The Chandler wobble (CW) is the Earth's free rotational eigenmode with a period of about 433 days; because it is damped, it must be continuously re-excited by angular momentum exchanges with the atmosphere, oceans, and continental waters. Bizouard, Remus, Lambert, Seoane and Gambis (2011) forward-integrated atmospheric and oceanic angular momentum over 1949-2009.5 and showed that atmosphere plus ocean explains most of the observed CW amplitude and phase variations, but left explicit residuals: a roughly 20-degree discrepancy between modeled and observed CW phase around the year 2000, an unquantified hydrological contribution, dataset-dependent errors in atmospheric and oceanic angular momentum (inter-product wind-term differences up to 0.7 milliarcseconds (mas) of polar motion in the Chandler band; ocean series without data assimilation and concatenated across runs), and an empirical optimum Q of about 84 inside a literature range of roughly 50-180. GRACE/GFO (Gravity Recovery and Climate Experiment and its Follow-On mission) era studies quantify hydrological and cryospheric excitation and competing, non-consensual explanations exist for the post-2015 CW collapse; Q estimates still span roughly 50-255 and its estimability from polar motion alone is actively disputed; assimilating ocean reanalyses now exist but their interannual excitation remains uncertain. The open problem is a quantitative, dataset-robust account reproducing the observed CW amplitude and phase over the full record spanned by the geophysical excitation data (from 1949 to the present), with a self-consistent period and quality factor.

Background

Earth's polar motion is the movement of the planet's rotation axis relative to the crust, observed since the nineteenth century by astronomical and, later, space-geodetic techniques. Its two dominant quasi-periodic components are the forced annual wobble, driven by the seasonal redistribution of air and water, and the Chandler wobble (CW), a free rotational eigenmode of the Earth with a period of about 433 days, discovered by S. C. Chandler in 1891. Because the Earth is viscoelastic, the CW would freely decay within a few decades unless continuously re-excited; its damping is described by the quality factor QQ (radians of oscillation per radian of energy loss, with a decay time 2Q/σ02Q/\sigma_0 of roughly 40 years for Q=100Q=100). Identifying the excitation that keeps the CW alive and modulates its amplitude and phase has been open since Chandler's discovery.

The excitation is expressed through angular momentum functions of the fluid geophysical layers: the atmospheric angular momentum (AAM, split into a mass or pressure term and a wind or motion term), the oceanic angular momentum (OAM, with bottom-pressure and current terms), and analogous hydrological and cryospheric terms. Linear rotation theory (the Liouville equation for a deformable Earth) relates these geophysical excitations to the complex pole coordinates p=x−iyp = x - iy. Two analysis strategies exist: the classical one transforms observed polar motion into a 'geodetic excitation function' and compares it with the fluid-layer angular momentum; the alternative adopted by Bizouard et al. (2011) forward-integrates the geophysical excitation and compares the modeled pole path directly with the observed one, isolating the CW with singular spectrum analysis (SSA), a data-adaptive decomposition that extracts quasi-periodic modes without assuming their periods. Rotational theory (Mathews, Herring and Buffett 2002) predicts a free period of 430.3 days with Q=88Q = 88, but observationally the period and especially QQ have remained contested: depending on data span and method, QQ estimates range from about 50 (Furuya and Chao 1996) to 180 (Vicente and Wilson 1997).

By the early 2000s a partial consensus held that the atmosphere and oceans together account for most of the CW excitation (Gross 2000; Seitz and Schmidt 2005). Bizouard, Remus, Lambert, Seoane and Gambis (2011) revisited the problem by forward-integrating AAM from the NCEP/NCAR reanalysis (a retrospective atmospheric analysis of the United States National Centers for Environmental Prediction and National Center for Atmospheric Research) and OAM from the ECCO ocean state estimate (Estimating the Circulation and Climate of the Ocean) over 1949-2009.5: the atmosphere dominates the amplitude variations before about 1970, the oceans drive the 1980s-1990s re-excitation, and an empirical optimum Q≈84Q \approx 84 yields the best regression between the modeled and observed Chandler modes. However, the modeled atmosphere+ocean phase still differs from the observed CW phase by roughly 20∘20^\circ around the year 2000 - an epoch inside a broader family of observed CW phase jumps and amplitude minima (Malkin and Miller 2010) - and the study left explicit gaps: continental hydrology was neglected, justified only by the predictive model of Celaya, Wahr and Bryan (1999); AAM products differ by up to 0.7 mas in the Chandler frequency band (1 mas, a milliarcsecond of polar motion, corresponds to about 3 cm of pole displacement on the surface), the discrepancy being attributed to the wind term; the longest ECCO OAM series (1949-2002, from the model run kf049f) was produced without data assimilation and had to be concatenated with another run to reach 2009.5; and no consensus on QQ existed. The question posed here is whether these residuals of the excitation budget can be closed.

Problem Statement

Provide a quantitative, physically attributed account of the Earth's variable Chandler wobble: identify and quantify the geophysical angular-momentum excitations - atmospheric, oceanic, continental hydrological, and cryospheric - constructed from geophysical data and models independently of the observed pole series, that, when integrated through the polar-motion (Liouville) equation with a self-consistent Chandler period and quality factor QQ, reproduce the observed Chandler wobble amplitude and phase variations over the record spanned by those excitation data: from 1949, the start of the atmospheric and oceanic angular momentum series forward-integrated by Bizouard et al. (2011) over their 1949.0-2009.5 analysis interval, to the present. The account must address, in particular: (i) remove the residual phase differences left by atmosphere-plus-ocean models around the year 2000, where Bizouard et al. (2011) found a roughly 20∘20^\circ discrepancy between modeled and observed Chandler phase, to within uncertainties justified independently of the excitation model under test rather than chosen so as to absorb the discrepancy; (ii) establish whether closing the residual budget requires a continental-water (and, where data permit, cryospheric) contribution beyond the neglect that Bizouard et al. (2011) justified by the predictive model of Celaya et al. (1999), and quantify that contribution where observational or model data permit, noting that over the pre-satellite-gravity portion of Bizouard et al.'s 1949.0-2009.5 analysis interval (in particular 1949-2002) no direct gravimetric observations exist, so any such quantification can only be model- or proxy-based; (iii) demonstrate that the attribution is robust against known dataset uncertainties, namely inter-product atmospheric angular momentum differences of order 0.7 mas in the Chandler band (dominated by the wind term) and oceanic angular momentum product dependence on data assimilation and series concatenation; and (iv) determine the Chandler period and QQ (or their time/frequency dependence) consistently with the excitation model, with uncertainties small enough to discriminate among - and to account for the method- and data-span dependence of - the currently discordant estimates (roughly QQ between 50 and 180 in the literature reviewed by Bizouard et al. (2011), and a 95% confidence interval of 56 to 255 for the recent estimate of Nastula and Gross (2015)), rather than merely overlap them. These facets are aspects of a single objective - closing the excitation budget of the observed variable Chandler wobble - rather than independent tests: they are resolved jointly by a single account that reproduces the observed amplitude and phase over the record with a self-consistent period and quality factor.

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