TOWARD PHYSICAL REALISM IN DEEP LEARNING FOR HYDROLOGY: A MASS CONSERVATION–GUIDED FRAMEWORK FOR LUMPED AND SPATIALLY DISTRIBUTED HYDROLOGIC MODELING

Abstract

Accurately simulating rainfall-runoff relationships is crucial for proactive flood forecasting and mitigation, efficient agricultural planning, and strategic urban development. Physically-based hydrologic models (PBMs), grounded in physical laws that govern hydrologic dynamics, have long served as the primary tools for rainfall-runoff simulation. However, the accuracy of PBMs is often limited by structural imperfections and by parameterizations that do not fully capture watershed behavior. With recent advances in artificial intelligence (AI) techniques and computational capacity, Deep Learning (DL) models have emerged as powerful data-driven alternatives. Numerous studies show that DL models can match or surpass the rainfall-runoff simulation accuracy achieved by PBMs. Among current DL model options, the Long Short-Term Memory (LSTM) network, despite being introduced decades ago, continues to serve as the dominant benchmark for rainfall-runoff simulation. At the same time, DL models have long been criticized for their limited interpretability, which restricts understanding of how they represent hydrologic processes internally and hinders their broader acceptance within the hydrology community. Recent efforts have therefore incorporated physical principles into DL architectures to promote physics-aware model design, yet important questions remain regarding how such constraints should be formulated so that model behavior better reflects real hydrologic processes. Together, these research gaps highlight the need to better understand both the accuracy limits of modern DL architectures and the role of physical principles in improving the interpretability and realism of rainfall-runoff simulation. Accordingly, this dissertation investigates how neural network architecture and physics-aware model design can advance rainfall-runoff simulation. Chapter 1 introduces the research background and presents the research questions and contributions. Chapter 2 evaluates whether a deep state space model (SSM), which has shown state-of-the-art performance in sequence modeling across many other fields, can provide meaningful improvements over the long-standing LSTM benchmark for rainfall-runoff simulation. Chapter 3 examines the mass conservation constraint in the Mass-Conserving LSTM (MC-LSTM), a physics-aware variant of LSTM designed to enforce water mass conservation, and investigates how this constraint influences model performance and hydrologic behavior. Chapter 4 develops a Mass Conservation Relaxed LSTM (MCR-LSTM), a new variant of MC-LSTM that introduces a more flexible conservation mechanism, and evaluates its hydrologic capability across 531 watersheds in the contiguous United States (CONUS). Chapter 5 extends mass conservation-guided model design from lumped to distributed hydrologic modeling through the development of the Physics-Enhanced Conservation-Augmented Network (PECAN). Chapter 6 summarizes the major findings of the dissertation and discusses future research directions. Through this structured investigation, the dissertation seeks to identify an effective balance between physical knowledge and AI flexibility, thereby advancing hydrologic modeling in both predictive performance and scientific insight.