MZ

Development and ApplicaƟons
of the HYDRUS and STANMOD SoŌware
Packages and Related Codes

S

S

:V

Jiří Šimůnek,* Mar nus Th. van Genuchten, and Miroslav Šejna
Mathema cal models have become indispensable tools for studying vadose zone flow and transport processes. We
reviewed the history of development, the main processes involved, and selected applica ons of HYDRUS and related
models and so ware packages developed collabora vely by several groups in the United States, the Czech Republic,
Israel, Belgium, and the Netherlands. Our main focus was on modeling tools developed jointly by the U.S. Salinity
Laboratory of the USDA, Agricultural Research Service, and the University of California, Riverside. This collaboraon during the past three decades has resulted in the development of a large number of numerical [e.g., SWMS_2D,HYDRUS-1D, HYDRUS-2D, HYDRUS (2D/3D), and HP1] as well as analy cal (e.g., CXTFIT and STANMOD) computer tools
for analyzing water flow and solute transport processes in soils and groundwater. The research also produced addi onal
programs and databases (e.g., RETC, Rose a, and UNSODA) for quan fying unsaturated soil hydraulic proper es. All of
the modeling tools, with the excep on of HYDRUS-2D and HYDRUS (2D/3D), are in the public domain and can be downloaded freely from several websites.

A: GUI, graphical user interface; UCR, University of California, Riverside; USSL, U.S. Salinity Laboratory.

S

involving ﬂow, transport, and biogeochemical processes in the subsurface environment requires
appropriate modeling tools consistent with the application. Whilecertain problems may be solved using relatively simple analytical or semianalytical models, other problems may require moresophisticated numerical models, either one- or multidimensional,
that simulate water ﬂow, solute transport, and a range of biogeochemical reactions. To have the ﬂexibility in optimally addressing
general as well as site-speciﬁc environmental problems, one may
thus need a toolbox containing a variety of computer programs ofvarying complexities. A large number of such computer tools havebeen developed jointly by the U.S. Salinity Laboratory (USSL)
and the University of California, Riverside (UCR) during a timespan of about 30 yr and released to the public. It is our objective
to describe the most pertinent of these computer programs anddiscuss several applications.

We describe here the history of development, the main processes involved, and selected applications of HYDRUS and related
models and software packages (Table 1). Our main focus is initially on the numerical HYDRUS models, their predecessors, andvarious modiﬁcations and extensions thereof [e.g., SWMS_2D,HYDRUS-1D, HYDRUS-2D, HYDRUS (2D/3D), and HP1]that resulted from the work of several groups of developers in
the United States, the Czech Republic, Israel, the Netherlands,
and Belgium. We also summarize several other modeling tools,
however, that were developed in close collaboration between the
USSL and UCR, such as the CXTFIT and STANMOD codes
for analytical transport modeling, as well as additional softwareand databases (e.g., RETC, Rosetta, and UNSODA) for analyzing unsaturated soil hydraulic properties. All of the tools anddatabases, with the exception of HYDRUS-2D and HYDRUS(2D/3D), are in the public domain. A CD containing the various codes and manuals is freely available from USSL. Most
codes can also be downloaded freely from both the HYDRUS
website (www.hydrus2d.com or www.pc-progress.cz [veriﬁed 3
Mar. 2008]) and the USSL site (www.ars.usda.gov/Services/docs.
htm?docid=15992 [veriﬁed 3 Mar. 2008]). It is beyond the scopeof this work to describe all applications for which the various
programs have been used. A comprehensive list of publications
showing a large number of applications can be found at www.
pc-progress.cz/Pg_Hydrus1D_References.htm (veriﬁed 3 Mar.
2008) for HYDRUS-1D and related software and at www.pcprogress.cz/Pg_Hydrus_References.htm (veriﬁed 3 Mar. 2008)
for HYDRUS-2D and its predecessors.

J. Šimůnek, Dep. of Environmental Sciences, Univ. of California, Riverside,
CA 92521; M.Th. van Genuchten, USDA-ARS, U.S. Salinity Lab., 450 West
Big Springs, Riverside, CA 92507; M. Šejna, PC-Progress, Ltd., Anglická 28,
120 00 Prague, Czech Republic. Received 23 April 2007. *Corresponding
author (Jiri.Simunek@ucr.edu).
Vadose Zone J. 7:587–600
doi:10.2136/vzj2007.0077© Soil Science Society of America
677 S. Segoe Rd. Madison, WI 53711 USA.
All rights reserved. No part of this periodical may be reproduced ortransmi ed in any form or by any means, electronic or mechanical,
including photocopying, recording, or any informa on storage andretrieval system, without permission in wri ng from the publisher.
www.vadosezonejournal.org · Vol. 7, No. 2, May 2008

587

T

1. The HYDRUS and related models and so ware packages.

HYDRUS

3.0

Opera ngsystemDOS

SOILCO2

5.0
6.0
1.0

UNSATCHEMHYDRUS-1D

Model

Version

Dimensions†

Brief descrip on (processes)‡

Reference

1

Variably saturated water flow and solute transport in porous media

DOS
DOS
DOS

1
1
1

2.0

Windows1

2.0

Windows1

3.0

Windows

1

1.0

DOS

2

2.0

DOS

2

CHAIN_2D

1.0

DOS

2

UNSATCHEM-2D

1.0

DOS

2

SWMS_3D

1.0

DOS

3

HYDRUS-2D

1.0
2.0

Windows
Windows

2
2

HYDRUS (2D/3D)

1.0

Windows

2, 3

Windows2

Windows

1, 2, 3

Windows

NA

Windows

NA

Windows

NA

Windows

1

Variably saturated water flow and solute transport in porous media
Variably saturated water flow and solute transport in porous media
Variably saturated water flow and transport of CO2 in porous media;
MVG
Variably saturated water flow and transport of major ions and CO2 in Šimůnek et al. (1996b)
porous media; MVG; 16 bit GUI
Variably saturated water flow and solute transport in porous media; Šimůnek et al. (1998b)root water and solute uptake; VG, MVG, BC; hysteresis in soil
hydraulic proper es; nonlinear solute transport; sequen al firstorder decay chains; temperature dependence of soil hydraulicand solute transport parameters; two-site sorp on model;
dual-porosity mobile–immobile water solute transport; inverse
problem; 32 bit GUI
Version 2.0 + Durner (1994) and Kosugi (1996) soil hydraulicŠimůnek et al. (2005)
property models; dual-porosity water flow; snow accumula on;compensated root water uptake; virus, colloid, and bacteriatransport; transport of major ions and CO2 (UNSATCHEM); 32 bit
GUI
Variably saturated water flow and solute transport in porous media; Šimůnek et al. (1992)
root water and solute uptake; MVG; linear solute transport
Version 1.0 + itera ve solvers for the system of linear equa ons;Šimůnek et al. (1994)
predecessor of the 1.0 version of HYDRUS-2DŠimůnek and van Genuchten
Version 2.0 of SWMS_2D + nonlinear solute transport; sequen al
first-order decay chains; gas diﬀusion; two-site sorp on model;(1994)
temperature dependence of soil hydraulic and solute transportparameters; predecessor of the 2.0 version of HYDRUS-2D
Variably saturated water flow and transport of major ions and CO2 in Šimůnek and Suarez (1993b)
porous media; MVG
Variably saturated water flow and solute transport in porous media; Šimůnek et al. (1995)
root water and solute uptake; MVG; linear solute transport;
itera ve solvers for the system of linear equa ons; predecessor of
the 1.0 version of HYDRUS (2D/3D)
SWMS_2D (2.0) + 16 bit GUIŠimůnek et al. (1996a)
CHAIN_2D + 32 bit GUI; dual-porosity mobile–immobile water solute Šimůnek et al. (1999a)transport; hysteresis in soil hydraulic proper es; inverse problem.
Šimůnek et al. (2006b),
HYDRUS-2D (2.0) + SWMS_3D + 32 bit GUI; two- and threedimensional variably saturated water flow and solute transportŠejna and Šimůnek (2007)
in porous media; VG, MVG, Durner (1994), and Kosugi (1996) soil
hydraulic property models; hysteresis in soil hydraulic proper es;
nonlinear solute transport; sequen al first-order decay chains; gas
diﬀusion; temperature dependence of soil hydraulic and solutetransport parameters; two-site sorp on model; dual-porosity
mobile–immobile water flow; virus, colloid, and bacteria transport;
constructed wetland module
So ware package for analyzing data collected with the tension diskŠimůnek and van Genuchten
infiltrometer; 32 bit GUI(2000)
Studio of analy cal models for analyzing solute transport, includingŠimůnek et al. (1999b)
CFitM (van Genuchten, 1980b), CFitIm (van Genuchten, 1981b),
Chain (van Genuchten, 1985), CXTFIT (Toride et al., 1995), 3ADE
(Leij and Bradford, 1994), N3DADE (Leij and Toride, 1997), andScreen (Jury et al., 1983); 32 bit GUI.
So ware package for analyzing soil hydraulic proper es; VG, BC,
Released online
Durner (1994), and Kosugi (1996) soil hydraulic property models;
32 bit GUI.
Hierarchical neural network pedotransfer func ons for the van
Schaap et al. (2001)
Genuchten–Mualem equa ons
Database serving as a repository of measured unsaturated soil
Leij et al. (1996)
hydraulic property data
One-dimensional water flow; transport of mul ple components;
Jacques and Šimůnek (2005)
mixed equilibrium–kine c biogeochemical reac ons; heattransport in variably saturated media

SWMS_2DDISKSTANMOD

2.0

RETC

ROSETTA

1.0

UNSODA
HP1

1.0

Kool and van Genuchten(1991)
Vogel et al. (1996)Šimůnek et al. (1998b)Šimůnek and Suarez (1993c)† 2 refers to two-dimensional and axisymmetrical three-dimensional; NA, not applicable.
‡ GUI, graphical user interface; BC, Brooks and Corey (1964); MVG, modified van Genuchten soil hydraulic func ons (Vogel and Císlerová, 1988).

