基于贝叶斯方法的水位流量关系——以东江干流为例

基于贝叶斯方法的水位流量关系——以东江干流为例 Stage-Discharge Relationship Based on Bayesian Methods——A Case Study of East River 顾西辉 GU Xihui 1 2 3 first-author 张强 ZHANG Qiang 1 2 3 陈晓宏 Chen Xiaohong 1 2 3 江涛 JIANG Tao 1 2 3 中山大学水资源与环境系 中山大学水资源与环境系 Department of Water Resources and Environment,Sun Yat-Sen University Department of Water Resources and Environment,Sun Yat-Sen University 中山大学华南地区水循环与水安全广东省普通高校重点实验室 中山大学华南地区水循环与水安全广东省普通高校重点实验室 Guangdong University Key Laboratory of Water Cycle and Security in South China,Sun Yat-Sen University Guangdong University Key Laboratory of Water Cycle and Security in South China,Sun Yat-Sen University 中山大学地理科学与规划学院/广东省城市化与地理环境空间模拟重点实验室 中山大学地理科学与规划学院/广东省城市化与地理环境空间模拟重点实验室 Geography and Planning School,Sun Yat-Sen University/Guangdong Key Laboratory of Urbanization and Geo-Simulation Geography and Planning School,Sun Yat-Sen University/Guangdong Key Laboratory of Urbanization and Geo-Simulation 以东江干流（珠江流域支流）河源、岭下和博罗3个测站水位-流量数据为例,运用贝叶斯方法拟合水位流量关系曲线中的幂律模型.以东江干流历年实测数据构建合理的先验分布为基础,结合似然函数,导出后验分布,并用马尔科夫链蒙特卡洛（MCMC）算法估计后验分布中的参数.结果表明:贝叶斯方法能够合理推断水位流量关系曲线中的幂律模型并结合MCMC算法进行参数估计,且能够提供拟合的水位流量关系曲线的95%置信区间;相比最大似然估计法,贝叶斯方法在曲线的外延性表现更好. This paper presents a Bayesian approach for fitting the power-law rating curve model to a set of stagedischarge measurements of Heyuan,Lingxia and Boluo,respectively,which are located in the East River.After creating a reasonable prior distribution with the previous stage-discharge measurements,the posterior distribution is derived with the likelihood function.Then an efficient MCMC algorithm for the parameters estimation is used.The study results show that:Bayesian approach is reasonable for fitting the power-law rating curve model and estimating the parameters with MCMC algorithm.Also,the 95%confidence interval is created by Bayesian approach;Bayesian approach performs better on extension of rating curves than the maximum likelihood estimation. 贝叶斯方法 马尔科夫链蒙特卡洛（MCMC）算法 水位流量关系曲线 置信区间 Bayesian methods Markov chain Monte Carlo（MCMC）algorithm rating curve confidence interval 10.14188/j.1671-8836.2014.04.027 P333 国家自然科学基金（41071020）;新世纪优秀人才支持计划资助项目 2014-04-01 2021-04-01 4 60