Comparison of Likelihood-Free Inference Approach and a Formal Bayesian Method in Parameter Uncertainty Assessment: Case Study with a Single-Event Rainfall–Runoff Model

Abstract

In the present study, DREAM(ZS) and DREAM(ABC) (which stands for differential evolution adaptive metropolis) algorithms were applied to determine the parameters’ uncertainty in a single-event rainfall–runoff model, and rainfall multipliers were also used to correct rainfall forcing errors. Moreover, DREAM(ZS), based on the original DREAM algorithm, and the DREAM(ABC) algorithm, as a likelihood-free inference approach, were both used to explore the posterior parameters in high-dimensional inference problems. Before comparing DREAM(ZS) with DREAM(ABC), some underlying assumptions of residual distribution were analyzed and then fulfilled to obtain a suitable likelihood function and also to provide a more reliable estimation of the parameters. Despite the use of an acceptable likelihood function in the DREAM(ZS) algorithm, the results confirm the advantage of the DREAM(ABC) for assessing the uncertainty in a single-event model and high-dimensional parameter spaces. Moreover, an acceptable distance function used in DREAM(ABC) is suggested to assess the uncertainty in a single-event rainfall-runoff model (HEC-HMS). Occasional flash floods occur in this study region and in large parts of Iran. The results of this study can, therefore, be useful for achieving more accurate predictions and planning for flood control management.