Parameter estimation for land-surface models using Neural Physics

TL;DR

The paper tackles parameter estimation for urban land-surface models by using Neural Physics to create a differentiable forward solver for a simple soil–surface energy balance system. It shows that single-depth soil temperature data lead to non-unique, correlated parameter estimates, while incorporating a second depth enables reliable recovery of key parameters such as thermal conductivity, heat capacity, and the combined heat transfer coefficient. The method is validated with synthetic data and applied to West Phoenix flux-tower observations, yielding plausible parameter values and good agreement with independent quantities. The study demonstrates a data-efficient, gradient-based calibration workflow that can inform urban microclimate modelling and potentially extend to more complex LSMs with further refinements.

Abstract

The Neural Physics approach is used to determine the parameters of a simple land-surface model using PyTorch's backpropagation engine to carry out the optimisation. 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 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 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.

Figures (5)

• Figure 1: Definition sketch of the domain with the governing equations and boundary conditions. Shown on the right are the nodes of the discretised problem.
• Figure 2: Flow diagram of the inverse model
• Figure 3: Scatter plots of initial vs final values for the synthetic data set of a) surface albedo $\alpha$, b) heat transfer coefficient $h$, c) Bowen ratio $\beta$, d) $h(1+\beta^{-1})$, e) Initial/interior temperature $T_b$, f) volumetric heat capacity $C$, g) thermal conductivity $\lambda$ and h) $\mu$ compared with their true values (black dotted line)
• Figure 4: Covariance plots of final parameter values for the synthetic dataset of a) $\beta$ against $h$; and b) $\lambda$ against $C$
• Figure 5: Comparison of modelled and recorded data for the West Phoenix flux tower dataset. a) Temperatures at 0.05 m and 0.15 m depth. b) Ground heat flux at 0.02 m depth. c) Outgoing long-wave radiation. d) Combined sensible-latent heat flux