Application of Bayesian framework for evaluation of streamflow simulations using multiple climate models

Abstract

Bayesian averaging of climate models is an important tool in streamflow predictions. Climate models have parametric and structural differences and thus have variable hydrological output. Performance of the individual climate models before they are averaged in a Bayesian framework should be consistent with their respective performance indices in a Bayesian framework to ensure that Bayesian averaging follows the physical process. Priors are required to compute posterior probability distributions in the Bayesian predictions. Robustness of Bayesian predictions therefore depends on use of a suitable prior. In this study, combinations of Bayesian regression model priors and regression parameter priors for streamflow prediction have been evaluated to investigate consistency of streamflow simulation performance of RCMs – individually outside the Bayesian framework, individually inside the Bayesian framework and collectively inside the Bayesian framework – using twelve widely used Bayesian formulations. The performance of RCM streamflow simulations outside the Bayesian framework is evaluated using widely used statistical indices: the Willmott’s index of agreement (d1), root mean square error (RMSE), and percent bias error (PBIAS). The performance inside the Bayesian framework is evaluated using posterior inclusion probability (PIP). Results suggest that performance of climate models inside Bayesian framework may not be the same as that outside Bayesian framework. Therefore, there is need for climate model performance evaluation both inside and outside Bayesian framework as a precursor to Bayesian prior selection. For example, the non-Empirical Bayes g-Local (non-EBL)-based Bayesian priors give consistent climate model performance inside and outside Bayesian framework, and therefore is the best prior for simulating high flows. Based on the participating climate models in low flow modelling, the results suggest that both EBL and non-EBL priors can be used in averaging low flow in the Bayesian framework.