Moving Spectral Variance and Coherence Analysis and Some Applications on Long Air Temperature Series

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Abstract
Climatic records of a long time series (e.g., centuries) may be nonstationary. Thus, the stability of the variance (power) spectrum over a sequence of time periods is examined. Moreover, it is important to use different algorithms and tests in cases where there is an unknown or problematical physical background. Variance spectra of Hohenpeissenberg (FRG) annual mean air temperatures are compared using two methods, autocorrelation spectral analysis (ASA) and maximum entropy spectral analysis (MESA). These spectra are then compared with corresponding spectra based on Northern Hemisphere mean air temperature reconstructions where the ASA and MESA results are very similar. The application of a moving (running, “dynamic”) variance spectrum analysis shows that, in general, the signals found in the customary “integrated” spectrum vary as time varies, namely in their occurrence, significance and “bandwidth.” These findings are presented in terms of either contour lines of the relative variance (MESA) or contour lines of the confidence levels exceeded (ASA), where 50-yr subsamples are “moved” in 10-yr steps. Similarly, coherence spectra can be computed in moving terms. As an example the Northern Hemisphere data are spectrally correlated with the corresponding central England and Philadelphia air temperature series. It is shown that the coherencies are not stable in time, and that the spectral characteristics throw considerable doubt on the reliability of the reconstructed Northern Hemisphere temperature series prior to 1881. In general, moving spectral analysis of climatic time series improves the interpretation of climatic change.

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