  More accurate, spatio-temporally, and physically consistent LST estimation
has been a main interest in Earth system research. Developing physics-driven
mechanism models and data-driven machine learning (ML) models are two major
paradigms for gapless LST estimation, which have their respective advantages
and disadvantages. In this paper, a physics-constrained ML model, which
combines the strengths in the mechanism model and ML model, is proposed to
generate gapless LST with physical meanings and high accuracy. The hybrid model
employs ML as the primary architecture, under which the input variable physical
constraints are incorporated to enhance the interpretability and extrapolation
ability of the model. Specifically, the light gradient-boosting machine (LGBM)
model, which uses only remote sensing data as input, serves as the pure ML
model. Physical constraints (PCs) are coupled by further incorporating key
Community Land Model (CLM) forcing data (cause) and CLM simulation data
(effect) as inputs into the LGBM model. This integration forms the PC-LGBM
model, which incorporates surface energy balance (SEB) constraints underlying
the data in CLM-LST modeling within a biophysical framework. Compared with a
pure physical method and pure ML methods, the PC-LGBM model improves the
prediction accuracy and physical interpretability of LST. It also demonstrates
a good extrapolation ability for the responses to extreme weather cases,
suggesting that the PC-LGBM model enables not only empirical learning from data
but also rationally derived from theory. The proposed method represents an
innovative way to map accurate and physically interpretable gapless LST, and
could provide insights to accelerate knowledge discovery in land surface
processes and data mining in geographical parameter estimation.
