Published June 24, 2016

Review and Analysis

Recent Developments andApplications of the HYDRUS
Computer Software PackagesJiří Šimůnek,* Martinus Th. van Genuchten,
and Miroslav Šejna
Core Ideas• Review of selected capabilities of
HYDRUS implemented since 2008
• New standard and nonstandard
specialized add-on modules significantly expanded capabilities of thesoftware• Review of selected applications of
the HYDRUS models published in VZJ
and elsewhere in recent years

The HYDRUS-1D and HYDRUS (2D/3D) computer software packages arewidely used finite-element models for simulating the one- and two- or
three-dimensional movement of water, heat, and multiple solutes in variably
saturated media, respectively. In 2008, Šimůnek et al. (2008b) describedthe entire history of the development of the various HYDRUS programs
and related models and tools such as STANMOD, RETC, ROSETTA, UNSODA,UNSATCHEM, HP1, and others. The objective of this manuscript is to review
selected capabilities of HYDRUS that have been implemented since 2008.
Our review is not limited to listing additional processes that were implemented in the standard computational modules, but also describes many
new standard and nonstandard specialized add-on modules that significantly expanded the capabilities of the two software packages. We also
review additional capabilities that have been incorporated into the graphical user interface (GUI) that supports the use of HYDRUS (2D/3D). Anotherobjective of this manuscript is to review selected applications of the HYDRUS
models such as evaluation of various irrigation schemes, evaluation of theeffects of plant water uptake on groundwater recharge, assessing the transport of particle-like substances in the subsurface, and using the models in
conjunction with various geophysical methods.
Abbreviations: CRS, cosmic-ray sensing; EC, electrical conductivity; ERT, electrical resistivity tomography; FEM, finite element mesh; GPR, ground-penetrating radar; GUI,graphical user interface; TDT, time-domain transmissometry.

The HYDRUS-1D and HYDRUS (2D/3D) software packages (Šimůnek etJ. Šimůnek, Dep. of Environmental
Sciences, Univ. of California, Riverside,
CA 92521, USA; M. Th. van Genuchten, Dep. of Mechanical Engineering,Federal Univ. of Rio de Janeiro, UFRJ,
Brazil and Dep. of Earth Sciences,
Utrecht Univ., the Netherlands; M.
Šejna, PC-Progress, Ltd., Prague,
Czech Republic.
*Corresponding
author (Jiri.Simunek@ucr.edu).

Vadose Zone J.
doi:10.2136/vzj2016.04.0033
Received 21 Apr. 2016.
Accepted 25 May 2016.
Open access.

© Soil Science Society of America.
This is an open access article distributed
under the CC BY-NC-ND license(http://creativecommons.org/licenses/
by-nc-nd/4.0/).

al., 2008b) are finite-element models for simulating the one- and two- or three-dimensional
movement of water, heat, and multiple solutes in variably saturated media, respectively. The
standard versions, as well as various specialized add-on modules, of the HYDRUS programs
numerically solve the Richards equation for saturated–unsaturated water flow and convection–dispersion type equations for heat and solute transport. The flow equation incorporates
a sink term to account for water uptake by plant roots as a function of water and salinity stress.
Both compensated and uncompensated water uptake by roots can be considered. The heattransport equation considers movement by both conduction and convection with flowing
water. The governing convection–dispersion solute transport equations are written in a relatively general form by including provisions for nonlinear, nonequilibrium reactions between
the solid and liquid phases and linear equilibrium reactions between the liquid and gaseous
phases. The transport models also account for convection and dispersion in the liquid phaseas well as diffusion in the gas phase, thus permitting the models to simulate solute transport
simultaneously in both the liquid and gaseous phases. Hence, both adsorbed and volatilesolutes, such as pesticides and fumigants, can be considered.

The solute transport equations further incorporate the effects of zero-order production,
first-order degradation independent of other solutes, and first-order decay and production
reactions that provide coupling between solutes involved in sequential first-order chain
reactions. Typical examples of such first-order degradation chains involve radionuclides,
various N species, pesticides, and many organic pollutants. Physical nonequilibrium

Vadose Zone Journal | Advancing Critical Zone Sciencesolute transport can be accounted for by assuming a two-region,
dual-porosity type formulation that partitions the liquid phase
into mobile and immobile regions. Attachment and detachment
processes and related filtration provisions are further included
to simulate the transport of viruses, colloids, bacteria, nanoparticles, and nanotubes. Many specialized modules, to be described
below, have been developed for both HYDRUS-1D and HYDRUS(2D/3D) to account for processes that cannot be handled by thestandard computational modules.

1). Version 4 substantially enhanced the capabilities of the modelcompared with Version 3. Version 4.01 additionally consideredvapor flow and the fully coupled transport of water, vapor, andenergy (Saito et al., 2006); an option to evaluate potential evapotranspiration using the Penman–Monteith combination equation(FAO, 1990) or the Hargreaves equation (Hargreaves, 1994); an
option to generate intraday variations in the evaporation and transpiration rates from their daily values; and full graphical support
for the HP1 program (Jacques et al., 2008a,b).

In 2008, Šimůnek et al. (2008b) reviewed the early history of the
HYDRUS and STANMOD software packages and related programs and modeling tools such as RETC, ROSETTA, UNSODA,UNSATCHEM, and HP1. Since then, several other HYDRUSrelated reviews appeared mostly focusing on a particular version
or type of application. For example, Šimůnek et al. (2012b) andvan Genuchten et al. (2012) reviewed the issues of calibrationand validation of the HYDRUS and STANMOD software packages, respectively, while Šimůnek et al. (2013a) reviewed various
specialized add-on modules (e.g., C-Ride, DualPerm, Fumigant,and UnsatChem) developed for HYDRUS (2D/3D). The main
objective of this paper is to review various new capabilities of the
HYDRUS programs that have been implemented since 2008. We
believe that such a review would be beneficial for the HYDRUS
community, which has grown dramatically during the past several
years. An additional objective is to review major types of applications of the different HYDRUS models and applicable add-ons
and to briefly discuss future plans and directions.

A detailed description of additional modifications and the different new options available in various HYDRUS-1D subversions(from 4.04 to 4.17) are given in Table 1. They include options to(i) evaluate tortuosity using the models of Moldrup et al. (1997,
2000) as an alternative to the Millington and Quirk (1961) model(Version 4.06), (ii) calculate soil surface temperatures and actual
evaporation fluxes for bare soils using the surface energy balance(Saito et al., 2006) (Version 4.07), (iii) provide support to the
HYDRUS package for MODFLOW (Twarakavi et al., 2008)(Version 4.07), (iv) consider both uncompensated and compensated root water uptake as well as both passive and active solute
uptake (Šimůnek and Hopmans, 2009) (Version 4.08), (v) use field
capacity as a possible initial condition using an equation suggested
by Twarakavi et al. (2009) (Version 4.16), (vi) trigger surface irrigation when a prescribed pressure head is reached at a specified depth(Dabach et al., 2013) (Version 4.16), and (vii) allow drainage fluxes
to horizontal drains to occur either through the bottom of the soil
profile or through a vertically distributed region in the saturated
zone (Version 4.17).

66HYDRUS Developments

since 2008

In the text below, we use various terms such as software package,code, model, module, and program. Although at times we will
use these terms interchangeably, we attempt to use them as follows. Under the terms model and module, we understand boththe conceptual and mathematical description of the problem aswell as its numerical implementation into a computer program.
The term model is a broader term in that it includes not only themain module (e.g., HYDRUS) but also multiple standard andnonstandard modules (e.g., UnsatChem or C-Ride). Under theterm program, we understand the numerical implementation of
the mathematical model into a computer language. And finally,
under the term software package, we understand a collection ofindividual files and resources (such as a GUI, help files, manuals,
computational modules, and test examples) that are put together
to provide certain functionality.

Standard Add-On Modules
Version 4 of HYDRUS-1D—similarly as Version 3—supports
two add-on modules simulating (i) carbon dioxide transportand production (Šimůnek and Suarez, 1993) and major ion reactions and transport (the UnsatChem module) (e.g., Šimůnek andSuarez, 1994), and (ii) the transport and general biogeochemical reactions between many different ions (the HP1 module)(Jacques et al., 2008a,b). More details about the HP1 module are
given below. Additionally, Version 4 of HYDRUS-1D supports
an add-on module simulating water flow and solute transport
in dual-permeability porous media (Gerke and van Genuchten,1993). This module, contrary to two other add-on modules (i.e.,
UnsatChem and HP1), can be run in both direct and inverse (calibration) mode. However, external optimization tools are required
to run UnsatChem and HP1 in the inverse mode (e.g., Jacques etal., 2012). While several applications of the UnsatChem and HP1
modules are described below, an overview of applications of the
DualPerm module were given by Köhne et al. (2009a,b)..

HYDRUS-1D

Nonstandard Modules

A major development with respect to HYDRUS-1D occurred in2008 when Version 4 (Šimůnek et al., 2008a) was released (Table

In addition to the standard HYDRUS-1D add-on modules, which
are fully supported by the HYDRUS-1D GUI and documented indetail in the HYDRUS-1D manuals and via online help, several

Main Module

VZJ | Advancing Critical Zone Sciencep. 2 of 25

Table 1. Selected new options implemented into HYDRUS-1D since 2008.
VersionNew options

4.01• Vapor flow (both thermal and isothermal)• Coupled water, vapor, and energy transport (thermal and isothermal, in the liquid and gaseous phases) (Saito et al., 2006)• Dual-permeability type water flow and solute transport (Gerke and van Genuchten, 1993)• Dual-porosity water flow and solute transport with solute transport subjected to two-site sorption in the mobile zone (Šimůnek and van
Genuchten, 2008)• Potential evapotranspiration calculated using the Penman–Monteith combination equation (FAO, 1990) or the Hargreaves equation(Hargreaves, 1994)• Seepage face boundary conditions with a specified pressure head
• Daily variations in evaporation and transpiration rates generated by HYDRUS from daily values• Full graphical user interface support for the HP1 program (Jacques et al., 2008a,b)

4.04• Option to specify the nonequilibrium phase concentrations to be initially at equilibrium with the equilibrium phase concentration• Option to specify initial conditions in total (instead of liquid) concentrations. The program then redistributes the solute mass into individual phases
based on distribution coefficients

4.05• Support for the dual-porosity (mobile–immobile water) model in HP1• Linking optimized parameters (which can be made the same) of different soil layers• Keeping a constant mobile water content in multiple layers (in the dual-porosity model) when optimizing the immobile water content

4.06• Tortuosity models by Moldrup et al. (1997, 2000) as an alternative to the Millington and Quirk (1961) model

