Interpolation of nonstationary air pollution processes: a spatial spectral approach

Spatial processes are important models for many environmental problems. Classical geostatistics and Fourier spectral methods are powerful tools for stuyding the spatial structure of stationary processes. However, it is widely recognized that in real applications spatial processes are rarely stationary and isotropic. Consequently, it is important to extend these spectral methods to processes that are nonstationary. In this work, we present some new spectral approaches and tools to estimate the spatial structure of a nonstationary process. More specifically, we propose an approach for the spectral analysis of nonstationary spatial processes that is based on the concept of spatial spectra, i.e., spectral functions that are space-dependent. This notion of spatial spectra generalizes the definition of spectra for stationary processes, and under certain conditions, the spatial spectrum at each Location can be estimated from a single realization of the spatial process. The motivation for this work is the modeling and prediction of ozone concentrations over different geopolitical boundaries for assessment of compliance with ambient air quality standards.