Challenges in Unifying Physically Based and Machine Learning Simulations Through Differentiable Modeling: A Land Surface Case Study

Differentiable geoscientific modeling has shown promise for leveraging machine learning (ML) to unify physically based and data-based modeling. Here, we critically analyze this promise in the context of large-scale parameter optimization with the Noah-MP land model as an example. The differentiable parameter learning framework is used to calibrate Noah-MP soil and vegetation parameters such that the simulated surface soil moisture better matches satellite observations over the contiguous US. We found that the optimized parameters only marginally improved soil moisture (average RMSE = 0.092 m³ m⁻³) upon uncalibrated Noah-MP (RMSE = 0.10 m³ m⁻³). Scaling and bias correction factors, often used in ML approaches for enhancing generalizability, were found to limit the transferability of the optimized physical parameters to the land model. The global objective function further compromises the algorithm's ability to simultaneously capture contrasting moisture regimes. Addressing these challenges is necessary to advance ML-based calibration frameworks to better learn and represent the constraints of the physical model.