4.07• Surface energy balance (i.e., the balance of latent, heat, and sensible fluxes) for bare soils (Saito et al., 2006)• Daily variations in meteorological variables can be generated by the model using simple meteorological models• Preliminary (at present rather simple) support of the HYDRUS package for MODFLOW (Twarakavi et al., 2008)

4.08• Uncompensated and compensated root water and solute (passive and active) uptake (Šimůnek and Hopmans, 2009)

4.12• Additional output (e.g., solute fluxes at observation nodes and profiles of various hydraulic conductivities [thermal and isothermal] and certain
fluxes [liquid, vapor, thermal, isothermal, and total])

4.13• New version (2.1.002) of HP1, a new graphical user interface supporting HP1• Automatic conversion of units for the threshold–slope salinity stress model from electric conductivities (dS m−1) to osmotic heads (m)4.15• Input of a sublimation constant and an initial snow layer• Conversion of constants (from electrical conductivity units to units of the osmotic potential) in the salinity stress response functions

4.16• Option to define field capacity as an initial condition (Twarakavi et al., 2009)• Display of wetting hydraulic functions for hysteretic soils• Triggered irrigation, that is, irrigation can be triggered when the pressure head at a particular observation node drops below a specified value(Dabach et al., 2013)• Interception can be considered with the standard HYDRUS input (without needing meteorological input)

4.17• Graphs for all meteorological/energy fluxes (when meteorological data are considered)• Drainage fluxes (to horizontal drains) can be either through the bottom of the soil profile or vertically distributed along the saturated zone.

additional nonstandard modules exist that can be freely downloaded from the HYDRUS website (http://www.pc-progress.com/
en/Default.aspx?h1d-library) together with many examples demonstrating their use as well as brief descriptions of the theories
behind the modules and their implementation. The nonstandard
computational modules significantly expand the capabilities ofthe HYDRUS-1D software. Although they can still be run fromthe standard HYDRUS-1D GUI, users are usually required tomanually provide an additional input file with supplementary
information needed for a particular module or to interpret selected
input and output variables differently from the standard versions.
Users may also need to prepare their own graphical output fromthe output text files. Six nonstandard computational modules havebeen developed so far. They pertain to centrifugal forces, freeze–
thaw processes, colloid-facilitated transport, colloid transport withtransient water contents, isotope transport, and root growth. The
nonstandard modules were developed mostly by ourselves, as well
as by various colleague as part of their research, and may become

VZJ | Advancing Critical Zone Sciencestandard HYDRUS modules in the future if sufficient interest
exists. They are briefly described below.
1. Centrifugal Forces: This nonstandard computational
module considers centrifugal forces in addition to gravitationand capillarity. Since this module can simulate, in both direct
and inverse modes, water flow and solute transport in atransient centrifugal field (Šimůnek and Nimmo, 2005), it canbe used to analyze data collected using high-speed centrifuges.
Note that high-speed centrifugal methods during the last few
decades have become relatively standard in many fields (suchas in soil physics, the petroleum industry, and environmental
and geotechnical engineering) for measuring saturated andunsaturated hydraulic conductivities or for studying various
flow and transport processes. Example applications of thismodule are given by Nakajima and Stadler (2006) and van den
Berg et al. (2009).
2. Freezing and Thawing: In addition to fully coupledtransport of water, vapor, and energy, this nonstandard module
considers the effects of freezing and thawing on water flow andp. 3 of 25

solute and heat transport processes (Hansson et al., 2004). The
module is not a standard in HYDRUS-1D since it runs only
for unsaturated soils and becomes unstable when the medium
reaches full saturation. The freezing and thawing module has
been used in studies by Watanabe et al. (2007) and Kurylyk and
Watanabe (2013).
3. Colloid-Facilitated Transport: This nonstandard computational module is essentially a one-dimensional versionof the C-Ride add-on module of HYDRUS (2D/3D). The
module considers particle transport and particle-facilitatedsolute transport (Šimůnek et al., 2006). The term particle isa general term used here for many substances having a relatively small but finite size (such as viruses, bacteria, pathogens,
nanoparticles, and nanotubes), the transport of which is usually described using a convection–dispersion type equation
with separate attachment, detachment, and straining terms.
Particle-facilitated solute transport (often referred to also as
colloid-facilitated transport when solutes are transported
sorbed to colloids) is often observed for many strongly sorbing contaminants such as heavy metals and radionuclides. This
computational module has been used by Pang and Šimůnek
(2006) among others.
4. Colloid Transport with Changing Water Contents:
This module can simulate particle transport, similarly as thestandard HYDRUS-1D computational modules, while additionally considering the effects of changes in the water content
on colloid and bacteria transport and attachment and detachment to or from solid–water and air–water interfaces (e.g.,Bradford et al., 2015). For example, when the air–water interface disappears during imbibition, particles residing on thisinterface are released into the liquid phase. Similarly, duringdrainage, particles residing at the solid–water interface may bedetached from this interface by capillary forces and released
into the liquid phase or become attached to the air–waterinterface.
5. Isotope Transport: This nonstandard module is a modified version of the standard solute transport formulationto account for isotope transport (Stumpp et al., 2012). The
module assumes that fractionation processes can be neglected
and that the relative concentration of isotopes (their d content)
does not increase at the upper boundary because of evaporation.
This is in contrast to the standard formulation during evaporation in HYDRUS-1D, where solutes concentrate at and near
the soil surface when water evaporates. Water and solutes in
the modified module will move at similar rates. The isotope
content taken up by roots during transpiration is then equal
to the soil solute concentration without having a fractionation
effect (Stumpp et al., 2012). This module has been successfully
used also by Stumpp and Hendry (2012), Huang et al. (2015),
and Sprenger et al. (2015).
6. Root Growth: This nonstandard computational module
can simulate root growth and its dependence on various environmental factors (Hartmann and Šimůnek, 2015). The root
growth module is based on approaches developed by Jones et

VZJ | Advancing Critical Zone Scienceal. (1991). The model assumes that various environmental factors, characterized by growth stress factors, can influence root
development under suboptimal conditions. Root growth andthe development of root-length density then depend on theseenvironmental factors when a stress factor approach is used. A
similar approach was implemented in the 2D part of HYDRUS(2D/3D) (Hartmann and Šimůnek, 2015).

HYDRUS (2D/3D)
A detailed list of recent developments, additional modifications,and new options in various versions (1.07 to 2.05) of HYDRUS(2D/3D) is given in Table 2. A major new release occurred in 2011
when Version 2 of HYDRUS (2D/3D) with its 3D-Professional
Level was made available. This version not only supports complex
general three-dimensional geometries that can be designed using
three-dimensional objects of general shapes but also includes
multiple specialized add-on modules that significantly expand
the number of processes that HYDRUS (2D/3D) can consider
and which were not available with the main standard module. The
add-on specialized modules (i.e., Fumigant, UnsatChem, Wetland,
DualPerm, C-Ride, Slope, and Slope Cube) are described below.

Main Computational Module
A number of special boundary conditions were implemented into
Version 2 of HYDRUS (2D/3D). These boundary conditions
include (i) a gradient bottom boundary condition (in addition to
the unit [free drainage] gradient boundary condition), (ii) a subsurface-drip boundary condition involving a drip characteristic
function that reduces irrigation fluxes based on the back pressure as described by Lazarovitch et al. (2005), (iii) a surface-drip
boundary condition with a dynamic wetting radius (Gärdenäs etal., 2005), (iv) a seepage-face boundary condition with a specified
pressure head (to accommodate a particular suction applied at thebottom of lysimeters), and (v) a triggered-irrigation boundary condition to allow irrigation to be triggered at a specified boundaryof the domain when the pressure head at a particular observation
node within the domain drops below a certain value (Dabach etal., 2013).
Two- and three-dimensional applications often require a large
number of finite elements to discretize large transport domains.
Even with powerful personal computers currently available, it isvirtually impossible to solve problems having more than about
half a million nodes within a reasonable computational time. To
decrease the required computational time, Hardelauf et al. (2007)
parallelized an earlier three-dimensional computational module of
HYDRUS (2D/3D), called SWMS_3D (Šimůnek et al., 2008b),
to obtain the ParSWMS code, which distributes problems with alarge number of elements over multiple processors working in parallel. While ParSWMS simulates water flow and solute transport
in 3D domains, it does not consider some of the advanced featuresof HYDRUS such as dual-porosity systems, hysteresis, and nonlinear and nonequilibrium solute transport. The ParSWMS programp. 4 of 25

Table 2. Selected options implemented into HYDRUS (2D/3D) since 2008.
Version
1.10
1.11
2.01

New options• Import of domain properties, initial, and boundary conditions from another project with a (slightly) different geometry or fine element mesh (both2D and 3D)• Tortuosity model by Moldrup et al. (1997, 2000) as an alternative to the Millington and Quirk (1961) model
Computational module:• Option to specify initial conditions in the total solute mass (previously only liquid phase concentrations could be specified); program thenredistributes the solute mass into separate phases based on distribution coefficients• Option to specify the nonequilibrium phase concentrations to be initially at equilibrium with the equilibrium phase concentrations• Gradient boundary conditions• Subsurface drip boundary conditions (with a drip characteristic function reducing irrigation flux based on the back pressure) (Lazarovitch et al.,2005)
• Surface drip boundary conditions with a dynamic wetting radius (Gärdenäs et al., 2005)• Seepage face boundary conditions with a specified pressure head
• Triggered irrigation, that is, irrigation can be triggered at a specified boundary when the pressure head at a particular observation node drops below acertain value (Dabach et al., 2013)• Time-variable internal pressure head or flux nodal sinks and sources (previously only constant internal sinks and sources were available)• Fluxes across mesh lines in the computational module for multiple solutes (previously only for a single solute)• HYDRUS calculates and reports surface runoff, evaporation, and infiltration fluxes for atmospheric boundary conditions• Water content dependence of solute reaction parameters using the Walker (1974) equation• Uncompensated and compensated root water and solute (passive and active) uptake (Šimůnek and Hopmans, 2009)• Option to consider a set of boundary condition records multiple times• Options related to the Fumigant transport module (e.g., removal of tarp, temperature dependent tarp properties, additional injection of a fumigant)• The UnsatChem module simulating transport of, and reactions between, major ions (Šimůnek and Suarez, 1994)• The new CWM1 constructed wetland module (Langergraber and Šimůnek, 2012)
Graphical user interface:• Support for complex general three-dimensional geometries (Professional Level)• Domain properties and initial and boundary conditions can be specified on Geometric Objects (defining the transport domain) rather than on thefinite element mesh
• Import of various quantities (e.g., domain properties and initial and boundary conditions) from another HYDRUS project even with a (slightly)
different geometry or fine element mesh
• Geometric objects can be imported using a variety of file formats (.TXT, .DXF, .SHP, …)• Display of results using isosurfaces• Support of ParSWMS (the parallelized version of SWMS_3D) (Hardelauf et al., 2007)

