Coupling Rainfal-Runoff and Shallow-Water Hybrid Models: A Reliability Test of Piecewise Versus End-to-End Learning

River-fed urban flooding is highly sensitive to boundary inflow hydrographs, yet many cities lack streamflow gauges at the location where the river enters the city. In such settings, inundation is typically governed by a coupled chain of processes: (a) routing from the nearest upstream gauge, (b) rainfall-driven lateral inflows from the intervening catchment, and (c) shallow-water dynamics within the city. Recent advances have progressed independently in deep learning and differentiable or hybrid formulations for each component, but this raises a central question: when these models are coupled, do errors propagate transparently, or do they compensate in ways that appear accurate while remaining physically biased? A key gap is demonstrating whether end-to-end coupling improves urban flood predictions or instead amplifies uncertainty and bias across modules.

We develop a hybrid framework that couples these three modules and supports both piecewise (module-wise) training and joint end-to-end learning, enabling explicit diagnosis of error propagation. A synthetic training dataset is generated using physics-based flood simulations to provide consistent supervision for runoff generation, routing behaviour, and inundation response. Evaluation then focuses on historical flood events in Surat, Gujarat, using remote-sensing inundation extent maps as an event-scale observational benchmark. The experimental design is structured to isolate the marginal effect of coupling by tracking how uncertainties in lateral inflow and routing translate into boundary hydrograph bias and, ultimately, mismatch in predicted inundation extent.

The analysis is framed around reliability rather than raw accuracy: it investigates when end-to-end coupling reduces boundary-condition uncertainty versus when it enables compensating errors that mask upstream bias at the urban scale. By comparing independently assessed sub-modules against the coupled system, the study aims to clarify how errors accumulate across the hydrology-to-inundation pipeline and under which hydrologic regimes. This provides a pathway toward reliable and rapid end-to-end hybrid systems for river-fed urban flood modeling.