NoahPy: a differentiable Noah land surface model for simulating permafrost thermo-hydrology

Abstract

Accurately representing permafrost in Earth System Models is a grand challenge that creates major uncertainty. A promising path forward is to create hybrid models that synergize process-based physics with deep learning, but this is fundamentally hindered by the non-differentiable nature of traditional land surface models (LSMs), which are incompatible with modern AI workflows. To overcome this limitation, we present NoahPy, a differentiable LSM developed by reconstructing the Noah LSM's governing partial differential equations into a process-encapsulated Recurrent Neural Network (RNN), with the heat–moisture solver forming the computational core. We first demonstrate that NoahPy very closely replicates the numerical behaviour of the modified Noah LSM, achieving Nash-Sutcliffe Efficiency (NSE) coefficients above 0.99 for both soil temperature and liquid water. We then show that at a permafrost site, the calibrated NoahPy achieves robust simulation performance for soil temperature (NSE > 0.9) and liquid water (NSE > 0.8). Critically, the differentiable workflow, when combined with the Adam optimizer, is significantly faster, more stable, and yields simulations with lower uncertainty compared to traditional Shuffled Complex Evolution (SCE-UA) calibration algorithm. NoahPy thus provides a foundational, “glass-box” framework that closes a key technical gap, enabling the development of the next generation of hybrid AI-physics models needed to more reliably predict the future of the cryosphere.