2.02• The DualPerm module simulating flow and transport in dual-permeability porous media (Gerke and van Genuchten, 1993)• The C-Ride module simulating particle transport and particle-facilitated solute transport (Šimůnek et al., 2006)• The HP2 module (coupled HYDRUS and PHREEQC) for simulating biogeochemical reactions• Option to use field capacity as an initial condition (Twarakavi et al., 2009)

2.03• Authorization of HYDRUS using a hardware key (HASP) in addition to a software key• Import of various quantities (such as the pressure head initial condition) from values defined at scattered points in the domain• Triggered irrigation (Dabach et al., 2013) was implemented into the UnsatChem module

2.04• The HYPAR module: a parallelized version of the standard two- and three-dimensional HYDRUS computational modules• The SLOPE module to analyze the stability of generally layered two-dimensional soil slopes, using HYDRUS-calculated water contents and pressure
heads

2.05

• The SLOPE CUBE (slope, stress, and stability) module for analysis of infiltration-induced landslide initiation and slope stability under variably
saturated soil conditions (Lu et al., 2010, 2012)

was developed for the LINUX or UNIX workstations using the
installed freeware MPI, PETSc, and PARMETIS. Hardelauf etal. (2007) demonstrated that an increase in the number of processors produces a proportional decrease in computational time.
Although the parallelized ParSWMS program cannot be run on
Windows-based PCs, since it requires LINUX or UNIX, its input
and output are fully supported by the HYDRUS GUI (Version 2).
An alternative to ParSWMS is the HYPAR module (acronymfor HYdrus PARallelized), which is a parallelized version of thestandard 2D and 3D HYDRUS computational modules. HYPAR
uses parallel programming tools to take advantage of new multicore and multiprocessor computers to significantly speed up

VZJ | Advancing Critical Zone Sciencetime-consuming simulations, especially those requiring a large
number of finite elements. HYPAR currently supports only calculations in a direct (forward) mode but not inverse (parameter
estimation) computations. HYPAR similarly does not support any
specialized add-on modules such as HP2, UnsatChem, Wetland,
and C-Ride.

Standard Add-On Modules
Several completely new specialized add-on modules have beendeveloped gradually for Version 2 of HYDRUS (2D/3D) toaccount for various processes not available in the standard software package. These new modules include the HP2, C-Ride,
DualPerm, UnsatChem, Wetland, and Fumigant modules. All
p. 5 of 25

of these modules simulate water flow and various solute transport processes in two-dimensional, variably saturated transportdomains and are fully supported by the HYDRUS GUI. Many ofthe processes included in these specialized modules of HYDRUS(2D/3D) are currently also available as part of HYDRUS-1D(described above).
1. The C-Ride Module: The C-Ride module simulates thetransport of particle-like substances (e.g., colloids, viruses,bacteria, and nanoparticles) as well as considers particlefacilitated solute transport (Šimůnek et al., 2006). Particlefacilitated transport is often observed for many strongly
sorbing contaminants such as heavy metals, radionuclides,
pharmaceuticals, pesticides, and explosives (see references inŠimůnek et al., 2006). These contaminants are predominantly
associated with the solid phase, which is commonly assumed to
be stationary. However, they may also sorb or attach to mobileand deposited (colloidal) particles such as microbes, humic
substances, suspended clay particles, and metal oxides, whichthen can act as pollutant carriers and hence provide a rapidtransport pathway for the pollutants. The C-Ride module
fully accounts for the dynamics of particles themselves (e.g.,
attachment and straining) as well as for solute transfer between
different phases such as kinetic or equilibrium sorption to thesoil phase and kinetic sorption to mobile or deposited colloids.
A schematic of the particle-facilitated solute transport model
as implemented into C-Ride is shown in Fig. 1.
2. The DualPerm Module: The DualPerm module simulates
preferential and nonequilibrium water flow and solute transport in dual-permeability media using the approach suggested
by Gerke and van Genuchten (1993). The module assumes thatthe porous medium consists of two interacting and overlapping regions: one associated with the interaggregate, macropore,or fracture system and one consisting of micropores (or intraaggregate pores) inside soil aggregates or within the soil or rockmatrix. Water flow can occur in both regions, albeit at different
rates. We note that this module cannot be applied to systems
involving discrete fracture and macropore networks. Modelingdetails are provided by Šimůnek and van Genuchten (2008).
Many applications of this HYDRUS (2D/3D) module, as well
as of the corresponding 1D module, are given by Köhne et al.
(2009a,b). Figure 2 shows an example for the infiltration ofwater from a tension disc infiltrometer (having a disc radius of
10 cm) into a 50-cm-wide and 150-cm-deep soil domain. Shownare calculated pressure head profiles in the matrix and fracturedomains for different ratios of the anisotropy hydraulic conductivity coefficients (i.e., K xA/KzA = 1, 10, and 0.1).
3. The UnsatChem Module: The geochemical UnsatChem
module has been implemented into all 1D, 2D, and 3D
HYDRUS versions. UnsatChem considers the transport ofmajor ions (i.e., Ca2+, Mg2+, Na+, K+, SO42−, CO32−, and Cl−)in conjunction with most or all relevant equilibrium and kinetic
geochemical reactions such as complexation, cation exchange,and precipitation and dissolution (e.g., of calcite, gypsum, anddolomite). Table 3 lists the various chemical species considered

VZJ | Advancing Critical Zone ScienceFig. 1. Schematic of the particle-facilitated solute transport module.
kac, attachment rate; kdc, detachment rate; kstr, straining rate; KD,
distribution coefficient; w, sorption rate; kaic, sorption rate constantto immobile particles; kdic, desorption rate constant to immobile
particles; kamc, sorption rate constant to mobile particles; kdmc,
desorption rate constant to mobile particles; other variables are
explained in the figure.

in UnsatChem. Possible applications of this module include
studies evaluating the sustainability of alternative irrigation
systems, salinization and reclamation of agricultural soils, andthe disposal of brine waters from mining operations (e.g., oiland gas production, shale fracking, or coal seam fracking). Ever
since its introduction some two decades ago (Šimůnek andSuarez, 1994), the Unsatchem module (especially its 1-D version) has been used widely in many applications (as describedin the Salinization and Sodification section).
4. The Wetland Module: The Wetland module simulates
aerobic, anoxic, and anaerobic transformation and degradation processes for organic matter, N, P, and S during treatmentof polluted wastewater in subsurface constructed wetlands(Langergraber and Šimůnek, 2012). Constructed wetlands areengineered water treatment systems that optimize the treatment processes taking place in natural environments. They
have become popular since they can be very efficient in treating
different types of polluted water using sustainable, environmentally friendly approaches. A large number of physical, chemical,
and biological processes are simultaneously active and may
mutually influence each other in constructed wetlands. The
Wetland module uses two biokinetic model formulations toaccount for complex conditions that may occur in various types
of wetlands: CW2D of Langergraber and Šimůnek (2005) for
aerobic and anoxic conditions and CWM1 of Langergraber
et al. (2009), which also considers anaerobic conditions. The
two Wetland modules were tested by Pálfy and Langergraber(2014) and Pálfy et al. (2015). Additional references of Wetland
module applications can be found at http://www.pc-progress.
com/en/Default.aspx?h3d2-wetland.
5. The Fumigant Module: The Fumigant module implements multiple additional options for simulating processes
related to the application and subsurface transport of fumigants,
which are not available in the standard HYDRUS models.
p. 6 of 25

Fig. 2. Pressure head profiles (cm) for(a) the matrix, (b) an isotropic fracture,
and anisotropic fractures with (c) KxA/KzA = 10 and (d) 0.1 (adapted fromŠimůnek et al., 2013a).

Table 3. Chemical species considered in the UnsatChem carbonate chemistry module.
Chemical species
1

Aqueous components

7

Ca 2+, Mg 2+, Na+, K+, SO 4 2−, Cl−, NO3−

2

Complexed species

10

CaCO3o, CaHCO3+, CaSO 4 o, MgCO3o, MgHCO3+, MgSO 4 o, NaCO3−, NaHCO3o, NaSO 4 −, KSO 4 −3Precipitated species

6

CaCO3, CaSO 4 ×2H2O, MgCO3 ×3H2O, Mg 5(CO3)4(OH)2×4H2O, Mg 2 Si3O7.5(OH)×3H2O, CaMg(CO3)2

4

Sorbed species

4

5

CO2–H2O species

7

Ca, Mg, Na, K
PCO2 , H2CO3*, CO32−, HCO3−, H+, OH−, H2O

6

Silica species

3

H4SiO 4 , H3SiO 4 −, H2 SiO 4 2−This module allows users to specify additional injections of
fumigants into the transport domain at a specific location at
a specific time as well as to consider the presence or absenceof a surface tarp, the temperature dependence of tarp properties, and the removal of tarp at a certain time. The Fumigant
module has been used recently to investigate the effects of different application scenarios (such as tarped broadcast, tarped
bedded shank injection, or tarped drip line-source application) and various factors (such as initial water content or tarp
permeability) on fumigant volatilization (Nelson et al., 2013;
Spurlock et al., 2013a,b). Figure 3 summarizes one example.
6. The Classic Slope Module: One frequent applicationof HYDRUS has been to obtain subsurface flow conditions(i.e., relative saturations and water fluxes) for subsequent slopestability analyses using other programs. This motivated us todevelop the Slope Stability (SLOPE) add-on module intended
mainly for stability tests of embankments, dams, earth cuts,
and anchored-sheeting structures. The influence of water
is modeled using the distribution of pore pressure, which isimported automatically from HYDRUS runs into the SLOPE
module at specified times, each of which can be analyzed separately. The slip surface in the SLOPE module is considered to be
circular and is evaluated using the Bishop, Fellenius–Petterson,
Morgenstern–Price, or Spencer method (Lu and Godt, 2013).
More details can be found in the user manual of this module.

VZJ | Advancing Critical Zone Science7. The Slope Cube Module: While the SLOPE module isbased on classical engineering soil mechanics theories and uses
the effective stress approach only for saturated conditions, a
new add-on module, SLOPE Cube (slope, stress, and stability) was recently developed to provide a unified effective stressapproach for both saturated and unsaturated conditions (Luet al., 2010). The module is intended to predict spatially andtemporally infiltration-induced landslide initiation and to carryout slope stability analyses under variably saturated soil conditions. Transient moisture and pressure-head fields are directly
obtained from the HYDRUS-2D model and subsequently used
to compute the effective stress field of hillslopes (Lu and Godt,2013). Furthermore, instead of the methodology of one-slopefor-one-factor safety in the classical slope stability analysis, the
SLOPE Cube module computes fields of the factor of safety
in the entire domain within hillslopes (Lu et al., 2012), thus
allowing identification of the development of potential failuresurface zones or surfaces.

