M

Vadose Zone Modeling:
IntroducƟon and Importance

S

S

:V

Z

Jirka Šimůnek* and Sco A. Bradford

Mof varying degree of complexity and dimensionality have been developed during the past
several decades to quantify the basic physical and chemical processes aﬀecting water ﬂow and pollutant
transport in the unsaturated zone. These models are now being used increasingly for a wide range of applications
in research and management of natural subsurface systems. Modeling approaches range from relatively simple analytical and semianalytical models to more complex numerical codes that permit consideration of a large number ofsimultaneous nonlinear processes. While analytical and semianalytical solutions are still used for relatively simple
applications, the ever-increasing power of personal computers, as well as supercomputers, and the development of
more accurate, numerically stable, and often parallelized (Hardelauf et al., 2007) solution techniques have givenrise to the much wider use of numerical models in recent decades (Šimůnek, 2005).
This special section of the Vadose Zone Journal documents the tremendous progress in vadose zone modelingover the last three decades. The section is divided into two parts. Part 1 includes six papers that describe the latest
developments or speciﬁc applications of some of the most widely used models for simulating various processes inthe vadose zone. These papers cover the following models (in the alphabetical order): HYDRUS (Šimůnek et al.,2008), MODFLOW-SURFACT (Panday and Huyakorn, 2008), STOMP (White et al., 2008), SWAP (van Dam
et al., 2008), TOUGH2 (Finsterle et al., 2008), and VS2DI (Healy, 2008). The authors of HYDRUS review theireﬀorts over some 30 yr in developing their various analytical and numerical tools (Šimůnek et al., 2008), while theauthors of TOUGH2 describe recent developments and new processes that have been considered in their model(Finsterle et al., 2008). Authors of MODFLOW-SURFACT (Panday and Huyakorn, 2008), VS2DI (Healy, 2008),
and SWAP (van Dam et al., 2008) provide basic descriptions of their models and their general capabilities. Finally,
authors of STOMP (White et al., 2008) present a sophisticated application of their model.
The second part of this special section includes 15 papers that describe modeling of speciﬁc vadose zone processes
or associated applications. Contributions include two papers that review colloid and colloid-facilitated contaminanttransport in the vadose zone (Bradford and Torkzaban, 2008; Flury and Qiu, 2008, respectively), two papers that
address reactive biogeochemical transport under transient ﬂow conditions (Jacques et al., 2008; Szegedi et al., 2008),
two papers related to multiphase ﬂow and remediation (Class et al., 2008; Hodges and Falta, 2008), and one paperthat reviews (Furman, 2008) and two papers that develop new tools for modeling surface–subsurface interactions(Twarakavi et al., 2008; van Walsum and Groenendijk, 2008). The topics of preferential and nonequilibrium ﬂow
and transport in the vadose zone are covered by Šimůnek and van Genuchten (2008) and Kodešová et al. (2008).
Individual papers deal with salt leaching under subsurface drip irrigation and saline, shallow groundwater conditions (Hanson et al., 2008), spatially distributed water ﬂuxes in soil under banana plants (Sansoulet et al., 2008),
modeling of processes in subsurface ﬂow constructed wetlands (Langergraber, 2008), and inverse modeling of
subsurface ﬂow and transport properties using recent advances in global optimization, parallel computing andsequential data assimilation (Vrugt et al., 2008). There are, however, some obvious gaps and uncovered processes,
such as coupled water, vapor and heat transport, and large-scale model applications, not addressed in this special
issue. Readers interested in these topics are referred, for example, to recent papers by Cahill and Parlange (1998),
Saito et al. (2006), or Twarakavi et al. (2008).

Part 1: Vadose Zone Models
This special section opens with two papers dedicated to the HYDRUS (Šimůnek et al., 2008) and TOUGH2(Finsterle et al., 2008) models. These models are commonly used by contributors to the Vadose Zone Journal. While
one of the HYDRUS models was used in more than 60 published manuscripts during the ﬁrst six years of the journal,

J. Šimůnek, Dep. of Environmental Sciences, Univ. of California-Riverside, Riverside, CA 92521; S.A. Bradford, USDA–ARS, U.S. Salinity Lab., 450 W. Big Springs Rd., Riverside, CA 92507. Received 22 Jan. 2008. *Corresponding author (Jiri.Simunek@ucr.edu).
Vadose Zone J. 7:581–586
doi:10.2136/vzj2008.0012© Soil Science Society of America
677 S. Segoe Rd. Madison, WI 53711 USA.
All rights reserved. No part of this periodical may be reproduced or transmi ed in any form or by any means, electronic or mechanical,
including photocopying, recording, or any informa on storage and retrieval system, without permission in wri ng from the publisher.

