Physics-constrained Gaussian process regression for soil moisture dynamics

Leilei He

doi:10.1016/j.jhydrol.2022.128779

2023-01-01

PRE

DOI：10.1016/j.jhydrol.2022.128779

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摘要

En 中文

Soil moisture (SM) is a crucial variable in the hydrological cycle and several recent studies have been conducted to model it using a hybrid strategy integrating physical-based and data-driven approaches. However, such methods pay little attention to the flaws of the introduced physics constraints, and the inherent nonlinearity of the soil flow process poses a challenge to their real-world application. In this study, a new physics-constrained scheme is proposed to exploit or avoid the adverse effects of the model error. Based on the reasonable assessment of model uncertainty, traditional physical model simulations are dynamically weighted to fuse into a data-driven framework based on Gaussian process regression (GPR) to utilize the respective strengths of both paradigms. For comparison, we also implement a scheme that introduces the gradient from the data as an implicit constraint. The effectiveness of the proposed paradigm is tested with a series of real-world cases. The results show that the physical model based on Richards' equation runs the risk of failing to guarantee even a basic water balance in real soil moisture simulations, which raises a red flag about the introduction of physics constraints, such as in the deep layers of the Goodwell site, the coefficient of determination (R2) predicted by the physical model is even less than 0.2 due to the neglect of the preferential flow process. In contrast, the proposed hybrid scheme significantly improves the accuracy and robustness of the soil moisture retrieval by weighing the reliability of the prediction results, with the R2 of the surface layer at Las Cruses site improving to 0.82 compared to 0.45 for the purely data-driven model. The comparison of the different forms of constraints further demonstrates the generalizability of our proposed constraint scheme.

Keyword:

Soil moisture

Physics-constrained

Hybrid modeling

Gaussian process regression

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