Hydrological post-processing based on approximate Bayesian computation (ABC)

This study introduces a method to quantify the conditional predictive uncertainty in hydrological post-processing contexts when it is cumbersome to calculate the likelihood (intractable likelihood). Sometimes, it can be difficult to calculate the likelihood itself in hydrological modelling, specially working with complex models or with ungauged catchments. Therefore, we propose the ABC post-processor that exchanges the requirement of calculating the likelihood function by the use of some sufficient summary statistics and synthetic datasets. The aim is to show that the conditional predictive distribution is qualitatively similar produced by the exact predictive (MCMC post-processor) or the approximate predictive (ABC post-processor). We also use MCMC post-processor as a benchmark to make results more comparable with the proposed method. We test the ABC post-processor in two scenarios: (1) the Aipe catchment with tropical climate and a spatially-lumped hydrological model (Colombia) and (2) the Oria catchment with oceanic climate and a spatially-distributed hydrological model (Spain). The main finding of the study is that the approximate (ABC post-processor) conditional predictive uncertainty is almost equivalent to the exact predictive (MCMC post-processor) in both scenarios.