www.vadosezonejournal.org · Vol. 7, No. 2, May 2008588

registered changes in the pressure head during the ﬁrst
iteration. Solute transport was described using the standard advection–dispersion equation that included linear
sorption, ﬁrst-order degradation in both the liquid andsolid phases, and zero-order production in both phases.
Several other numerical improvements were at the time
also implemented in SWMS_2D. These included solution of the mixed form of the Richards equation as
suggested by Celia et al. (1990), thus providing excellent
mass balances in the water ﬂow calculations, and higher
order corrections to the dispersion term (van Genuchten,
1978c) to improve the numerical solution of the transport equation. While SWMII could simulate water ﬂow
in two dimensions in either vertical or horizontal planes,
SWMS_2D extended the range of applications also to
F . 1. History of development of HYDRUS and related so ware packages. So ware
three-dimensional axisymmetrical ﬂow domains aroundpackages supported by graphical user interfaces are in color (2D, blue; 2D/3D, red).
a vertical axis of symmetry. Examples are ﬂow to a well,inﬁltration from a surface ring or tension disk inﬁltromDOS Numerical Models
eter, and inﬁltration from a surface or subsurface dripper.
UNSAT and SWMIIThe original version (1.1) of SWMS_2D used Gaussian elimThe two-dimensional HYDRUS models and their predecesination to solve the systems of linear algebraic equations resulting
sors have a long history (Fig. 1). The origin of these models canfrom discretization of the governing partial diﬀerential equations.
be traced back to the early work of Dr. Shlomo Neuman and colThe invoked solvers took advantage of the banded nature of thelaborators (Neuman, 1972, 1973, 1975; Neuman et al., 1974),
coeﬃcient matrices and, in the case of water ﬂow, of the symwho developed their UNSAT model at the Hydraulic Engineering
metric properties of the matrix. Since direct solution methods
Laboratory of Technion, Israel Institute of Technology, in Haifa,
have several disadvantages compared with iterative methods, espeIsrael, long before the introduction of personal computers. The
cially for relatively large problems, we supplemented the direct
UNSAT model was a ﬁnite element model simulating water ﬂow
solvers in Version 1.2 of SWMS_2D (Šimůnek et al., 1994)
in two-dimensional variably saturated domains as described withusing iterative solvers adopted from the ORTHOFEM software
the Richards equation (Richards, 1931). The model additionally
package of Mendoza et al. (1991). The system of linear algebraic
considered root water uptake as well as a range of pertinent boundequations for water ﬂow were solved using the preconditioned
ary conditions required to ensure wide applicability of the model.
conjugate gradient method, and for solute transport using the
The UNSAT model was later modiﬁed by Davis and Neuman
ORTHOMIN (preconditioned conjugate gradient squared) pro(1983) at the University of Arizona, Tucson, such that the model
cedure (Mendoza et al., 1991).
could be run on personal computers. This last version of UNSAT
Since SWMS_2D was in the public domain and distributed
formed the basis of the SWMII model developed by Vogel (1987)
freely by USSL on a CD or downloadable from the USSL website,
during his stay with Dr. Reinder Feddes and Dr. Han Stricker at
the code quickly became popular with many users. The HYDRUS
Wageningen University, Wageningen, the Netherlands.
website lists a large number of references, from various peerThe SWMII model signiﬁcantly extended the capabilities
reviewed journals, in which SWMS_2D was used. The search forand ease of use of UNSAT. The code simulated variably saturated
this list was performed using Google Scholar. Model applications
water ﬂow in two-dimensional transport domains, implemented
involved both agricultural and nonagricultural problems. Early
the van Genuchten soil hydraulic functions (van Genuchten,
agricultural applications included simulations of various irriga1980a) and modiﬁcations thereof (Vogel and Císlerová, 1988),
tion or drainage schemes (e.g., Benjamin et al., 1994; Meshkat
considered root water uptake by taking advantage of some of
et al., 1999) and the transport of various chemicals applied to
the features of the SWATRE model (Feddes et al., 1978), andagricultural soils (e.g., de Vos et al., 2000). Early nonagricultural
included scaling factors to enable simulations of ﬂow in heterogeapplications included studies of ﬂow and transport in heteroneous soils. The code also allowed the ﬂow region to be composed
geneous porous media (e.g., Tseng and Jury, 1994; Roth, 1995;
of nonuniform soils having an arbitrary degree of local anisotropy.
Roth and Hammel, 1996; Hammel and Roth, 1998). These studThe SWMII model was a direct predecessor of the SWMS_2D
ies showed that due to soil heterogeneity, water and solutes canmodel (Šimůnek et al., 1992) developed later at USSL.
ﬁnd ﬂow paths that are much more conductive than would be
expected from the average hydraulic conductivity.
SWMS_2DCHAIN_2DThe SWMS_2D model (Šimůnek et al., 1992) considerably
extended the capabilities of SWMII by including provisions forsolute transport. The speed and computational eﬃciency of thewater ﬂow calculations (still a major concern in the early and mid1990s) were increased by restricting calculations for the secondand subsequent iterations during the iterative solution process of
the Richards equation only to those parts of the ﬂow domain thatwww.vadosezonejournal.org · Vol. 7, No. 2, May 2008

The ﬁrst major upgrade of SWMS_2D was released under
the name CHAIN_2D (Šimůnek and van Genuchten, 1994).
This model greatly expanded on the capabilities of SWMS_2D
by including, among other things, sequential ﬁrst-order solutedecay chains and heat transport. The temperature dependenceof the soil hydraulic properties was included by considering the589

eﬀects of temperature on surface tension, dynamic viscosity, andthe density of water. The heat transport equation in CHAIN_2D
considered transport due to conduction and advection withﬂowing water. The solute transport equations considered advective–dispersive transport in the liquid phase, as well as diﬀusionin the gaseous phase. The transport equations also included provisions for nonlinear nonequilibrium reactions between the solidand liquid phases, linear equilibrium reactions between the liquidand gaseous phases, zero-order production, and two ﬁrst-orderdegradation reactions: one that was independent of other solutes,
and one that provided the coupling between solutes involvedin the sequential ﬁrst-order decay reactions. Typical examplesof sequential ﬁrst-order decay chains are the transport of radionuclides (van Genuchten, 1985), N species (e.g., Hanson etal., 2006), pesticides (Wagenet and Hutson, 1987), chlorinatedaliphatic hydrocarbons (Schaerlaekens et al., 1999; Casey andŠimůnek, 2001), hormones (Casey et al., 2003), and explosives(Dontsova et al., 2006). The additional solute transport processes in CHAIN_2D also allowed simulations of the transportof volatile contaminants, such as methyl bromine or 1,3-dichloropropene (e.g., Wang et al., 1997, 2000).

Even with the fast personal computers currently available, it isvirtually impossible to solve, within a reasonable computationaltime, problems having more than about half a million nodes ormore. To decrease the required computational time, Hardelauf
et al. (2007) parallelized SWMS_3D to develop PARSWMS,
which distributes problems with a large number of elements
across multiple processors working in parallel. The PARSWMS
code was developed for Linux or UNIX workstations using the
installed freewares MPI, PETSc, and PARMETIS. Hardelauf etal. (2007) demonstrated that doubling the number of processors
may decrease the computational time by up to nearly 50%.
The majority of applications of the diﬀerent DOS-based multidimensional numerical models discussed above involved relatively
simple geometrical domains since these codes were supported
only by simple ﬁnite element mesh generators for either structured quadrilateral or hexagonal geometries. Users were responsible
for preparing their own inputs characterizing the computational
domains and discretizing them into ﬁnite elements. Broader applicability and adoption of the codes could be accomplished only bydevelopment of graphical tools for easier domain design and theirdiscretization into ﬁnite elements. This was accomplished withthe second generation of the various modeling tools, starting with
Version 1.0 of HYDRUS-2D as described below.

UNSATCHEM-2D

The SWMS_2D model was further expanded by Šimůnek
and Suarez (1993b, 1994) to also simulate the transport of major
ions in variably saturated porous media, including major ion
equilibrium and kinetic nonequilibrium chemistry. The resulting
UNSATCHEM-2D code was intended for prediction of major
ion chemistry and water and solute ﬂuxes in soils during transient ﬂow. Since the solution chemistry in the unsaturated zone issigniﬁcantly inﬂuenced by variations in water content, temperature, and CO2 concentrations in the soil gas phase, all of thesevariables were included in the model. The CO2 transport andproduction model was based on the SOILCO2 model (Šimůnek
and Suarez, 1993a,c) described below. The major variables of thechemical system in UNSATCHEM-2D were Ca, Mg, Na, K, SO4,
Cl, NO3, H4SiO4, alkalinity, and CO2. The model accounted forvarious equilibrium chemical reactions between these components,
such as complexation, cation exchange, and precipitation–dissolution. For the precipitation–dissolution of calcite and dissolution of
dolomite, either equilibrium or multicomponent kinetic expressions could be used, which included both forward and backward
reactions. Other dissolution–precipitation reactions considered
included gypsum, hydromagnesite, nesquehonite, and sepiolite.
Since the ionic strength of soil solutions can vary considerably intime and space and often reach high values, both the modiﬁed
Debye–Hückel and Pitzer expressions were incorporated into themodel to calculate single ion activities.

HYDRUS

The one-dimensional HYDRUS models were initially developed
mostly independently of their multidimensional counterparts. It was
only with the later versions of the Windows-based HYDRUS-1D(Šimůnek et al., 1998c) and HYDRUS-2D (Šimůnek et al., 1999a)software packages that the various processes in these programs were
uniﬁed. Selected features of earlier one-dimensional codes, such as
SUMATRA-1 (van Genuchten, 1978b), WORM (van Genuchten,1987), and SWMI (Vogel, 1990) had been incorporated into theDOS-based one-dimensional HYDRUS models simulating waterﬂow and solute transport in one-dimensional variably saturated soils(HYDRUS 3.0 of Kool and van Genuchten, 1991; HYDRUS 5.0
of Vogel et al., 1996; HYDRUS 6.0 of Šimůnek et al., 1998b).
Most of these codes additionally also considered root water uptake,as well as solute transport subject to linear sorption, ﬁrst-orderdegradation in both the liquid and solid phases, and zero-orderproduction in both phases. Interestingly, there was at the time very
little common code and overlap between the diﬀerent versions of
the DOS-based HYDRUS codes. For example, the early UNSAT1
and SUMATRA-1 codes of van Genuchten (1978b,c) were basedon Hermitian cubic ﬁnite element schemes, which proved to be lesssuitable for highly nonlinear inﬁltration scenarios than those using
standard linear ﬁnite elements. Starting in 1998, the Windowsbased HYDRUS-1D (Šimůnek et al., 1998c) and HYDRUS-2D(Šimůnek et al., 1999a) software packages uniﬁed most or all of theprocesses and numerical procedures included in the various codes.

