水文变量高维非线性相关分析与水文模型结构不确定性评估  

High-dimensional nonlinear correlation analysis of hydrological variables and model structure uncertainty qualification

作　　者：龚伟[1] 杨大文[1] 

机构地区：[1]清华大学水沙科学与水利水电工程国家重点实验室,北京100084

出　　处：《水力发电学报》2013年第5期13-20,共8页Journal of Hydroelectric Engineering

基　　金：国家杰出青年科学基金(51025931);国家自然科学基金重点项目(50939004);水资源优化配置数字化技术及示范研究(201101004)

摘　　要：本文提出了采用互信息度量水文模型不确定性的基本方法。首先,采用互信息来描述水文变量之间的高维非线性相关关系,估计在现有水文数据条件下可能达到的最优模拟效果;然后,根据模拟结果与实测结果对比,估计模型结构的不确定性。由于互信息的估计方法独立于模型结构,可以作为模型结构不确定性评估指标。本文基于熵图法计算互信息,该方法基于严密的数学推理,对高维、非正态、非线性相关性有较强的识别能力;计算了中国滁洲流域和美国Leaf River流域的水文数据的互信息,并对比分析了HyMod模型和SVM模型对逐日径流的模拟效果,表明本文所提出的方法具有潜在的广泛应用前景。This paper puts forth a method based on mutual information to quantify model structure uncertainty ： first, use mutual information to measure the high-dimensional nonlinear correlation of hydrological variables, namely, the best achievable performance of a model with current available hydrological data; second, quantify model structure uncertainty according to the information offered by data and information contained in model simulation result. Because this method is independent of model structure, it is able to quantify model structure uncertainty. The proposed method is based on entropy spanning graph, which has a well established theoretical basis and is able to identify high-dimensional non-Gaussian nonlinear relationships. In this paper the hydrological data＇ s mutual information of two catchments, Chuzhou catchment, China and Leaf River catchment, USA, are computed and compared, and also the daily simulation results of HyMod and SVM. The results show that the proposed method potentially has extensive applied foreground.

关 键 词：水文学 防洪工程 模型不确定性 广义相关系数 信息熵 互信息 

分 类 号：TV11[水利工程—水文学及水资源]