Czech University of Life Sciences, Pragueand

PC-Progress, s.r.o., Prague

Proceedingsof the4 International Conferenceth

HYDRUS Software Applications
to Subsurface Flow andContaminant Transport Problems
March 21-22 2013
Prague, Czech RepublicCzech University of Life Sciences, Prague
Faculty of Agrobiology, Food and Natural ResourcesKamýcká 129
165 21 Praha 6 – Suchdol
Czech Republic
http://www.af.czu.cz/en/
PC-Progress s.r.o.
Korunní 2569/108a
Prague, 101 00
Czech Republic
http://www.pc-progress.com/en/Default.aspx

ISBN: 978-80-213-2380-3

Table of Content
Preface................................................................................................................................................5
Papers (Invited Presentations)
1. Jacques, D., J. Šimůnek, D. Mallants, and M. Th. van Genuchten, The HPx reactive
transport models: Summary of recent developments and applications.....................................7
2. Šimůnek, J., M. Šejna, D. Jacques, G. Langergraber, S. A. Bradford, and M. Th. van
Genuchten, New features of the HYDRUS computer software packages. ...............................17
Papers (Volunteered Presentations)
3. Abramson, A., E. Adar, and N. Lazarovitch, Investigating the impact of irrigation method
on profitability of smallholder gardening: Incorporating HYDRUS-1D into a decision
support system. .........................................................................................................................27
4. Anlauf, R., and P. Rehrmann, Simulation of water and air distribution in growing media. .....33
5. Antonov, D., D. Mallants, J. Šimůnek, and D. Karastanev, Application of the HYDRUS(2D/3D) inverse solution module for estimating of the soil hydraulic parameters of aquaternary complex in Northern Bulgaria. ...............................................................................47
6. Bezerra Coelho, B., C. R., M. S. Batalha, D. Jacques, M. C. Barbosa, and M. Th. van
Genuchten, Using HYDRUS-HP1 to estimate 226Ra transport in soils following the use ofphosphogypsum in agriculture. .................................................................................................53
7. Dabach, S., J. Šimůnek, A. Ben-Gal, J. Shi, and N. Lazarovitch, Optimization of triggered
irrigation using a system-dependent boundary condition in HYDRUS (2D/3D). ....................63
8. Diamantopoulos, E., S. C. Iden, and W. Durner, Modeling non-equilibrium water flow in
multistep outflow and multistep flux experiments. ..................................................................69
9. El-Nesr, M. N. B., A. Alazba, and J. Šimůnek, Dual-drip subsurface irrigation system: Can
it act as a hydraulic barrier? ......................................................................................................77
10. Filipović, V., R. Kodešová, and D. Petošić, Numerical modeling of water flow and nitrate
dynamics in zero tension plate lysimeters using HYDRUS-2D. ..............................................87
11. Glæsner, N., and H. H. Gerke, Single- and double porosity modeling of solute transport in
intact soil columns – effects of texture, slurry placement, and intermittent irrigation. ............95
12. Grinevskiy, S. O., and S. P. Pozdniakov, The use of HYDRUS-1D for groundwater
recharge estimation in boreal environments. ............................................................................107
13. Haile, S. S., and B. J. Merkel, Simulation of uranium tailing leaching using VS2DRT. .........119
14. Hlaváčiková, H., V. Novák, and M. Rodný, Infiltration into stony soil: modeling of theprocess using HYDRUS codes. ................................................................................................1271

15. Izadi, F. T., A. M. Damuchali, G. A. Fardi, and A. Khodadadi, Simulations of the impact ofdifferent rainfall intensities on reactive transport of metal contaminants from mine tailings.
..................................................................................................................................................135
16. Izadi, F. T., G. A. Fardi, A. Khodadadi, and M. Faridzad, Investigating the effect ofacidic rain on reactive transport of metal contaminants in groundwater. ...........................145
17. Kalin, J., B. Petkovšek, P. Montarnal, A. Genty, E. Deville, and J. Krivic, Comparison of
two numerical modeling codes for hydraulic and transport calculations in the near field. ......155
18. Kanzari, S., M. Hachicha, R. Bouhlila, and J. Battle-Sales, Characterization and modelingof water movement and salts transfer in a semi-arid region of Tunisia. ...................................165
19. Kanzari, S., I. Bâ, M. Hachicha, and R. Bouhlila, Characterization and modeling of waterand salt dynamics in a sandy soil under the effects of surface drip irrigation. .........................175
20. Karlsson, S. C., S. Dalahmeh, C. Lalander, and H. Jönsson, Hydraulic properties andreduction of COD, phosphorus and nitrogen in a sand filter used for greywater treatment –simulation and verification. ......................................................................................................183
21. Kato, C., T. Nishimura, H. Imoto, and T. Miyazaki, Predicting soil CO2 dynamics in arable
land of Andisol in western suburb of Tokyo. ...........................................................................191
22. Kébré, M. B., F. Cherblanc, F. Ouédraogo, Jean-Claude Bénet, and F. Zougmoré, Flow at
low water contents: A simple approach for inverse estimation of van Genuchten-Mualem
soil hydraulic parameters. .........................................................................................................203
23. Léger, E., A. Saintenoy, and Y. Coquet, Estimating saturated hydraulic conductivity fromsurface ground-penetrating radar monitoring of infiltration. ....................................................215
24. Leterme, B., and D. Jacques, Modeling Hg reactive transport in soil system using HP1. .......225
25. Leterme, B., M. Gedeon, and D. Jacques, Groundwater recharge modeling in the Netecatchment (Belgium) with HYDRUS-1D – MODFLOW package. .........................................235
26. Morvannou, A., N. Forquet, M. Vanclooster, and P. Molle, Which hydraulic model to use
for vertical flow constructed wetlands? ....................................................................................245
27. Nakhaei M. and J. Šimůnek, Estimating the soil hydraulic and thermal properties of
unsaturated porous media using HYDRUS-2D. .......................................................................257
28. Phogat, V., M. A. Skewes, M. Mahadevan, and J. W. Cox, Simulation of water and salinity
dynamics under different irrigation applications to an almond tree in pulsed and continuous
mode..........................................................................................................................................267
29. Pontedeiro, E. M., V. Ottoni, and M. Th. van Genuchten, HYDRUS-1D modelingapplications to waste disposal problems in Brazil. ...................................................................277
30. Pozdniakov, S., P. Wang, S. Grinevskiy, and J. Yu, Simulation of groundwater
evapotranspiration with HYDRUS-1D in desert environments. ..............................................289
31. Raij, I., N. Lazarovitch, A. Ben-Gal, U. Yermiyahu, and D. Jacques, Accounting forsolution composition in a plant roots active nutrient uptake model. ........................................2992

32. Ramos, T. B., J. Šimůnek, M. C. Gonçalves, J. C. Martins, A. Prazeres, and L. S. Pereira,
Modeling water and nitrogen fate in plots with sweet sorghum irrigated with fresh andblended saline waters using HYDRUS-2D. ..............................................................................307
33. Ružičić, S., Z. Kovac, M. Mileusnic, and K. Posavec, Longitudinal dispersivity
determination using conservative tracer in the field. ................................................................315
34. Sandhu, C., T. Fichtner, I. Hasan, and P.-W. Gräber, Predicting the impact of treatedwastewater infiltration on groundwater recharge by simulating reactive transport in theunsaturated zone. ......................................................................................................................323
35. Schwen, A., G. Bodner, and W. Loiskandl, Temporal variations of soil hydraulic properties
and its effect on soil water simulations.....................................................................................333
36. Šimůnek, J., D. Jacques, and M. Šejna, HP2/3: Extensions of the HP1 reactive transport
code to two and three dimensions. ............................................................................................345
37. Thaysen, E. M., E. Laloy, and D. Jacques, CO2 fluxes to aquifers beneath cropland:
Merging measurements and modeling. .....................................................................................355
38. Toride, N., and DaiWen Chen, Fate and transport of nitrogen in soils based on a couplednitrogen-carbon cycling model using the HP1 code. ................................................................365
39. Valdes-Abellan, J., J. Jiménez-Martínez, and L. Candela, HYDRUS application to assess
possible impacts of non-conventional water irrigation under two different vadose zone
monitoring strategies.................................................................................................................377
40. Xiao, H., J. Böttcher, and J. Šimůnek, Simulation of the heavy metal transport inunsaturated soils: Use of scale factors to quantify variable sorption isotherms. ......................385
41. Yurtseven, E., J. Šimůnek, S. Avci, and H. S. Öztürk, Comparison of HYDRUS-1D
simulations and ion(salt) movement in the soil profile subject to leaching..............................3953

Please reference the proceedings as follows:Šimůnek, J., M. Th. van Genuchten, and R. Kodešová (eds.), Proceedings of the 4thInternational Conference "HYDRUS Software Applications to Subsurface Flow andContaminant Transport Problems", March 21-22, 2013, Dept. of Soil Science and Geology,
Czech University of Life Sciences, Prague, Czech Republic, ISBN: 978-80-213-2380-3, pp. 404,
2013.
Please reference the individual papers as follows (adjust highlighted text as needed):
Authors, Title, Proceedings of the 4th International Conference "HYDRUS Software
Applications to Subsurface Flow and Contaminant Transport Problems", edited by J. Šimůnek,M. Th. van Genuchten, and R. Kodešová, March 21-22, 2013, Dept. of Soil Science andGeology, Czech University of Life Sciences, Prague, Czech Republic, ISBN: 978-80-213-23803, pp. ??-??, 2013.

4

Preface
These proceedings document presentations given at the Fourth International Conference on“HYDRUS Software Applications to Subsurface Flow and Contaminant Transport Problems,”
held in Prague, Czech Republic, March 21-22, 2013. Previous conferences in this series were
held in Utrecht in 2005, in Prague in 2008, and in Tokyo, also in 2008. The conferences focus on
the development and application of advanced numerical models simulating variably-saturated
flow, heat transport, and the transport of various contaminants or other solutes (such as nutrients,
pesticides, heavy metals, radionuclides, and pathogenic microorganisms) in soils andgroundwater. The conferences are designed to bring together users of the HYDRUS family ofcodes, as well as of related software, to review and exchange information on various aspects ofthe codes, future enhancements of the software, and their application to a range of soil,
environmental, hydrological, ecological and agricultural problems.
Since the first workshop in 2005, the community of HYDRUS users has been continuously
growing as evidenced by the number of downloads (over 10,000 times each of the past several
years) and visits to the HYDRUS web pages (on average several hundred each day). Hundreds ofjournal articles have now been published in which the HYDRUS codes have been used.
Feedback from users such as those attending the HYDRUS conference has been extremely
important in identifying particular strengths and weaknesses of the codes, and for defining
additional processes or features that should be included in the models. Feedback is also
continuously obtained from several discussion forums on the HYDRUS website, where users can
submit questions or suggestions about the models.
These proceedings contain 41 contributions from mostly HYDRUS software users, covering a
range of topics from the very fundamental to important practical applications. These
proceedings, as well as those of previous HYDRUS conferences, can be downloaded freely fromthe HYDRUS website at http://www.pc-progress.com.
We would like to thank the Czech University of Life Sciences and PC-Progress for hosting theconference in Prague. Our appreciation goes also to the many participants who travelled to
Prague from all continents. Special thanks are due to those that contributed to these proceedings.
Published studies in which the codes have been used always provide useful information for newusers. We believe that the software tools have served, and will continue to serve, an importantrole in especially vadose zone research.
The Editors
Jirka Šimůnek
Rien van Genuchten
Radka Kodešová

56The HPx Reactive Transport Models: Summary of Recent
Developments and Applications
Diederik Jacques1, Jiří Šimůnek2, Dirk Mallants3, and Martinus Th. van Genuchten4
1

Performance Assessments, Institute of Environment, Health and Safety, Belgian Nuclear Research Centre, Mol,
Belgium, djacques@sckcen.be2
Department of Environmental Sciences, University of California Riverside, CA, USA
3Land and Water, CSIRO, Adelaide, Australia
4
Department of Mechanical Engineering, Federal University of Rio de Janeiro, UFRJ, Rio de Janeiro, RJ, Brazil

Abstract
The HPx reactive transport codes were developed to simulate flow and transport processes in variably-

saturated porous media subject to a variety of low-temperature geochemical processes. The codes
combine the HYDRUS models for flow and transport (HYDRUS-1D version 4.16, and HYDRUS 2D/3Dversion 2.02) with the generic thermodynamic and kinetic model PHREEQC-2.17. As such, HPx expands
significantly the capabilities of the individual codes for multicomponent one-dimensional (HP1) and twodimensional (HP2) transport problems. This paper provides a brief summary of recent developments andapplications of HPx, such as (i) the inclusion of gas diffusion, (ii) extension to two-dimensional problems,(iii) inverse optimization, and (iv) feedback between changes in geochemical variables and transport
properties. HPx is a flexible tool which can be applied to flow and transport problems involving relatively
complex geochemical processes. A typical example is the geochemistry of mercury, which in acontaminated soil may be present in different forms and phases.

1. Introduction
The fate and transport of nutrients and contaminants in variably-saturated porous media is
influenced by a range of interacting physical, chemical, and biological processes (Jacques et al.,2008). Transport in soil systems is often further complicated by a multitude of coupledbiogeochemical reactions, the presence of spatially and temporally variable flow velocities, andspatial heterogeneities at different scales (for a review see Mallants et al., 2011). A numerical
tool that integrates these various processes offers unique possibilities for advanced modelbuilding and improving process understanding, ranging from sensitivity analyses of processes
and parameters, designing experiments, hypothesis testing by running virtual laboratories,
conceptual model validation using experimental data, and evaluation of different management orremediation practices. Based on the HYDRUS suite of models for one-dimensional (Šimůnek etal., 2008) and multi-dimensional problems (Šimůnek et al., 2011), and the generic
thermodynamic and kinetic geochemical model PHREEQC (Parkhurst and Appelo 1999), theHP1 (Jacques and Šimůnek, 2005) and HP2 (Šimůnek et al., 2012) modules were developed tohandle water flow, multi-component solute transport, heat transfer, and biogeochemical reactions
for a range of environmental soil quality applications. In this paper we provide a brief summaryof recent developments and various applications of the HPx modules.

72. Conceptual Basis of HPx
The HPx codes considerably extend upon the capabilities of the individual codes. For example,
the full range of water flow and solute transport formulations available in the standard HYDRUS
codes are now combined with the different geochemical models available in PHREEQC.
Contrary to the conventional advection-dispersion-reaction equations forming the basis of thestandard HYDRUS-1D and HYDRUS 2D/3D codes, the HPx modules account for interactions
between different aqueous components to simulate intra-aqueous degradation, transformation or
production processes, as well as heterogeneous equilibrium and kinetic processes. Using thecapabilities of PHREEQC, HPx allows thermodynamic equilibrium calculations for• aqueous speciation with different activity correction models (Davies, extended TruesdellJones, B-Dot, Pitzer, SIT - Specific ion Interaction Theory),• multi-site ion exchange sites for different conventions (Gaines-Thomas, Vanselow,
Gapon, or accounting for different selectivities considering the equivalent fraction
occupied by the cation by the Rothmund-Kornfeld or the active fraction model),• multi-site surface complexation sites with a non-electrostatic, the Dzombak and Morel, or
the CD_MUSIC model and different options to calculate the composition of the diffuse
double layer,• mineralogical assemblages,• solid-solutions consisting of multiple end members in an ideal solid solution or a binary
non-ideal solid solution using the Guggenheim approach for determining the activity
coefficients of the end members (Glynn and Reardon, 1990), and• gas exchange.
Kinetic calculations are furthermore used to describe mineral dissolution/precipitation (e.g.,based on transition state theories as shown by Lasaga (1998) and Brantley (2003)), nonequilibrium sorption processes, biogeochemical reactions, including first-order degradation
networks (e.g., C-sequestration, see below), Monod kinetics, and Michaelis-Menten kinetics(e.g., solute-dependent plant uptake coupled with root exudation as shown by Raji et al. (2013)).
HPx allows one to select uniform or dual-porosity models for water flow, and uniform,
mobile/immobile, or dual-porosity models for solute transport (Figure 1), as well as diffusive
processes in the gas phase. As opposed to many other reactive transport codes, HPx also
provides an option to account for the effects of root water and nutrient or contaminant uptake,including compensated water uptake and root growth (Šimůnek and Hopmans, 2008).
Furthermore, the HPx simulators can accommodate complex boundary conditions including
water and chemical exchange with streams and groundwater. Because geochemical gradients(e.g. changing redox conditions) are especially strong along such interfaces, only simulators thatprovide proper coupling between the various hydrological, geochemical and biological processes
involved are capable of providing accurate system descriptions.

8

Figure 1. Schematic of possible coupled flow–transport–reaction models available within HPx: auniform water flow and solute transport model (left), a uniform water flow model with amobile/immobile solute transport model (middle), and a dual-porosity water flow model with adual-porosity transport model (right). In the figure, εs is the volume fraction of solid phase, θa is
the air content, θw is the water content, θw,m is the mobile water content, θw,im is the immobile
water content, Sr,w represents root water uptake, Sr,s,i represents root uptake of solute i, Sc,i is a sinkor source term for solute i resulting from aqueous degradation or transformation processes, Γi andΓw are solute and water mass exchange terms between the mobile and the immobile water phases,
respectively, and Γwa, Γws, Γws,m, and Γws,im are heterogeneous mass exchange terms between thewater and air phases, the water and solid phases, the mobile water and solid phases, and theimmobile water and the solid phases, respectively (after Šimůnek and van Genuchten, 2008).

3. Recent Developments and Applications
This section describes several recent improvements and applications of HPx. Additional
examples are included in these proceedings for mercury transport and fate in soils (Leterme andJacques, 2013), CO2 production and transport in bare and planted mesocosmos (Thaysen et al.,2013), and active root nutrient uptake accounting for solution composition effects (Raji et al.,2013). The extension of the HPx code to two-dimensional flow and transport problems is
described in another contribution to these proceedings (Šimůnek and Jacques, 2013).
3.1. Gas Diffusion Coupled to Organic Matter Degradation
A recent addition to HPx is diffusion of components in the gas phase. We present here an
illustrative example that includes a process-based soil organic matter degradation model withthree immobile organic carbon pools (litter, humus, and biomass), external input of C into thesystem, and an inorganic pool (CO2). The model is based on previous work by Porporato et al.
(2003) as illustrated in Figure 2 (see also Batlle-Aguilar et al., 2011). The model consists of anumber of coupled nonlinear ordinary differential equations (see Fig. 2). There are several
differences with the original model of Porporato et al. (2003). For example, water flow ismodeled using the Richards equation with a root water uptake term (versus a probabilistic
modeling approach in Porporato et al., 2003), while heat transport is also considered. Two
inorganic pools are further included: CO2(g) and dissolved C, with thermodynamic exchange

9between the two pools. We additionally consider the temperature dependence of rate parameters,
and also included transport of inorganic C in the aqueous and gaseous phases.

Figure 2. Schematic of the soil organic matter model (left), the set of coupled non-linear ordinary
differential equations, and a list of symbols (after Porporato et al., 2003).

The rate parameters in Figure 2 for first-order decay and decomposition depend on the soil watercontent (described with the formulations of Porporato et al. (2003) and Manzoni and Porporato(2007)) and soil temperature. The latter effect is described using the temperature stress function
from the RothC model of Coleman and Jenkinson (2005). The effects of water content andtemperature stress were modeled as a multiplication of both factors. The combined effect oftransient variations in the water content and temperature in a soil profile during one year on the
stress factors is illustrated in Figure 3. Multiplication of the temperature and water content stressfactors leads to considerable variation in organic matter decomposition rates during the year
(Figure 3). Decomposition rates, relative to the reference rate value, range from zero (during dry
periods near the surface) up to 3.5 (during wet and warm periods).
Evolutions of the organic C pools during one year are shown in Figure 4. The different curves
follow smoothly the seasonal trends in temperature (and water content). The transformation anddecomposition of the organic C pools is also reflected in the general trend of soil CO2 gas. On
the other hand, water content changes on the shorter temporal scale seem to influence variationsin the soil CO2 partial pressure.

10

Figure 3. Temporal variations of water contents (top, left) and temperatures (top, right) in a soil
profile during a one year simulation. Resulting stress factors (bottom) for the decay anddecomposition rates.

3.2. Inverse Optimisation with UCODE
Coupled codes such as HP1 allow simultaneous optimization of various flow, transport, andgeochemical parameters using inverse methods. A recent application with HP1 is given by
Jacques et al. (2012), who combined HP1 with the general optimization tool UCODE (Poeter etal., 2005). The experimental data resulted from previously published laboratory experiments(Smiles and Smith, 2004) about the transport of major cations (Na, K, Mg, and Ca) during water
absorption into horizontal soil columns, which were terminated at different times. Experimental
data consisted of spatial distributions of the water content (θ), the Cl concentration, and total
aqueous and sorbed concentrations of the major cations. In addition to selected flow andtransport parameters (i.e., those describing the water retention and hydraulic conductivity
functions, as well as the dispersivity), cation exchange coefficients for the major cations and thecation exchange capacity were estimated. Another new aspect of this study was that two different
exchange models could be tested: the Gapon approach and a variable-selectivity model based on
the Rothmund-Kornfeld approach. The latter enables stronger binding of a species at lower
equivalent sorbed fractions (e.g., Bond, 1995). Calibrated profiles for Mg are shown in Figure 5.
The Rothmund-Kornfeld approach was found to perform slightly better than the Gapon
approach.

11

Exchangeable Mg (mmol/kg soil)

Figure 4. Time evolution of organic C pools (litter: top, left; humus: top, right; and biomass:bottom, left) and of gaseous CO2 concentrations (in atm, bottom, right) in a soil profile during a
one year simulation.

Mg (mol/kgw)

0.01

5

0.008

4

0.006

3

0.004

2

0.002

1

0

0

0

0.5
1
1.5
Distance / time0.5 (cm min-0.5)

2

0

0.5
1
1.5
Distance / time0.5 (cm min-0.5)

Figure 5. Simulated profiles of aqueous (left) and sorbed (right) Mg concentrations obtained with
the Gapon approach [solid lines] or the Rohtmund-Kornfeld approach [dashed lines], comparedwith experimental data [symbols: circles - 36 min, triangles - 106 min, and squares - 144 min]from water absorption and solute transport experiments using piggery effluent (Smith and Smiles,
2004) (adapted from Jacques et al., 2012).

12

2

The HP1-UCODE study was supplemented with information content (Hill and Tiedeman, 2007)
and surface contour analyses. As illustrated in Figure 6, the parameters of the Gapon exchange
approach were better identifiable as compared to the parameters of the Rothmund-Kornfeld
approach. Several parameters in the latter approach showed strong correlations. We refer to
Jacques et al. (2012) for details.
4

1.5

2

0

1
N CaNalog KRK CaNa

Log KGCa

3
1

2

0.5
1

-1

0
-1

0

1
log KGK

2

3

-1

0

1
log KRK KNa

2

3

0

1

2

3

4

log KRK CaNa

Figure 6. Contour plots of the objective function for (left) the exchange coefficient of K and Ca in
the Gapon approach (KGK and KGCa), (middle) the exchange constant between K and Na (KRKKNa),
and between Ca and Na (KRKCaNa) in the Rothmund-Kornfeld approach, and (right) the exchange
constant (KRKCaNa) and the nonlinear coefficient (NCaNa) for exchange between Ca and Na in theRothmund-Kornfeld approach (adopted from Jacques et al., 2012).

3.3. Coupling Between Geochemical Variables and Transport Properties
A useful new feature recently included in HP1 is an option to change the hydraulic and solutetransport properties as a function of evolving geochemical state variables. HP1 makes it possible
to account for changes in (i) the porosity (and hence the saturated water content), (ii) the
hydraulic conductivity, (iii) a scaling factor for the pressure head, (iv) aqueous and gaseous
phase pore geometry factors for calculating pore diffusion coefficients, (v) the dispersivity,(vi) the thermal capacity, (vii) the thermal conductivity, and (viii) the thermal dispersivity. HP1
does not provide any pre-defined conceptual or mathematical model to update the flow andtransport parameters, but uses the flexibility of the embedded BASIC interpreter for thispurpose. This permits users to define any user-specific relationship between the geochemical
state variables and the transport properties.
A typical example, illustrated in Figure 7, is diffusive leaching from a porous medium in contact
with more or less aggressive water. The example concerns leaching of a small concrete beam incontact with three types of water as indicated in the top part of Figure 7: (i) Rain W (wetdeposition only), (ii) Rain B (wet and bulk deposition), which has higher ion concentrations, and(iii) Soil water with a higher inorganic carbon content as a result of soil microbiologicalprocesses. In terms of concrete performance, the soil water type should be the most detrimental
since portlandite (Ca(OH)2) dissolution proceeds rapidly due to leaching and carbonation (i.e.,
portlandite dissolution followed by calcite precipitation as show by Jacques et al. (2010)). At thesame time, chemical dissolution of portlandite and precipitation of calcite change the physicalproperties such as porosity and tortuosity (e.g., Perko et al., 2010; Jacques et al., 2011).

13

Water flux
Solute diffusive flux
Concrete

1.6

5Rain W - 300 y
Rain W - 600 y
Rain B - 300 y
Rain B - 600 y
Soil - 300 y
Soil - 600 y

1.2
0.8

Calcite (mol/dm3)

Portlandite (mol/dm3)

4 cm

0.4
0

4
3
2
1
0

0

0.5

1

1.5

2

0

0.5

λ (mm/y0.5)

1.5

2

1.5

2

λ (mm/y0.5)
100Tortuosity factor

0.4
0.3

Porosity

1

0.2
0.1

10-1
10-2
-3

10

-4

0

10
0

0.5

1

1.5

0

2

0.5

1

λ (mm/y0.5)

λ (mm/y0.5)

Figure 7. Example showing the effect of coupling transport parameters to geochemical variables.
Results are for diffusive leaching of a small concrete beam. Shown are profiles of portlandite (topleft), calcite (top right), porosity (bottom left), and the tortuosity factor (bottom right) as afunction of the Boltzmann transform λ for three different water types and two different times.

Since calcite has a slightly larger molar volume than portlandite, porosity and tortuosity should
decrease if calcite precipitation leads to pore blockage without generation of internal stresses andsubsequent fracturing. Some of these processes are clearly evident from the results in Figure 7.
The portlandite profiles as a function of the Boltzmann transform (which should collapse to asingle curve in case of pure diffusive transport) are different among the three water types. In
particular, the portlandite dissolution front has progressed slightly further for water with apresumably less aggressive solution composition (Rain W). On the other hand, enhanced calcite
precipitation in the soil water case causes pore clogging and a strong reduction in the tortuosity
and the diffusion coefficient. As a result, the portlandite dissolution front is retarded compared tothe dissolution fronts when concrete is leached with the other two water compositions. A
porosity decrease is also simulated for the Rain B case, mainly due to precipitation of Mgbearing minerals.

14

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during land use change, A review, Agron. Sustain. Dev., 31, 251-275, 2011.
Bond, W. J., On the Rothmond-Kornfeld description of cation exchange, Soil Sci. Soc. Am. J., 59, 436443, 1995.
Brantley, S. L., 5.03 Reaction kinetics of primary rock-forming minerals under ambient conditions,
Treatise on Geochemistry, Elsevier, Volume 5, 73-117, 2003.
Coleman, K., and D. S. Jenkinson, RothC-26.3. A Model for Turnover of Carbon in Soil. Model
Description and Windows User Guide, IACR-Rothamsted, Harpender, 2005.
Glynn, P. D., and E. J. Reardon, Solid-solution aqueous-solution equilibria: Thermodynamic theory andrepresentation, Am. J. Sci., 290, 164-201, 1990.
Hill, M. C., and C. R. Tiedeman, Effective Groundwater Model Calibration with Analysis of Data:
Sensitivities, Predictions and Uncertainty, John Wiley & Sons, NJ, USA, 2007.
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Model HP1, Description, Verification and Examples, Version 1.0, SCK•CEN-BLG-998, Waste andDisposal, SCK•CEN, Mol, Belgium, 79 pp., 2005.
Jacques, D., J. Šimůnek, D. Mallants, and M. Th. van Genuchten, Modeling coupled hydrological andchemical processes: Long-term uranium transport following phosphorous fertilization, Vadose Zone
J., 7,698-711, 2008.
Jacques, D., J. Šimůnek, D. Mallants, M. Th. van Genuchten, and L. Yu, A coupled reactive transportmodel for contaminant leaching from cementitious waste matrices accounting for solid phasealterations, Proceedings Sardinia 2011, Thirteenth International Waste Management and Landfill
Symposium, 2011.
Jacques, D., C. Smith, J. Šimůnek, and D. Smiles, Inverse optimization of hydraulic, solute transport andcation exchange parameters using HP1 and UCODE to simulate cation exchange, J. Cont. Hydrol.,142-143, 109-125, 2012.
Jacques, D., L. Wang, E. Martens, and D. Mallants, Modelling chemical degradation of concrete duringleaching with rain and soil water types, Cem. Concr. Res., 40, 1306-1313, 2010.
Lasaga, A.C., Kinetic Theory in the Earth Sciences, Princeton University Press, Princeton, New Jersey,
1998.
Leterme, B., and D. Jacques, Modeling Hg reactive transport in soil systems using HP1, (this issue),
2013.
Mallants D., M. Th., van Genuchten, J. Šimůnek, D. Jacques, and S. Seetharam, Leaching ofcontaminants to groundwater. In ‘Dealing with Contaminated Sites’, (Ed F Swartjens), pp. 787-850.
DOI: 10.1007/978-90-481-9757-6_1, 2011
Manzoni, S., and A. Porporato, A theoretical analysis of nonlinearities and feedbacks in soil carbon andnitrogen cycles, Soil Biol. Biochem., 39, 1542-1556, 2005.
Parkhurst, D. L., and C. A. J. Appelo, User’s guide to PHREEQ C (Version 2) – A computer program forspeciation, batch-reaction, one-dimensional transport and inverse geochemical calculations, WaterResources Investigations, Report 99–4259, Denver, Co, USA, 312 pp., 1999.
Perko, J., D. Jacques, S. C. Seetharam, and D. Mallants, Long-term evolution of the near surface disposal
facility at Dessel, NIROND-TR 2010-04 E, 2010.
Poeter, E. P., M. C. Hill, E. R. Banta, S. Mehl, and C. Steen, UCODE_2005 and six other computer codes
for universal sensitivity analysis, calibration and uncertainty evaluation, U.S. Geological Survey
Techniques and Methods 6-A11, 2005.
Porporato, A., P. D’Odorico, F. Laio, and I. Rodrigues-Iturbe, Hydrological controls on soil carbon andnitrogen cycles. I. Modelling scheme, Adv. Water Resour., 26, 45-58, 2003.
Raji, I., N. Lazarovitch, A. Ben-Gal, U. Yermiyahu, and D. Jacques, Accounting for solution composition
in a plant roots active nutrient uptake model, (this issue), 2013.

15

Šimůnek, J. and J. W. Hopmans, Modeling compensated root water and nutrient uptake, EcologicalModeling, doi:10.1016/j.ecolmodel.2008.11.004, 220(4), 505-521, 2009.
Šimůnek, J., and M. Th. van Genuchten, Modeling nonequilibrium flow and transport processes using
HYDRUS, Vadose Zone J., 7(2), 782-797, 2008.
Šimůnek, J., M. Šejna, H. Saito, M. Sakai, and M. Th. van Genuchten, The HYDRUS-1D Software
Package for Simulating the One-Dimensional Movement of Water, Heat and Multiple Solutes in
Variably-Saturated Media, Version 4.08, HYDRUS Software Series 3, Department of Environmental
Sciences, University of California Riverside, Riverside, California, USA, 2008.
Šimůnek, J., M. Th. van Genuchten, and M. Šejna, Development and applications of the HYDRUS andSTANMOD software packages, and related codes, Vadose Zone Journal, 7(2), 587-600, 2008.
Šimůnek, J., M. Th. van Genuchten, and M. Šejna, The HYDRUS Software Package for Simulating Twoand Three-Dimensional Movement of Water, Heat, and Multiple Solutes in Variably-Saturated Media,
Technical Manual, Version 2.0, PC Progress, Prague, Czech Republic, pp. 258, 2011.
Šimůnek, J., D. Jacques, M. Šejna, and M. Th. van Genuchten, The HP2 Program for HYDRUS (2D/3D): A
Coupled Code for Simulating Two-Dimensional Variably-Saturated Water Flow, Heat Transport, andBiogeochemistry in Porous Media, Version 1.0, PC Progress, Prague, Czech Republic, 76 pp., 2012.
Šimůnek, J., D. Jacques, and M. Šejna, HP2/3: Extensions of the HP1 reactive transport code to two andthree dimensions, (this issue), 2013.
Smiles, D. E., and C. J. Smith, Absorption of artificial piggery effluent by soil: A laboratory study, Austr.
J. Soil Sci., 42, 961-975, 2004.
Thaysen, E., E. Laloy, and D. Jacques, CO2 fluxes to aquifers beneath cropland: Merging measurements
and modeling, (this issue), 2013.

16

New Features of the HYDRUS Computer Software Packages
Jirka Šimůnek1, Miroslav Šejna2, Diederik Jacques3, Günter Langergraber4,
Scott A. Bradford5, and Martinus Th. van Genuchten61Department of Environmental Sciences, University of California, Riverside, CA, USA, jiri.simunek@ucr.edu
2
PC-Progress, Ltd., Prague 2, Czech Republic, m.sejna@pc-progress.cz
3
Performance Assessments, Belgian Nuclear Research Institute, Mol, Belgium, djacques@sckcen.be4
Institute for Sanitary Engineering and Water Pollution Control, University of Natural Resources and Life Sciences,
Vienna (BOKU University), Austria, guenter.langergraber@boku.ac.at
5
U.S. Salinity Laboratory, USDA, ARS, Riverside, CA, USA, Scott.Bradford@ars.usda.gov
6
Department of Mechanical Engineering, Federal University of Rio de Janeiro, UFRJ, Rio de Janeiro, RJ, Brazil,rvangenuchten@hotmail.com

Abstract
The capabilities of the HYDRUS-1D and HYDRUS (2D/3D) software packages have been substantiallyexpanded since two earlier HYDRUS workshops held in Prague, Czech Republic (March 2008) andTokyo, Japan (June 2008). Multiple processes were added to both HYDRUS packages, including
compensated root water and solute uptake models and triggered irrigation. Computational modules ofboth packages have been made about 2-3 times faster by using capabilities of advanced processors andcompilers, such as using the loop vectorization. Major developments were introduced in version 2 of
HYDRUS (2D/3D). This version can now handle for the first time complex, general, three-dimensional
geometries, while domain properties, initial conditions, and boundary conditions can be specified ongeometrical objects, rather than on the finite element mesh. Completely new modules accounting forprocesses not available in the standard HYDRUS version were introduced. These new modules include
the HP2, C-Ride, DualPerm, UnsatChem, Wetland, and Fumigant modules. These new modules simulate
flow and transport processes in two-dimensional transport domains and are fully supported by the
HYDRUS graphical user interface. Several processes in these specialized modules of HYDRUS (2D/3D)
have been made also part of HYDRUS-1D.

1. Introduction
The HYDRUS-1D and HYDRUS (2D/3D) programs (Šimůnek et al., 2008) are finite element
models for simulating the one-, two- and three-dimensional movement of water, heat, andmultiple solutes in variably saturated media. The standard versions of HYDRUS programs
numerically solve the Richards equation for saturated-unsaturated water flow and convectiondispersion type equations for heat and solute transport. The flow equation incorporates a sinkterm to account for water uptake by plant roots. The heat transport equation considers movement
by both conduction and convection with flowing water. The governing convection-dispersion
solute transport equations are written in a very general form by including provisions fornonlinear nonequilibrium reactions between the solid and liquid phases, and linear equilibrium
reaction between the liquid and gaseous phases. Hence, both adsorbed and volatile solutes, suchas pesticides, can be considered. The solute transport equations also incorporate the effects ofzero-order production, first-order degradation independent of other solutes, and first-orderdecay/production reactions that provide the required coupling between the solutes involved in thesequential first-order chain. The transport models also account for convection and dispersion in17

the liquid phase, as well as diffusion in the gas phase, thus permitting the model tosimultaneously simulate solute transport in both the liquid and gaseous phases. HYDRUS
considers up to fifteen solutes, which can either be coupled in a unidirectional chain or moveindependently of each other. Physical nonequilibrium solute transport can be accounted for byassuming a two-region, dual porosity type formulation, which partitions the liquid phase into
mobile and immobile regions. Attachment/detachment theory, including the filtration theory, is
included to simulate transport of viruses, colloids, and/or bacteria.
Table 1. Selected new options in HYDRUS-1D (since 2008).
Version
4.04

4.05

4.06
4.07

4.08

4.12
4.13

4.15
4.16

New Options• Option to specify the nonequilibrium phase concentration initially at equilibrium with theequilibrium phase concentration• Option to specify initial conditions in total (instead of liquid) concentrations• Option to print fluxes instead of temperatures for observation nodes• HP1 – support of dual-porosity models• Linking of optimized parameters of different soil layers• Constant mobile water content in multiple layers (in the Mobile-Immobile Water Model) when
optimizing immobile water content• The Per Moldrup’s tortuosity models (Moldrup et al., 1997, 2000) were implemented as analternative to the Millington and Quirk (1960) model• Surface energy balance (i.e., the balance of latent, heat, and sensible fluxes) for bare soils• Daily variations of meteorological variables can be generated by the model using simple
meteorological models• Preliminary (at present rather simple) support of the HYDRUS package for MODFLOW• Compensated root water and solute (passive and active) uptake based on Šimůnek and Hopmans(2009)• Executable programs made about three times faster due to the loop vectorization• New additional output (e.g., solute fluxes for observation nodes and profiles of hydraulicconductivities (thermal and isothermal) and fluxes (liquid, vapor, and total))• Version 2.1.002 of HP1, new GUI supporting HP1• Conversions of the mass units for the threshold-slope salinity stress model from electric
conductivity to osmotic head
• Input of sublimation constant and initial snow layer• New conversions of constants (EC, osmotic potential) for the salinity stress response function• Option to set field capacity as an initial condition (Twarakavi et al., 2009)• Display of wetting hydraulic functions for hysteretic soils• Triggered irrigation• Interception can be considered with the standard HYDRUS input (without the need for
meteorological input)

We continue to expand the capabilities of the HYDRUS-1D and HYDRUS (2D/3D) software
packages and many new processes and options have been added since the two HYDRUS
workshops held in 2008 in Prague, Czech Republic (in March) and Tokyo, Japan (in June).
Multiple processes have been added to both HYDRUS packages since 2008, including thecompensated root water and solute uptake model and/or triggered irrigation, and many others.
Tables 1 and 2 list selected new processes and options that have been implemented in recent
versions of HYDRUS-1D and HYDRUS (2D/3D), respectively. Note that we continue to expand
the capabilities of the HYDRUS modeling environment (Table 2) by developing specialized18

modules for more complex applications that cannot be solved using its standard versions. In thismanuscript we list many of these changes and describe the new modules in more detail.

2. Specialized Modules
Completely new modules accounting for processes not available in the standard HYDRUS
version were introduced. These new modules include the HP2, C-Ride, DualPerm,
UnsatChem, Wetland, and Fumigant modules. All these modules simulate flow and transport
processes in two-dimensional transport domains and are fully supported by the HYDRUS
graphical user interface. Many processes included in these specialized modules of HYDRUS(2D/3D) are currently also available as part of HYDRUS-1D.
2.1. The HP1/HP2 Modules
The one-dimensional program HP1, which couples the PHREEQC geochemical code
(Parkhurst and Appelo 1999) with HYDRUS-1D, was first released in 2005 (Jacques andŠimůnek 2005), and successfully used in many applications. This comprehensive simulation tool
(HP1 is an acronym for HYDRUS-PHREEQC-1D) can simulate (1) transient water flow, (2) thetransport of multiple components, (3) mixed equilibrium/kinetic biogeochemical reactions, and(4) heat transport in one-dimensional variably-saturated porous media (soils). HP2 (Šimůnek etal., 2012d) is then a two-dimensional alternative of the HP1 module. Both HP1 and HP2 cansimulate a broad range of low-temperature biogeochemical reactions in water, the vadose zone
and/or ground water systems, including interactions with minerals, gases, exchangers andsorption surfaces based on thermodynamic equilibrium, kinetic, or mixed equilibrium-kinetic
reactions. More details about both modules are presented in several papers of these proceedings(e.g., Jacques et al., 2013; Šimůnek et al., 2013).
2.2. The C-Ride Modules
The C- Ride module (Šimůnek et al., 2012c) simulates the transport of particle-like substances(e.g., colloids, viruses, bacteria, and nanoparticles) and colloid-facilitated solute transport(Šimůnek et al., 2006), the latter often observed for many strongly sorbing contaminants such as
heavy metals, radionuclides, pharmaceuticals, pesticides, and explosives. These contaminants are
predominantly associated with the solid phase, which is commonly assumed to be stationary.
However, such contaminants may also sorb/attach to mobile and deposited colloidal particles(e.g., microbes, humic substances, suspended clay particles, and metal oxides), which then can
act as pollutant carriers and thus provide a rapid transport pathway for the pollutants. This
module fully accounts for the dynamics of colloid (attachment/straining) and solute(kinetic/equilibrium sorption to soil and mobile/deposited colloids) transfer between the different
phases. The schematic of the colloid-facilitated solute transport model is shown in Figure 1.

19

Table 2. Selected new options in HYDRUS (2D/3D) (since 2008).
Version
1.09
1.10
1.11
2.01

2.02

New Options• New more efficient algorithm for particle tracking• Import of domain properties, initial and boundary conditions from another project with (slightly)
different geometry or FE mesh (both 2D and 3D)• The Per Moldrup’s tortuosity models (Moldrup et al., 1997, 2000) were implemented as analternative to the Millington and Quirk (1960) model
Computational module:• Initial conditions can be specified in the total solute mass (previously only liquid phase
concentrations were allowed)• Initial equilibration of nonequilibrium solute phases with equilibrium solute phase• Gradient boundary conditions• A subsurface drip boundary condition (with a drip characteristic function reducing irrigation
flux based on the back pressure) (Lazarovitch et al., 2005)• A surface drip boundary condition with dynamic wetting radius (Gärdenäs et al., 2005)• A seepage face boundary condition with a specified pressure head
• Triggered Irrigation, i.e., irrigation can be triggered by the program when the pressure head at aparticular observation node drops below a specified value• Time-variable internal pressure head or flux nodal sinks/sources (previously only constantinternal sinks/sources)• Fluxes across meshlines in the computational module for multiple solutes (previously only for
one solute)• HYDRUS calculates and reports surface runoff, evaporation and infiltration fluxes for theatmospheric boundary• Water content dependence of solute reactions parameters using the Walker’s (1974) formula
was implemented• An option to consider root solute uptake, including both passive and active uptake (Šimůnek
and Hopmans, 2009)• An option to use a set of Boundary Condition records multiple times• Options related to the Fumigant transport (e.g., removal of tarp, temperature dependent tarp
properties, additional injection of fumigant)• The UNSATCHEM module simulating transport of and reactions between major ions
• The new CWM1 constructed wetland module
GUI:• Supports for complex general three-dimensional geometries (Professional Level)• Domain properties, initial conditions, and boundary conditions can be specified on "GeometricObjects" (defining the transport domain) rather than on the finite element mesh
• Import of various quantities (e.g., domain properties, initial and boundary conditions) fromanother HYDRUS projects even with (slightly) different geometry or FE mesh
• Geometric objects can be imported using DXF and TIN (triangular irregular network) files• Display of results using Isosurfaces• Support of ParSWMS (a parallelized version of SWMS_3D) (Hardelauf et al., 2006)• The DualPerm module simulating flow and transport in dual-permeability porous media• The C-Ride module simulating colloid transport and colloid-facilitated solute transport• The HP2 module (coupled HYDRUS and PHREEQC) for simulating biogeochemical reactions

20

Figure 1. Schematic of the colloid-facilitated solute transport model.

2.3. The DualPerm Module
The DualPerm module (Šimůnek et al., 2012b) simulates preferential and/or nonequilibrium
water flow and solute transport in dual-permeability media using the approach suggested by
Gerke and van Genuchten (1993). The module assumes that the porous medium consists of two
interacting regions: one associated with the inter-aggregate, macropore, or fracture system, andone comprising micropores (or intra-aggregate pores) inside soil aggregates or the rock matrix.
Water flow can occur in both regions, albeit at different rates. Modeling details are provided byŠimůnek and van Genuchten (2008). An example of the pressure head profiles for a tension disc(with a disc radius of 10 cm) infiltration experiment in the transport domain, 50 cm wide and 150
cm deep, in the matrix and fracture domains for different ratios of the anisotropy coefficients(KxA/KzA=1, 10, and 0.1) is shown in Figure 2.

Figure 2. Pressure head profiles for the matrix (left), isotropic fracture, and fracture with
KxA/KzA=10, and fracture with KxA/KzA=0.1 (right).

2.4. The UnsatChem Module
The geochemical UnsatChem module (Šimůnek et al., 2012a) has been implemented into boththe one- and two-dimensional computational modules of Hydrus. This module simulates the21transport of major ions (i.e., Ca, Mg, Na, K, SO4, CO3, and Cl) and their equilibrium and kinetic
geochemical interactions, such as complexation, cation exchange and precipitation-dissolution(e.g., calcite, gypsum, and/or dolomite). Possible applications include studies of the salinization/
reclamation of agricultural soils, sustainability of various irrigation systems, and the disposal ofbrine waters from mining operations. Since the computational driver for this module wasdeveloped some two decades ago (Šimůnek and Suarez, 1994), the UnsatChem module(especially its one-dimensional version) has found a wide use in many applications.
2.5. The Wetland Module
The Wetland module simulates aerobic, anoxic, and anaerobic transformation and degradation
processes for organic matter, nitrogen, phosphorus, and sulphur during treatment of polluted
wastewater in subsurface constructed wetlands (Langergraber and Šimůnek, 2012). Constructedwetlands are engineered water treatment systems that optimize the treatment processes found innatural environments. Constructed wetlands have become popular since they can be quite
efficient in treating different types of polluted water and provide sustainable, environmentallyfriendly solutions. A large number of physical, chemical and biological processes are
simultaneously active and may mutually influence each other. The Wetland module uses twobiokinetic model formulations [CW2D of Langergraber and Šimůnek (2005) and CWM1 of
Langergraber et al. (2009)] to account for complex conditions that may occur in various types of
wetlands. An example of the application of the Wetland module to simulate the spatial
distribution of heterotrophic organisms in a subsurface constructed wetland is shown in Figure 3.

Figure 3. Steady-state distribution of heterotrophic organisms in a subsurface constructedwetland.

2.6. The Fumigants Module
The Fumigants module implements multiple additional options that are required to simulate
processes related to fumigants applications and transport. This module allows users to specify anadditional injection of fumigants into the transport domain at a specified location at a specified
time and to consider the presence or absence of a surface tarp, a temperature dependence of tarp
properties, and its removal at specified time. The Fumigants module has been recently used toinvestigate the effect of different application scenarios, such as tarped broadcast, tarped bedded

22

shank injection and a tarped drip line-source application and various factors (e.g., initial watercontent, tarp permeability) on fumigant volatilization (Fig. 4) (Spurlock et al., 2013).

Figure 4. Tarped broadcast (left) and tarped bed drip scenarios (center). Volatilization fluxes fordifferent scenarios (adopted from Spurlock et al., 2013).

3. Graphical User Interface (GUI) of HYDRUS (2D/3D)
3.1. Geometries in the Professional Level of HYDRUS (2D/3D)
The latest 3D-Professional Level of HYDRUS supports complex general three-dimensional
geometries that can be formed from three-dimensional objects (Solids) of general shapes. Threedimensional objects are formed by boundary Surfaces, which can be either Planar surfaces orCurved surfaces (Quadrangle, Rotary, Pipe, or B-Spline). Figure 5 provides examples ofvarious curved surfaces, while Figure 6 shows how these individual objects can be combined toform complex three-dimensional geometries.

Figure 5. Examples of curved surfaces (Rotary, Pipe, B-Spline, and Quadrangle Surfaces).

23

Figure 6. Transport domains formed using planar (left) or curved (center, right) surfaces.

3.2. Domain Properties, Initial Conditions, and Boundary Conditions Specified on GeometricObjects
Various spatially variable properties (e.g., material distribution, initial conditions, boundary
conditions, domain properties, etc) can be specified in Version 2.0 of HYDRUS, either directlyon the Finite Element Mesh (FEM) (as done in Version 1.0), or on Geometric Objects (e.g.,boundary curves, rectangles, circles, surfaces, solids) (Fig. 7).

Figure 7. The transport domain with materials (left) and boundary conditions (right) specified onGeometric Objects.

3.3. Display of Standard and Alternative Variables
Many different spatially-variable properties can be displayed in the center “View” window of
HYDRUS GUI, depending on what processes are being simulated. These variables are divided
between standard variables, such as pressure heads, water contents, and/or liquid concentrations,and alternative variables, such as different types of water contents (mobile, immobile, and total) or
concentrations (liquid, solid, gas, or total). While the standard variables can be selected from the“Data” tab of the Navigator bar, the alternative variables can be selected from the View tab of theNavigator bar (Fig. 8).

24

Figure 8. Standard and alternative variables that can be displayed in the View window.

4. Conclusions
The HYDRUS models have served, and are serving, an important role in vadose zone research.
This is reflected by their frequent use in a variety of applications, many of them leading to peerreviewed publications (HYDRUS website lists over one thousand references, in which HYDRUS
has been used). The need for codes such as HYDRUS is further reflected by the frequency ofdownloading the program from the HYDRUS web site. For example, HYDRUS-1D was
downloaded more than 10,000 times in 2012 by users from some 50 different countries. The
HYDRUS web site receives on average some 700 individual visitors each day.

References

Gärdenäs, A., Hopmans, J. W., B. R. Hanson, and J. Šimůnek, Two-dimensional modeling of nitrateleaching for various fertigation scenarios under micro-irrigation, Agricultural Water Management, 74,
219-242, 2005.
Gerke, H. H., M. Th. van Genuchten, A dual-porosity model for simulating the preferential movement ofwater and solutes in structured porous media, Water Resources Research, 29, 305-319, 1993.
Hardelauf, H., M. Javaux, M. Herbst, S. Gottschalk, R. Kasteel, J. Vanderborght, and H. Vereecken,
PARSWMS: a parallelized model for simulating 3-D water flow and solute transport in variably
saturated soils, Vadose Zone Journal, 6(2), 255-259, 2007.
Jacques, D., and J. Šimůnek, User Manual of the Multicomponent Variably-Saturated Flow and Transport
Model HP1, Description, Verification and Examples, Version 1.0, SCK•CEN-BLG-998, Waste andDisposal, SCK•CEN, Mol, Belgium, 79 pp., 2005.
Jacques, D., J. Šimůnek, D. Mallants, and M. Th. van Genuchten, The HPx reactive transport models:
Summary of recent developments and applications, (this issue), 2013.
Langergraber, G., and J. Šimůnek, Modeling variably-saturated water flow and multi-component reactive
transport in constructed wetlands, Vadose Zone J., 4(4), 924-938, 2005.
Langergraber, G., D. Rousseau, J. García, and J. Mena, CWM1 - A general model to describe biokinetic
processes in subsurface flow constructed wetlands, Water Sci. Technol., 59(9), 1687-1697, 2009.
Langergraber, G., and J. Šimůnek, Reactive transport modeling of subsurface flow constructed wetlands,
Vadose Zone Journal, 11(2), doi:10.2136/vzj2011.0104, 14 pp., 2012.
Lazarovitch, N., J. Šimůnek, and U. Shani, System dependent boundary condition for water flow fromsubsurface source, Soil Sci. Soc. Am. J., 69(1), 46-50, 2005.

25

Millington, R. J., and J. M. Quirk, Permeability of porous solids, Trans. Faraday Soc., 57, 1200-1207,
1961.
Moldrup, P., T. Olesen, D. E. Rolston, and T. Yamaguchi, Modeling diffusion and reaction in soils: VII.
Predicting gas and ion diffusivity in undisturbed and sieved soils, Soil Sci., 162(9), 632-640, 1997.
Moldrup, P., T. Olesen, J. Gamst, P. Schjønning, T. Yamaguchi, and D. E. Rolston, Predicting the gas
diffusion coefficient in repacked soil: water-induced linear reduction model, Soil Sci. Soc. Am. J., 64,
1588-1594, 2000.
Parkhurst D. L., and C. A. J. Appelo, User’s guide to PHREEQ C (Version 2) – A computer program forspeciation, batch-reaction, one-dimensional transport and inverse geochemical calculations, WaterResources Investigations, Report 99–4259, Denver, Co, USA, 312 pp., 1999.
Šimůnek, J., and D. L. Suarez, Two-dimensional transport model for variably saturated porous media withmajor ion chemistry, Water Resources Research, 30(4), 1115-1133, 1994.
Šimůnek, J., Changming He, J. L. Pang, and S. A. Bradford, Colloid-facilitated transport in variablysaturated porous media: Numerical model and experimental verification, Vadose Zone Journal, 5(3),1035-1047, 2006.
Šimůnek, J. and J. W. Hopmans, Modeling compensated root water and nutrient uptake, EcologicalModeling, doi:10.1016/j.ecolmodel.2008.11.004, 220(4), 505-521, 2009.
Šimůnek, J., and M. Th. van Genuchten, Modeling nonequilibrium flow and transport processes using
HYDRUS, Vadose Zone Journal, 7(2), 782-797, 2008.
Šimůnek, J., M. Th. van Genuchten, and M. Šejna, Development and applications of the HYDRUS andSTANMOD software packages, and related codes, Vadose Zone Journal, 7(2), 587-600, 2008.
Šimůnek, J., M. Šejna, and M. Th. van Genuchten, The UNSATCHEM Module for HYDRUS (2D/3D)
Simulating Two-Dimensional Movement of and Reactions Between Major Ions in Soils, Version 1.0, PC
Progress, Prague, Czech Republic, 54 pp., 2012a.
Šimůnek, J., M. Šejna, and M. Th. van Genuchten, The DualPerm Module for HYDRUS (2D/3D) Simulating
Two-Dimensional Water Movement and Solute Transport in Dual-Permeability Porous Media, Version
1.0, PC Progress, Prague, Czech Republic, 32 pp., 2012b.
Šimůnek, J., M. Šejna, and M. Th. van Genuchten, The C-Ride Module for HYDRUS (2D/3D) Simulating
Two-Dimensional Colloid-Facilitated Solute Transport in Variably-Saturated Porous Media, Version 1.0,
PC Progress, Prague, Czech Republic, 45 pp., 2012c.
Šimůnek, J., D. Jacques, M. Šejna, and M. Th. van Genuchten, The HP2 Program for HYDRUS (2D/3D): A
Coupled Code for Simulating Two-Dimensional Variably-Saturated Water Flow, Heat Transport, andBiogeochemistry in Porous Media, Version 1.0, PC Progress, Prague, Czech Republic, 76 pp., 2012d.
Šimůnek, J., D. Jacques, and M. Šejna, HP2/3: Extensions of the HP1 reactive transport code to two andthree dimensions, (this issue), 2013.
Spurlock, F., J. Šimůnek, B. Johnson, and, A. Tuli, Sensitivity analysis of vadose zone fumigant transportand volatilization, Vadose Zone Journal, doi:10.2136/vzj2012.0130, (in press), 2013.
Twarakavi, N. K. C, M. Sakai, and J. Šimůnek, An objective analysis of the dynamic nature of field
capacity, Water Resources Research, 45, W10410, doi:10.1029/2009WR007944, 9 pp., 2009.
Walker, A., A simulation model for prediction of herbicide persistence, J. Environ. Quality, 3(4), 396401, 1974.

26

Investigating the Impact of the Irrigation Method on Profitabilityof Smallholder Gardening:
Incorporating HYDRUS-1D into a Decision Support System
Adam Abramson1, Eilon Adar1, and Naftali Lazarovitch2
1

Dept of Environmental Hydrology and Microbiology, Zuckerberg Institute for Water Research,adamab@bgu.ac.il and eilon@bgu.ac.il
2
Wyler Department of Dryland Agriculture, French Associates, Institute for Agriculture and Biotechnology of
Drylands, The Jacob Blaustein Institutes for Desert Research, Ben-Gurion University of the Negev,
Sede Boqer Campus, Midreshet Ben-Gurion, Israel, lazarovi@bgu.ac.il

AbstractDry-season irrigation in tropical developing regions provides many households with both nutritional andmonetary supplements. Optimizing production from these small-scale gardens is complicated by theunpredictability of water amounts available throughout the season, as well as the time, labor, and capitalconstraints common to subsistence livelihoods. Drip irrigation, known mostly for its high water use
efficiency, holds additional benefits of time savings in comparison to a conventional hand-watering of
smallholder gardens. The HYDRUS-1D software was incorporated into the Microsoft® Excel-based
Decision Support System (DSS) to model and compare the economic performance of these two irrigation
methods under a holistic range of agronomic, labor, and water parameter values. Results of thisinvestigation suggest that, due to the tradeoff between capital costs and time-savings, drip irrigation does
not always result in optimal net revenue as compared to hand-watering. We identified a linear relationshipbetween the rate of revenue earned and the ratio between water and time availability for both irrigation
methods. While these relationships are nearly identical, they reach a unique threshold value after whichwater becomes a limiting factor. The value of this threshold is lower for hand watering because theamount of water applied per unit of working time is less, thus labor becomes a limiting constraint at lower
water supply levels. Drip irrigation allows labor to earn higher revenue at sufficient water supplies. Thus,
it should be promoted where labor is relatively limiting.

1. Introduction
Dry-season irrigation in remote areas of tropical developing regions provides many householdswith both nutritional and monetary supplements. Often, smallholders depend on traditional(unimproved) water sources for meeting their irrigation needs, which are highly seasonal andmany times unreliable throughout the length of the season: dams, ponds, ephemeral streams, or
hand-dug shallow wells. Optimizing profits from these small-scale gardens is complicated by theunpredictability of water amounts available through the season as well as the time, labor, andcapital constraints common to subsistence livelihoods. In resource-poor communities, labor
commitments may replace cash payments for critical investments, such as water supplies, whencoupled to income generating activities, such as irrigation (Abramson et al., 2011). Millions ofsmallholder farmers face the above challenges daily.
Low-cost drip irrigation has emerged as a means to address these challenges through increased
water use efficiency, labor savings, and higher economic returns (Ngigi et al., 2005; Polak et al.,27

2003; Friedlander et al., 2013). A recent study quantified the time savings and economic gains
associated with drip irrigation for smallholders (Woltering et al., 2011). However, no studies
have investigated the economic advantages of drip irrigation against traditional hand-watering
while holistically considering all relevant constraints within a sufficiently robust modelingenvironment. These include agronomic factors as well as labor and water availability. This
study’s aim is to outline, through a representative scenario under a range of parameter values, thestrategic niche of drip irrigation against hand-watering in smallholder gardens.
2. Materials and Methods
Figure 1 presents a comparison of the time and capital costs of hand-watering and drip irrigation.

Figure 1. Relationship between work requirements, capital costs and irrigation method. Drip
irrigation saves time, but requires more initial capital than hand watering. Work requirement data
are adapted from Woltering (2011).

The HYDRUS-1D modeling environment (Šimůnek et al., 2008) was incorporated into a
Microsoft® Excel-based Decision Support System (DSS) for investigating the economics of rural
water development (Abramson, 2013). Modeled transpiration levels for field-grown tomato
under a range of irrigation rates (mm day-1) were obtained through a VBA-coded automation
mechanism of the HYDRUS-1D software within Excel. These transpiration results were thentranslated into actual crop yields according to the yield-transpiration relationship investigated by
Ben-Gal et al. (2003) for field-grown tomato. Various measures of time availability in the garden
were input into the DSS. For 100 irrigation levels discretized between 10% and 150% of PET,
total agricultural costs, comprised of capital and operation costs ($ m-2), were calculated alongwith modeled yields(kg m-2) and benefits ($ m-2).

28

In the DSS optimization scheme, two main constraints exist for determining the revenue
generated from irrigation: availability of labor (the time constraint) and the amount of available
water for irrigation (the water constraint). Optimal net benefit occurs at the maximum of:
Net Benefiti  Min (Time,Water Constra int s ) 
where i is irrigation level (mm day-1).
3. Results
In order to demonstrate the general trends of these factors, a single scenario was defined andimputed (Fig. 2).

Figure 2. Yield, net benefit, and total revenue by irrigation method and application rate. In this
scenario tomato is grown according to the yield-transpiration relationship derived by Ben-Gal(2003), PET is 5 mm, salinity is 0.1 dS m-1, produce earns $2 kg-1, and irrigation is conducted
over 3 seasons.

As expected, both total yield and net benefit increase linearly with irrigation application untilroughly 100% of PET. Due to the tradeoffs illustrated in Figure 1, with increasing irrigation
applications, work requirements also increase, resulting in less area that can be cultivated. The
optimal revenue is achieved in light of these two opposing factors.
Figure 3 demonstrates that where the time constraint is the limiting factor (i.e., allows less
irrigated area than available water), drip irrigation strongly outperforms hand watering. This isbecause of the time savings, which translates into higher irrigated areas and higher project
revenues. Figure 4 presents a generalized representation of these trends.

29

Figure 3. The relationship between irrigation application, labor availability, irrigation method,and project revenue for three scenarios: a) low (20 hr wk-1); b) intermediate (100 hr wk-1); and c)high (1,000 hr wk-1) labor availability. Dotted lines represent the peak revenue achieved.

30

Figure 4. The relationship between available water and labor against revenue earned, expressedby the variation of the revenue rate by the ratio of available water-to-labor. Linear regression of
the first (increasing) section of each line supports a constant, and nearly identical slope, which
represents the revenue earned per daily water supply available ($ (m-3 day-1)). The area to theright of the vertical dotted line represents scenarios where drip irrigation is advantageous to handwatering, and vice versa. The nearly identical slopes of the two regression lines and the unitary
values of R2 indicate that these trends are explained entirely by the factors investigated.

As the available water-to-labor ratio increases, the revenue rate reaches a threshold. The value of
this threshold is lower for hand watering because the amount of water applied per unit of timeworking is less, thus labor becomes a limiting constraint at lower water supply levels. Drip
irrigation allows labor to earn higher revenue where water supplies are sufficiently high in
relation to time commitments. Thus, it should be promoted where labor is relatively limiting.
The exact values of these figures will change according to the scenario investigated, but thesetrends will remain.
4. Conclusions
These results demonstrate the following:
1) While drip irrigation certainly does demonstrate applicability in low resource smallholder
economies, this may be limited to very water and/or labor scarce conditions. Given thetime-capital tradeoffs associated with the transition from subsistence to ‘developed’
economic status, drip irrigation finds its niche in the latter stages of this transition. Other
non-market benefits, however, such as increased water use efficiency, should be included
in development strategies.
2) The HYDRUS-1D software can be effectively automated for conducting Excel-based
analyses through simple algorithms.

31

References

Abramson, A., Decision Support System for assessing full cost recovery of water development in rural
Africa, PhD Thesis, Ben Gurion University of the Negev, Israel, 2013. DSS Available online atwww.outoftheground.org or https://dl.dropbox.com/u/24352729/DSS.zip
Abramson, A., N. Becker, Y. Garb, and N. Lazarovitch, Willingness to pay, borrow, and work for rural
water service improvements in developing countries, Water Resour. Res., 47, W11512,
doi:10.1029/2010WR010147, 2011.
Ben-Gal, A., L. Karlberg, P. Jansen, and U. Shani, Temporal robustness of linear relationships between
production and transpiration, Plant and Soil, 251(2), 211-218, 2003.
Friedlander, L., A. Tal, and N. Lazarovitch, Technical considerations affecting adoption of drip irrigationin sub-Saharan Africa, Agricultural water management, in press, 2013.
Ngigi, S., H. Savenije, J. N. Thome, J. Rockstrom, and F. Penning de Vries, Agro-hydrological evaluationof on-farm rainwater storage systems for supplemental irrigation in Laikipia district, Kenya,
Agricultural Water Management, 73, 21-41, 2005.
Polak, P., D. Adhikar, B. Nanes, D. Salter, and S. Suryawanshi, Transforming rural water access into
profitable business opportunities, In: Proceedings of the International symposium on Water, Poverty
and Productive Uses of Water at the Household Level, Muldersdrift, South Africa, 21-23 January,
2003.
Šimůnek, J., M. Th. van Genuchten, and M. Šejna, Development and applications of the HYDRUS andSTANMOD software packages, and related codes, Vadose Zone Journal, 7(2), 587-600, 2008.
Woltering, L., A. Ibrahim, D. Posternak, and J. Ndjeunga, The economics of low pressure drip irrigationand of hand watering for vegetable production in the Sahel, Agricultural Water Management, 99, 6773, 2011.

32

Simulation of Water and Air Distribution
in Growing Media
Ruediger Anlauf1 and Peter Rehrmann2
1

Faculty of Agricultural Sciences and Landscape Architectur, Osnabrueck University of Applied Sciences,
Osnabrueck, Germany, r.anlauf@hs-osnabrueck.de
2
Faculty of Agricultural Sciences and Landscape Architectur, Osnabrueck University of Applied Sciences,
Osnabrueck, Germany, p.rehrmann@hs-osnabrueck.de

Abstract
Understanding the water and air contents of growing media in plant containers is important for growers.
To optimize crop growth, the relative effect of substrate type and irrigation strategy on water uptake ofgrowing media must be known. Describing water uptake and distribution in the container with a dynamic
simulation model may overcome the disadvantages of static parameters such as container capacity and air
capacity. Water uptake and redistribution was investigated for an ebb-and-flow irrigation system with two
different growing media, a coarse white peat and a fine seedling substrate, at two flooding depths (1 and 4cm) and for three flooding durations (5, 10 and 15 min). The results were used to evaluate the use of
HYDRUS-1D to describe water uptake and redistribution. The hydraulic functions (water retention andhydraulic conductivity curves) needed for the simulation model were determined in the laboratory.
Hysteresis becomes especially important in irrigation systems where water is applied from the bottom of
the container, such as in ebb-and-flow irrigation.
Preliminary simulations with HYDRUS-1D showed that hysteresis in the water retention curve must be
taken into account for growing media to get reliable simulation results. Water retention drying curves
were determined through the use of a standard sand box apparatus. Wetting curves were determined withequipment that allowed water contents of growing media to be measured in an experimental container
with a constant flooding depth. Under the assumption that the water content at equilibrium is analogous to
the water retention curve, the water content of the growing media above the water table will correspond to
distinct pF values. Drying and wetting curves were parameterized to be used in HYDRUS-1D. The
simulation was divided into a flooding cycle with a constant head lower boundary condition and adrainage cycle with a seepage phase boundary condition. The simulated water content at the end of theflooding cycle was used as the initial condition for the drainage cycle. The results show that HYDRUS1D is able to describe water uptake and redistribution in containers filled with growing media sufficiently
well, but only if hysteresis in the water retention curve is taken into account. This correct representationof the water balance in plant containers is an important basis for future work on oxygen concentration
changes in growing media. Part of this study has been published elsewhere (Anlauf et al., 2012).

1. Introduction
Ebb-and-Flow irrigation is often used in horticultural practices to irrigate plant containers on
concrete floors. The depth of water during irrigation is usually 1 to 2 cm but can be as much as 5cm (Aendekerk, 1997; Raviv and Lieth, 2008). It is very important that the irrigation water isquickly and evenly distributed to realize a relatively uniform water level for all containers on thefloor. The water is drained after about 10 to 20 min and collected in a storage tank (Raviv andLieth, 2008).
1
33

It is known from practical experience that uneven water distributions in containers at different
positions on a concrete floor occur frequently. One of the main reasons is the necessary slope ofthe concrete floor (0.2 to 0.4%) to realize quick drainage of water (Raviv and Lieth, 2008).
Containers at a lower position will receive a higher irrigation depth and a longer irrigation timecompared to containers at higher positions (example in Figure 1). This may result in either
drought stress for the plants at some positions or too much moisture at others which then may
cause aeration and disease problems.

Edge position:
flooding depth 0.5 cm
for 10 min, often too dry

Center position:
flooding depth 3 cm
for 15 min, often too wet, notFigure 1. Example of uneven water distribution in containers at different positions on
a concrete floor.

The physical properties of growing media describing the quality of the substrate for different
horticultural uses are usually measured for standard conditions, such as container capacity andair capacity, both measured at a matric potential of -10 hPa. These methods are standardized(DIN EN 13041, 2010) and are widely accepted.
However, horticultural practices show that in some situations producers have problems related to
low oxygen supply, even with growing media with a high air capacity, while in other cases plants
with good growth and quality are produced using substrates of minor quality. This is not
surprising because the standard parameters describe a static condition, whereas in horticultural
practice a dynamic system exists in which the actual water and air contents fluctuateconsiderably with time, mainly due to the irrigation practices. Therefore, methods to describe thedynamic behavior of water and air in growing media, such as simulation models, seem to bepromising tools to more realistically describe actual situations in a container (Fonteno, 1993;
Heinen and de Willigen, 1995; Palla et al., 2008).
The use of simulation models to calculate water uptake and redistribution in plant containers
depending on irrigation depth, time, and type of material could be a cost-effective method.
Computer models are frequently and effectively used to simulate water movement in mineralsoils. Model applications for growing media are much less frequent and the quality of thesimulation is usually less good compared to mineral soils. Possible reasons are shrinking and234

swelling processes and the hysteretic behavior of the hydraulic functions. Both processes are ofmuch higher significance in growing media compared to mineral soils.
The objectives of this study were (i) to describe physical parameters related to water and gas
transport in different growing media, and (ii) to test the ability of HYDRUS-1D to describe watercontent, water uptake, and redistribution in the two materials. The final goal was to develop a
simple system to describe water and oxygen supply in growing media, based on a simulation
model, usable under practical conditions for growers. Study details of the effect of flooding
depth, flooding duration, and type of growing media on water uptake are given in Anlauf et al.
(2012).

2. Materials and Methods
2.1. Water Retention Curve
The physical properties of growing media are described with different specific parameters.
However, the use of these parameters is not always consistently used in literature. In this study,
we used the following definitions (De Boodt and Verdonck, 1972; Raviv and Lieth, 2008): total
porosity (TP) (combined volume of the liquid and gaseous phase of the medium), air capacity(AC) (volumetric percentage of the medium filled with air at a matric potential of 10 hPa, i.e.,the difference between the water content at 10 hPa and the total porosity), container capacity(CC) (volumetric water content at 10 hPa), easily available water (EAW) (difference between thevolumetric water contents at 10 and 50 hPa) and the water buffering capacity (WBC) (difference
between the volumetric water contents at 50 and 100 hPa).
The basis for modeling the behavior of water in porous media is the media’s pore structure,
which is reflected in the water retention curve and the unsaturated hydraulic conductivity
function. Both functions are necessary to simulate changes in the content and fluxes of water.
After drying, poor rewetting of the growing medium is often observed. Thus, the water content
of the substrate upon rewetting at a given matric potential will not reach its value measured
before drying. This is due to air inclusions or wetting problems of the organic material and iscalled hysteresis in the water retention curve (Raviv and Lieth, 2008). Hysteresis becomes
especially important in irrigation systems where the water is applied from the bottom of thecontainer, such as ebb-and-flow irrigation (Wever et al., 1997).
Applications of unsaturated flow models often assume unique, non-hysteretic water retention andhydraulic conductivity functions to characterize the hydraulic properties of a material. Such asimplification may be acceptable for flow simulations in mineral soils; growing media usuallyrequire a more realistic description involving hysteresis in the soil hydraulic properties (Heinen
and Raats, 1999; Naasz et al., 2005; Raviv and Lieth, 2008). The procedure for modelinghysteresis in the retention function in the HYDRUS model requires that both the main drying andmain wetting curves are known. In that case θr, θs and n are assumed constant for the drying andwetting curves (Šimůnek et al., 2008). Thus, α is then the only parameter to change whendescribing the main wetting and drying curves.

335

2.2. Initial and Boundary Conditions for the HYDRUS-1D Simulations
The initial water content (or matric potential) for all depths must be specified at the start of thesimulation. For the flooding cycle, a matric potential corresponding to the measured initial watercontent was specified for the depths above the water surface (-20 hPa or 32 % vol and -5000 hPa
or 18.7 % vol for the seedling substrate and white peat, respectively). At the water surface during
the flooding cycle (4 and 1 cm above the container bottom), a matric potential of 0 hPa was
specified, and at the container bottom, a matric potential of +4 and +1 hPa, respectively.
Between the container bottom and the water surface, a linear interpolation of the matric potential
was carried out. For the drainage cycle, the simulated water content at the end of the flooding
cycle was used as initial condition.
Due to the different physical conditions during flooding and drainage phases, different boundary
conditions have to be used (Figure 2). For both the flooding and drainage cycles, a constant zero
flux was used as the upper boundary condition, i.e. the assumption that there is no evaporationfrom the surface of the growing media during the short time period of 35 to 105 minutes.
The lower boundary condition during the flooding cycle is a constant matric potential of zero at
the water surface. During the drainage cycle, the lower boundary condition changes to a seepage
face boundary condition: as long as the lower end of the container is saturated, the pressure head
becomes zero and water may leave the container. If the matric potential becomes negative(unsaturated conditions), no more water may leave the container and the flux becomes zero.
Thus, the boundary condition changes from a constant zero potential to a constant zero flux(Šimůnek et al., 2008).

Figure 2. Boundary conditions for the simulation during flooding and drainage phase.

436

2.3. Model Quality Evaluation
To evaluate the quality of the simulations with HYDRUS-1D, different quality measures wereapplied: for a quick overview of the modeling quality, graphs measured against the simulated
values were drawn together with the linear regression, the correlation coefficient, and the 1:1
line. The points of good quality simulations should lie close to the 1:1 line, the slope of the linear
regression should be close to 1, and the correlation coefficient should be close to 1. Widely usedmeasures of agreement between measured and simulated values are the root mean squared error(RMSE) and the modeling efficiency (EF) (Wallach, 2006):
n

RMSE 

 X  P N1
 X i  Pi 2
N i 1i

EF  1  ni 12i X  X 
i 1

i

2

av

where N is the number of observations, Xi are the measured values, Pi the simulated (predicted)
values and Xav the average of the measured values. EF calculates the advantage of model resultscompared to using one average value. If the model gives perfect results, the predicted values Pi
will be equal to the measured values Xi and, thus, EF = 1. If the average of the measured values
is used as a predictor for every case, EF = 0. A model which is a worse predictor than the
average may result in EF < 0. A model with acceptable quality should have EF > 0.5.
2.4. Experimental Setup
The experimental container (Figure 3, left) is made up of six elements with an inner diameter of
10 cm. The total height is 15 cm, so that the shrinking of the substrate during irrigation anddrying can be considered. The topmost ring is 5 cm high; the following five rings have a heightof 2 cm each. The bottom of the container is replaced by a piece of gauze, which is stretchedaround the lower ring. The volume of the experimental container is 1.178 L. Three flooding
times (5 min, 10 min, and 15 min), two flooding depths (1 cm and 4 cm), and 3 drainage
durations (10 min, 30 min, and 90 min) were used. The flooding depths and durations wereselected according to usual practice. Each treatment was carried out in four replications. To
simulate the greenhouse floor, a specially made flooding tub is used (Figure 3, right).

Figure 3. Experimental containers with 10 cm inner diameter and 15 cm height.

537

2.5. Growing Media Used in the Study
Two types of substrate typically used in horticultural practice were chosen to carry out thisinvestigation: Lithuanian white peat and a commercially available seedling substrate (Figure 4).
The seedling substrate contains white peat, black peat and finely sieved cocos fiber. It is a
substrate which is used especially for salinity sensitive ornamental seedlings in trays.

Figure 4. Growing media used: Coarse white peat (left) and seedling substrate (right).

The chemical properties of the substrates used in this study (EC 1:5, pH 1:5) were determinedaccording to DIN EN 13037 (2009) and DIN EN 13038 (2009). Organic matter was determined
as ignition loss (DIN EN 13039, 2009): air dried and ground substrate samples are burnt at
550°C for 24 h in a muffle furnace. The residue is considered as mineral material and the ignition
loss as organic matter. Both are expressed as weight percent and related to dry matter content.
The particle size distribution of each substrate was determined using three 100 g oven dry
samples. Each sample was placed on a series of 5 sieves (ranging from 4 to 0.5 mm) and shaken
for 5 min at 160 shakes per min. Portions of substrate samples remaining on each screen were
weighed and expressed as the percentage of total sample weight. The mean weight diameter(MWD) was calculated according to Kemper and Rosenau (1986). Bulk density was determined
after VDLUFA (1991). Particle density (DP) was estimated from the gravimetric organic matter
content and the gravimetric mineral matter content (DIN EN 13041, 2010). The saturated
hydraulic conductivity was determined with an Eijkelkamp constant head infiltrometer (DIN
19683, 1998).
Water retention drying curves were determined using an Eijkelkamp standard sand box apparatus(Gabriels and Verdonck, 1991; DIN EN 13041, 2010) to measure the water content at pF 0.7,
1.0, 1.5 and 2.0. The TP was calculated as TP = (1 – DB/DP), where DB is bulk density (g·cm-3)
and DP is the particle density (g·cm-3). The water retention curve was parameterized after van
Genuchten (1980) from total porosity and the volumetric water content at the measured pF
values.
As growing media are known to show intensive hysteretic behavior, water retention wetting
curves were determined with the above mentioned experimental container made up of six
638

elements. The rings were filled with growing media with the same initial water content as in theexperiments (-20 hPa or 32%vol and -5.000 hPa or 18.7%vol for the seedling substrate and whitepeat, respectively) and with the same bulk density. A flooding depth of 1 cm was installed(Figure 5). Under the assumption that the water content at equilibrium is analogous to the water
retention curve (Raviv and Lieth, 2008), the water content of the media in the rings 2, 4, 6, and 8
cm above the water surface will correspond to pF log(2) [pF 0.3], pF log(4) [pF 0.6], pF log(6)[pF 0.78], and pF log (8) [pF 0.9]. The water retention wetting curve was parameterized byadjusting the parameter α (Šimůnek et al., 2008). The other van-Genuchten parameters were thesame as in the drying curve.

Figure 5. Experimental setup to determine the wetting water retention curve.

3. Results
3.1. Properties of the Growing MediaTable 1 shows some basic properties of the studied materials. The bulk densities of 0.130 and
0.139 g·cm-3 and the high organic matter content of 0.069 and 0.886 g·g-1 are typical for mostgrowing media. The seedling substrate had a larger percentage of fine particles (< 2 mm; 88.2%)
than the white peat (46.4%). The mean weight diameter was 1.15 mm for the seedling substrate
and 5.65 mm for the white peat. Consequently, one can expect a higher percentage of small
pores, more easily available water, and lower air capacity of the seedling substrate compared to
the white peat. This should also be reflected in the water retention curve.
Table 1. Properties of the studied materials.
DB
DP
OM
EC
(g·cm-3)(g·cm-3)(g·g-1)(mS· m-1)
White Peat
3.9
10
0.130
1.57
0.969
Seedling Substrate
5.5
25
0.139
1.63
0.886
pH (1:10), EC (1:10), DB: bulk density, DP: particle density,
OM: organic matter, FP: fine particles < 2 mm, MWD: Mean weight diameter
pH

7
39

FP
(%)
46.4
88.2

MWD
(mm)
5.65
1.15

3.2. Water Retention Curves
Major differences were observed in the water holding parameters of the two substrates (Table 2).
The total porosity and the water buffering capacity were nearly equal. The container capacity(CC; 0.88 and 0.71 cm3·cm-3) at 10 hPa and the easily available water (EAW; 0.44 and 0.26
cm3·cm-3) were significantly higher in the seedling substrate compared to the peat, while the air
capacity (AC; 0.03 and 0.21 cm3·cm-3) was significantly lower for the seedling substratecompared to the white peat. This agrees well with the particle size distribution that showed ahigh percentage of small particles in the seedling substrate compared to the peat. The measured
saturated hydraulic conductivity was slightly lower in the seedling substrate compared to thepeat, which also agrees with the smaller particle size.
Table 2. Physical properties of the two materials.
Material

White Peat
Seedling Substr.

Total
Porosity(TP)
cm3·cm-3
0.92
0.91

Container
Capacity(CC)
cm3·cm-3
0.71
0.88

Air
Capacity(AC)
cm3·cm-3
0.21
0.03

Easily Avail.
Water
(EAW)
cm3·cm-3
0.26
0.44

Water Buffering Capacity(WBC)
cm3·cm-3
0.06
0.05

Sat. Hydraulic
Conductivity(Ks)
cm·s-1
0.121
0.097

Figure 6 shows the drying and wetting water retention curves for both media. The vanGenuchten parameters θr, αw and n were fitted to the measured data by the least square
regression, whereas θs was fixed as the water content at saturation. The van Genuchten
parameters and the air entry values are given in Table 3.

Figure 6. Water retention curves (drying and wetting curves) for the white peat and the seedling
substrate.

840

Table 3. van Genuchten parameters for the water retention drying andwetting curves for the peat and the seedling substrate.
Parameterθs [cm³·cm-³]
θr [cm³·cm-³]
αd
αw
αw/αd
n
Air entry value [hPa]White Peat
0.920
0.187
0.232
1.600
6.90
1.411
-1

Seedling Substrate
0.910
0.373
0.055
0.320
5.82
3.022
-8

The air entry value (graphical determination according to Konyai et al., 2009) characterizes thematric potential at which the largest pores drain during drying, and air starts entering thematerial. The air entry value of the peat (-1 hPa) corresponds to a maximum pore size of
approximately 3 mm (Hillel, 1998). The air entry value of the much finer seedling substrate (-8hPa) corresponds to a maximum pore size of approximately 0.375 mm.
The residual water content θr of the van-Genuchten parameterization (0.37 and 0.19 cm3·cm-3 forthe seedling substrate and the peat, respectively) also characterizes much higher water content at
low matric potentials and thus lower air content. The wetting curves show a distinct hysteresis
for both substrates (Figure 6). To describe hysteresis, the α values were fitted to the measured
data by the least square regression (Table 3). The parameter αw, describing the shape of the wet
curve, was about 6 times larger than the parameter αd describing the drying curve. The measured
water content at high matric potentials (-5 to -10 hPa), where hysteresis shows its main effect,
was about 20% higher for both growing media for the drying curve compared to the wetting
curve. This corresponds well with investigations by other authors of hysteresis in peat substrates(Wever et al., 1997; Aendekerk, 1997).
3.3. Simulation Results
In the first step, the water uptake and redistribution was simulated without taking hysteresis into
account. As an example, figures 7a and b show the results of the simulation for a flooding
duration of 15 min, a flooding depth of 1 cm, and a drainage time of 90 min. Obviously, thesimulated water content is much higher than the measured one. In the bottommost layer, thesimulated water content exceeds the measured by 10 to 20%vol. In the topmost layer, thesimulated water content is about 40 to 50%vol higher than the simulated one. Thus, the model
highly over-estimates the amount of water entering the substrate by capillary forces. This fact isalso reflected in the significantly different drying and wetting water retention curves. To describewater content and water uptake correctly with the model, the hysteresis of the water retention
curve must be taken into account. Considering hysteresis, the simulation yields a completely
different picture (Figures 7c and d). Due to hysteresis, the water uptake into the initiallyrelatively dry substrate during the flooding period is much smaller. The measured and simulated
values agree much better. Therefore, the simulations for all cases measured were carried out
using the hysteretic water retention curves.
Table 4 shows numerical quality measures for the simulation of the water content in thecontainers. R2 (0.96 and 0.91 for the white peat and seedling substrate, respectively) is high. The
941

slope of the regression line (1.15 and 1.20) however, indicates that there is a tendency that themodel under-estimates low values and over-estimates high values. Similar but slightly better
results can be seen for the water uptake, where R2 is both 0.98 and the slope is 1.13 and 1.10 for
the white peat and seedling substrate, respectively. RMSE for the 1 cm flooding depth is less thanfor a 4 cm flooding depth, and there are no big differences in the simulation quality between thetwo investigated growing media. The modeling efficiency EF ranges from 0.70 to 0.97,
indicating a reasonable to very good simulation quality. The maximum total water uptake for thedifferent measurements in the experimental containers is approximately 550 cm³. Similar to thesimulation of the water content, the RMSE gives similar results for the simulated water uptake(Table 4): the simulation quality for 1 cm flooding depth is better than for a 4 cm flooding depth,
and there are no big differences in the simulation quality between the two growing media. EF isvery high, ranging from 0.95 to 0.99.

a)

b)

c)

c)
Figure 7. Water content (% vol) after 15 min of flooding, at a flooding depth 1 cm, and after 90
min of drainage, simulated without hysteresis (a, b) and with hysteresis (c, d) for the white peat
and the seedling substrate.

1042

Table 4. Quality measures for the simulation of the water content and water uptake.
MeasureWhite peat
Seedling substrate
4 cm
All
1 cm
4 cm
All
flooding
flooding flooding
depth
depth
depth
Simulation of water content
R2
0.977
0.956
0.961
0.920
0.868
0.910
Slope
1.040
1.225
1.150
1.211
1.139
1.197
RMSE (%vol)
6.67
8.36
7.56
3.56
8.96
6.81
EF
0.827
0.698
0.766
0.973
0.844
0.905
Simulation of the water uptake
R2
0.988
0.983
0.982
0.974
0.988
0.981
Slope
1.020
1.156
1.129
1.035
1.122
1.103
RMSE (cm³)
53.61
182.60134.5735.88
187.64135.09
EF
0.994
0.966
0.975
0.994
0.948
0.958
RMSE: root mean squared error; EF: modeling efficiency
1 cm
flooding
depth

4. Discussion and Conclusions
The model highly over-estimates the amount of water entering the substrate by capillary forces.
This fact is also reflected in the drying and wetting water retention curves which differ
significantly. To correctly describe water content and water uptake with the model, the hysteresisof the water retention curve must be taken into account. During the flooding period, the model
mainly uses the wetting water retention curve, whereas during the drainage and redistribution
phase, both curves and their connections are used: In the lower parts of the container, the watercontent mainly decreased during drainage and redistribution, resulting in the use of the drying
curve, whereas in the upper part of the container, some capillary rise of water takes place,
resulting in the use of the wetting curve.
The simulation results show that the simulation model, HYDRUS-1D is able to basicallydescribe water uptake and redistribution in containers filled with the two investigated growing
media. However, as these substrates show high hysteresis of the water retention curve, it isabsolutely necessary that the model takes this hysteresis into account. The regression lines of thesimulated against the measured values indicate that on average, the higher water contents areslightly over-estimated, whereas the lower water contents are under-estimated. A possible reason
is that the hysteresis of the water retention curve is not completely correctly described because
this hysteresis mainly governs the water uptake and distribution in the container. The descriptionof hysteresis is simplified in two aspects: 1) the wetting curve is described only by changing theparameter α of the van-Genuchten parameterization while the other parameters are kept constant.
This is done because the HYDRUS-1D version used has only this option to consider hysteresis,
while other authors suggest that hysteresis of growing media needs a more complex formulation(Naasz et al., 2005); 2) the determination of the wetting curve was done in a very simple way tomeasure the water content in different layers after water uptake took place and then relating thesevalues to the theoretical matric potential at equilibrium. This method should be evaluated andoptimized in future investigations. However, the use of HYDRUS-1D seems to be a promising
method to overcome the pure static description of physical properties of growing media, such as
11
43

available water capacity and air capacity, and moves toward a dynamic description of the water
movement in containers, with the ultimate goal of optimizing the production of horticultural
plants produced in growing media.

5. Outlook and Future Work
The final goal of the investigation was to develop a simple system to describe oxygen supply ingrowing media based on a simulation model. The basis for the simulation of oxygen in growing
media is a correct simulation of water uptake and redistribution. The next step will be measuringand modeling the dependency of the oxygen diffusion coefficient on air content for different
growing media in diffusion chambers with different bulk densities. Preliminary results show thatthe oxygen diffusion coefficient depends on water content and substrate density, which bothinfluence air content of growing media. There is a stable dependency of the oxygen diffusion
coefficient on air content, irrespective of the type of growing media (Schmitz et al., 2013). This
relation can best be described by the function of Moldrup (1997).
Another important factor to describe oxygen supply is the oxygen consumption for different
growing media, bulk densities, and water contents, which was determined by the Isermeyer
method and showed high variability depending on water, nutrient, and pH status of the growing
media (unpublished). Oxygen concentration profiles were measured for different growing media,
different densities, and under different irrigation situations with optical O2 sensors (unpublished).
In a final step, the public domain HYDRUS source code will be modified to take the changes inthe boundary conditions and the different ways to describe the oxygen diffusion coefficient into
account.

References
Aendekerk T. G. L., Decomposition of peat substrates in relation to physical properties and growth of
Chamaecyparis, Acta Hort., 450, 191-198, 1997.
Anlauf R., P. Rehrmann, and H. Schacht, Simulation of water uptake and redistribution in growing media
during ebb-and-flow irrigation, J Horticulture and Forestry, 4, 8-21, 2012.
Bradford, S. A., J. Šimůnek, M. Bettahar, M. Th. van Genuchten, and S. R. Yates, Modeling colloid
attachment, straining, and exclusion in saturated porous media, Environmental Science & Technology,
37, 2242-2250, 2003.
De Boodt, M., and O. Verdonck, The physical properties of the substrates in horticulture, Acta Hort., 26,
37-44, 1972
DIN 19683, Methods of Soil Investigations for agricultural engineering – Physical laboratory tests – Part
9: Determination of the saturated hydraulic water conductivity in the cylindrical core-cutter (inGerman), Beuth, Berlin, 1998.
DIN EN 13037, Soil Improvers and growing media – Determination of pH, German Version prEN
13037:2009, Beuth, Berlin, 2009.
DIN EN 13038, Soil Improvers and growing media – Determination of electric conductivity, German
Version prEN 13038:2009, Beuth, Berlin, 2009.
DIN EN 13039, Soil Improvers and growing media – Determination of organic content and ash. German
Version prEN 13039:2009, Beuth, Berlin, 2009.

12
44

DIN EN 13041, Soil Improvers and growing media – Determination of physical properties – Dry bulk
density, air volume, water volume, shrinkage value and total pore space, German Version prEN
13041:2010, Beuth, Berlin, 2010.
Fonteno, W. C., Problems and considerations in determining physical properties of horticultural
substrates, Acta Hort., 342, 197-204, 1993.
Gabriels, R., and O. Verdonck, Physical and chemical characterization of plant substrates: towards a
European standardization, Acta Hort., 294, 249-259, 1991.
Heinen, M., and P. de Willigen, Dynamics of water and nutrients in closed, recirculating sand bed
systems: Modeling water flow, nutrient transport, root water and nutrient uptake, Acta Hort., 401,
501-508, 1995.
Heinen, M., and P. A. C Raats, Hydraulic properties of root zone substrates used in greenhousehorticulture, In: M. Th. Van Genuchten et al. (ed.) Proc. Int. Workshop on the characterization andmeasurement of the hydraulic properties of unsaturated porous media, Univ. of California, Riverside,
467–476, 1999.
Hillel D., Environmental Soil Physics, Academic Press, San Diego,1998.
Kemper W.D. and R.C. Rosenau, Aggregate stability and size distribution, In: Klute, A. (ed), Methods ofsoil analysis, Part 1. 2nd ed Agron. Monogr. No 9. ADSA and SSSA, Madison WI, 425-441, 1986.
Konyai, S., V. Sriboonlue, and V. Trelo-Ges, The effect of air entry values on hysteresis of water
retention curve in saline soil, American Journal of Environmental Sciences, 5, 341-345, 2009.
Moldrup, P., T. Olesen, D. E. Rolston, and T. Yamaguchi, Modeling diffusion and reaction in soils: VII.
Predicting gas and ion diffusivity in undisturbed and sieved soils, Soil Science, 162, 632-640, 1997.
Naasz, R., J. C. Michel, and S. Charpentier, Measuring hysteretic hydraulic properties of peat and pine
bark using a transient method, Soil Sci. Soc. Am. J., 69, 13-22, 2005.
Palla, A., L. G. Lanza, and P. La Barbera, A green roof experimental site in the Mediterranean climate,
Proc. 11th Conf. on Urban Drainage, Edinburgh, UK, 31. Aug.-5. Sept., 2008.
Raviv, M. and J. H. Lieth, Soilless Culture: Theory and Practice, Elsevier, 2008.
Schmitz, D., R. Anlauf, and P. Rehrmann, Effect of air content on the oxygen diffusion coefficient ofgrowing media, Am. J. Plant Sci., 2013 (in press).
Šimůnek, J., M. Šejna, H. Saito, M. Sakai, and M. T. van Genuchten, The HYDRUS-1D Software
Package for Simulating the Movement of Water, Heat, and Multiple Solutes in Variably Saturated
Media, Version 4.0, HYDRUS Software Series 3, Department of Environmental Sciences, Universityof California Riverside, Riverside, California, USA, 2008.
van Genuchten, M. T., A closed form equation for predicting the hydraulic conductivity of unsaturated
soils, Soil Sci. Soc. Am. J., 49, 12-19, 1980.
VDLUFA, Bestimmung der Rohdichte (Volumengewicht) von gaertnerieschen Erden und Substratenohne sperrige Komponenten. Methodenbuch Band I: Die Untersuchung von Boeden. Darmstadt,
1991.
Wallach, D., Evaluating Crop models. In: Wallach, D., D. Makowski, J. W. Jones (Ed.), Working withdynamic crop models, Elsevier, 11-53, 2006.
Wever, G., A. A. van Leeuwen, and M. C. van der Meer, Saturation rate and hysteresis of substrates, Acta
Hort. , 450, 287-295, 1997.

13
45

14
46

Application of the HYDRUS (2D/3D) Inverse Solution Module for
Estimating the Soil Hydraulic Parameters of a Quaternary
Complex in Northern Bulgaria
Dimitar Antonov1, Dirk Mallants2, Jirka Šimůnek3, and Doncho Karastanev1
1

Geological Institute, Bulgarian Academy of Sciences, Sofia,
Bulgaria, dimia@geology.bas.bg, doncho@geology.bas.bg
2
CSIRO Land and Water, Urrbrae, South Australia, Dirk.Mallants@sciro.au
3
Department of Environmental Sciences, University of California Riverside, CA, USA, jiri.simunek@ucr.edu

Abstract
Characterizing hydraulic properties of the unsaturated zone at spatial scales commensurate with thenumerical model grid size is key to reliable predictive modeling of the fate and transport of contaminantsin the environment. We used the HYDRUS (2D/3D) model and inverse modeling to determine thehydraulic properties of a 10-m deep vadose zone from borehole infiltration tests. The investigated soil
profile is located in the Pleistocene loess complex near the town of Kozloduy, Northern Bulgaria, in thevicinity of the Kozloduy Nuclear Power Plant (NPP). Four constant-head infiltrometer tests were carriedout several meters below the ground surface to determine the unsaturated hydraulic properties of a silty
loess, clayey loess, clayey gravel, and a highly carbonated layer. Infiltration tests provided data on
cumulative infiltration and the movement of the wetting front in the initially unsaturated sediments
surrounding the infiltrometer. A cylindrical TRIME-IPH/T3 time-domain reflectometry probe was used tomeasure water content variations with time during the movement of the wetting front. An axisymmetricmodel was developed in HYDRUS (2D/3D) for each of the four infiltrometer tests. The inverse
optimization routine implemented in HYDRUS (2D/3D) was used to determine field-scale soil hydraulicparameters θr, θs, α, n, and Ks for all layers of interest. Results suggest the size of the affected volume ofsoil was large enough to reduce the effect of spatial variability and to produce effective field-scale
hydraulic parameters that are relevant for prediction of large-scale, variably-saturated water flow andradionuclide migration pathways at the Kozloduy NPP site.

1. Introduction
At present, only one nuclear power plant (NPP) is in operation in Bulgaria. Two reactors out of
six are still in operation near the town of Kozloduy, while the remaining four were shut down in
December 2002 (units 1 and 2) and December 2006 (units 3 and 4). A National Repository for
Low and Intermediate Level Radioactive Waste (LILW) from all the units is foreseen to be built
in the vicinity of the Kozloduy NPP. The investigated area represents an undulating landscapedeveloped on Pliocene clay covered with loess sediments, with the groundwater table usually
located in a clay formation at a depth of about 30 m (Antonov, 2002). For the purposes of asafety assessment for the LILW repository, an evaluation of radionuclide migration throughvariably-saturated, geological strata should be performed.
The fate and transport of contaminants in the geosphere is a multi-process phenomenon. It
usually involves the combination of several physical and chemical processes, such as convective

47

mass transport, hydrodynamic dispersion, molecular diffusion, adsorption/desorption, ionicexchange, precipitation/dissolution, radioactive decay, etc. (Jacques et al., 2008; Mallants et al.,2011). Hence, the relevant numerical simulators should incorporate all the above processes. The
most popular approaches to the mathematical description of water flow and mass transport
incorporate the Richards equation for variably-saturated flow and the Fickian-based convectiondispersion equation for solute transport (Mallants et al., 2011). Therefore, the characterization ofhydrological parameters and subsequent numerical modeling of water flow in the vadose zone isa key component in any contaminated site risk assessment. Accurate analysis of the unsaturated
flow regime requires an investigation of the stratification in soil and sediment profiles anddetermination of layer-specific hydraulic parameters by either laboratory or field tests. When thesoil is characterized by a complicated structure and texture, the results of laboratory tests carriedout on small samples may not fully capture properties of the unsaturated zone (Mallants et al.,1997). Examples of successful determination of the soil hydraulic parameters via different typesof field experiments, including for the purposes of migration analyses, can be found in Kodešová
et al. (1999) and Gvirtzman et al. (2008). This paper discusses the use of the HYDRUS (2D/3D)(Šimůnek et al., 2006) computer code to determine by inverse modeling hydraulic parameters ofthe vadose zone from borehole infiltration tests. The investigated 10-m deep soil profile islocated in the Pleistocene loess complex near the town of Kozloduy, Northern Bulgaria.
2. Theory and Methods
Water flow in variably-saturated soils is described using the Richards equation. A onedimensional form is given as follows:∂θ ∂  ∂h  =
K ( h )  + 1 ∂t ∂z  ∂z  (1)

where θ is the volumetric soil water content [L3L−3], t is time [T], z is the vertical coordinate(from a reference level) [L], K is the unsaturated hydraulic conductivity [LT−1], and h is the soil
water pressure head [L]. Numerical solution of Eq. (1) requires the knowledge of two highly
nonlinear functions, namely the soil water retention curve, θ(h), and the unsaturated hydraulicconductivity function, K(h). One of the most popular and flexible equations describing θ(h) was
developed by van Genuchten (1980). When coupled with the statistical pore size distribution
model of Mualem (1976), it gives a closed-form equation for K(h):θs − θrθ r +n m
1 + (α h )θ (h) = θ s K s K r ( h )K (h) =  K s

h<0

)

(

where

48

(2)
h≥0
h<0
h≥0

(3)

)

(

m
1


m
1
1
K=
S
−
−
S
r
e




l
e

2

(4)

and where θr and θs are, respectively, the residual and saturated water contents [L3L−3], α [L−1], n[−], and m (m=1−1/n) are empirical constants defining the shape of the curves, h is the soil waterpressure head [LT−1], l is an empirical constant [-], assumed equal to 0.5, Kr is the relative
hydraulic conductivity [-], Ks is the saturated hydraulic conductivity [LT−1], and Se is thesaturation degree given by:Se =θ − θrθs − θr(5)

According to the van Genuchten-Mualem model, knowledge of the five parameters θr, θs, α, n,and Ks allows quantification of the two functions θ(h) and K(h) (van Genuchten, 1980). The
values of these parameters for a given soil can be determined using field and/or laboratory tests(Mallants et al., 2007; Antonov et al., 2012). The software code HYDRUS (2D/3D) incorporates
the above-mentioned relations (Šimůnek et al., 2006). The automatic parameter optimization
routine implemented in HYDRUS (2D/3D) was used to optimize the parameters α and Ks (seefurther). The HYDRUS code adopts the minimization of the sum of squared residual (SSQ):=
SSQ∑(q − q )
N

i =1

p ,i

2

o ,i

(6)

where N is the number of the calibration points (note that here only the cumulative fluxes areused), qp,i is the ith predicted value, and qo,i is the ith observed value. The HYDRUS code uses
the Marquardt-Levenberg optimization algorithm to minimize the objective function (6).

