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The Lagrangian and Eulerian surface current signatures of a low-mode internal tide propagating through a turbulent balanced flow are compared in idealized numerical simulations. Lagrangian and Eulerian total (i.e., coherent plus incoherent) tidal amplitudes are found to be similar. Compared to Eulerian diagnostics, the Lagrangian tidal signal is more incoherent with comparable or smaller incoherence time scales and larger incoherent amplitudes. The larger level of incoherence in Lagrangian data is proposed to result from the deformation of an Eulerian internal tide signal induced by drifter displacements. Based on the latter hypothesis, a theoretical model successfully predicts Lagrangian autocovariances by relating Lagrangian and Eulerian autocovariances and the properties of the internal tides and jet. These results have implications for the separation of balanced flow and internal tides signals in the sea level data collected by the future Surface Water and Ocean Topography (SWOT) satellite mission.

International audience; The future wide-swath satellite altimeters, such as the upcoming Surface Water Ocean Topography (SWOT) mission, will provide instantaneous 2D measurements of sea level down to the spatial scale of O(10 km) for the first time. However, the validity of the geostrophic assumption for estimating surface currents from these instantaneous maps is not known a priori. In this study, we quantify the accuracy of geostrophy for the estimation of surface currents from a knowledge of instantaneous sea level using the hourly snapshots from a tide- and eddy-resolving global numerical simulation. Geostrophic balance is found to be the leading-order balance in frontal regions characterized by large kinetic energy, such as the western boundary currents and the Antarctic Circumpolar Current. Everywhere else, geostrophic approximation ceases to be a useful predictor of ocean velocity, which may result in significant high-frequency contamination of geostrophically computed velocities by fast variability (e.g., inertial and higher). As expected, the validity of geostrophy is shown to improve at low frequencies (typically urn:x-wiley:21699275:media:jgrc24720:jgrc24720-math-0001 0.5 cpd). Global estimates of the horizontal momentum budget reveal that the tropical and mid-latitude regions where geostrophic balance fails are dominated by fast variability and turbulent stress divergence terms rather than higher-order geostrophic terms. These findings indicate that the estimation of velocity from geostrophy applied on SWOT instantaneous sea level maps may be challenging away from energetic areas.

Two methods for the mapping of ocean surface currents from satellite measurements of sea level and future current vectors are presented and contrasted. Both methods rely on the linear and Gaussian analysis framework with different levels of covariance definitions. The first method separately maps sea level and currents with single‐scale covariance functions and leads to estimates of the geostrophic and ageostrophic circulations. The second maps both measurements simultaneously and projects the circulation onto 4 contributions: geostrophic, ageostrophic rotary, ageostrophic divergent and inertial. When compared to the first method, the second mapping moderately improves the resolution of geostrophic currents but significantly improves estimates of the ageostrophic circulation, in particular near‐inertial oscillations. This method offers promising perspectives for reconstructions of the ocean surface circulation. Even the hourly dynamics can be reconstructed from measurements made locally every few days because nearby measurements are coherent enough to help fill the gaps. Based on numerical simulation of ocean surface currents, the proposed SKIM mission that combines a nadir altimeter and a Doppler scatterometer with a 300 km wide swath (with a mean revisit time of 3 days) would allow the reconstruction of 50% of the near‐inertial variance around an 18 hour period of oscillation. Plain Language Summary Ocean surface currents are caused by a variety of phenomena that varies at different space and time scales. Here we mainly consider the two dominant contributions. The first is the current resulting from the quasi‐equilibrium between the sloping sea level and the Coriolis force, slowly evolving over a few days. The second is also associated with the Coriolis force, but out of equilibrium: oscillating currents caused by rapid changes of the wind with a narrow range of periods around a natural period of oscillation that increase with latitude from 12 hours at the poles. For many applications it is desirable to separate these two contributions, for example to compute transports associated to the slowly evolving component and to evaluate the amount of kinetic energy pumped by the wind, mostly in the fast oscillations. This separation is easy with hourly sampled in situ measurements, but few are available. Here we show that we can perform this separation using satellite passes with measurements of sea level and a swath of surface current vectors, as can be measured by proposed future satellites. The fast oscillations can be reproduced even if data is available every few days, thanks to their spatial patterns and temporal coherence.

