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This paper examines spectra of horizontal kinetic energy (HKE) in the surface and sub‐surface ocean, with an emphasis on internal gravity wave (IGW) motions, in global high‐resolution ocean simulations. Horizontal wavenumber‐frequency spectra of surface HKE are computed over seven oceanic regions from two global simulations of the HYbrid Coordinate Ocean Model (HYCOM) and three global simulations of the Massachusetts Institute of Technology general circulation model (MITgcm). In regions with high IGW activity, high surface HKE variance in the horizontal wavenumber‐frequency spectra is aligned along IGW linear dispersion curves. For both HYCOM and MITgcm, and in almost all regions, finer horizontal resolution yields more energetic supertidal IGW continuum spectra. The ratio of high‐horizontal‐wavenumber variance in semi‐diurnal and supertidal motions relative to lower‐frequency motions, a quantity of great interest for swath altimetry, depends on the model employed and the horizontal resolution within the model, implying that quantitative predictions of the partition between low‐ and high‐frequency motions taken from particular simulations should be treated with care. The frequency‐vertical wavenumber spectra, frequency spectra, and vertical wavenumber spectra from the models are compared to spectra computed from McLane profilers at nine locations. In general, MITgcm spectra match the McLane profiler spectra more closely at high frequencies (|ω| > 4.5 cpd). In both models, vertical wavenumber spectra roll off more steeply than observations at high vertical wavenumbers (m > 10−2 cpm). The vertical wavenumber spectra in such models is an important target for improvement, due to turbulence production and dissipation that takes place at high vertical wavenumbers. Plain Language Summary: Recently, a small but growing number of global ocean models have begun to employ simultaneous tidal and atmospheric forcing. At the same time, increasing supercomputer power has allowed for simulations of oceanic motions with increasing accuracy, increasing feature (spatial) resolution, and more frequent time slices. Global ocean models with fine grid spacing, and simultaneous tidal and atmospheric forcing, host a vigorous spectrum of high‐frequency waves that control mixing over most of the ocean water column, and are important for many operational oceanography challenges. As an example of the latter, high‐resolution global internal wave models have been used to study the relative partition of high‐frequency versus low‐frequency motions at the small horizontal scales that will be measured by the new Surface Water Ocean Topography mission. The partition described above depends on the model employed and the grid spacing employed within that model, meaning that conclusions about the partition are dependent on the model used to estimate it. Comparisons between the models and vertically profiling instruments indicate that resolving fine scale motions in the vertical direction, where ocean mixing takes place, is not yet handled well by the models. Modeling of fine‐vertical scale motions is therefore an important future research direction. Key Points: Vertical wavenumber spectra of internal gravity wave kinetic energy in two high‐resolution global models are compared to observed spectraModels under‐estimate motions at high vertical wavenumbers (small vertical scales), flagging this as a target for model improvementThe ratio of high‐ versus low‐frequency surface kinetic energy at small horizontal scales is dependent on the model and grid spacings employed [ABSTRACT FROM AUTHOR]

We investigate the seasonal variability of the semidiurnal internal tide steric sea surface height (SSSH) and energetics using 8-km global Hybrid Coordinate Ocean Model (HYCOM) simulations with realistic forcing and satellite altimeter data. In numerous previous studies, SSSH has been used to explore the seasonal changes in internal tides. For the first time, we compare the seasonal variability of the semidiurnal internal tide SSSH with the seasonal variability of the semidiurnal baroclinic energetics. We explore the seasonal trends in SSSH variance, barotropic to baroclinic conversion rate, kinetic energy, available potential energy, and pressure flux for the semidiurnal internal tides. We find that the seasonal cycle of monthly semidiurnal SSSH variance in the Northern Hemisphere is out of phase with the Southern Hemisphere. This north-south phase difference and its timing are in agreement with altimetry. The amplitudes of the seasonal variability in SSSH variance are about 10–15 % of their annual-mean values when zonally averaged. The normalized amplitude of the seasonal variability is higher for the SSSH variance than for the energetics. The largest seasonal variability is observed in Georges Bank and the Arabian Sea, where the seasonal trends of monthly SSSH variance and energetics are in phase. However, outside these hotspots, the seasonal variability in semidiurnal energetics is out of phase with semidiurnal SSSH variance and a clear phase difference between the Northern and Southern Hemispheres is lacking. While the seasonal variability in semidiurnal energy is driven by seasonal changes in barotropic to baroclinic conversion, semidiurnal SSSH variance is also modulated by seasonal changes in stratification. Surface intensified stratification at the end of summer enhances the surface perturbation pressures, which enhance the SSSH amplitudes. [ABSTRACT FROM AUTHOR]

