Long-term probabilistic streamflow forecast model with “inputs–structure–parameters” hierarchical optimization framework

Abstract

Accurate, reliable, and stable streamflow forecasts are essential for risk assessment and decision making in water resources management. Owing to the limited value of deterministic forecasting, probabilistic forecasting incorporating probability and confidence intervals is achieved by optimizing the predictors and forecast equation while identifying forecast error features. The combination of deterministic forecasts and error identification can facilitate water resources management. This study improved the traditional forecast model’s inputs selection, structure designation, and error parameters calibration to propose a long-term probabilistic streamflow forecast model with hierarchical optimization of the predictors, forecast equation, and errors characteristics. The model develops information entropy theory to screen the driving predictor set, the long short-term memory (LSTM) model to conduct deterministic forecasts, and the generalized autoregressive conditional heteroskedasticity (GARCH) model to identify time-varying errors. The proposed model, used in some case studies to forecast the monthly streamflow of two lakes, Hongze and Luoma lakes in China, was evaluated using the multidimensional index method considering “accuracy–reliability–stability” performance. The results revealed the following: (1) Predictor screening based on information entropy investigates the statistical characteristics of predictors, thereby improving the reliability of streamflow forecasts. (2) The LSTM model exploits the response between the driving predictors and streamflow, whereas GARCH model identifies the time-varying features of forecast errors effectively, which reduces the probability of forecast failure and increases the accuracy and stability of probabilistic forecasts. (3) Under current meteorological observation conditions and forecasting capability, the proposed forecasts can extend the maximum forecast lead time from 1 month to 3 months. (4) The proposed model improves the accuracy (root mean square error: 6.7%–34.8%), reliability (Brier score: 15.3%–27.9%), and stability (mistaken distance: 36.4–52.6%) in comparison with the benchmark of the two case studies, indicating that “inputs–structure–parameters” hierarchical optimization provides effective forecast information for water resources management.