Directional Wavenumber Spectrum of Internal Wave SSH Variance from Single Mooring Measurements

The upcoming Surface Water and Ocean Topography satellite mission will measure sea surface height with unprecedented horizontal resolution. At the smaller scales that will be accessible by SWOT, internal waves account for a significant fraction of the SSH variance in some regions. Whether those waves strongly project onto SWOT observations depends crucially on the directionality of the internal-wave field, yet most of the previous studies in the context of SWOT have assumed horizontal isotropy. We here develop a methodology for estimating the SSH variance directional wavenumber spectrum of internal waves based on interior observations at a single mooring. Following the mature field of surface-gravity waves, the directional spectrum is obtained from cross-spectra of simultaneous measurements of SSH and its slopes. Here the internal-wave SSH and its slopes are estimated via projection of the hydrostatic relation and the horizontal linear momentum equations onto baroclinic modes. We further convert the frequency-direction SSH variance spectrum into a wavenumber-direction SSH variance spectrum using the modal dispersion relationship of internal waves. Using data from a general circulation ocean model with embedded tides (a main source of internal waves in the ocean), we find that our method yields a directional SSH variance spectrum consistent with the directional spectrum calculated directly from 2D SSH snapshots. We apply our single-mooring method to study the directional properties of internal waves in the STRATUS XI Mooring, in the Southeast Pacific. At STRATUS XI, the internal-wave field was fairly directional, with most variance propagating in the meridional direction. As illustrated by the STRATUS XI application, our method provides a new tool to studying the projection of internal waves onto SWOT measurements and, more broadly, the energetics of internal waves in the global ocean.