基于随机微分方程的流域汇流模型  

Basin flow concentration model based on stochastic differential equation

作　　者：孙颖娜[1,2] 芮孝芳[3] 付强[2] 邢贞相[2] 

机构地区：[1]黑龙江大学水利电力学院,黑龙江哈尔滨150086 [2]东北农业大学,黑龙江哈尔滨150030 [3]河海大学水资源环境学院,江苏南京210098

出　　处：《水利学报》2011年第2期187-191,共5页Journal of Hydraulic Engineering

基　　金：黑龙江省教育厅科技项目(11531267);黑龙江大学博士基金;黑龙江省水利厅项目(HSKY2007-06)

摘　　要：针对水文过程中存在的许多随机不确定性因素,本文以Nash模型为基础,利用随机微分方程理论,在确定性汇流模型中引入随机输入项,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,为防洪决策提供预报值的不确定度,有利于降低水库调洪风险率。Since too many random uncertain factors exist 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 flow concentration model whose input terms have characteristics of white noise was established,and then,analytical solution and numerical solution of mean and variance of the outflow process were derived.In the mean time,the probability distribution of the outflow process at specific moment was attained with the help of mean and variance of the outflow process.The model can obtain the probabilities distribution of the outflow process by means of variance at specific moment,thus the uncertainties of the prediction are considered which can quantify the uncertainties of predictaion in flood control decision so as to consider the risk loss of decision.

关 键 词：随机微分方程 汇流模型 白噪声 概率 

分 类 号：P333[天文地球—水文科学]