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Satellite altimetry combined with data assimilation and optimal interpolation schemes have deeply renewed our ability to monitor sea surface dynamics. Recently, deep learning schemes have emerged as appealing solutions to address space‐time interpolation problems. However, the training of state‐of‐the‐art neural schemes on real‐world case‐studies is hindered by the sparse space‐time coverage of the sea surface of real altimetry data set. Here, we introduce an innovative approach that leverages state‐of‐the‐art ocean models to train simulation‐based neural schemes for the mapping of sea surface height and demonstrate their performance on real altimetry data sets. We analyze further how the ocean simulation data set used during the training phase impacts this performance. This experimental analysis covers both the resolution from eddy‐present configurations to eddy‐rich ones, forced simulations versus reanalyzes using data assimilation and tide‐free versus tide‐resolving simulations. Our benchmarking framework focuses on a Gulf Stream region for a realistic 5‐altimeter constellation using NEMO ocean simulations and 4DVarNet mapping schemes. All simulation‐based 4DVarNets outperform the operational observation‐driven and reanalysis products, namely DUACS and GLORYS. The more realistic the ocean simulation data set used during the training phase, the better the mapping. The best 4DVarNet mapping was trained from an eddy‐rich and tide‐free simulation data sets. It improves the resolved longitudinal scale from 151 km for DUACS and 241 km for GLORYS to 98 km and reduces the root mean square error by 23% and 61%. These results open research avenues for new synergies between ocean modeling and ocean observation using learning‐based approaches. Plain Language Summary: To train an artificial intelligence (AI) model, one need to describe a task using data and an evaluation procedure. Here we aim at constructing images related to the ocean surface currents. The satellite data we use provide images of the ocean surface with a lot of missing data (around 95% of missing pixels for a given day), and we aim at finding the values of the missing pixels. Because we don't know the full image, it is challenging to train an AI on this task using only the satellite data. However, today's physical knowledge makes it possible to numerically simulate oceans on big computers. For these simulated oceans, we have access to the gap‐free image, so we can train AI models by first hiding some pixels and checking if the model fill the gaps with the correct values. Here, we explore under which conditions AIs trained on simulated oceans are useful for the real ocean. We show that today's simulated oceans work well for training an AI on this task and that training on more realistic simulated oceans improve the performance of the AI! Key Points: We suggest utilizing ocean simulation data sets to train neural schemes for mapping real altimeter dataThe trained neural scheme improves the spatial scales resolved over the operational mapping product on a GulfStream case study by 30%Using more realistic simulation data sets improves the resulting neural mapping scheme by up to 20% in the spatial scales resolved [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]

The energy- and enstrophy-conserving momentum advection scheme (EEN) used over the last 10 years in NEMO is subject to a spurious numerical instability. This instability, referred to as the Symmetric Instability of the Computational Kind (SICK), arises from a discrete imbalance between the two components of the vector-invariant form of momentum advection. The properties and the method for removing this instability have been documented by Hollingsworth et al. (1983), but the extent to which the SICK may interfere with processes of interest at mesoscale- and submesoscale-permitting resolutions is still unkown. In this paper, the impact of the SICK in realistic ocean model simulations is assessed by comparing model integrations with different versions of the EEN momentum advection scheme. Investigations are undertaken with a global mesoscale-permitting resolution (1/4 °) configuration and with a regional North Atlantic Ocean submesoscale-permitting resolution (1/60 °) configuration. At both resolutions, the instability is found to alter primarily the most energetic current systems, such as equatorial jets, western boundary currents and coherent vortices. The impact of the SICK is found to increase with model resolution with a noticeable impact at mesoscale-permitting resolution and a dramatic impact at submesoscale-permitting resolution. The SICK is shown to distort the normal functioning of current systems, by redirecting the slow energy transfer between balanced motions to a spurious energy transfer to internal inertia-gravity waves and to dissipation. Our results indicate that the SICK is likely to have significantly corrupted NEMO solutions (when run with the EEN scheme) at mesocale-permitting and finer resolutions over the last 10 years. [ABSTRACT FROM AUTHOR]

