by classical Blackman-Tukey filters. MTM can thus detect small-amplitude organized variability with measurable statistical confidence. Kuo et al. (1990) applied MTM to demonstrate coherence between the instrumental temperature and carbon dioxide (CO2) records.

Yiou et al. (1991) applied evolutive spectral analysis based on MTM to the study of high-frequency paleoclimate variability in the Vostok ice core. In this context, it is important to notice that partial CO2 pressure in the air bubbles trapped in the core (Barnola et al., 1987) rises at the same time as the temperature recorded isotopically in the ice itself—for example, from the last glacial maximum into the Holocene, about 20,000 years ago. But temperature drops thousands of years before the CO2 level does, as happened with the shift from the previous climate optimum into the last glaciation, about 120,000 years ago. This indicates that, at least on paleoclimate time scales, temperature does not respond to CO2 changes alone, but may be influenced by other factors or may interact with CO2 in a nonlinear fashion that distinguishes between phase relations during warming and cooling episodes. On decade-to-century time scales, the still-incomplete atmospheric observational evidence is only marginally useful at present in diagnosing phase relationships among various internal and external variables (Karl et al., 1995, in this volume).

Singular spectrum analysis (SSA) was developed by Broomhead and King (1986) and Vautard and Ghil (1989). It uses data-adaptive basis functions that are the time analogs of empirical orthogonal functions (EOFs) in space (Preisendorfer, 1988; North and Kim, 1995). Pairs of such temporal EOFs can efficiently describe anharmonic, nonlinear oscillations. Using SSA on instrumental records of global surface air temperature (Jones et al., 1986; IPCC, 1990), Ghil and Vautard (1991) detected organized climate variability with peaks near 10, 15, and 25 years. The first two peaks were confirmed by considering the spatial coherence of the same temperature data set using SSA (Allen and Smith, 1994) and MTM (Mann and Park, 1993) respectively.

A 31-year peak was also found in 2,000-year-long tree-ring records from Tasmania by Cook et al. (1995, in this volume), and a 27-year peak in the Koch index of sea-ice extent around Iceland by Stocker and Mysak (1992). The longest continuous instrumental record of local surface air temperature is the central England record (Manley, 1974; Parker et al., 1991). Figure 1 displays the power spectrum of this 335-year-long record (Plaut et al., 1995). Similar interdecadal peaks were also found, using entirely different spectral methods, by Keeling and Whorf (1995, in this volume) in global temperature records. One plausible explanation for such internal variability on interdecadal time scales lies in changes of the ocean's thermohaline circulation (Weaver et al., 1991; Quon and Ghil, 1992).

Wallace (1995, in this section) separates carefully the interdecadal variability apparent in temperature records


Stack spectrum of the central England temperature record, using SSA combined with a low-order, robust, maximum-entropy method. Each line shows the power spectrum of a particular oscillation, isolated as a pair of temporal EOFs, essentially removing the broad-band variability in which the peaks are embedded (see text for details). (From Plaut et al., 1995; reprinted with permission of the American Association for the Advancement of Science.)

from higher-frequency variability due to the El Niño/ Southern Oscillation phenomenon and volcanic eruptions. He emphasizes the need for using satellite data in considering spatial details of natural and anthropogenic variability, especially for temperatures aloft.

To derive full benefit from sophisticated methods of signal detection and analysis, the same methods have to be applied to the existing data and to model simulations. This emphasizes again the need for intercomparing detailed, but short, GCM simulations with the longer, but less detailed, time series generated by simple and intermediate models, as well as with the data themselves. These comparisons need to be carried out in both the spatial and the temporal domains.

A rich panoply of atmospheric models has been developed over the last 40 years, from zero-dimensional EBMs to fully three-dimensional GCMs, passing through one- and two-dimensional EBMs, RCMs, and dynamic flow models. These models have been widely used to study anthropogenic climate change due to increases in aerosol loading or greenhouse-gas concentrations. Their use for the study of internal climate variability on the time scales of interest here has only begun.

Understanding climate response to external forcing, natural or anthropogenic, requires that one understand slow shifts in equilibrium behavior, and then—more important—slow shifts in internal variability. Even for the former, passive response, considerable uncertainty exists at present as to amplitude and timing. The IPCC estimates the global surface air temperature increase for a doubling of present CO2 concentration to be anywhere from 1.5°C to 4.5°C

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