Can We Infer Ocean Dynamics from Altimeter Wavenumber Spectra?

The wavenumber spectra of sea surface height (SSH) and kinetic energy (KE) have been used to infer the dynamics of the ocean. When quasi-geostrophic dynamics (QG) or surface quasi-geostrophic (SQG) turbulence dominate and an inertial subrange exists, a steep SSH wavenumber spectrum is expected with k-5 for QG turbulence and a flatter k-11/3 for SQG turbulence. However, inspection of the spectral slopes in the mesoscale band of 70 to 250 km shows that the altimeter wavenumber slopes typically are much flatter than the QG or SQG predictions over most of the ocean. Comparison of the altimeter wavenumber spectra with the spectra estimated from the output of an eddy resolving global ocean circulation model (the Hybrid Coordinate Ocean Model, HYCOM, at 1/25 resolution), which is forced by high frequency winds and includes the astronomical forcing of the sun and the moon, suggests that the flatter slopes of the altimeter may arise from three possible sources, the presence of internal waves, the lack of an inertial subrange in the 70 to 250 km band and noise or submesoscales at small scales. When the wavenumber spectra of SSH and KE are estimated near the internal tide generating regions, the resulting spectra are much flatter than the expectations of QG or SQG theory. If the height and velocity variability are separated into low frequency (periods greater than 2 days) and high frequency (periods less than a day), then a different pattern emerges with a relatively flat wavenumber spectrum at high frequency and a steeper wavenumber spectrum at low frequency. The stationary internal tides can be removed from the altimeter spectrum, which steepens the spectral slopes in the energetic internal wave regions. Away from generating regions where the internal wave

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 M 2 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 M 2 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 M 2 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 M 2 internal tides with NRMS < 0.5 are stationary over 25% of the deep ocean, particularly near the generation regions. The M 2 RMS variability tends to increase with increasing mean amplitude. However, the M 2 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. Key Points Internal tide stationarity measured by RMS variability normalized by amplitude Internal tide stationarity correlated with tidal amplitude Strong mesoscale eddies or currents decrease stationarity of internal tidesPeer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/107478/1/jgrc20664.pd

On eddy viscosity, energy cascades, and the horizontal resolution of gridded satellite altimeter products

Author Posting. © American Meteorological Society, 2013. This article is posted here by permission of American Meteorological Society for personal use, not for redistribution. The definitive version was published in Journal of Physical Oceanography 43 (2013): 283–300, doi:10.1175/JPO-D-11-0240.1.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 Π(K) computed in the isotropic wavenumber (K) domain. The paper utilizes idealized two-layer quasigeostrophic (QG) models, realistic high-resolution 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 Π(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.BKA received support from Office of Naval Research Grant N00014-11-1-0487, National Science Foundation (NSF) Grants OCE-0924481 and OCE- 09607820, and University of Michigan startup funds. KLP acknowledges support from Woods Hole Oceanographic Institution bridge support funds. RBS acknowledges support from NSF grants OCE-0960834 and OCE-0851457, a contract with the National Oceanography Centre, Southampton, and a NASA subcontract to Boston University. JFS and JGR were supported by the projects ‘‘Global and remote littoral forcing in global ocean models’’ and ‘‘Agesotrophic vorticity dynamics of the ocean,’’ respectively, both sponsored by the Office of Naval Research under program element 601153N.2013-08-0

Global modeling of internal tides within an eddying ocean general circulation model

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/91777/1/25-2_arbic_hi.pd

Indirect Evidence For Substantial Damping of Low-Mode Internal Tides In the Open Ocean

A global high-resolution ocean circulation model forced by atmospheric fields and the M2 tidal constituent is used to explore plausible scenarios for the damping of low-mode internal tides. The plausibility of different damping scenarios is tested by comparing the modeled barotropic tides with TPXO8, a highly accurate satellite-altimetry-constrained tide model, and by comparing the modeled coherent baroclinic tide amplitudes against along-track altimetry. Five scenarios are tested: (1) a topographic internal wave drag, argued here to represent the breaking of unresolved high vertical modes, applied to the bottom flow (default configuration), (2) a wave drag applied to the barotropic flow, (3) absence of wave drag, (4) a substantial increase in quadratic bottom friction along the continental shelves (with wave drag turned off), and (5) application of wave drag to the barotropic flow at the same time that quadratic bottom friction is substantially increased along the shelves. Of the scenarios tested here, the default configuration (1) yields the most accurate tides. In all other scenarios (2–5), the lack of damping on open ocean baroclinic motions yields baroclinic tides that are too energetic and travel too far from their sources, despite the presence of a vigorous mesoscale eddy field which can scatter and decohere internal tides in the model. The barotropic tides are also less accurate in the absence of an open ocean damping on barotropic motions, that is, in scenarios (3) and (4). The results presented here suggest that low-mode internal tides experience substantial damping in the open ocean

Toward Realistic Nonstationarity of Semidiurnal Baroclinic Tides in a Hydrodynamic Model

