A Bayesian Approach for the Spatiotemporal Interpolation of Environmental Data

Numerically based models are extensively used for many environmental applications, as for example, to assist in the prediction of weather phenomena (numerical weather prediction models), in risk assessment, or in pollutant emission control (air-quality models). These models often produce predictions for grid points over some temporal window, while observations are usually available as a set of spatially scattered values at individual locations (not coincident with the model grid points), so that the model assessment procedure, that is, the statistical evaluation of how well model output compares with observed data, should address the issue of comparing the grid-based model results with interpolated values estimated from observed data at a different spatial resolution. In this paper, a Bayesian inference procedure for the spatiotemporal interpolation of environmental data from irregularly spaced monitoring sites is presented. The spatial interpolation is based on the use of the predictive posterior distribution. It is shown how this procedure can be exploited to obtain statistically consistent interpolated values (at the same spatial resolution as that of model results) and valid standard errors for these estimates. Comparisons of the wind speed fifth-generat ion Pennsylvania State University-NCAR Mesoscale Model (MM5) results against grid-cell values estimated from observed data are presented