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In order to address the issue of limited common coverage and high cost in mapping ocean surface vector current by two (or more) high-frequency surface wave radars, this paper proposes a single-station surface wave radar vector current inversion algorithm. The feasibility of this algorithm has been validated in the Taiwan Strait. Based on the ocean dynamic characteristics of the Taiwan Strait, the algorithm utilizes the radial current obtained from a high-frequency surface wave radar (HFSWR) in Fujian Province to invert the ocean surface vector current. The surface vector current can be decomposed into three primary dynamic components: tidal currents, wind-driven currents, and geostrophic currents. Firstly, tidal current forecasting models and Ekman and Stokes theories are used to calculate the tidal and wind-driven currents in the Taiwan Strait, respectively. Subsequently, the directions of geostrophic currents in the Taiwan Strait are determined with sea surface height data, and the magnitudes of the geostrophic currents are constrained using the radial current from the single HFSWR. Finally, the three components are added together to obtain the vector current. Comparative results demonstrate that the efficacy of the algorithm has been validated through field experiments (with two HFSWRs and two drifting buoys) conducted in the southwestern of the Taiwan Strait. Further research is needed on the applicability of this algorithm to other sea areas and monitoring systems. [ABSTRACT FROM AUTHOR]

Satellite altimetry offers a unique approach for direct sea surface current observation, but it is limited to measuring the surface‐constrained geostrophic component. Ageostrophic dynamics, prevalent at horizontal scales below 100 km and time scales below 10 days, are often underestimated by ocean reanalyzes employing data assimilation schemes. To address this limitation, we introduce a novel deep learning scheme, rooted in a variational data assimilation formulation with trainable observations and a priori terms, that harnesses the synergies between satellite‐derived sea surface observations, namely sea surface height (SSH) and sea surface temperature (SST), to enhance sea surface current reconstruction. Numerical experiments, conducted using realistic simulations, in a case study area of the Gulf Stream, demonstrate the potential of the proposed scheme to capture ageostrophic dynamics at time scales of 2.5–3.0 days and horizontal scales of 0.5°–0.7°. The analysis of diverse observation configurations, encompassing nadir along‐track altimetry, wide‐swath SWOT (Surface Water and Ocean Topography) altimetry, and SST data, highlights the pivotal role of SST features in retrieving a significant portion of the ageostrophic dynamics (approximately 47%). These findings underscore the potential of deep learning and 4DVarNet schemes in improving ocean reanalyzes and enhancing our understanding of ocean dynamics. Plain Language Summary: Satellite altimetry provides a unique means for direct observation of sea surface currents, but it is confined to the geostrophic component, limiting the recovery of a substantial portion of mesoscale sea surface currents in operational products. To address this limitation, we present a novel deep learning framework, rooted in a variational data assimilation paradigm, that unlocks new avenues for leveraging the synergistic relationships between satellite‐derived sea surface observations, namely sea surface height and sea surface temperature. This innovative scheme demonstrates its remarkable potential to enhance sea surface current reconstruction and recover a substantial portion of the elusive ageostrophic dynamics. Numerical experiments, employing realistic simulations, in a case study area along the Gulf Stream, underscore the efficacy of our proposed approach. These findings support the pivotal role of physics‐informed deep learning in maximizing the utilization of available multimodal observation data sets and numerical simulations to elucidate partially observed sea surface dynamics. Key Points: We present end‐to‐end deep learning schemes to improve the reconstruction of total sea surface currents from satellite‐derived observationsExperiments in a region of the Gulf Stream support the synergistic analysis of sea surface temperature and sea surface height dataThe strain of sea surface dynamics is a proxy of the uncertainty of the retrieved estimation [ABSTRACT FROM AUTHOR]

For over 25 years, satellite altimetry has provided invaluable information about the ocean dynamics at many scales. In particular, gridded sea surface height (SSH) maps allow us to estimate the mesoscale geostrophic circulation in the ocean. However, conventional interpolation techniques rely on static optimal interpolation schemes, hence limiting the estimation of non-linear dynamics at scales not well sampled by altimetry (i.e., below 150–200 km at mid-latitudes). To overcome this limitation in the resolution of small-scale SSH structures (and thus small-scale geostrophic currents), a back-and-forth nudging algorithm combined with a quasi-geostrophic model, a technique called BFN-QG, has been successfully applied on simulated SSH data in observing system simulation experiments (OSSEs). The result is a significant reduction in interpolation error and an improvement in the space–time resolutions of the experimental gridded product compared to those of operational products. In this study, we propose that the BFN-QG be applied to real altimetric SSH data in a highly turbulent region spanning a part of the Agulhas Current. The performances are evaluated within observing system experiments (OSEs) that use independent data (such as independent SSH, sea surface temperature and drifter data) as ground truth. By comparing the mapping performances to the ones obtained with operational products, we show that the BFN-QG improves the mapping of short, energetic mesoscale structures and associated geostrophic currents both in space and time. In particular, the BFN-QG improves (i) the spatial effective resolution of the SSH maps by a factor of 20 %, (ii) the zonal and (especially) the meridional geostrophic currents, and (iii) the prediction of Lagrangian transport for lead times up to 10 d. Unlike the results obtained in the OSSEs, the OSEs reveal more contrasting performances in low-variability regions, which are discussed in the paper. [ABSTRACT FROM AUTHOR]

