Received: 13 October 2023

Accepted: 2 January 2024

DOI: 10.1002/vzj2.20310
Vadose Zone Journal

REVIEWS p e c i a l S e c t i o n : Tr i b u t e t o R i e n v a n G e n u c h t e n , R e c i p i e n t o f t h e 2 0 2 3 Wo l f P r i z e f o r A g r i c u l t u r e

Developments and applications of the HYDRUS computer
software packages since 2016Jiří Šimůnek1
Genuchten4,5

Giuseppe Brunetti2
Miroslav Šejna6

1 Department of Environmental Sciences,

University of California, Riverside,
Riverside, California, USA
2 Department of Civil Engineering,

University of Calabria, Rende, Italy
3 Performance Assessments, Belgian

Nuclear Research Institute, Mol, Belgium
4 Department of Nuclear Engineering,Federal University of Rio de Janeiro, UFRJ,
Rio De Janeiro, Brazil
5 Department of Earth Sciences, Utrecht

University, Utrecht, The Netherlands
6 PC-Progress, Ltd., Prague, Czech Republic

CorrespondenceJiří Šimůnek, Department of Environmental
Sciences, University of California,
Riverside, 900 University Ave., Riverside,
CA 92521, USA. Email:jiri.simunek@ucr.edu

Diederik Jacques3

Martinus Th. van

Abstract
The HYDRUS codes have become standard tools for addressing many soil, agricultural, environmental, and hydrological problems requiring the evaluation of various
subsurface physical, chemical, and biological processes. There are now many thousands of HYDRUS users worldwide, with thousands of applications of the HYDRUS
models appearing in the peer-reviewed literature. In this manuscript, we provide
an overview of the capabilities of the most recent Version 5 of HYDRUS, focusing primarily on features implemented since 2016. We briefly describe the standard
HYDRUS model and its standard and nonstandard specialized add-on modules thatsignificantly expand the capabilities of the software packages. The standard addon modules include HPx, UNSATCHEM, Wetland, Furrow, PFAS, COSMIC, DPU,SLOPE Cube, and Particle Tracking. Recent developments of the HYDRUS Package
for MODFLOW are also described, along with additional capabilities incorporated
into the graphical user interface supporting HYDRUS. Also discussed are newor improved options to simulate the fate and transport of environmental isotopes,
multi-cropping systems, compensated root water uptake, and hydraulic redistribution within the rootzone, which will be implemented in upcoming add-on modules.
Another objective is to review selected applications of the HYDRUS models, suchas evaluations of various irrigation, low-impact development (LID), and managed
aquifer recharge (MAR) schemes.

1

Abbreviations: AWI, air–water interface; COSMIC, COsmic-ray Soil
Moisture Interaction Code; CRNP, cosmic-ray neutron probe; CRWU,
compensated root water uptake; CW2D, constructed wetland
two-dimensional; CWM1, constructed wetland model 1; DPU, Dynamic
Plant Uptake; GUI, graphical user interface; HPM, HYDRUS Package for
MODFLOW; HR, hydraulic redistribution; LID, low-impact development;
MAR, managed aquifer recharge; PFAS, polyfluoroalkyl substances; RWU,
root water uptake; SHP, soil hydraulic property.

INTRODUCTION

During the past several decades, the HYDRUS codes havebecome standard tools for addressing many soil, agricultural,environmental, and hydrological problems involving a rangeof physical, chemical, and biological processes in the subsurface, particularly in the vadose zone. The HYDRUS models
remain one of the most widely used numerical tools for simulated processes in the subsurface. There are many thousandsof HYDRUS users (and institutions using HYDRUS) around

This is an open access article under the terms of the Creative Commons Attribution License, which permits use, distribution and reproduction in any medium, provided the original
work is properly cited.
© 2024 The Authors. Vadose Zone Journal published by Wiley Periodicals LLC on behalf of Soil Science Society of America.
Vadose Zone J. 2024;e20310.
https://doi.org/10.1002/vzj2.20310

wileyonlinelibrary.com/journal/vzj2

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the world, with many applications (also several thousand) of
the models being published in the peer-reviewed literature(see, e.g., Google Scholar). It is beyond the scope of this paper
to describe all applications for which the HYDRUS models
have been used. A comprehensive list of publications summarizing many one-dimensional (1D) applications of HYDRUS(over 2000) can be found at https://www.pc-progress.com/
en/Default.aspx?h1d-references. A similar list (over 1000) of
two-dimensional (2D) and three-dimensional (3D) applications of HYDRUS and its predecessors can be found at http://
www.pc-progress.com/en/Default.aspx?h3d-references.
The early history of the HYDRUS models and their predecessors, which can be traced back to the early 1970s, wasreviewed by Šimůnek et al. (2008). More recent accounts ofthe codes are described by Šimůnek et al. (2012, 2013, 2016,2018). Our objective here is not to provide a detailed history of
the HYDRUS models. Instead, we will focus mainly on developments after those previous reviews appeared, especiallyon the new capabilities of the current HYDRUS software
package and its specialized add-on modules. We thus aim to
describe the unique capabilities of the current HYDRUS software package relative to those described in the earlier reviewsby Šimůnek et al. (2016, 2018).
The manuscript is organized as follows. After this introduction, we provide in Section 2 a brief history of theWindows-based HYDRUS models. Section 3 summarizes thecurrent capability of the standard HYDRUS model, after
which we provide information about the standard (Section 4)
and nonstandard (Section 5) HYDRUS modules currently
available. In Section 6, we next discuss several new features
we plan to include in upcoming releases of the HYDRUS
software package, as well as the most common applicationsof the models. Section 7 discusses the HYDRUS use inundergraduate- and graduate-level courses and available textbooks. Finally, in Section 8, we will provide some summaries
and conclusions, along with a personal statement by the seniorauthor in the Appendix.

2
A BRIEF HISTORY OF THE
WINDOWS-BASED HYDRUS MODELSAs documented in our previous reports (Šimůnek et al., 2008,2016), the development of the HYDRUS software packages
during the first two decades of their existence followed two
separate paths. On the one hand, the HYDRUS-1D software
package (its four versions were released in 1998, 1998, 2005,
and 2008) focused on water flow and contaminant transport processes in 1D porous media. While the capabilities
and a list of processes that these sequential packages could
consider increased dramatically in its 20-year-long history(Šimůnek et al., 2008, 2016), the HYDRUS-1D package during its entire existence remained in the public domain andCore Ideas∙ An overview of the capabilities of the most recent
Version 5 of HYDRUS.
∙ The description of the standard and nonstandard
specialized HYDRUS add-on modules.
∙ A review of selected popular applications of the
HYDRUS models.
∙ Description of new or improved upcoming
HYDRUS add-on modules.

was freely downloadable. HYDRUS-2D, on the other hand,
was a 2D commercial software package. Its two versions werereleased in 1996 and 1998. In 2007, the HYDRUS-2D package was extended to consider three dimensions and renamed
HYDRUS (2D/3D). That software package was released inthree versions in 2007, 2011, and 2017, with each version
adding new computational and graphical capabilities andspecialized add-on modules (Šimůnek et al., 2016, 2018).
Interestingly, based on the number of citations, the manuscriptof Šimůnek et al. (2016), which was published in Vadose Zone
Journal, was ranked “as the most dominant article in the CTM(contaminant hydrology modeling) research field” by Guleria
and Chakma (2022), who carried out a bibliometric analysisof research articles published on this topic since 2010.

3

THE CURRENT HYDRUS MODEL

The last significant development in the family of the
HYDRUS models occurred in April 2022 when the two previously independent software packages, HYDRUS-1D (Version
4, for 1D applications) and HYDRUS (2D/3D) (Version 3,
for 2D and 3D applications), were merged into a single software package called HYDRUS. This new HYDRUS package
is listed as Version 5 to avoid confusion about the independent Version 4 of HYDRUS-1D and Version 3 of HYDRUS(2D/3D). The HYDRUS software package (Version 5) is a
Windows-based application for simulating water, heat, andsolute movement in 1D, 2D, or 3D variably saturated porous
media. The program was additionally extended with many
special (old and new) standard add-on modules (see Table 1).

3.1

Dimensionality and geometrical shapes

The HYDRUS program is a finite element model that cansimulate the movement of water, heat, and multiple solutes
in variably saturated media. It can analyze the flow andtransport of water and solutes in unsaturated, partially

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TA B L E 1

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Standard HYDRUS add-on modules.

Module nameDimensions

Description

HPx

1D, 2DThe HP1 and HP2 modules (Jacques & Šimůnek, 2005) are the result of coupling HYDRUS (1D
and 2D modules) with the PHREEQC-3 geochemical code (Parkhurst & Appelo, 2013). The HPx
modules contain modules simulating (1) transient water flow, (2) multicomponent transport, (3)mixed equilibrium/kinetic biogeochemical reactions, and (4) heat transport in 1D and 2D variably
saturated porous media (soils).

UNSATCHEM

1D, 2D, 3D

The UNSATCHEM module (Šimůnek & Suarez, 1994) can be used instead of the standard
HYDRUS solute transport module to simulate major ions’ fate, transport, and reaction chemistry.

Wetland2D

The Wetland module was developed to model biochemical transformation and degradation
processes in subsurface-flow-constructed wetlands. Two biokinetic model formulations can bechosen in the Wetland module: (1) CW2D (constructed wetland two-dimensional) (Langergraber& Šimůnek, 2005) and (2) CWM1 (constructed wetland model 1) (Langergraber et al., 2009).
Aerobic and anoxic transformation and degradation processes for organic matter, nitrogen, andphosphorus are described in CW2D, while aerobic, anoxic, and anaerobic processes for organic
matter, nitrogen, and sulfur are considered in CWM1.

C-Ride1D, 2D

The C-Ride module simulates variably saturated water flow, colloid transport, andcolloid-facilitated solute transport in porous media. The module accounts for transient variably
saturated water flow, both colloid and solute movement due to advection, diffusion, anddispersion, as well as for solute movement facilitated by colloid transport.

DualPerm

1D, 2DThe DualPerm module simulates 2D variably saturated water flow and solute transport indual-permeability media, that is, preferential and nonequilibrium water flow and solute transport(Gerke & van Genuchten, 1993; Šimůnek & van Genuchten, 2008; Šimůnek et al., 2003).

Furrow

2D

The Furrow module is a hybrid finite volume/finite element module describing coupledsurface–subsurface flow and transport processes during furrow irrigation and fertigation(Brunetti, Šimůnek, & Bautista, 2018). The numerical approach combines a 1D description ofwater flow and solute transport in an open channel with a 2D description of water flow and solutetransport in the subsurface.

PFAS

1D, 2D, 3D

The PFAS module includes options to consider sorption to the air–water interface and soluteconcentration effects on surface tension and viscosity (Silva et al., 2020).

Particle Tracking

1D

Zhou et al. (2021) implemented the Particle Tracking algorithm into HYDRUS. This module cancalculate soil water travel times and ages for different locations in the soil profile.

COSMIC

1D

The COSMIC module developed by Brunetti, Šimůnek, et al. (2019) calculates abovegroundneutron fluxes using the physically based COsmic-ray Soil Moisture Interaction Code (COSMIC)
of Shuttleworth et al. (2013).

DPU

1D, 2DThe DPU (Dynamic Plant Uptake) module developed by Brunetti, Kodešová, & Šimůnek (2019)
and Brunetti, Kodešová, et al. (2021) simulates the translocation and transformation of neutralcompounds in the soil–plant domain.

Fumigant

1D, 2D, 3D

The Fumigant module includes options to simulate the fate and transport of fumigants in soils (e.g.,
removal of a tarp, temperature-dependent tarp properties, additional fumigant injections).

