非均质土壤中二维非饱和土壤水分运动的随机分析

Stochastic Analysis of Two Dimensional Unsaturated Flow in a Heterogeneous Soil

以一水平向具有空间变异而垂直向为均质的二维非饱和流动区域中的均匀入渗问题为例，应用ＭｏｎｔｅＣａｒｌｏ随机模拟方法分析了土壤水分变量的随机统计特性及其一、二阶矩的时空分布规律。在随机分析过程中，将所研究的流动区域土壤水力特性的空间变异性以随空间位置变化的标定参数δ（ｘ）表示，并将标定参数δ（ｘ）视为一维随机空间函数的实现，应用随机生成模型来生成参数δ（ｘ）的随机样本。通过随机模拟分析得到：垂直方向上负压水头方差与平均负压水头近似呈一线性关系；随入渗时间的延长，不同深度处表征负压水头空间变异结构的自相关函数趋于一稳定结构。

The problem of two dimensional unsaturated flow in a hypothetical heterogeneous soil is analyzed by Monte Carlo simulation.It is assumed that the flow domain is scale hetergeneous along the horizontal direction but homogeneous in vertical direction,and the locally soil water flow can be described by the Richards equation.The heterogeneity in the soil hydraulic properties is represented by a scaling factor which is visualized as being a realization of a one dimensional spatial stochastic function,and the NNM model is used to generate realizations for the scaling factor. The spatial distribution of soil water pressure head is quantified in terms of its first and second order moment. The results indicate that the variance of pressure head is a function of its mean, the spatial covariances of pressure head assume their steady state form after a short period of infiltration.