Study on optimization and combination strategy of multiple daily runoff prediction models coupled with physical mechanism and LSTM

Accurate prediction of runoff is an important foundation for optimizing water resource allocation and reservoir scheduling operations. However, due to its complex characteristics such as time-varying and non-stationary, accurate prediction of the runoff process is very difficult. This paper proposes a novel approach for runoff forecasting by combining the physical mechanism models with the Long Short-Term Memory network (LSTM) method. Utilizing the simulation and description capabilities of physically based models, as well as the powerful nonlinear analysis provided by big data methods, a type of model selection and combination strategy is proposed incorporating 16 different physically based models with LSTM technology. Additionally, to accommodate the comprehensive analysis and evaluation of multi-model forecasting performance, this paper also proposed a comprehensive evaluation metric for runoff forecasting considering the characteristics of group models. The results of the case study demonstrate that this strategy can obtain model combinations suitable for different watershed characteristics and effectively improve the forecast accuracy of multiple models. Model combinations sorted by validation period RMSE and R2 should be a superior choice. When evaluating the runoff forecasting accuracy of obtained optimal model combination during the calibration period, the average reduction of Root Mean Square Error (RMSE) is 39.62%, and the average increase of Nash-Sutcliffe coefficient R2 is 7.49%. During the validation period, the average reduction of RMSE is 62.68% and the average increase of R2 is 24.24%. When the model combinations sorted by validation period F score, the obtained model combination increased RMSE by 22.7% and decreased R2 by 7.3% comparing to the model combination selected by RMSE and R2. It is indicated that the F score may not be suitable for evaluating model selection. The method proposed in this article can effectively improve the overall forecasting performance of a single forecasting model and has good practical value for promotion and application.