We investigate ocean dynamics at different scales in the Agulhas Current system, a region of important interocean exchange of heat and energy. While ocean observations and some of the most advanced climate models capture the larger mesoscale dynamics (> 100 km), the smaller-scale fronts and eddies are underrepresented. The recently launched NASA–CNES Surface Water and Ocean Topography (SWOT) wide-swath altimeter mission observes the smaller ocean geostrophic scales down to 15 km in wavelength globally. Here we will analyse different eddy diagnostics in the Agulhas Current region and quantify the contributions from the larger mesoscales observable today and the smaller scales to be observed with SWOT. Surface geostrophic diagnostics of eddy kinetic energy, strain, and energy cascades are estimated from modelled sea surface height (SSH) fields of the Massachusetts Institute of Technology general circulation model (MITgcm) latitude–longitude polar cap (LLC4320) simulation subsampled at 1/10 ∘. In this region, the smaller scales (<150 km) have a strong signature on the horizontal geostrophic strain rate and for all eddy diagnostics in the Western Boundary Current and along the meandering Agulhas Extension. We investigate the horizontal cascade of energy using a coarse-graining technique, and we observe that the wavelength range where the inverse cascade occurs is biased towards larger mesoscale wavelengths with today's altimetric sampling. We also calculate the projected sampling of the eddy diagnostics under the SWOT swaths built with the NASA–CNES simulator to include the satellite position and realistic noise. For the swaths, a neural network noise mitigation method is implemented to reduce the residual SWOT random error before calculating eddy diagnostics. In terms of SSH, observable wavelengths of 15 to 20 km are retrieved after neural network noise mitigation, as opposed to wavelengths larger than 40 km before the noise reduction. [ABSTRACT FROM AUTHOR]

Gridded sea surface height (SSH) maps estimated from satellite altimetry are widely used for estimating surface ocean geostrophic currents. Satellite altimeters observe SSH along one‐dimensional tracks widely spaced in space and time, making accurately reconstructing the two‐dimensional (2D) SSH field challenging. Traditionally, SSH is mapped using optimal interpolation (OI). However, OI artificially smooths the SSH field leading to high mapping errors in regions with rapidly‐evolving mesoscale features such as western boundary currents. Motivated by the dynamical relation between SSH and sea surface temperature (SST) and the notion that even the chaotic evolution of mesoscale ocean turbulence may contain repeating patterns, we outline a deep learning (DL) approach where a neural network is trained to reconstruct 2D SSH by synthesizing altimetry and SST observations. In the Gulf Stream Extension region, dominated by mesoscale variability, our DL method substantially improves the SSH reconstruction compared to existing methods. Our SSH map has 17% lower root‐mean‐square error and resolves spatial scales 30% smaller than OI compared against independent altimeter observations. Surface geostrophic currents calculated from our map are closer to surface drifter observations and appear qualitatively more realistic, with stronger currents, a clearer separation between the Gulf Stream and neighboring eddies, and the appearance of smaller coherent eddies missed by other methods. Our map yields significant re‐estimations of important dynamical quantities such as eddy kinetic energy, vorticity, and strain rate. Applying our DL method to produce a global SSH product may provide a more accurate and higher resolution product for studying mesoscale ocean turbulence. Plain Language Summary: Satellites observe small variations in the height of the sea surface but with large gaps in the observations. Having an estimate of the two‐dimensional sea surface height field allows one to estimate surface ocean currents, so filling in the gaps between the observations is an important problem. The traditionally‐used method for filling in the gaps between sea surface height observations struggles when there are lots of small‐scale, rapidly‐interacting ocean currents. We developed a deep learning (DL) model to estimate the sea surface height field more accurately. We achieved this by combining the sea surface height observations with satellite observations of sea surface temperature. The relationship between sea surface temperature and height is non‐trivial, but our DL model learned to use information from the sea surface temperature observations in the places where sea surface height wasn't observed to improve the accuracy of the sea surface height estimate. We applied and tested our method in the Gulf Stream and demonstrated that our sea surface height map is more accurate than that from the traditional method. Our method provides a more accurate sea surface height map which could allow us in future to learn new lessons about small‐scale surface currents in the ocean. Key Points: We developed a deep learning method that significantly improves the accuracy and resolution of gridded sea surface height anomaliesThis data‐driven method takes advantage of combining sea surface temperature and altimetry observationsInferred surface geostrophic currents are quantitatively and qualitatively more realistic than those from existing sea surface height maps [ABSTRACT FROM AUTHOR]

This study assesses the capability of Surface Quasi-Geostrophy (SQG) to reconstruct the three-dimensional (3D) dynamics in four critical areas of the Arctic Ocean: the Nordic, Barents, East Siberian, and Beaufort Seas. We first reconstruct the upper ocean dynamics from TOPAZ4 reanalysis of sea surface height (SSH), surface buoyancy (SSB), and surface velocities (SSV) and validate the results with the geostrophic and total TOPAZ4 velocities. The reconstruction of upper ocean dynamics using SSH fields is in high agreement with the geostrophic velocities, with correlation coefficients greater than 0.8 for the upper 400 m. SSH reconstructions outperform surface buoyancy reconstructions, even in places near freshwater inputs from river discharges, melting sea ice, and glaciers. Surface buoyancy fails due to the uncorrelation of SSB and subsurface potential vorticity (PV). Reconstruction from surface currents correlates to the total TOPAZ4 velocities with correlation coefficients greater than 0.6 up to 200 m. In the second part, we apply the SQG approach validated with the reanalysis outputs to satellite-derived sea level anomalies and validate the results against in-situ measurements. Due to lower water column stratification, the SQG approach's performance is better in fall and winter than in spring and summer. Our results demonstrate that using surface information from SSH or surface velocities, combined with information on the stratification of the water column, it is possible to effectively reconstruct the upper ocean dynamics in the Arctic and Subarctic Seas up to 400 m. Future remote sensing missions in the Arctic Ocean, such as SWOT, Seastar, WaCM, CIMR, and CRISTAL, will produce enhanced SSH and surface velocity observations, allowing SQG schemes to characterize upper ocean 3D mesoscale dynamics up to 400 m with higher resolutions and lower uncertainties. [ABSTRACT FROM AUTHOR]

