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 fully differentiable LSM developed by reconstructing the Noah LSM’s governing partial differential equations into a process-encapsulated Recurrent Neural Network (RNN). We first demonstrate that NoahPy perfectly 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 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 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.
The state-of-the-art land surface models (LSMs) have been reported to perform poorly in representing permafrost processes. To address this gap, the authors present NoahPy—a fully differentiable LSM developed by reconstructing the Noah LSM’s governing partial differential equations into a process-encapsulated recurrent neural network. NoahPy was compared with both the original and an improved version of the Noah LSM, and evaluated at a permafrost site. I find the model to be skillful and the results reasonable.
General Comments
1) Manuscript Structure
Introduction: It would be beneficial to restructure the introduction to better highlight the significance of permafrost, particularly as the authors aim to introduce the model to the permafrost research community. The section could begin by underscoring the importance of permafrost, followed by a critical review of how current LSMs represent permafrost processes, clearly outlining existing limitations. Addressing this gap, the authors should then introduce deep learning methods and explain how such approaches can provide an effective solution to improve permafrost modeling.
Discussion: The advantages and limitations are currently intermingled in this section. Please consider: (a) adding a brief outlook on future model development; and (b) using subsections to enhance the readability of the manuscript.
2) Language
The language should be improved throughout for clarity and academic tone.
Specific Comments:
“Essentially, all models are wrong, but some are useful.” (George E. P. Box, 1979)