www.vadosezonejournal.org · Vol. 7, No. 2, May 2008581

an entire special issue was recently dedicated to applications of
TOUGH2 [Vadose Zone Journal 6(1), 2008].
Šimůnek et al. (2008) review the history of development,
the main processes involved, and selected applications of a large
number of popularly used computer tools for studying vadosezone ﬂow and transport processes developed collaboratively
between the U.S. Salinity Laboratory, the University of California,
Riverside, and PC-Progress over the past 20 yr. These tools
include numerical models for one- or multidimensional variably
saturated ﬂow and transport [e.g., HYDRUS-1D, HYDRUS-2D,and HYDRUS (2D/3D)], analytical models for solute transport
in soils and groundwater (e.g., CXTFIT and STANMOD), andtools or databases for analyzing or predicting the unsaturated
soil hydraulic properties (e.g., RETC, Rosetta, and UNSODA).
These modeling tools cover a large number of processes, from
relatively simple one-dimensional solute transport problems tomultidimensional ﬂow and transport applications to relatively
complex problems involving a range of biogeochemical reactions.
An example of the latter is the HP1 (Jacques et al., 2008) program, which couples the HYDRUS-1D software package with the
PHREEQC geochemical code (Parkhurst and Appelo, 1999).
Finsterle et al. (2008) discuss fundamental and computational challenges in simulating vadose zone processes and present
examples of recent developments of the TOUGH suite of codes
aimed at addressing some of these issues. The TOUGH suite ofsimulators includes several related codes simulating, for example, nonisothermal multiphase ﬂow (e.g., TOUGH2, T2VOC),
reactive biogeochemical transport (TOUGHREACT) and rockmechanical processes (TOUGH-FLAC). Finsterle et al. (2008)
either list or discuss several recent applications of TOUGH. These
applications involve, for example, simulation of CO2 sequestration in brine-saturated formations while considering hysteresisand gas entrapment, evaluation of the presence of water andice on Mars while considering processes of freezing and thawing, and reactive biogeochemical transport. Key references to
described simulators and their recent advanced applications
are also provided.
Panday and Huyakorn (2008) describe the MODFLOWSURFACT model, the name of which indicates that this model
include modules developed for MODFLOW (Harbaugh et al.,2000), probably the most widely used groundwater ﬂow model,
to extend its capabilities to simulate unsaturated ﬂow, recharge,
fracture ﬂow, and contaminant transport. It is interesting to notethat the wide variety of MODFLOW SURFACT capabilities
is achieved by solving only one ﬂow equation and one transport equation. The Richards ﬂow equation can be solved withstandard retention functions, with bimodal or multimodal relative permeability curves, or with pseudo-soil retention functions.
The equation can also be recast in terms of air phase ﬂow toanalyze subsurface air ﬂow behavior. The transport equation can
include an immobile multicomponent nonaqueous phase liquid(NAPL) phase with equilibrium partitioning and mass transfer
between phases, as well as dual-porosity capabilities to analyzetransport in fractured media. Finally, two example problems arepresented that demonstrate the use of MODFLOW SURFACT
to evaluate alternative designs for dense nonaqueous phase liquid
remediation and to simulate the movement of a contaminant ina fractured system.

