O1, P1, N2 models of the global ocean tide on an elastic earth plus surface potential and spherical harmonic decompositions for M2, S2, and K1

Abstract

Because of the growing utility of having models of additional tidal constituents, this paper supplements models of M2, S2, and K1 presented previously in this journal with models of O1, P1, and N2 produced in exactly the same way. As before, the models satisfy specified elevation boundary conditions and are generated by fitting a small number of test functions to island data. Having models of three constituents in each band allows for estimates of cross‐band variations. Model admittances vary smoothly from place to place throughout the deep oceans, although significant variations can occur over distances as short as a few thousand kilometers; the most significant variations occur in the South Atlantic and Pacific oceans.

As before, this paper presents maps of the geocentric tide, the induced free space potential, the induced vertical component of the solid earth tide, and the induced vertical component of the gravitational field for each new component based on Farrell's 1972 Green's functions. In addition, since the tidal potential seen by an observer fixed to the surface of the solid earth is important to barotropic tidal velocity calculations and to tidal energy calculations in the deep ocean, maps of this quantity are also presented for all six constituents. The 1980 static Love number hypothesis of Schwiderski is compared with the presented Green's function results. Static Love numbers are calculated in the least squares sense. The static Love number is found to account for only part of the Green's function variability.

Spherical harmonic coefficients up to order 4 and the rms magnitude of the coefficients to order 15 are presented for each constituent. The rms magnitudes of the P1 and K1 coefficients normalized by their respective equilibrium amplitudes are compared to look for the effect of the diurnal core resonance as proposed by Sasao and Wahr in 1981. Although the second harmonic K1 rms magnitude is augmented by the predicted value of 1.04, this is curiously not true of the other spherical harmonic orders, as might be expected from the predicted increase in the forcing potential.