Improving the interpretability and predictive power of hydrological models: Applications for daily streamflow in managed and unmanaged catchments

In recent years, Machine Learning (ML) techniques have gained the attention of the hydrological community for their better predictive skills. Specifically, ML models are widely applied for streamflow predictions. However, limited interpretability in the ML models indicates space for improvement. Leveraging domain knowledge from conceptual models can aid in overcoming interpretability issues in ML models. Here, we have developed the Physics Informed Machine Learning (PIML) model at daily timestep, which accounts for memory in the hydrological processes and provides an interpretable model structure. We demonstrated three model cases, including lumped model and semi-distributed model structures with and without reservoir. We evaluate the first two model structures on three catchments in India, and the applicability of the third model structure is shown on the two United States catchments. Also, we compared the result of the PIML model with the conceptual model (SIMHYD), which is used as the parent model to derive contextual cues. Our results show that the PIML model outperforms simple ML model in target variable (streamflow) prediction and SIMHYD model in predicting target variable and intermediate variables (for example, evapotranspiration, reservoir storage) while being mindful of physical constraints. The water balance and runoff coefficient analysis reveals that the PIML model provides physically consistent outputs. The PIML modeling approach can make a conceptual model more modular such that it can be applied irrespective of the region for which it is developed. The successful application of PIML in different climatic as well as geographical regions shows its generalizability.