3. Field Infiltration Tests – Results and Discussion
Constant-head infiltration tests were carried out for determining the field-scale soil hydraulicproperties. Four such tests were carried out down to a depth of 10 m in the unsaturated
Pleistocene loess complex. Infiltration tests provided data on cumulative infiltration andprogression of the wetting front in the initially unsaturated sediments surrounding theinfiltrometers. A cylindrical time-domain reflectometry TRIME-IPH/T3 probe operated by the
TRIME-HD device was used to measure water content variations with time during the
progression of the wetting front. Special polycarbonate access tubes for the TRIME probe were
installed at 0.3 to 0.5 m from the infiltrometers. A more detailed description of the field andtechnical equipment layout could be found in Mallants et al. (2007). By means of an inverse
optimization routine implemented in the finite element code HYDRUS (2D/3D), field-scale soil
hydraulic parameters θr, θs, α, and n were derived for particular layers, namely silty loess, clayey
loess, clayey gravel, and a highly carbonated zone. For cemented layers, such as the clayey
gravel and the carbonated zone, collection of classical soil cores is not possible, leaving only
field determination as a reliable option for determining hydraulic properties (Fig. 1). The inverse
optimization is based on simulating the expected soil water redistribution history while adjusting49the soil hydraulic parameters until the best possible agreement is obtained between measured andcalculated cumulative infiltration and soil moisture profiles. An axisymmetric model wasdeveloped in HYDRUS (2D/3D) for each of the four infiltrometers (Fig. 2).

Figure 1. Carbonate concretions in the carbonated zone (left) and gravel concretions from thegravel layer (right).

The vertical dimension of the model was limited to the soil layers that would be immediately
influenced by infiltrating water (Fig. 2). The simulation starts with “guess” or “trial” values ofthe soil hydraulic properties; these values may be estimated using pedotransfer functions basedon particle size data, or by using some other prior information, e.g., laboratory tests data.
A

B

C

Figure 2. A) Conceptual models used in flow calculations. Vertical dimensions (in m) refer tomodel coordinates. B) An axisymmetrical quasi-3D model. C) Observed and calculated
cumulative infiltrations.

50

An initial optimization with three parameters, α, Ks, and n, showed a high correlation between α
and Ks, and a high standard error coefficient for n, indicating non-uniqueness of the solution.
Therefore, the n parameter was excluded from optimization. The parameter optimization routine
provided in HYDRUS (2D/3D) was invoked to further optimize the parameters α and Ks. The nparameter was kept constant at its initial value of 2 (obtained from initial trial runs). The resultsfrom parameter optimization for each of the modeled infiltrometers F-1b, F-1a, F-2, and F-3 areshown on Table 1. Overall good fits were obtained with hydraulic parameters being
representative of several cubic meters of soil.
Table 1. Parameter values obtained by an inverse optimization using HYDRUS (2D/3D).
Soil
description

Parameter

Best fitted
value
0.351
α [m-1]
Ks [ms-1]
6.03E-07*
Clayey loess
SSQ
0.0119
R2
0.997
0.497
α [m-1]n [-]4.29
Red clayKs [ms-1]
6.89E-07
SSQ
0.0118R2
0.997
0.0586α [m-1]
Ks [ms-1]
5.20E-07
Silty loess*SSQ
0.00281
R2
0.999
-1
3.00
α [m ]-1
Ks [ms ]1.06E-06
3
-3 **
0.431
θ
*
s [cm cm ]Clayey gravel
0.00251
SSQ(0.000605)**2R
0.999 (0.999)**-1
2.68
α [m ]
Ks [ms-1]
1.88E-07
Highly carbonated0.354
θs [cm3cm-3]
zone*
SSQ
0.00391
R2
0.998
*
**
Parameter n is fixed at 2; when θs fitted separately.

S.E. coefficient

Lower 95%

Upper 95%

0.03540.001440.450
0.02290.008490.000681.17
0.000739
0.000110.281
0.0492-0.3950.01400.04180.0436
0.701
0.089
0.411

0.490
0.0549
1.39
0.105

-

-

-

2.29
0.000246
0.0229--1.85
0.0158
0.308
-

7.21
0.01680.399-

0.07540.04635.30
0.09270.416

4. Conclusions
Field investigations have been performed in order to characterize the unsaturated zone in the
Pleistocene loess sediments near the town of Kozloduy, Northern Bulgaria. The values of the van
Genuchten model parameters have been derived from a series of field borehole infiltration tests
using an inverse optimization with the computer code HYDRUS (2D/3D). Due to the small
measurement scale of the laboratory test and the inability to obtain core samples from strongly
cemented layers, the use of a field-scale approach is the preferred option for obtaining hydraulicflow parameters representative of larger soil volumes typically used as grid elements innumerical models. Field-scale hydraulic parameters obtained at different locations were51

consistent, showing only little special variability. The use of a field infiltrometer set-up, in whicha relatively large volume of soil is affected by the constant head infiltration process, averages out
the effects of special variability. The use of field infiltration data in an inverse optimization
routine of the computer code HYDRUS (2D/3D) is a practical and reliable methodology toobtain field-scale hydraulic characteristics. Additional modeling work is required in theimplementation of the TRIME probe data into the objective function of the minimization
procedure.

References
Antonov, D., Loess near Kozloduy NPP as a medium for low and intermediate level radioactive waste disposal, PhD
Thesis, Geological Institute – BAS, 167 pp., 2002.
Antonov, D., D. Karastanev, D. Mallants, Determination of soil hydrologic parameters for multi-layered loesssediments using HYDRUS-2D and field infiltration experiments, Comptes endus de l`Academy bulgare desSciences, 65(12), 1717-1724, 2012.
Gvirtzman, H., E. Shalev, O. Dehan, and Y. Hazor, Large-scale infiltration experiments into unsaturated stratified
loess sediments: monitoring and modeling, Journal of Hydrology, 349, 214-229, 2008.
Jacques, D., J. Šimůnek, D. Mallants, and M. Th. Van Genuchten, odeling coupled hydrologic and chemical
processes: Long-term Uranium transport following Phosphorus fertilization, Vadose Zone Journal, 7(2), 698–
711, 2008.
Kodešová, R., S. E. Ordway, M. M. Gribb, and J. Šimůnek, Estimation of soil hydraulic properties with the cone
permeameter: Field studies, Soil Science, 164(8), 527-541, 1999.
Mallants, D., B. P. Mohanty, D. Jacques, and J. Feyen, Spatial variability of hydraulic properties in a multi-layeredsoil profile, Soil Science, 161, 167–181, 1996.
Mallants, D., B. P. Mohanty, A. Vervoort, and J. Feyen, Spatial analysis of saturated hydraulic conductivity in a soil
with macropores, Soil Technology, 10, 115–131, 1997.
Mallants, D., D. Karastanev, D. Antonov, and J. Perko, Innovative in-situ determination of unsaturated hydraulicproperties in deep loess sediments in North-West Bulgaria, Proceedings of the 11th International Conference on
Environmental Remediation and Radioactive Waste Management, Bruges, ICEM2007–7202, 733–740, 2007.
Mallants, D., M. Th. van Genuchten, J. Šimůnek, D. Jacques, and S. Seetharam, Leaching of contaminants togroundwater, Chapter 18, In: Dealing with Contaminated Sites. From Theory towards Practical Application (ed.
F. A. Swartjes), Dordrecht, the Netherlands, Springer, ISBN: 978-90-481-9756-9, 787–850, 2011.
Mualem, Y., A new model for predicting the hydraulic conductivity of unsaturated porous media, Water Resources
Research, 12, 513–522, 1976.
Šimůnek, J., N. J. Jarvis, M. Th. Van Genuchten, and A. Gärdenäs, Review and comparison of models for describing
non-equilibrium and preferential flow and transport in the vadose zone, Hydrology Journal, 272, 14–35, 2003.
Šimůnek, J., M. Th. van Genuchten, and M. Šejna, The HYDRUS Software Package for Simulating Two- and ThreeDimensional Movement of Water, Heat, and Multiple Solutes in Variably-Saturated Media, Technical Manual,
Version 1.0, PC Progress, Prague, Czech Republic, pp. 241, 2006.
van Genuchten, M. Th., A closed-form equation for predicting the hydraulic conductivity of unsaturated soils, Soil
Science Society of America Journal, 44, 892–898, 1980.

52

Using Hydrus-HP1 to Estimate 226Ra Transport in Soils Following
the Use of Phosphogypsum in Agriculture
Camila R. Bezerra Coelho1, Márcia S. Batalha1, Maria Claudia Barbosa1,
Diederik Jacques2, and Martinus Th. van Genuchten3
1Department of Civil Engineering, Federal University of Rio de Janeiro, UFRJ, Rio de Janeiro, RJ, Brazil
camila.rosabz@gmail.com, marciabatalha.nunes@gmail.com, mclaudia@coc.ufrj.br
2
Performance Assessments, Institute of Environment, Health and Safety, Belgian Nuclear Research Centre,
Mol, Belgium, djacques@sckcen.be3
Department of Mechanical Engineering, Federal University of Rio de Janeiro, UFRJ, Rio de Janeiro,
RJ, Brazil, rvangenuchten@hotmail.com

Abstract
Agricultural soils generally require the use of fertilizers and soil conditioners for optimal production.
Phosphate fertilizers produced from igneous phosphate rock often contain small amounts of naturalradionuclides (most notably 238U and 232Th), while the byproduct phosphogypsum (dihydrated calcium
sulfate) is enriched in 226Ra and 210Pb. Our study focused on the long-term (200 year) subsurface fate of226
Ra when phosphogypsum (PG) is applied annually for 27 years as an amendment to a typical Brazilian
Cerrado soil profile, after which PG applications ceased but agriculture continued. Expected water flow
and solute transport processes were estimated first using the standard HYDRUS-1D software package
assuming linear equilibrium transport, followed by simulations using the HP1 module of HYDRUS-1D.
Analyses with HP1 considered a range of geochemical and physical parameters affecting 226Ra transport
in the vadose zone, especially the effects of varying calcium concentrations resulting from the PG
applications. Several aspects related to the modeling approach, such using daily versus monthly averaged
weather data and assuming long-term steady-state flow conditions, are discussed also.

1.

Introduction

Natural radioactivity is common in most or all soils and rocks. This natural radioactivity may
change when fertilizers or amendments are used in agricultural operations to improve crop
production. For example, phosphate fertilizers often contain small amounts of radionuclides fromthe uranium (238U) and thorium (232Th) decay chains. During the phosphate production process,the naturally occurring U and Th decay series in the host rock are disrupted and some of theradionuclides tend to accumulate in both the fertilizer itself (approximately 86% of 238U and 70%
of 230Th) and the by-product phosphogypsum (about 80% of 226Ra and its daughter products)(Mazzilli et al., 2000; Papastefanou et al., 2006, Saueia and Mazzilli, 2006). For every ton ofphosphoric acid being produced (the basic constituent for the production of phosphate
fertilizers), about 4.8 tons of phosphogypsum (PG) is being generated. Because of its 226Ra
content, PG in many countries is considered a waste and stockpiled in very large quantities.
In Brazil, a major agricultural production area is the Cerrado region. Cerrado soils typically arehighly weathered, slightly acidic, leached, have a relatively low cation exchange capacity, andare poor in nutrients such as P, Ca and Mg. Natural gypsum has long been used as an amendment
or soil conditioner for such situations. Since PG is rich in P, Ca and Mg, many studies have53

advocated the use of PG as both a fertilizer and soil conditioner to reduce subsoil acidity and Al
toxicity, as well as to promote sodic soil reclamation and reduce soil erosion (Oster, 1982; Oates
and Caldwell, 1988; Embrapa, 2005; among others).
Detailed analyses are needed to understand the possible accumulation of radionuclides when fertilizers and/or phosphogypsum are being applied routinely over long periods of time to the same
field (Jacques et al., 2008; Batalha et al. 2011b). For this purpose we used the HYDRUS-1D
flow and transport simulator (Šimůnek et al., 2008) to predict the long-term fate and transport of226
Ra present in PG into and through the vadose zone to groundwater, assuming linear equilibrium transport. Rather than considering one single application, which should have very little impact on the environment (e.g., Rothbaum et al., 1979; Zielinski et al., 1997), the application is assumed to be repeated once every year for 27 years to a typical soil profile in the Cerrado regionof Brazil. The transport of 226Ra in the vadose soil is subsequently followed for another 170
years.
A recent study by Jacques et al. (2008) shows that radionuclide transport in soils is affected by arange of physical and geochemical processes. Their study focused on the transport of uranium
following the long-term use of phosphate fertilizers, as opposed to radium in this study. Since
radium and calcium released from applied PG may compete for the same sorption sites, several
simulations were performed using the HP1 (Jacques and Šimůnek, 2010) multicomponent
transport module of HYDRUS-1D. The module was obtained by coupling HYDRUS-1D with
the PHREEQC biochemical code (Parkhurst and Appelo, 1999). We were especially concerned
about the possible effects of varying calcium concentrations on 226Ra transport. Several aspects
related to the modeling approach, such as the use of daily versus monthly weather data and theeffect of assuming different transport regimes in the vadose zone (notably transient versus longterm steady-state flow) are discussed also. Additional details of the simulations are presented
elsewhere (Batalha et al., 2011, 2012).
2. Simulation Methodology
The scenario of concern is the repeated application of phosphogypsum to the same Cerrado soil
profile, and resultant 226Ra accumulation and transport in the vadose zone, and possibly into underlying groundwater. We considered a 2-m deep physically and chemically uniform soil profile,
without any preferential water flow. Since contaminant transport is very much affected by therates of water flow into and through the soil profile as a function of local weather conditions,transient precipitation and evaporation conditions were evaluated. Phosphogypsum was assumed
to be applied once each year for 27 years to the soil surface in the form of a short pulse withknown composition. Free drainage conditions were imposed at the bottom of the profile. In thisstudy we did not consider any uptake of water and solutes by plant roots.
Water flow in the soil profile is described using the standard Richards equation (Šimůnek et al.,2008):∂θ (h) ∂  ∂h  =
K ( h)  + 1  

∂z
∂z 
 ∂z  

54(1)

where h is the soil water pressure head [L], θ is volumetric water content [L3L-3], t is time [T], z
is the spatial coordinate (positive upward in this study) [L], and K is the hydraulic conductivity[LT-1].
The volumetric water content (θ) and the hydraulic conductivity (K) in Equation (1) are strongly
nonlinear functions of the pressure head, h. These functions are described here using the constitutive relationship of van Genuchten (1980) as follows:

(

)

h< 0
θ −θ r  1 + α h== Se ( h )        
h≥0θ s −θ  
r

1
n −m

(2a)



K=
( h ) K s Sel 1 − (1 − Se1/ m )m 

2

(2b)

where Se is effective saturation [L3L-3], θr and θs are the residual and saturated volumetric soil
water contents, respectively [-], Ks is the saturated hydraulic conductivity [LT-1], and α [L-1], n>1[-], m=1-1/n [-] and l [-] are mostly empirical shape factors. Following van Genuchten (1980),
the pore-connectivity parameter l was fixed at a value of 0.5.
Radionuclide transport was simulated initially with HYDRUS-1D using the standard linear equilibrium advection-dispersion equation:∂ (θ RC ) ∂ 
∂C

=   
− qC  − µθ RC
θ D
∂t
∂z 
∂z


(3)

where C is the solution concentration [ML-3], R the retardation factor [-], D is the dispersion coefficient [L2T-1], q is the Darcy-Buckingham volumetric flux [LT-1], and μ is the decay coefficient [T-1] for the particular radionuclide being considered (in our case 226Ra). Since the half-lifeof 226Ra (1600 years) is much greater than the time period of our study (200 years), radioactive
decay will not be considered here (i.e., μ=0). The parameters R and D in Eq. (3) are given by:

R= 1+

ρb K dθq=
D   
Ddτ + λ

θ

(4)

(5)

in which ρb is the bulk density of the soil [ML-3], Kd is the distribution coefficient for linear sorption [L3M-1], λ is the longitudinal dispersivity [L], Dd is the diffusion coefficient in free water[L2T-1], and τ is the porous medium tortuosity factor [-] given by θ7/3θs-2 (Millington and Quirk,
1961).

55

Geochemical transport involving phosphogypsum was represented by a system of Nm reaction
equations for the primary (or master) species, in canonical form given byNm∑ν A = A
ji

j

(6)

i

j =1

and correspondent mass action equations assuming equilibrium:Nm

K i = γ i Ci ∏(γ j C j )− v ji(7)

j =1

where Nm the number of master aqueous species, Aj and Ai are the chemical equations for the
master and secondary species, respectively, νji are stoichiometric coefficients of the reaction, Ki
is the equilibrium constant of a reaction, γi is the activity coefficient of the aqueous complex, andγj is the activity coefficient for the jth master species in solution.
Transport of each species is represented in the above manner by a set of Nm multicomponent
reactive transport equations of the form (Jacques et al., 2008):∂ (θ C j ) ∂ ∂C j
=− qC j  + R0, j
θ D
∂t
∂z 
∂z


(8)

where R0,j is the reaction term representing the sources/sinks for each aqueous component, Cj isthe total concentration of master species jNsC=
c j + ∑ν ji ci
j

(9)

i =1

in which Ns the number of secondary aqueous species, and ci is the concentration of secondary
species i.
For 226Ra sorption we assumed a relatively simple equilibrium approach that lumps all of thesorption processes onto the solid phase into a single linear isotherm in which the distribution coefficient is a nonlinear function of the calcium concentration, as described in Batalha (2011b).

K d = K d 0CCap(10)in which Kd is the reference distribution coefficient for 226Ra when the calcium activity is 1, CCa
is the calcium activity in soil solution, and p is an empirical parameter whose value was fixed at-0.4 as deduced from data in USEPA (2004).

56

3. Cerrado Soils and PG Application Data
Flow boundary conditions at the soil surface were defined by meteorological data (rainfall andtemperature) obtained from a weather station in the western part of Minas Gerais state in Brazil(17o 25′ 11′′ S, 46o 88′ 64′′ W) for the period 1982-2005. These values were repeated many times
for the long-term (200 year) simulations. Daily potential evapotranspiration rates were calculatedwith the Hargreaves equation (e.g. Jensen et al., 1997) from available weather data and the geographic location of the site. Data of the rainwater composition were taken from Maier et al.
(1992) and adapted for use in HP1 module: pH 6.3; 5.59 10-5 mol/L of Ca and 6.05 10-5mol/L of
Mg. The soil chosen for the study is a typical Brazilian Cerrado oxisol, whose physical andchemical data were obtained from Oliveira (2008). Chemical parameters are listed in Table 1.
The granulometric composition of the soil was 16% sand, 63% fine sand, 5% silt and 16% clay.
Values of the soil hydraulic parameters needed for the water flow simulations were estimatedfrom the soil textural data using the Rosetta neural network based pedotransfer functions of
Schaap et al. (1998) as implemented in HYDRUS-1D. The soil bulk density was taken to be 1.50
g/cm3. For solute transport we used a diffusion coefficient in free water (Dd) of 1.0 cm2/d, whilea dispersivity (λ) of 20 cm was used for the simulations involving transient flow and 30 cm forthe steady-state flow regime.
Table 1. Soil chemical parameters of the Cerrado oxisol.
_______________________________________________________________________________________________

P
Ca2+
K+
Mg2+
Al3+
_______________________________________
pH
mmol/L______________________________________________________________________________________________________---5.3
0.081
0.500
0.410
0.100
0.333
_______________________________________________________________________________________________

Simulations of the cumulative flux leaving the bottom of the 2m soil profile over a period of 27
years assuming transient water flow were used to define the recharge rate (0.152 cm/d) used forthe long-term simulations assuming steady-state flow. Equation (1) for this purpose must be
augmented with a set of initial and boundary conditions. For Equation (1) we assumed an initialpressure head of -100 cm, the presence of atmospheric boundary conditions at the soil surface(i.e., given precipitation and calculated potential evapotranspiration data), and a free drainage
condition (dh/dx=0) at the bottom of the profile.
For the phosphogypsum and 226Ra transport calculations we considered PG application rates thatare common in Brazil (1.000 kg/ha year). The annual application was pulsed in 1 cm of rainwaterin the wet season (November). Measurements of the amount of 226Ra in the PG were carried out
at the Poços de Caldas Laboratory of the Brazilian Nuclear Energy Commission (CNEN). Results indicated an activity of 252±26 Bq per kg of PG. Mass balance calculations produced values of 73.45 mmol/L of CaSO4 and 3.04 x 10-13 mol/L of 226Ra when applied in 1 cm of rainwater for the transient simulations, and values of 483.2 mmol/L of CaSO4 and 20 x 10-10 mmol/L of226
Ra when simulating the constant flow regime using an averaged flux of 0.152 cm/day. A distribution coefficient (Kd) of 2000 cm3/g was used for radium based on data provided by ISAM
(1999) as described in Batalha (2011a).

57

4. Results and Discussion
Figure 1 shows calculated net infiltration fluxes (actual evaporation minus precipitation) into thesoil profile for nine years using transient conditions of precipitation and potential evaporation.
Results indicates two main seasons (wet and dry) during the year. The simulations using daily
weather data from Minas Gerais state (Brazil) revealed no run-off.
2
0
-2
-4
-6
-8
-10
Figure 1. Net fluxes across the soil surface during the first 9 years of the simulations(negative fluxes are downward into the soil profile).

Cumulative drainage fluxes from the soil profile are showed in Figure 2. Results are for bothtransient flow using daily weather data (left) and monthly averaged precipitation and evaporation
data (right). The importance of using daily weather data can be evaluated by the slopes of thetwo plots. The results indicate an average recharge rate of 0.152 cm/day when using daily weather data, and a nearly 50% lower value of 0.079 cm/d when monthly averaged values for precipitation and potential evaporation are used. This means that time-averaging weather data (especially precipitation) can lead to significantly lower estimates of the recharge rate.
0

0

-200

-100

-400

-200

-600

-300

-800

-400

-1000

-500

-1200

-600

Figure 2. Calculated cumulative recharge rates from the soil profile during 27 years using daily(left) and monthly averaged (right) weather data.

58

Figure 3 compares calculated 226Ra concentration distributions in the soil profile assuming transient (left) and steady-state (right) flow conditions. Results for transient flow were obtained using observed daily weather data, while those for steady-state flow assumed a constant long-time
average recharge rate of 0.152 cm/d as deduced from the transient simulations (Fig. 2, left).
Since the transient regime produced a slightly more dispersed contaminant front, a higher longitudinal dispersivity (DL = 30 cm) for the steady flux scenario was used. The results in Figure 3
indicate that long-term predictions can be based equally well assuming steady-state water flow,rather than transient flow, provided the correct long-term deep drainage (recharge) rate is used
for the steady-state simulations.

0

0

-5

-5

-10

-10

-15

-15

-20

-20

-25

-25

-30

-30

-35

-35

-40

-40

-45

45
226

Figure 3. Calculated Ra concentrations after T0= 0, T1=9, T2=18, and T3=27 years assuming
transient weather data (left) and a constant long-term average recharge rate (right).

Figure 3 shows that after 27 years of PG application, essentially no 226Ra had reached a depth ofabout 30 or 40 cm. Subsequent transport after PG applications ceased, but while maintaining thesame water flow conditions, remained equally slow. This is shown in Figure 4 which presents
calculated 226Ra distributions in the soil profile after 27, 100 and 200 years. The plots show very
little movement into the lower part of the profile, with essentially no 226Ra reaching a depth of 1
m after 200 years. Cumulative amounts leached beyond 40 cm depth after 100 and 200 years
were estimated to be 3.58 x 10-13 and 1.85 x 10-12 mmol/cm2. Also notice that the maximum concentrations in the upper part of the profile decreased substantially with time.
Figure 5 shows the influence of the calcium concentration on 226Ra transport after 9, 18 and 27
years of phosphogypsum application. The plots compare simulations for a constant distribution
coefficient, Kd (left) and for a distribution coefficient that varies as a function of Ca2+ activity(right). Results indicate that Ca2+ resulting from the PG application has a major effect on boththe transport rate of 226Ra and the solution concentration. However, this trend is only present initially. Once the PG is no longer applied (after 27 years), calculated 226Ra curves slowly converged to the point that after 100 or 200 years they became very similar (results not further
shown here).

59

0
-20
-40
-60
-80
-100
-120
-140
-160
Figure 4. Calculated 226Ra concentrations after T0= 0, T1=27, T2=100, and T3=200 years (left).

0

0

-5

-5

-10

-10

-15

-15

-20

-20

-25

-25

-30

-30

-35

-35

-40

-40

45

45

Figure 5. Calculated 226Ra concentrations after T1= 9, T2=18, and T3=27 years, without (left) andwith (right) accounting for the effect of the Ca+ activity on the Kd of 226Ra.

5. Conclusions
In this paper we analyzed the fate and transport of 226Ra present in phosphogypsum when applied
for many years as an amendment to a typical Brazilian Cerrado soil used for crop production.
The main factors that influenced water flow and radionuclide transport were the deep drainage
flux determined by rainfall and evaporation and the use of daily precipitation and potential evaporation data. Results indicate that for the assumed long-term transport scenario (200 years andhaving relatively low 226Ra activities), steady-state flow conditions could be assumed without

60

significantly affecting the predictions. Most of the 226Ra remained in the upper 40 cm of the soil
profile.
The effect of PG derived calcium was important by decreasing the effective distribution coefficient of 226Ra, and as such increasing the transport rate. All of the simulations in this study assumed equilibrium water flow and solute transport conditions. We did not consider preferential
flow or nonequilibrium transport, or any other non-ideal transport process (such as colloidfacilitated transport). These processes could all lead to much higher rates of transport in the soil
profile (e.g., Šimůnek and van Genuchten, 2008).
In conclusion, we believe that modeling efforts such as those in this study using HYDRUS-1Dand HP1 are essential for detailed environmental assessment of the long-term use ofphosphogypsum or other naturally occurring radioactive materials (NORMs). They are especially needed for scenarios that cannot be easily monitored and/or occur over relatively long periodsof time.
References

Batalha, M. S., Multicomponent transport of contaminants released in the environment due tophosphogypsum use, MS dissertation in Mechanical Engineering, COPPE/UFRJ, Rio de Janeiro, RJ,
Brazil., 86 pp., 2011a (in Portuguese).
Batalha, M. S., C. R. Bezerra, M. C. Barbosa, D. Jacques, E. M. Pontedeiro and M. Th. van Genuchten,
Multicomponent transport of 226Ra present in phosphogypsum applied to a Brazilian Cerrado soil. VI
Brazilian Symposium on Geosynthetics, REGEO2011, Belo Horizonte, MG, Brazil, Nov. 21-14, 2011b(in Portuguese).
Batalha, M. S., C. B. Bezerra, D. Jacques, M. C. Barbosa, E. M. Pontedeiro, and M. Th. van Genuchten,
Multicomponent transport predictions of 226Ra in soil following the use of phosphogypsum,
WasteEng 2012,14th Int. Conf. on Engineering for Waste and Biomass Valorization, Oporto, Portugal,
2012.
Embrapa, Uso de Gesso Agrícola nos Solos do Cerrado, Empresa Brasileira de Pesquisa Agropecuária,Planaltina, Circular Técnica 32, 18 p., 2005.
Jacques, D., J. Šimůnek, D. Mallants, and M. Th. van Genuchten, Modeling coupled hydrological andchemical processes: Long-term uranium transport following phosphorous fertilization, Vadose Zone
J., 7,698-711, 2008.
Jacques, D. and J. Šimůnek, Notes on HP1, a software package for simulating variably-saturated water
flow, heat transport, solute transport, and biogeochemistry in porous media, HP1 Version 2.2., Open
Report, SCK•CEN-BLG-1068, Mol, Belgium, 129 p., 2010.
Jensen, D. T., G. H. Hargreaves, B. Temesgen, and R. G.Allen, Computation of ETo under nonideal conditions, J. Irrig. Drain. Eng., ASCE, 123(5), 394-400, 1997.
Maier, M. H., M. Takino, and L. L. Miyamaru, Alguns aspectos da composição da água da chuva, Acta
Limnol. Brasil., IV, 247-254, Brazil, 1992
Mazzili, B., V. Palmiro, C. Saueia, and M. B. Nisti, Radiochemical characterization of Brazilian
phosphogypsum, J. Environ. Radioactivity, 40, 113-122, 2000.
Millington, R. J., and J. M. Quirk, Permeability of porous solids, Trans. Faraday Soc., 57, 1200-1207,
1961.
Oates, K. M., and A. G. Caldwell, Use of by-product gypsum to alleviate soil acidity, Soil Sci. Soc. Am J.,
49, 915-918, 1988
Oliveira, K. A. P., Aplicação do fosfogesso na agricultura do Cerrado e suas implicações radiológicas,
Dissertação de Mestrado, CDTN/CNEN, Belo Horizonte, MG, Brazil, 2008.

61

Oster, J. D., Gypsum usage in irrigated agriculture: A review, Fertilizer Res., 3, 73-89, 1982.
Papastefanou, C., S. Stoulos, A. Ioannidou, and M. Manolopoulou, The application of phosphogypsum inagriculture and the radiological impact, J. Environ. Radioactivity, 89, 188-198, 2006.
Parkhurst, D. L., and C. A. J. Appelo, User's guide to PHREEQC (Version 2), A computer program forspeciation, batch-reaction, one-dimensional transport, and inverse geochemical calculations, Water Resources Investigations Report 99-4259, Denver, CO, 1999.
Rothbaum, H. P., D. A. McGaveston, T. Wall, A. E. Johnston, and G. E. G. Mattingly, Uranium accumulation in soils from long-continued applications of superphosphate, J. Soil Sci. 30, 147-153, 1979.
Saueia, C. H. R., and N. P. Mazzilli, Distribution of natural radionuclides in the production and use ofphosphate fertilizers in Brazil, J. Environ. Radioactivity, 89, 229-239, 2006.
Schaap, M. G., F. J. Leij, and M. Th. van Genuchten, Neural network analysis for hierarchical predictionof soil hydraulic properties, Soil Sci. Soc. Am. J., 62, 847-855, 1998.
Šimůnek, J., and M. Th. van Genuchten, Modeling nonequilibrium flow and transport processes using
HYDRUS, Vadose Zone J., 7(2), 782-797, 2008.
Šimůnek, J., M. Šejna, H. Saito, M. Sakai, and M. Th. van Genuchten, The HYDRUS-1D Software Package for Simulating the Movement of Water, Heat, and Multiple Solutes in Variably Saturated Media,
Version 4.0, HYDRUS Software Series 3, Department of Environmental Sciences, Univ. of California,
Riverside, CA, 2008.
U.S. Environmental Protection Agency, Understanding Variation in Partition Coefficient, Kd, Values.
Vol III, EPA 402-R-04-002C, EPA, Washington, DC, 2004
van Genuchten, M. Th., A closed-form equation for predicting the hydraulic conductivity of unsaturated
soils, Soil Sci. Soc. Am. J., 44, 892-898, 1980.
Zielinski, R.A., S. Asher-Bolinder, A. L. Meier, C. A. Johnson, and B. J. Szabo, Natural or fertilizerderived Uranium in irrigation drainage: A case study in southeastern Colorado, Appl. Geochem., 12, 921, 1997.

62

Optimization of Triggered Irrigation Using a System-Dependent
Boundary Condition in HYDRUS (2D/3D)
Sharon Dabach1, Jiří Šimůnek2, Alon Ben-Gal3, Jianchu Shi4, and Naftali Lazarovitch5
1

Seagram Center for Soil and Water Sciences, The Robert H. Smith Faculty of Agriculture, Food and Environment,
The Hebrew University of Jerusalem, Rehovot, Israel.
2
Department of Environmental Sciences, University of California Riverside, Riverside, California.
3
Soil, Water and Environmental Sciences, Agricultural Research Organization, Israel
4
Department of Soil and Water Sciences, College of Resources and Environment, China Agricultural University
5
The Jacob Blaustein Institutes for Desert Research, Ben-Gurion University of the Negev, Sede Boqer Campus, BenGurion, Israel.

Abstract
Improving the sustainability of irrigation systems requires the optimization of relevant
operational parameters, such as the irrigation threshold, the irrigation amount, and the sensor
location. However, little work has been done to investigate the relationship between irrigation
scheduling, irrigation threshold, water salinity, irrigation amount, and their dependence on thesensor location. Optimization of these parameters using field experiments would require
numerous experiments, time, and work. Instead, in this paper, we propose the use of the
HYDRUS (2D/3D) model as a tool for investigating different scenarios that occur in the field.

1. Introduction
Efficiency of water use in agriculture can be increased by improving irrigation scheduling, i.e.,
by optimizing the timing and amounts of water applications over the growing season. However,executing an efficient irrigation plan is challenging, due to many variables that must be taken
into consideration, including climate, crop type, irrigation method, salinity, and various systemconstraints (Howell, 1996). Several approaches can be used to initiate and terminate irrigation.
The most common approach is to initiate irrigation for a certain amount of time or by applying acertain water volume when a predetermined threshold is reached. Automated closed loop
irrigation systems, based on a threshold of soil pressure head or water content, have been shownto save water while maintaining high yields (Phene and Howell, 1984). Determining the proper
irrigation threshold has been studied extensively (e.g., Taylor, 1965; Phene and Howell, 1984;
Hodnett et al., 1990; Thompson et al., 2000; Hoppula and Salo, 2007). Nevertheless, most ofthese studies are empirically based and are valid only for a specific experimental setup: a crop
type, soil type, climatic conditions, location of the measuring device, irrigation method,
irrigation salinity, and the volume of applied water for each irrigation episode. However, fordifferent soils, climate, and vegetation, different combinations of a threshold and an irrigation
amount will yield different ranges of water available for plants, different root water uptake rates,and different water losses below the root zone. Optimization of these parameters, aimed atachieving better water use efficiency, should take into consideration the crop water uptake rate
and water application rates.

63

In this study, we examined the relationship between irrigation thresholds and applied amounts ofwater for different soils and climates using the HYDRUS (2D/3D) (Šimůnek et al., 2008) codethat numerically solves the Richards equation describing water flow and plant water uptake inhomogeneous or heterogeneous soils. HYDRUS has previously been utilized to study optimal
irrigation management (e.g., Cote et al., 2003; Lazarovitch et al., 2009). Additionally, we studied
the effect of sensor location in a heterogeneous soil on measurement variability and the effect ofwater salinity on the performance of a feedback irrigation system.

2. Materials and Methods
The HYDRUS (2D/3D) model was used for three different scenarios to evaluate (i) the effect of
the irrigation threshold on the quantity of applied water, (ii) the dependence of the variability ofobservation (irrigation triggering) points' measurements on their location (depth and distance)
relative to a dripper, and (iii) the effect of salinity of irrigation water on water use efficiency ofcrops. The triggered irrigation option in the HYDRUS (2D/3D) code was used for two
hypothetical soils, silt and clay loam (Carsel and Parrish, 1988), to determine an optimal
irrigation threshold that maximizes water use efficiency. The triggered irrigation option switcheda time-variable flux boundary condition, representing a surface dripper, from no flux to constantflux for a certain time duration when the pressure head in a predetermined observation point
reached the irrigation threshold (Dabach et al., 2013).
Scenario 1: For an irrigation amount of 10 mm, two hypothetical soils (silt and clay loam), andincreasingly larger potential transpiration rates (2, 4, 6, 7, and 10 mm d-1), the irrigationthreshold was adjusted until the ratio between irrigation and potential transpiration (ITp-1)
reached a value of 1. The simulations included irrigation and root water uptake processes.
Scenario 2: The effect of sensor placement on the performance of an automated irrigation
system was also investigated. Specifically, the variability of measurements by a sensor placed atvarious distances from a subsurface dripper, the total volume of applied water, and bottom
drainage were studied. The HYDRUS (2D/3D) software numerically simulated two-dimensional
water flow and root water uptake in a heterogeneous sandy loam soil (Carsel and Parrish, 1988)
with a subsurface dripper. Twelve heterogeneity realizations in soil hydraulic properties werecreated using random fields of scaling factors (Vogel et al., 1991) with a standard deviation of
0.5 and a correlation length of 5 cm in both x and z directions. Three pairs of observation points
were defined in the flow domain on each side and at distances of 10, 20, and 30 cm from thedripper. Each simulation was run for a different observation point, i.e., for every heterogeneity
realization, six simulations were performed. In each simulation, irrigation events were triggeredby a different observation point when the irrigation threshold was -60 cm. The irrigation amountwas 5 mm per irrigation pulse. The coefficients of variation were calculated for observation
points located at the same distance from the dripper (two in each realization times twelve
realizations).
Scenario 3: Triggered irrigation was additionally simulated with saline water in a sandy loam
soil (Carsel and Parrish, 1988). The simulation was axisymmetric with a surface drip source anda duration of 90 days. Various levels (from 0 to 4 mmol cm-3) of irrigation salinity were applied

64

from a surface drip source. The irrigation threshold was -80 cm, and the potential transpiration
rate was 4 mm day-1. Water use efficiency (WUE) was calculated from root water uptake (RWU)
divided by a total irrigation amount for the simulation duration.

3. Results and Discussion
Figure 1 shows the thresholds that yielded an ITp-1 value of 1 for silt and clay loam soils, as afunction of different potential transpiration rates, when a water volume of 10 mm per irrigation
pulse was used. The higher the daily potential transpiration rate, the higher the irrigationthreshold needed to achieve the ITp-1 value of 1. As plants grow during the season, theirtranspiration rate increases and so does their water demand. Therefore, the irrigation thresholdhas to be raised in order to compensate for an increasing water demand during the growing
season. Keeping the irrigation threshold constant while the potential transpiration rates rise
would result in more irrigation events since the threshold would be reached faster. Nevertheless,this would not produce a sufficient supply of water since the rate of the pressure head decreasedepends on water fluxes in the soil and is limited by the hydraulic conductivity. Therefore, toachieve optimal automatic triggering of irrigation via pressure head measurements, the irrigationthreshold must be adjusted according to changing potential transpiration rates.

Figure 1. Irrigation thresholds that yielded ITp-1 [-] values of 1 as a function of potential transpiration
for silt and clay loam soils with a water volume per irrigation equal to 10 mm.

Coefficients of variation for simulated pressure head measurements are presented in Figure 2 foreach of the three distances of the observation points from the dripper. The coefficient of variation
was increasing when water contents were changing rapidly in the soil. For observation points
located further away from the dripper, the water front did not reach them in all realizations at thesame time, and as a result the variation in measurements increased. On the other hand, as
observation points were placed further away from the dripper, the coefficient of variation
decreased because the rise in the pressure head due to irrigation was smaller. However, thecoefficient of variation of the total quantity of applied water increased considerably with the65distance of the observation point away from the dripper (results not shown). If the pressure headin the measurement location does not rise above the irrigation threshold after the irrigation pulse,then another irrigation pulse is triggered. Even though the variability in pressure headmeasurements was lower as the distance of the observation point increased, the hydraulicconductivity of the soil between the dripper and the observation point varies depending on thelocation of the observation point relative to the dripper. This variation in the hydraulicconductivity affects the travel time of the water front from the dripper to the observation point,
thus causing the variability in total applied water.

Figure 2. The coefficient of variation of simulated pressure heads at three distances (10 cm, 20 cm,
and 30 cm) from the dripper during a 1-week simulation.

As the salinity of irrigation water increased, WUE decreased (Figure 3). Salinity affects root
water uptake of plants, and indeed, simulations showed a steady decrease in RWU as salinity
increased. The drop in RWU resulted in a slower decrease in the pressure head, which resulted in
fewer irrigation events and hence less applied water while drainage was only slightly higher.
This combination of factors and processes converged to an undesirable result, in which thedecrease in RWU caused fewer irrigation events, which further raised soil salinity and decreased
RWU. The decrease in RWU was steeper than the decrease in the quantity of applied irrigationwater, and consequently, WUE declined with salinity. When irrigating with saline water, thetensiometer alone cannot efficiently be used to control irrigation. An additional sensor thatmonitors salinity is necessary in order to provide data needed for the decision to leach excess
salts from the root zone.

66

Figure 3. Water use efficiency (root water uptake divided by irrigation) as a function of the relative
salinity of irrigation water (water salinity divided by the C50 (3 mmol cm-3) parameter of van
Genuchten (1987).

4. Conclusions
Optimization and adjustment of the irrigation threshold throughout the growth season is neededto accommodate changing water uptake rates of the plants in systems that use pressure headmeasurements to trigger irrigation. The HYDRUS (2D/3D) code can be utilized to optimize
irrigation threshold values for specific boundary conditions and plant types. The boundary
conditions can be updated during the growing season, and used to determine new irrigationthresholds to compensate for increasing root water uptake by plants.
Variability of matric head measurements substantially increases during changes in soil water
status. When a rapid change in soil water contents occurs, whether naturally or artificially, it will
not occur at all locations simultaneously, and therefore variability will increase during times ofchange. Irrigation systems, which operate based on data from tensiometers, sometimes use analgorithm that turns off irrigation when the pressure head rises above a preset value. Our results
suggest that this algorithm should be avoided because of the increase in variation of thetensiometer measurements during irrigation. Instead, we recommend using an algorithm thatstops irrigation after a fixed volume of water has been applied.
When irrigating with saline water, a decrease in plant water uptake results in higher pressure
heads in the soil and hence fewer irrigations, which in turn causes higher soil salinity. Therefore,
when this is an issue, irrigation cannot be based only on sensors measuring the soil water status,
but must be complemented with salinity monitoring.
A numerical model is a good tool for optimizing irrigation regimes. However, many parameters
are involved in simulating triggered irrigation systems, and the operation of the numerical model
requires relatively extensive knowledge (i.e., root spatial distribution, soil spatial variability,
dripper wetting patterns, uptake fluxes), to which most farmers do not have access or realize onlyat the end of the season. Additional work is necessary in order to standardize and simplify the67

decision making process regarding sensor location, the value of the irrigation threshold, and thevolume of applied water in each irrigation pulse according to changing spatial variability,
irrigation methods, and crop conditions.

References
Carsel, R. F., and R. S. Parrish, Developing joint probability-distributions of soil-water retention
characteristics, Water Resources Research, 24, 755-769, 1988.
Cote, C. M., K. L. Bristow, P. B. Charlesworth, F. J. Cook, and P. J. Thorburn, Analysis of soil wetting
and solute transport in subsurface trickle irrigation, Irrigation Science, 22,143-156, 2003.
Dabach, S., N. Lazarovitch, J. Šimůnek, and U. Shani, Numerical investigation of irrigation schedulingbased on soil water status, Irrigation Science, 31, 27-36, 2011.
Hodnett, M. G., J. P. Bell, P. D. A. Koon, G. C. Soopramanien, and C. H. Batchelor, The control of drip
irrigation of sugarcane using index tensiometers - Some comparisons with control by the waterbudget method, Agricultural Water Management, 17, 189-207, 1990.
Hoppula, K. I., and T. J. Salo, Tensiometer-based irrigation scheduling in perennial strawberry
cultivation, Irrigation Science, 25, 401-409, 2007.
Howell, T. A., Irrigation scheduling research and its impact on water use, in: C. R. Camp, et al. (eds.)
Evapotranspiration and Irrigation Scheduling, San Antonio Convention Center, San Antonio, Texas,
pp. 1-15, 1996.
Lazarovitch, N., M. Poulton, A. Furman, and A. W. Warrick, Water distribution under trickle irrigation
predicted using artificial neural networks, Journal of Engineering Mathematics, 64, 207-218, 2009.
Maas, E. V., and C. J Hoffman, Crop salt tolerance – current assessment, ASCE Journal of Irrigation andDrainage Division, 103, 115-134, 1977.
Phene, C. J., and T. A. Howell, Soil sensor control of high-frequency irrigation systems, Transactions of
the ASAE, 27, 392-396, 1984.
Šimůnek, J., M. T. van Genuchten, and M. Šejna, Development and applications of the HYDRUS andSTANMOD software packages and related codes, Vadose Zone Journal, 7, 587-600, 2008.
Taylor, S. A., Managing irrigation water on the farm, Transactions of the ASAE, 8, 433-436, 1965.
Thompson, T. L., T. A. Doergo, and R. E. Godin, Nitrogen and water interactions in subsurface dripirrigated cauliflower: 1.Plant response, Soil Science Society of America Journal, 64, 406-441, 2000.
van Genuchten, M. Th., A numerical model for water and solute movement in and below the root zone,
Research Report No 121, U.S. Salinity Lab, ARS USDA, Riverside, CA, 1987.
Vogel, T., M. Cislerova, and J.W. Hopmans, Porous media with linearly variable hydraulic propertie,
Water Resourse research, 27, 2735–2741, 1991.

68

Modeling Non-equilibrium Water Flow in Multistep Outflow andMultistep Flux Experiments
Efstathios Diamantopoulos*1, Sascha C. Iden*2, and Wolfgang Durner*3*

Institut für Geoökologie, Technische Universität Braunschweig, Braunschweig, Germany,
1
ediamant@tu-bs.de, 2s.iden@tu-bs.de, 3w.durner@tu-bs.de

Abstract
During the last 50 years, experimental observations have shown that the soil hydraulic properties
estimated under static and dynamic flow conditions can substantially differ. These observations are often
described by the terms “dynamic non-equilibrium” or “dynamic effects.” The way in which hydraulicnon-equilibrium is expressed in experimental data depends on experimental boundary conditions. Duringexperiments with controlled pressure head boundary conditions, non-equilibrium effects appear as arelaxation in the cumulative outflow / system-averaged water content data, while the pressure head in thesoil column indicates hydrostatic equilibrium. For experiments with flux boundary conditions, nonequilibrium effects appear as a relaxation of the pressure head while the flux density and macroscopic
water content distribution appear static. These phenomena are often attributed to processes such as airwater-interface reconfiguration, pore-water blockage, air entrapment, dynamic contact angles, among
others. We have developed a model to quantitatively describe hydraulic non-equilibrium during variably
saturated flow. The model considers two continua at the macroscopic scale: one continuum is describedby the Richards equation and the second, associated with non-equilibrium water flow, by an extended
Richards equation using the non-equilibrium approach of Ross and Smettem. The new model called DNE
was implemented by extending the Hydrus-1D code. Numerical simulations with the DNE model
demonstrate its ability to describe the dynamic effects occurring in transient flow experiments very well.

1. Introduction
The Richards equation is the most widely used model for describing water flow in theunsaturated zone. It has a clear physical basis and its applicability has been proved in various
experimental studies in the laboratory and the field. The use of the Richards equation for the
purpose of prediction requires knowledge of the soil-water characteristics, i.e. the water retention
and the hydraulic conductivity curve. The water retention curve relates the water content θ withthe pressure head h and is parameterized by a monotonous function θ(h), which is easily used innumerical simulations. Traditional theory assumes that the water retention curve is independentof the soil water flow regime. However, observations reveal that water retention curves
determined under static equilibrium and dynamic conditions can differ. For this reason, theRichards equation often cannot describe observations of soil water dynamics in laboratory
experiments. These observations are often described as dynamic non-equilibrium (NE) effects
and are known since the work of Topp et al. (1967).
Diamantopoulos and Durner (2012) presented a comprehensive review on this phenomenon that
focused on dynamic NE observations, hypothesized causes and modeling approaches. In thiscontribution, we review only the key studies concerning NE. Topp et al. (1967) performedlaboratory experiments in sandy soils and measured the water retention curves (drainage) for69

three different flow cases: static, steady–state and dynamic. They drained their sample bycontrolling the pressure in the gas phase. They found that although the retention curves were
almost the same for static equilibrium and steady state flow experiments, the dynamic retention
curves significantly differed. Specifically, for the same pressure head value, the water content
was higher in the case of transient experiments compared with the other two cases. Similar water
dynamics are also observed in multistep outflow experiments (MSO). Figure 1 shows
experimental results for an MSO experiment presented by Diamantopoulos et al. (2012). After anapplied pressure step at the lower boundary, the pressure head in the soil quickly reaches theequilibrium state. However, the time series of cumulative outflow shows two stages. During thefirst stage, immediately after the change in the applied pressure head, a large volume of water
quickly flows out from the soil column. This is followed by a second stage with a much slower
flow in the column toward hydraulic equilibrium. The crucial point is that these data cannot be
described by the Richards equation because it cannot predict different equilibration times for θand h due to the tight coupling by the retention curve.

equilibrium in pressure headStage II

Stage I

Figure 1. Non-equilibrium water flow during an MSO experiment. After a pressure headchange at the boundary, the pressure head in the soil quickly equilibrates whereas outflow
of water continues.
Poulovassilis (1974) investigated the effect of water flow on the water retention curve byconducting constant flux infiltration experiments in a soil column equipped with fivetensiometers. After achieving uniform steady-state flow and uniform water content and pressure
head throughout the soil column, he sealed both ends of the soil column and placed ithorizontally. He observed that all tensiometers recorded a pressure head increase (suction
decrease) while the water content inside the column remained constant. Recently, Weller et al.
(2011) presented an automated method for direct measurements of hydraulic conductivity by asuccession of unit-gradient experiments. They applied constant fluxes at the upper boundary of
the soil column and set the pressure head at the lower boundary equal to the pressure head ofwater near the surface. Under these conditions, the hydraulic conductivity equals the applied flux
density. Their experiments started with a saturated soil column and the applied fluxes were70

decreased in steps. As was expected, pressure head measured in the soil dropped immediately
after each applied step, but rose to higher levels afterwards, even though the column-averaged
water content remained constant. Weller et al. (2011) also observed this phenomenon forincreasing fluxes, but in this case the pressure head decreased during the relaxation period.
Similar to what has been stated earlier, the observations of Poulovasillis (1974) and Weller et al.
(2011) cannot be described by the Richards equation because of its inherent assumption of aflux-invariant θ-h-K relationship.
The above studies reveal that for a given pressure head boundary condition, dynamic NE effects
appear as a relaxation in the cumulative outflow data (or water content), whereas for a given flux
boundary condition, they appear as a relaxation of the pressure head. Diamantopoulos et al.
(2012) proposed a model for describing dynamic NE water flow in the case of MSO
experiments. The model assumes two continua at the macroscopic scale. In the first continuum,
water flow is described by the Richards equation, whereas in the second continuum, water flow
is described by the Ross and Smettem (2000) model. In this article, we investigate the possibilityof describing the two major dynamic NE observations outlined above with this model.
2. Model2.1. Richards Equation
Variably saturated water flow in homogeneous porous media is generally described by theRichards equation:
∂θ
∂t

=

∂   ∂h  K   −1∂z   ∂z  

(1)

where θ [L3 L–3] is the water content, t [T] is time, z [L] is the vertical coordinate, positive
downwards, h [L] is the pressure head and K [L T-1] is the unsaturated hydraulic conductivity.
2.2. Dual–Fraction Non-Equilibrium Model (DNE)
The DNE model assumes two fractions of water in the same porous system, one fraction feq ininstantaneous equilibrium with the local pressure head, and the second fraction fne for which theequilibration of water content is time dependent. By assuming that the pressure heads in the tworegions quickly equilibrate relative to the movement of water in the main flow direction, themain equation describing water flow becomes (Diamantopoulos et al., 2012):(1 − f ne )
with

∂θ eq
∂t

+ f ne∂θ ne ∂  ∂h 
=  K (θ ) − 1∂t∂z  ∂z 

∂θ ne (θ eq − θ ne )
=
τ
∂t

71

(2)

(3)

where τ describes the equilibration of water content in the non-equilibrium region [T], and K is afunction of the water content θ. For more information about the model, the reader is referred to
Diamantopoulos et al. (2012).
2.3. Parameterization of Hydraulic Properties
The unsaturated soil hydraulic properties are parameterized with the van Genuchten–Mualem(VGM) model (van Genuchten, 1980). The retention function and the hydraulic conductivity
function (as a function of water content θ) are given by:θ + (θ s − θ r ) ⋅ (1 + αh ) − m , h < 0θ ( h) =  rθ s , h ≥ 0nSe =θ − θrθs − θr[(5)]

1/ m m 2

K ( Se ) = K s ⋅ Se 1 − (1 − Se
l

(4)

)

(6)

where, θ s and θ r [L3 L-3] are saturated and residual water contents, respectively, α [L-1], n [-],

1m [-] and l [-] are shape parameters and m = 1 − , n > 1.
n2.4. Inverse Modeling
The laboratory experiments were evaluated by inverse modeling. The objective function used for
determining the unknown parameters p from measurements of cumulative outflow and pressure
head data in the case of the MSO experiment and pressure head data in the case of the multistep
flux experiment is given by:
M

Nj

j =1

i =1

O( p ) = ∑ w j ∑ rij ( p ) 2(7)

where M is the number of the data groups used in the objective function ( M = 2 for MSO andM = 1 for multistep flux experiments), N j is the number of data for each group and r ij are theresiduals, i.e. the differences between observed and model–predicted data. The estimation of themodel parameters is done by minimizing Eq. (7) with respect to the parameter vector p. This wasachieved by the globally convergent evolutionary scheme SCE–UA (Duan et al., 1992).
Numerical simulations with both the Richards equation and the DNE model were done with amodified version of Hydrus-1D (Šimůnek et al., 2008).

72

3. Material and Methods
3.1. Multistep Outflow (MSO) Experiment
The DNE model was tested against experimental results from an MSO experiment presented by
Diamantopoulos et al. (2012). In that experiment, an undisturbed soil column 7.2 cm in heightwas collected from the subsoil horizon (35–45 cm) of a Luvisol (Schelle et al., 2011). The
column was placed on a 0.7 cm thick porous plate that was covered by a fine–pored diaphragm.
A tensiometer (T5, UMS Munich) was installed at a 1.8 cm depth measured from the top torecord pressure head. The sample was slowly saturated from the bottom. The initial watercontent was calculated from the water content at the end of the experiment, and the cumulative
water loss throughout the experiment. The bulk density, porosity and initial water content were1.67 g cm-3, 0.371 cm3 cm-3 and 0.334 cm3 cm-3, respectively. The saturated hydraulicconductivity of the plate (Kp) and soil (Ks) were 1.0 cm h-1 and 2.7 cm h-1, respectively. In the
inverse simulations with the Richards equation and the DNE model, both saturated conductivities
were fixed to these measured values.
3.2. Multistep Flux (MSF) Experiment
We tested the DNE model against experimental data from MSF experiments presented by Weller
et al. (2011). They obtained direct measurements of unsaturated hydraulic conductivity byimposing gravity flow to one sandy undisturbed soil column as was described in the introduction.
For more information about the material type or the experimental procedure, the reader isreferred to Weller et al. (2011).
4. Results
4.1. MSO
Figure 2 illustrates results of a sensitivity analysis in which the effect of the non-equilibrium
parameters τ and fne for a multistep outflow and inflow experiment were analyzed for a sandy
material. The first case (blue line) represents equilibrium flow described by the Richards
equation. Figure 2a shows the prediction of the DNE model for a drainage–imbibition
experiment and for increasing values of parameter τ (2, 4 and 8 h) when all the water is assumed
to be in non-equilibrium (fne = 1). This corresponds to the Ross and Smettem (2000) NE model,
which obviously is able to predict the basic observation that after an abrupt change in the appliedpressure head at the lower boundary, the pressure head in the soil equilibrates faster than the
cumulative outflow data. However, the equilibration dynamics always follow an exponential
form, which is in contrast to the observations. As described previously, outflow data often show
an equilibration in two stages. After each applied step, there is a quick outflow followed by aperiod with slower outflow. As shown in Figure 2b, this can be simulated by the DNE model.
Figure 2b shows that the greater the value of fne, the smaller the amount of water that leaves thesoil column after each applied pressure head.

73

a

b

Figure 2. Sensitivity analysis of DNE model for MSO experimental type.
(a): the effect of τ parameter; (b): the effect of fne parameter
Figure 3 shows measured and fitted outflow and pressure head data for a MSO experiment for aloamy sand soil. The experimental data show that after each pressure change at the lower
boundary, the equilibration of the pressure head data in the column is quicker than that of the
cumulative outflow data. The blue line illustrates that this cannot be described by the Richards
equation since it assumes simultaneous equilibration between pressure head and water content(or cumulative outflow). Accordingly, any attempt to describe the data leads to misfits. On thecontrary, the DNE model describes both the pressure head and outflow data very well. Anyremaining discrepancies between measured and simulated outflow data, especially in the second
and third step, can be attributed to the limited flexibility of the van Genuchten-Mualem model ofthe soil hydraulic properties. The fitted parameter τ and fne were 3.2 h and 0.76, respectively.

Figure 3. Observed and simulated cumulative outflow and pressure head data for an
undisturbed loamy sand. The fitted data are calculated using the Richards equation andthe dual-fraction non-equilibrium (DNE) model.

744.2. MSF
Figures 4a and b show results of a sensitivity analyses for both non-equilibrium parameters of
the DNE model for an MSF experiment. At the beginning, we assume a series of steady fluxes
decreasing stepwise corresponding to a drainage experiment; after 150 hours, we assume
increasing fluxes corresponding to an imbibition experiment. The Richards equation predicts thatafter an applied flux at the upper boundary, water content and pressure head in the soil
immediately change and assume the relationship defined by the soil water retention curve. Figure
4a shows that the DNE model can predict the capillary overshoot presented by Weller et al.
(2011) in both the drainage and imbibition sequence of the MSF experiment. At a constant valueof the fne parameter, increasing τ values result in slower equilibration of the pressure head after
each applied flux. Additionally, the magnitude of the pressure head drop after each flux change
is controlled by parameter fne (Figure 4b).

ab

Figure 4. Sensitivity analysis of DNE model for MSF experimental type.
(a): the effect of τ parameter; (b): the effect of fne parameter

Figure 5 shows the experimental and simulated data from the study of Weller et al. (2011). The
experimental data were digitized from figure 4 in Weller et al. (2011). Figure 5 shows that after a
stepwise change of the applied flux at the upper boundary, the pressure head drops as expected(drainage), but then it rises again to a higher value. The Richards equation predicts that after theestablishment of steady state flux with constant water content in the soil, the pressure headremains constant as well and corresponds to the pressure head value obtained from the retention
curve. This contradicts the experimental findings. In contrast, the DNE model predicts theobserved slow equilibration of the pressure head data even if the water content remains constantand the agreement between fitted model predictions and experimental data is excellent. The fitted
parameter τ and fne were 19 h and 0.37, respectively.

75

Figure 5. Observed and simulated pressure head data for an undisturbed sand (Weller etal., 2011). The fitted data are calculated using the Richards equation and the dual–
fraction non-equilibrium (DNE) model. The experimental data were digitized from
Figure 4 in Weller et al. (2011).
References

Diamantopoulos, E., and W. Durner, Dynamic non-equilibrium of water flow in porous media – A
review, Vadose Zone Journal, 11(3), doi:10.2136/vzj2011.0197, 2012.
Diamantopoulos, E., I. C. Iden, and W. Durner, Inverse modeling of dynamic non-equilibrium in waterflow with an effective approach, Water Resources Research, 48, W03503,
doi:10.1029/2011WR010717, 2012.
Duan, Q., S. Sorooshian, and V. Gupta, Effective and efficient global optimization for conceptual rainfallrunoff models, Water Resources Research, 28, 1015-1031, 1992.
Poulovassilis, A., The uniqueness of the moisture characteristics, Soil Science, 25, 27-33, 1974.
Ross, P. J., and K. R. J. Smettem, A simple treatment of physical nonequilibrium water flow in soils, Soil
Science Society of America Journal, 64, 1926-1930, 2000.
Schelle, H., S. C. Iden, and W. Durner, Combined transient method for determining soil hydraulicproperties in a wide pressure head range, Soil Science Society of America Journal, 75(5), 1-13, 2011.
Šimůnek, J., M. Th. van Genuchten, and M. Šejna, Development and applications of the HYDRUS andSTANMOD software packages, and related codes, Vadose Zone Journal, 7(2), 587-600, 2008.
Topp, G. C., A. Klute, and D. B. Peters, Comparison of water content-pressure head data obtained byequilibrium, steady state, and unsteady-state methods, Soil Science Society of America Proceedings,
31, 312-314, 1967.
van Genuchten, M. Th., A closed-form equation for predicting the hydraulic conductivity of unsaturated
soils, Soil Science Society of America Proceedings, 44, 892-898, 1980.
Weller, U., O. Ippisch, J. M. Köhne, and H. J. Vogel, Direct measurement of unsaturated hydraulicconductivity in sandy soil including temporal dynamics, hydraulic non-equilibrium and hysteresis,
Vadose Zone Journal, 10, 654-661, 2011.

76

Dual-Drip Subsurface Irrigation Systems:
Can it Act as a Hydraulic Barrier?
Mohammad El-Nesr, N. B.1, Abdurrahman Alazba1, and Jiří Šimůnek2
1

Alamoudi Chair for Water Researches, King Saud University, Riyadh, Saudi Arabia (drnesr@gmail.com).
2
Department of Environmental Sciences, University of California Riverside, Riverside, CA, USA.

Abstract
Subsurface drip irrigation systems, compared to other irrigation systems, enhance delivery of water andchemicals directly into the root zone. However, in light-textured soils, certain quantities of water may
percolate below the root zone due to the subsurface position of drip lines. The main objective of thispaper is to evaluate three technologies to enhance a spatial distribution of water and solutes in the rootzone and to limit downward leaching. The three technologies include a) a physical barrier, b) a dual-drip
system with concurrent irrigation, and c) a dual-drip system with sequential irrigation. To achieve thisobjective, we performed computer simulations and field experiments. Numerical simulations were carriedout using the HYDRUS (2D/3D) software for both bare and cultivated soils. The results indicate that thephysical barrier is more efficient than dual-drip systems in enhancing the water distribution in the rootzone while preventing downward leaching.

1. Introduction
Surface and subsurface drip irrigation systems are increasingly being used in arid regions withlimited water resources to irrigate agricultural crops. The subsurface drip irrigation (SDI)
systems, have an especially promising future due to their many advantages. The main advantagesof SDI, compared to surface drip irrigation (DI), include: a) a significant reduction of
evaporation, b) a direct injection of water and fertilizers into the root zone, and c) an easier andfor drip lines, safer, operation of machinery.
The proper design of SDI systems requires knowledge of the water distribution patterns aroundthe emitters that match the root extraction patterns and minimizes wetting of the soil surface anddeep percolation (Kandelous et al., 2011). The exact shape of the wetted volume and water
distribution depends on many factors, including soil hydraulic characteristics, initial soil
conditions, discharge rate, application frequency, root characteristics, evaporation, andtranspiration (Subbaiah, 2013). Additionally, the wetting pattern depends on the location of theemitter with respect to the soil surface. The wetting pattern is hemi-ellipsoidal or ellipsoidal
when the dripper is located on the soil surface or in the subsurface, respectively.
Generally, plants have higher root densities in the upper part of the root zone. Majumdar (2004)
indicated that in a soil profile with a uniform water content most plants extract about 40, 30, 20,
and 10% of their water needs from corresponding quarters of the root zone (Figure 1a). Despite asimilar wetting pattern under DI and SDI systems (Figure 1bc), a considerable amount of waterescapes from the root zone by percolating downwards or dispersing laterally in the soil beyond

77the reach of roots. Figure 1 indicates that the wetting pattern for the DI system is more similar to
the root distribution than for the SDI system, while more water leaches below the root zone in
the SDI system than in the DI system. El-Berry (1989) reported that the main avenue for water
losses under SDI is deep percolation, which is highest during the seedling stage and declines
with the growth of the root system.

Figure 1. A wetting pattern in the root zone: a) a distribution of a root water extraction, b) a
wetting pattern for a surface dripper, and c) a wetting pattern for a subsurface dripper.

Several investigators have tried to adjust the shape of the wetted zone to better match the root
extraction pattern (e.g., Phene et al., 1987; Barth, 1995; Welsh et al., 1995; Ismail et al., 2006).
Phene et al. (1987) showed that the wetted pattern around the buried emitter can be managed byadjusting the irrigation frequency and that more water moves toward the soil surface when theirrigation frequency is increased. Other investigators (e.g., Barth, 1995; Welsh et al., 1995) havesuggested placing an impermeable barrier below the lateral drip lines. This barrier can be madeof polyethylene (Barth, 1995) or metal (Welsh et al., 1995). However, there are some problems
concerning this physical barrier. For example, there are technical and economical problems with
digging a wide and deep trench to install the physical barrier.
Ismail et al. (2006) attempted to modify the wetting pattern by burying a secondary drip line
beneath the primary one, and by dividing the required water volume between the two drip lines.
This approach depends on the fact that water moves faster into the dry soil (due to a higher
pressure head gradient) than into the moist soil, and thus, when the secondary drip line moistens
the soil below the primary drip line, it forces water from the upper drip line to redistribute
upward and laterally, rather than moving downward. Hence, they called this technique “ahydraulic barrier”. This technique requires no wider trenching than the normal SDI trenching.
Their results showed that when applied in the field, the hydraulic barrier increased the total andmarketable yields of the Jerusalem artichokes by 12 and 48%, respectively, while the physicalbarrier increased the yields by 131 and 138%, respectively (Ismail et al., 2006). These results
clearly document the benefits of using such techniques to increase crop yields.
In order to efficiently design and manage SDI systems, several models (analytical and empirical)
have been developed to describe water flow from an emitting source (a point or line source) in
the soil (surface or subsurface) (e.g., Brandt et al., 1971; Warrick, 1985; Khalifa et al., 2004;
Sing et al., 2006). One of the most complete packages for simulating water, heat, and solute
movement in both two- and three-dimensional, variably-saturated, porous media is the HYDRUS
software package (Šimůnek et al., 2008). Many investigators have used this model to evaluate78either field or laboratory experiments, or other mathematical models (e.g., Skaggs et al., 2004;
Provenzano, 2007; Kandelous et al., 2011). The HYDRUS model enables its users to trace themovement of water and solutes and the wetting patterns in both simple and complex geometries
for homogeneous or heterogeneous soils, and for different combinations of initial and boundary
conditions.
The main objectives of this study therefore are (a) to simulate water flow for an SDI system
while considering both the physical barrier and the dual-drip system using the HYDRUS
package, (b) to numerically evaluate how these alternative techniques affect the movement ofwater, and (c) to evaluate whether or not the dual-drip system can act as a hydraulic barrier for
movement of water.
2. Material and Methods
2.1. Modeled Scenarios
To address our main objectives, we have chosen to evaluate the following alternative scenarios:
1. Two soil textures (sand and loam).
2. Different water applications:a. A single emitter without a physical barrierb. Two emitters operating concurrentlyc. Two emitters operating sequentiallyd. A single emitter with a physical barrier
Simulations were carried out for soils representing two textural classes: sand and loam. Soil
hydraulic parameters for the two textural classes were taken from the soil catalog provided by
the HYDRUS software (Carsel and Parish, 1988).

Figure 2. Location of the emitters and the physical barrier in the transport domain considered in
Hydrus simulations: a domain around a dripper is magnified in excerpts.

2.2. Initial and Boundary Conditions
The Hydrus (2D/3D) software package (version 2.02) (Šimůnek et al., 2008) is used in numericalsimulations for all modeled scenarios. The transport domain for all scenarios was considered to
be axisymmetrical around a vertical axis. Figure 2 shows the detail of the upper left corner of the79

transport domain, in which the emitters and a physical barrier are located. The transport domain
was 100 cm wide (radius) and 130 cm deep (depth). The (upper) emitter was located 15 cm
below the soil surface (Figure 2, left), while the secondary emitter (in scenarios b and c) was 25
cm below the soil surface (Figure 2, center). The physical barrier (when considered, scenario d)
was placed 27 cm below the soil surface and was considered to have a radius of 25 cm (Figure 2,
right).
Figure 3 shows the boundary conditions (BCs) considered in different scenarios in this study.
Boundary conditions that are placed in parenthesis are used only in some cases. In all simulated
scenarios, the upper boundary of the transport domain was subjected to atmospheric conditions,while the lower boundary of the domain was free drainage. Boundaries at both vertical sides
were assigned a “No Flux” boundary condition. Emitters were represented in all cases as half
circles with a radius of 1 cm, located on the left vertical boundary of the transport domain. The
upper emitter was assigned a “Variable Flux 1” BC. In scenarios b and c, in which two emitterswere considered, the second emitter was assigned a “Variable Flux 2” BC. In scenario d, thephysical barrier was simulated as a 1-cm thick impermeable barrier 25 cm wide with a “No Flux”
BC, (Figure 2d and Figure 3). Simulations were carried out for 2,880 minutes (i.e., 2 days).
Time-variable boundary conditions were used to simulate drip irrigation. The dripper discharge(Q) was considered to be 7.5 L/h, which is equivalent to a boundary flux (q) of about 10 cm/min
In scenarios with a single emitter (cases a and d), the irrigation flux was 10 cm/min. In scenarioswith two emitters (cases b and c), the irrigation flux at each emitter was 5 cm/min, thus
maintaining the same total discharge in all scenarios.

Figure 3. The transport domain with applied boundary conditions.

The operation sequence of different emitters in different scenarios is shown in Figure 4. In casesa and d with only one emitter, this emitter operates for 60 minutes every two days. In case b withtwo emitters, the two emitters have the same duration of operation, but with only 50% flux
applied to each of them. Finally, for cases c, cu, and cd with two emitters operating sequentially,
Figure 4 shows the pattern of each sequential operation. The secondary (deeper) emitter starts
operating either 30 or 120 minutes before the main (upper) emitter in cases c and cd, respectively,or 120 minutes after the upper emitter in case cu. Again, n these sequential scenarios, theirrigation flux to each emitter is i half of the flux in cases a and d.

80

Figure 4. Irrigation fluxes applied in different scenarios.

In the 'Results and Discussion' section below, we will provide graphical outputs for pressure
heads along vertical and horizontal cross-sections throughout the transport domain. Fivehorizontal cross-sections are at depths of 5, 10, 15, 25, and 35 centimeters, while seven verticalcross-sections are at distances of 5, 10, 15, 20, 30, 40, 50, and 60 cm away from the axis ofsymmetry.
3. Results and Discussion
3.1. Simulation Results for Water Flow
In this section, we will discuss the results of numerical simulations for scenarios a, b, c, and d,for both the loam- and sand-textured soils. For each soil texture we will discuss both watercontent profiles along horizontal and vertical cross-sections. Each figure will show water content
profiles for nine output times at an increasing time interval, i.e., 1, 5, 20, 60, 90, 360, 720, 1440,
and 2880 min after the beginning of infiltration. These water content profiles thus cover both theinfiltration and redistribution parts of the numerical experiment.
3.1.1. Bare Loamy Soil
Water Distribution along Vertical Cross-Sections
Figure 5 shows the vertical water content distributions at five vertical cross-sections at distancesof 5, 10, 15, 25, and 35 cm from the emitter(s) for the bare loamy soil for four analyzed scenarios(a, b, c, and d). Multiple curves represent outputs at different times.
The irrigation scheme can be clearly identified from the water content profiles after 1 min in the
5 cm from the emitter cross-section (Fig. 5; left). While water content profiles for cases a and dclearly show infiltration from a single emitter, for case b they show infiltration from twoemitters, and for case c only from the bottom emitter, since the upper emitter starts operating
only after 30 minutes. In case a, the area around the emitter (depths of 8-25 cm) at a distance of 5
cm reached saturation before 5 min. This area (at a 5-cm distance from the emitter) continues towiden until almost the entire root zone is saturated at the end of irrigation. The water content
profile after 60 min already reflects the redistribution process, since the irrigation flux stops at 60
min in all cases except c (as shown in Figure 4).

81

Figure 5. Vertical water content distributions at different distances (5, 10, 15, 25, and 35) awayfrom the dripper for different irrigation scenarios for a bare loamy soil.

Water content profiles are quite similar at a 10-cm distance from the emitter, except in case d,which shows some small differences in the upper 25 cm. Maximum water contents are reached incase c at times of 60 and 90 min. At a 15-cm distance from the emitter, the highest watercontents are reached in case d in the upper 25 cm, while the three other cases are quite similar.
At a 25-cm distance, only small increases in water contents can be observed over time. While thefirst increase in the water content is observed only after 60 min in cases b and c, this occurs
earlier (after 20 min) in cases a and d, due to the higher irrigation flux from a single emitter.
Interestingly, at a 25-cm distance, water content values appear in reverse order versus timecompared to water content values at shorter distances. While at this distance, water contents are
increasing for larger times, at shorter distances they are decreasing. This is due to theredistribution process, which both vertically and laterally drives water to distances further fromemitters. Finally, notice that water did not reach the 35-cm distance, except in case d between
depths of 10 and 25 cm.
Water Distribution along Horizontal Cross-Sections
Water content distributions for four analyzed cases are shown in Figure 6 at seven horizontal
cross-sections and at depths of 5, 10, 20, 30, 40, 50, and 60 cm. The same output times as in
Figure 5 are shown. The highest water contents are found at a depth of 20 cm, i.e., between themain and secondary emitters, which are placed at depths of 15 and 25 cm, respectively. In thisdepth, the soil stays saturated to a horizontal distance of about 20 cm for up to about 90 min incase c. In case d, water contents are highest compared to other scenarios at all times at depths of
5, 10, and 20 cm, while only a small amount of new water appears at a 30-cm depth at the far endof the physical barrier at later times (at about 360 min). This is due to the redistribution process,which is demonstrated in Figure 7. Figure 7 shows that the physical barrier is very effective in82

preventing leaching of water to deeper depths, as only small quantity of water flows around thebarrier.

Figure 6. Horizontal water content distributions at different depths (5, 10, 20, 30, 40, 50, and 60)
for different irrigation scenarios for a bare loamy soil.

Figure 7. Water content distributions at different times for case d for a bare loamy soil.

While water content profiles for the first three cases a, b, and c are quite similar in the top 30 cm(Figure 6), substantial differences occur at a depth of 40 cm and below. While in case a, at a
depth of 40 cm the maximum water content is only about 0.2, in both cases b and c, watercontents are as much as 0.38 at 90 min and 0.3 at 360 min. Only cases b and c show increases in83

water contents (up to 0.20) at later times due to the redistribution process (at times of 720, 1440,
2880 min). None of the analyzed cases delivered water down to a 60-cm depth.
3.1.2. Bare Sandy Soil
Water Distribution along Vertical Cross-Sections
Sandy soils have significantly higher hydraulic conductivities and infiltration rates than loamy
soils and significantly lower macroscopic capillary length. This causes water to move deeper andmuch less laterally into the sandy soil profile than in the loamy soil. Our simulations clearlyshow that in Figure 8. In cases b and c, water infiltrated down to 60 and 90 cm at a 5-cm distanceat times of 60 and 2880 min, respectively. On the other hand, the rest of the profile is much lesssaturated. Although water contents around emitters are higher than 0.40, water quickly
redistributes when irrigation stops. The highest water contents around the emitter at all times canbe observed in case d, because of the physical barrier, which prevents redistribution of water
downwards, while physical properties of the sandy soil prevent lateral redistribution. In case c,
the highest water contents are reached at 90 min when irrigation from the primary emitter stops.
There are only small differences in water content profiles between the first three cases after 360
min. This shows that none of the analyzed cases, except case d, improve the wetting pattern once
redistribution in the sandy soil starts. The same phenomena can be observed at cross-sections at
distances of 10 and 15 cm. On the other hand, in case d one can observe accumulation of water
above the physical barrier, as well as its bypassing during the redistribution process (at the 25and 35-cm cross-sections). This shows that the physical barrier indeed enhances water
redistribution in the root zone.

Figure 8. Vertical water content distributions at different distances (5, 10, 15, 25, and 35) awayfrom the dripper for different irrigation scenarios for a bare sandy soil.

Water Distribution along Horizontal Cross-Sections
One of the main benefits of the subsurface drip irrigation is that it keeps a dry soil surface. This
helps to reduce the loss of water due to evaporation and prohibits the growth of weeds at the soil
surface. Cases b and c have the lowest water contents in the top 5 cm of the soil profile (Figure849). This is caused mainly by the lower value of the discharge (5 cm/min) of the upper emitter inthe case of the dual-drip system compared to the single-drip system (10 cm/min). This may beconsidered one of the benefits of the dual-drip system.

Figure 9. Horizontal water content distributions at different depths (5, 10, 20, 30, 40, 50, and 60)
for different irrigation scenarios for a bare sandy soil.

At a 10-cm depth, the highest water contents for cases a and d occur at 20 min, while for case c
the highest water contents occur at times of 60 and 90 min. No noticeable differences are visible
between cases a, b, and c from time 360 min to 2880 min. In case d water laterally spreads
laterally both above (at higher values) and below the physical barrier, moving more than 40 cm
at times of 1440 and 2880 min, while in other cases the lateral spreading is at most 30 cm. At a
20-cm depth, the highest water contents were obtained in case d at almost all times. This reflects
the role of the physical barrier. Case c has the second highest water contents with a nearsaturation state for up to 90 minutes. This reflects the effect of the sequential operation of thedual-drip system. At depths of 30 and 40 cm, the highest water contents were obtained in case c
at 90 min, while the lowest water contents were obtained in case d due to the existence of thephysical barrier at a depth of 27 cm. In case d, there was almost no water content increase at a
depth of 50 cm and no increase at all at a depth of 60 cm. On the other hand, the dual-drip
scenarios (cases b and c) show a better distribution of water at a depth of 50 cm than case a.
4. Conclusions
Numerical simulations carried out in this study show that the application of a dual-drip system orthe installation of a physical barrier can significantly alter both the wetting pattern and spatial
distribution of applied solutes. Physical barriers simply prevent downward movement of all
substances (e.g., water, nutrients, and other chemicals) and thus their usefulness depends on85

whether we want to retain these substances in the root zone or if we prefer to flush them out. A
dual-drip system represents a powerful tool for manipulating the distribution of solutes in theroot zone, especially if the two emitters can be operated sequentially. Such a system allows
growers to control which solute to retain in the root zone and which one to discard by simply
altering the operation of the two drippers. However, this technology requires much more
research through the evaluation of larger numbers of possible scenarios involving different
solutes, different soils, and different operation scenarios, and especially, through evaluation
under field conditions.
Acknowledgments
The authors wish to express their gratitude to the National Plan of Science and Technology atKing Saud University for funding this research by the research project (10-WAT985-02). Thanks
are also due to Alamoudi Chair for Water Research, where this research is being carried out.
References

Barth, H. K., Resource conservation and preservation through a new subsurface irrigation system, Proc. of
the 5th International Microirrigation Congress, Florida, ASAE, 168-174, 1995.
Brandt A., E. Bresler, N. Dinar, I. Ben-Asher, J. Heller, and D. Goldberg, Infiltration from trickle source:
I. Mathematical model, Soil Sci. Soc. Am. J. Proc., 35, 675-682, 1971.
Carsel, R. F., and R. S. Parrish, Developing joint probability distributions of soil water retention
characteristics, Water Resour. Res., 24, 755-769, 1988.
El-Berry, A. M., Design and utilization of subsurface drip irrigation system for fodder production in arid
lands, Misr J. Agr. Eng., 6(2), 153-165, 1989.
Ismail, S. M., T. K. Zien El-Abedin, M. M. Wassif, and M. N. El- Nesr, Physical and hydraulic barriers
under surface and subsurface drip irrigation systems, The 14th annual conf. of Misr J. of Agr. Eng.
MSAE, 23(4), 1021-1034, 2006.
Kandelous, M. M., J. Šimůnek, M. Th. van Genuchten, and K. Malek, Soil water content distributions
between two emitters of a subsurface drip irrigation system, Soil Science Society of America Journal,
75(2), 488-497, 2011.
Khalifa H. E., A. M. El-Gindy, G. A. Sharaf, and Kh. A. Allam, Simulating water movement in sandy soil
under surface point source emitter. I. Model development, Misr J. Ag. Eng., 21(2), 341-361, 2004.
Majumdar, D. K., Irrigation Water Management: Principles and Practice, PHI Learning Pvt. Ltd, 2004.
Phene, C. J., K. R. Davis, R. B. Hutmacher, and R. L. McCormick, Advantages of subsurface drip
irrigation for processing tomatoes, Acta Horticulture, 200, 101-113, 1987.
Provenzano, G., Using HYDRUS-2D simulation model to evaluate wetted soil volume in subsurface drip
irrigation systems, J. Irrig. Drain. Eng., 133, 342–349, 2007.
Šimůnek, J., M. Th. van Genuchten, and M. Šejna, Development and applications of the HYDRUS andSTANMOD software packages, and related codes, Vadose Zone Journal, 7(2), 587-600, 2008.
Singh, D. K., T. B. S. Rajput, D. K. Singh, H. S. Sikarwar, R. N. Sahoo, and T. Ahmad, Simulation of soil
wetting pattern with subsurface drip irrigation from line source, Agricultural Water Management,83(1-2), 130–134, 2006.
Skaggs, T. H., T. J. Trout, J. Šimůnek, and P. J. Shouse, Comparison of HYDRUS-2D simulations of drip
irrigation with experimental observations, J. Irrig. Drain. Eng., 130, 304–310, 2004.
Subbaiah, R., A review of models for predicting soil water dynamics during trickle irrigation, Irrigation
Science, 31(3), 225-258, 2011.
Warrick, A. W., Point and line infiltration calculation of the wetted soil surface, Soil Sci. Soc. Am. J.
Proc., 49, 1581-1583, 1985.
Welsh, D. F., U. P., Kreuter, and J. D. Byles, Enhancing subsurface drip irrigation through vector flow,
Proc. of the 5th International Microirrigation Congress, Florida, ASAE, 688-693, 1995.

86

Numerical Modeling of Water Flow and Nitrate Dynamics in Zero
Tension Plate Lysimeters Using HYDRUS-2D
Filipović Vilim1, Radka Kodešová2, and Dragutin Petošić1
1

Department of Soil Amelioration, Faculty of Agriculture, University of Zagreb, Svetošimunska 25, 10000 Zagreb,
Croatia, vfilipovic@agr.hr2
Department of Soil Science and Soil Protection, Faculty of Agrobiology, Food and Natural Resources, Czech
University of Life Sciences, Kamýcká 129, Prague 6, Czech Republic, kodesova@af.czu.cz

Abstract
Lysimeter experiments attempt to represent as closely as possible actual field conditions. The ability ofzero tension plate lysimeters, installed in silty clay soils, to represent real field conditions, as well as theability of the HYDRUS-2D software package to simulate water flow and nitrate dynamics in these
conditions, were evaluated in this study. The relatively poor performance of the lysimeters during thevegetative period was mostly caused by a high water demand of the crops and possible diversion of water
to the sides of the zero tension plate lysimeter when the groundwater table was deep. The HYDRUS-2D
model was able to reproduce observed outflows to some degree. Water and solute diverged from the plate
towards the drier unsaturated soil when groundwater table was deep. Simulated distributions of thepressure heads and nitrate concentrations around the lysimeter plate illustrated that the lysimeter plate hada significant impact on the water regime and nitrate dynamics in the soil. This paper summarizes some of
the results published earlier by Filipović et al. (2013).

1. Introduction
Numerical simulations of water flow and urea-ammonium-nitrate reactions and transport in thevadose zone, while simultaneously accounting also for root water and nutrient uptake, canimprove our understanding of the dynamic nature of these processes under field conditions. This
insight could then be used to improve fertilizer application strategies. Many computer models
have been developed over the years to solve the problems of water, heat, and pollutant
movement in the vadose zone. Two of the most advanced and most widely used numericalmodels are HYDRUS-1D (Šimůnek et al., 2008) and HYDRUS 2D/3D (Šimůnek et al., 2011).
These programs have been used successfully to simulate fertigation and the transport of nitrogen(Hanson et al., 2006). Simulations were used also to optimize fertigation (with urea) and to
reduce fertilizer applications by 30% (Ravikumar et al., 2011). Experiments used to validate
mathematical models are frequently performed in the laboratory under controlled conditions
generally not typical of natural field conditions. Lysimeters may also be used to evaluate solutetransport models (Schoen et al. 1999), and to monitor the fate and mobility of contaminants(Ludwig et al., 2000). The goal of this study was to evaluate the efficiency of zero-tension platelysimeters to collect soil water samples and to assess soil water regime and nitrate leaching insoils influenced by a high groundwater table. Four zero-tension plate lysimeters were tested inrelatively fine-textured soils (silty clay) in 2007, 2008, 2009, and 2010. The ability of HYDRUS2D to reproduce observed water and nitrate outflows (collected by lysimeters) was also assessed.
Results were published by Filipović et al. (2013). Here we show data only for 2010.

87

2. Materials and Methods
2.1. Input Data and Soil Hydraulic Properties
The research area is located near Biđ Field in Eastern Croatia between 18º15' to 19º00' east
longitude and 44º45' to 45º20' north latitude. Climatic data were collected from the Gradište
meteorological station (45°09' N and 18°42' E). The study was performed at 4 locations. Soiltypes were classified as follows: Luvic Stagnic Phaeozem Siltic (Horizons: Ap-Bt-Bg-C) at
locations L1 and L2, Haplic Fluvisol Eutric Siltic (Horizons: Ap-A/Bw-Cg-Cr) at location L3,
and Haplic Gleysol Calcaric Eutric Siltic (Horizons: Ap-Bg-Cr-Cg) at location L4. Measured soil
textures are shown in Table 1.
Table 1. Soil texture, bulk density, and van Genuchten soil hydraulic parameters for the four lysimeters
L1 through L4 (Filipović et al., 2013).
(cm3 cm-3)(cm3 cm-3)

θr

Ks(cm day-1)

α (cm-1)

n

22

Bulk
density(g cm-3)
1.59

0.38

0

11

0.0026

1.18

63

33

1.57

0.37

0

15

0.0026

1.17

9

67

24

1.56

0.36

0

17

0.0018

1.26

30-75

2

61

37

1.55

0.37

0

12

0.00017

1.25

0-40

6

60

34

1.49

0.37

0

14

0.0016

1.20

40-90

6

60

34

1.55

0.38

0

9

0.0029

1.18

0-30

5

54

41

1.37

0.42

0

12

0.0014

1.20

30-70

3

54

43

1.55

0.41

0

14

0.0021

1.18

Location

Depth
(cm)

Sand
(%)

Silt
(%)

Clay
(%)

L1

0-40

13

65

40-75

4

0-30

L2
L3
L4

θs

Table 2. Information about crops, sowing and harvest dates, and fertilizer applications (Filipović et al.,2013).

2010

Year

Location

Crop

Sowingdate

Harvestdate

Application
date

L2

Barley13.11.2009

15.07.2010

01.04.2010

L3

Corn

04.05.2010

10.10.2010

04.05.2010

L4

Corn

01.05.2010

03.10.2010

01.05.2010

Fertilizer
NPK 15:15:15 260 kg/ha,
Urea 180 kg/ha
NPK 15:15:15 700 kg/ha,
Urea 180 kg/ha
NPK 15:15:15 600 kg/ha,
Urea 180 kg/ha

2.2. Lysimeter Experiment
One zero tension lysimeter was installed at each location at a depth of 50 cm. Nitrateconcentrations were determined with a continuous flow analyzer San+ (Skalar), while outflows
were collected manually. Daily elevations of the groundwater table were monitored using two
water level limnigraphs (Orphimedes-OTT Hydrometry). We recorded also all agriculturalactivities in the experimental fields, including sowing and harvesting dates, and the date and88amount of fertilizer application (Table 2). Location L1 was not used for the solute transport
simulations because only an organic fertilizer was applied at this location.
2.3. Model Description
The HYDRUS-2D model was used to simulate water flow and solute transport. The Richards
equation, which describes isothermal Darcian flow in a variably-saturated rigid porous medium,is solved numerically by the software. This equation may be written in a general form as follows:∂θ=∇ ( K ∇H ) − S w∂t(1)

where θ is the volumetric water content [L3L-3], K is the unsaturated hydraulic conductivity [LT1], H is the hydraulic head [L], Sw is a sink term accounting for plant water uptake [T-1], ∇ is thespatial gradient operator, and t is time (T).

Soil hydraulic functions were described using the van Genuchten-Mualem model (vanGenuchten, 1980). Table 1 lists the parameters values. Of these, the saturated water content, θs,
was measured, while the remaining parameters of the soil water retention curve (θr, α, and n)
were optimized using the RETC software (van Genuchten, 1991) by fitting the measured
retention data. Unsaturated hydraulic conductivities were predicted using the θs, θr, and n values,
the measured values of saturated hydraulic conductivity, Ks, and assuming the pore connectivity
parameter to be equal to the average of many soils (l=0.5) as suggested by Mualem (1976).
The governing solute transport equations, which solve the transport of each chemical species
separately, were simplified as follows:
For urea:∂θ c1= ∇ (θ D∇c1 ) − ∇ ( qc1 ) − µaθ c1 − S wc1
∂t

(2)

∂θ c2
∂s
+ ρ 2 = ∇ (θ D∇c2 ) − ∇ ( qc2 ) − µvθ c2 − µnθ c2 + µaθ c1 − S wc2
∂t
∂t

(3)

∂θ c3
= ∇ (θ D∇c3 ) − ∇ ( qc3 ) + µnθ c2 − S wc3∂t(4)

For ammonium:

For nitrate:

where ci is the liquid phase concentration of chemical species i (the subscripts 1, 2, and 3
represent urea, ammonium, and nitrate, respectively) [ML-3], D is the dispersion coefficienttensor [L2T-1], q is the volumetric flux density[LT-1], ρ is the bulk density of the soil [ML-3], s2 isthe adsorbed concentration of ammonium [MM-1], μa is a first-order rate constant [T-1]
representing nitrification of urea to ammonium, μv is a first-order rate constant [T-1] representing

89

volatilization of ammonium to ammonia and μn is a first-order reaction rate constant [T-1]
representing nitrification of ammonium to nitrate.
The parameters needed for simulating the transport of the various nitrogen species were set as
follows. The longitudinal dispersivity along the direction of flow was taken as 5 cm and thetransverse dispersivity as 0.5 cm. Molecular diffusion was neglected. The first-order reaction
constant representing nitrification of urea to ammonium (μa) was taken as 0.38 per day (Hanson
et al., 2006), the reaction constant representing nitrification of ammonium to nitrate (μn) was set
at 0.2 per day (Hanson et al., 2006), and the reaction constant for volatilization of ammonium toammonia (μv) was set at 0.0552 per day (Bolado Rodriguez et al., 2005). The distribution
coefficient for ammonium (Kd) was assumed to be 3.5 cm3g-1 (Hanson et al., 2006). The bulk
density was measured using undisturbed soil samples (Table 1).
The model was used to simulate the water regime and solute transport above and around thelysimeter plate assuming a radially symmetric flow domain. The assumed 2D transect was 150
cm wide radially, and 150 cm deep, with the lysimeter plate (Ø 50 cm) at a depth of 50 from thesoil surface. Initial conditions were defined as a hydrostatic equilibrium pressure head
distribution with the value of the pressure head at the bottom being zero (a groundwater table).
Atmospheric conditions with surface runoff were selected at the top. A seepage face was appliedat the top of the lysimeter plate. Root water uptake was calculated assuming potential
evapotranspiration, a given root depth and density, and using the Feddes water stress response
function (Filipović et al., 2013).
The initial ammonium and nitrate contents in soils were set in terms of nitrogen concentrations insoil water (expressed in mmol cm-3). No flux was considered at both lateral boundaries, and thesides and bottom of the lysimeter plate. A third-type boundary condition was used at remaining
boundaries. The concentration fluxes of nitrogen for all 3 applied species (urea, ammonium, or
nitrate) were calculated assuming molar mass and a number of atoms for each molecule(Filipović et al., 2013).
3. Results and Discussion
3.1. Water Flow
Observed and simulated results are shown in Figure 1. The simulated results depended upon
precipitation events, the transpiration intensity and the position of the groundwater table. The
water table in particular was found to have a major effect on pressure head distributions aroundthe lysimeter plate. No outflow was simulated when the water table was deep. Cumulative
outflow was then strongly affected by water diverging around the lysimeter, without any waterflowing through the lysimeter plate. The reason is that outflow will occur only when the soil
above the plate is fully saturated (e.g., the pressure head in the soil above the plate must reach apositive value). Outflows were simulated only after intensive rainfalls when the soil above theplate became saturated from below (i.e., when the water table was high and the soil profile
mostly saturated due to capillary rise from the water table).

90

Figure 1. Observed and simulated cumulative outflows from the four lysimeters in 2010. The
correspondence between measured and simulated values is expressed using the correlation
coefficient, r (Filipović et al., 2013).

The spatial distributions of the pressure head clearly indicate that water was diverging around theplate towards the dryer surrounding soil (as also discussed by Peters and Durner, 2009) and thatwater could also be supplied by capillary rise from the water table. Two examples of the pressure
head distribution are shown in Figure 2. Figure 2a shows pressure heads within a twodimensional transect (i.e., around the lysimeter plate) after rainfall when no outflow wassimulated. Figure 2b similarly shows pressure heads within the two-dimensional transect after
rainfall when considerable outflow was simulated. The figures clearly show either low or highpressure heads above the plate, which resulted into either no or high outflows, respectively.

Figure 2. Simulated pressure heads within the two-dimensional transect of lysimeter 4, 2010, day
71 (a, left) and 152 (b, right) (after Filipović et al., 2013).

913.2. Nitrate Transport
Cumulative nitrate outflow measured in different lysimeters and simulated using HYDRUS-2D
are presented in Figure 3. Values reflect cumulative water outflow rates (Fig. 2) and actual
nitrate concentrations above the lysimeter plate. Therefore, the correspondence between
observations and model outputs varies. This is reflected by the r values in Figure 3, which range
from 0.72 to 0.89. No outflow of urea was simulated because of root uptake and rapid conversion
into nitrate (urea and NPK are highly reactive fertilizers that start reacting immediately after theirdissolution in percolating water). Figure 4 shows the nitrate concentrations (79 days after thefertilizer application) after an extreme rainfall event in 2010. A considerable amount of nitratepassed in this case below the lysimeter plate due to large and intensive rainfall. Clearly, theamount of precipitation and its intensity strongly influenced the nitrate leaching process and its
dynamics in the observed soil profile. These are the most dominant processes determining nitratetransport and distributions in the soil.

Figure 3. Observed and simulated cumulative nitrate outflows from the three lysimeters in 2010.
The correspondence between measured and simulated values is expressed using the correlation
coefficient, r (after Filipović et al., 2013).

4. Conclusions
The ability of zero-tension plate lysimeters to collect soil water samples and to assess soil water
regimes and nitrate leaching in soils influenced by the groundwater table was evaluated in thisstudy. A poor efficiency during the vegetation period was caused mostly by high plant water
demand and possible lateral diversion of water when the groundwater table was deep. The
simulated water and nitrate outflows showed that the water regime was affected significantly by
the groundwater table, which was monitored in the field. Outflow was simulated only when thesoil above the plate was saturated from below, and during intensive rainfall periods.

92

Figure 4. Simulated nitrate concentrations within a two-dimensional transect of lysimeter 4, day
200 (Filipović et al., 2013).

Nitrate outflow always reflected the simulated outflow of water and the actual nitrateconcentrations above the lysimeter plate. The lysimeter plate generally acted as a barrier forwater flow and also solute transport. The HYDRUS-2D software package was able to reproduce
to some degree the observed water and nitrate outflows. Our results indicate that HYDRUS canbe very helpful for understanding and estimating the dynamics of water flow and nitrate transport
under real field conditions.
References

Bolado-Rodriguez, S., A. Alonso-Gaite, and J. Álvarez-Benedi, Characterization of nitrogentransformations, sorption and volatilization processes in urea fertilized soils, Vadose Zone J., 4, 329336, 2005.
Filipović, V., R. Kodešová, and D. Petošić, Experimental and mathematical modeling of water regime
and nitrate dynamics on zero tension plate lysimeters in soil influenced by high groundwater table,
Nutrient Cycling in Agroecosystems, 95, 23-42, 2013.
Hanson, B. R., J. Šimůnek, and J. W. Hopmans, Numerical modeling of urea-ammonium-nitratefertigation under microirrigation, Agricultural Water Management, 86, 102-113, 2006.
Ludwig, C., C. A. Johnson, M. Käppeli, A. Ulrich, and S. Riediker, Hydrological and geochemical factors
controlling the leaching of cemented MSWI air pollution control residues: A lysimeter field study, J.
Contam. Hydrol., 42, 253-272, 2000.
Mualem, Y., A new model for predicting the hydraulic conductivity of unsaturated porous media, Water
Resour. Res., 12(3), 513-522, 1976.
Peters, A., and W. Durner, Large zero-tension plate lysimeters for soil water and solute collection inundisturbed soils, Hydrol. Earth System Sci. Discussions, 6, 4637-4669, 2009.
Ravikumar, V, G. Vijayakumar, J. Šimůnek, S. Chellamuthu, R. Santhi, and K. Appavu, Evaluation offertigation scheduling for sugarcane using a vadose zone flow and transport model, Agric. Water
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Functions of Unsaturated Soils, Version 1.0, EPA Report 600/2-91/065, U.S. Salinity Laboratory,
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soils, Soil Sci. Soc. Am. J., 44(5), 892–898, 1980.

