An iterative geostatistical inverse method for steady flow in the vadose zone

An iterative geostatistical inverse approach is developed to estimate conditional effective unsaturated hydraulic conductivity parameters, soil-water pressure head, and degree of saturation in heterogeneous vadose zones. This approach is similar to the classical cokriging technique, and it uses a linear estimator that depends on covariances and cross covariances of unsaturated hydraulic parameters, soil-water pressure head, and degree of saturation. The linear estimator is, however, improved successively by solving the governing flow equation and by updating the residual covariance and cross-covariance functions in an iterative manner. As a result, the nonlinear relationship between unsaturated hydraulic conductivity parameters and head is incorporated in the estimation and the estimated fields are approximate conditional means. The ability of the iterative approach is demonstrated through some numerical examples.

[1]  W. Jury,et al.  A theoretical study of the estimation of the correlation scale in spatially variable fields: 2. Nonstationary fields , 1987 .

[2]  Thomas Harter,et al.  An efficient method for simulating steady unsaturated flow in random porous media: Using an analytical perturbation solution as initial guess to a numerical model , 1993 .

[3]  D. Mulla.  Estimating Spatial Patterns in Water Content, Matric Suction, and Hydraulic Conductivity , 1988 .

[4]  W. Yeh.  Review of Parameter Identification Procedures in Groundwater Hydrology: The Inverse Problem , 1986 .

[5]  Uri Shani,et al.  Analyses of infiltration events in relation to determining soil hydraulic properties by inverse problem methodology , 1991 .

[6]  Peter K. Kitanidis,et al.  Prediction of transmissivities, heads, and seepage velocities using mathematical modeling and geostatistics , 1989 .

[7]  R. Srivastava,et al.  Numerical Simulation of the Wicking Effect in Liner Systems , 1994 .

[8]  R. Willis,et al.  Groundwater Systems Planning and Management , 1987 .

[9]  Allan L. Gutjahr,et al.  Co-kriging for stochastic flow models , 1989 .

[10]  Charles F. Harvey,et al.  Mapping Hydraulic Conductivity: Sequential Conditioning with Measurements of Solute Arrival Time, Hydraulic Head, and Local Conductivity , 1995 .

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

[12]  P. C. Shah,et al.  Reservoir History Matching by Bayesian Estimation , 1976 .

[13]  Richard L. Cooley,et al.  Incorporation of prior information on parameters into nonlinear regression groundwater flow models: 1. Theory , 1982 .

[14]  J. Parker,et al.  Analysis of the inverse problem for transient unsaturated flow , 1988 .

[15]  G. Dagan,et al.  Stochastic identification of transmissivity and effective recharge in steady groundwater flow: 2. Case study , 1987 .

[16]  T. Harter,et al.  Conditional stochastic analysis of solute transport in heterogeneous, variably saturated soils , 1996 .

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

[18]  Allan L. Gutjahr,et al.  An Iterative Cokriging‐Like Technique for Ground‐Water Flow Modeling , 1995 .

[19]  Thomas Harter,et al.  Stochastic analysis of solute transport in heterogeneous, variably saturated soils , 1996 .

[20]  C. R. Dietrich,et al.  A stability analysis of the geostatistical approach to aquifer transmissivity identification , 1989 .

[21]  E. G. Vomvoris,et al.  A geostatistical approach to the inverse problem in groundwater modeling (steady state) and one‐dimensional simulations , 1983 .

[22]  S. P. Neuman,et al.  Estimation of Aquifer Parameters Under Transient and Steady State Conditions: 1. Maximum Likelihood Method Incorporating Prior Information , 1986 .

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

[24]  W. Yeh,et al.  Optimal Identification of Aquifer Diffusivity Using Quasilinearization , 1971 .

[25]  T.-C. Jim Yeh,et al.  A Geostatistical Inverse Method for Variably Saturated Flow in the Vadose Zone , 1995 .

[26]  T. Harter,et al.  A Numerical Model for Water Flow and Chemical Transport in Variably Saturated Porous Media , 1993 .

[27]  A. Warrick,et al.  Estimating Soil Water Content Using Cokriging1 , 1987 .

[28]  P. Kitanidis,et al.  An Application of the Geostatistical Approach to the Inverse Problem in Two-Dimensional Groundwater Modeling , 1984 .

[29]  S. P. Neuman,et al.  Estimation of aquifer parameters under transient and steady-state conditions: 2 , 1986 .

[30]  Jinqi. Zhang.  An iterative stochastic inverse approach for steady-state flow in heterogeneous, variably saturated porous media. , 1996 .

[31]  D. R. Nielsen,et al.  The Use of Cokriging with Limited Field Soil Observations 1 , 1983 .

[32]  Maliha S. Nash,et al.  Soil physical properties at the Las Cruces trench site , 1989 .

[33]  Minghui Jin,et al.  AN ITERATIVE STOCHASTIC INVERSE METHOD: CONDITIONAL EFFECTIVE TRANSMISSIVITY AND HYDRAULIC HEAD FIELDS , 1995 .