Article Type:
Research Article

Effective Hydraulic Parameters in Horizontally and Vertically Heterogeneous Soils for Steady-State Land–Atmosphere Interaction

Binayak P. Mohanty Department of Biological and Agricultural Engineering, Texas A&M University, College Station, Texas

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Jianting Zhu Desert Research Institute, Las Vegas, Nevada

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Print Publication:
01 Aug 2007
Collections:
The Global Energy and Water Cycle Experiment (GEWEX)
DOI:
https://doi.org/10.1175/JHM606.1
Page(s):
715–729
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Abstract

In this study, the authors investigate effective soil hydraulic parameter averaging schemes for steady-state flow in heterogeneous shallow subsurfaces useful to land–atmosphere interaction modeling. “Effective” soil hydraulic parameters of the heterogeneous shallow subsurface are obtained by conceptualizing the soil as an equivalent homogeneous medium. It requires that the effective homogeneous soil discharges the same mean surface moisture flux (evaporation or infiltration) as the heterogeneous media. Using the simple Gardner unsaturated hydraulic conductivity function, the authors derive the effective value for the saturated hydraulic conductivity Ks or the shape factor α under various hydrologic scenarios and input hydraulic parameter statistics. Assuming one-dimensional vertical moisture movement in the shallow unsaturated soils, both scenarios of horizontal (across the surface landscape) and vertical (across the soil profile) heterogeneities are investigated. The effects of hydraulic parameter statistics, surface boundary conditions, domain scales, and fractal dimensions in case of nested soil hydraulic property structure are addressed. Results show that the effective parameters are dictated more by the α heterogeneity for the evaporation scenario and mainly by Ks variability for the infiltration scenario. Also, heterogeneity orientation (horizontal or vertical) of soil hydraulic parameters impacts the effective parameters. In general, an increase in both the fractal dimension and the domain scale enhances the heterogeneous effects of the parameter fields on the effective parameters. The impact of the domain scale on the effective hydraulic parameters is more significant as the fractal dimension increases.

Corresponding author address: Binayak P. Mohanty, Department of Biological and Agricultural Engineering, Texas A&M University, 301 Scoates Hall, College Station, TX 77843-2117. Email: bmohanty@tamu.edu

This article included in the The Global Energy and Water Cycle Experiment (GEWEX) special collection.

Abstract

In this study, the authors investigate effective soil hydraulic parameter averaging schemes for steady-state flow in heterogeneous shallow subsurfaces useful to land–atmosphere interaction modeling. “Effective” soil hydraulic parameters of the heterogeneous shallow subsurface are obtained by conceptualizing the soil as an equivalent homogeneous medium. It requires that the effective homogeneous soil discharges the same mean surface moisture flux (evaporation or infiltration) as the heterogeneous media. Using the simple Gardner unsaturated hydraulic conductivity function, the authors derive the effective value for the saturated hydraulic conductivity Ks or the shape factor α under various hydrologic scenarios and input hydraulic parameter statistics. Assuming one-dimensional vertical moisture movement in the shallow unsaturated soils, both scenarios of horizontal (across the surface landscape) and vertical (across the soil profile) heterogeneities are investigated. The effects of hydraulic parameter statistics, surface boundary conditions, domain scales, and fractal dimensions in case of nested soil hydraulic property structure are addressed. Results show that the effective parameters are dictated more by the α heterogeneity for the evaporation scenario and mainly by Ks variability for the infiltration scenario. Also, heterogeneity orientation (horizontal or vertical) of soil hydraulic parameters impacts the effective parameters. In general, an increase in both the fractal dimension and the domain scale enhances the heterogeneous effects of the parameter fields on the effective parameters. The impact of the domain scale on the effective hydraulic parameters is more significant as the fractal dimension increases.

Corresponding author address: Binayak P. Mohanty, Department of Biological and Agricultural Engineering, Texas A&M University, 301 Scoates Hall, College Station, TX 77843-2117. Email: bmohanty@tamu.edu

This article included in the The Global Energy and Water Cycle Experiment (GEWEX) special collection.

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Journal of Hydrometeorology

  • Bresler, E., and Dagan G. , 1983: Unsaturated flow in spatially variable fields, 2. Application of water flow models to various fields. Water Resour. Res., 19 , 421–428.

