Abstract Emission reductions were mandated in the Clean Air Act Amendments of 1990 with the expectation that they would result in major reductions in the concentrations of atmospherically transported pollutants. The emission reductions are intended to reduce public health risks and to protect sensitive ecosystems. To determine whether the emission reductions are having the intended effect on atmospheric concentrations, monitoring data must be analyzed taking into consideration the spatial structure shown by the data. Maps of pollutant concentrations and fluxes are useful over different geopolitical boundaries, to discover when, where, and to what extent the U.S. Nation's air quality is improving or declining. Since the spatial covariance structure shown by the data changes with location, the standard kriging methodology for spatial interpolation cannot be used because it assumes stationarity of the process. We present a new methodology for spatial interpolation of non‐stationary processes. In this method the field is represented locally as a stationary isotropic random field, but the parameters of the stationary random field are allowed to vary across space. A procedure for interpolation is presented that uses an expression for the spectral density at high frequencies. New fitting algorithms are developed using spectral approaches. In cases where the data are distributed exactly or approximately on a lattice, it is argued that spectral approaches have potentially enormous computational benefits compared with maximum likelihood. The methods are extended to interpolation questions using approximate Bayesian approaches to account for parameter uncertainty. We develop applications to obtain the total loading of pollutant concentrations and fluxes over different geo‐political boundaries. Copyright © 2001 John Wiley & Sons, Ltd.
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