Abstract
Part of the debate over possible climate changes centers on the possibility that the changes observed over the previous century are natural in origin. This raises the question of how large a change could be expected as a result of natural variability. If the climate measurement of interest is modelled as a stationary (or related) Gaussian time series, this question can be answered in terms of (a) the way in which change is estimated, and (b) the spectrum of the time series. These computations are illustrated for 128 years of global temperature data using some simple measures of change and for a variety of possible temperature spectra. The results highlight the time scales on which it is important to know the magnitude of natural variability. The uncertainties in estimates of trend are most sensitive to fluctuations in the temperature series with periods from approximately 50 to 500 years. For some of the temperature spectra, it was found that the standard error of the least squares trend estimate was 3 times the standard error derived under the naïve assumption that the temperature series was uncorrelated. The observed trend differs from zero by more than 3 times the largest of the calculated standard errors, however, and is therefore highly significant.
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Bloomfield, P., Nychka, D. Climate spectra and detecting climate change. Climatic Change 21, 275–287 (1992). https://doi.org/10.1007/BF00139727
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DOI: https://doi.org/10.1007/BF00139727