HyPar

2D, 3D

HyPar is a parallelized version of the standard 2D and 3D HYDRUS computational modules.

SLOPE Cube

2D, 3D

The SLOPE Cube (Slope Stress and Stability) module was developed to provide a unified effective
stress approach for both saturated and unsaturated conditions (Lu et al., 2010). The module isintended to predict spatially and temporally infiltration-induced landslide initiations and conduct
slope stability analyses under variably saturated soil conditions.

SLOPE Classic

2D

The SLOPE Classic module is intended mainly for stability checks of embankments, dams, earth
cuts, and anchored sheeting structures.

saturated, or fully saturated porous media. The program
can model 1D vertical or horizontal flow, 2D vertical or
horizontal flow, 3D radial symmetry about the vertical axis,
or fully 3D domains. Invoked 3D domains may range from
simple hexahedral domains to more complex layered systems

and almost entirely general 3D domains (with very few
constraints on the system’s complexity). The program canhandle flow regions delineated by irregular boundaries. The
flow region, furthermore, may be composed of nonuniform
soils with an arbitrary degree of local anisotropy.

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3.2

Considered processes in HYDRUS

The HYDRUS program numerically solves the Richards
equation for variably saturated water flow and advection–
conduction/dispersion equations for heat and solute transport
in one, two, or three dimensions. The flow equation incorporates a sink term to account for water uptake by plant roots.
The heat transport equation considers transport due to conduction and convection with flowing water. The transport
equations also include provisions for nonlinear nonequilibrium reactions (sorption) between the solid and liquid phases,
linear equilibrium reactions between the liquid and gaseous
phases (allowing simulations of volatile chemicals), zeroorder production, and two first-order degradation reactions,one of which can be used to represent parent–daughter degradation reactions (e.g., degradation of organic substances, or
nitrification of nitrogen species). Chemical nonequilibrium
solute transport can be accounted for using a two-site sorption model (e.g., van Genuchten & Wagenet, 1989), which
divides the sorption sites into two groups. Sorption on the first
fraction of sorption sites is instantaneous, while sorption on
the remaining sites is kinetic. In addition, physical nonequilibrium solute transport can be accounted for by assuming
a two-region, dual-porosity type formulation that partitions
the liquid phase into mobile and immobile regions (e.g.,van Genuchten & Wierenga, 1976). Attachment/detachment
theory, including filtration theory, is additionally included
to enable simulations of the transport of viruses, colloids,
nanoparticles, and bacteria (e.g., Bradford et al., 2004).
The dispersion tensor includes terms reflecting the contribution of molecular diffusion, tortuosity, and hydrodynamic
dispersion.

3.3ŠIMŮNEK ET AL.

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Boundary conditions

The water flow part of the model can deal with (constant or
time-varying) prescribed pressure head and flux boundaries,
as well as boundaries controlled by atmospheric conditions.
Soil surface (atmospheric) boundary conditions may change
during the simulation from prescribed flux to prescribedhead-type conditions (and vice versa), accounting for infiltration, ponding, surface runoff, or actual evaporation processes.
The code can also handle a seepage face boundary, throughwhich water leaves the saturated part of the flow domain,and free drainage boundary conditions. Nodal drains can be
represented by a simple relationship derived from analog
experiments. Additional boundary conditions can deal withvarious surface and subsurface drip irrigation, triggered irrigation, and other unique irrigation scenarios (e.g., Gärdenäs
et al., 2005; Lazarovitch et al., 2023). Special interactions
between different types of boundary conditions, such as an

atmospheric boundary condition on a nonactive part of a seepage face or dynamic changes in water levels of external water
bodies, can also be considered. Finally, interactions between
surface water reservoirs (e.g., wells [e.g., Sasidharan et al.,2018, 2019, 2021], furrows [e.g., Bristow et al., 2020], andwetlands) and the subsurface can also be accounted for in
HYDRUS (Šimůnek et al., 2018).
For solute transport, the code supports both (constantand varying) prescribed concentration (Dirichlet or firsttype) and concentration flux (Cauchy or third-type) boundary
conditions. Additionally, a special boundary condition permitting gaseous diffusion through a stagnant boundary layer
above the soil surface is implemented for solute transport,
thereby allowing analyses of the fate and transport of volatile
chemicals such as fumigants (e.g., Spurlock et al., 2013).

3.4

Soil hydraulic property models

The soil hydraulic properties (SHPs) in HYDRUS can be
described using the analytical functions of Brooks and Corey(1964), Durner (1994), van Genuchten (1980), or Kosugi(1996), as well as modified van Genuchten-type analytical
functions that improve the description of the hydraulic properties near saturation (Vogel & Císlerová, 1988). Alternatively,
SHPs can be defined using lookup tables, thus expanding HYDRUS’s ability to consider other analytical models(e.g., Iden et al., 2021; Peters et al., 2021) or other shapes.
HYDRUS also incorporates hysteresis, assuming that drying
scanning curves are scaled from the main drying curve andwetting scanning curves from the main wetting curve (e.g.,
Kool & Parker, 1987; Lenhard et al., 1991). The code further
implements a scaling procedure to approximate variability inthe hydraulic properties of a given soil profile using a set of
linear scaling transformations that relate the individual soil
hydraulic characteristics to those of a reference soil (Vogelet al., 1991). Additionally, HYDRUS can generate stochastic spatial distributions of scaling factors for the pressure
head, water content, and hydraulic conductivity, which canbe either completely independent or constrained by Miller–
Miller similitude (Miller & Miller, 1956). The scaling factors
can be either normally or lognormally distributed.

3.5

Numerical methods

The governing equations are solved numerically in HYDRUS
using a Galerkin-type linear finite element method applied toa triangular or tetrahedral elements network. Integration intime is achieved using an implicit (backward) finite difference
scheme for water flow under both saturated and unsaturated
conditions, and central or implicit finite element schemes

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for solute transport. The resulting equations are solved iteratively by linearization and subsequent Gaussian elimination
for banded matrices, a conjugate gradient method for symmetric matrices, or the ORTHOMIN method for asymmetricmatrices. In order to improve solution efficiency in transientproblems, certain measures are taken, including automatictime step adjustment and ensuring that the Courant and Peclet
numbers are kept within preset levels. The water content termin the Richards equation for transient flow is evaluated using
the mass-conservative method proposed by Celia et al. (1990).
Upstream weighing is included as an option for solving thetransport equation to minimize numerical oscillations.

3.6

Inverse problems

The standard modules of HYDRUS (not the specialized
add-on modules except C-Ride and DualPerm in 1D) also
implement a Marquardt–Levenberg-type parameter optimization algorithm (Marquardt, 1963) for inverse estimation ofsoil hydraulic and/or solute transport and reaction parametersfrom measured transient or steady-state flow and/or transport
data. The procedure allows the estimation of several unknown
parameters from observed water contents, pressure heads,
concentrations, and instantaneous or cumulative boundary
fluxes (e.g., infiltration or outflow data). The parameter estimation procedure can also include additional retention or
hydraulic conductivity data. A penalty function can be used
to constrain optimized parameters to remain in some feasible
region (Bayesian estimation).
The capability of the standard HYDRUS module to directly
calibrate and optimize unknown parameters is very popularwith HYDRUS users, with nearly all HYDRUS applications
involving some calibration or fitting process. Most applications use the implemented Marquardt–Levenberg algorithm,
a gradient-based optimizer that provides a statistical basis
for assessing parameter uncertainty through confidence intervals. However, this local search strategy cannot guarantee
convergence to the global minimum. To address this limitation, multiple studies have coupled HYDRUS externallywith global search algorithms, such as Particle Swarm Optimizations (e.g., Brunetti et al. 2016a), Genetic Algorithms(e.g., Vrugt et al., 2001), and Shuffled Complex Evolution approaches (e.g., Vrugt et al., 2004; Wöhling et al.,2008). In an attempt to balance the exploration capabilities
of global search strategies and the exploitation features ofgradient-based optimizers, Brunetti, Stumpp, et al. (2022)
combined the Marquardt–Levenberg algorithm embedded in
HYDRUS with the Comprehensive Learning Particle Swarm
Optimization strategy. The resulting algorithm outperformed
both the Marquardt–Levenberg local search strategy and theglobal optimizer, Shuffled Complex Evolution, on multiple
benchmark problems.

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Optimization, sensitivity analyses, and uncertainty assessments are increasingly being implemented in conjunction
with HYDRUS. Global sensitivity analysis methods, such as
Sobol, Morris, E-FAST, and Random Balance Design-FAST,
have been used to investigate the influence of model parameters (e.g., soil hydraulic and solute reactive transport parameters) on the fitting accuracy (e.g., Brunetti et al., 2016b)
or on specific variables of interest (Brunetti, Kodešová,et al., 2021; Brunetti, Papagrigoriou, et al., 2021). Similarly, HYDRUS has been coupled externally with Bayesianinference algorithms for calibration and uncertainty assessment purposes (e.g., Brunetti, Šimůnek, et al., 2020; Brunetti,
et al., 2019; Guo et al., 2020; Schübl et al., 2022; Vrugt
et al., 2008; Wöhling & Vrugt, 2011). In this perspective,
Brunetti et al. (2023) recently compared Markov chain Monte
Carlo ensemble samplers for vadose zone inverse modeling,highlighting the advantages and limitations of using thesealgorithms in conjunction with HYDRUS. Samplers havebeen embedded into the HYDRUS source code, thus making it possible to incorporate them in the HYDRUS software
package.

4
STANDARD HYDRUS ADD-ON
MODULESThe capabilities of the HYDRUS software packages havebeen expanded significantly by including various standard
and nonstandard specialized add-on modules described in thefollowing two sections. The standard add-on modules are
fully incorporated and supported by the HYDRUS graphical user interfaces (GUIs) and documented in detail in thetechnical and user manuals and via online help. This is not
the case for several nonstandard add-on modules (described
below in Section 5), which require additional work outside theGUI.
Common to all HYDRUS add-on modules is that they
simulate variably saturated water flow and heat and solutetransport in porous media. The specialized add-on modules provide additional capabilities, such as general reactive
transport (using the HP1 and HP2 models) or reactive
transport with specific chemistry (notably the Wetland and
UNSATCHEM modules). Other modules provide additionalmodeling capabilities, such as to account for preferential flow(the DualPerm module), colloid-facilitated solute transport(the C-Ride module), or the transport of polyfluoroalkyl substances (PFAS) (the PFAS module) or fumigant (the Fumigant
module) compounds. Some add-on modules are available forall three dimensions, while others are available only for aparticular dimension (e.g., 1D or 2D; see Table 1). In thesubsections below, we will discuss only the modules thathave been added since 2016, were expanded meaningfully(e.g., having some new capabilities or new dimensions), or

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Vadose Zone Journal

have been used in interesting applications. We will not discuss modules already available in 2016 (and thus described inŠimůnek et al., 2016).

