Statistics – Computation
Scientific paper
Apr 1988
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1988rspta.324..513c&link_type=abstract
Philosophical Transactions of the Royal Society of London. Series A, Mathematical and Physical Sciences, Volume 324, Issue 1581,
Statistics
Computation
21
Scientific paper
As a sequel to Cartwright et al. (Phil. Trans. R. Soc. Lond. A298, 87-139 (1980)) (C.E.S.V.) an extended series of oceanic tidal pressure measurements in the Atlantic Ocean is described and the spatial properties of their spectral components are analysed. The principal linear admittances vary widely across the ocean basins, and clearly indicate the positions of the major amphidromes. Constants for the leading harmonics M2 and S2 are defined everywhere along the parallel of 53.6 degrees N and along a section from Natal (Brazil) and west Africa by interpolation between measurements. From a unique set of seven one-year deep pressure records between 57 degrees N and the Equator, the radiational component of S2 is shown to have similar magnitude and phase anomaly to values previously known only at coastal stations, confirming its intrinsically atmospheric forcing. From the same records, nonlinear terms in the semidiurnal band are found to be irregular and indistinguishable from noise. From the full set of data, the M4 overtide is generally small and erratic, probably affected in some areas by low-stability internal waves. The long-period tides Mm and Mf are clearly identified in the equatorial zone as coherent motions with slight phase variations. Their amplitudes are significantly greater than those deduced from the `self-consistent equilibrium theory' of Agnew & Farrell (Geophys. Jl R. astr. Soc. 55, 171-181 (1978)). The M1 tide, linearly driven from the third-degree harmonic of the potential, has been extracted from multiyear records at 13 representative coastal stations in both hemispheres. It is shown to agree well with a synthesis of normal modes of oscillation computed by Platzman (J. Phys. Oceanogr. 14 (10), 1521-1550 (1984)), provided a general phase adjustment of about 60 degrees is made to the synthesized phases. The other third-degree term M3 is well extracted from most of the pelagic stations but is found to be too finely structured in space for easy interpolation. Attempts are made to model the M3 tide from sums of normal modes and from Proudman functions (defined in section 5a) with only moderate success, owing to noisy coastal data. High solar harmonics from the atmospheric tide penetrate to the ocean bottom, and are especially noticeable at low latitudes. The ter-diurnal solar pressure close to S3 is shown to have similar spectral characteristics in midocean to that calculated from the fourth harmonic of the radiational potential of Munk & Cartwright (Phil. Trans. R. Soc. Lond. A259, 533-581 (1966)). At coastal stations, however, the S3 line itself dominates, probably because of the thermal responses of the conventional tide gauge and of shallow coastal waters. Representative diurnal and semidiurnal harmonics are mapped spatially by the `objective analysis' procedure of Sanchez et al. (Mar. Geod. 9 (1), 71-91 (1985)), with a set of basis (Proudman) functions computed for the Atlantic-plus-Indian Oceans by D. B. Rao. Data from both oceans are used in the fits but the results are probably most accurate in the Atlantic Ocean on account of the greater concentration of pelagic data. The first 100 Proudman functions out of 470 computed by Rao are found to fit the M2 data (50 for O1) optimally, without `over-fitting'. Goodness of fit is biased towards areas of greater amplitude. Most of the known features of tidal maps are reproduced fairly well, but the anti-amphidrome of M2 in the Indian Ocean has too large amplitude. Inaccuracy is attributed to the dearth of pelagic tidal data in the Indian Ocean. The same constituents are similarly mapped by empirically fitting sums of Platzman's normal mode functions to the same data. Numbers of basis functions here should, in principle, be restricted by the need for reasonably small values of (natural frequency of mode minus tidal frequency). About 20 Platzman modes give a reasonable mapping of O1, less successfully for M2, but the fits are generally less good than those from 50-100 Proudman functions. A calculation of the work done by the Moon on the Atlantic tidal field defined by the Proudman-function synthesis confirms that this parameter is the net sum of nearly cancelling positive and negative zones, and is therefore sensitive to small errors in the tidal field. In summary, there remains a mismatch between the precision and detail of tidal parameters known at a finite number of measuring points and spatial interpolations derived from present computational schemes.
Cartwright David Edgar
Spencer Ralph
Vassie J. M.
Woodworth Philip L.
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