SWMS_3D

The SWMS_3D model (Šimůnek et al., 1995) was a
direct extension of the SWMS_2D code (Version 1.2) to threedimensional ﬂow and transport problems. The model uses theﬁnite element method with tetrahedral linear ﬁnite elements tosolve the Richards equation for water ﬂow and the advection–
dispersion equation with linear sorption for solute transport inthree-dimensional transport domains.
Three-dimensional applications often require a large numberof ﬁnite elements to discretize realistically large transport domains.
www.vadosezonejournal.org · Vol. 7, No. 2, May 2008

SOILCO2Šimůnek and Suarez (1993a,c) additionally developed apredictive simulation model, SOILCO2, to simulate one-dimensional water ﬂow and multiphase transport of CO2 based on
the Richards and advection–dispersion equations, respectively.
The model also included heat transport and a CO2 production
module. Transport of CO2 was assumed to occur in both theliquid and gas phases. The gas transport equation accounted for590

production of CO2 and uptake of CO2 by plant roots associatedwith root water uptake. The CO2 production model considered
microbial as well as root respiration, which both depend on watercontent, temperature, plant growth, salinity, and plant and soil
characteristics. Heat ﬂow was included in the model since several
CO2 transport parameters and various partitioning and production coeﬃcients are strongly temperature dependent. An early
application of SOILCO2 to ﬁeld data was presented by Suarez
and Šimůnek (1993).
Although all of the above DOS-based programs are still
publicly available (most can still be downloaded from the USSL
web site), none is currently being developed further since they
have been replaced with Windows-based programs or modules
as described below.

van Genuchten (Vogel and Císlerová, 1988) type analytical functions. The heat transport equation considers conduction as wellas advection with ﬂowing water. The solute transport equations
assume advective–dispersive transport in the liquid phase anddiﬀusion in the gaseous phase. The transport equations further
include provisions for nonlinear and nonequilibrium reactions
between the solid and liquid phases, linear equilibrium reactions
between the liquid and gaseous phases, zero-order production,and two ﬁrst-order degradation reactions: one that is independentof other solutes, and one that provides the coupling between solutes involved in sequential ﬁrst-order decay reactions. In addition,
physical nonequilibrium solute transport can be accounted forby assuming a two-region, dual-porosity type formulation thatpartitions the liquid phase into mobile and immobile regions.
The HYDRUS-1D software may be used to analyze waterand solute movement in unsaturated, partially saturated, or fully
saturated homogeneous layered media. The code incorporates
hysteresis by assuming that drying scanning curves are scaled
from the main drying curve and wetting scanning curves fromthe main wetting curve. Root growth is simulated by meansof a logistic growth function, while root water uptake can be
simulated as a function of both water and salinity stress. The
HYDRUS-1D software package additionally implements a
Marquardt–Levenberg type parameter estimation technique(Marquardt, 1963; Šimůnek and Hopmans, 2002) for inverse
estimation of soil hydraulic (Šimůnek et al., 1998d; Hopmans
et al., 2002) and solute transport and reaction (Šimůnek et al.,2002) parameters from measured transient or steady-state ﬂow
or transport data. The programs are, for this purpose, written insuch a way that almost any application that can be run in a directmode can equally well be run in an inverse mode and thus formodel calibration and parameter estimation. The inverse option
has proved to be very popular with many users, leading to a large
number of applications ranging from relatively simple laboratory
experiments, such as one- and multistep outﬂow or evaporation

Windows-Based Numerical Models
Even with well-documented technical or user manuals available, one major problem often preventing the use of DOS-based
numerical codes is the extensive work generally required for datapreparation, ﬁnite element grid design, and graphical presentation of the output results (Šimůnek et al., 1996a). The widespread
adoption of numerical models requires techniques that make iteasier for users to create, manipulate, and display large data ﬁles,and to facilitate interactive data management. Introducing suchtechniques frees users from cumbersome manual data processing
and should enhance the eﬃciency in which programs are being
implemented for a particular example. To avoid or simplify the
preparation and management of relatively complex input dataﬁles and to graphically display ﬁnal simulation results, we started
in 1995 developing interactive graphical user interfaces (GUIs)
for the Microsoft Windows environments that resulted in several
software packages described below. While the earlier Windowsbased versions were still 16-bit applications, all software packages
released starting in 1998 were 32-bit applications.
HYDRUS-1DThe HYDRUS-1D software packages(Šimůnek et al., 1998c, 2005) (Fig. 2) were basedon the latest DOS Version 6.0 of HYDRUS(Šimůnek et al., 1998b). Three major upgradesof HYDRUS-1D have been released so far. Whilethe diﬀerence between Versions 1.0 and 2.0 was
mainly technical (16- vs. 32-bit applications,
respectively), Version 3.0 (Šimůnek et al., 2005)
represented a major upgrade with several new processes included in the software package. Version
2.0 of HYDRUS-1D (Šimůnek et al., 1998c)
may be used to simulate the one-dimensional
movement of water, heat, and multiple solutes invariably saturated media. The program uses linear
ﬁnite elements to numerically solve the Richards
equation for saturated–unsaturated water ﬂow andFickian-based advection–dispersion equations forboth heat and solute transport. The ﬂow equation also includes a sink term to account for water
uptake by plant roots as a function of both waterand salinity stress. The unsaturated soil hydraulic F . 2. Main window of the HYDRUS-1D so ware package. The preprocessing part isproperties can be described using van Genuchten on the le and post-processing part on the right. Individual input and output com(1980a), Brooks and Corey (1964), and modiﬁed mands are accessible either using menus or directly from the main window.
www.vadosezonejournal.org · Vol. 7, No. 2, May 2008591

experiments to more elaborate ﬁeld problems involving multiple
soil horizons and chemicals. We refer to the HYDRUS website
for speciﬁc examples.
The HYDRUS-1D package uses a Microsoft Windows-based
GUI to manage the input data required to run the program, as
well as for nodal discretization and editing, parameter allocation,
problem execution, and visualization of results. All spatially distributed parameters, such as those for various soil horizons, root
water uptake distribution, and the initial conditions for water,
heat, and solute movement, are speciﬁed in a graphical environment. The program oﬀers graphs of the distributions of thepressure head, water content, water and solute ﬂuxes, root water
uptake, and temperature and solute concentrations in the subsurface at preselected times. Also included is a small catalog of
unsaturated soil hydraulic properties (Carsel and Parrish, 1988) as
well as pedotransfer functions based on neural networks (Schaap
et al., 2001).
Version 3.0 of HYDRUS-1D (Šimůnek et al., 2005) includes
several new features compared with Version 2.0. Among the newfeatures are additional analytical functions for soil hydraulic properties (Durner, 1994; Kosugi, 1996), compensated root water
uptake, and various provisions for simulating nonequilibrium
ﬂow and transport (Šimůnek et al., 2003; Šimůnek and van
Genuchten, 2008). The ﬂow equation for the latter purpose canconsider dual-porosity-type ﬂow, with a fraction of the watercontent being mobile and a fraction immobile. The transport
equations additionally were modiﬁed to allow consideration of
kinetic attachment–detachment processes of solutes to the solid
phase, and hence of solutes having a ﬁnite size. This attachment–
detachment feature has been used by many recently to simulate
the transport of viruses (e.g., Schijven and Šimůnek, 2002), colloids (e.g., Bradford et al., 2002, 2003, 2004), and bacteria (e.g.,
Gargiulo et al., 2007a,b, 2008). The HYDRUS-1D software further includes modules for simulating CO2 transport and major
ion chemistry modules, adopted from the UNSATCHEM-2D(Šimůnek and Suarez, 1993b) and UNSATCHEM programs(Šimůnek et al., 1996b). Gonçalves et al. (2006) recently
demonstrated the use of these new modules by simulating multicomponent major ion solute transport in soil lysimeters irrigatedwith waters of diﬀerent qualities. The HYDRUS-1D package
was used in this application to described ﬁeld measurements of
the water content, overall salinity, and concentration of individual soluble cations, as well as the Na adsorption ratio and theexchangeable Na percentage.
The water ﬂow part of HYDRUS-1D has been recently usedby Seo et al. (2007) in the HYDRUS package for MODFLOW(Harbaugh et al., 2000) to represent the eﬀects of vadose zone
processes in this widely used groundwater ﬂow model. Being
fully incorporated into the MODFLOW program, the HYDRUS
package provides MODFLOW with recharge ﬂuxes at the watertable, while MODFLOW provides HYDRUS with the positionof the groundwater table that is used as the bottom boundary
condition. Twarakavi et al. (2008) compared the HYDRUS package to other contemporary modeling approaches and evaluated its
performance for three case studies of increasing complexity.
Finally, we emphasize that HYDRUS-1D is continuously
being updated with new processes. Although the new features are
not always immediately made available publicly, they are usuallyshared immediately with colleagues so that they can be properly
www.vadosezonejournal.org · Vol. 7, No. 2, May 2008

tested before their general release. For example, Scanlon et al.
(2003) and Saito et al. (2006) used a version of HYDRUS-1D thatconsiders coupled water, vapor, and energy movement in soils, aswell as mass and energy balances at the soil surface, while Hansson
et al. (2004) also considered freeze–thaw processes. Šimůnek etal. (2001), Haws et al. (2005), Köhne et al. (2004, 2006), Pot
et al. (2005), and Kodešová et al. (2008), among many others,
used a version of HYDRUS-1D that considers the dual-permeability ﬂow and transport model of Gerke and van Genuchten(1993). Pang and Šimůnek (2006) evaluated bacteria-facilitated
Cd transport in gravel columns using the HYDRUS-1D codewith capabilities to simulate colloid-facilitated solute transport(Šimůnek et al., 2006a). Finally, Šimůnek and Nimmo (2005)
used a version that allowed simulations of water ﬂow in accelerated centrifugal ﬁelds.
HYDRUS-2D

Most or all processes in HYDRUS-1D were included also in
HYDRUS-2D, including water uptake by plant roots as a function of both water and salinity stress, a range of soil hydraulicfunctions, solute decay chains, hysteresis, provisions for nonlinear and nonequilibrium reactions, physical nonequilibrium(dual-porosity) type solute transport, and parameter estimation
capabilities. While Version 1.0 of HYDRUS-2D (Šimůnek etal., 1996a) was based on the SWMS_2D model (Šimůnek etal., 1994), Version 2.0 (Šimůnek et al., 1999a) was derived fromCHAIN_2D (Šimůnek and van Genuchten, 1994). A uniquefeature of HYDRUS-2D is that it can handle ﬂow regions delineated by irregular boundaries as well as three-dimensional regions
exhibiting radial symmetry about the vertical axis. The code
includes the MeshGen2D mesh generator (Lain and Šejna, 1992;Šejna et al., 1994), which was speciﬁcally designed for variably
saturated subsurface ﬂow and transport problems. The mesh generator may be used for deﬁning very general domain geometries
and for discretizing the transport domain into an unstructured
ﬁnite element mesh.
Similarly as discussed above for HYDRUS-1D,HYDRUS-2D, before having been recently fully replaced with
HYDRUS (2D/3D) as described below, was continuously being
updated with new features and processes. New dynamic boundary
conditions suitable for various microirrigation schemes implemented into HYDRUS-2D were used, for example, by Gärdenäs
et al. (2005), Lazarovitch et al. (2005), and Hanson et al. (2006).
Hansson et al. (2005) simulated water ﬂow patterns in ﬂexible
pavements with a version of HYDRUS-2D that considered, in
addition to subsurface ﬂow, also the surface runoﬀ describedusing the kinematic equation.
HYDRUS (2D/3D)

The HYDRUS (2D/3D) software package (Šimůnek et al.,2006c; Šejna and Šimůnek, 2007) (Fig. 3) is an extension andreplacement of HYDRUS-2D (Version 2.0) and SWMS_3D.
This software package is a complete rewrite of HYDRUS-2D
and its extensions for two- and three-dimensional geometries.
In addition to features and processes available in HYDRUS-2Dand SWMS_3D, the new computational modules of HYDRUS(2D/3D) consider (i) water ﬂow and solute transport in a dualporosity system, thus allowing for preferential ﬂow in fractures
or macropores while storing water in the matrix (Šimůnek et592