International audience; Several methods that reconstruct the three-dimensional ocean dynamics from sea level are presented and evaluated in the Gulf Stream region with a 1/60° realistic numerical simulation. The use of sea level is motivated by its better correlation with interior pressure or quasi-geostrophic potential vorticity (PV) compared to sea surface temperature and sea surface salinity, and, by its observability via satellite altimetry. The simplest method of reconstruction relies on a linear estimation of pressure at depth from sea level. Another method consists in linearly estimating PV from sea level first and then performing a PV inversion. The last method considered, labeled SQG for surface quasi-geostrophy, relies on a PV inversion but assumes no PV anomalies. The first two methods show comparable skill at levels above -800 m. They moderately outperform SQG which emphasizes the difficulty of estimating interior PV from surface variables. Over the 250-1,000 m depth range, the three methods skillfully reconstruct pressure at wavelengths between 500 and 200 km whereas they exhibit a rapid loss of skill between 200 and 100 km wavelengths. Applicability to a real case scenario and leads for improvements are discussed.

Understanding how internal tides distort and lose coherence as they propagate through the ocean has been identified as a key issue for interpreting data from the upcoming wide-swath altimeter mission SWOT. This study addresses that issue through the analysis of numerical experiments where a low mode internal tide propagates through a quasi-geostrophic turbulent jet. We present a set of reduced equations based on vertical mode projections that describe the dynamics of the low-mode internal tides as they propagate through the slower turbulent field. Diagnostics of the terms responsible for the interaction between the wave and the slow circulation are computed from the numerical outputs. The large scale change of stratification, on top of eddies and jet meanders, contributes significantly to these interaction terms which is shown to be consistent with an independent scaling analysis. The sensitivity of interaction terms to a degradation of the slow field spatial and horizontal resolution indicates that current day observing systems (Argo network, altimetry) may lack spatial resolution in order to correctly predict internal tide evolution. The upcoming SWOT satellite mission may improve upon this situation. The number of vertical modes required to properly estimate interaction terms is discussed. These results advocate development of a simplified model based on solving a modest number of the reduced equations subject to a prescribed mesoscale field and internal tide sources. Such a model would constitute an inexpensive way to calculate the distortion and loss of coherence of low-mode internal tides as they propagate through mesoscale circulation.

Taking advantage of alternative expressions for potential vorticity (PV) in divergence forms, we derive balances between volume integral of PV and boundary conditions, that are then applied to practical computations of PV: • We propose a new method for diagnosing the Ertel potential vorticity from model output, that preserves the balances; • We show how the expression of PV can be derived in general coordinate systems. This is here emphasised with isopycnic coordinates by generalising the PV expression to the general Navier-Stokes equations; • We propose a generalised derivation for the Haynes-McIntyre impermeability theorem, which highlights the role of the bottom boundary condition choice (e.g. no-slip vs free-slip) and mixing near the bottom boundary for the volume integral of PV. The implications of balances between volume integral of PV and boundary conditions are then analysed for specific processes at various scales: • At large scale, we show how an integral involving surface observations (derived from satellite observations) is linked to the integral of PV within a layer (between two isopycnals). This surface integral can be calculated for models and observations and can be used for validation; • At mesoscale or sub-mesoscale, we analyse the relationship between net PV anomalies and net surface density anomalies for idealised vortices and 2D fronts. This can help determining vortex or jet structures for idealised studies or empirical methodologies; • We also confirm and integrate previous results on the modification of PV within a bottom boundary layer into a single diagnostic taking into account the effect of density and velocity modifications by diabatic processes along the topography and diapycnal mixing within the boundary layer.

