贝叶斯框架的Copula季节水文干旱预报模型构建及应用

Bayesian Probabilistic Forecasting of Seasonal Hydrological Drought Based on Copula Function

根据季节径流量相关特性,利用标准径流指数（SRI）,通过优选Copula函数和径流量分布函数,构建贝叶斯框架的Copula季节水文干旱预报模型,并对阿克苏河西大桥水文站进行实证分析。结果表明：1 Gamma、Lognormal、Normal、Gumbel、Exponential 5种分布函数中,Gamma、Gumbel能较好拟合夏、秋季径流量;2 Gumbel-Hougaard、Clayton、Frank 3种Copula函数中,Clayton能较好联结夏、秋季径流量分布函数;3构建模型预报表明,2001~2009年秋季发生干旱概率较低（24%~38%）,以轻微、中度干旱为主,而2010年发生干旱的概率极高（95%）,发生异常干旱的概率偏高（81%）,与实际发生的干旱情况基本一致;4贝叶斯框架下构建的Copula模型能准确预报季节水文干旱发生,减少预报的不确定性,为特定区域干旱预报提供了一条新的途径。

Forecasting of hydrological drought plays an important role in the decision-making process of water resources management.Bayesian networks provide an elegant tool to reflect the autocorrelation in the runoff record and develop the conditional probabilities,furnishing a framework for various types of probabilistic drought forecasting.This study presents a Bayesian probabilistic forecasting model based on best-fitted first-order copula functions.Standardized runoff index（SRI） is used to characterize the historical hydrological droughts and forecast probabilistic drought by season runoff correlations of a target season with the previous seasons in future.We used the Xidaqiao hydrological station in the Aksu River,sub-basin of the Trim River Basin of Xinjiang as a case,and apply the Bayesian probabilistic forecasting model to forecast the probability of autumn drought during the period 2000-2010 based on data from the previous summer,and testing the accuracy of the model.The results show that the probability of an autumn drought in the Aksu River Basin during2001-2009 was low（24%-38%）,with mainly abnormal and moderate droughts,whereas drought was very likely to occur in 2010（95%）,with the probability of occurrence of an exceptional drought being as high as 81%.The model is reliable and can forecast hydrological drought in the next season when current hydrological conditions are known.And the model can quantitatively express the uncertainty of hydrological drought and then improve its prediction accuracy.It does not require the linear assumption of normality and has a wide range of applications.The model provides an useful tool for uncertainty modeling through a probabilistic representation of model parameter uncertainty,developing conditional probabilities for given forecast variables,and returning the highest probable forecast along with an assessment of the uncertainty around that value.However,this study only selects the highest seasonal correlation as a condition,and further studies of hydrological drought forecasting are needed using high-dimensional copula functions.Furthermore,it＇s a very urgent task to use more hydrological sites to forecast regional hydrological drought.