城市洪涝治理方案以及排涝设施规模建设都与城市暴雨强度和外江洪水位息息相关,因此需要对暴雨强度与外江洪水位联合概率分布进行深入研究.以武汉市为例,采用Copula函数建立小时尺度城市暴雨强度和外江洪水位的联合分布,使用极大似然估计值(Max-Likelihood)、模型选择准则、RMSE和NSE拟合优度来评估不同Copula模型的性能,利用局部优化(Local optimization,LO)和马尔科夫链蒙特卡洛(Markov chain Monte Carlo,MCMC)方法来分析Copula模型的不确定性.结果表明:暴雨强度和外江洪水位两要素存在明显的正相关,1 h最大连续降水量和最大日水位相关性最高,最优联合分布函数为Gumbel Copula函数;模型不确定性分析表明MCMC模拟的最优参数与理论参数值基本吻合,效果明显优于局部优化算法,且模型不确定性结果与拟合优度评价结果一致,进一步验证了联合分布函数参数的有效性.相同频率情况下,单变量值低于两变量联合频率对应的暴雨强度和外江洪水位值,高于两变量同现频率对应的暴雨强度和外江洪水位值;两变量同现重现期高于单变量设计重现期,而联合重现期低于单变量设计重现期.同频率下的暴雨强度与水位的组合风险率都远远低于单变量情况下的频率值,50 a以上排涝风险率大于设计暴雨重现期,但最大不超过联合风险率.
Uncertainty-based study on the joint distribution of multi-scale rainfall intensity and water level in the outer flood river
The urban flood management program and the scale construction of drainage facilities are closely related to the urban rainstorm intensity and the flood level of the outer river,so it is necessary to conduct an in-depth study on the joint probability distribution of rainstorm intensity and the flood level of the outer river.Taking Wuhan City as an example,the Copula function is used to establish the joint distribution of hourly-scale urban rainstorm intensity and outer-river flood level,and the performance of different Copula models is evaluated by using the Max-Likelihood estimator,the model selection criterion,the RMSE and the NSE goodness-of-fit.The Local optimization(LO)and Markov chain Monte Carlo(MCMC)methods are used to analyze the uncertainty of Copula models.The results are as follows.There is an obvious positive correlation between the heavy rainfall intensity and the flood level of the outer river,and the correlation between the 1-h maximum continuous precipitation and the maximum daily water level is the highest,and the optimal joint distribution function is the Gumbel Copula function.The uncertainty analysis of model shows that the optimal parameters of the MCMC simulation basically match with the theoretical parameter values,which is obviously superior to the local optimization algorithm.The results of the model uncertainty are consistent with that of the evaluation of the goodness-of-fit,which further verifies the validity of the parameters of the joint distribution function.Under the same frequency,the univariate values are lower than the values of heavy rainfall intensity and outer flood river level corresponding to the two-variable joint frequency,and higher than those corresponding to the two-variable co-occurring frequency.The two-variable co-occurring reproduction period is higher than that of the single-variable design reproduction period,and the joint reproduction period is lower than that of the single-variable design reproduction period.The combined risk rate of both storm intensity and flood level at the same frequency is much lower than the frequency value in the univariate case,and the risk rate of drainage above 50 a is greater than that of the design storm return period,but the maximum risk rate does not exceed the joint risk rate.
Copula functionjoint probability distributiongoodness of fitjoint return period
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