Two global ocean models ranging in horizontal resolution from 1/12° to 1/48° are used to study the space and time scales of sea surface height (SSH) signals associated with internal gravity waves (IGWs). Frequency‐horizontal wavenumber SSH spectral densities are computed over seven regions of the world ocean from two simulations of the HYbrid Coordinate Ocean Model (HYCOM) and three simulations of the Massachusetts Institute of Technology general circulation model (MITgcm). High wavenumber, high‐frequency SSH variance follows the predicted IGW linear dispersion curves. The realism of high‐frequency motions (> 0.87  cpd) in the models is tested through comparison of the frequency spectral density of dynamic height variance computed from the highest‐resolution runs of each model (1/25° HYCOM and 1/48° MITgcm) with dynamic height variance frequency spectral density computed from nine in situ profiling instruments. These high‐frequency motions are of particular interest because of their contributions to the small‐scale SSH variability that will be observed on a global scale in the upcoming Surface Water and Ocean Topography (SWOT) satellite altimetry mission. The variance at supertidal frequencies can be comparable to the tidal and low‐frequency variance for high wavenumbers (length scales smaller than ∼50 km), especially in the higher‐resolution simulations. In the highest‐resolution simulations, the high‐frequency variance can be greater than the low‐frequency variance at these scales.

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High horizontal‐resolution ( 1/12.5° and 1/25°) 41‐layer global simulations of the HYbrid Coordinate Ocean Model (HYCOM), forced by both atmospheric fields and the astronomical tidal potential, are used to construct global maps of sea surface height (SSH) variability. The HYCOM output is separated into steric and nonsteric and into subtidal, diurnal, semidiurnal, and supertidal frequency bands. The model SSH output is compared to two data sets that offer some geographical coverage and that also cover a wide range of frequencies—a set of 351 tide gauges that measure full SSH and a set of 14 in situ vertical profilers from which steric SSH can be calculated. Three of the global maps are of interest in planning for the upcoming Surface Water and Ocean Topography (SWOT) two‐dimensional swath altimeter mission: (1) maps of the total and (2) nonstationary internal tidal signal (the latter calculated after removing the stationary internal tidal signal via harmonic analysis), with an average variance of 1.05 and 0.43 cm2, respectively, for the semidiurnal band, and (3) a map of the steric supertidal contributions, which are dominated by the internal gravity wave continuum, with an average variance of 0.15 cm2. Stationary internal tides (which are predictable), nonstationary internal tides (which will be harder to predict), and nontidal internal gravity waves (which will be very difficult to predict) may all be important sources of high‐frequency “noise” that could mask lower frequency phenomena in SSH measurements made by the SWOT mission.

In recent years, high-resolution ("eddying") global three-dimensional ocean general circulation models have begun to include astronomical tidal forcing alongside atmospheric forcing. Such models can carry an internal tide field with a realistic amount of nonstationarity, and an internal gravity wave continuum spectrum that compares more closely with observations as model resolution increases. Global internal tide and gravity wave models are important for understanding the three-dimensional geography of ocean mixing, for operational oceanography, and for simulating and interpreting satellite altimeter observations. Here we describe the most important technical details behind such models, including atmospheric forcing, bathymetry, astronomical tidal forcing, self-attraction and loading, quadratic bottom boundary layer drag, parameterized topographic internal wave drag, shallow-water tidal equations, and a brief summary of the theory of linear internal gravity waves. We focus on simulations run with two models, the HYbrid Coordinate Ocean Model (HYCOM) and the Massachusetts Institute of Technology general circulation model (MITgcm). We compare the modeled internal tides and internal gravity wave continuum to satellite altimeter observations, moored observational records, and the predictions of the Garrett-Munk (1975) internal gravity wave continuum spectrum. We briefly examine specific topics of interest, such as tidal energetics, internal tide nonstationarity, and the role of nonlinearities in generating the modeled internal gravity wave continuum. We also describe our first attempts at using a Kalman filter to improve the accuracy of tides embedded within a general circulation model. We discuss the challenges and opportunities of modeling stationary internal tides, non-stationary internal tides, and the internal gravity wave continuum spectrum for satellite altimetry and other applications. Introductionhis book chapter is about global modeling of oceanic internal tides and the oceanic internal gravity wave continuum. The chapter focuses on hydrodynamical modeling, rather than empirical modeling, of such motions. Due to the operational oceanography theme of the book in which this chapter resides, we focus on high-spatial-resolution numerical models run over relatively short time scales-i.e., simulations that could form the dynamical backbone of operational models-rather than on lower-resolution models run over decades or centuries for climate forecasting purposes. In this introductory section, after defining internal gravity waves and internal tides, we discuss the motivation for, requirements for, and history of global modeling of internal tides and the internal gravity wave continuum. A subsequent section focuses on the technical details underlying such models, such as atmospheric forcing, bathymetry, astronomical tidal forcing, self-attraction and loading, quadratic bottom boundary layer drag, parameterized topographic internal wave drag, shallow-water tidal equations, and a brief synopsis of internal wave theor...

The jets in the equatorial Pacific Ocean of a realistically forced global circulation model with a horizontal resolution of 1/12.5° cause a strong loss of phase coherence in semidiurnal internal tides that propagate equatorward from the French Polynesian Islands and Hawaii. This loss of coherence is quantified with a baroclinic energy analysis, in which the semidiurnal‐band terms are separated into coherent, incoherent, and cross terms. For time scales longer than a year, the coherent energy flux approaches zero values at the equator, while the total flux is ∼500 W/m. The time variability of the incoherent energy flux is compared with the internal‐tide travel‐time variability, which is based on along‐beam integrated phase speeds computed with the Taylor‐Goldstein equation. The variability of monthly mean Taylor‐Goldstein phase speeds agrees well with the phase speed variability inferred from steric sea surface height phases extracted with a plane‐wave fit technique. On monthly time scales, the loss of phase coherence in the equatorward beams from the French Polynesian Islands is attributed to the time variability in the vertically sheared background flow associated with the jets and tropical instability waves. On an annual time scale, the effect of stratification variability is of equal or greater importance than the shear variability is to the loss of coherence. In the model simulations, low‐frequency equatorial jets do not noticeably enhance the dissipation of the internal tide, but merely decohere and scatter it.