www.vadosezonejournal.org · Vol. 7, No. 2, May 2008

Healy (2008) presents ﬁrst a brief overview of approaches
for simulating water, solute, and heat transport through variably
saturated porous media, including a brief description of the mostwidely used numerical models. He then discusses assumptions
involved in the development of the VS2DI package and presents
examples of its uses for a variety of applications. These examples
include an evaluation of the inﬂuence of the unsaturated zone
on piezometer responses in unconﬁned aquifers during aquifer
tests, an estimation of ground–surface water exchange, and ananalysis of water movement in soils in response to evapotranspiration. Finally, he analyzes advantages and limitations of the VS2DI
package for diﬀerent applications.
In their paper, van Dam et al. (2008) review both the mainand special features of the one-dimensional SWAP model. While
the main features—water ﬂow, and solutes and heat transport in
the vadose zone—are similar as in the above models, SWAP has
several unique features. These include generic crop growth, swelling and shrinking processes, versatile top boundary conditions,macroporous ﬂow, and relatively complex interactions, althoughhandled in a simpliﬁed manner, of soil water with groundwaterand surface water. van Dam et al. (2008) also review several casestudies of SWAP applications that appeared in recent literature.
These applications involve an evaluation of agricultural waterproductivity, regional nutrient management, and groundwater
conservation by surface water management. To conclude theirpaper, van Dam et al. (2008) provide their vision of the future
SWAP developments for the coming 5 to 10 yr.
Finally, authors of STOMP (White et al., 2008) present
a sophisticated application of their model to investigate the
distribution and remediation (soil vapor extraction) of carbon
tetrachloride in the deep vadose zone at the Hanford site, near
Richland, WA. High-resolution simulations were executed inthree dimensions using layered and heterogeneous distributionsof soil properties. The use of only a single processor to solve thisproblem with STOMP was not practical because of the complexity of the problem and the long simulation times. To overcome
these limitations, White et al. (2008) present the developed andapplication of a scalable version of STOMP for faster execution
on parallel computers.

Part 2: Modeling of Vadose Zone Processes
While the ﬁrst part of this special section is devoted tonumerical models simulating water ﬂow, heat transport, and contaminant transport in the vadose zone, the second part presents
reviews of important vadose zone processes and applications ofmodels simulating these processes.
Colloid and Colloid-Facilitated Contaminant Transport

The ﬁrst two papers in this part review processes involvedin colloid and colloid-facilitated contaminant transport in thevadose zone. Pore-scale processes and models relevant for colloidtransport and retention in unsaturated porous media are thoroughly reviewed by Bradford and Torkzaban (2008). While themajority of literature devoted to colloid transport studies theseprocesses at the laboratory column scale, this review discusses ourcurrent knowledge of physical and chemical mechanisms, factors,
and models of colloid transport and retention at the smaller scales:interface, collector, and pore. Bradford and Torkzaban (2008) ﬁrst
study the interaction energy and adhesive, hydrodynamic, and582

non–Derjaguin–Landau–Verwey–Overbeek forces and/or torques
that act on colloids near the solid–water and air–water interfaces.
They discuss the hydrodynamic mechanisms, such as lifting, sliding, and rolling, that can cause colloid removal from an interface.
Then they numerically solve the Navier–Stokes equation at thecollector scale, that is, around a single solid grain or an air bubble,
and evaluate the potential for colloid attachment in the presenceof hydrodynamic forces from a balance of applied and adhesive
torques. Here, they discuss processes such as diﬀusion, interception, and sedimentation that aﬀect colloid attachment. Finally,
they carry out similar analysis at the pore scale that diﬀers fromthe collector scale by the presence of small pore spaces associatedwith multiple interfaces and zones of relative ﬂow stagnation andwhere new processes such as straining, wedging, retention at the
triple point, bridging, or mechanical ﬁltration can take place.
Flury and Qiu (2008) review the current knowledge andmodeling of colloid-facilitated contaminant transport in thevadose zone. Their review indicates that colloid-facilitated transport models consider mechanisms that control both colloid andsolute (contaminant) transport, their mutual interactions, andmass transfer to and from the solid and air phases. The presenceof an air phase in the vadose zone is reported to aﬀect colloidfacilitated contaminant transport in several ways; for example.
colloids can be trapped in immobile water, strained in thin waterﬁlms and in the smallest regions of the pore space, or attachedto the air–water interface itself. Flury and Qiu (2008) indicatethat modeling of colloid-facilitated contaminant transport in thevadose zone has mostly been theoretical, tested only with column
experiments; ﬁeld applications are still lacking.

mathematical package MATLAB, simulating either one-dimensional or radial solute transport with PHREEQC. Their paper
presents both the model development and its veriﬁcation. In its
most complex application presented here, RhizoMath is able todescribe the observed eﬀects of citrate exudates on the simultaneous transport of arsenate and phosphate that compete forsurface binding sites with each other and with other oxyanions
such as citrate.
Mul phase Flow and Remedia on

