中文摘要：

将降雨视为随机场，考虑降雨人渗补给量与地下水埋深的关系，采用二维稳定一非稳定潜水运动的KLPC模型，分析了降雨的空间变异性对水头均值、方差和协方差的影响，利用变异系数描述了水头、流速和水动力弥散系数的变异程度。结果表明，KLPC算法的随机模型具有优越的计算效率；水头方差随降雨场方差和相关长度的增大而增大；在降雨空间变异的条件下，水头随机场呈现出明显的非平稳特性且具有各向异性结构；在非稳定流中，水头协方差表现出“扩散”和“平移”的特性；水头的变异程度较小，在随机模拟中可以不考虑降雨空间变异对地下水流动的影响；但水头的变异导致了流速和水动力弥散系数强烈的变异性，在溶质运移的随机分析中需要予以充分重视。

英文摘要：

On the basis of Karhunen-Loeve expansion and polynomial chaos expansion （KLPC） methods a model describing the 2-D steady-unsteady groundwater flow is established. In the model the distribution of precipitation is regarded as random field and the relationship between infiltration and groundwater depth is taken into account. By using this model the effects of random characteristics of precipitation on mean water head, variance and covariance are analyzed and the variability of water head, flow velocity and hydrodynamic dispersivity can be expressed by variability coefficients. The result shows that the variance of water head increases with the increase of variability of precipitation as well as the increase of correlation length. Under the condition of isotropic and homogeneous random precipitation the water head exhibits the characteristics of strong nonstationarity and anisotropy. In case of transient flow the spatial structure of the random pressure head field changes with time and space. The variability of precipitation can be neglected in stochastic analysis because of its small effect on groundwater flow. The variability of pressure head results in significant variability of flow velocity and dispersivity.