Nonstandard Modules
As with HYDRUS-1D, several additional nonstandard computational HYDRUS (2D/3D) add-on modules were developedthat are not fully supported by HYDRUS (2D/3D) nor have they
been fully documented. These nonstandard add-on modules canagain be downloaded from the HYDRUS website (http://www.
pc-progress.com/en/Default.aspx?h3d-applications) together with
p. 7 of 25

Fig. 3. Tarped broadcast (left) and tarped bed (center) fumigation scenarios and calculated volatilization fluxes for different (broadcast, bed, and drip)
scenarios (adopted from Spurlock et al., 2013a).

many examples demonstrating their use and a brief description of
the theory behind the modules and their implementation. As with
HYDRUS-1D, the nonstandard computational modules can still
be run from the standard HYDRUS (2D/3D) GUI, but users areusually required to provide an additional input file with supplementary information needed by a particular module or to interpret
various input and output variables differently. Three such nonstandard computational add-on modules have been developed thus far:
1. Centrifugal Forces: This nonstandard computational
module deals with centrifugal forces in addition to gravitationaland capillary forces. In addition to considering processes in 2D
transport domains, this module has similar capabilities as thecorresponding HYDRUS-1D module (Šimůnek and Nimmo,2005) as explained above.
2. Overland Flow: The Overland Flow nonstandard module
can consider, in addition to subsurface flow and transport,
overland flow and transport processes. While the standard
HYDRUS modules assume that once the infiltration capacity
is exceeded, any excess water is instantaneously removed bysurface runoff, this module considers flow of this excess wateralong the soil surface. The module can account for overland
flow (runoff) once the soil infiltration capacity has beenreached, can redistribute water on the land surface by moving it
to lower parts of a hillside where the water could infiltrate if thelocal soil infiltration capacity has not been reached, or where it
can remain as runoff. While subsurface flow is still describedusing the Richards equation, overland flow is simulated using
the kinematic wave equation (Köhne et al., 2011).
3. Carbon Dioxide Transport and Production: This
nonstandard module extends the capabilities of the 2D
UnsatChem module discussed earlier. While the standard
version of UnsatChem assumes that the spatial distribution of
CO2 concentrations is constant in time (contrary to the 1D
UnsatChem model, which considers transient CO2 transport),
this specialized nonstandard module can also simulate CO2transport and production (Šimůnek and Suarez, 1993). The
module accounts for diffusion of CO2 in both liquid and gas
phases, CO2 production, and uptake of CO2 by plant roots.

VZJ | Advancing Critical Zone ScienceThe CO2 production model considers both microbial and root
respiration, which are dependent on water content, temperature,and plant and soil characteristics. The new module wasdeveloped so that it can be run using the HYDRUS (2D/3D)
graphical user interface, similarly as all other standard andnonstandard add-on modules.

The Graphical User Interfaceof HYDRUS (2D/3D)
Geometries in the Professional Levelof HYDRUS (2D/3D)
While the 3D-Layered Level of HYDRUS can support only layered geometries that are built above a two-dimensional base, the3D-Professional Level supports complex general three-dimensional
geometries that can be formed from three-dimensional objects(solids) having very general shapes. Three-dimensional objects areformed by boundary surfaces that can be both planar surfaces andcurved surfaces (quadrangles, rotaries, pipes, or B-splines). Figure
4 shows examples of various curved surfaces, while Fig. 5 shows
how these individual objects can be combined to form complex
3D geometries.

Domain Properties and Initial and Boundary
Conditions Specified on Geometric Objects
Various spatially variable properties (such as materials, initialconditions, boundary conditions, and domain properties) canbe specified in Version 2.0 of HYDRUS either directly on the
FEM, as done previously also in Version 1.0, or independently of
the FEM on geometric objects (e.g., boundary curves, rectangles,
circles, surfaces, solids) as shown in Fig. 6. The main advantage ofthe latter approach is that when the FEM is changed (e.g., whenconvergence is not achieved for a given FEM), these properties
are not automatically lost but can be reassigned immediately tothe new FEM from their initial definition on geometric objects.
Many other improvements were implemented into Version 2.0 of
HYDRUS (2D/3D) to make the program easier to use. Particularly
useful are options to (i) import domain properties and initial andp. 8 of 25

Fig. 4. Examples of curved
surfaces (rotary, pipe, B-spline,
and quadrangle surfaces).

Fig. 5. Transport domains formed using planar (left) or curved (center, right) surfaces.
Fig. 6. The transport domain
showing the assumed materials (left)
and boundary conditions (right) as
specified on Geometric Objects.

boundary conditions from existing HYDRUS projects even fromprojects with a (slightly) different geometry or FEM, (ii) importgeometric objects using a variety of formats (e.g., .TXT, .DXF,.SHP), and (iii) display results using isosurfaces. Table 2 lists several other options.

HP1 and HP2
The one-dimensional program HP1 (Jacques et al., 2008a,b),
which couples the PHREEQC geochemical program (Parkhurst
and Appelo, 1999) with HYDRUS-1D, has been used successfully in many applications since its release in 2005 (see HP1and HP2 Applications section below). The two-dimensional
extension, HP2, was released in 2013 as an add-on module to
HYDRUS (2D/3D) (Šimůnek et al., 2012a). HPx, which is anacronym for HYDRUS-PHREEQC-xD (1D or 2D), is a relatively

VZJ | Advancing Critical Zone Sciencecomprehensive simulation module that can be used to simulate(i) transient water flow, (ii) the transport of multiple components,(iii) mixed equilibrium and kinetic biogeochemical reactions, and(iv) heat transport in one- and two-dimensional variably saturated
porous media. The HP1 and HP2 modules are suitable for a broad
range of low-temperature biogeochemical reactions in water, thevadose zone, and ground water systems including interactions withminerals, gases, exchangers, and sorption surfaces based on thermodynamic equilibrium, kinetic, or mixed equilibrium–kinetic
reactions.
HP1 and HP2 both allow thermodynamic equilibrium calculations
for multiple chemical reactions and other features such as (i) aqueous speciation with different activity correction models (Davies,
extended Truesdell–Jones, B-Dot, Pitzer, and SIT-Specific Ion
p. 9 of 25

Interaction Theory), (ii) multisite ion exchange sites with exchange
described using different models (Gaines–Thomas, Vanselow, orGapon), (iii) multisite surface complexation sites with a nonelectrostatic, the Dzombak and Morel or CD_MUSIC models anddifferent options to calculate compositions of the diffuse double
layer, (iv) mineralogical assemblages, (v) solid–solutions, and (vi)gas exchange. Kinetic calculations can be used to describe mineraldissolution and precipitation, nonequilibrium sorption processes,
biogeochemical reactions including first-order degradation networks,
Monod kinetics, and Michaelis–Menten kinetics.
Recent additions to the capabilities of HP1 are (i) diffusion of components (e.g., O2 or CO2) in the gas phase and (ii) an option tochange the hydraulic and solute transport properties as a functionof evolving geochemical state variables. For example, precipitationand dissolution may lead to changes in porosity and corresponding changes in the soil water retention and hydraulic conductivity
functions. Similarly, bacterial growth and clogging can affectporosity and corresponding physical properties. HP1 makes it
possible to account for changes in (i) the porosity (and hence thesaturated water content), (ii) the hydraulic conductivity, (iii) a
scaling factor for the pressure head, (iv) aqueous- and gas-phasepore-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 require
any predefined conceptual or mathematical model to update theflow and transport parameters but rather uses the flexibility ofthe embedded BASIC interpreter for this purpose. This permits
software users to define any user-specific relationship between thegeochemical state variables and the transport properties (Jacqueset al., 2013).

The HYDRUS Package for MODFLOWThe HYDRUS Package for MODFLOW was developed by
Twarakavi et al. (2008) to account for water fluxes into andthrough the vadose zone in conjunction with the three-dimensional modular finite-difference ground water model MODFLOW(Harbaugh et al., 2000). The package for MODFLOW consistsof two submodels that interact in space and time (Fig. 7): (i) the

HYDRUS submodel for flow in the vadose zone and (ii) the
MODFLOW submodel for ground water flow. The HYDRUS
package considers all of the main processes and factors affecting
fluxes in the vadose zone as incorporated in HYDRUS-1D suchas precipitation, infiltration, evaporation, redistribution, capillaryrise, plant water uptake, water accumulation on the soil surface,surface runoff, and soil moisture storage. Being fully incorporated into the MODFLOW program, the HYDRUS package
provides MODFLOW with recharge fluxes into groundwater,while MODFLOW provides HYDRUS with the position of thegroundwater table that is used as the bottom boundary condition. The performance of the HYDRUS package was analyzed by
Twarakavi et al. (2008) for various case studies involving different
spatial and temporal scales. The package has been used in several
studies including Deme (2011) and Leterme et al. (2013).

66Selected HYDRUS

Applications

The different versions of HYDRUS models have been used over theyears for a large number of applications. We refer to the HYDRUS
web site (http://www.pc-progress.com/en/Default.aspx) for an
extensive list of various examples. The list currently contains
over 850 and 550 references of HYDRUS-1D and HYDRUS(2D/3D) applications, respectively. The types of applications arevery broad, ranging between agricultural problems evaluating different irrigation schemes, the effects of plants on the soil waterbalance and groundwater recharge (see Agricultural Applications
section below), to many environmental applications simulating
the transport of different solutes and particle-like substances (seeTransport of Particle-Like Substances section) as well as evaluating
the effects of land use and environmental changes. While many
early applications focused mostly on subsurface flow processes, therelatively general formulation of the transport and reaction terms
in the HYDRUS models makes it possible to simulate the fate
and transport of many different solutes including nonadsorbing
tracers, radionuclides (e.g., Pontedeiro et al., 2010; Matisoff et al.,2011; Merk, 2012; Xie et al., 2013), mineral N species (e.g., Li etFig. 7. Schematic of the HYDRUS package for MODFLOW.

