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The Tibetan Plateau (TP) has experienced rapid warming in recent decades. However, the meteorological stations of the TP are scarce and mostly located at the eastern and southern parts of the TP where the elevation is relatively low, which increases the uncertainty of regional and local climate studies. Recently, the remotely sensed land surface temperature (LST) has been used to estimate the surface air temperature (SAT). However, the thermal infrared based LST is prone to cloud contamination, which limits the availability of the estimated SAT. This study presents a novel all sky model based on the rule-based Cubist regression to estimate all sky daily average SAT using LST, incident solar radiation (ISR), top-of-atmosphere (TOA) albedo and outgoing longwave radiation (OLR). The model is trained using station data of the Chinese Meteorological Administration (CMA) and corresponding satellite products. The output is evaluated using independent station data with the bias of -0.07 degrees C and RMSE of 1.87 degrees C. Additionally, the 25-fold cross validation shows a stable model performance (RMSE: 1.6-2.8 degrees C). Moreover, the all sky Cubist model increases the availability of the estimated SAT by nearly three times. We used the all sky Cubist model to estimate the daily average SAT of the TP for 2002-2016 at 0.05 degrees x 0.05 degrees. We compared our all sky Cubist model estimated daily average SAT with three existing data sets (i.e., GLDAS, CLDAS, and CMFD). Our model estimation shows similar spatial and temporal dynamics with these existing data sets but outperforms them with lower bias and RMSE when benchmarked against the CMA station data. The estimated SAT data could be very useful for regional and local climate studies over the TP. Although the model is developed for the TP, the framework is generic and may be extended to other regions with proper model training using local data.