Research And Application On Mid-Long Term Streamflow Forecasting Based On Entropy Spectral Theory

Mid-long term monthly streamflow forecasting can provide a basis for the full utilization for reservoir operation,flood control and power generation,river ecological restoration,irrigation and shipping.In northwestern China,streamflow is the most important source of water for industry and agriculture,but it also limits the development of local industry and agriculture.Therefore,improving the accuracy of streamflow forecasting can provide a reasonable basis for optimal allocation of water resources.There are many factors affecting streamflow.Under the influence of various factors,the regularity and variation characteristics of streamflow are also complex.Monthly streamflow time series often show periodic and random characteristics.Entropy spectral analysis and time series analysis is applied to characterize stochastic pattern and periodic pattern,respectively.The entropy spectral theory combines entropy spectral analysis and auto-regression model to provide a new idea for monthly streamflow forecasting.BESA,CESA and RESA model is discussed and applied to monthly streamflow at Yingluoxia station,Zamuzi station,Jiutiaoling station,Xiangtang station and Tangnaihai station,and average relative error(RE),root mean square error(RMSE),and correlation coefficient.(R)and decision coefficient(DC)are selected as performance metrics of model.Matlab2010 b is used to achieve the calibration and verification of the model.The spectral density and prediction accuracy estimated by the three models are compared,based on the optimal training period length.The main conclusions are following:(1)For BESA model,the 26 years streamflow data is determined as the optimal training period length at each station,based on the model order,training period and verification period forecasting performance.Comparing the spectral density function obtained by the BESA with the spectral density function obtained by FFT,it is found that the spectral density function of the BESA is smoother than the FFT.At the same time,BESA and FFT both detected the 12-month primary period but BESA did not detect the secondary period which should have existed.The streamflow process at each station are forecasted well by BESA model.DC of the validation period for Yingluoxia station,Zamuzi station,Jiutiaoling station,Xiangtang station and Tangnaihai station are 0.859,0.734,0.716,0.797 and 0.545,respectively.(2)For CESA model,19 years,33 years,17 years,16 years and 17 years streamflow data is determined as the optimal training period length at Yingluoxia station,Zamuzi station,Jiuchiling station,Xiangtang station and Tangnaihai station,respectively,which based on the model order,training period and verification period forecasting performance.Comparing the spectral density function obtained by the CESA with the spectral density function obtained by FFT,it is found that the spectral density function of the CESA is smoother than the FFT.At the same time,CESA and FFT both detected the 12-month primary period and secondary period,through the peak of CESA's spectral density function are both wide and low.The streamflow process at each station are forecasted well by CESA model.DC of the validation period for Yingluoxia station,Zamuzi station,Jiutiaoling station,Xiangtang station and Tangnaihai station are 0.882,0.748,0.739,0.818 and 0.547,respectively.(3)Since the solution method of RESA is similar to that of CESA,the optimal training period of RESA model is the same as the CESA model.When RESA is used to solve the spectral density function,it is necessary to artificially assign a prior spectral density function,which is influenced by subjective factors.Therefore,the spectral density function estimated by RESA is not discussed in this research.The RESA model is used to test monthly streamflow forecasting for each hydrological station,after determining the prior spectral density function.DC of the validation period for Yingluoxia station,Zamuzi station,Jiutiaoling station,Xiangtang station and Tangnaihai station are 0.885,0.714,0.758,0.859 and 0.579,respectively.(4)The spectral density functions of BESA and CESA are more smooth than FFT,and they are all able to estimate the 12-month primary period of the monthly streamflow time series well,with no shifted.However,the spectral density function of BESA sometimes cannot detect the sub-periods.On the other hand,the spectral density function of CESA can accurately detect the sub-periods of multi-period time series.Comparing the forecasting accuracy of BESA model,CESA model and RESA model,we find that all three models can be used for monthly streamflow forecasting.The RESA model has the highest forecasting accuracy,the CESA model is the second,and the BESA model has the lowest forecasting accuracy.However,the BESA model has the highest forecasting accuracy in non-flood period.And the prediction accuracy of RESA and CESA models in the flood season is relatively higher.