Earth-Sun distance and Chandler Wobble

Continuing from The Pacemaker of the Chandler Wobble, Grumbine 2014:

The Chandler Wobble (CW) is a small variation in the orientation of the earth’s rotational axis [Chandler, 1891]. It has a period near 433 days [Liao and Zhou, 2004] (0.8435cycles per year, 0.0023095 cycles per day). Some source of energy for the Chandler Wobble  must exist because it dies out on a time scale of decades [Munk and MacDonald, 1960] if energy is not continuingly added. Gross [2000] found that atmosphere-ocean forcing on the earth’s rotation, computed in an ocean general circulation model driven by observed  meteorological parameters, provided that forcing. [O’Connor et al., 2000] also found wind forcing of the ocean to drive the pole tide. This source was questioned [Wunsch, 2001] partly on the grounds that the ocean was displaying a very narrow band response, but there was no reason to believe that the forcing itself was narrow band.

I suggest that the atmosphere-ocean variability near the Chandler Wobble period, among others, is paced by variation in earth-sun distance. The earth-sun distance, in addition to annual and semi-annual variations due to the elliptical shape of the earth’s orbit, varies due to perturbations from the moon (29.53 day period and others), Venus (292, 584, 417, 1455, ... days), and Jupiter (399, 199, 439, 489, ... days). The size of these variations is small, the largest being the 29.53 day lunar synodic period (31*10−6 Astronomical Units), amounting to approximately 0.08 W/m2 on a plane perpendicular to the sun at the top of the atmosphere. See Table 1 for more precise periods and the amplitudes of distance variations corresponding to them.

Horizons [Giorgini et al., 1996] was used to provided 6-hourly earth-sun distance and osculating elements for 1 Jan 1962 00 UTC through 31 Dec 2008 18 UTC. Table 1 was derived by harmonic analysis of those data at precise frequencies to determine purely cyclic variations in the earth-sun distance. The leading terms are, of course, the annual and semi-annual cycles from the elliptical orbit. Following this, however, are perturbations in Earth-Sun distance due to the moon, Venus, and Jupiter. Note that the orbital elements are not precisely locked to the periods given. The osculating (instantaneous) orbital elements vary; the osculating year varies from 364 to 366 days, for instance [Giorgini et al., 1996]. Consequently, there are residuals near the annual period. But they are far smaller than the main line. The anomalistic year, 365.259635 days [Observatory and Observatory, 2001], is the period between successive perihelia. This has been found to be the appropriate period for climate temperature analysis rather than the tropical (vernal equinox to vernal equinox) year [Thomson, 1995]. As we will be drawing the conclusion that earth-sun distance is important, even for small variations, the anomalistic year is the self-consistent one to use here. 

Previous analyses of orbital variation at relatively high frequency (high compared to, e.g., Milankovitch periods [Milankovich, 1941]) have used annual average orbital parameters [Borisenkov et al., 1985; Loutre et al., 1992], precluding them from examining periods shorter than 2 years and aliasing some of the periods examined here. Also, those works were examining the earth’s tilt, rather than earth-sun distance. Gravitational torques have been examined previously as the main driver of the Chandler Wobble and rejected [Munk and MacDonald , 1960; Lambeck , 1980], which means only non-gravitational external forces, such as earth-sun distance, force Chandler Wobble at these periods, if any external sources do. 

Table 1:

Table 1: Summary of frequency (cycles per tropical year), amplitude, phase, period and origins.

The code lists the number of cycles per lunar sidereal month, per year (here I list both the tropical year and anomalistic year – tropical year is used for motions involving the moon, Jupiter, and Venus), Venus's sidereal year, and Jupiter's sidereal year, respectively (M T A V J).

Frequency	Amplitude	Phase	Period	Code
(cpy)	(10-6 AU)		(dy)	M	T	A	V	J
0.99995	16712.75	-177.9	365.260	0	0	1	0	0
1.99990	139.69	-175.8	182.630	0	0	2	0	0
12.36825	30.84	63.5	29.531	1	-1	0	0	0
0.91566	15.92	-143.5	398.884	0	1	0	0	-1
1.25100	15.63	31	291.961	0	-2	0	2	0
1.83132	9.27	-99.7	199.442	0	2	0	0	-2
0.62550	5.12	16.2	583.923	0	-1	0	1	0
0.87653	4.79	107.5	416.690	0	-4	0	3	0
0.83136	2.93	-137.3	439.332	0	1	0	0	-2
0.08430	2.58	70.2	4332.589	0	0	0	0	1
1.87649	2.54	-136	194.641	0	-3	0	3	0
2.99986	1.76	-173.9	121.753	0	0	3	0	0
1.75306	1.54	-98.5	208.345	0	-8	0	6	0
0.25103	1.53	-145.4	1454.951	0	-3	0	2	0
2.50199	0.91	61.5	145.981	0	-4	0	4	0
0.74706	0.64	146.4	488.908	0	1	0	0	-3
13.36821	0.57	-114.4	27.322	1	0	0	0	0
11.36829	0.56	61.3	32.128	1	-2	0	0	0
3.12749	0.37	-103.8	116.785	0	-5	0	5	0
0.50207	0.36	-71.8	727.476	0	-6	0	4	0
3.75299	0.20	94.1	97.320	0	-6	0	6	0
0.37446	0.14	156.7	975.374	0	2	0	-1	0

Horizons  -- go here for more data.