Figure 6

Two maximum-entropy spectra of the global surface temperature anomaly, expressed as power (logarithmic scale) versus frequency, in cycles per year. The temperature record used to determine the spectra was expressed as the difference between the flexible spline plotted in Figure 3 and the very stiff spline from curve "1" of Figure 4, panel 1. The solid curve indicates a spectrum with the number of poles, M, equal to 250; the dashed curve shows a spectrum with M equal to 150. The periods of the prominent peaks of the former, in years, are shown in standard characters, those of the latter by figures in italics.

Another study of nearly the same temperature record by Ghil and Vautard (1991) used a combined singular spectrum and multi-taper analysis that provides an F-test for the significance of the peaks. Their study confirms the significance, at the 97 percent confidence level, of the peaks that we found near 6, 9, 15, and 21 years, and showed evidence of several of the other peaks listed in Table 1.

Accepting the peak periods revealed by the second spectrum of Table 1 for further study, we have fit the slightly smoothed temperature record of Figure 5, panel 1, using a non-linear least-squares method (Bevington, 1969, subroutine CURFIT) to a series of sine and cosine functions having the periods indicated for peaks in the MEM spectrum, omitting only very weak peaks and any peaks with periods less than 1.7 years.

The reconstructed time series obtained by summing these 24 computed sinusoidal spectral oscillations reproduces the main peaks and troughs of the original record (Figure 5, panel 2). If individual warming and cold events are scrutinized, admittedly the fit is far from perfect. Allowing, however, that the lowest period of oscillation in the reconstruction is 1.8 years, one cannot expect a wholly consistent representation of times and amplitudes of short-term interannual fluctuations such as those related to El Niño events. As we verified by carrying out a further reconstruction using 48 harmonics that included oscillations with periods as low as 1.0 years, the correctness of the phasing and amplitudes for short-term interannual fluctuations can be improved by including higher-frequency oscillations in the fit to the temperature data. The amplitudes of the lower-frequency oscillations, which are those of importance to the present study, were only negligibly altered by the addition of higher frequencies in the fit.

The amplitudes of the sinusoidal functions are listed in Table 1. Of the 24 spectral oscillations in the reconstruction, only the two noted earlier, having periods of 9.3 and 10.2 years, occur near to the decadal time scale. Summed, these produce oscillations with an average period of 9.7 years and a maximum amplitude, peak to peak, of 0.15°C. They beat with a recurrence period of 102 years (half of the period of the long-term oscillation produced by the difference of the two shorter-period oscillations) and exhibit interference



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