Fine‐scale motions (<100 km) contribute significantly to the exchanges and dissipation of kinetic energy in the upper ocean. However, knowledge of ocean kinetic energy at fine‐scales (in terms of density and transfers) is currently limited due to the lack of sufficient observational data sets at these scales. The sea‐surface height measurements of the upcoming Surface Water and Ocean Topography (SWOT) altimeter mission should provide information on kinetic energy exchanges in the upper ocean down to 10–15 km. Numerical ocean models, able to describe ocean dynamics down to ∼10 km, have been developed in anticipation of the SWOT mission. In this study, we use two state‐of‐the‐art, realistic, North Atlantic simulations, with horizontal resolutions ∼1.5 km, to investigate the distribution and exchanges of kinetic energy at fine‐scales in the open ocean. Our results show that the distribution of kinetic energy at fine‐scales approximately follows the predictions of quasigeostrophic dynamics in summertime but is somewhat consistent with submesoscale fronts‐dominated regimes in wintertime. The kinetic energy spectral fluxes are found to exhibit both inverse and forward cascade over the top 1,000 m, with a maximum inverse cascade close to the average energy‐containing scale. The forward cascade is confined to the ocean surface and shows a strong seasonality, both in magnitude and range of scales affected. Our analysis further indicates that high‐frequency motions (<1 day) play a key role in the forward cascade and that the estimates of the spectral fluxes based on geostrophic velocities fail to capture some quantitative aspects of kinetic energy exchanges across scales. Plain Language Summary: The dynamics of oceanic motions with scales <100 km (fine‐scales) are currently not well known. This is due to the lack of sufficient observational datasets at these scales in the ocean. There are suggestions from recent studies that this class of motions impacts the distribution and exchanges of kinetic energy in the ocean. To better understand fine‐scale motions, the Surface Water and Ocean Topography (SWOT) satellite has been assembled. SWOT is expected for lunch in 2022 and will provide an unprecedented view of the ocean down to a wavelength of 10–15 km. In anticipation of the SWOT mission, numerical ocean models capable of resolving fine‐scale oceanic motions have been designed and implemented. In this study, we use two of these simulations to investigate how kinetic energy is exchanged between oceanic motions at fine‐scales. Our results show that submesoscale turbulence (a class of oceanic turbulence at fine‐scale) and high‐frequency motions affect the kinetic energy exchanges by providing a route to kinetic energy toward dissipation. Also, we found that kinetic energy exchanges based on the future SWOT data set might underestimate the true magnitude of the transfer of kinetic energy toward finer scales. Key Points: We used two submesoscale permitting ocean models of the North Atlantic Ocean to investigate kinetic energy exchanges at fine‐scalesKE fluxes at fine‐scales are strongly impacted by submesoscale turbulence with a stronger forward cascade in winter within the mixed‐layerNot accounting for ageostrophic motions yields a significant underestimation of the forward cascade [ABSTRACT FROM AUTHOR]

The deformation radius is widely used as an indication of the eddy length scale at different latitudes. The radius is usually calculated assuming a flat ocean bottom. However, bathymetry alters the baroclinic modes and hence their deformation radii. In a linear quasigeostrophic two-layer model with realistic parameters, the deep flow for a 100-km wave approaches zero with a bottom ridge roughly 10m high, leaving a baroclinic mode that is mostly surface trapped. This is in line with published current meter studies showing a primary EOF that is surface intensified and has nearly zero flow at the bottom. The deformation radius associated with this ''surface mode'' is significantly larger than that of the flat bottom baroclinic mode. Using World Ocean Atlas data, the surface radius is found to be 20%-50% larger over much of the globe, and 100% larger in some regions. This in turn alters the long Rossby wave speed, which is shown to be 1.5-2 times faster than over a flat bottom. In addition, the larger deformation radius is easier to resolve in ocean models. [ABSTRACT FROM AUTHOR]

Estimates of 3D ocean circulation are needed to improve our understanding of ocean dynamics and to assess their impact on marine ecosystems and Earth climate. Here we present the OMEGA3D product, an observation-based time series of (quasi-)global 3D ocean currents covering the 1993–2018 period, developed by the Italian Consiglio Nazionale delle Ricerche within the European Copernicus Marine Environment Monitoring Service (CMEMS). This dataset was obtained by applying a diabatic quasi-geostrophic (QG) diagnostic model to the data-driven CMEMS-ARMOR3D weekly reconstruction of temperature and salinity as well as ERA Interim fluxes. Outside the equatorial band, vertical velocities were retrieved in the upper 1500 m at 1/4 ∘ nominal resolution and successively used to compute the horizontal ageostrophic components. Root mean square differences between OMEGA3D total horizontal velocities and totally independent drifter observations at two different depths (15 and 1000 m) decrease with respect to corresponding estimates obtained from zero-order geostrophic balance, meaning that estimated vertical velocities can also be deemed reliable. OMEGA3D horizontal velocities are also closer to drifter observations than velocities provided by a set of reanalyses spanning a comparable time period but based on data assimilation in ocean general circulation numerical models. The full OMEGA3D product (released on 31 March 2020) is available upon free registration at https://doi.org/10.25423/cmcc/multiobs%5fglo%5fphy%5fw%5frep%5f015%5f007 (Buongiorno Nardelli, 2020a). The reduced subset used here for validation and review purposes is openly available at 10.5281/zenodo.3696885 (Buongiorno Nardelli, 2020b). [ABSTRACT FROM AUTHOR]

