Nonlinear Segmental Runoff Ensemble Prediction Model Using BMA

In this study, a novel nonlinear segmental runoff ensemble forecast model based on the Bayesian model averaging (BMA) algorithm (NLTM-BMAm(P-III)) is proposed based on multimodel ensemble prediction for forecasting monthly runoff and quantifying forecast uncertainty. Four nonlinear time series models were used as ensemble members, and runoff segmented intervals were divided based on P-III type hydrological frequency curves. On this basis, the BMA algorithm was used to obtain the weight sets of each interval after the Box‒Cox transformation. Finally, the mean and probability forecasts were obtained using the weighted average method and the Monte Carlo method. The model was applied to monthly runoff forecasts at eight hydrological stations in the Hei River Basin and two hydrological stations in the Wei River Basin; and compared with the whole-segment simple averaging model NLTM-SMA, the whole-segment Bayesian averaging model NLTM-BMA1 and the segmented Bayesian averaging model with normal distribution partitioning NLTM-BMAm(Normal). The results show that (1) the BMA algorithm yields more reliable forecasts than the SMA algorithm, (2) Segmentation criteria appropriate for the runoff distribution can improve the forecasting accuracy, which would otherwise be reduced, and (3) Compared with the NLTM-SMA and NLTM-BMA1 models, the NLTM-BMAm(P-III) model yields a higher CR value, demonstrating that the segmented ensemble forecasting model can improve the accuracy of probability prediction by considering the diversity of ensemble members. Additionally, the BMA algorithm has good applicability in the segmented ensemble model. The model provides a new method for medium- and long-term runoff forecasting.