Introducing entropy-based Bayesian model averaging for streamflow forecast

Abstract

Bayesian Model Averaging (BMA) is a well-known statistical post-processing approach for probabilistically merging individual forecasts. In BMA, the posterior distribution of the predictand variable is determined by implementing the law of total probability. Therefore, possessing an ensemble of independent members (mutually exclusive) with the highest information content about observation variability (collectively exhaustive) is the main inherent assumption of the original BMA method. Mutually exclusive and collectively exhaustive are two contradictory criteria. Although constructing an ensemble of members that fully satisfied these two properties is practically impossible, providing a balance between them is a key requirement for enhancing the BMA performance. Through coupling BMA with Shannon entropy of information theory, this study proposes an entropy-based selection procedure to construct an ensemble of streamflow forecasts by better addressing the aforementioned contradictory criteria prior to performing the BMA. We investigate the effects of using ensembles with the aforementioned properties by comparing the results of original BMA with the proposed entropy-based BMA (En-BMA) for short- to medium-range daily streamflow forecasts in two different watersheds. The results indicate that the En-BMA leads to better results particularly for high flow predictions. Both probabilistic and deterministic high flow forecasts are more accurate and reliable when using the En-BMA approach. However, for the average flow forecasts, there are no clear differences in the general performance of both methods. The improvements observed are more pronounced for shorter lead-times and less pronounced, but still present, for longer lead times.