Keywords: climate models, spatial Gaussian random field, Bayesian hierarchical models, Markov Chain Monte Carlo
Climate scientists have been developing a lot of climate models for variables of interest, like temperature, pressure, based on physical dynamics. Due to different techniques in implementing the climate models and the uncertainty in the climate system, the variable values are not identical from different model outputs. Actually, they can be treated as a representation of the climate system. Many statistics scientists keep working on sensible statistical models to combine different climate model outputs, but most of them assume all the climate model outputs are exchangeable. In fact, many climate models may have similar origins or share common components, leading to dependence among each model. In this work, we present a Bayesian hierarchical model to account for the model dependence, which gives a good inference for the underlying process for the variable of interest. In addition, we use spatial Gaussian random field to allow for spatial correlation in the modeling, offering us a sensible map for the inference on the future state of the climate.