Contamination of the vadose zone with NAPLs poses a risk
to soil and water quality at many hazardous waste sites. Two
papers related to multiphase ﬂow and remediation of NAPLs inthe vadose zone are included here.
Class et al. (2008) demonstrate how dominant multiphaseﬂow and transport processes at a NAPL-contaminated site canchange over distinct timescales. For example, multiphase ﬂow
is the dominant mechanism at early times following the releaseof a NAPL into the subsurface, whereas compositional and/or
nonisothermal eﬀects become more important at longer timescales and/or during active remediation. The authors propose
and illustrate how models of varying complexity can be sequentially coupled to simulate such problems. Adjusting the model
complexity to the dominant processes results in signiﬁcant savings of computation time and thus enables the user to makepredictions for complex flow and transport scenarios overlonger time spans.
Hodges and Falta (2008) numerically investigate the ability of cold air injection to control the vertical movement of thesteam during steam ﬂooding in the shallow vadose zone. Cold air
injection is found to provide good control of the vertical steam
movement when using approximately equal air and steam volumetric ﬂow rates, but it may also result in the need to treat a larger
volume of contaminated air. These authors report that the mosteﬀective design for steam ﬂooding appears to be a low-permeability surface cap in conjunction with air injection above thesteam injector.

Biogeochemical Transport

Two articles demonstrate the use of biogeochemical transportand reactions models that simultaneously consider water ﬂow,
solute transport and complex chemical reactions. Both models
are based on the geochemical speciation model PHREEQC(Parkhurst and Appelo, 1999).
Jacques et al. (2008) ﬁrst review interactions between physical and biogeochemical processes in the vadose zone and theirmutual feedbacks. They then present a hypothetical example
involving the migration of several chemical species over a 200-yr
time period. In this application, they use the multicomponent
transport model HP1 (Jacques and Šimůnek, 2005) that resulted
from coupling of the HYDRUS-1D water ﬂow and solute transport model (Šimůnek et al., 2008) with PHREEQC to evaluate
the potential environmental impact of long-term applicationsof mineral fertilizers containing small amounts of uranium toagricultural soils. They account for interactions between uraniumand organic matter, phosphate, and carbonate, consider surface
complexation as the major solid-phase interaction, and couple allgeochemical processes with transient soil water ﬂow. Jacques etal. (2008) demonstrate how transient water contents and ﬂuxes
aﬀect soil pH and hence, the retention, bioavailability, and ﬂuxes
of various solute components. Leaching of uranium from the soil
proﬁle occurred faster in the transient ﬂow simulation than in
the steady-state simulation, as a result of the interplay betweenchanging hydrological and geochemical soil conditions.
Szegedi et al. (2008) present the RhizoMath model for simulating coupled solute transport and speciation in the rhizosphere.
RhizoMath resulted from coupling routines developed in the
www.vadosezonejournal.org · Vol. 7, No. 2, May 2008

Surface–Subsurface Processes

The cycling of water in the environment involves water in theatmosphere, surface waters, and water in the subsurface. Whilewater ﬂuxes between these three domains are continuous anddirectly aﬀect each other, water movement and storage in individual domains are usually described by specialized models thatconsider only one domain, while the other two domains are represented simply as boundary conditions, and thus, interactions
between individual domains are greatly simpliﬁed. The same isalso true for the subsurface, where specialized models exist for
the vadose zone and the groundwater. To describe mutual interactions between the three domains, the specialized models need
to be coupled. In his review, Furman (2008) focuses on diﬀerent
ways of coupling hydrological models for surface and subsurface
domains. He ﬁrst reviews the governing equations for surface
and subsurface ﬂow, and the coupling physics and mathematics. He starts with relatively complex systems and shows how
these systems are frequently simpliﬁed. He then discuses thephysical alternatives for internal (between surface and subsurface)boundary conditions and numerical alternatives for coupling thesystems. He identiﬁes four diﬀerent coupling schemes: uncoupled,583