94

Single and Double Porosity Modeling of Solute Transport in
Intact Soil Columns – Effects of Texture, Slurry Placement, andIntermittent Irrigation
Nadia Glæsner1,2,3 and Horst H. Gerke3
1

Faculty of Science, University of Copenhagen, Frederiksberg, Denmark, nadia.glaesner@gmail.com
2
Faculty of Science and Technology, Aarhus University, Tjele, Denmark,3
Leibniz-Zentrum für Agrarlandschaftsforschung (ZALF) e.V., Müncheberg, Germany, hgerke@zalf.de

Abstract
We investigated using single and double porosity models implemented in HYDRUS-1D
numerical code, solute transport and solute mass exchange between pore water regions in intact
soil columns (20 cm diameter, 20 cm high) under variably-saturated flow conditions during
injection and surface application of dairy slurry manure in three soil textures, and duringcontinuous and intermittent irrigation. All models tested were able to describe breakthroughcurves of nonreactive slurry components (Br tracer applied to slurry) and a tritium tracer appliedwith irrigation water for all experimental conditions. Simulation of intermittent irrigation with
HYDRUS software was limited by the option of a fixed bottom seepage face value, which could
not be changed in time according to experimental conditions. The problem was provisionally
fixed by restarting the program with the modified bottom conditions at experimentally definedtimes using the calculated final distribution of state variables as new initial conditions. Bothsingle and double porosity water flow and mobile-immobile solute transport models predicted
decreased solute mass exchange when injecting slurry into the soil profile compared with surface
application in a loam, but not in the more coarse-textured soils. These results suggest protectionof slurry compounds when placed inside the soil matrix in finer-textured soils compared withplacement of slurry at the soil surface. Introducing rainfall interruptions (and variably-saturatedflow) led to higher leaching of injected slurry compounds compared with steady flow conditions.
These results were explained by increased mass exchange from immobile to mobile pore water
regions during interruptions. The model based analysis suggests considering more natural
boundary conditions when trying to obtain improved understanding of nutrient leaching afterslurry application.

1. Introduction
Leaching of plant nutrients from agricultural fields is causing eutrophication problems of surface
waters worldwide. Nutrient losses especially occur from fields subjected to land application ofanimal manure in areas of high livestock production (Coelho et al., 2007; Kronvang et al., 2009).
In order to minimize leaching of agricultural chemicals to the subsurface and aquatic
environments, the effects of different soil management strategies are being evaluated (e.g.,
Maguire et al., 2011).

95

Injection of animal slurry into arable topsoil was proposed as an alternative to surface application
to reduce ammonia gas emissions (Webb et al., 2010). Injection of dairy slurry has additionallybeen shown to reduce leaching of slurry components (Glæsner et al., 2011a,b) in loamy soils
when compared with surface application; the effect was less obvious for the sandy soils. Early
tracer appearance in the loam indicated the effects of preferential flow (e.g., Flühler et al., 1996;
Gerke, 2006) and physical non-equilibrium solute transport (e.g., van Genuchten and Dalton,1986). Physical non-equilibrium in the loamy soil could be explained by the existence of a twodomain pore system (van Genuchten and Wierenga, 1976) characterized by a mobile and an
immobile (aggregate or less mobile soil matrix) pore water region.
Solute transport in column experiments has often been studied assuming steady-flow conditions(de Jonge et al., 2004; Glæsner et al., 2011a), thereby simplifying model analysis by neglecting
soil hydraulic properties. Under steady flow conditions, breakthrough curves (BTCs) of
percolation experiments can be analyzed with analytical solutions of the convection-dispersion
equation (CDE); for instance, with the program CXTFIT (Toride et al., 1995). Transfer of steadyflow laboratory column experimental data to field conditions however, can be criticized because
the steady flow assumption rarely occurs. It is more realistic to have rain infiltration periods
followed by dry periods, generating variably-saturated flow of water and locally varying porewater velocities (Wehrer and Totsche, 2003). While diffusion-limited solute mass transfer canalready occur under steady-flow conditions, an additional mass exchange by transfer of water
between the mobile and immobile pore regions has to be considered for intermittent flow
conditions with physical non-equilibrium (e.g., Gerke, 2006; Jarvis, 2007).
This study aims at identifying the possible role of mass exchange between mobile and immobile
pore regions during different slurry placements (surface application and injection) and irrigation
regimes (steady-flow and intermittent irrigation). Based on the description of a set of soil column
percolation experiments, the aim is achieved by a stepwise increase in model complexity using
an analytical CDE model and numerical single and double porosity models. The analysis
required i) choosing the most appropriate flow and transport model types, ii) determining
parameters for each model type (again from simple to more complex), iii) identifying limitations
given by experimental data at certain modeling steps, and iv) defining particular initialconditions and treatment of the boundary conditions for the injection case. The final aim was tocouple experimental results with detailed understanding of the underlying mechanisms ofleaching losses of slurry compounds.
2. Experimental Design and Modeling Approach
2.1. Experimental Design
Although experimental conditions are thoroughly described in the papers of Glæsner et al.
(2011a,c), a short description is given here. Intact soil columns (20 cm diameter, 20 cm height)
were excavated from the plough layer of an agricultural field in Denmark with a natural gradientof clay content; loamy sand, sandy loam, and loam. The effects of no slurry application, surface
application of slurry, and injection of slurry were all studied (Glæsner et al., 2011a). The finertextured loamy soil with injected slurry was furthermore studied during continuous irrigation and96intermittent irrigation at a rate of 2 mm h-1 (Glæsner et al., 2011c). The experiments were carriedout in triplicate.
All intact soil columns, excavated at field capacity, were initially saturated and subsequently
drained on tension tables to -100 cm. The columns were then transferred to an irrigation/leaching
setup; irrigation was initiated, and a suction of -5 cm was applied at the lower boundary after 2.5– 12.5 h irrigation to ensure unsaturated conditions. Experiments were carried out for
approximately 5 days, and during intermittent irrigation, suction was increased to -20 cm during
irrigation interruptions.
Dairy slurry manure was initially homogenized and spiked with KBr (2.69 g L-1), and thenapplied to the soil columns 52–53 h prior to initiation of the leaching experiment at an amountcorresponding to 25 t ha-1. Slurry was either evenly distributed at the soil surface or injected in a
1 cm wide and 10 cm long band, placed 5 cm from the edge of the cylinder and 8 cm below thesoil surface. The columns received a pulse of 2.5 mm 3H2O after steady outflow was reached.
2.2. Modeling Approach
For simulating tracer movement (3H2O), we used the equilibrium (EQ) and non-equilibrium(NEQ) convection-dispersion equations (CDE); model parameters were fitted using the CXTFIT
program (Toride et al., 1995) as implemented in STANMOD software (Šimůnek et al., 2008).
For simulating solute transport under steady-state (continuous irrigation) and variably-saturated
flow conditions (intermittent irrigation), we used: i) the single porosity model for uniform
equilibrium-type flow and solute transport (SP-EQM), in which the volumetric water content, θ(cm3 cm-3), the solute concentration, c (g L-1), and the solute mass, cθ, are defined for a single
porosity soil, ii) the combination of equilibrium water flow (EQ water) with mobile-immobile
solute transport (SP-MIM solute), and iii) the double porosity model for non-equilibrium mobileimmobile type water flow and solute transport (DP-MIM) (cf., Šimůnek and van Genuchten,2008). These models were numerically solved as implemented in the HYDRUS-1D program(Šimůnek et al., 2008).
The double porosity and MIM approaches partition the bulk soil into fractions for mobile andimmobile pore-water regions for the volumetric water content, θ, and the solute mass as θ = θim +θm and cθ = cimθim + cmθm, respectively. Equations and parameters used in this paper are as in
Toride et al. (1995) and Šimůnek et al. (2008).
2.2.1. Stepwise Parameter Estimation
The parameter estimation was carried out stepwise as illustrated in Figure 1. The 3H2O-BTCs
were first analyzed with CXTFIT. The EQM model was used to fit an initial value of D to the3
H2O-BTCs for all columns, assuming a retardation factor of R = 1. These initial D values wereused in the NEQM to further optimize the values of D, β, and ω to obtain λ, as well as θim, and αs
to be used in HYDRUS. The best fit was based on the lowest possible MSE (mean square error),
low correlation between parameters, and low 95% confidence intervals as calculated in CXTFIT.

97

The β parameter (mobile water fraction) was used in the DP-MIM transport simulation (seebelow).

Figure 1. Overview of the complex stepwise analysis of mass exchange in the leachingexperiments, illustrating the data input from small cores and larger intact columns, breakthroughcurves (BTC) for 3H2O and Br for steady flow (top row), variably-saturated flow and transport
during surface application and injection (of slurry) for intermittent irrigation (bottom), and theresulting exchange rates and the used programs, models, flow and transport parameter
derivations.

Soil Hydraulic Model Parameters
From the experimental conditions (Glæsner et al., 2011a, b, c), the volumetric water contents at-5 and -100 cm from each intact soil column as well as eight values of the water retention curvefrom 100 cm3 intact core samples were available for each soil texture-type in the pressure headrange between -4 and -300 cm. Two approaches were carried out to find optimized single
porosity vGM (van Genuchten, 1980) soil hydraulic parameters:A) Soil hydraulic functions were estimated using pedotransfer functions with the ROSETTA
program (Schaap et al., 2001) as implemented in HYDRUS. ROSETTA estimates werebased on data of texture, bulk density, and water content at -100 cm, which we usedinstead of that at -330 cm. Since the ROSETTA fit did not match the two retention values
at -5 and -100 cm available for each soil column, the value of θs was manually adjusted
based on the vGM equation (van Genuchten, 1980), such that the fitted matched the98observed θ-value at -5 cm. With the manually fitted θs and the ROSETTA fitted θr, n andα values as initial estimates, the α-values of the vGM function were again optimized
using the RETC program (van Genuchten et al., 1991), assuming m=1-1/n to fit theretention values at -5 and -100 cm. The values of Ks were fitted such that K(h) function(van Genuchten, 1980) matched the observed K-value at h =-5 cm.
B) The water retention data from 100 cm3 soil cores of each texture were fitted with the
RETC program using the optimized vGM-parameters from step A) as initial estimates.
The value of θs was fixed, and θr, n, and α were fitted. For the loam, the optimized values
for n were not allowed to drop below n = 1.2 (fixed minimum) to avoid numericalproblems. The resulting α and n values based on soil core retention data were applied to
all columns of each texture class, whereas θs and θr values were adjusted to match themeasured water contents at -100 cm and -5 cm of each individual column using the vGM
equation (van Genuchten, 1980).
The parameter sets were finally tested by describing the experiments with the vGM parameters in
HYDRUS, such that simulated θ-values were matching the measured ones during drainage (at 100 cm) and irrigation (at -5 cm) for each column.
For the double porosity flow model parameters, the identical values of α and n obtained fromabove were used for both mobile and immobile pore water regions in order to minimize
parameter identification. The fractions θm and θim were obtained from CXTFIT results (above).
For the loamy sand and the sandy loam columns, the mobile pore water region θsm and θrm were
defined as 0.9-times, and the immobile region θsIm and θrIm as 0.1-times the values of the vGMparameters. For the loam, θsm and θrm were 0.4-times, and θsIm and θrIm were 0.6-times the valuesof the vGM parameters. Values of the water exchange coefficient, αw, were fitted using the
optimization routine provided in the HYDRUS program.
Solute Transport and Mass Exchange Parameters
The transport parameter θim obtained with CXTFIT from 3H2O solute transport was not further
fitted; however, λ and αs of columns subjected to injection were fitted in HYDRUS using the
average values of the parameters from columns of the same texture that were subjected to surface
application as initial values. For analyzing Br leaching, we used the parameters obtained from3
H2O as initial estimates in all columns and then fitted the values of λ and αs for Br in HYDRUS.
For intermittent irrigation, solute transport parameters, λ and αs, obtained during steady flow,
were used as initial estimates in HYDRUS and then fitted to the effluent data of the respective
soil columns.
2.2.2. Initial and Boundary Conditions
Conditions in HYDRUS were different for columns subjected to surface application or injectionof slurry (mixed with Br). Surface application of slurry was treated as a flux boundary condition
with a flux rate of 32.4 cm d-1 for 10 min, assuming that a pulse of 70 mL of water in appliedslurry per column was mixed within the first 1 cm layer for 10 min after application at day 11 (2days prior to irrigation).

99

Slurry injection as an initial condition was assumed to be fully mixed with the soil of a verticallayer of 2.5 cm in 6.5 - 9 cm depth for the loamy sand and the sandy loam, and a layer of 7 cm
thickness in 4 - 11 cm depth for the loam columns. The full mix of slurry and soil in the layers of
the whole column was required when assuming a 1D vertical model. The slurry injection
introduced Br and additional water. This application-induced increase in water contents wasconsidered proportional to the available water storage porosity, hence the vertical thickness of
the injection layer was chosen the smallest layer possible that could store the additional slurrywater without exceeding the porosity. Due to a larger fraction of smaller pores in the loam(Glæsner et al., 2011a), the higher water-filled porosity at -100 cm at the time of slurry injection
resulted in the assumed larger layer for the loam in which slurry was mixed as compared to theother two soils.
Upper boundary conditions in HYDRUS were set to atmospheric with a surface layer. The lower
boundary was set to a seepage face condition of 0 cm when irrigation was initiated; hereafter, aseepage face condition of -5 cm was imposed after 2.5 - 12.5 hours. These changes of lower
boundary conditions required us to split the simulation runs in a series of interrupted model
periods per run. Hence, end conditions of a previous period were applied as initial conditions inthe subsequent period during each simulation run. Transport of 3H2O was described asconcentration flux at the upper boundary and with zero concentration gradient at the lower
boundary, whereas Br was described (see above) in the initial condition in the form of a resident
concentration. The flow domain was spatially discretized using 200 nodes.
3. Leaching of Irrigation Tracer (3H2O)
Simulations using ROSETTA-derived parameters for 3H2O transport yielded only small
differences as compared to those results obtained with the optimized RETC retention parameterset (data not shown). We, therefore, used optimized RETC retention parameters in all solutetransport simulations.
The NEQM in CXTFIT fitted the 3H2O BTCs before slurry application better than the EQM in
all soil textures (Fig. 2), even though the NEQM fit improved more with increased clay content,
as the degree of nonequilibrium transport increased with increasing clay content observed byearlier breakthrough and larger tailing (e.g., Flühler et al., 1996). In HYDRUS, applying DPMIM did, however, not improve the fitting of 3H2O in an injected column during continuous
irrigation compared with the simpler models (Fig. 3, left).
Simulations of intermittent irrigation conditions improved with increasingly complex models
from SP-EQ to SP-MIM to DP-MIM (Fig. 3, right). One explanation for improved simulation
with increasingly complex models for the increased complex experimental setup during
intermittent conditions could be the inclusion of solute and water exchange in the more complex
models, as increased exchange of solute as well as of water is expected as new pressure andconcentration gradients arise within the soil when pores are emptied for water during
interruptions.

100

0.06

Loamy sand

0.05

Loamy sandLoamy sand

Sandy loam

Sandy loam

EQM
NEQM 1
NEQM 2

0.04
0.03
0.02
0.01
0.00

Sandy loam
0.05

C/C0

0.04

Col 19 vs Col 20
Col 19 vs Col 21
Col 22 vs Col 23
Col 22 vs Col 24
Col 25 vs Col 26
Col 25 vs Col 27

Col 1 vs Col 2
Col 1 vs Col 3

0.03
0.02
0.01

Col 28 vs Col 29
Col 28 vs Col 30
Col 31 vs Col 32
Col 31 vs Col 33
Col 34 vs Col 35
Col 34 vs Col 36

0.00

Loam

Loam

Loam

0.05
0.04
0.03
0.02
0.01
0.00
0.0

0.5

1.0

1.5

2.0

0.0

0.5

1.0

1.5

2.0

0.0

0.5

1.0

1.5

2.0

2.5

Pore volumes V/V0

Figure 2. 3H2O BTCs in surface applied triplicate columns from the three soil textures using EQM
and NEQM in CXTFIT for curve fitting for steady flow (continuous irrigation).
0.035

3

H2O C/C0

0.030
data
SP-EQ
SP-MIM
DP-MIM

0.025
0.020
0.015
0.010
0.005
0.000
13

14

15

16

13

14

15

16

17

18

Time (days)

Figure 3. 3H2O BTCs after injection with continuous (left) and intermittent (right) irrigation using
SP-EQ (dotted line), SP-MIM (dashed line), and DP-MIM (solid line) in HYDRUS. Only one
column from each experiment is shown. Open symbols represent samples collected during
interruptions; vertical solid lines represent interruptions; and vertical dotted lines represent
initiation of irrigation.

Water exchange during continuous irrigation occurred only from mobile to immobile pore water
regions (positive values) (Fig. 4). Water exchange during intermittent irrigation occurred frommobile to immobile pore regions during irrigation and from immobile to mobile pore regions(negative values) during irrigation interruptions (Fig. 4), resulting in lower cumulative mass
exchange of water from mobile to immobile pore regions during intermittent conditions.

101

0.18

Cumulative water exchange

cumulative cm

0.14

Cont. Irrigation
Int. Irrigation

0.10

0.06

0.02

-0.02
13.0

13.5

14.0

14.5

15.0

15.5

16.0

Days

Figure 4. Cumulative water exchange for continuous and intermittent irrigation using the DPMIM approach.

The importance of water exchange for solute transport is evident, as a substantially larger
exchange of 3H2O occurred when applying DP-MIM compared with SP-MIM (Fig. 5). This is
explained by the additional advective solute mass exchange of 3H2O caused by assuming waterexchange between the pore regions in the DP-MIM. However, for solute exchange, higher
cumulative 3H2O exchange from mobile to immobile pore regions is recorded for intermittent
irrigation as compared with continuous irrigation, which is due to “diffusive” mass exchange of3
H2O being the main mechanism for 3H2O exchange caused by concentration differences
between pore regions compared to “advective” exchange of 3H2O with water caused by pressure
head gradients. The high fluctuations in cumulative water exchange (Fig. 4) are therefore not so
evident in the cumulative 3H2O exchange (Fig. 5). This was further confirmed by decreased mass
recovery of leached 3H2O when changing the boundary conditions from continuous (86.6 %) tointermittent (76.4 %) irrigation (Glæsner et al., 2011c).
50

Cumulative 3H2O exchange

Cumulative Br exchange

Cumulative mg L-1 cm-2

Cumulative DPM cm-2

8000

6000

4000

2000

0
13.0

Cont. Irrigation 2 mm h-1 SP-MIM
Cont. Irrigation 2 mm h-1 DP-MIM
Int. Irrigation 2 mm h-1 SP-MIM
Int. Irrigation 2 mm h-1 DP-MIM

13.5

14.0

14.5

15.0

15.5

0
-50
-100
-150
-200
-250
13.0

16.0

Int. Irrigation 2 mm h-1 SP-MIM
Int. Irrigation 2 mm h-1 DP-MIM
Cont. Irrigation 2 mm h-1 SP-MIM
Cont. Irrigation 2 mm h-1 DP-MIM

13.5

14.0

14.5

15.0

15.5

16.0

Days

Days

Figure 5. Cumulative 3H2O and Br exchange for continuous and intermittent irrigation simulatedwith the SP-MIM and DP-MIM approaches.

102

4. Leaching of Slurry Tracer (Bromide)
Bromide BTCs, when slurry was applied both to the soil surface and injected into the soil, were
simulated less well than 3H2O, but the models still gave good simulation fits (Fig. 6). That BTCs
of Br were less well fitted compared with 3H2O reflects that Br was applied with slurry which
has a different consistency and viscosity than water (Kumar et al., 1972; Frey et al., 2012).
Injection of slurry decreased mass recovery of bromide (60.2 %) compared with surface
application (80.6 %) in the loam soil, but not in the other soils (Glæsner et al., 2011a). The
authors suggested this to be due to protection of solutes from the few preferential flow paths inthe more fine-textured soil. This hypothesis was confirmed in this study by lower cumulative
mass exchange from immobile to mobile pore regions during injection compared with surface
application in the loam, whereas no difference was observed in the loamy sand and sandy loam
when using SP-MIM, even though no statistical significance was found (Table 1). The highly
heterogeneous nature of the different columns challenges statistical analysis of the results.

0.03
data
SP-EQ
SP-MIM
DP-MIM

Bromide C/C0

0.02

0.01

0.00
0.03

0.02

0.01

0.00
13

14

15

16

17

18 13

14

15

16

17

18 13

14

15

16

17

18

Time (days)

Figure 6. Bromide BTCs after injection with continuous (upper) and intermittent irrigation(lower) using SP-EQ (dotted line), SP-MIM (dashed line), and DP-MIM (solid line) in HYDRUS.
Open symbols represent samples collected during interruptions; vertical solid lines representinterruptions; and vertical dotted lines represent initiation of irrigation.

103

Table 1. Averaged cumulative mass exchange of Br after 1.2 eluted PV using SP-MIM and DPMIM. Positive values represent exchange from mobile to immobile pore regions, whereas
negative values represent exchange from immobile to mobile pore regions. Statistical differencesat the 5% level are given by different letters.
Experiment
Loamy sand – surface application
Loamy sand – injection
Sandy loam – surface application
Sandy loam – injection
Loam – surface application
Loam – injection

SP-MIM
mg L-1 cm-2
-0.01 (0.00)a-0.61 (0.49)a-0.01 (0.00)a-4.64 (1.14)a-127.45 (28.4)a-58.46 (0.13)aDP-MIM
mg L-1 cm-2
-16.79 (13.7)a-3.11 (1.04)a-17.91 (14.4)a-1.42 (0.81)a-140.27 (8.46)a-124.21 (8.59)aLoam – injection - continuous
Loam – injection - intermittent-127.73 (21.5)a-175.02 (3.18)a-170.23 (47.1)a-272.56 (4.20)aDuring intermittent conditions, in similarity to 3H2O, simulation fits increased with increasedmodel complexity (Fig. 6). The Br mass exchange values were all negative (Fig. 5), indicatingthat exchange of injected Br is only directed from the immobile to the mobile pore water region,
which corresponds well with Br being placed within the intact columns at -100 cm, when only
pores <30 µm were saturated. Though the water content of the slurry added to higher poreclasses being saturated, Br was assumed to diffuse into the water-filled porosity at the time of
application, hence the immobile region. Mass recovery of Br in the effluent during continuous
irrigation (45.5% ± 2.5) was lower than during intermittent irrigation (59.3% ± 5.2) (Glæsner etal., 2011c). This is fully supported by the cumulative exchange analysis, demonstrating higher
mass exchange from immobile to mobile pore regions during intermittent irrigation (Fig. 5),
thereby resulting in higher effluent mass recovery.

5. Conclusions
The role of mass exchange was analyzed using different models implemented in HYDRUS-1D.
Both single and double porosity water flow and mobile-immobile solute transport models
described the data well. However, as experimental conditions became more complex, the more
complex models described the data better by including solute and water exchange between porewater regions. Injection decreased leaching of solutes compared with surface application in aloam, but not in the more coarse-textured soils, which could be described by decreased soluteexchange from immobile to mobile pore regions in the loam by the model based analysis.
Introducing rainfall interruptions (and variably-saturated flow) led to higher leaching of injectedslurry compounds compared with steady flow conditions, explained by increased mass exchange
from immobile to mobile pore water regions during interruptions in the model based analysis.
The results suggest considering more natural boundary conditions when trying to obtain
improved understanding of nutrient leaching after slurry application.

104

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Quality, 40, 292-301, 2011.
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Šimůnek, J., and M. Th. van Genuchten, Modeling nonequilibrium flow and transport processes using HYDRUS,
Vadose Zone Journal, 7(2), 782-797, 2008.
Šimůnek, J., M. Th. van Genuchten, and M. Šejna, Development and applications of the HYDRUS and STANMOD
software packages, and related codes, Vadose Zone Journal, 7(2), 587-600, 2008.
Toride, N., F. J. Leij, and M. Th. van Genuchten, The CXTFIT code for estimating transport parameters fromlaboratory or field tracer experiments, Version 2.0, Research Report No. 137, US Salinity Laboratory, USDA,
ARS, Riverside, CA, USA, 1995.
van Genuchten, M. Th., A closed-form equation for predicting the hydraulic conductivity of unsaturated soils, Soil
Science Society of America Journal, 44, 892-898, 1980.
van Genuchten, M. Th., and P. J. Wierenga, Mass-transfer studies in sorbing porous-media. 1. Analytical solutions,
Soil Science Society of America Journal, 44, 473-480, 1976.
van Genuchten, M. Th., and F. N. Dalton, Models for simulating salt movement in aggregated field soils, Geoderma,
38, 165-183, 1986.
Van Genuchten, M. Th., F. J. Leij, and S. R. Yates, The RETC code for quantifying the hydraulic functions of
unsaturated soils, Version 1.0, EPA Report 600/2-91/065, US Salinity Laboratory, USDA, ARS, Riverside, CA,
USA, 1991.
Webb. J., B. Pain, S. Bittman, and J. Morgan, The impacts of manure application methods on emissions ofammonia, nitrous oxide and on crop response – a review, Agriculture, Ecosystem and Environment, 137, 39-46,
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2003.

105

106

The Use of HYDRUS-1D for Groundwater Recharge Estimationin Boreal Environments
Sergey O. Grinevskiy1 and Sergey P. Pozdniakov2
1

Hydrogeology division, Geological Department, Moscow State University, Leninskie Gory, MSU, Moscow, Russia,
sogrin@geol.msu.ru
2
Hydrogeology division, Geological Department, Moscow State University, Leninskie Gory, MSU, Moscow, Russia,
sppozd@geol.msu.ru

Abstract
The well-known package HYDRUS-1D (Šimůnek et al., 2009) was used for groundwater recharge
simulations based on long term meteorological data with daily resolution. For a boreal climate with a long
winter period, initial meteorological data such as precipitation cannot be used directly as the atmosphericboundary condition in HYDRUS. This data must be preprocessed to take snow accumulation and snow
melting, evaporation from snow and vegetation cover, and soil freezing-defrosting processes into account.
For this purpose, SurfBal (Grinevskii and Pozdnyakov, 2010), a special preprocessing code for simulating
surface water and energy balances and generating upper boundary conditions for HYDRUS-1D wasdeveloped. SurfBal calculates surface water balance using known daily values of precipitation, solar
radiation, and maximum and minimum temperatures. It calculates interception by canopy, surface (leafand snow) evaporation, snow accumulation, consolidation of snowpack and its melting and surface
runoff, as well as initial potential values of evaporation, transpiration, and input water fluxes for
HYDRUS-1D. The results of water balance and groundwater recharge simulations using SurfBal and
HYDRUS-1D for climate conditions of the south-western part of Moscow Artesian Basin show the
principal role of the spring-period surface-soil water budget for groundwater recharge under various
landscapes and soil cover, and the effects of various groundwater level depths.

1. Introduction
The methodological principles of regional estimation of groundwater recharge (GWR) by
atmospheric water infiltration are based on simulation of the water balance on the land surface
and unsaturated flow inside the soil cover and vadose zone to groundwater level (GWL). These
processes are generally identical for the uniform, typical natural conditions of GWR, which arecharacterized by a combination of meteorological conditions, type of surface and vegetation, soil
and underlying vadose zone properties, as well as GWL depth. So the results of simulation of
GWR, obtained for each type (combination) of such conditions, may be extrapolated for thecorresponding part of the river basin (Crosbie et al., 2010; Grinevskii and Pozdnyakov, 2010).
In small-scale, regional consideration, the typical conditions of GWR are formed by the complex
of meteorological, landscape, vegetation, soil and hydrogeological factors, which jointly
influence the recharge heterogeneity (Fig. 0).

107

Groundwater recharge factors

LandscapeSurface type:forestgrassland
tillageswamp
water area
urban land

Relief:Tableland
Slope
BottomExposure
South
North

Meteorological
Precipitation
Temperature
Humidity
Solarradiation

Hydrogeological

Drainageconditions

Groundwater level
depth, z (m)0-1 m (flood land)
W<0
1-3 m (river terrace) W = f (z)
3-5 m (slope) W = f (z)>5 m (watershed) W=сonst

Vadose zone texture:
Dispersed :Sand
Sandy Loam
Loam
Clay
Rocky

Soil texture
Sandy
Loamy Sandy
Loamy

Figure 1. Main regional factors of groundwater recharge.

Main features of boreal climate with regard to GWR processes are:- the total precipitation exceeds total potential evapotranspiration, so the dry index is less thanone;
- the long winter season with temperatures below zero causes a high amount of solid
precipitation, accumulated in snow cover;- winter thaws are usually very short and rare, and the upper part of the soil is frozen, so thewater seepage into the soil is negligible during winter season;- the snow melting period is usually short and intensive, which causes the high volume ofsnowmelt runoff.
All these features result in special variable upper boundary meteorological and flow conditions
for unsaturated flow simulations using HYDRUS-1D. The program code SurfBal was developed
to simulate the processes of precipitation and heat energy transformations on the land surface inorder to generate the upper boundary meteorological conditions for HYDRUS.
2. Model of Precipitation and Heat Energy Transformations on the Land Surface(SurfBal)The SurfBal integrates the next water budget equation at the surface:dV= P − E LS − S − v p ; V=VS + VL; ELS = EL + ESdt

(1)

where V is the total volume of water accumulated on vegetation (VL) and in snowpack (VS), P is
the precipitation rate, ELS is the total surface evaporation, including evaporation from canopy

108

(EL) and snow cover (ES), S is the surface runoff, and vp is the potential infiltration into the soil
profile. Solution of Eq. (3) with daily time step gives a value of v ip for i-th day, which is passed
to HYDRUS-1D as the upper boundary condition:(2)

v ip = P i ± ∆VS − ∆VL − S i − ESi − ELi

where ∆VS and ∆VL equal daily changes of water volumes, accumulated in snow and on leaves,respectively.
Tracking the temperature records, SurfBal calculates the interception of liquid precipitation by
the canopy PL (if the mean daily air temperature is above zero) as the well-known bucket model(Vinogradov, 1988):
 P i ii
= K L LAI i
PLi = Λi 1 − exp i , Λi = Pmax
− V Li , Pmax Λ 


(3)

According to this approach, total intercepted water is less than maximum storage Pmax,
depending on the daily value of LAI and water retention constant KL = 0.2 mm (Liang et al.,1994). So, a daily variation of water accumulated by canopy depends on interception as well as
leaf evaporation EL, which is proportional to potential evapotranspiration ET0 (Liang et al.,1994):∆V = V − V
i
L

i
L

i −1
L

=P −E ;iL

i
L

 V Li i Pmax 

E Li = ETi 0 

2/3

(4)

Daily values of potential evapotranspiration ET0 are calculated based on air temperature and net
solar radiation data by the Penman-Montheith or Priestley-Taylor methods (Allen, 2001).
The modified model of Gelphan and Kuchment (Kuchment and Gelfan, 1996) is used to
calculate snow depth dynamic and the release of melting water at the soil surface. Dynamics ofthe snow depth HS at the surface is simulated by depth-averaged equations for the snow state,considered as a three-phase system that includes solid phase ice with the density ρi, water withdensity ρw, and void space. The model takes into account accumulation of snow during
precipitation when air temperature T <0, snowmelt, snow metamorphism, sublimation, refreezingof melting water, and its flow to the soil surface through snowpack:dΗ s=  Ps χ 0 − ( L + ES ) χ I −1  − Vρdtd( IH s=) χ ( Ps − L − ES + Si )dtd(θ H s ) = ( Pr + L − Vm − EW − Si )
dt

109

(5)

where I and θ are parts of ice and water in snow volume, χ 0 = ρ w ρ s−01; χ = ρ w ρi−1 , Ps and Pr aresnowfall and rainfall rates, respectively, and Si is the rate of refreezing of melt water for T<0,which is calculated as:(6)

Si = K i T
where Ki≈4.5 mm/ deg0,5/day is the empirical coefficient of water-ice phase transformations.

The total sublimation of ice ES and evaporation of liquid water EW from snowpack depends on
potential evapotranspiration ET0 (Budagovskii, 1981):
 β i ETi 0 , when VSi > β i ETi 0 i; β = exp(-δ LAIi ); 0.45< δ <0.55( ES + EW )i =
 i
0
i
i
when VS < β ETi
VS ,(7)

Vρ is the snowpack self-compression rate due to its weight:=Vρ 0.5 K v ρ s H s2 exp (ξ1T − ξ 2 ρ s )(8)

The snow melting rate L depends on the temperature and the current snow density ρs with theempirical coefficient of snow melting Ks:

T <0
0;
L=
 K s ρ sT ; T ≥ 0(9)

Vm is the release rate of melting water to the soil surface due to gravity-dominated flow of water
through the unsaturated snowpack:θ − θ max
3.5=
; θ ≥ θ max
K f θ ; θ
1 − I − θ max
Vm = 
0;θ < θ max

(10)

where Kf is the snow hydraulic conductivity, and θmax is the maximum water retention by snow.
The current snow density is:ρs =ρi I + ρ wθHs

and fresh snow density ρs0 is the function of air temperature:

110

(11)

 ρ min ;
T − Tminρ=; ρ min + ( ρ max − ρ min )
s0
Tmin

ρ ;
 max

T < Tmin
Tmin ≤ T < 0

(12)

T ≥0

The well-known curve number method (USDA, 1985) is used for calculations of daily surface
runoff. When T<0, daily curve number value CN depends on thawed or frozen status of topsoil(Schroeder et al., 1993). The beginning of soil defrosting may be identified by a reverse weighedaverage of air temperature for the last ten days Tth>0 and a current snowpack thickness Hs<0.2m, with the empirical delay factor ε:
t

=
Tth

∫ T (τ ) exp(−ε (t − τ ))dτ

(13)

t −tl

Because potential evapotranspiration ET0 characterizes total available water losses to atmosphere
due to energy limits of the landscape, the remaining daily part of ET0, except for losses by snow
ES and leaf EL evaporation, can be estimated:
ET p0 = ET 0 − E S − E L(14)This value is the limit for soil evaporation and plant transpiration, which can be divided into theirpotential values E 0p и TR 0p (Budagovskii, 1981):

E p0 = β ETp0 , TR p0= (1 − β )ETp0(15)

where β is obtained from eq. (7).
The results of SurfBal calculations - daily values of inflow v p , and potential evaporation E 0p
and transpiration rates TR 0p - describe upper boundary conditions for the soil profile and arepassed to HYDRUS-1D as the atmospheric boundary condition.
3. Site and Data Description and GWR Model Parameters
With a total area of 49 600 km2, the investigated region is the south-western part of Moscow
Artesian Basin (MAB) and is located in the center of the European part of Russia. This is theperiphery, the edge of MAB, where the regional recharge of carboniferous aquifers takes place.
Mean annual precipitation varies in a south-north direction from 600 to 700 mm; mean air
temperature ranges from 5.0oC to 4.6oC. These differences are correlated with river runoff,
which also changes from 160 mm to 200 mm per year from south to north. For further
investigations, the observed daily values of total precipitation, mean, and minimum andmaximum air temperatures from 6 meteorological stations for a period of about 50 years were111

used. The representative weather stations for different major river basins of the region wereselected by the statistical analysis and correlation between precipitation and river runoff.
The areal division of the region using the typical recharge conditions, including landscape,vegetation and soil type, as well as the dominant texture of the underlying vadose zone and meanannual GW level depths, was made. And for each type of GWR conditions, the model of surface
and vadose zone water balance was developed for a fifty year simulation period.
The main parameters of the surface water balance model (SurfBal) are presented in Table 1. CN
values in the curve number method reflect the mean areal runoff properties of the catchment.
Typical curve numbers were used as preliminary values and then were verified by river runoff
observations on stream gage stations.
Table 1. Main parameters of the SurfBal model.
Landscape type

Model parameter

Field
0-3
4-6
1
0.45
70
88
94

LAI, min-max, [-]Snow melting rate, Ks [cm4/deg/g/day]Snow melting delay, ε, day-1
δ, [-]
sandy soil
Curve number,CN, [-]
loamy soil
clayey soil

Forest2-8
1.5-3.5
3
0.55
40
83
90

The snowpack dynamic model allows calibration of its parameters by comparing simulated andobserved snow depth during winter (Fig. 2). Main fitting parameters in this simulation stage are
Kv, Ks, Kf and ξ1, ξ2 in eqs. (8-10).

Figure 2. Simulated (lines) and observed (dots) snow depths for the 3-year period.

The soil profile for the unsaturated flow simulation consists of three model layers, which reflect
an average typical structure of the vadose zone (Grinevskii, 2010). The upper layer is the soil

112

horizon of the A type (humus horizon) and has the maximum variability of soil properties.
Moreover, water retention curve (WRC) characteristics not only depend on the lithologicaltexture, but also on the type of surface vegetation. The second soil layer, the illuvial soil horizonof the B type, usually has a lower permeability than expected for such soil texture because of the
inflow of the organic matter from topsoil. The third model layer simulates the underlying parent
rock material (horizon C), whose properties are almost unchanged by pedogenic processes andwell-corresponded to the soil texture. Vertical model distribution of this layer is limited by GWL
depth.
Average characteristics of WRC van Genuchten equations (van Genuchten, 1980) for threesimulated soil profile layers, depending on soil texture and type of vegetation cover (for theupper layer) were calculated using the well known program, Rosetta (Schaap et al., 2001) andnumerous soil data (Grinevskii, 2010), and were used for GWR simulation (Table 2). Data in
Table 2 show that WRC parameters for the top soil differ depending on the type of vegetation
cover. Besides this, the influence of vegetation cover leads to anomalous values of parameter α,which decrease from loamy to sandy soil, unlike those for the underlying layers.
Table 2. Average van Genuchten WRC parameters for different soil layers, soil texture and types of
surface landscape (Grinevskii, 2010).
Soil texture /Landcape
Loam / Forest
Loam / Field
Loamy sand / Forest
Loamy sand / Field
Sand / Forest
Sand / Field
Loam
Sandy Loam
Sand
Clay
Loam
Sandy Loam
Sand

θr
-

θs
-

α,
m-1

Layer 1– Soil horizon A
0,041
0,525
1,00
0,054
0,525
1,17
0,038
0,532
0,79
0,033
0,500
1,08
0,029
0,482
0,34
0,030
0,413
0,55
Layer 2 – Soil horizon B
0,055
0,427
0,60
0,038
0,412
0,90
0,022
0,366
1,25
Layer 3 – Soil horizon C
0,057
0,380
0,74
0,052
0,383
0,49
0,034
0,379
1,39
0,018
0,370
2,06

n
-

Ks,
m/d

1,388
1,352
1,486
1,494
2,280
1,744

0,562
0,049
0,73
0,27
3,85
1,50

1,352
1,442
1,578

0,07
0,21
1,21

1,145
1,269
1,361
1,581

0,007
0,04
0,20
2,96

For root water uptake calculations, the S-shape function, which describes the water uptake stressresponse function φ(h) in HYDRUS-1D (Šimůnek et al., 2008), was used:ϕ ( h) =1τ
1 + (h h50 )(16)

where h50 represents the pressure head at which the root water extraction rate is reduced by 50%,and τ is an empirical parameter. The beginning of decreasing root water extraction (φ(h) <1) due

113to drying conditions in dependence of WRC and it’s specific points (field capacity and wilting
point) was defined by Li et al. (2006). Following this, values of h50 for different soil andvegetation types were calculated (Table 3) using average WRC parameters (Table 2) as(Grinevskii, 2011):

h − hwpθ −θh *θ *; h* 50 =; θ * 50 wp= 0.5=
h fc − hwp
θ fc − θ wp
TR p0 /(TR p0 ) max(17)

where θfc and θwp are water content at field capacity and wilting point, hfc and hwp arecorresponding pressure heads, TR p0 and ( TR 0p )max equals average and maximum potential
transpiration rate during the vegetation period. In eq. (17) hfc = -3.36 m and hwp = -153 m, andthe corresponding θfc and θwp were calculated from WRC. Values of τ, which reflect different
rates of decreasing root water extraction ability due to drying conditions for trees and grasses,
were obtained by the best fit of calculated and observed φ(h) curves (Sudnitsyn, 1979). The
exponent tau was set smaller for trees produce a slower decreasing φ(h) curve, due to the trees’
best adaptability to water stress conditions.
The root distribution model takes into account the differences in root zone structure and depth
for various vegetation and soil textures. The exponential function (Gale and Grigal, 1987) of theroot distribution with depth was used for trees with bar root system. For grass vegetation with afibrous root system we used another root distribution function, offered by Hoffman and van
Genuchten (Šimůnek et al., 2008). Parameters of the root water uptake model thus reflect thetype of vegetation as well as soil texture (Table 3).
Table 3. Parameters of the root water uptake model (Grinevskii, 2011).
Vegetation type
Trees
Grass

Soil

h50, mLoam
Loamy sand
Sand
Loam
Loamy sand
Sand

-37.3
-33.3
-15.0
-45.5
-31.9
-24.0

τ
2
4

Average root
depth, m
1.0
1.5
2.0
0.15
0.3
0.5

4. Simulation Results and Discussion
Using daily precipitation and temperature data and SurfBal and HYDRUS-1D parameters fordifferent types of vegetation cover and soil and vadose zone textures, as presented above, daily
and mean annual values of GWR (for the 50 year period) for each type of natural conditions
were calculated. These mean annual GWR values were extended to areas with similar GWR
conditions across the investigated region (Grinevskii and Pozdnyakov, 2010). Differences inlandscape, soil and groundwater conditions cause significant variability of mean annual GWR
rates – from 15 to 144 mm/year (Figure 3).

114

Figure 3. Differences in simulated mean annual GWR due to landscape and soil conditions (forGWL depth >5 m).

Simulation results also show the strong landscape and soil type influence on seasonal surface andvadose zone water balance variations (Fig. 4). The total sum of annual evapotranspiration isalmost the same, but for woody vegetation, the main part is the plant transpiration. In fieldlandscapes, the main part is evaporation. The principal differences for various landscapes are inspring surface runoff, which forms during a short snow melting period (Grinevskii and
Novoselova, 2011). There is an intensive peak of water seepage to the soil in forest landscapes,
where snow isn’t melting as fast. Exactly during this period the upper inflow to the soil isstrongly variable and differs from precipitation data. This is the main reason for the landscapedifferences in annual GW recharge and its seasonal variability (Fig. 4).

Figure 4. Simulated mean seasonal variations of surface runoff, potential infiltration to the soil
and GWR due to landscape and soil conditions (for GWL depth >5 m).

Figure 5. Mean annual GWR (W) as a function of GWL depth (Z) for different landscapes andsoil types.

115

Landscape and soil conditions also influence the relationship between mean annual GWR and
GWL depth (Fig. 5). Simulation results show that mean annual GWR increases with depth only
to a certain limit, wp, and can be approximated with the Pashkovskii equation (Shestakov et al.,1982):( γ)

w(z) =wp − ( wp − w0 ) exp − z(18)where w0 and γ are fitted parameters. For shallow groundwater levels, the mean annual GWR
becomes negative as a rule, which means that the upward flow in the vadose zone by theevapotranspiration processes dominates the downward flow. This means groundwater discharge
by evapotranspiration. The w0 is thus an asymptotic negative value, where GWL depth z=0, andis close to ET0. The critical GWL depth z0, where mean annual GWR w(z)=0, can be obtained
from eq. (18). Therefore, for every landscape and soil type, z < z0 means GW evapotranspiration
discharge (w(z) < 0) and vice versa: when z > z0, w(z) > 0, which means recharge conditions.
Acknowledgments. This work was supported by RBRFoundation via grants 11-05-00478-а
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117

118

Simulation of Uranium Tailing Leaching using VS2DRT
Sosina S. Haile and Broder J. Merkel
Department of Geology, Technische Universität Bergakademie Freiberg, Gustav-Zeuner-Str. 12,09596 Freiberg/Sa., Germany, wedatnsos@yahoo.com and merkel@geo.tu-freiberg.de

Abstract
Uranium contamination of surface and ground waters from uranium tailings is a serious
environmental problem in many countries that have uranium mining. Reactive transport models
can be used to predict the potential environmental impacts of new uranium tailing sites, as wellas to assess a level of contamination from existing uranium tailing sites. Hence, reactive
transport models are useful tools to visualize potential threats, as well as to emanate dangerous
situations, and to design preventive and remedial measures to protect and rehabilitate water
resources. In the present study, a newly developed, two-dimensional, multi-species coupled
reactive transport model, VS2DRT, is used to simulate uranium tailing leaching. The problem
was adapted from HYDROGEOCHEM 5.0 and HP2 manuals and deals with the release andsubsequent migration of uranium from a uranium tailing pile toward ground water and a nearby
river. The simulation does not involve redox reactions and shows the application of VS2DRT in
simulating uranium migration in the subsurface.
1. Introduction
Uranium is a natural, radioactive and hazardous element which exists in three isotope forms of
U238, U235, and U234 in trace amounts in the environment. The discovery of radium by Marie
Curie led to uranium mining in the first half of the 20th century for the production of radium(Carvalho, 2012). After World War II, uranium was mined widely for production of nuclear
weapons and later for nuclear power plants to produce energy. The radioactive and hazardous
nature of waste materials from uranium mining and milling was poorly recognized during thefirst uranium boom in the 1940s to 1960s (Robinson, 2004).
Uranium tailing refers to a uranium ore residue, which contains the radioactive decay products ofuranium and heavy metals that are deposited in ponds. There is a huge volume of tailing waste
around the world, with an estimated volume of 938 million cubic meters produced at more than
4000 mines (IAEA, 2004). Living in a uranium mining area may lead to exposure toradionuclides from mining, mill tailings, dust, and contaminated water and foodstuff (Matias,
2008). Although the major environmental impacts of uranium tailings are the failure of tailingdams and exposure to radiation, contamination of groundwater and/or surface water by leakageof contaminated water from tailing ponds is a serious concern. For example, in Australia in 1994,
the uranium tailing Olympic Dam released up to 5 million m3 of contaminated water into the soil
(IAEA, 2004). More recently, in 2012 in Sotkamo, Kainuu province, Finland, leakage from a
gypsum pond resulted in higher uranium concentrations in the nearby Snow River, exceeding
more than tenfold the allowable threshold level (http://www.wise-uranium.org/mdaf.html).

119

Reactive transport modeling of contaminants from uranium tailing dams or ponds could be used
as a predictive tool to estimate the extent of contamination and to take remedial measures torehabilitate the site. Hence, reactive transport models such as HYDROGEOCHEM 5.0 (Yeh etal., 2004), HP2 (Šimůnek et al., 2012), and VS2DRT (Haile, 2013) could be useful tools tosimulate possible leaching of uranium from passive as well as active tailing sites. In this paper,
we introduce a new reactive transport model, VS2DRT, which could be used to simulateleaching of uranium and other heavy metals from uranium tailings. The HP2 test example
involving leaching of uranium tailing is adapted here to show the applicability of VS2DRT forsuch cases.
2. VS2DRT Simulation of Leaching of Uranium Tailings
2.1. Description of VS2DRT
VS2DRT is a new reactive transport model for variably-saturated porous media. VS2DRT
couples the single solute transport program, VS2DT (Healy R., 1990), and the heat transport
program, VS2DH (Healy and Ronan, 1996), with the hydro-geochemical program, PHREEQC(Parkhurst and Appelo, 1999). VS2DRT uses a non-iterative operator splitting approach tocouple the programs. This approach involves solving the transport and chemical reactions
sequentially in one time step. VS2DRT has capabilities to simulate the flow of water, heattransport, multi-solute transport, various equilibrium reactions such as cation exchange,
adsorption, dissolution/precipitation, and various kinetic reactions in variably-saturated porous
media. However, VS2DRT does not consider gas phase flow, the effect of chemical reactions on
hydraulic properties, and the density of water.
2.2. The Case of Leaching of Uranium Tailings
This problem was adapted from the HYDROGEOCHEM 5.0 and HP2 manuals. The problem
deals with a hypothetical case of a uranium mill-tailing disposal and a subsequent release andmigration of uranium to groundwater and a river. The schematic representation of the domain of
simulation is presented on Figure 1. The tailings pile is located on a flat surface which slopes
down to a river. The hydraulic properties of soil and tailing are presented in Figure 2. The
surface of the tailing pile was defined as the flux boundary with an infiltration rate of 0.0139
m/day. The top boundary, except for the surface of the tailing pile, has a flux boundary condition
with an infiltration rate of 0.00139 m/day. The bottom boundary is considered to be impervious.
The left side of the simulation domain below the water table has a 5 m pressure head. The riverbottom and the vertical nodes on the right side of the river have a 4 m pressure head boundary
condition. The initial pressure head and uranium profiles are presented in Figures 3 and 4,
respectively. The light green color on the top right corner in Figure 3 is out of the simulation
domain.

120

Figure 1. Schematic representation of the uranium tailing problem.

Figure 2. van Genuchten hydraulic parameters used for the soil and tailing piles.

Figure 3. The pressure head profile at the beginning of the simulation (0 days).

121

Figure 4. The uranium (mole/ kg of water) profile at the beginning of the simulation (0 days).

The list of chemical reactions and their thermodynamic equilibrium constants considered for thiscase are presented in Table 1. The simulation here does not consider redox reactions. The
aqueous solution inside the tailing piles, outside the tailing, and at the boundaries are presented
in Table 2. The simulation was conducted for 1000 days with a time step of 1 day.
Table 1. Reactions and log K used for a uranium tailing problem (Šimůnek et al., 2012).
Reaction
Aqueous Complexation Reactions considered
H2O ↔ H+ + OHCa2+ + CO32- ↔ CaCO3
Ca2+ + H+ + CO32- ↔ CaHCO3+
Ca2+ + SO32- ↔ CaSO3
Ca2+ + 2H+ + PO43- ↔ CaH2PO4+
Ca2+ + PO43- ↔ CaPO4Ca2+ + H+ + PO43- ↔ CaHPO4
Ca2+ + H2O ↔ H+ + CaOHFe2+ + SO42- ↔ FeSO4
Fe2+ + H2O ↔ H+ + FeOHFe2+ + 2H2O ↔ 2H+ + Fe(OH)2
Fe2+ + 3H2O ↔ 3H+ + Fe(OH)3Fe2+ + 4H2O ↔ 4H+ + Fe(OH)42UO22+ + H2O ↔ H+ +(UO2)(OH)+
2UO22+ + 2H2O ↔ 2H+ +(UO2)2(OH)22+
3UO22+ + 4H2O ↔ 4H+ +(UO2)3(OH) 42+
3UO22+ + 5H2O ↔ 5H+ +(UO2)3(OH) 5+
4UO22+ + 7H2O ↔ 7H+ +(UO2)4(OH) 7+
3UO22+ + 7H2O ↔ 7H+ +(UO2)3(OH) 7UO22+ + CO32- ↔ (UO2)(CO3)
UO22+ + 2CO32- ↔ (UO2)(CO3) 22UO22+ + 3CO32- ↔ (UO2)(CO3) 342UO22+ + CO32- + 3H2O ↔ 3H+ + (UO2)2(CO3)(OH) 3UO22+ + SO42- ↔ (UO2)(SO4)
UO22+ + 2SO42- ↔ (UO2)(SO4) 222H+ + UO22+ + PO43- ↔ H2(UO2)(PO4)+
3H+ + UO22+ + PO43- ↔ H2(UO2)(PO4)2+
Ca2+ + 4H+ + UO22+ + 2PO43- ↔ CaH4(UO2)(PO4) 22+

122

No

Log K

R1
R2
R3
R4
R5
R6
R7
R8
R9
R10
R11
R12
R13
R14
R15
R16
R17
R18
R19
R20
R21
R22
R23
R24
R25
R26
R27
R28

-14
3.22
11.43
2.31
20.96
6.49
15.08
-12.582.2-9.5-20.57-31.00-43.00-5.3-5.68-11.88-15.82-21.9-28.34
9.65
17.08
21.7
-1.18
2.95
4.0
23.2
22.90
45.24

Ca2+ + 5H+ + UO22+ + 2PO43- ↔ CaH5(UO2)(PO4) 23+
H+ + CO32- ↔ HCO32H+ + CO32- ↔ H2CO3
H+ + SO42- ↔ HSO4H+ + PO43- ↔ HPO422H+ + PO43- ↔ H2PO43H+ + PO43- ↔ H3PO4
Precipitation-Dissolution Reactions
Ca2+ + SO42- ↔ CaSO4 (s)Ca2+ + CO32- ↔ CaCO3 (s)Ca2+ + 3PO43- + H2O ↔ H+ + Ca5(OH)(PO4)3(s)Fe2+ + CO32- ↔ FeCO3 (s)Ca2+ + 2UO22+ + 2PO43- ↔ Ca(UO2)2(PO4)2(s)4Ca2+ + H+ + 3PO43- ↔ CaH(PO4)3(s)Ca2+ + H+ + PO43- ↔ CaH(PO4) (s)Ca2+ + 2H2O ↔ 2H+ + Ca(OH)2 (s)3Fe2+ + 2PO43- ↔ Fe3(PO4)2(s)Fe2+ + 2H2O ↔ 2H+ + Fe(OH)2 (s)UO22+ + 2H2O ↔ 2H+ + (UO2) (OH)2 (s)UO22+ + CO32- ↔ (UO2)(CO3) (s)Fe2+ + 2UO22+ + 2PO43- ↔ Fe(UO2)2(PO4)2(s)H+ + UO22+ + PO43- ↔ H(UO2) (PO4)2(s)

R29
R30
R31
R32
R33
R34
R35

46.00
10.32
16.67
1.99
12.32
19.55
21.74

R36
R37
R38
R39
R40
R41
R42
R43
R44
R45
R46
R47
R48
R49

4.62
8.48
40.47
10.50
48.61
48.20
19.30
-21.9033.30-12.10
-5.40
14.11
46.00
25.00

Table 2. Initial and boundary solutions for a uranium tailing problem (Šimůnek et al., 2012).
Species
Ca2+
CO32UO22+
PO43SO42H+
Fe2+

Inside the Tailing(mole/kg of water)
1.0 x 10-2
1.0 x 10-2
5.0 x 10-4
1.0 x 10-6
2.0 x 10-1
3.5 x 10-2
2.0 x 10-1

Outside the Tailing(mole/kg of water)
1.0 x 10-2
1.5 x 10-3
1.0 x 10-7
1.0 x 10-6
2.0 x 10-2
1.0 x 10-7
1.0 x 10-3

Boundary solution(mole/kg of water)
1.0 x 10-3
1.5 x 10-3
1.0 x 10-8
1.0 x 10-6
1.0 x 10-4
1.0 x 10-7
1.0 x 10-3

3. Result and Discussion
The results of the VS2DRT simulation are presented in Figures 5, 6, and 7 for uranium at 250,
500, and 1000 days, respectively. At 250 days, the uranium plume spreads toward the groundwater, which is located at a depth of about 12 m. At 500 days, the uranium plume continues tospread in ground water and moves toward the river, which is located about 100 m along the xaxis. At 1000 days, ground water is completely polluted with uranium with concentrations ashigh as 0.0004 mole/kg of water. Uranium continues spreading toward the river with aconcentration of 0.00005 mole/kg of water.

123

Figure 5. The uranium (mole/ kg of water) profile at 250 days.

Figure 6. The uranium (mole/kg of water) profile at 500 days.

Figure 7. The uranium (mole/kg of water) profile at 1000 days.

Figure 8 shows the uranium profile at 250 and 500 days based on the HP2 simulation. The
uranium plumes show similar patterns for both HP2 and VS2DRT models. The difference
between HP2 and VS2DRT simulation results could be due to spatial and temporal
discretizations used. HP2 uses a finite element method, and for the current problem, it used atime step of 0.0001 day. However, VS2DRT uses a finite difference method, and for the current
problem, it used a time step of 1 day. The effect of the pumping well considered in the HP2
simulation is also not included in VS2DRT.
Generally, both HP2 and VS2DRT can be used for 2D reactive transport modeling in variablysaturated porous media. The advantage of VS2DRT is that it is a public domain program while
HP2 is a commercial one.

124

Figure 8. Uranium (mole/kg of water) profiles at (a) 250 days and (b) 500 days based on the HP2
simulation (Šimůnek et al., 2012).

4. Conclusions
Reactive transport programs such as VS2DRT are useful tools to visualize the possible spatial
and temporal distributions of contaminants in the subsurface. Coupling of VS2DT and VS2DH
with PHREEQC has boosted the applicability of VS2DT to simulate multi-solute transport with awide variety of equilibrium and kinetic reactions. The hypothetical case presented here showsthat VS2DRT can be used to predict the uranium plume pattern at variable times. In real world
applications, the accuracy of the simulation depends on the hydraulic and chemical properties
and the initial and boundary conditions for flow and chemical solutions. Moreover, the grid size
and the time steps used for the numerical simulations play a huge role. It is good practice toverify the numerical simulations with measured or observed values whenever possible in order tohave more confidence in the obtained results and in decisions made based on numericalsimulations.
References

Carvalho, F. P., Marie Curie and the Discovery of Radium. In Merkel, B., and M. Schipek (eds.), The
New Uranium Mining Boom, pp. 3-17, Berlin, Springer, 2012.
Haile, S. S., VS2DRT: Variably Saturated Two Dimensional Reactive Transport, Freiberg, Saxony,
Germany, 2013.
Healy, R., Simulation of solute transport in variably saturated porous media with supplemental
information on modifications to U.S. Geological Survey's Computer Program VS2D, Denver,
Colorado, U.S. Geological Survey, 1990.
Healy, R., and A. Ronan, Documentation of Computer Program VS2DH for simulation of energy
transport in Variably saturated porous media--modification of the US Geological Survey's computer
program VS2DT, Denver, Colorado, U.S. Geological Survey, 1996.
IAEA, The long term stabilization of uranium mill tailings, Vienna, International Atomic Energy Agency,
2004.

125

Matias, O. N., Assessment of groundwater quality and contamination problems ascribed to an abandoned
uranium mine (Cunha Baixa region), Environ Geol., 1799–1810, 2008.
Parkhurst, D., and C. Appelo, User's guide to PHREEQC (version-2) a computer program for speciation,
batch-reaction, one-dimensional transport, and inverse geochemical calculations, Denver, Colorado,
U.S. Geological Survey, 1999.
Robinson, P., Uranium Mill Tailings Remediation Performed by the US DOE: An Overview, US DOE,
2004.
Šimůnek, J., D. Jacques, M. Šejna, and M. Th. van Genuchten, The HP2 Program for HYDRUS (2D/3D):
A Coupled Code for Simulating Two-Dimensional Variably-Saturated Water Flow, Heat Transport, andBiogeochemistry in Porous Media, Version 1.0, PC Progress, Prague, Czech Republic, 76 pp., 2012.
Yeh, G.-T., J. Sun, P. M. Jardine, W. D. Burgos, Y. Fang, M.-H. Li, and M. D. Siegel,
HYDROGEOCHEM 5.0: A Three-Dimensional Model of Coupled Fluid Flow, Thermal Transport,
and HYDROGEOCHEMical Transport through Variably Saturated Conditions - Version 5.0, US
DOE, 2004.
http://www.wise-uranium.org/mdaf.html

126

Infiltration Into a Stony Soil: Modeling of the Process Using
HYDRUS Codes
Hana Hlaváčiková, Viliam Novák, and Marek Rodný
Institute of Hydrology, Slovak Academy of Sciences, Račianska 75, 83102 Bratislava, Slovakia
hlavacikova@uh.savba.sk

Abstract
Stony soils are composed of fractions (rocks and fine particles) with different hydrophysicalcharacteristics. Consequently, effective hydrophysical characteristics are needed for simulations of waterflow in stony soils. In the following contribution, the effective hydraulic conductivity of a stony soil was
estimated using the HYDRUS-2D numerical experiment. Next, infiltration into soils with different
stoniness was performed using the derived effective characteristics and the HYDRUS-1D model. Ponded
and rainfall infiltrations were modeled (with the rainfall intensity lower than the saturated hydraulicconductivity of a stony soil) with the aim of evaluating the influence of different stoniness on the processof water flow in stony soils.

1. State of the Art
Soils containing a significant fraction of rocks (stones, skeleton), generally denoted as stonysoils, are located mainly in forest and mountainous areas. According to Poesen and Lavee(1994), Western Europe contains about 30% of such soils; in the Mediterranean region stonysoils cover around 60% of the territory. According to Šály (1976), the major portion of Slovak
forest soils (up to 80%) contain stones, while the stone content increases with depth.
Furthermore, about 47% of Slovak agricultural soils are referred to as stony soils (Hraško andBedrna, 1988). Shape, size, degree of weathering, and geological origin of the soil skeleton canstrongly influence the soil hydrophysical properties, mainly the retention capacity and hydraulicconductivity. Therefore, it is important to characterize the properties of the stony skeleton and its
distribution in the soil profile. Obtained information could be used to elucidate the influence ofstones on soil water transport processes. It can be expected that the stone content in soils will
reduce the effective cross-sectional area through which water flows. Furthermore, an increase instoniness results in higher tortuosity of soil pores, which consequently leads to a lower hydraulicconductivity of the stony soil (Ravina and Magier, 1984, Childs and Flint, 1990; Novák et al.,2011; Bouwer and Rice, 1984; Ma et al., 2010). On the other hand, the shrinking-swelling
phenomena could lead to the presence of temporal lacunar pores (voids along soil/stoneinterface), which could consequently cause the presence of preferential flow, and thus anincrease in the saturated hydraulic conductivity (Sauer a Logsdon, 2002; Shi et al., 2008; Verbist
et al., 2009; Zhou et al., 2009). Moreover, it could be hypothesized that the degree of preferential
flow in such soils will be proportionally related to the stone content and its spatial distribution.
In this study we present an original method for estimating the effective hydraulic conductivity ofstony soils (Kse) based on the HYDRUS-2D numerical simulations. Moreover, HYDRUS-1D
simulations were performed for soils with different stoniness under different infiltration

127

conditions. Simulated upper and bottom boundary fluxes for soils with different stoniness were
evaluated and discussed.

2. Soil Characteristics
2.1. Effective Saturated Hydraulic Conductivity of a Stony Soil
Effective saturated hydraulic conductivities and retention curves need to be estimated for aquantitative description of soil water movement in stony soils. The representative elementaryvolume (REV) used for the determination of the above-mentioned soil hydraulic properties isdependent on the size of rock fragments. For example, for a soil containing stones with anaverage diameter of 10 cm, a REV of 1 m3 is needed. Since it is extremely technically difficult toperform physical experiments with this size of soil sample, solutions based on virtualization ofclassical laboratory experiments are taking place. In this study, a classical Darcy´s experiment
was simulated using the HYDRUS-2D model (Šimůnek et al., 2008b). Impermeable stones of aspheroidal shape (approximated as circles in a 2D cross-sectional area) were equally distributedin the virtual soil sample with a volume of 1 m3. Furthermore, steady-state water flow wassimulated using the unit hydraulic gradient (1 cm of water pressure head was applied as theupper and bottom boundary conditions). The rate of water flow through the REV therefore
equals the effective saturated hydraulic conductivity Kse (Novák et al., 2011). Results of thenumerical experiments were used to adjust the formula of Ravina and Magier (1984) to the form
presented in Novák et al. (2011):
K se = (1− a.Rv )K fe(1)

where Kse is the effective saturated hydraulic conductivity [cm h-1], Kfe is the saturated hydraulicconductivity of a fine-textured soil fraction [cm h-1], a is a parameter that incorporates thehydraulic resistance of the rock fragments to water flow and depends on soil texture anddimensions of rock fragments [-] (e.g., a = 1.1 was estimated for sandy loam and spherical rockfragments of a 10-cm diameter), and Rv stands for a relative volume fraction of stones [cm3cm-3](stoniness).
2.2. Effective Water Retention Curve of a Stony Soil
The relationship between water contents and pressure heads for stony soils can be estimatedusing the method presented by Bouwer and Rice (1984). In this method, the bulk volumetricwater content of a stony soil is expressed from the volumetric water content of a fine soil fraction
alone (eq. 2). Bouwer and Rice (1984) have neglected the retention capacity of the rockfragments.

θ se = (1 − Rv )θ fe(2)

where θse is the bulk volumetric water content of a stony soil [cm3cm-3], θfe is the volumetricwater content of a fine soil fraction alone [cm3cm-3], and Rv is the relative volume fraction ofstones [cm3cm-3].

128

3. Infiltration into Soils with Different Stoniness
The impact of different stoniness on the upper and bottom boundary water fluxes during
infiltration through the stony soil was evaluated using HYDRUS-1D (Šimůnek et al., 2008a).
Two qualitatively different upper boundary conditions were used to evaluate the stony soil
behavior during infiltration. A Dirichlet boundary condition with a 2 cm layer of water ponded
on the soil surface was used to simulate ponded infiltration. The second case involved simulating
infiltration from precipitation with an 80 mm/h rainfall intensity and three hours duration (anextremely high rainfall event). However, the rainfall intensity was lower than the saturated
hydraulic conductivity of a stony soil with 50% stoniness. Under this condition, surface runoff
did not occur. Furthermore, the effective hydraulic properties were determined for the sandy
loam soil from the study site Červenec (1500 m a.s.l.) located in the Western High Tatra Mts.
Infiltration was modeled using the standard (single domain) description of hydraulic properties(van Genuchten, 1980; Mualem, 1976).
Infiltration into four virtual soil profiles with a depth of 95 cm and different stoniness (Rv = 0,
10, 30, and 50%) were modeled. During the simulation, evaporation from the soil surface and thewater retention of the rock fragments were neglected. For all modeled soil profiles, the initialconditions were set as vertically uniform (h = -1000 cm). The bottom boundary was defined as afree drainage boundary. The spatial distribution of rock fragments in the soil profile wasassumed to be uniform in order to be compatible with ideas presented in the HYDRUS-2D
numerical experiment.
4. Results and Discussion
The parameters of effective retention curves and effective saturated hydraulic conductivities
reflecting different stoniness are presented in Table 1. As can be seen in Figure 1, under ponded
conditions the infiltration rates are negatively correlated with the amount of stones present in thesoil (stoniness). As is demonstrated in Figures 2 and 3, cumulative infiltration rates and fluxes
through the bottom boundary under saturated conditions are lower for stony soils in comparison
with soil without stones (0% stoniness). This is due to the fact that rock fragments reduce theeffective cross-sectional area through which water flows. Hydraulic conductivities of the matrix
soil fraction in forest stony soils are usually high. Therefore, it can be expected, even in the caseof heavy rains, that surface runoff will rarely occur in the mild temperate climatic zone. This fact
was already confirmed by a study of Holko et al. (2011) for the same catchment.
Table 1. Effective soil hydraulic parameters determined for the Červenec study site.

θr (-)

Rv 0%

Rv 10%

Rv 30%

Rv 50%

0.05

0.045

0.035

0.025

θs (-)

0.495

0.44550.346

0.2475α (-)

0.01809

0.01810.01740.0181n (-)

1.09439

1.09439

1.09491.09439

Ks (cm.h-1)

19.79

17.61

13.26

8.91

129

Figure 1. Modeled infiltration rates and bottom boundary fluxes for soils with different stoninessunder ponded conditions.

Figure 2. Modeled cumulative infiltration amounts for soils with different stoniness.

Figure 3. Cumulative outflow through the bottom boundary of a soil layer 95 cm thick, during
infiltration shown in Figure 2. Outflow rates for soils with different stoniness (Rv) are shownusing color lines.

130

The situation is completely different if infiltration under unsaturated conditions (the rainfall
intensity is lower than the saturated hydraulic conductivity) is modeled (compare Figs. 4 and 5).
As a result, an increase in the penetration depth of the infiltration front (Figure 5), and also in thebottom boundary flux (Figs. 3 and 6), is higher for stony soils compared to the soil withoutstones. Moreover, the penetration depth and bottom outflow are positively correlated with thestone content (Figs. 4 and 5). These phenomena could be explained by reduced water retention
capacity of a stony soil. Since stones present in the soil limit the volume of fine soil matrix, lessinfiltrating water is needed to increase the water content in the matrix of the stony soil and its
related unsaturated hydraulic conductivity. Consequently, a faster movement of pollutants into
deeper soil layers could be expected for soils with high stone content.

Figure 4. Soil water content profiles during ponded infiltration with the initial soil matrix waterpressure head h= -1000 cm and θi = 0.38. a) a homogeneous soil without stones, (Rv = 0.), b) a
stony soil with stoniness of 50% (Rv = 0.5), a total water content, and c) a stony soil withstoniness of 50% (Rv = 0.5), a matrix water content.

Figure 5. Soil water content profiles during rainfall infiltration. Rain intensity was 80 mm/h, rain
duration 3 h, the initial soil matrix water pressure head h= -1000 cm and water content θi = 0.38.
a) a homogeneous soil without stones, (Rv = 0.), b) a stony soil with stoniness of 50% (Rv = 0.5), a
total water content, and c) a stony soil with stoniness of 50% (Rv = 0.5), a matrix water content.

131

Figure 6. Cumulative rain infiltration (full line, rain duration 3 h) into a stony soil and cumulative
outflows (color lines) from the bottom boundary of a soil with different stoniness (Rv).

5. Conclusions
In this paper, the effective saturated hydraulic conductivities reflecting different soil stoninesswere calculated by the HYDRUS-2D numerical model, which was used to simulate the classic
Darcy’s experiment. Furthermore, soil water retention curves for stony soils were estimatedunder an assumption of zero retention capacity of the rock fragments. Obtained effective
hydraulic characteristics were then used to simulate the infiltration process using HYDRUS-1D.
Calculated cumulative infiltration rates during ponded infiltration were lower for stony soils
compared to a soil without stones (0% stoniness). When an infiltration from rainfall wasmodeled (on the assumption that the rainfall intensity was lower than the saturated hydraulicconductivity of a stony soil), a faster penetration of the infiltration front and higher cumulative
bottom fluxes were calculated for soils containing stones. Moisture front penetration depths andrelated bottom fluxes were positively correlated with the stone content.
Acknowledgement
This contribution was partially supported by grant agency of the Slovak Academy of Sciences
VEGA, project No. 2/0032/13 and is the result of the project implementation ITMS
26240120004 Centre of excellence for integrated flood protection of land supported by the
Research & Development Operational Programme funded by the ERDF.
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Package for Simulating the One-Dimensional Movement of Water, Heat, and Multiple Solutes in
Variably-Saturated Media, Version 4.0, Hydrus Series 3, Department of Environmental Sciences,
University of California Riverside, Riverside, CA, USA, pp. 281, 2008a.
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van Genuchten, M. Th., A closed-form equation for predicting the hydraulic conductivity of unsaturated
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Verbist, K., J. Baetens, W. M. Cornelis, D. Gabriels, C. Torres, and G. Soto, Hydraulic conductivity as
influenced by stoniness in degraded drylands of Chile, Soil Sci. Soc. Am. J., 73(2), doi:
10.2136/sssaj2008.0066, 471-484, 2009.
Zhou, B., M. Shao, and H. Shao, Effects of rock fragments on water movement and solute transport in a
Loess Plateau soil, C.R. Geoscience, 341, doi: 10.1016/j.crte.2009.03.009, 462-472, 2009.

133

134

Simulations of the Impact of Different Rainfall Intensities on
Reactive Transport of Metal Contaminants from Mine Tailings
Fatemeh Izadi Tame1, Ali Motalebi Damuchali2, Gholamreza Asadollah Fardi3,and Ahmad Khodadadi4
1

Civil Engineering Department, Kharazmi University, Tehran, Iran, fateme.izadi66@gmail.com, fardi@tmu.ac.ir
2
Environmental Engineering, Kharazmi University, Tehran, Iran; a.m.damuchali@gmail.com
3
Civil Engineering Department of Kharazmi University, Tehran, Iran; fardi@tmu.ac.ir
4
Engineering Faculty, Tarbiat Modares University, Tehran, Iran; akdarban@modares.ac.ir

Abstract
Contamination of aquifers underlying mining areas is one of many environmental problems that can beevaluated using numerical models in order to delineate possible measures minimizing contamination ofgroundwater and neighboring river systems. Interpreting the geochemistry of the system and achieving agood understanding of the processes involved is necessary to mitigate environmental damage. Extensive
internal risk prediction models often fail to predict where catastrophes will arise. In this study, thepotential risk of metal contamination around mining sites is evaluated, and the sensitivity of reactive
transport of metals to different leachate fluxes is estimated. The numerical model PHREEQC was used tosimulate the transport of three metals (Cd, Ni and Mn) from zinc leaching plant tailings in Zanjan, Iran,with variable leachate fluxes during 30 days. The simulations showed that different rainfall rates induce
different metal speciations. Decreasing water contents lowered the soil solution pH and produced new
cation exchange conditions. The simulation results were generally in good agreement with experimental
data. Incompatibility of modeled and experimental data for some scenarios may be attributed to theassumption of linear cation retardation in PHREEQC. Of the three metals considered, modeled Ni
concentrations differed the most from experimental results of the different scenarios. We conclude thatvariations in water fluxes can significantly influence metal mobility and availability, and hence thatspecific risk assessments for past and present hydrological regimes are needed for mining disposal sites.

1. Introduction
Soil and groundwater contamination by heavy metals released from mining activities is aworldwide environmental problem. Heavy metals and other contaminants may be released frommining sites, especially from waste dumps or tailing ponds. Uncontrolled releases of thesepollutants will contaminate soil and groundwater, which in turn poses serious threats to both theenvironment and human health because of toxicity and non-degradability of the metals.
The migration of contaminants from a waste disposal site usually involves one or more of thefollowing processes: (1) advective, dispersive, and diffusive mass transport through the tailings,(2) chemical reactions within the soil solution, (3) interaction between the soil solution and thesoil solids, such as adsorption, ion exchange, and precipitation, and (4) biodegradation.
Heavy metals in tailings exist in different forms, such as exchangeable or adsorbed, with thespecific form having an important effect on their mobility and bioavailability. Heavy metals inavailable forms (i.e., exchangeable or adsorbed to the surface of clays, organic matter, or oxides

135with weak bonding strength) are easily moved and dispersed in an ecosystem. On the other hand,
metals bound with organic ligands or held within a crystal lattice are not easily separated andmoved (Fletcher et al., 1981). Therefore, areas near the mines should be continuously monitored
using observation wells to control and prevent groundwater pollution. Such monitoring is quite
expensive and time consuming. Due to these economic reasons and the complexity ofgeochemical processes affecting metal reactive transport, various mathematical simulation
models have been developed for assessing groundwater vulnerability to contamination and water
resources management. These models have been found to be promising tools to unravel thecomplex interactions between soil physical and biogeochemical processes for all types ofproblems, including the impact of natural processes and anthropogenic activities on soil
evolution (Jacques et al., 2008).
Seuntjens et al. (2002) studied how physical and chemical properties affected field-scale Cd
transport in a heterogeneous soil profile. Using Monte Carlo simulations, they demonstrated thatvariations in field-scale Cd fluxes were dominated by variations in the deposition rate and theparameters of the Freundlich sorption isotherm. Using geochemical analyses and investigationsof samples from mine tailings and water resources adjacent to the Piscinas River in Sardinia,
Italy, Concas et al. (2005) concluded that a decrease in the pH will increase metal dissolution andtransport from mine tailings. Tipping et al. (2006) used the CHUM-AM model to investigate thebehavior of atmospherically-deposited metals (Ni, Cu, Zn, Cd and Pb) in Cumbria, UK, andconcluded that the main processes controlling cationic metals are competitive partitioning to soilorganic matter, chemical interactions in solution, and chemical weathering. Michel et al. (2007)
applied mathematical and empirical models to investigate nickel and cadmium transport in silty
and sandy soils in north Germany and concluded that lower pH level increases metal transport inacidic soils.
In another study, Van der Grift and Griffioen (2008) investigated Cd and Zn leaching from apolluted soil using saturated and unsaturated zone flow and reactive transport models. They
concluded that metal contamination depended on the surface water loadings, the geohydrologic
and geologic structure of the site, soil type and the dominant land use. Hanna et al. (2007) used
PHREEQC to study the transport of zinc and lead in soils and concluded that the model can
predict metal transport in acidic conditions, and that decreasing pH increases metal transport.
Gordon et al. (2009) used geochemical modeling of Ni and Cd transport and found that
decreasing pH levels will cause an increase in Ni and Cd mobility in silt and sandy soils.
Horvath et al. (2009) in another study employed column leaching tests to investigate metaltransport from mine tailings to water resources and showed that the adopted method was suitable
for metal transport analyses.
The Zanjan zinc leaching plant, located 12 km from Zanjan, Iran, processes ore from theaffiliated Anguran mine into zinc sheet metal. Tailings or “cake” of this operation are enriched innickel (Ni) and cadmium (Cd). The objective of our study was to determine how different
rainfall rates affected nickel (Ni), cadmium (Cd), and manganese (Mn) transport from thesetailings, using the PHREEQC geochemical model.

1362. Materials and Methods
2.1. Simulations
This section defines some of the governing equations for the physical and biogeochemical
processes used in the reactive transport code. PHREEQC2 (Parkhurst and Appelo, 1999) wasused to simulate different scenarios with different flow rates for a period of 30 days. PHREEQC
is a geochemical model that can be used for water and soil environments. The code has thecapability to model several one-dimensional transport processes, including diffusion, advection,
advection and dispersion, and advection and dispersion with diffusion into stagnant zones. All ofthese processes can be combined with equilibrium and kinetic chemical reactions. The softwareuses the Advection-Reaction-Dispersion (ARD) equation to simulate transport as follows∂C∂C∂ 2C ∂q=−v+ DL 2 −
∂t
∂x
∂x
∂t

(1)

where C, t, v, x, q, and DL are concentration in water (mol/kgw), time (s), pore water flow
velocity (m/s), distance (m), concentration in the solid phase (expressed as mol/kgw in the pores)
and the hydrodynamic dispersion coefficient (m2/s), respectively. The first term on the right sideof (1) represents advective transport, the second term dispersive transport, and the third term thechange in concentration in the solid phase due to reactions.
The relationship between the hydrodynamic dispersion coefficient, the effective diffusion
coefficient (De) and the dispersivity (λL) is as follows:D=
De + λL v
L(2)

The usual assumption is that v and DL are equal for all solute species, so that C can be the total
dissolved concentration of an element, including all redox species. The transport part of equation(1) is solved with an explicit finite difference scheme that is forward in time, central in space fordispersion, and upwind for advective transport (Parkhurst and Appelo, 1999). The chemicalinteraction term for each element is calculated separately from the transport part for each time
step and is the sum of all equilibrium and non-equilibrium reaction rates. The numericalapproach follows the basic components of the ARD equation in a split-operator scheme(Yanenko, 1971).
The process of metals cation exchange can be modeled effectively with the software for onedimensional transport. However, it is not possible to directly enter the initial flow rate into thesoftware. Hence, the leached solution from the tailing columns corresponds to the flow rate andneeds to be described in the software for each transport procedure. This approach substantiallyprolongs the run times.
2.2. Simulation Efficiency
The modeling efficiency (EF), a measure of correspondence between measured and modeled
results, is calculated using the equation (Loague and Green, 1990):

137∑ (x − x ) −∑ ( y − x )EF =∑ (x − x )
2

n

n

i
n
i 1
=i 1 =
n
2
i =1

i

i

2

(3)

i

n

where xi, yi, xn, and n are measured values, modeled predictions, the arithmetic mean ofmeasured values, and the number of measured and modeled values, respectively. When modeledpredictions perfectly match the measured ones, EF is equal to 1. A negative value indicates thatthe modeled predictions describe the data less well than the mean of the observations.
2.3. Ni-Cd Cake Compounds
The deposited waste material was studied using the X-ray fluorescence test (XRF). Its physicalproperties were reported by Hashem Zadeh (2003) and Sedaghat (2007). Elemental analysis
indicated that the waste material contains high concentrations of metals: 40.4% Zn, 11.2% Cd,
3.3% Ni, 1.4% Cu, and 0.8% Pb. Table 1 shows the types and quantities of elements in a 100 g
Ni-Cd cake sample. A 1 kg sample was sieved by Sedaghat (2007) using 18, 35, 60, 80, 100,
120, 140, 170, 200, 230, and 270 mesh sieves.
Table 1. Quantities of elements in 100 g Ni-Cd Cake.
Compounds
Na2O
MgO
Al2O3
SiO2
SO3
CaO
MnO

Percentage
10.94
0.57
0.19
0.36
8.40
0.31
0.17

Elements
Cd
Ni
Cu
Zn
Pb
LOI

Percentage
11.1
3.34
1.40
40.4
0.80
22.1

Sedaghat (2007) worked experimentally on the same site and conducted 30-day leaching tests on
1,441 g of the Ni-Cd cake in each of the three 6-cm internal diameter columns. The columns
were 50 cm long, with the tailings in each column occupying 40 cm. The effluent of each column
was analyzed after 1, 3, 7, 13, 20, and 30 days. Parameters and their different levels used in thesimulation scenarios are summarized in Table 2. The experimental data of Sedaghat (2007), andthe same parameters and boundary conditions, were used also in this study.
Table 2. Simulation parameters.
Compounds
Flow (cc/min)
Time (day)Level 10.5
1138

Level 2
1
13

Level 3230

2.4. Using the PHREEQC Model
Input into the PHREEQC code is identified using special Keywords. Using the SOLUTION
keyword one can define types and concentrations of elements and their composition in thecolumns. The exchange reactions and one-dimensional transport parameters can be simulatedusing the EXCHANGE and TRANSPORT keywords, respectively. Equilibrium and exchange
constants for chemical species of the tailing columns were taken from the MINTEQ database(Allison et al., 1990).
3. Results and Discussion
As mentioned earlier, understanding and modeling multicomponent reactive transport at the field
scale is necessary for the design of remediation strategies in groundwater pollution problems andfor risk assessment evaluations. While numerical and analytical methods are generally available
to address multicomponent reactive transport problems at the local scale, it is not clear whether
these methods can be extended to the field scale. The simulation results of this study will be
evaluated and compared against the experimental results.
Three ﬂow rates (low, moderate, and high) were selected to simulate natural processes. While a
ﬂow rate of 0.5 cc/min (cc stands for cubic centimeters), which produces laminar ﬂow , was thelowest rate that could be reliably established in the laboratory, the 2 cc/min rate was the highest
flow rate since ponding occurred at higher flow rates (Sedaghat, 2007). Also, the MeteorologicalOrganization of the Islamic republic of Iran reported a maximum daily rainfall rate of 55
mm/day for Zanjan. The number of time steps was defined for each flow rate in PHREEQC.
Cadmium leaching concentrations were found to decrease with increasing flow rates. Cadmium
concentrations declined with time during the 30-day period. Leaching concentrations weredecreasing dramatically during the first 7 days and then only gradually as illustrated in Figure 1.

Figure 1. Simulated and measured leaching cadmium concentrations for various flow rates.

139

Figure 2 compares the modeled and measured nickel concentrations. Leached nickel
concentrations also decreased with increasing flow rates. Similarly as for cadmium, the nickel
concentrations dropped quickly during the first 7 days and then more gradually at later times.

Figure 2. Simulated and measured leaching nickel concentrations for various flow rates.

The removal of manganese from tailing columns is presented in Figure 3. The behavior ofmanganese for various flow rates was similar to that of the other heavy metals. Higher inflow in
general produced lower manganese leaching concentrations. The leached Mn concentrations
decreased over time for all flow rate scenarios. Simulation efficiencies for the various flow ratescenarios are presented in Table 3.

Figure 3. Simulated and measured leaching manganese concentrations for various flow rates.

140

Table 3. Simulation efficiencies for the different flow rate scenarios.
Flow rate (cc/min)Cadmium
NickelManganese

0.5
0.22
0.2
0.74

1
0.61
0.3
0.44

2
0.21
0.62
0.7

Michel et al. (2007) investigated the removal of Ni and Cd from acidic sandy and silty soils
using empirical and mathematical modeling. The simulation efficiency in their study was
between 0.35 and 0.85 for different scenarios, while the effects of chemical and other parameters
were not considered. In a study of the effect of increasing pore water flow on zinc and leadtransport using PHREEQC, Hanna et al. (2007) observed poor correspondence between
predicted and measured results. They concluded that the differences were due to the inability ofthe software to consider the strong metal-binding capacity of the soil.
In our study we found good agreement between model predictions and experimental results formost scenarios. However, the ratio of the leached volume of water to the pore volume of thetailing columns was high for all scenarios, which may explain observed differences between
simulated results and experimental data. Several reasons may have contributed to the poorcorrespondence between measured and simulated concentrations of some of the scenarios. One isthe assumption of linear cation retardation in PHREEQC. Retardation reflects the activity of acation species in an exchange reaction, which in PHREEQC is defined as

R=

1 + CEC
C(4)

where R is the retardation, CEC is the cation exchange capacity expressed in mol/kg water) andC is the species concentration (mol/kg water). In some scenarios, for example at lower pH,
chemical reactions could compensate for the effects of linear retardation and improve thecorrespondence between modeled and measured data.
The differences between simulated and experimental results can be explained in part also by
simplification of the problem to a one-dimensional domain, and ignoring possible heterogeneities
in the porous medium. Large scale transport in spatially heterogeneous field systems is usuallydifferent from transport observed in homogeneous media, and more often of a non‐Fickian
nature. Realistic hydro-geological applications must directly or indirectly account for thisheterogeneity. Under certain conditions, the asymptotic large scale transport of conservative
species can be described by the advection‐dispersion equation (ADE) with upscaled transportparameters (Dagan, 1989; Gelhar, 1993). The asymptotic limit is typically given by time, after
which the species distribution is spread out over a volume whose dimensions are much larger
than the largest heterogeneity scale. At pre-asymptotic times, however, which are relevant formost hydrogeological problems, data (e.g., Adams and Gelhar, 1992) often display what is
known as anomalous (non‐Fickian) or nonergodic (Kitanidis, 1998) behavior. This implies thatconcentrations then are not easily simulated using an ADE, even when allowing for upscaled
parameters (Carrera, 1993). Different nonlocal methods have been developed to describe theeffective transport of conservative species at intermediate distances, such as continuous time141

random walks (CTRW) (Berkowitz and Scher, 1998; Berkowitz et al., 2006), fractional
advection‐dispersion equations (fADE) (Benson et al., 2000), multi-rate mass transfer (MRMT)
formulations (Haggerty and Gorelick, 1995; Silva et al., 2009), and memory functions (Carrera
et al., 1998). Regardless of using nonlocal methods, the same problem as considered in this study
could be solved using other similar software, such as the HYDRUS family of programs or the
coupled reactive transport code HP1.
4. Conclusions
The transport of heavy metals was evaluated in our study using PHREEQC for various flow ratescenarios. The modeled results matched experimental data collected on laboratory columns fairly
well, which suggests that geochemical modeling may be an alternative and economic method toinvestigate metal transport from mine tailings for various environmental situations. In all cases,
lower flow rates produced higher concentrations of metals leached from the Zanjan tailings. Of
the three metals considered, the modeled Ni concentrations were least similar to collected datafor different leaching scenarios.
Acknowledgment
The first author would like to express her appreciation to Dr. Jirka Šimůnek, Dr. Diederik
Jacques, and Miss Elnaz Siami for their kind help and guidance.
References

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E., 57(5), 5858–5869, 1998.
Berkowitz, B., A. Cortis, M. Dentz, and H. Scher, Modeling non-Fickian transport in geologicalformations as a continuous time random walk, Rev. Geophys., 44, RG2003, 2006.
Carrera, J., An overview of uncertainties in modelling ground water solute transport, J. Contam. Hydrol.,13(1-4), 23–48, 1993.
Carrera, J., X. Sánchez-Vila, I. Benet, A. Medina, G. Galarza, and J. Guimera, On matrix diffusion:
Formulations, solution methods and qualitative effects, Hydrogeol. J., 6(1), 178–190, 1998.
Concas, A., C. Ardou, A. Cristini, P. Zuddas, and G. Cao, Mobility of heavy metals from tailings tostream waters in a mining activity contaminated site, Chemosphere, 63, 244-253, 2005.
Dagan, G., Flow and Transport in Porous Formations, Springer, Berlin, 1989.
Fletcher, W. K., Handbook of Exploration Geochemistry 1, Elsevier Science Publishers B.V, Amsterdam,
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Gelhar, L. W., Stochastic Subsurface Hydrology, Prentice Hall Publication, Old Tappan, New York,
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Gordon, G. W., T. W. Lyons, G. L. Arnold, J. Roe, B. B. Sageman, and A. D. Anbar, When do blackshales tell molybdenum isotope tales, Geology, 37(6), 535–538, 2009.
Hanna, K., L. Lassabatere, and B. Bachet, Zinc and Lead transfer in a contaminated road soil:
experimental study and modeling, J. Hazard. Materials, 161, 1499-1505, 2007.
Haggerty, R., and S. M. Gorelick, Multiple-rate mass transfer for modeling diffusion and surface
reactions in media with pore scale hetero geneity, Water Resour. Res., 31(10), 2383–2400, 1995.
Hashemzadeh, M., Study of the machinery methods for quantity and quality analysis of mineral, MSc
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and G. Damian, Risk assessment of heavy metals in abandoned mine lands as significant
contamination problem in Romania, Geophys. Res. Abstracts, 11, p. 8916, EGU General Assembly,
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Islamic Republic of Iran Meteorological Organization, Climate Statics. http://www.irimo.ir, accessed
Nov. 20 2012.
Jacques, D., J. Šimůnek, D. Mallants, and M. Th. van Genuchten, Modelling coupled water flow, solutetransport and geochemical reactions affecting heavy metal migration in a podzol soil, Geoderma, 145(3-4), 449-461, 2008.
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Michel, K., M. Roose, and B. Ludwig, Comparison of different approaches for modelling heavy metaltransport in acidic soils, Geoderma, 140, 207-214, 2007.
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143

144

Investigating the Effect of Acidic Rain on Reactive Transport ofMetal Contaminants in Groundwater
Fatemeh Izadi Tame1, Gholamreza Asadollah Fardi2, Ahmad Khodadadi3, Mohammad Faridzad4
1

Civil Engineering Department, Kharazmi University, Tehran, Iran; fateme.izadi66@gmail.com,
2
Civil Engineering Department of Kharazmi University, Tehran, Iran; fardi@tmu.ac.ir
3
Engineering Faculty, Tarbiat Modares University, Tehran, Iran; akdarban@modares.ac.ir
4
School of Civil Engineering, Sharif University of Technology, Tehran, Iran; m.farizdad@yahoo.com

Abstract
Multicomponent reactive transport in porous media is a complex process owing to a combination ofvariability in the processes involved and the inherent heterogeneity of nature. In recent years, various
multicomponent reactive transport models have been developed to study the mobility of potentially toxic
heavy metals in the subsurface. Heavy metals and other contaminants may be released from mining sites,
especially from waste dumps and tailing ponds. Soil and groundwater contamination due to mining
activities is an important environmental problem worldwide. Because of their abundance and potential
toxicity, Pb2+, Zn2+, and Cd2+ figure prominently among inorganic contaminants of greatest concern inmine tailings. This study investigated the effect of pH on the transport of these metals through lead andzinc leaching plant tailings in Lakan, Iran. The HP1 model and PHREEQC database were used tosimulate the transport of the metals through a saturated soil at the laboratory column scale during a 15day time period. The simulations assumed local equilibrium. As expected, a lower pH increased metaltransport. However, although the simulation results generally agreed well with results of the column
study, they indicated that physical and chemical parameters must be carefully determined for use in thesimulations. Improvements in the results are expected when using multi-dimensional models and a kinetic
modeling approach for the reactions involved.

1. Introduction
Despite significant progress in science and technology, environmental problems are increasing at
the national, regional, and international levels. Correlations between industrial activities andenvironmental contamination make it difficult to expect substantial industrial development
without some impact on the environment. The production of inorganic wastes in mining
operations has always been an important issue and a threat to the environment, especially thesubsurface. These wastes often contain high levels of heavy metals, which constitute a major
threat to human populations, aquatic species, plants, ecosystems, and groundwater quality ingeneral because of their biological non-degradability and stability in the environment. Largescale mining can especially adversely affect the environment. Iran, as a developing country, stillneeds to develop much of its mining activities. Unfortunately, a lack of necessary standards forproper processing and waste burial make environmental pollution more probable in Iran.
Leaching of heavy metals from surface soils to deeper layers, and the risk of groundwaterpollution, depend on the retention, mobilization, and transport of heavy metals in soils. Specificadsorption, ion exchange, and precipitation of various solid phases are the main processes
responsible for the retention of heavy metals. Previous studies indicate that the pH is one of themost important factors affecting the transport and sorption of heavy metals (Chotpantarat et al.,145

2011). Changes in the chemical composition or pH of the soil solution may impact the sorptionof elements on organic matter or iron oxides.
Decision makers need predictions of the fate of heavy metals in soils to design management
strategies that minimize adverse environmental impacts. Accurate simulations of pollutant
transport require a coupled reactive transport code that integrates the physical processes of waterflow and advective-dispersive solute transport with a range of biogeochemical processes. Manymodels have been developed to simulate and predict the fate and transport of pollutants in porous
media (e.g., Šimůnek, 2007; Šimůnek et al., 2008b). The most commonly-used models are basedon advection-dispersion equations and consider such mechanisms as advection, dispersion,
sorption, and degradation.
Wu et al. (1998) showed that at lower pH levels, Cd and Pb precipitation will cause a sharp
decrease in their external concentrations. Pang et al. (2002) showed that the breakthrough curves(BTCs) of Cd, Zn, and Pb in gravel columns with pore water velocities ranging from 3 to 60
m/day displayed long tailing, suggesting that non-equilibrium sorption conditions occurred in thegravel columns due to high pore water velocities. Using geochemical analyses and investigationsof samples from mine tailings and water resources adjacent to the Piscinas River in Sardinia,
Italy, Concas et al. (2005) concluded that a decrease in the pH level increased metal dissolution
and transport from mine tailings. Pot et al. (2005) used different physical and chemical
equilibrium and non-equilibrium transport models to simulate the impact of various rainfall
intensities on herbicide transport. Their study showed that physical/chemical non-equilibrium
conditions were dominant. Michel et al. (2007) used mathematical and empirical models toinvestigate nickel and cadmium transport in silty and sandy soils and concluded that a decreasein the pH will increase the transport of heavy metals in acidic soils. Using HP1 model, Jacques etal. (2008) further showed that reducing the inflow intensity will cause a decrease in the pH level,
thereby promoting monovalent cations to sorb on the cation exchange complex, and bivalentcations to desorb into the soil solution. Simulating the effect of pH on Pb, Mn, Zn, and Ni
transport using HYDRUS-1D, Chotpantarat et al. (2011) found that increasing the pH of the
inflow solution will increase the retardation of heavy metals. They also showed that the use of a
two-site model (TSM) for sorption produced a better match with measured heavy metal BTCs
than linear or nonlinear Langmuir type equilibrium models.
The main objective of this research was to investigate the effect of aqueous pH conditions on thesorption and transport of three heavy metal ions, Cd2+, Pb2+, and Zn2+, using the HP1 numericalmodel, to evaluate the model’s utility in simulating the transport of heavy metals in soil columns,
and to investigate the sorption behavior of heavy metals in soil columns.
2. Materials and Methods
2.1. General Features of Study Area
The Lakan lead and zinc processing plant is located 46 km Southwest of Arak City in theMarkazi Province, Iran. The geographical location of this site is 33°42’5”N latitude and49°43’26”E longitude. The Lakan plant is located in a temperate mountainous zone with hot

146summers and cold winters. Annual variations in temperatures are very high, ranging from -20 ºC
in the winter to +35 ºC in the summer.
2.2. Soil Physical and Chemical Properties
The deposited waste material had been studied previously by Marzban (2008) using X-ray
fluorescence (XRF) tests. Table 1 shows the types and quantities of elements in a 100 g sample.
Table 1. Quantities of elements in a 100 g sample.
Compounds
Na2O
MgO
AL2O3
SiO2
SO3
K2O
CaO
BaO

Percentage
0.5
0.8
3.5
66.6
4.5
0.7
9.5
0.4

Compound/Element
MnO
Ni
Zn
Pb
Cd
P2O5
Fe2O3
LOI

Percentage
0.3
0.0146
1.15
1.5
0.005
0.9
2.9
6.73

Using tailings from the same site, Marzban (2008) conducted 15-day leaching tests on 180 g
samples in three 2.7-cm internal diameter columns in which the tailings occupied heights of 21
cm. The effluent from each column was analyzed after 3, 7, 10, and 15 days. Physical propertiesof the tailing dam soil as reported by Marzban (2008) are presented in Table 2.
Table 2. Physical properties of tailing dam soil.
Soil Property
Bulk Volume
WeightPore Volume
Specific Volume
Bulk density
Specific density
Solid fraction
Porosity

Unit
(mL)
(g)
(mL)
(mL)
(g/mL)(g/mL)-

Value
150
221.77
40
110
1.48
2.02
0.73
0.27

2.3. Transport ModelAll calculations in this paper were carried out using version 2.2 of HP1 (Jacques et al., 2010).
The HP1 reactive transport simulator, obtained by weak coupling of HYDRUS-1D and
PHREEQC-2, was developed and designed to address multicomponent geochemical transport
processes in the vadose zone. The software integrates a broad range of physical andbiogeochemical processes, as described in the original manuals of HYDRUS-1D (Šimůnek et al.,2008ab), PHREEQC-2 (Parkhurst and Appelo, 1999), and HP1 (Jacques et al., 2010). HYDRUS1D was originally designed mostly for simulating water flow, solute transport, and heat transport147

in soils from the soil column scale to the field scale. The program can numerically solve theRichards equation for saturated-unsaturated water flow and the advection-dispersion equation forsolute and heat transport. In this software, the solute transport module also considers equilibriumand non-equilibrium advection-dispersion in the liquid phase, and nonlinear equilibrium physicaland chemical sorption. Important to note is that both the HYDRUS-1D and HP1 models accountfor soil heterogeneity at the macroscopic scale by using scaling factors (Vogel et al., 1991), andat the microscopic scale by using dual-porosity or mobile/immobile type flow models (Šimůnek
et al., 2003). HP1 implements a weak coupling method in which the governing equations forwater flow, heat transport, and solute transport are solved sequentially. The multicomponent
reactive transport equations are solved using a non-iterative sequential approach, meaning thatthe physical part is solved first without any chemical interactions, while the chemical reactions
that are uncoupled in space and coupled over the components are solved subsequently (Jacqueset al., 2008). A flow chart of the operator-splitting approach used in HP1 was given in Jacques etal. (2006). Although operator-splitting errors may occur with this approach, Jacques et al., (2006,2008) showed that very accurate results can be obtained by carefully selecting the spatial andtemporal discretizations.
2.3.1. Soil Hydraulic Properties
Six analytical models are available in HP1 to describe the soil hydraulic properties, including thefunction of Brooks and Corey (1964), van Genuchten (1980), and Vogel and Cislerova (1988). In
this study the van Genuchten-Mualem model (van Genuchten, 1980) was used to describe thewater retention and hydraulic conductivity (K(h)) functions:θs - θr θr +[1+ |α h|n]mθ ( h) = 

θs


h<0
h≥0
2

K ( h ) = K s Sel [1 - (1 - Se1 / m ) m ]S e ( h) =1
[1+ |α h|n]m

(1)

(2)
(3)

where θ(h) is the soil water content [-] as a function of the pressure head, h [L], θs is thesaturated water content [-], θr is the residual water content [-], Ks is the saturated hydraulicconductivity [LT-1], Se is the effective water content [-], α, m, and n are empirical parameters of
the retention curve (m=1-1/n for n>1), and K(h) is the unsaturated hydraulic conductivity [LT-1].
The pore connectivity/tortuosity factor (l) used in the simulations was set to 0.5 for all simulation
scenarios. This value was recommended by Mualem (1976) and is a default value used for soils
in the HYDRUS software.
2.3.2. Water Flow Equation
A combination of the mass balance equation with the Darcy-Buckingham law results in the
Richards equation describing water flow in variably-saturated porous media. The onedimensional form of the Richards equation can be written as:148∂θ (h) ∂ 
 ∂h

=
K (h)  + cos α   − S (h)

∂t
∂z 
 ∂z


(4)

where h is the water pressure head [L], θ is the volumetric water content [-], t is time [T], z is thespatial coordinate [L] (positive upward), S is the sink term [L3L-3T-1], α is the angle between theflow direction and the vertical axis, and K is the unsaturated hydraulic conductivity [LT-1].
2.3.3. Solute Transport Equation
Solute transport in porous media can be described with the one-dimensional convectivedispersive equation (CDE):∂θ C ∂ρb S ∂ ∂C  ∂qwC
+=
θ D
−
∂t
∂t
∂z 
∂z 
∂z

(5)

in which C is the solute concentration in solution [ML-3], S is the sorbed solute concentration[MM-1], ρb is the soil bulk density, qw is the volumetric water flux [LT-1], and D is the effective
dispersion coefficient [L2T-1]. The effective dispersion is given by Bear (1972):=Dθ λL qw + θτ D0(6)

where λL is the longitudinal dispersivity [L], D0 is the aqueous ionic or molecular diffusion
coefficient of a solute in water [L2T-1], and τ is the tortuosity factor given by (Milington and
Quirk, 1961):

τ=

θ 7/3
θ s2

(7)

By manipulating Equation (5), the modified convective-dispersive equation is obtained asfollows:
∂C
∂ 2C
∂C
(8)
=
R
D 2 −v∂t∂z∂zwhere R is the retardation factor given by the following equation:R=

1 + ρb K dθ(9)in which Kd is the partitioning coefficient of solute [L3M-1] and v the average pore water velocity[LT-1].
2.3.4. Numerical Simulations
The water flow and solute transport equations were solved numerically using the HP1 code
(Jacques et al., 2010). The upper and lower boundary conditions for water flow were assumed to149

be a constant pressure head, and for solute transport to be a concentration flux BC (third type)and a zero concentration gradient (free drainage), respectively. In the HP1 model, the Galerkinfinite element method with a space weighting scheme was selected, while the time derivatives
for the solute transport solution were approximated using a Crank-Nicholson finite difference
scheme. All simulations were conducted over a period of 15 days. The column height was 21 cm
and the inflow rate 1 cc/min (cc stands for cubic centimeters), while acid concentrations were 0,0.12, and 0.29 g/L. Selected parameter values (Levels 1, 2, and 3) used in the simulation
scenarios are summarized in Table 3.
Table 3. Simulation parameters and levels.
Compounds
pH
Time (day)Level 1
7
3

Level 2
6
10

Level 35
15

2.3.5. Modeling Efficiency
The modeling efficiency (EF) was calculated for the measured and modeled data using (Loague
and Green, 1990)∑ (x − x ) −∑ ( y − x )EF =∑ (x − x )
2

n

n

i
n
i 1
=i 1 =
n
2
i =1

i

i

i

2

(10)

n

where xi, yi, xn and n are measured values, model predictions, arithmetic means of the measured
values, and the number of measured and modeled values, respectively. When model predictions
perfectly match the measured data, EF is equal to 1. A negative value indicates that thepredictions describe the data less than the mean of the observations.
3. Results and Discussion
3B

The effects of pH on the transport of Cd, Zn, and Pb are shown in Figure 1. Taking into accountthe fact that the pH of rain in the Arak city is 5.5, three input solutions with pH values of 5, 6,
and 7 were selected for the study, similarly as in the experiments carried out by Marzban (2008)
and Darban et al. (2012). Maximum removal of Cd, Zn, and Pb was achieved after three days
using the input solution with pH of 5. The removal concentrations of these three metals were 0.4,
16.38, and 1.21 mg/L, respectively. The lower removal concentrations of Cd and Pb, comparedto Zn, is likely due to precipitation of Cd and Pb species, especially at lower pH levels. The
higher removal of metals with decreasing pH is reasonable, since higher pH indicates lower
quantities of H+ ions and an increase in the retardation factor of heavy metals as shown by
Chotpantarat et al. (2011), among many others. The removal concentrations of the three metals
after 15 days are shown in Table 4.