VZJ | Advancing Critical Zone Sciencep. 10 of 25

al., 2015), pesticides (Pot et al., 2005; Dousset et al., 2007; Köhne
et al., 2009b), chlorinated aliphatic hydrocarbons (e.g., Kasaraneni
et al., 2014; Ngo et al., 2014), hormones (e.g., Casey et al., 2005;
Arnon et al., 2008; Chen et al., 2013), antibiotics (e.g., Wehrhan
et al., 2007; Unold et al., 2009; Chu et al., 2013; Engelhardt et al.,2015), explosives and propellants (e.g., Dontsova et al., 2006, 2009;
Alavi et al., 2011), as well as many particle-like substances such as
viruses, colloids, bacteria, nanoparticles, and carbon nanotubes(see Transport of Particle-Like Substances section).
An important advantage of the HYDRUS models is thatthey are not limited to any particular spatial or temporal scale.
HYDRUS-1D has been applied to scales involving very short laboratory soil columns, soil profiles of one to several meters deep (e.g.,
Ramos et al., 2011, 2012; Neto et al., 2016), as well as to soil profiles several hundred meters deep (Scanlon et al., 2003). HYDRUS(2D/3D) has been used similarly for transport domains ranging
from <1 m wide to transects of several tens or hundreds of meters
wide and for both laboratory (e.g., Rühle et al., 2013, 2015) andfield-scale applications (e.g., Yakirevitch et al., 2010; Pachepsky etal., 2014). Still, we do not recommend HYDRUS for very large
3D domains such as entire catchments (Šimůnek et al., 2012b).
Solutions of the Richards equation require relatively fine spatial
discretizations especially where and when large pressure gradients
may occur such as at and near the soil surface where variable climatological conditions may cause steep gradients in the pressure
head. Spatial discretizations of even a relatively small catchment
can quickly lead to a finite element mesh (FEM) containing millions of nodes, thus impacting available computational resources.
By comparison, no inherent limitations exist for the temporal scale,
which can be very short for small-scale laboratory flow studies tohundreds of thousands of years for studies evaluating the effectsof the past and current climate (e.g., Scanlon et al., 2003; Leterme
et al., 2012) or for long-term environmental risk analyses of radioactive contaminants (Pontedeiro et al., 2010) provided that thematerial properties, such as soil hydraulic and transport properties,
remain constant during the simulation.
A very common use of the HYDRUS models is for inverse estimation of soil hydraulic, solute transport, and heat transportparameters from measured steady-state or transient data. BothHYDRUS models implement a Marquardt–Levenberg-type
parameter estimation technique (Marquardt, 1963; Šimůnek
and Hopmans, 2002) in such a way that almost any applicationthat can be run in a direct mode (i.e., when all parameters andinitial and boundary conditions are specified and predictions aremade) can be run equally well in the inverse mode. Hence, themodels are effective for various model calibration and parameter
estimation applications (Šimůnek et al., 2012b). Because of its
generality, the inverse option in HYDRUS has proved to be very
popular with many users, leading to a large number of applications. Model calibration and inverse parameter estimation canbe performed with the HYDRUS software packages using either

VZJ | Advancing Critical Zone Science

a relatively simple, gradient-based, local-optimization approachbased on the Marquardt–Levenberg method, which is directly
implemented into the HYDRUS models, or more complex global
optimization methods (e.g., Vrugt, 2016), which need to be run
separately of HYDRUS. We refer readers to a recent review of various HYDRUS applications for model calibration and parameter
estimation by Šimůnek et al. (2012b).
It is beyond the scope of this paper to list all possible applicationsof the HYDRUS models. The breadth of applications is muchlarger than we expected when we initially started developing themodels some 25 yr ago. We briefly note here several different types
of applications that are not further discussed below. One is thehydrologic performance of green-roof systems using HYDRUS-1D(Hilten et al., 2008) or HYDRUS (2D/3D) (Palla et al., 2009;
Li and Babcock, 2015; Charpentier, 2015; Brunetti et al., 2016).
Water flow in highly heterogeneous waste rock piles was evaluated by Fala et al. (2005), Buczko and Gerke (2006), Dawood
and Aubertin (2014), and Namaghi et al. (2014). Abramson etal. (2014a,b) further used HYDRUS in a decision support system
to investigate the costs and benefits of groundwater access andabstraction for non-networked rural supplies. In yet other studies, Hassan et al. (2008), Finch et al. (2008), Sinclair et al. (2014),
and Morrissey et al. (2015) modeled effluent distributions andpossible groundwater pollution problems from on-site wastewater
treatment systems. We refer to the HYDRUS website for a more
complete list of applications.

Agricultural Applications
Agricultural applications of the HYDRUS modules often involve
evaluations of various irrigation schemes (e.g., Cote et al., 2003; BenGal et al., 2004; Gärdenäs et al., 2005; Dabach et al., 2013), studiesof root water uptake and groundwater recharge (e.g., Turkeltaub
et al., 2014; Neto et al., 2016), and the transport of agriculturalcontaminants (Wehrhan et al., 2007; Unold et al., 2009; Engelhardt
et al., 2015). For example, Gärdenäs et al. (2005) used HYDRUS(2D/3D) to evaluate water and N leaching scenarios for threedifferent microirrigation systems (surface and subsurface drip andsprinkler irrigation) and five different fertigation strategies. Siyal
et al. (2012) and Šimůnek et al. (2016) similarly used HYDRUS(2D/3D) to evaluate the effect of alternative fertigation strategies
and furrow surface treatments on plant water and N use. Li etal. (2014a, 2015) and Dash et al. (2015) used HYDRUS-1D toassess water flow processes and the N balance of a rice paddy field.
Others used the HYDRUS models to evaluate the effects of various
irrigation practices on soil salinization and sodification (e.g., Corwin
et al., 2007; Hanson et al., 2008; Ramos et al., 2011). In the section
below, we briefly review applications of the HYDRUS models todrip and furrow irrigation practices, irrigation and soil salinization
problems, and groundwater recharge. The examples are included
here to show the wide spectrum of applications that are possible with
the HYDRUS models. We again refer to the HYDRUS website formany other applications.
p. 11 of 25

Drip Irrigation
Modeling surface or subsurface drip irrigation has been a popularapplication of HYDRUS (2D/3D). Ever since Skaggs et al.
(2004) successfully compared HYDRUS-2D simulations of drip
irrigation with experimental observations, the model has beenfound helpful for evaluating soil water content patterns around
drip emitters. Using ISI’s Web of Science, we identified morethan 80 manuscripts (listed at http://www.pc-progress.com/en/
Default.aspx?h3d-references) in which HYDRUS (2D/3D) wasused to simulate drip and trickle irrigation. While the emittersin some studies were simulated as equivalent line sources (Skaggs
et al., 2004), other studies considered the emitters to be a point
source (Lazarovitch et al., 2009a; Kandelous and Šimůnek, 2010).
Kandelous et al. (2011) discussed under what conditions drip
emitters can be represented as a point source in an axisymmetrical
2D domain, a line source in a planar 2D domain, or a point source
in a fully 3D domain (Fig. 8). They concluded that an axisymmetric
2D representation could be used only before wetting patterns start
to overlap and a planar 2D model only after the wetting fronts
from neighboring emitters fully merged. Only a 3D model could
describe subsurface drip irrigation in its entirety.
HYDRUS has also been used to verify various analytical andempirical models for estimating the position of a wetting front
with time, which is useful for designing or operating drip irrigation systems (Cook et al., 2006; Warrick and Lazarovitch, 2007;
Lazarovitch et al., 2009a; Hinnell et al., 2010; Kandelous andŠimůnek, 2010). The effects of emitter rate, pulsing, and antecedent water content on water distribution patterns were studied by
Skaggs et al. (2010). Dabach et al. (2015) evaluated optimal tensiometer placement for high-frequency subsurface drip irrigation
management in heterogeneous soils. The effects of high-frequency
pulsing of drip irrigation in heterogeneous soils were also studied
by Assouline et al. (2006) and Mubarak et al. (2009).
Soil water and salinity distributions under different treatmentsof drip irrigation were simulated by Hanson et al. (2008, 2009),

Fig. 8. Water content distributions in a subsurface, drip-irrigatedsoil profile simulated as (A) a three-dimensional system with two
point sources, (B) a two-dimensional system with a line source, and(C) an axisymmetrical, two-dimensional system with a point source(modified from Kandelous et al., 2011).

VZJ | Advancing Critical Zone Science

Roberts et al. (2008, 2009), Shan and Wang (2012), Selim et al.
(2012, 2013), and Phogat et al. (2014), among others. Still others
used the HYDRUS models to evaluate N leaching for different
fertigation strategies using drip irrigation (Li et al., 2004, 2005;
Gärdenäs et al., 2005; Hanson et al., 2006; Ajdary et al., 2007).

Furrow Irrigation
The HYDRUS (2D/3D) software, and its predecessors such as
SWMS-2D and HYDRUS-2D, also has been used widely tosimulate water flow and solute transport in furrow irrigation
systems. We identified more than 25 papers addressing these topics(e.g., Benjamin et al., 1994; Abbasi et al., 2003a,b, 2004; Rocha
et al., 2006; Wöhling et al., 2004a,b, 2006; Mailhol et al., 2007;
Warrick et al., 2007; Wöhling and Schmitz, 2007; Wöhling and
Mailhol, 2007; Crevoisier et al., 2008; Lazarovitch et al., 2009b;
Ebrahimian et al., 2012, 2013a,b; Siyal et al., 2012; Zerihun etal., 2014; Šimůnek et al., 2016). A more complete list is given at
http://www.pc-progress.com/en/Default.aspx?h3d-references.
Still, we note that the HYDRUS models as such only consider
processes in the subsurface and not overland flow. Hence, whena two-dimensional soil profile perpendicular to the actual furrow
is considered, they cannot fully account for flow in the third
dimension such as the advance and recession of water in a furrow.
A full three-dimensional model that accounts for surface fluxes
in the furrow and subsurface flow processes is required to fully
describe complex three-dimensional furrow-irrigated systems(e.g., Wöhling et al., 2004b, 2006; Wöhling and Schmitz, 2007;
Wöhling and Mailhol, 2007; Zerihun et al., 2014).
A typical early application of HYDRUS-2D to furrow irrigation is given by Benjamin et al. (1994) who simulated fertilizer
distributions in the soil profile following broadcast fertilization
using conventional- and alternate-furrow irrigation. Abbasi etal. (2003a,b, 2004) in later studies obtained close agreement
between measured and predicted soil water contents and soluteconcentrations along a blocked-end furrow cross-section using
HYDRUS-2D. Mailhol et al. (2007) and Crevoisier et al. (2008)
similarly found good results with HYDRUS-2D when simulatingpressure heads, nitrate concentrations, and N leaching in seasonalstudies of conventional- and alternate -furrow irrigated systems
while including both root water and nutrient uptake. Rocha etal. (2006) further performed a sensitivity analysis to investigate
the effects of different soil hydraulic properties on flow processes
below furrows.
In related work, Wöhling and Schmitz (2007) developed a numerical program that coupled HYDRUS-2D with a 1D surface flow
and a crop growth model. Their code was used to predict advanceand recession times, soil water contents, and crop yield (Wöhlingand Mailhol 2007). Ebrahimian et al. (2012) subsequently usedthe HYDRUS-1D and HYDRUS-2D models to simulate waterflow and nitrate transport processes following conventionalfurrow irrigation, fixed alternate-furrow irrigation, and variable
p. 12 of 25