A deeper knowledge about geostrophic ocean surface currents in the northern Nordic Seas supports the understanding of ocean dynamics in an area affected by sea ice and rapidly changing environmental conditions. Monitoring these areas by satellite altimetry results in a fragmented and irregularly distributed data sampling and prevents the computation of homogeneous and highly resolved spatio-temporal datasets. In order to overcome this problem, an ocean model is used to fill in data when altimetry observations are missing. The present study provides a novel dataset based on a combination of along-track satellite-altimetry-derived dynamic ocean topography (DOT) elevations and simulated differential water heights (DWHs) from the Finite Element Sea ice Ocean Model (FESOM) version 1.4. This innovative dataset differs from classical assimilation methods because it substitutes altimetry data with the model output when altimetry fails or is not available. The combination approach is mainly based on a principal component analysis (PCA) after reducing both quantities by their constant and seasonal signals. In the main step, the most-dominant spatial patterns of the modeled differential water heights as provided by the PCA are linked with the temporal variability in the estimated DOT from altimetry by performing a principal component synthesis (PCS). After the combination, the annual signal obtained by altimetry and a constant offset are re-added in order to reference the final data product to the altimetry height level. Surface currents are computed by applying the geostrophic flow equations to the combined topography. The resulting final product is characterized by the spatial resolution of the ocean model around 1 km and the temporal variability in the altimetry along-track derived DOT heights. The combined DOT is compared to an independent DOT product, resulting in a positive correlation of about 80 %, to provide more detailed information about short periodic and finer spatial structures. The derived geostrophic velocity components are evaluated by in situ surface drifter observations. Summarizing all drifter observations in equally sized bins and comparing the velocity components shows good agreement in spatial patterns, magnitude and flow direction. Mean differences of 0.004 m s -1 in the zonal and 0.02 m s -1 in the meridional component are observed. A direct pointwise comparison between the combined geostrophic velocity components interpolated onto the drifter locations indicates that about 94 % of all residuals are smaller than 0.15 m s -1. The dataset is able to provide surface circulation information within the sea ice area and can be used to support a deeper comprehension of ocean currents in the northern Nordic Seas affected by rapid environmental changes in the 1995–2012 time period. The data are available at 10.1594/PANGAEA.900691. [ABSTRACT FROM AUTHOR]

Based on analysis of observational data it has been suggested that a negative feedback of ice–ocean stress coupling may limit freshwater accumulation in the Beaufort Gyre (BG). In this paper we explore how this feedback can significantly contribute to BG stabilization in an anticyclonic wind regime. We use an ice–ocean model and turn on and off the feedback in simulations to elucidate the role of the feedback. When a persistent anticyclonic wind anomaly is applied over the BG, liquid freshwater content (FWC) increases because of enhanced Ekman downwelling. As a consequence, ocean surface geostrophic currents speed up. However, the spinup of sea ice is weaker than the acceleration of surface geostrophic currents during wintertime, because of strong sea ice internal stress when ice concentration is high and ice is thick. This leads to cyclonic anomalies in the ice–ocean relative velocity and stress over the BG. The resultant seasonal Ekman upwelling anomaly reduces freshwater accumulation by about 1/4 as compared to a simulation with the negative feedback turned off in a control experiment, with a reduction range of 1/10–1/3 in all experiments conducted. We show that the feedback is more effective when the model's mesoscale eddy diffusivity is smaller or when sea ice internal stress is stronger. Finally, we argue that the ice–ocean stress feedback may become less significant as the Arctic warms and sea ice declines. [ABSTRACT FROM AUTHOR]

A process-oriented numerical modeling study was conducted to investigate the formation and underlying forcing of an anticyclonic eddy train observed in the northern South China Sea. Observations showed that long-lived anticyclonic eddies formed an eddy train along an eastward separated jet across the northern South China Sea in summer. The eddy train plays a critical role in regulating ocean circulation in the region. Forced by the southwesterly monsoon and prevailing dipole wind stress curl in the summer, the northward coastal jet separates from the west boundary of the South China Sea basin and overshoots northeastward into the basin. The anticyclonic recirculation of the separated jet forms the first anticyclonic eddy in the eddy train. The jet meanders downstream with a strong negative shear vorticity that forms a second and a third anticyclonic eddy along the jet's path. These three eddies form the eddy train. These eddies weaken gradually with depth from surface, but they can extend to approximately 500 m deep. The inherent stratification in the region regulates the three-dimensional scale of the anticyclonic eddies and constrains their intensity vertical extension by weakening the geostrophic balance within these eddies. Analyses of the vorticity balance indicate that the eddy train's negative vorticity originates from the beta effect of northward western boundary current and from the subsequent downstream vorticity advection in the jet. The jet separation is a necessary condition for the formation of the eddy train, and the enhanced stratification, increased summer wind stress, and associated negative wind stress curl are favorable conditions for the formation of the anticyclonic eddies. [ABSTRACT FROM AUTHOR]

The problem of localized dense water formation over a sloping bottom is considered for the general case in which the topography forms a closed contour. This class of problems is motivated by topography around islands or shallow shoals in which convection resulting from brine rejection or surface heat loss reaches the bottom. The focus of this study is on the large-scale circulation that is forced far from the region of surface forcing. The authors find that a cyclonic current is generated around the topography, in the opposite sense to the propagation of the dense water plume. In physical terms, this current results from the propagation of low sea surface height from the region of dense water formation anticyclonically along the topographic contours back to the formation region. This pressure gradient is then balanced by a cyclonic geostrophic flow. This basic structure is well predicted by a linear quasigeostrophic theory, a primitive equation model, and in rotating tank experiments. For sufficiently strong forcing, the anticyclonic circulation of the dense plume meets this cyclonic circulation to produce a sharp front and offshore advection of dense water at the bottom and buoyant water at the surface. This nonlinear limit is demonstrated in both the primitive equation model and in the tank experiments. [ABSTRACT FROM AUTHOR]

