Differentiable Parameter Learning Framework for Calibration of Hydrological Model Parameters

Hydrological models, such as rainfall-runoff and groundwater models, require the accurate calibration of multiple unobserved parameters to function effectively. While various methods, including genetic and evolutionary algorithms, have been developed for this purpose, traditional calibration techniques often fall short. They tend to focus on individual locations, leading to suboptimal, local solutions and results in discontinuous parameter estimates, even in geographically similar adjacent regions. To address these challenges, we propose a differentiable Parameter Learning (dPL) framework that harnesses the power of deep learning for the comprehensive calibration of hydrological model parameters across both temporal and spatial domains. This innovative approach moves beyond the constraints of traditional methods by integrating the extensive learning capabilities of deep learning to achieve more consistent and accurate parameter estimation. In this study, we apply the dPL framework to the HBV (Hydrologiska Byråns Vattenbalansavdelning) rainfall-runoff model, a conceptual lumped model that represents an entire watershed as a system comprising a soil layer, an upper tank, and a lower tank. The study area encompasses the upstream regions of five government-managed rivers of Taiwan, covering six distinct watersheds, each with unique geographical characteristics. The results demonstrate that the dPL framework not only outperforms traditional calibration methods but also enhances physical coherence and generalizability. These findings highlight the potential of the dPL framework as a robust tool for hydrological model calibration.

Keyword：differentiable Parameter Learning Framework，HBV Rainfall-Runoff Model，Surrogate Model，Long Short-Term Memory (LSTM)