We propose a novel inverse-modelling approach which estimates the parameters of a simple land-surface model (LSM) by assimilating data into a differentiable physics-based forward model. The governing equations are expressed within a machine-learning framework using the Neural Physics approach, allowing direct gradient-based optimisation of time-dependent parameters without the need to derive and maintain adjoint formulations. The model parameters are updated by minimising the mismatch between model predictions and synthetic or observational data. Although differentiability is achieved through functionality in machine-learning libraries, the forward model itself remains entirely physics-based and no part of either the forward model or the parameter estimation involves training. In order to test the approach, a synthetic dataset is generated by running the forward model with known parameter values to create a time series of soil temperature that serves as observations for an inverse problem in which the parameters are assumed unknown and subsequently estimated. We show that it is not possible to obtain a reliable estimate of the parameters using a time series of soil temperature observed at a single depth. 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 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.

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