Towards Interpretable Physical-Conceptual Catchment-Scale Hydrological Modeling using the Mass-Conserving-Perceptron

We investigate the applicability of machine learning technologies to the development of parsimonious, interpretable, catchment-scale hydrologic models using directed-graph architectures based on the mass-conserving perceptron (MCP) as the fundamental computational unit. Here, we focus on architectural complexity (depth) at a single location, rather than universal applicability (breadth) across large samples of catchments. The goal is to discover a minimal representation (numbers of cell-states and flow paths) that represents the dominant processes that can explain the input-state-output behaviors of a given catchment, with particular emphasis given to simulating the full range (high, medium, and low) of flow dynamics. We find that a HyMod Like architecture with three cell-states and two major flow pathways achieves such a representation at our study location, but that the additional incorporation of an input-bypass mechanism significantly improves the timing and shape of the hydrograph, while the inclusion of bi-directional groundwater mass exchanges significantly enhances the simulation of baseflow. Overall, our results demonstrate the importance of using multiple diagnostic metrics for model evaluation, while highlighting the need for properly selecting and designing the training metrics based on information-theoretic foundations that are better suited to extracting information across the full range of flow dynamics. This study sets the stage for interpretable regional-scale MCP-based hydrological modeling (using large sample data) by using neural architecture search to determine appropriate minimal representations for catchments in different hydroclimatic regimes.