To investigate further a possible relationship between tidal forcing and temperature appears to us to be worthwhile, because the oceanic tide raising forces vary in strength predictably over a wide range of time scales. If they should be shown to influence temperature on any time scale, they may explain periodic changes in weather and climate on other time scales as short as fortnightly and as long as the Milankovitch cycles.

2.

Air Temperature Analysis and Sunspots

To test the hypothesis of tidal forcing of temperature we have adopted a global compilation of temperature data over both land and in surface sea water (14), expressed as an anomaly beginning in 1855 and updated through mid-1995 (P. D. Jones, personal communication). We accept Jones’ premise that sea surface and marine air temperatures follow each other closely on interannual time scales, so that combined land and marine temperature data portray global average variations in surface air temperature.

The large scatter in monthly averaged global temperature data (dots plotted in Fig. 1) is not a strong encouragement to look for cyclic phenomena. Nevertheless, if the data are fit to a flexible nodal spline (15, 16) (solid curve in Fig. 1) to suppress the high frequency scatter, periods of persistently warmer and cooler conditions are indicated. Many of the warmer periods occurred at times of El Niño events (ref. 17, p. 623), suggesting coherent interannual variability.

To detect possible fluctuations in global temperature on interannual time scales, we have fit monthly averages with nodal splines of successively greater stiffness (Fig. 2, Top), chosen to produce increasing degrees of low-pass filtering of the data. The choices were subjective, but are not critical to the outcome, because nearly the same distinct patterns are produced over a considerable range of stiffnesses. The stiffest spline (curve labeled 1) shows only a tendency for global air temperature to rise irregularly since 1855. The difference between the two looser splines produces an approximately decadal bandpass (Middle), whereas the difference between the stiffest and loosest curves shows a broad, low frequency bandpass (Bottom).

In Fig. 3 , a record of sunspot numbers (18) is compared with the near-decadal bandpass of temperature of Fig. 2. As shown by broken lines, four near-decadal peak temperatures immediately before 1905 were close to sunspot minima, while four immediately after 1960 were close to sunspot maxima. For several decades near 1920, peak temperatures in the bandpass were only about 6 years apart and did not correlate with sunspots at all. These results are thus consistent with the earlier findings reported by Herman and Goldberg (3), of an intermittent correlation of temperature with sunspots and a reversal of phase.

FIG. 1. Global surface temperature anomaly (combined land and marine) from 1855 through mid-1995 in degrees C (ref. 14 and P. D. Jones, personal communication). Monthly averages are shown as dots. The solid line is a spline fit (15) of these data with a standard error, s, of 0.107°C.

To examine further the oscillatory character of the global temperature record, we have computed its spectrum (Fig. 4) by the maximum entropy method (19), which is highly sensitive to spectral line detection. We have afterwards established the amplitudes and phases of 24 identified spectral peaks by least-squares fits, to avoid the problem that the maximum entropy method is not quantitatively reliable with respect to amplitudes and cannot establish phase relationships (20). Our method has been described in detail previously (21) and is applied here to an updated temperature record.

FIG. 2. Spline fits of the global temperature anomaly of Fig. 1 together with associated bandpasses. (Top) Global trends depicted by three superimposed spline fits (15), one consisting of a very stiff spline fit to yearly averages (dotted curve 1, s of 0.106°C), and two consisting of splines of lesser stiffness fit to monthly averages (dashed curve 2 and solid curve 3, ss of 0.161 and 0.148°C, respectively). (Middle) Decadal bandpass (curve 3 minus curve 2). (Bottom) Low frequency bandpass (curve 3 minus curve 1).

We reconstructed the time series of temperature by summing the resultant 24 computed sinusoidal spectral oscillations. Near the decadal time scale, a strong harmonic with a period of 9.3 years, when summed with a sideband at 10.3 years

FIG. 3. Comparison of mean sunspot number (ref. 18, 12-month running mean, upper curve) with the decadal bandpass of global surface temperature in degrees C, of Fig. 2 (Middle).



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