Sea Surface Height Signatures of Internal Gravity Waves

Sea surface height (SSH) is a fundamental variable in physical oceanography and is the key observable quantity in global satellite altimetry. SSH is a complicated manifestation of many oceanic processes, and, as such, exhibits variability over a wide range of space and time scales. It is well known that tides are of first order importance in SSH, but SSH contributions outside of this narrow band are also of great interest. Satellite altimetry has become an invaluable tool in the study of the global ocean. However, the long repeat period (of order ten to 40 days) of altimeters implies that high-frequency motions will be aliased in altimeter records. In order to study the lower-frequency SSH variability, the aliased high-frequency variability must first be accurately removed. Some of these high-frequency motions, such as the stationary component of surface and internal tides, can be adequately removed even from aliased records, via harmonic analysis or response methods, as long as the signal-to-noise ratio is relatively high. However, the challenge of removing SSH signals associated with motions that are less predictable, for instance, the non-stationary component of the internal tides, or the internal gravy wave (IGW) continuum, is much greater. To quantify the magnitude of this challenge, high resolution global general circulation ocean models are used to simulate and study internal tides, the IGW continuum, and other contributions to sea surface variability. Using these models, we examine the space- and time-scales of SSH variability. For instance, we compute frequency- horizontal wavenumber (ω − K) spectral densities over a several oceanic regions that collectively represent different regimes of global ocean variability. These ω − K spectral densities show high energy along lines representing the linear dispersion relations predicted by the Sturm-Liouville problem for internal waves. In many oceanic regions, the high-frequency motions dominate the small-scale (high-wavenumber) SSH spectra. This has implications for upcoming wide-swath satellite altimeter missions, which will focus on high-wavenumber SSH spectra. In addition to quantifying the frequency-horizontal wavenumber spectral densities, we estimate the SSH variance in subtidal, tidal, and supertidal phenomena through the use of frequency spectral densities. This temporally driven approach allows us to create global maps of SSH variance in these frequency bands. The global band-integrated maps are further divided into steric and non-steric SSH components, which further helps to delineate different classes of oceanic motions. These global band-integrated maps provide both results consistent with previous studies (e.g., of subtidal steric SSH, dominated by mesoscale eddies and well-measured by current generation satellite altimeters), as well as unprecedented global maps of the non-stationary component of the internal tides and of the IGW continuum. As global general circulation ocean models have only begun to be able to partially resolve the IGW continuum, we believe that our estimate represents a lower bound of variance in the IGW continuum, and will likely increase with increased horizontal and vertical resolution of ocean models. Indeed, comparisons of the models used here with in-situ data strongly suggest that the mod- els used here underestimate the IGW continuum, while representing other motions with a higher accuracy.PhDApplied PhysicsUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttps://deepblue.lib.umich.edu/bitstream/2027.42/138555/1/savagea_1.pd