Atlas of ocean tidal charts and maps, Part I: The semidiurnal principal lunar tide M₂

Abstract

In this paper the author presents the NSWC ocean tide model of the semidiurnal principal lunar (M₂) tide in an atlas of ocean tidal charts and maps. The model is the computer result of a unique combination of mathematical and empirical techniques, which was introduced, extensively tested, and evaluated by Schwiderski (1978a, 1980a, b, 1983e). The computed M₂ amplitudes and phases are tabulated along with all specially labeled empirical input data on a 1° × 1 ° grid system in 42° × 71° overlapping charts covering the whole oceanic globe. Corresponding global and arctic corange and cotidal maps are included to provide a quick overview of the major tidal phenomena. Significant qualitative and quantitative features are explained and discussed for proper application. In particular, the charted harmonic constants may be used to compute instantaneous M₂ ocean tides with an accuracy of better than 5 cm any time and anywhere in the open oceans. Limitations of this accuracy in coastal waters and border seas are mentioned.

The following four sections of this paper deal with brief reviews, detailed evaluations, and simple improvements of general and special applications of the NSWC ocean tide model. In spite of the numerous and diverse applications with potential possibilities of erroneous interpretations, the results are gratifying without exceptions. For instance, it is concluded that the computed low‐degree spherical harmonic coefficients of the M₂ ocean tide model agree with recent empirical satellite solutions as closely as one could wish for within the elaborated nonmodel error bounds. Detailed computations of all significant tidal energy terms produced the following noteworthy results: The rate of supplied tidal energy of 3.50Z10¹² Watt matches Cartwright's (1977) estimate of 3.5Z10¹² Watt. The rate of energy loss by bottom friction and displacement over the shelves is 1.50Z10¹² Watt, which fits into Miller's (1966) estimated range of (1.4–1.7)Z10¹² Watt, with a clear bias toward his preferred lower bound. Perhaps most remarkably, the computed range (0.41–0.60)Z10¹² Watt for the rate of deep bottom friction work done by the unresolved fluctuating (internal or baroclinic) currents contains in its center Munk's (1966) estimate of 0.5Z10¹² Watt and lies safely below Wunsch's (1975) extreme upper bound of 0.7Z10¹² Watt, which both authors derived for the rate of energy needed to sustain the internal tidal circulations. As is commonly believed, the results substantiate the fact that the total rate of ocean eddy dissipation (into heat) by the averaged (surface or barotropic) currents and their fluctuating comotions is negligible within three significant figures. Finally, the total tidal energy budget of the oceans is perfectly balanced in realistic terms. Budget deficits in earlier tide models were traced to the following tacit assumptions: The ocean bottom tide is doing positive work on the oceans against the ocean tide. In fact, the bottom displacement work by the ocean tide against the bottom tide is an energy loss at the rate of 1.64Z10¹² Watt. The transfer of G. I. Taylor's quadratic bottom friction term from the Irish Sea to the global oceans without accounting for major differences in area resolution scales is directly responsible for significant budget deficits in semiempirical estimates. In contrast, the hydrodynamically more consistent and realistic linear law of bottom friction encountered no serious transplantation difficulties.