A simple quasigeostrophic model is used to examine the outflow from a river, estuary, or strait into a coastal ocean. As shown by Johnson et al., these quasigeostrophic outflows are accurately described by analytical long-wave solutions. This paper first uses these solutions and contour dynamics simulations to discuss the behavior of coastal outflows. Second, it extends the model and the long-wave theory to consider the effects of ambient currents, tides, winds, or a variable source flux. Third, consideration of the momentum flux at the source is used to understand the turning of the current, showing that steady solutions conserve momentum, hence resolving the momentum imbalance paradox of Pichevin and Nof. Finally, a new numerical scheme to compute steady outflow boundaries is developed. The model focuses on the key dynamics driven by the source velocity and the generation of vorticity as the buoyant fluid adjusts. The simplicity of the model, and insight given by the long-wave solutions, enables a full understanding of the dynamics. The outflows display a range of behaviors, including indefinitely growing near-source bulges, steady boundary profiles with varying offshore width, bidirectional currents, and rarefying or eddy-like leading heads, all of which can be understood with the long-wave theory. Despite the simplicity of the model, the results show good agreement in comparison with observations, experiments, and numerical models. [ABSTRACT FROM AUTHOR]

This study deals with the physical properties and 3D structures of the wave motions with finite wavelengths of O(100-550) km in the tropical western North Pacific and their variation as propagating from the Pacific to the South China Sea (SCS) using conductivity-temperature-depth observations taken in October and November 2005 and concurrent satellite altimeter data. Three wave components with wavelength bands of O(100), O(200), and O(550) km are derived from the isopycnal undulation signals along 21°, 18°, and 15°N using the ensemble empirical mode decomposition analysis. Their maximum amplitudes are over 100 m in the layer of 1000-2000 m. Phase speeds are derived from cruise-observed vertical profiles of zonal-mean geostrophic flow velocity and the Brunt-Väisälä frequency based on linear quasigeostrophic wave theory with background flow and topography. The speeds are also derived from concurrent sea level anomaly data with the objective Radon transform method. They are close to that of the first baroclinic mode of theoretical solutions, implying that the observed wave motions possess the physical properties of Rossby waves (RWs). The vertical structures of the first generalized modes are derived from cruise observations at three sections. It is shown that the RWs continuously propagate from the Pacific to the SCS, and the available potential energy of RWs 1 and 2 intensify 3-4 times in the Luzon Strait and the SCS compared to that in the Pacific. [ABSTRACT FROM AUTHOR]

The spatial structure of the upper ocean heat budget in the Antarctic Circumpolar Current (ACC) is investigated using the ⅙°, data-assimilating Southern Ocean State Estimate (SOSE) for 2005-10. The ACC circumpolar integrated budget shows that 0.27 PW of ocean heat gain from the atmosphere and 0.38 PW heat gain from divergence of geostrophic heat transport are balanced by −0.58 PW cooling by divergence of Ekman heat transport and −0.09 PW divergence of vertical heat transport. However, this circumpolar integrated balance obscures important zonal variations in the heat budget. The air-sea heat flux shows a zonally asymmetric pattern of ocean heat gain in the Indian and Atlantic sectors and ocean heat loss in the Pacific sector of the ACC. In the Atlantic and Indian sectors of the ACC, the surface ocean heat gain is primarily balanced by divergence of equatorward Ekman heat transport that cools the upper ocean. In the Pacific sector, surface ocean heat loss and cooling due to divergence of Ekman heat transport are balanced by warming due to divergence of geostrophic heat advection, which is similar to the dominant heat balance in the subtropical Agulhas Return Current. The divergence of horizontal and vertical eddy advection of heat is important for warming the upper ocean close to major topographic features, while the divergence of mean vertical heat advection is a weak cooling term. The results herein show that topographic steering and zonal asymmetry in air-sea exchange lead to substantial zonal asymmetries in the heat budget, which is important for understanding the upper cell of the overturning circulation. [ABSTRACT FROM AUTHOR]

Understanding of the three-dimensional circulation in the South China Sea (SCS) is crucial for determining the transports of water masses, energy, and biogeochemical substances in the regional and adjacent larger oceans. The circulation's kinematic and dynamic natures, however, are largely unclear. Results from a three-dimensional numerical ocean circulation model and geostrophic currents, derived from hydrographic data, reveal the existence of a unique, three-layer, cyclonic-anticyclonic-cyclonic (CAC) circulation in the upper (<750 m), middle (750-1500 m), and deep (>1500 m) layers in the SCS with differing seasonality. An inflow-outflow-inflow structure in Luzon Strait largely induces the CAC circulation, which leads to vortex stretching in the SCS basin because of a lateral planetary vorticity flux in each of the respective layers. The formation of joint effects of baroclinicity and relief (JEBAR) is an intrinsic dynamic response to the CAC circulation. The JEBAR arises from the CAC flow-topography interaction in the SCS. [ABSTRACT FROM AUTHOR]

A quasigeostrophic model is developed to diagnose the three-dimensional circulation, including the vertical velocity, in the upper ocean from high-resolution observations of sea surface height and buoyancy. The formulation for the adiabatic component departs from the classical surface quasigeostrophic framework considered before since it takes into account the stratification within the surface mixed layer that is usually much weaker than that in the ocean interior. To achieve this, the model approximates the ocean with two constant stratification layers: a finite-thickness surface layer (or the mixed layer) and an infinitely deep interior layer. It is shown that the leading-order adiabatic circulation is entirely determined if both the surface streamfunction and buoyancy anomalies are considered. The surface layer further includes a diabatic dynamical contribution. Parameterization of diabatic vertical velocities is based on their restoring impacts of the thermal wind balance that is perturbed by turbulent vertical mixing of momentum and buoyancy. The model skill in reproducing the three-dimensional circulation in the upper ocean from surface data is checked against the output of a high-resolution primitive equation numerical simulation. [ABSTRACT FROM AUTHOR]