150

0.50
0.40
0.30
0.20
0.10

Concentration (Mg/L)

Concentration (Mg/L)

Concentration (Mg/L)

Zn Simulation

Cd Simulation

20.00
15.00
10.00
5.00

0.00

0.00
0

5

10

15

0

20

Time (day)

5

10

15

20

Pb Simulation
1.40
1.20
1.00
0.80
0.60
0.40
0.20
0.00

pH=5
pH=6
pH=7
0

10

20

Time (day)Time (day)Figure 1. Effect of pH on Cd, Zn, and Pb transport and removal.
Table 4. Removal concentrations of heavy metals in mg/L after 15 days.
Element/pH
Cd
Zn
Pb

pH=5
0.04
2.62
0.24

pH=6
0.02
2.44
0.07

Allowable limits for concentrations of zinc, lead, and cadmium in groundwater according to the
U.S. Environmental Protection Agency (US EPA, 1993) are 5, 0.005, and 0.01 ppm,
respectively. The results in Table 4 indicate that the concentrations of Cd and Pb in solution
exceeded the EPA limits. They also exceeded the Iranian standard for drinking water (Standard
No. 1053). Similar findings were reported by Darban et al. (2012). Heavy metal mobility
followed the order Zn2+ > Pb2+ > Cd2+ . The same results for similar conditions were reported
by Wu et al. (1998), except for Pb. This difference can be attributed to the lower simulation
efficiency for Pb in our study. As reported also by Wu et al. (1998), Darban et al. (2012), andNguyen at al. (2010), the removal concentrations were lower for neutral solutions, as comparedto more acidic solutions, because of precipitation of metals under neutral aquatic conditions.
Experimental and simulated concentrations for Cd, Zn, and Pb after 7 days are presented inTable 5, while the simulation efficiencies for different pH levels are listed in Table 6. Comparing
the simulated and the experimental results, the highest efficiency was achieved for Cd removal
concentrations, followed by Zn and Pb.
Table 5. Experimental and simulated removal concentrations of heavy metals (in mg/L).
Element
Cd
Zn
Pb

pH=6 (Experiment)
0.041
4.47
0.039

pH=6 (Simulation)
0.054
5.24
0.15

pH=5 (Experiment)
0.053
5.46
0.078

pH=5 (Simulation)
0.08
5.32
0.052

Table 6. Modeling efficiencies for the heavy metals removal concentrations at two pH values.
Element/pH
Cd
Zn
Pb

pH=6
0.80
0.77
0.79

pH=5
0.69
0.5
0.29

151

Average
0.75
0.63
0.54

Brown et al. (1998) attributed the differences in their observed and simulated results to the local
equilibrium assumption. They indicated that due to the slow reaction kinetics and limited
interactions of solid phase surfaces with solutes, the dominant process could not be effectively
described using the assumption of local equilibrium in their simulation. Pot et al. (2005)
concluded that the physical/chemical non-equilibrium models were also more effective insimulating herbicide transport. Michel et al. (2007) investigated the removal of Ni and Cd from
acidic sandy and silty soils using empirical and mathematical modeling. They found thesimulation efficiencies between 0.35 and 0.85 for different scenarios. The effects of different
chemicals or other transport and reaction parameters were not considered.
Jacques et al. (2008) found that decreasing the pH level will increase bivalent cations removal
concentrations. A comparison of our results with results reported by Motalebi et al. (2012) showsthat the PHREEQC and HP1 models had approximately the same efficiency for Cd reactive
transport, perhaps because of the saturated flow conditions in both studies.
Relatively good agreement between model predictions and experimental results was obtained inour study. Some small differences between the experimental and simulated results were observed
only during the first few days of the simulations. The presence of dissolved organic matter(DOM) may have influenced the mobility and retention of heavy metals in soils. The formationof complexes with DOM can be especially important for Pb (Weng et al., 2002; Tipping et al.,2003). The lower simulated removal concentrations of metals may be attributed to the formationof complexes during the first few days of simulation.
Another possible reason for the differences may be the fact that the soil hydraulic conductivity
was assumed to be constant during the simulations. In reality, the hydraulic conductivity changes
with changes in pH, which should affect the heavy metal precipitation rate. In general,disagreement between the model and the data (lower modeling efficiencies) of some of the
scenarios can be attributed also to uncertainty in the value of some parameters, simplification of
the transport process to a one dimension, ignoring the effects of macropores and other transport
processes in natural soil (such as bioturbation), and/or local physical or chemical nonequilibrium processes.
4. Conclusions
4B

In this study, the effects of pH on reactive transport of Cd, Zn, and Pb from Lakan mine tailings
were investigated using the HP1 model. Metal removal concentrations were predicted using the
HP1 model. Simulation results were compared with previously published experimental results
and the results of other researchers. Overall, the HP1 model successfully simulated water flow
and solute transport in the columns, considering the limitations in the experimental data.
Using different pH levels for the inflow solution, the following conclusions were reached:• The retardation of heavy metals followed the order Zn2+>Pb2+>Cd2+• Decreasing pH values produced higher metal removal concentrations• The removal concentrations of Cd and Pb exceeded the allowable EPA and Iranian’s
1053 standard thresholds• The simulations for Cd had the highest modeling efficiency, followed by Zn and Pb

152

•

•

•

Predicted early removal concentrations did not successfully match the observed data,
likely due to the presence of sharp solute fronts, failure to establish local equilibrium,
insufficient time for complete soil solid phase and soil solution reactions, or temporalvariations in the physical properties. Some of the differences could be attributed also to
the formation of complexes at the beginning of simulations.
Differences between modeling and experimental results for some scenarios could also be
attributed to uncertainty in the values of some parameters, simplification of the transport
process to 1D, ignoring the effects of macropores and other transport mechanisms
occurring in soils (such as bioturbation), local physical/chemical non-equilibrium, or
uncertainty in the dominant chemical processes and their parameters.
PHREEQC and HP1 models had approximately the same modeling efficiency for the Cd
reactive transport simulations.

More research is needed to explore the various physico-chemical and biological processes that
control the potential solubility of toxic metals from mine tailings. The use of two- and threedimensional models, as well as kinetic modeling, is recommended to more accurately simulate
reactive transport in actual field conditions.
Acknowledgments
The authors give heartfelt thanks to Dr. Jirka Šimůnek for his kind help and guidance during thetime of this research.
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154

Comparison of Two Numerical Modeling Codes for Hydraulic andTransport Calculations in the Near Field
Jan Kalin1, Borut Petkovšek1, Philippe Montarnal2, Alain Genty2, Estelle Deville2, Jure Krivic3
1

Slovenian National Building and Civil Engineering Institute, Ljubljana, Slovenia, jan.kalin@zag.si,
borut.petkovsek@zag.si
2
CEA/Saclay, DM2S, Gif-sur-Yvette, France, philippe.montarnal@cea.fr, alain.genty@cea.fr, estelle.deville@cea.fr
3Geolgical Survey of Slovenia, Ljubljana, Slovenia, jure.krivic@geo-zs.si

Abstract
In past years, the Slovenian PA/SA team has performed many generic PA/SA studies for the future
Slovenian LILW repository, most recently a Special Safety Analysis (SSA) for the Krško site. The
modeling approach taken was to split the problem into three parts: near-field (detailed model of therepository), far-field (i.e., geosphere) and biosphere. In the SSA, the code used to perform near-fieldcalculations was HYDRUS-2D. Recently, the team has begun to cooperate with CEA/Saclay and, as aresult of this cooperation, began investigations into using the Alliances numerical platform for near-fieldcalculations in order to compare the overall approach and calculated results. This article presents thecomparison between these two codes for a silo-type repository that was considered in the SSA. We will
present the physical layout and characteristics of the repository and develop and implement a hydraulicand transport model of the repository in Alliances. Some analysis of the sensitivity to mesh fineness andto a simulation timestep has been performed and will also be presented. The compared quantity will be
the output flux of radionuclides on the boundary of the model. We will compare the results and commenton differences/similarities.

1. Introduction
In the previous years the Slovenian Performance Analysis/Safety Assessment (PA/SA) team has
performed many studies for the future low and intermediate level waste repository. The mostrecent one was a Special Safety Analysis (SSA) (Petkovšek et al., 2006) for three proposedpreliminary designs, including a silo-type subsurface repository.
In the SSA, the code used to perform near-field calculations was HYDRUS-2D (HYDRUS,
2013). However, the team investigated the possibility of using Alliances (Montarnal et al., 2006)- a numerical platform co-developed by CEA, ANDRA and EDF for the numerical simulation of
nuclear waste disposal - to perform near-field transport and other calculations. In the decision
process one of the tasks was to repeat the near-field calculations for the silo-type repository with
Alliances and compare results with those obtained with HYDRUS.
2. System Description
The silo-type subsurface repository is buried in a silty soil. It is a cylindrical concrete structurewith a 12.8 m inner radius, 0.9 m thick walls and an inner height of 33 m after closure. The spaceinside the repository is filled with layers of 70 waste-containing concrete blocks with external155

dimensions 2.45m × 2.45m × 3.2m. Any remaining space between the blocks and silo walls isfilled with drainage gravel. The whole of the repository lies underneath the water table so thehydraulic conditions in the soil and in the repository are saturated. There is a general horizontal
hydraulic gradient of 0.00118 in the aquifer.

Figure 1. Horizontal section through repository.

Since the hydraulic flow is driven by an external horizontal gradient and the repository iscompletely below the water table, the end effects of top and bottom of the silo can be neglected
and the model simplifies to horizontal flow in 2D. The red rectangle in figure 1 marks theboundary of the 40 m × 20 m modeled domain. The other three red lines mark the boundaries
between different regions of the repository; from the center outwards: the boundary between
waste containing blocks and drainage gravel, the boundary between drainage gravel and a silowall, and the boundary between a silo wall and silt. The direction of the gradient was chosen sothat the water flows from left to right.
3. Hydraulic Calculations
The hydraulic conditions are saturated, so the only parameters needed are the saturated hydraulicconductivities of materials, listed in Table 1.
Barrier degradation was simulated by artificially changing the hydraulic conductivities ofmaterials at specified times. Up to 10,000 years, there is no degradation. It is assumed thatbetween 10,000 and 100,000 years, the silo wall degrades. This is simulated by increasing thehydraulic conductivity of the silo wall to that of the silt. After 100,000 years, the containers alsodegrade so that their hydraulic conductivity increases to that of the silt.

156

Table 1. Saturated hydraulic conductivities of materials.
Material
Silt
Concrete (silo and containers)
Drainage GravelKs [m/s]
10-7
10-10
10-3

Figure 2. Darcy velocity field in m/s, no degradation, Alliances result.

Figure 2 shows the Darcy velocity field in the un-degraded state. The velocity field looks right,
but when the Darcy velocities in the middle of the repository were compared, there were large
discrepancies between the Alliances and HYDRUS results, as can be seen in Table 2.
Table 2. Darcy velocities (in m/s) in the middle of the repository.
Degradation
0
1
2

Alliances
4.96×10-18
6.32×10-16
6.31×10-13

HYDRUS
1.74×10-13
5.44×10-13
1.19×10-10

It turned out that the calculations for the SSA were simplified. In the attempts to calculate thehydraulic field and transport with HYDRUS, the team ran into problems. The difference between
hydraulic conductivities of drainage gravel and concrete is 7 orders of magnitude. This caused
numerical instabilities on the boundaries between these two materials, especially in the bottom
right corner region of the repository. The team worked around this by assigning the hydraulicconductivity of silt to the drainage gravel, effectively substituting the drainage gravel with silt
and reducing the difference to 3 orders of magnitude.

157

The hydraulic field was recalculated with the two hydraulic conductivities that were used for the
SSA. As shown in Table 3, the comparison between Darcy velocities in the middle of therepository shows a much better agreement between Alliances and HYDRUS.
Table 3. Darcy velocities (in m/s) in the middle of the repository, 2 hydraulic conductivities.
Degradation
0
1
2

Alliances
3.95×10-14
1.94×10-13
1.18×10-10

HYDRUS
1.74×10-13
5.44×10-13
1.19×10-10

Ratio
4.4
2.8
1.0

4. Transport Calculations
The processes considered were advection, diffusion, dispersion, sorption and radioactive decay(including chains). The total radionuclide flux through the downstream (right) boundary of themodeled domain was measured, and the height and position of the flux peak compared to theresults obtained with HYDRUS.
Of all the radionuclides in the inventory, only those whose half-lives are long enough that theystand a chance of exiting from the repository were considered. The full inventory and transportparameters for the considered radionuclides can be found in (Kalin et al., 2010).
The calculations in SSA stopped at 106 years because that was all that was required for the study
and because of the slow calculation speed of HYDRUS. However, since peaks for someradionuclides were not reached, it was decided to run calculations up to 1010 years. By that time,
all the radionuclides have either decayed or have been washed out of the system. It is assumed
that the waste is uniformly spread between the containers and within each container and that it iscompletely dissolved in water at the beginning of the simulation. This is unrealistic, since inreality, the radionuclides would first need to be leeched from solids, but it is conservative. A
previous unpublished study determined that all concentrations everywhere are far below
solubility limits, so these are reasonable assumptions.
4.1. Mass Balance and Timestep Sensitivity Analysis
All the timesteps were performed using the fully implicit scheme (Press et al., 2007), which is
unconditionally stable - one can increase timestep between successive steps (and decrease thereal time for simulations) almost arbitrarily. But there’s a trade-off in the loss of accuracy. To
determine the optimum balance between computational speed and accuracy, a timestep
sensitivity analysis was performed.
A strongly sorbed radionuclide, 129I, was used to check accuracy. Decay was turned off, whichmeans that at the end of the simulation, the cumulative flux (time integral of flux) exiting themodel must match the amount put in the repository at the start of simulation.

158

Figure 3 shows the results of calculations. The vertical axis is the ratio of cumulative flux tostarting amount. One can see that even with relatively large timesteps, the mass balance is off
only by 15%. In most other cases the accuracy is better than 3%. For further calculations, such a
discretization was chosen that the mass balance for 129I is accurate to 0.5% (far above what’s
needed for the comparison), but still relatively little real time is needed to perform thecalculations.

Figure 3. Timestep sensitivity.

4.2. Results and ComparisonFirst, the mass balances were checked by turning off the decay. All the cumulative fluxes were
within 1% of the input activities.
Figure 4 shows the results with decay and Table 4 contains the numerical comparison between
results obtained with Alliances and with HYDRUS. The “Ratio” column is the ratio of HYDRUS
peak flux height versus Alliances peak flux height.

159

Figure 4. Transport results.
Table 4. Transport comparison.
RN
238
U
234
U
230
Th
226
Ra
241
Am
227
Np
233
U
229
Th
36
Cl
129
I
99
Tc
94
Nb
59
Ni
14
C
137
Cs
90
Sr
63
Ni
3
H

Half+life [y]4.50×10+09
2.45×10+05
7.68×10+04
1.59×10+03
4.29×10+02
2.14×10+06
1.59×10+05
7.33×10+03
3.10×10+05
1.59×10+07
2.10×10+05
2.00×10+04
7.59×10+04
5.70×10+03
3.00×10+01
2.90×10+01
9.99×10+01
1.20×10+01

Alliances
Max [bq/y]
At [y]
5.03×10-02
1.25×10+07
5.03×10-02
1.25×10+07-04
2.30×10
1.25×10+07-03
5.74×10
1.25×10+07-52
8.86×10
5.50×10+03-02
5.24×10
1.13×10+07-02
6.49×10
1.13×10+07-04
2.95×10
1.13×10+07+00
1.78×10
1.50×10+05-01
3.81×102.75×10+05-01
7.61×10
4.13×10+05-04
6.99×10
2.88×10+05+02
7.70×10
2.88×10+05-11
4.13×10
1.63×10+05-181
3.54×102.00×10+04-41
2.31×107.00×10+02-32
6.28×10
1.38×10+03-10
5.47×10
2.50×10+02

HYDRUS
Max [bq/y]
At [y]
2.35×10-06
6.10×10+05
5.83×10-06
6.45×10+05-08
2.23×10
7.61×10+05-07
5.51×10
7.63×10+05

Ratio
4.68×10-01
1.16×10-01
9.68×10-01
9.60×10-01

4.55×10-08
1.08×10-10
9.20×10-25
3.66×10+01
8.30×10-01
5.06×10-01
6.59×10-03
1.40×10+03
1.42×10-17

3.96×10+05
3.96×10+05
6.86×10+02
1.64×10+05
3.23×10+05
7.35×10+05
2.81×10+05
3.37×10+05
9.44×10+05

8.69×10-01
1.66×10-01
3.11×10-01
20.54
2.18
0.67
9.42
1.82
3.44×10-07

5.71×10-07

2.13×10+02

1045.47

As noted earlier, the calculations in the SSA were done only for the first 106 years. Consideringthat the peaks in the case of the 238U chain occur at 1.25×107y in Alliances results, these sets ofresults cannot be compared. Similarly in the case of the 241Am chain, the peaks in Alliances
results occur at 1.13×107y (except for the 241Am itself, which rapidly decays into 237Np), so again
the results cannot be compared.
The fluxes of 137Cs, 90Sr, and 63Ni are so low that they can be neglected; indeed, in the SSA they
were not even considered.

160

The difference in 14C peak fluxes is over 7 orders of magnitude, but this can be explained bydecay. The peak in Alliances results occurs at 7.8×105y before peak in HYDRUS results, while
the half-life of 14C is 5.7×103y. The difference in peak times is thus 136 half-lives, and much
more 14C decays in the HYDRUS case.
In any case, the peak fluxes for 14C are very low - on the order of 10-11bq/y for Alliances and 10bq/y for HYDRUS. At values this low, there’s already a chance of numerical problems, not tomention that values this low are completely undetectable in nature and pose absolutely no
problem as far as doses are concerned

17

Next are the 36Cl and 94Nb, where the HYDRUS results are around an order of magnitude higher.
No immediate explanation was found for this.
Values for 129I, 99Tc and 59Ni, however, match very well - within a factor of two. This is very
good for the purposes of PA/SA, as 129I and 59Ni are exactly the two radionuclides that contributethe most to the total dose.
This leaves us with 3H, where the difference is three orders of magnitude. 3H is not sorbed, i.e.,
not retarded. Additionally, it has a short half-life of only 12y, so a small difference of 5% in peak
position (at around 220 y) can alter the peak height by a factor of two. Recalling also that there’s
still an appreciable difference in hydraulic conductivities between different regions and that thesedifferences caused problems in HYDRUS, it was decided to investigate the effect of mesh on 3Htransport.
5. Sensitivity to Mesh Density
To check sensitivity to mesh density, the whole calculation (from mesh generation onwards) was
repeated with two finer meshes. Figure 5 shows the details of the mesh in the critical region —the bottom right corner of the repository.

Figure 5. Mesh details.

From left to right the following meshes are depicted: “NetGen2D, very fine mesh” (“NGv”, themesh used for the calculations so far), “Triangles, fine mesh” (“TRf”) and “Triangles, very finemesh” (“TRv”). The calculations were run for 1000 years for 3H and for 1010 years for 129I.

161

Figure 6. Mesh sensitivity for 3H.

Figure 6 shows the effects of different meshes for 3H. Different timestep discretizations weretried, but this did not appreciably affect the results. However, the position and height of the peak
are strongly influenced by the mesh details. It seems that the finer the mesh is, the later the peakoccurs. In other words, the coarser mesh appears to overestimate the Darcy velocities.

Figure 7. Mesh sensitivity for 129I.

162

Figure 7 shows the effects of different meshes for 129I. Note that in this case, only the default
timestep discretization was used, as the calculation for the TRv mesh took almost five days on anIntel 2 GHz Core 2 Duo with 800 MHz FSB and 2 GB of memory.
The coarser mesh again has the effect of allowing a contaminant to appear earlier (and to disappear later). The position of the peak does not change (this cannot be verified in the figure, but
was checked in the output data). This is understandable, as the majority of the contaminantappears after 105y, when the barriers have all degraded and there is no difference in hydraulicconductivities.
6. Conclusions and Further Work
From the study of mesh sensitivity we can conclude that, especially for the short-lived
radionuclides, the mesh details can have a strong influence on the results. For future calculations,the density of the mesh should be increased in the critical areas (around the boundaries between
materials) and kept about the same elsewhere. It would be impractical to use the TRv mesh, as
the transport calculations for all radionuclides would take around three months.
On the other hand, for the significant radionuclides (59Ni and 129I), the results are very close to
the ones obtained by HYDRUS, meaning that in some cases the coarser mesh may be adequate.
In any case, the sensitivity to mesh details needs to be investigated further before performing“real” calculations.
It would also be interesting to run transport calculations with the hydraulic fields from three
hydraulic conductivities and compare them with results with two hydraulic conductivities. Ifanything, the mesh details should be even more influential, as the differences between hydraulicconductivities are much bigger.
Last, but not least, Alliances had an enormous advantage in speed for this type of problem, i.e.,the calculation of Darcy velocity field and transport in saturated conditions. It took a few days of
calculations to produce results for 106 years with HYDRUS and a few hours to produce resultsfor 1010 years with Alliances - an advantage of 105 in the ratio of real time to simulation time.
At the time when the comparison was performed, HYDRUS did not have any means to automatetransitions between degradations - human intervention was necessary to save radionuclide
concentration fields produced with one level of degradation, calculate Darcy velocity field forthe next level of degradation, and use the saved concentration fields as the initial conditions forconcentrations. Since Alliances uses Python (Python, 2013) as the underlying language, it waseasy to automate the transitions, thus no human intervention was necessary to obtain final results.
This capability was used in an unpublished study and allowed us to perform sensitivity analysis,
not only to physical parameters, but also to the mesh, as it is possible to programmaticallygenerate mesh .

163

References

HYDRUS 2D/3D for Windows, http://www.pc-progress.com/en/Default.aspx?HYDRUS-3d, retrieved on
27/03/2013.
Kalin, J., et al., Comparison of two numerical modelling codes for hydraulic and transport calculations in
the near-field, Nucl. Eng. Des., doi:10.1016/j.nucengdes.2010.04.026, 2010.
Montarnal, Ph, A. Bengaouer, C. Chavant and L. Loth, ALLIANCES: Simulation Platform for Nuclear
Waste Disposal, proceedings of CMWR’06, Copenhagen, Denmark, http://proceedings.cmwrxvi.org/getFile.py/access?contribId=205&amp;sessionId=10&amp;resId=0&amp;materialId=paper&
amp;confId=a05, 2006.
Petkovšek, B., J. Kalin, J. Krivic, G. Omahen, P. Pavšič, R. Ratej. Izdelava ocene lastnosti in varnosti
odlagališča v sklopu PVA za potencialno lokacijo Vrbina (T2226-1): revizija 1. Ljubljana: Zavod za
grabeništvo Slovenije, 2006.
Press, W. H., S. A. Teukolsky, W. T. Vetterling and B. P. Flannery, Numerical Recipes: The Art of
Scientific Computing, 3rd. ed., p.1045 Cambridge University Press, 2007.
Python Programming Language – Official Website, http://www.python.org/, retrieved on 27/03/2013.

164

Characterization and Modeling of Water Movement and Salts
Transfer in a Semi-arid Region of Tunisia
Sabri Kanzari1*, Mohamed Hachicha1, Rachida Bouhlila2, and Jorge Battle-Sales3
1National Institute of Research of Rural Engineering, Waters and Forests of Tunis, Tunisia
National Engineering School of Tunis, Modeling in Hydraulic and Environment Laboratory, Tunisia
3
University of Valencia - Department of Plant Biology, Valencia, Spain*
Corresponding author, sabri.kanzari@gmail.com

2

Abstract
The semi-arid region of Bou Hajla (Kairouan – Central Tunisia) is exposed to the risk of salinization ofsoils and aquifers. A characterization of water movement using TDR probes installed down to a depth of
4 m and salts transport using soil sampling was conducted to highlight this risk. At the same time,
climatic parameters were monitored. The results were collected over a time period of approximately one
year (from June 12, 2006 to May 08, 2007). Water movement and salts transport were simulated using theHydrus-1D model. Inverse modeling was used to optimize the required soil hydraulic parameters. It was
found that the simulated profiles of the volumetric water content and the electrical conductivity wereclose to those measured. The calculated RMSE values were low, indicating the reliability of Hydrus-1D tosimulate the hydro-saline dynamics under field conditions.
Keywords: Soil, Salinization, Hydrus-1D, Aquifer, Semi-arid region, Tunisia.

1. Introduction
Besides the scarcity of water resources and their often poor quality in arid regions, there is apotential shortage of these resources that could be exacerbated by climate change; especiallywhen irrigation is a determinant factor of the agricultural intensification (Mermoud et al., 2005;
Khan et al., 2006). In several regions, this intensification led to the endoreisation of thehydropedologic watershed (Mhiri et al., 1998). In addition, the use of saline waters in these areas
induces, in the short-term, salinization of soils and, over time, the salinization of aquifers.
Modeling of water movement and solute transport is useful for analyzing the effects of irrigation
with saline water and predicting its impacts on soils, crops, and groundwater, as well as fordeveloping sustainable management practices for irrigation and fertilization (Gonçalves et al.,2006).
Considerable progress has been made in recent decades in numerical modeling (van Genuchtenand Šimůnek, 2004). The most commonly used models use a deterministic approach, which isbased primarily on the numerical solution of the Richards equation for variably-saturated waterflow and the advection-dispersion equation for solute transport. These models are important tools
for analyzing water and solute dynamics in the vadose zone. However, their use in the fieldremains limited (Suarez and Šimůnek, 1997; Gonçalves et al., 2006) due to the large amount ofcritical input data they require, such as the soil hydraulic properties, solute transport parameters,
and climatic data.

165

In the context of arid regions that are essentially endorheic and depend on saline aquifers, it isnecessary to prevent soil salinization and the contamination of these aquifers. Risk assessment of
the salinization process is usually based on a quantitative approach, which requires anunderstanding of salts transport phenomena, which are driven by water movement through theunsaturated soil zone to the aquifer (Milnes and Perrochet, 2005).
Tunisia has limited water resources (4.8 billion of m3), which are very often salted. Over half ofavailable water resources, essentially those of Central Tunisia, have a salinity of more than 3 g l1
. Besides the scarcity and poor quality, overexploitation of groundwater results in the depletionof these resources. In the region of Bou Hajla on the plain of Kairouan in Central Tunisia,
salinization of soils and aquifers is a widespread phenomenon, making groundwater resources
unsuitable for irrigation (with saline water of about 6 g l-1) (Hachicha et al., 2005). In the shortterm, the impact of salinity on soils and crops occurs particularly in summer when evaporation ishigh. In the long-term, irrigation with saline water can degrade the overall system formed by thesoil and groundwater.
The objectives of this paper are (a) to evaluate water movement and salt transport in the soil
profile by studying variations of water and salt profiles as they depend on weather events, (b) tohighlight the risk of salinization of the aquifers, and (c) to calibrate and validate Hydrus-1D(Šimůnek et al., 2005) for modeling the hydro-saline dynamics in the semi-arid context ofCentral Tunisia.
2. Materials and Methods
2.1. The Plot, Soil and Irrigation Water
The region of Bou Hajla is located about 30 km southeast of the city of Kairouan in central
Tunisia. It is situated between a mountain range to the west and an area of sabkhas (salt flats) inthe east and south, receiving surface waters and groundwater flowing from the mountains. The
region is characterized as having an arid climate and a temperate winter. Rainfall is highlyvariable with an annual average of about 250 mm. Evapotranspiration is about 1600 mm perannum. An experimental plot (35°15’47.58’’N; 10°4’17.16’’E) was selected from a farmer’s
field about 9 km south of the village of Bou Hajla, having surface soils of sandy texture (00.6 m) and a high clay content to a depth of 2 m. Below this depth, the texture is sandy to sandysilty (Table 1). Irrigation water comes from a surface well about 20 m deep, with a pumping rateof approximately 3 l s-1, and a water quality corresponding to a TDS (total dissolved solids) of
6.5 g l-1, an ECi (electric conductivity of irrigation water) of 7 dS m-1, and an SAR (sodium
adsorption ratio) of about 7.5.

166

Table 1. Soil particle size analysis.
Depth (m)Clay (%)

Loam (%)

Sand (%)

Texture0 – 0.6
0.6 – 1.1
1.1 – 1.8
2 – 2.5
2.5 – 33 – 3.5
3.5 – 3.7
3.7 –4

11.5
15.5
13.0
4.0
10.0
11.0
10
17.0

4.5
6.5
6.0
8.0
14.0
14.0
19.0
22.7

81.5
77.5
70.5
81.0
76.0
56.0
55.0
47.5

Sand
Sand clay
Sand clay
Sand
Sand loam
Sand loam
Sand loam
Sand clay

2.2. Experimental Methods
The analysis of soil and aquifer salinization was performed by monitoring the soil water content
using time domain reflectometry (TDR), and the soil salt content by using soil sampling.
- Water content monitoring: Water content was monitored using TDR probes installed at
depths of 0.1, 0.5, 1, 1.5, 2, 3, and 4 m. Monitoring of the soil water profile in situ by the
TDR sensors was launched at the time of installation (Apr/05/2006).
- Soil salt content monitoring: Soil salt profiles were monitored to a depth of 4 m. Soilsalinity was determined using soil samples and the method of the soil diluted extract(soil/water ratio of 1/5). A relationship established by Hachicha (2005) has been used toconvert EC(1/5) into the electrical conductivity of the saturated paste extract:
ECe=7.4*EC(1/5). Three salt profiles were observed on the following dates: December 26,
2006, February 2, 2007, and May 8, 2007.
- Monitoring climate parameters: An automated weather station from the Campbell
Company has been installed in Bou Hajla since April, 2004. It includes a set of sensors
and a communication interface for data transfer, which includes an anemometer formeasuring speed and wind direction, a bucket rain gauge, a temperature sensor, a relative
humidity device, and a pyranometer for measuring solar radiation. Monitoring of eachparameter is done hourly, and daily data is obtained by averaging data collected over 24hours. An ET0 software (Raes, 2007) was used to estimate daily evapotranspiration (ET0)from the collected data.
2.3. Input Parameters of Hydrus-1DThe soil hydraulic parameters were determined from the particle size distribution and the bulk
density of the soil using the Rosetta model (Schaap et al., 2001) implemented in Hydrus-1D.
Values obtained by pedotransfer functions were adjusted to volumetric water content andelectrical conductivity values measured in the field using inverse modeling described byŠimůnek et al. (2005), as a method of optimizing parameters by matching results of numericalsolutions with experimental data. Inverse modeling has been used for the determination of the
shape parameters α and n, and the saturated hydraulic conductivity (Ks), the most sensitive
parameters to water flow according to Lu and Zhang (2002). Initial values of the soil hydraulicparameters are presented in Table 2. The residual water content, θr, and the saturated water167

content, θs, were estimated from the particle size distribution using the Rosetta (Schaap et al.,2001) pedotransfer functions.
As for solute transport parameters, dispersions coefficients (Disp) were taken from the literature(Vanderborght and Vereecken, 2007) for each type of texture. The adsorption coefficients (Kd) ofsalts were determined using the batch experiment for different layers. The upper boundary
condition was set to the atmospheric boundary condition (BC) with a surface water layer, which
requires an input of rainfall and evaporation calculated from climate data. Free drainage wasused as the lower BC. Concentration flux BC was used as the upper boundary condition forsolute transport. The results of the model were evaluated by both graphical and statisticalmethods. In the graphical approach, the measured and simulated volumetric water contents andsoil salinities were plotted as a function of the soil depth at different times. The statistical
approach involved the calculation of the root mean square error (RMSE):n

RMSE =∑ ( p − m )²
i =1

i

n

i

×

1
m

(5)

where pi are the predicted values, mi are the measured values, m is the average value ofobserved data, and n is the number of observations.
3. Results
3.1. Characterization of Water Movement and Salt Transport
All water content profiles have the same distinct shape, from which four layers can be
distinguished: two layers with high variations of water contents and two layers with smallchanges in water contents (Fig. 1).
The layers with high variations in water contents are characterized by the following:- In the topsoil, primarily between depths of 0 and 0.7 m, the soil water content varies between
the field capacity (36%) and the permanent wilting point (14%) in the silty sand material.
This layer is directly exposed to evaporation, rainfall, and irrigation (absent during thisperiod).
- In the deep layer, located at a depth of approximately 2 m, the water content varies between
the field capacity (35%) and the permanent wilting point (14%) in the silty clay material(Musy and Soutter. 1991). Variations in water contents in the deep soil layer can be
explained by deep drainage and the influence of the clay material on top.
The layers with minimal changes in water contents correspond to the following:- The soil stratum with a thickness of about 1 m, located between the topsoil and the soil layer
starting at a depth of 2 m. This layer is a first zero-flux plane, which retains low levels ofwater. The texture is similar to the one found at the soil surface, i.e., a very permeable silty
sand.

168

Figure 1. Soil water content profiles at different
times.

-

Figure 2. Variations of the soil salinity profiles atdifferent times.

The soil layer at a depth of about 3 m, located between the soil layer at 2 m and the one at
depths greater than 4 m. This layer is a second zero-flux plane that moderately retains water.
The texture is sandy-silty and is also quite permeable.

Five layers, corresponding to the four layers distinguished above in the examination of watercontents, can be identified from the three available saline profiles (Fig. 2):- In the topsoil, between depths of 0 and 0.7 m, salinity (ECe) varies between 3 and 7 dS m-1.
The high salinity value is due to the winter planting season in 2006, when a barley crop was
irrigated with water having a salinity of 7 dS m-1. Fall rains appear to have completelyleached salts.
- The soil layer located about 2 m deep is a very salted layer, with an ECe higher than 20 dS m1. The silt-clay material reduces water infiltration, leading to the accumulation of salts.
Rainfall also influences the content of salts in this layer, which allows for the transfer of salts
to greater depths (Alimi-Ichola and Gaidi, 2006).
- The soil layer between depths of 0.7 and 1 m, which corresponds with the first zero-flux
plane, is comprised of a highly permeable sandy-silty material, which does not appear toretain salt, but is a salts transfer zone.
- The soil layer down to a depth of 3 m, the second zero-flux plane with average salinity,
seems to retain a portion of the salts arriving from the above saline layer. Although the soil
layer located at a 4-m depth does not appear as a place for water retention, the ECe reachedexcessive levels equivalent to the soil layer located at approximately 2 m. However, this soil

169

layer differs from the 2 m layer, because it remains salinized and accumulates salts, while the
2 m layer is desalinized. Although it is difficult to make further conclusions without further
information regarding the constitution of the soil, it seems likely that a soil layer similar tothat of the 2 m layer exists, playing a similar role in water retention and accumulation ofsalts. This soil layer seems to be located at a deeper level and may reach a degree of salt
accumulation comparable to the previous level. The salt storage calculated for different dates
shows an export of salts below the 4 m depth during the winter period (-0.623 t ha-1). An
infiltration test was accompanied by an import of salts, which is reflected in the salinestorage on May 08, 2007. This highlights the risk of salinization of the aquifer.
3.2. Modeling the Hydrosaline Dynamics
Calibration of Hydrus-1D was performed for a time period of 134 days, with a daily time step(from December 26, 2006 to May 08, 2007). Inverse modeling was used in the calibration of
Hydrus-1D against the water content profiles. The solute transport parameters (dispersion andadsorption coefficients) were adjusted several times in order to find an adequate match between
the measured and simulated salinity profiles. The print times were set to 57th and 134th days tomatch the salinity profiles measured on February 27, 2007 and May 8, 2007, respectively. The
initial profiles of the volumetric water content and soil electrical conductivity are those of
December 26, 2006. The depth of the soil profile is 4 m. There are five distinct soil strata,
identified through the characterization of the dynamics of water contents and salinities in
Sections 3.1 and 3.2. The depths of different soil layers are as follows: 0 - 0.7, 0.7 - 1, 1 - 2, 2 –3, and 3 - 4 m. Observation points were added to depths that correspond to the locations of TDR
probes (0.1, 0.5, 1.5, 2, 3, and 4 m). The soil hydraulic parameters (θr, θs, α, n, and Ks) were
determined by inverse modeling with a correlation coefficient, r², between measured data
(volumetric water contents and electric conductivities) and modeling results, equal to 0.94.
Optimized values of the dispersion and adsorption coefficients for each soil material are given in
Table 2.
Validation of calibrated results was performed on the water content and electrical conductivity
profiles measured on July 22, 2008. The same input data were used, and only the upper boundary
conditions were changed. Values of evaporation and precipitation were extended to day 577 inthis simulation.
Table 2. Input parameters of Hydrus-1D.
Soil hydraulic parameters

Solute transport parameters

cm3 cm-3
0.372

cm-1
0.0254n-Ks
cm d-1Bd
cm3 g-1

Disp
cm-1

Kd
-

0-0.7

cm3 cm-3
0.0543

1.77

128.

1.38

17

0.10

0.7-1

0.05360.373

0.0195

1.62

97.

1.35

6

0 .1

1-2

0.04540.382

0.0474

1.61

142.

1.60

40

0.3

2-3

0.055

0.386

0.01892

1.37

21.

1.54

17

0.05

3-4

0.055

0.386

0.0173

1.375

54.

1.60

40

0.03

Depth (m)

θr

θs

α

170

Figure 3. Measured and predicted water content and salinity profiles for calibration times.

The water content and salinity profiles measured and simulated for the two calibration times areshown in Figure 3. Calibrated results showed a strong correlation between simulated andmeasured values. The RMSE values calculated for the 57th and 134th days of simulation are 0.06
cm3cm-3 and 0.028 cm3cm-3 for water content profiles, and 0.35 dS m-1 and 0.26 dS m-1 forsalinity profiles, respectively.

Figure 4. Measured and predicted water content and ECe profiles on 577th day ofthe simulation.

Similar results were found in the validation stage. Good agreement between simulated andmeasured soil water contents and electrical conductivities were found for the 577th day of thesimulation (Figure 4). The RMSE value for the water content profile was 0.043 cm3cm-3, and forthe electrical conductivity profile it was 0.21 dS m-1. These values are close to 0, which indicatesthe reliability of the model for the reproduction of water movement and transfer of salts under
the field conditions.
3.3. Discussion
The Hydrus-1D model was able to simulate the dynamics of water and salts, as indicated by low
values of RMSE. The inverse parameter estimation method was able to optimize the soil
hydraulic parameters and to achieve a good correlation between measured and simulated data.
However, it was unable to provide precise values of these parameters, due to the effects of spatial
heterogeneity and the soil microstructure organization. An increase in the number ofmeasurement points in time and space is suggested in order to better understand the variation of171

soil water and salts contents (Köhne et al., 2009). The characterization of these parameters andthe use of a hydro-structural approach for modeling the water and solute dynamics in the soil, asutilized in the Kamel model (Braudeau et al., 2009), can be a good alternative to our approachand could also demonstrate the limits of the approach used in this paper.
The salts balance, calculated at a depth of 4 m, is additive, which increases the risk of aquifer
contamination. It is essential to monitor the groundwater level and the aquifer quality in order todetermine possible contamination of groundwater by irrigation with saline water and to assess
this risk. Also, the consideration of cultures and the design of some irrigation management
scenarios for the farmers in the region are needed, in order to better assess the magnitude of thesecondary salinization and to find appropriate management strategies (Forkutsa et al., 2009).
Finally, it will be interesting to study the effects of torrential rains on the leaching of salts in thesemi-arid region of Bou Hajla. These rains may have a regulatory role on the salts dynamic in the
topsoil (Armstrong et al., 1998). All these recommendations will be considered in future research
work and papers.
4. Conclusions
The effect of irrigation with saline water on soils and aquifers was studied in an experimental
plot in Bou Hajla, central Tunisia. Deep characterization and simulation of salt and water content
of the soil over the course of one year reveals the significant effects of infiltration after rainfall.
As changes in climate affect soil evaporation at certain layers, it can be seen that the infiltration
effect is dependent upon climate. The greatest effect is seen at depths greater than 3 m, and at aclay layer at 2 m, which is surrounded by sandy loam materials. This particular layer appears toplay a major role in the movement of water and in the transfer of salts. Indeed, the salinity
profiles highlight the phenomenon of reversibility of salts movement toward the soil surface, butalso its accumulation in the clay layer where the value of electrical conductivity exceeds 20 dS
m-1. This layer reduces the transfer of salts into the aquifer, but does not seem to prevent themaltogether. Thus, the region of Bou Hajla is subject to the salinization of its soils, which is further
aggravated by aquifer over-exploitation and a decrease in aquifer piezometric levels. This may
result in a reversal of the direction of groundwater flow, and thus exacerbate the intrusion ofsaline waters from surrounding sabkhas (salt flats).
References

Alimi-Ichola, I., and L. Gaidi, Influence of the unsaturated zone of soil layer on the solute migration,
Engineering Geology, 85, 2-8, 2006.
Armstrong, A. S. B., T. W. Tanton, and D. W. Rycroft, The effect of ped size. simulated rainfall durationand frequency on the leaching of salts from clay topsoils, Agricultural Water Management, 37, 133143, 1998.
Braudeau, E., R. H. Mohtar, N. E. Ghezal, M. Crayol, M. Salahat, and P. Martin, A multi-scale “soilwater structure” model based on the pedostructure concept, Hydrol. Earth Syst. Sci. Discuss., 6,
1111–1163, 2009.
Forkutsa, I., R. Sommer, Y. P. Shirokova, J. P. A. Lamers, K. Kienzler, C. Tischbein, P. L. Martius, and
G. Vlek, Modeling irrigated cotton with shallow groundwater in the Aral Sea Basin of Uzbekistan: II.
Soil salinity dynamics, Irrig. Sci., 27, 319-330, 2009.

172

Gonçalves, M. C., J. Šimůnek, T. B. Ramos, J. C. Martins, M. J. Neves, and F. P. Pires, Multicomponent
solute transport in soil lysimeters irrigated with waters of different quality, Water Resources
Research, 42, W08401, doi:10.1029/2006WR004802, 17 pp., 2006.
Hachicha, M., M. Mansour, S. Rejeb, R. Mougou, H. Askri, and J. Abdelgawad, Applied Research for theUtilization of Brackish/Saline Water in Center of Tunisia: water use. salinity evolution and crop
response. salinity evolution and crop response, Proceedings of International Salinity Forum,
Riverside, 25-27 April 2005, 213-216, 2005.
Khan, S., R. Tariq, C. Yuanlai, and J. Blackwell, Can irrigation be sustainable? Agricultural Water
Management, 80, 87-99, 2006.
Köhne, J. M., S, Köhne, and J. Šimůnek, A review of model applications for structured soils: a) Water
flow and tracer transport, Journal of Contaminant Hydrology, 104, 4-35, 2009.
Lu, Z., and D. Zhang, Stochastic Analysis of transient flow in heteregeneous variably saturated porous
media: The van Genuchten-Mualem constitutive model, Vadose Zone Journal, 1, 137-149, 2002.
Mermoud, A ., T. D. Tamini, and H. Yacouba, Impact of different irrigation schedules on the waterbalance components of an onion crop in semi-arid zone, Agricultural Water Management, 77, 282295, 2005.
Mhiri, A., J. Tarhouni, M. Hachicha, and F. Lebdi, Approche systématique des risques de salinisation par
endoréisation anthropique, Revue Etude et gestion des sols, 5(4), 257-268, 1998.
Milnes, E., and P. Perrochet, Direct simulation of solute recycling in irrigated areas, Advances in Water
Resources, 29, 1140-1154, 2005.
Raes, D., The ET0 calculator – Reference Manual, K. U. Leuven University, Belgium, 36 pp., 2007.
Schaap, M. G., F. J. Leij, and M. Th. van Genuchten, Rosetta: A computer program for estimating soil
hydraulic parameters with hierarchical pedotransfer functions, J. Hydrol., 251, 163-176, 2001.
Šimůnek, J., K. Huang, M. Šejna, and M. Th. van Genuchten, The HYDRUS-1D Software Package forSimulating the One-Dimensional Movement of Water, Heat, and Multiple Solutes in VariablySaturated Porous Media, International Ground Water Modeling Center, Colorado School of Mines,
Golden, Colorado, 162 pp., 2005.
Suarez, D. L., and J. Šimůnek, UNSATCHEM: Unsaturated water and solute transport model withequilibrium and kinetic chemistry, Soil Sci. Soc. Am. J., 61, 1633–1646, 1997.
Vanderborght, J., and H. Vereecken, Review of Dispersivities for Transport Modeling in Soils, Vadose
Zone Journal, 6, 29–52, 2007, 2007.
van Genuchten, M. Th., and J. Šimůnek, Integrated modeling of vadose zone flow and transport
processes, in Unsaturated Zone Modelling: Progress, Challenges and Applications, Frontis Ser. vol.
6, edited by R. A. Feddes, G. H. de Rooij, and J. C. van Dam, 37–69, Springer, New York, 2004.

173

174

Characterization and Modeling of Water and Salt Dynamics in a
Sandy Soil Under the Effects of Surface Drip Irrigation
Sabri Kanzari1*, Ibrahima Bâ2, Mohamed Hachicha1, and Rachida Bouhlila2
1National Institute of Research of Rural Engineering, Waters and Forests of Tunis, Tunisia
National Engineering School of Tunis, Modeling in Hydraulic and Environment Laboratory, Tunisia*
Corresponding author, sabri.kanzari@gmail.com

2

Abstract
In the global context of water scarcity and salinization, there is a more pressing need for an efficient useof irrigation water through alternative, localized irrigation techniques. Experimental characterization andtwo-dimensional modeling of water movement and salts transport is important for managing such
irrigation systems. However, experimental observations rarely accompany most numerical modelingstudies of two-dimensional water flow and solute transport under drip irrigation. For this purpose, twosandy soil monoliths were instrumented with TDR probes to monitor water contents and Watermark
sensors to monitor soil pressure heads. Soil salinity was measured using the method of the soil diluted
extract (soil/water ratio of 1/5). Preliminary tests on small monoliths were carried out to determine soil
hydraulic parameters of this soil. The two monoliths were saturated with either distilled or saline waters(with electrical conductivity of 4 dS m-1). Experimental results show important vertical movement ofwater and the formation of a saline bulb around a depth of 20 cm.
Modeling of water movement and solute transport was performed with Hydrus-2D. Four sets of soil
hydraulic parameters were evaluated against data from the monolith irrigated with distilled water. The
best results were obtained with the parameters estimated using the RETC software and the retention curve
data measured by the evaporation method. Model validation was performed on the data obtained from themonolith irrigated with saline water. Modeling results showed a good agreement between measured andpredicted values. A scenario highlighting the effect of significant evaporation (8 mm day-1) during anirrigation cycle revealed a potential for soil salinization with the formation of a saline bulb of medium
salinity (3.5 dS m-1) around the emitter. This bulb extends to a depth of 30 cm. In the long-term, after
several cycles of irrigation, the salinity risk can be aggravated and affect the soil physical properties andconsequently, crops production.

1. Introduction
In arid and semi-arid regions, soil salinity remains one of the most crucial and widespreadenvironmental problems in agriculture, in addition to an increasing demand on water resources
and water quality degradation. To cope with these twin problems, a wide range of irrigation
systems, including surface drip irrigation, have been developed. Surface drip irrigation is widelyused in agriculture in recent decades because of its many advantages in terms of water economy,
water efficiency, and limitation of soil salinization. Thus, increasing water demand, water quality
degradation, and soil salinization have aroused a great interest in understanding the processes
governing water movement and solute transport in unsaturated soils through numerical modeling.
This requires a reliable characterization of soil hydraulic properties and solute transportparameters. However, measuring these parameters is expensive and often difficult to implement.

175

Indirect methods and laboratory measurements are increasingly used by researchers. Meanwhile,
several numerical models have been developed to study water and salts dynamics under drip
irrigation (Al-Qinna and Abu-Awwad, 2001). For example, Skaggs et al. (2004) comparedmeasured values of water contents under surface drip irrigation to those simulated using Hydrus2D. Zhou et al. (2007) also compared simulated values of water contents by Hydrus-2D withthose simulated by a two-dimensional model APRI under the dripper. However, these days there
are only few studies that focus on soil salinization risks with surface drip irrigation. In Tunisia,
there is also a lack of studies that focus on numerical modeling in the management of water andsoil salinity under drip irrigation.
The objectives of this paper are to experimentally characterize and model two-dimensional waterand solute dynamics in a sandy soil under surface drip irrigation and to study the effects of highevaporation on the distribution of water content and soil salinity.
2. Materials and Methods
2.1. Experimental Design and Measurements
Two monoliths of a sandy soil (93% sand, 4% silt and 3% clay) were used (Fig. 1). Theirdimensions were: 60 cm along the x-axis, 60 cm along the z-axis, and 10 cm along the y-axis. In
each monolith, given the symmetry of the problem, five TDR probes were placed on the rightside at the following coordinates: one probe 45 cm below the emitter axis, two probes at a depthof 30 cm at x = 0 cm and x = 15 cm, and two probes at a depth of 10 cm depth at x = 0 cm and x= 15 cm. The dripper was placed in the center (x = 0 cm, z = 0 cm) at the surface of the monolith.
The first monolith was irrigated at a flow rate of 0.316 L h-1 with fresh water (0.5 dS m-1) and thesecond monolith at a flow rate of 0.490 L h-1 with saline water (4 dS m-1). Water was applied for4 h 45 min and 4 h 25 min to the first and second monoliths, respectively. The water content wasmonitored using TDR probes. The 2001 Trase model from the Soil Moisture Corp Company wasused. The TDR probes were adapted to salinity and previously calibrated. The salinity of the soil
was determined on soil samples using the method of the soil diluted extract (soil/water ratio of
1/5) at the same measurement points.
2.2. Modeling of Water Movement and Solute Transport
Only the right side of the monolith was simulated using Hydrus-2D (Šimůnek et al., 1999). The
geometric domain is defined for the two monoliths as before: width = 30 cm and height = 60 cm.
The emitter, represented by a quarter of a circle with a radius of 1 cm, is placed 1 cm below theorigin of the coordinate system, i.e., in the center, 1 cm below the surface of the monolith. The
simulations were carried out over periods of 2,685 min and 2,800 min, respectively, for the firstand second monolith. The first monolith was used to evaluate the model with four different setsof soil hydraulic parameters, and the second to validate the model. As an initial condition, theaverage water contents measured by TDR probes in each depth were used. The average watercontent for the probes located at a depth of 10 cm was 12%. This value was assigned uniformly
to the portion of the soil between the soil surface and a depth of 20 cm. The same approach wasused for the following 20-cm thick soil layer by taking the average of probes located at a depth176

of 30 cm. For the soil profile between depths of 40 and 60 cm, the water content value measured
by a probe located at a 45-cm depth was used. The initial electrical conductivity was assumed to
be uniform and equal to 0.5 dS m-1.

Figure 1. Monolith and measurement points.

Water flow

Solute Transport

Figure 2. Water flow (left) and solute transport (middle) boundary conditions.

Soil hydraulic properties were estimated using either:- the van Genuchten catalog (1991) (denoted as vG)- Rosetta pedotransfer functions (Schaap at al., 2001 ) (denoted as R), and- the evaporation method (Kanzari et al., 2012), using fresh water (0.5 dS m-1) (denoted asFW) and saline water (4 dS m-1) (denoted as SW).

177

Table 1. Soil hydraulic parameters determined by the four methods.
θs (cm3cm-3)

θr (cm3cm-3)

α (cm-1)n (-)

Ks (cm d-1)

vG

0.43

0.0001

0.036

1.56

24.9

R

0.43

0.0001

0.145

2.68

24.9

FW

0.749

0.134

0.00959

4.34

712.8

SW

0.831

0.0444001086

2.75

712.8

SourceThe results of model simulations were evaluated using graphical and statistical methods. In thegraphical approach, the measured and simulated volumetric water contents and soil salinities
were plotted as a function of soil depth using Surfer 8.0. The statistical approach involved thecalculation of the root mean square error (RMSE).
3. Results
3.1. Characterization of Water Movement and Solute Transport
Figure 3 below shows the distribution of the water content and soil salinity for the two monoliths
at different times. The vertical movement of water is more important than the lateral movement.
For monolith 2, the salts bulb extends down to a depth of 30 cm.

Monolith 1
0.5 dS m-1

Monolith 2
4 dS m-1

Figure 3. Measured water contents (left) and soil salinities (right) for the two monoliths.

3.2. Hydrus-2D Calibration
Hydrus-2D was calibrated against the experimental data on water and salts dynamics in monolith
1 using four different sets of hydraulic properties. According to the graphical and statisticalevaluation, the parameters estimated using the evaporation method with fresh water provided thebest agreement between predicted and measured values.

178

Figure 4. Measured and simulated (using four different sets of soil hydraulic parameters) water content
and soil salinity distributions for Monolith 1.
Table 2. RMSE Values.
Value

FW

SW

R

vG

RMSE: Water Contents
RMSE: ECe

0.140
0.379

0.206
0.372

0.199
0.388

0.256
0.374

3.3. Hydrus-2D Validation
Validation of Hydrus-2D was carried out using the experimental results from Monolith 2. Goodagreement between measured and simulated values was obtained. The wetting bulb and salts
accumulation were more important. At the end of the irrigation cycle, the soil was dry and low
soil salinity around the dripper was observed.
3.4. Effects of High Evaporation
A scenario with a high evaporation rate (8 mm day-1) was studied numerically using the same
input parameters for monolith 2 during a 3 month long irrigation cycle (1 irrigation per week)with a 25 mm irrigation volume of 4 dS m-1 saline water. 25 mm is approximately the irrigation
volume applied to the second monolith. The results show that at the end of the irrigation, soil
salinity is low under the dripper down to a depth of about 10 cm and that salts migrated to adepth of 30 cm with an ECe of 3.5 dS m-1.

179

Figure 5. Simulated and measured water and salts distributions for Monolith 2.

Figure 6. Soil salinity and water content profile under a high evaporation rate.

4. Conclusions
In this study, a good agreement between simulated and measured soil water contents and saltcontents was found using Hydrus-2D. The effect of high evaporation (8 mm day-1) during anirrigation cycle revealed a risk of soil salinization. In the long term, after several irrigation
cycles, this risk can be aggravated and affect the soil physicochemical properties and crop
growth.
References

Al-Qinna, M. I., and A. M. Abu-Awwad, Soil and water: Wetting patterns under trickle source in arid
soils with surface crust, Journal of Agricultural Engineering Research, 8(3), 301-305, 2001.
Kanzari S., M. Hachicha, and R. Bouhlila, Laboratory method for estimating soil water retention
properties of an unsaturated soils, Walailak Journal of Science and Technology, 9(4), 361-367 2012.

180

Schaap, M. G., F. J. Leij, and M. T. van Genuchten, ROSETTA: A computer program for estimating soil
hydraulic parameters with hierarchical pedotransfer functions, Journal of Hydrology, 251, 163-176,
2001.
Šimůnek J., M. Šejna, and M. Th. van Genuchten, The Hydrus-2D Software Package for Simulating TwoDimensional Movement of Water, Heat, and Multiple Solutes in Variably Saturated Media, Version
2.0, IGWMC-TPS-53, International Ground Water Modeling Center, Colorado School of Mines,
Golden, Colorado, 251pp., 1999.
Skaggs, T. H.,T. J. Trout, J. Šimůnek, and P. J. Shouse, Comparison of HYDRUS-2D simulations of drip
irrigation with experimental observations, ASCE Journal of Irrigation and Drainage Engineering,
130(4), 304–310, 2004.
Zhou Q., S. Kang, L. Zhang, and L. Fusheng, Comparison of APRI and Hydrus-2D models to simulate
soil water dynamics in a vineyard under alternate partial root zone drip irrigation, Plant and Soil,
291(1-2), 2007.
van Genuchten, M. Th., A closed-form equation for predicting the hydraulic conductivity of unsaturated
soils, Soil Sci. Soc. Am. J., 44, 892-898, 1980.

181

182

Hydraulic Properties and Reduction of COD, Phosphorus andNitrogen in a Sand Filter used for Greywater Treatment –Simulation and Verification
Susanna Ciuk Karlsson1, Sahar Dalahmeh2, Cecilia Lalander3, and Håkan Jönsson4
Department of Energy and Technology, Swedish University of Agricultural Sciences, Uppsala, SWEDEN,
susanna.ciuk.karlsson@slu.se, 2sahar.dalahmeh@slu.se, 3Cecilia.Lalander@slu.se, 4Hakan.Jonsson@slu.se

1

Abstract
A vertical flow sand filter is a simple, effective and inexpensive system for treating greywater. The
performance of sand filters treating artificial greywater was tested in the laboratory over a time period of
113 days. The filters consisted of columns (0.2 m diameter) filled with sand to a height of 0.6 m. The
hydraulic properties of the filters were measured as well as the inflow and outflow concentrations of
COD, BOD5, total and phosphate phosphorus and total-, ammonia- and nitrate nitrogen. To get a better
quantitative understanding of the treatment processes inside the filters, the HYDRUS-CW2D computer
software was used to simulate the filters. The simulation of water flow through the filter could be wellfitted to the measured flow by adjusting three model parameters: the air entry value, the pore size
distribution index, and the pore connectivity parameter. For the COD reduction the simulated results
agreed well with experimental data after an adjustment of the microbial lysis parameters of HYDRUSCW2D. The simulated reduction of COD was 65 %, while a 72 % reduction was measured for the filtersin the lab. Simulated reduction of phosphorus in the sand filter effluent corresponded well to themeasured reduction: the simulated reduction of phosphorus was 72 % while the experimental filters
achieved a 79 % reduction. Also, the simulated effluent concentrations of nitrate compared quite well tothe measured values. Almost no reduction (4 %) in total nitrogen took place in the experimental filters,
which agreed with the simulated reduction (0 %). For the phosphorus and nitrate components in
HYDRUS-CW2D, so far no changes have been made to the default parameters.

1. Introduction
Physical water scarcity affects one fifth of the world’s population today, and over the coming
years water scarcity is likely to increase (Molden, 2007). About 90 % of the globally produced
wastewater is left untreated, resulting in extensive pollution of natural water resources (Drechsel
et al., 2010). An estimated 5.4 billion people have access to pit toilets or no toilet, which means
their household wastewater is constituted of greywater (water from bath, shower and wash)(WHO, 2006). Greywater contains suspended solids, various household chemicals, oil, and tosome extent, pathogenic microorganisms. Source-separated greywater is, however, usually lesspolluted than common wastewater or industrial wastewater (Morel and Diener, 2006). Greywatercan, after suitable treatment, be a sustainable resource for irrigation, cleaning and strengthening
the groundwater by infiltration (WHO, 2006). A vertical flow sand filter could prove to be asimple, effective and inexpensive system for treating greywater.
The performance of a sand filter treating artificial greywater was tested in the laboratory over atime period of 113 days. The filter consisted of a column (0.2 m diameter) filled with sand to a183

height of 0.6 m. Duplicates of the sand filter were simultaneously tested. The filters wereintermittently loaded three times a day; the loading was performed as a rapid flush emerging
from sprinklers installed on top of the filter columns. The size and timing of the loadings wereintended to correspond to the greywater yield of a typical rural community household in Jordan(Abu Ghunmi et al., 2008). The hydraulic properties of the filters were measured as well as the
inflow and outflow concentrations of COD, BOD5, total and phosphate phosphorus, and total-,ammonia- and nitrate nitrogen.
To get a better quantitative understanding of the treatment processes inside the filters, the
HYDRUS-CW2D computer software (Langergraber and Šimůnek, 2005) was used to simulate
the filters. The simulation results were compared to the measured observations for verification.
The idea was to verify if HYDRUS-CW2D could simulate the capacity of a system using verticalflow sand filters for treatment of household greywater.
The simulation of water flow through the filter could be well fitted to the measured flow byadjusting three model parameters: the air entry value (α, [cm-1]), the pore size distribution index(n, [-]), and the pore connectivity parameter (l, [-]). The simulation of reactive transport ofnutrients within the filter compared quite well to the experimental observations. The simulated
reduction of COD was 65 % while a 72 % reduction was measured for the filters in the lab(Table 5). Simulated reduction of phosphorus in the sand filter effluent corresponded well to themeasured reduction: the simulated reduction of phosphorus was 72 % while the experimental
filters achieved a 79 % reduction (Table 5). Also, the simulated effluent concentration of nitratecompared quite well to the measured values. Almost no reduction (4 %) in total nitrogen took
place in the experimental filters, which agreed with the simulated reduction (0 %) (Table 5).
HYDRUS-CW2D was to a large extent successfully used to simulate the capacity of a systemusing vertical flow sand filters for the treatment of household greywater. Using HYDRUSCW2D for running simulations has so far improved our understanding of the lab scale sandfilters by elucidating that some water bypasses the filter by running alongside the filter column
walls. The simulations also indicated that the biological activity and COD reduction mainly took
place in the very top of the filter, thereby agreeing with experimental observations.
2. Materials and Methods
The experimental setup consisted of a column (0.2 diameter) filled with sand up to 60 cm.
Several characteristics of the sand were measured (Table 1). To facilitate drainage anddistribution of loadings, a 0.1 m layer of coarse gravel was placed at the bottom of the column.
Some large pieces of gravel were placed on top of the sand to even out the distribution ofincoming greywater. The loadings were set to be automatically conducted as short, intermittent
bursts following the same schedule (Table 2) each day for 113 days.
The artificial greywater was prepared by mixing standard nutrient broth, dishwashing gel,shampoo, washing powder and maize oil with tap water. To include indigenous bacterial flora, asmall amount of wastewater from a nearby Swedish municipal sewage treatment plant was also
added. Various characteristics of the artificial greywater were measured (Table 3).

184

Table 1. Characteristics of the sand filter material used in the experiment set up (Dalahmeh et al., 2012).
Parameter
pH [SU]
Loss on ignition [%]Effective size [mm]Uniformity coefficient [-]Bulk density [kg m-3]
Particle density [kg m-3]
Porosity [%]Surface area [m2g-1]
Hydraulic conductivity [cm h-1]

Sand
7.9
<1
1.4
2.2
1690
2570
34
0.136
360

Table 2. Loading schedule for the irrigation of the filter.
Time
Amount of water [L]

9:00
0.7

16:00
0.1

20:00
0.2

Table 3. Characteristics of the artificial greywater used in the experiment set up (Dalahmeh et al., 2012).
Parameter
pH [SU]Electrical conductivity, EC, [µS cm-2]
Biochemical oxygen demand, BOD5, [mgL-1]
Chemical oxygen demand, COD, [mgL-1]
Total organic carbon, TOC, [mgL-1]
Methylane blue activity substances, MBAS, [mgL-1]
Total phosphorus, Tot-P, [mgL-1]
PO4-P, [mgL-1]
Total nitrogen, Tot-N, [mgL-1]

Concentration in artificial greywater
7.8 ± 0.3
1960 ± 140
425 ± 56890 ± 130304
30 ± 104.2 ± 0.2
2.1 ± 0.475 ± 10

The filter effluent was collected in a bucket placed on top of a digital scale connected to acomputer that recorded the weight once a minute. Weight and time recorded in this manner gave
a thorough estimate of the cumulated effluent flow of the filter. Samples from both influent
greywater and filter effluent were collected and analyzed regularly during the experiment.
To get a better quantitative understanding of the treatment processes inside the filter, the
HYDRUS-CW2D computer software was used to simulate the filter. HYDRUS-CW2D was firstused to model the hydraulics of the filter. A large number of simulations with varied empiricalcoefficients α, n, and l were carried out and compared to the experimental data. The areas
between simulated curves and measured curve for cumulative water flow were calculated andused as a measure to determine the best fit (Table 4), as the least area indicates the best fit.
After a good fit to measured values had been established, the reactive transport of nutrients was
also modeled. Some assumptions were made to adjust the concentrations of pollutants in theartificial greywater (Table 3) to values of the components in CW2D. COD in CW2D is divided
into three fractions: readily biodegradable soluble COD (CR); slowly biodegradable soluble

185

COD (CS) and inert soluble COD (CI). It was assumed that CR equals measured BOD5 (Table3). BODu was taken into consideration to determine the CS fraction. BODu can be expected toequal the total amount of biodegradable COD (Ghunmi, 2011). It was assumed that BODu could
be determined from the measured BOD5 by dividing BOD5 with a factor 0.7, according toliterature values (Ghunmi, 2011). The calculation of CR, CS, and CI was thereafter done by:
CR = BOD5
CS = BOD5/0.7-CR
CI = COD-CR-CS

(1)
(2)
(3)

To evaluate the performance of the filters, the efficient % reduction (%red) was calculated foreach parameter with available data by using:%red =

cin − cout
*100
cin

(4)

where cin is the influent concentration and cout is the filter effluent concentration.
3. Results
3.1. Hydraulic Model
When configuring the empirical coefficients, different sets of values of coefficients α, n, and l,gave a broad variety to the outcome of the simulated cumulative flow. The values that were
finally judged to give a good enough fit of simulated data onto the experimental data arepresented in Table 4.
Table 4. Values of empirical coefficients used in the final simulation.
Empirical coefficients
Air entry value, α [cm-1]
Pore size distribution index, n [-]Pore connectivity parameter, l [-]Estimated best fit values
0.06
2.68
1

Observations from the duplicate sand filter showed that there were some variations in thehydraulic behavior between the same type of filters (Figure 1). The simulated cumulative water
flux was deemed as a good enough intermediate fit to the two sets of experimental data, although
the simulated water flux deviated somewhat from the measured flux after the second loading(Figure 1).

186

Figure 1. Cumulative water fluxes: simulated data compared to experimental data from the mainsand filter (SAND1) and its duplicate (SAND2).

3.2. Reactive Transport Model
The simulated heterotrophic bacteria appeared to grow continuously (Fig. 2a) while theautotrophic bacteria appeared to reach a steady state of constant growth after 30 days. The
simulated microorganisms appeared to be concentrated to the top 20 cm of the filter, with thelargest concentrations (17.6 mg COD g-1 DW; 12 µg COD g-1 DW and 13 µg COD g-1 DW forheterotrophic bacteria, Nitrosomonas, and Nitrobacter, respectively) at the very top of the filter(Figure 2b).
From the empirical experiment, the measured values of effluent pollutant concentrations wereconsidered as steady state values. To compare measurements with simulated observations, themean values of the simulated effluent pollutant concentrations were calculated for days 56-113(Table 5). CR, CS, and CI concentrations in the simulated inflow (Table 5) were calculated basedon the concentrations in the artificial greywater (Table 3), according to equations 1-3.

187

Figure 2. (a) Growth of heterotrophic microorganisms at different depths in the filter, 0 cm being
the top of the filter. (b) Amount of microorganisms over a filter depth during day 113 of thesimulation.

Table 5. Simulated and measured mean values of the filter effluent concentrations of pollutants (fromsimulation timespan 56-113 days).
Parameter

Simulated
Measured filter
greywater
effluent
concentrations
concentrations[mgL-1][mgL-1]
CR
425
108
CS
180
46
CI
278
91
COD
885
245
IP
2
0.4
TP
4.2
0.9
NO3N
1
57
NH4N
0.5
4
NO2N*
TN**
75
72
* NO2N was not measured**simulated TN could not be established within the model

188

Simulated filter
effluent
concentrations[mgL-1]
0
0
308
308
0.5
1.2
47
0.1
0
-

Measured%red [%]

Simulated%red [%]

75
74
67
72
83
79
4

99.9
100
65
78
72
79
-

4. Discussion
The simulation of flow dynamics was considered successful since a close fit of simulated andmeasured data was achieved for the cumulative flux. It was demonstrated that calibration of
empirical coefficients α, n, and l was necessary to achieve a good fit. The coefficients werechosen by matching the curves of simulated and measured cumulative fluxes, similar to a studyof the simulation of a subsurface vertical flow constructed wetland for CSO treatment (Dittmer etal., 2005). It is possible that a measured retention curve for the sand used as filter material could
provide further insight on which empirical coefficient values to use (van Genuchten, 1980).
The measurements on the physical filter indicated that the filter operated under pseudo steadystate conditions because the observed concentrations of pollutants in the filter effluent did notvary from day to day. However, the simulations demonstrated constant growth of heterotrophic
microorganisms in the filter (Fig. 2a), which contradicts the observed behavior of the physicalfilter. In order to calibrate the simulated growth of biomass, some quantitative measurements ofbiomass should be performed on the physical filter. A study of microbial biocoenosis has been
carried out on vertical subsurface flow constructed wetlands treating municipal wastewater(Tietz et al., 2006). The result of the study by Tietz et al. (2006) was used further in acomparative study of measured and simulated distributions of microbial biomass in subsurface
vertical flow constructed wetlands (Langergraber et al., 2007). In the study, carried out byLangergraber et al. (2007), different heterotrophic lysis rate constants were varied to fit
simulated data to measured data of biomass, which proved successful. A similar attempt tocalibrate the simulated biomass growth in vertical flow sand filters treating greywater would be asuitable continuation in order to correct the current model.
Regardless of the inconsistency of the constant growth of biomass in the simulations, thesimulated performance matched the performance of the physical filter quite well. The simulated
reduction of COD was 65 % while a 72 % reduction was measured for the physical filter (Table
5). Simulated reduction of phosphorus in the sand filter effluent corresponded well to themeasured reduction: the simulated reduction of phosphorus was 72 %, while the physical filter
achieved a 79 % reduction (Table 5). Also, the simulated effluent concentrations of nitratecompared quite well to the measured values. Almost no reduction (4 %) in total nitrogen took
place in the physical filter, thereby agreeing with the simulated reduction (0 %) (Table 5).
References

Abu Ghunmi, L., G. Zeeman, J. V. Lier, and F. Fayyed, Quantitative and qualitative characteristics ofgrey water for reuse requirements and treatment alternatives: The case of Jordan, Water Science &Technology, 58(7), 1385-1396, 2008.
Dalahmeh, S., M. Pell, B. Vinnerås, L. Hylander, I. Öborn, and H. Jönsson, Efficiency of bark, activatedcharcoal, foam and sand filters in reducing pollutants from greywater, Water Air Soil Pollut.,
Published online: 29 March 2012.
Dittmer, U., D. Meyer, and G. Langergraber, Simulation of a subsurface vertical flow constructed wetland
for CSO treatment, Water Science & Technology, 51(9), 225-232, 2005.

189

Drechsel, P., C. A. Scott, L. Raschid-Sally, M. Redwood, and A. Bahri, A. (eds.), Wastewater irrigationand health: Assessing and mitigating risks in low-income countries, Earthscan-IDRC-IWMI, UK,404, 475-478, 2010.
Ghunmi, L. A., G. Zeeman, M. Fayyad, and J. B. van Lier, Grey water biodegradability, Biodegradation,
22, 163-174, 2011.
Langergraber, G. and J. Šimůnek, Modeling variably-saturated water flow and multi-component reactive
transport in constructed wetlands, Vadose Zone Journal, 4(4), 924-938, 2005.
Langergraber, G., A. Tietz, and R. Haberl, Comparison of measured and simulated distribution of
microbial biomass in subsurface vertical flow constructed wetlands, Water Science & Technology,
56(3), 233-240, 2007.
Molden, D. (Ed), Water for food, Water for life: A Comprehensive Assessment of Water Management inAgriculture, Earthscan/IWMI, p. 11, 2007.
Morel, A, and S. Diener, Greywater Management in Low and Middle Income Countries, Sandec, Eawag,
Switzerland, ISBN: 978-3-906484-37-2, 2006.
Tietz, A., A. Kirschner, G. Langergraber, K. Sleytr, and R. Haberl, Characterization of microbial
biocoenosis in vertical subsurface flow constructed wetlands, Science of Total Environment, 380,
163-172, 2007.
van Genuchten, M. Th., A closed-form equation for predicting the hydraulic conductivity of unsaturated
soils, Soil Science Society of America Journal, 44, 892-898, 1980.
WHO, Guidelines for the safe use of wastewater, excreta and greywater, Vol. IV. Excreta and Greywater
Use in Agriculture, Geneva: World health organization, 2006.

190

Predicting Soil CO2 Dynamics in Arable Land of Andisol in
A Western Suburb of Tokyo
Chihiro Kato1, Taku Nishimura1, Hiromi Imoto1, and Tsuyoshi Miyazaki2
1

Graduate School of Agricultural and Life Sciences, The University of Tokyo, Tokyo, JAPAN,
kato@soil.en.a.u-tokyo.ac.jp
2
Professor Emeritus at the University of Tokyo, Tokyo, JAPAN

Abstract
Recently, carbon capture and storage by soils is recognized as an important function of agricultural fields.
When discussing global warming mitigation such as proper agricultural practices and/or an appropriate
depth of composting in agricultural lands for soil carbon storage, not only CO2 efflux, but also profiles of
CO2 concentrations in soil air are important. In this study, we evaluated the performance of the SOILCO2
model in predicting soil CO2 dynamics, especially CO2 concentrations at various depths in an arable bareland of Andisol. We attempted to experimentally determine two soil parameters required for the CO2
production model, the optimal CO2 production rate and the parameter of a depth-dependent CO2
production function, by measuring CO2 efflux from the surface and a vertical distribution ofconcentrations of dissolved organic carbon, respectively. Soil CO2 concentrations, water contents, andtemperatures were continuously monitored for about a half year at three different depths. Simulated
results were compared with the observed data for model validation. We concluded that the soil parameters
were properly determined, especially for the upper layer, and that the soil CO2 dynamics in the arable
bare land could be well predicted using the SOILCO2 model.

1. Introduction
Soil retains two to three times more carbon (C) than the atmosphere (Sundquist, 1993). Soil is an
important source and sink of C, and soil respiration plays an important role in soil CO2
dynamics. Recently, it has become more and more important and necessary to predict the soil
CO2 dynamics in agricultural lands. Carbon capture and storage (CCS) are recognized asimportant functions of agricultural fields, and the capacity for the C storage of agricultural lands
has been discussed. For example, the application of compost to agricultural fields has been
attempted to increase the C storage in soils (Ministry of Agriculture, Forestry and Fisheries ofJapan, 2008). Effects of various management practices, such as drainage, tillage, and fertilizer
applications on the soil organic C dynamics have been investigated in various parts of the world(e.g., Lal and Kimble, 1997).
When predicting the soil C storage and discussing global warming mitigations such as proper
agricultural practices and/or an appropriate depth of composting in agricultural lands, both CO2
fluxes and profiles of CO2 concentrations in soil air are important. However, most previous
studies dealing with modeling of soil CO2 dynamics have focused on predicting the soil CO2
efflux, and few have evaluated the model performance with respect to simulated profiles of soil
CO2. It is mainly because of the two following difficulties remaining in simulating vertical
distributions of soil CO2 concentrations.

191

First, there is no acceptable way of determining parameters describing the soil CO2 production
and transport. There are many ways to empirically describe the vertical distribution of the CO2
production rate, which varies with land use such as agricultural fields and forests. Uncertainty insoil hydraulic parameters were also said to have strong impact on simulated CO2 dynamics,
because the volumetric water content directly affects the soil respiration rate, and indirectly CO2
diffusion (Buchner et al., 2008).
Second, lack of monitoring data for model validation has been problematic for predicting soil
CO2 dynamics. Validation of models simulating soil CO2 dynamics has been done mainly using
the data of CO2 flux from the soil surface rather than continuously monitored data of CO2 atvarious depths. Recently, a gas permeable resin, which allows gas to pass but excludes liquidwater from outside, has been used to monitor soil gas without disturbing the soil air phase. Katoet al. (2013) reduced the size and improved responsiveness of the CO2 monitoring system toconduct continuous monitoring at various depths.
The purpose of this study is to predict the soil CO2 dynamics, which includes both CO2 fluxes
from the soil surface and profiles of CO2 concentrations in the arable bare land in the western
suburb of Tokyo, using the SOILCO2 module of HYDRUS-1D (Šimůnek et al., 2008). In thisstudy, we tried to experimentally determine two CO2 production parameters dealing with theamount and distribution of the respiratory substrate in soil. Continuous monitoring of soil CO2
concentrations was conducted over half a year to obtain data for evaluating the model
performance. Soil water contents and temperatures were also monitored and simulated results
were compared with observed values.
2. Materials and Methods
2.1. Study Site and Field Monitoring
For model validation, continuous monitoring was conducted at the Institute for Sustainable
Agro-ecosystem Services of the University of Tokyo (ISAS-UT; N 35°44′13″, E 139°32′30″) in
Nishi-Tokyo City, a western suburb of Tokyo, for approximately half a year from 28th Aug.,2010 to 31st March, 2011. The soil between depths of 0 and 35 cm was Kuroboku andisol (soiltexture: Loam), and between depths of 35 and 100 cm was Tachikawa loam andisol (soil texture:
Light Clay). A 10-m2 area was kept bare until the end of the monitoring using weed
management.
Time-domain reflectometry (TDR) sensors (self-made) and copper-constantan typethermocouples were used to monitor soil water contents and soil temperatures, respectively, at
depths of 3, 5, 7, 10, 20, 30, 50, and 80 cm. TDR sensors were connected to the TDR100 Timedomain reflectometer (Campbell Scientific Inc., United States) and both TDR100 andthermocouples were connected to a CR10X data logger (Campbell Scientific Inc., United States)(Kato et al., 2011). Non-Dispersive Infrared type CO2 sensors GMM 221 (Vaisala Co. Ltd.,
Finland) were used for measuring soil CO2 concentrations at depths of 10, 20, and 50 cm. Each
CO2 sensor (GMM221) was sealed in a gas-permeable silicone tube (Kato et al., 2013). These
CO2 sensors were connected to a CR1000 data logger (Campbell Scientific Inc., United States).

192

All data were collected every 20 minutes. CO2 efflux from the surface during daytime wasmeasured with a closed chamber method in both summer (28th Jul., 2011) and winter (20th Dec.,
2010). Meteorological data was obtained from the ISAS-UT and AMeDAS (AutomatedMeteorological Data Acquisition System, Japan Meteorological Agency) weather stations
located in the city of Fuchu, about 10 km south from the experimental field.
2.2. Numerical Models
The SOILCO2 model first calculates soil water flow and heat transport since the CO2 production
is sensitive to both soil water contents and soil temperatures. The governing equation for onedimensional water flow in bare fields is the Richards equation. Heat transport can be describedwith the convection-dispersion equation when the effects of water vapor diffusion are neglected:∂C p T
∂t

=

∂q T
∂ 
∂T 
λ (θ w )  − C w w

∂z
∂z 
∂z 

(1)

where Cp and Cw are volumetric heat capacities of the moist soil and liquid water, respectively. λis the thermal conductivity of the moist soil and qw [L T-1] is soil water flux.
In SOILCO2, the one-dimensional CO2 transport in bare fields can be described as follows:∂ ( caθ a + cwθ w ) ∂
∂c
∂c
∂
∂
θ a Ddif _ s a + θ w Ddisp _ s w + qwcw + P
=
∂t
∂z
∂z ∂z
∂z ∂z

(2)

where ca and cw are the volumetric concentrations of CO2 in the gas and dissolved phase [L3L-3],
respectively, Ddif_s is the effective soil matrix diffusion coefficient of CO2 in the gas phase [L2T1], Ddisp_s is the effective soil matrix dispersion coefficient of CO2 in the dissolved phase [L2T-1],
and θa and θw are the volumetric fractions of air and water [L3L-3], respectively. P is the CO2
production term. The term on the left-hand side of eq. (2) represents changes in the total CO2
concentration in the soil. The first, second, and third terms of the right-hand side correspond to
gaseous soil CO2 flux by diffusion, dissolved CO2 flux by water dispersion, and by convection,
respectively. In this study, convective transport of CO2 in response to the total pressure gradient
was assumed to be negligible compared to diffusion.
The total dissolved CO2 concentration, cw, defined as the sum of aqueous CO2(aq) and H2CO3, isrelated to the CO2 concentration in the gas phase by Henry’s law as follows:(3)

cw = K CO 2 RTca

where KCO2 is the Henry’s law constant [MT2M-1L-2], R is the universal gas constant (=8.314 JKmol-1) [ML2T-2K-1M-1], and T is the absolute temperature [K]. The dispersion coefficient Ddisp_s
and the diffusion coefficient Ddif_s are defined according to Millington and Quirk (1961):

1

Ddisp _ s= Ddisp _ wτ w + λw

qw

θw

= Ddisp _ w

193

θ w7 / 3
p

2

+ λw

qw

θw

(4)

=
Ddif _ s D=
Ddif _ adif _ aτ a

θa7 / 3p2

(5)where Ddisp_w and Ddif_a are the dispersion coefficient of CO2 in the aqueous phase and the
diffusion coefficient of CO2 in the air, respectively, τw and τa are the tortuosity factors [LL-1] inboth phases, respectively. p is the porosity [L3L-3], which is assumed to be equal to the saturated
water content θs, and λw is the dispersivity in the water phase [L].
Soil CO2 in bare fields is assumed to be produced by soil microorganisms. In this study,
respiration by plant roots was ignored.
P = γ s = γ s 0 ∏ f si

(6)i

∏ f = f (z ) f (T ) f (c ) f (h )
si

1

2

3

a

4

(7)

i

where γs [L3L-3T-1] is the CO2 production rate by soil microorganisms, which is calculated as the
reduced optimal production rate γs0 by soil microorganisms for the entire soil profile at 20oC
under optimal water, solute, and CO2 concentration conditions, with the various environmental
factors described by reduction coefficients fsi. In this study, four environmental factors weretaken into account; f1(z) for depth, f2(T) for temperature, f3(ca) for the CO2 concentration or O2
concentration, and f4(h) for soil moisture.
The reduction coefficient for depth, f1(z), represents a profile of the potential CO2 production rateor respiration rate by soil microorganisms when other conditions such as moisture andtemperature are vertically uniform. In SOILCO2, the exponential function is used:
f1 ( z ) = ae − az(8)where a is an empirical constant [L-1]. The exponential function is multiplied by the constant a toinsure that the integral from the soil surface to the infinite depth of the function f1(z) is equal tounity.
The dependence of the soil CO2 production, f2(T), on temperature is described using theArrhenius equation:

 E (T − T20 ) 
f 2 (T ) = exp  RTT20 (9)where f2(T) = 1 when temperature is T20 = 293.15 and K = 20oC. R is the universal gas constant,and E is the activation energy of the reaction [ML2T-2n-1], which was treated as a constant in thisstudy.
In SOILCO2, the impact of O2 deficiency f3(ca) is not described as a function of soil moisture butof the CO2 concentration using the Michaelis-Menten equation:194

f 3 ( ca ) =cb
0.21 - ca=
cb + K M 0.42 - ca - K m*

(10)

where KM is the Michaelis constant [L3L-3T-1] for O2, that is, O2 concentration cb at which theoxygen uptake rate q is equal to 1/2 qmax, which is half of the maximum oxygen uptake rate [L3L3 -1
T ], and K*m is the Michaelis constant for the CO2 concentration. Because f3(ca) is not equal tounity when ca = 0, the value of the optimal production γs0 must be adjusted accordingly (Šimůnek
and Suarez, 1993).
Since SOILCO2 describes the effects of O2 stresses using f3(ca), no reduction in the coefficient,f4(h), occurs even close to saturation:=f 4 ( h) 1=
f 4 ( h)h ∈ (h2 , ∞)log h − log h3
log h2 − log h3(11)h ∈ (h3 , h2 )=f 4 ( h) 0h ∈ (−∞, h3 )where h2 and h3 are the pressure heads when the CO2 production is optimal and when it ceases[L], respectively. More details about the model description can be found in Šimůnek and Suarez(1993).
2.3. Determinations of Parameters2.3.1. Soil Hydraulic and Thermal Properties
The soil profile was divided into three layers based on the soil texture and the dry bulk density;
overlying Kuroboku andisol between 0 and 35-cm depths was subdivided into two layers,“Plowed” for depths of 0~15 cm, and “Hardpan” for depths of 15~35 cm, and underlying“Tachikawa loam andisol” for the soil layer deeper than 35 cm below the soil surface. The
Durner-Mualem model (Durner, 1994) was used for predicting water retention curves andunsaturated hydraulic conductivities for each soil:
Se =

(

)

(

)

θ − θrn −mn −m= w1 1 + αh
+ w2 1 + α 2 hθs − θr

K ( S e ) = K s (w1S e1 + w2 S e 2 ) ×
l

1

1

2

2

(w α [1 − (1 − S ) ] + w α [1 − (1 − S
1

1m m
e1

1

2

2

(w1α1 + w2α 2 )(12)
1 m2 m 2
e2

)

])

2

(13)

where θr is the residual volumetric water content [L3L-3], Ks is the saturated hydraulicconductivity [LT-1], Se is the effective saturation [dimensionless], αi [L-1] , l, mi (=1-1/ni), and ni[dimensionless] are empirical parameters, and wi are weighing factors (i=1,2). These hydraulicparameters in eq. (12) and (13), θr, Ks, αi , l, ni, and wi for “Plowed” and “Hardpan” layers were
determined using an inverse analysis and the evaporation method (Šimůnek et al., 1998). Since

195Kuroboku andisol is highly aggregated and it is difficult to reproduce the behavior of theundisturbed field soil on disturbed repacked soil samples (Kato et al., 2011), undisturbed soilcores sampled from each layer were used for the evaporation experiments.
The saturated volumetric water content, θs, plays an important role in predicting CO2 diffusion
through air-filled pores in a variably-saturated soil. In this study, porosity of the field soil was
assumed to be equal to θs. The modified version of SOILCO2 was used so that we could conduct
calculations using the Durner-Mualem model. Soil thermal properties, i.e., soil thermal
conductivities and volumetric heat capacities of Kuroboku and Tachikawa loam andisols wereobtained from Kato et al. (2011).
2.3.2. CO2 Production and Transport Parameters
Several laboratory experiments have shown that the soil respiration rate positively correlateswith the amount of dissolved organic carbon (DOC) (e.g., Sato and Seto, 1999). In this study, aprofile of the DOC concentration was measured in order to determine the parameter “a” in f1(z),assuming that DOC can represent “readily decomposable organic matter” in soil. Field soil was
sampled at 12 different depths between 0 and 90 cm. DOC of each soil sample was extractedwith deionized water at the soil-water ratio of 1:5 and then the total organic carbon (TOC) of theextracts was analyzed using the TOC analyzer (TOC-VCPH, SHIMADZU Co. Ltd, Japan).
The optimal CO2 production rate by soil microorganisms for the entire profile at 20oC, γs0, wasdetermined based on the measured soil CO2 efflux from the soil surface in the field at daytime on
28th July, 2010, assuming that the rate of the CO2 production of the entire soil profile is equal to
the CO2 efflux. Since the air temperature at that time was about 28oC, the measured value wascorrected for the temperature difference using the reduction function of temperature f2(T) (eq.
(12)) and then divided by f3(ca=0) = 0.91. Other parameters needed to simulate the CO2 transportand production were obtained from Suarez and Šimůnek (1993) and Buchner et al. (2008). In thesimulation, the CO2 production and transport parameters were assumed to be constant through ayear.
2.4. Initial and Boundary Conditions
In the simulation, the soil profile was considered to be 1000 cm deep with a spatial discretizationof 1 cm, assuming that the underlying Tachikawa loam layer was distributed down to 1000 cm.
Since the exact distributions of soil water contents, temperatures, and CO2 concentrations on thefirst day of the simulation period were unknown, initial conditions, at midnight of 1st Jan. 2010,
were determined by a 1-yr preliminary simulation (Kato et al., 2011), assuming that the initial
distribution of the soil water pressure head and temperature for the preliminary simulation was 100 cm H2O and 20oC, respectively. The initial condition for the soil CO2 concentration at thesurface in the preliminary simulation was set at 0.035%, which is the average atmospheric CO2
concentration. The soil CO2 concentration then linearly increased to the measured value at a
depth of 50 cm at 24:00 on 31st Dec., 2010 (=0.45 %). The deeper layer had the same initial CO2
concentrations as those at a depth of 50 cm.

196

Boundary conditions (BCs) for water movement at the soil surface were hourly precipitations
observed at ISAS-UT and daily potential evaporation rates, which were obtained from theMeteoCrop data base (Kuwagata et al., 2011). A free drainage condition was used at the bottomof the soil profile. Continuous surface temperatures, calculated using the sinusoidal function anddaily maximum and minimum soil surface temperatures, were used as the upper BC for heattransport calculations. These temperatures were independently simulated using HYDRUS-1Dver. 4.14 (Šimůnek et al., 2008; Kato et al., 2011). A zero temperature gradient was used as thebottom BC. The upper BC for CO2 transport at the soil surface was the constant CO2
concentration at the atmospheric value of 0.035%. The lower BC was also a zero CO2concentration gradient (Suarez and Šimůnek, 1993; Buchner et al., 2008).
3. Results and Discussion
Estimated water retention curves and unsaturated hydraulic conductivities of each soil layer are
shown in Figure 1.
(b)

(a)

-1

Hydraulic conductivity [cm d ]

0.8
0.7
0.6
0.5
0.4
0.3

Kuroboku (Plowed)

0.2

Kuroboku (Hardpan)

0.1

Tachikawa (Subsoil)

110

1.E+03103
110
1.E+01-1
1.E-0110

1.E-0310-3
1.E-0510-5
1.E-07
10-7

0
100
1000
Suction [cmH2O]

0

10000

0.2
0.4
0.6
0.8
Vol. water content [cm3 cm -3]

1

Figure 1. Estimated (a) water retention curves and (b) unsaturated hydraulic conductivities ofeach soil.
-1

0

2

DOC [μgC
drysoil-1]DOC[μgCg -g-1
dry-soil]
4
6
8

10

0
a=0.10520
Depth[cm]Vol. water content [cm3 cm-3]

0.9

40

Measured
a=0.0460
80
100

Figure 2. Comparison of the measured profile of DOC concentrations and depth-dependentfunctions of CO2 production rates for different a coefficients, f1(z).

197The profile of measured soil DOC concentrations per unit of soil mass is shown in Figure 2. It
decreases with depth from the surface to a depth of 30 cm, and is almost constant in the
Tachikawa loam layer. In Figure 2, the profile of measured DOC was compared with f1(z). Here,
since f1(z) is the normalized function, f1(z) was multiplied by the ratio of measured and calculated
values at a depth of 2.5 cm. Since the parameter “a” in f1(z) is empirical and there is no common
method to determine its value, first, a=0.105, after Suarez and Šimůnek (1993) and Buchner etal. (2008), was employed. In this case, a decrease in f1(z) with increasing depth was more rapid
than expected from the measured DOC profile. Since a smaller “a” gives larger values of f1(z) in
deeper layers, a value of 0.04 was employed as “a” in an attempt to fit the measured DOC.
Again, f1(z) was multiplied by the ratio of measured and calculated values at a depth of 2.5 cm(Fig. 2). When a=0.04, the model described the decrease in the vertical distribution of themeasured DOC profile in the upper 30-cm-thick soil layer well, though the calculated values
were still smaller than measured ones below a depth of 40 cm. In simulations presented in thisstudy, both values of 0.04 and 0.105 were employed as “a” and their results were compared.
Figure 3a shows a comparison of observed and simulated soil water contents at depths of 10, 20,
and 50 cm. Data could not be obtained due to sensor and/or datalogger problems from 22nd Sept.
till 14th Oct., 2010. The model described fluctuations in the soil water content well, reflecting
rainfall and evaporation. Although there was no rainfall for 47 days from 24th Dec., 2010 to 8th
Feb., 2011, except for rains of 0.3 mm on 25th Jan. and 0.1 mm on 27th Jan., 2011, the measured
soil water content at depths of 10 and 20 cm decreased very little, and the model underestimatedthe soil water content during this period. It is possible that air temperatures were below afreezing point and ice occurred in the soil profile, while the SOILCO2 model does not takefreezing and frost into account (Kato et al., 2011).

Figure 3. Comparison of observed and simulated (a) soil water contents and (b) soil temperaturesat depths of 10, 20, and 50 cm.

198

Simulated soil temperatures at depths of 10, 20, and 50 cm are compared with observed data in
Figure 3b. The simulated results agreed with the observed values fairly well. Soil temperatures,
especially those at depths of 10 and 20 cm, were underestimated in winter. The upper boundary
condition for soil heat transport was surface temperature, which was independently calculatedwith the HYDRUS-1D model using the energy balance equation. The underestimation oftemperatures seems to coincide with the underestimation of soil water contents. A lack ofconsideration of the latent heat of freezing and the heat capacity of ice in the heat flow equation
presumably resulted in the underestimation of the soil temperature in winter and thus inputtedsurface temperatures in winter likely led to the underestimation of soil temperatures.
Figure 4 shows a comparison of observed and simulated soil CO2 concentrations at depths of 10,
20, and 50 cm. Daily rainfall depth is also shown. Seasonal changes in CO2 concentrations wereobserved at all three depths in the field monitoring. This seasonal variation was associated withseasonal changes in soil temperature, e.g., soil CO2 concentrations decreased with decreasing soil
temperatures. Observed CO2 concentrations suddenly increased when rainfall occurred. This
could be because the rise in the soil water content following rainfall events (Fig. 3a) enhanced
activities of microorganisms and decreased the diffusion coefficient (Kato et al., 2013). The
model could describe these seasonal variations and responses to rainfall well.
When the experimentally determined value of 0.04 was employed for a in f1(z), simulated results
agreed well with the observed soil CO2 concentrations at both depths of 10 and 20 cm, while themodel underestimated soil CO2 concentrations at a depth of 20 cm when a literature-based
a=0.105 was used.

Figure 4. Comparison of observed and simulated soil CO2 concentrations at depths of 10, 20, and50 cm.

199

The CO2 concentration at a depth of 50 cm was overestimated when the experiment-based
a=0.04 was employed. This result suggests that the CO2 production from the soil layer below 50
cm may be smaller than that expected from the DOC distribution. Not only the quantity of DOC,
but also its quality may determine the respiration rate by soil microorganisms. Boyer and
Groffman (1996) investigated the vertical distribution of the water extractable DOC (WEDOC)
and biodegradable DOC (BDOC). They showed that WEDOC diminished with depth and,furthermore, the percentage of BDOC to the total WEDOC pool decreased with depth. Wagai
and Sollins (2002) compared the biodegradability of WEDOC and leachable DOC in forest soils,
and their results suggest that the leachable DOC was not always labile. In the experimental field,
some of DOC in the deeper layer must have been leached from the surface layer and less labile,and thus the CO2 production rate of deeper soil is small.
4. Conclusions
In this study, we evaluated the performance of the SOILCO2 model in predicting soil CO2
dynamics, especially soil CO2 concentrations at various depths in arable bare land. For thesimulation, we have tried to experimentally determine two parameters that are related to therespiratory substrate of the soil. The optimal CO2 production rate, “γs0” was determined using theCO2 efflux from the soil surface measured during the summer season. The parameter of the depth
dependent coefficient, “a”, which describes a profile of respiratory substrate, was determinedfrom a measured profile of the dissolved organic carbon (DOC). For the model validation, thesoil CO2 concentrations, soil water contents, and soil temperatures were continuously monitored
for approximately half a year at three different depths. Seasonal and daily changes in soil watercontents and soil temperatures, which both affect the production and transport of soil CO2, were
well described with the SOILCO2 model. Simulated behavior of the soil CO2 concentration, suchas seasonal variations and responses to rainfall, agreed well with the observed values, especiallyin upper layers.
The model tended to overestimate the soil CO2 concentration in deeper layers when an
experiment-based parameter “a” was employed, although soil water contents and temperatures
were properly predicted. It may be because labile DOC tends to degrade rapidly and some of the
DOC present in deeper layers could have been leached from the surface and not highly labile.
We concluded that the soil CO2 dynamics in arable bare land could be predicted well using the
SOILCO2 model. To improve simulation results of CO2 concentrations, especially in deeper
layers, it may be necessary to consider the relationship between the water extractable DOC(WEDOC) and the biodegradable DOC (BDOC) in soil.
Acknowledgement
This study was partly supported by JSPS Research Fellowships for Young Scientists andResearch Program on Climate Change Adaptation (RECCA) of Ministry of Education, Culture,
Sports, Science and Technology. We appreciate Mr. S. Hatano, Mr. H. Kubota, and Mr. K.
Yatsuda of ISAS-UT for their help in using the field and meteorological data. We would also
like to thank Prof. Šimůnek for his help in using a modified version of the SOILCO2 program.

