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Natural Climate Variability on Decade-to-Century Time Scales
for the sake of continuity includes a datum for that year.) Qualitatively, the extension prior to A.D. 900 looks similar to, and therefore homogeneous with, the later period. In the next section, we will describe the spectral properties of this record, which indicate the probable existence of interdecadal oscillatory modes in the SH climate system that have persisted over the past 2290 years. Later, we will take a detailed look at these oscillations through time and speculate on mechanisms that might be responsible for their existence.
Cook et al. (1992) examined the power spectrum of the Tasmanian temperature reconstruction estimated for the period A.D. 900-1989. Using both Blackman-Tukey and maximum-entropy spectral analysis (Jenkins and Watts, 1968; Marple, 1987), they found evidence for statistically significant (a priori p < 0.05) peaks in the spectrum at approximately 30, 56, 80, and 180 years. Cook et al. (1992) did not examine the properties of these apparent oscillations in the series. However, they speculated that the 30- and 56 year modes could be reflecting similar oscillations in the SH climate system associated with different wave-number flow regimes of the circumpolar zonal westerlies in the 40° to 50°S latitude zone (Enomoto, 1991).
The extended temperature reconstruction described earlier provides us with a rare opportunity to validate the existence of these apparent oscillations. Clearly, if they disappear from the early portion of the extended record, then the physical basis for the existence for these modes is doubtful. For this purpose, we split the series into two essentially independent 1145-year segments covering the intervals from 300 B.C. to A.D. 844 (early period) and A.D. 845 to 1989 (late period).
The Blackman-Tukey power spectra for these periods are shown in Figure 2 (estimates are shown only for periods greater than 10 years). As expected, the late-period spectrum
Blackman-Tukey spectra of the first and second halves of the Tasmanian temperature reconstruction. Each half is 1145 years long. The spectra are shown only for periods greater than 10 years. Note the similarity between the spectra in the low-frequency end.
has peaks very close in frequency to those found previously, the principal difference being that the longest-period oscillation is now 190 years. The early-period spectrum likewise has peaks in the same vicinity, although there are some differences. The 190-year peak is more subdued in the earlier period, and the 30-year peak has virtually disappeared. In contrast, the 56- and 80-year peaks found in the late period are present in the early period at closely associated frequencies and with similar power. If the bandwidths of the 56-, 80-, and 190-year peaks in the late-period spectrum are taken into account, the frequencies of the associated peaks in the early-period spectrum are fully covered. The same formal coverage applies for the power estimates in the early period if 80 percent confidence intervals are computed for the late-period peaks. Thus, in terms of both frequency and power, there is little that significantly distinguishes the spectra of the early and late periods at approximately 56, 80, and 190 years. In contrast, the 30-year peak appears to be less stable through time. This result covering the past 2290 years suggests that the putative oscillations are not statistical artifacts.
For completeness, the spectrum of the entire series is shown in Figure 3. The identified periods differ slightly due to the increased record length. All four peaks of interest here exceed the a priori 95 percent confidence level (dashed line), on the basis of a first-order Markov null-continuum model.
SINGULAR SPECTRUM ANALYSIS
The previous spectral analyses revealed the probable existence of oscillatory behavior in warm-season Tasmanian temperatures over the past 2290 years. However, changes in amplitude and phase are indicated, which necessitates a more thorough examination of these oscillations in the time domain. For this purpose we used singular spectrum analysis (SSA), a data-adaptive technique that is particularly well suited for isolating weak signals embedded in red noise (Vautard and Ghil, 1989). SSA decomposes a time series into signal and noise sub-spaces by applying principle components analysis (PCA) to the autocorrelation function (ACF) of that process. Vautard and Ghil (1989) refer to the eigenvectors produced by PCA as empirical orthogonal functions (EOFs) and the eigenvalues as singular values, hence SSA. A pure oscillation embedded in red noise, whose average period is shorter than the length of the ACF, will be composed of an even-and-odd EOF pair. The EOF pair will resemble the shape of the oscillation and be in quadrature (i.e., 90° out of phase). The EOF loadings can be thought of as digital filter weights that are used to estimate the waveform. For this purpose, only the even (or symmetric) EOF, which preserves phase, is used here. Vautard and Ghil (1989) refer to these recovered waveforms as principal components (PCs). The final step of SSA is spectral analysis