College of Ocean Science and Engineering, Shanghai Maritime University, Shanghai 201306, China and Center for Marine Environmental and Ecological Modelling, Shanghai Maritime University, Shanghai 201306, China E-mail:
Water Sci Technol. 2021 Mar;83(5):1085-1102. doi: 10.2166/wst.2021.032.
A new parameter optimization and uncertainty assessment procedure using the Bayesian inference with an adaptive Metropolis-Hastings (AM-H) algorithm is presented for extreme rainfall frequency modeling. An efficient Markov chain Monte Carlo sampler is adopted to explore the posterior distribution of parameters and calculate their uncertainty intervals associated with the magnitude of estimated rainfall depth quantiles. Also, the efficiency of AM-H and conventional maximum likelihood estimation (MLE) in parameter estimation and uncertainty quantification are compared. And the procedure was implemented and discussed for the case of Chaohu city, China. Results of our work reveal that: (i) the adaptive Bayesian method, especially for return level associated to large return period, shows better estimated effect when compared with MLE; it should be noted that the implementation of MLE often produces overy optimistic results in the case of Chaohu city; (ii) AM-H algorithm is more reliable than MLE in terms of uncertainty quantification, and yields relatively narrow credible intervals for the quantile estimates to be instrumental in risk assessment of urban storm drainage planning.
提出了一种新的参数优化和不确定性评估方法，该方法使用贝叶斯推断和自适应 Metropolis-Hastings (AM-H) 算法，用于极端降雨频率建模。采用有效的马尔可夫链蒙特卡罗抽样器来探索参数的后验分布，并计算与估计降雨深度分位数幅度相关的不确定性区间。此外，还比较了 AM-H 和传统最大似然估计 (MLE) 在参数估计和不确定性量化方面的效率。并针对中国巢湖市的情况实施和讨论了该程序。我们的工作结果表明：（i）与 MLE 相比，自适应贝叶斯方法（特别是对于大重现期相关的重现期水平）表现出更好的估计效果；需要注意的是，在巢湖市的情况下，MLE 的实施往往会产生过于乐观的结果；（ii）AM-H 算法在不确定性量化方面比 MLE 更可靠，并且为分位数估计产生相对较窄的置信区间，这对于城市暴雨水排水规划的风险评估很有帮助。