F . 3. Main window of the HYDRUS (2D/3D) so ware package. Input and output data are accessible using the data tree of the naviga on baron the le . The computa onal domain with its finite element discre za on, various domain proper es, ini al and boundary condi ons, andresults are displayed in one or mul ple view windows in the middle. Various tools for manipula ng data in the view window are available on
the edit bar on the right. The tabs in the view window allow fast access to diﬀerent type of data.

al., 2003), (ii) root water uptake with compensation, (iii) the
spatial root distribution functions of Vrugt et al. (2001), (iv) the
soil hydraulic property models of Kosugi (1996) and Durner(1994), (v) the transport of viruses, colloids, and bacteria using
an attachment–detachment model, ﬁltration theory, and blocking functions (e.g., Bradford et al., 2004), (vi) a constructedwetland module (only in two dimensions) (Langergraber andŠimůnek, 2005, 2006), (vii) the hysteresis model of Lenhard et al.
(1991) to eliminate pumping by keeping track of historical reversal points, (viii) new print management options, (ix) dynamic,
system-dependent boundary conditions, (x) ﬂowing particles in
two-dimensional applications, and (xi) calculations of actual andcumulative ﬂuxes across internal mesh lines.
New features of the GUI of HYDRUS (2D/3D) include,
among other things, (i) a completely new GUI based on high-end
three-dimensional graphics libraries, (ii) the Multiple Document
Interface architecture with multiple projects and multiple views,(iii) a new organization of geometric objects, (iv) a navigation window with an object explorer, (v) many new functions
improving the user friendliness, such as drag-and-drop andcontext-sensitive pop-up menus, (vi) improved interactive tools
for graphical input, (vii) options to save cross-sections and meshwww.vadosezonejournal.org · Vol. 7, No. 2, May 2008lines for charts within a given project, (viii) a new display options
dialog where all colors, line styles, fonts, and other parameters ofgraphical objects can be customized, (ix) extended print options,(x) extended information in the Project Manager (including project previews), and (xi) an option to export input data for theparallelized PARSWMS code (Hardelauf et al., 2007).
An interesting application of HYDRUS (2D/3D) is presented by Sansoulet et al. (2008), who simulated transient spatial
distributions of water ﬂuxes in a three-dimensional transportdomain under a banana (Musa sp.) plant.
DISC

The DISC software package (Šimůnek and van Genuchten,
2000) is a dramatic simpliﬁcation of HYDRUS-2D for analyzing tension disk inﬁltrometer data by parameter estimation.
The DISC code numerically solves the Richards equation forsaturated–unsaturated water ﬂow in a three-dimensional region
exhibiting radial symmetry about the vertical axis. The software
includes the Marquardt–Levenberg (Marquardt, 1963) parameter
optimization algorithm for inverse estimation of soil hydraulicproperties from measured transient cumulative inﬁltration andrelated data obtained during a typical tension disk permeameter593

experiment (Šimůnek and van Genuchten, 1996, 1997). Šimůnek
and van Genuchten (1997) concluded that the best practicalscenario for estimating soil hydraulic parameters from a tension
disk inﬁltration experiment is to use the cumulative inﬁltration
curve measured at several consecutive tensions applied to thesoil surface, in conjunction with knowledge of the initial andﬁnal water content. These results suggest that one should be able
to use information typically being collected with a tension disk
inﬁltrometer to estimate not only the unsaturated hydraulic conductivity function but, without further experiments, also the soil
water retention curve (Šimůnek et al., 1998a). The applicabilityof the suggested inverse technology using ﬁeld data was recently
demonstrated by Ramos et al. (2006).

Jacques et al. (2003, 2008a,b), Jacques and Šimůnek (2005),
and Šimůnek et al. (2006b) demonstrated the versatility of HP1
on several examples such as (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 medium
with a pH-dependent cation exchange complex, (iv) inﬁltration ofa hyperalkaline solution in a clay sample (this example consideredkinetic precipitation–dissolution of kaolinite, illite, quartz, calcite, dolomite, gypsum, hydrotalcite, and sepiolite), (v) long-termtransient ﬂow and transport of major cations (Na+, K+, Ca2+, andMg2+) and heavy metals (Cd2+, Zn2+, and Pb2+) in a soil proﬁle,(vi) Cd leaching in acid sandy soils, (vii) radionuclide transport(U and its aqueous complexes), and (viii) the fate and subsurface
transport of explosives (trinitrotoluene [TNT] and its daughter
products 4-amino-2,6-dinitrotoluene [4ADNT], 2-amino-4,6dinitrotoluene [2ADNT], and 2,4,6-triaminotoluene [TAT]).

UNSATCHEM

The UNSATCHEM software package (Šimůnek etal., 1996b) resulted from combining various features from
SOILCO2 (water ﬂow, heat transport, and CO2 transport),
UNSATCHEM-2D (major ion chemistry), and Version 1.0
of HYDRUS-1D (especially the GUI). We refer to the originalcodes for detailed descriptions of the many processes that werecombined into UNSATCHEM. The UNSATCHEM package
allows simulations of one-dimensional water ﬂow, heat transport,
multiphase transport of CO2, transport of major ions, and major
ion equilibrium and kinetic nonequilibrium chemistry in variably saturated porous media. The model as such can consider theeﬀects of varying water content, temperature, CO2–producing
microbiological activity, and CO2 transport in the soil environment on geochemical transport. The UNSATCHEM code wasused to evaluate alternative strategies for sodic soil reclamationby Šimůnek and Suarez (1997), while an application assessing As
oxyanion transport in gold mine heap leach facilities was demonstrated by Decker et al. (2006), the latter using a modiﬁed version
that included additional species such as As and pyrite. Major ion
chemistry and CO2 transport modules of UNSATCHEM were
fully incorporated into Version 3.0 of HYDRUS-1D.

AnalyƟcal Solute Transport Models
Parallel to the development of numerical models, joint collaborative work at USSL and UCR also produced a large numberof analytical models for solute transport. These solutions pertained
to one-dimensional equilibrium transport (e.g., van Genuchten,
1981a,b; van Genuchten and Alves, 1982), one-dimensional nonequilibrium transport (van Genuchten and Wierenga, 1976; van
Genuchten and Wagenet, 1989; Toride et al., 1993), two- andthree-dimensional equilibrium transport (Leij et al., 1991), andtwo- or three-dimensional nonequilibrium transport (Leij et al.,1993). Much of this work has been incorporated into a seriesof computer programs for both forward and inverse analyses ofsolute transport in soils and groundwater. The ﬁrst computercodes for inverse estimation of solute transport parameters were
the CFITM (van Genuchten, 1980b) and CFITIM codes (vanGenuchten, 1981b), which considered the analysis of laboratory
soil column breakthrough curves in terms of equilibrium andnonequilibrium transport models, respectively. These models were
updated by Parker and van Genuchten (1984) to yield the widelyused CXTFIT code. This program allowed analysis of column
breakthrough data, as well as distributions vs. depth. The CFITM,
CFITIM, and CXTFIT models were the ﬁrst computerizedparameter estimation codes for estimating selected equilibriumand nonequilibrium transport parameters from observed laboratory and ﬁeld data. They provided a much-needed alternative
to the then widely accepted but much more approximate trial
and error or graphical methods for analyzing laboratory or ﬁeld
transport data (van Genuchten and Wierenga, 1986).
The CXTFIT code of Parker and van Genuchten (1984) waslater updated by Toride et al. (1995) to allow analysis of a muchbroader range of laboratory and ﬁeld data. The program permitted more ﬂexible initial and boundary conditions, included moregeneral zero- and ﬁrst-order production or decay scenarios, andconsidered both local-scale equilibrium and nonequilibrium processes in the stochastic stream-tube models. The CXTFIT codealso included a variety of stochastic stream-tube models that consider the eﬀects of areal variations in the pore-water velocity on
ﬁeld-scale transport. The CXTFIT models were later extended
by Leij and Bradford (1994) to three-dimensional equilibriumtransport to produce the 3DADE software package, and by Leij
and Toride (1997) to three-dimensional nonequilibrium trans-

HP1

The most complex modeling tool in terms of available
chemical and biological reactions was recently developed bycoupling HYDRUS-1D with the PHREEQC geochemical code
(Parkhurst and Appelo, 1999). This coupling resulted in a newcomprehensive simulation tool, HP1 (acronym for HYDRUS1D–
PHREEQC, Version 1) (Jacques and Šimůnek, 2005; Jacques etal., 2006). The combined code contains modules simulating (i)transient water ﬂow in variably saturated media, (ii) the transportof multiple components, (iii) mixed equilibrium–kinetic biogeochemical reactions, and (iv) heat transport. The HP1 programis a signiﬁcant expansion of the individual HYDRUS-1D and
PHREEQC programs by combining and preserving most of their
original features and capabilities into a single numerical model.
The code still uses the Richards equation for variably saturated
ﬂow and advection–dispersion type equations for heat and solutetransport; however, the program can now simulate also a broad
range of low-temperature biogeochemical reactions in water, thevadose zone, and groundwater systems, including interactions
with minerals, gases, exchangers, and sorption surfaces, basedon thermodynamic equilibrium, kinetics, or mixed equilibrium–
kinetic reactions.
www.vadosezonejournal.org · Vol. 7, No. 2, May 2008594

port to yield the N3DADE code. All of the abovetransport codes, except N3DADE, were developedfor both the forward and inverse analyses.
The various analytical transport models above
were all DOS-based codes. A major development
next was their inclusion in the public-domain
Windows-based STANMOD (STudio of ANalytical
MODels) computer software package (Šimůnek
et al., 1999b) (Fig. 4). In addition to CFITM,
CFITIM, CXTFIT, 3DADE, and N3DADE,STANMOD also included the CHAIN code of
van Genuchten (1985) for analyzing the advective–
dispersive transport of up to four solutes involved
in sequential ﬁrst-order decay reactions (e.g., forradionuclide decay chains or the simultaneous
movement of various interacting N or organic
chemicals). Another one-dimensional analyticalmodel included in STANMOD is the screening
model of Jury et al. (1983) for describing the transport, degradation, and volatilization of soil-applied
volatile organic chemicals. The STANMOD package hence is a very ﬂexible tool for approximate
analysis of one- two-, or multidimensional solutetransport problems in soils and groundwater.

F . 4. Graphical display of results obtained with the STANMOD so ware package.

tion model of Kosugi (1996) and the dual-porosity formulation
proposed initially by Durner (1994). In addition to the inverse
options available in RETC, we also added a direct option for calculating the soil hydraulic functions from speciﬁed parameters.

Unsaturated Soil Hydraulic
Property SoŌware

Rose aA third area of collaborative software development at USSLand UCR has been in the area of hydraulic property estimation,
leading to the RETC code for analyzing soil hydraulic property
data, the Rosetta software for estimating the hydraulic properties
using pedotransfer functions, and the UNSODA soil hydraulicproperty database. These three software packages are brieﬂy summarized below.

