A TEST FOR INHOMOGENEOUS VARIANCE IN TIME-AVERAGED TEMPERATURE DATA

Many climatic applications, including detection of climate change, req uire temperature time series that are free from discontinuities introd uced by nonclimatic events such as relocation of weather stations. Alt hough much attention has been devoted to discontinuities in the mean, possible changes in the variance have not been considered. A method is proposed to test and possibly adjust for nonclimatic inhomogeneities in the variance of temperature time series. The method is somewhat ana logous to that developed by Karl and Williams to adjust for nonclimati c inhomogeneities in the mean. It uses the nonparametric bootstrap tec hnique to compute confidence intervals for the discontinuity in varian ce. The method is tested on 1901-88 summer and winter mean maximum tem perature data from 21 weather stations in the midwestern United States . The reasonableness, reliability, and accuracy of the estimated chang es in variance are evaluated. The bootstrap technique is found to be a valuable tool for obtaining confidence limits on the proposed varianc e adjustment. Inhomogeneities in variance are found to be more frequen t than would be expected by chance in the summer temperature data, ind icating that variance inhomogeneity is indeed a problem. Precision of the estimates in the test data indicates that changes of about 25%-30% in standard deviation can be detected if sufficient data are availabl e. However, estimates of the changes in the standard deviation may be unreliable when less than 10 years of data are available before or aft er a potential discontinuity. This statistical test can be a useful to ol for screening out stations that have unacceptably large discontinui ties in variance.