degenerated uncoupled, iteratively coupled, and fully coupled.
Finally, he discusses how various, widely used models, deal withcoupling of processes in diﬀerent zones.
Although water ﬂow through the variably saturated (vadose)zone is an important part of the hydrologic cycle because itinﬂuences partitioning of water among various ﬂow components—runoﬀ, inﬁltration, evapotranspiration, groundwater
recharge, and vadose zone storage—vadose zone ﬂow processes
have rarely been properly represented in large-scale hydrologicalmodels. While Furman (2008) deals mainly with the problem ofcoupling surface and subsurface models, Twarakavi et al. (2008)
review various approaches that can be used to account for processes in the vadose zone when simulating groundwater ﬂow with
MODFLOW (Harbaugh et al., 2000). In particular, Twarakavi
et al. (2008) evaluate the newly developed HYDRUS package
for MODFLOW and compare it with other available approaches.
Because the HYDRUS package solves the Richards equation
for water movement in the vadose zone, it can thus consider
processes, such as precipitation, inﬁltration, evaporation, redistribution, capillary rise, plant water uptake, water accumulation at
the ground surface, surface runoﬀ, and soil moisture storage andtherefore can evaluate the eﬀects of these processes on groundwater ﬂow and storage. The authors present several test examples
of increasing complexity to document the functionality of the
HYDRUS package in the MODFLOW environment.
An alternative approach to account for vadose zone ﬂuxes
in groundwater modeling is presented by van Walsum and
Groenendijk (2008). They describe an approach in which asequence of steady-state water content proﬁles (for the vadosezone) is used to perform dynamic simulations. The appropriate
proﬁles are selected on the basis of water balances at the aggregate scale of control volumes. The performance of the simpliﬁed
approach is evaluated by comparing results to those of a modelthat solves the Richards equation.

dual-porosity physical and two-site chemical nonequilibrium
models to complex dual-permeability models that consider both
physical and chemical nonequilibrium. The presented models
form a hierarchical system from which diﬀerent formulations
can be selected for diﬀerent applications, depending on available
information and data. Šimůnek and van Genuchten (2008) present several examples calculated with the diﬀerent nonequilibrium
approaches to show the eﬀect of various transport and reaction
parameters and to demonstrate the consequences of increased
complexity in the models. They also discuss implications for theformulation of the inverse problem.
The impact of soil micromorphological features on water ﬂow
and herbicide transport in three diﬀerent soil types is discussed
by Kodešová et al. (2008). Micromorphological properties characterizing the soil pore structure were studied on images of thinsoil sections taken with a camera. The soil micromorphologicalimages were used to analyze soil porous systems, to count pores ofdiﬀerent diameters, to distinguish the possible characters of water
ﬂow, and to select appropriate numerical models for three diﬀerent soil types. Soil hydraulic properties for selected models werethen estimated using a multistep outﬂow and ponded inﬁltration
experiments, and numerical inversion. Finally, ﬁeld observationsof water ﬂow and herbicide transport were successfully simulatedusing single-porosity and either dual-porosity or dual-permeability ﬂow and transport models in HYDRUS-1D.
Agricultural Applica ons

Most early models for studying variably saturated water ﬂow
in the vadose zone were initially used in agricultural research to
optimize moisture conditions for crop production. This focus has
increasingly shifted to environmental research, with the primaryconcern now being the subsurface fate and transport of a wide
range of contaminants, such as pesticides, nutrients, pathogens,pharmaceuticals, viruses, bacteria, colloids, toxic trace elements,
radionuclides, and/or fumigants, but also the evaluation of water
recharge through the vadose zone. In the category of agricultural
applications, there are two papers, the ﬁrst one dealing with saltleaching under subsurface drip irrigation (Hanson et al., 2008)
and the second evaluating spatially distributed water ﬂuxes underbanana plants (Sansoulet et al., 2008).
Hanson et al. (2008) use the HYDRUS-2D software package to evaluate salt leaching under conditions found in many
commercial ﬁelds in the San Joaquin Valley, California. Heredrip irrigation is often used in ﬁelds that have saline, shallow
ground water. HYDRUS-2D was used in this study to estimate
actual leaching fractions, including localized leaching below the
drip emitter. Simulations were conducted for diﬀerent amounts
of applied water, water table depths, and irrigation water salinity.
The spatially varying soil wetting patterns that occur under drip
irrigation caused the localized leaching. Results show that somelocalized leaching occur even for water applications of 60% of
the potential evapotranspiration, typically considered to be severe
deﬁcit irrigation. The authors conclude that the commonly usedﬁeldwide water balance approach is inappropriate for estimating
actual leaching fractions under drip irrigation.
Sansoulet et al. (2008) used suction lysimeters to collectspatially distributed water ﬂuxes in an Andisol under banana
plants. The main cause for the spatial heterogeneity of recharge
ﬂuxes at the 1-m depth was not the spatial variability of theNonequilibrium and Preferen al Flow