To refine the understanding of how the Southern Ocean responds to recent intensification of the southern annular mode (SAM), a regional ocean model at two eddy-permitting resolutions was forced with two synthetic interannual forcings. The first forcing corresponds to homogeneously intensified winds, while the second concerns their poleward intensification, consistent with positive phases of the SAM. Resulting wind-driven responses differ greatly between the nearly insensitive Antarctic Circumpolar Current (ACC) and the more sensitive meridional overturning circulation (MOC). As expected, eddies mitigate the response of the ACC and MOC to poleward-intensified winds. However, transient eddies do not necessarily play an increasing role in meridional transport with increasing resolution. As winds and resolution increase, meridional transport from standing eddies becomes more efficient at balancing wind-enhanced overturning. These results question the current paradigms on the role of eddies and present new challenges for eddy flux parameterization. Results also indicate that spatial patterns of wind anomalies are at least as important as the overall change in intensity in influencing the Southern Ocean's dynamic response to wind events. Poleward-intensified wind anomalies from the positive trend in the SAM are far more efficient in accelerating the ACC than homogeneous wind anomalies. [ABSTRACT FROM AUTHOR]

Abstract: Horizontal stirring by time-varying mesoscale flows contributes to forming submesoscale tracer filaments. In this paper, we propose a parameterization of the passive transport associated with filamentation by mesoscale flows for use in O(10km) resolution ocean models. Theoretical motivations are provided for modelling subgrid stirring by the resolved mesoscale flows with an anisotropic generalization of Smagorinsky operator. For level coordinate models, an isoneutral formulation of the proposed subgrid operator is provided. The proposed subgrid operator is diagnosed with DRAKKAR global 1/4° eddy-resolving model output. In the Southern Ocean, the parameterization is shown to provide diffusivities peaking at about 400m2 s−1. If applied prognostically, the proposed subgrid operator could drive meridional heat transports of about .5PW at 45°S. This suggests that a significant fraction of the transport by mesoscale flows could be associated with tracer features of scale smaller than our model grid size (∼20km at 45°S). A large contribution to this transport is associated with differential advection by the time-mean flow at subgrid scale. [Copyright &y& Elsevier]

The subsurface variability of potential temperature and salinity south of Australia along 130°°E is studied over a 25-yr period (1980--2004). The study is done with fields provided by a global eddy-permitting model of the DRAKKAR project forced by atmospheric reanalysis. The analysis performed by C. Sun and D. R. Watts with in situ hydrographic data is repeated. Sun and Watts have investigated the EOF modes in streamfunction space along the World Ocean Circulation Experiment (WOCE) SR3 section. In particular, they found that an EOF mode, which they called the ''pulsation mode,'' strongly dominates subsurface thermohaline variations. Here, it is found that, in the model, an EOF mode with spatial structure similar to the Sun and Watts pulsation mode dominates subsurface thermohaline variations in streamfunction space. The mode displays a maximum of variability at the Subantarctic Front (SAF) between Subantarctic Mode Water (SAMW) and Antarctic Intermediate Water (AAIW). The associated time series exhibits an intermittent interseasonal frequency (3--6 months), especially during three periods (1983--84, 1990, and 1994--96). Some energy is also found with a 4-yr period. Further analyses reveal that the pulsation mode can also be observed in physical space. The pulsation mode is found to be related to movements of the SAF constrained by the bathymetry of the Southeast Indian Ridge. The pulsation mode displays many similarities with cold-core eddy events rather than being related to variations of the westerly wind stress, as previously proposed. The impact of those events on SAMW properties remains unclear. [ABSTRACT FROM AUTHOR]

The authors evaluate the response of the Southern Ocean to the variability and multidecadal trend of the southern annular mode (SAM) from 1972 to 2001 in a global eddy-permitting model of the DRAKKAR project. The transport of the Antarctic Circumpolar Current (ACC) is correlated with the SAM at interannual time scales but exhibits a drift because of the thermodynamic adjustment of the model (the ACC transport decreases because of a low renewal rate of dense waters around Antarctica). The interannual variability of the eddy kinetic energy (EKE) and the ACC transport are uncorrelated, but the EKE decreases like the ACC transport over the three decades, even though meridional eddy fluxes of heat and buoyancy remain stable. The contribution of oceanic eddies to meridional transports is an important issue because a growth of the poleward eddy transport could, in theory, oppose the increase of the mean overturning circulation forced by the SAM. In the authors’ model, the total meridional circulation at 50°S is well correlated with the SAM index (and the Ekman transport) at interannual time scales, and both increase over three decades between 1972 and 2001. However, given the long-term drift, no SAM-linked trend in the eddy contribution to the meridional overturning circulation is detectable. The increase of the meridional overturning is due to the time-mean component and is compensated by an increased buoyancy gain at the surface. The authors emphasize that the meridional circulation does not vary in a simple relationship with the zonal circulation. The model solution points out that the zonal circulation and the eddy kinetic energy are governed by different mechanisms according to the time scale considered (interannual or decadal). [ABSTRACT FROM AUTHOR]

