On the Nature and Origin of Atmospheric Annual

This paper is an attempt to obtain better constraints on the forcings of the trend and annual components of both global sea-level pressure and variations in the Earth’s rotation, and to test the hypothesis that there might be a causal link between them. Lopes et al. (2022a) undertook the singular spectral analysis (SSA) of the evolution of mean sea-level atmospheric pressure (SLP) since 1850. In addition to dominant trends, a eleven quasi-periodic components were identified, with (pseudo-) periods of ∼130, 90, 50, 22, 15, 4, 1.8, 1, 0.5, 0.33, and 0.25 years, corresponding to the Jose, Gleissberg, Hale and Schwabe cycles, to the annual cycle and its first three harmonics. These periods are already known to be characteristic of the space-time evolution of the Earth’s rotation axis: the rotation pole (RP) also undergoes periodic motions longer than 1 year, at least up to the Gleissberg ∼90 yr cycle (Chandler 1891a,b; Markowitz 1968; Kirov et al. 2002; Lambeck 2005; Zotov et Bizouard 2012; Chao et al. 2014; Zotov et al. 2016; Lopes et al. 2017; Le Mouel et al. ¨ 2021; Lopes et al. 2021, 2022a). They are encountered in solar physics (Gleissberg 1939; Jose 1965; Coles et al. 2019; Charvatova et Strestik 1991; Scafetta 2010; Le Mouel et al. ¨ 2017; Usoskin 2017; Scafetta 2020; Courtillot et al. 2021; Scafetta 2021) and terrestrial climate (Wood et al. 1974; Morth et Schlamminger ¨ 1979; Morner ¨ 1984; Schlesinger et Ramankutty 1994; Lau and Weng 1995; Courtillot et al. 2007, 2013; Le Mouel et al. ¨ 2019a; Scafetta et al. 2020; Connolly et al. 2021). arXiv:2206.12133v1 [physics.geo-ph] 24 Jun 2022 2 V. Courtillot et al.: SLP Annual and Semi-annual Oscillations The rotation velocity is usually expressed as the length of day (lod); it contains periods of 1 year and shorter, but also (though they are weaker) longer periods from 11 yr to 18.6 yr (Guinot 1973; Ray et Erofeeva 2014; Le Mouel et al. ¨ 2019b; Dumont et al. 2021; Petrosino et Dumont 1995). Lopes et al. (2022a) showed that the secular variation of lod since 1846 Stephenson et Morrison (1984) and RP have been carried by an oscillation whose period fits the Gleissberg cycle. RP consists to first order of 3 SSA components that together amount to more than 85% of the total signal variance Lopes et al. (2017): the Markowitz (1968) drift, the Chandler (1891a,b) free oscillation (actually a double component with periods ∼433 and ∼434 days), and the forced annual oscillation. Polar drift does not have a universally accepted explanation (Stoyko 1968; Hulot et al. 1996; Markowitz et Guinot 2022; Deng et al. 2021). The two other oscillatory components (Chandler and annual) are obtained using the Liouville-Euler system, that describes the motion of a spherical rotating solid body (e.g. Lambeck (2005), chapter 3, system 3.2.9). Polar drift has been discussed in Le Mouel et al. ¨ (2021) and Lopes et al. (2022a) and the free Chandler wobble in Lopes et al. (2021). In the present paper, we focus on the third major component, the forced annual oscillation. This oscillation is often assumed to be forced by the Earth’s fluid envelopes, hence also by climate variations (e.g. Gross et al. (2003), Lambeck (2005) chapter 7, Bizouard et Seoane (2010); Chen et al. (2019)). The fact that the observed Chandler period (433-434 days) is not equal to the theoretical value of the Euler period (306 days) has been interpreted in terms of Earth elasticity. The annual period is forced by interactions with fluids. Variations in the Sun-Earth distance, hence of the corresponding gravitational forces, displace the fluid atmosphere and ocean; exchanges in angular moment affect RP and lod. The annual oscillation of the rotation pole RP (coordinates m1 and m2) would therefore be due to the presence of the fluid envelopes. If Earth were devoid of fluid envelopes, the annual oscillation should not exist, which would contradict both the theory and observations of motion of a Lagrange top (Landau and Lifchitz 1984). Wilson et Haubrich (1976) recall that Spitaler (1897, 1901) “demonstrated that the annual wobble was forced, at least in part, by the seasonal migration of air masses on and off the Asian continent”.

 

Jeffreys (1916) showed that the annual fluctuation in water storage on the continents was also important. Munk et Mohamed (1961) re-examined the sources of annual wobble excitation and concluded that the air mass effect accounted for much but not all of the annual wobble, and water storage did not explain the remainder. Reservations appear in chapter 7 of Lambeck (2005), Seasonal Variations, page 146, who writes: “The principal seasonal oscillation in the wobble is the annual term which has generally been attributed to a geographical redistribution of mass associated with meteorological causes. Jeffreys, in 1916, first attempted a detailed quantitative evaluation of this excitation function by considering the contributions from atmospheric and oceanic motion, of precipitation, of vegetation and of polar ice. Jeffreys concluded that these factors explain the observed annual polar motion, a conclusion still valid today, although the quantitative comparisons between the observed and computed annual components of the pole path are still not satisfactory”. In summary, the interpretation of the forced annual component of polar motion is still hypothetical and fails to be validated by a numerical model. In a previous analysis of global sea-level pressure (SLP), we found that trends since 1950 were very stable in time and space (Lopes et al. 2022b) and were organized in a dominant 3-fold symmetry about the rotation axis in the northern hemisphere (NH) and a 3 or 4-fold symmetry in the southern hemisphere (SH) (Lopes et al. 2022b). These features could be interpreted as resulting from Taylor-Couette flow. In this paper, we return to the pressure data and focus on the annual oscillation.

