基于随机微分方程的流域汇流模型的构建

针对水文过程中存在的许多随机不确定性因素，本文以n=3的Nash模型为基础，利用随机微分 方程理论，引入随机输入项，建立了输入具有白噪声特性的随机Nash汇流模型，求解得到出流过程均值和方差的解析解和数值解，并利用出流过程的均值和方差确定各时刻出流过程的概率分布。该方法借助于各时刻的方差得到流量过程的分布概率，从而考虑预报的不确定性，为防洪决策中提供预报值的不确定度以考虑风险损失。

Establishing Basin Concentration Model Based on Stochastic Differential Equation

According to many random uncertain factors existing in hydrological processes, the theory of stochastic differential equation is adopted and random input term is introduced, on the basis of the Nash model of n=3, Nash stochastic concentration model whose input terms have characteristics of white noise was established, at the end, analytical solution and numerical solution of mean and variance of the outflow process were derived. At the same time, the probability distribution of the outflow process in each time was gotten with the help of mean and variance of the outflow process. This model in this article can obtain the probability distribution of the outflow process by means of variance at each time, thus uncertainty of the prediction was considered. which can quantify of uncertainty of predictand in flood control decision so as to consider the risk loss of decision.