Model evaluation and spatial interpolation by Bayesian combination of observations with outputs from numerical models

Constructing maps of dry deposition pollution levels is vital for air quality management, and presents statistical problems typical of many environmental and spatial applications. Ideally, such maps would be based on a dense network of monitoring stations, but this does not exist. Instead, there are two main sources of information for dry deposition levels in the United States: one is pollution measurements at a sparse set of about 50 monitoring stations called CASTNet, and the other is the output of the regional scale air quality models, called Models-3. A related problem is the evaluation of these numerical models for air quality applications, which is crucial for control strategy selection. We develop formal methods for combining sources of information with different spatial resolutions and for the evaluation of numerical models. We specify a simple model for both the Models-3 output and the CASTNet observations in terms of the unobserved ground truth, and we estimate the model in a Bayesian way. This provides improved spatial prediction via the posterior distribution of the ground truth, allows us to validate Models-3 via the posterior predictive distribution of the CASTNet observations, and enables us to remove the bias in the Models-3 output. We apply our methods to data on SO2 concentrations, and we obtain high-resolution SO2 distributions by combining observed data with model output. We also conclude that the numerical models perform worse in areas closer to power plants, where the SO2 values are overestimated by the models.