A subseasonal-to-seasonal runoff forecasting framework under uncertainty: application of numerical weather predictions and a Bayesian maximum entropy-based data fusion technique

This study proposes a methodology for subseasonal-to-seasonal (S2S) runoff forecasting by developing a data fusion model to enhance numerical weather prediction (NWP) outputs. Initially, monthly precipitation data from NWP models are bias-corrected and downscaled using quantile mapping. Subsequently, S2S precipitation forecasts are further improved via a Bayesian maximum entropy (BME)-based data fusion model. An uncertainty analysis is conducted to assess the effectiveness of these models in reducing forecast uncertainty, with results compared against an artificial neural network (ANN)-based data fusion approach. The proposed methodology is applied to the Zarrinehrud basin in Iran, a critical water source of Lake Urmia, the world's second-largest hyper-saline lake. Findings demonstrate that the data fusion models – particularly the BME-based approach – significantly enhance the S2S precipitation forecasts of NWP models. For instance, the d-factor values for individual NWP models (e.g., ECMWF) improved by 50%. Consequently, the refined precipitation forecasts yielded highly accurate runoff predictions. In the S2S runoff forecasting phase, model efficiency criteria achieved Pearson correlation (ρ) = 0.87, Nash-Sutcliffe efficiency (NSE) = 0.75, and Kling-Gupta efficiency (KGE) = 0.87 h.