Numerical models such as the HYDRUS codes simulating variably saturated ﬂow all require information about theunsaturated soil hydraulic properties. Considering that direct
measurements of the soil hydraulic properties is relatively tedious,
diﬃcult, and time consuming, many have attempted to predict

RETC

Much of the hydraulic property research at USSL started
with the publication of van Genuchten’s (1980a) study in which
statistical pore-size distribution models for the unsaturated soil
hydraulic conductivity (Mualem, 1976) were combined with arelatively ﬂexible equation for the soil water retention curve toyield closed-form constitutive relationships that could be readily
incorporated in numerical simulators like HYDRUS. The van
Genuchten equations have become quite popular in the subsurface hydrologic literature (Kundzewicz and Koutsoyiannis, 2007)
by providing an attractive alternative to the then popularly usedequations of Brooks and Corey (1964). The hydraulic functions
were ﬁrst programmed in the SOHYP model (van Genuchten,
1978a), but later extended in the RETC code (van Genuchten etal., 1991) using fewer restrictions on the van Genuchten m and nparameters. The programs may be used to predict the unsaturated
hydraulic conductivity from observed soil water retention dataassuming that one observed conductivity value (not necessarily atsaturation) is available. The RETC program also permits ﬁtting ofanalytical functions simultaneously to observed water retention
and hydraulic conductivity data. In 1999, we supplemented the
RETC program with a GUI (Fig. 5) similar to STANMOD, andexpanded the program to also include the lognormal distribuwww.vadosezonejournal.org · Vol. 7, No. 2, May 2008

F . 5. Display by RETC of hydraulic conduc vity data fi ed with thevan Genuchten-Mualem model (van Genuchten, 1980a).
595

soil hydraulic properties from more easily measured surrogate soil
properties, such as soil texture and other more readily available
information. Relationships between the soil hydraulic and other(textural) properties are commonly called pedotransfer functions(PTFs). Pedotransfer functions have been developed using various mathematical and statistical approaches, such as regression orneural network analyses (Schaap et al., 1998, 2001). Pedotransfer
functions can be used to predict either the soil hydraulic properties directly, such as the water content at speciﬁed pressure heads
or the saturated hydraulic conductivity, or parameters in the analytical models used for the soil hydraulic properties.
Schaap et al. (1998) calibrated hierarchical neural network
PTFs for the van Genuchten–Mualem equations on a large database of soil hydraulic and related properties, and implemented theresulting PTFs into the Rosetta software package (Schaap et al.,2001). Figure 6 shows a dialog window from the HYDRUS-1D
software package that implements the Rosetta Lite module (asimpliﬁcation of Rosetta) of Schaap et al. (2001) to predict van
Genuchten (1980a) soil hydraulic parameters using ﬁve diﬀerent
levels of input data. The simplest model (Model 1) uses the average of ﬁtted hydraulic parameters within a textural class in the
USDA textural triangle. These averages provide an alternative tothe class-average values obtained by Carsel and Parrish (1988).
The four other models in Rosetta use progressively more detailed
input data, starting with the sand, silt, and clay fractions (Model2), then adding a measured bulk density value (Model 3), andadditionally requiring water contents at 33 (Model 4) and 1500
(Model 5) kPa suctions (i.e., at 330 and 15,000 cm), which are
traditionally considered to be the ﬁeld capacity and permanent
wilting point, respectively. All estimated hydraulic parametersin Rosetta itself are accompanied by uncertainty estimates that
permit an assessment of the reliability of Rosetta’s predictions.
These uncertainty estimates were generated by combining theneural networks with the bootstrap method (for more information, see Schaap and Leij, 2000; Schaap et al., 1998, 2001).

urated soil hydraulic property data (water retention, hydraulicconductivity, and soil water diﬀusivity), and related soils information (particle-size distribution, bulk density, organic matter
content, etc.) potentially useful for theoretical analysis of thehydraulic properties. The initial DOS-based version of the database was released in 1996 (Leij et al., 1996), but later updated(Nemes et al., 2001) in Microsoft Access 97 format to provide
more ﬂexibility in data entry and retrieval and possible interfacing with other programs. The database can be used to: (i) store
and edit data; (ii) search for data sets based on user-deﬁned query
speciﬁcations; (iii) write the contents of selected data sets to an
output device; and (iv) describe the unsaturated hydraulic datawith closed-form analytical expressions. The UNSODA database
may be used as a source of surrogate hydraulic data or for thedevelopment and evaluation of indirect methods for estimating
the unsaturated hydraulic properties. The latest version contains
information on close to 800 soil samples from around the world.
The UNSODA database allows analysis of the unsaturated soil
hydraulic data using the parametric models of Brooks and Corey(1964) and van Genuchten (1980a), although users can easily
add additional hydraulic models. Several studies have relied ondata from the UNSODA database to analyze alternative constitutive relationships (e.g., Leij et al., 1997; Kravchenko andZhang, 1998; Kosugi, 1996; Schaap and van Genuchten, 2006),
for predicting the hydraulic properties from particle-size data
(e.g., Arya et al., 1999a,b), and for deriving PTFs (Schaap et al.,
1998; Schaap and Leij, 2000).

User Feedback and SoŌware Support

The various programs discussed here, especially the HYDRUS
and STANMOD codes and their predecessors, have been usedover the years in a large number of applications. We refer tothe HYDRUS website (www.hydrus2d.com) for an extensive
list of examples. As an example, we list here several references
for a single application: drip irrigation and associated processes.
References include Meshkat et al. (1999), Assouline (2002),
UNSODA
Schmitz et al. (2002), Cote et al. (2003), Skaggs et al. (2004),
The UNSODA (UNsaturated SOil Hydraulic DAtabase)Beggs et al. (2004), Li et al. (2005), Lazarovitch et al. (2005,
database was developed to serve as a repository of measured unsat2007), Gärdenäs et al. (2005), and Hanson et al. (2006, 2008).
Many other example applications have been compiled (seeRassam et al., 2003, 2004; Selker, 2004). Feedback from users
like these has been extremely helpful in identifying strengths
and weaknesses of the codes, deﬁning additional processes orfeatures that should be included, and for identifying coding
errors. Much of the feedback and user support during thelast 10 yr has been through the Frequently Asked Questions(FAQs) and troubleshooting pages of the HYDRUS web site.
The HYDRUS web site also hosts several discussion
forums where users, after registering, can submit questions
about the diﬀerent software packages and how to use themfor their particular applications. Users there can also discussvarious topics related to modeling or respond to questions
posted by other users. The large number of users of these
discussion forums has made the forums nearly self-supportingin terms of software support and feedback. This is importantbecause of the shear number of software questions that otherwise had to be answered by the software developers only.
We note that the HYDRUS website also provides tutorials
F . 6. The Rose a Lite dialog window from the HYDRUS-1D so ware package.
for several software packages, including brief downloadable

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

596

A

videos in which these tutorials are performed step by step, thus
allowing software users to teach themselves interactively about
the basic components of the software, including the process ofdata entry and display of calculated results. We also dramatically extended the documentation for several software packages.
For example, the installation of the latest HYDRUS (2D/3D)
is accompanied by 240 pages of information in the technicalmanual, a 200-page user manual, and more than 1000 pagesof online context-sensitive help. Each Windows-based software
package furthermore comes with a suite of test problems, mostof which are described in detail in the corresponding technicalmanuals. Major sources of information for new users are always
previously published studies in which the programs have beenused. Of course, a major satisfaction for software developers like
us is to see the programs being actively used in various applications, and to see results of the applications published in theliterature. We therefore are continuously updating the list of such
publications at www.pc-progress.cz/Pg_Hydrus1D_References.
htm for HYDRUS-1D and related software packages, and at www.
pc-progress.cz/Pg_Hydrus_References.htm for HYDRUS-2D (or2D/3D) and its predecessors.

This work is based on work supported in part by the Terrestrial Sciences Program of the Army Research Oﬃce (Terrestrial Processes andLandscape Dynamics and Terrestrial System Modeling and Model Integration), by the National Science Foundation Biocomplexity programs
no. 04-10055 and NSF DEB 04-21530, and by SAHRA (Sustainabilityof Semi-Arid Hydrology and Riparian Areas) under the STC Programof the National Science Foundation, Agreement no. EAR-9876800.

References
Arya, L.M., F.J. Leij, P.J. Shouse, and M.Th. van Genuchten. 1999a. Relationship between the hydraulic conductivity function and the particle-size distribution. Soil Sci. Soc. Am. J. 63:1063–1070.
Arya, L.M., F.J. Leij, M.Th. van Genuchten, and P.J. Shouse. 1999b. Scaling
parameter to predict the soil water characteristic from particle-size distribution data. Soil Sci. Soc. Am. J. 63:510–519.
Assouline, S. 2002. The eﬀects of microdrip and conventional drip irrigation onwater distribution and uptake. Soil Sci. Soc. Am. J. 66:1630–1636.
Beggs, R.A., G. Tchobanoglous, D. Hills, and R.W. Crites. 2004. Modelingsubsurface drip application of onsite wastewater treatment system eﬄuent. p. 92–103. In On-Site Wastewater Treatment, Proc. Natl. Symp. on
Individual and Small Community Sewage Systems, 10th, Sacramento, CA.
21–24 Mar. 2004. Am. Soc. Agric. Eng., St. Joseph, MI.
Benjamin, J.G., H.R. Havis, L.R. Ahuja, and C.V. Alonso. 1994. Leaching andwater ﬂow patterns in every-furrow and alternate-furrow irrigation. Soil
Sci. Soc. Am. J. 58:1511–1517.
Bradford, S.A., M. Bettehar, J. Šimůnek, and M.Th. van Genuchten. 2004.
Straining and attachment of colloids in physically heterogeneous porous
media. Vadose Zone J. 3:384–394.
Bradford, S.A., J. Šimůnek, M. Bettehar, M.Th. van Genuchten, and S.R. Yates.
2003. Modeling colloid attachment, straining, and exclusion in saturated
porous media. Environ. Sci. Technol. 37:2242–2250.
Bradford, S.A., S.R. Yates, M. Bettehar, and J. Šimůnek. 2002. Physical factors
aﬀecting the transport and fate of colloids in saturated porous media. Water Resour. Res. 38(12):1327, doi:10.1029/2002WR001340.
Brooks, R.H., and A.T. Corey. 1964. Hydraulic properties of porous media. Hydrol. Pap. 3. Colorado State Univ., Fort Collins.
Carsel, R.F., and R.S. Parrish. 1988. Developing joint probability distributionsof soil water retention characteristics. Water Resour. Res. 24:755–769.
Casey, F.X.M., G.L. Larsen, H. Hakk, and J. Šimůnek. 2003. Fate and transport of17β-estradiol in soil-water systems. Environ. Sci. Technol. 37:2400–2409.
Casey, F.X.M., and J. Šimůnek. 2001. Inverse analyses of the transport of chlorinated hydrocarbons subject to sequential transformation reactions. J. Environ. Qual. 30:1354–1360.
Celia, M.A., E.T. Bououtas, and R.L. Zarba. 1990. A general mass-conservative
numerical solution for the unsaturated ﬂow equation. Water Resour. Res.
26:1483–1496.
Cote, C.M., K.L. Bristow, P.B. Charlesworth, F.J. Cook, and P.J. Thorburn.
2003. Analysis of soil wetting and solute transport in subsurface trickle
irrigation. Irrig. Sci. 22:143–156.
Davis, L.A., and S.P. Neuman. 1983. Documentation and user’s guide: UNSAT2—Variably saturated ﬂow model. Final Rep. WWL/TM-1791-1.
Water, Waste & Land, Ft. Collins, CO.
Decker, D.L., J. Šimůnek, S.W. Tyler, Ch. Papelis, and M. Logsdon. 2006. Variably saturated reactive transport of arsenic in heap leach facilities. Vadose
Zone J. 5:430–444.
de Vos, J.A., D. Hesterberg, and P.A.C. Raats. 2000. Nitrate leaching in a tiledrained silt loam soil. Soil Sci. Soc. Am. J. 64:517–527.
Diodato, D.M. 2000. Review: HYDRUS-2D. Ground Water 38:10–11.
Divine, C.E. 2003. STANMOD software review. Southwest Hydrol. 3:37.
Dontsova, K.M., S.L. Yost, J. Šimůnek, J.C. Pennington, and C. Williford. 2006.
Dissolution and transport of TNT, RDX, and Composition B in saturated
soil columns. J. Environ. Qual. 35:2043–2054.
Durner, W. 1994. Hydraulic conductivity estimation for soils with heterogeneous pore structure. Water Resour. Res. 32:211–223.
Feddes, R.A., P.J. Kowalik, and H. Zaradny. 1978. Simulation of ﬁeld water use
and crop yield. John Wiley & Sons, New York.
Gärdenäs, A., J.W. Hopmans, B.R. Hanson, and J. Šimůnek. 2005. Two-dimensional modeling of nitrate leaching for various fertigation scenarios under
micro-irrigation. Agric. Water Manage. 74:219–242.

