The accuracy of state-of-the-art global barotropic tide models is assessed using bottom pressure data, coastal tide gauges, satellite altimetry, various geodetic data on Antarctic ice shelves, and independent tracked satellite orbit perturbations. Tide models under review include empirical, purely hydrodynamic ("forward"), and assimilative dynamical, i.e., constrained by observations. Ten dominant tidal constituents in the diurnal, semidiurnal, and quarter-diurnal bands are considered. Since the last major model comparison project in 1997, models have improved markedly, especially in shallow-water regions and also in the deep ocean. The root-sum-square differences between tide observations and the best models for eight major constituents are approximately 0.9, 5.0, and 6.5 cm for pelagic, shelf, and coastal conditions, respectively. Large intermodel discrepancies occur in high latitudes, but testing in those regions is impeded by the paucity of high-quality in situ tide records. Long-wavelength components of models tested by analyzing satellite laser ranging measurements suggest that several models are comparably accurate for use in precise orbit determination, but analyses of GRACE intersatellite ranging data show that all models are still imperfect on basin and subbasin scales, especially near Antarctica. For the M 2 constituent, errors in purely hydrodynamic models are now almost comparable to the 1980-era Schwiderski empirical solution, indicating marked advancement in dynamical modeling. Assessing model accuracy using tidal currents remains problematic owing to uncertainties in in situ current meter estimates and the inability to isolate the barotropic mode. Velocity tests against both acoustic tomography and current meters do confirm that assimilative models perform better than purely hydrodynamic models.

[1] Global comparisons of barotropic and internal tides generated in an eddy-resolving ocean circulation model are made with tidal estimates obtained from altimetric sea surface heights and an altimetry-constrained tide model. As far as we know, our Hybrid Coordinate Ocean Model (HYCOM) simulations shown here and in an earlier paper are the only published high-resolution global simulations to contain barotropic tides, internal tides, the general circulation, and mesoscale eddies concurrently. Comparing the model barotropic tide with a global data-assimilative shallow water tide model shows that the global tidal elevation differences are approximately evenly split between discrepancies in tidal amplitude and phase. Both the model and observations show strong generation of internal tides at a limited number of "hot spot" regions with propagation of beams of energy for thousands of kilometers away from the sources. The model internal tidal amplitudes compare well with observations near these energetic tidal regions. Averaged over these regions, the model and observation internal tide amplitude estimates agree to approximately 15% for the four largest semidiurnal constituents and 23% for the four largest diurnal constituents. Away from the hot spots, the comparison between the model and altimetric amplitude is not as good due, in part, to two problems, errors in the model barotropic tides and overestimation of the altimetric tides in regions of strong mesoscale eddy activity. Examining the general energy distribution of the simulated internal tide is an important first step in the evaluation of internal tides in HYCOM.

Motivated by the recent interest in ocean energetics, the widespread use of horizontal eddy viscosity in models, and the promise of high horizontal resolution data from the planned wide-swath satellite altimeter, this paper explores the impacts of horizontal eddy viscosity and horizontal grid resolution on geostrophic turbulence, with a particular focus on spectral kinetic energy fluxes P(K) computed in the isotropic wavenumber (K) domain. The paper utilizes idealized two-layer quasigeostrophic (QG) models, realistic highresolution ocean general circulation models, and present-generation gridded satellite altimeter data. Adding horizontal eddy viscosity to the QG model results in a forward cascade at smaller scales, in apparent agreement with results from present-generation altimetry. Eddy viscosity is taken to roughly represent coupling of mesoscale eddies to internal waves or to submesoscale eddies. Filtering the output of either the QG or realistic models before computing P(K) also greatly increases the forward cascade. Such filtering mimics the smoothing inherent in the construction of present-generation gridded altimeter data. It is therefore difficult to say whether the forward cascades seen in present-generation altimeter data are due to real physics (represented here by eddy viscosity) or to insufficient horizontal resolution. The inverse cascade at larger scales remains in the models even after filtering, suggesting that its existence in the models and in altimeter data is robust. However, the magnitude of the inverse cascade is affected by filtering, suggesting that the wide-swath altimeter will allow a more accurate determination of the inverse cascade at larger scales as well as providing important constraints on smaller-scale dynamics.

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.

