A Deep State Space Model for Rainfall-Runoff Simulations

The rainfall-runoff relationship is a fundamental concept in hydrology. It describes how rainfall is transformed into surface runoff through interconnected hydrologic processes, such as infiltration, evapotranspiration, and the exchange of water between surface and subsurface flows (Beven & Kirkby, 1979). Thoroughly understanding these hydrologic processes and subsequently achieving accurate simulations of the rainfall-runoff relationship are critical for proactive flood forecasting and mitigation, efficient agricultural planning, and strategic urban development (Beven, 2012; Knapp et al., 1991; Moradkhani & Sorooshian, 2008). Physically-based hydrologic models (PBMs), grounded in physical laws that govern hydrologic dynamics, are the standard tools for simulating rainfall-runoff relationships (Beven, 1996). However, the highly nonlinear nature of various hydrologic processes often challenges PBMs, limiting their accuracy in diverse conditions (Beven, 1989; Clark et al., 2017). Consequently, there is a growing need for innovative approaches to address the limitations of PBMs. Deep learning (DL) has emerged as an alternative to PBMs, showing success in capturing the complex, nonlinear patterns in rainfall-runoff simulations. The hydrology community also explores the applicability of DL models in rainfall-runoff simulations across diverse temporal scales and geospatial locations.