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COMMENTS

Response to "Comments on ‘A Set of Analytical Benchmarks to Test Numerical Models of Flow and Transport in Soils’"

^a Agrosphere Institute, ICG-IV, Forschungszentrum Jülich GmbH, D-52425 Jülich, Germany
^b Department of Environmental Sciences and Land Use Planning, Université Catholique de Louvain (UCL), Croix du Sud, 2 Bte 2, B-1348 Louvain-La-Neuve, Belgium
^c Bureau de Recherches Géologique et Minièries, BRGM, Avenue Claude Guillemin, F-45060 Orleans Cedex 02, France
j.vanderborght{at}fz-juelich.de

The comments by Groenendijk et al. (2006) nicely illustrate the usefulness of analytical benchmarks for code developers to test and improve numerical models. These benchmarks may also be useful for model users to validate whether the numerical settings (e.g., space and time discretiztion, convergence and iteration parameters, discretiztion and/or linearization of the hydraulic functions) that they use guarantee sufficient accuracy of the numerical solution. The problem addressed by Groenendijk et al. (2006) actually points to the importance of these settings to obtain an accurate solution. As a consequence, some model developers tend to fix these settings in the model code, thus providing less flexibility and opportunities for model users to make errors. However, numerical settings are to a certain extent problem-specific, so default settings, which are accurate for most cases, may be inappropriate for some special conditions.

Groenendijk et al. (2006) suggest that the parameterization used for the clay soil is an extreme case that seems to lack any physical basis. The parameterization of the hydraulic functions of the clay soil is based on a catalog in the HYDRUS-1D software (Simunek et al., 1998), which was derived from the database of Carsel and Parrish (1988). The n value of the van Genuchten retention function (van Genuchten, 1980) for clay soils in this database is small and close to 1.1. The HYPRES database (Wösten et al., 1999) also suggests a value of n close to 1.1 for very fine-textured soils. Therefore, our parameterization of the Mualem–van Genuchten hydraulic functions may be considered realistic for a clay soil. However, for small n values, the physical meaning of the Mualem–van Genuchten hydraulic functions near saturation can be questioned. To address this problem, Vogel and Cislerova (1988) proposed a modification of the K(h) function which is actually identical to the hidden linearization in the SWAP model.

Although the course of the hydraulic conductivity function and its linear approximation close to saturation were shown to have an important impact on the predicted pressure head profiles in the steady-state flow scenario for the clay soil, they seemed to be less relevant for predictions of water fluxes and solute transport under natural boundary conditions (see Fig. 11c and 12c of Vanderborght et al., 2005).

REFERENCES

• Carsel, R.F., and R.S. Parrish. 1988. Developing joint probability-distributions of soil-water retention characteristics. Water Resour. Res. 24:755–769.[CrossRef]
• Groenendijk, P., J.G. Kroes, and J.C. van Dam. 2006. Comments on "A set of analytical benchmarks to test numerical models of flow and transport in soils". Available at www.vadosezonejournal.org. Vadose Zone J. 5:xxx–xxx (this issue).
• Simunek, J., M. Sejna, and M.Th. van Genuchten. 1998. The Hydrus-1D software package for simulating the one-dimensional movement of water, heat, and multiple solutes in variably saturated media. Version 2.0. IGWMC-TPS 70. Int. Ground Water Modeling Center, Colorado School of Mines, Golden, CO.
• Vanderborght, J., R. Kasteel, M. Herbst, M. Javaux, M. Vanclooster, D. Thiery, C. Mouvet, and H. Vereecken. 2005. A test of numerical models for simulating flow and transport in soils using analytical solutions. Available at www.vadosezonejournal.org. Vadose Zone J. 4:206–221.[Abstract/Free Full Text]
• van Genuchten, M.Th. 1980. A closed-form equation for predicting the hydraulic conductivity of unsaturated soils. Soil Sci. Soc. Am. J. 44:892–898.[Abstract/Free Full Text]
• Vogel, T., and M. Cislerova. 1988. On the reliability of unsaturated hydraulic conductivity calculated from the moisture retention curve. Transp. Porous Media 3:1–15.
• Wösten, J.H.M., A. Lilly, A. Nemes, and C. Le Bas. 1999. Development and use of a database of hydraulic properties of European soils. Geoderma 90:169–185.[CrossRef][ISI]

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