A Test for Inhomogeneous Variance in Time-averaged Temperature Data

Mary W. Downton National Center for Atmospheric Research,* Boulder, Colorado

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Richard W. Katz National Center for Atmospheric Research,* Boulder, Colorado

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Abstract

Many climatic applications, including detection of climate change, require temperature time series that are free from discontinuities introduced by nonclimatic events such as relocation of weather stations. Although 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 analogous to that developed by Karl and Williams to adjust for nonclimatic inhomogeneities in the mean. It uses the nonparametric bootstrap technique to compute confidence intervals for the discontinuity in variance. The method is tested on 1901–88 summer and winter mean maximum temperature data from 21 weather stations in the midwestern United States. The reasonableness, reliability, and accuracy of the estimated changes in variance are evaluated.

The bootstrap technique is found to be a valuable tool for obtaining confidence limits on the proposed variance adjustment. Inhomogeneities in variance are found to be more frequent than would be expected by chance in the summer temperature data, indicating 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 available. However, estimates of the changes in the standard deviation may be unreliable when less than 10 years of data are available before or after a potential discontinuity. This statistical test can be a useful tool for screening out stations that have unacceptably large discontinuities in variance.

Abstract

Many climatic applications, including detection of climate change, require temperature time series that are free from discontinuities introduced by nonclimatic events such as relocation of weather stations. Although 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 analogous to that developed by Karl and Williams to adjust for nonclimatic inhomogeneities in the mean. It uses the nonparametric bootstrap technique to compute confidence intervals for the discontinuity in variance. The method is tested on 1901–88 summer and winter mean maximum temperature data from 21 weather stations in the midwestern United States. The reasonableness, reliability, and accuracy of the estimated changes in variance are evaluated.

The bootstrap technique is found to be a valuable tool for obtaining confidence limits on the proposed variance adjustment. Inhomogeneities in variance are found to be more frequent than would be expected by chance in the summer temperature data, indicating 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 available. However, estimates of the changes in the standard deviation may be unreliable when less than 10 years of data are available before or after a potential discontinuity. This statistical test can be a useful tool for screening out stations that have unacceptably large discontinuities in variance.

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