Comparing Bayesian Model Averaging and Reliability Ensemble Averaging in Post-Processing Runoff Projections under Climate Change

This study investigated the strength and limitations of two widely used multi-model averaging frameworks—Bayesian model averaging (BMA) and reliability ensemble averaging (REA), in post-processing runoff projections derived from coupled hydrological models and climate downscaling models. The performance and weight distributions of five model ensembles were thoroughly compared, including simple equal-weight averaging, BMA, and REAs optimizing mean (REA-mean), maximum (REA-max), and minimum (REA-min) monthly runoff. The results suggest that REA and BMA both can synthesize individual models’ diverse skills with comparable reliability, despite of their different averaging strategies and assumptions. While BMA weighs candidate models by their predictive skills in the baseline period, REA also forces the model ensembles to approximate a convergent projection towards the long-term future. The type of incorporation of the uncertain future climate in REA weighting criteria, as well as the differences in parameter estimation (i.e., the expectation maximization (EM) algorithm in BMA and the Markov Chain Monte Carlo sampling method in REA), tend to cause larger uncertainty ranges in the weight distributions of REA ensembles. Moreover, our results show that different averaging objectives could cause much larger discrepancy than that induced by different weighting criteria or parameter estimation algorithms. Among the three REA ensembles, REA-max most resembled BMA because the EM algorithm of BMA converges to the minimum aggregated error, and thus emphasize the simulation of high flows. REA-min achieved better performance in terms of inter-annual temporal pattern, yet at the cost of compromising accuracy in capturing mean behaviors. Caution should be taken to strike a balance among runoff features of interest.