Spatial averaging of unsaturated flow equations under infiltration conditions over areally heterogeneous fields: 1. Development of models

Unsaturated flows within subsurface regions control many large-scale hydrological and environmental processes. This study addresses the issue of spatial averaging of unsaturated flow equations at field scales. Two models for horizontally averaged unsaturated flow have been developed from two different approaches in this study. The spatially horizontally averaged Richards equation (SHARE) model is represented by a system of two coupled partial differential equations for the mean water saturation in each horizontal soil layer and the cross-covariance of the saturated hydraulic conductivity and the water saturation in each horizontal soil layer in a heterogeneous field. As an alternative to the spatial averaging/perturbation approach which was used for SHARE, a spatially horizontally averaged form of Green-Ampt model is obtained by field scale spatial horizontal averaging of the local soil water dynamics which are represented approximately by rectangular profiles. This strategy leads to analytical solutions for average water content and the results can be upscaled to large spatial areas. The computational effort required to evaluate such analytic expressions is trivial in comparison with that of the numerical solution of Richards equation. The averaged Green-Ampt model, though approximate, yields good results when large variations exist in the soil properties in the horizontal directions.

[1]  R. Allan Freeze,et al.  Three-Dimensional, Transient, Saturated-Unsaturated Flow in a Groundwater Basin , 1971 .

[2]  David Russo,et al.  Soil Hydraulic Properties as Stochastic Processes: I. An Analysis of Field Spatial Variability , 1981 .

[3]  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 .

[4]  W. R. Gardner.  SOME STEADY‐STATE SOLUTIONS OF THE UNSATURATED MOISTURE FLOW EQUATION WITH APPLICATION TO EVAPORATION FROM A WATER TABLE , 1958 .

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

[6]  R. Freeze.  A stochastic‐conceptual analysis of one‐dimensional groundwater flow in nonuniform homogeneous media , 1975 .

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

[8]  W. Green,et al.  Studies on Soil Phyics. , 1911, The Journal of Agricultural Science.

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

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

[11]  J. R. Macmillan,et al.  Stochastic analysis of spatial variability in subsurface flows: 2. Evaluation and application , 1978 .

[12]  R. L. Cooley.  Some new procedures for numerical solution of variably saturated flow problems , 1983 .

[13]  Allan L. Gutjahr,et al.  Stochastic analysis of spatial variability in two‐dimensional steady groundwater flow assuming stationary and nonstationary heads , 1982 .

[14]  David Russo,et al.  Effect of Field Variability in Soil Hydraulic Properties on Solutions of Unsaturated Water and Salt Flows 1 , 1981 .

[15]  R. Allan Freeze,et al.  Stochastic analysis of steady state groundwater flow in a bounded domain: 2. Two‐dimensional simulations , 1979 .

[16]  Allan L. Gutjahr,et al.  Stochastic analysis of spatial variability in subsurface flows: 1. Comparison of one‐ and three‐dimensional flows , 1978 .

[17]  J. Philip.  THE THEORY OF INFILTRATION: 1. THE INFILTRATION EQUATION AND ITS SOLUTION , 1957 .

[18]  Roger David Braddock,et al.  THE THREE‐PARAMETER INFILTRATION EQUATION , 1982 .

[19]  J. Philip,et al.  THE THEORY OF INFILTRATION: 4. SORPTIVITY AND ALGEBRAIC INFILTRATION EQUATIONS , 1957 .

[20]  Daniel Hillel,et al.  Applications of soil physics , 1980 .

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

[22]  Peter K. Kitanidis,et al.  Transmissivity of a heterogeneous formation , 1993 .

[23]  J. W. Biggar,et al.  Spatial variability of the leaching characteristics of a field soil , 1976 .

[24]  Roger E. Smith.  Approximate Soil Water Movement by Kinematic Characteristics1 , 1983 .

[25]  G. Dagan,et al.  Upscaling of permeability of anisotropic heterogeneous formations: 2. General structure and small perturbation analysis , 1993 .

[26]  D. Or,et al.  ERROR ANALYSES OF SIMPLIFIED UNSATURATED FLOW MODELS UNDER LARGE UNCERTAINTY IN HYDRAULIC PROPERTIES , 1992 .

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

[28]  D. R. Nielsen,et al.  Spatial Variability of Field‐measured Soil‐water Characteristics , 1985 .

[29]  Aristotelis Mantoglou,et al.  A theoretical approach for modeling unsaturated flow in spatially variable soils: Effective flow models in finite domains and nonstationarity , 1992 .

[30]  Allan L. Gutjahr,et al.  Stochastic models of subsurface flow: infinite versus finite domains and stationarity , 1981 .

[31]  Rao S. Govindaraju,et al.  Spatial averaging of unsaturated flow equations under infiltration conditions over areally heterogeneous fields 2. Numerical simulations , 1994 .

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

[33]  David Russo,et al.  Determining soil hydraulic properties by parameter estimation: On the selection of a model for the hydraulic properties , 1988 .

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

[35]  J. W. Biggar,et al.  Spatial Variability of Field-Measured Infiltration Rate1 , 1981 .

[36]  Curtis L. Larson,et al.  Modeling infiltration during a steady rain , 1973 .