Conclusions
Collaboration between the USSL and the UCR during thepast 30 yr has resulted in the development of a large numberof popularly used computer tools for studying vadose zone
ﬂow and transport processes. These tools include numericalmodels for one- or multidimensional variably saturated ﬂow
and transport (e.g., HYDRUS-1D and HYDRUS-2D), analytical models for solute transport in soils and groundwater (e.g.,
CXTFIT and STANMOD), and tools or databases for analyzing or predicting the unsaturated soil hydraulic properties(e.g., RETC and UNSODA). The wide use of these models isin large part due to their ease of use because of the availabilityof interactive GUIs. The modeling tools cover a large numberof processes, from relatively simple one-dimensional solutetransport problems to multidimensional ﬂow and transportapplications at the ﬁeld scale, including relatively complex
problems involving a range of biogeochemical reactions. An
example of the latter is the HP1 program that couples the
HYDRUS-1D software package with the PHREEQC geochemical code.
We believe that the software tools have served, and areserving, an important role in vadose zone research. This is
reﬂected by their frequent use in a variety of applications (manyof them leading to peer-reviewed publications) and the favorable reviews the programs have received recently. For example,
the HYDRUS-2D software package was reviewed by Diodato(2000) and Tyler (2004). The STANMOD software package wasreviewed by Divine (2003), the HYDRUS-1D software package
by Scanlon (2004), and the latest HYDRUS (2D/3D) programby McCray (2007). The need for codes such as HYDRUS andSTANMOD is further reﬂected by the frequency of downloading from the HYDRUS website. For example, HYDRUS-1D
was downloaded more than 200 times in March 2007 by users
from 30 diﬀerent countries, and more than 1000 times in 2006.
The HYDRUS website receives, on average, some 700 individual
visitors each day.

www.vadosezonejournal.org · Vol. 7, No. 2, May 2008597

Gargiulo, G., S.A. Bradford, J. Šimůnek, P. Ustohal, H. Vereecken, and E.
Klumpp. 2007a. Transport and deposition of metabolically active and stationary phase Deinococcus radiodurans in unsaturated porous media. Environ. Sci. Technol. 41:1265–1271.
Gargiulo, G., S.A. Bradford, J. Šimůnek, P. Ustohal, H. Vereecken, and E.
Klumpp. 2007b. Bacteria transport and deposition under unsaturated conditions: The role of the matrix grain size and the bacteria surface protein. J.
Contam. Hydrol. 92:255–273.
Gargiulo, G., S.A. Bradford, J. Šimůnek, P. Ustohal, H. Vereecken, and E.
Klumpp. 2008. Bacteria transport and deposition under unsaturated conditions: The role of water content and bacteria surface hydrobophicity. Vadose Zone J. 7:406–419 (this issue).
Gerke, H.H., and M.Th. van Genuchten. 1993. A dual-porosity model for simulating the preferential movement of water and solutes in structured porous
media. Water Resour. Res. 29:305–319.
Gonçalves, M.C., J. Šimůnek, T.B. Ramos, J.C. Martins, M.J. Neves, andF.P. Pires. 2006. Multicomponent solute transport in soil lysimeters irrigated with waters of diﬀerent quality. Water Resour. Res. 42:W08401,
doi:10.1029/2005WR004802.
Hammel, K., and K. Roth. 1998. Approximation of asymptotic dispersivity ofconservative solute in unsaturated heterogeneous media with steady state
ﬂow. Water Resour. Res. 34:709–715.
Hanson, B.R., 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).
Hanson, B.R., J. Šimůnek, and J.W. Hopmans. 2006. Numerical modeling of
urea–ammonium-nitrate fertigation under microirrigation. Agric. Water
Manage. 86:102–113.
Hansson, K., L.-Ch. Lundin, and J. Šimůnek. 2005. Modeling water ﬂow patterns in ﬂexible pavements. Transp. Res. Rec. 1936:133–141.
Hansson, K., J. Šimůnek, M. Mizoguchi, and L.-Ch. Lundin. 2004. Water ﬂow
and heat transport in frozen soil: Numerical solution and freeze/thaw applications. Vadose Zone J. 3:693–704.
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.
Open File Rep. 00-92. USGS, Denver, CO.
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.
Haws, N.W., P.S.C. Rao, J. Šimůnek, and I.C. Poyer. 2005. Single-porosityand dual-porosity modeling of water ﬂow and solute transport in subsurface-drained ﬁelds using eﬀective ﬁeld-scale parameters. J. Hydrol.
313:257–273.
Hopmans, J.W., J. Šimůnek, N. Romano, and W. Durner. 2002. Inverse modeling of transient water ﬂow. p. 963–1008. In J.H. Dane and G.C. Topp(ed.) Methods of soil analysis. Part 4. Physical methods. SSSA Book Ser. 5.
SSSA, Madison, WI.
Jacques, D., and J. Šimůnek. 2005. User manual of the multicomponent variably-saturated ﬂow and transport model HP1: Description, veriﬁcation,and examples. Version 1.0. BLG-998. Waste and Disposal, SCK⋅CEN,
Mol, Belgium.
Jacques, D., J. Šimůnek, D. Mallants, and M.Th. van Genuchten. 2003. The
HYDRUS-PHREEQC multicomponent transport model for variablysaturated porous media: Code veriﬁcation and application. p. 23–27. In E.
Poeter et al. (ed.) MODFLOW and More 2003: Understanding throughmodeling. Proc. Conf., Golden, CO. Sept. 2003. Int. Ground Water Modeling Ctr., Colorado School of Mines, Golden.
Jacques, D., J. Šimůnek, D. Mallants, and M.Th. van Genuchten. 2006. Operator-splitting errors in coupled reactive transport codes for transient variably saturated ﬂow and contaminant transport in layered soil proﬁles. J.
Contam. Hydrol. 88:197–218.
Jacques, D., J. Šimůnek, D. Mallants, and M.Th. van Genuchten. 2008a. Modeling coupled water ﬂow, solute transport and geochemical reactions aﬀecting heavy metal migration in a podzol soil. Geoderma (in press).
Jacques, D., J. Šimůnek, D. Mallants, and M.Th. van Genuchten. 2008b. Modeling coupled hydrologic and chemical processes: Long-term uraniumtransport following phosphorus fertilization. Vadose Zone J. 7:698–711(this issue).

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

Jury, W.A., W.F. Spencer, and W.J. Farmer. 1983. Behavior assessment model for trace organics in soil: I. Description of model. J. Environ. Qual.
12:558–564.
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).
Köhne, J.M., S. Köhne, and J. Šimůnek. 2006. Multi-process herbicide transport in structured soil columns: Experiment and model analysis. J. Contam. Hydrol. 85:1–32.
Köhne, J.M., B. Mohanty, J. Šimůnek, and H.H. Gerke. 2004. Numerical evaluation of a second-order water transfer term for variably saturated dual-permeability models. Water Resour. Res. 40:W07409,
doi:10.1029/2004WR003285.
Kool, J.B., and M.Th. van Genuchten. 1991. HYDRUS: One-dimensionalvariably saturated ﬂow and transport model, including hysteresis androot water uptake. Version 3.3. Res. Rep. 124. U.S. Salinity Lab., Riverside, CA.
Kosugi, K. 1996. Lognormal distribution model for unsaturated soil hydraulicproperties. Water Resour. Res. 32:2697–2703.
Kravchenko, A., and R. Zhang. 1998. Estimating the soil water retention curvefrom particle-size distriutions: A fractal approach. Soil Sci. 163:171–179.
Kundzewicz, Z.W., and D. Koutsoyiannis. 2007. Editorial—Quantifying theimpact of hydrological studies. Hydrol. Sci. J. 52:3–17.
Lain, J., and M. Šejna. 1992. Unstructured triangular meshes and TVD schemes
for ﬂuid ﬂow computations. p. 83–94. In K. Kozel (ed.) Numerical methods solving 2D and 3D inviscid and viscous ﬂows, Proc. Seminar, 2nd,
Prague. Sept. 1992. Czech Tech. Univ., Prague, Czech Republic.
Langergraber, G., and J. Šimůnek. 2005. Modeling variably saturated water ﬂow
and multi-component reactive transport in constructed wetlands. Vadose
Zone J. 4:924–938.
Langergraber, G., and J. Šimůnek. 2006. The multi-component reactive transport module CW2D for constructed wetlands for the HYDRUS software
package. Manual, Version 1.0. HYDRUS Softw. Ser. 2. Dep. of Environ.
Sci., Univ. of California, Riverside.
Lazarovitch, N., J. Šimůnek, and U. Shani. 2005. System dependent boundary condition for water ﬂow from subsurface source. Soil Sci. Soc. Am. J.
69:46–50.
Lazarovitch, N., A.W. Warrick, A. Furman, and J. Šimůnek. 2007. Subsurface
water distribution from drip irrigation described by moment analyses. Vadose Zone J. 6:116–123.
Leij, F.J., W.J. Alves, M.Th. van Genuchten, and J.R. Williams. 1996. Unsaturated soil hydraulic database, UNSODA 1.0 user’s manual. Rep.
EPA/600/R-96/095. USEPA, Ada, OK.
Leij, F.J., and S.A. Bradford. 1994. 3DADE: A computer program for evaluating
three-dimensional equilibrium solute transport in porous media. Res. Rep.
134. U.S. Salinity Lab., Riverside, CA.
Leij, F.J., W.B. Russell, and S.M. Lesch. 1997. Closed-form expressions for water
retention and conductivity data. Ground Water 35:848–853.
Leij, F.J., T.H. Skaggs, and M.Th. van Genuchten. 1991. Analytical solutions forsolute transport in three-dimensional semi-inﬁnite porous media. Water
Resour. Res. 27:2719–2733.
Leij, F.J., and N. Toride. 1997. N3DADE: A computer program for evaluating
nonequilibrium three-dimensional equilibrium solute transport in porous
media. Res. Rep. 143. U.S. Salinity Lab., Riverside, CA.
Leij, F.J., N. Toride, and M.Th. van Genuchten. 1993. Analytical solutions for
non-equilibrium solute transport in three-dimensional porous media. J.
Hydrol. 151:193–228.
Lenhard, R.J., J.C. Parker, and J.J. Kaluarachchi. 1991. Comparing simulated
and experimental hysteretic two-phase transient ﬂuid ﬂow phenomena.
Water Resour. Res. 27:2113–2124.
Li, J., J. Zhang, and M. Rao. 2005. Water ﬂow and nitrate transport under surface drip fertigation. Trans. ASAE 48:627–637.
Marquardt, D.W. 1963. An algorithm for least-squares estimation of nonlinear
parameters. SIAM J. Appl. Math. 11:431–441.
McCray, J. 2007. HYDRUS: Software review. Southwest Hydrol. 6(1):41.
Mendoza, C.A., R. Therrien, and E.A. Sudicky. 1991. ORTHOFEM user’s
guide. Version 1.02. Centre for Groundwater Res., Univ. of Waterloo, Waterloo, ON, Canada.
Meshkat, M., R.C. Warner, and S.R. Workman. 1999. Modeling of evaporation
reduction in drip irrigation system. J. Irrig. Drain. Eng. 125:315–323.

