Hierarchical Bayesian space-time estimation of monthly maximum and minimum surface air temperature

Surface air temperature (SAT) is a critical metric that is used to assess regional warming and cooling patterns, and maximum and minimum SATs are required to evaluate the model predictions of climate extremes. Since station SAT data are irregularly distributed, land surface temperature (LST) values derived from Moderate Resolution Imaging Spectroradiometer (MODIS) data are used to estimate regional SAT by using linear regression methods. The deviations between SAT and LST are largely dependent on space and time, which hampers the estimation of linear regression, especially for the maximum SAT. To obtain accurate regional SAT estimates, a three-stage hierarchical Bayesian (HB) model is proposed that incorporates the MODIS LSTs as model covariates and specifies the deviations with structured dependence of MODIS LST fields. Sampling of model parameters and estimation of SAT values are implemented under the Bayesian paradigm using a Markov Chain Monte Carlo algorithm. Sensitivity analyses involving various model configurations and running processes are discussed to help build a robust HB model. The model's performance is evaluated using station measurements that are not used in the modeling process, with RMSEs of 2.15 K (0.75%) and 1.97 K (0.73%) for monthly maximum and minimum SATs, respectively. The evaluation indicates that HB modeling is an effective method to estimate SAT from MODIS LST. The verified HB model with the covariate inputs of both MODIS daytime and nighttime LSTs is used to reproduce monthly maximum and minimum SATs that are spatially continuous over the Qinghai province in Northwestern China for 2003-2011. From the comparison between MODIS LST and HB-estimated SAT, it is found that the spatial structure and warming patterns of LST and SAT show significant distinctions, implying that they cannot be substituted for one another when assessing the regional warming trends. The spatial heterogeneity of HB model estimation is able to provide thorough insights into regional SAT status changes that could otherwise be biased by station deployment.