Multi-variable Medium And Long-term Streamflow Prediction Models Based On Bayesian Inference

The highly nonlinear and non-stationary nature of runoff series under the changing environment makes the existing hydrological forecasting methods challenging.The prediction results of many current hydrological forecasting models are deterministic,and uncertainties in model inputs,model structure and model parameters usually lead to uncertainty in model prediction results.Bayesian inference-based models can quantitatively describe forecast results in the form of probability distributions,and output point forecasts and forecast interval results.Credible intervals are typically used to quantify uncertainty.Many previous studies have modeled individual hydrological stations by using prior runoff as a forecast factor.Although some prediction accuracy can be achieved,the forecasting effect is strongly influenced by the statistical characteristics of the runoff series.Some studies consider adding meteorological data and climate factors to improve forecast accuracy,but there is relatively little modeling of simultaneous forecasts from different stations under the same climatic conditions.This study constructs univariate and multivariate models based on Bayesian inference methods for daily runoff data in the Yellow River basin(including the Wei River basin).This paper reviews the current research progress of hydrological forecasting,points out the problems of hydrological forecasting methods,and investigates the daily runoff series of hydrological stations in the Yellow River basin.The mean absolute error(MAE),root mean square error(RMSE),RMSE-observed standard deviation ratio(RSR),Nash-Sutcliffe efficiency coefficient(NSE)and correlation coefficient(R)are used to assess the point prediction ability of the model.The containment ratio(CR)and the average bandwidth(IW)are used to assess the interval prediction ability of the model.The main conclusions obtained from this study are as follows.(1)In this paper,we construct univariate autoregressive(AR)models based on No-U-Turn Sampler(NUTS)and Variational Inference(VI)algorithms,referred to as BAR＿NUTS and BAR＿VI models.The univariate models were applied to the forecasting of daily runoff series from seven hydrological stations in the Yellow River basin.It is shown that the fitting and prediction ability of BAR＿NUTS and BAR＿VI models are basically the same.The containment rates of both the BAR＿NUTS and BAR＿VI models were close to 1 during the training and testing periods,but the IW values of the former were lower.This indicates that the BAR＿NUTS model outperforms the BAR＿VI model in terms of quantifying uncertainty.Therefore,the prediction uncertainty of the BAR＿NUTS model is much smaller.(2)In this paper,a univariate long short-term memory neural network model(LSTM)based on the VI algorithm is constructed,and a Bayesian optimization algorithm is used to determine the number of neurons in the hidden layer to establish BO-BLSTM model.BLSTM models based on 10 and 20 hidden layer neurons are constructed,respectively,and are denoted as BLSTM-10 and BLSTM-20 models.The results of the study show that the BLSTM-10 model has good prediction effect considering the computation time and model complexity.Changing the number of neurons does not improve the prediction accuracy and reduce the uncertainty.(3)In this paper,a univariate hybrid model is constructed.The residuals of the BAR＿NUTS,BLSTM-VI and BLSTM-10 models are corrected using the Complete ensemble empirical mode decomposition with adaptive noise(CEEMDAN)algorithm and the Bayesian Optimization(BO)based Support Vector Regression(SVR)model to build the CEE-SBAR-NUTS,CEE-SBAR-VI and CEE-SBLSTM models.The results show that the error correction hybrid model can significantly improve the accuracy of fitting and prediction of BAR＿NUTS,BAR＿VI and BLSTM-10 models.(4)The multivariate runoff forecasting model is established based on the geographic location of hydrological stations and the relationship between upstream and downstream.The BVAR model modeled the daily runoff series of Zhangjiashan,Xianyang,Lintong,Zhuangtou,and Jiaokou hydrological stations in the Weihe River basin.The results of the study show that there are differences in the prediction performance of BVAR models for the same hydrological station with different combinations of stations.The fitting accuracy of the BVAR model in the training period is relatively low and does not differ much from the fitting results of the BAR＿NUTS,BAR＿VI,BLSTM-10,BLSTM-20,and BO-BLSTM models.However,the predictive accuracy of the BVAR model increased significantly during the testing period.Analysis of the interval prediction shows that the BAR＿NUTS and BAR＿VI models have lower fit uncertainty in the training period.However,the BVAR model has lower interval prediction uncertainty in the testing period.Multivariate daily runoff series as input variables of the model can provide richer information than univariate series,which is beneficial to improve the prediction accuracy.The multivariate BVAR model has better out-of-sample predictions compared to the univariate model.For areas with limited meteorological data,the BVAR model is able to obtain satisfactory prediction results using runoff data from nearby hydrological stations.(5)The prediction results of the models in the flood season show that the error correction hybrid CEE-SBAR-NUTS,CEE-SBAR-VI and CEE-SBLSTM models can improve the prediction accuracy of the univariate models in the flood season.For the five hydrological stations in the Weihe River basin selected for this paper,the BVAR model outperformed the error-corrected hybrid model in terms of prediction accuracy in the flood season,significantly improving the accuracy of the univariate model in the flood season.