河相关系的随机微分方程建模与研究

由气候变化等环境突变引起的水沙输入条件和边界条件的不确定性给河流地形特征的考察与模拟增加了困难。本文通过建立随机微分方程,研究了典型的河相关系特征变量(包括比降、河宽、水深、流速)随时间变化的概率分布演化规律。随机方程的随机输入项分别由3种噪声模型进行模拟,包括单独的高斯白噪声、组合的高斯白噪声加泊松噪声,和组合的分数白噪声加泊松噪声模型。方程中的未知参数使用一种复合型的极大似然非参数估计法进行估计。使用蒙特卡洛方法将方程应用于黄河下游高村-孙口段,结果较好地展示了河相关系对随机扰动的潜在响应,特别是,计算的随机平均值与测量值有较好的同步度。通过模型比较发现,既能反映非线性又能反映突变性特征的分数-泊松扩散模型是较适合模拟河相关系随机演化的模型,以此为基础的河流功率可作为系统性评估河流动态演化特征的优选指标。本文提出的分析河相关系的新方法,可根据指定精度用于设计和监测河流系统,既有理论价值又有实际意义。

Modeling and research of stochastic differential equations for hydraulic geometry relationship

Uncertainty in flow-sediment input and channel boundary of restriction caused by environmental change (such as clclimatic events) pose difficulties for the accurate acquisition of information on river mor-phology dynamics.In this study,a set of stable stochastic differential equations (SDEs) are developed to simulate the dynamic probability distributions of typical hydraulic geometry variables represented by slope,width,depth and velocity with varying bankfull discharge at certain moment in river system.The random parts of each equation are modeled based on single Gaussian white noise and further on compound Gauss-ian/Fractional white noise plus Poisson noise.Consistent estimate of the SDEs parameters are conducted us-ing a composite nonparametric MLE method.The stochastic models are examined with Monte Carlo simula-tion in a lower Yellow River case,and results successfully reveal the potential responses of hydraulic geom-etries to stochastic disturbance,and especially,the average trends mainly run to synchronize with the mea-sured values.Comparisons among the three models confirm the advantage of Fractional jump-diffusion mod-el,and through further discussion,stream power on the basis of such model is concluded as the better sys-tematic measure of river dynamics.The proposed stochastic approach is new to the field of fluvial relation-ships,and its application could help to design and monitor river system with the specified accuracy require-ments.