regions where the semi-diurnal component predominates, such as in the north Atlantic Ocean ( 35 ). Sequence C events during this same period contributed strong forcing nearly midway between several of these 6-year events, but this did not lead to a sustained 3-year periodicity at P_e/2 because the other two associated 18-year sequences were too weak.

Millennial Repetitions. The perigean eclipse cycle also influences tidal events on the millennial time scale because the return time for near coincidence of events of this cycle with perihelion is approximately 1,800 years. We propose that the repeat time of millennial extremes in tide raising forces, discussed below, relates to this return time, although the actual timing of such millennial events must be irregular, being sensitive to the exact time of syzygy (ref. 23, pp. 201–249). The near coincidence of perihelion with this cycle in the present millennium occurred near the time of a climactic tidal event in A.D. 1433 (ref. 6, p. 220).

Our final objective is to demonstrate that the times of strong tidal forcing, based on astronomical factors, correlate with cool periods in the global temperature record at 6- to 10-year intervals. In Fig. 7 are shown four bandpasses of the global temperature anomaly obtained by either spectral analysis or spline fits. The upper three were shown previously; the lowest, including higher frequencies, is new. Also shown, by vertical hatched lines, are the times of selected tidal events as in Fig. 6 . In referring to tidal events that occurred near the date of perihelion, we will cite the year of the event as though it occurred in January, unless we give the exact date.

We first draw attention to the climactic tidal events of December 31, 1880, and January 8, 1974 (thick vertical hatched lines). Close to these dates (hereafter referred to as 1881 and 1974), spectrally derived oscillations in temperature, found by maximum entropy spectral analysis on the decadal time scale (curve 1, Decadal), show maximum rates of cooling, as indicated by the curve descending across the zero anomaly line. Thus, unlike the comparison of near-decadal temperature variations with the sunspot cycle (see Fig. 3 ), there is no shift in phase with respect to tidal forcing between centuries.

Next, still on the decadal time scale (curve 1), we examine the phasing of temperature variations with the timing of other tidal events (vertical hatched lines). The near coincidence of the climactic tidal events of 1881 and 1974 with maximum cooling rates did not extend to other decades, because the nearly 10-year intervals between cool periods exceeded the 9-year intervals between tidal events. The near-decadal temperature variations, nevertheless, have characteristics suggestive of tidal forcing. They are expressed as the sum of two harmonics (9.31 years and 10.23 years, see Fig. 4 ), which are close to the 9th and 10th harmonics of the 93-year tidal cycle. Also, they reinforced each other maximally close to the climactic tidal events of 1881 and 1974, and interfered maximally in the 1920s when the succession of 9-year tidal events was interrupted by an offset of 2.87 years. These two harmonics thus match the 93-year tidal cycle with its staggered sequences of 9-year events as well as can be expected for a single pair of spectral harmonics.

A broader spectral bandpass including nine oscillations (Curve 2, Low Frequency/Spectral) shows additional relations of temperature to tidal events. This bandpass shows oscillations in phase with those of Curve 1, before 1900 and after 1945, when Curve 1 shows reinforcement, but 6-year oscillations between these dates, when Curve 1 shows interference. Except near the times of the climactic tidal events of 1881 and 1974, tidal events tended to coincide with temperature minima rather than maximum cooling rates. After the 9-year tidal event of 1863, as already noted above, these cool periods occurred approximately 1 year further apart than the tidal events. As a consequence, a decadal cool event, occurring in 1883, lagged the Sequence B tidal event of 1881, to the extent that the latter nearly coincided with the maximum decadal cooling rate. Moreover, the next such cool period, in 1893, lagged the Sequence B* tidal event by so much that it nearly coincided with a Sequence C* event, and was thus in phase with subsequent 6-year temperature oscillations.

That these relationships are not an artifact of spectral analysis is shown by a lowpass spline fit (Curve 3, Low Frequency/Spline), which typically shows cool periods at the same times as by spectral analysis. This analysis, however, also shows the hint of a cool period near 1899, reinforcing the possibility that 6-year oscillations extended back to 1893. Thus, the 10-year spacing of cool events from 1863 to 1893 suggest an association with tidal forcing related to the perigean eclipse cycle; this forcing perhaps hastened (see Fig. 6 ) by the lesser strengths of the Sequence B* tidal events compared with Sequence C* events after 1900. (The tidal events of 1890 and 1893 indeed were of nearly equal strength.) The phasing of the temperature record with tidal events after 1956 is similar to that after 1863, leaving open the further possibility of similar tidal forcing 93 years after the events described for the late 19th century. Cool periods in a high-pass spline fit of temperature (Curve 4, High Frequency) also tend to coincide with 6- and 9-year tidal events. The cooling events of 1893 and 1899, discussed above, are seen to have been quite intense, although brief.

In summary, since 1855, cool periods of global extent at near-decadal tidal intervals have typically occurred in episodes lasting about half a century, before, during, and after climactic tidal events spaced about a century apart. Between these episodes, also for about half a century, cool periods tended to occur synchronously with strong tidal events at 6-year inter-

Contents (R1-R4)

Climate change and carbon dioxide: An introduction (1-2)

Tribute to Roger Revelle and his contribution to studies of carbon dioxide and climate change (3-7)

Equilibration of the terrestrial water, nitrogen, and carbon cycles (8-11)

Potential responses of soil organic carbon to global environmental change (12-19)

Global air-sea flux of CO2: An estimate based on measurements of sea-air pCO2 differences (20-27)

Characteristics of the deep ocean carbon system during the past 150,000 years: CO2 distributions, deep water flow patterns, and abrupt climate change (28-35)

Direct observation of the oceanic CO2 increase revisited (36-41)

The observed global warming record: What does it tell us? (42-48)

Possible forcing of global temperature by the oceanic tides (49-56)

Spectrum of 100-kyr glacial cycle: Orbital inclination, not eccentricity (57-62)

Can increasing carbon dioxide cause climate change? (63-70)

Gases in ice cores (71-77)

Tree rings, carbon dioxide, and climatic change (78-81)

Geochemistry of corals: Proxies of past ocean chemistry, ocean circulation, and climate (82-89)

A long marine history of carbon cycle modulation by orgital-climatic changes (90-97)

Dependence of global temperatures on atmospheric CO2 and solar irradiance (98-107)