Semidiurnal baroclinic tide sea surface height (SSH) variance and semidiurnal nonstationary variance fraction (SNVF) are compared between a hydrodynamic model and altimetry for the low‐ to middle‐latitude global ocean. Tidal frequencies are aliased by ∼10‐day altimeter sampling, which makes it impossible to unambiguously identify nonstationary tidal signals from the observations. In order to better understand altimeter sampling artifacts, the model was analyzed using its native hourly outputs and by subsampling it in the same manner as altimeters. Different estimates of the semidiurnal nonstationary and total SSH variance are obtained with the model depending on whether they are identified in the frequency domain or wave number domain and depending on the temporal sampling of the model output. Five sources of ambiguity in the interpretation of the altimetry are identified and briefly discussed. When the model and altimetry are analyzed in the same manner, they display qualitatively similar spatial patterns of semidiurnal baroclinic tides. The SNVF typically correlates above 80% at all latitudes between the different analysis methods and above 60% between the model and altimetry. The choice of analysis methodology was found to have a profound effect on estimates of the semidiurnal baroclinic SSH variance with the wave number domain methodology underestimating the semidiurnal nonstationary and total SSH variances by 68% and 66%, respectively. These results produce a SNVF estimate from altimetry that is biased low by a factor of 0.92. This bias is primarily a consequence of the ambiguity in the separation of tidal and mesoscale signals in the wave number domain.Key PointsHydrodynamic models incorporating mesoscale dynamics and tides are beginning to resolve stationary and nonstationary baroclinic tidesThe ratio of nonstationary to total semidiurnal variance computed from altimetry and HyCOM simulations agrees at low and middle latitudesComparisons of analysis methodologies show that total and nonstationary semidiurnal variances are underestimated in altimetry on averagePeer Reviewedhttps://deepblue.lib.umich.edu/bitstream/2027.42/152034/1/jgrc23624_am.pdfhttps://deepblue.lib.umich.edu/bitstream/2027.42/152034/2/jgrc23624.pd

Remote Internal Wave Forcing of Regional Ocean Simulations Near the U.S. West Coast

Low mode internal waves are able to propagate across ocean basins and modulate ocean dynamics thousands of kilometers away from their generation sites. In this study, the impact of remotely generated internal waves on the internal wave energetics near the U.S. West Coast is investigated with realistically forced regional ocean simulations. At the open boundaries, we impose high-frequency oceanic state variables obtained from a global ocean simulation with realistic atmospheric and astronomical tidal forcing. We use the Discrete Fourier Transform (DFT) technique in separating ingoing and outgoing internal tide energy fluxes at the open boundaries in order to quantify internal tide reflections. Although internal tide reflections are reduced with increasing sponge viscosity and/or sponge layer width, reflection coefficients (λ) can be as high as 73%. In the presence of remote internal waves, the model variance and spatial correlations become more in agreement with both mooring and altimetry datasets. The results confirm that an improved internal wave continuum can be achieved in regional models with remote internal wave forcing at the open boundaries. However, care should be taken to avoid excessive reflections of internal waves from the interior at these boundaries

Effects of stencil width on surface ocean geostrophic velocity and vorticity estimation from gridded satellite altimeter data

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/90421/1/2011JC007367.pd

Effects of stencil width on surface ocean geostrophic velocity and vorticity estimation from gridded satellite altimeter data

This paper examines the effect of “stencil width” on surface ocean geostrophic velocity and vorticity estimated from differentiating gridded satellite altimeter sea surface height products. In oceanographic applications, the value of the first derivative at a central grid point is generally obtained by differencing the sea surface heights at adjacent grid points. This is called a “three-point stencil centered difference”. Here the stencil width is increased from three to five, seven, and nine points, using well-known formulae from the numerical analysis literature. The discrepancies between velocities computed with successive stencils decreases with increasing stencil width, suggesting that wide stencil results are more reliable. Significant speed-dependent biases (up to 10–20%) are found between results computed from three-point stencils versus those computed from wider stencils. The geostrophic velocity, and the variance of geostrophic velocity, are underestimated with thin stencils. Similar results are seen in geostrophic velocities computed from high-resolution model output. In contrast to the case when three-point stencils are used, wider stencils yield estimates of the anisotropy of velocity variance that are insensitive to the differences in grid spacing between two widely used altimeter products. Three-point stencils yield incorrect anisotropies on the 1/4° anisotropic AVISO grid; we recommend the use of 7-point stencils. Despite the demonstrated inadequacies of the three-point stencils, the conclusions of earlier studies based on them, that the zonally averaged midlatitude eddy kinetic energy field is nearly isotropic, are found to pertain also with wider stencils. Finally, the paper also examines the strengths and limitations of applying noise-suppressing differentiators, versus classic centered differences, to altimeter data

Accuracy Assessment of Global Internal-Tide Models Using Satellite Altimetry

Altimeter measurements are corrected for several geophysical parameters in order to access ocean signals of interest, like mesoscale or sub-mesoscale variability. The ocean tide is one of the most critical corrections due to the amplitude of the tidal elevations and to the aliasing phenomena of high-frequency signals into the lower-frequency band, but the internal-tide signatures at the ocean surface are not yet corrected globally. Internal tides can have a signature of several centimeters at the surface with wavelengths of 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 correction of all tidal variability becomes mandatory to access accurate measurements of other oceanic signals. 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. The results show a significant altimeter variance reduction when using internal-tide corrections in all ocean regions where internal tides are generating or 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. This work led to the implementation of a new internal-tide correction (ZARON\u27one) in the next geophysical data records version-F (GDR-F) standards