tions in temperature, we have fit the individual data points of Figure 3 to three additional smoothing splines of successively greater stiffness (Figure 4, panel 1), chosen to produce increasing degrees of low-pass filtering of the monthly data (Enting, 1987). The choices were subjective, but are not critical to the outcome, because distinct decadal patterns can be produced over a considerable range of stiffnesses. These three spline fits were run on both monthly and yearly averaged data, and the resulting curves showed essentially no difference. The stiffest spline (the curve labeled ''1") shows only a tendency for global air temperature to rise irregularly since 1855. The two looser splines (curves "2" and "3"), whose difference is shown in panel 2, are nearly identical to the spline curves whose difference produced the approximately decadal band-pass of temperature that is shown in Figure 1. The difference between curves " 1" and "2" (Figure 4, panel 3) approximates a band-pass centered near 20 years, while the difference between curves "1 " and "3" (Figure 4, panel 4) approximates a broader band-pass showing temperature fluctuations on both decadal and bidecadal time scales.

To examine further the spectral character of the global temperature record of Jones and co-workers, we have computed a series of spectra of their record by the maximum entropy method (MEM) (Press et al., 1989). This method of spectral analysis includes both the Thomson multitaper method and the fast fourier transform (FFT) method. Its results are particularly suitable for trying to resolve closely spaced frequencies (Press et al., 1989; Berger et al., 1990). We afterwards established the amplitudes and phases of the identified spectral peaks by least-squares fits of sinusoidal functions, since the maximum entropy method, as discussed by Sonett (1983), is not quantitatively reliable with respect to amplitudes and cannot establish phase relationships.

FIGURE 4

Global temperature anomaly from 1855 through 1989, based on annual averages of the data in Figure 3 (Use of monthly data showed negligible difference at these decadal frequencies.) Panel 1: Three superimposed spline fits. The dotted curve "1" is a very stiff spline (s equal to 0.106°C); the dashed curve "2" and solid curve "3" are looser spline curves (s's of 0.095°C and 0.075°C). Panel 2: Curve "3" minus curve "2". Panel 3: Curve "2" minus curve "1". Panel 4: Curve "3" minus curve "1".



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