Large-scale baroclinic instability is investigated as a potential source of Rossby waves and large-scale variability in the ocean. This baroclinic instability is first reviewed in a 2.5-layer model. As already noticed by several authors, the instability arises in westward surface mean flow when the phase velocities of the two vertical modes are made equal by mean flow influence. This large-scale instability is stronger at low latitudes and thus is likely to happen in the westward return flow of the subtropical gyres. Further investigations with a continuous stratification quasigeostrophic model show that the instability is stronger where the mean flow projects negatively on the second baroclinic mode (imposing positive vertical modes at the surface). The linear stability calculation is then performed on Argo-derived mean flow along with mean stratification data. The results show that the unstable regions are situated at low latitudes in every oceanic basin, in western boundary currents, and in some part of the Antarctic Circumpolar Current. The location of these unstable regions is well correlated with the region of negative projection of the mean flow on the second baroclinic mode. Given that the unstable mode growth times are generally smaller than 6 months at low latitudes, these unstable modes are likely to be observable in satellite altimetry. Therefore, results of the present article suggest that the large-scale instability is indeed a source of large-scale variability at low latitudes. [ABSTRACT FROM AUTHOR]

This study demonstrates that oceanic vertical velocities can be estimated from individual mooring measurements, even for nonstationary flow. This result is obtained under three assumptions: (i) weak diffusion (Péclet number ≫ 1), (ii) weak friction (Reynolds number ≫ 1), and (iii) small inertial terms (Rossby number ≪ 1). The theoretical framework is applied to a set of four moorings located in the Southern Ocean. For this site, the diagnosed vertical velocities are highly variable in time, their standard deviation being one to two orders of magnitude greater than their mean. The time-averaged vertical velocities are demonstrated to be largely induced by geostrophic flow and can be estimated from the time-averaged density and horizontal velocities. This suggests that local time-mean vertical velocities are primarily forced by the time-mean ocean dynamics, rather than by, for example, transient eddies or internal waves. It is also shown that, in the context of these four moorings, the time-mean vertical flow is consistent with stratified Taylor column dynamics in the presence of a topographic obstacle. [ABSTRACT FROM AUTHOR]

The interannual variability of the upper-ocean circulation forced by seasonally varying monsoonal wind is investigated in a two-layer quasigeostrophic (QG) model, with the aim to understand the low-frequency variability of the South China Sea (SCS) circulation. It is demonstrated that the seasonally varying monsoonal wind can force the upper-ocean circulation with significant internal variability, which is mainly associated with the intrinsic nonlinear dynamics of the summer double-gyre system. This arises from the fact that the intrinsic variability, characterized by the Rossby wave adjustment in the winter single-gyre system, is much weaker than that in the summer double-gyre system driven by the intergyre eddy potential vorticity flux through barotropic instability. [ABSTRACT FROM AUTHOR]

The west-to-east crossover of boundary currents has been seen in mean circulation schemes from several past models of the Red Sea. This study investigates the mechanisms that produce and control the crossover in an idealized, eddy-resolving numerical model of the Red Sea. The authors also review the observational evidence and derive an analytical estimate for the crossover latitude. The surface buoyancy loss increases northward in the idealized model, and the resultant mean circulation consists of an anticyclonic gyre in the south and a cyclonic gyre in the north. In the midbasin, the northward surface flow crosses from the western boundary to the eastern boundary. Numerical experiments with different parameters indicate that the crossover latitude of the boundary currents changes with f0, β, and the meridional gradient of surface buoyancy forcing. In the analytical estimate, which is based on quasigeostrophic, β-plane dynamics, the crossover is predicted to lie at the latitude where the net potential vorticity advection (including an eddy component) is zero. Various terms in the potential vorticity budget can be estimated using a buoyancy budget, a thermal wind balance, and a parameterization of baroclinic instability. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

Absolute geostrophic currents in the North Pacific Ocean are calculated from the newly gridded Argo profiling float data using the P-vector method for the period of 2004-11. The zonal geostrophic currents based on the Argo profile data are found to be stronger than those based on the traditional World Ocean Atlas 2009 ( WOA09) data. A westward mean geostrophic flow underneath the North Equatorial Countercurrent is identified using the Argo data, which is evidenced by sporadic direct current measurements and geostrophic calculations in history. This current originates east of the date line and transports more than 4 × 106 m3 s−1 of water westward in the subsurface northwestern tropical Pacific Ocean. The authors name this current the North Equatorial Subsurface Current. The transport in the geostrophic currents is compared with the Sverdrup theory and found to differ significantly in several locations. Analyses have shown that errors of wind stress estimation cannot account for all of the differences. The largest differences are found in the area immediately north and south of the bifurcation latitude of the North Equatorial Current west of the date line and in the recirculation area of the Kuroshio and its extension, where nonlinear activities are vigorous. It is, therefore, suggested that the linear dynamics of the Sverdrup theory is deficient in explaining the geostrophic transport of the tropical northwestern Pacific Ocean. [ABSTRACT FROM AUTHOR]

Surface ocean dynamics play a key role in the Earth system, contributing to regulate its climate and affecting the marine ecosystem functioning. Dynamical processes occur and interact in the upper ocean at multiple scales, down to, or even less than, few kilometres. These scales are not adequately resolved by present observing systems, and, in the last decades, global monitoring of surface currents has been based on the application of geostrophic balance to absolute dynamic topography maps obtained through the statistical interpolation of along-track satellite altimeter data. Due to the cross-track distance and repetitiveness of satellite acquisitions, the effective resolution of interpolated data is limited to several tens of kilometres. At the kilometre scale, sea surface temperature pattern evolution is dominated by advection, providing indirect information on upper ocean currents. Computer vision techniques are perfect candidates to infer this dynamical information from the combination of altimeter data, surface temperature images and observing-system geometry. Here, we exploit one class of image processing techniques, super-resolution, to develop an original neural-network architecture specifically designed to improve absolute dynamic topography reconstruction. Our model is first trained on synthetic observations built from a numerical general-circulation model and then tested on real satellite products. Provided concurrent clear-sky thermal observations are available, it proves able to compensate for altimeter sampling/interpolation limitations by learning from primitive equation data. The algorithm can be adapted to learn directly from future surface topography, and eventual surface currents, high-resolution satellite observations. [ABSTRACT FROM AUTHOR]