At times, high-resolution images of sea surface roughness can provide stunning details of submesoscale upper-ocean dynamics. As interpreted, transformations of short-scale wind waves by horizontal current gradients are responsible for those spectacular observations. Those observations could prove particularly useful to validate numerical ocean models that reach increasingly high resolutions. Focusing on surface roughness at optical wavelengths, two steps have recently been performed in that direction. First, it was shown in a previous paper by Rascle et al. that surface roughness variations not only trace surface current divergence but also other characteristics of the current gradient tensor, mainly the strain in the wind direction. The wind direction with respect to the current gradient thus stands out as an important interpretative parameter. The second step is the purpose of the present paper, where the effect of the viewing direction is investigated. To this end, the authors discuss pairs of quasi-simultaneous sun-glitter images, taken from different satellite positions, to provide different viewing configurations, namely, quasi-orthogonal azimuth angles at similar zenith angles. As evidenced, upwind and crosswind viewing observations can be markedly different. As further confirmed with idealized numerical simulations, this anisotropy well traces anisotropic surface current areas, while more isotropic contrasts likely trace areas dominated by surface divergence conditions. These findings suggest the potential to directly separate divergence from other deformations by using high-resolution roughness observations at multiple azimuth view angles.

International audience; Recent realistic high resolution modeling studies show a net increase of submesoscale activity in fall and winter when the mixed layer depth is at its maximum. This submesoscale activity increase is associated with a reduced deepening of the mixed layer. Both phenomena can be related to the development of mixed layer instabilities, which convert available potential energy into submesoscale eddy kinetic energy and contribute to a fast restratification by slumping the horizontal density gradient in the mixed layer. In the present work, the mixed layer formation and restratification was studied by uniformly cooling a fully turbulent zonal jet in a periodic channel at different resolutions, from eddy resolving (10 km) to submesoscale permitting (2 km). The effect of the submesoscale activity, highlighted by these different horizontal resolutions, was quantified in terms of mixed layer depth, restratification rate and buoyancy fluxes. Contrary to many idealized studies focusing on the restratification phase only, this study addresses a continuous event of mixed layer formation followed by its complete restratification. The robustness of the present results was established by ensemble simulations. The results show that, at higher resolution, when submesoscale starts to be resolved, the mixed layer formed during the surface cooling is significantly shallower and the total restratification almost three times faster. Such differences between coarse and fine resolution models are consistent with the submesoscale upward buoyancy flux, which balances the convection during the formation phase and accelerates the restratification once the surface cooling is stopped. This submesoscale buoyancy flux is active even below the mixed layer. Our simulations show that mesoscale dynamics also cause restratification, but on longer time scales. Finally, the spatial distribution of the mixed layer depth is highly heterogeneous in the presence of submesoscale activity, prompting the question of whether it is possible to parameterize submesoscale effects and their effects on the marine biology as a function of a spatially-averaged mixed layer depth.

The propagation of remotely generated superinertial internal tides constitutes a difficulty for the modelling of regional ocean tidal variability which we illustrate in several ways. First, the M2 tidal solution inside a control region located along the Southern California Bight coastline is monitored while the extent of the numerical domain is increased (up to 512 x 512 km). While the amplitude and phase of sea level averaged over the region is quasi-insensitive to domain size, a steady increase of kinetic energy, predominantly baroclinic, is observed with increasing domain size. The increasing flux of energy into the control region suggests that this trend is explained by the growing contribution from remote generation sites of internal tide which can propagate up to the control region. Increasing viscosities confirms this interpretation by lowering baroclinic energy levels and limiting their rate of increase with domain size. Doubling the grid spacing allows consideration of numerical domains 2 times larger. While the coarse grid has lower energy levels than the finer grid, the rate of energy increase with domain size appears to be slowing for the largest domain of the coarse grid simulations. Forcing the smallest domain with depth-varying tidal boundary conditions from the simulation in the largest domain produces energy levels inside the control region comparable to those in the control region for the largest domain, thereby confirming the feasibility of a nested approach. In contrast, simulations forced with a subinertial tidal constituent (K1) show that when the propagation of internal tide is limited, the control region kinetic energy is mostly barotropic and the magnitudes of variations of the kinetic energy with domain size are reduced. (C) 2012 Elsevier Ltd. All rights reserved.

