摘要
Stochastic approaches are useful to quantitatively describe transportbehavior over large temporal and spatial scales while accounting for the influence of small-scalevariabilities. Numerous solutions have been developed for unsatu-rated soil water flow based on thelognormal distribution of soil hydraulic conductivity. To our knowledge, no available stochasticsolutions for unsaturated flow have been derived on the basis of the normal distribution ofhydraulic conductivity. In this paper, stochastic solutions were developed for unsaturated flow byassuming the normal distribution of saturated hydraulic conductivity (K_s). Under the assumptionthat soil hydraulic properties are second-order stationary, analytical expressions for capillarytension head variance (σ_h^2 ) and effective hydraulic conductivity (K_ii~*) in stratified soilswere derived using the perturbation method. The dependence of σ_h^2 and K_ii~* on soil variabilityand mean flow variables (the mean capillary tension head and its temporal and spatial gradients) andmean flow conditions (wetting and drying) were systematically analyzed. The calculated variance ofcapillary tension head with the analytical solution derived in this paper was compared with fieldexperimental data. The good agreement indicates that the analytical solution is applicable toevaluate the variance of capillary tension head of field soils with moderate variability.
Stochastic approaches are useful to quantitatively describe transportbehavior over large temporal and spatial scales while accounting for the influence of small-scalevariabilities. Numerous solutions have been developed for unsatu-rated soil water flow based on thelognormal distribution of soil hydraulic conductivity. To our knowledge, no available stochasticsolutions for unsaturated flow have been derived on the basis of the normal distribution ofhydraulic conductivity. In this paper, stochastic solutions were developed for unsaturated flow byassuming the normal distribution of saturated hydraulic conductivity (K_s). Under the assumptionthat soil hydraulic properties are second-order stationary, analytical expressions for capillarytension head variance (σ_h^2 ) and effective hydraulic conductivity (K_ii~*) in stratified soilswere derived using the perturbation method. The dependence of σ_h^2 and K_ii~* on soil variabilityand mean flow variables (the mean capillary tension head and its temporal and spatial gradients) andmean flow conditions (wetting and drying) were systematically analyzed. The calculated variance ofcapillary tension head with the analytical solution derived in this paper was compared with fieldexperimental data. The good agreement indicates that the analytical solution is applicable toevaluate the variance of capillary tension head of field soils with moderate variability.
基金
This work was supported by the National NaturaI Science Foundation of China(Grant Nos:59509007,59879028)
the Major State Basic Research Development Program of China(Grant No:G1999045700)
the Fok Ying Tung Education Foundation.(Grant No:71027)