.[1] The slopes of the wavenumber spectra of sea surface height (SSH) and kinetic energy (KE) have been used to infer "interior" or surface quasi-geostrophic (QG or SQG) dynamics of the ocean. However, inspection of spectral slopes for altimeter SSH in the mesoscale band of 70 to 250 km shows much flatter slopes than the QG or SQG predictions over most of the ocean. Comparison of altimeter wavenumber spectra with spectra from an eddy resolving global ocean circulation model (the HYbrid Coordinate Ocean Model, HYCOM, at 1/12.5 equatorial resolution), which has embedded tides, suggests that the flatter slopes of the altimeter SSH may arise from three possible sources: (1) presence of strong internal tides, (2) shift of the inertial sub-range to smaller scales and (3) altimeter noise. Artificially adding noise to the model tends to flatten the spectra for low KE regions. Near internal tide generating regions, spectral slopes in the presence of internal waves are much flatter than QG or SQG predictions. Separating the variability into high and low frequency (around periods of 2 days), then a different pattern emerges with a flat high-frequency wavenumber spectrum and a steeper low-frequency wavenumber spectrum. For low mesoscale KE, the inertial sub-range, defined by the nearly flat enstrophy band, moves to smaller scales and the mesoscale band of 70 to 250 km no longer represents the inertial sub-range. The model wavenumber spectra are consistent with QG and SQG theory when internal waves and inertial sub-range shifts are taken into consideration.Citation: Richman, J. G., B. K. Arbic, J. F. Shriver, E. J. Metzger, and A. J. Wallcraft (2012), Inferring dynamics from the wavenumber spectra of an eddying global ocean model with embedded tides,

Motivated by the potential of oceanic mesoscale eddies to drive intrinsic low-frequency variability, this paper examines geostrophic turbulence in the frequency–wavenumber domain. Frequency–wavenumber spectra, spectral fluxes, and spectral transfers are computed from an idealized two-layer quasigeostrophic (QG) turbulence model, a realistic high-resolution global ocean general circulation model, and gridded satellite altimeter products. In the idealized QG model, energy in low wavenumbers, arising from nonlinear interactions via the well-known inverse cascade, is associated with energy in low frequencies and vice versa, although not in a simple way. The range of frequencies that are highly energized and engaged in nonlinear transfer is much greater than the range of highly energized and engaged wavenumbers. Low-frequency, low-wavenumber energy is maintained primarily by nonlinearities in the QG model, with forcing and friction playing important but secondary roles. In the high-resolution ocean model, nonlinearities also generally drive kinetic energy to low frequencies as well as to low wavenumbers. Implications for the maintenance of low-frequency oceanic variability are discussed. The cascade of surface kinetic energy to low frequencies that predominates in idealized and realistic models is seen in some regions of the gridded altimeter product, but not in others. Exercises conducted with the general circulation model suggest that the spatial and temporal filtering inherent in the construction of gridded satellite altimeter maps may contribute to the discrepancies between the direction of the frequency cascade in models versus gridded altimeter maps seen in some regions. Of course, another potential reason for the discrepancy is missing physics in the models utilized here.

The dynamics of the flow field surrounding New Zealand are investigated using a series of global ocean models. The physical mechanisms governing the direction, magnitude, and location of the East Australian Current (EAC), the Tasman Front, the East Auckland Current (EAUC), and the East Cape Current (ECC) are studied using numerical simulations whose complexity is systematically increased. As new dynamics are added to each successive simulation, their direct and indirect effects on the flow field are examined. The simulations have horizontal resolutions of 1/8Њ, 1/16Њ, or 1/32Њ for each variable, and vertical resolutions ranging from 1.5-layer reduced gravity to 6-layer finite depth with realistic bottom topography. All simulations are forced by the Hellerman and Rosenstein monthly wind stress climatology. Analysis of these simulations shows that several factors play a critical role in governing the behavior of the examined currents. These factors include 1) mass balance of water pathways through the region, 2) gradients in the wind stress curl, 3) nonlinear flow instabilities, and 4) upper-ocean-topographic coupling due to mixed baroclinic and barotropic instabilities. Transport streamfunctions of a linear reduced gravity model reproduce the large-scale features well but produce an EAUC that flows counter to the observed direction. The residual of the mass balance of the transport through the Tasman Sea, the basinwide transport at 32ЊS, and the transport of the South Pacific subtropical gyre east of New Zealand determines the direction of the EAUC. The 6-layer nonlinear model allows isopycnal outcropping, which changes the transport through the Tasman Sea and produces an EAUC flowing in the observed direction. Gradients in the zonally integrated wind stress curl field determine the coastal separation points of the EAC, the EAUC, and the ECC, while a combination of nonlinear flow instabilities and upper-ocean-topographic coupling contribute to the formation of meanders in the Tasman Front. Increased resolution results in greater mixed baroclinicbarotropic instabilities and thus more upper-ocean-topographic coupling and surface variability, giving a more accurate simulation of topographically controlled mean meanders in the Tasman Front.

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.