    • Crossref
    • Search Google Scholar
    • Export Citation

  • Brooks, R. H., and Corey A. T. , 1964: Hydraulic properties of porous media. Colorado State University Hydrology Paper 3, 27 pp.

  • Carsel, R. F., and Parrish R. S. , 1988: Developing joint probability distributions of soil water retention characteristics. Water Resour. Res., 24 , 755–769.

    • Crossref
    • Search Google Scholar
    • Export Citation

  • Dagan, G., and Bresler E. , 1983: Unsaturated flow in spatially variable fields, 1. Derivation of models of infiltration and redistribution. Water Resour. Res., 19 , 413–420.

    • Crossref
    • Search Google Scholar
    • Export Citation

  • Desbarats, A. J., 1998: Scaling of constitutive relationships in unsaturated heterogeneous media: A numerical investigation. Water Resour. Res., 34 , 1427–1435.

    • Crossref
    • Search Google Scholar
    • Export Citation

  • Gardner, W. R., 1958: Some steady state solutions of unsaturated moisture flow equations with applications to evaporation from a water table. Soil Sci., 85 , 228–232.

    • Crossref
    • Search Google Scholar
    • Export Citation

  • Gelhar, L. W., and Axness C. L. , 1983: Three-dimensional stochastic analysis of macrodispersion in aquifers. Water Resour. Res., 19 , 161–180.

  • Harter, T., and Zhang D. , 1999: Water flow and solute spreading in heterogeneous soils with spatially variable water content. Water Resour. Res., 35 , 415–426.

    • Crossref
    • Search Google Scholar
    • Export Citation

  • Harter, T., and Hopmans J. W. , 2004: Role of vadose zone flow processes in regional scale hydrology: Review, opportunities and challenges. Unsaturated Zone Modeling: Processes, Applications, and Challenges, R. A. Feddes, G. H. de Rooij, and J. C. van Dam, Eds., Kluwer, 179–208.

  • Hassan, A. E., Cushman J. H. , and Delleur J. W. , 1997: Monte Carlo studies of flow and transport in fractal conductivity fields: Comparison with stochastic perturbation theory. Water Resour. Res., 33 , 2519–2534.

    • Crossref
    • Search Google Scholar
    • Export Citation

  • Hewett, T. A., 1986: Fractal distribution of reservoir heterogeneity and their influence on fluid transport. Preprints, Annual Technical Conf. and Exhibition, New Orleans, LA, Society of Petroleum Engineers, 1–16.

    • Crossref
    • Export Citation

  • Jenny, H., 1941: Factors of Soil Formation: A System of Quantitative Pedology. McGraw-Hill, 281 pp.

  • Kim, C. P., and Stricker J. N. M. , 1996: Influence of spatially variable soil hydraulic properties and rainfall intensity on the water budget. Water Resour. Res., 32 , 1699–1712.

    • Crossref
    • Search Google Scholar
    • Export Citation

  • Kim, C. P., Stricker J. N. M. , and Feddes R. A. , 1997: Impact of soil heterogeneity on the water budget of the unsaturated zone. Water Resour. Res., 33 , 991–999.

    • Crossref
    • Search Google Scholar
    • Export Citation

  • Koster, R. D., and Coauthors, 2004: Regions of strong coupling between soil moisture and precipitation. Science, 305 , 1138–1140.

  • Mohanty, B. P., and Mousli Z. , 2000: Saturated hydraulic conductivity and soil water retention properties across a soil-slope transition. Water Resour. Res., 36 , 3311–3324.

    • Crossref
    • Search Google Scholar
    • Export Citation

  • Mohanty, B. P., Kanwar R. S. , and Horton R. , 1991: A robust-resistant approach to interpret spatial behavior of saturated hydraulic conductivity of a glacial till under no-tillage system. Water Resour. Res., 27 , 2979–2992.

    • Crossref
    • Search Google Scholar
    • Export Citation

  • Mohanty, B. P., Kanwar R. S. , and Everts C. J. , 1994: Comparison of saturated hydraulic conductivity measurement methods for a glacial-till soil. Soil Sci. Soc. Amer. J., 58 , 672–677.