An idealized model is developed for the three-dimensional response of a coastal basin (e.g., lagoon, bay, or estuary) to time-periodic wind stress. This model handles basins that are deeper and/or shallower than an Ekman depth with wind forcing frequencies ranging from subinertial to superinertial. Here the model is used to describe how the response (current and sea level) of a basin deeper than one Ekman depth depends on the wind forcing frequency. At low subinertial frequencies, the response is similar to the steady wind case and is hence called “quasi steady.” There is a near-surface Ekman transport to the right of the wind balanced by a return flow at depth. Lateral bathymetric variations introduce an along-basin circulation that decays with increasing frequency and sets the extent of the quasi-steady response in the frequency domain. At the inertial frequency, the wind forces a damped resonant response with large vertical shear and weak depth-integrated flow. This result is potentially important for coastal basins located near ±30° latitude and forced by a diurnal breeze. At superinertial frequencies, the response becomes irrotational and is amplified near seiche frequencies. The response to a sudden onset of wind is computed in the time domain and confirms that the slow growth of the along-basin circulation controls the spinup process. The response of basins shallower than an Ekman depth, and the validity of the model inside semienclosed basins, are also discussed.

The role of wind-driven upwelling in stratifying a semiarid bay in the Gulf of California is demonstrated with observations in Bahia Concepcion, Baja California Sur, Mexico. The stratification in Bahia Concepcion is related to the seasonal heat transfer from the atmosphere as well as to cold water intrusions forced by wind-driven upwelling. During winter, the water column is relatively well-mixed by atmospheric cooling and by northwesterly, downwelling-favorable, winds that typically exceed 10 m/s. During summer, the water column is gradually heated and becomes stratified because of the heat flux from the atmosphere. The wind field shifts from downwelling-favorable to upwelling-favorable at the beginning of summer, i.e., the winds become predominantly southeasterly. The reversal of wind direction triggers a major cold water intrusion at the beginning of the summer season that drops the temperature of the entire water column by 3–5 °C. The persistent upwelling-favorable winds during the summer provide a continuous cold water supply that helps maintain the stratification of the bay.

International audience; The local wind-driven circulation off southern San Diego is addressed with two complementary statistical and dynamical frameworks based on observations and idealized numerical model simulations. The observations including surface currents from high-frequency radars, subsurface currents from a nearshore mooring, and wind records at a local wind station are analyzed with the idealized ocean model (MITgcm) simulations using realistic bottom topography and spatially uniform wind stress forcing. Statistically estimated anisotropic local wind transfer functions characterize the observed oceanic spectral response to wind stress separately in the x (east-west) and y (north-south) directions. We delineate the coastal circulation at three primary frequencies [low (σ L=0.0767 cycles per day (cpd)), diurnal (σ D=1 cpd), and inertial (σ f=1.07 cpd) frequencies] with the momentum budget equations and transfer functions. At low frequency, the magnitudes of transfer functions are enhanced near the coast, attributed to geostrophic balance between wind-driven pressure gradients and the Coriolis force on currents. The response diminishes away from the coast, returning to the balance between frictional and Coriolis terms, as in the classic Ekman model. On the contrary, transfer functions in the near-inertial frequency band show reduced magnitudes near the coast primarily due to friction, but exhibits the enhanced seaward response as a result of the inertial resonance. The idealized model simulations forced by local wind stress can identify the influences of remote wind stress and the biases in the data-derived transfer functions.