 

We show in Figure 5 polar maps of the mean amplitude of the annual component (oscillation), for each season since 1850, 4 V. Courtillot et al.: SLP Annual and Semi-annual Oscillations Fig. 3: iSSA annual component of sea level pressure SLP from 1850 to the Present. (a) Envelopes of oscillations of iSSA annual components of polar motion m (blue curve, right scale) and global sea-level pressure SLP (black curve, left scale). (b) Trends of the pole movement (blue curve) and atmospheric pressure SLP (black curve) extracted by iSSA. Fig. 4: Annual enveloppes and trends extracted from pole movement and SLP and in Figure 6 polar maps of the mean of the semi-annual component. In Figure 5, in the Spring SH, there is a very regular pattern at the intersections of the 20◦S to 50◦S annulus and the southern tips of the three southern continents (Africa, Australia and South America). There is a smaller dipole with its negative part centered almost perfectly on the South pole, and its positive part centered on 70◦S, 105◦W. In the Fall, the pattern is the same but with a reversal in sign. In the Summer, there is a positive band between 15 and 25°S latitude from Madagascar to New Caledonia (40°-170°E) and a small negative spot near the South pole (Winter is the same with a sign reversal). The positive annulus is actually also seen, much weaker, in the Atlantic and Pacific oceans. The NH is rather different with, in the Spring, a large negative area over Asia from the Red Sea to Japan and extending in latitude from 80◦N to 15◦N. This large “anomaly” (using geophysical language) extends negative arms towards Senegal and over the western USA. Over the year, the “anomaly” changes sign.

 

Still in the Summer, there are two sizeable positive anomalies over the northern Atlantic and Pacific Oceans between 40◦N and 60◦N. In the SH, the large mean annual pressure variations occur over the Southern continents; in the NH, the Asian continental “anomaly” dominates, though two significant features occur over the northern parts of the oceans. Because the Asian “anomaly” and the two (opposite sign) anomalies in the North Atlantic and Pacific are separated by almost 180° in longitude, their maxima being always in phase, their contributions to the seasonal excitation function tend to cancel (Lamb 1972). The semi-annual component (Figure 6) has stronger patterns of symmetry. The SH features a very stable 3-fold symmetry (triskel); three large anomalies form an equilateral triangle centered on 70◦E, 30◦W and 210◦W, between latitudes 40◦S and 60◦S, a large anomaly of opposite sign is centered on the South Pole (the maximum is actually offset from the SP by 20◦E towards the 120◦E meridian), and an anomaly with the same sign as that over the pole, but located over southern Africa. The NH has weaker anomalies forming an irregular triangle with apices near the North Pacific (40◦N, 165◦E), Baffin Sea (40◦N, 50◦W) and Iran (30◦N, 60◦W). The bottom two maps in Figure 7 are the Spring maps for the annual and semi-annual components. We can compare the maps of Figures 5, 6 and 7 for the annual, semi-annual and trend components with corresponding figures from the reference treatise of Lamb (1972), reproduced in Appendix C .Recall that taken together these three components suffice to capture about 85% of the total signal variance. Figures 4-12 and 4-13 for instance (reproduced in Appendix C as Figures C1aand Figure C1b) show Lamb’s representation of the average mean sea level pressure over (respectively) the northern and southern hemispheres in the 1950s.

 

There is very good agreement for the northern hemisphere (Figure 10a): the January map from Lamb and our Winter map show the dominant “dipole” with the large high pressure (HP) over Asia and the low pressure (LP) over the northern Pacific. The April and Spring maps do not agree so well. The July map from Lamb and our Summer map both show a large LP over Asia and two HPs over the northern Pacific and northern Atlantic. The October map from Lamb and our Autumn map show a weaker HP over Asia. For the southern hemisphere (Figure 10b), agreement between the two sets of maps is significantly less; the Winter vs January maps both feature a HP centered on Antarctica and a LP extending from Madagascar to Australia, and the reverse in Summer/July. Our Spring (respectively Autumn) maps feature strong HPs (respectively LPs) on the southern tips of the southern continents. This sharp pattern V. Courtillot et al.: SLP Annual and Semi-annual Oscillations 5 is not really seen so well in Lamb’s (1972) maps (Appendix C). Lamb’s Figure 3-17 (reproduced in Appendix C as Figure C2) represents the annual mean distribution of atmospheric pressure at sea level for the time span 1900-40 for the northern hemisphere and 1900-50s for the southern hemisphere. This can be compared to our maps of the trend (Lopes et al. (2022b), and Figure 7, top row).

 

The agreement is quite good: the 3 fold symmetry of the northern hemisphere and the 4 fold symmetry of the southern hemisphere are even clearer in the Lopes et al. (2022b) maps using the iSSA method to extract the trend (i.e. the main component) from the data. As concluded by Lamb (1972) the effects of geography modify the circumpolar circulation much more in the northern than in the southern hemisphere; “ The broad zonal character of the long-period mean circulation is as permanent as the circumpolar arrangement of the heating and cooling zones and the circumpolar vortex aloft”. It appears to us that such maps are not available in the published literature; the maps from the southern hemisphere are particularly interesting, and so is the triskel in Figure 7 (top left). Specialists may wish to analyze these maps in more detail; they can be provided on simple request. (a) During springs (b) During summer.