A new method is proposed for extrapolating subsurface velocity and density fields from sea surface density and sea surface height (SSH). In this, the surface density is linked to the subsurface fields via the surface quasigeostrophic (SQG) formalism, as proposed in several recent papers. The subsurface field is augmented by the addition of the barotropic and first baroclinic modes, whose amplitudes are determined by matching to the sea surface height (pressure), after subtracting the SQG contribution. An additional constraint is that the bottom pressure anomaly vanishes. The method is tested for three regions in the North Atlantic using data from a high-resolution numerical simulation. The decomposition yields strikingly realistic subsurface fields. It is particularly successful in energetic regions like the Gulf Stream extension and at high latitudes where the mixed layer is deep, but it also works in less energetic eastern subtropics. The demonstration highlights the possibility of reconstructing three-dimensional oceanic flows using a combination of satellite fields, for example, sea surface temperature (SST) and SSH, and sparse (or climatological) estimates of the regional depth-resolved density. The method could be further elaborated to integrate additional subsurface information, such as mooring measurements. [ABSTRACT FROM AUTHOR]

The cross-shelf dynamics up- and downstream of the separation of the South Pacific Ocean's Western Boundary Current (WBC) are studied using two years of high-resolution velocity and temperature measurements from mooring arrays. The shelf circulation is dominated by the East Australian Current (EAC) and its eddy field, with mean poleward depth-integrated magnitudes on the shelf break of 0.35 and 0.15 m s−1 up- and downstream of the separation point, respectively. The high cross-shelf variability is analyzed though a momentum budget, showing a dominant geostrophic balance at both locations. Among the secondary midshelf terms, the bottom stress influence is higher upstream of the separation point while the wind stress is dominant downstream. This study investigates the response of the velocity and temperature cross-shelf structure to both wind and EAC intrusions. Despite the deep water (up to 140 m), the response to a dominant along-shelf wind stress forcing is a classic two-layer Ekman structure. During weak winds, the shelf encroachment of the southward current drives an onshore Ekman flow in the bottom boundary layer. Both the bottom velocity and the resultant bottom cross-shelf temperature gradient are proportional to the magnitude of the encroaching current, with similar linear regressions up- and downstream of the WBC separation. The upwelled water is then subducted below the EAC upstream of the separation point. Such current-driven upwelling is shown to be the dominant driver of cold water uplift in the EAC-dominated region, with significant impacts expected on nutrient enrichment and thus on biological productivity. [ABSTRACT FROM AUTHOR]

A framework for parameterizing eddy potential vorticity fluxes is developed that is consistent with conservation of energy and momentum while retaining the symmetries of the original eddy flux. The framework involves rewriting the residual-mean eddy force, or equivalently the eddy potential vorticity flux, as the divergence of an eddy stress tensor. A norm of this tensor is bounded by the eddy energy, allowing the components of the stress tensor to be rewritten in terms of the eddy energy and nondimensional parameters describing the mean shape and orientation of the eddies. If a prognostic equation is solved for the eddy energy, the remaining unknowns are nondimensional and bounded in magnitude by unity. Moreover, these nondimensional geometric parameters have strong connections with classical stability theory. When applied to the Eady problem, it is shown that the new framework preserves the functional form of the Eady growth rate for linear instability. Moreover, in the limit in which Reynolds stresses are neglected, the framework reduces to a Gent and McWilliams type of eddy closure where the eddy diffusivity can be interpreted as the form proposed by Visbeck et al. Simulations of three-layer wind-driven gyres are used to diagnose the eddy shape and orientations in fully developed geostrophic turbulence. These fields are found to have large-scale structure that appears related to the structure of the mean flow. The eddy energy sets the magnitude of the eddy stress tensor and hence the eddy potential vorticity fluxes. Possible extensions of the framework to ensure potential vorticity is mixed on average are discussed. [ABSTRACT FROM AUTHOR]

It is shown that geostrophic vertical shear estimates can be recovered from seismic (i.e., acoustic) images of thermohaline structure. In the Southern Ocean, the Antarctic Circumpolar Current forms a loop within the Falkland Trough before it flows northward into the Argentine Basin. Seismic profiles that cross this loop show the detailed structure of different water masses with a horizontal resolution of O(10 m). Coherent seismic reflections are tilted in response to current flow around the Falkland Trough. Average slopes were measured on length scales that are large enough to ensure that the geostrophic approximation is valid (i.e., with a Rossby number <0.1). By combining shear estimates with satellite altimetric measurements and acoustic Doppler current profiles, geostrophic velocities can be calculated throughout the data volume. This technique for estimating geostrophic vertical shear from legacy seismic images yields useful information about the spatial and temporal variation of mesoscale circulation. [ABSTRACT FROM AUTHOR]

It is shown that geostrophic vertical shear estimates can be recovered from seismic (i.e., acoustic) images of thermohaline structure. In the Southern Ocean, the Antarctic Circumpolar Current forms a loop within the Falkland Trough before it flows northward into the Argentine Basin. Seismic profiles that cross this loop show the detailed structure of different water masses with a horizontal resolution of O(10 m). Coherent seismic reflections are tilted in response to current flow around the Falkland Trough. Average slopes were measured on length scales that are large enough to ensure that the geostrophic approximation is valid (i.e., with a Rossby number <0.1). By combining shear estimates with satellite altimetric measurements and acoustic Doppler current profiles, geostrophic velocities can be calculated throughout the data volume. This technique for estimating geostrophic vertical shear from legacy seismic images yields useful information about the spatial and temporal variation of mesoscale circulation. [ABSTRACT FROM AUTHOR]

