A Differentiable Regionalizable Hydrological-Hydraulic Chainage basin scale assimilation of SWOT Altimetry.

The accurate calibration of hydrological models remains a challenge, particularly in data-scarce regions or where downstream hydraulic complexities influence upstream signatures. We present a novel, end-to-end differentiable optimization framework that couples the conceptual distributed rainfall-runoff model SMASH with the physics-based 1D shallow-water model DassFlow. This framework enables the calibration of hydrological parameters by assimilating downstream water level observations, specifically targeting high-resolution data from the SWOT (Surface Water and Ocean Topography) mission.

The core innovation is a multi-component hydrological-hydraulic gradient computation, we chain the PyTorch-based autograd system of SMASH with the Fortran-based adjoint of DassFlow-1D. This allows for the exact propagation of sensitivities from hydraulic cost functions back to hydrological inputs via the chain rule. To address the ill-posedness of the inverse problem, several constraints and regularizations are considered, including descriptor to parameter regionalization mappings and a background-error covariance term. 

We demonstrate this approach on the Garonne watershed, showing that conceptual parameters can be effectively constrained by propagating gradients through a heterogeneous-code coupling. This work proves the feasibility of "physics-informed" regionalized hydrological hydraulic calibration and provides a scalable path for integrating satellite altimetry into operational rainfall-runoff hydrodynamic modeling. This method is transposable to other bassins globaly and other water surface signatures (geometrical or velocity) and will deployed in eo-hydrolab.