The variation of the Earth's axis of rotation with respect to its mean geographic pole with a period around 435 days and an amplitude varying between 0.002" to 0.30" is called the Chandler Wobble after Seth Carlo Chandler, who first in 1891 confirmed its existence through observations of latitude. Such a free mode of oscillation was expected to exist and, although its period is adequately explained, neither the source of the changes in the angular momentum that excite it have been identified nor the sink of its energy (Lambeck, 1988). The changes in the centrifugal forces produce a signal in sea level at the same frequency. Whether the response of sea level to the Chandler wobble (the Pole Tide ) is equilibrium or dynamic will determine if the oceans can be a substantial sink of the energy of the wobble, and, therefore, will possibly constrain an alternative mechanism, namely mantle anelasticity at low frequencies. As the pole tide is not due to astronomical forcing, as are the luni-solar tides, and has the ability to modify what is presumably its generation mechanism (i.e. the Chandler Wobble), there is no a priori reason for expecting an equilibrium response.
The study of tide gauge data has shown that in some areas around the world there is a statistically significant signal at frequencies similar to those expected for the pole tide, and with amplitude of a few centimetres, several times larger than expected from the equilibrium theory (see, for example, Haubrich and Munk, 1959). The North and the Baltic Seas are the areas where sea level analysis reveals the largest amplitudes at around the Chandler Wobble frequency.
As model-based estimates of the pole tide in the open ocean resulted in values close to equilibrium (see, for example, Dickman, 1988), and attempts to explain its departure from equilibrium in the North Sea area resulted in a requirement of a non-equilibrium response in the open ocean (Dickman and Preisig, 1986), meteorological forcing in the North Sea and the Baltic became an increasingly stronger alternative assumption (O'Connor, 1986; Trupin and Wahr, 1990).
In order to investigate:
1) the possibility of a resonance that may enhance the sea level response at this frequency in the North Sea, and
2) the possible meteorological forcing of the pole tide,
a two dimensional tide-surge model (Flather et al., 1991) was used.
The storm surge component in the model is generated by meteorological forcing based on wind and pressure fields produced by the Norwegian Meteorological Institute. The model tide comprises eight main constituents of the diurnal and semi-diurnal species, namely Q1, O1, P1, K1, N2, M2, S2 and K2.
In one experiment, the model was forced by the 8 diurnal and semi-diurnal tidal constituents and the equilibrium pole tide. No resonance was observed thus excluding a basin oscillation. In a second experiment, the model was forced by the same eight tidal constituents and realistic meteorological forcing for the period 1955-1984. The mean monthly sea level values from 15 tide gauges at the coasts of the North Sea that had at least twenty-five complete years during the same period are compared to data from the corresponding grid points of the model. The tide gauge data come from the Permanent Service for Mean Sea Level database (Spencer and Woodworth, 1993).
The monthly mean sea level values as measured by the tide gauges (after removing the long term mean value) at one of the stations (Buesum) are shown in figure 1 (top). The middle plot in the same figure shows the modelled mean monthly values at the same location. The similarity is remarkable. The residual values (figure 1, bottom) are much smoother with a pronounced annual variation, most probably due to the steric cycle.
The power spectra of the three time series shown in figure 1 are shown in figure 2. Subtraction of model values from the tide gauge data reduces the energy across its spectrum at almost all frequencies by an order of magnitude. Only at the annual frequency does it fail to describe the sea level variations, clearly because the tide-surge model does not include any description of seasonal density changes. Remarkably at the Chandler wobble frequency, the model removes most of the energy from the tide gauge data and leaves the residuals (dashed line) with power comparable to that of the equilibrium pole tide calculated from the formulation of J.Wahr and with data supplied by S.Manabe and M.Feissel.
The meteorological input to the model was examined to investigate the origin of energy at the pole tide frequency. The power spectrum of the east-west wind stress component was found to include statistically significant energy at the Chandler Wobble frequency, while the north-south component was not above the noise level at that frequency.
Therefore, without the need of a non-equilibrium oceanic pole tide, the sea level variability at the Chandler Wobble frequency can be explained for the North Sea in terms of meteorology alone. It is unknown, however, whether the wind-stress signal is connected to the wobble of the axis of rotation of the Earth, either as a product of the wobble or as an excitation mechanism of the wobble. These questions remain the subject of further research.
References
Dickman S.R., The self-consistent dynamic pole tide in non-global
oceans, Geophys.J., 94, 519-543, 1988.
Dickman S.R. and J.R.Preisig, Another look at North Sea pole tide
dynamics, Geophys.J.R. astr.Soc., 86, 295-304, 1986.
Flather R., R. Proctor and J. Wolf, Oceanographic forecast
models, pp. 15-30 in Computer Modelling in the Environmental
Sciences (ed. D.G. Farmer and M.J. Rycroft). Oxford: Clarendon
Press, 1991.
Haubrich R. and W. Munk, The pole tide, J.Geophys.Res., 64, 2373
- 2388,
1959.
Lambeck K., The Earth's variable rotation: some geophysical
causes, pp. 1-20 in The Earth's rotation and reference frames for
geodesy and geodynamics. (ed. A.K.Babcock and G.A. Wilkins). IAU,
1988.
O'Connor W.P., The 14-month wind stressed residual circulation
(pole tide) in the North Sea, NASA Technical Memorandum 87800,
1986.
Spencer N.E. and P.L. Woodworth, Data Holdings of the Permanent
Service of Mean Sea Level, Bidston Observatory, 1993.
Trupin A. and J.Wahr, Spectroscopic analysis of global tide gauge
sea level data, Geophys.J.Int., 100, 441-453, 1990.
For a more detailed description of this research and a complete list of references see:
Tsimplis M.N., R.A. Flather and J.M.Vassie. 1994. The North Sea pole tide described through a tide-surge numerical model. Geophysical Research Letters, 21(6), 449-452.
Or contact:
Mickey Tsimplis mnt@pol.ac.uk