4.1

HPx

The current HPx modules (Jacques et al., 2018; HP1 for 1D
and HP2 for 2D) couple the PHREEQC-3 geochemical code
(Parkhurst & Appelo, 2013) with the HYDRUS computational modules. The 1D version HP1 (the first HP1 versions
were coupled with PHREEQC-2; Parkhurst & Appelo, 1999)
was first released in 2005 (Jacques & Šimůnek, 2005; Jacqueset al., 2008a, 2008b) and used successfully in many applications. The 2D equivalent of HP1, that is, HP2, was released in2012. HPx is a comprehensive simulation module that can beused to simulate (1) transient water flow, (2) the transport ofmultiple components, including diffusion in the gas phase andexchange with the atmosphere, (3) mixed equilibrium/kinetic
biogeochemical reactions, and (4) heat transport in 1D or
2D variably saturated porous media. The HPx modules cansimulate a broad range of low-temperature biogeochemical
reactions in water, the vadose zone, and/or groundwater systems, including interactions with minerals, gases, exchangers,
and sorption surfaces based on thermodynamic equilibrium,
kinetic, or mixed equilibrium/kinetic reactions. Additionally,
the framework allows the use of flow and transport parameters
based on the geochemical state at a given time and location in
the domain (Jacques et al., 2018); example applications canbe found in Xie et al. (2015) and Valdes-Abellan et al. (2017).
The most significant changes implemented recently in the
HPx software are (1) more flexibility, reuse, and reproducibility of model structures and input, (2) the use of alternative
geochemical solvers, and (3) better integration of graphicaluser elements (see Section 2.4 in the Supporting Information). Elements contributing to the first point are (1) full
implementation of an alternative scripting language (MyBasic, https://paladin-t.github.io/my_basic), which is a more
modern and structured BASIC-like scripting language with
object-oriented programming possibilities, (2) options to run
Python (Version 3.8) scripts during run time, (3) dynamic definition and use of inline variables in the input files, and (4) agraphical component to define global variables (more details
are in Section 2.4 in the Supporting Information). Using thegraphical component to define global variables, relatively
complex parameter input tables can be created for a given
project. Examples (available on request) have been developed to assess the acidification of pyrite-rich soils (Mosley
et al., unpublished data, 2024), the implementation of the Tippings model for sorption of heavy metals on organics (Lofts& Tipping, 2011), and cement hydration and aging.
Recently (and currently only available upon request), the
PHREEQC geochemical calculations can be replaced by (1)ŠIMŮNEK ET AL.

ORCHESTRA (Meeussen, 2003), which solves similar geochemical systems as PHREEQC but also allows for the
implementation of alternative geochemical models because
the model equations are not in the source code but defined inseparate text files, and (2) script functions defined by users
in the input file. An application of the latter is replacinga (time-consuming) full geochemical solver with a (faster)
statistical metamodel derived using machine learning algorithms. Laloy and Jacques (2022) used Python scripts andlibraries to replace geochemical calculations with a deep neural network or a k-nearest neighbors model for 1D or 2D
cement leaching problems. Depending on the complexity ofthe model, speedups compared with a single-thread run of thefull geochemical model ranged between 10 and 30 times, withresults very close to theoretical values calculated by assuming
a zero cost for the geochemical calculations. Another example of the U transport application is given by Prasianakis et al.
(unpublished data, 2024).
Some interesting applications have been implemented in
the HPx module since 2016. In addition to the carbon cycling
study of Jia et al. (2021), Thaysen, Jessen, et al. (2014)
and Thaysen, Jacques, et al. (2014) demonstrated that HPx
and other generic coupled reactive transport models provide
a flexible framework for implementing soil organic matter dynamics such as those of multiple carbon pools, theeffects of biomass, and the fate of gaseous carbon dioxide. Jacques et al. (2018) demonstrated the effects of soil
environmental variables (e.g., water content and temperature) on the degradation rate constant and the migration ofsolid organic matter by bioturbation. Another set of applications concerns the fate of major elements and contaminants
in soil profiles and saturated media (e.g., Bruneel et al.,2021; Jiang et al., 2021; Latrille et al., 2021). Colloids andcolloid-facilitated solute transport were simulated using HPx
by Zhou et al. (2016) and Makselon et al. (2017). The
latter used the DVLO theory to calculate the attachment efficiency during variable geochemical conditions. Applicationsof pyrite oxidation in acid sulfate soils are given by Knabeet al. (2018), who implemented pyrite oxidation under nitratereducing conditions in aquifers, and by Salo et al. (2023) andMosley et al. (unpublished data, 2024), who simulated geochemical changes in acid sulfate soils following prolonged
drought events due to climate change. Tremosa et al. (2020)
assessed the weathering of shale tailings by combining transient water flow, mobile–immobile regions, and gas diffusion
with geochemical reactions. Besides environmental applications, coupled reactive transport tools are also useful for
more engineering-oriented problems, such as the durability ofbuilding materials and waste repositories. Although not many
applications have been published on these topics using HPx(e.g., Santiago et al., 2023), examples of other similar genericcoupled reactive transport models illustrate the feasibility
and interest of modeling complex, large-scale engineering

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applications (see Claret et al. [2022] for deep radioactive
waste repositories).
The HPx modules are general reactive transport models inwhich users need to define the geochemical system themselves. As a result, these modules provide users with a lotof freedom in designing their particular geochemical system,
which facilitates their application to a very wide range of subsurface contaminant transport problems. On the other hand,the following two modules (i.e., UNSATCHEM and Wetland)
are modules with specific chemistry in which the geochemical system is predefined, which restricts their application to
problems involving the prescribed chemical system. However,
the two modules with specific chemistry are much easier to
use and are computationally far more efficient than the moregeneral HPx models.

4.2

UNSATCHEM

The UNSATCHEM geochemical module (Šimůnek & Suarez,
1994, 1997) is the oldest HYDRUS module. This module
was initially a standalone software package simulating carbon dioxide’s 1D transport and production and the transportof major ions in variably saturated porous media, including
major ion equilibrium and kinetic nonequilibrium chemistry.
UNSATCHEM simulates the transport of major ions (i.e.,
Ca2+ , Mg2+ , Na+ , K2+ , SO4 2− , CO3 2− , and Cl− ) and theirequilibrium and kinetic geochemical interactions, such ascomplexation, cation exchange, and precipitation–dissolution(e.g., of calcite, gypsum, and dolomite). UNSATCHEM was
first incorporated in 2005 as a standard add-on module into
Version 3 of HYDRUS-1D, but then also in 2012 as a 2D
module into HYDRUS (2D/3D) (Šimůnek et al., 2016), andin 2022 as a 3D module into HYDRUS (2D/3D). The current
Version 5 of HYDRUS thus supports UNSATCHEM in all
three dimensions.
While the number of applications of the UNSATCHEM
module is narrower than for the HPx modules, a tremendous number of very practical and important agriculturaland environmental applications can be evaluated using thismodule. The number of applications of the UNSATCHEM
module has dramatically increased since 2016. Existing applications include studies evaluating the sustainability of various
irrigation systems, especially those using saline groundwater (e.g., Phogat, Mallants, Cox, Šimůnek, Oliver, & Awad,
2020; Phogat, Mallants, Cox, Šimůnek, Oliver, Pitt, et al.,2020; Ramos et al., 2019), the disposal of brine waters frommining operations (e.g., Mallants, Šimůnek, & Torkzaban,
2017; Mallants, Šimůnek, Th. van Genuchten, et al., 2017), or
the salinization/reclamation of agricultural soils (e.g., Phogat
et al., 2021; Ramos et al., 2023).

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4.3

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Wetland

The Wetland module simulates aerobic, anoxic, and anaerobic transformation and degradation processes for organic
matter, nitrogen, phosphorus, and sulfur during the treatmentof polluted wastewater in subsurface constructed wetlands(Langergraber & Šimůnek, 2012). The Wetland module uses
two biokinetic model formulations (constructed wetland twodimensional [CW2D] of Langergraber & Šimůnek [2005] andconstructed wetland model 1 [CWM1] of Langergraber et al.
[2009]) to account for complex conditions that may occur
in various types of wetlands. CW2D considers aerobic andanoxic transformation and degradation processes for organic
matter, nitrogen, and phosphorus, whereas CWM1 considers
aerobic, anoxic, and anaerobic processes for organic matter, nitrogen, and sulfur. Both biokinetic model formulations
were developed for constructed wetlands treating municipal
wastewater; they can be applied only to 2D problems.
No significant changes have been implemented into the
Wetland module since 2016. However, there have been many
interesting applications of this module. For example, Pucher
et al. (2017) used the HYDRUS Wetland module to optimize the depth of a zeolite layer in a one-stage vertical flow
wetland. Similarly, Pucher and Langergraber (2018) used
the module to evaluate the functioning of vertical flow wetlands with filter media of different grain sizes. Yasinta et al.
(2019) and John et al. (2020) simulated aeration intensity ina saturated vertical upflow constructed wetland. Jayswal andRodríguez (2021) evaluated the effects of temperature andloading frequency on the performance of vertical subsurfaceflow constructed wetlands. Khan et al. (2022) furthermore
assessed the capability of the HYDRUS wetland module tosimulate flow and nitrogen removal processes in pilot-scale
treatment peatlands under frost and no-frost conditions. A listof other applications of the Wetland module can be foundon the HYDRUS website (https://www.pc-progress.com/en/
Default.aspx?h3d2-wetland).

4.4

Furrow

The Furrow module simulates coupled surface–subsurface
flow and transport processes during furrow irrigation and fertigation (Brunetti, Šimůnek, & Bautista, 2018). To reduce thecomplexity and computational cost, the solver uses a pseudo3D numerical approach (in 1D and 2D) (Figure 1). The 3D
furrow domain is horizontally divided into N elements, associated with a cell-centered 1D finite volume scheme used toresolve overland flow processes spatially. Each element j ischaracterized by a 2D finite element discretization of the soil
domain, which is used to simulate subsurface processes.

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ŠIMŮNEK ET AL.

Vadose Zone Journal

furrow fertigation experiment conducted in the United States(Brunetti, Šimůnek, & Bautista, 2018).

4.5

PFAS

The PFAS module was developed to simulate, under dynamic
vadose zone conditions, the fate and transport of PFAS, often
called “forever chemicals.” When evaluating the transport of
PFAS compounds in the subsurface, one needs to consider,in addition to standard transport, sorption, and degradation
processes (as considered in the standard HYDRUS modules),sorption onto the air–water interface (AWI) (Silva et al., 2020;
Silva, Šimůnek, Guelfo, et al., 2022). In that case, the termin HYDRUS that accounts for the distribution of a solute
between the liquid and gaseous phases (i.e., for volatile chemicals such as ammonia, pesticides, or fumigants) is replaced
by a new term accounting for solute sorption onto the AWI as
follows:
F I G U R E 1 Schematic of the modeled transport domain in the
Furrow module consisting of a trapezoidal open channel and a soil
profile (Qinj is the solute injection rate [L3 T−1 ], Cinj is the soluteconcentration [ML−3 ], Qir is the irrigation inflow rate [L3 T−1 ], ET isevapotranspiration, P is precipitation, h is the water depth in the furrow[L], L is the length of the furrow [L], dx is the discretization length [L],hmax is the maximum allowed water depth in the furrow [L], bw is the
furrow bottom width [L], Tw is the top furrow width [L], and SS is theside slope).

