near 1925 (Figure 5, panel 3). The pattern of interference and reinforcement is distinct because the amplitudes of the separate oscillations, as found by the least-squares fits to the sinusoidal functions, are nearly equal.
Two additional strong spectral oscillations are found in the temperature spectrum at approximately the bidecadal time scale, with periods of 15.6 and 21.7 years. Summed, they have a maximum amplitude of 0.14°C and beat with a period of 55 years (Figure 5, panel 4), which is close to half the beat period of the decadal harmonics. They also exhibit interference in the 1920s, at almost the same time as the decadal oscillations. Furthermore, their summed oscillations, with an average period of 18.1 years, essentially impose variable amplitudes on the decadal oscillations. The addition of weaker harmonics with periods of 6.7, 7.6, 12.2, and 31 years to form a broad low-pass filter of the detrended temperature record does not cancel out this beat pattern (Figure 5, panel 5). The decadal oscillations are still present, with the strongest temperature maxima where the bidecadal oscillations enhance the decadal signal. Between 1905 and 1940, however, only oscillations with periods close to 6 years appear, as was the case for the spline-fit differences of panels 2 and 4 of Figure 4.
As shown in Figure 7, the sinusoidal oscillations of Figure 5, which are derived from spectral analysis, show essentially the same patterns as those previously derived from spline fits. The decadal and bidecadal oscillations are equally prominent, whether they are obtained by spectral analysis or by the use of smoothing splines. Thus, the amplitudes and phases obtained by spectral analysis do not appear to be falsified by the restricted number of degrees of freedom of the spectral compositing.
We conclude that the decadal oscillations that have appeared in the temperature record since the late 1950s may be characteristic of the longer-term record as well. If so, the bidecadal oscillations seen in Figures 5 and 7 may also be characteristic of the longer record, especially since they appear to be an amplitude modulation of the decadal oscillations. Both pairs of oscillations are intermittent, however, being essentially absent for about 35 years near the middle of the temperature record.