598

Mualem, Y. 1976. A new model for predicting the hydraulic conductivity ofunsaturated porous media. Water Resour. Res. 12:513–522.
Nemes, A., M.G. Schaap, F.J. Leij, and J.H.M. Wosten. 2001. Description of
the unsaturated soil hydraulic database UNSODA. Version 2.0. J. Hydrol.
251:151–162.
Neuman, S.P. 1972. Finite element computer programs for ﬂow in saturated–unsaturated porous media. 2nd Annu. Rep. Project A10-SWC-77. Hydraulic Eng. Lab., Technion, Haifa, Israel.
Neuman, S.P. 1973. Saturated–unsaturated seepage by ﬁnite elements. J. Hydraul. Div. Am. Soc. Civ. Eng. 99:2233–2250.
Neuman, S.P. 1975. Galerkin approach to saturated–unsaturated ﬂow in porous
media. p. 201–217. In R.H. Gallagher et al. (ed.) Finite elements in ﬂuids.
Vol. 1. Viscous ﬂow and hydrodynamics. John Wiley & Sons, London.
Neuman, S.P., R.A. Feddes, and E. Bresler. 1974. Finite element simulation of ﬂow
in saturated–unsaturated soils considering water uptake by plants. 3rd Annu.
Rep. Project A10-SWC-77. Hydraulic Eng. Lab., Technion, Haifa, Israel.
Pang, L., and J. Šimůnek. 2006. Evaluation of bacteria-facilitated cadmium transport in gravel columns using the HYDRUS colloid-facilitated solute transport model. Water Resour. Res. 42:W12S10,
doi:10.1029/2006WR004896.
Parker, J.C., and M.Th. van Genuchten. 1984. Determining transport parameters from laboratory and ﬁeld tracer experiments. Bull. 84-3. Virginia
Agric. Exp. Stn., Blacksburg.
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-Resour. Invest. Rep.
99-4259. USGS, Denver, CO.
Pot, V., J. Šimůnek, P. Benoit, Y. Coquet, A. Yra, and M.-J. MartínezCordón. 2005. Impact of rainfall intensity on the transport of two
herbicides in undisturbed grassed ﬁlter strip soil cores. J. Contam. Hydrol. 81:63–88.
Richards, L.A. 1931. Capillary conduction of ﬂuid through porous mediums.
Physics 1:318–333.
Ramos, T.B., M.C. Goncalves, and J.C. Martins. 2006. Estimation of soil hydraulic properties from numerical inversion of tension disk inﬁltrometerdata. Vadose Zone J. 5:684–696.
Rassam, D., J. Šimůnek, and M.Th. van Genuchten. 2003. Modeling variably
saturated ﬂow with HYDRUS-2D. ND Consult, Brisbane, Australia.
Rassam, D., J. Šimůnek, and M.Th. van Genuchten. 2004. Modeling variably
saturated ﬂow with HYDRUS-2D. (Japanese transl., N. Toride,and M. Inoue [ed.]) Jpn. Irrig. and Drain. Soc., Tokyo.
Roth, K. 1995. Steady state ﬂow in an unsaturated, two-dimensional, macroscopically homogeneous, Miller-similar medium. Water Resour. Res.
31:2127–2140.
Roth, K., and K. Hammel. 1996. Transport of conservative chemical throughan unsaturated two-dimensional Miller-similar medium with steady state
ﬂow. Water Resour. Res. 32:1653–1663.
Saito, H., 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).
Scanlon, B. 2004. Review of HYDRUS-1D. Southwest Hydrol. 3(4):37.
Scanlon, B., K. Keese, R.C. Reedy, J. Šimůnek, and B. Andraski. 2003. Variations in ﬂow and transport in thick desert vadose zones in response to paleoclimatic forcing (0–90 kyr): Monitoring, modeling, and uncertainties.
Water Resour. Res. 39(7):1179, doi:10.1029/2002WR001604.
Schaap, M.G., and J.J. Leij. 2000. Improved prediction of unsaturated hydraulicconductivity with the Mualem–van Genuchten model. Soil Sci. Soc. Am.
J. 64:843–851.
Schaap, M.G., F.J. Leij, and M.Th. van Genuchten. 1998. Neural network
analysis for hierarchical prediction of soil water retention and saturated
hydraulic conductivity. Soil Sci. Soc. Am. J. 62:847–855.
Schaap, M.G., F.J. Leij, and M.Th. van Genuchten. 2001. Rosetta: A computer
program for estimating soil hydraulic parameters with hierarchical pedotransfer functions. J. Hydrol. 251:163–176.
Schaap, M.G., and M.Th. van Genuchten. 2006. A modiﬁed Mualem–van Genuchten formulation for improved description of the hydraulic conductivity near saturation. Vadose Zone J. 5:27–34.

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

Schaerlaekens, J., D. Mallants, J. Šimůnek, M.Th. van Genuchten, and J. Feyen.
1999. Numerical simulation of transport and sequential biodegradation ofchlorinated aliphatic hydrocarbons using CHAIN_2D. Hydrol. Processes
13:2847–2859.
Schijven, J., and J. Šimůnek. 2002. Kinetic modeling of virus transport at ﬁeld
scale. J. Contam. Hydrol. 55:113–135.
Schmitz, G.H., N. Schutze, and U. Petersohn. 2002. New strategy for optimizing water application under trickle irrigation. J. Irrig. Drain. Eng.
128:287–297.
Šejna, M., and J. Šimůnek. 2007. HYDRUS (2D/3D): Graphical user interface
for the HYDRUS software package simulating two- and three-dimensional movement of water, heat, and multiple solutes in variably-saturated media. Available at www.pc-progress.cz (veriﬁed 20 Feb. 2008). PC-Progress,
Prague, Czech Republic.
Šejna, M., J. Šimůnek, D.L. Suarez, and M.Th. van Genuchten. 1994. Unstructured mesh generation and its application in models of two-dimensionaltransport processes. p. 97. In 1994 Agronomy abstracts. ASA, Madison, WI.
Selker, J. 2004. Book review: Modelling variably saturated ﬂow with HYDRUS2D. Vadose Zone J. 3:725.
Seo, H.S., J. Šimůnek, and E.P. Poeter. 2007. Documentation of the HYDRUS
package for MODFLOW-2000, the U.S. Geological Survey modular
ground-water model. GWMI 2007-01. Int. Ground Water Modeling Ctr,,
Colorado School of Mines, Golden.
Šimůnek, J., R. Angulo-Jaramillo, M.G. Schaap, J.-P. Vandervaere, and M.Th. van
Genuchten. 1998a. Using an inverse method to estimate the hydraulic properties of crusted soils from tension disc inﬁltrometer data. Geoderma 86:61–81.
Šimůnek, J., C. He, J.L. Pang, and S.A. Bradford. 2006a. Colloid-facilitatedtransport in variably saturated porous media: Numerical model and experimental veriﬁcation. Vadose Zone J. 5:1035–1047.
Šimůnek, J., and J.W. Hopmans. 2002. Parameter optimization and nonlinear ﬁtting. p. 139–157. In J.H. Dane and G.C. Topp (ed.) Methods of soil analysis.
Part 4. Physical methods. SSSA Book Ser. 5. SSSA, Madison, WI.
Šimůnek, J., K. Huang, and M.Th. van Genuchten. 1995. The SWMS_3D code forsimulating water ﬂow and solute transport in three-dimensional variably saturated media. Version 1.0. Res. Rep. 139. U.S. Salinity Lab., Riverside, CA.
Šimůnek, J., K. Huang, and M.Th. van Genuchten. 1998b. The HYDRUS codefor simulating the one-dimensional movement of water, heat, and multiple
solutes in variably-saturated media. Version 6.0. Res. Rep. 144. U.S. Salinity Lab., Riverside, CA.
Šimůnek, J., D. Jacques, J.W. Hopmans, M. Inoue, M. Flury, and M.Th. van
Genuchten. 2002. Solute transport during variably saturated ﬂow inverse
methods. p. 1435–1449. In J.H. Dane and G.C. Topp (ed.) Methods of soil
analysis. Part 4. Physical methods. SSSA Book Ser. 5. SSSA, Madison, WI.
Šimůnek, J., D. Jacques, M.Th. van Genuchten, and D. Mallants. 2006b. Multicomponent geochemical transport modeling using the HYDRUS computer software packages. J. Am. Water Resour. Assoc. 42:1537–1547.
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., and J.R. Nimmo. 2005. Estimating soil hydraulic parameters fromtransient ﬂow experiments in a centrifuge using parameter optimization technique. Water Resour. Res. 41(4):W04015, doi:10.1029/2004WR003379.
Šimůnek, J., M. Šejna, and M.Th. van Genuchten. 1996a. The HYDRUS-2D
software package for simulating water ﬂow and solute transport in twodimensional variably saturated media. Version 1.0. IGWMC-TPS-53. Int.
Ground Water Modeling Ctr., Colorado School of Mines, Golden.
Šimůnek, J., M. Šejna, and M.Th. van Genuchten. 1998c. The HYDRUS-1D
software package for simulating the one-dimensional movement of water, heat, and multiple solutes in variably-saturated media. Version 2.0.
IGWMC-TPS-70. Int. Ground Water Modeling Ctr., Colorado Schoolof Mines, Golden.
Šimůnek, J., M. Šejna, and M.Th. van Genuchten. 1999a. The HYDRUS-2D software package for simulating two-dimensional movement of water, heat, andmultiple solutes in variably saturated media. Version 2.0. IGWMC-TPS-53.
Int. Ground Water Modeling Ctr., Colorado School of Mines, Golden.
Šimůnek, J., and D.L. Suarez. 1993a. Modeling of carbon dioxide transportand production in soil: 1. Model development. Water Resour. Res.
29:487–497.
Šimůnek, J., and D.L. Suarez. 1993b. UNSATCHEM-2D code for simulating two-dimensional variably saturated water ﬂow, heat transport, carbon

