Modeling and interpreting hydrological responses of sustainable urban drainage systems with explainable machine learning methods

Abstract

Abstract. Sustainable urban drainage systems (SuDS) are decentralized stormwater management practices that mimic natural drainage processes. The hydrological processes of SuDS are often modeled using process-based models. However, it can require considerable effort to set up these models. This study thus proposes a machine learning (ML) method to directly learn the statistical correlations between the hydrological responses of SuDS and the forcing variables at sub-hourly timescales from observation data. The proposed methods are applied to two SuDS catchments with different sizes, SuDS practice types, and data availabilities in the USA for discharge prediction. The resulting models have high prediction accuracies (Nash–Sutcliffe efficiency, NSE, >0.70). ML explanation methods are then employed to derive the basis of each ML prediction, based on which the hydrological processes being modeled are then inferred. The physical realism of the inferred hydrological processes is then compared to that would be expected based on the domain-specific knowledge of the system being modeled. The inferred processes of some models, however, are found to be physically implausible. For instance, negative contributions of rainfall to runoff have been identified in some models. This study further empirically shows that an ML model's ability to provide accurate predictions can be uncorrelated with its ability to offer plausible explanations to the physical processes being modeled. Finally, this study provides a high-level overview of the practices of inferring physical processes from the ML modeling results and shows both conceptually and empirically that large uncertainty exists in every step of the inference processes. In summary, this study shows that ML methods are a useful tool for predicting the hydrological responses of SuDS catchments, and the hydrological processes inferred from modeling results should be interpreted cautiously due to the existence of large uncertainty in the inference processes.