Zero-inertia approximations of the hydrodynamic wave andadvection equation are used to describe water flow and solutetransport in the open channel. This reduces model complexity
and computational cost and enables one to simulate open- andblocked-ended channels. The standard 2D HYDRUS computational module calculates infiltration, describes water flow
and solute transport, and may include root water and nutrient
uptake in each element j. The overland and subsurface modules are coupled sequentially in time. In particular, at time t,water levels in the channel are used in HYDRUS as Dirichletboundary conditions to calculate infiltration in all elements.
The resulting infiltration vector is then used to solve overland flow using a fourth-order Runge–Kutta scheme, thereby
calculating the water level at the next time step. Soil watercontents, pressure heads, and concentrations in each element
are stored and updated during the simulation, thus enabling
one to thoroughly appraise surface and subsurface water andsolute movement along the furrow.
The robustness of the proposed Furrow module was examined and confirmed by mesh and time-step sensitivity analyses(Brunetti, Šimůnek, & Bautista, 2018). The model was theoretically validated by comparison with simulations conductedusing the well-established WinSRFR model and experimentally validated by comparison with field-measured data from a

𝜕𝑎v 𝑐g
𝜕𝑡

=

𝜕Γ𝐴aw
,
𝜕𝑡

(1)

where av is the air content [L3 L−3 ], cg is the gas-phase concentration [ML−3 ], t is time [T], Γ is the interfacial adsorbed
concentration (i.e., mass or moles per unit area of the interface, or ML−2 ), and Aaw is the air–water interfacial area,
which has dimensions of [L2 L−3 ] or [L−1 ]. Under transient
flow conditions, the air–water interfacial area is a dynamic
variable that increases during drying and decreases during
wetting, with a corresponding exchange of PFAS compounds
between the two phases across the AWI. The air–water interfacial area Aaw in the PFAS module is calculated directly fromthe pressure head–saturation relationship (e.g., Bradford et al.,2015):𝜃𝜌 𝑔

𝜃

𝐴aw (𝜃) = 𝜎1 ∫𝜃 s 𝑃aw (𝜃)𝑑𝜃 = 𝜎w ∫𝜃 s ℎ (𝜃) 𝑑𝜃,aw

aw

𝑑𝐴aw (𝜃)𝑃𝜌 𝑔ℎ= 𝜎aw = 𝜎w ,
𝑑𝜃
aw
aw

(2)

where σaw is the air–water surface tension [MT−2 ], Paw is thecapillary pressure [ML−1 T−2 ], θs is the saturated water content [L3 L−3 ], ρw is the density of water [ML−3 ], and g is thegravitational acceleration [LT−2 ]. Since there is still an ongoing discussion about the suitability of Equation (2) (e.g., Silva,Šimůnek, & McCray, 2022) for simulating the fate and transport of PFAS, we additionally implemented a user-specified
constant km , which allows one to scale the interfacial area
Aaw .
The interfacial adsorbed concentration, Γ, can be calculated
directly using the Freundlich–Langmuir adsorption isothermas:Γ=Γmax 𝐾L 𝑐 𝛽
𝐾H 𝑐 𝛽
=,1 + 𝐾L 𝑐 𝛽
1 + 𝐾L 𝑐 𝛽(3)15391663, 0, Downloaded from https://acsess.onlinelibrary.wiley.com/doi/10.1002/vzj2.20310, Wiley Online Library on [15/02/2024]. See the Terms and Conditions (https://onlinelibrary.wiley.com/terms-and-conditions) on Wiley Online Library for rules of use; OA articles are governed by the applicable Creative Commons License

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Vadose Zone Journal

where Γmax [ML−2 ] is the maximum surface concentration(i.e., at the solubility limit), and KH (for linear sorption,[L3 M−1 ]; for Freundlich sorption, [L3β M−β ]), β [–], and KL[L3β M−β ] are empirical coefficients.
The two-site sorption concept (similar to sorption onto thesolid phase) can be used for solute sorption on the AWI:
Γ = Γe + Γ k ,(4)where sorption, Γe [ML−2 ], on one fraction of the AWI
sites (the Type-1 sites) is assumed to be instantaneous, while
sorption, Γk [ML−2 ], on the remaining (Type-2) AWI sites
is considered to be time dependent. Sorption on the Type2 nonequilibrium AWI sites is assumed to be a first-orderkinetic rate process. The mass balance equation for the Type-2
AWI sites in the presence of degradation is given by[]
𝐾H 𝑐 𝛽𝜕Γkk− Γ − 𝜇AWI Γk , (5)= 𝜔AWI (1 − 𝑓AWI )𝜕𝑡
1 + 𝐾L 𝑐 𝛽
where ωAWI is the first-order rate constant [T−1 ].
A scaling technique is additionally used in the PFAS module to express concentration effects on the soil hydraulicfunctions. The primary impact of surface-active organic
solutes on unsaturated flow is through the dependence of thesoil water pressure head, h [L], on surface tension, σ [MT−2 ],and the contact angle, ω [–], and of the hydraulic conductivity, K [LT−1 ], on kinematic viscosity, ν [L2 T−1 ]. The capillarypressure head of the target liquid can then be scaled withsurface tension σ as follows:
( )
𝜎
(6)
= ℎ0 𝛼h ,ℎ = ℎ0𝜎0where αh is the pressure head scaling factor [–], h0 is the reference soil water pressure head [L], and σ0 is the reference
surface tension [MT−2 ]. The dependence of surface tension
on solute concentration can be described as (Adamson & Gast,
1997; Henry et al., 2001):
(
)
𝜎(𝑐)
𝑐
= 1 − 𝑏 ln
+1 ,
𝜎0
𝑎

(7)

where a [L3 M−1 ] and b [–] are constants for the compound ofinterest, σ(c) is the surface tension at concentration c, and σ0 is
the surface tension at a reference concentration c0 . Similarly,
the concentration-dependent unsaturated hydraulic conductivity, K(θ, c), of the target liquid can then be scaled with thekinematic viscosity ν as follows:
𝐾 (𝜃, 𝑐) =

(𝜈 )
0

𝜈

(
)
(
)
( )
𝐾0 𝜃, 𝑐0 = 𝛼𝐾 𝐾0 𝜃, 𝑐0 = 𝛼𝐾 𝐾 ∗ ℎ∗ ,(8)9 of 29

where αK is the hydraulic conductivity scaling factor [–] andK0 is the hydraulic conductivity at reference concentration c0 .
The dependence of viscosity on the solute concentration is(Smith & Gillham, 1999)()]−1
𝜈(𝑐) [𝑐= 1 − 𝑒 ln
,
+1
𝜈0
𝑑

(9)

where d [L3 M−1 ] and e [–] are constants for the compound ofinterest, ν(c) is the kinematic viscosity at concentration c, andν0 is the kinematic viscosity at reference concentration c0 .
The options to consider equilibrium sorption to the AWI
and the concentration effects on viscosity and surface tension were first implemented in Version 5.01 of HYDRUS only
for 1D and 2D, but later extended to 3D in Version 5.03.
Two-site sorption to the AWI has become available only in
Version 5.03. Since the PFAS module has been released only
recently, there have not yet been any published applicationsof this module other than from our team (Silva et al., 2020;
Silva, Šimůnek, & McCray, 2022). This is despite immenseinterest in this module by the research community because of
public and regulatory agencies’ increased awareness about theenvironmental dangers of polyfluoroalkyl compounds.

4.6

Particle Tracking

The Particle Tracking algorithm from Šimůnek (1991) was
recently implemented into the Particle Tracking module of
HYDRUS-1D (Zhou et al., 2021) and then in Version 5 of
HYDRUS as a 1D add-on module. The module tracks the
position of hypothetical particles, either initially defined in
the soil profile or released at its boundaries (e.g., with rainfall
or irrigation). New particles may be created or leave the soil
profile through the soil surface and the bottom, depending on
the actual development of the moisture profile. The results ofthis module can be used to calculate soil water travel times
and water ages at different locations in the soil profile.
The Particle Tracking algorithm is based on water balancecalculations using soil water profiles simulated by numerically solving the Richards equation. The first monitored
particle below the soil surface is at depth z = z0 and timet = t0 . Between this particle and the soil surface is an amountof water W0 [L], which can be calculated by integrating thewater content between positions z0 and L:
𝐿

𝑊0 =

∫

𝜃(𝑧, 𝑡0 )𝑑𝑧.

(10)

𝑧0

During time interval (t0 , t1 ), an amount of water N [L]passes through the soil surface depending on surface fluxes

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ŠIMŮNEK ET AL.

Vadose Zone Journal

such as rainfall, irrigation, and evaporation:

The resulting mass balance equation has then the following
form:

𝑡1

𝑁=

∫

[𝐸(𝑡) − 𝐼(𝑡)] 𝑑𝑡,(11)𝑧b(𝑡 )1

𝑡0∫ 𝜃(𝑧, 𝑡1 )𝑑𝑧 = ∫ 𝜃(𝑧, 𝑡0 )𝑑𝑧 − ∫ ∫ 𝑆(𝑧, 𝑡)𝑑𝑧𝑑𝑡.

𝑧a(𝑡 )

where E(t) [LT−1 ] is actual evaporation and I(t) [LT−1 ] isactual infiltration from precipitation or irrigation. During thesame interval, the layer between the soil surface and the monitored particle is depleted by water uptake from the root zone
by a transpired amount S [L]:
𝑡1

𝑆=

𝐿

𝑆(𝑧, 𝑡)𝑑𝑧𝑑𝑡,

∫ ∫

(12)

𝑡0 𝑧(𝑡)where S(z,t) is the sink (extraction) term [T−1 ]. At time t1 , one
hence has the following quantity of water W1 [L] between thesoil surface and the monitored particle:
𝑊1 = 𝑊0 − 𝑁 − 𝑆.

(13)

Equation (13) shows that W1 is the initial amount of water
enriched by infiltration and reduced by evaporation and root
water uptake (RWU). The monitored particle is then locatedat a depth of z = z1 , which can be calculated from the massbalance equation:
𝐿

∫

𝑡1

𝐿

𝜃(𝑧, 𝑡1 )𝑑𝑧 =𝑧1∫

𝜃(𝑧, 𝑡0 )𝑑𝑧 −

𝑧0

∫

𝑡1

[𝐸(𝑡) − 𝐼(𝑡)] 𝑑𝑡 −

𝑡0

∫ ∫

𝐿

𝑆(𝑧, 𝑡)𝑑𝑧𝑑𝑡.

𝑡0 𝑧(𝑡)(14)
By repeating the solution of this equation for the time
sequence (t0 , t1 , . . . , tn ), one obtains a sequence of depths (z0 ,z1 , . . . , zn ) defining the trajectory of the observed particle.
The locations of the other particles further down in the soil
profile can be calculated analogously, except that the amountof water is now balanced between the next two neighboring particles. The amount of water W0 (W1 ) between two
neighboring particles at time t0 (t1 ) is as follows:𝑧b(𝑡 )𝑧b(𝑡 )

0

𝑊0 =

∫

1

𝜃(𝑧, 𝑡0 )𝑑𝑧 and𝑊1 =𝑧a(𝑡 )∫

𝜃(𝑧, 𝑡1 )𝑑𝑧.

(15)𝑧a(𝑡 )

01

During time interval (t0 , t1 ), the amount of water between
the two neighboring particles is depleted by the transpiration
amount S:
𝑡1 𝑧b (𝑡)𝑆=

𝑊1 = 𝑊0 − 𝑆,𝑧b(𝑡 )
𝑡1 𝑧b (𝑡)0∫ ∫𝑡0 𝑧a (𝑡)𝑆(𝑧, 𝑡)𝑑𝑧𝑑𝑡.