Images of sea surface roughness-for example, obtained by synthetic aperture radars (SAR) or by radiometers viewing areas in and around the sun glitter-at times provide clear observations of meso- and sub-mesoscale oceanic features. Interacting with the surface wind waves, particular deformation properties of surface currents are responsible for those manifestations. Ignoring other sources of surface roughness variations, the authors limit their discussion to the mean square slope (mss) variability. This study confirms that vortical currents and currents with shear in the wind direction shall not be expressed in surface roughness images. Only divergent currents or currents with no divergence but strained in the wind direction can exhibit surface roughness signatures. More specifically, nondivergent currents might be traced with a 45 degrees sensitivity to the wind direction. A simple method is proposed in order to interpret high-resolution roughness images, where roughness variations are proportional to partial derivative u/partial derivative x + alpha partial derivative v/partial derivative y, a linear combination of the along-wind and crosswind current gradients. The polarization parameter a depends upon the sensor look direction and the directional properties of the surface waves selected by the sensor. The use of multiple look directions or possible acquisitions with different wind directions shall thus help to retrieve surface currents from surface roughness observations.

International audience; The present study investigates the reconstruction of the 3D dynamics of a turbulent mesoscale eddy field driven at a depth by a baroclinic instability of the Phillips type. It uses a high-resolution primitive equation simulation as a testbed. The method of reconstruction is based on potential vorticity principles and extends an earlier approach (Lapeyre and Klein, J Phys Oceanogr 36:165-176, 2006) to a regime where the signature of surface density anomalies on the dynamics is weak. The crux and the originality of the reconstruction lie in the estimation from sea surface height and surface density anomalies of the interior quasigeostrophic potential vorticity (PV) anomalies and its subsequent inversion. The estimation of PV anomalies relies on the vertical correlation between PV anomalies and on the knowledge on stratification and horizontal gradients of background PV. PV anomalies are accurately estimated over the first 500 m of the water column and over a wide range of wavenumbers. Density anomalies play a minor role in the PV estimation, though their omission leads to an overestimation of PV by a factor of less than 2 at scales of order 20 km and less. Inversion of the estimated PV leads to a geostrophic streamfunction which in turn provides reliable reconstructions of the relative vorticity and vertical velocity (via the omega equation).

High-resolution numerical experiments of ocean mesoscale eddy turbulence show that the wind-driven mixed layer (ML) dynamics affects mesoscale motions in the surface layers at scales lower than O(60 km). At these scales, surface horizontal currents are still coherent to, but weaker than, those derived from sea surface height using geostrophy. Vertical motions, on the other hand, are stronger than those diagnosed using the adiabatic quasigeotrophic (QG) framework. An analytical model, based on a scaling analysis and on simple dynamical arguments, provides a physical understanding and leads to a parameterization of these features in terms of vertical mixing. These results are valid when the wind-driven velocity scale is much smaller than that associated with eddies and the Ekman number (related to the ratio between the Ekman and ML depth) is not small. This suggests that, in these specific situations, three-dimensional ML motions (including the vertical velocity) can be diagnosed from high-resolution satellite observations combined with a climatological knowledge of ML conditions and interior stratification.

Internal gravity waves of tidal frequency are generated as the ocean tides push water upward onto the continental shelf. Such waves also arrive at the continental slope from deep water and are heavily modified by the change in water depth. The wave generation and wave shoaling effects have an additional level of complexity where a canyon is sliced into the continental slope. Recently, steps have been taken to simulate internal tides in canyons, to understand the physical processes of internal tides in canyons, and also to compute the ramifications on sound propagation in and near the canyons. Internal tides generated in canyons can exhibit directionality, with the directionality being consistent with an interesting multiple-scattering effect. The directionality imparts a pattern to the sound-speed anomaly field affecting propagation. The directionality also means that short nonlinear internal waves, which have specific strong effects on sound, can have interesting patterns near the canyons. In addition to the directionality of internal tides radiated from canyons, the internal tide energy within the canyons can be patchy and may unevenly affect sound.