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.

翻译：我们提出了一种新颖的逆建模方法，通过同化数据到可微分的基于物理的正向模型中，来估计简单地表模型（LSM）的参数。控制方程采用神经物理方法在机器学习框架内表达，从而无需推导和维护伴随公式，即可直接对时间相关参数进行基于梯度的优化。模型参数通过最小化模型预测与合成数据或观测数据之间的不匹配来更新。尽管可微性是通过机器学习库的功能实现的，但正向模型本身完全基于物理原理，正向模型和参数估计的任何部分均不涉及训练。为测试该方法，我们使用已知参数值运行正向模型生成合成数据集，获得土壤温度时间序列作为逆问题的观测数据，其中参数被假设为未知并随后进行估计。结果表明，仅使用单个深度的土壤温度时间序列无法获得可靠的参数估计。利用两个深度的测量数据可获得可靠的参数估计，但无法区分潜热通量和感热通量。我们还将该方法应用于美国凤凰城的城市通量塔数据，结果表明，在使用观测的有效地表反照率时，热导率、体积热容以及组合感热-潜热传递系数均能被可靠估计。