This study investigates the seasonal variations of the mixed-layer salinity anomalies(MLSAs) under the decadal variability of the Kuroshio Extension (KE) in theKuroshio-Oyashio Confluence Region (KOCR: 35–40˚ N, 140–150˚ E). Our analysis revealsthat the seasonal variation trend of the MLSA is almost opposite in the stable andunstable states of the KE. In the stable (unstable) state, the increasing (decreasing)MLSA in the KOCR reaches its maximal positive (minimal negative) value in latesummer and then decreases (increases) gradually. An exploration of the budgetof the MLSA shows that ocean dynamics explain more than half of the seasonalMLSA changes in the two states and exceed the contribution of atmospheric forcing(approximately 18%). The leading oceanic processes include advection of the meanmixed-layer salinity by anomalous Ekman and geostrophic currents and advection ofthe MLSA by mean geostrophic currents, which explain 13.80%, 12.90%, and20.73% (11.59%, 13.36%, and 24.90%) of the MLSA temporal changes in the stable(unstable) states, respectively. The difference in the MLSA between the two states isprimarily derived from the discrepancies in the anomalous ocean currents in theKOCR and south of Japan, salinity anomalies in the south of Japan, and sea surfacetemperature anomalies affecting atmospheric forcing between the two modes of the KE.Moreover, the most apparent influences are concentrated in summer and early autumnbecause of the shallower mixed layer in terms of atmospheric forcing and obviousvelocity changes and the distribution of climatological salinity for ocean processes. [ABSTRACT FROM AUTHOR]

Kinetic energy wavenumber spectra provide information on the regime of turbulent energy exchanges across scales in the ocean. This is why a lot of efforts have focused on assessing how the slopes of ocean surface kinetic energy wavenumber spectra compare with the slopes predicted by simplified models of ocean dynamics (QG, SQG) in the quasi-two dimensional turbulence inertial range. Analyses of high resolution ocean circulation models suggest that the slopes of ocean surface kinetic energy wavenumber spectra lie between the prediction of QG ($k^{-3}$) and SQG ($k^-2$) models with strong spatial variations modulated by the levels of surface eddy kinetic energy. Analysis from altimetry also show constrasted results, within the limits set by the resolution capability of current generation altimeters. In this study we focus on quantifying the rate of turbulent kinetic energy exchange and the inverse cascade of energy through advective nonlinearity in the mesoscale inertial range. Our analysis is based on model output from a kilometric grid resolution, North Atlantic, sub-mesoscale permitting ocean circulation model configurations based on NEMO. The novelty of this study is to focus specifically on kinetic energy exchanges within the inertial range, which is defined as the scales between the dominent energy containing scale (integral scale) and the models effective resolution (where numerical dissipation becomes significant). Our results show that north of 30°N the energy containing scale of mesoscale eddies decreases with latitude following the first Rossby radius of deformation (Rd) while the nonlinearity of eddies (ratio of the Rhine scale Rh to integral scale) increases with latitude. Within the inertial range, we find that surface kinetic energy wavenumber spectra show slopes close to $k^{-3}$. Model turbulent regimes are therefore comparable with QG predictions in most of the North Atlantic Ocean north of 30°N, in both high and low eddy kinetic energy regions. Analysis of KE transfers due to advective nonlinearity further show that, in most of the North Atlantic, KE is injected at scales close to Rd and cascades towards larger scales. In regions of weak nonlinearity this inverse cascade is arrested close to the Rhine scales (Rh). Our result also show that estimates of KE transfers based on geostrophic currents significantly underestimate the inverse cascade, which questions our ability to infer oceanic energy cascade from altimetry and the future SWOT mission. [ABSTRACT FROM AUTHOR]

Satellite altimetry enables to obtain the Sea Surface Height (SSH) variations along the satellite tracks. More and more accurate observations are available near the coasts thanks to advances in the data processing and to technological innovations. As a consequence, fine-scale coastal structures (eg down to 30-50 km, depending on their signature in SSH) can be regularly monitored. However, in terms of geostrophic current derived from the SSH altimetry gradients, intercomparisons with in situ observations show regularly that their amplitude is underestimated. This is due to the signal-over-noise ratio associated to altimetry measurements, which results in a loss of information. If we want to optimize the use of altimetry in coastal studies, it is important to quantify what current component can/can't be observed. This is the objective of this work.The North-Western Mediterranean Sea (NWMed) has become a pilot area for coastal altimetry studies. It is a particularly interesting area in terms of coastal ocean dynamics, associated to a large number of fine scale structures. It also benefits from a large number of in situ current observations (ADCP, gliders, HF radars). In this study, the objectives are to quantify the SSH signature of dedicated coastal processes in the NWMed and to analyse the spatio-temporal scales associated. We focus on the Northern Current (or NC, less than 60 km wide) which flows cyclonally along the Italian, French and Spanish coasts. We use a high resolution numerical model (Symphonie) which is first validated against independent in situ datasets. Then it is used to quantify the SSH signature of the NC at two distinct locations along the French coast. We then compared the results obtained with the spatio-temporal variations observed in satellite altimetry data and quantify and study the differences. We also analyze the origin of the differences observed between different types of in situ current observations and altimetry data : their respective spatial/temporal resolution, track orientation, differences in location, geostrophic vs total current component,... Finally, this study also allows us to understand the intrinsic differences obtained from different types of ocean current observations. [ABSTRACT FROM AUTHOR]

This response addresses the three comments by A. Polonsky on 'A Global Analysis of Sverdrup Balance Using Absolute Geostrophic Velocities from Argo.' [ABSTRACT FROM AUTHOR]