ENVIRONMETRICS Environmetrics 2001; 12: 673±690 DOI: 10.1002/env.468) Temperature trends in the United States Robert Lund, 1 * Lynne Seymour 1 and Karen Kafadar 2 1 Department of Statistics, The University of Georgia, Athens, GA 30602-1952, U.S.A 2 Department of Mathematics, The University of Colorado - Denver, Denver, CO 80217-3364, U.S.A SUMMARY Linear temperature trends and their uncertainties from data at 359 recording stations in the contiguous United States are investigated. A statistical model is developed that accounts for changes in the site location of each station, the seasonal means and variances inherent in monthly temperature series, and the temporal and spatial correlations found in such data. Least squares estimates of the seasonal trend parameters in the model are derived, as well as appropriate standard errors that take into account the site changes, periodicities and temporal correlations present in the data. The estimates and their standard errors at each station are then spatially analyzed to identify geographical patterns of temperature change across the United States. Copyright # 2001 John Wiley & Sons, Ltd. key words: time series; linear trend; least squares; standard error; correlation; seasonality 1. INTRODUCTION Temperature trends have substantial effects on both environmental and human resources and hence are important quantities to estimate. Even slight changes in temperatures can affect many aspects of life. The objective of this article is to develop accurate estimates of long-term temperature trends from monthly temperature time series, as well as realistic standard errors that account for all prominent statistical features in the data. For each temperature recording station, these features include temporal correlation, changepoints induced by changes in station location, and seasonal cycles in the ®rst two moments of the data. To characterize geographical patterns of temperature change, a spatial analysis of the trends is performed. Many authors have analyzed temperature changes by estimating linear trends cf. Roden, 1966; Jones and Kelly, 1983; Pruscha, 1986; Jones, 1988; Karoly, 1989; Vinnikov et al., 1990). Temperature trends in North America and the United States speci®cally have also been studied cf. Diaz and Quayle, 1980; Karl et al., 1995; Walsh, 1997). The global temperature trend studies of Ellsaesser et al. 1986), Hansen and Lebedeff 1987), Trenberth 1990) and van Loon 1991) also contain information about temperature trends in the United States. Our methods make three contributions to temperature trend analyses. The ®rst contribution involves the development of accurate standard errors for the trend estimates. If temporal correlations in the data are ignored, the standard error of the trend estimate can underestimate the true standard Received 14 June 2000 Copyright # 2001 John Wiley & Sons, Ltd. Accepted 12 September 2000 *Correspondence to: R. Lund, Department of Statistics, The University of Georgia, Athens, GA 30602-1952, U.S.A.