Mapping and Wavenumber Resolution of Line-Integral Data for Observations of Low-Mode Internal Tides

Abstract

Abstract Techniques are developed for using line-integral tomography data to estimate the spectra, maps, and energy of low-mode internal-tide radiation; the extension of these techniques to other phenomena is obvious. Sparse arrays of line integrals over paths 300–1000 km long can generally determine the direction of propagation of semidiurnal radiation well, but the magnitude of the wavenumbers is ambiguous because of sidelobes in the spectrum. Both wavenumber magnitude and direction can generally be determined for diurnal internal-tide radiation. Spectra for the semidiurnal and diurnal internal tides are estimated for the region of the Atlantic Ocean between Puerto Rico and Bermuda using data obtained during the Acoustic Mid-Ocean Dynamics Experiment (AMODE) in 1991–92. Simulations of semidiurnal internal-tide radiation, consisting of wave packets or highly irregular wave crests, are used to show that the line-integral data provide better mapping resolution than point data, but the best results are, of course, obtained when both types of data are used. As a practical example of the formalism of these simulations, maps of M2 internal-tide variability are derived from the AMODE tomography data. Because the inverse problem is underdetermined with the sparse arrays that are deployed in the ocean, the inverse solution generally underestimates the energy of the radiative field. In the simulations employed here, the energy is underestimated by 33% ± 10%, but the exact amount by which the energy is underestimated is dependent on the assumptions made for the simulations, such as the array geometry and the nature of the tidal variability.