alternate-furrow irrigation using different fertigation strategies.
Ebrahimian et al. (2013a,b) similarly used the 1D surface and 2D
subsurface models to study scenarios that could minimize nitratelosses in two different alternate-furrow fertigation systems.
In a more recent study, Šimůnek et al. (2016) developed a furrowirrigation submodule for HYDRUS (2D/3D) (Fig. 9) to evaluate
the effects of furrow soil surface treatment and fertigation timing onroot water and solute uptake, deep drainage, and solute leaching ina loamy soil. Simulations showed that although more water was lostby evaporation in treatments with plastic placed along the furrow
bottom than in the control treatments, more water was available
for transpiration and less water was drained from the soil profile forthese treatments. While some of the above studies involved only simulations (e.g., Rocha et al., 2006; Warrick et al., 2007; Lazarovitch
et al., 2009b), several used HYDRUS (2D/3D) to calibrate and test
predictions against experimental data (e.g., Abbasi et al., 2003a,b,
2004; Wöhling and Mailhol 2007; Crevoisier et al., 2008; Zerihun
et al., 2014), thus providing confidence that the model can adequately describe these complex systems.

Salinization and Sodification
Saline waters are used often for irrigating agricultural crops inregions having limited water resources, thus potentially causing salinization and sodification of irrigated agricultural lands.
Efficient irrigation and leaching management practices are criticalin these regions to prevent or limit soil salinization when rainfall
is not sufficient to leach accumulated salts during or following
irrigation. The HYDRUS models have been used in several studies to evaluate the sustainability of various irrigation schemeswith respect to salinization and sodification processes, to assess
reclamation of saline or sodic soils, and to evaluate the movementof salts after the accidental release (or possible beneficial application) of saline waters resulting from mining operations (e.g.,
Jakubowski et al., 2014). Such problems can be addressed with
HYDRUS using two approaches. One would be to use the standard HYDRUS models by assuming that salinity behaves moreor less like an inert tracer and hence is now subject to chemical
reactions (e.g., Hanson et al., 2008; Dudley et al., 2008; Roberts
et al., 2009; Groenveld et al., 2013). An alternative is to use theUnsatChem module, which considers the transport and reactions between major ions (e.g., Gonçalves et al., 2006; Ramos etal., 2011). While the former approach does not permit such processes as cation exchange, dissolution of mineral amendments (e.g.,
gypsum or calcite), or precipitation of these minerals when the soil
solution becomes oversaturated; the latter approach allows one toconsider those geochemical processes and the effects of salts andsoil water quality on soil properties.
The UnsatChem modules (especially its 1D version) has beenused in many applications as exemplified by Kaledhonkar andKeshari (2006), Kaledhonkar et al. (2006, 2012), Schoups et al.
(2006), Skaggs et al. (2004), Corwin et al. (2007), and Rasouli
et al. (2013), among others. Gonçalves et al. (2006) and Ramos etal. (2011, 2012) demonstrated the applicability of these modules
to simulating multicomponent major ion transport in soil lysimeters irrigated with waters of different quality. While Gonçalves
et al. (2006) used the UnsatChem module of HYDRUS-1D (Fig.
10), Ramos et al. (2011) used both the standard HYDRUS-1Dand UnsatChem modules. Ramos et al. (2011) compared results
obtained with the two modules and discussed their respective
advantages and disadvantages. For example, the UnsatChem
module requires much more input information (e.g., the solution
composition of irrigation waters and Gapon exchange constants
for all soil horizons) and runs much slower (~20 times) than thestandard HYDRUS-1D model. While both HYDRUS-1D modules were used by Ramos et al. (2011) to describe field data of thewater content and overall salinity as expressed in terms of electricalconductivity (EC), the UnsatChem module was additionally used
to describe the concentrations of individual soluble cations as well
as of the Na adsorption ratio and the exchangeable Na percentage.
Whereas EC values were calculated using different methodologies(treated as a nonadsorbing tracer in the standard module and calculated from concentrations of individual ions in UnsatChem), thetwo modules produced very similar results during the irrigationseasons. The main differences were found when soil water contents
decreased significantly below field capacity, in which case the standard HYDRUS transport module simply increased EC linearly as
the soil dried out, while the UNSATCHEM module produced anonlinear increase in EC as a result of cation exchange (Ramos etFig. 9. Schematic of the transportdomain showing the main hydrologicalfluxes (left) and initial and boundary
conditions (right) of a furrow irrigation
system (modified from Šimůnek et al.,2016).

VZJ | Advancing Critical Zone Sciencep. 13 of 25

Fig. 10. Measured and simulated(using the UnsatChem module)
soluble Na concentrations (top) andNa adsorption ratios (SAR) at a depthof 10 cm for lysimeters irrigated withwaters of different quality (A, B, and
C). I, irrigation period; R, rainfall
period. Adapted from Gonçalves et al.
(2006).

al., 2011). Larger differences in EC values predicted with the twomodules would have been observed if the soil solution had become
oversaturated with respect to calcite and gypsum.
Important conclusions about the practical implications of salinity
management were obtained in several studies such as by Corwin
et al. (2007) and Hanson et al. (2008). Corwin et al. (2007) used
the UnsatChem module to demonstrate that leaching requirements would be lower when estimated with a transient modelingapproach than when using a more standard steady-state approach.
Adapting leaching requirements based on the transient approach
would produce significant savings in terms of irrigation water volumes. Hanson et al. (2008) showed that while the conventionalor water balance approach for estimating leaching fractions predicts little or no leaching when applied water levels are less thanpotential evapotranspiration, field data and HYDRUS modelingshowed considerable leaching around the drip lines. The spatiallyvarying soil wetting patterns that occur during drip irrigation
causes localized leaching near the drip lines (Hanson et al., 2008),
thus allowing for more profitable production of various crops (e.g.,
processing tomato [Solanum lycopersicum L.]) than with other irrigation methods.

Root Water and Nutrient Uptake
The HYDRUS models now include a relatively comprehensive
macroscopic root water and solute uptake module (Šimůnek andHopmans, 2009) to account for both water and salinity stresseffects on water uptake while also accounting for possible active
and passive root solute uptake. Root water and solute uptake

VZJ | Advancing Critical Zone Sciencefurthermore can be treated as being either noncompensated orcompensated.
HYDRUS-1D allows users to externally prescribe a timevariable rooting depth either using the logistic growth function
or in a tabulated form. Such a feature is currently not available
in HYDRUS (2D/3D), which forces the spatial distribution ofroots in the root zone to remain constant during the simulations.
Both models also do not allow the spatial extent of the rooting
zone to change actively as a result of environmental stresses. To
overcome these deficiencies, several studies either further modified
the HYDRUS models (or their predecessors such as CHAIN-2D
or SWMS-3D) or coupled the models with various crop-growthor root-growth models. For example, Javaux et al. (2008, 2013)
developed R-SWMS, a three-dimensional root-growth model that
couples the model of Somma et al. (1998) (based on SWMS-3D)
with the model of Doussan et al. (1998).
For these same reasons, Zhou et al. (2012) coupled HYDRUS-1D
with the WOFOST (Boogaard et al., 1998) crop-growth modeland used the resulting model to simulate the growth and yieldof irrigated wheat (Triticum aestivum L.) and maize (Zea mays
L.) (Li et al., 2012, 2014b). Han et al. (2015) similarly coupled
HYDRUS-1D with a simplified crop-growth version used in the
Soil and Water Assessment Tool (SWAT) to simulate the contribution and impact of groundwater on cotton (Gossypium hirsutumL.) growth and root zone water balance. Wang et al. (2014a,
2015b) coupled the crop-growth model EPIC (Williams et al.,1989) with CHAIN-2D and HYDRUS-1D to assess the effects
p. 14 of 25

of furrow and sprinkler irrigation, respectively, on crop growth.
Hartmann and Šimůnek (2015) furthermore implemented into
both HYDRUS-1D and HYDRUS (2D/3D) the root-growthmodel developed by Jones et al. (1991). Their model assumes thatvarious environmental factors as characterized by growth stress factors can influence root development under suboptimal conditions.

Transport of Particle-Like Substances
The governing convection–dispersion solute transport equations, as solved numerically in the HYDRUS models, allow
consideration of kinetic attachment and detachment processes ofparticle-like substances to the solid phase. The term particle-like
substance is used to represent colloids, viruses, pathogens, bacteria,
nanoparticles, nanotubes, and related constituents, whose subsurface transport is often modeled using the convection–dispersion
equation with certain attachment, detachment, and straining
terms. This approach is used widely even though the various constituents can have dramatically different shapes and sizes withsizes varying from nanometers to micrometers. Modeling theirtransport represents one of the most popular applications of the
HYDRUS models. We identified more than 80 manuscripts inwhich HYDRUS was used for simulating the transport of particlelike substances (see references at http://www.pc-progress.com/en/
Default.aspx?h1d-lib-bacteria).
The particle-transport option was used first by Schijven andŠimůnek (2002) to simulate the transport of viruses at the field
scale using both HYDRUS-1D and HYDRUS-2D. They modified the models by including two kinetic attachment–detachment
processes involving two different sorption sites and then used theprograms to simulate the removal of bacteriophages MS2 and
PRD1 by dune recharge and deep-well injection. Many others sincethen have used the HYDRUS models to simulate virus transport
in laboratory columns (e.g., Torkzaban et al., 2006a,b; Zhang et al.,2012; Frohnert et al., 2014) as well as field systems (e.g., Schijven
et al., 2013).
The HYDRUS models have been used similarly as tools tounderstand and predict various complexities of colloid andmicrobial transport in the subsurface under different conditions.
For example, Bradford et al. (2002, 2003, 2004) evaluatedthe effects of attachment, straining, and exclusion on the fate
and transport of colloids in saturated porous media. Gargiulo
et al. (2007a,b, 2008) evaluated the effects of such factors as
matrix grain size, water content, metabolic activity, and surface
proteins on bacterial transport and deposition in saturated andunsaturated media. Torkzaban et al. (2010) and Bradford et al.
(2012) additionally evaluated the effects of dynamic changes in thesolution ionic strength on the transport and release of colloids andmicroorganisms in soils. Bradford et al. (2015) further considered
the effects of changing water contents on E. coli D21g transport
and attachment and detachment to or from solid–water andair–water interfaces. We emphasize that at present a specialized

VZJ | Advancing Critical Zone Science

nonstandard HYDRUS-1D module must be used to consider theeffects of changes in solution chemistry and water contents on
the transport and release of colloids (see Nonstandard Modules
section)The HYDRUS models are increasingly being used also to simulate the fate and transport of various nanoparticles and nanotubes
in the environment. For example, Liang et al. (2013a,b), Ren andSmith (2013), Cornelis et al. (2013), Neukum et al. (2014), andWang et al. (2015a) evaluated the sensitivity of the transport andretention of stabilized silver nanoparticles to various physicochemical factors in column studies and undisturbed soil. Kasel
et al. (2013a,b) and Mekonen et al. (2014) evaluated the effects of
input concentration, grain size, and saturation on the transportof multiwalled carbon nanotubes. Such studies are important forproviding new knowledge about the processes affecting the environmental fate of particle like substances, which in turn allows us
to continuously update the HYDRUS models.

