Probabilistic Physics-Guided Deep Neural Networks With Recurrence and Attention Mechanisms for Interpretable Daily Streamflow Simulation

As Deep Neural Networks (DNNs) are being increasingly employed to make important simulations in rainfall-runoff contexts, the demand for interpretability is increasing in the hydrology community. Interpretability is not just a scientific question, but rather knowing where the models fall flat, how to fix them, and how to explain their outcomes to scientific communities so that everyone understands how the model arrives at specific simulations This paper addresses these challenges by deciphering interpretable probabilistic DNNs utilizing the Deep Autoregressive Recurrent (DeepAR) and Temporal Fusion Transformer (TFT) for daily streamflow simulation across the continental United States (CONUS). We benchmarked TFT and DeepAR against conceptual to physics-based hydrologic models. In this setting, catchment physical attributes were incorporated into the training process to create physics-guided TFT and DeepAR configurations. Our proposed physics-guided configurations are also designed to aggregate the patterns across the entire data set, analyze the sensitivity of key catchment physical attributes and facilitate the interpretability of temporal dynamics in rainfall-runoff generation mechanisms. To assess the uncertainty, the modeling configurations were coupled with a quantile regression by adding Gaussian noise $N\left(0,\sigma \right)$ with increasing standard deviation to the individual catchment attributes. Analysis suggested that the physics-guided TFT was superior in predicting daily streamflow compared to the original TFT and DeepAR as well as benchmark hydrologic models. Predictive uncertainty intervals effectively bracketed most of the observational data by simultaneous simulation of various percentiles (e.g., 10th, 50th, and 90th). Interpretable physics-guided TFT proved to be a strong candidate for CONUS daily streamflow simulations.