Hysteresis and state‐dependent anisotropy in modeling unsaturated hillslope hydrologic processes

This paper describes a series of soil water tracer experiments and approaches taken to numerically model the flow and transport behavior observed in the field experiments. These experimental and numerical results strongly suggest that current widely held views and commonly applied modeling approaches are flawed in many cases for unsaturated flow, and provide strong supporting evidence for a variable, state-dependent anisotropy in the hydraulic conductivity of an unsaturated medium. This phenomenon has been previously postulated in a number of independent theoretical and experimental investigations. In general, the previous studies identify layered heterogeneity as a primary cause of the macroscopic anisotropy. In addition, we show how hysteresis in the soil moisture characteristics (θ-ψ relationship) can cause a lexturally homogeneous porous media profile to behave anisotropically under transient unsaturaied conditions. Recognizing that both of these factors (layered heterogeneity and capillary hysteresis) contribute the anisotropic behavior observed in the tracer experiments, we attempt to quantify the relative magnitude of their contributions in a numerical modeling investigation. For the numerical modeling study we use a finite element flow and transport code, and introduce a simple procedure for incorporating variable anisotropy into a predictive numerical model. To determine the relative magnitude of textural heterogeneity and capillary hysteresis as causes of the observed macroscopic anisotropy, we employ a diagnostic modeling approach. The results of the diagnostic modeling study indicate that textural heterogeneity is by far the most important contributor to the variable macroscopic anisotropy observed at the field site. The diagnostic simulations further show that the variable anisotropy approach is well suited to modeling field-scale problems. Subsequently, a sensitivity analysis was performed to determine how climate, geologic and topographic structure, and media lithology affect flow and transport behavior when soils were specified to have a variable macroscopic anisotropy. The results of this study clearly indicate that variable state-dependent anisotropy is a real and significant process at the field site and that modeling with consideration of variable anisotropy strongly affects model predictions.

[1]  Van Genuchten,et al.  A closed-form equation for predicting the hydraulic conductivity of unsaturated soils , 1980 .

[2]  Aristotelis Mantoglou,et al.  Capillary tension head variance, mean soil moisture content, and effective specific soil moisture capacity of transient unsaturated flow in stratified soils , 1987 .

[3]  J. T. McCord,et al.  Toward validating state-dependent macroscopic anisotropy in unsaturated media : field experiments and modeling considerations , 1991 .

[4]  D. Zasłavsky,et al.  Surface Hydrology: III°Causes of Lateral Flow , 1981 .

[5]  A. Gutjahr,et al.  Stochastic Analysis of Unsaturated Flow in Heterogeneous Soils: 2. Statistically Anisotropic Media With Variable α , 1985 .

[6]  D. Zasłavsky,et al.  Surface Hydrology: IV°Flow in Sloping, Layered Soil , 1981 .

[7]  T.-C. Jim Yeh,et al.  One‐dimensional steady state infiltration in heterogeneous soils , 1989 .

[8]  D. R. Nielsen,et al.  Spatial variability of field-measured soil-water properties , 1973 .

[9]  Allen M. Shapiro,et al.  Stochastic analysis of one‐dimensional steady state unsaturated flow: A Comparison of Monte Carlo and Perturbation Methods , 1983 .

[10]  A. Klute,et al.  A numeric method for estimating infiltration, redistribution, drainage, and evaporation of water from soil , 1969 .

[11]  H. Bouwer.  Infiltration of Water into Nonuniform Soil , 1969 .

[12]  Aristotelis Mantoglou,et al.  Stochastic modeling of large‐scale transient unsaturated flow systems , 1987 .

[13]  P. Huyakorn,et al.  A three‐dimensional finite‐element model for simulating water flow in variably saturated porous media , 1986 .

[14]  D. B. Stephens.  Groundwater flow and implications for groundwater contamination north of Prewitt, New Mexico, U.S.A. , 1983 .

[15]  Jan W. Hopmans,et al.  Two‐dimensional steady state unsaturated water flow in heterogeneous soils with autocorrelated soil hydraulic properties , 1988 .

[16]  Y. Mualem,et al.  Anisotropy of Unsaturated Soils , 1984 .

[17]  P.S. Huyakorn,et al.  VAM2D: Variably saturated analysis model in two dimensions , 1989 .

[18]  I J Winogard,et al.  Radioactive waste disposal in thick unsaturated zones. , 1981, Science.

[19]  D. B. Stephens,et al.  Statistical and Stochastic Analyses of Hydraulic Conductivity and Particle-Size in a Fluvial Sand1 , 1983 .

[20]  Aristotelis Mantoglou,et al.  Effective hydraulic conductivities of transient unsaturated flow in stratified soils , 1987 .

[21]  J. Bear,et al.  Comments on “A three-dimensional finite-element model for simulating water flow in variably saturated porous media” by Peter S. Huyakorn et al. , 1987 .

[22]  P. Huyakorn,et al.  Techniques for Making Finite Elements Competitve in Modeling Flow in Variably Saturated Porous Media , 1984 .

[23]  D. B. Jaynes,et al.  Comparison of soil-water hysteresis models , 1984 .

[24]  Jacob Bear,et al.  Effective and relative permeabilities of anisotropie porous media , 1987 .

[25]  J. R. Philip.  RECENT PROGRESS IN THE SOLUTION OF NONLINEAR DIFFUSION EQUATIONS , 1974 .

[26]  Allan L. Gutjahr,et al.  Stochastic Analysis of Unsaturated Flow in Heterogeneous Soils: 1. Statistically Isotropic Media , 1985 .

[27]  D. Zasłavsky,et al.  Surface Hydrology: I—Explanation of Phenomena , 1981 .

[28]  Gedeon Dagan,et al.  Unsaturated flow in spatially variable fields: 1. Derivation of models of infiltration and redistribution , 1983 .

[29]  Dennis McLaughlin,et al.  Application of stochastic methods to the simulaton of large-scale unsaturated flow and transport , 1988 .

[30]  J. Rubin,et al.  Numerical Method for Analyzing Hysteresis-Affected, Post-Infiltration Redistribution of Soil Moisture1 , 1967 .

[31]  L. Gelhar,et al.  OBSERVATIONS OF SPATIAL VARIABILITY OF SOIL‐WATER PRESSURE IN A FIELD SOIL , 1986 .

[32]  J. T. McCord,et al.  Lateral moisture flow beneath a sandy hillslope without an apparent impeding layer , 1987 .

[33]  Allan L. Gutjahr,et al.  Stochastic Analysis of Unsaturated Flow in Heterogeneous Soils: 3. Observations and Applications , 1985 .

[34]  D. B. Stephens,et al.  Dependence of anisotropy on saturation in a stratified sand , 1988 .