Applications Involving Geophysical Data
As discussed below (HYDRUS Applications Published in VZJ),
the HYDRUS models are often used (we identified 34 papers) instudies involving the use of various geophysical methods including
electrical resistivity tomography (ERT), ground-penetrating radar(GPR), cosmic-ray sensing (CRS), and electric magnetic resonance.
For example, electrical resistivity surveys and HYDRUS modelingwere used by Batlle-Aguilar et al. (2009) to investigate axisymmetrical infiltration patterns and by Lehmann et al. (2013) to observe
the evolution of soil wetting patterns preceding a hydrologicallyinduced landslide. A large number of studies involved the complementary use of HYDRUS modeling and GPR data (e.g., Laloy etal., 2012; Jadoon et al., 2012; Scholer et al., 2013; Moghadas et al.,2013; Busch et al., 2013; Léger et al., 2014; Tran et al., 2014) orcosmic-ray neutron probes (e.g., Franz et al., 2012; Bogena et al.,2013; Lv et al., 2014; Villarreyes et al., 2014). While the depth ofpenetration for GPR may be up to 10 to 15 m, its spatial extent
is quite limited. By comparison, CRS monitors water contents
mainly near the soil surface but over much larger areas. Although
CRS methods do not provide a horizontal or vertical resolution forsoil moisture, it averages water contents over tens of hectares andthus can provide very useful data for agriculture and hydrological models at the hectometer scale. Other studies using magnetic
resonance imaging and time-lapse electromagnetic induction are
given by Pohlmeier et al. (2009) and Robinson et al. (2012), respectively. Additional applications of HYDRUS, in conjunction withgeophysical methods, are discussed below.

Groundwater Recharge Applications
Historically, one of the most common applications (~40 papers)of the HYDRUS models have been to estimate subsurface water
fluxes and groundwater recharge and how these processes areaffected by soil surface and root zone conditions such as precipitation, evaporation, and the presence or absence of plants (e.g.,
p. 15 of 25

Scanlon et al., 2002, 2003; Garcia et al., 2011; Kurtzman and
Scanlon, 2011; Kodešová et al., 2014; Fan et al., 2015; Turkeltaub
et al., 2014; Dafny and Šimůnek, 2016; Neto et al., 2016). For
example, Dafny and Šimůnek (2016) showed that for the coastal
plain of Israel, groundwater recharge dramatically decreases as apercentage of precipitation from ~30% to ~10 and 1% for conditions with bare sandy loess and sandy loess with vegetative coversof 26 and 50%, respectively.
The impact of changing land use on groundwater recharge wasinvestigated in several other studies (e.g., Le Coz et al., 2013;
Ibrahim et al., 2014; Turkeltaub et al., 2014, 2015). Of these,
Le Coz et al. (2013) found an increase in groundwater recharge
because of changes from rainfed to irrigated cropping conditions
in a semiarid region. Turkeltaub et al. (2015) evaluated the impactof switching crop type on water and solute fluxes in deep vadosezones. Similarly, changes in groundwater recharge in response to
the expansion of rainfed cultivation in the Sahel, West Africa, were
evaluated by Ibrahim et al. (2014). Another related application is
to anticipate the sensitivity of groundwater recharge to changes
in climate in response to greenhouse effects (e.g., Leterme et al.,2012; Newcomer et al., 2014; Pfletschinger et al., 2014; Wineet al., 2015). Additional applications of HYDRUS for evaluating groundwater recharge are given below in the Groundwater
Recharge Applications section and on the HYDRUS website.

HP1 and HP2 Applications
The versatility of HP1 was demonstrated by Jacques et al. (2008a,b)
by means of several examples including (i) the transport of heavy
metals (Zn2+, Pb2+, and Cd2+) subject to multiple cation exchange
reactions, (ii) transport with mineral dissolution of amorphous
SiO2 and gibbsite [Al(OH)3], (iii) heavy-metal transport in a
porous medium having a pH-dependent cation exchange complex,(iv) infiltration of a hyperalkaline solution in a clay sample (thisexample considered kinetic precipitation or dissolution of kaolinite,
illite, quartz, calcite, dolomite, gypsum, hydrotalcite, and sepiolite),(v) long-term transient flow and transport of major cations (Na+,K+, Ca 2+, and Mg 2+) and heavy metals (Cd 2+, Zn2+, and Pb2+)
in a soil profile, (vi) cadmium leaching in acid sandy soils, (vii)radionuclide transport, and (viii) long-term uranium migration inagricultural field soils following mineral P fertilization.
More recent HP1 applications include evaluations of (i) laboratory
and field experiments involving the treatment of Hg-contaminatedsoils with activated C (Bessinger and Marks, 2010; Leterme et al.,2014), (ii) CO2 production and transport in bare and planted
mesocosms (Thaysen et al., 2014a), (iii) the effects of lime and concrete waste on vadose zone C cycling (Thaysen et al., 2014b), (iv)chemical degradation of concrete during leaching with rain anddifferent types of water (Jacques et al., 2010), and (v) the effects ofchemical degradation on the hydraulic properties of concrete suchas porosity, tortuosity, and the hydraulic conductivity (Jacques etal., 2013). Jacques et al. (2012) additionally combined HP1 with

VZJ | Advancing Critical Zone Science

the general optimization UCODE program (Poeter et al., 2005) toinversely optimize hydraulic, solute transport, and cation exchange
parameters pertaining to column experiments subject to transientwater flow and solute transport with cation exchange.
HP1 has recently been used also to solve a number of benchmark problems that were developed for model developers todemonstrate model conformance with norms established by thesubsurface science and engineering community (Steefel et al.,2015). These benchmarks involved (i) multirate surface complexation and 1D dual-domain multicomponent reactive transportof U(VI) (Greskowiak et al., 2015), (ii) generation of acidity asa result of sulfide oxidation and its subsequent effect on metal
mobility above and below the water table (Mayer et al., 2015), and(iii) implementation and evaluation of permeability–porosity andtortuosity–porosity relationships associated with mineral precipitation and dissolution processes (Xie et al., 2015).
The versatility of the two-dimensional HP2 was demonstrated
recently by Šimůnek et al. (2012b) on several examples: (i) sodic
soil reclamation using furrow irrigation to demonstrate the cationexchange features of HP2 and (ii) the release and migration of
uranium from a simplified uranium mill tailings pile toward ariver. These examples included the processes of water flow, solutetransport, precipitation and dissolution of the solid phase, cationexchange, complexation, and many other reactions.

Selected HYDRUS Applications Published in
Vadose Zone Journal in 2013 to 2015
Vadose Zone Journal (VZJ) has been a frequent outlet for
manuscripts documenting various HYDRUS applications.
HYDRUS-1D and HYDRUS (2D/3D) were used in over 100
and 50 VZJ papers, respectively. This means that almost 20% of
peer-reviewed journal articles using the HYDRUS models havebeen published in VZJ. This trend continued in recent years: 18,
14, and eight papers using HYDRUS appeared in VZJ in 2013,2014, and 2015, respectively. In the sections below, we provide an
overview of HYDRUS applications that have appeared in VZJ in
recent years and which partly mirror the main types of applications
discussed above.

Groundwater Recharge Applications
The largest number of HYDRUS papers in VZJ simulated subsurface water fluxes and groundwater recharge (e.g., Dickinson et al.,2014; Pfletschinger et al., 2014; Rieckh et al., 2014; Turkeltaub etal., 2014; Fan et al., 2015; and Guber et al., 2015). Of these, Guber
et al. (2015) used HYDRUS-2D to evaluate a new subsurface
water retention technology consisting of subsurface polyethylene
membranes installed within the soil profile to improve rootzone water storage and to limit downward recharge fluxes. Fanet al. (2015) used both HYDRUS-1D and HYDRUS (2D/3D)
to model the effects of plant canopy and roots on soil moistureand deep drainage in forested ecosystems. Dickinson et al. (2014)
p. 16 of 25

used HYDRUS-1D to verify the appropriateness of a proposed
screening tool for delineating areas with constant groundwater recharge. Turkeltaub et al. (2014) used data collected with adeep vadose zone monitoring system to calibrate HYDRUS-1Dand subsequently used the software to investigate the temporalcharacteristics of groundwater recharge and how recharge may beaffected by climate change. Similarly, Pfletschinger et al. (2014)
used HYDRUS-1D to evaluate the effects of climate shifts in arid
areas on groundwater recharge. Rieckh et al. (2014) further used
HYDRUS-1D to evaluate water and dissolved C fluxes in an eroding soil landscape and their dependence on terrain position, while
Le Coz et al. (2013) used HYDRUS-1D to evaluate how a change
from rainfed to irrigated cropping in a semiarid region will affectgroundwater recharge.

Applications Involving Geophysical Data
The second largest group of HYDRUS applications published in
VZJ comprised studies that use data collected with various geophysical methods (e.g., Montzka et al., 2013; Grunat et al., 2013;
Moghadas et al., 2013; Ganz et al., 2014; Thoma et al., 2014; Lv
et al., 2014; Dimitrov et al., 2014, 2015; and Persson et al., 2015).
For example, several issues related to data assimilation, which
involved both HYDRUS modeling and ERT or GPR were studied by Grunat et al. (2013), Moghadas et al. (2013), Ganz et al.
(2014), Thoma et al. (2014), and Persson et al. (2015). Of thesevarious studies, Persson et al. (2015) used HYDRUS-2D to simulate laboratory experiments involving dye movement in a glasstank. They successfully compared modeled horizontal velocities
with those obtained by image analysis and ERT. Experimental andnumerical results both showed that horizontal velocities in thecapillary fringe are more or less identical to those in the saturated
zone. Ganz et al. (2014) used HYDRUS-3D to simulate ponded
infiltration into a water-repellent sand and successfully compared
their numerical results with ERT observations. They discussed theimportance of considering hysteresis for water repellent soils. Lv etal. (2014) calibrated HYDRUS-1D using soil moisture measurements from a network of time-domain transmissometry (TDT)probes and then compared both measured and modeled water content values against cosmic-ray neutron probe estimates. Finally, aseries of papers by Dimitrov et al. (2014, 2015) and Montzka etal. (2013) used the HYDRUS-1D model to inversely derive soil
hydraulic parameters and surface soil water contents using L-band
brightness temperatures. All of these studies demonstrate how
numerical modeling of subsurface flow processes can be used to
optimize the analysis of geophysical data.