200

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202

Flow at Low Water Contents: A Simple Approach for Inverse
Estimation of van Genuchten-Mualem Soil Hydraulic Parameters
Marcel Bawindsom Kébré1,2, Fabien Cherblanc1, François Ouédraogo2,
Jean-Claude Bénet1, and François Zougmoré2
1

LMGC, CNRS, Université Montpellier 2, Place Eugène Bataillon 34000 Montpellier, France,
mkebre@hotmail.com
2
LAME, UFR-SEA, Université Ouagadougou, Avenue Charles de Gaulle 03 BP 7021, Burkina Faso

Abstract
The unsaturated soil hydraulic properties (the soil water characteristic and relative permeability curves)
are key hydrodynamic parameters in the fields of soil science and civil engineering. Because of the strong
dependency of these properties on water content, their determination is subject to considerable
experimental and numerical problems. Difficulties increase when the soil approaches oven-dry
conditions, a situation often encountered in arid and semi-arid areas. Moreover, computational costs of
estimating the hydrodynamic properties can be relatively high also. After a short review of alternativemodeling approaches for the hydraulic functions from saturation to oven-dryness, we present atheoretical-numerical approach, along with a relatively simple, robust and inexpensive experimental
method for inverse determination of van Genuchten/Mualem soil hydraulic parameters. For gravimetricwater contents greater than 0.04, numeral results agreed well with experimental data, while somediscrepancies were observed at very low water contents.

1. Introduction
The process of water flow in soils has been the focus of intensive research in the fields ofagronomy, hydrology and geomechanics. The amount and energy status of water in a soil canaffect considerably the soil hydraulic properties. While knowledge of the two extreme states ofwater in a soil (saturated and very dry conditions) seems well advanced, the unsaturated state atmedium to low water contents deserves further investigation. This condition is usuallyencountered in soil surface layers where strong interactions occur between soil and roots,
microorganisms or building foundations. In arid and semi-arid zones, precise knowledge ofphysical flow processes at low water contents would allow development of more effective tools
for water resources management.
The Richards equation is commonly used to describe water flow in the unsaturated zone of soils.
Other formulations based on thermodynamics (Fremond and Nicolas, 1990) and/or thethermodynamics of irreversible processes (Bénet, 1981) lead to similar equations. Application ofthese equations in all cases requires initial and boundary conditions, as well as relationships
between the gravimetric or volumetric water content (w in kg.kg-1, and θ in m3.m-3, respectively)
and the water flow rate. One can show that the suction or matric potential ψ (in Pa) and thematric head h (in m), both widely used in soil hydrology, are closely related to the chemical
potential μ (J.kg-1) (Bénet et al., 2012). The relationship between matric potential, chemical203

potential and matric head is given by μ=ψ/ρw=gh, where ρw is the density of water, taken as 1000
kg.m-3, and g the acceleration of gravity (m.s-2). These relationships reflecting the soil hydraulicproperties are conventionally expressed using two functions, namely the water retention function
denoted by w(μ) and the hydraulic conductivity function K(μ) or K(w). Additional processes may
be included in the flow equation such as liquid-gas phase change (or evaporation), which isimportant especially in arid regions.
All of the above functions and processes must be known from saturation to oven-dry conditions
where measurements are especially challenging (Sakai et al., 2009). Physical and technicaldifficulties include possible cavitation of tensiometers (limiting their use up to about 80 J.kg-1)
and lack of continuity in the liquid phase of the soil when a saturated porous plate is used beyond
500 J.kg-1 (e.g., using the axis translation procedure as implemented by Baker and Frydman,2009). In addition, acquisition of the data can be very time consuming and costly. For thesereasons most studies are limited to situations between saturation and some intermediate state ofsoil water, corresponding to the range of operation of the most common experimental devices(Sakai et al., 2009; Fujimaki and Inoue, 2003; Fujimaki et al., 2004).
Inverse methods are now increasingly used to identify the hydraulic properties of unsaturated
porous media. They offer a very flexible approach by allowing a range of numerical optimization
algorithms (e.g., Levenberg-Marquart, conjugate gradient methods, genetic algorithms and neuralnetwork approaches). In soil hydrology, the approach generally used for inverse problems issolution of the Richards equation in conjunction with some infiltration/drainage orevaporation/condensation experiment (Durner et al., 1999; Fujimaki et al, 2004; Peters andDurner, 2008; Schindler et al., 2010; Sakai et al., 2009). A major difficulty of inverse problems is
to find analytical or empirical models that accurately represent the hydraulic properties at very
low water contents.
In this paper, we first review the problem of obtaining accurate descriptions of the soil hydraulicproperties (the soil water characteristic and relative hydraulic conductivity curves) over the fullrange of water contents, but especially at relatively low water contents. The soil water
characteristic curve is a representation of the relationship between soil water suction and watercontent. For suction ψ (Pa), we prefer to use the equivalent concept of water chemical potential μ(J.kg-1), which provides a link between the physics of water in porous media andthermodynamically open systems. We next propose a theoretical-numerical model for isothermal
water flow, which will be used in the inverse problem formulation. The selected state variables
are the gravimetric water content, w, and the water vapor pressure, pv. A simple, robust and very
cheap experimental method for the inverse determination of the soil hydraulic properties is thenpresented. The soil hydraulic functions in this study are based on the van Genuchten model(1980) for the soil water characteristic and the van Genuchten (1980) - Mualem (1976) model forthe unsaturated hydraulic conductivity. The ROSETTA code (Schaap et al., 2001) is further used
to provide initial estimates of the model parameters. Various scenarios with regard to the residual
water content, wr, Mualem’s tortuosity parameter, L, and the saturated hydraulic conductivity,
Ksat, will be simulated and discussed.

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2. Characterization of Soil Hydraulic Properties at Low Water Contents
2.1. The Soil Water Characteristic
Despite the relatively small amounts of water retained, accurate representation of soil water
characteristic curves at the dry end is important for modeling biological processes including plantwater uptake and microbial activity in arid environments (Tuller and Or, 2005). Accurate
measurement over the full range of water contents is a delicate task. Most or all methods formeasuring the water potential have limitations, especially at intermediate and very low values of
the water content (its pendular and hygroscopic states). Very often the curve is completed byextrapolation, which can lead to instabilities in numerical codes (Lu et al, 2008). Experimental
methods (infiltration and/or drainage, evaporation and condensation) associated with inverse
problems also suffer from shortcomings, including in the instrumental devices, and are mostly
robust only at the higher water contents (i.e., the funicular state) where the liquid phase iscontinuous. All this raises the question of the validity at low water contents of the matric head water content relationship, h - θ, usually a key function to describe the physics of unsaturated
flow. Indeed, this range of the water content comprises the pendular state where the liquid andvapor phases presumably are discontinuous, and the hygroscopic state where only the gas phaseis continuous, while water is being strongly adsorbed onto the solid phase. This is why we prefer
the use of the water chemical potential to describe the movement of water in all of its states. Oneof the fundamental properties of the chemical potential stipulates that at local thermodynamic
equilibrium, the potential of a component present in two phases should be the same (Callen,1985). Experimentally well-defined methods (e.g., Bénet et al., 2012) should apply to allimportant parts of the soil water characteristic curve, from saturation to oven dryness.
The models most commonly used in the literature to represent the soil water characteristic curve(Brooks and Corey, 1964; van Genuchten, 1980) often fail to reproduce experimental data at very
low water contents (Sakai et al., 2009). Many researchers therefore developed new models or
extended existing models to the full range of water contents. Campbell and Shiozawa (1992)
used data at very high chemical potentials (in absolute value) to establish an equation reflecting
the phenomenon of water adsorption on the surface of particles in the soil matrix. They modified
the model of van Genuchten (1980) to improve the calibration of data at low water contents. The
adsorption equation (Campbell and Shiozawa, 1992) was used later also by others (e.g., Fayer
and Simmons, 1995; Khlosi et al., 2006) as an additional correction to the classical models at the
low water contents. Fredlund and Xing (1994) opted for a different mathematical expression tobetter fit experimental data in this range. Junction models are now also available (e.g., Rossi and
Nimmo, 1994; Webb, 2000; Zhang et al., 2011). Recent evaluations have highlighted thestrengths and weaknesses of the various models. For example, Sillers and Fredlund (2001) notedthat the Fayer and Simmons (1995) correction of van Genuchten’s (1980) soil water
characteristic model with m = 1.0 gave excellent results for about 200 soils from the USDA
database over the entire range of moisture contents, while avoiding the controversial concept ofresidual water content. Using data from 137 soils of the UNSODA database, Khlosi et al. (2008)
compared eight analytical models describing the complete soil water characteristic curve. They
found that the model of Khlosi et al. (2006) with four fitting parameters was most consistent forsoils covering a broad range of densities, organic matter contents and textures.

205

2.2. The Unsaturated Hydraulic Conductivity
Unlike the soil water characteristic curve, very few studies have been devoted to the hydraulicconductivity over the full range of water contents (Zhang, 2011). One problem involves thephysical processes that govern the flow of water at low water contents. While capillary models
based on theories by Purcell (1949), Childs and Collis (1950), Burdine (1953), Kunze (1968) and
Mualem (1976) for estimating the unsaturated hydraulic conductivity are generally fairly accurate
at high water contents, they often underestimate the permeability at low water contents (Sakai etal. 2009). Hydraulic conductivity expressions that have been validated over the full range ofwater contents often are relatively complex and sometimes difficult to use within an inverse
optimization program. As for the physical flow phenomena at low water contents, Tuller and Or(2001), Peters and Durner (2008) and Zhang (2011) use the concepts of film flow at low watercontents to establish hydraulic conductivity models over the full range of water contents. The
model of Tuller and Or (2001) is mathematically very complex and not easily associated with oneof the classical models for the soil-water characteristic curve. Those of Peters and Durner (2008)
and Zhang (2011) add an extra term accounting for capillary flow according to the theories of
Mualem (1976) and Burdine (1953), and another term describing film flow around solid particles
in the soil matrix. However, some of these models remain very complex, especially when used in
an inverse procedure.

3. Theoretical-Numerical Model for Water Flow in Arid Soils
A natural soil can be idealized as a triphasic porous medium by considering a solid, a liquid and agaseous phase, with the gaseous phase consisting of two components: dry air and water vapor.
From an experimental point of view, appropriate state variables for water flow modeling are thegravimetric water content, w, defined as the ratio between the apparent mass densities of liquid,ρl, and solid ρs (i.e., w= ρl/ρs), and the vapor partial pressure of the gas phase, pv (Pa) linked tothe apparent density of vapor, ρv, through the ideal gas law:
pv =

ρ v RT
φg M w(1)

where R (J.kg-1) is the ideal gas constant and Mw (kg.mol-1) the molar mass of water. The volume
fraction of the gas phase φg is related to the water content w by:

φg =

Vg
V

= 1−

ρs
ρ
− w s*
*
ρs
ρl

(2)

Three elementary processes are considered: liquid flow governed by capillary and gravity effects,
vapor diffusion in the gas phase, and liquid-gas phase changes of water. The main assumptions
are that the temperature is uniform and constant, the solid skeleton is rigid, the total gas pressure
is constant and uniform, and hence also that convective flow in the gas phase is negligible.

206

Fundamental mass balance equations for water in liquid and gas phases are then written as:∂w+ ∇.(ρ l v l ) = − ρˆ∂tMw ∂(φ g pv ) + ∇.J v = + ρˆ
RT ∂t

ρs

(3)
(4)

The liquid filtration flux, denoted by ρ l v l in Equation (3) is described with Darcy's law extended
to unsaturated conditions. Extension of the above description to very low water contents isquestionable since the concept of liquid pressure is meaningless (Nitao and Bear, 1996). An
alternative proposed by Bénet et al. (2012) is to rely on the chemical potential, which is definedover the full range of water contents. This thermodynamic potential is a function of the watercontent described by the soil-water retention curve obtained by merging measurements usingclassical tensiometry and sorption isotherms. Therefore, water flow can be governed by theequation:ρ l v l = − K sat k rρ l*g(∇µ l − g )(5)where µl (J.kg-1) is the mass chemical potential of liquid water, g (m.s-2) is the gravity
acceleration vector, kr is the relative permeability function and Ksat (m.s-1) the hydraulicconductivity at saturation. The mass density of water ρ l* is taken to be 1000 kg.m-1.
The vapor diffusion flux, denote by Jv in Equation (4), is classically described using a first-order
Fick's law of the form:
J v = Dvs ∇ρ v*(6)

in which Dvs is the effective vapor diffusion coefficient in the soil:
Dvs = τφ g Dva(7)

where τ is the tortuosity, which can be described using functions given by Penman (1940),
Millington and Quirck (1961) or Moldrup et al. (1997), and Dva the free diffusion coefficient ofvapor in air. Standard correlations give a value of 26.1 × 10-6 m.s-2 for Dva at 30°C.
From thermodynamic considerations of liquid-gas phase changes, it can be shown that thevolumetric rate of phase change is proportional to the chemical potential difference of water
between the liquid and vapor states. A detailed theoretical development of this phase change has
been given by Bénet et al., (2009).

207

The nonlinear equations (3) and (4) are strongly coupled through the phase change term ρ̂ , aswell as through the soil physical characteristics that depend on the water content: φg(w), Dvs(w),and kr(w). The governing equations were discretized using a finite-volume formulation on a onedimensional regular mesh, with the unknowns w and pv located at the center of grid blocks. A
first-order upstream scheme was used to describe the convective term appearing in liquid massbalance Equation (3). Temporal integration was performed based on a fully implicit scheme toensure numerical stability. Nonlinearities were dealt with by using a Newton-Raphson method
which produced accurate convergence with relatively moderate time steps.

4. Materials and Methods
4.1. Morphological Characteristics and Soil Moisture
The material under investigation is a natural soil from Nasso, Burkina-Faso. The soil sample wastaken from the top layer of soil (0-30 cm depth). The analysis by dry sieving after washing(standard NF P94-056) for particles having diameters greater than 80 µm and a sedimentation
analysis (standard NF P94-057) for smaller particles, indicated that the soil contained 95% sand,
2% silt and 3% clay (USDA classification). Soil texture is hence sand. The dry soil density
measured at the site gave an average value of 1688 kg.m-3. Points of the soil water characteristic(desorption data) were obtained by combining two methods: using a pressure plate apparatus atconstant temperature (30°C) for water in the funicular state (saturations up to μ = -500 J.kg-1) anda desorption device (using saturated solutions at equilibrium) to complete the curve in thehygroscopic state (from -5000 to -3× 105 J.kg-1). Figure 1 shows the measured data as well as therelationship between the chemical potential and the water content based on the model of van
Genuchten (1980) as identified using the RETC code of van Genuchten et al. (1991).

Figure 1. Measured and fitted soil water characteristic curves (gravimetricwater content, w, as a function of the chemical potential, μ).

208

4.2. Measured Water Content Profiles
The objective of the experimental study was to establish profiles of water content in a
homogeneous soil column. The upper half of the PVC column used for this purpose (20 cm highand 7.5 cm inner diameter) was packed with soil having a desired initial gravimetric watercontent of 0.06, and the lower half with soil having a gravimetric water content of 0.02. Bothparts of the column were compacted to the field-measured dry density. The sealing ends of thecolumns were coated with a thick plastic film. Crafted columns were stored in a thermo-regulatedchamber. Evaporative phenomena were negligible. The mass of the column was assumed to beconstant. The experiment consisted in a redistribution of water on both sides of the interface dueto the gradient of the moisture content (or chemical potential). A destructive method was used formeasurement of gravimetric water contents by weighting after oven-drying at 105°C for 48
hours. The soil columns for this purpose were sliced using a mechanical device to determine the
distributions of the water content along the column at given time intervals. The mechanicaldevice permitted slices of soil of only 5 mm thick. Ideal conditions of the experiment were suchthat only the physical phenomenon of water flow in the column occurred (e.g., flow of water inthe liquid phase from the top part). Phase changes could be neglected since air within the column
was presumably saturated.
4.3. Inverse Analysis
The inverse analysis was based on solutions of the theoretical model given by Equations (3) and(4) using a nonlinear Newton-Raphson method. The chemical potential as a function of the watercontent was described using the model van Genuchten (1980) and the relative permeability
function using the van Genuchten (1980) - Mualem (1976) equation as follows:
S=
e

n −m
w( µ ) − wr 
= 1 + ( αµ ) wsat − wrm) S eL 1 − (1 − Se1/ m ) kr ( Se=



2

(8)
(9)

where wr and wsat are the residual and saturated gravimetric water contents, respectively, α (> 0 in
kg.J-1), n (> 1) and L are fitting parameters, m=1-1/n as suggested by van Genuchten and Nielsen(1985), and Se is effective saturation. In this study we selected the above original van Genuchten
equations rather than the complicated modified expressions advocated by Schaap and van
Genuchten (2006).
Two minimization programs were used next in the inverse analysis to find optimal hydraulicparameter values based on obtaining the minimum average squared difference between measured
and calculated values: one based on the Levenberg-Marquardt (1963) algorithm, and anotherusing the Nelder-Mead Downhill Simplex method (Nelder and Mead, 1965). All optimizations
produced a value of zero for the residual water content (wr = 0), while the saturated watercontents wsat was fixed at 0.208 kg.kg-1 as estimated from the measured porosity of the soil.

209

Since laboratory saturated permeability tests (rigid-wall or flexible-wall permeameters) often
show considerable errors (e.g., Chapuis, 2012) with predicted values sometime deviating
considerably from measured values due to macroporosity or other effects (Schaap and Leij, 2000;
Schaap and van Genuchten, 2006), we decided to keep Ksat as a free (adjustable) parameter in the
inverse analysis.
Table 1. Assumed optimization scenarios and imposed parameter constraints
Scenario
S1
S2
S3
ROS

Free parameters
Ksat (m.s-1)
n, m, Ksat (m.s-1)
Ksat (m.s-1)
α, n, Ksat (m.s-1)

Fixed parameters
wr = 0, α, n, m = 1-1/n, L = 0.5
wr = 0, α, L = 0.5
wr = 0, α, n, m = 1-1/n, L = -6.5
wr = 0, L = 0.5

Lower bond
10-10n>1, m>0
10-10
-//-

Upper bound10-3
n<10, m<1
10-3
-//-

Several optimization scenarios were considered as summarized in Table 1. Scenario S1
corresponds to an optimization of the saturated permeability (Ksat) with the model parameters
w(μ) deduced from the fitted soil water characteristic curve in Figure 1. Scenario S2 consideredboth m and Ksat, to be the optimization parameters. The parameter m in Equation (9) is in thatcase independent of n in Equation 8. In a third scenario, S3, following the work of Schaap andLeij (2000), Peters et al. (2011), Peters and Durner (2008) and Zhang (2011), we fixed L at anegative value (-6.5) and focused on the optimization of Ksat. The other parameters kept thevalues associated with Figure 1. In a fourth scenario, denoted ROS, we optimized all parametersof Equations 8 and 9. The initial values were estimated from textural properties and the density
using the ROSETTA code (Schaap and al., 2001). Parameter constraints were further introduced
to ensure realistic physical descriptions of the hydraulic functions. Inspired by the work of van
Genuchten and Nielsen (1985); Ippisch et al. (2006) and Peters et al. (2011), we used thefollowing constraints: 1<n<10, 0<m<1, and 0<α<15. Following Schaap and Leij (2000) and
Schaap and van Genuchten (2006), we further imposed the constraint 10-10<Ksat<10-3 on thesaturated hydraulic conductivity of our sandy soil.
5. Results and Discussion
Table 2 summarizes the estimated values for optimization scenarios (S1, S2, S3, ROS), including
values of the Root Mean Square Error (RMSE). Figures 2 and 3 show the experimental andsimulated profiles according to the scenarios presented in Table 1. Figure 2 is for scenario S1,
while Figure 3 shows results for all scenarios at different times (1, 3, 5 and 13 days).
Table 2. Optimized values of van Genuchten/Mualem model parameters.
αnkg.J-1
S1
0.95271.3922
S2
0.95271.3922
S3
0.95271.3922
ROS
13.1034
1.0 *+minimum limit imposed*
minimum limit imposed, nopt = 0.86735
Scenariom
1- 1/n0.62881- 1/n1- 1/n

210

Ksat
m.s-1
3.6946.10-5
2.3698.10-7
10-10 +
4.3277.10-5

RMSE
0.002652
0.002068
0.006482
0.002286

Figure 2. Experimental and simulated water content profiles for scenario S1.

Figure 3. Experimental and simulated water content profiles for optimization scenarios
S1, S2, S3, and ROS at different times (1, 3, 5 and 13 days).

211

The results presented in Table 2 and Figures 2 and 3 show that the inverse analysis inconjunction with the assumed numerical model (section 3) leads to a good match with theexperimental data. The inverse procedure based on the Levenberg Marquart method was found to
be quite robust by producing unique solutions. The computational time depended on the numberof parameters to be optimized and the invoked initial values. The Nelder-Mead method (1985),
on the other hand, was found to be very time-consuming.
Except for case S3, all scenarios using the van Genuchten model for w(μ) and the van
Genuchten-Mualem model for the unsaturated hydraulic conductivity accurately described theflow of water at relatively high water contents. Below 0.03, however, significant discrepancies
are apparent in Figure 2. When the parameter n of Equation 8 was optimized along with m (kept
independent of n) and Ksat (i.e., scenario S2), the inverse analysis gave the best results in terms ofyielding the lowest value of RMSE. However, the optimized value for Ksat (2.3698 × 10-7 ms-1)
was very small compared to typical values for a sandy soil, as can be observed in the work of
Schaap and Leij (2000). Taking into account the textural properties of the soil, optimizing allparameters (α, n, m = 1-1/n, Ksat) and using initial estimates provided by ROSETTA (Schaap etal., 2001) produced excellent results (RMSE = 0.002286). This case may well prove the mostpromising for characterizing the hydraulic properties of unsaturated soils. The cost of the method
is very small considering the simplicity of the experimental method, including the use of initial
estimates as predicted with ROSETTA from soil texture.
Optimizing Ksat according to scenario S3 produced the lowest value of the saturated hydraulicconductivity (Ksat = 10-10 ms-1), while only a fair match was obtained at the lower water contents.
This case also failed to reproduce the observed gradients in the moisture profile in the centre of
the column at intermediate water contents.
6. Conclusion
Determining the unsaturated soil hydraulic properties at very low water contents is still a major
challenge. Existing numerical and experimental methods have many limitations in the very dry
range. The theoretical model we proposed in this paper is based on the chemical potential, which
provides a fundamental thermodynamic link between the physics of water flow in porous media
and the thermodynamics of open systems. A numerical inverse procedure was developed to
identify the parameters associated with the models of van Genuchten (1980) for the soil-water
characteristic curve and the van Genuchten (1980) - Mualem (1976) formulation for theunsaturated hydraulic conductivity. Experimental water content profiles were obtained using avery simple experimental setup. The optimized parameters remained within their physical limits,in agreement with literature values. They closely described the results as shown by relatively
small RMSE values. However, discrepancies were still observed at very low water contents. An
alternative is to rely on the general model of van Genuchten and Nielsen (1985) with independentm and n values, which gives more flexibility to match the experimental results in the low watercontent range

212

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214

Estimating Saturated Hydraulic Conductivity from Surface
Ground-Penetrating Radar Monitoring of Infiltration
Emmanuel Léger1, Albane Saintenoy2, and Yves Coquet3
1

Université Paris Sud, UMR8148 IDES, Orsay, France, emmanuel.leger@u-psud.fr
Université Paris Sud, UMR8148 IDES, Orsay, France, albane.saintenoy@u-psud.fr
3
Université Orléans, ISTO/OSUC.,Orléans, France, yves.coquet@univ-orleans.fr

2

Abstract
In this study we used Hydrus-1D to simulate water infiltration from a ring infiltrometer. We generated
water content profiles at each time step of infiltration, based on a particular value of the saturated
hydraulic conductivity while knowing the other van Genuchten parameters. Water content profiles wereconverted to dielectric permittivity profiles using the Complex Refractive Index Method relation. We thenused the GprMax suite of programs to generate radargrams and to follow the wetting front using arrival
time of electromagnetic waves recorded by a Ground-Penetrating Radar (GPR). Theoretically, the depthof the inflection point of the water content profile simulated at any infiltration time step is related to thepeak of the reflected amplitude recorded in the corresponding trace in the radargram. We used thisrelationship to invert the saturated hydraulic conductivity for constant and falling head infiltrations. We
present our method on synthetic examples and on two experiments carried out on sand. We further
discuss the possibility of estimating two other van Genuchten parameters, n and α, in addition to thesaturated hydraulic conductivity.

1. Introduction
Soil hydraulic properties, represented by the soil water retention θ(h) and hydraulic conductivity
K(h) functions, dictate water flow in the vadose zone, as well as partitioning between infiltration
and runoff. Their evaluation has important implications for modeling available water resources
and for flood forecasting. It is also crucial in evaluating the soil capacity to retain chemical
pollutants and in assessing the potential for groundwater pollution.
The determination of parameters defining the van Genuchten soil water retention function (vanGenuchten, 1980) is usually done using laboratory experiments, such as the hanging watercolumn (Dane and Hopmans, 2002). On the other hand, the hydraulic conductivity can be
estimated either in the laboratory, or in situ using infiltration tests. Among the large number ofexisting infiltration tests (Angulo-Jaramillo, 2002), the single (Müntz et al., 1905) or double ring
infiltrometers (Boivin et al., 1987) provide the field saturated hydraulic conductivity by applying
a positive pressure on the soil surface, while the disk infiltrometer (Perroux et White, 1988;
Clothier and White, 1981) allows for reconstruction of the hydraulic conductivity curve byapplying different pressures smaller than or equal to zero. For infiltration tests, the volume of
infiltrated water versus time is fitted to infer the soil hydraulic conductivity at or close tosaturation. These tests are time-consuming and difficult to apply to landscape-scale forecastingof infiltration. Furthermore, their analysis involves various simplifying assumptions, partly due
to the ignorance of the shape of the infiltration bulb.

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Geophysical monitoring methods, mainly electrical (Battle-Aguilar et al., 2009) andelectromagnetic methods, have been carried out during the infiltration process. Among them, theGround-Penetrating Radar (GPR) is based on electromagnetic (EM) wave propagation. It ishighly sensitive to variations in water contents, which are directly related to the dielectric
permittivity (Huismann et al., 2003). This method thus appears to be an accurate tool formonitoring the wetting front movement during infiltration (Saintenoy et al., 2008).
2. Methods
We studied infiltration of a 5-cm thick water layer inside of a single ring infiltrometer in a sandy
soil. The schematic of the apparatus is presented in Figure 1. The single ring infiltrometer is a 1mm thick aluminum cylinder of a 60-cm diameter, approximately 20-cm high, buried in the soil
to a depth of 10 cm. We set up a GPR antennae (namely the transmitter T and the receiver R) at a
variable distance from the edge of the cylinder, labeled x in Figure 1. In all of our field
experiments, we used a Mala RAMAC system with antennae centered on 1600 MHz, shielded at
the top. We then covered the inner part of the cylinder with a plastic waterproof sheet. The
plastic sheet allowed us to fill the cylinder with water and create an initial 5-cm thick waterlayer, while preventing infiltration into the sand before starting data acquisition. The beginningof the acquisition was launched by pulling away the plastic sheet to trigger water infiltration. The
GPR system was set to acquire a trace every 10 s. With this apparatus, we performed two typesof infiltration: i) a falling head infiltration consisting of pulling away the plastic sheet andleaving water to infiltrate into the sand freely with no additional refill, and ii) a constant head
infiltration, when water was continuously added to the ring to maintain a 5-cm thick water layer
during the infiltration experiment. In the following examples we will show how we can use the
GPR data acquired every 10 s during the infiltration experiment to estimate the saturated
hydraulic conductivity.

Figure 1. Schematic of the apparatus at its initial state.

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3. Falling Head Infiltration
3.1. Numerical Example
3.1.1. Forward Modeling
The falling head infiltration experiment was simulated using Hydrus-1D (Šimůnek et al., 1996,
2008; Šimůnek and van Genuchten, 1996). The soil profile was 50 cm deep, was assumed to behomogeneous, and was divided into 1001 layers. To describe the soil hydraulic properties of themedium, we used the van Genuchten-Mualem (van Genuchten, 1980) hydraulic conductivity andwater retention functions, which require 5 parameters, namely the saturated water content, θs, theresidual water content, θr, two fitting parameters, α and n, and the saturated hydraulicconductivity, Ks. For our numerical example, we set θs=0.43, θr=0.07, α=0.019 cm-1, n=8.67, andKs=0.120 cm/min. We used an atmospheric boundary condition (BC) with no rain and noevaporation at the soil surface and a free drainage BC at the bottom. To simulate the 5-cm layerof water, the initial condition was set to a 5 cm pressure head in the top node. We simulated thefirst 10 minutes of the experiment with a time step of 10 s, i.e., with 60 water content snapshots.
Using the CRIM relation (Birchak et al., 1974; Roth et al., 1990), each water content snapshot
was converted to permittivity profiles (made of 1001 points), considering a three-phase media:
sand (considered as pure silica), water, and air. Each one of these permittivity profiles (Fig. 2a)
were the input for the GprMax2D program (Giannopoulos, 2004), based on finite difference time
domain modeling, the output of which is one simulated GPR trace acquired at the antenna
position (set at the surface of the medium, in the middle with X=0.3 m in Fig. 1). The simulated
GPR monitoring of the infiltration process is shown in Figure 2b. The horizontal axis is thenumber of traces simulated by GprMax2D, two traces being separated by 10 seconds, as Hydrus1D profiles are. The vertical axis is the Two-Way Travel time (TWT) of the EM wave amplitude
coming back to the receiver.
On the profile presented in Figure 2b, we denote one particular reflection, labeled A. Its arrival
time is increasing as the wetting front moves deeper. This reflection is interpreted as comingfrom the wetting front. The reflections labeled A' and A'' are primary and secondary multiples ofreflection A. The reflection labeled B is the wave traveling in the air directly between the twoantennae. After the 40th trace, the 5-cm layer of water has been infiltrated and drainage isstarting. As a consequence, the permittivity of the upper part of the medium decreases. The EM
wave velocity is inversely proportional to the square root of permittivity (Huisman et al., 2003).
Then the TWT of the reflection A increases more slowly, creating a change of slope in thereflection time curve (Fig. 2b). In Figure 2c, we display two curves: the TWT of the maximum
peak of a reflection A (obtained from Fig. 2b) and the TWT calculated by a ray-path algorithm,
going from the GPR antennae to the inflection point of ε(z) curves (indicated by crosses in Fig.
2a), as proposed by Saintenoy and Hopmans (2011). We attribute the difference between thesetwo curves to some numerical dispersion of the signal, a problem that we will address later.

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3.1.2. Inversion
We used the TWT obtained from the radargram of Figure 2b as data to be fitted to derive thesaturated hydraulic conductivity, assuming the other 4 parameters are known. Using Hydrus-1D,
we generated 60 water content snapshots using the saturated hydraulic conductivity in the range
from 0.01 to 1 cm/min, with a step of 0.001 cm/min. For each value of Ks, we calculated the
TWT by the ray-path algorithm from the surface to the inflection point of the ε(z) curves. We
computed the Root Mean Square Error (RMSE) between these times and the data. The RMSE
was minimized for Ks=0.129 cm/min, which is higher than the value used for simulating the data,i.e., Ks=0.120 cm/min.

Figure 2. Falling head infiltration from a 5-cm thick water layer. a) Permittivity profiles: eachcurve is plotted every 10 s; crosses represent the inflection points of each curve. b) Radargram
simulated with GprMax2D; reflection A is coming from the wetting front, B is the direct wave, A'
and A'' are multiples of reflection A. c) TWT computed with an optical path algorithm, directlyfrom the permittivity profiles.

3.2. Experimental Example
3.2.1. Experimental Data and its Analysis
The experiment took place in a quarry of Fontainebleau sand in Cernay-La-Ville (Yvelines,
France). The middle of the antennae was positioned 11 cm away from the cylinder wall (x = 11
cm in Fig. 1). The 5-cm water layer was fully infiltrated after about 10 minutes, although incertain areas of the soil surface this time has been slightly shorter. The recorded GPR data areshown in Figure 3. We recorded during 30 minutes, with a time window of 15 ns, transmitting218and receiving each 10 seconds (stacking 4 measurements). We subtracted the average trace andapplied an Automatic Gain Control to the data. The sand parameters have been determined inlaboratory by several classical hanging water column experiments, fitted by the van Genuchten
retention curve. Assuming a 5% uncertainty of the optimized parameters, we obtained θr=0.062±0.003, θs=0.39±0.01, α=0.023±0.001, and n=6.7±0.3. We considered in our model that the sandwas homogeneous. Gravimetric measurements on field samples gave us an initial volumetricwater content of θi=0.09±0.01. In the profile presented in Figure 3, we denote three particularreflections. The one interpreted as coming from the infiltration front, labeled A, is visible during
the first 30 minutes of the acquisition, with an arrival time varying from 2 ns down to 9 ns. The
other reflections are interpreted in Léger and Saintenoy (2012). We determined the arrival timeof the A reflection peak and inverted the saturated hydraulic conductivity using the samealgorithm as for the synthetic case. We obtained the minimum of the objective function for
Ks=0.131 cm/min. In parallel, we also carried out disk infiltrometer experiments using the multipotential method (Ankeny et al., 1991; Reynolds and Elrick, 1991). We obtained a value of thesaturated hydraulic conductivity of KDisk=0.108±0.01 cm/min.

Figure 3. Experimental GPR data acquired during the falling head infiltration (from a 5 cm initialwater layer). Reflection A is the reflection coming from the wetting front.

3.2.2. Uncertainty Analysis
We assumed a 5% relative uncertainty of four van Genuchten parameters and the initial watercontent of the sand. These parameters directly influence the arrival time curves used to computethe misfit function. Figure 4 shows variations associated with each of these parameters. It
appears that the uncertainty in α has the strongest influence on the arrival time curves. As an
attempt to evaluate the uncertainty in the saturated hydraulic conductivity retrieved from GPR
data fitting, we made some quadratic error summation associated with each of the parameters.
The total quadratic error has the expression of, whereδti, δtr, δts, δα, and δn are RMSE due to uncertainties in θi, θr, θs, α, and n. The RMSE is thesummation of the two curves for each parameter, presented in Figure 4. δgpr =0.1 ns is assumed
to be the error on picking, and δA1go=0.01 ns is the RMSE between the arrival times generated by
the optical path-algorithm and the GprMax modeling (Fig. 2c). The total quadratic error was219

estimated at δtot=0.101 ns. From the objective function curve, all Ks in the interval [0.04; 0.263
cm/min] have a misfit value to our data of less than 0.111 ns, with the minimum at 0.131
cm/min. We think that this wide interval of possible Ks is over-estimated by our rough error
determination.

Figure 4. Influence of the parameter uncertainties on the arrival time difference, between thearrival time generated with each parameter and the arrival time generated with optimal
parameters.

4. Constant Head Infiltration
4.1. Numerical Example
In the second case, a water layer of 5 cm above the ground is kept constant during the entire
experiment. Similarly as above, using the same van Genuchten parameters as in the first
synthetic example (θs=0.43, θr=0.07, α=0.019 cm-1, n=8.67, and Ks=0.120 cm/min), we modeled
infiltration of water inside a ring infiltrometer by applying a constant pressure head of 5 cm tothe top node during 10 minutes. The permittivity profiles are presented in Figure 5a, with eachcurve plotted every 10 s as in the previous case. Figure 5b shows the radargram simulated with
GprMax2D. As can be seen, the reflection labeled A, describing the position of the infiltration
front, is returning at increasing times because infiltration is being constantly fed by the constantponding depth, contrary to the previous falling head case. In Figure 5c, we computed the TWT of
the wetting front, using the ray path algorithm and the picking of A reflection coming from theradargram in Figure 5b.
Assuming the four van Genuchten parameters θr, θs, α, and n are known, we inverted for thesaturated hydraulic conductivity by minimizing the differences between the arrival times of thewetting front reflection obtained by the ray path-algorithm and the arrival times picked from theradargram in Figure 5b. The objective function was minimized for Ks=0.128 cm/min, which isagain larger than the value used for simulating the data: Ks=0.120 cm/min.

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4.2. Experimental Example
The experiment took place in the same quarry of Fontainebleau sand as the previous experiment.
The middle of antennae was positioned in the middle of the ring (x = 30 cm in Fig. 1). The
recorded GPR data are shown in Figure 6. We recorded during 80 minutes, with a time windowof 30 ns (in Fig. 6, we only present a part of the radargram), transmitting and receiving each 5
seconds and with no stacking. In the radargram in Figure 6, we subtracted the average trace andapplied an AGC gain to the data. We used the van Genuchten parameters determined in thelaboratory using the hanging column experiments, and we measured on sand samples an initial
volumetric water content of θi=0.07±0.02.

Figure 5. Constant head infiltration with 5 cm of water. a) Permittivity profiles, each curve isplotted every 10 s. Crosses represent the inflection points. b) Radargram simulated with
GprMax2D, reflection A is the wetting front, B is the direct wave, A' and A'' are multiples. c)
Two Way Travel Time, computed with an optical path algorithm directly from the permittivity
profiles.

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Figure 6. GPR data acquired during a constant head (5 cm) infiltration. Reflection A is thereflection coming from the wetting front.

In the profile presented in Figure 6, the arrival time of reflection A ranges from 0 at the
beginning of the experiment to about 6 ns after 10 min. We picked the arrival time of thereflection A peak and computed the objective function using the same procedure as described
before. We obtained the minimum of the objective function for Ks=0.110 cm/min. This value has
to be again compared with the one obtained by the disk infiltrometer experiment,
KDisk=0.108±0.01 cm/min. Using the same procedure as presented in the earlier field example,
we found a total quadratic error of δtot =0.131 ns, which gives a range of possible values for thesaturated hydraulic conductivity, Ks =[0.035; 0.213] cm/min.
5. Toward a Three Parameter Inversion
From our uncertainty analysis (Fig. 4), we pointed out the high sensitivity of our inversion to theparameter α. The solution may be in inverting our GPR measurements for α and n in addition toKs, assuming θs and θr known. We computed misfit diagrams of the arrival times, to analyze
which parameters can be easily inverted by our algorithm and which cannot. The procedure ofcalculating misfit diagrams is presented in Figure 6d. We carried out this analysis for both
infiltration cases. We set one of the three parameters and plotted the misfit diagram for the twoothers. In Figure 6, we present the misfit diagrams obtained for the constant head infiltration. In
Figure 6, we present similar diagrams for the falling head infiltration. When Hydrus-1D did notconverge for a given combination of parameters, we set the misfit equal to 10 (dark red areas in
Figures 6abc). The misfit diagram (Ks,α) in Figure 6b does not exhibit a correlation between
those two parameters, and informs us about the possibility of inverting (Ks,α) while knowing n.
The two other diagrams show the difficulty of obtaining the correct value of n. Indeed, thisparameter is directly related to the slope of the retention curve ∂θ / ∂h , and thus also to ∂θ / ∂z at
the infiltration front. This information is not present in the TWT of the inflection points used forthe misfit computations.
Figure 7 presents misfit diagrams for the falling head infiltration, calculated using the sameprocedure as above. The upper boundary condition in Hydrus-1D was set to a variable pressure222

head. Note again that each time when Hydrus-1D did not converge, the misfit was set equal to 10(dark red zones in the graph). Graphs 7a and 7c are completely different than in the previous
case. They imply that having information on the evolution of the water layer thickness from theexperiment itself is providing additional information that can help resolve the uniquenessproblem for the n parameter. This case needs to be explored in the future in more detail.

Figure 7. Misfit diagrams for the constant head boundary condition: a) n-α diagram, b) Ks-α
diagram, and c) Ks-n diagram. Black stars represent minimum.

Figure 8. Misfit diagrams for the falling head boundary condition: a) n-α diagram, b) Ks-α
diagram, and c) Ks-n diagram. Black stars represent minimum.

223

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developments, Soil and Tillage Research, 55, 1–29, 2000.
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19(10), 755–762, 2005.
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Léger, E., and A. Saintenoy, Surface ground-penetrating radar monitoring of water infiltration inside aring infiltrometer, In 14th International Conference on Ground Penetrating Radar, Shanghai, 2012.
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224

Modeling Hg Reactive Transport in Soil Systems Using HP1
Bertrand Leterme and Diederik Jacques
Performance Assessments, Institute Environment, Health and Safety, Belgian Nuclear Research Centre, Mol,
Belgium, bleterme@sckcen.be, djacques@sckcen.be

Abstract
We developed a reactive transport model for simulating mercury (Hg) fate and transport in theunsaturated zone, in order to gain insight into the environmental fate of Hg originating from contaminatedsoil. The code was implemented using the module HP1 (Jacques et al., 2006; 2008), which couples
HYDRUS-1D (Šimůnek et al., 2008) for water and solute transport with PHREEQC (Parkhurst andAppelo, 1999) for geochemical reactions. The main processes accounted for in the model are Hg aqueous
speciation (including complexation with dissolved organic matter (DOM), humic and fulvic acids (HAand FA), and thiol groups), Hg sorption to solid organic matter (SOM, while also distinguishing between
humic and fulvic acids and thiol groups), dissolution of solid phase Hg (e.g., cinnabar HgS(s)), dissolutionof Hg non-aqueous phase liquid (NAPL), sunlight-driven HgII reduction to Hg0, Hg0 diffusion in the gas
phase and volatilization, and DOM sorption to soil minerals. Using a 50-year time series of daily weather
data from Dessel (Belgium) and a 1-m deep sandy soil with deep groundwater (free drainage, oxic
conditions), we implemented a sensitivity analysis using the elementary effects method (Morris, 1991).
The most sensitive parameters determining Hg leaching or retardation were found to be the equilibrium
constant for Hg sorption to humic and fulvic acids (i.e., the most abundant sorption sites in SOM), theinitial concentration of Hg, and the concentration of DOM in the soil solution.

1. Introduction
Mercury (Hg) poses threats to human health and the environment, notably due to its persistencein the environment and its ability to bioaccumulate in ecosystems and the food chain.
Anthropogenic sources are major contributors to the release of mercury into the atmosphere,
water and soil. Soil contamination not only results from direct spills, but also indirectly, forexample via deposition of prior atmospheric emissions. The main sources of mercury in soils aremercury mining activities, gold and silver mining (Hg0 is used to amalgamate the metal),manufacturing (e.g., chlor-alkali plants, or manometer spills), wood preservation, and cemeteries(release of mercury from dental amalgams).
Mercury in soils can be present in different phases: the solid phase (most frequently cinnabar(HgS) and montroydite (HgO)), the solution phase (mainly Hg2+ bound to organic or inorganic
ligands, but also methylmercury CH3Hg+ and dissolved Hg0), the gas phase (Hg0 or
dimethylmercury (CH3)2Hg), and the non-aqueous liquid phase (NAPL), which may containespecially elemental mercury Hg0 and is more dense than water. This complexity of multiple
phases makes modeling of mercury transport in soils a particularly challenging task. As such,knowing the history of a given contaminated site is important because Hg species present in soils
are closely related to the type of industry or activity that caused the contamination. The age of an
Hg contaminated site is also important since the kinetics of phase transformations and retention
processes may be relatively slow.

225

This study is focused on Hg fate and transport in the unsaturated zone following direct soil
contamination from human activities. Our main objective was to develop a reactive transportmodel in order to gain insight into the fate and transport processes of Hg in soils under oxic
conditions. The relative importance of different processes and parameters is assessed by meansof with a sensitivity analysis based on the Morris (1991) method of elementary effects. The
analysis is carried out for different initial speciations (dissolved, solid phase or NAPL) of Hg
contamination.
2. Conceptual Model and Numerical Implementation in HP1
Figure 1 shows the conceptual model implemented in the HP1 simulator (Jacques et al., 2006;2008). Aqueous complexation is treated using the database IM003_THERMODDEM (Blanc etal., 2012), augmented with some Hg speciation data from Skyllberg (2012). However,complexation with organic ligands is not included in IM003_THERMODDEM. Therefore, four
hypothetical organic compounds (Ya, Yb and Yc representing oxygen sites of humic and fulvic
acids, and Ys representing thiol groups) were added (Table 1, left column). Based on exchange
capacity data, approximately 99% of the dissolved organic matter (DOM) ligands were modeled
as humic and fulvic acids (88%, 11% and 1% for Ya, Yb and Yc, respectively), and about 1% as
thiols (Gustafsson, 2001; Skyllberg, 2008).
Colloidal transport of Hg (Sen and Khilar, 2006; Zhu et al., 2012) is implicitly considered by thetransport of Hg bound to DOM. While numerical solutions exists for simulating more
realistically colloid formation and migration exist (Šimůnek et al., 2006), they generally demand
numerous specific parameters that were not available for the present case.
For Hg sorption to soil organic matter (SOM) we used the EXCHANGE command of PHREEQC for
simulating multiple proton/ion exchangers. Similarly to Hg complexation with DOM, four
reactive surface sites were considered (Table 1, right column): Xa, Xb, Xc (representing the~99% oxygen exchange sites from fulvic and humic acids) and Xs (representing ~1% thiol
exchange sites). Sorption of DOM on soil minerals was modeled using the PHREEQC function
SURFACE for surface complexation, with a Langmuir isotherm and parameters fitted by
Kothawala et al. (2008).
Starting with Hg2+ in the aqueous phase, mercury volatilization requires two steps: (i) reductionof HgII to Hg0, and (ii) a phase change from Hg0(aq) to Hg0(g). Our model at present wasdeveloped for oxic conditions, which thermodynamically does not favor volatilization. For thisreason we decided to implement a (pseudo-first-order) kinetic reaction in HP1 for the reductionof HgII to Hg0(aq) (cf. Figure 1).
Two other kinetic reactions were necessary to allow dissolution of cinnabar (HgS(s)) and NAPL
(cf. Figure 1). Cinnabar dissolution is dependent upon DOM (Waples et al., 2005) andrepresented by a zero-order rate equation, while NAPL dissolution is modeled by means of afirst-order rate law (this was done somewhat arbitrarily due to the absence of data on Hg NAPL
dissolution).

226

Figure 1. Conceptual model of Hg speciation and reactions in the solid, aqueous and gas
phases. Initial mercury contamination can be simulated as non-aqueous phase liquid (NAPL),
solid, or aqueous phase.
Table 1. Equilibrium constants for Hg-DOM complexes (left column) and for sorptionof Hg to SOM (ion exchange assemblage; right column).
Complexation Hg-DOM
HYa + 0.5Hg

Sorption Hg-SOM= Hg0.5Ya + H

−1.1

(a)

Hg

2+

+ 2Xa = HgXa2

+

−7.6

(a)

Hg

2+

+ 2Xb = HgXb2

−1.8

(a)

Hg

2+

+ 2Xc = HgXc2+

2+= Hg0.5Yb + H

2+= Hg0.5Yc + H

HYb + .5Hg
HYc + .5Hg

2+

Log k

+

+

+

−3

+

+

+

+

HYa + HgOH = HgOHYa + H
HYb + HgOH = HgOHYb + H
HYc + HgOH = HgOHYc + H
2HYs + Hg
(a)
(b)

2+

+

= HgYs2 + 2H

−
−

−

+

−

+

−

+

−

(a)

HgOH + Xa = HgOHXa

1.8

(a)

HgOH + Xb = HgOHXb

2.0

(a)

HgOH + Xc = HgOHXc

22.0

(b)

Hg

2+

+ 2HXs = HgXs2 + 2H+

Log k
3.5

(a)

4.3

(a)

5.08

(a)

7.7

(a)

7.7

(a)

10.2

(a)

15.4

(b)

Bessinger and Marks (2010)
Skyllberg (2008)

Within the context of Hg contamination from anthropogenic sources, mercury uptake byvegetation and atmospheric wet and dry deposition could be ignored since they generally
generate relatively small Hg fluxes compared to those included in our model.

227

3. Sensitivity Analysis
We applied Hg reactive transport model to a synthetic case, consisting of a 1-m course-textured
soil having a uniform SOM content in the top 30 cm, initial Hg contamination in the top 10 cm,
and a grass cover with uniform rooting depth until 30 cm (no Hg uptake). The soil surface
hydraulic boundary condition consisted of atmospheric input (precipitation and potential
evapotranspiration rates) obtained from a 50-year time series of daily observations in Dessel(Belgium). The lower hydraulic boundary condition was set to free drainage in order to ensure
oxic conditions.
Given these assumptions, a sensitivity analysis (SA) was performed using the elementary effects
method of Morris (1991). Sampling trajectories were randomly designed across parameter space(each parameter range being divided into p levels), with successive deviations in the trajectories
resulting in quantification of the elementary effects. One computes then µ (the averageelementary effect) which assesses the overall influence of the factor on the output, and also σ(standard deviation) which estimates the ensemble of the factor’s higher order effects (i.e., nonlinear and/or interaction effects). Campolongo et al. (2007) further proposed the use of µ* (themean of the absolute value of elementary effects) as an indicator of parameter sensitivity toidentify model non-monoticity (i.e. when for a given factor elementary effects of opposite signs
cancel each other in the measure of µ).
Thirteen parameters were included in the SA (Table 2), while the following model outputs wereselected: leached Hg, Hg still in the originally polluted horizon, and Hg below the top 30-cm
thick horizon (all expressed as % of the initial Hg contamination). The SA was repeated at threedifferent simulation times (after 5, 25 and 50 years) and with three different contamination
sources (cinnabar, Hg NAPL and aqueous mercuric chloride). Only a few representative results
are presented hereafter.
Figure 2 shows plots of µ vs. σ and µ* vs. σ for the percentage of Hg being leached after 50 years
in case of cinnabar being the contamination source. Among the parameters tested, X4 (DOM
concentration of infiltrating rainwater) had the highest sensitivity. This is due to (i) HgII
migration occurring mainly via Hg-DOM complexes and (ii) cinnabar dissolution rate depending
upon the DOM concentration of soil water. Other parameters showing a high sensitivity were X1(initial cinnabar concentration) and X8 (log k Hg-DOM (thiols)). For X1, the high sensitivity waspartly explained by the model output being expressed in a relative way (% of initial Hg), and byincomplete cinnabar dissolution over the simulation time.
Figure 3 shows plots of the concentration of HgII in the leachate over time, obtained from one SA
simulation using cinnabar as the contamination source. Results indicate that HgII leaching occurs
after only about 30 years. Also, after the initial breakthrough, the variability in the HgII
concentration spans about two orders of magnitude. These are important findings, for example
within the context of designing a sampling strategy, or for planning (temporal) objectives of soil
remediation and/or risk assessment.

228

Table 2. List of parameters included in the sensitivity analysis, and their lower and upper bounds(uniform distributions).
Factor
X1

Unit
Initial Hg concentration

X2

Cinnabar dissolution rate

X3

Hg reduction rate

X4

Lower bound

mg kg
−1

day

−1

135

gOC

−1

II

day

DOM (in rainwater boundary solution)

mg L

−1

13500

4.59×10
6.91×10−1

X5

Exchange capacity of HA and FA (SOM top 30 cm)

meq dmX6

Exchange capacity of thiols (SOM top 30 cm)

meq dmX7

log k complexation Hg-DOM (HA and FA)-

X8

log k complexation Hg-DOM (thiols)

X9

log k sorption Hg-SOM (HA and FA)

X10

log k sorption Hg-SOM (thiols)

X11

KL sorption DOM to soil minerals

9−3Upper bound−4(a)1.42×10−7−2 (a)

6.91×10

(c,d)

90

−5

(c,d)

7.95

159

0.0705

1.41

HgYa2
−2.2
HgYb2: −15.2
HgYc2: −3.6
HgOHYa: −6.0
HgOHYb:0.9
HgOHYc : 1.0

−0.55
−3.8
−0.9
−1.5
3.6
4.0

-

11.0

44.0

-

HgXa2:
HgXb2:
HgXc2:HgOHXa:HgOHXb:HgOHXc:

−3

7.7
-

X12

Smax max. adsorption capacity of DOM to minerals

mg kg

X13

NAPL dissolution rate

day

−1

109

7.0
8.6
10.16
15.4
15.4
20.4
30.8

5.6×10
−1

1.75
2.15
2.54
3.85
3.85
5.1

−4

(g)

8.64×10

1.23×10−2 (g)

601
−5

(g)

8.64×10−3(a)Waples et al. (2005)
Scholtz et al. (2003)(c)
Mertens et al. (2007)(d)
Don and Schulze (2008)(e)Skyllberg (2008)(f)
Bessinger and Marks (2010)(g)
Kothawala et al. (2008)(b)

Figure 4 presents results for the percentage of Hg still present in the top horizon (0-10 cm) after
50 years, with Hg NAPL being the contamination source. Parameter X9 (log k Hg-SOM (HA,FA)) was the most sensitive parameter. The corresponding parameter for thiols, X10, showed nosensitivity due to the high proportion of HA and FA sites compared to thiols. Factor X1 (Hginitial concentration) was the second most important parameter. This parameter is characterizedby µ values indicating non-monotonic behavior of the model. Nonlinearities and interactions
with other parameters are also important for X9 and X1 (high σ values).

229

Figure 2. Plots of µ vs. σ and µ* vs. σ for elementary effects of the percentage Hg leaching after
50 years, using 5 trajectories and cinnabar (HgS(s)) was the contamination source.

Figure 3. HgII concentration (µg L−1) in the leachate over time, from one of the 60 HP1 runs of
the sensitivity analysis using cinnabar (HgS(s)) as the contamination source.

Two simulations illustrating model nonlinearity and the interaction effects are shown in Figure 5.
Figure 5a indicates that no more Hg is present in the top horizon (0-10 cm) after 50 years, while
the percentage is still 32.5% of the initial Hg in Figure 5b (= the maximum of all simulations of
the 5 trajectories). Both simulations were carried out using the same initial concentration (X1)
and a low value of X9. Differences between the two simulations is mainly due to interactions
between X1 and X6 (exchange capacity of thiols). Even though thiol sorption sites are lessabundant than HA and FA sites, the interaction of low X1 and high X6 in Figure 5b means that
thiols in SOM are sufficient to retain a significant percentage of the initial Hg in the topsoil.

230

Figure 4. Plots of µ vs. σ and µ* vs. σ for elementary effects of the percentage Hg still in thesurface horizon initially polluted after 50 years, using 5 trajectories and Hg NAPL ascontamination source.

(a)

(b)

Figure 5. Depth distribution over time of Hg sorbed to SOM at t = 0, 5, 10, 25 and 50 years fortwo simulations with contrasting percentages of Hg in the top horizon after 50 years: 0% for (a)and 32.5% for (b). The initial contamination Hg NAPL was (135 mg[Hg]/kg[soil]).

Overall (i.e., including results not shown in this paper), parameter sensitivity for a given model
output was found to depend on the type of mercury contamination. However, trends could be
drawn by ranking the 13 parameters based on the sensitivity after 25 and 50 years for all types ofcontamination. For leaching, the most sensitive parameters were X1, X9 and X4 (decreasing
sensitivity ; see Table 2 for parameter names and ranges). For the percentage of Hg remaining in
the topsoil, the ranking was: X9, X1 and X4. For Hg below the horizon of contamination (1130 cm), the most sensitive parameters were X9, and X1, X4, X2, X13. Parameters that could
generally be considered negligible based on the SA results were X3, X7, X11, X12.
Simulated Hg volatilization was found to be negligible (<0.1%). This is mainly due to the factthat the reduction rate depends on the total HgII concentration in the aqueous phase, i.e. the freespecies of Hg2+, the inorganic and organic aqueous complexes of HgII, not being sorbed. Since

231

HgII concentration in the aqueous phase were relatively low at all times, Hg reduction andvolatilization were consequently very limited.
4. Conclusions
The HP1 module of HYDRUS-1D was used to implement a numerical model of mercury fate
and transport in soils. The processes included in the model are relevant for oxic conditions andpollution from anthropogenic sources. These simulated processes were Hg transport andspeciation in the gaseous and aqueous phases, Hg sorption to SOM, cinnabar and Hg NAPL
dissolution, HgII reduction and volatilization, and DOM sorption to minerals. Hg-DOM
complexes in the aqueous phase were considered as a surrogate for colloid transport.
Three different phases of initial mercury contamination were tested: solid (cinnabar), nonaqueous phase liquid Hg, and aqueous mercuric chloride. The dominant processes for Hg fate insoils were identified by means of a parameter sensitivity analysis using the method of elementary
effects. Overall, the most sensitive parameters were the equilibrium constant for Hg sorption to
humic and fulvic acids (i.e., the most abundant sorption sites of SOM), the Hg initialconcentration, and the DOM concentration of the infiltrating rainwater. Interactions between
factors and nonlinear effects as measured by the elementary effect method were generally
important. They depended on the type of contamination and on the time at which the indicators
were evaluated.
More comprehensive modeling of the DOM cycle in soils should improve performance of themodel, given the importance of DOM and SOM on Hg dynamics. Finally, we note that no model
calibration was performed in the present study, but this is considered a necessary step in the
future.
Acknowledgements
The present study is part of the IMaHg project (Enhanced knowledge in mercury fate andtransport for Improved Management of Hg soil contamination), which aims at providing
recommendations to improve management of sites contaminated by mercury within the
SNOWMAN funding framework. This particular work was done with financial support of the
Public Waste Agency of Flanders (OVAM).
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Bessinger, B. A., and C. D. Marks, Treatment of mercury-contaminated soils with activated carbon: Alaboratory, field, and modeling study, Remediation J., 21(1), 115-135, 2010.
Blanc, P., Lassin, A., and P. Piantone, THERMODDEM, A database devoted to waste minerals, BRGM,
Orléans, France, 2012. http://thermoddem.brgm.fr
Campolongo, F., J. Cariboni, and A. Saltelli, An effective screening design for sensitivity analysis oflarge models, Environ. Modelling & Software, 22(10), 1509-1518, 2007.
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contrasting soil types, Biogeochemistry, 91(2), 117-131, 2008.

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Gustafsson, J. P., Modeling the acid-base properties and metal complexation of humic substances with theStockholm Humic Model, J. Colloid and Interface Sci., 244(1), 102, 2008.
Jacques, D., J. Šimůnek, D. Mallants, and M. Th. van Genuchten, Operator-splitting errors in coupled
reactive transport codes for transient variably saturated flow and contaminant transport in layered soil
profiles, J. Contam. Hydrol., 88, 197–218, 2006.
Jacques, D., J. Šimůnek, D. Mallants, and M. Th. van Genuchten, Modeling coupled water flow, solutetransport and geochemical reactions affecting heavy metal migration in a podzol soil, Geoderma,145(3-4), 449-461, 2006.
Kothawala, D. N., T. R. Moore, and W. H. Hendershot, Adsorption of dissolved organic carbon tomineral soils: A comparison of four isotherm approaches, Geoderma, 148(1), 43-50, 2008.
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organic carbon fluxes under bare soil, J. Environ. Qual., 36(2), 597-606, 2007.
Morris, M. D., Factorial sampling plans for preliminary computational experiments, Technometrics,
33(2), 161-174, 1991.
Parkhurst, D. L., and C. A. J. Appelo, User's guide to PHREEQC (Version 2), A computer program forspeciation, batch-reaction, one-dimensional transport, and inverse geochemical calculations, WaterResources Investigations Report 99-4259, U.S. Department of the Interior, U.S. Geological Survey,
Denver, Colorado, USA, 1999.
Scholtz, M. T., B. J. Van Heyst, and W. H. Schroeder, Modelling of mercury emissions from backgroundsoils, Sci. Total Environ., 304(1-3), 185-207, 2003.
Sen, T. K., and K. C. Khilar, Review on subsurface colloids and colloid-associated contaminant transport
in saturated porous media, Adv. Colloid Interface Sci., 119(2-3), 71-96, 2006.
Šimůnek, J., C. He, L. Pang, and S. A. Bradford, Colloid-facilitated solute transport in variably saturated
porous media, Vadose Zone J., 5(3), 1035-1047, 2006.
Šimůnek, J., M. Šejna, H. Saito, and M. Th. van Genuchten, The HYDRUS-1D Software Package forSimulating the Movement of Water, Heat, and Multiple Solutes in Variably Saturated Media, Version
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Skyllberg, U., Competition among thiols and inorganic sulfides and polysulfides for Hg and MeHg in
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233

234

Groundwater Recharge Modeling of the Nete Catchment(Belgium) Using the HYDRUS-1D – MODFLOW Package
Bertrand Leterme, Matej Gedeon, and Diederik Jacques
Performance Assessments, Institute Environment, Health and Safety, Belgian Nuclear Research Centre, Mol,
Belgium, bleterme@sckcen.be, mgedeon@sckcen.be, djacques@sckcen.be

Abstract
The HYDRUS-1D and MODFLOW software packages were coupled to produce a groundwater model ofthe Nete catchment (northern Belgium) that would improve simulations of near-surface hydrologicalprocesses, including temporal and spatial variabilities in groundwater recharge rates. The present paper
reports the practical implementation of the HYDRUS package for MODFLOW. Several issues are
discussed: the choice and design of MODFLOW zones for coupling to one-dimensional HYDRUS
profiles; time discretization of the MODFLOW and HYDRUS components, numerical oscillations andrelated warm-up periods; and the presence of seepage water in zones of shallow groundwater. In thisstudy we delineated MODFLOW zones on the basis of groundwater depths as obtained with a calibrated
steady-state version of the model. Transient simulations are then compared with observed groundwater
depths derived from a piezometer network. We summarize a number of priorities and issues that need tobe addressed in order to improve the model and achieve sound coupling of the two parts at the catchment
scale, while keeping computation times reasonable.

1. Introduction
A groundwater model for the Nete catchment (Belgium) was previously developed assuming
constant (in space and time) recharge (Gedeon and Wemaere, 2008). The model was calibrated
for steady-state conditions using a uniform groundwater recharge rate of 289 mm y−1. One way
to introduce more realism in the spatial and temporal characterization of groundwater recharge is
to couple the groundwater model to an unsaturated zone model. A review of surface-subsurface
coupling methods and models is provided by Furman (2008). Recent examples using
MODFLOW (Harbaugh et al., 2000) as the subsurface component include Xu et al. (2012) and
Morway et al. (2013). Seo et al. (2007) developed a module that couples HYDRUS-1D(Šimůnek et al., 2008) to MODFLOW-2000, but until now only applications on synthetic cases
have been documented (Twarakavi et al., 2008).
This case study documents the implementation of the HYDRUS-MODFLOW package for the
Nete catchment in northern Belgium. The groundwater modeling domain for MODFLOW was
discretized into cells of 400×400 m each (9644 active cells in the top layer; see Figure 1). The
vertical thickness of active layers in the model varied between 0 and 200 m as some layers werewedged out.

235

Figure 1. Surface discretization and cross-section of the groundwater model developed
using MODFLOW.

2. Implementation of the HYDRUS Package for MODFLOW
2.1. Zone Definition
Zones within the MODFLOW discretization identify cells to which each unsaturated soil profile
applies. In theory, the number of zones can vary between 1 and the total number of active cells in
the top layer (9644 in the present case). In practice, a compromise is needed between increasing
model realism (i.e., including more zones) and keeping reasonable CPU time (i.e., limiting thenumber of zones). For a given MODFLOW zone, the depth to groundwater in each cell isaveraged to determine the hydraulic head at the bottom of the corresponding HYDRUS soil
profile (details in Seo et al., 2007). The time-averaged flux at the bottom of the soil profile isapplied to each cell in the zone as recharge during the time step. Therefore, the expected depth togroundwater should be taken as the first criterion for defining relatively homogeneous
MODFLOW zones, in order to limit precision losses due to averaging between the MODFLOW
and HYDRUS models. In our study, the expected groundwater depth was taken from thecalibrated steady-state model of Gedeon and Wemaere (2008).

236

Other logical criteria for defining MODFLOW zones relate to surface processes. For given
atmospheric input (i.e., precipitation time series), it is expected that different soil types andvegetation covers will significantly affect the fluxes calculated with HYDRUS, which then are
applied to the MODFLOW cells. For this reason we used the soil association map (Maréchal andTavernier, 1974) as a possible geographical criterion to define MODFLOW zones. Soil hydraulicparameters were taken from the AARDEWERK database (Van Orshoven and Vandenbroucke,1993). Spatial information of land cover was extracted from a 2001 Landsat image (AGIV,
2011), which we further aggregated to obtain six main classes: surface water (1%), impervious(urban areas; 13%), grass (16%), deciduous trees (7%), coniferous trees (14%), and crop (maize;
49%).
We next developed a pre-processing script in Python that enables one to generate a zone arrayand HYDRUS soil profiles by specifying criteria of groundwater depth intervals, soil types, andland cover types (vegetation). The resulting number of zones can be easily tuned by changing theselection criteria.
For the work reported here, different simulations were performed using different numbers ofzones obtained by changing only the groundwater depth intervals. Soil and land cover types were
kept constant, being a typical podzol with a grass cover for the whole study area (except surface
waters which were already included in the groundwater model). Despite the reduced complexity,
several issues had to be addressed while coupling of the separate HYDRUS and MODFLOW
models. These issues are discussed hereafter.
2.2. Seepage Water
A significant part of the study area can be characterized as a relatively shallow aquifer. This is
illustrated in Figure 2 where zones 1 and 2 correspond to estimated groundwater depths being
less than 2 m (on the basis of the calibrated steady-state model). For zones having shallow
groundwater, it became apparent that the average groundwater depth transmitted from
MODFLOW to HYDRUS frequently exceeded the soil surface. This may partly be aconsequence of the spatial resolution (i.e., averaging of groundwater depths and/or topography),or could reflect a lack of precision of the calibrated groundwater model in certain areas. For
example, the calibrated hydraulic conductivity of aquifer layers is closely linked to the imposed
steady-state recharge rate.
The HYDRUS package could not properly handle this problem and produced convergenceproblems. We therefore modified the code to allow the excess water to be removed as seepage
from the soil surface. For zones 1 to 3 (which accounted for approximately two thirds of thestudy area), Figure 3 shows the number of MODFLOW cells in which seepage was simulated
during the last time step of the simulation (model with 20 zones). The simulated seepage wasfound to be very important for zone 1 (shallowest groundwater).

237

Figure 2. Map of the Nete catchment with 20 MODFLOW zones. Black dots represent locationsof the piezometers available for comparison of simulated vs. observed groundwater depth.

# cells

2500
2000
1500

GW depth < 0 (seepage)
GW depth > 0

1000

500
0

Zone 1(gw 0-1m)

Zone 2(gw 1-2m)

Zone 3(gw 2-3m)

zone definition withsteady-state model results

Figure 3. Total number of MODFLOW active cells with or without seepage during the last time
step of a 10-year simulation (+10 years warm-up) for the coupled model using 20 zones. Only the
first three zones are shown.

238

2.3. Warm-up Period
For all simulations tested (assuming a different number of zones, and using transient or steadystate atmospheric input), we noted oscillations in the fluxes being exchanged between HYDRUS
and MODFLOW during some initial time period of the simulation (Figure 4). While this could
be a consequence of the removal of seepage water, the oscillations were not limited to zones
having shallow groundwater (e.g., see Figure 4(b)). The oscillations could eventually lead to
non-convergence, especially when the number of zones was very low or the number of couplingtime steps were insufficient during the early stress periods.
(a)

0

(b)

30

60

90

120

150

180

210

240

270

300

330

360

0

Groundwater depth (m)

5

Zone1

10

Zone2

15

Zone3
Zone4

20

Zone5

25

Zone6

30
35

Figure 4. First year of transient simulation with the coupled HYDRUS-MODFLOW package
using 6 zones, showing oscillations during approximately the first 180 days in (a) the total
discharge rate (left vertical axis) and the potential evaporation (E0), transpiration (T0) andrecharge rates (right axis), as well as the exchange flux between the unsaturated and saturated
zones (right axis), all in mm d-1, and (b) averaged groundwater depths (m) for each zone.

Even while the numerical solution eventually stabilized, we noted that relatively long warm-up
periods were necessary to avoid oscillations (at least several years). This was partly due to thepresence of zones with a deep groundwater table, which required several years before
atmospheric input migrated through the unsaturated zone. This is illustrated in Figure 5, which
compares HYDRUS profile water contents and fluxed at the bottom of the profile for two zones

239

with different groundwater depths. We therefore used a warm-up period of ten years in
subsequent simulations (see section 2.4) to ensure results independent of the initial conditions.

(a)

(b)

Figure 5. Water contents (blue color scale; cm3 cm−3) and fluxes (red dots; mm d−1) at the bottomof the HYDRUS profile during the first 5 years of a simulation with 10 zones. Results are for (a)zone 2 (initial groundwater depth between 2.5 and 5 m) and (b) zone 9 (initial groundwater depth
between 20 and 25 m).

2.4. Comparison with Piezometer Data
For a 10-year simulation (plus a 10-year warm-up period) with 20 zones, the recharge rate varied
between 226 and 392 mm y−1 for the different zones (Figure 6). In the present case, thevariability between the zones was due only to variability in the groundwater depth translated todifferent positions of the bottom boundary condition in the HYDRUS profiles. This because asingle combination of soil type, land cover and atmospheric boundary conditions was considered.
For the entire Nete catchment, the average simulated recharge rate was 274 mm y−1, and theaverage seepage rate 32 mm y−1 (mainly in zone 1 with initial groundwater table < 1 m). Net
simulated recharge was thus 242 mm y−1. Previous estimates of the groundwater recharge rate in
the area ranged from 237 to 486 mm y−1 (see the review in Hardy et al., 2001).

Figure 6. Average annual recharge rate in the period 2000-2009 for the 20 MODFLOW zones.

240

For each zone, simulated groundwater depths were compared with data available from a networkof piezometers in the study area (Figure 2 indicates piezometer locations). This comparison isshown in Figure 7 for zones 1 to 3. Results indicate that the average simulated groundwater
depths generally reflect seasonal fluctuations (higher water table at the end of winter). In zone 1,
the simulated groundwater depth was close to zero due to seepage in many of the cells (cf.
section 2.2), while piezometer data showed groundwater depths in the range 1.5-3.0 m most of
the time. In zones 2 and 3, average calculated depths corresponded approximately to theobservations.
We emphasize that until now no calibration was attempted with the model (which was previously
calibrated for steady-state conditions using a single recharge rate). There are possibilities toimprove the simulation by calibrating the number of zones and including more soil types andland covers. Also, the consistency and reliability of the piezometer observations need to beverified since different data sources were combined. Figure 7 shows that piezometricobservations do not show an overall increasing groundwater depth from zone 1 to zone 3,
contrary to the simulated groundwater depths. This may partly be due to the resolution of the
MODFLOW cells and the corresponding DEM (400×400 m), which were too coarse comparedto point measurements such as piezometers.
3. Conclusions and Perspectives
This paper presents a case study of coupling surface and subsurface models for the Netecatchment. A few practical issues during implementation of the HYDRUS-MODFLOW package
are described. The main issues are related to the use of homogeneous MODFLOW zones(section 2.1), the occurrence of seepage in areas of shallow groundwater (section 2.2), andoscillatory behavior of the model during the initial time steps and the resulting need for a
relatively long warm-up period (section 2.3). Results of a simulation with 20 zones werecompared to piezometer data (section 2.4).
The main issue to address in the future is probably the treatment of seepage. Currently, this water
is not routed to rivers, which makes it impossible to obtain a consistent water balance over thewhole catchment. Moreover, currently simulated seepage rates seem too high and do notcorrespond to rates that have been observed in the catchment. This is probably due to therelatively large area covered by zones 1 and 2, and to assumed hydraulic parameters of thegroundwater model. These parameters need to be re-calibrated to allow for more precise recharge
drainage rates. The re-calibration will be done using transient groundwater level observations.
In parallel, the sensitivity of the model to the number of zones should be quantified. This would
lead to an optimization of the number of zones. Important information for this is the variability inthe simulated zone groundwater depth within a zone (cf., red shadowed area in Figure 7). A highstandard deviation in a given zone indicates that splitting that zone may improve the results. On
the other hand, analysis of HYDRUS sensitivities to groundwater depth prior to coupling could
also provide valuable information. For example, having more zones may be beneficial inintervals of groundwater depth where the sensitivity is high (i.e., where actual ET is influenced
by groundwater;Maxwell and Kollet, 2008), while having fewer zones may be possible inintervals with deeper groundwater (i.e., where groundwater is disconnected from the surface).

241Figure 7. Comparison of observed (blue) and simulated (red) groundwater depths for zones 1 to 3
for a simulation with 20 zones. The shadowed red area is the average calculated depth (± 1standard deviation) of all cells pertaining to a given zone.

242

Future simulations are planned, including for more soil types and land cover classes. This should
improve model realism (e.g., having very low or no recharge in urbanized areas), but could
require a (much) higher number of zones. One major issue here is the relatively long simulation
time. The 10-year (plus 10-year warm up) simulation presented here took about 4 h on a standard
computer. This is relatively high considering the need of multiple runs for calibration and/or
sensitivity analyses. As such, an optimal design of the warm-up period, of MODFLOW stressperiods and of the time steps could possibly improve CPU time. We also believe that the model
eventually needs to be calibrated against observed piezometer data.
References

AGIV, Bodemgebruiksbestand, opname 2001, Agentschap voor Geografische Informatie Vlaanderen, 2011,
available at www.agiv.be/gis (accessed March 15th, 2013).
Furman, A., Modeling Coupled Surface-Subsurface Flow Processes: A Review, Vadose Zone J., 7(2), 741-756,
2008.
Gedeon, M., and I. Wemaere, Conceptual uncertainty assessment for a catchment scale model, Calibration andReliability in Groundwater Modelling. Credibility of Modelling, ModelCare 2007, Copenhagen, Denmark, 9-13
September 2007 IAHS, Wallington, United Kingdom, 2008.
Harbaugh, A. W., E. R. Banta, M. C. Hill, and M. G. McDonald, MODFLOW-2000, The U.S. Geological Survey
Modular Ground-Water Model User Guide to Modularization Concepts and the Ground-Water Flow Process,
USGS, Denver, CO., 2000.
Hardy, L., D. Mallants, and G. Volckaert, Hydrogeological model for the safety evaluation: groundwater flow andtransport calculations for the nuclear zone Mol-Dessel, R-3550, Waste & Disposal Department, SCK-CEN Mol,
Belgium, 2001.
Maréchal, R., and R. Tavernier, Pédologie : commentaires des planches de la carte des associations de sols, Livret
explicatif des planches 11A et 11B de l’Atlas de Belgique du Comité National de Géographie, 4-64, 1974.
Maxwell, R. M., and S. J. Kollet, Interdependence of groundwater dynamics and land-energy feedbacks underclimate change, Nature Geosciences, 1, 665-669, 2008.
Morway, E. D., R. G. Niswonger, C. D. Langevin, R. T. Bailey, and R. W. Healy, Modeling variably saturated
subsurface solute transport with MODFLOW-UZF and MT3DMS, Groundwater, 51(2), 237-251, 2013.
Seo, H. S., J. Šimůnek, and E. P. Poeter, Documentation of the HYDRUS Package for MODFLOW-2000, the U.S.
Geological Survey Modular Ground-Water Model. Golden, CO, Colorado School of Mines, 96 p., 2007.
Šimůnek, J., M. Šejna, H. Saito, M. Sakai, and M. Th. van Genuchten, The Hydrus-1D Software Package forSimulating the Movement of Water, Heat, and Multiple Solutes in Variably Saturated Media, Version 4.0,
HYDRUS Software Series 3, Department of Environmental Sciences, University of California Riverside,
Riverside, California, USA, 2008.
Twarakavi, N. K. C., J. Šimůnek, and S. Seo, Evaluating interactions between groundwater and vadose zone using
the HYDRUS-based flow Ppckage for MODFLOW, Vadose Zone J., 7(2), 757-768, 2008.
Van Orshoven, J., and D. Vandenbroucke, Guide de l'utilisateur de Aardewerk, Base de données de profils
pédologiques, K. U. L. IRSIA-COBIS Instituut voor Land-en Waterbeheer, Leuven, Belgium, 1993.
Xu, X., G. Huang, H. Zhan, Z. Qu, and Q. Huang, Integration of SWAP and MODFLOW-2000 for modelinggroundwater dynamics in shallow water table areas, J. Hydrol., 412-413, 170-181, 2012.

243

244

Which Hydraulic Model to Use for Vertical Flow
Constructed Wetlands?
Ania Morvannou1, Nicolas Forquet1, Marnik Vanclooster2, and Pascal Molle1
1

Irstea, Freshwater Systems, Ecology and Pollution Research Unit, 5 rue de la Doua, CS70077, 69626
Villeurbanne cedex, France, ania.morvannou@irstea.fr, nicolas.forquet@irstea.fr, pascal.molle@irstea.fr
2Earth and Life Institute, Environmental Sciences, Université Catholique de Louvain, Croix du Sud 2 Box
2, B-1348 Louvain-la-Neuve, Belgium, marnik.vanclooster@uclouvain.be

Abstract
Modeling water flow in a Vertical Flow Constructed Wetland (VFWC) is a prerequisite to simulate
wastewater treatment using process based filtering models. The material used in a VFCW is often very
susceptible to generate preferential flow. If this occurs, water will bypass much of the soil porous matrix
in a largely unpredictable way. Even if it is possible to simulate water content variations within a VFCW,
one cannot correctly model outflow using the standard van Genuchten-Mualem functions if preferential
flow occurs. Various modeling approaches have been proposed to overcome this problem. These
approaches mostly try to describe flow and transport separately in the preferred flow paths and in slow orstagnant pore regions. The objective of this study was to investigate and simulate the hydrodynamic
behavior and solute transport through a simplified representation of a French VFCW by using both theclassical equilibrium flow model and a non-equilibrium dual-porosity (mobile-immobile) type model withwater content mass transfer as included in the HYDRUS-1D software package. Modeling results werecompared to a solute breakthrough curve obtained from a tracer experiment carried out on an existing
VFCW. Inlet concentrations were first corrected to account for tracer losses and experimental
uncertainties. Both the hydraulic parameters of the mobile and immobile regions ( θ rm / θ sm and θ rim / θ sim )and the transfer coefficient (ω) were optimized to fit the experimental tracer breakthrough curve.
Comparison of measured and simulated tracer breakthrough curves indicates that the non-equilibrium
approach seems to be more appropriate for simulating preferential flow.

1. Introduction
Constructed wetlands (CWs) provide an attractive wastewater treatment technology for small
communities (< 2000 people-equivalents; p.e.) since their simplicity of operation, low cost andreliable treatment efficiency often fit with the limited resources of small communities for
wastewater treatment. Irstea (formerly Cemagref) developed an innovative first-stage typesystem for vertical flow constructed wetlands (VFCWs) containing gravel instead of sand. The
first-stage system directly accepts raw wastewater without needing a preliminary settling tank.
Despite obtaining good treatment efficiencies, Molle et al. (2008) indicated that the treatment
efficiency could be improved if the hydraulic behavior of the VFCW were better understood.
While a French VFCW initially contain only gravel, after some years of operation a sludge layer
develops at the filter surface, with the filter medium slowly turning into a medium made up of
gravel and organic matter. Water retention is then mainly caused by organic matter in the filter.
Consequently, both gravitational and capillary flow due to gravel and the presence of organic

245matter, respectively, must be considered (Maier et al., 2009). The macroporosity associated withthe coarse material and the network of reed stalks may serve as preferential flow paths throughwhich water can bypass much of the porous matrix. Moreover, during rest periods the sludge
generally dries fast, often leading to visible cracks that facilitate preferential flow paths throughthe sludge layer, especially at the beginning of a feeding period (Molle et al., 2006). Nonequilibrium conditions in pressure heads are thus created between preferential flow paths and thematrix pore region. VFCWs thus far have been depicted as a porous medium with continuous
properties. Variably saturated water flow is then usually modeled using the Richards equation
assuming that the water content and pressure head are at equilibrium at each node. These
equilibrium models cannot be used for simulating preferential flow in structured media (Gerke,
2006; Köhne et al., 2009). Moreover, even if it is possible to simulate water content variations
within a VFCW using equilibrium models, outflow cannot be correctly modeled with thestandard van Genuchten-Mualem functions (Morvannou et al, submitted). A model accounting
for non-equilibrium water flow and solute transport would hence be more appropriate.
Preferential flow models thus far have not been applied to flow and transport processes in
VFCWs. By comparison, many preferential flow studies have been carried out in the soil andhydrologic sciences for simulating water flow and/or solute transport in saturated andunsaturated porous media (Šimůnek et al., 2001; Haws et al., 2005; Köhne et al., 2006; Maier etal., 2009). Šimunek et al., (2003, 2008) carried out extensive literature reviews of existingmodels. Most of the models assume the simultaneous consideration of two or more domains forthe same porous medium. Four different preferential flow models have been implemented in the
HYDRUS software package (Šimůnek et al., 2006). These models have in common that waterflow in the preferential flow paths is still simulated using the Richards equation and solutetransport using the convection-dispersion equation. However, they differ in the way flow andtransport in and between the ‘‘fast” (macropore domain) and “slow” or stagnant (matrix domain)pore spaces are modeled. A disadvantage of these approaches is that they increase thecomputational demand of the model as well as the number of required model parameters, someof which may be very difficult to estimate (Šimůnek and van Genuchten, 2008).
The purpose of this paper is to study and simulate the hydrodynamic behavior and solutetransport in a simplified representation of a VFCW by using both the classical equilibrium and a
non-equilibrium model formulation available in the HYDRUS-1D software package. We usedthe dual-porosity model since it represents the simplest non-equilibrium approach with thefewest possible parameters, while still facilitating both non-equilibrium flow and solutetransport. Modeling results will be compared with a solute breakthrough curve obtained from a
tracer experiment carried out on an existing VFCW to determine which approach is mostappropriate. We also tried a more realistic approach for calibrating the dual-porosity model.
2. Materials and Methods
2.1. Tracer Experiment
The Evieu wastewater treatment plant (200 p.e.) in Ain, France, has been in operation since2004. The first stage plant consists of three VFCWs receiving raw wastewater. A pump sump at
the plant inlet is used for mechanical screening using a 5 cm mesh screen. Each filter is fed

246according to a feeding/rest regime of 3.5/7 days. Effluent from the first stage is then routed to asecond pump sump and separated between the second stage’s vertical and horizontal flow
constructed wetlands according to the experimental objectives (Molle et al., 2008). All beds areplanted with Phragmites australis.
A fluorescein infiltration experiment was carried out from 04/15/2010 to 04/19/2010,
corresponding to the entire feeding period, on one of the VFCW of the first stage of thewastewater treatment plant. The selected vertical filter (28 m², 2.9 m wide x 9.7 m long) was
designed according to French recommendations. From the bottom to the top, the filter contains a
15-cm thick drainage layer (grain size of 30-60 mm), a 10-cm transition layer (grain size 15-25mm) and a 60-cm gravel layer (d10 = 2.46 mm; UC = d60/d10 = 1.39; average porosity of 40.4%).
Since the filter had been working at nominal load for 7 years, a sludge layer of about 20 cm had
developed at the top of the filter. The VFCW is fed by raw wastewater in batches of 5 cm at a
rate of 1.23 m3/h/m² on average. During spells of dry weather, 8 separate batches are processed
per day. Water is drained using a 160-mm diameter drainage pipe (0.42 m of pipe per m²), whichallowed passive aeration from the bottom as well.
For the tracer experiment, 1.98 g of fluorescein was diluted in a batch volume (1973 L) andapplied to the filter. This application was equal to 0.07 g/m², having a solution fluorescein
concentration of 0.001 g/L. We note that not all the fluorescein was applied in only one batch as
expected; some remained in the pump sump (despite attempts to empty the sump after eachbatch), which was then applied subsequently with the next batch. Unfortunately, the remaining
concentration could not be determined. Some fluorescein after application also remained on topof the filter due to the low permeability and heterogeneity of the sludge deposit. After the
fluorescein application, its concentration was recorded at the VFCW outlet (using an online
fluorimeter PELI 1300 Case; Peli Products, USA) along with the outflow rate (measured with aventure flume) at time intervals of 1 minute throughout the tracer experiment.
Water contents were recorded at the same time using TDR probes, but only during the first batchof the tracer experiment. TDR probes were inserted at three different depths of the filter (13, 31
and 47 cm below the VFCW top surface) and connected through multiplexers to a signal
generator/analyzer (model TDR100, Campbell ScientificTM, Logan, UT). Results were recorded
using a datalogger (model CR1000, Campbell ScientificTM Logan, UT). Measurements weremade at 20 second time intervals.
2.2. Dual-Porosity Models
The aim of this section is not to provide a full mathematical description of various dual-porosity
models. For this purpose readers are referred to Šimůnek et al. (2003, 2008). Our objectives areto emphasize how dual-porosity models can represent preferential flow and to highlight how
complexity is increased by additional parameters. According to Šimůnek et al. (2003),
preferential flow has two main characteristics: (1) an ability to quickly propagate by “bypassing
a large part of the matrix pore-space”, and (2) the presence of non-equilibrium between the waterpressure head within the macropores and the water content in the matrix. Non-equilibrium is a
key concept of preferential flow modeling. Classical descriptions of flow in variably saturated
porous media based on the Richards equation presume that the water pressure head and water247

content are always at equilibrium, and that they are linked by means of a certain water retention
relationship (e.g., the van Genuchten function). This assumption does not hold in situations
where preferential flow occurs.
Dual-porosity models do not aim to physically represent the paths of rapid flow (it would be very
challenging to map every macropore at the scale of a VFCW), but rather attempt to incorporate
their effects in a representative elementary volume (REV) to serve as a basis for modeling.
Figure 1 comparatively shows how macropores can be observed in the filter and how they can bemodeled at the REV scale.

Figure 1. Schematic representation of macropores and preferential flow paths in a VFCW (left)
and the corresponding conceptual physical non-equilibrium (mobile-immobile) model for waterflow and solute transport (right).

Dual-porosity models assume that flow only takes place within the macropores (the mobile
region), whereas flow in the remainder of the medium is neglected. Water in the matrix hence
constitutes the immobile region. The hydraulic parameters (α, n and Ks) are representative offlow in the macropores and therefore must be adjusted, especially Ks, to produce rapid flow. The
total porosity is divided between the mobile ( θ sm ) and the immobile ( θ sim ) regions. This brings
additional complexity to the model. For example, for a given saturated hydraulic conductivity,
the larger the mobile region, the slower the flow in the preferential flow path. For the sake ofsimplicity we considered the residual water content to be zero for both regions.
Non-equilibrium flow is modeled by adding a time-dependent parameter (ω) to the relationshipbetween the water content in the immobile region and the water content in the mobile region (thelatter being linked to the water pressure head). This is an important feature that allows waterexchange to occur at a different time scale than the main gravitational drainage process. The
parameter ω represents another increase in model complexity and needs to be calibrated for eachmaterial in the model.
2.3. Model Description
Because of significant ponding during the feeding process (~5 cm/m²), we assumed that thewater distribution laterally was homogeneous. Consequently, we modeled water flow and solute248transport in one dimension with HYDRUS-1D. In contrast to previous studies carried out on thesame VFCW where we considered four layers (a sludge layer, a first gravel-sludge layer, asecond gravel-sludge layer, and a final layer consisting mostly only of gravel), in this study welimited the domain to only two layers: a sludge layer and a gravel-only layer. Since the numberof parameters in the dual-porosity model is higher than in the equilibrium model, a simplified
representation of the VFCW facilitates modeling and understanding of non-equilibrium flow.
The one-dimensional mesh used for the simulations consisted of 101 equidistant nodes. The top
boundary condition was a time-dependent atmospheric condition with the threshold value forsurface runoff set at 10 cm. The wastewater load duration and flow rate were specified, whileevapotranspiration was neglected. When the incoming flow rate exceeded the infiltration
capacity, ponding of water above the surface was taken into account until the level reached 10
cm. This value was never observed in our case. The bottom boundary condition was a seepage
face. Initial conditions were set to hydrostatic equilibrium.
2.4. Tested Hydraulic Models
Water flow and solute transport were simulated using two different modeling approaches: theclassical equilibrium model and a dual-porosity non-equilibrium model. Two dual-porosity
models are available in HYDRUS-1D depending upon how the mass transfer rate(Γw) is modeled: either being proportional to the difference in effective water contents of the tworegions, or to the difference in effective pressure heads (Gerke and van Genuchten, 1993). We
used the first approach because it requires far fewer parameters. One then does not need to know
the retention function for the matrix region explicitly, but only its residual and saturated watercontents. The second approach should provide a more realistic description of the exchange ratesince the difference in pressure heads between the macropore and matrix regions is the actual
driving force. However, the mass exchange term may then become more unstable numerically(Šimůnek et al., 2003).
Using the first approach, the mass transfer rate Γw for water between the mobile and immobile
regions is given byθ m − θ rm θ im − θ rim ∂θ im= ω Sem − Seim = ω  m
− im
m
im 
∂t
θ s − θ r θ s − θ r 
which in our case simplifies to:θ m θ im 
Γw = ω  m − im θ s θ s 
Γw =

[

]

(1)

(2)

where θm and θim are the mobile and immobile water content, respectively, θ rm and θ rim are themobile and immobile residual water content, respectively, θ sm and θ sim are the mobile andimmobile saturated water content, respectively, ω is a first-order rate coefficient (T-1), and Sem
and Seim are effective fluid saturations of the mobile and immobile regions, respectively.

249

For the equilibrium model we used hydraulic parameter values determined from a previous study(Morvannou, 2012), while for the dual-porosity model some of the hydraulic parameters(notably θ sm , αm, nm, λ, and θ sim ) were adapted from Morvannou (2012), whereas others werearbitrarily fixed ( θ rm , Ks, θ rim , and ω) (Table 1).
One major objective of this study was to obtain better insight into the hydrodynamic and solutetransport processes taking place inside a VFCW. In a first attempt we simulated the tracer
application for only one pulse. In order to evaluate if the observed multiple tracer peaks could be
due to tracer remaining in the sump or at the surface of the filter, we also tested a case with sevenpulses of decreasing concentrations. Modeling results obtained with the equilibrium and nonequilibrium models were compared in terms of concentrations and cumulative fluxes computedat the outlet.
2.5. Calibration of the Dual-Porosity Model
A second objective of our study was to calibrate the dual-porosity model. For this purpose we
divided the gravel-sludge layer into two layers to be able to account for the decreasing gradientin organic matter content versus depth and to compare simulation results with water contents
measured with TDR probes installed in the filter. The one-dimensional mesh and the top andbottom boundary conditions were the same as those used for the previous simulations. The setupof the initial conditions necessitated a prior initialization step. We could not use measured watercontents (from TDR probes) since they did not provide a continuous water content profile at theinitial time and caused convergence problems (Radcliffe and Šimůnek, 2010). Our priorinitialization step consisted of repeating a batch simulation until the pressure heads reached apseudo-permanent state. We then selected the time at which the simulated water content profile
matched the measured initial water contents. The corresponding water pressure profile wasconsidered as initial condition.
Inlet tracer concentrations were adapted from the tracer concentrations measured at the outlet.
For this we applied four batches with decreasing tracer concentrations. Both the hydraulicparameters of the mobile and immobile regions ( θ rm / θ sm and θ rim / θ sim ) and the transfer
coefficient (ω) were subsequently optimized to fit the experimental tracer breakthrough curve.
3. Results and Discussion
3.1. Tracer Experiment
Figure 2 presents the tracer concentration measured at the outlet of the VFCW and thecumulative percentage of the tracer recovery. The total tracer recovery was 62%, which indicatessome loss of fluorescein. This loss could be due to photodegradation of the tracer in the ponded
water above the surface, tracer retention on organic matter (adsorption) and uncertainties in theflow and concentration measurements.

250

Figure 2. Tracer experimental breakthrough curve and cumulative tracer recovery percentage.

Figure 2 highlights two main issues. One is the presence of not just one but several peaks in theobserved breakthrough curve (Fig. 2, (1)). Even if the tracer was mixed only once with theincoming wastewater, it seemed like the tracer application was carried out in several steps (e.g.,remaining tracer in the sump and on filter surface). The tracer left the filter very quickly during
the first batch, thus pointing out the presence of preferential flows in the filter. Another issue is achange in the shape of the breakthrough curve. After the first seven peaks, the tracer
concentration decreased when a new batch arrived and then increased logarithmically towards a
new equilibrium (Fig. 2; (2)).
3.2. Modeling Results
Table 1 presents the hydraulic parameter values used for the equilibrium and non-equilibrium
models.
Table 1. Values of the hydraulic parameters of the VFCW used in HYDRUS-1D.

Layer
1

θr
[-]
0.64

Equilibrium ModelθsΑ[-][1/cm]
0.84
0.12

2

0.00

0.44

0.50

n
[-]
1.80

Ks
[cm/s]
2.50

λ
[-]
0.50

3.20

100

0.50

Dual-Porosity Model

θ rm

θ sm

nm
[-]

Ks
[cm/s]

λ
[-]

θ rim

θ sim

[-]

αm
[1/cm]

[-]

ω
[1/s]

Layer
1

0.00

0.05

0.12

1.80

5

0.50

0.20

0.79

0.05

2

0.00

0.10

0.50

3.20

100

0.50

0.20

0.34

0.00

[-]

251

[-]

Figure 3 shows the simulated concentrations and fluxes obtained with the equilibrium and nonequilibrium models. Also shown are results obtained with only one tracer pulse, and those withseven tracer pulses.

Figure 3. Simulated concentrations (left) and cumulative fluxes (right) for one pulse (top) andseven pulses (bottom) for the equilibrium and non-equilibrium dual-porosity models.

A comparison of the simulated tracer breakthrough curve obtained with the two models showsthat the tracer left the filter faster when using the dual-porosity model than with the equilibrium
model. Also, we note that the equilibrium model was not able to reproduce the shape inversion of
the experimental tracer breakthrough curve (Fig. 2; (2)). The dual-porosity formulation on theother hand provided the same shape inversion due to tracer transfer into the immobile region andits release back into the mobile liquid after each batch. This suggests that preferential flow
effects modeled in terms of mobile and immobile water are very important for matching theobserved fluorescein tracer transport characteristics.
We further note that when only one batch with tracer was applied, it was not possible to simulate
the multiple peaks of the tracer shown in Figure 2. It was necessary to apply the tracer several
times to reproduce the tracer peaks observed at the beginning of the tracer experiment.
If one only compares the cumulative tracer fluxes from the outlet of the filter, no importantdifferences can be seen between the equilibrium and non-equilibrium results. Indeed, cumulative
fluxes are not sensitive enough for comparing the modeling results whereas tracer concentrations
provide much more information about the non-equilibrium processes that occur in the filter.

252

Overall, the comparison of measured and simulated tracer breakthrough curves indicates that the
non-equilibrium approach provides to the more appropriate model for simulating preferential
flow paths.
3.3. Calibration Results
Table 2 presents the hydraulic parameter values of the dual-porosity model used for both thetracer concentrations obtained at the outlet of the filter and the water contents recorded in the
VFCW.
Table 2. Hydraulic parameter values used for calibration of the dual-porosity model representing
VFCW behavior in HYDRUS-1D.
nm
[-]

Ks
[cm/s]

λ
[-]

θ rim

θ sim

[-]

αm
[1/cm]

[-]

ω
[1/s]

0.00

0.01

0.12

1.80

5

0.50

0.70

0.83

0.040

2

0.00

0.02

0.50

3.20

25

0.50

0.38

0.39

0.005

3

0.00

0.05

0.50

3.20

25

0.50

0.34

0.36

0.005

θ rm

θ sm

Layer
1

[-]

[-]

Figure 4 presents measured and simulated concentrations obtained from the tracer experimentand the dual-porosity model using parameter values shown in Table 2. Figure 5 compares
simulated water contents presents using the dual-porosity model with measured values obtainedwith the TDR probes.

13 cm

31 cm
47 cm

Figure 4. Measured (black line) andsimulated (red line) concentrations from thetracer experiment and the dual-porosity
model, respectively.

Figure 5. Measured (dots) and simulated (lines)
water contents from the TDR probes and the dualporosity model at different depths, respectively.

253

After adjusting some of the hydraulic parameters, the simulation using the dual-porosity model(Fig. 4) showed a good match with the measured data (RMSE = 1.47.10-5). We could identify thefour pulses corresponding to the four inlet concentrations at the beginning of the tracer
experiment. After these four batches we observed the same tendency as seen in Figure 2 (2): thetracer concentration decreased immediately after each loading and then increased logarithmicallyto some equilibrium value until a new batch was applied.
The results in Figure 5 indicate that water retention decreased with depth, mostly because oflower organic matter contents deeper in the filter. Also, even with only having water contents
recorded during the first tracer batch, Figure 5 shows that simulated water contents of the sludge
layer (13 cm) where very close to the observed water contents (RMSE = 9.1.10-3). While stillreasonable, simulated water contents for the first (31 cm) and second (47 cm) gravel-sludge
layers were far less accurate (RMSE values were 0.39 and 0.43, respectively). In all, the dualporosity model hence was able to simulate both the tracer breakthrough curve and the watercontents at different depths of the VFCW.
4. Conclusions
A comparison was carried out between the classical equilibrium flow model and a nonequilibrium (dual-porosity) type model for simulating the hydrodynamic behavior and the solutetransport in a simplified representation of a French VFCW. The HYDRUS-1D software package
was found used for modeling the flow and transport processes. Modeling results were compared
to a solute breakthrough curve obtained from a tracer experiment carried out in an existing
VFCW. This allowed us to determine the most appropriate modeling approach.
The comparison between measured and simulated tracer breakthrough curves indicates that thetracer left the filter faster when simulated with the dual-porosity model than with the classicalequilibrium model. The dual-porosity results were consistent with the experimental tracer
breakthrough data. Moreover, the dual-porosity model provided the same shape inversion due tothe tracer transfer into the immobile region and its release back into the mobile region after eachbatch. The dual-porosity model also was able to closely match observed water contents at
different depths of the filter. We conclude that the non-equilibrium approach is the more
appropriate model for simulating preferential flow paths in a French-type VFCW.
References

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Science, 169(3), 382-400, 2006.
Gerke, H. H., and M. Th. van Genuchten, A dual-porosity model for simulating the preferential
movement of water and solutes in structured porous media, Water Resources Research, 29(2), 305–
319, 1993.
Haws, N. W., P. S. C. Rao, J. Šimůnek, and I. C. Poyer, Single-porosity and dual-porosity modeling ofwater flow and solute transport in subsurface-drained fields using effective field-scale parameters,
Journal of Hydrology, 313(3–4), 257–273, 2005.
Köhne, J. M., S. Köhne, and J. Šimůnek, Multi-process herbicide transport in structured soil columns:
experiments and model analysis, Journal of Contaminant Hydrology, 85, 1–32, 2006.