Internal tides (ITs) play a critical role in ocean mixing, and have strong signatures in ocean observations. Here, global IT sea surface height (SSH) in nadir altimetry is compared with an ocean forecast model that assimilates de‐tided SSH from nadir altimetry. The forecast model removes IT SSH variance from nadir altimetry at skill levels comparable to those achieved with empirical analysis of nadir altimetry. Accurate removal of IT SSH is needed to fully reveal lower‐frequency mesoscale eddies and currents in altimeter data. Analysis windows of order 30–120 days, made possible by the frequent (hourly) outputs of the forecast model, remove more IT SSH variance than longer windows. Forecast models offer a promising new approach for global internal tide mapping and altimetry correction. Because they provide information on the full water column, forecast models can also help to improve understanding of the underlying dynamics of ITs. Plain Language Summary: Tidal flow over topographic features on the seafloor generates vertical displacements along the interfaces of ocean layers that have different densities. These vertical displacements at tidal frequencies are known as internal tides. Internal tide displacements are largest well below the sea surface, but also display a sea surface height (SSH) signature that is large enough to be measured by satellite altimeters. Removing internal tide signals from satellite altimeter SSH allows for a more accurate accounting of non‐tidal features, including slowly evolving ocean currents and eddies, that are also measured by altimeters. Here, we show that supercomputer ocean forecast simulations of the global internal tide field are able to remove internal tide SSH from satellite altimeter measurements with a skill level that is comparable to the skill of internal tide SSH removal based upon analysis of the satellite altimeter data itself. Thus, forecast models offer a complementary method for this important task. In addition, forecast models provide information on the entire ocean water column, not just the sea surface. Finally, the hourly outputs of forecast models allow for a greater variety of tidal analysis record lengths than can be achieved with altimeter outputs, which report sea surface height fields much less frequently. Key Points: Global ocean forecast models can accurately simulate both long‐term (phase‐locked) internal tides and their short‐term modulationsOcean forecast models offer a useful complement to empirical models for mapping internal tides and correcting altimetry for internal tidesIn regions of strong internal tides, optimal variance reduction in nadir altimetry is attained through short‐term tidal analyses (∼60 days) [ABSTRACT FROM AUTHOR]

The decay of the low‐mode internal tide due to the superharmonic energy cascade is investigated in a realistically forced global Hybrid Coordinate Ocean Model simulation with 1/25° (4 km) horizontal grid spacing. Time‐mean and depth‐integrated supertidal kinetic energy is found to be largest near low‐latitude internal tide generation sites, such as the Bay of Bengal, Amazon Shelf, and Mascarene Ridge. The supertidal kinetic energy can make up to 50% of the total internal tide kinetic energy several hundred kilometers from the generation sites. As opposed to the tidal flux divergence, the supertidal flux divergence does not correlate with the barotropic to baroclinic energy conversion. Instead, the time‐mean and depth‐integrated supertidal flux divergence correlates with the nonlinear kinetic energy transfers from (sub)tidal to supertidal frequency bands as estimated with a novel coarse‐graining approach. The regular spaced banding patterns of the surface‐intensified nonlinear energy transfers are attributed to semidiurnal mode 1 and mode 2 internal waves that interfere constructively at the surface. This causes patches where both surface tidal kinetic energy and nonlinear energy transfers are elevated. The simulated internal tide off the Amazon Shelf steepens significantly near these patches, generating solitary‐like waves in good agreement with Synthetic Aperture Radar imagery. Globally, we find that regions of high supertidal energy flux also show a high correlation with observed instances of internal solitary waves. Plain Language Summary: Ocean tides generate internal waves at steep ridges and continental shelves in a stratified ocean. In some regions with strong tidal forcing, surface intensified stratification, and weak background rotation, these waves are observed to steepen into solitary‐like waves. In this process, energy is transferred from the tidal band to higher (supertidal) frequencies and wavenumbers. This study investigates "internal tide steepening" in a realistically forced global Hybrid Coordinate Ocean Model (HYCOM) simulation with a 4‐km horizontal grid spacing. In our simulation, supertidal internal wave energy accounts for about 5% of the total energy available to internal tides equatorward of ±25°. However in some regions, such as the Amazon Shelf and Bay of Bengal, this ratio can be as much as 50%. Along the internal tide beams, the supertidal energy transfers are enhanced in regular spaced "patches" where longer and faster mode 1 semidiurnal internal tides overtake the shorter and slower mode 2 internal tides. In these patches the surface velocities of these waves constructively superpose, enhancing the surface kinetic energy and nonlinear energy transfers. At the Amazon Shelf, sharp‐crested solitary‐like waves that emerge in these patches in the HYCOM simulation are in good agreement with satellite observations. Although nonlinear internal tides are simulated in our global ocean model simulation, higher resolutions are needed to better resolve the energy cascade to smaller scales. Key Points: Supertidal energy (>2.67 cycles per day [cpd]) is elevated at low latitudes, making up to 50% of total tidal energy (>0.9 cpd) in some areasSupertidal flux divergence and surface tidal energy reveal banding patterns due to the interaction between mode 1 and 2 internal tidesSupertidal flux divergence is due to energy transfers from internal tides to higher‐harmonic frequencies as computed with coarse graining [ABSTRACT FROM AUTHOR]