Wang et al. (2015a) evaluated the transport and retention of
polyvinylpyrrolidone-coated silver nanoparticles in natural soils.

Other HYDRUS Applications
Several other applications of the HYDRUS software packages
models have appeared in VZJ. Two such applications in 2015
focused on the effects of root water uptake on soil moisture dynamics and deep drainage or recharge. Fan et al. (2015) used both
HYDRUS-1D and HYDRUS (2D/3D) to model the effects ofspatial distributions of the plant canopy, rainfall, and roots on soil
moisture and deep drainage in a coastal sand dune forest of subtropical Australia. Périard et al. (2015) used HYDRUS (2D/3D)
to simulate root water uptake by romaine lettuce (Lactuca sativa
L.) and to evaluate the effect of moisture deficit on tip burn, aphysiological disorder that can lead to a complete loss of harvest.
A similar HYDRUS-1D study for evaporation was performed laterby Huang et al. (2013).
The HYDRUS models were further used in a large number ofstudies to inversely optimize various soil hydraulic and solutetransport parameters (Rühle et al., 2015; Qu et al., 2014; Lv et al.,2014; Caldwell et al., 2013; Schelle et al., 2013). Of these studies, Qu et al. (2014) used HYDRUS-1D to inversely estimate van
Genuchten (1980) soil hydraulic parameters from field soil watercontent measurements at multiple locations to evaluate the spatial variability of the soil water content. Lv et al. (2014) calibrated
HYDRUS-1D by optimizing soil hydraulic parameters using soil
moisture measurements from a network of TDT probes, while
Zhao et al. (2013) used the multistep outflow method to determine
the soil hydraulic properties of a frozen soil.
Several specialized HYDRUS modules, as discussed above, havebeen used also in multiple VZJ publications. For example, Spurlock
et al. (2013a,b) used the fumigant module to evaluate soil fumigant
transport and volatilization to the atmosphere for different types
of fumigant applications. The HP1 module was used further ina study by Thaysen et al. (2014b) to evaluate the effects of lime
and concrete waste on carbon cycling in the vadose zone. Skaggs
et al. (2014) used the UnsatChem module in a global sensitivity
analysis to simulate crop production with degraded waters, whereas
Lassabatere et al. (2014) used the dual-permeability flow module
to evaluate a new analytical model for calculating cumulative
infiltration into dual-permeability soils.

Transport of Particle-Like Substances

66HYDRUS Books andAs discussed above, the HYDRUS models are often used toevaluate the transport of particle-like substances such as colloids,
bacteria, viruses, or nanoparticles. Two manuscripts addressingthese topics appeared in VZJ. Wang et al. (2014b) used HYDRUS
to study physical and chemical factors influencing the transportand fate of E. coli in soil affected by preferential flow, while

As numerical models, such as the HYDRUS software packages,
are becoming increasingly more accurate, comprehensive, andnumerically efficient, their application to a large number oftheoretical and practical problems is becoming more and morewidespread. For these reasons, the Windows-based HYDRUS

VZJ | Advancing Critical Zone Science

Proceedings

p. 17 of 25

models are now rapidly becoming useful tools for teaching
the principles of water, solute, and heat movement in soils andgroundwater, even for users with very little direct knowledge ofsoil physics and related disciplines and with limited mathematicalexpertise. As a result, the HYDRUS software packages have beenused to advantage in several soil physics and hydrology related
textbooks (e.g., Rassam et al., 2003; Radcliffe and Šimůnek, 2010;
Lazarovitch and Warrick, 2013; Shukla, 2013). Below, we give a
brief account of the more recent books and conference proceedings.
Radcliffe and Šimůnek (2010), in their textbook Soil Physics with
HYDRUS: Modeling and Applications, describe a broad range ofrelatively standard soil physics topics. They used various tools
from the HYDRUS family of programs (Šimůnek et al., 2008b)
to make the topics more accessible to students. For example, the
RETC software is used to describe and quantify the unsaturated
soil hydraulic properties, while HYDRUS-1D software was used
to demonstrate infiltration, evaporation, and percolation processesof water in soils having different textures and layering. The software is also used to demonstrate various heat and solute transport
problems in these systems including the effect of physical andchemical nonequilibrium conditions. The HYDRUS (2D/3D)
software is used further to describe two-dimensional flow in fieldsoils, hillslopes, boreholes, and within capillary fringes. The effectsof various transport and reaction parameters on solute transport
are also evaluated. Using information in this book, users can run
HYDRUS and related models for different scenarios and with different parameters, thus obtaining more insight into the physics ofwater flow and contaminant transport. The book can also be used
for self-study on how to use the HYDRUS models.
Another book, Exercises in Soil Physics, was edited by Lazarovitch
and Warrick (2013) to complement available soil physics and vadosezone hydrology texts by providing additional practical exercises. The
topics of soil physics are explored using nine categories: solid phase,soil water relations, saturated water flow, unsaturated flow, fieldwater flow processes, chemical fate and transport, heat and energy
transport, soil gases and transport, and soil variability. Several
problems involving variably saturated water flow and root water
uptake are solved using HYDRUS-1D. Some of the solute transport
problems involved sorbing, nonsorbing, degrading, nondegrading,and volatile solutes with different degrees of dispersion and aresolved using STANMOD. Finally, ROSETTA and RETC areused in forward calculations of the soil water retention curve andfor inverse calculation of the soil hydraulic properties of the van
Genuchten and other soil hydraulic models.
A very extensive HYDRUS-1D tutorial, Soil Physics: An
Introduction, was published by Shukla (2013). This textbook
focused on coupled liquid water, water vapor, and heat transport
in the unsaturated zone of a sandy loam, furrow-irrigated onion
field (Deb et al., 2011). Readers are provided with a very detailed
description of most HYDRUS-1D input and output windows

VZJ | Advancing Critical Zone Science

used in the tutorial including details on how the required input
parameters can be obtained and how the output is to be interpreted.
Three special workshops dedicated to various applications of the
HYDRUS models have been conducted since 2008. The second,
third, and fourth HYDRUS workshops or conferences were organized in Prague, Czech Republic (in 2008), in Tokyo, Japan (in2008), and again in Prague (in 2013), respectively. A large number
of HYDRUS applications presented at these conferences have been
published in the conference proceedings (Šimůnek and Kodešová,2008; Saito et al., 2008; and Šimůnek et al., 2013b), which canbe downloaded freely from the HYDRUS website (http://www.
pc-progress.com/en/Default.aspx).

66Concluding Remarks

As numerical models are becoming much more efficient,comprehensive, and numerically accurate, their application to alarge number of theoretical and practical problems is becoming
increasingly widespread. This is true not just for the HYDRUS
models but also for other models addressing various soil, hydrologic
and environmental science, and engineering problems such as the
TOUGH models (Finsterle et al., 2008), STOMP (White et al.,2008), SWAP (van Dam et al., 2008), VS2DI (Healy, 2008), andmany other models as discussed by Vereecken et al. (2016). As
we noted earlier in our 2008 paper (Šimůnek et al., 2008b), we
believe that these various models and modeling tools have served,
and will continue to serve, an extremely important role in vadosezone research.
In this paper we illustrated a large number of applications of
HYDRUS-1D and HYDRUS (2/3D) and its standard andnonstandard specialized add-on modules that significantly
expanded the versatility of the models. The popularity of the
HYDRUS models and related models (notably, STANMOD,
RETC, UNSATCHEM, and HP1) is reflected by their increasing
use in a variety of applications and publications. That these models
serve a purpose is certainly reflected by the number of downloads
from the HYDRUS website (http://www.pc-progress.com/en/
Default.aspx). HYDRUS-1D has been downloaded more than
40,000 times since the program was made freely available (7738
times in 2015 alone), STANMOD 6000 times (>1000 times
in 2015), and RETC nearly 11,000 times (2260 times in 2015).
The website received nearly 140,000 visitors in 2015, while morethan 30,000 people are registered users, mostly from the UnitedStates, China, Germany, France, Australia, Colombia, Israel, andTurkey (in this order). We hope to continue further development
and improvement of these models in the near future as part of acontinual cycle of improvement.
While much effort has gone into the development of the HYDRUS
models, we also realize that model development and validation andverification never end. In terms of future work, one major priority
p. 18 of 25

for us is to formalize most or all of the nonstandard modules that
thus far are included only in an approximate manner and without
much documentation. In terms of HYDRUS-1D, these nonstandard modules deal with centrifugal forces, freeze–thaw processes,
colloid-facilitated transport, colloid transport with changing watercontents, isotope transport, and root growth (see HYDRUS 1D:
Nonstandard Modules section above). Nonstandard HYDRUS(2D/3D) modules concern centrifugal forces, overland flow,
and CO2 transport and production [see HYDRUS (2D/3D):
Nonstandard Modules section above]. Especially important is thecoupling of the HYDRUS models with surface runoff processes to
produce a more comprehensive surface–vadose zone–groundwater modeling environment. Also needed in the future are further
improvements in the accuracy and computational efficiency ofthe numerical solutions of the governing equations to facilitate
larger-scale applications and continual updates of some of thecomponents of the HYDRUS software packages and related
models (like RETC and STANMOD) to make them more compatible with the 64-bit Windows 10 operating systems and future
Windows versions.
We further realize that models remain a reflection of what is
known—or thought to be known—about prevailing subsurface
water flow and solute processes and our ability to capture those
processes in usable mathematical formulations and related computer software. Many scientific and organizational challenges
remain in this respect to advance systematic modeling of all of
the physical, chemical, and biotic processes operative in the vadosezone and relevant connections with both groundwater and aboveground surface hydrologic and atmospheric processes. We refer toVereecken et al. (2016) for a wide-ranging discussion of these
aspects within the general context of modeling soil processes.

Acknowledgments

We greatly acknowledge USDA NIFA (projects CA-R-ENS-5047-RR and CA-RENS-7274-H) for the financial support.

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