254

Köhne, J. M., S. Köhne, and J. Šimůnek, A review of model applications for structured soils: a) Water
flow and tracer transport, Journal of Contaminant Hydrology, 104, 4–35, 2009.
Maier, U., C. DeBiase, O. Baeder-Bederski, and P. Bayer, Calibration of hydraulic parameters for largescale vertical flow constructed wetlands, Journal of Hydrology, 369(3-4), 260-273, 2009.
Molle, P., A. Liénard, A. Grasmick, and A. Iwema, Effect of reeds and feeding operations on hydraulicbehavior of vertical flow constructed wetlands under hydraulic overloads, Water Research, 40(3),606-612, 2006.
Molle, P., S. Prost-Boucle, and A. Liénard, Potential for total nitrogen removal by combining verticalflow and horizontal flow constructed wetlands: a full-scale experiment study, EcologicalEngineering, 34(1), 23-29, 2008.
Morvannou, A., Dynamic modelling of nitrification in vertical flow constructed wetlands. Sciencesagronomiques et ingénierie biologique, Université catholique de Louvain, 184p, 2012.
Morvannou, A., N. Forquet, M. Vanclooster, and P. Molle, On the characterization of the hydraulicproperties of the filter material of a Vertical Flow Constructed Wetland, (Submitted).
Radcliffe, D., and J. Šimůnek, Soil Physics with HYDRUS: Modeling and Applications, CRC Press,
Taylor and Francis Group, 373 p, 2010.
Šimůnek, J., O. Wendroth, N. Wypler, and M. Th. van Genuchten, Non-equilibrium water flow
characterized by means of upward infiltration experiments, European Journal of Soil Science, 52, 1324, 2001.
Šimůnek, J., N. J. Jarvis, M. Th. van Genuchten, and A. Gärdenäs, Review and comparison of models fordescribing non-equilibrium and preferential flow and transport in the vadose zone, Journal of
Hydrology, 272(1-4), 14-35, 2003.
Šimůnek, J., D. Jacques, M. Th. van Genuchten, and D. Mallants, Multicomponent geochemical transportmodeling using the HYDRUS computer software packages, Journal America Water Resources
Association, 42(6), 1537-1547, 2006.
Šimůnek, J., and M. Th. van Genuchten, Modeling nonequilibrium flow and transport with HYDRUS,
Vadose Zone Journal, 7(2), 782–797, Special Issue “Vadose Zone Modeling”, 2008.

255

256

Estimating the Soil Hydraulic and Thermal Properties of
Unsaturated Porous Media Using HYDRUS-2D
Mohammad Nakhaei1 and Jirka Šimůnek2
1

Department of Geology, Kharazmi University, Tehran, Iran, nakhaei@khu.ac.ir
Department of Environmental Sciences, University of California Riverside, Riverside, USA,
Jiri.Simunek@ucr.edu

2

Abstract
The combined effects of soil temperature and water input on water flow and redistribution processes
under field conditions have not been fully investigated. The objective of this study was to estimate the van
Genuchten unsaturated soil hydraulic parameters and several heat transport parameters (the coefficients inthe thermal conductivity functions) from observed temperature and infiltration data during a single ring
infiltration field experiment. Real-time sensors built by the authors were used to monitor soil
temperatures at depths of 40, 80, 120, and 160 cm during 10 hours. Water temperature in the single
infiltration ring was simultaneously monitored at the same location. The soil thermal conductivity wasestimated from cumulative infiltration and temperature measurements by solving the two-dimensional,
inverse water flow and heat transport problem using HYDRUS-2D. Preliminary results are presented
showing favorable agreement between simulated soil temperatures during the ring infiltration experimentand corresponding observed values.

1. Introduction
The importance of the unsaturated zone as an integral part of the hydrological cycle has long
been recognized. The zone plays an important role in many aspects of hydrology, including
infiltration, soil moisture storage, evaporation, plant water uptake, groundwater recharge, runoff,and erosion. Initial studies of the unsaturated zone focused primarily on water supply studies,inspired in part by attempts to optimally manage the root zone of agricultural soils for maximum
crop production. The past several decades has seen considerable progress in the conceptual
understanding and mathematical description of water flow and heat transport in the unsaturated
zone.
Unsaturated water flow in porous media is generally described using the Richards equation. The
solution of this equation requires knowledge of soil hydraulic functions, θ(h) and K(h). Currently
there are many laboratory and field methods to determine these nonlinear functions (e.g., Klute,
1986; Dirksen, 1991). Most methods require restrictive initial and boundary conditions, which
can make measurements very time-consuming and expensive. When an inverse modelingapproach is used, the unknown hydraulic parameters are estimated by minimizing deviations
between observed variables and model-predicted output (e.g., Kool et al., 1987; Kool and Parker,
1988).
Models of the simultaneous movement of water and heat in the vadose zone are indispensable for
evaluating the water and energy balance of subsurface environments for both agriculture and257

engineering applications, especially in arid and semi-arid regions. Although it is widely
recognized that the movement of water and heat are closely coupled and strongly affect eachother, their mutual interactions are rarely considered in practical applications. The effect of heattransport on water flow is often neglected, arguably because of model complexity and a lack ofdata to fully parameterize the model, but partly also because user friendly simulation codes are
not readily available. Exceptions are the HYDRUS codes (Šimůnek et al., 2006, 2008), which
implement solutions for the coupled movement of water and heat in the subsurface. The
HYDRUS programs numerically solve the Richards equation for saturated-unsaturated waterflow and the convection-conduction equation for heat transport. The heat transport equationconsiders the transport due to conduction and convection with flowing water. The program may
be used to analyze water and heat movement in unsaturated, partially-saturated, or fully-saturated
porous media.
The objective of this study was to estimate soil hydraulic and heat transport parameters bycollecting data during a ring infiltration experiment, including temperature data collected atseveral depths under the center of the ring, while using the parameter estimation options
incorporated in the HYDRUS-2D software package (Šimůnek and Hopmans, 2002; Hopmans etal., 2002).
2. Material and Methods
2.1. Study Area
The study area is located at the campus site of the Kharazmi University in the city of Karaj ofAlborz province, 48 kilometer outside Tehran, Iran. The altitude is 1,297 m above sea level, andthe annual average precipitation approximately 300 mm. The annual average temperature isabout 16°C. The geology is dominated by the Karaj tuff formations. Soils developed from thisbedrock are ssandy loams with a low content of clay (40% sand, 55 % silt, 5% clay). The
vegetation cover is very sparse.
2.2. Single Ring Infiltration Experiment
To study water movement and heat transport we instrumented the soil profile with a single 40 cm
diameter infiltration ring (Fig. 1a) and 4 thermal sensors at depths of 40, 80, 120 and 160 cm(Fig. 1b). The measurement period was from 8.00 to 18.00 on 4th April 2012. Two soil samples
were first collected to characterize soil texture, and then to measure bulk density and the initialwater content. The soil samples were analyzed in the sedimentology laboratory of Kharazmi
University. Water content was measured in the middle of the profile at a depth of 100 cm. Air
temperature was 20oC, and initial soil temperatures at the observation depths were 17.5 oC.
The temperature of the infiltration water was 61oC during the whole experiment. The final
steady-state infiltration rate was also measured and subsequently used for calculating thesaturated hydraulic conductivity of the soil using the Wooding (1968) equation (cited from
Radcliffe and Šimůnek, 2010, page 106).

258

Figure 1a. Single infiltration ring.

Figure 1b. Location of four thermal sensors.

2.3. Numerical Model
The HYDRUS-2D software package was used to model the soil water dynamics and heattransport assuming an axisymmetric transport domain (Šimůnek et al, 2006).
2.3.1. Soil Hydraulic PropertiesHYDRUS implements the soil-hydraulic functions of van Genuchten (1980) who used thestatistical pore-size distribution model of Mualem (1976) to obtain a predictive equation for theunsaturated hydraulic conductivity function in terms of soil water retention parameters. The
expressions of van Genuchten (1980) are given by Eq. 1 and Eq. 2:

θs - θr θr +[1+ |α h|n]mθ ( h) = 
 θ
s


h<0

(1)

h≥0
2

K ( h ) = K s Sel [1 - (1 - Se1 / m ) m ](2)

in which θr and θs denote the residual and saturated water content [-], respectively; Ks is thesaturated hydraulic conductivity [LT-1], α is the inverse of the air-entry value (or bubblingpressure) [L-1], n is a pore-size distribution index [-], and l is a pore-connectivity parameterassumed to be 0.5 [-].
2.3.2. Temperature Dependence of the Soil Hydraulic Functions
A scaling technique similar to one used to describe the spatial variability of soil hydraulicproperties is used in HYDRUS to express the dependence of the soil hydraulic functions on259

temperature. Based on capillary theory that assumes that the influence of temperature on the soil
water pressure head can be quantitatively predicted from the influence of temperature on surface
tension, Philip and de Vries (1957) derived the following equation:

dh h dσ=
dT σ dT(3)

where T is temperature [K] and σ is the surface tension at the air-water interface [MT-2]. From(3) it follows that:

hT =

σT
href = α h* href
σ ref

(4)

where hT and href (σT and σref) are pressure heads (surface tensions) at temperature T andreference temperature Tref, respectively; and αh* is the temperature scaling factor for the pressure
head. Following Constantz (1982), the temperature dependence of the hydraulic conductivity canbe expressed as follows:=
KT (θ )

µ ref ρ T=
K ref (θ ) α K* K ref (θ )µ T ρ ref(5)where Kref and KT denote hydraulic conductivities at the reference temperature Tref and soil
temperature T, respectively; µref and µT (ρref and ρT) represent the dynamic viscosity [ML-1T-1](density of soil water [ML-3]) at temperatures Tref and T, respectively; and αK* is the temperaturescaling factor for the hydraulic conductivity.
2.3.3. Heat Transport
Neglecting the effects of water vapor diffusion, two- and three-dimensional heat transport can be
described as (Sophocleous, 1979):

C p (θ )

∂T
∂ 
∂T 
∂T
=
λij (θ ) - Cw qi∂t ∂xi ∂x j 
∂xi(6)

where λij(θ) is the apparent thermal conductivity of the soil [MLT-3K-1] (e.g. Wm-1K-1) and Cp(θ) and Cw are the volumetric heat capacities [ML-1T-2K-1] (e.g. Jm-3K-1) of the porous medium
and the liquid phase, respectively. The volumetric heat capacity is defined as the product of thebulk density and the gravimetric heat capacity. The first term on the right-hand side of (6)represents heat flow due to conduction, while the second term accounts for heat being260

transported by flowing water. In this study we did not consider the transfer of latent heat byvapor movement. According to de Vries (1963) the volumetric heat capacity can be expressed as:

C p (θ ) = Cnθ n + Coθ o + Cwθ + Ca av ≈ (1.92θ n + 2.51θ o + 4.18θ ) 106( J m -3 o C-1 )(7)

where θ refers to a volumetric fraction [L3L-3], and the subscripts n, o, g, w represent the solid
phase, organic matter, gas phase and liquid phase, respectively.
2.3.4. Apparent Thermal Conductivity Coefficient
The apparent thermal conductivity, λij(θ), combines the thermal conductivity λ0(θ) of the porous
medium (solid plus water) in the absence of flow, and the macro-dispersivity, which is assumed
to be a linear function of the velocity (de Marsily, 1986). In analogy with the dispersion
coefficient for solute transport, the apparent thermal conductivity λij(θ) is given by (Šimůnek andSuarez, 1993):

λij (θ ) = λT Cw | q | δ ij + (λL - λT )cw

q j qi|q |+ λ0 (θ )δ ij(8)where q is the absolute value of the Darcian fluid flux density [LT -1], δij is the Kronecker delta
function, and λL and λT are the longitudinal and transverse thermal dispersivities [L],respectively. The volumetric heat capacity of the liquid phase is included here in the definition of
the thermal conductivity in order to have the dimensions of the thermal dispersivities in length
units (de Marsily, 1986). The thermal conductivity, λ0(θ), accounts for the tortuosity of theporous medium, and is described with the simple equation (Chung and Horton, 1987):

λ0 (θ ) =b1 + b2θ + b3θ 0.5(9)where b1, b2 and b3 are empirical parameters [MLT-3K-1] (e.g. Wm-1K-1).
2.4. Numerical Model
2.4.1. Transport Domain
The transport domain was 200 cm wide and 200 cm deep. The domain was discretized into 441
nodes and 400 triangular finite elements. Calculations were carried out over a period of 10 hours.

261

2.4.2. Initial and Boundary Conditions
The initial water content considered in the simulation (0.041 cm3/cm3) was measured in the field.
A soil profile temperature of 17.5oC as measured in the field was used as the initial condition forheat transport.
All sides of the flow region were considered to be impervious, except for a small portion aroundthe origin at the ponded surface inside the ring infiltrometer where a constant water content was
imposed, and for the bottom of the soil profile where a free drainage condition was imposed (Fig.
2a). The volumetric water content of 0.43 cm3/cm3 was used as the water flow boundary
condition under the single infiltration ring. A third-type heat transport boundary condition wasused for nodes under the single infiltration ring with a constant temperature of 61oC, representing
hot water infiltrating into the soil profile. A third-type heat transport boundary condition was
also invoked at the bottom of the soil profile (Fig. 2b). No-flux boundary conditions were used
for both water flow and heat transport along all other boundary nodes.

Figure 2. Imposed boundary conditions for water flow (left) and heat transport (right) for
the single ring infiltrometer experiment investigated in this study.

3. Results and Discussion
The experimental infiltration data were used to estimate the soil hydraulic characteristics of thesilt loam field soil profile. The steady-state infiltration rate from the ring was 0.00166 cm/s,
while we used a macroscopic capillary length of 8.3 cm typical of a sandy loam (Radcliffe andŠimůnek, 2010). We subsequently used the predicted saturated hydraulic conductivity of 0.0011
cm/sec as an initial estimate in the inverse solution. Measured soil temperatures at four262

observation depths and the cumulative infiltration were used to optimize selected soil hydraulicand heat transport parameters.
Figure 3 shows an example of the simulated output obtained with the HYDRUS-2D model. The
plots show the final water contents and temperatures in the soil profile. Figure 4 compares
simulated and measured cumulative infiltration rates (left) and simulated and measured
temperatures in the soil profile at depths of 40, 80, 120 and 160 cm. Temperatures optimized
with the model fitted the measured temperatures well. Also, the coefficient of determination
indicated a good fit. We conclude that we were able to estimate selected soil hydraulic andthermal parameters quite well, although some questions remain about the uniqueness of the
optimized values.

Figure 3. Final simulated water contents (left) and temperatures (right) in the soil profile.

Figure 4. Simulated and observed cumulative fluxes (left) and temperatures (right).

263

Figure 6 shows the optimized soil characteristic curve, θ(h), and the unsaturated hydraulicconductivity function, K(h), for the silt loam soil. Tables 1 and 2 show the initial estimates (forthose parameters that were optimized) of the soil hydraulic and heat transport properties,
respectively.

Figure 6. Optimized soil characteristic curve (left), θ(h), and hydraulic conductivity function(right), K(h).
Table 1. Initial estimates of soil hydraulic parameters.
=========================
Residual moisture content
Saturated moisture content
First coefficient
Second coefficient
Saturated conductivity
Pore connectivity factor

(WCR)
(WCS)
(ALPHA)(N)(CONDS)
(L)

.001
.43
.035
1.5
.001067.500

Table 2. Initial estimates of heat transport parameters.
=========================
Solid fraction...............................(Qn).............
Organic matter fraction......................(Qo).............
Heat dispersivity longitudinal...............(DisperHL).......
Heat dispersivity transverse.................(DisperHT).......
Parameter B1.................................(B1).............
Parameter B2.................................(B2).............
Parameter B3.................................(B3).............
Heat capacity - solid…………....................(Cn).............
Heat capacity - organic matter...............(Co).............
Heat capacity - water........................(Cw).............

.600
.001
2.000
.200
.2400E+02.3000E+02.1500E+03.1920E+05.2510E+05.4180E+05

Finally, the optimized soil hydraulic and heat transport parameters obtained by solving theinverse problem using the HYDRUS-2D program are presented in Table 3. Figure 7 shows acomparison of the optimized thermal conductivity function λ(θ) for our silt loam soil with thosefor the three main textural classes of clay, loam, and sand (Chung and Horton, 1987). The results
indicate that the optimized thermal conductivity function is very similar to the default functions,thus demonstrating the robustness of the numerical inverse solution when using only measured
soil temperatures and cumulative infiltration during the field ring infiltration experiment.

264

Table 3. Final optimized soil hydraulic and heat transport parameters.
WCR, θr
0.0

WCS, θs

ALPHA, α[cm-1]
0.075

0.43

Thermal Conductivityv [W/m/K]

3

n
1.51

CONDS, Ks[cm/sec]
0.001322b1[kg cm s-3 K-1]
43.3

b2

[kg cm s-3 K-1]
29.6

b3

[kg cm s-3 K-1]
106.0

clay
loam
sand
soil

2.5
2
1.5
1
0.5
0
0

0.1

0.2
0.3
Water Content [-]

0.4

0.5

Figure 7. Comparison of the optimized thermal conductivity function λ(θ) with those for threemain textural classes (clay, loam, and sand).

4. Conclusions
In this study we used HYDRUS-2D to simulate infiltration of relatively warm water from asingle ring infiltrometer into a silt loam soil profile and to estimate the soil thermal andhydraulics properties by inverse solution from collected experimental data. We showed thattemperatures collected at four sensors at four different depths with cumulative infiltration could
provide the required information for simultaneous estimation of the soil thermal and hydraulicproperties. However, using available collected data, we could prove the uniqueness of ourestimated parameters. Therefore, in a subsequent study we will be collecting additional data
(especially pressure heads and water contents at different locations, as well as independently
measured retention and hydraulic conductivity functions) to be able to better evaluate results of
our inverse analysis. We also plan to include nonreactive chemicals in the infiltrating warm
water to study the possibility of inverse modeling for additionally estimate solute transport
properties.

265References

Chung S.-O., and R. Horton, Soil heat and water flow with a partial surface mulch, Water Resour. Res.,23(12), 2175-2186, 1987.
Constantz, J., Temperature dependence of unsaturated hydraulic conductivity of two soils, Soil Sci. Soc.
Am. J., 46(3), 466-470, 1982.
de Marsily, G., Quantitative Hydrogeology, Academic Press, London, 1986.
de Vries, D. A., The thermal properties of soils, In: Physics of Plant Environment, edited by R. W. van
Wijk, pp. 210-235, North Holland, Amsterdam, 1963.
Dirksen, C., Unsaturated hydraulic conductivity, In: Soil Analysis: Physical methods, K.A. Smith andC.E. Mullins (eds.), 209-269, Marcel Dekker, Inc., New York, 1991.
Hopmans, J. W., J. Šimůnek, N. Romano, and W. Durner, Inverse Modeling of Transient Water Flow, In:
Methods of Soil Analysis, Part 1, Physical Methods, Chapter 3.6.2, Eds. J. H. Dane and G. C. Topp,
Third edition, SSSA, Madison, WI, 963-1008, 2002.
Klute, A. (ed.), Methods of Soil Analysis, Part 1., 2nd ed., Agronomy Monograph, 9, 635-662, ASA and
SSSA, Madison, WI, 1986.
Kool, J. B., and J. C. Parker, Development and evaluation of closed-form expressions for hysteretic soil
hydraulic properties. Water Resour. Res., 23(1), 105-114, 1987.
Kool, J. B., J. C. Parker, and M. Th. van Genuchten, Parameter estimation for unsaturated flow andtransport models - A review, J. Hydrol., 91, 255-293, 1987.
Mualem, Y., A new model for predicting the hydraulic conductivity of unsaturated porous media, Water
Resour. Res., 12(3), 513-522, 1976.
Philip, J. R., and D. A. de Vries, Moisture movement in porous materials under temperature gradients,
Trans. Am. Geophys. Union, 38, 222-232, 1957.
Radcliffe D. E, and J. Šimůnek, Soil Physics with HYDRUS, CRC Press, Taylor & Francis Group, Boca
Raton, FL, ISBN: 978-1-4200-7380-5, pp. 373, 2010.
Šimůnek, J., and D. L. Suarez, UNSATCHEM-2D code for simulating two-dimensional variably
saturated water flow, heat transport, carbon dioxide production and transport, and multicomponent
solute transport with major ion equilibrium and kinetic chemistry, Version 1.1, Research Report No.
128, U. S. Salinity Laboratory, USDA, ARS, Riverside, CA, 1993.
Šimůnek, J., and J. W. Hopmans, Parameter Optimization and Nonlinear Fitting, In: Methods of Soil
Analysis, Part 1, Physical Methods, Chapter 1.7, Eds. J. H. Dane and G. C. Topp, Third edition, SSSA,
Madison, WI, 139-157, 2002.
Šimůnek, J., M. Šejna, and M. Th. van Genuchten, The HYDRUS Software Package for Simulating Twoand Three-Dimensional Movement of Water, Heat, and Multiple Solutes in Variably-Saturated
Media, User Manual, Version 1.0, PC Progress, Prague, Czech Republic, 2006.
Šimůnek, J., M. Th. van Genuchten, and M. Šejna, Development and applications of the HYDRUS andSTANMOD software packages, and related codes, Vadose Zone Journal, 7(2), 587-600, 2008.
Sophocleous, M., Analysis of water and heat flow in unsaturated-saturated porous media, Water Resour.
Res., 15(5), 1195-1206, 1979.
van Genuchten, M. Th., A closed-form equation for predicting the hydraulic conductivity of unsaturated
soils, Soil Sci. Soc. Am. J., 44, 892-898, 1980.
Wooding, R. A., Steady infiltration from large shallow circular pond, Water Resour. Res., 4, 1259-1273,
1968.

266

Simulation of Water and Salinity Dynamics under Different
Irrigation Applications to an Almond Treein Pulsed and Continuous Mode
Vinod Phogat1,*, Mark A. Skewes1, M. Mahadevan1, and James W. Cox1,21South Australian Research and Development Institute, G.P.O. Box 397, Adelaide, SA 5001
Vinod.Phogat@sa.gov.au, Mark.Skewes@sa.gov.au, Mahalakshmi.Mahadevan@sa.gov.au, Jim.Cox@sa.gov.au
2
The University of Adelaide, PMB1 Glen Osmond SA 5064
james.w.cox@adelaide.edu.au

Abstract
The quantification of the components of water balance is essential for designing strategies for improving
irrigation efficiency and water productivity of crops under different irrigation systems and for minimizing
the offsite movement of nutrients out of the rhizosphere. HYDRUS-2D was used to simulate seasonal
water balance and salinity distribution under full pulsed (FIp), sustained deficit pulsed (SDIp; 65% ETC),
and full continuous (FIc) irrigation of an almond tree using a surface drip. The weekly measured andpredicted values of moisture content at different distances from the dripper and at different soil depths
matched well, showing only a small variation in RMSE values. The sap flow underestimated almondwater uptake by 31% as compared to the modeled value in SDIp. Water uptake efficiency under SDIp
(68%) was higher compared to full water application conditions under FIp and FIc (54-55%). The leaching
fraction was estimated to be 0.14 under SDIp and 0.25 in FIp and FIc treatments. The higher irrigation
amounts under 100% ETC treatments (FIp and FIc) largely contributed to non-productive water fluxes(deep drainage losses and evaporation). The seasonal water uptake by almond under pulsed (FIp) andcontinuous irrigation (FIc) remained almost at par, indicating that pulsing didn’t provide any added
advantage, although it is a viable alternative to slow discharge continuous irrigation. The averagemodeled soil solution salinity (ECsw) of the soil profile also remained below the threshold for the yield
reduction during the growing season in all treatments. The irrigation water productivity (WPI) increased
substantially (37%), yield was reduced by 8% and about 35% of irrigation water was saved undersustained deficit irrigation (SDIp) as compared to full irrigation (FIp). It was concluded that SDIp is apromising deficit irrigation strategy for almond cultivation in Australia. These outcomes can be utilized to
improve irrigation efficiency and system design for drip irrigation of almond trees.

1. Introduction
Fierce competition among water users, frequent droughts, and scarce water resources in Australia
put enormous pressure on irrigation systems and drive a requirement for more efficient irrigation
practices. Hence, 90% of almond plantation in Australia is under a high efficiency drip system of
irrigation. Various water saving interventions, like pulsing of irrigation and sustained deficit
irrigation, are being followed for managing water efficiently and increasing the waterproductivity. However, dynamics of water fluxes above and in the soil exert a pronounced
impact on plant water uptake, deep drainage, and solute distribution in the soil profile and thus
significantly influence processes of water and solute movement in the rhizosphere (Phogat et al.,2013). Therefore, evaluating seasonal dynamics in plant water uptake and deep drainage is267

needed, so that improvements in the usage of scarcely available water can be attained and toenhance water productivity.
The temporal and spatial dynamics of water fluxes through the soil-plant-atmosphere continuum
can be better understood using numerical simulation models, provided that the precisely
measured values of input parameters are used for modeling simulations. Out of the numerous
models, varying in degree of sophistication and complexity and presently available for
evaluating the soil water movement (Subbaiah, 2013), HYDRUS has been extensively used forthe analysis of micro irrigation systems involving a varied range of soil, water, and cropconditions (Gardenas et al., 2005; Hanson et al., 2006; Kandelous et al., 2012; Phogat et al.,2012ab, 2013; Ramos et al., 2012). Although modeling has been done extensively for problems
related to drip irrigation systems using the HYDRUS software, only a few studies have been
substantiated with field validation.
The present study uses HYDRUS-2D modeling and the field data recorded for an almond tree
over a season to evaluate the water balance and salinity dynamics under full irrigation and stressconditions, and to evaluate the impact of pulsing and continuous drip irrigation on the dynamics
of water fluxes, including plant water uptake and deep drainage. Understanding the daily water
fluxes during the crop season under high frequency irrigation would have large implications fordevising the irrigation scheduling and improving water productivity of almond under stressconditions.
2. Materials and Methods
2.1. Details of Field Experiment
The experiment was conducted at Clark Taylor farms, a commercial almond [Prunus dulcis(Mill.) Webb] orchard in Berri, South Australia (34°20'S and 140°35'E) from July, 2009 to May,
2010. The orchard was planted in 1998 with the rows oriented north–south and a spacing of 6.7
m between rows and 6.1 m within a row. Since the soil was more or less uniform, a mean soil
particle size distribution of 88.5% sand, 1.9% silt, and 9.6% clay, and a bulk density of 1,610 kg
m-3 were considered in this study. The trees were managed and fertilized following current
commercial practices. The total rainfall received during the study period was 220 mm. The daily
ETC for the irrigation purpose was calculated from Epan values of the previous day multipliedwith suitable crop factors.
The orchard was surface drip irrigated, with a pulsed irrigation treatment of 100% ETC (FIP),
sustained deficit irrigation of 65% ETC (SDIp), and a continuous irrigation treatment of 100%
ETC (FIc), covering an area of 1.89, 0.97, and 0.7 ha, respectively. The treatments were initiatedfrom 20th August, 2009 after one month of a profile establishment stage. Profile establishment
resulted in the application of an equal amount of irrigation (85 mm) in each treatment. The
seasonal salinity of irrigation water ranged between 0.2 to 0.52 dS m-1.
Each row of trees had two laterals, one on either side of the row at 1 m offset from the tree trunk.
The pulsed treatments (FIp and SDIp) were irrigated with a cycle of one hour on and one hour268

off, with an average flow rate of the drippers of 3.87 l h-1. For continuous treatment (FIc), themeasured flow rate was 2.00 l h-1 per dripper. The number of drippers per tree was approximately
12 for the pulsed treatments and 15 for the continuous treatment, as the dripper distance inpulsed and continuous treatments was 100 cm and 80 cm, respectively.
Neutron probe access tubes were installed at a lateral distance of 0, 20, 40, 60, 80, and 100 cm
from the dripper (Fig. 1) to a depth of 160 cm to monitor the profile soil water distribution at
weekly intervals, at every 10 cm depth up to a depth of 100 cm, and then every 20 cm between
depths of 100 and 160 cm.

Figure 1. A schematic view of a model domain, plant spacing, and measuring gadgets.

Sap flow measurements were performed on two trees under pulsed treatments (SDIp and FIp) andwere based on the heat pulse method outlined by Green et al. (2003) to quantify the water uptake
by an almond tree. However, the sap flow installation was delayed and measurements wereobtained only from 25th November onward.
2.2. Numerical Modeling
Soil water and soil water salinity distributions below the drip line were simulated with theversion 2.x of the computer simulation model HYDRUS (2D/3D). This new HYDRUS softwaremodule can simulate two- and three-dimensional variably saturated water flow, heat movement,
and transport of solutes involved in sequential first-order decay reactions. In addition, the modelallows for specification of root water uptake, which affects the spatial distribution of water andsoil water salinity between irrigation cycles. The details about the model can be obtained fromŠimůnek et al. (2011) and Šejna et al. (2011).
2.3. Input Parameters
Though seasonal irrigations of almond were based on Epan and crop factors, the potential ETC
was calculated from the reference evapotranspiration (ET0) values collected from the269

Bookpurong meteorological station, situated 150-200 m away from the experimental site,
following the dual crop coefficient method (Allen et al., 1998), to serve as an input for themodel. The seasonal potential transpiration (Tpot) amounts to 1,380 mm, and potential
evaporation (Es) for the same period was 414 mm. The estimates of optimized soil hydraulicparameters used for the modeling simulations were: θr = 0.06, θs = 0.37, Ks = 276.6 cm day-1, α= 0.0316 cm-1 and n = 2.52. The value of l was taken as 0.5 as recommended.
The almond root distribution was described using the Vrugt et al. (2001) two-dimensional model
adapted in HYDRUS. The parameters used in the model for almond were: zm = 150 cm, z* = 30
cm, xm = 335 cm, x* = 25 cm, px = 2.918, pz = 3.214. The values of empirical coefficients weretaken from Vrugt et al. (2001), and were optimized for almond.
The reducing effects of both soil water pressure head and osmotic head on root water uptake
were included, assuming their effects were multiplicative. The following parameters of themodel were used: h1 = −10, h2 = −25, h3max, = −500, h3min = −800, h4 = −8000 cm; r2,high = 0.5 cm
d-1, and r2,low = 0.1 cm d-1. The threshold model was used to describe osmotic effects using athreshold ECe = 1.5 dS m-1 and a slope of 19%.
Spatial distribution of salinity in the transport domain was simulated using the convection–
dispersion equation for a nonreactive tracer. Such simulations cannot account for complex
processes such as precipitation or dissolution of solid phases (e.g., gypsum or calcite) or cationexchange. Longitudinal dispersivity was considered to be 20 cm and transverse dispersivity was
2 cm.
The water content initial conditions were based on values measured by the neutron probe, which
varied from 0.05 to 0.08 cm3cm-3 in F1p, 0.07-0.14 cm3cm-3 in SDIp, and 0.04-0.06 cm3cm-3 incontinuous (F1c) drip irrigation. Similarly, the initial soil solution salinity (ECswi) in the soil
profile varied from 3.89 to 7.22 dS m-1, 3.63-8.3 dS m-1, and 4.55-7.95 dS m-1 in F1p, SDIp, andF1c treatments, respectively. Initial soil water salinities were based on field measurements madeat the start of the experiment and estimated from measurements of the saturated soil extract(ECe). The water flow boundary conditions are shown in Figure 1. In the case of solute transport,
the boundary condition representing salinity is a third-type Cauchy boundary condition thatprescribes the salt movement during defined irrigation intervals.
Simulations were made for hourly pulsed and continuous irrigation treatments during a period of
316 days. The simulated surface drip irrigation system design characteristics were typical of thedrip systems used for the field experiment on almond, as shown in Figure 1. The model domain
was 200 cm deep and 335 cm wide (one fourth of the bed spacing used for the almondproduction). The domain was discretized into 5,087 finite elements with a very fine grid aroundthe dripper (0.3 cm) and gradually increasing elements farther from the drip (up to 9.8 cm). The
measured salinity of irrigation water (ECiw) was used as a time variable boundary condition. The
drip irrigation was simulated assuming an infinite line source to be a good representation of thedrip irrigation system. The root mean square error (RMSE) was calculated to compare theexperimental and predicted values of water content.

270

3. Results and Discussion
The model-produced, weekly values of water content were compared with measured values atvarious horizontal and vertical locations in the domain in all treatments. For example, themeasured and simulated water contents in full pulsed treatment (FIp) at a distance of 20 cm fromthe dripper, averaged for all depths is shown in Figure 2. The simulated water content values
matched the neutron probe measured data well, except within a short period during midseason of
the crop. The RMSE values ranged from 0.01 to 0.08, 0.01-0.06, and 0.01-0.05 cm3cm-3 in full
pulsed (F1p), pulsed deficit (SDIp), and full continuous (F1c) irrigation, respectively. Similarvariations between measured and simulated moisture regimes have also been reported in othermodeling studies (Phogat et al. 2012ab, 2013). This comparison confirms that the model
successfully captured the dynamics of water movement in the soil throughout the cropping
season under both scenarios of the water application. However, the small differences between
measured and simulated water contents are likely due to model errors caused by restrictive
assumptions regarding the geometry of the rooting system, homogeneity of soil hydraulicproperties within the spatial domain, and the prescribed root water uptake model.

Water content (cm3 cm-3)

Simulated water balance components obtained for different treatments are shown in Table 1.
Seasonal water uptake in sustained deficit treatment (SDIp) was reduced by 13.9%, compared tofull pulsed irrigation. However, water uptake under full pulsed (F1p) and full continuous (FIc)
irrigations remained almost equal. On the other hand, root water uptake efficiency under stresstreatment (68%) was much higher compared to normal water application conditions (54-55%) in
FIp and FIc treatments.
0.18
0.15
0.12
0.09
0.06

measuredsimulated

0.03
0

205

240

275

317

357
29
DOY

70

105

144

Figure 2. The comparison of weekly measured and simulated water contents in full pulsed
irrigation (FIp) at a distance of 20 cm from the dripper.

A significant reduction was observed in deep drainage flux for scenarios under stress, which was
drastically reduced under SDIp as compared to full irrigation (Table 1). Only 14% of total water
applied escaped the crop root zone in SDIp, compared to 25% in full irrigation treatments (FIpand FIc). However, among full irrigation scenarios, pulsing had a little impact on the deep
drainage because it was slightly higher (13 mm) under pulsing (FIp), and the soil storage was 20
mm higher under continuous irrigation (FIc). Apparently, large changes in the soil storage (53271and 73 mm) reflected the depth of the soil in the model domain (200 cm) and the fact that the soil
was quite dry at the beginning of the simulation, and uniformly wet across the model domain at
the end of the simulation, as a result of irrigation and rainfall events.
Table 1. Water balance components in different treatments under pulsed and continuous irrigation.
Parameters
Irrigation
Rainfall
Root water uptake
Evaporation
Deep drainage
Soil storage

SDIp
FIp
FIc
Difference (FIp & FIc)---------------------(mm)----------------(%)
1104
1686
1668
18
1.1
220
220
220
905
1051
1026
25
2.4
238
310
311
-1
-0.3
190
489
476
13
2.7
(-) 8
53
73
-20
-37.7

Water uptake (mm)Daily root water uptake rates calculated by HYDRUS-2D were compared with the sap flow
measured transpiration by almond during 25th Nov, 2009 to 31st May, 2010 in full pulsed (FIp),
as well as for stress (SDIp) treatments. The comparison for full irrigation has been illustrated in
Figure 3. It can be seen that HYDRUS very well sensed the diurnal fluctuations in the water
uptake driven by the evapotranspirational demand, and the model also predicted water uptake
fluctuations very well, in accordance with the sap flow measurements. However, the magnitudeof modeled water uptake was higher than the sap flow measurements until the almond harvest
and, subsequently, both matched well. Sap flow measurements estimated 492 mm water uptake
during this period, compared to 659 mm predicted by the model, and compared with the 1,167
mm of water applied through irrigation and rainfall. Hence, sap flow measurements
underestimated water uptake by almond by about 25% under full irrigation and 31% under the
stress treatment. We believe that the assumption of wood thickness, and wood and sap
composition for the estimation of the correction factor may have resulted in the underestimationof water uptake by sap flow. Several other reasons for underestimations are also outlined in
Phogat et al. (2013).
16

Simulated

12

Sap flow84
0

329 344 359

9

24

39

54 69
DOY

84

99 114 129 144

Figure 3. Comparison of simulated daily water uptake and sap flow water uptake by almond infull pulsed (FIp) irrigation.

272

The deep drainage was not evenly distributed over the season (Figure 4). There was higher
leaching early in the season (August) and after harvest in Feb-April, together amounting to 50%of the total seasonal leaching in FIp and FIc treatments, whereas more than 50% drainage in SDIp
occurred in July-August (a profile establishment stage), and thereafter the drainage volume wasdrastically reduced to negligible amounts during the midseason, increasing again during MarchApril after the harvest of kernels. Hence, during the July-August and Feb-April periods, thewater requirement of almond was less than the water application. This implies that there is aneed to revise the used crop coefficients (Kc), and reschedule irrigation applications during these
periods so that these unnecessary water losses can be controlled.
Model simulations were also performed for the seasonal salinity distribution in the soil profile,and average soil solution salinity (ECsw) data is presented in Figure 5. The ECsw values remained
similar in both full irrigation treatments (FIp and FIc) because the salt transport in a light-textured
soil is predominantly governed by the dynamics of water movement, which was similar in both
treatments. The average ECsw values in the soil below the dripper ranged from 0.47 to 3.38 dS m1
and 0.49 to 3.67 dS m-1 in FIp and FIc treatments, respectively.

Drainage (mm)

120
100
80
60
40
20
0

SDIp
FIp
FIc

July, Aug, Sept, Oct, Nov, Dec, Jan, Feb, Mar, Apr, May,
09 09 09 09 09 09 10 10 10 10 10

Figure 4. Simulated deep drainage (mm) under pulsed deficit (SDIp), full pulsed (F1p), and fullcontinuous (F1c) drip irrigation of almond.

4
SDIp
FIp
FIc

ECsw (ds/m)

3
2
1
0

202 221 240 282 308 324 365
DOY

43

78

91

106 148

Figure 5: Simulated soil solution salinity (ECsw) distribution in pulsed deficit (SDIp), full pulsed(FIp) and continuous (FIc) drip irrigation of almond.

273

The soil solution salinity (ECsw) under SDIp was initially lower because the initial soil watercontent was substantially higher compared to FIp and FIc treatments and consequently, higher
leaching was observed during the profile establishment and early growth period. However, from
September onward the salinity in SDIp was much higher and continued to increase until
December, when it reached a maximum value of 3.55 dS m-1, after which it decreased
continuously until April, 2010. This occurred due to relatively lower water content in the soil
under stress conditions in SDIp up until December, and then dilution due to increased soil watercontents after December, although little drainage was evident until March. However, the salinity
remained below the threshold for almond (ECe 1.5 dS m-1) throughout the growing season in all
the treatments.

1.4
1.2
1
0.8
0.6
0.4
0.2
0

Kc
ETc

300
250
200
150
100

ETC (mm)Kc

HYDRUS-2D-calculated values of actual monthly evaporation and transpiration were summed
up to calculate the monthly crop coefficients of almond (Figure 6). The midseason Kc’s of 1.23,
1.22, 1.31, and 1.11 for October, November, December, and January, respectively, weresignificantly higher than the FAO 56 value of 0.9, which is applied to a temperate climate andno-stress conditions. However, the values of Kc obtained in the present study matched well withthose reported by Stevens et al. (2012) for a sprinkler-irrigated almond in this region. They
reported that higher Kc values for midseason were due to the prevalence of non standard weather
conditions and high advective conditions in the region.

50
0

Figure 6. Estimated monthly crop coefficients (Kc) and crop evapotranspiration (ETC) of almond.

Experimental and simulated values of water balance were utilized to calculate the waterproductivity of almonds under full and deficit irrigation (Figure 7). It can be seen that irrigationwater productivity (WPI) under stressed conditions (SDIp) increased substantially (37%) ascompared to full irrigation (FIp). It is inferred that almonds are among the species capable ofmaintaining high gains in the water productivity under increasing soil water deficit (Girona et al.,2005). The estimated irrigation water productivity (WPI) in this investigation was appreciably
higher than that reported in several other studies, where it varied from 0.20-0.33 kg m-3 (Egea etal., 2010). The data indicates that, for regions with a severe water scarcity, SDIp appears to be a
promising deficit irrigation strategy for almond trees, as it increased WPI by 37%, reduced yield
only by 8%, and saved about 34.5% of irrigation water in comparison to full irrigation (FIp).

274

20.00

16.86

16.00
12.00

SDIp
FIp

11.04

8.00

5.34 5.84

4.00

0.48 0.35

0.00
Irrigation(ML/ha)Yield (t/ha)

Productvity(t/ML)

Figure 7. Almond water productivity under full irrigation (FIp) and stress conditions (SDIp).

4. Conclusions
The study concludes that HYDRUS-2D simulated water fluxes and soil salinity dynamics underdrip-irrigated almond very well. This work identifies significant drainage during the months ofAugust and Feb-April, when the tree water demand was less than had previously been assumed.
The model-produced values of evapotranspiration were utilized to evaluate the monthly crop
coefficients and the crop water productivity. Recalculations of crop coefficients (Kc) as a resultof this work have the potential to lead to significant water savings and water efficiency
improvements. The study also revealed that SDIp seems to be one of the most promising reduced
irrigation application options available for improving irrigation efficiency.
Acknowledgements
The authors wish to thank Clark Taylor Farms for access to the orchard for field work and JirkaŠimůnek for modeling support. The financial support of the Almond Board of Australia isgratefully acknowledged.
References

Allen, R. G., L. S. Pereira, D. Raes, and M. Smith, Crop evapotranspiration guidelines for computing cropwater requirements, FAO Irrigation and Drainage Paper No. 56, FAO, Rome, Italy, 1998.
Egea, G., P. A. Nortes, M. M. Gonzalez-Real, A. Baille, and R. Domingo, Agronomic response and waterproductivity of almond trees under contrasted deficit irrigation regimes, Agricultural Water
Management, 97, 171–181, 2010.
Gärdenäs, A. I., J. W. Hopmans, B. R. Hanson, and J. Šimůnek, Two-dimensional modeling of nitrateleaching for various fertigation scenarios under micro irrigation, Agricultural Water Management, 74,
219–242, 2005.
Girona, J., M. Mata, and J. Marsal, Regulated deficit irrigation during the kernel-filling period andoptimal irrigation rates in almond, Agricultural Water Management, 75, 152–167, 2005.
Green, S., B. Clothier, and B. Jardine, Theory and practical application of heat pulse to measure sap flow,
Agronomy Journal, 95, 1371–1379, 2003.

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Hanson, B. R., J. Šimůnek, and J. W. Hopmans, Evaluation of urea–ammonium–nitrate fertigation withdrip irrigation using numerical modeling, Agricultural Water Management, 86, 102–113, 2006.
Kandelous, M. M., T. Kamai, J. A. Vrugt, J. Šimůnek, B. Hanson, and J. W. Hopmans, Evaluation of
subsurface drip irrigation design and management parameters for alfalfa, Agricultural Water
Management, 109, 81–93, 2012.
Phogat, V., M. Mahadevan, M. A. Skewes, and J. W. Cox, Modelling soil water and salt dynamics underpulsed and continuous surface drip irrigation of almond and implications of system design, Irrigation
Science, 30(4), 315-333, 2012a.
Phogat, V., M. A. Skewes, J. W. Cox, and M. Mahadevan, Modelling the impact of pulsing of drip
irrigation on the water and salinity dynamics in soil in relation to water uptake by an almond tree,
WIT Transactions on Ecology and Environment, 168, 101-113, WIT Press, ISSN 1743-3541,
doi:10.2495/SI120091, 2012b.
Phogat, V., M. A. Skewes, M. Mahadevan, J. W. Cox, Evaluation of soil plant system response to pulsed
drip irrigation of an almond tree under sustained stress conditions, Agricultural Water Management,
118, 1-11, 2013.
Ramos, T. B., J. Šimůnek, M. C. Goncalves, J. C. Martins, A. Prazeres, L. S. Pereira, Two-dimensionalmodeling of water and nitrogen fate from sweet sorghum irrigated with fresh and blended saline
waters, Agricultural Water Management, 111, 87-104, 2012.
Šejna, M., J. Šimůnek, and M. Th. van Genuchten, The HYDRUS software package for simulating twoand three-dimensional movement of water, heat, and multiple solutes in variably-saturated media,
User Manual, Version 2, PC Progress, Prague, Czech Republic, pp. 280, 2011.
Šimůnek, J., M. Th. van Genuchten, and M. Šejna, The HYDRUS software package for simulating twoand three-dimensional movement of water, heat, and multiple solutes in variably-saturated media,
Technical Manual, Version 2, PC Progress, Prague, Czech Republic, pp. 258, 2011.
Stevens, R. M., C. M. Ewenz, G. Grigson, S. M. Conner, Water use by an irrigated almond orchard,
Irrigation Science, 30(3), 189-200, 2012.
Subbaiah, R., A review of models for predicting soil water dynamics during trickle irrigation, Irrigation
Science, 31(3), 225-258, doi:10.1007/s00271-011-0309-x, 2013.
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Soil Science Society of America Journal, 65, 1027-1037, 2001.

276

HYDRUS-1D Modeling Applications to Waste Disposal
Problems in Brazil
Elizabeth M. Pontedeiro, Victoria Ottoni, and Martinus Th. van Genuchten
Departments of Nuclear, Civil and Mechanical Engineering, COPPE, Federal Universityof Rio de Janeiro, UFRJ, Rio de Janeiro, RJ, 21945-970, Brazil
bettinadulley@hotmail.com, viottoni@gmail.com, rvangenuchten@hotmail.com

Abstract
This paper summarizes three studies in which HYDRUS-1D was used to investigate the performance ofdifferent types of waste disposal sites in Brazil: a conventional mining installation containing naturally
occurring radioactive materials (NORMs), a municipal landfill, and a radioactive waste repository. In thefirst application we used HYDRUS-1D to predict long-term (tens of thousands of years) radionuclidetransport vertically through both the landfill and the underlying unsaturated zone, and then laterally ingroundwater. The second study concerned water fluxes into and through a municipal solid waste (MSW)
landfill in the city of Rio de Janeiro. We considered two cover systems that could minimize percolation
through the landfill. One used a capillary barrier made from MSW compost, and the other one avegetation cover using either grass or native vegetation. The third application involved a near-surface
repository containing 137Cs wastes resulting from decontamination of Goiania city in Brazil after the 1987
accident with a CsCl teletherapy source. Long-term simulations were carried out of 137Cs transport fromthe repository through the concrete liner below the waste and the underlying vadose into groundwater.
The examples show the flexibility of HYDRUS-1D to address different types of problems.

1. Introduction
Numerical models such as the HYDRUS codes (Šimůnek et al., 2008a) are increasingly used forpredicting or analyzing water flow and contaminant transport processes in the subsurface,
including the vadose zone. In this paper we summarize three recent applications of HYDRUS-1D
to waste disposal problems in Brazil. One application involves the disposal of NORM mining
wastes (i.e., wastes containing naturally occurring radioactive materials) in an industrial landfill.
HYDRUS-1D (Šimůnek et al., 2008b) was used to predict long-term radionuclide transportvertically through both the landfill and the underlying unsaturated zone, and then laterally ingroundwater. Calculations were carried out for both a best-case scenario assuming equilibriumtransport in a fine-textured subsurface, and a worst-case scenario involving preferential flow.
The second study concerned water fluxes into and through a municipal solid waste (MSW)
landfill in the city of Rio de Janeiro. Two different cover systems were considered that would
minimize infiltration of rain water into the landfill. One used a capillary barrier made from MSW
compost, and the other one a vegetation (evapotranspiration) cover using either grass or native
vegetation from the area.
The third application considered a near-surface repository containing 137Cs wastes resulting fromdecontamination of Goiania city in Brazil after the 1987 accident with a CsCl teletherapy source.

277

The study provided estimates of water fluxes through the soil cover into and through therepository and concrete liners of the repository towards underlying groundwater. Performance ofthe cover system and engineered barriers was followed for 400-years, which included accounting
for the effects of concrete degradation. Simulations were further carried out of 137Cs transport
from the repository through the concrete liner below the waste and the underlying vadose
towards groundwater below the site.
2. NORM Waste Disposal Site
The first application concerned the subsurface transport of radionuclide decay chains (notably
the 238U and 232Th series) leached from a conventional mining installation in Amazonia
processing ore containing natural occurring radioactive materials (NORMs). The disposal site
contained slags having radionuclide concentrations many times higher as compared to theoriginal ore. Dimensions of the disposal unit were 70 m wide by 100 m long and 6.0 m deep.
Initial radionuclide concentrations were 71 Bq/g for 238U and 234U, 67 Bq/g for 230Th, 63 Bq/g for226
Ra and 4.8 Bq/g for 210Pb. The slag waste layer had a measured bulk density (ρb) of 1.89
g/cm3. Hydraulic properties of the waste were estimated from drainage experiments on large
lysimeters containing slags from the site. Batch measurements produced radionuclide
distribution coefficients (Kd) very close to those of a clay soil (ISAM, 1998), except for Ra,
whose Kd value was closer to that of sand. For these reasons we used Kd values typical of clay for
U, Th, and Pb (1.6, 5.8, and 0.54 m3/kg, respectively), and the measured value (0.88 m3/kg) for
Ra. An impermeable liner under the waste layer (a requirement of the Brazilian regulatory
agency) was not considered in our analysis.
The unsaturated zone below the waste layer consisted of reddish Belterra clay as described by
Dennen and Norton (1977) and Truckenbrodt and Kotschoubey (1981). Soil texture, bulk density(1.3 g/cm3) and the saturated hydraulic conductivity (Ks = 21 m/y) were locally measured. Other
parameters of Belterra clay were taken from Belk et al. (2007), except for the soil hydraulicparameter α (we used a value of 4.5 m-1). The saturated zone contained red saprolite interspersedwith lighter-colored lenses derived from feldspars. The phreatic aquifer had an average thicknessof 4.5 m, with a natural hydraulic gradient of 0.0562. Geotechnical essays produced Ks values
between 4.2 x10-5 and 7.9x10-4 cm/s. For our calculations we used a value of 1.7 x 10-4 cm/s.
Average annual precipitation measured in the area was 2,430 mm, and the average
evapotranspiration rate (as calculated with the Penman-Monteith equation) was 1,610 mm.
Adjusted for runoff, the long-term average recharge rate at the site was estimated to be 657
mm/y. This recharge rate was used as a surface flux boundary condition for the steady-state
simulations of water flow through the site and into groundwater.
We used HYDRUS-1D to first predict radionuclide transport vertically through both the landfill
and the underlying unsaturated zone, and then one-dimensional laterally in groundwater.
Calculations were carried out for both a best-case scenario assuming equilibrium transport, and aworst-case scenario with preferential flow as modeled using the physical nonequilibrium (dualporosity) formulation of van Genuchten and Wierenga (1976). The performance assessment was
carried out using a leaching and off-site small farm scenario (Pontedeiro et al., 2010).

278

Radionuclides transported in groundwater were assumed to be intercepted by a well 100 m down
gradient of the landfill. For the safety analysis we used concentrations of the aquifer at the well.
Figure 1 shows the effect of preferential flow separately through the waste later, the vadose zone
and the aquifer. For preferential flow we assumed a value of 0.5 for the fraction immobile water,and different values of the mass transfer coefficient (denoted here by the parameter β in year-1).
Results indicate that the highest U concentrations in the leachate leaving the waste were obtainedfor equilibrium transport. This shows that preferential flow (smaller value of β) of rain water
through the waste leads to less pollution of the subsurface. This situation is reversed whenpreferential flow occurs in the unsaturated zone below the waste, or in the phreatic aquifer.
Preferential flow then leads to more rapid transport and higher concentrations.
4.5x104

5x104

vadose zone

waste layer
4.0x104

4x104

3.5x104

U (Bq m-3)

U (Bq m-3)

3.0x104
3x104

equilibrium
β=1
β = 0.1
β = 0.01
β = 0.001

2x104

equilibrium
β=1
β = 0.1
β = 0.01
β = 0.001

4

2.5x102.0x104
1.5x104
1.0x104

1x104

5.0x103
0.0

0
0

20000

40000

60000

80000

0

100000

20000

60000

80000

100000groundwater - well

2.2x104

equilibrium
β=1
β = 0.1
β = 0.01
β = 0.001

4

2.0x101.8x104
1.6x104

U (Bq m-3)

40000

time (y)time (y)1.4x104
1.2x104
1.0x1048.0x1036.0x1034.0x1032.0x103
0.0
0

20000

40000

60000

80000

100000time (y)Figure 1. Calculated uranium concentrations versus time in the waste layer (upper right), thebottom of the vadose zone (upper right) and the downgradient well (bottom). Results are fordifferent values of the mass transfer coefficient β (year-1).

Figure 2 shows results of the safety assessment for both equilibrium transport and the situation
where preferential flow would occur in all three regions simultaneously (waste, vadose zone,
groundwater). A safety assessment is often used to provide evidence that human health and theenvironment are protected as much as possible in the future. The scenario used here assumes thatthe downgradient well was the only available source of water for direct consumption by
residents, and for irrigation and animal use. We refer to Pontedeiro et al. (2010) for details. The
results in Figure 2 show that preferential flow causes the risks to shift to much earlier times, but

279

that the maximum or annual risk is not much affected by preferential flow. Most of the risk in
Figure 2 was caused by uranium followed by thorium.

Uranium

2.5x10-5

Annual Risk

2.0x10-5

1.5x10-5

equilibrium
preferential flow

1.0x10-5

5.0x10-6

0.0
0

20000

40000

60000

80000

100000time (y)Figure 2. Calculated annual risk assuming equilibrium transport and preferential flow.

3. Municipal Solid Waste Landfill
The second case study concerned water flow into and through a municipal solid waste (MSW)
landfill in the Nova Iguaçu suburb of Rio de Janeiro (Fig. 3). The landfill occupies an area of 1.2
million m2 and contains mostly non-hazardous wastes (classified as Class IIA and IIB according
to Brazilian standards). The location includes, among other things, a central treatment plant forthe collected leachate and a biogas collection facility to generate electricity. Two studies werecarried out to investigate the performance of a final cover that would minimize infiltration into
the waste. One was a capillary barrier made from MSW compost, while a second scenario
considered a vegetative cover using grasses or native species.

Figure 3. Aerial view of the Nova Iguaçu landfill showing four sub-landfills.

280

Table 1. Physical and soil hydraulic parameters of the waste.

ρb
Ks(g/cm3) (cm/day)
0.632
233

θs
cm3/cm3)
0.53

θr(cm3/cm3)
0.25

α(cm-1)
0.20

n
(-)
1.98

l
(-)
0.50

Local data were used as much as possible. The average saturated hydraulic conductivity (Ks) of
the cover soil was measured to be 2.3 cm/day. Hydraulic parameters were estimated frommeasured soil texture data of the fines (on average 32% clay, 19% silt, and 49% sand) using the
Rosetta pedotransfer functions in HYDRUS-1D, and adjusted for gravel (4%). Hydraulicparameters for the waste were taken from Breitmeyer (2011) and are listed in Table 1.
For all simulations we considered the intermediate (during operation) and final cover layers tohave a thickness of 60 cm, and the waste layer to be 500 cm thick. In order to calibrate themodel, we initially modeled each vertical landfill cell separately. For this we considered theinfluence of rainfall and evaporation on each cell independently, with the premise that theamount of liquid generated by each cell was fully captured by the drainage network of thelandfill, and that the overall recharge rate was simply the sum of the deep drainage rates of allcells combined. It was estimated to be 0.257 m/y (0.0703 cm/day) using local weather data andpotential evapotranspiration rates calculated with the equation of Hargreaves (1975). The
simulations were performed for profiles varying from 1 to 10 meters, after which the individual
cells were superimposed to cover the entire landfill. The total amount of leachate simulated for
Sub-Landfill1 during 2010 was found to be 27,020 m3, which compared well with the measured
drainage volume of 33,100 m3.

Figure 4. Composition of the capillary barrier system and underlying waste.

281

Figure 5. Cumulative drainage fluxes at a depth of 3 m assuming the capillary barrier to have athickness of 30 cm (left) and 50 cm (right).

Another option we analyzed was the use of vegetation on the cover: either grass with roots
uniformly distributed in the top 20 cm, or native vegetation (brachiaria humidicola) with roots
having a distribution as reported by Costa (2002). The recharge rate with grass was estimated tobe 0.0467 cm/day, as compared to 0.0367 cm/day for the native vegetation.
Figure 6 summarizes the drainage calculations. The use of a capillary barrier or vegetation on topof the landfill resulted in a water flux reduction of about 38% for a capillary barrier layer of 30
cm, 42% for a capillary barrier of 50 cm, 34% for grass and 48% for brachiaria. Our results
confirm literature findings that vegetative covers (also referred to often as evapotranspiration
covers) can significantly reduce water flow rates through a landfill by promoting root water
uptake and hence evapotranspiration (e.g., EPA, 2003; McGuire et al., 2009), not only in arid
and semi-arid regions but also in more humid areas. Additional details of this study are given by
Ottoni (2010).

Figure 6. Comparison of calculated drainage rates from a landfill containing a compacted surface
soil, capillary barriers (CBs) of 30 and 50 cm, and vegetative covers using grass and vegetation
native to Rio de Janeiro, Brazil282

4. The Goiania Repository
In September 1987 a major accident occurred with a 137Cs teletherapy source in Goiania, Brazil(Paschoa et al., 1993; Heilbron et al., 2002). The accident caused widespread contamination ofradioactive material (1375 Ci of 137Cs) in the town of Goiania. Subsequent cleanup generated
about 3,500 m3 of solid radioactive wastes (about 6,000 tons of material). The wastes were
disposed in a near-surface repository built in concrete. The purpose of this study was to performa safety assessment of the low level radioactive waste deposit containing 137Cs over a time
period of about 400 years.
The study was designed to provide estimates of water infiltrating through the soil cover above
the repository into and through the repository and its concrete liners towards underlying
groundwater. This was done by applying first a detailed water balance to the soil coveraccounting for local precipitation and evapotranspiration rates, including root water uptake bygrass on the cover. All calculations were carried out using HYDRUS-1D. Estimates wereobtained of the infiltration of water from the cover through the concrete surface of the repository
into and through the radioactive waste and underlying concrete liner. These flow rates were used
next to simulate long-term 137Cs transport from the repository through the bottom concrete liner
into the underlying vadose zone until reaching the groundwater aquifer below the repository.
Radionuclide transport calculations accounted for the effects of 137Cs sorption and radioactive
decay. Simulations provided estimates of possible future radionuclide fluxes into groundwater,thus permitting an evaluation of potential consequences to the environment and possible
exposure to the public.
The subsurface repository was built in concrete, having dimensions of 19.6 m length, 60 m widthand 6.20 m high, and with 20 cm thick concrete walls. A 50-cm thick uniform soil cover wasplaced on top of the repository and vegetated with grass. The waste inside the repository
consisted mostly of compacted soil contaminated with 137Cs (4.38 m). Figure 7 gives an aboveground view of the repository. A schematic cross-section of the facility and underlying vadosezone is shown in Figure 8. The repository is located at 16° 45′ 32″ S, 49° 26′ 16″ W, about 770
m above sea level.

Figure 7. View of the Goiania repository.

283

Figure 8. Schematic of the Goiania repository and underlying vadose zone.

CNEN, the Brazilian Nuclear Regulatory Agency, defined a maximum annual dose for the publicof 0.25 mSv/y for a low-level radioactive waste repository. Two safety assessments were
performed in the past (Heilbron et al., 2002). The present study was carried out 10 years later aspart of the enforcement of national regulations. Modeling of the repository was done in two
steps. First the behavior of the cover was studied assuming some degradation of the concrete
liners with time (400 years). Fluxes through the upper liner into the repository obtained in thismanner were used next to estimate 137Cs transport rates from the waste vertically down towards
the water table.
For the soil cover we used soil hydraulic parameters from a typical Cerrado soil (Batalha, 2010)
containing 53% of sand, 10% of silt and 37% clay. The initial hydraulic properties for theconcrete were taken from Schneider (2012). The soil cover above the upper concrete wall wasmodeled as a 50 cm layer covered by grass (30 cm rooting depth). Potential evapotranspiration
rates (Fig. 9) needed for the simulations were obtained with the equation of Hargreaves (1975)
using 10 years of temperature and precipitation data from a local weather station. These data
were repeated 40 times to cover the 400 year total simulation period. For the root water uptake
calculations we used the model of Feddes et al. (1978).
The saturated hydraulic conductivity (Ks) of the upper and lower concrete walls (liners) wereassumed to decrease slowly due to natural degradation. We approximated this degradation
process with a discrete function, using Ks=0.00315 m/year for the first 100 years, 0.0315 m/year
for the next 100 years, and 0.315 m/year between 200 and 400 year. The porosity wassimultaneously doubled after 100 and 400 years, while keeping the same values for the otherhydraulic parameters of the concrete.
The contaminated waste layer in the repository was taken to be 4.38 m thick, situated over a 20cm thick concrete liner and a 4 to 5 m thick vadose zone (Fig. 8) depending on fluctuations of thewater table. Hydraulic properties of the waste layer were measured (Pereira, 1996), including thebulk density (1.7 g/cm3) and for the calculations it was measured a value of 463 cm3/g for the Kd
in that layer. The relatively bulk density of the waste reflected compaction of the 137Cs

284

contaminated soils. The concrete liner below the waste was assumed to have the same
unsaturated hydraulic properties as the degraded upper concrete cover. A partitioning coefficient(Kd) of 10 cm3/g was used for the concrete (Aguiar, 2006). Hydraulic properties and Kd of thevadose zone were measured (Pereira, 1996), with a bulk density of 1.3 g/cm3 and mean value of
430 cm3/g for the Kd.

Figure 9. Calculated potential evapotranspiration rates.

Simulations for the infiltration of water from the cover through the upper concrete liner into therepository gave the following results: 0.00280 m/year for the initial period (0 to 100 years),
0.0290 m/year from 100 to 200 years, and 0.238 m/year for the period from 200 to 400 years.
These infiltration rates were subsequently used for the 137Cs transport equations. Figure 10 shows
calculated 137Cs concentrations of fluid leaving the waste layer and moving into the lower
concrete liner. The three local concentration maxima in the curve are a consequence of the three
conductivities used to approximate the concrete degradation process, leading to three flow rates
and causing a different maximum during each for the three stages of concrete degradation. 137Csconcentrations eventually approach zero because of radioactive decay.

Figure 10. Calculated 137Cs concentrations at the bottom of the waste layer.

285

Figure 11. Calculated 137Cs concentration at three locations in the vadose zone below the lower
concrete liner.

5. Conclusions
In this paper we summarized three studies in which the HYDRUS-1D software package wasused to investigate the performance of different types of waste disposal sites in Brazil: aconventional mining installation containing naturally occurring radioactive materials (NORMs),
a municipal solid waste landfill, and a low-level radioactive waste repository. The three
examples show the flexibility of HYDRUS-1D in being able to address different types ofproblems at involving different time and spatial scales. All calculations were based on thestandard equilibrium formulation for variably-saturated flow (the Richards equation). Solutetransport in the first example considered both equilibrium transport and some preferential flow asmodeled with a dual-porosity type physical nonequilibrium transport formulation. The
HYDRUS-1D code was found to be very appropriate and extremely easy to use for the required
calculations.
References

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Cenários de Liberação de Radionuclídeos por Infiltração de Água, DSc Thesis, Department of
Nuclear Engineering, COPPE, Federal University of Rio de Janeiro, UFRJ, Rio de Janeiro, Brazil,
2006.
Batalhá, M. S., C. R. Bezerra, E. M. Pontedeiro, and M. Th. van Genuchten, Environmental fate of naturalradioactive contaminants in fertilizers and phosphogypsum, Proc. ENCIT 2010, 13th Brazilian
Congress of Thermal Sciences and Engineering, Dec. 5-10, 2010, Uberlandia, MG, Brazilian Soc.
Mech. Sci. & Eng., ABCM, Brazil, 2010.
Belk, E. L., D. Markewitz, T. C. Rasmussen, E. J. M. Carvalho, D. C. Nepstad, and E. A. Davidson,
Modeling the effects of through fall reduction on soil water content in a Brazilian Oxisol under amoist tropical forest, Water Resour. Res., 43, W08432, doi:10.1029/2006WR005493, 2007.

286

Breitmeyer, R. J., Hydraulic Characterization of Municipal Solid Waste, Ph.D. Dissertation, University of
Wisconsin, Madison, WI, 192 p, 2011.
Costa, F. da; R. O. Pereyra, S. Paciomik, and J. B. R. de Abreu, Distribuição vertical de características
morfológicas do sistema radicular de Brachiaria humidicola, Pasturas Tropicales, 24(3), 14-20, 2012.
Dennen, W. D. and H. A. Norton, Geology and geochemistry of bauxite deposits in the lower Amazon
basin, Econ. Geol., 72, 82-89, 1977.
Feddes, R. A., P. J. Kowalik, and H. Zaradny, Simulation of Field Water Use and Crop Yield, John Wiley& Sons, New York, NY, 1978.
Felice, L. B., Aplicação do Código Computacional HYDRUS-1D na Avaliação de Segurança de Depósito
de Rejeitos Radioativos; Estudo de Caso: Repositório de Rejeitos Radioativos de Abadia de Goiás,
MSc Thesis, Department of Nuclear Engineering, Institute of Military Engineering, IME, Rio deJaneiro, Brazil, 2013.
Hargreaves, G. H., Moisture availability and crop production, Trans. Am. Soc. Agric. Eng., 18(5), 980984, 1975.
Heilbron, P. F., E. M. Pontedeiro, R. M. Cotta, J. P. Guerrero, and N. Ruperti, Reassessment of the safetyof the Goiania repositories, Internal Report, CNEN, Rio de Janeiro, Brazil, 2002.
ISAM, Derivation of quantitative acceptance criteria for disposal of radioactive waste to near surface
facilities: development and implementation of an approach, Safety Report, Version 3.0, IAEA,
Vienna, Austria, 1999.
McGuire, P. E., B. J. Andraski, and R. Archibald, Case study of a full-scale evapotranspiration cover, J.
Environ. Eng., 135, 3, 316-332, doi:10.1061/(ASCE)1090-0241, 2009.
Pashoa, A. S., A. Tranjan Filho, and J. J. Rosenthal, Revisiting Goiânia: Toward a final repository forradioactive waste, Topical Report, IAEA Bulletin, 1, 28-31, 1993.
Roberts, L., Radiation accident grips Goiania, Science, 238, 1-28-1031, 1987.
Pereira, J. C. A, Determinação da Velocidade de Migração e das Razões de Partição de 137Cs em Solosda Região do Futuro Repositório de Rejeitos de Abadia de Goiás, Goiás. MS. Thesis, Pontifícia
Universidade Católica do Rio de Janeiro, Departamento de Química, 1996.
Ottoni, V., Análise Numérica de Fluxo da Base de Aterros de Resíduos Solidos, MS Thesis, Department
of Civil Engineering, COPPE, Federal University of Rio de Janeiro, UFRJ, Rio de Janeiro, Brazil,
2010.
Pontedeiro, E. M., M. Th. van Genuchten, R. M. Cotta and J. Šimůnek, The effects of preferential flow
and soil texture on risk assessments of a NORM waste disposal site, J. Hazard. Mater., 174, 648-655,
doi:10.1016/j.jhazmat.2009.09.100, 2010.
Schneider, S., D. Jacques, and D. Mallants, Determining hydraulic properties of concrete and mortar byinverse modeling, Mater. Res. Soc. Symp. Proc., 1475, 367-372, Materials Research Society, DOI:
10.1557/opl.2012.601, 2012.
Šimůnek, J., M. Th. van Genuchten, and M. Šejna, Development and applications of the HYDRUS andSTANMOD software packages and related codes, Vadose Zone J., 7, 587-600, 2008a.
Šimůnek, J., M. Šejna, H. Saito, M. Sakai, and M. Th. van Genuchten, The HYDRUS-1D Software
Package for Simulating the Movement of Water, Heat, and Multiple Solutes in Variably Saturated
Media, Version 4.0, HYDRUS Software Series 3, Department of Environmental Sciences, Universityof California, Riverside, California, USA, 315 pp., 2008b.
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Geociências. 11: 203-208, 1981.
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287

288

Simulation of Groundwater Evapotranspiration with
HYDRUS-1D in Desert Environments
Sergey Pozdniakov1, Ping Wang2, Sergey Grinevskiy1, and Jingjie Yu2
1

Department of hydrogeology, Moscow State University, GSP-1, Leninskie Gory, Moscow, 119899, Russia
sppozd@geol.msu.ru
2
Key Laboratory of Water Cycle & Related Land Surface Processes, Institute of Geographic Sciences and Natural
Resources Research, Chinese Academy of Sciences, 11A, Datun Road, Chaoyang District, Beijing, 100101, P. R.
China
wangping@igsnrr.ac.cn

Abstract
It is well known that water tables fluctuate in many arid/semiarid areas both daily, seasonally, andannually in response to phreatophyte consumption of groundwater via evapotranspiration (Ridolfi et al.,2007). In this study the pattern of daily and seasonal groundwater fluctuations in a desert area ofnorthwest China was analyzed. In addition, a one-dimensional saturated-unsaturated soil water flow
model HYDRUS-1D (Šimůnek et al., 2008) was used to simulate daily and seasonal water tablefluctuations induced by groundwater evapotranspiration (ETG). Simulations were conducted for four
different soil profiles (sand, loam, silt, and sandy clay) and two typical vegetation covers (Populus andTamarix) with temporal variability of precipitation, potential evaporation, and transpiration input data,
which was produced using special preprocessing code SurfBal 3.60. The results show that a strong linear
relationship exists in all model settings between the ETG values and the standard diversion of water tablefluctuations. The proposed methodology is expected to provide a basis for assessment of groundwater
evapotranspiration using diurnal water table fluctuations in arid and semi-arid areas.

1. Introduction
The lower Heihe River in northwestern China is characterized by a continental climate that isextremely hot in the summer and severely cold in the winter. According to observational datafrom 1960 to 2011 gathered at the local weather station, the mean annual air temperature was
8.95 °C, with a range from -35.3 °C (9 February, 1964) to +43.7 °C (28 July, 2010). The meanannual precipitation was only 34.5 mm, while the average annual potential evaporation (ET0)was about 1413 mm, which was 40 times greater (Wang et al., 2013). The predominant natural
plant species in this area is characterized by phreatophytes (e.g., Populus euphratica andTamarix ramosissiman), which relies on groundwater for survival (Wang et al., 2011; Zhao etal., 2004). Groundwater evapotranspiration (ETG) from the phreatophyte vegetation is an
important part of the water balance in this area; however, the ETG estimate still remains achallenge for the regional water resources assessment. Many studies have linked diurnal watertable fluctuations to evapotranspiration resulting from groundwater use by phreatophytes,
particularly in arid and semiarid areas (Bauer et al., 2004; Gribovszki et al., 2008; Loheide II,2008; Soylu et al., 2012). In this paper, the daily and seasonal water table fluctuations in theriparian zone were analyzed by using monitoring of groundwater dynamics during the period ofApril, 2010 – March, 2012. Moreover, water table fluctuations induced by riparian289

evapotranspiration were simulated with a one-dimensional, saturated-unsaturated soil water flow
model.
2. Diurnal and Seasonal Water Table Fluctuations
The selected groundwater monitoring well, with a depth of 12 m, is located within a riparianzone of the lower Heihe River. The groundwater levels were recorded in 30-minute intervals by
Schlumberger Mini-Diver pressure transducers with an uncertainty of ±5 mm (Fig. 1). Analysisof the groundwater levels showed that a diurnal fluctuation existed in the water table during theperiod from May to September; however, these diurnal fluctuations were smaller during winter.
To test the hypothesis that groundwater evapotranspiration impacts diurnal water tablefluctuations, the detrended analysis of water level time series was conducted using the BAYSEA
procedure (Akaike, 1980). In this analysis, it is supposed that the fluctuation of the groundwaterlevel depth Zgw can be written as a superposition of a seasonal trend Zy, a daily cycle zd, andresidual zr fluctuations, i.e.:

Z gw = Z y + zd + z r(1)

Then, the monthly standard deviation (Zsd) of a detrended water level was analyzed. The increaseof Zsd in the summer and its decrease in the winter should indicate that the drawdown of thewater table in the summer is related to groundwater evapotranspiration.
Figure 2 shows the amplitude of the diurnal water table fluctuation for typical summer (July) andwinter (January) periods. There is a notable daily fluctuation in the water table during summer,with an amplitude of about 2 cm; however, such a diurnal fluctuation did not show in the winter.
Analysis of the standard deviation of the water table (Zsd) during the entire period showed that
Zsd is almost unchanged in winter (about 0.3 cm). It is noted that Zsd increased significantly in
May and obtained the maximum in June-July (Figure 2), indicating an increasing amplitude ofdiurnal fluctuations in the groundwater table during summer. Therefore, the analysis of daily
fluctuations in the groundwater level indicates that the groundwater evapotranspiration during
summer is the main cause of diurnal fluctuations in the water level and the cause of its seasonal
decline.

Water level depth, m

0

1

2

3

2010-4-1

2010-10-1

2011-4-1

2011-10-1

2012-4-1

Figure 1. Water level depth in a riparian well for the period of 2010-2012.

290

Figure 2. Diurnal fluctuations of the water table (Zf, cm) and its monthly standard deviation (Zsd,cm).

3. Simulation of Evapotranspiration
A one-dimensional, vertical saturated-unsaturated profile within the groundwater discharge zone
due to evapotranspiration (Figure 3) was used to investigate the relationship between the mean
groundwater depth, diurnal and seasonal water table fluctuations, and evapotranspiration. We
consider a homogeneous soil with an active shallow root zone that extends from the soil surface
to a depth Zr (cm). A groundwater table occurs at a depth Zg (cm) below the soil surface. The
upper boundary of this profile is the soil surface and the lower boundary is located below thedepth of seasonal groundwater level fluctuations within the zone of predominantly vertical flow.
Let’s suppose that the lower boundary of the profile is the boundary with a given flow rate R(t).
The root system is distributed along the profile and intakes water with a net rate ET(t) that
depends on the potential evapotranspiration and the root water uptake reduction according to the
S-shape model (Šimůnek et al., 2008).

291

T(t)
P(t)

E(t)

R(t)
Figure 3. Sketch of the water table position and plant root distribution in the soil column.

Four typical soil profiles were selected for test: sand, loam, silt and sandy clay. The parametervalues of the van Genuchten model used in the simulations are shown in Table 1.
Table 1. Mean textural and hydraulic properties of four typical sediment profiles (Loheide et al., 2005).

The species selected at this site were two drought-deciduous shrubs, Populus and Tamarisk, thedominant phreatophytes in the lower Heihe river basin. They all have dimorphic root systems
that can reach a depth of 30 m and show the evidence of a hydraulic lift. Root distributions are
fixed during the simulations and are used to weight the water uptake function. The root
distribution of the Populus has the following normalized function (Zhu et al., 2009):

292

 1
 3L ,
 r
3
L ,
 r
b( z r ) =  5 , 8 Lr
 1 ,
 2 Lrz r ∈ (0;0.30 Lr )z r ∈ (0.30 Lr ;0.50 Lr )z r ∈ (0.50 Lr ;0.90 Lr )z r ∈ (0.90 Lr ;1.00 Lr )(2）

where zr is the z coordinate of the soil surface, and Lr is the root depth.
Similarly, the following normalized function of the root distribution of the Tamarisk (Xu and Li,2009) was used in the simulation:z ∈ (0; 0.12 Lr )0
 13z ∈ (0.12 Lr ; 0.46 Lr )( z − 0.12 Lr ), 32 Lr32b( z r ) = 0.13 +( z − 0.46 Lr ), z ∈ (0.46 Lr ; 0.75 Lr )
29 Lr


50
( z − 0.75 Lr ), z ∈ (0.75 Lr ; 0.94 Lr )
0.45 +
Lr19
5
( z − 0.95 Lr ), z ∈ (0.94 Lr ; 1.00 Lr )
0.95 +

Lr
6


(3）

The groundwater table fluctuations were simulated using the HYDRUS-1D software package(Šimůnek et al., 2008), and the temporal variability of precipitation, potential evaporation, andtranspiration input data were produced using the special preprocessing code SurfBal 3.60
(Grinevskii and Pozdnyakov, 2010) that creates an Atmosph.in input file for Hydrus-1D.
The first series of numerical experiments studied the relationship between the mean groundwater
depth and groundwater evapotranspiration ETG. Different constant head values were used on thelower boundary and the same atmospheric boundary conditions at the top in each simulation run.
The meteorological variables that form the atmospheric boundary conditions were taken fromobservational data from 1960 to 2011. Thus, each simulation run covers 50-years total time witha daily resolution of atmospheric boundary conditions. The processing of simulation results by
estimating average transpiration and plotting it versus the mean groundwater depth for aparticular run shows the strong relationship between transpiration and the depth to groundwaterlevel (Fig. 4). Taking into account that cumulative infiltration of precipitation for these
conditions is too small in comparison with cumulative transpiration, the relationship shown in
Figure 4 reflects the dependence of groundwater evapotranspiration on the mean groundwater
depth. Figure 4 also shows the results of estimating groundwater ET by using data of a summer
decline trend of the observed groundwater level in monitoring wells, using a precondition thatthe summer increase of the seasonal groundwater depth ∆ Zy is the result of evapotranspiration,
i.e.:

293

Groundwater Evaportranspiration rate, mm/day
0

0.4

0.8

1.2

1.6

2

Groundwater Depth, m

0

2

4
Hydrus simulation results
Estimation by using well data

6

Figure 4. Simulated and estimated groundwater evapotranspiration rate.

ETG = S y

∆Z y
∆t

(4)

where ∆t is the length of summer period.
One can see from this figure that simulations, as well as observations, show the decrease in the
groundwater evapotranspiration with the increase of the mean groundwater depth.
In the second series of simulations we considered the relationship between daily groundwaterlevel fluctuations and the evapotranspiration rate. The constant low boundary head that reflects
the groundwater table depth of 200 cm below the soil surface and four different plant root depths(150 cm, 200 cm, 210 cm, and 250 cm) were used in this series of simulations. The simulation
time for each run was three years with diurnal fluctuations of potential evapotranspiration. The
diurnal fluctuation of potential evapotranspiration was simulated using the Fayer’s model
adopted in Hydrus-1D. To recognize small daily fluctuations of groundwater, the 5-m deep soil
profile was discretized using a fine finite element mesh with 500 nodes. The simulation results
were processed using the BAYSEA procedure to estimate the statistics of simulated diurnal
groundwater level fluctuations.

294

Figure 5. Water table fluctuations after the BAYSEA detrended analysis.

Figure 5 illustrates the diurnal fluctuation in groundwater levels in a 30-min simulation fordifferent soil types and vegetation covers. Clearly, groundwater levels in all scenarios showedseasonal fluctuations. Strong diurnal fluctuations in the groundwater level could be found during
summer, while such diurnal fluctuations were not observed during winter. In addition, for low
hydraulic conductivity aquifers (silt and sandy clay), root water uptake induces a considerable
water table depression. However, for coarse aquifers (sand and loam) the water table depression
is lower because the decreasing storage can be readily recovered due to high hydraulicconductivities. To compare with the Tamarix, the root water uptake of Populus caused a smaller
water table decline because of the difference in root distribution.
Figure 6 shows that a strong linear relationship exists in all model settings between the ETG
values and the standard deviation of water table fluctuations. This indicates that it is possible toestimate monthly groundwater evapotranspiration based on the analysis of the standard deviationof diurnal water table fluctuations.

295

Figure 6. The relationship between daily average evapotranspiration (ET_AVE, cm/day) and thestandard deviation of water table fluctuations (SDG, cm).

4. Conclusion and Future Work
This study is an ongoing process report on developing the theoretical and numerical framework
for estimating groundwater evapotranspiration using data about the mean groundwater depth, aseasonal groundwater trend, and diurnal water table fluctuations in the desert environments. The
dynamic behavior patterns of the groundwater level at most wells are characterized by adeclining trend during the period from spring to autumn and a slightly rising trend in the wintermonths, which relates to ETG. Estimating ETG by using seasonal trend and Hydrus simulations
showed a strong dependence of ETG on mean groundwater depths. The proposed method of
estimating ETG by using diurnal groundwater fluctuation statistics can be used for wells locatedin environments with the deep root zone, while the problem of how to take into account the
dynamic of specific yield still remains. The potential for future work is to analyze the influenceof the atmospheric evaporative demand, the soil hydraulic properties, and the vegetation
parameters (e.g., leaf area index, root density distribution) on quantifying the relationshipbetween groundwater evapotranspiration and water level fluctuations.

296

Acknowledgements
This work is supported by the Visiting Professorship for Senior International Scientists, Chinese
Academy of Sciences (№ 2012T1Z0037), the NSFC-RFBR Program 2013 – 2014 (№13-0591161), the National Natural Science Foundation of China (№ 91025023 and 41271049), theNational Basic Research Program of China (973 Program) (№ 2009CB421305) and the RussianFederation Basic Research Foundation grant (№13-05-91161-ГФЕН_а)
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Zhu, Y., L. Ren, T. H. Skaggs, H. Lü, Z. Yu, Y. Wu, and X. Fang, Simulation of Populus euphratica root
uptake of groundwater in an arid woodland of the Ejina Basin, China, Hydrological Processes,
23(17), 2460-2469, doi:10.1002/hyp.7353, 2009.

297

298

Accounting for Solution Composition in a Plant Roots Active
Nutrient Uptake Model
Iael Raij1, Naftali Lazarovitch1, Alan Ben-Gal2, Uri Yermiyahu2, and Diederik Jacques3
1

The Jacob Blaustein Institutes for Desert Research, Ben-Gurion University of the Negev, Sede Boqer Campus, BenGurion, Israel
2
Soil, Water and Environmental Sciences, Agricultural Research Organization, Israel
3
Belgian Nuclear Research Centre, Belgium

Abstract
The objective of this study was to include the nutrient uptake deficiency stress in the genericmulticomponent transport model, HP1 (the geochemical code PHREEQC coupled to the transient waterand solute transport model HYDRUS-1D). The first step was the incorporation of a combined passiveactive root nutrient uptake model in HP1 (Jacques et al., 2006). The nutrient uptake model is based on themodel of Silberbush et al. (2005). For example, Ca is taken up by passive and active processes, in which
the parameters of the Michaelis-Menten active uptake model depend on the solution chemistry.
Simulations were compared with experimental data from four irrigation treatments with different Na(-Cl)
concentrations. The results are a preliminary attempt to predict uptake of different ions under varying
conditions of salinity. Results for Na and K are promising.

1. Introduction
Plant nutrient uptake is controlled by both the plant and soil system (Feddes and Raats, 2004).
Under saline conditions, plants are stressed through different processes, including reduced
osmotic potential of the soil solution, specific ion toxicity, and ion competition (Taiz and Zeiger,
2002). Models can take into account the effects of general salinity characterized by electricalconductivity (EC) by decreasing water uptake as a result of a lower osmotic potential. In
addition, models that calculate specific active uptake of solutes can decrease the uptake as afunction of the concentration of specific toxic ions (Hopmans and Bristow, 2002). Generally,models that focus on water movement and solute transport in the soil will use the first approach,and plant based models will use the second approach. However, real field conditions are complex
and their modeling demands integration of principles of soil and plant science (Hopmans andBristow, 2002).
In this framework of coupling various soil and plant factors, Šimůnek and Hopmans (2009)presented an improvement to the classic macroscopic scale approach. In the classic approach(e.g., HYDRUS can serve as an example of the model for water movement and solute transport
in unsaturated conditions), nutrient uptake is represented by a passive sink term based on root
water uptake. The improved model includes active as well as passive nutrient uptake and uptake
reduction due to salinity, in an attempt to connect soil modeling with root uptake modeling. A
main limitation of this model is that uptake of a solute is independent of concentrations,activities, or speciation of the other solutes in the soil solution (Šimůnek and Hopmans, 2009).

299

Silberbush et al. (2005) proposed a root nutrient uptake model in which active uptake is specificfor each solute according to Michaelis-Menten kinetics and takes into account salinity conditions(as a function of Na+ and Cl- concentrations) as well as passive nutrient uptake with water. Thismodel is applied to a soilless culture of known hydraulic properties and follows a Darcy typeflow.
The objective of the current study was to describe a model that combines the generic multicomponent solute transport model, HP1 (geochemical code PHREEQC coupled to the transientwater movement and solute transport model HYDRUS-1D), with a multi-component passive andactive root solute uptake model (with parts taken from Silberbush et al. (2005)). The model
integrates the strengths of both plant and soil approaches and will help explain and understandthe root nutrient uptake deficiency stress under different salinity conditions. In addition, themodel will help to separate the passive nutrient uptake reduction due to osmotic stress and thespecific nutrient uptake reduction due to specific ion toxicity (Na-Cl, in this case).
2. HP1 Implementation of the Nutrient Uptake Model
The three subparts of the Silberbush et al. (2005) uptake model (passive uptake for Na, active
uptake for K, and combined passive and active uptake for Ca) were implemented in HP1(Jacques and Simůnek, 2005).
2.1. Passive Na root water uptake with maximum uptake flux controlled by solution
chemistry
The generic passive uptake model is defined by Eq (1):pa ( x, t ) = min[ sw ( x, t ) min c ( x, t ) , cmax  ,Aroot ( x, t ) J p ,max (ω ( x, t ) ) ,if c ( x, t ) > cr

p p ( x, t )]  =0

(1)

otherwise

where pa(x,t) is the actual passive nutrient uptake rate [ML-3T-1] for a given depth x [L] and timet [T], sw(x,t) is the root water uptake rate [L3L-3T-1], c(x,t) is concentration [ML-3], cmax is the
maximum allowed concentration for root uptake [ML-3], Aroot(x,t) is the root surface area [L2L-3],
Jp,max is the maximum allowed passive nutrient uptake rate [ML-2T-1], ω(x,t) is the geochemical
condition at x and t, pp is the potential passive nutrient uptake rate [ML-3T-1], and cr is the criticalconcentration below which passive root uptake is zero [ML-3]. This expression is generic as it
limits uptake by (i) a maximum allowable concentration for uptake (min[c(.),cmax]), (ii) a
maximum nutrient uptake flux (min[sw(.)min[c(.),cmax], Aroot(.)Jp,max(.)], and (iii) a maximum
potential root uptake. Uptake below a critical value, cr, equals zero.
Passive uptake of Na is controlled by the root water uptake rate (sw) or by the coefficient ofpassive Na influx, PNam (as in Silberbush et al. (2005)).

300

Three possible variants of this general equation are defined (in all variants, uptake is not limited
by a potential uptake, i.e., pp = 4 mol m-3 s-1 in Eq. (1)):•••

Variant 1: Passive Na uptake is not limited (i.e., cmax = 4 mol m-3, Jp,max = 4 m-2 s-1, and cr= 0 mol m-3 in Eq. (1)). The charge balance in the soil solution is controlled by an
exudation of protons, which results in pH changes in the soil solution.
Variant 2: Na uptake is only limited by a maximum Na concentration (i.e., Jp,max = 4 m-2
s-1 and cr = 0 mol/m³ in Eq. (1)). The charge balance in the soil solution is controlled by
an exudation of protons.
Variant 3: Na uptake is only limited by a maximum allowable Na uptake flux and is zero
below cr (i.e., cmax = 4 mol m-3 in Eq. (1)). Jp,max depends on the soil solution chemistry as
shown in Eq. (2). In Silberbush et al. (2005), the Ca concentration will affect the active
Na uptake. In this implementation to HP1, the uptake of Na is only passive, so this factor
is included in the passive uptake according to Eqs. (1) and (2).

( )J p ,max= 2.5 ×10−11 c Na c Ca

−0.24

(2)

Note also that passive uptake is zero when cmax = 0 mol m-3. In Eq. (2), cNa and cCa areconcentrations of Na and Ca, respectively.
2.2. Active K uptake with Michaelis-Menten kinetic rate parameters dependent on solution
chemistry
Active nutrient uptake is described by the Michaelis-Menten rate equation:aa ( x, t ) = Aroot ( x, t ) J a ,max (ω ( x, t ) )c( x, t ) − cmin
K m (ω ( x, t ) + (c( x, t ) − cmin )(3)

where aa(x,t) is the actual active nutrient uptake [ML-3T-1], Ja,max is the maximum allowed active
uptake [ML-2T-1], Km is the Michaelis-Menten constant [ML-3], and cmin is the minimum
concentration below which active uptake is zero [ML-3].
Both Ja,max (mol m-2 s-1) and Km (mol m-3) parameters depend on Na concentrations as describedin Silberbush et al. (2005) (Eqs. (4) and (5), respectively).

J a ,max =5.12 ×10−8 exp(−0.023c Na )(4)

K m= 0.0127 + 2.34 × 10−4 c Na

(5)

2.3. Simultaneous passive and active Ca uptake with Michaelis-Menten parameters
dependent on solution chemistry
In Šimůnek and Hopmans (2009), passive uptake is calculated first, and if it cannot supply thepotential demand, active uptake is activated. In our HP1 implementation, passive and active
uptake are calculated simultaneously as:301

ra ( x, t=) pa + aa= β sw ( x , t ) c ( x , t ) +(6)+ Aroot ( x, t ) J a ,max (ω ( x, t ) )c( x, t ) − cmin
K m (ω ( x, t ) + (c( x, t ) − cmin )where ra(x,t) is the actual root uptake [ML-3T-1], and β is he fraction of root water uptake active
in Ca uptake [-]. Ja,max varies with Na concentrations as described in Silberbush et al. (2005) (Eq.
(7) in mol cm-2 d-1). Km and β are constants.

(

J a ,m ax = 8.64 × 8.90 ×10−9 1 − 2.56 × 10−4 c Na)

(7)

3. Numerical Example and Experimental Data
The nutrient uptake model was implemented in a generic problem described as:• 1 m deep loamy soil. Soil hydraulic characteristics are described using the van
Genuchten-Mualem model (van Genuchten, 1980).
• The bottom of the soil profile has a constant pressure head of 0 cm. The initial conditionat the top is -10 cm with a linear decrease in pressure heads from the top to the bottom.
• A constant potential evaporation and transpiration of 0.01 and 0.15 cm day-1,
respectively. Between days 20 and 23, and between days 60 and 63, there is irrigation of
1 cm day-1.
• The plant has a uniform root distribution down to a depth of 30 cm. The water stress
reduction function of Feddes et al. (1978) is taken with values: P0 = -10 cm, POpt = -25
cm, P2H = -200 cm, P2L = -800 cm, P3 = -8000 cm, r2H = 0.5 cm day-1, r2L = 0.1 cm day-1.
For simplicity, the area of the root surface is taken to be 1 cm2dm-3 soil.
• The same four irrigation treatments used in the laboratory experiment are simulated(Table 1). Initial solution chemistry in the soil corresponds to the solution of Treatment 1.
Table 1. Solution composition for different treatments, concentrations in ppm.

pH
Na
Cl
NH4
NO3
P
K
Ca
Mg

Treatment 1(0 mM NaCl)
5.7
3.5
10.6
6.6
79.7
16.5
65.3
78.8
19.7

Treatment 3(5 mM NaCl)
5.7
100.4
185.1
6.6
79.6
16.7
65
79.4
19.4

Treatment 5(10 mM NaCl)
5.7
201.5
371.6
6
80.7
17.4
67.1
81.9
19.9

Treatment 7(20 mM NaCl)
5.8
415.9
760.4
5.9
83.6
19
71.5
85.9
20.2

The dataset used to validate this model was from a laboratory experiment with sweet basil(Ocimum basilicum) grown in lysimeters. The controlled upper boundary conditions consisted of302different salinity treatments (Table 1). The bottom boundary conditions were measured toaccount for a complete water and macro-nutrient balance. Transpiration, growth, and nutrient
uptake of sweet basil as a function of irrigation water amount, nutrient concentration, and salinity
were measured over time, and compared with calculated data of K, Ca, and Na.
4. Numerical Results

10

-1

10

-2

10

-3

10

-4

10

-5

Variant 1

Treatment 1
Treatment 3
Treatment 5
Treatment 7

0

Cumulative Passive Na uptake (mol)Cumulative Passive Na uptake (mol)Cumulative Passive Na uptake (mol)As a first illustration, three different variants of passive uptake for the first subpart are shown in
Figure 1. Because uptake is limited by a maximum concentration, cumulative uptake is smaller
in variant 2 compared to variant 1, and also the differences between the treatments with higher
Na concentrations is smaller compared to variant 1. Limiting the Na uptake by a maximum
uptake flux has a large impact on the cumulative uptake (at least with the current parametersetting).

10-5
10

-6

10

-7

10

-8

10

-9

25

50
75
Time (days)

100

-1

10

Variant 2
-2

10

-3

10

-4

10

-5

10

0

25

50
75
Time (days)

100

Variant 3

10-10
0

25

50
75
Time (days)

100

Figure 1. Cumulative passive Na for four salinity treatments simulated with three variants.

Numerical results from the combined implementation of the three subparts of the model ofSilberbush et al. (2005) (with variant 3 for passive Na uptake) are shown in Figure 2, in which
cumulative uptake of three specific ions under four different salinity treatments (Table 1) are
shown. As salinity in irrigation water increases, Na uptake increases, K uptake decreases, and Ca
uptake slightly increases.

303

-6

Cumulative Na uptake (mol)5x10Treatment 1
Treatment 3
Treatment 5
Treatment 7

-6

4x10

-6

3x10

-6

2x10

-6

1x10

0

0x10

0
Cumulative K uptake (mol)1.5x10-3204060Time (days)

80

100

80

100

Treatment 1
Treatment 3
Treatment 5
Treatment 7

1.0x10-3-4

5.0x100.0x100
0

20-2

Cumulative Ca uptake (mol)2.0x104060Time (days)

Treatment 1
Treatment 3
Treatment 5
Treatment 7-2

1.5x10-2

1.0x105.0x10-3
0

0.0x10

0

20

40
60
Time (days)

80

100
DJA_2012_005

Figure 2. Cumulative Na, K, and Ca uptake for four salinity treatments.

The last result shows a comparison between the model and experimental data from basil grownin lysimeters (Figure 3). Relative uptake of Na, K, and Ca is plotted against four different EC
values of irrigation water (differences in EC are due to different levels of NaCl added). Modeled
values of Na and K are close to measured data. Ca shows disparities between measurements andmodel at high salinity values, indicating that not all parameters for simulations are accurate.

304

Figure 3. Relative uptake of Na, K, and Ca under various salinities. Comparison between the HP1model simulations (lines) and experimental data (points) from basil plants grown in lysimeters.

5. Discussion and Conclusions
We have coupled a soil-focused model with a plant-focused model and have demonstrated thepotential of linking the Silberbush et al. (2005) nutrient uptake model with HP1 (Jacques et al.,2006). Passive Na, active K, and passive and active Ca uptake with solution-dependent
parameters were all integrated in a water movement and solute transport numerical model, as
illustrated in the numerical experiment with HP1. Preliminary results are promising thoughparameters still need to be calibrated for different soils, climates, and crops.
What is ground-breaking in this model is the separation of the nutrient deficiency stress due tocertain ions (e.g., Na or Cl) from the osmotic stress they pose. This will allow the functions
describing water uptake reduction due to salinity (Maas and Hoffman, 1977; van Genuchten and
Hoffman, 1984) to be strictly used to model osmotic stress (Ben-Gal et al., 2009), so that theadditional stress due to the reduction in nutrient uptake and specific ion toxicity may then bequantified separately.
References

Ben-Gal, A., H. Borochov-Neori, U. Yermiyahu, and U. Shani, Is osmotic potential a more appropriate
property than electrical conductivity for evaluating whole-plant response to salinity? Envir. Exp. Bot.,65, 232–237, 2009.
Feddes, R. A., P. J. Kowalik, and H. Zaradny, Simulation of Field Water Use and Crop Yield, John Wiley& Sons, New York, NY, 1978.
Feddes, R. A., and P. A. C. Raats, Parameterizing the soil-water-plat root system, in: R. A. Feddes, G. H.
Rooij, and J. C. van Dam, (Eds.), Unsaturated Zone Modeling: Progress, Challenges andApplications, Kluwer Academic, Dordrecht, pp. 95–141, 2004.
Hopmans, J. W., and K. L. Bristow, Current capabilities and future needs of root water and nutrient
uptake modeling, Adv. Agr., 77, 103–183, 2002.
Jacques, D., and J. Šimůnek, User Manual of the Multicomponent Variably-Saturated Flow andTransport Model HP1: Description, Verification, and Examples, Version 1.0, SCK•CEN-BLG-998,
Waste and Disposal, SCK•CEN, Mol, Belgium, 79 pp., 2005.

305

Jacques, D., J. Šimůnek, D. Mallants, and M. Th. van Genuchten, Operator-splitting errors in coupled
reactive transport codes for transient variably saturated flow and contaminant transport in layered soil
profiles, J. Cont.Hydrol., 88, 197–218, 2006.
Maas, E. V., and G. J. Hoffman, Crop salt tolerance. Current assessment, J. Irr.Drain. Div., 103, 115–
134, 1977.
Silberbush, M., J. Ben-Asher, and J. E. Ephrath, A model for nutrient and water flow and their uptake byplants grown in a soilless culture, Plant and Soil, 271, 309–319, 2005.
Šimůnek, J., and J. W. Hopmans, Modeling compensated root water and nutrient uptake, Ecol. Model.,220, 505–521, 2009.
van Genuchten, M. Th., A closed-form equation for predicting the hydraulic conductivity of unsaturated
soils, Soil Sci. Soc. Am., 44, 892–898, 1980.
van Genuchten, M. T., and G. J. Hoffman, Analysis of crop salt tolerance data, In: I. Shainberg, and J.
Shalhevet, (Eds.), Soil Salinity Under Irrigation: Processes and Management, Springer Verlag, New
York, pp. 258–271, 1984
Taiz, L., and E. Zeiger, Plant Physiology, 3rd ed., Sinauer, 2002.