Preferential and nonequilibrium ﬂow and transport are often
considered to hamper accurate predictions of contaminant transport in soils and fractured rocks (Šimůnek et al., 2003). Since
several reviews of nonequilibrium ﬂow have recently appeared,or will soon appear, in the literature (Šimůnek et al., 2003;
Gerke, 2006; Köhne et al., personal communication, 2008), we
do not include an additional review here. Instead, this special
section includes one paper (Šimůnek and van Genuchten, 2008)
that reviews the wide range of approaches for simulating preferential ﬂow and transport in the HYDRUS-1D model, andanother (Kodešová et al., 2008) that discusses the impact of soil
micromorphological features on nonequilibrium water ﬂow andherbicide transport in soils.
The large number of physical and chemical nonequilibrium
approaches available in the latest version of HYDRUS-1D aredescribed by Šimůnek and van Genuchten (2008). Since nonequilibrium models for water ﬂow have been reviewed relatively
recently (Šimůnek et al., 2003), this paper focuses mainly on
solute transport. The various models are divided into threegroups: physical nonequilibrium transport models, chemical
nonequilibrium transport models, and physical and chemical
nonequilibrium transport models. These models range from classical models simulating uniform ﬂow and transport to traditional
www.vadosezonejournal.org · Vol. 7, No. 2, May 2008584

subsurface environment but rather, uneven inﬁltration of water
due to aboveground interception and redistribution of rainfall
by the plant canopy that caused signiﬁcant stemﬂow. Drainage
volumes under the banana stem were up to six times higher thanelsewhere, as these other areas were sheltered from direct rainfall
by the banana leaves and received only throughfall. Collected
experimental data and spatially distributed drainage ﬂuxes arewell reproduced by the HYDRUS software package, simulating
three-dimensional variably saturated water ﬂow for boundary
conditions reﬂecting spatially varying inﬁltration ﬂuxes. Sansoulet
et al. (2008) question the common practice of applying fertilizers
and pesticides at the foot of the plant, as the abundant stemﬂow
may leach soluble nutrients or pesticides from the root zone into
deeper horizons and eventually into the groundwater.

Linux operating systems, there is also a need to develop parallelized versions of these models that can run on regular PCs withmulticore processors.
Future advances in vadose zone modeling will also be limited
by our basic understanding of the fundamental physics, chemistry,and biology that occurs in the subsurface environments. As ourknowledge increases and this information is incorporated intomodels, more physically meaningful tools can be generated tohelp study and manage the vadose zone.
While not covered in this special section, research on new
numerical techniques, linear and nonlinear solvers, grid generation, parallel computing techniques, visualization, optimization
techniques, and other areas (USDOE, 2001) is taking placethat will have an important impact on future developments in
vadose zone modeling. Additionally, there is a need to develop
and implement spatial and temporal error estimators and adaptive local grid and time-step reﬁnement algorithms into vadosezone models to automatically minimize these errors. To facilitate
the use of numerical models by regulators and consulting practitioners, it would be extremely helpful to develop algorithms thatwould automatically alert users about a model’s possible limitations or that could even automatically select more accuratealternative approaches.

Constructed Wetlands

Langergraber (2008) provides a thorough review of numerical
tools available for modeling various biogeochemical processes insubsurface constructed wetlands, that is, engineered systems thatprovide a natural way for simple, inexpensive, and robust wastewater treatment. Understanding the constructed wetland function
is diﬃcult since a large number of coupled physical, chemical,
and biological processes occur simultaneously. Numerical models
are thus indispensable for understanding these complex systems.
Langergraber (2008) reviews ﬁve models of diﬀerent complexitythat consider variably saturated ﬂow and transport, as well as
typical wetland reactions. Several example applications of themulticomponent reactive transport module CW2D of HYDRUS(Langergraber and Šimůnek, 2006) are given.

A
We would like to express our thanks to Jan Hopmans, the editor of
the Vadose Zone Journal, for giving us the opportunity to serve as guest
editors. We have appreciated this chance to be in close contact withmany of our colleagues, both authors and reviewers, who contributed
to this special section. We are conﬁdent that every reader of this journal
will ﬁnd a few papers of interest in our special section on vadose zone
modeling. Thus, go ahead, download these papers, and start reading.

