Spatial Interpolation of Nonstationary Environmental Processes

Atmospheric pollutant concentrations and fluxes are measured at points, estimated by models in grids, and desired by the community as total loadings over areas defined by ecological or geo-political boundaries. The spatial distribution of the pollutant concentrations and fluxes is determined by the spatio-temporal distribution of sources, the weather, seasonal cycles, land cover, plant growth rate, topography, and other factors. The present generation of regional scale air quality models can consider these factors in estimating pollutant concentrations and fluxes in a grid, while the networks run by EPA measure these variables at 50 sites irregularly spaced in the eastern U.S. Because spatial patterns of pollutant fluxes and concentrations are nonstationary, standard methods of spatial interpolation are inadequate. Therefore, we present a new methodology for spatial interpolation of nonstationary fields, that we call "high frequency kriging" and will be used to interpolate the EPA point measurements to desired geographic areas. We prove that the validity of local interpolation procedures, such as kriging, depend on the spatial variation, over the domain of interest, of the ratio of the variance of the process and the range of spatial autocorrelation. We present a method to stabilize this ratio and then efficiently obtain the loading of pollutant concentrations and fluxes over different geo-political boundaries. The methodology presented here is based on analyses using local spectral representations of the spatial process.