Parameter estimation for land-surface models using Neural Physics

We propose a novel inverse-modelling approach that estimates the parameters of a simple land-surface model (LSM) by assimilating data into a differentiable, physics-based forward model formulated using convolutional operations. The governing equations are expressed within the Neural Physics framework, allowing direct gradient-based optimisation of time-dependent parameters without the need to derive and maintain adjoint formulations. The model parameters are estimated by minimising the mismatch between model predictions and synthetic or observational data. Although differentiability is enabled through machine-learning libraries, the forward model itself remains entirely physics-based and neither the forward model nor the parameter estimation procedure involve training. To evaluate the approach, we first generate synthetic observations of soil temperature by running the forward model with known parameter values and subsequently treat these parameters as unknown in an inverse problem. We show that observations of soil temperature at a single depth are insufficient to reliably constrain the model parameters. Using observations at two depths, however, does yield reliable parameter estimates, although the individual contributions of latent and sensible heat fluxes cannot be distinguished. We also apply the approach to urban flux tower data from Phoenix, United States, and show that the thermal conductivity, volumetric heat capacity and the combined sensible-latent heat transfer coefficient can be reliably estimated whilst 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, demonstrating that the Neural Physics framework can be used to accurately determine the parameters of the particular LSM used here. This model is intentionally simple and does not include, for example, a subsurface moisture model. This simplicity facilitates an exploration of parameter identifiability, confounding and equifinality.