考虑降雨空间变化的随机产汇流模型

引入两个负指数型差值函数,估计降雨量的概率分布,以此描述流域降雨空间变异性问题.将降雨量空间统计分布与垂向混合产流模型耦合进行产流量计算,即对地表径流,采用超渗产流模式,根据降雨与土壤下渗能力的联合分布推求其空间分布;对地面以下径流,采用蓄满产流模式,以地表渗入量的均值作为输入,进行简化处理以提高其实用性;最终推导出总产流量概率分布函数计算公式.将流域概化成一个线性水库,并根据随机微分方程理论,推导任一计算时段洪水流量的概率分布,从而构建了一个完整的随机产汇流模型.以淮河支流黄泥庄流域为例进行应用研究,结果表明,该模型可提供洪水过程的概率预报,可用于防洪风险分析,若以概率分布的期望值作为确定性预报,亦具有较高精度.

Development of a stochastic runoff model considering spatial variability of rainfall

Two negative exponential difference functions were introduced to estimate the probability distribution of rainfall for describing the spatial variability of rainfall over the basin. Then calculation formula of probability distribution of total runoff was conducted by a vertically-mixed runoff yield model. The joint distribution of rainfall and infiltration capability was deduced to calculate surface runoff according to the infiltration excess mechanism. Furthermore, the groundwater runoff was estimated with mean value of infiltration according to the saturation excess mechanism to improve the practicability. Thus, the probability distribution function of total runoff could be deduced. In the flow concentration calculation, the basin was generalized to a linear reservoir, and the probability function of discharge at any time interval could be obtained according to the stochastic differential equation theory. Therefore, a complete stochastic runoff model was developed. As an example, this model was applied to flood simulation in the Huangnizhuang Basin locating at a tributary of Huaihe River. Results showed that the model could provide the probabilistic flood forecasts for the risk analysis of flood control. Meanwhile, the deterministic result (i.e., the mathematical expectation of discharge probability distribution function) had a high forecast accuracy.