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Acquiring cloudy land surface temperature (LST) is crucial for terrestrial ecosystem monitoring and global climate observation. Although numerous methods have been proposed to retrieve cloudy-sky LST using microwave remote sensing, the physical significance of these methods is inadequate due to their oversimplification of the effects of atmospheric components and clouds. To obtain accurate cloudy-sky LST, by simultaneously considering the influences of water vapor and cloud properties on LST, a physics-based LST retrieval algorithm is developed for cloudy skies with adjacent three brightness temperatures (BTs) at 18.7, 23.8, and 36.5 GHz vertically polarization. We develop this algorithm by building a simulated database, which includes a large range of BTs, surface emissivities, air temperatures, and water vapor contents. Meanwhile, various cloudy atmospheric profiles are constructed to reveal multifarious weather conditions. The test results with the simulated database show that the algorithm has good accuracy with an RMSE of 1.75 K and MAE of 1.33 K under cloudy weather. Sensitivity analysis indicates that precipitable water vapor (PWV) and cloud liquid water (CLW) are indispensable for correcting cloudy LST. In particular, LST accuracy shows an evident sensitivity to PWV, and RMSEs are reduced with an increase in PWV. Meanwhile, the proposed algorithm was applied to AMSR-E BTs and ERA5 profile dataset over the China region in 2008 and validated with ground-based air temperatures. Results indicate that RMSEs between retrieved LSTs and true LSTs are 3.47 K for cloudy weather, and there is better performance at high water vapor status, with an RMSE of 2.05 K.