End-to-End Differentiable Auto-Calibration of a Distributed Glacio-Hydrological Model Using Physically Consistent Routing

Dinesh Joshi, Rijan Bhakta Kayastha, Kundan Lal Shrestha

Distributed glacio-hydrological models are essential for simulating runoff processes in glacier-fed Himalayan basins, yet their application is often constrained by extensive data requirements, high computational costs, and reliance on manual, trial-and-error calibration. Recent auto-calibration approaches using stochastic optimization or machine learning have shown promise, but they frequently suffer from limited physical interpretability, high computational demand, or the absence of physically con-sistent routing formulations, restricting their applicability to spatially distributed models. In this study, we present an end-to-end differentiable, gradient-based auto-calibration framework for the PCRaster-based PyGDM glacio-hydrological model. The framework integrates a physically consistent, mass-conserving routing scheme based on an eight-direction flow network, im-plemented in TensorFlow and optimized using Accelerated Linear Algebra (XLA). This formulation enables gradient propa-gation through all hydrological processes, including surface runoff generation, subsurface flow, and river routing, allowing simultaneous calibration of spatially and temporally varying parameters directly from discharge observations. Spatially distrib-uted subsurface parameters and monthly varying surface and cryospheric parameters are optimized using automatic differenti-ation and constrained within physically meaningful ranges through sigmoid-based reparameterization. To address the lack of spatial discharge observations, a flow-accumulation-based pseudo-observed discharge field is constructed to support spatially distributed calibration. The framework is evaluated in the glacier-fed Bheri Basin, Nepal, and benchmarked against a manually calibrated PyGDM simulation. Results demonstrate that the proposed approach outperforms manual calibration, achieving higher predictive skill during both calibration (NSE = 0.85; VD = −6.56) and validation (NSE = 0.86; VD = −0.06) periods, while requiring substantially reduced human intervention. The learned parameters exhibit coherent spatial, elevation-depend-ent, land-use-specific, and seasonal patterns that remain physically interpretable and consistent with hydrological understanding of Himalayan catchments. The study demonstrates that fully differentiable, physically constrained routing is critical for robust end-to-end calibration of distributed hydrological models. The proposed framework offers a scalable, computationally efficient, and physically interpretable solution for auto-calibration in data-limited, glacier-fed basins, with broad applicability to high-resolution hydrological modeling and climate impact assessments.