    • Crossref
    • Search Google Scholar
    • Export Citation

  • Molz, F. J., and Boman G. K. , 1993: A fractal-based stochastic interpolation scheme in subsurface hydrology. Water Resour. Res., 29 , 3769–3774.

  • Montoglou, A., and Gelhar L. W. , 1987a: Stochastic modeling of large-scale transient unsaturated flow systems. Water Resour. Res., 23 , 37–46.

  • Montoglou, A., and Gelhar L. W. , 1987b: Capillary tension head variance, mean soil moisture content, and effective specific soil moisture capacity of transient unsaturated flow in stratified soils. Water Resour. Res., 23 , 47–56.

    • Crossref
    • Search Google Scholar
    • Export Citation

  • Montoglou, A., and Gelhar L. W. , 1987c: Effective hydraulic conductivities of transient unsaturated flow in stratified aquifer. Water Resour. Res., 23 , 57–67.

    • Crossref
    • Search Google Scholar
    • Export Citation

  • Nielsen, D. R., Biggar J. W. , and Erh K. T. , 1973: Spatial variability of field-measured soil-water properties. Hilgardia, 42 , 215–260.

  • Peyton, R. L., Gantzer C. J. , Anderson S. H. , Haeffner B. A. , and Pfeifer P. , 1994: Fractal dimension to describe soil macropore structure using X ray computed tomography. Water Resour. Res., 30 , 691–700.

    • Crossref
    • Search Google Scholar
    • Export Citation

  • Robin, M. J. L., Gutjahr A. L. , Sudicky E. A. , and Wilson J. L. , 1993: Cross-correlated random field generation with the direct Fourier transform method. Water Resour. Res., 29 , 2385–2397.

    • Crossref
    • Search Google Scholar
    • Export Citation

  • Rubin, Y., and Or D. , 1993: Stochastic modeling of unsaturated flow in heterogeneous soil with water uptake by plant roots: The parallel columns model. Water Resour. Res., 29 , 619–631.

    • Crossref
    • Search Google Scholar
    • Export Citation

  • Russo, D., 1992: Upscaling of hydraulic conductivity in partially saturated heterogeneous porous formation. Water Resour. Res., 28 , 397–409.

  • Russo, D., 1993: Stochastic modeling of macrodispersion for solute transport in a heterogeneous unsaturated porous formation. Water Resour. Res., 29 , 383–397.

    • Crossref
    • Search Google Scholar
    • Export Citation

  • Russo, D., 1995a: On the velocity covariance and transport modeling in heterogeneous anisotropic porous formations: 2. Unsaturated flow. Water Resour. Res., 31 , 139–145.

    • Crossref
    • Search Google Scholar
    • Export Citation

  • Russo, D., 1995b: Stochastic analysis of the velocity covariance and the displacement covariance tensors in partially saturated heterogeneous anisotropic porous formations. Water Resour. Res., 31 , 1647–1658.

    • Crossref
    • Search Google Scholar
    • Export Citation

  • Smith, R. E., and Diekkruger B. , 1996: Effective soil water characteristics and ensemble soil water profiles in heterogeneous soils. Water Resour. Res., 32 , 1993–2002.

    • Crossref
    • Search Google Scholar
    • Export Citation

  • van Genuchten, M. Th, 1980: A closed-form equation for predicting the hydraulic conductivity of unsaturated soils. Soil Sci. Soc. Amer. J., 44 , 892–898.

    • Crossref
    • Search Google Scholar
    • Export Citation

  • Warrick, A. W., and Yeh T-C. J. , 1990: One-dimensional, steady vertical flow in a layered soil profile. Adv. Water Resour., 13 , 207–210.

  • Wheatcraft, S. W., and Tyler S. W. , 1988: An explanation of scale-dependent dispersivity in heterogeneous aquifers using concepts of fractal geometry. Water Resour. Res., 24 , 566–578.

    • Crossref
    • Search Google Scholar
    • Export Citation

  • Wheatcraft, S. W., Sharp G. A. , and Tyler S. W. , 1990: Fluid flow and solute transport in fractal heterogeneous porous media. Dynamics of Fluids in Hierarchical Porous Media, J. H. Cushman, Ed., Academic Press, 528 pp.

