A hybrid method to tackle conditional systematic errors of hydrological models

Machine learning has been used in hydrological applications for decades. Recent studies, after a systematic comparison, have shown that machine learning models (more precisely, deep learning with thousands of nodes) can outperform even the most sophisticated physically based models. Furthermore, one of the basic criticisms, that machine learning produces black box models, has been addressed by researchers, who have indicated how this black box can be made transparent to obtain explainable/interpretable results. However, the main disadvantage of the machine learning approaches (especially deep learning, which may employ hundreds of thousands of parameters) remains the CPU-intensive training process. This disadvantage can be overcome by employing hybrid modelling frameworks that combine simple machine learning models with parsimonious hydrological models. The drawback of these parsimonious approaches is the susceptibility of the latter to conditional systematic errors, which propagate through the modelling framework and cannot be eliminated by simple machine learning networks (employing complex networks would nullify the sought benefit of reduced CPU times). In this study, we suggest methods to cope with this kind of error and achieve a modelling performance close to the best achievable with the available data.