(16)

1

𝑧a(𝑡 )
0(17)

𝑡0 𝑧a (𝑡)Again, by repeating the solution of this equation for the time
sequence (t0 , t1 , . . . , tn ), one obtains a trajectory (z0 , z1 , . . . ,zn ) of the particle in question.
The Particle Tracking algorithm itself proceeds as follows:
From the known position of the particles at the beginning of
the time interval, the pre-solved development of the moistureprofile, and the actual values of infiltration, evaporation, andtranspiration, the new position of the first monitored particle
is calculated using Equation (14). The new positions of allother particles are then calculated using Equation (17). New
particles may be created or leave the profile at the soil surface and the bottom of the soil profile, depending upon thetransient development of the moisture profile. Those particles
can be released after a certain amount of water passes throughthe soil surface or with each rainfall. In the latter case, the ageof each rainfall can be tracked throughout the soil profile.
By calculating the trajectories of flowing particles, themovement of inert substances not subject to dispersion can bemodeled. The average concentration within particular regions
between the two neighboring particles can be determinedeasily from the initial concentration (defined for individual regions) and from a decrease in the water content ofthese layers due to the extraction term S. The initial position of particles can be defined geometrically (at specified
depths) or based on mass balance calculations (by water
storage). Similarly, the release of new particles at the boundary can be defined chronologically (at specified times) or
meteorologically (rainfall events or depths).
We demonstrate here some typical results of the Particle
Tracking module using a dataset reported by Stumpp et al.
(2012), who provided all necessary details about the data(which can also be downloaded from the HYDRUS website).
Figure 2 shows the trajectories of hypothetical particles initially in the soil profile and generated at the soil surface.
The Particle Tracking module additionally provides various
particle statistics, such as the initial, final, and total number of particles, the number of particles released at the top
and bottom of the profile, the beginning (when released) andend (when leaving the profile) days for each particle, andthe particle residence/travel time (Figure 3). Users can use
this information to obtain a frequency distribution of particle
travel times.
The Particle Tracking module additionally provides information about the age of individual particles since they are
released, from which one can interpolate the age of water at

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Particle trajectories calculated by the Particle Tracking module.

FIGURE 3

Particle statistics and travel times reported by the Particle Tracking module.

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FIGURE 2

11 of 29
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Vadose Zone Journal

FIGURE 4

Water age as a function of time and depth calculated with the Particle Tracking module.

FIGURE 5
water uptake.

Precipitation and the average age of water taken up by plant roots, as calculated with the Particle Tracking module. RWU, root

different locations in the soil profile (Figure 4) and the average age of water taken up by roots at any time (Figure 5). This
information may be useful for designing various irrigation
schemes or for selected ecological applications.
The average age of water taken up by roots (the entire
root system), RWUAge, at any particular time is evaluated asfollows:∫ 𝑆(𝑧)Age(𝑧)𝑑𝑧

RWUAge =𝐿R∫ 𝑆(𝑧)𝑑𝑧

𝐿R

growth cycle, they took up mainly relatively young water fromthe surface layer. Once the roots reached deeper layers, they
started taking up older water from deeper soil layers. However, since the root density was assumed to decrease linearly
from the top to the bottom of the root zone, most water taken
up by roots was relatively young water throughout the growing
cycle (Figure 5).

∫ 𝑆(𝑧)Age(𝑧)𝑑𝑧

=

𝐿R

𝑇a

, (18)

where S is RWU [T−1 ] and Age is the water age at a particular location (interpolated from the age of particles evaluatedby the Particle Tracking module). Winter wheat was grown in
the lysimeters reported by Stumpp et al. (2012). The root zone
increased from 0 to 100 cm during one growing cycle of about
90 days. Since the roots were relatively shallow early in the

4.7

COSMICThe COsmic-ray Soil Moisture Interaction Code (COSMIC)
module (Brunetti, Šimůnek, et al., 2019) was mainly developed to enable the assimilation of cosmic-ray neutron probe(CRNP) data by HYDRUS. The CRNP measures fast neutrons
produced by nuclear interactions between incoming cosmic
rays and elements of the Earth’s atmosphere (Zreda et al.,2008). When cosmic rays reach the soil surface, they penetrate

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Vadose Zone Journal

13 of 29F I G U R E 6 Schematic of the COSMIC module, showing the coupling of HYDRUS with the COSMIC operator. The soil profile consists of two
soil horizons with variable water contents (the left bottom figure). The above ground neutron fluxes are given in N h−1 .

to a certain depth and are scattered back into the atmosphere.
The scattering process is regulated mainly by hydrogen, which
implies that the fast neutron intensity at the near-ground levelis directly related to the near-surface soil moisture content.
While the penetration depth of CRNP measurements varies
between 15 cm for wet soils and 55 cm for dry soils, theirmeasurement footprint can reach a radius of up to 240 m,
significantly larger than the typical spatial correlation lengthof soil moisture patterns. Due to this large sample volume,
CRNP data can be used to understand the hydraulic behaviorof the near-surface soil layer and infer effective SHPs for land
surface models.
The COSMIC module addresses this scientific need bycoupling HYDRUS with the physically based COSMIC of
Shuttleworth et al. (2013) (Figure 6). The two models arecoupled sequentially in time. At each time step, the soil moisture profile simulated by HYDRUS is passed to the COSMIC
operator, which calculates the aboveground neutron intensity.
This enables the COSMIC module to simulate the soil’s transient hydrological behavior and a time series of abovegroundneutron intensities. In its direct mode, the COSMIC module creates standard HYDRUS outputs and stores the timeseries of neutron intensities in an independent output file. In
its inverse mode, COSMIC can be combined with transient
CRNP data and other relevant information (e.g., soil moisture) to estimate soil hydraulic parameters inversely (Barbosa
et al., 2021; Brunetti, Šimůnek et al., 2019).

4.8

DPU

Plant roots generally take up water and solutes moving in therhizosphere due to the transpiration demand. While water sustains plant growth and its hydraulic functioning, chemicals arebioaccumulated in different plant tissues, where they are eventually metabolized into daughter compounds. The uptake andaccumulation of environmental contaminants in edible partsof a plant can pose a major risk to human health. Hence, it
is paramount to develop numerical tools to track the fate ofchemicals in the soil–plant system, which can also be used forphytoremediation design purposes.
The DPU (i.e., Dynamic Plant Uptake) module addresses
this need and extends the capability of HYDRUS to simulate
the translocation and transformation of neutral compounds
in the soil–plant domain (Brunetti, Kodešová, et al., 2019).
As shown schematically in Figure 7, this is accomplished bycoupling HYDRUS with a modified version of the multicompartment DPU model of Trapp (2007), which discretizes theplant into four compartments (i.e., roots, stem, leaves, andfruits). The following processes are considered in the DPU
module: (a) translocation of compounds with the transpiration
stream from roots to the stem and from the stem to leaves andfruits, (b) volatilization of compounds in the stem, leaves, andfruits, (c) gaseous and particle deposition from air to the stem,
leaves, and fruits, (d) dilution of compounds by plant growthin all compartments, and (e) sorption and metabolization of

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FIGURE 7

Schematic of the modeled system in the dynamic plant uptake (DPU) module.

compounds in all compartments. At each time step, HYDRUS
computes and passes the actual root water and solute uptake
flux to the DPU part, which calculates the mass balance andconcentrations of the compound(s) in each compartment. The
resulting numerical framework, which accounts for multiple
metabolization pathways in plant tissues, was successfully
used to predict the translocation and transformation of carbamazepine in green pea plants (Brunetti, Kodešová, et al.,2021). The currently available DPU module is fully incorporated into the HYDRUS software package and currently exists
for 1D and 2D applications while still being limited to neutral compounds. Brunetti, Kodešová, et al. (2022) extended
and validated the DPU module for ionizable chemicals, but
their approach is not yet included in the HYDRUS software
package.

4.9ŠIMŮNEK ET AL.

Vadose Zone Journal

SLOPE Cube

The SLOPE Cube (or SLOPE3 ; Slope Stress and Stability)
module was developed in cooperation with Dr. Ning Lu fromthe Colorado School of Mines as a supplemental 2D module of HYDRUS (2D/3D) to simulate 2D transient fields ofsoil moisture, soil suction, suction stress, total and effective
stresses, slope displacement, and a local factor of safety. The
module was originally available as a 2D add-on in 2015 andextended to 3D in 2019. The module, which uses a unified
effective stress approach for saturated and unsaturated conditions (Lu et al., 2010), is intended to predict spatially andtemporally infiltration-induced landslide initiation and carryout slope stability analyses for variably saturated soil conditions. Transient moisture and pressure head fields are obtained
directly with HYDRUS and then used to compute effective
stress and displacement fields in hillslopes (Lu & Godt, 2013).
Instead of using a one-factor safety methodology for the entire

slope, common in conventional slope stability analyses, the
SLOPE Cube module computes a field of the safety factors
for the whole domain within the hillslope (Lu et al., 2012),
thus allowing identification of potential failure surface zones
or surfaces.
Three new advancements were implemented in SLOPE
Cube far beyond traditional physically based landslide models. One is the utilization of pressure head-based effective
stress to unify the description of effective stress distribution in hillslopes under variably saturated conditions. Anotheradvancement is the computation of the transient hillslope
displacement field caused by variations in effective stress.
A third advancement involves implementing the recently
established concept of a local factor of safety to capture
the evolution of stress paths toward a failure state in hillslopes. The implemented hydromechanical framework has
been extensively validated through decades of field monitoring, case studies, and laboratory and field testing, as
documented thoroughly by Lu and Godt (2013).

4.10

HYDRUS Package for MODFLOW

There have also been further improvements in the “HYDRUS
Package for MODFLOW” (HPM) (Beegum et al., 2018, 2019,2020). The HPM, originally developed by Twarakavi et al.
(2008), accounts for the main processes and factors affecting
fluxes in the vadose zone as incorporated in HYDRUS1D. These include precipitation, infiltration, evaporation,
redistribution, capillary rise, plant water uptake, water ponding on the soil surface, surface runoff, and soil moisturestorage. The resulting package provided information about
groundwater recharge to the 3D modular finite-difference
groundwater model MODFLOW (Harbaugh et al., 2000). The
coupled model (HPM+MODFLOW) proved to be effective

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in addressing spatially variable saturated–unsaturated hydrologic processes at the regional scale by allowing for spatiallyand temporarily variable water fluxes at the soil surface andin the root zone, considering complex layering in the unsaturated zone, and permitting alternating recharge and discharge
fluxes.
The original coupled algorithm assumed that the groundwater table in the HPM profile remained constant throughout
an entire MODFLOW time step. This often resulted in unrealistic sudden inflow and/or outflow fluxes at the bottom of
the HPM profile when the groundwater table was updated
at the next time step. Beegum et al. (2018) developed amethodology to eliminate these sudden bottom fluxes by
updating/modifying the pressure head profile at the bottomof the HPM profile after every MODFLOW time step. They
showed that the new coupling algorithm effectively eliminated unrealistic sudden variations in the bottom flux of the
HPM profiles.
A major limitation of HPM was that it could not simulate solute transport along with water flow and thus could
not be used for evaluating groundwater contamination scenarios. This limitation was overcome by Beegum et al. (2019),
who integrated the solute transport part of HYDRUS-1D into
HPM for the unsaturated zone and MT3DMS for the saturated zone. The resulting update of the coupled model can
now simulate solute transport involving many biogeochemical
processes and reactions in the vadose zone, including firstorder degradation, volatilization, linear or nonlinear sorption,
one-site kinetic sorption, two-site sorption, and two-kineticsite sorption. Beegum et al. (2019) verified the developedmodel using HYDRUS (2D/3D) and showed that the model
effectively simulates the movement of water and contaminants in saturated–unsaturated flow domains. Beegum et al.
(2020) further demonstrated the use of MODFLOW with
the HYDRUS-1D package and MT3DMS by investigating
atrazine contamination in the Zwischenscholle aquifer in Germany. Additional applications of HPM have been reported by
Dandekar et al. (2018), Samuel et al. (2020), Szymkiewicz
et al. (2018), Zeng et al. (2019), Dai and Guo (2020), andSarma and Singh (2021), among others.

