Brian K. Arbic

Accuracy assessment of global barotropic ocean tide models

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 M2 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.

Spectral energy fluxes in geostrophic turbulence : Implications for ocean energetics

Abstract The energy pathways in geostrophic turbulence are explored using a two-layer, flat-bottom, f-plane, quasigeostrophic model forced by an imposed, horizontally homogenous, baroclinically unstable mean flow and damped by bottom Ekman friction. A systematic presentation of the spectral energy fluxes, the mean flow forcing, and dissipation terms allows for a comprehensive understanding of the sources and sinks for baroclinic and barotropic energy as a function of length scale. The key new result is a robust inverse cascade of kinetic energy for both the baroclinic mode and the upper layer. This is consistent with recent observations of satellite altimeter data over the South Pacific Ocean. The well-known forward cascade of baroclinic potential and total energy was found to be very robust. Decomposing the spectral fluxes into contributions from different terms provided further insight. The inverse baroclinic kinetic energy cascade is driven mostly by an efficient interaction between the baroclinic velo...

Global energy dissipation rate of deep-ocean low frequency flows by quadratic bottom boundary layer drag: computations from current-meter data

The global energy dissipation rate of deep-ocean low-frequency flows by quadratic bottom boundary layer drag is estimated in three ways. First, an average over the dissipations computed from the near-bottom velocities recorded by 290 moored current meters is multiplied by the World Ocean area. Second, near-global maps of surface velocities derived from satellite altimetry data are used to estimate the bias due to the sparse spatial coverage of the moorings. Third, a relationship between bottom and surface flows, computed over the mooring locations, is used to estimate global maps of bottom flows from the surface data. All three methods suggest that at least 0.2 TW of the wind-power input into geostrophic flows is dissipated in deep water by quadratic bottom drag. Implications for the oceanic overturning circulation, and for oceanic mesoscale eddy dynamics, are briefly discussed.

On tidal resonance in the global ocean and the back-effect of coastal tides upon open-ocean tides

Abstract The resonance of semi‐diurnal tidal elevations is investigated with a forward numerical forced damped global tide model and an analytical model of forced‐damped tides in a deep ocean basin coupled to a shelf. The analytical model contains the classical half‐wavelength and quarter‐wavelength resonances in the deep ocean and shelf, respectively, as well as a forcing‐scale dependence which depends on the ratio of the phase speed of open‐ocean gravity waves to that of the astronomical forcing. In the analytical model, when the deep ocean and shelf resonate separately at the same frequency, the resonance in the coupled system shifts to frequencies slightly higher and lower than the original frequency, such that a ‘double bump’ is seen in plots of elevation amplitude versus frequency. The addition of a shelf to a resonant open ocean tends to reduce open‐ocean tides, especially when the shelf is also near resonance. The magnitude of this ‘back‐effect’ is controlled by shelf friction. A weakly damped resonant shelf has a larger back‐effect on the open‐ocean tide than does a strongly damped shelf. Numerical simulations largely bear out the analytical model predictions, at least qualitatively. Idealized simulations show that continents enhance tides by enabling the half‐wavelength resonance. Simulations with realistic geometry and topography but varying longitudinal structure in the astronomical forcing display an influence of the forcing scale on tidal amplitudes somewhat similar to that seen in the analytical model. A frequency sweep in the semi‐diurnal band in experiments with realistic geometry and topography reveals weakly resonant peaks in the amplitudes of several shelf regions and in the globally averaged open‐ocean amplitudes. Finally, the back‐effect of the shelf upon the open ocean is seen in simulations in which locations of resonant coastal tides are blocked out and open‐ocean tidal elevations are significantly altered (increased, generally) as a result.

On Quadratic Bottom Drag, Geostrophic Turbulence, and Oceanic Mesoscale Eddies

Abstract Many investigators have idealized the oceanic mesoscale eddy field with numerical simulations of geostrophic turbulence forced by a horizontally homogeneous, baroclinically unstable mean flow. To date such studies have employed linear bottom Ekman friction (hereinafter, linear drag). This paper presents simulations of two-layer baroclinically unstable geostrophic turbulence damped by quadratic bottom drag, which is generally thought to be more realistic. The goals of the paper are 1) to describe the behavior of quadratically damped turbulence as drag strength changes, using previously reported behaviors of linearly damped turbulence as a point of comparison, and 2) to compare the eddy energies, baroclinicities, and horizontal scales in both quadratic and linear drag simulations with observations and to discuss the constraints these comparisons place on the form and strength of bottom drag in the ocean. In both quadratic and linear drag simulations, large barotropic eddies develop with weak dampin...

