Spatial Interpolation, Network Bias, and Terrestrial Air Temperature Variability

Variations in air temperature have profound impacts on our planetary environment. Estimating air temperature variability, therefore, is of considerable importance not only for environmental analyses, but for assessing social and economic impacts as well. Although a variety of approaches (e.g., mathematical modeling, analysis of satellite and paleoclimatic data) are used to analyze air temperature variability, estimates made from observational station networks still are considered the most reliable. Estimates of air temperature change made from station data, nonetheless, are subject to several types of error. While observational errors have been identified at station locations, errors related to using sparse and highly irregular spatial and temporal distributions of stations (i.e., network bias) have not been assessed adequately. Since irregularly spaced data usually are interpolated to obtain a terrestrial average, methods of spatial analysis clearly play a role in determining estimates of air temperature change. Through graphical and statistical analysis, several spherically-based interpolation methods--inverse distance -weighting, triangular surface patches, and smoothing by functional minimization--are evaluated and compared. Analysis of spatial interpolation errors also provides information about the strengths and weaknesses of the station network. Cross validation and other resampling methods are used to evaluate interpolation methods and the station network for both air temperature anomalies and raw air temperatures. Cross validation analysis of air temperature anomalies suggests that errors are nontrivial and, for some years, interpolation error may be as large as estimates of temperature trends over the last century. Resampling from the station network also suggests substantial network induced variability in estimates of global change. By removing spatial variability, reducing air temperatures to anomalies from a station mean does reduce interpolation error relative to raw air temperatures. At the same time, however, valuable information needed for physically based studies (e.g., radiative emission, phase changes of water, etc.) is removed. To obtain reliable air temperature space-time series, information from a high -resolution climatology is incorporated to reduce interpolation error.