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Hydrus 2D-3D

Year of publication:
Hydrus 2D-3D


J. Šimůnek1, M. Šejna2, and M. Th. van Genuchten3

1Department of Environmental Sciences

University of California Riverside, Riverside, CA, 92521

2PC-Progress s.r.o.
Korunní 2569/108a
Prague, 101 00, Czech Republic

3Department of Mechanical Engineering

Federal University of Rio de Janeiro, Brazil





The Hydrus (2D/3D) Model Description

HYDRUS is a Microsoft Windows based modeling environment for the analysis of water flow and solute transport in variably saturated porous media. The HYDRUS program is a finite element model for simulating the two- and three-dimensional movement of water, heat, and multiple solutes in variably saturated media. The HYDRUS program numerically solves the Richards equation for saturated-unsaturated water flow and convection-dispersion type equations for heat and solute transport. The flow equation incorporates a sink term to account for water uptake by plant roots. The heat transport equation considers movement by conduction as well as convection with flowing water. The governing convection-dispersion solute transport equations are written in a very general form by including provisions for nonlinear nonequilibrium reactions between the solid and liquid phases, and linear equilibrium reaction between the liquid and gaseous phases. Hence, both adsorbed and volatile solutes, such as pesticides, can be considered. The solute transport equations also incorporate the effects of zero-order production, first-order degradation independent of other solutes, and first-order decay/production reactions that provide the required coupling between the solutes involved in the sequential first-order chain. The transport models also account for convection and dispersion in the liquid phase, as well as diffusion in the gas phase, thus permitting the model to simulate solute transport simultaneously in both the liquid and gaseous phases. At present, HYDRUS considers up to fifteen solutes, which can either be coupled in a unidirectional chain or move independently of each other. Physical nonequilibrium solute transport can be accounted for by assuming a two-region, dual porosity type formulation, which partitions the liquid phase into mobile and immobile regions. Attachment/detachment theory, including the filtration theory, is included to simulate transport of viruses, colloids, and/or bacteria.

The Unsaturated Soil Hydraulic Properties are described using van Genuchten [1980], Brooks and Corey [1964] and modified van Genuchten type analytical functions. Modifications were made to improve the description of hydraulic properties near saturation. The HYDRUS code incorporates hysteresis by using the empirical model introduced by Scott et al. [1983] and Kool and Parker [1987]. This model assumes that drying scanning curves are scaled from the main drying curve, and wetting scanning curves from the main wetting curve.

HYDRUS also implements a scaling procedure to approximate hydraulic variability in a given soil profile by means of a set of linear scaling transformations which relate the individual soil hydraulic characteristics to those of a reference soil.

The governing flow and transport equations are solved numerically using Galerkin type linear finite element schemes. Integration in time is achieved using an implicit (backwards) finite difference scheme for both saturated and unsaturated conditions. Additional measures are taken to improve solution efficiency for transient problems, including automatic time step adjustment and adherence to preset ranges of the Courant and Peclet numbers. The water content term is evaluated using the mass conservative method proposed by Celia et al. [1990]. Possible options for minimizing numerical oscillations in the transport solutions include upstream weighing, artificial dispersion, and/or performance indexing.

HYDRUS implements a Marquardt-Levenberg type parameter estimation technique for inverse estimation of selected soil hydraulic and/or solute transport and reaction parameters from measured transient or steady-state flow and/or transport data. The procedure permits several unknown parameters to be estimated from observed water contents, pressure heads, concentrations, and/or instantaneous or cumulative boundary fluxes (e.g., infiltration or outflow data). Additional retention or hydraulic conductivity data, as well as a penalty function for constraining the optimized parameters to remain in some feasible region (Bayesian estimation), can be optionally included in the parameter estimation procedure.





Scientific articles

Šimůnek, J., M. Th. van Genuchten, and M. Šejna, Development and applications of the HYDRUS and STANMOD software packages and related codes, Vadose Zone Journal, doi:10.2136/VZJ2007.0077, Special Issue “Vadose Zone Modeling”, 7(2), 587-600, 2008.


Technical information

Operating system(s):

Intel Pentium or higher processor, 16 Mb RAM, hard disk with at least 20 Mb free disk space, VGA graphics (High Color recommended), MS Windows 95, 98, NT, 2000, XP, Vista (32/64-bit), Windows 7 (32/64-bit) and Windows 8 (32/64-bit).

Licence: Commercial program (

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