306

Modeling Water and Nitrogen Fate in Plots with Sweet Sorghum
Irrigated with Fresh and Blended Saline Waters using
HYDRUS-2D
Tiago B. Ramos1, Jiří Šimůnek2, Maria C. Gonçalves1,3, José C. Martins3, Ângela Prazeres3, andLuís S. Pereira1
1

CEER, Institute of Agronomy, Technical University of Lisbon, Lisbon, Portugal,
tiago_ramos@netcabo.pt
2
Department of Environmental Sciences, University of California Riverside, Riverside, CA, USA,jiri.simunek@ucr.edu
3National Institute of Agronomic and Veterinarian Research, INIAV, Oeiras, Portugal,
maria.goncalves@iniav.pt

Abstract
The Alentejo region in southern Portugal faces water scarcity and environmental problems as a result ofhigh atmospheric demands and irregular rainfall. In the last few years, the HYDRUS software package
has been calibrated and validated in order to minimize human-induced salinization, sodification, and nonpoint source pollution from agricultural fertilization in the region. This paper describes results from anexperiment where HYDRUS-2D, while considering drip irrigation scenarios with different levels of
nitrogen and salty waters, was used to assess the fate of nitrogen in a plot planted with sweet sorghum.
HYDRUS-2D simulated water contents ECsw, N-NH4+, and N-NO3− concentrations continuously between
2007 and 2010, while producing RMSE between simulated and measured data of 0.030 cm3 cm−3, 1.764
dS m−1, 0.042 mmolc L−1, and 3.078 mmolc L−1, respectively. Actual transpiration varied between 264 and334 mm depending upon the crop season and the irrigation treatment. Sweet sorghum showed to be
tolerant to saline waters only during one crop season. After that, the continuous use of saline waters led tosoil salinization and to root water uptake reductions due to the increasing salinity stress. N uptake andleaching were dependent on the amount of water flowing through the root zone, the amount of N applied,the form of N in the fertilizer, and the timing and number of fertigation events. The effect of the osmotic
stress on nitrogen leaching was only minimal. The yield function developed from N-NO3− uptake and dry
biomass yield (R2 = 0.71) estimated the N needs to be between 130 and 180 kg/ha. The simulations with
HYDRUS-2D were thus useful to understand the best strategies toward increasing nutrient uptake andreducing nutrient leaching.

1. Introduction
The Alentejo region of southern Portugal normally exhibits high summer temperatures and very
low rainfall that limits crop production. In this water scarce region, irrigation plays afundamental economical and social role but has exacerbated several environmental problems as aresult of poor irrigation and water management practices. Human-induced salinization,
sodification, and non-point source pollution from agricultural fertilization are among therecognized problems. Therefore, a sound irrigation policy must be established to avoid andmitigate these risks. Such policy may include the adoption of less water and nutrient demanding307

crops, and should be based on a quantitative understanding of the subsurface movement of waterand dissolved chemicals.
Modeling of subsurface water flow and the transport of major soluble ions in and below the rootzone is essential for predicting groundwater quality, implementing better irrigation andfertilization practices (Cameira et al., 2003), and quantifying salinization and alkalization
hazards. Thus, the HYDRUS software package (Šimůnek et al., 2008) has been used in the last
few years to better understand the main physical and chemical processes involved whenirrigating with waters of different quality and to help establish sound irrigation practices for thesoils in the region.
Gonçalves et al. (2006) first analysed transient water flow and solute transport in three soil
lysimeters with waters of different quality over a period of 3 years using the UNSATCHEM
module implemented in HYDRUS-1D. In this study, HYDRUS-1D successfully described watercontents, overall salinity, concentration of major soluble cations (Ca2+, Mg2+, K+, and Na+),sodium adsorption ration, and exchangeable sodium percentage.
Later, Ramos et al. (2011) addressed the transport and reactions of salts and nitrogen species inthe soil profile in an integrated way. The UNSATCHEM module was again used to simulate theoverall salinity and major cations in two soils with coarse and medium textures during a longterm experiment, while the general solute transport module of HYDRUS-1D was used to model
nutrient fate (N-NO3- and N-NH4+). This study allowed a better understanding of soluteinteractions between the solid and liquid phases and the complex reactions involved in solutetransport. The study further allowed understanding of the basic relations between nutrient uptake,leaching and the salinity stress caused by the use of saline waters.
Although the modeling approaches carried out were successful in modeling soil water dynamics
and solute transport in field conditions, these two studies were only one-dimensional andneglected water and solute fluxes and pressure head and concentration gradients in the horizontal
direction. Additionally, one-dimensional models fail to adequately simulate micro-irrigation
systems (such as drip emitters, drip tape, and micro-sprinklers), which can efficiently apply
water and nutrients in the right amounts and precise locations throughout a field (e.g., Gärdenäs
et al., 2005). Since drip irrigation is often used in Portugal, it seemed more appropriate to findmodeling approaches that are better able to represent complex physical and chemical processes
that take place in the soil profile under this irrigation system.
The main objective of this study was to use the HYDRUS-2D software package to model
nitrogen fate in a field with sweet sorghum while considering different drip fertigation and water
quality scenarios. Field data was used to calibrate and validate HYDRUS-2D for predicting (i)soil water contents and fluxes, (ii) the electrical conductivity of the soil solution (ECsw), (iii)water uptake reductions due to the use of saline waters, and (iv) N-NH4+ and N-NO3−
concentrations in the soil and their leaching. Water and nutrient balances were calculated basedon model predictions. A complete description of this study is reported by Ramos et al. (2012b).

308

2. Material and Methods
2.1. Field Experiment
The field experiment was conducted at the Alvalade Experimental Station (37º 56’ 48’’ N and 8º
23’ 40’’ W), southern Portugal, from May, 2007 to April, 2010. The field experiment involved
irrigation of sweet sorghum (Sorghum bicolor (L.) Moench) with synthetic saline waters blended
with fresh irrigation waters and waters with nitrogen (NH4NO3) during three crop seasons. The
blended amounts varied between the 12 experimental plots, while the total amount of water
applied per irrigation event and per crop season, as well as the quality of the irrigation waters
before blending, remained identical in all plots.
The total amount of water applied was 425, 522, and 546 mm in 2007, 2008, and 2009,
respectively. Application amounts averaged 15, 16, and 17 mm per irrigation event in 2007,2008, and 2009, respectively. Nitrogen fertilization was applied in 4 (2007), 6 (2008), and 3(2009) irrigation events during the vegetative stage (July). The EC of the fresh waters, saline
waters, and waters with fertilizer was 0.8, 7.6-10.6, and 6.8-9.5 dS m-1, respectively. N-NH4+ andN-NO3- concentrations in the waters with fertilizer varied between 67.7-95.0 mmolc L-1.
In the plots with the highest application of synthetic saline waters, and in those irrigated onlywith the locally available fresh water, TDR probes with waveguides from the Trase System (Soil
Moisture Equipment Corp., Goleta, CA) and ceramic cups were installed at depths of 20, 40, and60 cm to measure soil water contents and collect soil solutions, respectively. The soil solution
was monitored for ECsw and the concentrations of N-NH4+ and N-NO3-. The dry biomass of
sweet sorghum was determined at the end of each crop season by harvesting all sorghum plants
in each experimental plot and oven drying them at 70 ºC to a constant weight.
2.2. Modeling Approach
Modeling of water flow and solute transport was carried out for all experimental plots irrigatedwith the highest application of synthetic saline waters and only with the water available in theregion. The HYDRUS-2D software package (Šimůnek et al., 2008) was used to simulate thetransient axisymmetrical (or radially symmetrical) three-dimensional movement of water andnutrients in the soil. The transport domain was set as a rectangle with a width of 37.5 cm (halfthe lateral spacing, i.e., the half-distance between triple joint laterals placed along the sorghumrows) and a depth of 100 cm (Figure 1). The flux boundary condition with the flux q was definedas:q=volume of applied water
surface wetted area × duration(1)

where the volume of applied water [L3] varied for different irrigation events, the surface wettedarea [L2] was approximately 1,256 cm2 (i.e., 3.14 x 202), and the irrigation duration was adjusted
to permit water to infiltrate into the soil without producing positive surface pressure heads and toallow for the application of irrigation waters of different qualities within a particular irrigation
event.

309

Figure 1. Location of observation points within the soil profile (a) and an axisymmetrical domain
geometry with the finite element discretization used in HYDRUS-2D simulations (b).

HYDRUS-2D numerically solved the Richards equation for describing the variably-saturated
water flow in a radially symmetric domain and the convection-dispersion equation for solutetransport. The soil hydraulic properties were described using the van Genuchten-Mualem model(van Genuchten, 1980). Since the fertilizer used in our study was NH4NO3, nitrification φ [ML-3
T-1] of the N-NH4+ species to N-NO3- was assumed to be the main N process occurring in thesoil. This process was described by means of a sequential first-order decay chain as follows:

φN − NH =−φN − NO =− µ w, N − NH θ cN − NH − µ s , N − NH ρ c N − NH
+
4

−
3

+
4

+
4

+
4

+
4

(2)

where c, and c are solute concentrations in the liquid phase [ML-3] and solid phase [MM-1],
respectively, μw and μs (set to 0.2 d-1) are the first-order rate constants for solutes in the liquidand solid phases [T-1], respectively, θ is the volumetric water content [L3L-3], and ρ is the soil
bulk density [ML-3]. The first-order reaction terms, representing nitrification of N-NH4+ to NNO3-, thus act as a sink for N-NH4+ and as a source for N-NO3-. The distribution of solutes
between the solid and liquid phases was described by means of a linear adsorption isotherm.
Only N-NH4+ was assumed to adsorb to the solid phase (Kd of 3.5 cm3g-1).
The Richards and the CDE equations incorporate a sink term to account for water uptake byroots. Water and salinity stresses were defined according to the functions proposed by Feddes etal. (1978) and the Maas (1990) salinity threshold and slope function, respectively. Soilevaporation and plant transpiration rates were obtained by combining the daily values ofreference evapotranspiration (ET0), determined with the FAO Penman-Monteith method and thedual crop coefficient approach (Allen et al., 1998). Nutrient uptake was simulated by considering
unlimited passive uptake for nitrogen species (Šimůnek and Hopmans, 2009). Model validation
was carried out by comparing field measured values with HYDRUS-2D simulations while using
the root mean square error (RMSE) for quantifying model uncertainty.

310

3. Results and Discussion
Figure 2 compares the measured and simulated water contents at 40 cm depth in plots with thehighest application of the saline and fresh waters. Water contents increased to full saturation near
the emitter after an irrigation or rain event, and then decreased gradually during the following
hours and days, until the next irrigation or rain event took place. Deeper depths showed smaller
water content variations since root water uptake and soil evaporation were more pronounced atshallower depths. A RMSE of 0.030 cm3 cm-3 was found between measured and simulated
values.
Water content (cm3 cm-3)

0.5
0.4
0.3
0.2
0.1 Season
1

Season2

Season3

Measured data (Plot with saline waters)
Measured data (Plot with fresh waters)
HYDRUS-2D simulation (Plot with saline waters)
HYDRUS-2D simulation (Plot fresh waters)

0.0
18-05-07 04-12-07 21-06-08 07-01-09 26-07-09 11-02-10 30-08-10

Time

Figure 2. Measured and simulated water content at 40 cm.

Potential transpiration (Tp) varied between 360 and 457 mm. Tp values obtained in plots irrigatedwith saline waters were generally lower that those obtained in plots irrigated with fresh waters.
However, the differences were found to be very small since sweet sorghum is moderately tohighly tolerant to salinity (Maas, 1990). Actual transpiration (Ta) varied between 264 and 334
mm. Tp reductions due to water stress (21.9-27.4%) were a function of the adopted irrigation
schedule. In plots irrigated with saline waters, Tp was further reduced by 2.3-7.0% due to salinity
stress. The salinity stress became increasingly higher as a result of soil salinization and thecontinuous and increasing amount of synthetic saline waters being applied in each experimental
plot (Figure 3). The RMSE obtained between measured and simulated ECsw was 1.764 dS m-1.
Nitrogen leaching was directly related to water flow through the bottom boundary of the soil
domain. The movement of N out of the root zone also depended on the amount of applied N, theform of N in the fertilizer, and the time and number of fertigation events. Based on model
simulations, most N-NH4+ was rapidly nitrified into N-NO3-, not reaching depths deeper than 20
cm (Figure 4). Leaching of nitrogen occurred mainly in the N-NO3- form (Figure 5). The higher
the number of fertigation events, the lower the amount of N applied per event, and thus the lower
the amount of leached N-NO3-. Nutrient uptake by plant roots occurred mainly in the N-NO3form as well. The number of fertigation events also significantly influenced the amount of NNO3- taken up by plant roots. The effects of the salinity stress on nutrient uptake (and inversely
on nutrient leaching) was relatively small since sweet sorghum has a medium to high tolerance tosalinity, and consequently there were only small reductions in transpiration due to the increase of
the osmotic stress.

311

Figure 3. Simulated distributions of the electrical conductivity of the soil solution in plots
irrigated with saline (left) and fresh (right) waters during sowing (top) and harvest (bottom) of
each crop season. The drip emitter was located in the top left corner of each contour plot.

The RMSE obtained while comparing measured and simulated N-NH4+ and N-NO3concentrations were 0.042 and 3.078 mmolc L-1, respectively. Deviations between measured dataand simulated variables were related to field measurements, model input and model structure
errors. Here we would like to note that the approach followed for modeling the transport of the N
species (eq. 2) is relatively simple, and can only consider N processes that are involved in asequential-first order decay chain, such as nitrification, denitrification, and volatilization. Other

Figure 4. Simulated distributions of N-NH4+ concentrations in plot irrigated with saline waters
during crop season 2. The dripper was located in the top left corner the contour plots.

312

Figure 5. Simulated distributions of N-NO3-concentrations in plot irrigated with saline waters
during crop season 2. The dripper was located in the top left corner the contour plots.

nitrogen reactions, with probable relevance for long-term applications such as ours, simply
cannot be accounted for using this approach. However, from an agronomical perspective where
the efficient use of the fertilizer applied is one of the main objectives to achieve, the approach isadequate.
Figure 5 shows the relationship between the N-NO3- plant uptake calculated using HYDRUS-2D
and the experimentally determined dry biomass yield expressed using a logarithmic function
with a R2 of 0.71. This logarithmic function fitted to experimental data shows that an additional
incremental increase of N-NO3- uptake produced diminishing returns in the total dry biomass
response, with optimum levels being reached at 130-180 kg/ha (Ramos et al., 2012a).

Dry biomass (kg/ha)

30000

data from plots with saline waters
S from plots with fresh waters
data

25000
20000
15000
y = 2818.59Ln(x) + 6223.58

10000

2

R = 0.71
5000
0

50

100

150

200

250

300

N-NO3- uptake (kg/ha)

Figure 5. Relationship between the N-NO3- uptake (x), as simulated by HYDRUS-2D, and the dry
biomass yield (y).

4. Conclusions
HYDRUS-2D successfully estimated the fate of nitrogen in field plots grown with sweetsorghum in Alentejo. In this water-scarce region, where even saline waters can be viewed as animportant source of irrigation water during drought seasons, the use of marginal waters showed313

viability for irrigating sweet sorghum during a limited time period (one crop season).
Furthermore, the relatively low water needs (360-457 mm) and N requirements (130-180 kg/ha)of sweet sorghum makes it a good alternative when compared to other traditional crops grown in
the region. The leaching of N out of the root zone depended closely on drainage, the amount of N
applied, the form of N in the fertilizer, and the time and number of fertigation events. The
modeling approach helped us understand the best irrigation and fertigation management practices
to be adopted in future practical applications for increasing nutrient uptake and reducing nutrient
leaching.
Acknowledgments
This research was performed within the framework of the Project EUTROPHOS (PTDC/AGRAAM/098100/2008) of the Fundação para a Ciência e a Tecnologia (FCT). T. B. Ramos was
funded by the FCT grant SFRH/BD/60363/2009.
References

Allen, R. G., L. S. Pereira, D. Raes, and M. Smith, Crop Evapotranspiration – Guidelines for Computing
Crop Water Requirements, Irrigation and Drainage Paper, 56, FAO, Rome, Italy, 1998.
Cameira, M. R., R. M. Fernando, and L. S. Pereira, Monitoring water and NO3-N in irrigated maize fields
in the Sorraia watershed, Portugal. Agricultural Water Management, 60, 199-216, 2003.
Feddes, R. A., P. J. Kowalik, and H. Zaradny, Simulation of field water use and crop yield, Simulation
Monographs Pudoc, Wageningen, The Netherlands, 1978.
Gärdenäs, A., J. W. Hopmans, B. R. Hanson, and J. Šimůnek, Two-dimensional modeling of nitrateleaching for various fertigation scenarios under micro-irrigation, Agricultural Water Management, 74,
219–242, 2005.
Gonçalves, M. C., J. Šimůnek, T. B. Ramos, J. C. Martins, M. J. Neves, and F. P. Pires, Multicomponent
solute transport in soil lysimeters irrigated with waters of different quality, Water Resources
Research, 42, W08401, 2006.
Maas, E. V., Crop salt tolerance, In: K. K. Tanji (Ed.), Agricultural Salinity Assessment and Management,
Manual Eng. Pract., vol. 71, pp. 262–304, Am. Soc. of Civ. Eng., Reston, Va., 1990.
Ramos, T. B., J. Šimůnek, M. C. Gonçalves, J. C. Martins, A. Prazeres, N. L. Castanheira, and L. S.
Pereira, Field Evaluation of a multicomponent solute transport model in soils irrigated with saline
waters. Journal of Hydrology, 407, 129-144, 2011.
Ramos, T. B., N. L. Castanheira, M. C. Gonçalves, M. L. Fernandes, M. I. Januário, M. E. Lourenço, F.
P. Pires, and J. C. Martins, Effects of increasing levels of nitrogen fertigation and sodium on sweetsorghum yield components, Pedosphere, 22, 785-794, 2012a.
Ramos, T. B., J. Šimůnek, M. C. Gonçalves, J. C. Martins, A. Prazeres, and L. S. Pereira, Twodimensional modeling of water and nitrogen fate from sweet sorghum irrigated with fresh andblended saline waters, Agricultural Water Management, 111, 87-104, 2012b.
Šimůnek, J. and J. W. Hopmans, Modeling compensated root water and nutrient uptake, EcologicalModeling, 220, 505-521, 2009Šimůnek, J., M. Th. van Genuchten, and M. Šejna, Development and applications of the HYDRUS andSTANMOD software packages, and related codes, Vadose Zone Journal, 7(2), 587-600, 2008.
van Genuchten, M. Th., A closed form equation for predicting the hydraulic conductivity of unsaturated
soils, Soil Science Society of America Journal, 44, 892-898, 1980.

314

Longitudinal Dispersivity Determination Using Conservative
Tracer in the FieldRužičić Stanko1, Zoran Kovac2, Marta Mileusnic1, and Kristijan Posavec2
1

Department of Mineralogy, Petrology and Mineral Resources, Faculty of Mining, Geology and Petroleum
Engineering, University of Zagreb, Pierottijeva 6, 10000 Zagreb, Croatia, sruzicic@rgn.hr
2
Department of Geology and Geological Engineering, Faculty of Mining, Geology and Petroleum Engineering,
University of Zagreb, Pierottijeva 6, 10000 Zagreb, Croatia

Abstract
Determination of solute transport parameters in the unsaturated zone is of great importance forgroundwater pollution risk assessment. The subject of this study was Fluvisol soil developed on thefloodplain of the Sava River. The goal of the study was estimation of longitudinal dispersivity, one of themain solute transport parameters. A field experiment using conservative tracer calcium chloride wascarried out. The investigated site is situated about eight hundred meters from the right bank of the Sava
River at Kosnica regional well field. Longitudinal dispersivity was estimated by inverse modelingchloride concentration using HYDRUS-1D. Due to the collapse of the pedological pit during applicationof the tracer and sampling of percolating solution, the field experiment was not completed. Therefore,
estimation of longitudinal dispersivity was performed on an incomplete data set.

1. Introduction
Solute transport at the field scale can be very complex because of the presence of several
physical, chemical, and biological soil processes that may vary over space and time.
Longitudinal dispersivity (λ), which is one of the main solute transport parameters, depends on
the scale of measurement. This parameter is often determined in the field (e.g., Seuntjens et al.,
2001; Stumpp et al., 2009; Severino et al., 2010). Common tracers are calcium chloride andpotassium bromide. In this study, calcium chloride was used. The sorption potential of calcium
chloride is relatively low and its suitability has been demonstrated in the unsaturated zone
(Akhtar et al., 2003; Heilig et al., 2003; Dişli, E., 2010). Inverse optimization techniques,
wherein differences between observed and predicted values are minimized, is increasingly used
to estimate solute transport parameters (e.g., Jacques et al., 2002; Šimůnek et al., 2002; Moradi etal., 2005; Jacques et al., 2012). Numerical models for inverse modeling are STANMOD(Šimůnek et al., 1999b) and HYDRUS-1D (Šimůnek et al., 2008). STANMOD also includes
several analytical models for solute transport problems. The CXTFIT code (Toride et al., 1999)
is the most widely used (e.g., Fonseca et al., 2009; Zhang et al., 2011; Wang et al., 2013).
The goal of the study was estimation of longitudinal dispersivity which is one of the main solutetransport parameters.

315

2. Materials and Methods
2.1. Site Description and Experimental Design
The study area is located near Zagreb, the capital city of Croatia, in the second zone of sanitary
protection of the water abstraction site, Kosnica (45°46' N; 16°05' E). The soil is classified after
FAO classification (FAO, 2006) as a Fluvisol (Horizons: A-AC-C-2C/Cl-3Cl-4Cl/Cr-5Cr).
Separately, undisturbed and disturbed samples of investigated horizons were taken from thepedological pit for laboratory analyses. Undisturbed samples (soil-cores) were analyzed for bulk
density, porosity, water capacity, air capacity, and sediment density. The soil particle size
distribution was determined on disturbed samples using wet sieving and sedimentation. Soil bulk
density was determined using the standard soil-core method. Analytical results are shown in
Table 1. The texture of this type of soil is mainly loamy, in some parts clayey with loam. Resultsfrom grain size analysis and bulk densities of soil samples were used for prediction of soil
hydraulic parameters. Soil hydraulic parameters (θs, θr, α, Ks, n and l) were calculated using
Rosetta lite (Schapp et al., 2001) software (Table 1).
Table 1. Soil texture, bulk density and van Genuchten soil hydraulic parameters (Ružičić et al., 2012).

A

0-19

24

66

10

Bulk
density(gcm-3)
1.04

0.428

0.055

30

0.0043

1.70

AC

19-68

14

77

9

1.36

0.466

0.055

36

0.0052

1.70

C68-110

57

38

5

1.39

0.371

0.033

61

0.0218

1.44

2C/Cl

110-140

44

47

9

1.37

0.373

0.041

35

0.0096

1.54

4Cl/Cr140-190

38

50

12

1.41

0.372

0.047

24

0.0077

1.58

5Cr

190-215

56

39

5

1.43

0.362

0.032

51

0.0223

1.444

Soilhorizons

Depth
(cm)

Sand
(%)

Silt
(%)

Clay
(%)

(cm3 cm-3)

θs(cm3 cm-3)

θr

Ks(cm day-1)

α (cm-1)nParameters such as water content, electrical conductivity and soil water tension are essential formodeling of solute transport. Therefore, a 2.1 m pedological pit, in which field measurement
instruments were installed, was dug at the investigated location (Fig. 1). Two TDR (time domainreflectrometry) and two EC (electrical conductivity) probes (Fig. 1), as well as two tensiometers,
were installed at different depths (TDR: 40 and 110 cm; EC: 50 and 120 cm; tensiometers: 40 cm
and 110 cm). Furthermore, four suction lysimeters were installed at four different depths (40, 80,
150 and 190 cm).

316

Figure 1. Investigative pedological pit with TDR probes and EC-probes.

The surface of the plot above the lysimeters and monitoring equipment to which the tracer wasapplied is approximately 0.7 m2. Before application, the plot was leveled, cleaned of allvegetation and enclosed in order to prevent tracers run off. The plot was irrigated with a 200 l
tracer solution over two hours. During the experiment, water content (using TDR probes) andelectrical conductivity (using EC probes) were measured every twenty minutes. Due to
unexpected problems with the suction lysimeters installed at deeper depths, the percolating
solution was sampled only at a depth of 40 cm. Chloride concentrations in leachate wereanalyzed using ion chromatography (ICS–1000 Ion Chromatography System, Dionex).
2.2.

Modeling

One-dimensional water flow in an unsaturated zone is based on the modified Richards equation(Richards, 1931):∂θ (h) ∂  ∂h  
K ( h)  + 1  
=

∂t
∂z 
 ∂z  (1)

where z is the vertical coordinate (positive upward from water table) [L], t the time (s), h thepressure head [L], θ the volumetric water content [L3L-3] and K the hydraulic conductivity [LT1].
An empirical model of van Genuchten (1980) is used to describe the water retention
characteristics, θ(h):θs − θrθ ( h) =θr +m
1 + α h n 




317

h<0

(2)

where θr is the residual water content [L3L-3], θs the saturated water content [L3L-3], α [L-1], nand m [-] are shape parameters.
In this study, conservative solute transport is described using the convection–dispersion equation(CDE) in the following form:∂θ c ∂ ∂c  ∂θ vc=
θ D  −∂t∂z ∂z  ∂z(3)

where C is chloride concentration [M L-3] in soil solution, v the average pore water velocity [LT1] and D the hydrodynamic dispersion coefficient [L2 T-1].
Pore water velocity is calculated using Darcy's law:

v=

q

θ

(4)

where q is the Darcy flux [LT-1] and θ the porosity [-].
The HYDRUS-1D model (Šimůnek et al., 2008) was used for estimation of the solute transportparameter, namely the longitudinal dispersivity.
A pressure head of 145 cm was set as the initial condition for water flow through the model
domain. This pressure head presents average values from the tensiometer installed at 40 cm
depth. The model domain is delineated by the water flux on the upper boundary and the knownpressure head as the boundary condition on the bottom of profile (constant pressure head).
The initial chloride concentration (0.023 mg cm-3) was set as input (tracer) concentration at the
top of the model domain, while chloride contents through the soil profile were set as chloride
concentrations in soil water (expressed in mg cm-3). For the upper and lower boundary
conditions, a third type condition, representing the flux concentration, was used.
3. Results
3.1. Field ExperimentElectrical conductivity and water content measured during the experiment are presented in
Figures 2a and 2b. Electrical conductivity measured at 50 cm depth shows an immediate increase
from 430 μS cm-1 to 550 μS cm-1 in the 20 minutes after the starting time of tracer application(9:00AM). Electrical conductivity measured at a deeper depth (120 cm) shows a slight increase
from 230 μS cm-1 to 270 μS cm-1 after one hour and forty minutes. Water content measured at a
depth of 40 cm also shows an immediate increase from 35.0 % to 36.4 % in 20 minutes after thestarting time of tracer application. Water content measured at a deeper depth (110 cm) shows aslight increase from 27.8% to 29.1% after one hour and twenty minutes. Chloride concentrationsof percolating water samples from the lysimeter installed at 40 cm are shown in Table 2.

318

Figure 2. a) Diagram of water content for period of two hours and forty minutes, b) Diagram ofelectrical conductivity for period of two hours and forty minutes.
Table 2. Chloride concentrations of percolating water.
Sampled time (min)Observed concentration (mg cm-3)

93
98
108
110
114
116
120

0.02120.02280.02320.02780.02940.02330.0262

Pore water velocity was analytically calculated using eq. 4. Table 3 presents estimated saturated
hydraulic conductivity, porosity, hydraulic gradients, pore water velocities, and dispersivity.
Table 3. Estimated saturated hydraulic conductivity, porosity, hydraulic gradients,
pore water velocities, and dispersivity.
Kavg. (cm day-1)

θavg.(-)

33

0.46

v (cm min-1)

i (-)
imin

0.5

vmin

0.025

imax

4

vmax

0.2

λ* (cm)2

Kavg - average hydraulic conductivity for horizons A and AC, θavg - average porosity for horizons A andAC, imin - minimal hydraulic gradient calculated from tensiometer readings, imax - maximal hydraulicgradient calculated from tensiometer readings, vmin - minimal pore water velocity for imin, vmax - maximal
pore water velocity for imax, λ* - estimated dispersivity with HYDRUS-1D.

319

3.2. Modeling
The diagram in Figure 3 shows that the calcium chloride concentration of 0.023 mg cm-3 (which
is applied at the top of the soil) decreased to 0.013 mg cm-3 in 30 minutes. After that period,
concentration rose to 0.025 mg cm-3 in 120 minutes. A longitudinal dispersivity of 2 cm gave thebest fitting of simulated and observed values. The time that the lysimeter needed to intake
enough water for the first sample was 93 minutes (Fig. 3). Due to collapse of the pedological pit
during application of the tracer and sampling of percolating solution, the field experiment was
not completed.

Figure 3. Diagram of concentration in time. Legend: - N1-predicted curve at 40 cm depth using
HYDRUS 1D, x D1-observed values from suction lysimeter.

4. Conclusions
Longitudinal dispersivity was inversely estimated using data gained by a field experiment in
Fluvisol using the HYDRUS-1D model. Calcium chloride was used as a conservative tracer. The
percolating solution was sampled by a suction lysimeter installed at a depth of 40 cm.
Monitoring equipment was used for input parameters and calculation of dispersivity. Pore watervelocities were calculated using Darcy's law. Both velocities were used for estimation ofdispersivity. The HYDRUS 1D model gave a dispersivity value of 2 cm. Due to collapse of thepedological pit during application of the tracer, estimation of longitudinal dispersivity was
performed on an incomplete data set. The value of dispersivity is therefore doubtful.
Acknowledgments
The work was carried out as part of the GENESIS project on groundwater systems(http://www.thegenesisproject.eu) financed by the European Commission 7FP contract 226536
and Croatian Ministry of Science, Education and Sport (no. 195-1953068-2704 to G.D.).

320

References

Akhtar, M. S., T. S. Steenhuis, B. K. Richards, and M. B. McBride, Chloride and Lithium transport inlarge arrays of undisturbed silt loam and sandy loam soil columns, Vadose Zone Journal, 2, 715–727,
2003.
Dişli, E., Batch and column experiments to support heavy metals (Cu, Zn and Mn) transport modeling inalluvial sediments between the Mogan Lake and the Eymir Lake Gölbaşi, Ankara, Ground Water
Monitoring & Remediation 30(3), 125–139, 2010.
FAO, World reference base for soil resources 2006, A framework for international classification,correlation and communication, World Soil Resources Reports No. 103, FAO, Rome, 2006.
Fonseca, B., A. Teixeira, H. Figueiredo, and T. Tavares, Modelling of the Cr(VI) transport in typical soilsof the North of Portugal, Journal of Hazardous Materials, 167, 756–762, 2009.
Heilig, A., T. S. Steenhuis, M. T. Walter, S. J. Herbert, Funneled flow mechanisms in layered soil: field
investigations, Journal of Hydrology, 279, 210–223, 2003.
Jacques, D., J. Šimůnek, A. Timmerman, and J. Feyen, Calibration of Richards’ and convection–
dispersion equations to field–scale water flow and solute transport under rainfall conditions, Journalof Hydrology, 259, 15–31, 2002.
Jacques, D., C. Smith, J. Šimůnek, and D. Smiles, Inverse optimization of hydraulic, solute transport, andcation exchange parameters using HP1 and UCODE to simulate cation exchange, Journal ofcontaminant Hydrology, 142-143, 109-125, 2012.
Moradi, A., K. C. Abbaspour, and M. Afyuni, Modelling field-scale cadmium transport below the rootzone of a sewage sludge amended soil in an arid region in Central Iran, Journal of ContaminantHydrology, 79, 187– 206, 2005.
Richards, L. A., Capillary conduction of liquids through porous mediums, Physics, 1(5), 318–333, 1931.
Ružičić, S., M. Mileusnić, and K. Posavec, Building conceptual and mathematical model for water flow
and solute transport in the unsaturated zone at Kosnica Site, Mining-Geological-Petroleum
Engineering Bulletin, 25, 21-31, 2012.
Schaap, M. G., F. J. Leij, and M. Th. van Genuchten, Rosetta: A computer program for estimating soil
hydraulic parameters with hierarchical pedotransfer functions, Journal of Hydrology, 251, 163-176,
2001.
Seuntjens, P., D. Mallants, N. Toride, C. Cornelis, and P. Geuzens, Grid lysimeter study of steady statechloride transport in two Spodosol types using TDR and wick samplers, Journal of ContaminantHydrology, 51, 13–39, 2001.
Severino, G., A. Comegna, A. Coppola, A. Sommella, and A. Santini, Stochastic analysis of a field-scale
unsaturated transport experiment, Advances in Water Resources, 33, 1188–1198, 2010.
Stumpp, C., G. Nützmann, S. Maciejewski, and P. Maloszewski, A comparative modeling study of a dual
tracer experiment in a large lysimeter under atmospheric conditions, Journal of Hydrology, 375, 566–
577, 2009.
Šimůnek, J., M. Th. van Genuchten, M. Šejna, N. Toride, and F. J. Leij, The STANMOD computer
software for evaluating solute transport in porous media using analytical solutions of convectiondispersion equation, Version 1.0, and 2.0, IGWMC-TPS-71, International Ground Water ModelingCenter, Colorado School of Mines, Golden, Colorado, 32 pp., 1999.
Šimůnek, J., D. Jacques, J. W. Hopmans, M. Inoue, M. Flury, and M. Th. van Genuchten, Solute transport
during variably–saturated flow – Inverse methods. Chapter 6.6 in Methods of Soil Analysis: Part 1.
Physical Methods, 1435–1449, 3rd ed., J. H. Dane and G. C. Topp (eds.), Madison, Wisc., SSSA,
2002.
Šimůnek, J., M. Šejna, H. Saito, M. Sakai, and M. Th. van Genuchten, The HYDRUS-1D Software
Package for Simulating the Movement of Water, Heat, and Multiple Solutes in Variably Saturated
Media, Version 4.0, Hydrus Software Series 3, Department of Environmental Sciences, University ofCalifornia Riverside, Riverside, CA, USA, pp. 315, 2008.

321

Toride N., F. J. Leij, and M. Th. van Genuchten, The CXTFIT code for estimating transport parametersfrom laboratory or field tracer experiments, Version 2.0, Research Report No. 137, U.S. Salinity
Laboratory, USDA, Riverside, CA, 1999.
van Genuchten, M. Th., A closed form equation for predicting the hydraulic conductivity of unsaturated
soils, Soil Science Society of America Journal, 44(5), 892–898, 1980.
Zhang, S., M. Jin, and Q. Sun, Experiment and numerical simulation on transportation of ammonia
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1332, 2011.
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322

Predicting the Impact of Treated Wastewater Infiltration on
Groundwater Recharge by Simulating Reactive Transport in theUnsaturated Zone
Cristina Sandhu, Thomas Fichtner, Issa Hasan, and Peter-Wolfgang Gräber
Faculty of Environmental Sciences, Institute for Waste Management and Contaminated Sites Treatment
Dresden University of Technology – Pratzschwitzer Straße 15, 01796 Pirna – Germany,
cristina.sandhu@tu-dresden.de,thomas.fichtner@tu-dresden.de,issa.hasan@tu-dresden.de,peterwolfgang.graeber@tu-dresden.de

Abstract
Due to demographic increase and climate change, it is necessary to look at alternative ways to replenish
groundwater resources. One possibility is to infiltrate treated wastewater directly into the ground and use
the filtering capacity of the soil. To prevent the pollution of groundwater, one must ensure that not only
the quality of treated wastewater is suitable for infiltration, but also that the soil has good filtration
capacities. This is a sustainable alternative to groundwater recharge if natural precipitation is insufficient,
especially in semi-arid and arid areas. This paper presents the results of a project investigating theinfiltration of treated wastewater from small-scale wastewater treatment plants (WTPs) into theunsaturated soil zone. These small-scale WTPs use a preliminary sedimentation, followed by a biofilm
reactor and secondary treatment. Consequently, the treated wastewater has a high quality and is therefore
suitable for direct infiltration into the unsaturated soil zone. To forecast the transport and thetransformation processes and the concentration of infiltrated treated wastewater into the unsaturated zone,
different scenarios were modeled with the help of the software, PCSiWaPro®. For this purpose, thesoftware tool PCSiWaPro® was further enhanced to include wastewater transport and transformation as
well as the small-scale sewage treatment plants classes. To account for the relevant biogeochemical
reactions, PCSiWaPro® was coupled to the geochemical software PHREEQC. To validate the enhanced
simulation software, column experiments were conducted. The results from column experiments andfrom modeling have improved the understanding of the complex processes in the unsaturated zone and its
relationship with the saturated zone. It is now possible to efficiently design and operate small-scale
wastewater treatment plants and to predict groundwater recharge.

1. Introduction
According to the European Water Frame Directive (EU-WFD, 2000), all the member states mustachieve a good chemical and ecological status for all water bodies until 2015. The EU-WFD
establishes quality criteria that takes into account the local characteristics of the groundwater
body and its chemical status and introduces measures to prevent or limit its pollution. As a large
proportion of the groundwater recharge comes from the treated wastewater, important steps incollecting and disposing it have been taken. But there is still significant groundwater recharge
originating from small-scale wastewater treatment plants (WTPs). Until now, the treatedwastewater has been directly discharged via drainage pipes. Since both discharge methods are
expensive, the concept of infiltrating the treated wastewater directly into the ground for smallscale individual systems is being investigated.

323

The main objective of this work is to develop a software tool for simulating the transport andtransformation of contaminants in variable saturated porous media coming from WTPs, based onlaboratory and field experiments. Thus, the results of the modeling and the experiments canfurther improve the designs of small-scale WTPs, increase their operational efficiency, andrecharge groundwater.
2. Modeling Unsaturated Zone Processes
2.1. Theoretical Background
The water flow process in variably-saturated porous media can be described using the Richards
equation (Richards, 1931), which considers both unsaturated and saturated regions
simultaneously:∂θ ∂   A ∂h=
+ K izA  − S
 K  K ij∂t ∂xi  
∂x j


(1)

where θ is the volumetric water content [L3L-3], h is the capillary pressure head [L], xi (i=1, 2)
are the spatial coordinates [L], t is the time [T], KijA are components of a dimensionlessanisotropy tensor KA, K is the unsaturated hydraulic conductivity function [LT-1], and S is asink/source term [T-1], which is considered here as the amount of water removed by roots ofplants. Since the capillary pressure head is a dependent variable and both the hydraulicconductivity K and the volumetric water content θ are dependent on the pressure head, theRichards equation is highly non-linear. Therefore, the solution process has to be conducted in an
iterative manner. The unsaturated soil hydraulic properties are described by using the equations
developed by van Genuchten (1980) and Mualem (1976). The water content in an unsaturated
porous medium depends on the capillary pressure head in the pores, given by:θ (hc ) = θ s +θs − θr[1 + (α ⋅ h ) ]1n 1− n(2)cin which θr and θs denote the residual and saturated water contents, and the exponent n is the van
Genuchten parameter.
The partial differential equation governing two-dimensional chemical transport during transientwater flow in a variably-saturated porous media is given by:∂θc ∂ρs ∂ ∂c  ∂qi c
+
=
θ
Dij
−
+ µ wθc + µ s ρs + γ wθ + γ s ρ − Scs∂t∂t ∂xi ∂x j  ∂xi(3)

where c is the solute concentration [ML-3], s is the sorbed concentration [ML-3], qi is the ith
component of the volumetric flux [LT-1], and µw and µs are the first-order rate constants for324solutes in the liquid and solid phases [T-1], respectively; γw and γs are zero-rate constants for theliquid [ML-3T-1] and the solid phases [T-1]; ρ is the bulk density [ML-3], S is the sink/source termin the water flow equation (1), cs is the concentration of the sink/source term [ML-3], and Dij isthe dispersion coefficient tensor [L2T-1]. The four zero-and first-order rate constants may be used
to represent biodegradation, volatilization, precipitation and radioactive decay.
2.2. Software Tool PCSiWaPro®
The PCSiWaPro® is a software tool developed at the TU Dresden. It is based on a soil physicalmodel implemented in the numerical code SWMS_2D, developed by Šimůnek et al., (1994). The
PCSiWaPro® can simulate 1D and 2D vertical plane or axially symmetrical flow and transport
processes in the unsaturated zone under steady-state and transient conditions. It numericallysolves the Richards equation (1) and the convection-dispersion equation, using the finite
elements method. Moreover, it has a flexible choice of boundary conditions, the consideration ofhysteresis-like processes in the unsaturated zone, and a parameter identification algorithm. It
considers sorption and zero- and first-order degradation. To account for hydrological conditions(e.g., precipitation, evapotranspiration, surface runoff, root water uptake), PCSiWaPro® iscoupled with a Weather Generator module (WettGen) (Nitsch et al., 2007, Blankenburg, 2008).
As this numerical tool is intended for application by enterprises that investigate contaminanttransport in groundwater and the degree of pollution of different contaminated sites, there issubstantial demand to develop a complex software tool that covers all areas of interest (i.e.,surface, unsaturated and saturated zone). Therefore, PCSiWaPro® is also coupled to thegeochemical software PHREEQC (Appelo et al., 2005) to consider the relevant bio-geochemical
reactions in the unsaturated zone (inter-dependent complexation reactions, cation exchange,
precipitation-dissolution, volatilization, redox-reactions), and to the groundwater flow andcontaminant transport simulation tool model PCGEOFIM (Boy et al., 2005) shown in Figure 1.

Figure 1. Conceptualization of coupled numerical codes for simulating surface, unsaturated andsaturated zone processes.

2.3. Software Tool PHREEQC
The well known bio-geochemical program, PHREEQC (Parkhurst, 1995), is based on an ionassociation aqueous model and is capable of a variety of chemical equilibrium reactions,kinetically determined reactions, solution and precipitation processes, and ion exchange325

processes. In several databases, the chemical properties of the individual substances and thepossible reaction equations are stored. In a control file, the definition of the solution and theresultant chemistry of the solution are calculated.
2.4. Coupling PCSiWaPro® and PHREEQC
PCSiWaPro® accounts for sorption, retardation, and zero- and first-order degree degradation, andin the case of wastewater, it is also necessary to consider biogeochemical reactions. The wellknown geochemical model PHREEQC was chosen to be coupled with PCSiWaPro® due to its
modular structure and extensive geochemical databases.
While PCSiWaPro® simulates the transport of water and wastewater in the unsaturated soil zone,
PHREEQC focuses on the bio-geochemical reactions. The simulation tool has to consider
different soil types, small-scale sewage treatment plant classes, as well as a mixture ofcontaminants and their inter-relations. Therefore, a set of databases for soil types, typical organicand inorganic wastewater contaminants, sewage treatment plant classes, and boundary conditions
have all been further implemented to make the tool more user-friendly (Figure 2).

Figure 2. Coupling of numerical simulation codes and databases.

Figure 3 illustrates the program structure of the coupling between the two numerical models. In
the discretized time domain of the numerical model, the three simultaneous and dependent
processes of flow, transport and reaction are separated using a non-iterative splitting approach
where ∆t is the length of the coupling step. The coupling time step is further reduced in the caseof geochemical reactions if necessary. As a result of decoupling, concentrations are assumed
independent of reactions in the solute transport calculations. Likewise, the liquid phase saturationis considered independent of concentrations and reactions during flow calculation. During thegeochemical step, performed by PHREEQC, the solution composition is considered independentof both flow and transport.

326

The coupling scheme between the PCSiWaPro® and PHREEQC takes places online, whichmeans that for each time step, the codes exchange the following data:
1. Simulation of the water flow for the calculation of the convective transport performed by
PCSiWaPro® (independent of concentrations and reactions)
2. Simulation of solute transport for each individual substance performed by PCSiWaPro®
(independent of reactions)
3. Calculation of the bio-geochemical equilibrium and kinetics reactions for each node
performed by PHREEQC (independent of flow and transport). The changes in theconcentrations after the reactive step are the new initial concentrations for the nexttransport time step calculation. The concentrations in the immobile phase remain in thecorresponding node and play no role for the mass transfer. A maximum one-day time stepfor the reaction is necessary to depict a realistic illustration of interactions between waterand nutrient budgets.

Figure 3. Coupling between the PCSiWaPro® and PHREEQC in a 2D cross-section.

3. Validation Through Column Experiments
As the software PCSiWaPro® is further developed to include small–scale WTPs, it is necessary
to validate the results of the numerical simulations. Accordingly, a series of column experiments
were performed in the laboratory to answer following:• Which soil has the best natural attenuation capacity in order to ensure a good seepage
water quality?
• How does the treated wastewater quality influence the infiltration capacity of soils(clogging aspect)?
• How do the infiltration rate characteristics (continuous/pulse, amount) influence theinfiltration and natural attenuation capacity?
• Does the thickness of the unsaturated zone have a significant impact on the residence
time of the seepage water and the natural attenuation capacity?

327

The experiments consisted of three columns, each with a different soil type described in Table 1.
The in situ soil from the case study sites of Kleinopitz and Biehain in Saxony (Germany) wasused for the column experiments. The 150 cm long columns were made of Plexiglas having aninternal diameter of 15 cm. The treated effluent was infiltrated in the upper part of the column
with the help of a peristaltic pump. Infiltration occurred eleven times daily, according to human
diurnal water consumption. To determine the soil water potential in the column, two
tensiometers were installed at different heights. Moreover, to have on overview of thetemperature, a soil temperature sensor was attached. The measured data was directly recorded ona data logger.
Table 1. Soil parameters and initial conditions.
Soil typeθs

Coarse sand withgravel (KRB23)
Medium silty sand
(KRB10)Medium sandy silt
(B5)

van Genuchten parametersθrαInfiltrationrate[m3 d-1]

Precipitation[mm y-1]

Duration ofexperiments[d][cm3cm-3][cm3cm-3][cm-1]

n
[-]

0.38

0

0.15

1.34

0.1

676

365

0.38

0

0.2

1.23

0.1

676

365

0.38

0

0.262

1.35

0.1

676

185

The quality of the inflow wastewater into the column and outflow was determined and comparedto the legal limit for drinking water according to the German Drinking Water Directive (TWO:
Die Trinkwasserverordnung, 2012) as listed in Table 2.
Table 2. Quality of some investigated parameters/contaminants and their legal limit.
Unit
Concentration
in inflow
Legal limit
TWO, 2012)

pH
[-]

COD
[mg L-1]

DOC[mg L-1]

NO2-- N
[mg L-1]

NO3--N[mg L-1]

NH4+-N[mg L-1]

TKN[mg L-1]

Pges[mg L-1]

E.coli/100 ml

65

90

18.5

102

57.6

15.2

16.5

19.2

269

6.59.5

-

-

0.15

11.3

0.39

-

0

In the column with medium sandy silt (red line in Figure 4–left), a complete reduction ofammonium could be observed during the experimental duration of 185 days. However, an
increase in the nitrate concentration was observed due to nitrification (Figure 4–right). The
nitrate concentrations in the effluent were about 20 mg L-1 higher than the concentrations in theinfiltrated wastewater. In the medium silty sand, a complete reduction of ammonium could beobserved after 250 days. This result was achieved by decreasing the amount of infiltrated treatedwastewater. An increase of nitrate could also be registered for this time. The reduction of theammonium in the coarse sand with gravel was only between 25% and 50% and subject to major
fluctuations. Due to the sufficient oxygen present in the soil column, denitrification was notobserved.

328

Figure 4. Ammonium Nitrogen (left) and Nitrate-Nitrogen (right) behavior in different soils(Blue- inflow; Green–coarse sand with gravel; Purple–medium silty sand; Red–medium sandy
silt)

The reduction of COD and removal of DOC, TKN, and Total Phosphorous is presented in Table
3. It is observed that the highest removal of all parameters occurs in medium sandy silt. A higher
removal was observed for COD and DOC in coarse sand with gravel, compared to medium silty
sand. On the other hand a higher removal was observed for TKN and Total Phosphorous for
medium silty sand, compared to coarse sand with gravel.
Table 3. Removal of COD, DOC, TKN, and Total Phosphorous observed during column experiments.
Soil class
Coarse sand with gravel (KRB23)
Medium silty sand (KRB10)
Medium sandy silt (B5)

COD
[%]
70
50
90

DOC
[%]
40
20
75

TKN
[%]
30
70
80

PTotal
[%]
0
75
100

The reason for the low removal efficiency in the coarse sand with gravel and medium silty sandwas the prevalent, non–optimal environmental conditions for the occurrence of biologicaldegradation in the columns (low pH–value due to lower buffering capacity of soil). Anotherreason for low removal efficiency in the coarse sand with gravel and medium silty sand was theshort residence time of the treated wastewater in the soil caused by the higher hydraulicconductivity. However, in the medium sandy silt, ideal conditions are present, as can bedemonstrated by the highest removal of the concentrations of the infiltrated wastewater.
Although the medium silty sand and the medium sandy silt have similar soil physical properties
as shown in Table 1, the natural attenuation is more efficient in medium sandy silt due to thehigher portion of fine grained silt compared to medium silty sand. Consequently, the finer
grained soil type provides a larger specific surface area for the geochemical processes to occur.
4. Example Application
The PCSiWaPro® software was applied to the Kleinopitz case study site to predict the on-sitetransport of treated wastewater. A 2D numerical model was prepared (Figure 5) using input

329

parameters and data (Table 1) obtained from the field and laboratory experiments to simulate theseepage of the treated effluent from small–scale WTPs (Tomoda, 2012). The upper boundary
condition was the atmosphere, while the lower boundary represents the groundwater table.

Figure 5. Graphical representation of the numerical model.

Several questions needed to be answered before performing a solute transport and reactions
simulations, the most important being:• Does the thickness of the unsaturated zone significantly impact the residence time of thewastewater and natural attenuation capacity?
• Where should the infiltration area be located to prevent contamination of any possible
drinking water well?
• Which soil hydraulic parameters influence the seepage of the treated effluent?
The results in Figure 6 show the groundwater recharge from different scenarios, where thegroundwater table depths of 10 m, 6.5 m, and 3.5 m have been used. Two different infiltration
rates of 0.1 and 0.3 m3d-1 for three different soil types were applied. When an infiltration rate of
Qin =0.1 m3d-1 is applied (Figure 6–left) to all three different groundwater table depths, the travel
time is always fastest for medium sand (compared to medium silty sand and medium sandy silt).
As expected, the minimum travel time of 25 days to a GW table depth of 10 m is shortest for
medium sand, compared to 27 and 33 days for medium silty sand and medium sandy silt,
respectively. Irrespective of the depth of the GW table, a maximum groundwater recharge of 0.1
m3d-1 is eventually attained for an equal infiltration rate of 0.1 m3d-1.
In case of medium sand and medium silty sand, when an infiltration rate of 0.3 m3d-1 is applied,
the minimum travel times are similar for both soil types. Thus the minimum travel time is 2, 6,
and 10 days for a GW table depth of 3.5, 6.5 and 10 m, respectively. An eventual equivalentgroundwater recharge rate (compared to the infiltration rate) of 0.3 m3d-1 is also attained for thesesoil types but at a relatively faster rate compared to an infiltration rate of 0.1 m3d-1 over a 60 day
simulation period. The short travel time of water through the unsaturated zone to thegroundwater table implies insufficient time for geochemical reactions to optimally occur. Only
the medium sandy silt, with longer travel times, lower groundwater recharge rates, and greater
depths to the groundwater table, could be a good candidate for infiltrating treated effluent fromsmall scale WTPs, as also demonstrated by the column experiments.

330

Figure 6. Groundwater recharge for different groundwater tables (GwT) and infiltration rates(Qin) (blue–medium silty sand green–medium sandy silt, red–medium sand.

5. Conclusions
This paper presented a coupled finite element model that uses PCSiWaPro® for simulating waterand solute transport in an unsaturated zone and the geochemical model PHREEQC for its
capability of simulating chemical equilibrium and non–equilibrium reactions. The numericalmodel was validated by column experiments, where different soil types, infiltration rates andeffluent qualities were considered. From the column experiments and the numerical simulation,
one can conclude that medium sandy silt is the best suited soil type for infiltrating the treatedeffluent from small–scale WTPs because it has the longest travel time, and therefore sufficient
time for bio–chemical reactions to take place. However due to the shallow depth to the GW table(up to 10 m), it is important to limit the infiltration rates to 0.1 m³ d-1 or less.
The most difficult task in simulating the solute transport in unsaturated soils is the effective
characterization and quantification of the effects of the chemical reactions on transport
processes. In this context, one of the advantages of coupling is that PCSiWaPro® completely
integrates the PHREEQC geochemical model, and thereby allows the user access to a large rangeof chemical reactions. It provides the ability to include the effects of a large number of different
types of chemical processes on solution compositions on a per time–step basis. Anotheradvantage is the extensive databases, which make the numerical PCSiWaPro® code a userfriendly software tool, especially when the necessary data collection cannot be performed
through laboratory and field investigations. To demonstrate the robustness of the coupling
scheme between the codes, the numerical software still needs to be extensively verified for more
complex systems.

331

Acknowledgements
The authors thank the German Federal Ministry of Education and Research (BMBF) for thefinancial support of the research project “RESS-199-016 ESEK –Ganzheitliches System zur
Errichtung von Kleinkläranlagen; TP 3: Entwicklung eines Entscheidungshilfesystem und
Validierung durch Laborversuche” (“Integrated system for designing and operating a small-scale
sewage treatment plant – Development of an expert system and validation using laboratory
experiments”), whose results were presented in this paper.
References

Appelo, C. A. J., and D. Posma, Geochemistry, Groundwater and Pollution, CRC Press, Taylor & Francis
Group, 2005.
Blankenburg, R., and O. Kemmesis, SiWaPro DSS a computer aided leaching forecast tool, ConSoil
Conference Abstract, 2008.
Boy, S. and D. Sames, PCGEOFIM®, Anwenderdokumentation, Ingenieurbüro für Grundwasser Leipzig
GmbH, (in German, internal use only), 2005.
EU Directive 2000/60/EC of the European Parliament and the Council of 23 October 2000 establishing aframework for Community action in the field of water policy, 2000.
Gräber, P.-W., et al., SiWaPro DSS, Beratungssystem zur Simulation von Prozessen der unterirdischen
Zonen, Simulation in Umwelt- und Geowissenschaften, Buchverf, Wittmann Jochen und Müller Mike,
Hrsg. Müller Mike. - Leipzig, Shaker Verlag, ISBN 3-8322-5132-4, (in German), 2006.
Jacques, D., J. Šimůnek, D. Mallants, and M. Th. van Genuchten, Modeling coupled hydrogeological andchemical processes in the vadose zone: a case study of long-term uranium transport following mineral
P-fertilization, Vadose Zone Journal, 7(2), 698-711, 2008.
Langergraber, G., and J. Šimůnek, Reactive transport modeling of subsurface flow constructed wetlands,
Vadose Zone Journal, 11(2), doi:10.2136/vzj2011.0104, 14 pp., 2012.
Mualem, Y, A new model for predicting the hydraulic conductivity of unsaturated porous media, Water
Resources Research, 12(3), 513-522, 1976.
Nitsch, B., and P.-W. Gräber, Anwendung synthetischer Niederschlagszeitreihen bei der Strömungsmodellierung der ungesättigten Bodenzone, Simulation in Umwelt- und Geowissenschaften,
Workshop Berlin, Shaker Verlag, Bereich Umweltinformatik, (in German), 2007.
Parkhurst, D. L., and C. A. J. Appelo, User’s guide to PHREEQ C (Version 2) – A computer program forspeciation, batch-reaction, one-dimensional transport and inverse geochemical calculations, WaterResources Investigations, Report 99–4259, Denver, Co, USA, 312 pp., 1999.
Radcliffe, D., and J. Šimůnek, Soil Physics with HYDRUS: Modeling and Applications, CRC Press, Taylor &Francis Group, Boca Raton, FL, ISBN: 978-1-4200-7380-5, pp. 373, 2010.
Richards, L. A., Capillary conduction of liquids through porous mediums, Physics, 1(5), 318–333, 1931.
Šimůnek, J., T. Vogel, and M. Th. van Genuchten, The SWMS-2D code for simulating water flow andsolute transport in two-dimensional variably saturated media, Research Report No. 132, U.S. Salinity
Laboratory, USDA, ARS, Riverside, CA, 1994.
Šimůnek, J., and M. Th. van Genuchten, Modeling nonequilibrium flow and transport processes using
HYDRUS, Vadose Zone Journal, 7(2), 782-797, 2008.
Šimůnek, J., M. Th. van Genuchten, and M. Šejna, Development and applications of the HYDRUS andSTANMOD software packages, and related codes, Vadose Zone Journal, 7(2), 587-600, 2008.
Tomoda, N., Sensitivitätssanalyse mittels Softwaretool PCSiWaPro® von hydrogeologischen undhydrologischen Kenngrößen bei Versickerung von gereinigten Abwassers aus Kleinkläranlagen(Bachelor Thesis, in German, internal use only), 2012.
Die Trinkwasserverordnung: Verordnung über die Qualität von Wasser für den menschlichen Gebrauch,Art. 1 ÄndVO vom 5. Dezember 2012, BGBl. I S. 2562, 2012.
van Genuchten, M. Th., A closed-form equation for predicting the hydraulic conductivity of unsaturated
soils, Soil Science Society of America Journal, 44, 892-898, 1980.

332

Temporal Variations of Soil Hydraulic Properties
and its Effect on Soil Water Simulations
Andreas Schwen1, Gernot Bodner2, and Willibald Loiskandl11Institute of Hydraulics and Rural Water Management, University of Natural Resources and Life Sciences (BOKU),
Vienna, Austria; andreas.schwen@boku.ac.at2
Institute of Agronomy and Plant Breeding, University of Natural Resources and Life Sciences (BOKU), Vienna, Austria

Abstract
Simulating water dynamics in the soil compartment close below the surface is challenging since this part ofthe soil profile inhibits large temporal dynamics as a response to climate and crop growth. For accurate
simulations the soil hydraulic properties have to be properly known. These properties may be subject totemporal changes as a response to both tillage and natural impact factors. The impact of different tillage
techniques – conventional (CT), reduced (RT), and no-tillage (NT) – on the soil hydraulic properties and theirtemporal dynamics were observed by repeated experiments using tension infiltrometers. The experimental
data was analyzed in terms of the near-saturated hydraulic conductivity, inversely estimated parameters of thevan Genuchten/Mualem (VGM) model, and the water-conducting porosity. In a second step, the inversely
estimated VGM parameters were incorporated into a soil water simulation. By using temporally variableversus constant sets of VGM parameters, the impact on soil water balance components was tested. Simulated
water dynamics were compared to observed data in terms of the soil water content and water storage in thenear-surface soil profile (0-30 cm). The results show that the near-saturated hydraulic conductivity was in theorder CT > RT > NT, with larger treatment-induced differences where water flow is dominated bymesopores. The VGM model parameter αVG was in the order CT < RT < NT, with high temporal variations
under CT and RT, whereas the parameter n was hardly affected. The results give indirect evidence that NTleads to greater connectivity and smaller tortuosity of macropores, possibly due to biological activity and abetter established soil structure. Simulations with temporally constant hydraulic parameters led tounderestimations of soil water dynamics in winter and early spring and overestimations during late spring andsummer. The use of temporally variable hydraulic parameters significantly improved simulation performancefor all treatments, resulting in average relative errors below 13%. Since simulation results agreed withobserved water dynamics in two seasons, the applicability of inversely estimated hydraulic properties for soil
water simulations was demonstrated. Our results also showed that simulations addressing applied questions inagricultural water management can be improved by time-variable hydraulic parameters.

1. Introduction
For many applied questions in the fields of crop production and agronomy, soil water dynamics areof fundamental importance. Modeling can be a valuable tool to optimize its management (RogerEstrade et al., 2009). Such soil water modeling requires an accurate description of soil hydraulicproperties, i.e. the soil water retention function θ(h) and the hydraulic conductivity function K(h).
Generally, these constitutive functions are assumed to be unchanged over time in most simulation
studies. However, there is extensive empirical evidence that soil hydraulic properties are subject totemporal changes particularly in the near-saturated range where soil structure essentially influences
water flow characteristics (Daraghmeh et al., 2008; Or et al., 2000). The structure of soil top layers
is especially subject to changes over time, caused by wetting/drying cycles, biological activity, andagricultural operations (Leij et al., 2002; Mubarak et al., 2009). Soil tillage and management affectthe hydraulic properties with consequences for the storage and movement of water, nutrients and333pollutants, and for plant growth (Strudley et al., 2008; Xu and Mermoud, 2003). The temporalvariability of hydraulic properties can even exceed differences induced by crops, tillage, or land use(Alletto and Coquet, 2009; Bodner et al., 2008; Bormann and Klaassen, 2008; Hu et al., 2009; Zhou
et al., 2008).
Compared to deeper soil layers, soil moisture close to the surface (0-30 cm) is subject to rapidchanges as response to rainfall, infiltration, evaporation, and root water-uptake. Despite its
importance for the supply of water and nutrients for crops, simulation of this highly dynamic soil
compartment is difficult and requires adequate sets of hydraulic parameters (Šimůnek et al., 2003).
For modeling nutrient or contaminant transport and for the assessment of different tillage methods,
soil water simulations should be introduced that account for time-variable hydraulic properties(Mubarak et al., 2009; Or et al., 2000). However, few studies have addressed this task. For instance,
Or et al. (2000) introduced a model that describes temporal changes of the soil retention properties
after tillage based on the pore-size distribution. Recently, Schwärzel et al. (2011) used the model todescribe landuse-induced changes of the retention properties, but the model has not been applied toa more complex time series of measured hydraulic parameters.
To capture temporal variations in the soil hydraulic properties, suitable measurement methods haveto be applied. As most of the temporal changes are expected to occur in the structural pores, due tochanges in different groups of macro- and mesopores, field methods are preferable to laboratory
methods (Angulo-Jaramillo et al., 2000; Hu et al., 2009; Yoon et al., 2007). To determine the nearsaturated hydraulic properties of agricultural soils directly in the field, tension infiltrometry has
become a commonly used method (Angulo-Jaramillo et al., 1997; Messing and Jarvis, 1993;
Reynolds et al., 1995). Before now, hardly any study assessed the applicability of inversely
estimated parameters in soil water simulations.
The main hypothesis underlying the presented study was that soil water simulations can be
improved by accounting for temporal changes of near-surface soil hydraulic properties. Thus, theobjectives of this study were 1) to capture temporal changes of soil hydraulic properties by repeatedtension infiltrometer measurements, 2) to implement time-variable soil hydraulic properties in a soil
water simulation. This study also aims to assess the feasibility of inversely estimated hydraulicparameters in soil water simulations. We acknowledge that this proceedings paper has been subject
to previous publications (Schwen et al., 2011ab).
2. Materials and Methods
2.1. Experimental Site
Measurements were obtained on an arable field near Raasdorf, Lower Austria (48°14′N 16°35′E).
Climatic data have been recorded at the site since 1998 (Figure 1). The reference evapotranspiration
ET0 was calculated using the Penman-Monteith equation. The site has a mean annual precipitation R
of 546 mm, a mean temperature of 9.8 °C, a mean relative humidity of 75%, and an annual reference
evapotranspiration ET0 of 912 mm. A field trial was established in 1997 to assess the following soil
cultivation techniques: 1) Conventional tillage (CT) with moldboard ploughing and seedbed
preparation using a harrow prior crop seeding; 2) Reduced tillage (RT) with a chisel plough to
10 cm for seedbed preparation; and 3) No-tillage (NT) using direct seeding technique.

334

The soil can be classified as Chernozem in the WRB (IUSS, 2007). The humous A-horizon (030 cm) is followed by an AC-horizon (30-60 cm) over the mature silty sediments (C-horizon,>60 cm). Due to particle size analysis (Table 1), the texture throughout the profile can be classified
as silt loam according to the FAO classification (FAO, 1990). The organic carbon content was
24 g kg−1 in the topsoil. In the two seasons analyzed for this study (2008/09 and 2009/10) the site
was cropped with winter wheat (Triticum aestivum L.) in mid October and harvested in mid July of
the following year (Figure 1).
Soil water content in the field was continuously measured over two consecutive seasons using
capacitance moisture sensors (C-Probe, Adcon Telemetry GmbH, Austria). For each treatment, three
replicate probes were installed in depths of 10, 20, 40, 60, and 90 cm. The measurement interval was
15 min, and data was averaged to daily values. The probes were installed after seeding in November
and removed from the field prior to harvest in July in both analyzed seasons. The water storage inthe soil profile to a depth of 0.30 m S was derived from the water content measurement.

Figure 1. Soil water regime, climatic conditions, and times of measurements: Volumetric watercontent θ, measured in 10 cm depth for the different tillage treatments (mean of three replicate
sensors), air temperature T (grey line); rainfall R (peaks), and times of infiltration measurements(diamonds), soil tillage (triangle), and crop growing period. The grey areas indicate frost periods.

2.2.

Sampling and Infiltration Measurements

Infiltration measurements were made nine times, starting immediately before crop seeding in
October 2008 and continuing until shortly before harvest in July 2010, using three tension
infiltrometers (Soil Measurement Systems Inc., Tucson, AZ) of the design described by Ankeny etal. (1988). The supply pressure heads were −10, −4, −1, and 0 cm: the first two were maintained forapproximately 50-60 min, and the last two for about 10-20 min. Preliminary tests found thesedurations to be sufficient to achieve steady-state infiltration. For each treatment, three replicate
infiltration measurements were carried out. Before each infiltration measurement, soil samples were335

taken with steel cores near the measurement location to obtain the initial water content θi.
Immediately after each measurement, another core sample was collected directly below theinfiltration disc to quantify the final water content θf, bulk density ρb, and total porosity φ. We used
Wooding’s solution (1968) as described by Reynolds and Elrick (1991) and Ankeny et al. (1991) todetermine K(h) from the infiltration measurements. More details can be found in Schwen et al.
(2011).
One soil profile per treatment was excavated and sampled with soil cores in depths of 5 cm, 40 cm,
and 70 cm with three replicates during July 2009. The hydraulic properties of the subsoil layers were
determined using pressure plate extractors (Soil Moisture Inc., USA) at h = 0.2, 0.5, 1.0, 2.0 and 3.0
bar. The RETC code (van Genuchten et al., 1991) was used to fit the parameters of the van
Genuchten/Mualem model (referred to as VGM, van Genuchten, 1980; Table 1).
Table 1. Physical soil properties and hydraulic parameters at the experimental site. Texture (content of sand,silt and clay), bulk density ρb, saturated water content θs, saturated hydraulic conductivity Ks, and the VGM
model parameters αVG and n are listed.
Depth
cm
0-30
30-60
60-90

2.3.

Tillage
CT

Sand
Silt
Clay
———— kg kg-1 ————
0.27
0.54
0.20
0.35
0.47
0.18
0.31
0.57
0.12

ρb
g cm-3
1.38
1.27
1.36

θs
m3 m-3
0.48
0.52
0.49

Ks
m d-1

αVG
m-1

n
-

0.40
0.31

6.77
1.15

1.168
1.571

0-30
30-60
60-90

RT

0.27
0.35
0.31

0.54
0.47
0.57

0.20
0.18
0.12

1.38
1.23
1.38

0.48
0.54
0.48

0.30
0.31

5.57
1.55

1.234
1.452

0-30
30-60
60-90

NT

0.27
0.35
0.31

0.54
0.47
0.57

0.20
0.18
0.12

1.42
1.27
1.39

0.47
0.52
0.48

0.30
0.31

12.34
1.40

1.169
1.575

Inverse Estimation of Soil Hydraulic Parameters

The inverse analysis of tension infiltrometer data required a numerical solution of the modified
Richards’ equation. The initial and boundary conditions were defined as proposed by Šimůnek et al.
(1998). To describe the unsaturated soil hydraulic properties, we used the van Genuchten/Mualem
model (van Genuchten, 1980). We formulated the objective function (OF) that is minimized during
parameter estimation by combining the cumulative infiltration data, the K(h) values calculated by
Wooding’s analysis, and θf. OF minimization was accomplished using the Levenberg-Marquardt
nonlinear minimization method (Marquardt, 1963), as provided by the program HYDRUS 2D/3D(Šimůnek et al., 2006). For a numerical solution, a quasi-3D (axisymmetric) model geometry waschosen, as described by Šimůnek et al. (1998). Initial values for the parameters were derived fromthe soil’s texture using the Rosetta pedotransfer package (Schaap et al., 2001; input parameters: soil
texture and ρb). To reduce the amount of unknown variables, for all parameter estimations l was set
constant at 0.5 (Ramos et al., 2006), and θr was fixed at 0.065 m3 m−3, as predicted by Rosetta(Lazarovitch et al., 2007). Ks was set to the value obtained by Wooding’s analysis (Lazarovitch etal., 2007; Schwen et al., 2011ab; Yoon et al., 2007). The remaining parameters θs, αVG, and n wereinversely estimated.

336

Representative mean parameters for each cultivation treatment were derived using the scaling
approach. Following the approach of Schwärzel et al. (2011) and Vereecken et al. (2007), a
conventional scaling procedure was applied in which scaling factors were estimated by minimizing
the residual sum of square differences between the data and the scaled K(h) and θ(h) reference
curves.
2.4.

Simulation with Time-variable Hydraulic Parameters

Soil water dynamics were simulated with a daily temporal discretization for the wheat growing
seasons (Oct. 2008 – July 2009 and Oct. 2009 – July 2010; Figure 1). The vertical 1D Richards’
equation was solved numerically using the Earth Science Module within Comsol Multiphysics(Comsol AB). According to the observed soil horizons for the different tillage treatments, thegeometry was divided into three layers: the surface soil (A-horizon) was between 0 and 0.15 m for
RT and NT, and 0 - 0.30 m for CT, the AC-horizon down to 0.60 m, and the subsoil (C-horizon)
from 0.60 m to 1.00 m.
Potential evaporation Epot and transpiration Tpot were derived using the FAO 56 dual crop coefficientmethod (Allen et al., 1998). We used tabulated values for the crop coefficient Kc (Kc ini = 0.4,
Kc mid = 1.15, Kc end = 0.25, Allen et al., 1998) and observed crop development stages. We
acknowledge that we did not calculate Epot and Tpot as treatment-specific but assumed them to be thesame for the different tillage treatments. R and Epot, the latter reduced by a h-dependent reduction
function, were applied as the upper boundary condition (Bodner et al., 2007). Tpot was implemented
via a sink term using a growth function, a linear decreasing root distribution function (Prasad, 1988),
and a h-dependent reduction function according to Feddes et al. (2001) and Wu et al. (1999). The
lower boundary was defined by a unit gradient condition.
Simulations were made with constant and time variable VGM parameters (αVG, Ks, and θs) of theupper soil layer for all tillage methods. The measured parameter values were connected using cubic
splines to allow a continous description. Since the temporal variability was expected to be negligible
in the lower soil horizons, the hydraulic parameters were set constant (Table 1). To get a comparison
between observed and predicted values, Oi and Pi, the average relative error (ARE) was calculated asfollows (Popova and Pereira, 2011):

ARE =1 N  Oi − Pi ∑
N i =1  Oi (1)Here, N is the number of observations. For further comparison between Oi and Pi, regressions of theform Pi = slope × Oi + intercept were performed (Moret et al., 2007) and the determination
coefficient R2 was calculated. Root mean square errors (RMSE) were also calculated by (Ji et al.,2009; Popova and Pereira, 2011):

1 N
2
RMSE =  ∑ (Pi − Oi ) 
N 1


337

1/ 2

(2)

To account for the spatial variability of the observed values, Oi used in the differences was defined
as mean (Oi) ± standard deviation.
3. Results and Discussion
3.1.

Climatic Conditions and Soil Water Content

For the present study two consecutive wheat growing seasons were analyzed. R between October 15,
2008 and July 13, 2009 was 398 mm, which is in line with the long-term average. Remarkably, there
was hardly any rain during April and May 2009 (Figure 1). Between October 15, 2009 and July 12,2010, the rainfall was 395 mm. Potential evapotranspiration Etpot in the seasons 2008/09 and2009/10 was 366 and 332 mm, respectively, which can be divided into Epot (117 and 101 mm), andTpot (249 and 231 mm). In the growing seasons 2008/09 and 2009/10 the climatic water balance
resulted in a surplus of 32 mm and 63 mm, respectively.

Figure 2. Simulated vs. measured volumetric soil water content θ in a depth of 10 cm (upper plots)
and water storage S in the near-surface soil profile (0-30 cm; lower plots). θ and S (mean ± standard
deviation) were measured using three replicate sensors per treatment in depths of 10, 20, and 40 cm(grey areas). The gaps in winter are due to frost periods (Figure 1). The results of simulations using
constant and time-variable hydraulic properties are shown for the tillage treatments CT (a), RT (b),and NT (c).

338

In response to climatic conditions and crop growth, the soil water content varied over time (Figure1). With high water contents in winter and early spring and dryer periods between April and June
2009, the first analyzed year shows a broad variety of soil moisture conditions. Since there wassufficient rainfall in spring 2010, the soil moisture in the season 2009/10 was more balanced. During
frost periods in winter, the shallow sensors did not give meaningful values so they had to be
excluded from further analysis (Figure 1). Only small differences in the near-surface water content
occurred between treatments CT and RT, whereas NT resulted in significant higher soil moisture
contents. This agrees with findings of Moret et al. (2007) and Moreno et al. (1997).
The variability within a treatment indicated by the replicate probes was considerably high (Figure2). Since technical problems with the moisture sensors could be ruled out due to careful dataprocessing, this variability might be attributed to the natural spatial variability in the hydraulicproperties. As the variability was smallest for CT and slightly larger for RT, it reflects the effect of
spatial homogenization of repeated tillage operations. Contrarily, considerable differences among
the replicate sensors under NT indicate a high spatial variability, especially in the season 2008/09.
Under NT, the variability was much smaller in the season 2009/10 than in 2008/09. This may be
explained by the fact that the probes were removed before harvest in July and reinstalled at slightly
different positions after seeding in October 2009.
3.2.

Temporal Dynamics of Soil Hydraulic Properties

The temporal variability of soil hydraulic properties and its underlying water-conducting porosity atthe experimental site has been discussed in detail by Schwen et al. (2011a). In both analyzed
seasons, Ks and θs under CT and RT strongly decreased after tillage during winter (Figure 1), whichmight be due to rainfall-induced pore sealing and settling (Cameira et al., 2003; Mubarak et al.,2009; Xu and Mermoud, 2003). The decrease is followed by a gradual increase in spring andsummer, possibly induced by biological activity, root development, and wetting / drying cycles, as
proposed by Mubarak et al. (2009). Beside considerable higher Ks values in October 2009 and June
2010, NT showed only small temporal variability and no systematic dynamic. The high Ks values in
the non-tilled soil may be due to the existence of preferential flow paths (earthworm burrows), as
reported by Moreno et al. (1997).
Regarding the VGM model parameters, n showed only small temporal dynamic for all treatments.
However, αVG showed a considerable temporal dynamic. This dynamic was smallest for NT,
indicating the relatively greater temporal stability of the hydraulic properties under this treatment(Schwen et al., 2011a). We found no systematic trend that reasonably explains the temporal dynamicof αVG for both analyzed seasons. Possibly, this indicates that temporal dynamics of the VGM
parameters are quite complex, even for the tilled treatments (CT, RT). Therefore, we did not apply apore-size evolution model (e.g., Or et al., 2000), but used cubic splines to continuously describe thehydraulic parameters.
3.3.

Performance of Near-Surface Water Simulations

The present study focuses on the simulation of water movement and storage in the highly dynamic
near-surface soil compartment (0-30 cm). Therefore in the following, only the results for theuppermost soil layer are discussed. However, we acknowledge that we found a good agreement339

between measured and simulated soil water contents in the deeper soil layers for all simulations. For
quality assessment of the simulations, we compared simulated and measured values of θ10 and S
using Eq. 9 and 10. Overall, the simulations resulted in soil water dynamics that agreed with themeasured range for all treatments (Figure 2). Since the hydraulic parameters that were used in the
topsoil were estimated inversely from tension infiltrometer measurements, this demonstrates thegeneral applicability of this method for soil water simulations.
However, the degree of agreement between simulated and measured soil water dynamics differedamong the tillage treatments and between simulations with temporally constant and variable
hydraulic parameters. We observed that simulations with time-constant sets of hydraulic parameters
tend to underestimate θ10 and S in winter and spring (November 2008 – March 2009 and November
2009 – April 2010), whereas they resulted in overestimations during late spring and summer (Juneand July 2009 and 2010). Contrarily, application of time-variable hydraulic parameters significantly
increased the agreement of both θ10 and S for all tillage treatments in both seasons. This was also
reported by Xu and Mermoud (2003). Compared to simulations with constant parameters, values of
ARE for θ10 and S approximately halved and the RSME for S was reduced by up to 93% (Table 2).
RSME values of θ10 for CT, RT, and NT were 0.042, 0.062, and 0.074 m3 m-3, respectively (Table2), and thus in the same range as reported by Moret et al. (2007). As the ARE values for θ10 and S
were below 13%, the simulation results were satisfactory (Ji et al., 2009).
Within simulations with time-variable hydraulic parameters, the best agreement was found for CTwith ARE and RSME values for θ10 of 0.09 and 0.042 m3 m-3, respectively, (Table 2) and acorrelation of R2 = 0.81 (Figure 3), followed by NT (ARE = 0.09, R2 = 0.78). Simulations for RT
resulted in slightly larger differences and showed the weakest correlation (R2 for θ10 = 0.65, Figure3). For all treatments, the agreement was better in the season 2008/09 than in 2009/10.
These results show that the accuracy of simulations of the near-surface soil water dynamics can besubstantially improved by applying time-variable hydraulic parameters. The presented approach
might help to improve the quality of soil water simulations, not only for the assessment of different
tillage methods, but also for other applied questions in agricultural water management.
To capture temporal and management-induced dynamics in the near-surface soil hydraulicproperties, adequate and expeditious methods have to be applied. As demonstrated by this study,
repeated tension infiltrometer measurements followed by the described data analysis procedure canmeet this requirement. However, to derive physically-based descriptions of the complex temporaland management-induced dynamics of soil hydraulic properties, more research is necessary. We
suggest that future research should focus on measurements at different temporal scales that might becorrelated to underlying changes in the soil’s structure.
Table 2. Performance of the soil water simulation. Sums of relative differences SRD and root mean squaredifferences RSMD are listed for the volumetric water content in 10 cm depth, θ10, and the water storage S in
the near-surface soil profile (0-30 cm). Results for simulations with constant and time-variable hydraulicparameters are shown for all tillage treatments.

340

Tillage
CT
RT
NT

Season2008/20092009/2010
Overall
2008/20092009/2010
Overall
2008/20092009/2010
Overall

SRD (-)
const.
var.
0.11
0.07
0.32
0.11
0.21
0.09
0.13
0.08
0.31
0.13
0.21
0.10
0.15
0.07
0.35
0.12
0.24
0.09

θ10

RSMD (m3 m-3)
const.
var.
0.037
0.035
0.080
0.049
0.062
0.042
0.065
0.072
0.077
0.045
0.072
0.062
0.060
0.073
0.101
0.073
0.083
0.074

S (0-30 cm)
SRD (-)
RSMD (mm)const.
var.
const.
var.
0.05
0.01
5.4
2.1
0.16
0.02
14.3
2.8
0.11
0.01
10.7
2.5
0.09
0.03
10.0
4.0
0.25
0.08
23.9
9.5
0.17
0.05
18.1
7.2
0.02
0.001
2.7
0.2
0.20
0.03
22.3
3.9
0.10
0.01
15.6
2.7

4. Conclusion
The present study reveals the applicability of repeated tension infiltrometer measurements to capture
temporal and tillage-induced changes in soil hydraulic properties. As classical simulations of the soil
water use temporally constant hydraulic parameters, we used a Richards’ equation water simulationthat enables the flexible definition of these important control quantities. Simulated water content andstorage in the near-surface soil compartments under different tillage treatments were compared tomeasured data. The performance of the simulation could be improved significantly using timevariable hydraulic parameters, regardless the tillage. By giving meaningful results, our simulations
demonstrate the applicability of inversely estimated hydraulic parameters for soil water simulations.
Acknowledgement
The content of this proceedings paper has been published previously in Schwen et al. (2011ab).
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344

HP2/3: Extensions of the HP1 Reactive Transport Code to Two
and Three DimensionsJiří Šimůnek1, Diederik Jacques2, and Miroslav Šejna3
1

Department of Environmental Sciences, University of California Riverside, Riverside, CA, USA,jiri.simunek@ucr.edu
2
Performance Assessment, Belgian Nuclear Research Institute, Mol, Belgium, djacques@sckcen.be3
PC-Progress, Ltd., Prague 2, Czech Republic, m.sejna@pc-progress.cz

Abstract
A large number of interacting physical, chemical, and biological processes determine the fate of major
cations and anions, contaminants (e.g., heavy metals, pesticides), and colloids in soil systems. Also,modeling of soil CO2 sequestration requires consideration of water flow, heat transport, gas diffusion, andmicrobiological soil respiration processes. The HP1 simulator (Jacques et al., 2008) is a state-of-the-art
model that was specifically developed to evaluate these and similar processes in the unsaturated zone.
HP1 couples the one-dimensional variably-saturated flow and transport model HYDRUS-1D (Šimůnek etal., 2008) with the generic geochemical model PHREEQC (Parkhurst and Appelo, 1999). Although HP1
is a versatile code for implementing different geochemical and transport conceptual models in variablysaturated porous media, one of its main limitations is that flow and transport is restricted to one
dimension. However, there are many applications that require consideration of various processes in either
two- or three-dimensions. Typical examples are flow and transport in soil systems with tiled drains, orwith drip and furrow irrigation, or in sloped, layered or heterogeneous systems. Therefore, PHREEQC has
recently been coupled also with HYDRUS (2D/3D) (Šimůnek et al., 2011) to handle flow and transport
problems, which require a higher dimensionality (HP2/3), and this manuscript describes the capabilitiesof this new tool. Typical two-dimensional flow and transport problems illustrating the capability of the
HP2 simulator are presented in this manuscript. The HP2/3 code uses the graphical user interface ofHYDRUS (2D/3D) (Šejna et al., 2011) for input and output processing, enabling definitions and finite
element discretization of very complex flow domains.

1. Introduction
The one-dimensional program HP1, which couples the PHREEQC geochemical code
(Parkhurst and Appelo 1999) with HYDRUS-1D, was first released in 2005 (Jacques andŠimůnek 2005). This comprehensive simulation tool (HP1 is an acronym for HYDRUSPHREEQC-1D) can simulate (1) transient water flow, (2) the transport of multiple components,(3) mixed equilibrium/kinetic biogeochemical reactions, and (4) heat transport in onedimensional variably-saturated porous media (soils). The code uses the Richards equation forsimulating one-dimensional variably-saturated water flow and advection-dispersion typeequations for heat and solute transport. However, the loosely coupled program can also simulatea broad range of low-temperature biogeochemical reactions in water, the vadose zone and inground water systems, including interactions with minerals, gases, exchangers and sorption
surfaces based on thermodynamic equilibrium, kinetic, or mixed equilibrium-kinetic reactions.
HP1 uses the operator-splitting approach with no iterations during one time step (a non-iterative
sequential modeling approach).

345

Jacques and Šimůnek (2005), and Šimůnek et al. (2006), and Jacques et al. (2008ab, 2013),
demonstrated the versatility of HP1 in several examples, which included a) the transport ofheavy metals (Zn2+, Pb2+, and Cd2+) subject to multiple cation exchange reactions, b) transportwith mineral dissolution of amorphous SiO2 and gibbsite (Al(OH)3), c) heavy metal transport ina medium with a pH-dependent cation exchange complex, d) infiltration of a hyperalkaline
solution in a clay sample (this example considers kinetic precipitation-dissolution of kaolinite,
illite, quartz, calcite, dolomite, gypsum, hydrotalcite, and sepiolite), e) long-term transient flow
and transport of major cations (Na+, K+, Ca2+, and Mg2+) and heavy metals (Cd2+, Zn2+, and Pb2+)
in a soil profile, f) cadmium leaching in acid sandy soils, g) radionuclide transport, and h) longterm uranium migration in agricultural field soils following mineral P-fertilization.
Although HP1 is a versatile code for implementing different geochemical and transport
conceptual models in variably-saturated porous media, one of its main limitations is that flow
and transport is restricted to one dimension. However, there are many applications, such as flow
and transport in soil systems with tiled drains, or with drip and furrow irrigation, or in sloped,
layered or heterogeneous systems, that require consideration of various processes in either twoor three-dimensions. Therefore, PHREEQC has recently been coupled also with HYDRUS(2D/3D) (Šimůnek et al., 2011) to handle flow and transport problems, which require a higher
dimensionality (HP2/3), and this manuscript describes the capabilities of this new tool.
HP2/3 have, apart from the dimensionality (2D or 3D, respectively), the same capabilities as
HP1. The HP2/3 module may be used to analyze water flow, solute movement, and biogeochemical
reactions in unsaturated, partially-saturated, or fully saturated two- and three-dimensional porous
media. HP2/3 can handle flow domains delineated by irregular boundaries. The flow region itself
may be composed of nonuniform soils having an arbitrary degree of local anisotropy. Flow andtransport can occur in the vertical plane, the horizontal plane, or in a three-dimensional region
exhibiting radial symmetry about a vertical axis. The water flow part of the model considers
prescribed head and flux boundaries, as well as boundaries controlled by atmospheric conditions.
The HP2/3 code uses the graphical user interface of HYDRUS (2D/3D) (Šejna et al., 2011) for
input and output processing, enabling definitions and finite element discretization of very
complex flow domains. Typical two-dimensional flow and transport problems illustrating thecapability of the HP2 simulator are presented in this manuscript.
2. HYDRUS (2D/3D) Graphical User Interface for HP2/3
The HP2 code is fully incorporated into the HYDRUS (2D/3D) software package, and hence isinstalled automatically, together with selected examples, when one obtains HYDRUS (2D/3D)
and HP2 licenses and downloads HYDRUS from the Hydrus website. Here, we focus mostly on
the implementation of the HP2 module into HYDRUS (2D/3D). We will not discuss processes thatare related to geometry design, finite element discretization, variably-saturated water flow, heattransport, solute transport, or initial and boundary conditions, which are described in detail in the
HYDRUS (2D/3D) documentation (Šimůnek et al., 2011; Šejna et al., 2011). Nor will we discuss346

processes and reactions related to biogeochemical reactions that are described in detail in the
PHREEQC (Parkhurst and Apello, 1998] and HP1 (Jacques and Šimůnek, 2005, 2010) manuals.
2.1. Common Features with HP1
Similarly as HP1, the HP2 module is activated in the "Main Processes" window by selecting the"Solute Transport" check box and the "HP2 (Hydrus + Phreeqc)" radio button. The number of"Components" is again selected in the "Solute Transport - General Information" window. Largeparts of this window (e.g., iteration criteria) are disabled, since they are not relevant to HP2applications. Also the "HP2/3 Components and Database Pathway" window, in which users haveto select the thermodynamic database to be used with HP2 calculations and to list all main
components, is the same as in HP1.
2.2. HP2/3 Definitions Window
The main difference between HP1 and HP2 is in how PHREEQC-related inputs (i.e., those thatare printed into the PHREEQC.IN input file) are handled. The "HP2/3 Definitions" window has
been completely rewritten and reorganized. While in HP1, we had one "HP1 Definitions"window with four external text editors (Fig. 1), in HP2/3, the external text editors were converted
into four Internal pages (Fig. 2) (1 - Additions to Thermodynamic Database, 2 - Definitions of
Solution Compositions, 3 - Geochemical Model, and 4 - Addition Output), which can all beviewed directly in the "HP2/3 Definitions" window. One additional Page (5 - Database Viewer),in which one can view the selected thermodynamic database, has been added. The five pages canbe selected in the top left corner ("List of Pages") of the "HP2/3 Definition" window (Fig. 2).

Figure 1. HP1 Definitions window with four external edit windows.

This allowed us to include a section called, "Keywords (double-click to insert)" (bottom leftpart), which offers the most commonly used PHREEQC Keywords that are used in the first four
PHREEQC Pages. The Keywords are hierarchically organized in a tree-like structure in sevenmain groups: Solution Definition, Geochemical Model, Output, Chemical/Physical Reaction,
Database, Advanced, and Miscellaneous. A single click opens a particular tree subsection and adouble click copies the selected keyword to the Editor Window. This arrangement should
dramatically simplify the work of HP2/3 users, and prevent many common errors that they may

347

have made with HP1. Note the most commonly used Solution Keywords in Figure 2 below density, -isotope, -pe, -pH, -redox, -temperature, -units, and -water.

Figure 2. HP2/3 Definitions window with an open page Definitions of Solution Compositions.

Additional new commands were included below the Editor window. For example, the "New
Solution" appears below the "Definitions of Solution Compositions" page in Fig. 2. Clicking thiscommand will result in including a template for a new solution (Fig. 3). This solution will have atemperature of 25oC, a pH of 7, be in equilibrium with the atmospheric content of oxygen andhave zero concentrations of Ca2+ and Cl-.
solution 1001
-temp 25
-units mmol/kgw-pH 7 charge
Ca 0
Cl 0
O(0) 1 O2(g) -0.68

Figure 3. A template for a New Solution.

Similar commands (e.g., Add Exchange, Surface, Equilibrium Phases, and Kinetics) appear
below the "Geochemical Model" page. These commands can be used to include templates fordefining cation exchange, surface complexation, and precipitation/dissolution reactions. For
more details about the HP2/3 related GUI, see the HP2 Manual (Šimůnek et al., 2012a).

348

2.3. HP2/3 Output
The output for the HP2 module is similar to the output for the standard HYDRUS module and forstandard variables, such as pressure head, water contents, and so on. Multiple variables can bedisplayed in the View window (Figure 4). Main components defined in the "HP2/3 Components
and Database Pathway" window, variables selected in the "HP2 Print and Punch Controls"
window, and variables specified in the "Additional Output" page of the "HP2/3 Definitions"window (Fig. 2) can be displayed this way.
Figure 4 below shows the "Results - Graphical Display" part of the Data Tab of the Navigator
Bar for the Leaching of the Uranium Tailings example given below (Section 3.2). From the HP2variables, the first seven are the main components (Total_H, Total_O, Ca, C, U, P, S, and Fe)
defined in the "HP2/3 Components and Database Pathway" window, the next two (pH and pe) arevariables selected in the "HP2 Print and Punch Controls" window, and finally the last four
(calcite, gypsum, ratherfordine and siderite) are mineral phases specified in the "Additional
Output" page of the "HP2/3 Definitions" window.

Figure 4. The "Results - Graphical Display" part of the Data Tab of the Navigator Bar for the HP2
module.

3. Example Problems with HP2
Most of the HP1 examples discussed above in the Introduction and provided with the HP1
installation have been rerun using HP2 to verify correct implementation of various componentsof the coupled program. Two additional two-dimensional examples are discussed below. All ofthese examples can be downloaded from the HYDRUS/HP2 website (the links are provided
below).

349

3.1. Furrow Irrigation with Cation Exchange
A furrow irrigation problem, similar to the one used in the UNSATCHEM manual (Šimůnek etal., 2012b), was used to simulate two-dimensional infiltration of gypsum saturated water into asodic soil. The example thus simulates a sodic soil reclamation problem and demonstrates thecation exchange feature of HP2. The schematic representation of the flow domain for theconsidered furrow irrigation is presented in Figure 5, together with the finite element mesh. It is
assumed that every other furrow is flooded with water and that the water level in the irrigatedfurrow is kept constant at a level of 6 cm. Due to symmetry, it is necessary to carry out thesimulation only for the domain between the axis of two neighboring furrows. Free drainage isused as the bottom boundary condition and zero flux is considered on the rest of the boundary.
The initial pressure head condition is -200 cm, and the soil hydraulic properties for silt are used.
15

15

40

15

15

15

85

100 cm100 cmFigure 5. Schematic representation and finite element mesh of the flow domain for the furrow
irrigation system.

The calculation was run at a constant temperature of 25 oC. The bulk density of the soil was
taken as 1.4 g cm-3 and molecular diffusion as 2 cm2day-1. Longitudinal and transverse
dispersivities were equal to 2 and 0.2 cm, respectively.
The solution composition of the water initially present in the soil profile is that of the following
highly sodic water: CaT=1.0 MgT=0.0, NaT=5.0, KT=0.0, SO4T=3.5, ClT=0.0 mmol L-1. The
cation exchange capacity is equal to 7.143 mmol kg-1 (10 mmol dm-3) and is divided between
exchangeable calcium and sodium (it is equilibrated with the solution). The solution compositionof the irrigation water was almost gypsum saturated: CaT=16.3, MgT=0.0, NaT=4.4, KT=0.0,
ClT=5.0, SO4T=16.0 mmolL-1. As a consequence of the reactions of the irrigation water with the350exchanger composition, cation exchange was the dominant chemical processes in the soil profile.
Cation exchange is treated as an instantaneous process in the model.
Figure 6 below presents the exchangeable concentrations of sodium to demonstrate typical output of
HP2. The exchange phase concentrations reflect the changes in aqueous Na and Ca concentrations.

Figure 6. Exchangeable concentrations of sodium (mol kgw-1) profiles at times: a) 0.5, b) 1, c) 3, andd) 5 days.

3.2. Leaching of the Uranium Tailings
This problem was inspired by one reported by Yeh and Tripathi (1991), and we have modified it
to make it more realistic. The problem considers the release and migration of uranium from a
simplified uranium mill tailings pile towards a river. The schematic of the transport domain isshown in Figure 7. The mill tailings pile is located adjacent to a surface that slopes down to ariver. The medium has the hydraulic properties of a loam with the saturated hydraulicconductivity of Ks = 3.78 m/day.
The horizontal bottom of the region is impermeable. The vertical left edge has the Dirichletboundary condition with a groundwater table 12 m above the bottom of the transport domain(exactly in the middle of the boundary). The top boundary (except for the mill tailing pile and theriver) has a flux boundary condition with a net rainfall rate of 0.139 cm/day. The horizontal
region on the top of the mill tailings pile is a Cauchy flow boundary with an infiltration rate of
1.39 cm/day. The nodes on the vertical line on the right side and the nodes on the river bottom351

have the Dirichlet boundary condition reflecting the position of water in the river (4.5 m above
the bottom of the transport domain). A hypothetical pumping well with a withdrawal rate of
271.58 cm2/day is located at (x, z) = (400, 100). The region is discretized using a structured FE
mesh with 1564 elements and 852 nodes.
Cauchy Flow
= 0.139 dm/day
Mill Tailing
Pile

Infiltration Rate
= 0.0139 dm/day
Dirichlet Flow
Nodes

240 dmPumping Well

39 dm
1,050 dm

Figure 7. Problem description for the Uranium Tailing Problem (Yeh and Tripathi, 1991).

Chemical Reactions (35 Aqueous Complexation Reactions):

CaCO3(aq), CaHCO3+, CaSO4(aq), CaH2PO4+, CaPO4-, CaHPO4 (aq), CaOH+, FeSO4 (aq), FeOH+, Fe(OH)2 (aq),
Fe(OH)3-, Fe(OH)42-, (UO2)(OH)+, (UO2)2(OH)22+, (UO2)3(OH)42+, (UO2)3(OH)5+, (UO2)4(OH)7+, (UO2)3(OH)7-,(UO2)(CO3)(aq), (UO2)(CO3)22-, (UO2)(CO3)34-, (UO2)2(CO3)(OH)3-, (UO2)(SO4)(aq), (UO2)(SO4)22-,
H2(UO2)(PO4)+, H3(UO2)(PO4)2+, CaH4(UO2)(PO4)22+, CaH5(UO2)(PO4)23+, HCO3-, H2CO3(aq), HSO4-, HPO42-,
H2PO4-, and H3PO4

and Precipitation-Dissolution Reactions (14):

CaSO4(s), CaCO3(s), Ca5(OH)(PO4)3(s), FeCO3(s), Ca(UO2)2(PO4)2(s), Ca4H(PO4)3(s), CaH(PO4)(s), Ca(OH)2(s),Fe3(PO4)2(s), Fe(OH)2(s), (UO2)(OH)2(s), (UO2)(CO3)(s), Fe(UO2)2(PO4)2 (s), and H(UO2)(PO4)(s)and their thermodynamic equilibrium constants considered in this example are listed in Table 3of the HP2 manual. For reactive hydrogeochemical transport, the problem consists of eightcomponents: Total H, Total O, Ca, C, uranium, sulfate, phosphate, and Fe. A total of 35 species
and 14 minerals is defined for the problem; redox reactions were not considered. Table 1 lists
concentrations of the tailing and recharge waters.
Table 1. Initial and boundary compositions of recharge water and pore water in the tailings and regions
outside of the tailing for the uranium tailing problem.
Species

Inside the Tailing

Outside the Tailing

Recharge Water

Ca2+

1.0 x 10-2

1.0 x 10-2

1.0 x 10-3CO32-

1.0 x 10-2

1.5 x 10-3

1.5 x 10-3

UO22+

5.0 x 10-4

1.0 x 10-7

1.0 x 10-8PO43-

1.0 x 10-6

1.0 x 10-6

1.0 x 10-6SO42-

2.0 x 10-1

2.0 x 10-2

1.0 x 0-4H+

2.0 x 10-1

1.0 x 10-31.ox 10-3

Fe2+

3.5 x 10-2

1.0 x 10-7

1.0x 10-7

352

The steady-state pressure heads and velocity fields are depicted in Figure 8. Uranium
concentration profiles are shown in Figure 9. pH, calcite, and gypsum profiles are shown in
Figure 10.

Figure 8. The steady-state pressure head (cm) (top) and flux (cm/d) (bottom) profiles for the Tailing
Pile Leaching example.

Figure 9. Uranium concentration profiles at time 0 (left), and 500 (right) d for the Tailing Pile
Leaching example.

Figure 10. pH (top), calcite (mol/L) (middle), and gypsum (mol/L) (bottom) profiles after 1000 d for
the Tailing Pile Leaching example.