How stationary are the internal tides in a high‐resolution global ocean circulation model?

The stationarity of the internal tides generated in a global eddy-resolving ocean circulation model forced by realistic atmospheric fluxes and the luni-solar gravitational potential is explored. The root mean square (RMS) variability in the M2 internal tidal amplitude is approximately 2 mm or less over most of the ocean and exceeds 2 mm in regions with larger internal tidal amplitude. The M2 RMS variability approaches the mean amplitude in weaker tidal areas such as the tropical Pacific and eastern Indian Ocean, but is smaller than the mean amplitude near generation regions. Approximately 60% of the variance in the complex M2 tidal amplitude is due to amplitude-weighted phase variations. Using the RMS tidal amplitude variations normalized by the mean tidal amplitude (normalized RMS variability (NRMS)) as a metric for stationarity, low-mode M2 internal tides with NRMS < 0.5 are stationary over 25% of the deep ocean, particularly near the generation regions. The M2 RMS variability tends to increase with increasing mean amplitude. However, the M2 NRMS variability tends to decrease with increasing mean amplitude, and regions with strong low-mode internal tides are more stationary. The internal tide beams radiating away from generation regions become less stationary with distance. Similar results are obtained for other tidal constituents with the overall stationarity of the constituent decreasing as the energy in the constituent decreases. Seasonal variations dominate the RMS variability in the Arabian Sea and near-equatorial oceans. Regions of high eddy kinetic energy are regions of higher internal tide nonstationarity.

Impact of Parameterized Internal Wave Drag on the Semidiurnal Energy Balance in a Global Ocean Circulation Model

AbstractThe effects of a parameterized linear internal wave drag on the semidiurnal barotropic and baroclinic energetics of a realistically forced, three-dimensional global ocean model are analyzed. Although the main purpose of the parameterization is to improve the surface tides, it also influences the internal tides. The relatively coarse resolution of the model of ~8 km only permits the generation and propagation of the first three vertical modes. Hence, this wave drag parameterization represents the energy conversion to and the subsequent breaking of the unresolved high modes. The total tidal energy input and the spatial distribution of the barotropic energy loss agree with the Ocean Topography Experiment (TOPEX)/Poseidon (TPXO) tidal inversion model. The wave drag overestimates the high-mode conversion at ocean ridges as measured against regional high-resolution models. The wave drag also damps the low-mode internal tides as they propagate away from their generation sites. Hence, it can be considered...

On Eddy Viscosity, Energy Cascades, and the Horizontal Resolution of Gridded Satellite Altimeter Products*

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 altimeterdata is robust.However,themagnitudeofthe inverse cascadeis affectedbyfiltering,suggestingthat 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.

Internal tide generation by abyssal hills using analytical theory

[1] Internal tide driven mixing plays a key role in sustaining the deep ocean stratification and meridional overturning circulation. Internal tides can be generated by topographic horizontal scales ranging from hundreds of meters to tens of kilometers. State of the art topographic products barely resolve scales smaller than � 10 km in the deep ocean. On these scales abyssal hills dominate ocean floor roughness. The impact of abyssal hill roughness on internal-tide generation is evaluated in this study. The conversion of M2 barotropic to baroclinic tidal energy is calculated based on linear wave theory both in real and spectral space using the Shuttle Radar Topography Mission SRTM30_PLUS bathymetric product at 1/120 � resolution with and without the addition of synthetic abyssal hill roughness. Internal tide generation by abyssal hills integrates to 0.1 TW globally or 0.03 TW when the energy flux is empirically corrected for supercritical slope (i.e., � 10% of the energy flux due to larger topographic scales resolved in standard products in both cases). The abyssal hill driven energy conversion is dominated by mid-ocean ridges, where abyssal hill roughness is large. Focusing on two regions located over the Mid-Atlantic Ridge and the East Pacific Rise, it is shown that regionally linear theory predicts an increase of the energy flux due to abyssal hills of up to 100% or 60% when an empirical correction for supercritical slopes is attempted. Therefore, abyssal hills, unresolved in state of the art topographic products, can have a strong impact on internal tide generation, especially over mid-ocean ridges.

Geostrophic Turbulence in the Frequency–Wavenumber Domain: Eddy-Driven Low-Frequency Variability*

AbstractMotivated 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 mod...