Hybrid model for daily runoff interval predictions based on Bayesian inference

The highly non-linear and nonstationary nature of runoff events in changing environments makes accurate and reliable runoff forecasting difficult. We propose a hybrid model by integrating an autoregressive (AR) model, Bayesian inference, a complete ensemble empirical mode decomposition with adaptive noise (CEEMDAN) algorithm, Bayesian optimization, and support vector regression. Two Bayesian inference methods (the No-U-Turn Sampler (NUTS) and variational inference) were used to calculate the parameters of the AR model to obtain a Bayesian AR (BAR) model. Credible intervals were used to analyse the uncertainty of the parameters and model prediction results. The above model is applied to the daily runoff predictions of hydrological stations in the Yellow River basin of China. The results show that (1) the hybrid model can improve the prediction accuracy and (2) the NUTS algorithm-based model provides a narrower reliable interval and performs better in uncertainty analyses.