353

4. Important Links
http://www.pc-progress.com/en/Default.aspx?h3d2-HP2: web page providing brief description of
the HP2 module and listing all main documents (reports and manuscripts) related to this module.
http://www.pc-progress.com/en/Default.aspx?H3D2-lib-HP2: Examples demonstrating the HP2
program using one-dimensional (for comparison with HP1) and two-dimensional (those
discussed above) problems.
http://www.pc-progress.com/Documents/HYDRUS3D_HP2_Manual.pdf: HP2 manual.
References

Jacques, D., and J. Šimůnek, User Manual of the Multicomponent Variably-Saturated Flow and Transport
Model HP1, Description, Verification and Examples, Version 1.0, SCK•CEN-BLG-998, Waste andDisposal, SCK•CEN, Mol, Belgium, 79 pp., 2005.
Jacques, D., J. Šimůnek, D. Mallants, and M. Th. van Genuchten, Modelling coupled hydrogeological andchemical processes in the vadose zone: a case study of long-term uranium transport following mineral
P-fertilization, Vadose Zone Journal, 7(2), 698-711, 2008a.
Jacques, D., J. Šimůnek, D. Mallants and M. Th. van Genuchten, Modelling coupled water flow, solutetransport and geochemical reactions affection heavy metal migration in a Podzol soil, Geoderma, 145,
449-461, 2008b.
Jacques, D., J. Šimůnek, D. Mallants, M. Th. van Genuchten, The HPx reactive transport models:
Summary of recent developments and applications, (this issue), 2013.
Parkhurst D. L., and C. A. J. Appelo, User’s guide to PHREEQ C (Version 2) – A computer program forspeciation, batch-reaction, one-dimensional transport and inverse geochemical calculations, WaterResources Investigations, Report 99–4259, Denver, Co, USA, 312 pp., 1999.
Šejna, M., J. Šimůnek, and M. Th. van Genuchten, The HYDRUS Software Package for Simulating Twoand Three-Dimensional Movement of Water, Heat, and Multiple Solutes in Variably-Saturated Media,
User Manual, Version 2.0, PC Progress, Prague, Czech Republic, pp. 280, 2011.
Šimůnek, J., D. Jacques, M. Th. van Genuchten, and D. Mallants, Multicomponent geochemical transportmodeling using the HYDRUS computer software packages, J. Am. Water Resour. Assoc., 42(6),1537-1547, 2006.
Šimůnek, J., M. Th. van Genuchten, and M. Šejna, Development and applications of the HYDRUS andSTANMOD software packages, and related codes, Vadose Zone Journal, 7(2), 587-600, 2008.
Šimůnek, J., M. Šejna, H. Saito, M. Sakai, and M. Th. van Genuchten, The HYDRUS-1D software
package for simulating the one-dimensional movement of water, heat and multiple solutes invariably-saturated media, Version 4.08, HYDRUS Software Series 3, Department of Environmental
Sciences, University of California Riverside, Riverside, California, USA, 2008.
Šimůnek, J., M. Th. van Genuchten, and M. Šejna, The HYDRUS Software Package for Simulating Twoand Three-Dimensional Movement of Water, Heat, and Multiple Solutes in Variably-Saturated Media,
Technical Manual, Version 2.0, PC Progress, Prague, Czech Republic, pp. 258, 2011.
Šimůnek, J., D. Jacques, M. Šejna, and M. Th. van Genuchten, The HP2 Program for HYDRUS (2D/3D): A
Coupled Code for Simulating Two-Dimensional Variably-Saturated Water Flow, Heat Transport, andBiogeochemistry in Porous Media, Version 1.0, PC Progress, Prague, Czech Republic, 76 pp., 2012a.
Šimůnek, J., M. Šejna, and M. Th. van Genuchten, The UNSATCHEM Module for HYDRUS (2D/3D)
Simulating Two-Dimensional Movement of and Reactions Between Major Ions in Soils, Version 1.0, PC
Progress, Prague, Czech Republic, 54 pp., 2012b.
Yeh, G. T., and V. S. Tripathi, A model for simulating transport of reactive multispecies components:
Model development and demonstration, Water Resour. Res., 27, 3075-3094, 1991.

354

CO2 Fluxes to Aquifers Beneath Cropland:
Merging Measurements and Modeling
Eike M. Thaysen1, Diederik Jacques2, and Eric Laloy2
1

Department of Chemical and Biochemical Engineering, Center for Ecosystems and Environmental Sustainability,
Technical University of Denmark, Kgs. Lyngby, Denmark, emth@kt.dtu.dk
2
Institute for Environment, Health, and Safety, Belgian Nuclear Research Centre (SCK•CEN), Mol, Belgium,
djacques@sckcen.be, elaloy@sckcen.be

Abstract
Carbon dioxide (CO2) fluxes in the vadose zone are influenced by a complex interplay of biological,
chemical and physical factors. To determine the controls behind dissolved inorganic carbon (DIC)
percolation to aquifers, CO2 fluxes in planted soil mesocosms were described with the SOILCO2 model
formulation (Šimůnek et al., 1993) that was implemented into the HP1 module of the Hydrus 1D software
package. Water flow, cation exchange, and supersaturation for amorphous aluminum hydroxide weremodeled. The model provided a good fit to measured water content and outflow time series. Also, themeasured DIC efflux, CO2 partial pressure (pCO2), and CO2 efflux were simulated well throughout mostof the experimental period. However, alkalinity was significantly overestimated, indicating additional
acidity production in the mesocosms. CO2 fluxes were strongly influenced by a higher root growth in themesocosms as compared to the field, which caused steep increases in pCO2. The model showed that thehigh pCO2 triggered weathering of calcite, leading to increases in alkalinity. DIC percolation lacked
accompanying increases, indicating an overestimation of the DIC percolation estimated from measured
pCO2, alkalinity, and water flux.

1. Introduction
The global flux of carbon dioxide (CO2) into the groundwater is less than 1% of the diffusion
flux of CO2 from soils to the atmosphere (Kessler et al., 2001). Although estimates of leachinglosses of carbon are scarce, available estimates indicate that leaching of dissolved carbon fromsoils constitutes a significant fraction of the annual carbon (C) budgets of croplands (Kindler etal., 2011). C is leached from soils as dissolved organic carbon (DOC), dissolved methane (CH4),
and dissolved inorganic carbon (DIC). DIC originates from either soil respiration, dissolution ofcarbonate minerals, or atmospheric CO2. The latter contribution is negligible because of the low
atmospheric partial pressures of CO2 (pCO2) (Kindler et al., 2011). The amount of DIC varies
with the soil pCO2, pH, and temperature (Clark et al., 1997). However, our understanding ofproduction and transport of CO2 in the soil (Jassal et al., 2005) and of the exchange of CO2
between soils, plants, and the atmosphere is incomplete (Sugden et al., 2004).
In this work, experimentally determined CO2 fluxes in the vadose zone of large planted soil
mesocosms were modeled using the HP1 module of the Hydrus-1D software package (Jacques etal., 2010) in order to identify the main drivers controlling DIC transport to aquifers.

355

2. Methodology
2.1. Experimental Data
Soil from the A and C horizons of a carbonated alluvial sediment was collected and packed into
plexiglas cylinders (length: 83 cm, diameter: 19 cm) above a bottom plate with an embedded
suction disc (Thaysen et al., in review). The hydraulic connection between the C horizon and thesuction disc was optimized by means of a thin layer of quartz flour and a layer of quartz flour
mixed with the C horizon.
Barley (Hordeum vulgare L. cv Anakin) was sown into the mesocosms at a seeding density of
280 plants m-2. The mesocosms were incubated in climate chambers and maintained at mean
daily air and night temperatures of 18 °C and 13 °C, respectively. Plants were irrigated with a
50% strength Hoagland solution (Hoagland et al., 1950) with an alkalinity of 0.05 meq L-1. Root
length was measured at five time points on the outside of the mesocosm walls.
Volumetric water content (VWC) and temperature within the mesocosms were logged at ten
minute intervals with 5 TM and EC-TM sensors and EM50 (Decagon Devices, USA) andCR1000 loggers (Campbell Scientific, UK). To increase measurement accuracy, sensors were
calibrated to the A and C horizon conditions according to the guidelines of the manufacturers.
Samples of soil air and soil water were collected weekly and analyzed for CO2 partial pressure(pCO2) and alkalinity, respectively. Soil air pCO2 was measured on a 7890A GC System with a
FID detector in combination with a methanizer (Agilent Technologies, DK). Alkalinity wasdetermined using the Gran Titration method (Gran, 1952).
The exchange of CO2 between the mesocosm and the atmosphere was measured at regularintervals using the static closed chamber technique (Ambus et al., 2007). During measurement,
the concentration of CO2 in the chamber space (V= 22.6 L) was continuously closed-loop
sampled with an environmental gas monitor (EGM-2, PP-Systems, USA), and the flux was
estimated from the concentration change, volume, and measurement time.
The DIC concentration in the percolating water was calculated from the pCO2, the alkalinity inthe soil solution, and the temperature at the mesocosm bottom (∼62-76 cm) using PHREEQC
software (Parkhurst et al., 2011), while assuming chemical equilibrium between gaseous CO2,
CO2(g), and solution H2CO3*, HCO3-, and CO32-. The DIC concentration was multiplied by thewater flux to obtain the DIC flux to the groundwater.
2.2. Modeling of Experimental Results
Results from only one planted mesocosm are discussed in this paper. The mesocosm consisted ofthree materials. The first and second layers were the A and C horizons located between 0-30 and
31-80 cm depths, respectively. The suction plate, the quartz flour layer, and the layer of quartz
flour mixed with the C horizon were grouped in the third material between depths of 80-83 cm.

356

Model Setup
Water flow was described by the Richards equation and the constitutive relations of the van
Genuchten-Mualem model without hysteresis (Mualem, 1978; van Genuchten, 1980). Upper
boundary conditions for the water flow were atmospheric conditions with a surface boundary
layer. At the bottom, a variable pressure head boundary condition was chosen. Maximum
allowed pressure head at the soil surface was zero. Potential evapotranspiration was estimatedusing the Blaney Criddle formula (Blaney et al., 1962). Water retention parameters wereobtained from inverse modeling of the water flow in an unplanted mesocosm (data not shown)using Hydrus-1D (Šimůnek et al., 2013) and a global stochastic optimization algorithm (Vrugt etal., 2009).
Heat transport was not included in the model as temperatures in the mesocosm were almost
constant. Temperatures declined from the top to the bottom of the mesocosm due to theproximity of heat emitting lamps at the mesocosm top, high volumetric water content (VWC) in
the A horizon and the higher heat capacity of water compared to air. Hence, constant boundaries
of 22 and 18°C were used at the mesocosm top and bottom, respectively, with a linear
interpolation in between. The model domain was discretized in 157 nodes with the highest nodedensities at the mesocosm top and at the interfaces of soil materials.
CO2 production was modeled through implementation of equations and parameters for CO2
production from SOILCO2 (Šimůnek et al., 1993; Suarez et al., 1993). The parameter a,
describing the depth dependency of microbial respiration, was set to 0.04 cm-1, and the boundary
layer height (BLH) was set at 0.05 m. The dependency of CO2 production on root growth wasaccounted for by 1) a distribution factor and (measured) root depth (as is done for root water
uptake) and 2) by introducing a linear root biomass increase, RMI [M], (Eq. 2). The latter wasadded to account for a 2-5 times higher total root mass in mesocosms than in the field (Table 1)(Biscoe et al., 1975; Xu et al. 1992; Malhi 2002). It was anticipated that(2)

RMI
= Rinit + r * time

where Rinit [M] is the initial root mass at simulation time= 0 [T] and r is the growth rate [MT-1].
For our simulations Rinit was set to 0.1 g and r was 0.21 g day-1.
Table 1. Root growth as a function of depth in mesocosms as measured 70 days after sowing.
Depth
(cm)

Root mass (g)(means ± SE)

0-10

8.1 ± 0.5

10-20

3.5 ± 0.3

20-30

2.6 ± 0.330-42

0.5 ± 0.1

42-58

0.3 ± 0.1

58-80

<0.01

Root mass per soil
horizon (%)

Total root mass(g m-2)91.7 ± 0.9
527.4 ± 14.7
8.3 ± 0.9357

CO2 transport in the gas and water phases and phase distribution were described as stated withinHP1. For more details the reader is referred to Šimůnek et al. (2013). The measured pore watercomposition was supersaturated for amorphous aluminum hydroxide, Al(OH)3(a). Therefore, thesaturation index (SI) of Al(OH)3(a) was set at 0.8 and 0.6 for the A and C horizons, respectively.
The cation exchange capacity was estimated from the soil organic matter and clay content,
resulting in values of 9.2*10-2 and 4.2*10-3 eq dm-3 for the A and C horizons, respectively. The
exchanger composition was calculated from the soil water composition on day 40 and contained
3.90*10-2 Ca2+, 6.51*10-3 Mg2+, 6.62*10-4 K+, 1.39*10-4 Na+, 1.32*10-4 Al(OH)2- and 4.04*105
Al3+ mol dm-3 in the A horizon, and 1.7*10-3 Ca2+, 2.863*10-3 Mg2+, 1.06*10-4 K+, 1.52*10-4
Na+, 2.4*10-5 Al(OH)2- and 1.41*10-5Al3+ mol dm-3 in the C horizon. To simplify thesimulations, the influence of nutrients in the irrigation water was neglected.
3. Results and Discussion
3.1. Water Flow
Water flow throughout the soil profile was generally well described (forward simulation fromfitted parameters in an unplanted mesocosm, Fig. 1). However, due to a pressure drop across the
suction disc that offset boundary conditions and the lack of retention parameters for material
three, outflow and VWC in the soil profile could not be matched with high accuracy at the sametime. Water logging at the mesocosm bottom (76 cm) was overestimated but cumulative outflow
was simulated correctly.

Figure 1. Measured and modeled water content profile and cumulative drainage.

358

3.2. Profiles of CO2 and Alkalinity
The pCO2 increased with plant growth. The magnitude of the pCO2 could be simulated but themodel could not capture all fluctuations in pCO2 (Fig. 2). The diffusion gradient was matchedquite well on days 7, 21 and 35. However, the measured gradients on days 27 and 40 weresignificantly steeper than the simulated ones. The addition of dependency of CO2 production on
the root biomass increase caused a steady increase in pCO2 with root growth. On the other hand,the distribution of the production within the soil profile is defined by the normalized root
distribution. However, the current implementation of the evolution of the normalized root
distribution in HYDRUS simulates a downward shift of the center of mass of the roots (Šimůnek
et al., 2013). This downward shift of the region of the highest root abundance seems to be anerroneous assumption for a mesocosm in which ~90% of the root biomass is found in the upper
30 cm after harvest, and root growth declines exponentially from the top (Table 1). Root mass
always declines with soil depth (Malhi et al., 2002) and exponential decreases have often beenreported (e.g., Xu et al., 1992; Mandal et al. 2003; Rong-hua et al., 2008).
The observed peak pCO2 in mesocosms was 2-5% higher than observed at a corresponding fieldsite (Voulund, Denmark, 56°2’35.7”N, 9°8’101.1”E). Peak pCO2 levels were also 5-7% higher
than in a previous field study addressing CO2 dynamics under actively growing winter wheat in asilt loam soil at similar soil temperatures and VWC (Buyanovsky et al., 1983). The higher pCO2
in mesocosms is probably caused by the higher root length in mesocosms as compared to thefield.
The alkalinity increased throughout the experimental period (Fig. 2). Increases in alkalinity could
be modeled, but simulated values were twice the measured values. Increases in alkalinity can beunderstood from 1) increased dissolution of CO2(g) into soil water as the pCO2 in mesocosms
increases (Eq. 2) and 2) the consumption of carbonic acid, H2CO3, during dissolution of calcite,
CaCO3, that causes 3) increases in [HCO3-] (Eq. 3).
CO2(g) + H2O ↔ H2CO3 ↔ HCO3- + H+

Figure 2. Measured and modeled time course of soil air pCO2, alkalinity, and saturation index(SI) for calcite.

359

(2)

H2CO3 + CaCO3 ↔ 2HCO3- + Ca2+

(3)

Calcite dissolution on day 40 (Fig. 2) could be approximated by the model in the C horizon but
was underestimated in the A horizon, which can be ascribed to the underestimation of pCO2 on
day 40. The larger increases in alkalinity in the simulation as compared to the measured values
indicate additional alkalinity-consuming acid production in the mesocosm that is not covered by
the model. This could be organic acids released by the roots although several authors havesuggested that organic acid concentrations in nutrient-rich bulk soil are generally low (Drever etal., 1994; Ryan et al., 2001) to non-detectable (Baars et al., 2008). Alternatively, watering with anutrient solution low in alkalinity might also have decreased the soil alkalinity due to the
combined effects of flushing and cation exchange with sediment-bound base cations. It is also
possible that modeling of proton exchange, which has been shown to act as a source of acid in
NaHCO3 water in which calcite dissolves (Appelo, 1994), could produce the measured profilesof alkalinity. The incorporation of additional acid-producing processes in future model work isplanned and is expected to improve model fits to experimental data.
3.3. CO2 Fluxes out of the Mesocosm
The simulated ecosystem respiration (ER) was slightly lower than the measured ER at days 0-30
(Fig. 3) although the diffusion gradients for pCO2 were simulated well on days 7-21 and 35 (Fig.
2). Simulated ER was much lower than measured ER on days 30-40 (Fig. 3). This is due to theunderestimation of the pCO2 in the A horizon towards the end of the experiment as discussed in
Section 3.2. Due to the much higher pCO2 in mesocosms, measured ER was larger than what has
been reported in the field under similar environmental conditions (Buyanovksy et al., 1986;
Buyanovsky et al., 1983; Feizene et al., 2008). The simulated CO2 efflux follows the applied
irrigation pattern with lower efflux during irrigation events.

Figure 3. Measured and modeled time course of ecosystem respiration (ER) and DIC percolation.

DIC percolation was predicted well although alkalinity was largely overestimated (Fig. 3).
According to theory (Appelo et al., 2005), the DIC concentration can be calculated from pCO2

360

and soil alkalinity. DIC percolation is then described by the product of the [DIC] and thedrainage flux (e.g., Kindler et al., 2011; Walmsley et al., 2011). As the drainage from themesocosm was simulated well (Fig. 1), the large overestimation of alkalinity was expected toincrease DIC percolation compared to the measured. While differences between the measured
and simulated DIC percolation might be due to the fact that the measured DIC percolation was
estimated from a weekly “snap shot” of the pCO2 and the alkalinity, as has been suggested byWalmsley et al. (2011), these inconsistencies need further investigation. The average [DIC] of
2.5 ± 0.02 mmol L-1 was in the range of previously reported values for cropped carbonated soil:
Luvisol with sand-loam texture ([DIC]: 1.90 mmol L-1) (Siemens et al., 2012) and calcaric
Cambisol with silt-loam texture ([DIC]: 5.9 mmol L-1) (Kindler et al., 2011).
4.

Conclusion

CO2 fluxes in the vadose zone of planted mesocosms were strongly influenced by root growththat caused steep increases in CO2, triggering the dissolution of calcite with subsequent increasesof alkalinity. The applied simple model was able to simulate the main tendencies in the data andaided in the comprehension of the underlying biogeochemical processes. The model stressed that
additional acid-producing processes occurred in the mesocosm that were not detectable fromexperimental results alone. Incorporation of the latter in future model work is planned and is
expected to improve model fits to experimental data. Modeling results further indicated that
pCO2 profiles are strongly linked to the root distribution and that the downward shift of thecenter root mass with plant age (root growth) would need to be revised to improve the model.
Acknowledgements
The authors thank Rasmus Jakobsen, Søren Jessen, and Jirka Šimůnek for their support anddiscussion.
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364

Fate and Transport of Nitrogen in Soils Based on a Coupled
Nitrogen-Carbon Cycling Model Using the HP1 CodeNobuo Toride and DaiWen Chen
Graduate School of Bioresources, Mie University, Tsu, 514-8507, Japan, ntoride@bio.mie-u.ac.jp

Abstract
In order to predict the fate and transport of nitrogen in soils as a result of decomposition of organic
matter, we implemented within the PHREEQC program a coupled carbon and nitrogen cycling model
based on the LEACHM code. Decay processes from organic carbon (Org-C) to biomass carbon (Bio-C),
humus carbon (Hum-C), and carbon dioxide were described using first-order kinetics. Bio-C was recycled
into the organic pool. Decomposition of Org-N was related to the carbon cycle using the C/N ratio.
Mineralization and immobilization were determined based on available NH4-N and the nitrogen demand
for the formation of biomass and humus. Nitrogen transformations were also described with first-orderchain reactions. The carbon and nitrogen cycling model described with PHREEQC was linked with
HYDRUS-1D using the HP1 code. Various nitrogen transport scenarios were demonstrated for theapplication of organic matter to a variable-saturated soil under nonisothermal conditions.

1. Introduction
Nitrogen in soil can change its form through various microbial activities such as mineralizationof ammonium from organic matter, nitrification from ammonium, and denitrification from
nitrate. Nitrogen mineralization rates depend upon the rate of degradation of organic carbon, theN content of organic matter, and the carbon-to-nitrogen (C/N) ratio of the decomposition
products. Because the biomass product usually has a higher C/N ratio than the parent manure,incorporation of biomass gradually increases the C/N ratio of the parent organic pool. The C/Nratios of humus and biomass determine how much N transforms to humus and biomass, while
any excess N is released as mineral NH4. If sufficient N for the production of humus and biomass
is not released by mineralization, mineral N will be immobilized from the soil. In order to predictthe dynamics and transport of nitrogen as a result of decomposition of organic matter in soils, itis necessary to link a coupled carbon and nitrogen cycling model with a water flow and solutetransport model.
The LEACHM code (Hutson, 2005) used a coupled carbon and nitrogen cycling model
developed by Johnsson (1987). Although LEACHM has been used widely for nitrogen transport
problems, it is currently difficult to further modify the code for various applications. Furthermore,
the basic properties of the coupled carbon and nitrogen cycling model have not been investigatedthoroughly. In this study we firstly describe first-order kinetic equations for the carbon andnitrogen cycles in soils using the PHREEQC program (Parkhurst and Appelo, 1999). Then, thecoupled cycling model is linked with the water flow and solute transport model of HYDRUS-1D(Šimůnek et al., 2005) within the HP1 code (Jacques and Šimůnek, 2010). Various nitrogentransport scenarios are demonstrated for the application of organic matters to a variable-saturated
soil under nonisothermal conditions.

365

2. Coupled Nitrogen and Carbon Cycling Model
2.1. Degradation of Organic Matter
Figure 1 shows the coupled nitrogen and carbon cycling model of Johnsson et al. (1987) as
implemented in LEACHM (Hutson, 2005). The blue lines are for the carbon cycle and the blacklines for the nitrogen cycle. Numbers in the figure represent the reaction routes specified in thediscussion that follows. Two types of principal organic matter were defined: a first cycling poolfor litter and a slow cycling pool for stabilized humus. Separate litter pools were used for organic
matter having different decay rates and carbon-to-nitrogen (C/N) ratios, such as plant residue andmanure. Decay processes from organic carbon (Org-C) to biomass carbon (Bio-C), humus
carbon (Hum-C), and carbon dioxide were described with a first-order kinetic. The biomass wasrecycled into a decomposable litter pool, forming a litter-decomposer complex. Decomposition
from the Org-N to Bio-N and Hum-N were related to the carbon cycle using the C/N ratios of theorganic matter, biomass and humus. Mineralization of ammonium (NH4-N) from organic matterand immobilization of NH4-N to organic matter were determined based on the available NH4-N
and the N demand for the formation of biomass and humus.
Carbon dioxide③Decomposable Pool 1

Plant residue
①

❺

②

③

④

Decomposable Pool 2

Humus

❻

②

Manure①❻❺

Biomass

Biomass❽❼

Urea

Carbon route
Nitrogen route❾❼

Ammonium(NH4-N)❿

Nitrate(NO3-N)⓫N2 gasPlant uptake
Leaching (water flow)

Figure 1. Coupled nitrogen and carbon cycling model based on the LEACHM code.

2.2. Carbon Cycle
Organic carbon (Org-C) in the organic pool i (= 1, 2) degrades into three components (routes 1, 2
and 3 in Figure 1): microbial biomass carbon (Bio-C), humus carbon (Hum-C), and carbon
dioxide (CO2):
Org-C → Bio-C + Hum-C + CO 2

366

(1)

First-order kinetic is used for the degradation of organic carbon:
dCOrg-Ci ( d )dt= − kOrgi COrg-C(2)

where C is concentration, expressed as mass per volume of soil, and kOrg is the first-order rate
coefficient. In order to distinguish the route and direction of the reactions in Figure 1, thesubscript (d) is used for degradation while the subscript (p) is used for production in the rateequations. The rate coefficient depends on temperature and water content, with a correction
factor according to Johnsson et al. (1987).
The fractions of three products in Eq. (1) are assumed to be invariant. The efficiency factor, fe,
determines the relative production of CO2 and biomass plus humus while the humification factor,
fh, determines the split between biomass and humus as follows:fe =∆Bio-C + ∆Hum-C∆Bio-C + ∆Hum-C+∆CO 2∆Hum-Cfh =∆Bio-C + ∆Hum-C

(3)
(4)

The fraction of each mineralized product can be described with these two factors: fe (1 − fh ) for∆Bio-C, fe fh for ∆Hum-C, and 1 − fe for ∆CO2. Johnsson et al. (1987) used fe = 0.5 and fh = 0.2 intheir examples, assuming fractions of ∆Bio-C, ∆Hum-C, and ∆CO2 are 0.4, 0.1, and 0.5,
respectively. The fraction of persistent humus production may depend on the type of organic
matter (Brady and Weil, 2008). Since fe and fh can be different for the different organic pools, thesubscript i (= 1, 2) is used in this paper to distinguish between these two factors.
The production rate of Bio-C, Hum-C, and CO2 of the organic pool i (= 1, 2) can be related to thedegradation rate of Org-C (routes 1, 2, 3):dCBio-Ci ( p )=− f ei (1 − f hi )dt
dCHum-Ci ( p )dt
dCCO2i ( p )dt= − f ei f hi=−(1 − f ei )dCOrg-Ci ( d )dtdCOrg-Ci ( d )dtdCOrg-Ci ( d )
dt

(5)
(6)
(7)

Hum-C further decomposes into CO2 and the degradation rate is also described with first-orderkinetics (route 4):
dCHum-C( d )dt= − kHum − C CHum-C

Note that kHum-C is much smaller than kOrgi since humus is a persistent substance.

367

(8)

The net reaction rate for each carbon component can be described with a mass balance for all theroutes in Figure 1. The net reaction rate for Org-C is the sum of degradation described using Eq.
(2) and Bio-C production described with Eq. (5), which is recycled in the organic pool (routes 2,
3):dCOrg − Cidt=
− kOrg i COrg − Ci + f ei (1 − f hi ) kOrg i COrg − Ci

(9)The net reaction rate for Hum-C is the sum of degradation according to Eq. (8) and production
from the organic pools according to Eqs. (2) and (6) (routes 2, 4):
2
dCHum-C=−kHum − C CHum − C + ∑ f ei f hi kOrg i COrg − Ci
dt
i =1

(10)

Carbon dioxide is produced from the organic pools according to Eq. (7) and Hum-C according to
Eq. (8) (routes 3, 4):
2
dCCO2
=
(1 − f ei ) kOrg i COrg −Ci + kHum −CCHum −C
∑
dt
i =1

(11)

Note that since the biomass is recycled in the organic pool as shown by the second term on theright hand side of Eq. (9), Bio-C does not explicitly appear in the net rate equations.
2.3. Nitrogen Cycle
Organic nitrogen (Org-N) decomposes to microbial biomass nitrogen (Bio-N) and humus
nitrogen (Hum-N) as in the case of carbon of Eq. (1):Org − N → Bio − N + Hum − N(12)

The C/N ratios, r, for organic matter, biomass and humus are defined asrOrg i=COrg − Ci
CBio − CiCHum − C=, rBio=, rHumCOrg − Ni
CBio − NiCHum − N(13)

Note that rOrg i changes with time as the organic matter degrades, whereas rBio and rHum, areconstant (≈ 10).
The degradation rate of Org-N in Eq. (12) can be related to the degradation rate of Org-C using
rOrg i as
dCOrg − Ni (d)dt=

1 dCOrg − Ci (d)rOrg i
dt

368

(14)

The production rates for Bio-N and Hum-N are also transformed to the carbon concentration
rates and further related with the degradation rate for the organic carbon using Eqs. (5) and (6):f (1 − f hi ) dCOrg − Ci (d)1 dCBio − Ci (p)= − ei
dt
rBio
dt
rBio
dt
dCHum − N(p)f f dCOrg − Ci (d)1 dCHum − C(p)== − ei hi
dt
rHum
dt
rHum
dt

dCBio − Ni (p)

=

(15)
(16)

The difference between the nitrogen supplies from Org-N and the demands for Bio-N and HumN production gives the production rate of ammonium (NH4-N):
dCNH4i (p)dtdCOrg − Ni (d)  dCBio − Ni (p) dCHum − N(p) 
=
−
−
+

dt
dt
dt



 1
f (1 − f hi ) f ei f hi  dCOrg − Ci (d)
=
−
− ei
−

r
rBio
rHum 
dt
 Org i 1
f (1 − f hi ) f ei f hi 
=
− ei
−

 kOrg i COrg − CirBiorHum 
 rOrg i(17)

In case of rBio = rHum = r0, Eq. (17) can be simplified as
 1
f  dCOrg − Ci (d)=−− ei 
rdtdt
 Org i r0 
 1
f 
= 
− ei  kOrg i COrg − Cir Org i r0 

dCNH4i (p)(18)

When the NH4-N production rate described with Eq. (17) or (18) is positive, the surplus nitrogenis used for the mineralization of NH4-N. On the other hand, when the production rate is negative,
immobilization of NH4-N occurs to compensate the nitrogen deficiency (route 7). If fei and r0 are
constant, the sign of the parenthesis in Eq. (18) simply depends on the rOrg i value. A negative
production rate for rOrg i > r0 / fei leads to immobilization while a positive production rate for rOrg i< r0 / fei results in mineralization. In case fei = 0.5 and r0 = 10, the immobilization occurs for rOrg i> 20 while the mineralization for rOrg i < 20.
The net reaction rate for each nitrogen component can be described with a mass balance scheme
similarly as shown in Figure 1 for the carbon cycle. The net reaction rate for Org-N is the sum of
reductions due to ammonium production as given by Eq. (18) and Hum-N production as given by
Eq. (16) (routes 6, 7):369

dCOrg − Nidt

dCNH4 (p) dCHum − N(p)
=
−
−
dt
dt
 1
f (1 − f hi ) 
=
−
− ei
 kOrg i COrg − Cir0 rOrg i(19)Notice that Bio-N production does not explicitly appear in Eq. (19) since Bio-N is recycled in theorganic pool (route 5). Although a similar expression can be obtained when rBio ≠ rHum, forsimplicity we assume in the discussion to follow that rBio = rHum (= r0).
Hum-N also produces ammonium as a result of first-order degradation (route 8):
dCHum − N(d)dt

= − kHum-N CHum − N(20)

The net reaction rate for Hum-N is degradation and production from the organic pools as
described with Eq. (16) (route 6):
dCHum − N
1 2=
−kHum-N CHum − N + ∑ f ei f hi kOrg i COrg − Cidtr0 i =1(21)

As in the case of carbon, since kHum-N << kOrgi, it is possible to neglect Hum-N degradation as
given by Eq. (20) for relatively short time periods.
2.4. Immobilization of Ammonium
If the C/N ratio for organic matter, rOrgi, is smaller than r0/fei, mineralization of NH4-N
ammonium occurs according to Eq. (18). In that case, the NH4-N concentration does not affectthe degradation rate of organic matter. On the other hand, in case rOrgi is larger than r0/fei, thebiomass and humus are produced using the immobilized NH4-N. If the NH4-N concentration issmall enough for immobilization, the decay rate may slow down because of NH4-N deficiency.
According to the LEACHM program (Hutson, 2005), three immobilization stages can be defined
depending upon the available amount of NH4-N.
If the amount of Org-Ci degradation per day according to Eq. (2) is given as ∆COrg-Ci, the amountof immobilized NH4-N per day, ∆CNH4, can be related with ∆COrg-Ci using Eq. (18):
 1
f 
∆C
=
− ei  ∆COrg − CiNH4 rOrg i r0 

(22)

It is assumed that not more than one tenth of the total NH4-N concentration including solution
and adsorbed phases, CNH4, is available for each organic pool per day. The maximum amount ofdegradable Org-Ci per day can be defined as:370∆COrg −Ci , Max =CNH4

rOrg i r0

10 r0 − rOrg i f ei

(23)

Three immobilization stages can be defined depending on the ∆COrg-Ci, max value:
Stage 1:

Stage 2:

Stage 3:∆COrg-Ci, max > ∆COrg-Ci
Since enough NH4-N exists, immobilization does not affect the degradation rate of theorganic pool.
∆COrg-Ci > ∆COrg-Ci, max > 0.1∆COrg-Ci
The degradation rate of the organic pool is now reduced by multiplying Eq. (2) with
∆COrg-Ci, max/∆COrg-Ci because of a deficiency in available NH4-N. The reduction,
however, is not less than 10 %.
∆COrg-Ci, max < 0.1∆COrg-Ci
When the available NH4-N is further reduced, ∆COrg-Ci, max becomes less than
0.1∆COrg-Ci. In this case, immobilization for biomass and humus production ceases.
Degradation of Org-C now only produces CO2 without biomass and humus
production at the 10 % rate of Eq. (2). Degradation of Org-N according to Eq. (14)mineralizes only NH4-N. Hence, the C/N ratio for the organic pool, rOrg i, does notchange since no immobilization of NH4-N occurs. When the NH4-N concentration
increases, ∆COrg-Ci, max becomes greater than 0.1∆COrg-Ci. However, the immobilizationof Stage 2 starts using the mineralized NH4-N.

Since ∆COrg-Ci, max is defined for each organic pool, the immobilization stage can be different
between the organic pools. Although we consider two organic pools as in the case of the
LEACHM program, it is straightforward to increase the number of organic pools by simply
letting i run from 1 to n in the summations of the above equations.
2.5. Nitrogen transformation
The inorganic N pools in Figure 1 consist of urea, ammonium and nitrate. The degradation
processes of inorganic N are also described using first-order kinetics. Urea fertilizers are rapidlytransformed to NH4-N in soils:
dCUrea= −kUrea CUrea
dt

(24)

where kUrea is the ammonification constant. The net reaction rate for NH4-N is the sum ofnitrification (route 10), mineralization from urea (route 9) and humus (route 8), andmineralization or immobilization for biomass and humus production as described with Eq. (18)(route 7):
2 
dCNH4
f 
1
=
−knit CNH4 + k Urea CUrea + kHum − N CHum − N / r0 + ∑ − ei  kOrg i COrg − Ci

dt
r0 
i =1  rOrg i

371

(25)

where knit is the nitrification constant. When the available NH4-N for immobilization is limited,
the last term is modified for Stages 2 and 3 of the immobilization process. The net reaction rate
for the nitrate is denitrification and production from NH4-N:
dCNO3=−kden CNO3 + knit CNH4
dt

(26)

where kden is the denitrification constant.
2.6. Transport of Ammonium and Nitrate
Transport of nitrogen in soils can be predicted by coupling the first-order kinetic equations forthe carbon and nitrogen cycles with the convective-dispersive equation (CDE). The total
concentration, C, expressed as solute mass per volume of soil, can be related with the soluteconcentration, Cl, expressed as solute mass per volume of soil solution, and adsorbed
concentration, S, expressed as adsorbed mass per mass of dry soil as follows:=
C θ Cl + ρb S

(27)

where θ is the volumetric water content, and ρb is the soil bulk density. Adsorption of urea andammonium is described with the Freundlich isotherm:
S = K d Cl n(28)

where Kd and n are constants. Nitrate is assumed to be a nonreactive solute. The CDE for urea,
ammonium, and nitrate are given by:∂Cl ,Uera  ∂qw Cl ,Uera∂CUera ∂ =− kUrea CUera θ DUera
−
∂t
∂z 
∂z 
∂z

∂Cl ,NH4  ∂qw Cl ,NH4
∂CNH4 ∂ =
− knit CNH4 + kUrea CUrea + kHum − C CHum − C / r0
 θ DNH4
−
∂t
∂z 
∂z 
∂z
2 
f 
1
+ ∑
− e  kOrg i COrg − Cir0 
i =1  rOrg i∂θ Cl ,NO3 ∂ ∂Cl , NO3  ∂qwCl ,NO3=
+ knit CNH4 − kdenθ Cl ,NO3
 θ DNO3
−
∂t
∂z 
∂z 
∂z

(29)

(30)

(31)

where D is the dispersion coefficient, qw is the volumetric water flux density, z is the vertical
position, and t is time.
The first-order kinetic equations for the carbon and nitrogen cycles can be described with the
PHREEQC program, which can be readily implemented into HYDRUS-1D using the HP1 codefor solute transport simulations.

372

3. Examples
We demonstrated the decomposition processes of organic matter and resultant nitrogen transport
in soils for transient water flow and nonisothermal conditions. A constant flux of water of 0.5 cm
d-1 was applied to the surface of a 100-cm deep silty soil profile having an initial pressure head hiof -2000 cm. The soil bulk density, ρb, is 1.5 g cm-3. Constant temperature boundary conditions
were applied: 40 °C at the surface and 10 °C at the bottom. Four types of organic matter withdifferent C/N ratios (= 5, 20, 30, and 100) were uniformly applied from the surface to 25 cm
depth. The amount of carbon per volume of soil was 0.152 mg cm-3, while the carbon content
was taken to be the same for each type of organic matter. Linear adsorption was assumed for
NH4-N with Kd = 2.5. A negligible amount of NH4-N initially existed and the initial CNH4 was set
at 3.9 ×10-5 g kg-1. A single carbon pool (i = 1) was used with kOrg = 0.04 d-1, kHum-C = kHum-N =0.0001 d-1, fe = 0.5, fh=0.2, and r0 = 10. Nitrification was neglected, knit = 0 d-1. Figures 2 and 3
show volumetric water content and temperature profiles during infiltration. Results for low andhigh C/N rations with mineralization are presented below in sections 3.1 and 3.2, respectively.
0

0
0d
5

-20

10

-40

z (cm)z (cm)

-20

20

20

0d

-40

40
-60

-60

100

40
-80

-80
100
-100
0.1

0.2

0.3

0.4

-100
10

0.5

Figure 2. Volumetric water content profiles during
infiltration into silt with a constant flux of 0.5 cm d-1.

20

30

40

Temperature (oC)

Theta (-)

Figure 3. Temperature profiles during infiltration
into silt with boundary conditions of 40 °C at thesurface and 10 °C at the bottom.

3.1. Low C/N Ratio with Mineralization
When the C/N ratio of organic matter is below 20 (=r0/fe), sufficient N for humus and biomass
production results in the mineralization of NH4-N. Since the NH4-N concentration did not affectthe degradation rate of the organic matter, Org-C concentrations were identical for C/N = 5 and
20 (Fig. 2). Faster degradation near the surface was due to effects of temperature. At 40 days,
Org-C and Org-N became almost negligible and the C/N ratio became close to 10 (=r0 ).
Increased mineralization resulted in higher NH4-N concentrations for C/N = 5.

373

0

0
1

3

0d

5
-10

0d
3
-10

10

10

5
10

20

z (cm)

-20
40

40

0d

0d

1

5

20

z (cm)

1

3

-20

10
20

40

-30

-30

5

20

40

-40

-40

C/NInitial=20

C/NInitial=5

-50

-50
0

0.04

0.08

0.12

0.04

0.16

0.08

0.12

0

0.16

0.01

0.02

0.03

0.04

0.01

0.02

0.03

0.04

COrg-N (mg cm-3 soil)-3

COrg-C (mg cm soil)

Figure 2. Organic carbon (Org-C) concentration
profiles for C/N = 5 and 20 with mineralization ofammonium.

Figure 3. Organic nitrogen (Org-N) concentration
profiles for C/N = 5 and 20 with mineralization ofammonium.

0

0
1 0d

0d
3

5
10

3

-10

10

20
-20

10d

1d

5

5

20

40

z (cm)-10z (cm)

C/NInitial=20

C/NInitial=5

40

40
-30

-30

20
10

-20

20
40

-40

-40

C/NInitial=20

C/NInitial=5

C/NInitial=20

C/NInitial=5

-50

-50
0

10

20

30

10

20

30

0

0.005

0.01

0.015

0.02

0.005

0.01

0.015

0.02

CT-NH -N (mg cm-3 soil)

C/N (-)

4

Figure 5. Total ammonium (NH4-N) concentration
profiles for o C/N = 5 and 20 with mineralization ofammonium.

Figure 4. C/N ratio profiles in the organic pool for C/N= 5 and 20 with mineralization of ammonium.

3.2. High C/N Ratio with Immobilization
On the other hand, when the C/N ratio of organic matter was above 20 (=r0 / fe), NH4-N in a soil
is immobilized for humus and biomass production. The N deficiency now slowed down the
degradation process in that it took more than 200 days until the degradation almost finished for
C/N = 100. As shown in Figure 7, C/N became less than 20 near the surface in case of C/N = 30,
indicating mineralization started near the surface whereas immobilization continued in the lower
part of the soil. Stage 3 immobilization continued for C/N =100. During this stage, very slow
degradation at a 90 % reduced rate produced only CO2 and NH4-N without biomass and humus
production. Stage 2 stated in the lower part of the soil at 100 days because of NH4-N supply fromthe upper part of the profile.
374

0

0
0d
10

-10

60

200

100

20

-30

-20

100

-30

-40

0

0.04

0.08

0.12

0.16

0.04

0.08

0.12

200

-40

C/NInitial=100

C/NInitial=30-50

C/NInitial=100

C/NInitial=30

-50

0.16

0

0.002

-3

COrg-C (mg cm soil)

0.004

0.006

0.002

0.004

0.006

COrg-N (mg cm-3 soil)

Figure 6. Organic carbon (Org-C) concentration
profiles for C/N = 30 and 100 with immobilization ofammonium.

Figure 7. Organic nitrogen (Org-N) concentration
profiles for C/N = 30 and 100 with immobilizationof ammonium.

0

0

10d

0d

10
20

0d

40

-10
60

20

400

60

-20

10d

z (cm)-10z (cm)

100

60

100

z (cm)z (cm)

-10

20
40

40
-20

40

10

20

0d

0d
20 10

0d

200

100

100

40

-20

40
100

-30

-30

-40

-40

100
200

C/NInitial=100

C/NInitial=30

C/NInitial=30

C/NInitial=100

-50

-50
0

10

20

30

40

40

80

120

C/N (-)

00.0004 0.0008 0.0012 0.0016 0.0004 0.0008 0.0012 0.0016

CT-NH -N (mg cm-3 soil)
4

Figure 9. Total ammonium (NH4-N) concentration
profiles for C/N = 30 and 100 with immobilizationof ammonium.

Figure 8. C/N ratio profiles in the organic pool for C/N= 30 and 100 with immobilization of ammonium.

4. Conclusions
The carbon and nitrogen cycling model used in the LEACHM code was reformulated using the
PHREEQC program and linked with HYDRUS-1D using the HP1 code. We confirmed that theHP1 code could accurately calculate carbon and nitrogen cycles and various nitrogen transportscenarios as a result of the application of organic matter to a variably-saturated soil profile under
nonisothermal conditions. We further showed that coupled carbon and nitrogen cycling is
especially important when organic matter with a high C/N ratio is applied to a soil. Although weonly showed results for a single organic pool, it is possible to demonstrate various interactions
between the different organic matter pools. We are planning to extend the program to include
multiple organic pools, passive and active root uptake, CO2 diffusion in the gas phase, cation and375

anion exchange for ammonium and nitrate, and several other chemical reactions judged to beimportant.
ReferencesŠimůnek, J., M. Th., van Genuchten, and M. Šejna, The HYDRUS-1D software package for simulating
the one-dimensional movement of water, heat, and multiple solutes in variably-saturated media,
Version 3.0, HYDRUS Software Series 1, Department of Environmental Sciences, University ofCalifornia Riverside, Riverside, CA, 270 pp., 2005.
Hutson., J. L., Leaching Estimation and Chemistry Model, Version 4.1, School of Chemistry, Physics andEarth Sciences Flinders University Adelaide, Australia, pp. 135, 2005.
Jacques, D., and J. Šimůnek, Notes on HP1 – a software package for simulating variably-saturated water
flow, heat transport, solute transport, and biogeochemistry in porous media, HP1 Version 2.2,
SCKCEN, Mol, Belgium, 2010.
Johnsson, H., L. Bergstörm, P.-E. Jansson, and K. Paustian, Simulated nitrogen dynamics and losses in alayered agricultural soil, Agric. Ecosyst. Environ., 18, 333-356, 1987.
Parkhurst, D. L., and C. A. J. Appelo, User’s guide to PHREEQC (Version 2): A computer program forspeciation, batch-reaction, one-dimensional transport, and inverse geochemical calculations, WaterResour. Invest. Rep. 99-4259, USGS, Denver, CO, pp. 312, 1999.

376

HYDRUS Application to Assess Possible Impacts of NonConventional Water Irrigation under Two Different Vadose Zone
Monitoring Strategies
Javier Valdes-Abellan1, J. Jiménez-Martínez2, and L. Candela3
1

Department of Civil Engineering, University of Alicante, Alicante, Spain, javier.valdes@ua.es
2
Geosciences Rennes, UMR 6118 CNRS, Université de Rennes I. Rennes, France,
joaquin.jimenez-martinez@univ-rennes1.fr
3Department of Geotechnical Engineering and Geosciences, UPC-Barcelona, Jordi Girona 1-3, 08034 Barcelona,
Spain, lucila.candela@upc.edu

Abstract
Scarcity of water resources is one of the major problems that faces many arid and semi-arid areas where
potential socio-economic development is often hindered by the lack of water. This has led to the use ofnon-conventional water sources such as desalinated brackish groundwater and/or seawater for urban andagricultural demands. Applications of non-conventional water to the vadose zone may produce various
impacts such as changes in soil hydraulic properties, among others. In this context, monitoring vadosezone water dynamics is key to studying these possible impacts. According to the available literature,different monitoring systems and strategies have been carried out independently, while comparative
studies between different monitoring techniques have received less attention.
In this study, an experimental plot was set with automatic and non-automatic sensors to measure thevolumetric water content (θ) and the soil pressure head (h) down to a depth of 1.5 m. Water flow
simulations for automatically and non-automatically collected data were carried out using HYDRUS-1D.
A good agreement between simulated and experimental data was observed for both automatic and nonautomatic data acquisitions. General trends were captured as expected, except for outlier values. Slightdifferences were found between hydraulic properties obtained from laboratory determinations and fitted
by inverse modeling for both data acquisition strategies. Differences of up to 14% in the bottom drainage
were obtained between both strategies. According to our results, automatic sensors were more accurate,
and thus more appropriate, for detecting subtle changes in soil hydraulic properties as a consequence of
non-conventional water use. Nevertheless, if the aim of the research is to control the general trend ofwater dynamics, then there are no significant differences between both data acquisition systems.
The current work presented here is the first part of the study carried out before the geochemical processes
responsible for expected changes in the soil hydraulic properties as a consequence of non-conventional
water use are analyzed. This second part will be carried out using the HP1 model, which couples the
HYDRUS and PHREEQC models.

1. Introduction
In semi-arid regions with endemic water scarcity, which imposes constraints on socio-economic
development (Lattemann and Höpner, 2008), the use of non-conventional resources (such as
desalinated water, treated water, and waste-water) for agricultural purposes is increasing during
recent years. The potential impacts of the use of non-conventional water on soil, plants, or377

aquifer media may include changes in soil hydraulic properties due to mineral precipitation, root
growth blockage and plant uptake of pollutants, and/or contaminant leaching to groundwater(Calderón-Preciado et al., 2011; Candela et al., 2007; Mandal et al., 2008). In addition, thisirrigation water is usually characterized by high electric conductivity values while highevapotranspiration rates may prevail in arid areas. The combination of these two factors may
enhance soil salinization, which ultimately causes damage to crop yield (Kanzari et al., 2012).
To assess these possible impacts, having a careful monitoring procedure of the vadose zone at afield scale is a very important issue. Field monitoring can be carried out using different devices,
the number of which is continuously increasing following the latest technological developments.
Among them, methods range from classical ceramic cup tensiometers and gravimetricdetermination of soil water contents from oven-dried samples to Time Domain Reflectometry(TDR) technology. These methods can be classified as manually managed, i.e., with nonautomatic data acquisition, or with automatic data acquisition using more sophisticated sensors,which makes monitoring less time-consuming but with an increasing initial investment.
Although automatic and non-automatic monitoring strategies have been commonly used
separately in the past in order to study different aspects of the vadose zone (Jiménez-Martínez etal., 2009; Wallis et al., 2011; Wollschläger et al., 2009), the selection of a monitoring strategy
has not been completely justified in these studies. However, studies in which different
monitoring strategies have been simultaneously set up and compared have not been carried out.
In this work, a comparative study between an automatic and non-automatic monitoring strategy
for the same experimental plot is presented. Two different flow simulations were carried out
using HYDRUS for different data sets (the monitoring period extended over 9 months). A
conservative tracer test has also been modeled in order to validate the previous water flux results.
2. Methodology and Field Experiment
An experimental plot of 9 x 5 m located on the campus of the University of Alicante (Spain) was
set up. On the plot, a mixture of turf grass (St. Agustine grass, Stenotaphrum secundatum, andray grass, Lolium perenne) was grown to mimic the current management of the campus
landscape. The plot was irrigated using micro-sprinklers, providing a quasi-uniform water input
over the land surface.
Installed measurement devices included manual or non-automatic instruments, which consistedof ten Jet Fill tensiometers (Soil Moisture®) for h measurements installed at depths of 30, 45, 60,
90, and 120 cm (2 tensiometers in each depth), and two 44 mm (i.d.) polycarbonate access tubes
installed down to a depth of 1.9 m for θ measurements using a TRIME FM TDR portable probe(IMKO®). The probe was previously calibrated in the lab following the manufacturer’s
recommendations and also specifically calibrated following previous study procedures (Laurent
et al., 2001; Laurent et al., 2005; Varble and Chávez, 2011). Installation of non-automatic
equipment was done from the plot surface, aided by hand auger equipment (Eijkelkamp®).
Vertical installation was carefully performed in order to prevent preferential flows along the sidewalls of the equipment itself. Automatic data acquisition consisted of five 5TE sensors (Decagon

378

Devices ®) installed at depths of 20, 40, 60, 90, and 120 cm for θ measurements, and one MPS-1
sensor installed at a depth of 60 cm for h measurements. All automatic sensors were controlled
by the data-logger, CR1000 (Campbell Scientific®). Installation of automatic sensors took placehorizontally in an 80 cm wide and 150 cm deep excavated trench. Horizontal holes (40-50 cmlong) were drilled in the trench walls for sensor installation in order to reduce the boundary
effects. Subsequently, the holes were re-filled with the same soil material extracted during the
excavation, in an attempt to keep the original soil conditions (e.g., bulk density). The side-wall of
the trench was covered with a plastic film and finally, the trench was refilled with the soilmaterial, creating a non-flow boundary condition for further modeling purposes.

Figure1. Scheme of the experimental plot with the configuration of automatic and non-automatic
devices.

2.1. Data Gathering
Data acquisition started on September 1st, 2011, five weeks after the devices’ installation. Nonautomatic θ measurements were taken twice per week, while h measurements were taken threetimes per week. An hourly measurement frequency was used regarding automatic dataacquisition. A five-minute frequency was used in November, 2011, in order to capture theinfiltration dynamics following extreme rainfall events that took place in this period.
Meteorological data were recorded every 30 minutes by a meteorological station located 900 m
away from the plot.
2.2. Numerical Modeling
Water flow through the vadose zone was modeled using HYDRUS-1D (Šimůnek et al., 2009),
which numerically solves the governing Richards equation describing flow in partially-saturated
porous media (Richards, 1931):∂θ∂   ∂h  =K  + 1  − S∂t ∂z   ∂z


379

(1)

One dimensional modeling was selected based on the assumption of horizontal uniformity overthe experimental plot and vertical flow being a dominant direction of flow in the experiment.
Daily time steps were considered in the modeling process. Collected data in smaller time steps(as those values obtained with automatic data collection) were averaged over daily intervals.
The soil hydraulic properties were modeled using the van Genuchten-Mualem constitutive
relationships (Mualem, 1976; van Genuchten, 1980):

θs − θr
1−1/ nθ r +
1 + αh n θ ( h) = 



θ s

{

h<0

(2)

h≥0

}

1−1/ n 2

K=(h) K s Sel 1 − 1 − Sen /( n −1) (3)In order to reduce the number of free parameters, we considered l = 0.5, which is a common
assumption regarding this model. The remaining parameters were estimated from laboratory data
and by inverse fit.
Atmospheric boundary conditions (BC) were considered at the soil surface, and free drainage BC
on the bottom of the soil profile. Daily evaporation and transpiration rates were computed
following the Penman-Monteith method (Allen et al., 1998). A modified Feddes root water
uptake model (Feddes et al., 1978; Wesseling and Brandyk, 1985) was considered for modelingthe influence of the plants The key parameters of the model adopted for the current crop (grass)
were: h1= -10 cm, h2= -25 cm, h3.1= -240 cm, h3.2= -360 cm, and h4= -8000 cm. Root growth was
not considered due to the selected species being completely developed at the beginning of thesimulation period.
2.3. Tracer Test
A conservative tracer test with a LiBr solution was carried out in order to assess water flow andto estimate dispersivity coefficients for different soil layers. The Br- tracer application was used
due to the low background concentration of Br in the soil profile. On June 27th, 2012, a solutionof LiBr (25 L with a LiBr concentration of 131.73 mmol/L) was sprinkled over 10 m2 of the plot.
Undisturbed soil samples were collected (7, 37 and 57 days after injection) at different depths.
Subsequently, the total bromine concentration (Br) was determined using X-ray fluorescence,
following the methodology proposed by Abderrahim et al. (2011). To simulate Br- transport in
the soil profile, soil hydraulic parameters obtained from the flow model with automatic data wereused.
3. Results and Discussion
An important difference between the two monitoring strategies was the amount of collected data.
1489 versus 400 daily values were collected by an automatic and non-automatic monitoring
strategy, respectively. Following identical and parallel procedures, θ and h measured values for380both data sets were simulated by means of HYDRUS-1D. Figure 2 shows the observed andsimulated values of θ for the automatic and non-automatic equipment at different depths. A good
agreement is observed between the experimental and modeled data for both collection strategies.
Recorded and simulated h values are shown in Figure 3. Note that automatic sensors properly
capture the peak events, while the non-automatic ones present a smoother behavior, which can bea consequence of the acquisition frequency. On the other hand, a greater dispersion of h data isfound for the non-automatic acquisition system. Several statistics were calculated for pressure
head (h) and volumetric water content (θ) data at all depths observed by both automatic and nonautomatic devices. A summary of the results is provided in Table 1.

Figure 2. Observed and simulated θ values collected by an automatic (a) and non-automatic (b)monitoring strategy. Water input data (irrigation plus precipitation) is depicted on the secondary
vertical axis.

Figure 3. Observed and simulated h values collected by an automatic (a) and non-automatic (b)monitoring strategy. Water input data (irrigation plus precipitation) is depicted on the secondary
vertical axis.

381

Table 1. Goodness of fit measures for simulations and experimental data.
Acquisition

Automatic

Non-automatic

Statistic
RMSE
EF
R2
RMSE
EF
R2

Volumetric water content, θPressure head, h
60 cm

30 cm

45 cm

60 cm

90 cm 120 cm All

0.21
0.72

0.05
0.81

0.04
0.74

0.02
0.94

-

0.05
0.5

0.04
0.76

0.16
0.80

0.07
0.00

0.05
0.43

0.10
0.24

0.12
-0.02

0.14
-0.37

0.10
0.44

All (h and θ)

0.96
0.98

Despite of good agreement between both simulations and experimental data, computed drainage
flux through the bottom boundary was equal to 230 and 196 mm for automatic and nonautomatic data acquisitions, respectively. This is a difference of 14.8% between both models,
which is an important difference when attempting to assess groundwater recharge from a semiarid area point of view.
The results of the tracer test performed to assess the flow model and to derivate transportparameters are shown Figure 4. A good agreement between measured and predicted total
bromide (Br) concentrations along the soil profile was observed, which validates the flow model.

Figure 4. Measured and predicted values of total Br concentrations in soil at 7 (a), 37 (b), and 57(c) days after the tracer application.

4. Conclusions
The analysis proposed in this study has provided insights into soil and vadose zone monitoring
strategies to assess water dynamics and changes in soil hydraulic properties. However,monitoring results for hydraulic parameters were complex, indicating that one of the main
limitations is the inability to measure the effective properties representing the overall system.

382

The instruments used normally explore a domain that is notoriously too small to describe average
properties. Field measurements obtained with non-automatic (vertically-installed) instruments
need to be carefully analyzed since the installation process can lead to preferential flow along thedevice walls, even when careful installation procedures are followed. It should be noted that if
previously determined information on soil characteristics obtained in the laboratory is not taken
into account, unrealistic soil hydraulic parameters can be obtained from simulated values of bothautomatic and non-automatic data.
The HYDRUS simulations were able to reproduce the behavior of a field-scale plot instrumented
with automatic and non-automatic data acquisition systems. A good agreement between thepredicted and measured soil water contents and pressure heads was obtained. However, theoverall trend was predicted better than extreme episodes, which has been also observed by otherresearchers. Significant differences between the modeled parameters obtained from the nonautomatic and automatic experimental data were observed. On average, the statistical evaluation
revealed that fits of the θ data proved better than those of the h data. This fact could be related tothe equilibration time required by the pressure head devices to obtain reliable measurements. For
the tracer test, a good agreement between measured and predicted total bromine (Br)concentrations in the soil profile was obtained, which validates the flow model.
This work only represents the first step of the study, before the geochemical processes
responsible for the expected changes in the soil hydraulic properties as consequence of the use ofnon-conventional water is analyzed. This purpose will be carried out using the coupled
HYDRUS and PHREEQC model HP1.
References

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crop water requirements. FAO Irrigation and Drainage Papers, Food and Agriculture Organization of
the United Nations, Rome, 1998..
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emerging contaminants and related compounds in an agricultural irrigation network, Science of the
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Candela, L., S. Fabregat, A. Josa, J. Suriol, N.Vigués, and J. Mas, Assessment of soil and groundwater
impacts by treated urban wastewater reuse. A case study: Application in a golf course (Girona,
Spain), Science of the Total Environment, 374(1), 26-35, 2007.
Feddes, R. A., P. J. Kowalik, and H. Zaradny, Simulation of Field Water Use and Crop Yield, Wiley,
1978.
Jiménez-Martínez, J., T. H. Skaggs, M. Th. van Genuchten, and L. Candela, A root zone modelling
approach to estimating groundwater recharge from irrigated areas, Journal of Hydrology, 367(1-2),
138-149, 2009.
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movement and salts transfer in a semi-arid region of Tunisia (Bou Hajla, Kairouan) - Salinization riskof soils and aquifers, Computers and Electronics in Agriculture, 86, 34-42, 2012.
Lattemann, S., and T. Höpner, Environmental impact and impact assessment of seawater desalination,
Desalination, 220(1-3), 1-15, 2008.
Laurent, J.-P., P. Ruelle, N. Bréda, A. Chanzy, and C. Chevallier, On the use of the TDR TRIME-TUBE
system for profiling water content in soils, TDR'01 Evanstons, Illinois, USA, pp. 1-10, 2001.

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384

Simulation of the Heavy Metal Transport in Unsaturated Soils:
Use of Scale Factors to Quantify Variable Sorption Isotherms
Han Xiao1, Jürgen Böttcher2, and Jiří Šimůnek3
1

Institute of Soil Science, Leibniz University of Hannover, Hannover, Germany, xiao@ifbk.uni-hannover.deInstitute of Soil Science, Leibniz University of Hannover, Hannover, Germany, boettcher@ifbk.uni-hannover.de
3
Department of Environmental Sciences, University of California, Riverside, CA 92521, USA, jiri.simunek@ucr.edu
2

Abstract
Heavy metals are toxic soil pollutants that are retarded in soils by sorption at the solid phase. At a small
scale (of a soil sample), the sorption process can be observed and quantified using sorption isotherms.
However, most environmental problems have to be treated and solved at large scales (e.g., a field scale).
At the field scale, heavy metal sorption isotherms are commonly highly variable in space. This spatial
variability makes a representative quantification of the sorption process (e.g., for the soil protection or forthe management of soil functions) and its consideration in reactive transport modelling (e.g., forgroundwater protection) difficult. Many transport simulation studies therefore treat soils as homogeneous
to avoid the need for complex datasets and calculations. In this study we used a recently developed
method of scale sorption factors to quantify the spatial variability of heavy metal sorption in soils at thefield scale. This method reduces the variability of sorption isotherms into a single average relation while
preserving their variation through the scale factors. We investigated the spatial variability of heavy metal
sorption isotherms for an agricultural field on a Luvisol developed over a loess material near Hannover,Germany. Fifty samples were taken from A and B horizons along a 250-m transect. Sorption isotherms
for heavy metals and soil properties, such as pH, CEC, and texture, were measured and scale factors were
calculated. The heavy metal transport was simulated with the HYDRUS model using a unique reference
sorption isotherm (derived using the scale procedure or mixed soil samples). Spatial variability ofsorption at every sampling point was further represented using a scale factor, which was either directly
calculated (using a scaling procedure) or indirectly estimated (using regression models with anotherheavy metal or from soil properties). For comparison, variability of sorption was also simulated using theoriginal, measured Freundlich parameters.
The results show that scale factors are well suited for predicting spatially variable retardation andtransport of heavy metals in soil, although a certain reduction of variability is to be expected. In the caseof extreme situations, transport simulations with scale factors are not well suited to describe the depth
distribution of heavy metal concentrations, especially when using indirectly calculated scale factors.

1. Introduction
Both agricultural (He et al., 2005; Nicholson, 2003) and environmental (Bradl, 2005) sciences
treat heavy metals as an important environmental factor because of their negative impact on theecosystem. Soils are either gradually contaminated by heavy metals due to their long-term
depositions, or suddenly due to various industrial leaks or intentional applications of various
compounds (e.g., sewage sludge, manure). The fate and transport of heavy metals in soils
depends mainly on their reactive properties, with sorption reactions being the most importantones (Alloway, 1995). The soil can then act as a storage container for these contaminants. A lot

385

of studies reported spatial distributions of heavy metals in the subsurface (Yang, 1989;
Camobreco, 1996; Ingwersen et al., 2006). However, much attention has been paid to transport
processes in one-dimensional soil columns, without extending the transport into two or three
dimensions. Soil spatial heterogeneity, which makes the sorption highly variable, is the main
reason for the lack of extending transport studies into higher dimensions.
Sorption processes cause the retardation of heavy metals in soils (Sparks, 2003). Hence, thequantification of sorption isotherms and their spatial variability is a prerequisite to quantify thespatial variability of heavy metal transport in soils. To simulate heavy metal displacement at thefield scale, Streck et al. (1997) used a parallel soil column approach. Altfelder et al. (2007) havestudied the combination of uncertainty and variability to predict field-scale heavy metaltransport. These authors have quantified sorption isotherms through pedotransfer functions(PTF). Deurer and Boettcher (2007) have compared PTF and a scaling method for sorption
isotherms (Böttcher, 1997) to upscale the small scale transport variability and concluded thatmean sorption behavior derived through scaling resulted in smaller uncertainty of heavy metaltransport prognoses.
Scaling was used first in soil hydrology to quantify the variation of water retention (Miller andMiller, 1956, Russo and Bresler, 1980; Raats et al., 2006). Following the basic ideas and rules ofscaling (Tillotson and Nielsen, 1984), Böttcher (1997) has developed a method to calculate scale
factors for spatially variable sorption isotherms and successfully applied this method to Cd
sorption in sandy soil. Furthermore, Böttcher (1997) showed that the scale factors for sorption
isotherms were correlated with some soil physicochemical properties. Therefore, indirect
calculation of scale factors for sorption from physicochemical soil properties (indirect scaling
procedure) seems possible. If so, scale factors may be derived by direct or indirect procedures.
This would extend the use of scale factors from statistical description of spatially variable
sorption isotherms (direct scaling procedure) to a broadened application in the prediction ofreactive transport processes in soil by the indirect scaling procedure.
In this study, scenarios of heavy metal (Cadmium, Zinc and Copper) transport in unsaturated soil
using the direct and indirect scaling procedure were simulated with HYDRUS-2D (Šimůnek etal., 2011). The main objective was to prove the performance of the two scaling procedures insimulating spatially variable heavy metal transport compared to simulations with original
sorption data.

2. Material and Methods
2.1. Soil Samples
The soil samples (undisturbed and disturbed) were taken from an agricultural field on a Luvisol
developed in loess material near Hannover, Germany. 50 samples were taken along a 250 m
transect at every five meters from 0 to 30 cm (topsoil) and 30 to 60 cm (subsoil). For eachhorizon, one mixed sample was made from the 50 soil samples to measure a mean sorption
isotherm that is needed as a reference in the indirect scaling procedure (see 2.4.2).

386

2.2. Laboratory Analyses
The undisturbed soil samples were used to measure the bulk density and water content. The
disturbed soil samples were air dried and sieved. Then the samples were used to measure therelevant soil physicochemical properties (Table 1).
Table 1. Soil physicochemical properties used to quantify the scale factors and the measurements method(source: Utermann et al., 2005).
Soil property [Unit]
Texture [%]pH(CaCl2) [-]Total carbon [%]Total carbonate [%]Total organic carbon (OC) [%]Oxalate extractable oxide by Fe, Mn and Al(Feox, Mnox, Alox) [mg/kg]
Effective cation exchange capacity (CECeff)[mmol/kg]*^

MethodPipette method after Koehn (<63µm)
Dry sieving (>63µm)
DIN* 19683-2
Potentiometric by use of a glass electrode in 0.001 M CaCl2
DIN ISO^ 10390:1997
C-N-S elementary analysis
DIN ISO 10694
Gas volumetric
DIN ISO 10693 (1997)
Difference between Total carbon and total carbonate
Extraction with oxalic acid ammonium oxalate
DIN 19684-6
Measure with flame-AAS
Percolation with 0.1 M BaCl2
Modified by DIN 19684-8
Measure of Ca, Mg, K, Na, Fe, Mn and Al with ICP-OES,
determination of H+-ions-concentration from pH-Value

German Institute for Standardization
International Organization for Standardization

Sorption isotherms were measured in a batch experiment. Heavy metal solutions (concentrations
range from 0 to 20 mg/L for Cadmium, 75 mg/L for Zinc and 40 mg/L for Copper) were added
to the soil water suspensions. A Ca(NO3)2 electrolyte solution was also added to maintain thenatural ionic strength. After 24 h of shaking, the suspensions were centrifuged for 15 minutes.
Heavy metal concentrations were then measured in the supernatant by ICP-OES.
2.3. Parameterization of Heavy Metal Sorption Isotherm
From measured sorption data, sorption isotherms were calculated, and the Freundlich equation(Bradl, 2005) was used to describe the isotherms.
S = K Cn(1)

In the Freundlich equation, S is the sorbed fraction [µg/kg], C is the solution concentration[µg/L], and K and n are parameters, adjusted by fitting the equation to the measured data.
2.4. Scaling of Sorption Isotherms
The scaling rule of sorption isotherms derived by Böttcher (1997) is:

387

(2)
C * = α 2Ci
where C* is the scaled concentration, Ci is a measured concentration, and α is the scale factor.
2.4.1

Direct Scaling Procedure

In the direct scaling procedure, mean concentrations describing the reference isotherm are first
derived as scale means (Böttcher, 1997) from:R
M r , j = R ∑
 r =1
2

( C )

−1

r, j





−2

(1)

Second, scale factors are calculated under the constraintR∑a R =1
r =1

−1

(2)

r

by minimization of the sum of squares (in logarithmic space)SS=∑∑ ( ln M
RJ=r 1 =j 1r, j− 2 ln ar − ln Cr , j )2(3)

to obtain α as:
Jr


−1
=
α exp ( 2 J r ) ∑ ( ln M r , j − ln Cr , j ) 
r =1



(6)

In the equations above, r is the number of soil samples (R = maxima) and j is the number of data
points on the respective sorption isotherm (J = maxima). C represents the individual measured
concentration, and M is the scale mean concentration.
The ratio (SSbefore-SSafter)/SSbefore is used to quantify the scaling efficiency. More details are given
in Böttcher (1997).
2.4.2

Indirect Scaling Procedure

Both scale factors for sorption isotherms and scale factors for soil properties were calculated
based on principles outlined in Tillotson and Nielsen (1984). Using correlations between heavy
metal sorption and soil properties, an indirect scaling procedure was also developed.
The concept of indirect scaling is based on the assumption that the measured sorption isothermof mixed samples is comparable with the mean sorption isotherm derived from the direct scaling388

procedure, and that scale factors can be calculated from scale factors from soil properties
relevant to sorption using multiple linear regression:

α in =
α * + aα pH + bα clay + cα OC + ...

(7)

where αin is the scale factor of indirect scaling and α* is an intrinsic scale factor, αpH, αclay andαOC are calculated scale factors of soil properties, and a, b, and c are fitting parameters of linear
regression.
2.5. Simulation of Heavy Metal Transport with HYDRUS
In unsaturated soil, the water flow is usually vertical. Hence, the simultaneous heavy metaltransport is also vertical and can be described by the widely used convection-dispersion equation(CDE) under steady flow conditions (Radcliffe and Šimůnek, 2010).
As sampling was carried out along a transect at every 5 m, the geometry in HYDRUS-2D was set
as a rectangle with a length of 250 m and a depth of 0.6 m. The rectangles were divided into 50
columns, each with topsoil and subsoil horizons. Each column has a single set of water flow andsolute transport parameters. The infiltration rate was 250 mm per year (Deurer, 2007). The input
concentrations were set to 100 for Cd, 8000 for Zn, and 2000 μg/L for Cu. The simulation time
was set to 500 years for Cd and Zn and 100 years for Cu.
Three scenarios were set up. Scenario I was simulated using the original measured sorption
parameters. In scenario II, the reference isotherms (Table 3) for the soil horizons were used, andthe scale factors from the direct scaling procedure were applied to calculate the sorption
isotherms for the soil columns. In scenario III, sorption isotherms for the columns were
calculated from the isotherm of the mixed soil sample, and the scale factors from the indirect
scaling procedure.

3. Results
3.1. Sorption Isotherm Parameters and Physicochemical Soil Properties
Table 2 lists the mean and the coefficient of variation (CV) of the measured soil properties andthe Freundlich parameters.
Differences between soil properties in topsoil and subsoil are low. The pH values are high,causing strong heavy metal sorption in topsoil and subsoil. The sorption parameter K of Cd and
Zn in subsoil is much higher than in topsoil, possibly because of a higher pH in the subsoil,
though n is more or less the same. K and n of Cu behave differently, which may be attributed tothe higher OC content in the topsoil. Most CVs in Tab. 2 are low, except the CV of CECeff and K.
This finding hints at a correlation between CEC and K, as already published by others (e.g.,
Buchter et al., 1989, Springob and Böttcher, 1998).

389

Table 2. Summary statistics of soil properties and isotherm parameters.
pH

CECeff

OC

sand

clay

silt

%

%

%

%

-

Feox

Alox

Mnox

Topsoil

6.9

96.8

1.18

3.8

11

85

2617

581

356

Subsoil

7.2

72.9

0.31

3.3

12

85

2621

603

228

%

%

%

%

%

%

%

%

%

Topsoil

2

40

10

9

1

12

4

4

10

Subsoil

2

42

17

13

2

10

5

6

17

Mean

CV*
*
^

K
n
(Cd)

K
n
(Zn)

K
n
(Cu)

[]^

[]

[]

1407
0.81
2271
0.80
%
34
7
33
6

7498
0.51
13509
0.49
%
24
5
17
7

247
1.34
123
1.66
%
34
6
49
9

CV - Coefficient of Variation
Units of K are [µg1-nLn/kg], and units of n are [-]3.2. Reference Isotherm and Scale Factors
A summary of sorption isotherm parameters and scale factors from direct and indirect scaling
procedures and their statistics are presented in Table 3. Because the mean of scale factors isalways 1 (compare to eq. 4), the range of scale factors with the coefficient of variation is given.
CVs of scale factors α appear to be lower than CVs of K in Table 2, and higher than CVs of n inconsideration of residual sum of squares. As shown in Table 3, the scaling efficiencies (derived
for direct scaling) are mostly high. This confirms earlier findings of Böttcher (1997) and Deurer
and Böttcher (2007), who showed that for sandy soils, successful scaling of sorption isotherms ispossible.
Table 3. α and reference isotherms from direct and indirect scaling procedures, and statistical parameters.
Heavy
metal

HorizonSamplesize

Direct scaling procedure
R-SI*
SE^
Range [-]%
CV [%]αIndirect scaling procedure
Adj. R2
SImixed#Range [-]
CV [%]

αin

0.67
S=1394C0.80
85
0.51
0.513
S=1398C0.83
1310
subsoil50
0.87
S=2248C0.79
92
0.42
0.503
S=2229C0.77
1613
Zn
topsoil50
0.71
S=7482C0.51
88
0.55
0.505
S=8709C0.49
1411
subsoil50
0.81
S=13638C0.49
75
0.29
0.248
S=15612C0.44
14
7Cu
topsoil50
0.23
S=245C1.33
78
0.13
0.443
S=275C1.30
53
subsoil50
0.39
S=118C1.64
89
0.32
0.612
S=161C1.59
10
8* Reference sorption isotherm, ^ Scaling efficiency, # Sorption isotherm derived from mixed sample
Cd

topsoil

50

390

The values of "Adj. R2" for indirect scale factors are low, indicating only weak correlation
between measured soil properties and scale factors. The reasons could be a relatively small
sample size and low CVs of soil properties, among other things. The reference sorption isothermsof the direct scaling procedure correspond quite well with sorption isotherms of the indirect
scaling procedure (measured at mixed soil samples). This demonstrates that scale means aremeaningful estimators to upscale soil sorption properties from point measurements to the field
scale.
3.3. Evaluation of Heavy Metal Transport
The simulated heavy metal concentrations are shown in Figure 1. The spatial variation ofconcentration depth distributions along the transect between the different simulation scenarios isbasically the same for each heavy metal. However, the extent of transport variability is in theorder of Scenario I > II > III. These results indicate that the application of scale factors for
sorption isotherms, especially indirect scale factors, causes a certain reduction of the variabilityof heavy metal retardation in soil, while the typical transport behavior of the metals ismaintained.
Unlike Cd and Cu, Zn shows a very good match between model results simulated with theoriginal topsoil sorption data or scale factors, regardless of the scaling procedure. This is very
probably due to two reasons. First, Zn topsoil has a scaling efficiency of 88% (Table 3), which ishigher than for Cd (85%) and Cu (78%). Second, Zn topsoil has low CVs of sorption isotherm
parameters K (CV=24%) and n (CV=5%). Compared to Cd and Cu, these values are closer to theCVs of α and αin (Table 3). Also, Nanos and Martín (2012) found that Zn concentrations in soil
are not as spatially variable as Cd and Cu concentrations.
On the other hand, the simulation scenarios for the highly spatially variable heavy metal Cu
demonstrate a disadvantage of sorption scale factors. Maximum Cu concentration has alreadybeen transported to a depth larger than 60 cm only in column 13 (from the left of the transect,Fig. 1) if simulated with the original sorption data (Scenario I). If simulated with direct scale
factors (Scenario II) or indirect scale factors (Scenario III), respectively, Cu in column 13
traveled only slightly deeper or to a rather similar depth, compared to surrounding columns (Fig.
1). The reason for this behavior may be explained by comparing Freundlich parameters K andscale factors. The original Freundlich K at column 13 is 98.7 µg1-nLn/kg. Obviously, Cu
retardation at this point (column 13) is relatively low. In contrast, the mean K of a directly
calculated reference isotherm and K of a mixed sample are 244.8 and 274.8 µg1-nLn/kg,
respectively. I.e., the ratios are 0.4 and 0.36, respectively. But the corresponding squared scale
factors α2 (eq. 2) are 0.82 and 0.91. Thus, using scale factors, a much stronger retardation of Cu
is simulated in column 13. This shows that scale factors, and especially scale factors of theapplied indirect scaling procedure (uncertain as indicated by low Adj. R2, Table 3), are not well
suited to describe extreme situations at single points in space.
Summarized, the simulated scenarios show that scale factors are well suited for predicting
spatially variable retardation and transport of heavy metals in soil, although a certain reductionof variability is to be expected. In the case of extreme situations, transport simulations with scale
factors are not well suited to describe the depth distribution of heavy metal concentrations.

391

0

I
-60cm
0

II

Cd
-60cm
0

III
-60cm

0

100 μg/L

100 μg/L

0

I
-60cm
0

II

Zn
-60cm
0

III
-60cm

0

8000 μg/L

8000 μg/L

0

I

-60cm
0

II

Cu
-60cm
0

III

-60cm

0

2000 μg/L

2000 μg/L

Figure 1. The simulation scenarios of heavy metal transport with I: the original sorption
procedure, II: the direct scaling procedure, and III: the indirect scaling procedure.

392

4. Conclusions
We demonstrated that the calculation of scale factors is a convenient and effective method (dueto high scaling efficiency) for deriving the mean sorption isotherm at the field scale. We
conclude that scale factors have the potential to describe the spatial variability of heavy metaltransport well if the variability of sorption isotherms is not too high, as it is, for example, in thecase of Zn. In extreme situations (very week heavy metal sorption) at single points, scale factors
may not be sufficiently effective to simulate sorption or retardation. In such a case, the indirect
scaling procedure especially fails because of the high uncertainty of the multiple regression.
However, in general, the applied indirect scaling procedure tends to even out the variability ofheavy metal transport, and thus cannot be recommended as an effective tool for heavy metaltransport prediction. Further studies should concentrate on developing an improved indirect
scaling procedure, possibly including other sorption relevant soil properties such as a specificsoil surface area.

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394

Comparison of HYDRUS-1D Simulations and Ion (Salt)
Movement in the Soil Profile Subject to Leaching
Engin Yurtseven1, Jiří Šimůnek2, S. Avcı3, and H. S. Öztürk41

Department of Farm Structures and Irrigation, Faculty of Agriculture, University of Ankara, 06110 Dışkapı,
Ankara, Turkey, yurtsev@ankara.edu.tr
2
Department of Environmental Sciences, University of California, Riverside, CA 92521, USA, jiri.simunek@ucr.edu
3
Department of Farm Structures and Irrigation, Faculty of Agriculture, University of Ankara, 06110 Dışkapı,
Ankara, Turkey, sertan.avci@gmail.com
4
Department of Soil Science, Faculty of Agriculture, University of Ankara, 06110 Dışkapı, Ankara, Turkey,
H.Sabri.Ozturk@agri.ankara.edu.tr

Abstract
There is an increasing trend to require more efficient use of water resources, both in urban and rural
environments. Drainage water can be beneficially reused for agricultural irrigation before being discarded
after its use. The quality of the discarded water depends on many factors, including the irrigation water
quality and irrigation management, i.e., the salt content and the quantity of irrigation water to be applied
during the vegetation period.
A variety of analytical and numerical models have been developed during the past several decades topredict water and solute transfer processes between the soil surface and groundwater table. The
HYDRUS-1D software package is one of such models simulating water movement and solute transport in
the soil. In this study, we use HYDRUS-1D to analyze water flow and solute transport in soil columns
115 cm long and with a diameter of 40 cm, irrigated with waters of different quality at different leachingrates. Three different irrigation water salinities (0.25, 1.5, and 3.0 dS/m) and four leaching fractions (10,20, 35, and 50% more water than required) were used in a fully randomized, factorial design experiment.
Each experiment was run in three replicates, resulting in a total of 36 lysimeters. Following every
irrigation, drainage waters were collected using the plastic pods situated under each lysimeter. Water
fluxes, concentrations of individual ions (Na+, K+, Ca2+, Mg2+, Cl-, SO42-, CO32-, and HCO3-), EC of thesoil solution, and SAR were monitored at five depths (20, 40, 60, 80, and 100 cm) in all soil columns. The
soil used for the experiments was SCL. In all leaching experiments, the salts accumulated in the profile
due to irrigation with salty water could be leached out from the soil. More soluble salts, such as Cl-,
leached more easily than the less soluble salts, such as CO3-2 and HCO3-.
The results showed that HYDRUS-1D was able to successfully simulate soil water salinity and movementof salts (ions) in the soil profile. The RMSE values for all treatments and for different soil depths varied
for EC (dS/m) between 2.50-5.21 and 1.36-4.38 and for SAR between 1.26-3.18 and 1.45-1.88 during thefirst (2010) and second (2011) experimental year, respectively. The RMSE values for ions Ca2+, Mg2+,
Na+, K+, SO42-, and Cl- were between 0.50-24.14 in 2010, and 0.28-14.25 in 2011. HYDRUS-1D proved
to be a powerful tool for analyzing solute concentrations related to overall soil salinity.

1. Introduction
Salinization is, due to the presence of various ions in irrigation water, the most widespread
problem in irrigated areas with arid and/or semi-arid climate throughout the world. Salinization

395

generally occurs when salts accumulate in the soil profile, depending on the relationship between
irrigation applied by farmers, natural precipitation, evapotranspiration, and leaching. When theconcentration of salts exceeds a level harmful to crops, crop yields decrease and fruit quality
worsens. It is unavoidable that some salts accumulate in the root zone since all waters used for
irrigation inevitably contain soluble ions, concentrations of which depend on the type of water
source. The higher the content of salts in irrigation water, the faster the process of soil
salinization. Evaporation and transpiration are the predominant mechanisms causing theaccumulation of salts in irrigated agricultural soils. Both evaporation and transpiration processes
remove water from the soil, while leaving salts behind and increasing their concentrations inremaining soil water (Corwin et al., 2007; Gonçalves et al., 2006). Therefore, the higher theevaporation and/or transpiration rates, the faster the soil salinization. The increase of salinity ofwater due to evaporation is often called evapoconcentration.
Salinity restrains root water uptake of plants by increasing the osmotic pressure in soil water andthus making it more difficult for plants to extract water from the soil. Some components ofsalinity may cause specific-ion toxicity and imbalance the nutritional stability of plants. In
addition, the salt composition of soil water influences the composition of cations in the exchange
complex of soil particles, which may significantly influence soil permeability and tilth(Yurtseven and Sönmez, 1992; Corwin et al., 2007).
Soils not only contain a mixture of salts, but the distribution of these salts is not uniform
spatially, nor constant with a soil depth and/or time. Non uniformity within a field is caused inlarge part by irrigation systems that do not supply water evenly (Hoffman and van Genuchten,1983). Excessive salts accumulated in soil profiles of irrigated lands can be leached out byadding more water than required to meet the evapotranspiration needs of the crops. The ratio ofadditional irrigation water, with respect to evaporation and transpiration, is usually expressed asa leaching fraction (LF) or a leaching requirement (LR), which are identical mathematicalexpressions, but with different meanings. The LF is simply a ratio of the total amount of water
passing through the soil profile to the total amount of applied irrigation water. On the other hand,
the LR is defined as the fraction of infiltrated water that must pass through the root zone to keep
soil salinity from exceeding a level that would significantly reduce crop yield under steady-state
conditions with associated good management and uniformity of leaching (USSL Staff, 1954;
Rhoades, 1974).
Many methods are available to determine the impact of irrigation water quality and existing farm
irrigation management in soil salinity. The most precise assessment of salinity is taking soil
samples and carrying out laboratory analyses of salinity and its components using several typesof laboratory instruments and methods. However, classical methods of evaluating soil salinity aretime demanding, expensive, and require a lot of effort, yet cannot completely cover the spatial
and temporal variability at the field scale (Rasouli et al., 2012). On the other hand, it is possible
to use ground-based geophysical measurements of the apparent soil electrical conductivity (ECa),such as electrical resistivity (ER) or electromagnetic induction (EM) surveys (Corwin and Lesch,2003), to assess soil salinity across individual fields. However, even these types of methods are
too time-consuming to be applied cost-effectively at larger scales, i.e., at regional scales (Lobel
et al., 2010). For this reason, quicker and cheaper methods and tools are required to assess soil
salinity for decision-making needs.

396

Mathematical models that can consider various soil, climate, and crop factors have beensuggested as useful tools for evaluating the optimum management strategies for saline conditions(Ramos et al., 2011; Rasouli et al., 2012). A variety of analytical and numerical models havebeen developed during the past several decades to predict water and solute transfer processes
between the soil surface and groundwater table. The HYDRUS-1D software package (Šimůnek
et al. 2008) is one of such models simulating water movement and solute transport in the soil.
The objective of this study is to use HYDRUS-1D to analyze water flow and solute transport insoil columns irrigated with waters of different quality at different leaching rates, and to assess its
applicability for practical applications.
2. Material and Methods
2.1. Experimental Conditions
The experiment was carried out on soil columns 115 cm long and 40 cm diameter constructedfrom plastic pipes obtained by cutting 6 m long waste-water pipes. The soil columns were
installed as outdoor lysimeters at the experimental field of the Agricultural College of Ankara
University. The columns were filled with a sieved soil collected from the experimental field of
the Agricultural College. The texture of the soil was classified as Silt Clay Loam with 58% sand,
21% silt, and 21% clay. The CEC (Cation Exchange Capacity) of the soil was 177.2 mmolc kg-1.
Each column was equipped with TDR (Soil Moisture, TRACE) probes at four different depths(15, 35, 50, and 75 cm).
Large pots were placed below the bottom of the columns to collect drainage water after eachirrigation application. Drainage waters and soil samples collected monthly during the irrigation
period were analyzed for salt contents and individual components, i.e., EC, pH, Na+, K+, Ca2+,
Mg2+, Cl-, SO42-, CO32-, HCO3-, NO2-, NO3-, NH4+. Soil samples were taken at five different soil
depths (20, 40, 60, 80, and 100 cm). The study was carried out on 36 soil columns using threeirrigation water salinities (0.25, 1.5, and 3 dS m-1; denoted below as treatments T1, T2, and T3)
with NaCl and CaCl2 salts, four leaching rates (10, 20, 35, and 50% more water than required;denoted below as treatments Y1, Y2, Y3, and Y4), and three replicates in fully randomized,
experimental design.
The soil was first irrigated at the seeding time of alfalfa (i.e., the soil was at the field capacity).
Volumes of applied irrigation water and water drained from the bottom of the columns during
each irrigation event were measured so that actual evapotranspiration of the crop could beobtained for each treatment. Actual evapotranspiration was calculated from the difference
between irrigation and drainage depths. During a given time interval, the water balance is:
ET = I + P − D − ∆S(1)where (all values are cumulative during a particular time interval) ET is evapotranspiration (cm),
I is irrigation (cm), P is precipitation (cm), D is drainage (cm), and ΔS is the change in storedsoil water (cm).

397

The experiments were conducted in the first year (2010) between May 1st and October 8th and in
the second year (2011) between May 1st and October 13th. Irrigation times, amounts of appliedand drainage waters, and the soil sampling dates are given in Table 1.
The amounts of irrigation water were calculated for the non-saline treatments and fromgravimetrically measured soil water contents and TDR measurements. Total amounts of drainage
water were measured during the experiments as well so that leaching fractions (LF) could be
calculated. Leaching fractions were calculated using the formula below (Ayers and Westcot,
1985):LF =Drainage Water Amount*100
Irrigation Water Amount(2)

Table 1. Irrigation and drainage water amounts (average of T1 - non-saline treatments), application times,
and soil sampling dates for both the first (2010) and second (2011) year experiments.
1

2

Irrig. time (Julian day)Irrigation water (L)Drainage water (L)Soil sampling

18
12,88
2,07
June 1

38
12,88
1,63
July 2Irrig. time (Julian day)Irrigation water (L)Drainage water (L)Soil sampling

67
28,33
5,00
June 27

86
28,33
4,85
July 28

3

4
2010

49
67
12,88
25,25
1,63
5,49
Aug 2
Sept 1
2011
100
117
30,9
30,9
5,09
4,88
Aug 30 Sept 30

5

6

7

8

9

79
25,25
4,52
Oct 4

96
30,9
7,3

110
30,9
5,91

127
30,9
5,51

143
30,9
1,76

131
25,75
4,64

149
25,75
4,30

2.2. Model Description
The HYDRUS-1D program numerically solves the Richards equation for variably-saturated
water flow and the convection-dispersion equation for heat and solute transport. The flow
equation incorporates a sink term to account for water uptake by plant roots. The heat transport
equation considers transport due to conduction and convection with flowing water. The solutetransport equations consider convective-dispersive transport in the liquid phase, as well as
diffusion in the gaseous phase. The transport equations also include provisions for nonlinear andnon-equilibrium reactions between the solid and liquid phases, linear equilibrium reactions
between the liquid and gaseous phases, zero-order production, and two first-order degradation
reactions: one which is independent of other solutes, and one which provides the coupling
between solutes involved in sequential, first-order decay reactions. In addition, physical nonequilibrium solute transport can be accounted for by assuming a two-region, dual-porosity type
formulation which partitions the liquid phase into mobile and immobile regions.
Attachment/detachment theory, including the filtration theory, is included to simulate transportof viruses, colloids, and/or bacteria.
The program may be used to analyze water and solute movement in unsaturated, partiallysaturated, or fully saturated porous media. The soil profile itself may be composed of different

398

soil layers. The water flow part of the model can deal with prescribed head and flux boundaries,
boundaries controlled by atmospheric conditions, and free drainage boundary conditions.
The UnsatChem module (Šimůnek and Suarez, 1994) of the HYDRUS-1D software package(Šimůnek et al., 2008), simulating the major ion chemistry/transport and carbon dioxide transport, isused in this study.
2.3. Statistical Analysis
In addition to a visual check, field measured values were compared with the results of the
HYDRUS-1D simulations using the mean absolute error (MAE), the root mean square error(RMSE), and the relative error (RE). Which are defined as follows;
=
MAE

1 N
∑ Oi − Pi
N i =1(3)N

RMSE =∑ O −P
i =1

i

N −1
RMSE
RE =
Obsavgi(4)(5)

where Oi and Pi are observed and model-predicted values in units of a particular variable, N is
the number of observations, and Obsavg is the mean observed value. In general, RMSE ≥ MAE.
The degree to which the RMSE value exceeds MAE is usually a good indicator of the presence
and extent of outliers, or the variance of the differences between the modeled and observed
values (Legates and McCabe, 1999; Kobayashi and Salam, 2000). RE was used to evaluate thequality of the RMSE value. The simulation is considered to be excellent when a relative error isless than 10%, good if it is greater than 10% and less than 20%, fair if it is greater than 20% andless than 30%, and poor if it is greater than 30% (Loague and Green, 1991).
3. Results and Discussion
The HYDRUS-1D simulations were carried out for two experimental years of 2010 and 2011. A
simulation time period started on May 1st of both 2010 and 2011 and ended on October 8th and13th, 2010 and 2011, respectively, which corresponded to the irrigation period of alfalfa inrelation with the climatological factors. Nine and six irrigations were applied during the first andsecond year, respectively. The leaching fractions, calculated (Eq. 2) using the ratio between
irrigation and drainage water amounts, were 12, 17, 20, and 22 % in 2010, and 8, 16, 23, and 28% in 2011, experimental years for Y1, Y2, Y3, and Y4 treatments, respectively.
The main physical and chemical parameters of the soil are given in Table 2. The solution
concentrations of irrigation waters are given in Table 3.

399

The soil was sandy clay loam (SCL) with a water holding capacity of 74.4 mm m-1, and a bulk
soil density of 1.31 g cm-3. At the beginning of the experiment, pH and the EC of the saturation
extract were 8.18 and 0.816 dS cm-1, respectively. CEC and exchangeable cations were measured
in the laboratory on soil samples. CEC was 177.15 mmolckg-1, and the exchangeable cations
were Ca2+=125.85, Mg2+=41.35, Na+=4.85, and K+=4 mmolckg-1. Actual crop ET and the total
annual rainfall were 1595.7 and 136.7 mm in 2010, respectively, and 1124.1 mm and 189.4 mm
in 2011, respectively.
Table 2. Physical and chemical soil characteristics (initial conditions).
Sand (%)
Silt (%)
Clay (%)
TextureBulk density (g cm-3)
EC (dS m-1)
Soluble cations (mmolc L-1)
Ca2+
Mg2+
Na+
K+
Alk
SO42Cl-

58
21
21
SCL
1.31
0.816

SAR ((mmolc L-1)0.5)
Soil hydraulic parameters
Ks (cm day-1)
α (cm-1)
n

4.9
2.265
1.48
0.275
4.595
3.045
1.28

Exc. cations (mmolc kg-1)
Ca2+
Mg2+
Na+
K+
CEC (mmolc kg-1)
Actual average ET (cm day-1)
Total rainfall (cm)

0.78
31.44
0.059
1.48
0.1
0.39

θr
θs

125.8541.35
4.85
4177.150.985 (2010), 0.667 (2011)13.67 (2010), 18.94 (2011)

Table 3. Ion contents of irrigation waters used in the experiments (mmolc L-1).
Water 1 (T1)
Water 2 (T2)
Water 3 (T3)

Ca2+
0.7
13.24
26.12

Mg2+
1.14
0.56
0.57

Na+
0.43
1.94
3.56

K+
0.07
0.04
0.05

Alk
1.6
1.9
1.9

SO420.24
0.35
0.37

Cl0.5013.08
27.74

Tracer0
00Simulation results were evaluated against measured data using several statistical measures (eqs.
3, 4, and 5), providing information about how well the model approximated collected
experimental data. The results of the statistical analysis are given in Table 4. The statisticalmeasures are given for each depth (20, 40, 60, 80, and 100 cm), as well as for the entire soil
profile, as an average over the entire experimental year (2010 and 2011).
In general, the MAE and RMSE values increased and RE values decreased with the increasing
soil depth. Also, almost in all experiments, the soil salt and ion concentrations increased withdepth. As an example, the measured and simulated values of the soil Cl- and EC, with depths ofthe soil profile for both years and for the T2Y4 and T3Y4 treatments, are shown in Figure 1.

400

Table 4. Results of the statistical analysis.
Depth

0

20

MAE
RMSE
RE
MAE
RMSE
RE

1.75
2.50
1.58

3.01
4.07
0.85

MAE
RMSE
RE
MAE
RMSE
RE

0.94
1.26
1.74

1.72
2.15
0.60

MAE
RMSE
RE
MAE
RMSE
RE

10.90
17.18
1.29

15.11
19.00
0.90

MAE
RMSE
RE
MAE
RMSE
RE

1.97
2.49
3.29

8.60
12.24
1.14

MAE
RMSE
RE
MAE
RMSE
RE

3.00
3.89
1.97

10.67
15.03
0.98

MAE
RMSE
RE
MAE
RMSE
RE

0.87
1.10
3.42

13.92
24.09
1.62

MAE
RMSE
RE
MAE
RMSE
RE

15.54
23.03
1.67

12.87
18.95
1.16

2010
40
60
EC (dS m-1)
2.33
2.65
2.76
3.24
0.72
0.73
2.67
3.73
0.85
SAR
1.46
1.47
1.72
1.80
0.44
0.42
1.75
2.22
0.56
Ca2+
11.46 12.08
13.67 14.30
0.87
0.78
12.82
16.20
0.88
Mg2+
6.74
8.06
8.18
9.43
0.93
0.95
7.74
9.94
1.09
Na+
9.16 10.93
11.09 12.60
0.79
0.78
11.56
14.97
0.96
SO428.83 11.25
12.42 15.55
1.27
1.26
11.95
18.03
1.41
Cl10.20 7.03
15.41 9.85
1.20
0.66
10.95
17.03
1.02

80

100

Depth

0

20

3.48
3.93
0.75

4.61
5.21
0.82

MAE
RMSE
RE
MAE
RMSE
RE

0.96
1.36
0.86

1.45
1.64
0.55

2.33
2.66
0.49

2.60
3.18
0.56

MAE
RMSE
RE
MAE
RMSE
RE

1.03
1.54
2.12

1.36
1.65
1.02

12.67
14.95
0.75

14.62
17.39
0.77

MAE
RMSE
RE
MAE
RMSE
RE

7.35
10.83
0.81

8.38
10.88
0.68

9.49
10.58
0.95

11.65
13.03
0.97

MAE
RMSE
RE
MAE
RMSE
RE

0.93
1.26
1.66

2.62
3.46
0.93

16.09
17.60
0.82

19.51
22.63
0.91

MAE
RMSE
RE
MAE
RMSE
RE

1.33
1.77
0.89

2.39
2.79
0.55

15.85
19.77
1.15

20.95
24.14
1.08

MAE
RMSE
RE
MAE
RMSE
RE

0.93
1.60
4.99

3.24
4.25
1.07

8.25
12.89
0.70

11.79
18.72
0.79

MAE
RMSE
RE
MAE
RMSE
RE

9.09
13.15
0.95

6.91
9.19
0.56

401

2011
40
60
EC (dS m-1)
1.72
1.77
2.04
1.99
0.68
0.61
2.05
2.68
0.77
SAR
1.35
1.54
1.65
1.88
0.83
0.90
1.30
1.63
0.76
Ca2+
9.34
9.52
12.85 11.67
1.02
0.82
8.47
11.60
0.81
Mg2+
3.20
4.35
3.71
5.05
0.85
0.85
3.68
4.85
1.00
Na+
2.11
2.91
2.87
3.88
0.50
0.57
3.29
4.82
0.71
SO423.26
3.56
4.71
4.65
1.10
1.06
3.49
5.80
1.38
Cl9.608.67
14.25 11.81
1.00
0.69
8.47
12.02
0.70

80

100

2.77
3.35
0.73

3.61
4.38
0.80

1.24
1.45
0.47

1.30
1.58
0.46

8.06
12.32
0.85

8.19
10.91
0.70

5.40
6.36
0.90

5.60
6.90
0.96

4.71
6.30
0.64

6.30
8.11
0.72

4.77
9.52
1.58

5.15
6.85
1.09

7.99
10.37
0.52

8.53
12.65
0.59

Figure 1. Measured (M) and simulated (S) Cl and soil EC values for both experimental years(2010 an 2011) and for the T2Y4 and T3Y4 treatments.

402

The RMSE values for all treatments and for different soil depths varied for EC (dS m-1) between
2.50-5.21 and 1.36-4.38 and for SAR between 1.26-3.18 and 1.45-1.88 during the first (2010) andsecond (2011) experimental year, respectively. The RMSE values for ions Ca2+, Mg2+, Na+,SO42-, and Cl- were between 0.50-24.14 in 2010, and 0.28-14.25 in 2011.
4. Conclusions
The results showed that HYDRUS-1D was able to successfully simulate soil water salinity andmovement of salts (ions) in the soil profile. The model described better scenarios with lower
values of salt concentrations (EC). Similar results were obtained for individual ion
concentrations. The same results were reported by other researchers (e.g., Gonçalves et al., 2006;
Ramos et al., 2011). HYDRUS-1D proved to be a powerful tool for analyzing soluteconcentrations related to overall soil salinity.
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404

Proceedings of the 4th International Conference HYDRUS Software Applications to
Subsurface Flow and Contaminant Transport Problems
Edited by J. Šimůnek, M. Th van Genuchten, and R. Kodešová
Czech University of Life Sciences Prague
Faculty of Agrobiology, Food and Natural Resources
Department of Soil Science and Soil Protection
Czech Republic
CD Proceedings
50
404 pages
First Printing
2013
ISBN: 978-80-213-2380-3