Influence of spatial sampling and interpolation on estimates of air temperature change

When observed air temperatures are analyzed spatially, irregularly sampled data are usually interpolated in some fashion. As a result, methods of spatial analysis clearly play a role in determining the size and variability of estimated air temperature changes, both spatially and temporally. Through graphical and statistical analysis, 3 spherically based interpolation methods inversedistance weighting, triangulated surface patches, and thin-plate splines are evaluated and compared using air temperature anomaly data. Analysis of errors resulting from spatial interpolation provides information about the strengths and weaknesses of historical station networks. Analysis of differences between the 3 interpolation methods suggests that similar spatial patterns are produced, but with some regional disparities. Mean absolute differences between interpolation methods can be over 0.4 "C for some sparse statlon networks and as low as O.l°C for dense station networks. When averaged spatially, however, the differences tend to offset one another, producing time series of terrestrial average air temperature anomalies that are largely independent of spatial interpolation method. Using cross validation to analyze spatial interpolation errors suggests that sparse station networks can produce nontrivial interpolation errors. Station networks from the late 1800s produce average interpolation errors of nearly 0.5"C, errors that are similar in magnitude to spatial standard deviations of air temperature anomalies. Denser station networks, typical of the 1950s and 1960s, produce average interpolation errors as low as 0.2OC. While these regional interpolation errors do not appear to influence estimates of terrestrial average air temperature, they do raise additional concerns regarding our ability to detect small climatic signals at regional scales.