5
NONSTANDARD HYDRUS ADD-ON
MODULES
Several nonstandard computational modules significantly
expand the capabilities of the HYDRUS-1D, HYDRUS(2D/3D), and HYDRUS software packages. Although they
still can be run from the standard HYDRUS GUIs, users
are usually required to provide manually an additional input
file with supplementary information needed for a particular
module or to interpret selected input and/or output variables
differently from the standard versions. Users may also need to

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prepare their own graphical output from the output text files.
Most of the nonstandard modules can be downloaded freely
from the HYDRUS website, together with many examples
demonstrating their use and brief descriptions of the theories
behind the modules and their implementation (for details, see
Table 2 or the HYDRUS website).
A few of the standard HYDRUS add-on modules were initially posted only as nonstandard modules, but they were later
included as standard packages with full graphical support
when the scientific community showed considerable interestin their use. Examples are C-Ride, Fumigant, and PFAS. Nonstandard HYDRUS modules currently listed in Table 2 likely
will be included in the standard HYDRUS software packagesin the future.
We are currently developing several additional nonstandard modules, which we intend to convert into standard
packages. They involve the modules discussed below in Section 6, such as the Isotope module (Section 6.1), the extended
RWU module (Section 6.2), and the Brunswick module(Section 6.3).

6
DISCUSSION OF RECENTDEVELOPMENTS AND APPLICATIONSIn this section, we will first discuss some of the most recent
developments, including processes and options we intend toinclude in upcoming releases of HYDRUS as either standard or nonstandard add-on modules, depending upon theinterest of the research community. New features include
options to consider the fate and transport of environmental
isotopes (Section 6.1), double vegetation as required in multicropping systems (Section 6.2), more physically based RWU
models compared to the currently available Feddes model(Section 6.3), and more complex descriptions of the SHPs,
such as the capillary and noncapillary parts of the water
retention and hydraulic conductivity functions (Section 6.4).
The second part of this section provides an overview ofsome of the most common applications of the HYDRUS models or those we see as obtaining broader prominence. They
include alternative irrigation applications (Section 6.5), evaluations of the hydraulic functioning of various low-impact
developments (LIDs) (Section 6.6), and applications involving different managed aquifer recharge (MAR) technologies(Section 6.7).

6.1

Environmental isotopes

The standard third-type (Cauchy type) boundary condition
defining the solute flux at the upper boundary is as follows:−𝜃𝐷𝜕𝑐+ 𝑞𝑐 = 𝑞0 𝑐0 ,
𝜕𝑥

(19)

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ŠIMŮNEK ET AL.

Vadose Zone Journal

TA B L E 2

Nonstandard HYDRUS add-on modules.

Module nameDimensions

Description

Centrifuge

1D

The Centrifuge module for HYDRUS-1D simulates water flow and solute transport in a centrifuge
with time-variable rotations (e.g., Šimůnek & Nimmo, 2005).

Isotopes

1D

The Isotopes module for HYDRUS-1D modifies the upper solute transport boundary condition by
allowing isotopes not to accumulate at the upper boundary due to evaporation (in contrast to thestandard treatment of solutes during evaporation, where solutes stay behind in the soil whilewater is removed) without considering fractionation processes (Stumpp et al. 2012). This option(with constant fractionation) is now available in Version 5 of HYDRUS.

ColThetaTr

1D

The ColThetaTr module for HYDRUS-1D (both direct and inverse) simulates transient watercontent effects on colloid transport and the attachment/detachment of colloids from the air–waterinterface (Bradford et al., 2015).

RootGrowth

1D, 2D

The RootGrowth module was developed by Hartmann et al. (2018) as a supplemental module of the
HYDRUS software package (both HYDRUS-1D and HYDRUS [2D/3D]) to model root growth
as a function of different environmental stresses.

Freeze1D

The Freeze module considers freezing/thawing processes and their impact on flow and transport(Hansson et al., 2004; Zheng et al., 2021).

Tillage

The Tillage module performs tillage mixing (averaging or homogenizing water contents and soluteconcentrations due to tillage over a specified depth) at specified times (Mallman et al., 2014).

Overland2D

The Overland module considers overland flow (described using a kinematic wave equation) on an
atmospheric boundary (van Genuchten & Šimůnek, 2004).

Carbon

2D

The nonstandard Carbon module extends the standard UNSATCHEM module to also consider the
production and transport of carbon dioxide in soils, as in the 1D version of UNSATCHEM(Šimůnek & Suarez, 1993).

where q0 represents the water flux [LT−1 ] and c0 is the concentration associated with the flux [ML−3 ]. When the water
flux is directed into the soil profile (e.g., rainfall or irrigation),c0 is the concentration of the incoming fluid. No solutes are
assumed to leave the soil with evaporation at the atmosphericboundary, and hence c0 in Equation (19) is then zero.
This standard treatment of the upper boundary condition
for solute transport was modified by Stumpp et al. (2012) toaccount for isotope transport. They assumed that isotope fractionation processes could be neglected and that the relative
concentration of isotopes (δ content) will not increase at theupper boundary due to evaporation, and thus, that water andsolutes will move at similar rates during evaporation. This
contrasts with the standard treatment of solutes during evaporation in HYDRUS-1D, where solutes stay behind in thesoil while water is removed. This modification resulted ina nonstandard Isotope module, which has been successfully
used by Huang et al. (2015), Sprenger et al. (2015, 2016),
Brinkmann et al. (2018), and Nasta et al. (2023), among others. For example, Sprenger et al. (2016) used the modified
model to infer soil water residence times at different depths,
while Brinkmann et al. (2018) used the model to estimate theresidence time distribution of soil water and to identify the
temporal origin of water taken up by Picea abies and Fagus
sylvatica.
Ignoring evaporative enrichment, as done in the modified
HYDRUS-1D, still leads to underestimations of the 2 H and
18 O concentrations in the topsoil, which may be more sig-

nificant in regions with higher evaporative losses (Sprenger
et al., 2018). For this reason, we modified the Isotope module of Stumpp et al. (2012) further by considering constantevaporative fractionation when c0 in (19) is equal to the surface concentration, c(L,t), multiplied by a fractionation factor
rFract . This factor equals 0.0 when all solutes are left behindin the soil (the standard treatment of solutes), equals 1.0
when fractionation is completely neglected and hence whenwater and solutes (or isotopes) move at similar rates, and falls
between 0 and 1 (close to 1) when evaporation fractionationis considered to be constant. This modified Isotope module is
now a standard option in HYDRUS (Version 5).
The Isotope module was further modified by Zhou et al.
(2021), who considered the dependence of evaporation fractionation on environmental factors, such as atmosphere temperature and relative humidity, using the Craig and Gordon(1965) and Gonfiantini (1986) models. The resulting formulation has been used successfully in multiple applications (e.g.,
Post et al., 2022; Zhou et al., 2022, 2023). For example, Post
et al. (2022) used the code to estimate groundwater recharge
rates using soil water isotope profiles in two contrasting dune
types on Langeoog Island in Germany.

6.2

Double vegetation

Intercropping systems have been widely used worldwide
due to their high economic benefits, field productivity, and

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16 of 29

Vadose Zone Journal

land-, water-, and nitrogen-use efficiency. Intercropping is anagricultural practice where two crops (e.g., tomato and corn)
are grown simultaneously in one field. The practice is often
coupled with drip irrigation and mulching to increase crop
yields and land- and water-use efficiencies. However, evaluating interspecies nutrition competition and the effects ofdifferent spatial arrangements of intercropping species on thespatial distributions of soil water content, temperature, andnitrogen concentration is much more complex than when asingle crop species is present.
The standard HYDRUS models consider only single vegetation with a single root zone and a single stress response
function. The sink term in the Richards equation representing
RWU for such a system is described using the macroscopic
approach of Feddes et al. (1978):𝑆(ℎ) = 𝛼(ℎ)𝑏(𝑧)𝑇p ,(20)

where S is RWU [T−1 ], α is the stress response function [–], b represents the spatial distribution of roots in the rootzone [L−1 ], and Tp is the potential transpiration [LT−1 ]. The
HYDRUS code was modified to consider the effects of multiple species and their competition for various resources (e.g.,water and nutrients) as follows (Chen et al., 2020, 2022):
𝑆(ℎ) = 𝑆c (ℎ)+𝑆t (ℎ)=𝛼c (ℎ)𝑏c (𝑧)𝑇pc + 𝛼t (ℎ)𝑏t (𝑧)𝑇pt , (21)where subscripts c and t refer to two vegetations (e.g., corn andtomato). Each crop has its own root distribution and potential
transpiration rate, thus reflecting different growth cycles withdifferent root growth and leaf area parameters. The model
additionally allows the specification of different root waterand solute uptake parameters for the different crops, which
affects the spatial distribution of water and nutrients between
irrigation cycles. While only the 1D formulation is given
above, the same formulation was also implemented in the 2D
code.
The modified HYDRUS code (its 2D version) with double vegetation was used successfully to evaluate soil nitrate
dynamics and interspecies water and nitrogen competition
in a tomato–corn intercropping system with different spatial arrangements (i.e., different number of rows of different
species) by Chen et al. (2020, 2022).

6.3

RWU models

The spatiotemporal pattern of RWU depends on multiple
factors, including soil moisture availability and plant root
biomass distribution. The nonuniformity of soil moisture andits impact on RWU is often mitigated by various coexistingprocesses, such as compensated root water uptake (CRWU)
and hydraulic redistribution (HR). CRWU represents the abil-

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ity of plants to preferentially extract water from the wet zone tooffset a reduction in RWU from the water-stressed zone (e.g.,
Jarvis, 1989; Šimůnek & Hopmans, 2009). On the other hand,
HR refers to the passive transfer of soil moisture through theroot system from a relatively wet soil zone to drier soil layers
under reduced transpiration demand.
RWU in most or all previous HYDRUS versions is
described using the macroscopic approach of Feddes et al.
(1978). The approach is now generalized in HYDRUS suchthat the model can simulate root water and solute uptake,account for the effects of both water and salinity stress on
RWU, and additionally consider possible active and passiveroot contaminant or nutrient uptake (Šimůnek & Hopmans,
2009). Root water and solute uptake processes can be treatedas being noncompensated or compensated (Jarvis, 1989),
while users can select the degree of compensation (Šimůnek
& Hopmans, 2009). Environmental stresses and compensation in this approach are considered purely empirical, withthe model unable to simulate additional processes such as
hydraulic lift.
To overcome the limitation of HYDRUS not being able toconsider these processes and to demonstrate the importanceof simultaneously considering CRWU and HR in estimating
daily transpiration and RWU distributions under nonuniform
soil moisture conditions, Thomas et al. (2024) implemented
multiple mechanistic RWU models, including those of deJong van Lier et al. (2006, 2008, 2009, 2013), Couvreur et al.
(2012), Couvreur, Vanderborght, Beff, et al. (2014), Couvreur, Vanderborght, Draye, et al. (2014), and Nimah andHanks (1973a, 1973b), in addition to the existing models
of Jarvis (1989) and Feddes et al. (1978). The applications
demonstrated much flexibility to account for the various processes involved. Implementing the models into the HYDRUS
platform to simultaneously consider CRWU and HR andmaking them available to HYDRUS users should improve
the accuracy of RWU predictions, and it will undoubtedly
facilitate and encourage future research in this area.

6.4

Soil hydraulic properties

As noted earlier, SHPs can be described in HYDRUS
using multiple analytical models for the water retention andhydraulic conductivity functions, including those by van
Genuchten (1980), Brooks and Corey (1964), Durner (1994),
and Kosugi (1996), as well as modified van Genuchten functions (Vogel & Císlerová, 1988). Alternatively, SHPs can be
defined using lookup tables, thereby expanding HYDRUS’s
ability to consider other analytical models or more generalshapes.
Much research has been carried out recently to derive analytical models that improve the description of SHPs in thevery dry range (e.g., Iden et al., 2021; Peters, 2013; Peters

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ŠIMŮNEK ET AL.