Inverse Problem

References

In the ﬁrst part of their article, Vrugt et al. (2008) review thecurrent state-of-the-art of inverse modeling for estimating unsaturated ﬂow and transport processes. They provide the historicalbackground and summarize various solution algorithms used
to solve the parameter estimation problem. In the second part,
they discuss their recent work on improved optimization anddata assimilation methods for inverse estimation of distributed
ﬂow and transport model parameters using parallel computing
capabilities. Finally, in the third part, they demonstrate these
new methods with three case studies involving the calibration ofa fully coupled three-dimensional vapor extraction model, themultiobjective inverse estimation of soil hydraulic properties ofa one-dimension ﬂow model, and the simultaneous estimation ofparameters and states in a groundwater solute mixture model.

Bradford, S.A., and S. Torkzaban. 2008. Colloid transport and retention in unsaturated porous media: A review of interface-, collector-, and pore-scale
processes and models. Vadose Zone J. 7:667–681 (this issue).
Cahill, A.T., and M.B. Parlange. 1998. On water vapor transport in ﬁeld soils.
Water Resour. Res. 34:731–739.
Class, H., R. Helmig, and I. Neuweiler. 2008. Sequential coupling of models
for contaminant spreading in the vadose zone. Vadose Zone J. 7:721–731(this issue).
Finsterle, S., C. Doughty, M.B. Kowalsky, G.J. Moridis, L. Pan, T. Xu, Y. Zhang,and K. Pruess. 2008. Advanced vadose zone simulations using TOUGH.
Vadose Zone J. 7:601–609 (this issue).
Flury, M., and H. Qiu. 2008. Modeling colloid-facilitated contaminant transport in the vadose zone. Vadose Zone J. 7:682–697 (this issue).
Furman, A. 2008. Modeling coupled surface–subsurface ﬂow processes: A review.
Vadose Zone J. 7:741–756 (this issue).
Gerke, H.H. 2006. Preferential ﬂow descriptions for structured soils. J. Plant
Nutr. Soil Sci. 169:382–400.
Hanson, B., J.W. Hopmans, and J. Šimůnek. 2008. Leaching with subsurface
drip irrigation under saline, shallow groundwater conditions. Vadose Zone
J. 7:810–818 (this issue).
Harbaugh, A.W., E.R. Banta, M.C. Hill, and M.G. McDonald. 2000. MODFLOW-2000, the U.S. Geological Survey modular ground-water model
user guide to modularization concepts and the ground-water ﬂow process.
USGS, Denver, CO, Reston, VA.
Hardelauf, H., M. Javaux, M. Herbst, S. Gottschalk, R. Kasteel, J. Vanderborght,
and H. Vereecken. 2007. PARSWMS: A parallelized model for simulating
three-dimensional water ﬂow and solute transport in variably saturated
soils. Vadose Zone J. 6:255–259.
Healy, R.W. 2008. Simulating water, solute, and heat transport in the subsurface
with the VS2DI software package. Vadose Zone J. 7:632–639 (this issue).
Hodges, R.A., and R.W. Falta. 2008. Vertical conﬁnement of injected steam in thevadose zone using cold air injection. Vadose Zone J. 7:732–740 (this issue).

Future Outlook
Historically, vadose zone models were used essentially only innational laboratories or by premium research institutes and universities. Today, sophisticated numerical models are available toevery college student or consulting practitioner. Although more
and more complex numerical models are being developed, someof these tools can only be accessed by a few highly specialized
individuals or teams. There is therefore an increasing need tomake these tools available and accessible to the public by thedevelopment of graphics-based user interfaces that can tremendously simplify the use of these tools. Similarly, while many of
the advanced numerical models have been parallelized to run
on supercomputers or computer clusters running either Unix or
www.vadosezonejournal.org · Vol. 7, No. 2, May 2008585