The total variance and decorrelation of the semidiurnal internal tide (IT) are examined in a 32-day segment of a global run of the HYbrid Coordinate Ocean Model (HYCOM). This numerical simulation, with 41 vertical layers and 1/25 degree horizontal resolution, includes tidal and atmospheric forcing allowing for the generation and propagation of IT to take place within a realistic eddying general circulation. The HYCOM data are in turn compared with global observations of the IT around 1,000 dbar, from Argo float park phase data and mooring records. HYCOM is found to be globally biased low in terms of total variance and decorrelation of the semidiurnal IT over timescales shorter than 32 days. Except in the Southern Ocean, where limitations in the model causes the discrepancy with in situ measurements to grow poleward, the spatial correlation between the Argo and HYCOM inferred total variance suggests that the generation of low-mode semidiurnal IT is globally well captured by the model. [ABSTRACT FROM AUTHOR]

In order to access the targeted ocean signal, altimeter measurements are corrected for several geophysical parameters among which the ocean tide correction is one of the most critical, but the internal tide signature at the surface are not yet corrected globally. Internal tides can have a signature of several cm at the surface with wavelengths about 50-250 km for the first mode and even smaller scales for higher order modes. The goals of the upcoming Surface Water Ocean Topography (SWOT) mission and other high- resolution ocean measurements make the correction of these small scale signals a challenge, as the separation of all tidal variability from other oceanic signals becomes mandatory. In this context, several scientific teams are working on the development of new internal tide models, taking advantage of the very long altimeter time series now available, which represent an unprecedented and valuable global ocean database. The internal tide models presented here focus on the coherent internal tide signal and they are of three types: empirical models based upon analysis of existing altimeter missions, an assimilative model, and a three-dimensional hydrodynamic model. A detailed comparison and validation of these internal tide models is proposed using existing satellite altimeter databases. The analysis focuses on the four main tidal constituents M2, K1, O1 and S2. The validation process is based on a statistical analysis of multi-mission altimetry including Jason-2 and Cryosphere Satellite-2 data, taking advantage of the long-term altimeter databases available. The results show a significant altimeter variance reduction when using internal tide corrections on all ocean regions where internal tides are generating/propagating. A complementary spectral analysis also gives some estimation of the performance of each model as a function of wavelength, and some insight into the residual non-stationary part of internal tides in the different regions of interest. [ABSTRACT FROM AUTHOR]

Temperature variance and kinetic energy (KE) from two global simulations of the HYbrid Coordinate Ocean Model (HYCOM; 1/12° and 1/25°) and three global simulations of the Massachusetts Institute of Technology general circulation model (MITgcm; 1/12°, 1/24°, and 1/48°), all of which are forced by atmospheric fields and the astronomical tidal potential, are compared with temperature variance and KE from a database of about 2,000 moored historical observations (MHOs). The variances are computed across frequencies ranging from supertidal, dominated by the internal gravity wave continuum, to subtidal, dominated by currents and mesoscale eddies. The most important qualitative difference between HYCOM and MITgcm, and between simulations of different resolutions, is in the supertidal band, where the 1/48° MITgcm lies closest to observations. Across all frequency bands examined, the HYCOM simulations display higher spatial correlation with the MHO than do the MITgcm simulations. The supertidal, semidiurnal, and diurnal velocities in the HYCOM simulations also compare more closely with observations than do the MITgcm simulations in a number of specific continental margin/marginal sea regions. To complement the model‐MHO comparisons, this paper also compares the surface ocean geostrophic eddy KE in HYCOM, MITgcm, and a gridded satellite altimeter product. Consistent with the model‐MHO comparisons, the HYCOM simulations have a higher spatial correlation with the altimeter product than the MITgcm simulations do. On the other hand, the surface ocean geostrophic eddy KE is too large, relative to the altimeter product, in the HYCOM simulations. [ABSTRACT FROM AUTHOR]