Vadose Zone Journal

et al., 2021; Seki et al., 2023; Weber et al., 2019, 2020). Whilethese models can be accommodated in HYDRUS using the
input of lookup tables, we nevertheless included one such formulation directly in HYDRUS. In collaboration with Stathis
Diamantopoulos and Tobias Weber, we implemented theirgeneralized modular framework (Weber et al., 2019), which
partitions the SHP functions into capillary and noncapillary(e.g., water in corners and/or films) parts. The water retention
curve is, for this purpose, considered to be a weighted sum of aparametric capillary retention function, Sc (h) (one of the analytical functions referred to above), and a new general modelfor the noncapillary saturation function, Snc (h) (Weber et al.,2019):
𝜃(ℎ) = 𝜃cs 𝑆c (ℎ) + 𝜃ncs 𝑆nc (ℎ),(22)

where θcs [–] and θncs [–] are the saturated water contentsof the capillary and the noncapillary parts, respectively. The
hydraulic conductivity function, K(h) [LT−1 ], is then obtained
similarly. The capillary part of K(h) is obtained by adopting
Mualem’s integral, while the noncapillary part of K(h) is estimated directly from the new noncapillary saturation function(Weber et al., 2019), leading to𝐾(ℎ) = 𝐾c (ℎ) + 𝐾nc (ℎ) = 𝐾sc 𝐾rc (𝑆c ) + 𝐾snc 𝐾rnc (𝑆c ),(23)
where Kc (h) is the hydraulic conductivity of liquid waterin completely filled capillaries and Knc is the hydraulicconductivity of noncapillary (e.g., corner flow, film flow)
liquid water [LT−1 ]. Additionally, Krc (Sc ) [–] is the relative hydraulic conductivity associated with completely filledcapillaries, Krnc (Snc ) [–] is the saturation-dependent relative
conductivity of the noncapillary part, and Ks is the traditional
total saturated hydraulic conductivity [LT−1 ], which is partitioned into the saturated capillary conductivity, Ksc , and thenoncapillary conductivity, Ksnc .
Since the generalized modular framework of Weber et al.
(2019) can be combined with all soil hydraulic functions currently available in HYDRUS (i.e., Brooks & Corey, 1964;
Kosugi, 1996; van Genuchten, 1980; Vogel & Císlerová,1988), it provides significant additional flexibility to how
SHPs can be described in HYDRUS. The resulting module
currently has a working title, the Brunswick module. Lastly, apedotransfer function is also provided to convert the parameters of van Genuchten (1980) to the parameters of the Weberet al. (2019) model (Weber et al., 2020).

6.5

Irrigation applications

The number and breadth of HYDRUS applications in the literature have increased dramatically in recent years and aremuch larger than expected when we first started developing
the models. The type of applications is very broad, ranging from environmental applications simulating the transportof different solutes and particle-like substances to agricultural problems evaluating alternative irrigation schemes andthe effects of plant covers on the soil water balance andgroundwater recharge (Šimůnek et al., 2016).
Irrigation applications have always been one of the mostcommon HYDRUS applications. They have been the focusof hundreds of studies evaluating different irrigation methods (e.g., basin, sprinkler, furrow, and surface and subsurfacedrip), their scheduling (e.g., the timing of irrigation and its
amount), and solute-related factors (e.g., fertigation, chemigation, salinization, and sodification) (Lazarovitch et al., 2023).
For example, HYDRUS has been used in over 200 peerreviewed journal articles to assess various issues associatedwith drip irrigation. While a complete understanding of complex irrigation systems requires laborious, time-consuming,and expensive field investigations, which invariably involve
only a limited number of treatments, fully calibrated processbased models such as HYDRUS can quickly evaluate different
irrigation management strategies without the need for laborintensive fieldwork. The HYDRUS models for these reasons
have become invaluable tools for studying complex and interactive water flow and solute transport processes in various
irrigation systems.
Lazarovitch et al. (2023) provided a recent review of thecurrent modeling capabilities of HYDRUS to evaluate different irrigation methods. They provided not only a descriptionof how HYDRUS can be used to model different irrigation techniques and solute-related topics such as fertigation,
chemigation, and salinization/sodification, but also a long listof references of manuscripts in which HYDRUS was used forthese applications. Other topics discussed in Lazarovitch et al.
(2023) include special boundary conditions implemented in
HYDRUS for various irrigation methods, optimization of irrigation systems, special irrigation methods, and the effectsof spatial variability. The manuscript emphasizes the advantages and opportunities of using HYDRUS to describe basic
processes in the root zone of irrigated plants that support sustainable irrigated agriculture. Especially valuable to
HYDRUS users, the manuscript provides a link to a webpage
from which all the HYDRUS project files of the discussed
examples can be downloaded.
Another more narrowly focused review was written by
Morianou et al. (2023). They looked at HYDRUS applications
for simulations of water dynamics, RWU, and solute transport
under drip irrigation of the four most common categories oftree crops (citrus, olive, avocado, and deciduous fruit/nuts).
Morianou et al. (2023) identified 22 papers dealing with this
topic, most of which involved surface drip irrigation, while
three also focused on subsurface drip irrigation.

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6.6

Low-impact developments

There has been an explosion of applications of the HYDRUS
models to simulate flow and transport in various LIDs thathave proven to be valuable alternatives for stormwater management and hydrological restoration of urban areas. LIDs
include many different systems such as bioretention cells,
infiltration wells/trenches, stormwater wetlands, wet ponds,
level spreaders, permeable pavements, swales, green roofs,
vegetated filter/buffer strips, sand and gravel filters, smaller
culverts, or water harvesting systems (Brunetti et al., 2017).
One of the limiting factors in the wide use of LIDs is alack of adequate modeling tools that can be used to design
LIDs that function properly for particular climate conditions.
LID modeling requires an accurate description of multiple and interacting hydrological processes. Although several
stormwater models can be applied to LID analyses, most ofthem do not incorporate accurate descriptions of the hydrological processes involved. The HYDRUS models may overcome
this limitation.
Most LID applications with HYDRUS involved analysesof the overall hydrological functioning and effects of substrates used in green roofs, bioretention cells, and permeable
pavements. Green roofs are complex systems consisting ofa growing medium (usually a soil, which may be layered)and a waterproofing membrane, which are fully or partiallycovered with vegetation and may include additional features
such as a drainage layer and an irrigation system. By retaining, delaying, and evapotranspirating stormwater, green roofs
increase the resilience of urban areas against flooding. Theirhydrological efficiency is strongly influenced by the hydraulicproperties of the soil substrate, which is designed to belightweight, to support vegetation, and to avoid surface water
ponding. These features are generally achieved by mixing
carbon-enriched soils with lightweight aggregates (e.g., volcanic lapillus or pumice), which confer a multimodal pore size
distribution to the substrate. The resulting hydraulic behavior is strongly unsaturated and can be adequately describedby the Richards equation. Many evaluated the effectivenessof green roofs using HYDRUS, including Brunetti, Papagrigoriou et al. (2020), Peczkowski et al. (2018), Sandoval
et al. (2017), Soulis et al. (2017), and Zhang, Lin et al.
(2021). Several studied various factors affecting the hydrological functioning of green roofs, such as different substrates(Zhang, Lin et al., 2021), a storage layer (Li et al., 2019),
storm events (Peng et al., 2019), compaction (Sandoval &Suárez, 2019), different substrate depths and vegetation covers (Soulis et al., 2017), having no vegetation (Brunetti, Porti,
et al., 2018), and layering (Brunetti et al., 2016b; Wang et al.,2021). HYDRUS can be used to simulate not only water flowin green roofs, but also solute transport. Recently, Brunetti,
Papagrigoriou, et al. (2021) used HYDRUS to reproduce

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observations from an experimental campaign about nitrogenturnover in green roofs irrigated with domestic wastewater.
HYDRUS predicted high nitrogen turnover rates supported by
the unsaturated conditions in the soil.
Strong unsaturated hydraulic behavior is also a common
trait of permeable pavements, which is another LID consistingof a surface layer (e.g., porous concrete or turf blocks), a bedding layer (e.g., coarse sand), and a base layer (e.g., stones).
The multilayered structure increases the stormwater retention
capacity, delays subsurface runoff peaks, and avoids surface
runoff. The hydrological efficiency of permeable pavements
can be increased further by infiltrating subsurface runoff into
the underlining soil, thereby reducing the pressure on urban
drainage systems. Analyses of the hydrological functioningof permeable pavements with HYDRUS were carried out
by Brunetti et al. (2016a), Brunetti, Šimůnek, Turco, et al.
(2018), da Silva Ribas et al. (2021), and Turco et al. (2017),
among others.
Finally, a bioretention cell is a stormwater device designed
to capture and treat the first portion of runoff from impervious surfaces. The first flush into the cell often contains alarge portion of the pollutants that leave an impermeable area.
Examples of HYDRUS applications to evaluate the functioning of bioretention cells are given by Stewart et al. (2017), Liet al. (2021), Lisenbee et al. (2021), and Hečková et al. (2022).

6.7

Managed aquifer recharge

Evaluating problems associated with MAR is another areawith a dramatically increasing number of HYDRUS applications. Uncontrolled groundwater use worldwide has resulted
in overexploitation, pollution, and other unintended consequences such as land subsidence, destruction of groundwaterdependent ecosystems, and alterations in the hydrologicalcycle. MAR, which refers to the intentional recharge ofgroundwater for future recovery or environmental benefit, has
emerged as an important tool for achieving groundwater sustainability. MAR uses various technologies for intentional
diversion, including the transport, storage, infiltration, andrecharge of excess surface water (Sasidharan et al., 2021;
Sprenger et al., 2017).
As an example, MAR can be accomplished using technologies such as aquifer storage and recovery, flooding land
(Flood-MAR), flooding agricultural land (Ag-MAR), infiltration basins (IB), and vadose zone recharge devices suchas stormwater disposal wells, vadose zone trenches, or drywells (Sasidharan et al., 2021). HYDRUS has been used toevaluate many of these technologies. The most common application has been studies of the hydrological functioning ofdrywells (e.g., Glass et al., 2020; Helles & Mogheir, 2023;
Moreno et al., 2023; Sasidharan et al., 2018, 2019, 2020,

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Vadose Zone Journal2021) and infiltration basins (e.g., Cannavo et al., 2018; Glasset al., 2020; Lu et al. 2021; Nieec et al., 2021; Qi et al.,2021). The reservoir boundary condition in HYDRUS, forwhich the water level in a well or infiltration basin depends
on the rate of water injection or pumping along with water
infiltration or exfiltration, has most often been used in theseapplications (e.g., Glass et al., 2020; Sasidharan et al., 2018,2019).
Various factors influencing infiltration from drywells andinfiltration basins, such as spatial soil heterogeneity (e.g.,
Sasidharan et al., 2019, 2020, 2021) and clogging (Glass et al.,2020), have been evaluated in the above studies. Several havecompared the hydrological functioning of drywells with infiltration basins (e.g., Glass et al., 2020; Sasidharan et al., 2021),
the surface area required by these technologies (Sasidharan
et al., 2021), or how infiltration from an infiltration basin canbe enhanced substantially using drywell techniques (Helles& Mogheir, 2023; Sasidharan et al., 2021). While Sasidharan et al. (2021) considered a single drywell in the center of acircular infiltration basin, which only requires a 2D axisymmetrical formulation, Helles and Mogheir (2023) considereda more complicated 3D transport domain with an infiltration
basin containing 18 drywells.
The references in this section have all used a multidimensional version of HYDRUS. A much higher number of MAR
applications (not further given here) used HYDRUS-1D. The
generic geochemical module PHREEQC in HPx was recently
used to represent redox conditions and site geochemical evolutions during MAR, which made it possible also to accountfor alterations in the hydraulic conductivity due to clogging
or field operations (Rodríguez-Escales et al., 2020). Given theincreasing shortage of water resources worldwide, HYDRUS
undoubtedly will be used in future studies evaluating current
and new MAR technologies.

