Space–time modeling of 20 years of daily air temperature in the Chicago metropolitan region

Abstract

AbstractWe analyze 20 years of daily minimum and maximum air temperature data in the Chicago metropolitan region and propose a parsimonious model that describes their mean function and the space–time covariance structure. The mean function contains a long‐term trend, annual and semiannual harmonics, and physical covariates such as latitude, distance to the Lake Michigan, and winds, each interacted with the harmonic terms, thus allowing the effects of physical covariates to vary smoothly over time. The temporal correlation at a given location is described using an ARMA(1,2) model. The residuals (innovations) from this models are treated as independent replications of a spatial process with covariance structure in the Matérn class. The space–time covariance structure parameters are allowed to vary seasonally. Using the estimated covariance structure, we interpolate the temperature to a fine grid in the Chicago metropolitan region. This procedure borrows information from temporally and spatially adjacent data. The methods presented in this paper should be useful to approach other environmental problems where the data are discrete and regular in time but irregular in space. Copyright © 2008 John Wiley & Sons, Ltd.