The Neural Networks for Partial Differential Equations (NN4PDEs) approach is used to determine the parameters of a simple land-surface model using PyTorch's backpropagation engine. In order to test the inverse model, a synthetic dataset is created by running the model in forward mode with known parameter values to create soil temperature time series that can be used as observations for the inverse model. We show that it is not possible to obtain a reliable parameter estimation using a single observed soil temperature time series. Using measurements at two depths, reliable parameter estimates can be obtained although it is not possible to differentiate between latent and sensible heat fluxes. We apply the inverse model to urban flux tower data in Phoenix, United States, and show that the thermal conductivity, volumetric heat capacity, and the combined sensible-latent heat transfer coefficient can be reliably estimated using an observed value for the effective surface albedo. The resulting model accurately predicts the outgoing longwave radiation, conductive soil fluxes and the combined sensible-latent heat fluxes.
View on arXiv@article{huang2025_2505.02979,
title={ Parameter estimation for land-surface models using machine learning libraries },
author={ Ruiyue Huang and Claire E. Heaney and Maarten van Reeuwijk },
journal={arXiv preprint arXiv:2505.02979},
year={ 2025 }
}