Vine Copula与贝叶斯模型平均结合的月径流预测及应用

Prediction and application of monthly streamflow based on Vine Copula coupled Bayesian model averaging

准确可靠且预见期较长的月径流预测对水资源配置、防汛抗旱以及生态环境保护等具有重要意义。径流变化与降水、气温、潜在蒸散发以及前期径流等存在密切联系。鉴于Vine Copula可以灵活地将多个随机变量的边缘分布函数通过Copula对的形式联结起来构造多维联合分布函数以及贝叶斯模型平均(Bayesian Model Averaging,BMA)在处理多模型集合预报方面的优势,该研究基于BMA集合多个Vine Copula模型提出了一种BVC径流预测模型(简称BVC模型),应用于黄河流域上游4个水文站(唐乃亥站、民和站、红旗站和折桥站)的月径流预测,采用确定性系数(R2)、纳什效率系数(Nash-Sutcliffe Efficiency coefficient,NSE)和均方根误差(Root Mean Squared Error,RMSE)评价模型的预测性能。结果表明,验证期内预见期为1~3个月时,BVC模型在各水文站的R2均大于等于0.83、NSE均大于等于0.78且RMSE均维持在较低水平;与随机森林(Random Forest,RF)模型和长短期记忆神经网络(Long Short-Term Memory Neural Network,LSTM)模型相比,BVC模型能够很好地预测各水文站月径流的变化过程,特别是月径流极值的变化。研究表明BVC模型在预见期为1~3个月时的月径流预测性能明显优于RF模型和LSTM模型。该研究构建的BVC模型为流域的水资源管理和风险评估等提供参考。

Streamflow(channel runoff)is one of the paramount components in the hydrological cycle from the land to waterbodies.Reliable prediction of monthly streamflow in the long lead time is of great significance for the water resource allocation,flood defense,drought mitigation,and ecological environment.The streamflow over time is closely related to precipitation,temperature,potential evapotranspiration,and antecedent streamflow.Fortunately,vine copulas can easily establish the multivariate distribution function by decomposing multidimensional variables into pair copula constructions.And,the Bayesian Model Averaging(BMA)provides outstanding advantages in multi-model ensemble prediction.In this study,a novel streamflow prediction model was proposed to integrate the multiple vine copula models with BMA,(i.e.,Bayesian model averaging ensemble Vine Copula(BVC)model).The monthly streamflow predictions of Tangnaihai,Minhe,Hongqi,and Zheqiao hydrological stations in the upstream of Yellow River basin were selected as four cases.The spatial average of precipitation,temperature,and potential evapotranspiration data were calculated across the watershed controlled by each hydrological station.The precipitation,temperature,potential evapotranspiration,and streamflow in each month were firstly fitted with the best marginal distribution functions from the pool of Normal,Gamma,Weibull,and Log-Normal functions.The vine copulas model was leveraged to couple these variables(incorporated four explainable variables and a predicted variable)under five-dimensional situations.The BMA was then employed to combine the streamflow predictions of these candidate vine copula models to reduce the uncertainties caused by distinct variable ordering of individual vine copula model.Finally,the Random Forest(RF)model and the Long Short-Term Memory neural network(LSTM)model were adopted as two reference models.The results show that the best-fitted marginal distributions for precipitation,temperature,potential evapotranspiration,and streamflow were Gamma,Normal,Weibull,and Log-Normal based on the chi-square test,respectively.The minimum coefficient of the determination(R~2)(Nash-Sutcliffe Efficiency coefficient(NSE))was all above 0.83(0.78)and the Root Mean Squared Error(RMSE)was all sustained at a lower level for the 1-3-month lead streamflow predictions using the BVC model during the validation period(1963-2006).Compared with the RF model,the BVC model greatly was captured the variations in the monthly streamflow at these hydrological stations,especially for the extreme streamflow.The prediction performances of BVC and RF models were further evaluated by leveraging the precipitation,temperature,potential evapotranspiration,and streamflow time series over the driest and wettest seasons(corresponding to the average lowest and highest streamflow of three consecutive months during 1963-2006,respectively).Among them,the driest season was found in the January-March period at four hydrological stations;the wettest season was in the July-September period at the Tangnaihai and Hongqi hydrological stations,whereas the Minhe and Zheqiao hydrological stations were found in the August-October period.Similarly,in comparison with the RF model,the BVC model yielded a better performance for streamflow predictions with 1-3-month lead times during the driest and wettest seasons,and the minimum R~2(NSE)values all exceeded 0.57(0.61).Moreover,the BVC model also outperformed the RF and LSTM models for the 1-3-month lead times during the validation period(2007-2016),in terms of R~2,NSE,and RMSE.The findings can provide a theoretical framework for streamflow prediction,and can serve as a guidance for water resources management and risk assessment.