Jacques, D., and J. Šimůnek. 2005. User manual of the multicomponent variably-saturated ﬂow and transport model HP1: Description, veriﬁcationand examples. Version 1.0. BLG-998 Rep. SCK•CEN, Mol, Belgium.
Jacques, D., J. Šimůnek, D. Mallants, and M.Th. van Genuchten. 2008. Modeling coupled hydrological and chemical processes in the vadose zone: Review and case study of long-term uranium transport following phosphorus
fertilization. Vadose Zone J. 7:698–711 (this issue).
Kodešová, R., M. Kočárek, V. Kodeš, J. Šimůnek, and J. Kozák. 2008. Impact ofsoil micromorphological features on water ﬂow and herbicide transport insoils. Vadose Zone J. 7:798–809 (this issue).
Langergraber, G. 2008. Modeling of processes in subsurface ﬂow constructedwetlands: A review. Vadose Zone Journal 7:830–842 (this issue).
Langergraber, G., and J. Šimůnek. 2006. The multi-component reactive transport module CW2D for constructed wetlands for the HYDRUS software
package. Hydrus Software Ser. 2. Dep. of Environmental Sciences, Univ.
of California, Riverside.
Panday, S., and P.S. Huyakorn. 2008. MODFLOW SURFACT: A state-ofthe-art use of vadose zone ﬂow and transport equations and numerical
techniques for environmental evaluations. Vadose Zone J. 7:610–631(this issue).
Parkhurst, D.L., and C.A.J. Appelo. 1999. User’s guide to PHREEQC (Version
2): A computer program for speciation, batch-reaction, one-dimensionaltransport and inverse geochemical calculations. Water-Resources Investigations, Rep. 99-4259. USGS, Denver, CO.
Saito, H.J., J. Šimůnek, and B. Mohanty. 2006. Numerical analyses of coupled water, vapor, and heat transport in the vadose zone. Vadose Zone
J. 5:784–800.
Sansoulet, J., Y.-M. Cabidoche, P. Cattan, S. Ruy, and J. Šimůnek. 2008. Spatially distributed water ﬂuxes in an Andisol under banana plants: Experiments
and three-dimensional modeling. Vadose Zone J. 7:819–829 (this issue).
Šimůnek, J., N.J. Jarvis, M.Th. van Genuchten, and A. Gärdenäs. 2003. Review
and comparison of models for describing non-equilibrium and preferential
ﬂow and transport in the vadose zone. J. Hydrol. 272:14–35.
Šimůnek, J. 2005. Models of water ﬂow and solute transport in the unsaturated
zone. p. 1171–1180. In M.G. Anderson and J.J. McDonnell (ed.) Encyclopedia of hydrological sciences. John Wiley & Sons, Chichester, UK.
Šimůnek, J., and M.Th. van Genuchten. 2008. Modeling nonequilibrium ﬂow
and transport processes using HYDRUS. Vadose Zone J. 7:782–797(this issue).
Šimůnek, J., M.Th. van Genuchten, and M. Šejna. 2008. Development andapplications of the HYDRUS and STANMOD software packages and related codes. Vadose Zone J. 7:587–600 (this issue).
Szegedi, K., D. Vetterlein, H. Nietfeld, R. Jahn, and H.-U. Neue. 2008. New
tool RhizoMath for modeling coupled transport and speciation in therhizosphere. Vadose Zone J. 7:712–720 (this issue).
Twarakavi, N.K.C., J. Šimůnek, and S. Seo. 2008. Evaluating interactions between groundwater and vadose zone using HYDRUS-based ﬂow package
for MODFLOW. Vadose Zone J. 7:757–768 (this issue).
USDOE. 2001. A national roadmap for vadose zone science and technology:
Understanding, monitoring, and predicting contaminant fate and transport in the unsaturated zone. DOE/ID-10871. Idaho National Engineering and Environmental Laboratory, Idaho Falls, ID.
van Dam, J.C., P. Groenendijk, R.F.A. Hendriks, and J.G. Kroes. 2008. Advances of modeling water ﬂow in variably saturated soils with SWAP. Vadose
Zone J. 7:640–653 (this issue).
van Walsum, P.E.V., and P. Groenendijk. 2008. Quasi steady-state simulation of
the unsaturated zone in groundwater modeling of lowland regions. Vadose
Zone J. 7:769–781 (this issue).
Vrugt, J.A., P.H. Stauﬀer, Th. Wöhling, B.A. Robinson, and V.V. Vesselinov.
2008. Inverse modeling of subsurface ﬂow and transport properties: A review with recent advances in self-adaptive global optimization, sequential
data assimilation, and parallel computing. Vadose Zone J. 7:843–864 (thisissue).
White, M.D., M. Oostrom, M.L. Rockhold, and M. Rosing. 2008. Scalable
modeling of carbon tetrachloride migration at the Hanford site using the
STOMP simulator. Vadose Zone J. 7:654–666 (this issue).

www.vadosezonejournal.org · Vol. 7, No. 2, May 2008586