    • Crossref
    • Export Citation

  • Yang, J., Zhang R. , and Wu J. , 1996: An analytical solution of macrodispersivity for adsorbing solute transport in unsaturated soils. Water Resour. Res., 32 , 355–362.

    • Crossref
    • Search Google Scholar
    • Export Citation

  • Yeh, T-C. J., 1989: One-dimensional steady state infiltration in heterogeneous soils. Water Resour. Res., 25 , 2149–2158.

  • Yeh, T-C. J., Gelhar L. W. , and Gutjahr A. L. , 1985a: Stochastic analysis of unsaturated flow in heterogeneous soils, 1. Statistically isotropic media. Water Resour. Res., 21 , 447–456.

    • Crossref
    • Search Google Scholar
    • Export Citation

  • Yeh, T-C. J., Gelhar L. W. , and Gutjahr A. L. , 1985b: Stochastic analysis of unsaturated flow in heterogeneous soils, 2. Statistically anisotropic media with variable α. Water Resour. Res., 21 , 457–464.

    • Crossref
    • Search Google Scholar
    • Export Citation

  • Yeh, T-C. J., Gelhar L. W. , and Gutjahr A. L. , 1985c: Stochastic analysis of unsaturated flow in heterogeneous soils, 3. Observation and applications. Water Resour. Res., 21 , 465–471.

    • Crossref
    • Search Google Scholar
    • Export Citation

  • Zaslavsky, D., 1964: Theory of unsaturated flow into a non-uniform soil profile. Soil Sci., 97 , 400–410.

  • Zhan, H., and Wheatcraft S. W. , 1996: Macrodispersivity tensor for nonreactive solute transport in isotropic and anisotropic fractal porous media: Analytical solutions. Water Resour. Res., 32 , 3461–3474.

    • Crossref
    • Search Google Scholar
    • Export Citation

  • Zhang, D., Wallstrom T. C. , and Winter C. L. , 1998: Stochastic analysis of steady-state unsaturated flow in heterogeneous media: Comparison of the Brooks–Corey and Gardner–Russo models. Water Resour. Res., 34 , 1437–1449.

    • Crossref
    • Search Google Scholar
    • Export Citation

  • Zhu, J., and Mohanty B. P. , 2002a: Upscaling of hydraulic properties for steady state evaporation and infiltration. Water Resour. Res., 38 .1178, doi:10.1029/2001WR000704.

    • Search Google Scholar
    • Export Citation

  • Zhu, J., and Mohanty B. P. , 2002b: Spatial averaging of van Genuchten hydraulic parameters for steady-state flow in heterogeneous soils: A numerical study. Vadose Zone J., 1 , 261–272.

    • Crossref
    • Search Google Scholar
    • Export Citation

  • Zhu, J., and Mohanty B. P. , 2003a: Effective hydraulic parameters for steady state vertical flow in heterogeneous soils. Water Resour. Res., 39 .1227, doi:10.1029/2002WR001831.

    • Search Google Scholar
    • Export Citation

  • Zhu, J., and Mohanty B. P. , 2003b: Upscaling of hydraulic properties in heterogeneous soils. Scaling Methods in Soil Physics, Y. Pachepsky, D. E. Radcliffe, and H. M. Selim, Eds., CRC Press, 97–117.

    • Crossref
    • Export Citation

  • Zhu, J., and Mohanty B. P. , 2004: Soil hydraulic parameter upscaling for steady state flow with root water uptake. Vadose Zone J., 3 , 1464–1470.

  • Zhu, J., and Mohanty B. P. , 2006: Effective scaling factor for transient infiltration in heterogeneous soils. J. Hydrol., 319 , 96–108.

  • Zhu, J., Mohanty B. P. , Warrick A. W. , and van Genuchten M. Th , 2004: Correspondence and upscaling of hydraulic functions for steady-state flow in heterogeneous soils. Vadose Zone J., 3 , 527–533.

    • Crossref
    • Search Google Scholar
    • Export Citation

  • Zhu, J., Mohanty B. P. , and Das N. N. , 2006: On the effective averaging schemes of hydraulic properties at the landscape scale. Vadose Zone J., 5 , 308–316.

    • Crossref
    • Search Google Scholar
    • Export Citation
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