基于随机方法的饱和-非饱和带水流时间尺度性研究

Rainfall infiltration and groundwater recharge are important hydrological processes for water flow in saturated-unsaturated systems. It is difficult, if not impossible, to measure precisely infiltration and recharge due to complexity of these variables. Therefore, Our knowledge of temporal scaling of infiltration and recharge is limited. However, it is relatively easy to measure groundwater level and soil moisture content. The fluctuations of groundwater level and soil moisture content are dynamic responses of the saturated-unsaturated system to infiltration and recharge, and thus contain significant amount of information about the nature of infiltration and recharge. Therefore, it is necessary to investigate the temporal variability of groundwater level and soil moisture content in order to understand infiltration and recharge processes. In this study we will to solve the stochastic differential equation of saturated-unsaturated flow use a non-stationary spectral analysis to investigate temporal scaling of infiltration, recharge, groundwater level and soil moisture content and their relationship. Spatiotemporal stochastic differential equation of saturated-unsaturated flow will be solved by probabilistic collocation method, and the effects of heterogeneity of hydraulic conductivity on the flow temporal scaling will be investigated. In order to verify results of stochastic analysis, we will also conduct numerical simulations of integrated hydrologic modeling of surface and ground water for a realistic case. It is expected to reveal physical meaning behind the temporal scaling of saturated-unsaturated flow and to improve our understanding of the saturated-unsaturated flow system with the study proposed in this project.

降水入渗和地下水补给是饱和-非饱和带的主要水循环过程。由于受多种因素影响而难以直接测量，对降水入渗和地下水补给过程的时间尺度性认识还较为有限。土壤含水率和地下水位容易直接测量。它们的波动是饱和-非饱和带水流系统对这两个过程的动态响应并隐含降水入渗和地下水补给的重要信息。因此，研究土壤含水率和地下水位的时间变异性有助于理解以上两个复杂的过程。本项目采用非平稳谱方法求解饱和-非饱和水流随机微分方程，研究土壤含水率和地下水位与降水入渗和地下水补给之间的时间尺度性关系；利用随机配点法求解饱和-非饱和水流时空随机微分方程，分析非均质对水流时间尺度性的影响；并选定典型流域进行地表-地下水耦合模拟,验证随机分析的结论。拟通过理论分析与典型流域水文模拟，揭示饱和-非饱和带水流的时间尺度性及其物理意义，为深刻理解饱和-非饱带水循环规律提供理论支撑。

降水入渗和地下水补给是饱和-非饱和带的主要水循环过程，由于受多种因素影响而难以直接测量，对降水入渗和地下水补给过程的时间尺度性认识还较为有限。土壤含水率和地下水位容易直接测量，它们的波动是饱和-非饱和带水流系统对这两个过程的动态响应并隐含降水入渗和地下水补给的重要信息。因此，研究土壤含水率和地下水位的时间变异性有助于理解以上两个复杂的过程。本研究利用非平稳谱方法和随机数值矩方法求解了饱和-非饱和带水流时空随机偏微分方程，分析了各水文变量间统计矩及功率谱的关系，选取了一个典型流域，建立了地表-地下水耦合数值模型，模拟了地表水流、非饱和带水流和地下水流的全耦合过程。研究结果发现，降水入渗是非饱和-饱和水流分形波动的主要来源，在分形降水入渗条件下地下水位呈现分形波动，在分数布朗降水入渗条件下土壤含水率呈现分形波动；非均质性减弱水流波动的短期相关性，影响水流分形的性质，但不产生分形的水流波动；地下含水系统是一个低通分形的滤波器，降雨、入渗和河流径流为单分形过程，蒸散发、地下水补给和基流为双分形过程，地下水含水层把单分形的地表径流过程过滤为多（双）分形地下水流过程。本研究的创新点是系统地研究了水流在非饱和-饱和带中的波动特征，揭示了地下水流分形波动的成因及影响因素，本研究的结果为深刻理解饱和-非饱带水循环规律提供理论基础。