Tian et al. (2026) NoahPy: a differentiable Noah land surface model for simulating permafrost thermo-hydrology

Identification

• Journal: Geoscientific model development
• Year: 2026
• Date: 2026-01-06
• Authors: Wenbiao Tian, Hu Yu, Shuping Zhao, Yuhe Cao, Wenjun Yi, Jiwei Xu, Zhuotong Nan
• DOI: 10.5194/gmd-19-57-2026

Research Groups

• State Key Laboratory of Climate System Prediction and Risk Management, Nanjing Normal University, Nanjing, China
• Key Laboratory of Ministry of Education on Virtual Geographic Environment, Nanjing Normal University, Nanjing, China
• North Information Control Research Academy Group Co., Ltd., Nanjing, China
• College of Forestry, Northeast Forestry University, Harbin, China
• Jiangsu Center for Collaborative Innovation in Geographical Information Resource Development and Application, Nanjing, China

Short Summary

This paper introduces NoahPy, a differentiable land surface model (LSM) for permafrost thermo-hydrology, developed by re-implementing the modified Noah LSM within a PyTorch-based Recurrent Neural Network (RNN) framework. NoahPy accurately replicates the original model's behavior and enables significantly faster, more stable, and lower-uncertainty parameter optimization using gradient-based methods compared to traditional approaches.

Objective

• To develop NoahPy, a differentiable land surface model for simulating permafrost thermo-hydrology, by reconstructing the modified Noah LSM's governing partial differential equations into a process-encapsulated Recurrent Neural Network (RNN) within a Python framework.
• To validate NoahPy's numerical equivalence to the original Fortran-based modified Noah LSM.
• To demonstrate NoahPy's capability for robust and efficient gradient-based parameter optimization using observational data from a permafrost site, and compare its performance against traditional calibration algorithms.

Study Configuration

• Spatial Scale:
  • Numerical equivalence validation: Three randomly selected grid cells on the Qinghai-Tibet Plateau (QTP) (28.75° N, 93.85° E; 34.75° N, 98.25° E; 37.55° N, 100.55° E).
  • Backpropagation and performance comparison: Tanggula (TGL) permafrost site on the QTP.
  • Soil column depth: 15.2 meters (18 layers) for numerical equivalence; 40 meters (20 layers, with specific depths up to 14.8 meters) for TGL site.
• Temporal Scale:
  • Numerical equivalence validation: Simulation period 2000–2010, with a 500-year spin-up using 1999 data.
  • Backpropagation and performance comparison: Simulation period 1 April 2007 to 31 December 2010; training period 1 April 2007 to 31 December 2009; validation period 1 January 2010 to 31 December 2010.

Methodology and Data

• Models used:
  • NoahPy: A differentiable land surface model implemented in Python using PyTorch, based on the modified Noah LSM.
  • Modified Noah LSM: A Fortran-based version of the Noah LSM (v3.4.1) with improvements for permafrost applications.
  • Original Noah LSM (v3.4.1).
  • Optimization algorithms: Adam optimizer (gradient-based, for NoahPy), Shuffled Complex Evolution (SCE-UA) algorithm (gradient-free, for modified and original Noah LSMs).
• Data sources:
  • China Meteorological Forcing Dataset (ITP-forcing) for 2000–2010 (for numerical equivalence validation).
  • MSTD dataset for soil types and 1:1,000,000 China Vegetation Type Map (for numerical equivalence validation).
  • Daily meteorological observations from the TGL station (air temperature, wind speed, relative humidity, incoming shortwave and longwave radiation, precipitation) for 1 April 2007 to 31 December 2010 (for backpropagation validation).
  • In-situ observations of active layer soil temperature and liquid water content from the TGL site (for model calibration and validation).

Main Results

• NoahPy faithfully reproduces the numerical behavior of the Fortran-based modified Noah LSM, achieving Nash-Sutcliffe Efficiency (NSE) coefficients above 0.999 and near-zero bias (< 0.01) for both soil temperature and liquid water content across all tested depths.
• At the Tanggula permafrost site, the calibrated NoahPy demonstrates robust simulation performance, with NSE values exceeding 0.9 for soil temperature and 0.8 for liquid water content.
• The differentiable NoahPy, when combined with the Adam optimizer, achieves significantly faster convergence (within approximately 100 iterations) and greater stability (narrower 95% uncertainty band) during parameter optimization compared to the traditional SCE-UA algorithm.
• While all models perform well for shallow soil temperature (NSE > 0.9), NoahPy and the modified Noah LSM significantly outperform the original Noah LSM in deep soil, which exhibits a pronounced cold bias (Root Mean Square Error (RMSE) of 1.68 °C at 2.45 meters) and poor liquid water simulation (NSE of -0.09 at 2.45 meters).
• Statistical analysis (Friedman and Dunn's post-hoc tests) confirms that NoahPy and the modified Noah LSM perform significantly better than the original Noah LSM, with NoahPy offering practical advantages in optimization efficiency and lower uncertainty.

Contributions

• Development of NoahPy, the first differentiable land surface model specifically improved for permafrost thermo-hydrology, by re-implementing the modified Noah LSM in a PyTorch-based Python framework.
• Closes a critical technical gap by enabling gradient-based optimization for a complex process-based permafrost model, making it compatible with modern artificial intelligence (AI) workflows.
• Provides a "glass-box" modeling framework that maintains physical interpretability while allowing for efficient, end-to-end training and seamless integration into hybrid AI-physics models.
• Demonstrates that differentiable modeling significantly enhances the speed, stability, and robustness of parameter calibration compared to traditional gradient-free methods.
• Lays foundational groundwork for the next generation of hybrid Earth System Models, enabling more reliable predictions of cryosphere changes and addressing long-standing parameter uncertainty challenges in permafrost modeling.

Funding

• National Key Research and Development Program of China (grant no. 2022YFF0711703)
• National Natural Science Foundation of China (grant nos. 42171125 and 42571149)

Citation

@article{Tian2026NoahPy,
  author = {Tian, Wenbiao and Yu, Hu and Zhao, Shuping and Cao, Yuhe and Yi, Wenjun and Xu, Jiwei and Nan, Zhuotong},
  title = {NoahPy: a differentiable Noah land surface model for simulating permafrost thermo-hydrology},
  journal = {Geoscientific model development},
  year = {2026},
  doi = {10.5194/gmd-19-57-2026},
  url = {https://doi.org/10.5194/gmd-19-57-2026}
}