7

HYDRUS USE IN CLASSROOMS

Because of their ease of use and the advanced GUIs, the
HYDRUS models have become popular tools for teaching theprinciples of water, solute, and heat movement in soils andgroundwater in undergraduate- and graduate-level courses.
Even users with little direct knowledge of soil physics andrelated disciplines and limited mathematical expertise canbenefit from the models. As a result, the HYDRUS software
packages have been discussed extensively also in several soil
physics and hydrology-related textbooks (e.g., Jury & Horton,
2004; Lazarovitch & Warrick, 2013; Radcliffe & Šimůnek,2010; Rassam et al., 2003, 2018; Shukla, 2014) that can bereadily used in university classrooms.
In 2003, Rassam et al. published a book that provided
detailed guidance on using HYDRUS-2D to simulate variably
saturated water flow and solute transport in soils. The bookŠIMŮNEK ET AL.

mainly focused on the technical aspects of defining transportdomains, describing their discretization, and interpreting simulated results rather than explaining the underlying flow andtransport processes in soils. Thus, the book was aimed at users
familiar with the involved physical processes. The book waslater translated into Japanese by Nobuo Toride and Mitsuhiro
Inoue (Rassam et al., 2004). On the other hand, Soil Physics
by Jury and Horton (2004) was likely the first textbook that
attempted to explain basic flow and transport processes tostudents using the HYDRUS-1D software package.
Radcliffe and Šimůnek (2010) later wrote a textbook called
Soil Physics with Hydrus that covers different soil physics topics and is widely used in university classrooms worldwide.
They used the HYDRUS family of programs to help students
understand the basic topics better. While the RETC software
was used to evaluate the unsaturated SHPs, HYDRUS-1D
was used to demonstrate the processes of water infiltration,
evaporation, and percolation in soils with varying texturesand layers. They also showed how the software can be used
for heat and solute transport in these systems, including
how physical and chemical nonequilibrium conditions canaffect water flow and contaminant transport. The HYDRUS(2D/3D) software was used further to describe 2D flow withinfield soils, hillslopes, boreholes, and capillary fringes. The
software can also evaluate how different transport and reaction parameters affect solute transport. Using the informationin this book, students can run HYDRUS and related models for different scenarios and parameters, thereby gaining
more insight into the physics of water flow and contaminanttransport. The book by Radcliff and Šimůnek (2010) is also
suitable for self-studies on how to use the HYDRUS models since all examined problems can be downloaded from the
HYDRUS website (https://www.pc-progress.com/en/Default.
aspx?h3d-book).
A book called Exercises in Soil Physics was published by
Lazarovitch and Warrick (2013) to complement existing soil
physics and vadose zone hydrology textbooks by providing
practical exercises. The text explores various topics related tosoil physics, including solid-phase characteristics, soil water
relations, saturated water flow, unsaturated flow, field waterflow processes, chemical fate and transport, heat and energy
transport, soil gases and their transport, and soil variability. Using HYDRUS-1D, the book further provides solutions
to several problems related to variably saturated water flow
and RWU. Additionally, STANMOD is used to solve solutetransport problems involving sorbing, nonsorbing, degrading,nondegrading, and volatile solutes with different degrees ofdispersion. Finally, the book uses ROSETTA and RETC to
calculate the soil water retention curve and to determine theunsaturated soil hydraulic functions of van Genuchten (1980)
and other soil hydraulic models.
In his textbook Soil Physics: An Introduction, Shukla(2014) published an extensive HYDRUS-1D tutorial focused15391663, 0, Downloaded from https://acsess.onlinelibrary.wiley.com/doi/10.1002/vzj2.20310, Wiley Online Library on [15/02/2024]. See the Terms and Conditions (https://onlinelibrary.wiley.com/terms-and-conditions) on Wiley Online Library for rules of use; OA articles are governed by the applicable Creative Commons License

20 of 29

on the unsaturated zone of a sandy loam furrow-irrigatedonion field (Deb et al., 2011). He covered coupled liquidwater, water vapor, and heat transport. Readers are provided
a detailed description of the HYDRUS-1D input and output
windows, including instructions on obtaining the necessary
input parameters and interpreting the output.
In 2018, Rassam et al. published an introductory eBook,
The HYDRUS-1D Software Package for Simulating the Movement of Water, Heat, and Multiple Solutes in Variably
Saturated Media: Tutorial, containing a series of example
problems for version 4.16 of HYDRUS-1D. The eBook aimed
to provide HYDRUS-1D users with hands-on software package experience and to help them familiarize themselves withthe overall organization of the GUI, including the main input
and output dialog windows. The tutorial eBook discusses
many examples of various complexities that can be easily
downloaded from the HYDRUS website (https://www.pcprogress.com/en/Default.aspx?h1d-tut-TutorialBook).
A very recent contribution to the HYDRUS textbooks
was provided in Chinese by Hu (2023). Entitled Theory
and Applications of Environmental Soil Physics with the
HYDRUS Model, the book includes theoretical developments
and detailed instructions on using the HYDRUS-1D and
HYDRUS (2D/3D) software packages. Although HYDRUS isalready widely used in China, this textbook will make it evenmore accessible to the Chinese audience, and it will likely leadto its broader use in classrooms and for various applicationsin the country.

8

SUMMARY AND CONCLUSIONSWe believe that the HYDRUS suite of codes is well-suited toaddress the many environmental challenges humanity and ourplanet face, including soil and groundwater pollution problems, a lack of fresh water, soil salinization, climate change,
and many other issues. The HYDRUS codes may be used for
relatively simple 1D water flow and solute transport problems
as well as for far more extensive multidimensional flow andtransport applications at the field scale, including relatively
complex problems involving a range of biogeochemical reactions. Examples of the latter include the HPx modules that
couple the HYDRUS software packages with the PHREEQC
geochemical code, which can consider a wide range of biogeochemical reactions, and the Wetland, UNSATCHEM, andDPU modules, which consider various more specific geochemical systems. Much attention has recently been paid
especially to the PFAS module for evaluating the fate andtransport of PFAS in the subsurface and the Particle Tracking
module for determining recharge travel times or the averageage of water taken up by plant roots.
An important aspect of the HYDRUS models is that they
are supported by relatively sophisticated interactive GUIs,

Vadose Zone Journal

21 of 29

making them easy to use and likely a major reason for theirwide use. The GUI is continuously updated to make the codes
as attractive as possible for nonexpert users and to facilitateclassroom learning. Feedback from users is constantly being
used to improve the codes, to identify particular strengths andweaknesses of the models, and to define additional processesor features that could be included in the models. We believe
the codes and associated manuals are essential in transferring
vadose zone research and development technologies to boththe scientific community and practitioners.
For these reasons, we believe that the HYDRUS models
have provided and will continue to provide an important service to the soil, environmental, and hydrological communities
evaluating various fluid flow and biogeochemical processes in
especially variably saturated subsurface systems.
AU T H O R C O N T R I B U T I O N S
Jirka Simunek: Conceptualization; formal analysis; investigation; methodology; project administration; resources;
software; writing—original draft. Giuseppe Brunetti: Conceptualization; formal analysis; investigation; methodology;
software; writing—original draft. Diederik Jacques: Conceptualization; formal analysis; investigation; methodology;
software; writing—original draft. Martinus van Genuchten:
Conceptualization; formal analysis; investigation; methodology; software; supervision; writing—original draft. Miroslav
Sejna: Conceptualization; formal analysis; investigation;
methodology; software; supervision; writing—original draft.
ORCIDJiří Šimůnek https://orcid.org/0000-0002-0166-6563
Martinus Th. van Genuchten https://orcid.org/0000-00031654-8858
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S U P P O RT I N G I N F O R M AT I O N
Additional supporting information can be found online in the
Supporting Information section at the end of this article.

ŠIMŮNEK ET AL.

How to cite this article: Šimůnek, J., Brunetti, G.,
Jacques, D., van Genuchten, M. Th., & Šejna, M.
(2024). Developments and applications of the
HYDRUS computer software packages since 2016.
Vadose Zone Journal, e20310.
https://doi.org/10.1002/vzj2.20310

APPENDIX A: PERSONAL NOTE BY THE SENIORAUTHOR
This VZJ special issue is a tribute to Rien van Genuchten,
who, while a coauthor of this manuscript, has not been directly
involved in writing this appendix. Allow me (a senior authorof this article) to make some personal remarks on how Rien
has influenced my career and those of many others.
My journey in numerical modeling started in the mid-1980s
when I became part of a small group in Prague, at that time far
behind the Iron Curtain, that was trying to develop one- andmultidimensional, variably saturated water flow and solutetransport models on a personal computer (an Atari ST). I
am using “personal” in its literal meaning instead of mainframes and computers owned by institutions. The Atari was
the personal property of Prof. Milena Císlerová, who enabled
a few of us (including Tomáš Vogel and Radka Kodešová) towork on her computer to test various numerical schemes andtechniques. This was when most governmental research institutions in Czechoslovakia had no or only minimal computer
access. Our work was greatly helped by a visit from Rien in1985 (I did not meet Rien at that time as I was in a conscription service in the army), who left with us many of his reprints
and technical reports documenting his early models, as well
as a box of punch cards with the source code. These reports
documented in detail alternative numerical schemes (fromfinite differences to linear and Hermitian cubic finite element
schemes with and without mass lumping) implemented in
Rien’s codes. I was an eager learner and tester of these various
numerical schemes.
It is well known that Rien has been a mentor and promoter of many people in our research discipline, especially his
numerous visitors, coworkers, and collaborators, relentlessly
facilitating their continued career development in various
ways. Especially remarkable was his support of scientists from
non-Western countries that were not free or had just started
opening their borders. He invited young scientists from Hungary, Czechoslovakia, East Germany, the Soviet Union, andIran, providing them with new opportunities that were otherwise unavailable to them at the time. I wrote a letter to Rien

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in the late 80s, informing him about my work, and soon, I
received an invitation to join his group in Riverside. Unfortunately, I did not obtain an exit visa (a special visa that the
governments in Eastern Europe used at the time to control
their population), and I had to wait until the communist government was overthrown in 1989 before I could embark on mytrip to California in 1990.
Rien has been a great mentor to me since I arrived in the
United States as a graduate student. He became my mentor
and later a friend and a partner after I graduated. I continued to work with him as a postdoc, a research assistant,and eventually a professor. Since then, we have developed(with significant contributions from other coauthors of thismanuscript, as well as some others) some of the most widelyused numerical models in subsurface hydrology. Before join-

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ing the University of California, Riverside’s faculty (in 2002),
I traveled with Rien to all six continents to teach students andresearchers worldwide how to use our numerical models anddeveloped many friendships and collaborations. Our teaching job was tremendously helped by the work of Miroslav
Šejna, my old high school friend from Czechia, who in the
mid-90s developed the first versions of the sophisticated GUIs
that made HYDRUS codes much easier and intuitive to use.
The software then made its way very quickly into university classrooms and the offices of environmental consulting
companies.
As documented by this manuscript, our close collaboration
with Rien and Mirek (and later with Diederik and Giuseppe)
continues until today. I will be forever grateful for Rien’s
mentorship and friendship in the past and future decades.

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