599

dioxide production and transport, and multicomponent solute transportwith major ion equilibrium and kinetic chemistry. Version 1.1. Res. Rep.
128. U.S. Salinity Lab., Riverside, CA.
Šimůnek, J., and D.L. Suarez. 1993c. The SOILCO2 code for simulating one-dimensional carbon dioxide production and transport in variably saturated porous media. Version 1.1. Res. Rep. 127. U.S. Salinity Lab., Riverside, CA.
Šimůnek, J., and D.L. Suarez. 1994. Major ion chemistry model for variably
saturated porous media. Water Resour. Res. 30:1115–1133.
Šimůnek, J., and D.L. Suarez. 1997. Sodic soil reclamation using multicomponent transport modeling. J. Irrig. Drain. Eng. 123:367–376.
Šimůnek, J., D.L. Suarez, and M. Šejna. 1996b. The UNSATCHEM software
package for simulating one-dimensional variably saturated water ﬂow, heattransport, carbon dioxide production and transport, and multicomponent
solute transport with major ion equilibrium and kinetic chemistry. Version
2.0. Res. Rep. 141. U.S. Salinity Lab., Riverside, CA.
Šimůnek, J., and M.Th. van Genuchten. 1994. The CHAIN_2D code for simulating two-dimensional movement of water ﬂow, heat, and multiple solutes
in variably-saturated porous media. Version 1.1. Res. Rep. 136. U.S. Salinity Lab., Riverside, CA.
Šimůnek, J., and M.Th. van Genuchten. 1996. Estimating unsaturated soil hydraulic properties from tension disc inﬁltrometer data by numerical inversion. Water Resour. Res. 32:2683–2696.
Šimůnek, J., and M.Th. van Genuchten. 1997. Estimating unsaturated soil hydraulic properties from multiple tension disc inﬁltrometer data. Soil Sci.
162:383–398.
Šimůnek, J., and M.Th. van Genuchten. 2000. The DISC computer software foranalyzing tension disc inﬁltrometer data by parameter estimation. Version
1.0. Res. Rep. 145. U.S. Salinity Lab., Riverside, CA.
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. 2005. The HYDRUS-1D software package for simulating the one-dimensional movement of water, heat,and multiple solutes in variably-saturated media. Version 3.0. HYDRUS
Softw. Ser. 1. Dep. of Environ. Sci., Univ. of California, Riverside, CA.
Šimůnek, J., M.Th. van Genuchten, and M. Šejna. 2006c. The HYDRUS software package for simulating two- and three-dimensional movement ofwater, heat, and multiple solutes in variably-saturated media: Technicalmanual. Version 1.0. PC-Progress, Prague, Czech Republic.
Šimůnek, J., M.Th. van Genuchten, M. Šejna, N. Toride, and F.J. Leij. 1999b.
The STANMOD computer software for evaluating solute transport in porous media using analytical solutions of convection–dispersion equation.
Versions 1.0 and 2.0. IGWMC-TPS-71. Int. Ground Water Modeling
Ctr., Colorado School of Mines, Golden.
Šimůnek, J., T. Vogel, and M.Th. van Genuchten. 1992. The SWMS_2D code forsimulating water ﬂow and solute transport in two-dimensional variably saturated media. Version 1.1. Res. Rep. 126. U.S. Salinity Lab., Riverside, CA.
Šimůnek, J., T. Vogel, and M.Th. van Genuchten. 1994. The SWMS_2D code forsimulating water ﬂow and solute transport in two-dimensional variably saturated media. Version 1.2. Res. Rep. 132. U.S. Salinity Lab., Riverside, CA.
Šimůnek, J., O. Wendroth, and M.Th. van Genuchten. 1998d. A parameter estimation analysis of the evaporation method for determining soil hydraulicproperties. Soil Sci. Soc. Am. J. 62:894–905.
Šimůnek, J., O. Wendroth, N. Wypler, and M.Th. van Genuchten. 2001. Nonequilibrium water ﬂow characterized from an upward inﬁltration experiment. Eur. J. Soil Sci. 52:13–24.
Skaggs, T.H., T.J. Trout, J. Šimůnek, and P.J. Shouse. 2004. Comparison of HYDRUS-2D simulations of drip irrigation with experimental observations.
J. Irrig. Drain. Eng. 130:304–310.
Suarez, D.L., and J. Šimůnek. 1993. Modeling of carbon dioxide transport andproduction in soil: 2. Parameter selection, sensitivity analysis, and comparison of model predictions to ﬁeld data. Water Resour. Res. 29:499–513.
Toride, N., F.J. Leij, and M.Th. van Genuchten. 1993. A comprehensive set ofanalytical solutions for nonequilibrium solute transport with ﬁrst-orderdecay and zero-order production. Water Resour. Res. 29:2167–2218.
Toride, N., F.J. Leij, and M.Th. van Genuchten. 1995. The CXTFIT code for estimating transport parameters from laboratory or ﬁeld tracer experiments.
Version 2.0. Res. Rep. 137. U.S. Salinity Lab., Riverside, CA.
Tseng, P.-H., and W.A. Jury. 1994. Comparison of transfer function and deterministic modeling of area-averaged solute transport in a heterogeneouswww.vadosezonejournal.org · Vol. 7, No. 2, May 2008

ﬁeld. Water Resour. Res. 30:2051–2063.
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).
Tyler, S. 2004. Review of HYDRUS-2D. Southwest Hydrol. 3:37.
van Genuchten, M.Th. 1978a. Calculating the unsaturated hydraulic conductivity with a new, closed-form analytical model. Res. Rep. 78-WR-8. Water
Resour. Program, Dep. of Civil Eng., Princeton Univ., Princeton, NJ.
van Genuchten, M.Th. 1978b. Numerical solutions of the one-dimensional
saturated–unsaturated ﬂow equation. Res. Rep. 78-WR-9. Water Resour.
Program, Dep. of Civil Eng., Princeton Univ., Princeton, NJ.
van Genuchten, M.Th. 1978c. Mass transport in unsaturated–saturated media:
One-dimensional solutions. Res. Rep. 78-WR-11. Water Resour. Program,
Dep. of Civil Eng., Princeton Univ., Princeton, NJ.
van Genuchten, M.Th. 1980a. A closed-form equation for predicting the hydraulic conductivity of unsaturated soils. Soil Sci. Soc. Am. J. 44:892–898.
van Genuchten, M.Th. 1980b. Determining transport parameters from solute displacement experiments. Res. Rep. 118. U.S. Salinity Lab., Riverside, CA.
van Genuchten, M.Th. 1981a. Analytical solutions for chemical transport withsimultaneous adsorption, zero-order production and ﬁrst-order decay. J.
Hydrol. 49:213–233.
van Genuchten, M.Th. 1981b. Non-equilibrium transport parameters frommiscible displacement experiments. Res. Rep. 119. U.S. Salinity Lab., Riverside, CA.
van Genuchten, M.Th. 1985. Convective–dispersive transport of solutes involved
in sequential ﬁrst-order decay reactions. Comput. Geosci. 11:129–147.
van Genuchten, M.Th. 1987. A numerical model for water and solute movement in and below the root zone. Res. Rep. 121. U.S. Salinity Lab.,Riverside, CA.
van Genuchten, M.Th., and W.J. Alves. 1982. Analytical solutions of the onedimensional convective–dispersive solute transport equation. Tech. Bull.
1661. U.S. Gov. Print. Oﬃce, Washington, DC.
van Genuchten, M.Th., F.J. Leij, and S.R. Yates. 1991. The RETC codefor quantifying the hydraulic functions of unsaturated soils. USEPA,
Washington, DC.
van Genuchten, M.Th., and R.J. Wagenet. 1989. Two-site/two-region models
for pesticide transport and degradation: Theoretical development and analytical solutions. Soil Sci. Soc. Am. J. 53:1303–1310.
van Genuchten, M.Th., and P.J. Wierenga. 1976. Mass transfer studies in sorbing
porous media: I. Analytical solutions. Soil Sci. Soc. Am. J. 40:473–480.
van Genuchten, M.Th., and P.J. Wierenga. 1986. Solute dispersion coeﬃcientsand retardation factors. p. 1025–1054. In A. Klute (ed.) Methods of soil
analysis. Part 1. Physical and mineralogical methods. 2nd ed. Agron.
Monogr. 9. ASA and SSSA, Madison, WI.
Vogel, T. 1987. SWMII: Numerical model of two-dimensional ﬂow in a variably
saturated porous medium. Res. Rep. 87. Dep. of Hydraul. and Catchment
Hydrol., Agricultural Univ., Wageningen, the Netherlands.
Vogel, T. 1990. Numerical modeling of water ﬂow in non-homogeneous soil
proﬁle. (In Czech.) Ph.D. diss. Czech Technical Univ., Prague.
Vogel, T., and M. Císlerová. 1988. On the reliability of unsaturated hydraulicconductivity calculated from the moisture retention curve. Transp. PorousMedia 3:1–15.
Vogel, T., K. Huang, R. Zhang, and M.Th. van Genuchten. 1996. The HYDRUS code for simulating one-dimensional water ﬂow, solute transport,
and heat movement in variably-saturated media. Version 5.0. Res. Rep.
140. U.S. Salinity Lab., Riverside, CA.
Vrugt, J.A., M.T. van Wijk, J.W. Hopmans, and J. Šimůnek. 2001. One-, two-,and three-dimensional root water uptake functions for transient modeling.
Water Resour. Res. 37:2457–2470.
Wagenet, R.J., and J.L. Hutson. 1987. LEACHM: Leaching estimation andchemistry model. A process-based model of water and solute movement,
transformations, plant uptake and chemical reactions in the unsaturated
zone. Continuum 2. Dep. of Agronomy, Cornell Univ., Ithaca, NY.
Wang, D., J.A. Knuteson, and S.R. Yates. 2000. Two-dimensional model simulation of 1,3-dichloropropene volatilization and transport in a ﬁeld soil. J.
Environ. Qual. 29:639–644.
Wang, D., S.R. Yates, and J. Gan. 1997. Temperature eﬀect on methyl bromide
volatilization in soil fumigation. J. Environ. Qual. 26:1072–1079.

600