New aspects of the equilibrium pole tide

Summary. We have developed a new spherical harmonic algorithm for the calculation of the loading and self-gravitating equilibrium pole tide. Based on a suggestion of Dahlen, this approach minimizes the distortions in tide height caused by an incomplete representation of the ocean function. With slight modification our approach easily could be used to compute self-gravitating and loading luni-solar tides as well.
Using our algorithm we have compared the static pole tide with tide observations at a variety of locations around the world. We find statistically significant evidence for pole tide enhancements in mid-ocean as well as the shallow seas.
We have also re-investigated the effect of the static tide on the Chandler wobble period. The difference between the wobble period of an oceanless, elastic earth with a fluid core (Smith & Dahlen) and the period of an earth minus static oceans yields a 7.4-day discrepancy. We conclude from tide observations that much of the discrepancy can probably be accounted for by non-equilibrium pole tide behaviour in the deep oceans.     

The quarter-diurnal tide in the English Channel

summary . The English Channel is modelled by a simplified geometry which enables a quasi-analytic solution to be obtained for the semidiurnal tide. This solution is then used to calculate the forced components of the quarterdiurnal tide from the non-linear terms in the equations of motion.     

Tidal gravity and ocean tide loading in Europe

b
The results are presented from tidal gravity measurements at five sites in Europe using LaCoste and Romberg ET gravimeters. Improvements that we have made to the accuracies of these gravimeters are discussed. It is shown that the 'standard' calibration of the International Center for Earth Tides, used for worldwide tidal gravity profiles, is 1.2 per cent too high. The M₂ and O₁ observations are compared with model calculations of the Earth's body tide and ocean tide loading and it is shown that there is a very significant improvement in the agreement between observations and models compared to that obtained with previous tidal gravity measurements. For O₁, where the ocean tide loading and attraction in central Europe is only 0.4 per cent of the body tide, our measurements verify that the Dehant-Wahr anelastic body tide model gravimetric factor is accurate to 0.2 per cent. It is also shown that the effects of lateral heterogeneities in Earth structure on tidal gravity are too small to explain the large anomalies in previously published tidal gravity amplitudes. The observations clearly show the importance of conserving tidal mass in the Schwiderski ocean tide model. For sites in central Europe, the M₂ and O₁ observations and the models are in agreement at the 0.1 μgal (10⁻⁹ m s⁻²) level and tidal corrections to this accuracy can now be made to absolute gravity measurements.     

Comparison of tide model outputs for the northern region of the Antarctic Peninsula using satellite altimeters and tide gauge data

This study compares the common harmonic constants of the O₁, K₁, P₁, Q₁, M₂, S₂, N₂, and K₂ tidal constituents from eight global and four regional tide models with harmonic constants from satellite altimeter and tide gauge data for the northern region of the Antarctic Peninsula (58°S–66°S, 53°W–66°W). To obtain a more representative comparison, the study area was divided into three zones with different physical characteristics but similar maximum tidal amplitude variations: Zone I (north of 62°S), Zone II (south of 62°S and west of the Antarctic Peninsula), and Zone III (between 62°S and 64.3°S, and east of 58.5°W). Root sum square (RSS) values are less than or equal to 3.0, 4.2, and 8.4 cm for zones I, II, and III, respectively. No single model shows superior performance in all zones. Because there are insufficient satellite altimetry observations in the vicinity of Matienzo Base (64.9761°S, 60.0683°W), this station was analyzed separately and presents the greatest values of both root mean square misfit and RSS. The maximum, minimum, and average amplitude values of the constituents that follow in importance after the eight common tidal constituents, and which have amplitudes greater than 1 cm, are also analyzed.     

Modelling the pole tide and its effect on the Earth's rotation

Summary. The pole tide is the response of the ocean to incremental centrifugal forces associated with the Chandler wobble. The tide has a potentially important effect on the period and damping of the wobble, but it is at present not well constrained by observations. Here, we construct both analytical and numerical models for the pole tide. The analytical models consider the tide first in a global ocean and then in an enclosed basin on a beta-plane. The results are found to approach equilibrium linearly with decreasing frequency and inversely with increasing basin depth. The numerical models solve Laplace's tidal equations over the world's oceans using realistic continental boundaries and bottom topography. The results indicate that the effects of the non-equilibrium portion of the deep ocean tide on the Chandler wobble period and damping are negligible.     

Extraction of the M2 ocean tide from SEASAT altimeter data

Summary. Three complementary methods for the extraction of the M2 ocean tide using SEASAT altimetry are presented and compared. The first method (that developed by Cartwright & Alcock), which provides 'point measurements'of the tide at the crossovers of the SEASAT repeat orbit ground track, has been applied to a study of the tide in tropical ocean areas. The other two methods involve spatial expansions of M2 in terms of either surface spherical harmonics (in the case of the method developed by Mazzega) or Platzman normal modes of the world ocean. The results obtained by each method from only one month of SEASAT data reproduce many features of the tide represented in recent tidal models, and promise well for satellite altimetry as a future source of tidal knowledge.