Possible excitation of the Chandler wobble by the geophysical annual cycle Kosek Wiesław Space Research Centre, Polish Academy of Sciences Seminar at the U.S. Naval Observatory Washington D.C. December 2003

Chandler wobble excitation Electromagnetic torques acting on the CMB play a negligible role in excitation of the CW (Rochester and Smylie 1965). Cumulative effect of large earthquakes was a noticeable contribution to the CW excitation (O’Connel and Dziewonski 1976; Mansinha et al. 1979). Seismic excitation was far too small to explain the CW excitation (Souriau and Cazenave 1985, Gross 1986). The contribution of meteorological sources to the CW excitation was estimated as % by Ooe (1978). The 14.7 month signal found in the surface air pressure calculated in a coupled ocean-atmosphere general circulation model was identified as the “atmospheric pole tide” CW, so the changes in atmospheric mass distribution excite and maintain the CW and neither earthquakes nor the fluid core are significant contributions (Hameed and Currie 1989). The joint ocean-atmosphere excitation compares substantially better with the observed excitation at the annual and Chandler frequencies than when only atmosphere is considered (Ponte et al. 1998).

Chandler wobble excitation (cont.) The importance of the OAM and AAM to the excitation of the Chandler and annual wobbles were found to be of the same order (Ponte and Stammer 1999). The atmospheric wind and IB pressure variations maintain a major part of the observed CW, however the wind signal dominates over the IB pressure term in the vicinity of the Chandler frequency (Furuya et al. 1996; Aoyama and Naito 2001). Celaya et al. (1999) using the results of a coupled atmosphere-ocean- land climate model, concluded that some combination of atmospheric and oceanic processes have enough power to excite the CW. Using an 11-year time series of the OAM Brzeziński and Nastula (2002) concluded that, within the limits of accuracy, the coupled system atmosphere/ocean fully explains the CW in The most important mechanism exciting the CW in was ocean-bottom pressure fluctuations, which contribute about twice as much excitation power as do atmospheric pressure fluctuations (Gross 2002).

Data Pole coordinates data IERS EOPC04 in – and EOPC01 in (IERS 2003). The geodetic excitation (GE) functions, were computed from the IERS EOPC04 pole coordinates data using the time domain Wilson and Haubrich (1976) deconvolution formula (Chandler period equal to, quality factor ). Atmospheric angular momentum (AAM) excitation functions - - equatorial components of the effective atmospheric angular momentum reanalysis data in from the U.S. NCEP/NCAR, the top of the model is 10 hPa (Barnes et al. 1983, Salstein et al. 1986, Kalnay et al. 1996, Salstein and Rosen 1997, AER 2002), Oceanic angular momentum (OAM) excitation functions - equatorial components of global oceanic angular momentum mass and motion terms from Jan 1980 to Mar 2002 with 1 day sampling interval (Gross et al. 2003), Ocean model: ECCO (based on MITgcm).

Pole coordinates data EOPC01EOPC

The mean determination error of x, y pole coordinates data

The FTBPF amplitude spectra of complex-valued pole coordinate data in

The most energetic oscillations of polar motion computed by the FTBPF Chandler Annual

The amplitude and phase variations of the Chandler and annual oscillations computed by the LS in 3 year time intervals, the Niño indices

The amplitude of the Chandler oscillation and its first difference computed from the x – i y data by the FTBPF and by the LS method in 5 year time intervals

Transformation of x, y pole coordinates data to polar coordinate system radius angular velocity length of polar motion path mean pole

The mean pole computed by the Ormsby LPF - filter length,- number of data, - cutoff frequency, - cutoff period, - roll-off termination frequency. - pole coordinates data,

Corr. Coeff

The time-frequency coherence between the radius and angular velocity computed using the Morlet Wavelet Transform

The FTBPF time-frequency amplitude spectra of polar motion radius and angular velocity

The length of polar motion path and the envelope of the Chandler oscillation

Variable beat period of the Chandler and annual oscillations - from the phase variations of the Chandler and annual oscillations - from the phase variations of the 6-7 yr oscillation of the radius

Beat period variations computed from the LS phase variations of the Chandler and annual oscillations

Beat period estimated from the phase variations of the 6-7 yr oscillation of the radius. The LS amplitudes and phases computed in 12, 13 year time intervals

The period of the 6-7 yr oscillation in the radius computed from the LS phases in 12, 13 year time intervals. Beat period of the Chandler and annual oscillations computed from the LS phases in 5 and 6 year time intervals. First derivative of the Chandler amplitudes computed by the LS in 4, 5 and 6 year time intervals Corr. Coeff Corr. Coeff

The Morlet Wavelet Transform spectro-temporal coherences between the complex-valued geodetic (GE) and the atmospheric (AAM) as well as the sum of the atmospheric and oceanic (AAM+OAM) excitation functions.

The LS amplitude variations of the annual oscillation computed in four-year time intervals from the geodetic GE, atmospheric AAM and the sum of atmospheric and oceanic AAM+OAM excitation functions.

The LS phase variations of the annual oscillation referred to the epoch computed in four-year time intervals from the geodetic GE, atmospheric AAM and the sum of atmospheric and oceanic AAM+OAM excitation functions.

The LS phase variations of the annual oscillation computed in 3 and 4 year time intervals of the AAM+OAM excitation functions. The change of the Chandler amplitude computed by the LS in 4, 5 and 6 year time intervals. Corr.coef

The phase of the annual oscillation in the AAM+OAM excitation functions decreases The phase of the annual oscillation in polar motion decreases The period of the annual oscillation in polar motion increases The beat period of the Chandler and annual oscillations increases The change of the Chandler amplitudeincreases The excitation mechanism of the Chandler wobble

Conclusions Amplitudes and phases of the Chandler oscillation are smoother than those of the annual oscillation. The phase of the annual oscillation had maximum values and the beat period of the Chandler and annual oscillation had minimum values before the biggest 1982/83 and 1997/98 El Niño events. Long period variations with periods greater than six years in the length of polar motion path are due to variable amplitude of the Chandler oscillation. The change of the Chandler amplitude increases with the increase of the beat period of the annual and Chandler oscillations and decreases with the phase of the annual oscillation of the coupled atmospheric/ocean excitation. The increase of the beat period means that the period of the annual oscillation increases and becomes closer to the Chandler one. Thus, the Chandler amplitude increases during decrease of the phase of the annual oscillation of polar motion and of the sum of the atmospheric and oceanic angular momentum excitation functions. Thus, the Chandler wobble may be excited during decrease of the phase of the annual geophysical cycle.

ABSTRACT It was found that the change of the Chandler oscillation amplitude is similar to the change of the beat period of the Chandler and annual oscillations and to the negative change of the phase of the annual oscillation of the coupled atmospheric/ocean excitation. The beat period increases due to decrease of the phase of the annual oscillation, which means that the annual oscillation period increases and becomes closer to the Chandler one. The exchange of the atmospheric angular momentum and ocean angular momentum with each other and with the solid earth at the frequency equal approximately to 1 cycle per year represents the ‘geophysical annul cycle’ which can be expressed by the annual oscillation in the sum of the atmospheric and oceanic angular momentum excitation functions. The phase variations of this annual cycle are possibly responsible for the Chandler wobble excitation.