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A sudden surge of data has created new challenges in water management, spanning quality control, assimilation, and analysis. Few approaches are available to integrate growing volumes of data into interpretable results. Process-based hydrologic models have not been designed to consume large amounts of data. Alternatively, new machine learning tools can automate data analysis and forecasting, but their lack of interpretability and reliance on very large data sets limits the discovery of insights and may impact trust. To address this gap, we present a new approach, which seeks to strike a middle ground between process-, and data-based modeling. The contribution of this work is an automated and scalable methodology that discovers differential equations and latent state estimations within hydrologic systems using only rainfall and runoff measurements. We show how this enables automated tools to learn interpretable models of 6 to 18 parameters solely from measurements. We apply this approach to nearly 400 stream gaging sites across the US, showing how complex catchment dynamics can be reconstructed solely from rainfall and runoff measurements. We also show how the approach discovers surrogate models that can replicate the dynamics of a much more complex process-based model, but at a fraction of the computational complexity. We discuss how the resulting representation of watershed dynamics provides insight and computational efficiency to enable automated predictions across large sensor networks. 

Wireless sensor networks support decision-making in diverse environmental contexts. Adoption of these networks has increased dramatically due to technological advances that have increased value while lowering cost. However, real-time information only allows for reactive management. As most interventions take time, predictions across these sensor networks enable better planning and decision making. Prediction models across large water level and discharge sensor networks do exist. However, they have limitations in their accessibility, automaticity, and data requirements. We present an open-source method for automatically generating computationally cheap rainfall-runoff models for any depth or discharge sensor given only its measurements and location. We characterize reliability in a real-world case study across 200,000 km, evaluate long-term accuracy, and assess sensitivity to measurement noise and errors in catchment delineation. The method’s accuracy, computational efficiency, and automaticity make it a valuable asset to support operational decision making for diverse stakeholders including bridge inspectors and utilities.