This paper is focused on the spontaneous transient adjustment of a buoyant lens of water with uniform density, initially at rest in the vicinity of the equator. For parameters typical of the western Pacific warm pool, the adjustment is shown to generate finite-amplitude wave motions with period ∼8 days, which are not covered by the standard theory of linear equatorial waves. This mechanism may be at the origin of inertial motions at the early stages of ENSO events in the western Pacific Ocean. The lens adjustment is studied within the 11/2-layer reduced-gravity approximation on the equatorial β plane, using the high-resolution finite-volume numerical methods that are specially designed to handle outcropping isopycnals. Under the reduced-gravity approximation, a buoyant region of light water with outcropping boundaries in the vicinity of the equator is described by two parameters: the meridional-to-zonal scale aspect ratio δ and the ratio γ of the Coriolis force to the pressure force on its meridional boundary. For realistic parameters (δ ∼ 10-1; γ ∼ 1), the lens, initially at rest, spreads eastward in accord with nonrotating gravity current dynamics, whereas its westward extrusion is arrested so that the western edge splits into two anticyclonic vortices. Meanwhile finite-amplitude westward-propagating inertial wave motions develop at the interface between the spreading current and the ambient fluid. The inertial wave structure is shown to be consistent with the structure of stable wave modes predicted by linear analysis of small amplitude perturbations superimposed on a zonally symmetric equatorial current with outcropping isopycnals. A Wentzel–Kramers–Brillouin–Jeffreys ray-tracing analysis indicates that the inertial wave is emitted during the early stage of the gravity current evolution and then dispersed on the spreading current. [ABSTRACT FROM AUTHOR]

A clear-cut signature of a wave-breaking event is irreversible modification of the mean flow. In this paper, we provide examples of different breaking mechanisms and show that breaking scenario of equatorial waves in the β-plane shallow water model is determined by the degree of balance between the zonal component of the Coriolis force and the pressure gradient. Our analysis is based on a specially designed numerical method which guarantees two essential conditions to simulate nonlinear equatorial waves: (i) the scheme converges toward weak solutions including shocks and (ii) preserves the steadiness of balanced stationary solutions. This allows for accurate diagnostics of Lagrangian invariants of motion such as passive tracer density or potential vorticity. For unbalanced waves, the lack of balance leads to shock formation in finite time. In shock fronts, the variation of the dissipation rate induces a nonadvective potential vorticity flux and violates the local potential vorticity conservation valid for smooth solutions. This dissipative breaking mechanism is generic for unbalanced waves and is associated with enhanced mixing. For long, balanced (Rossby) waves, breaking consists in appearance of recirculation regions. It results in the formation of propagating patterns, the equatorial modons, which trap fluid particles. Such breaking occurs during the propagation of Rossby wave packets with positive geopotential anomaly and is strengthened by decreasing fluid depth. The modons are robust and collide quasielastically with Kelvin waves. [ABSTRACT FROM AUTHOR]

An important characteristic of geophysically turbulent flows is the transfer of energy between scales. Balanced flows pass energy from smaller to larger scales as part of the well‐known upscale cascade, while submesoscale and smaller scale flows can transfer energy eventually to smaller, dissipative scales. Much effort has been put into quantifying these transfers, but a complicating factor in realistic settings is that the underlying flows are often strongly spatially heterogeneous and anisotropic. Furthermore, the flows may be embedded in irregularly shaped domains that can be multiply connected. As a result, straightforward approaches like computing Fourier spatial spectra of nonlinear terms suffer from a number of conceptual issues. In this paper, we develop a method to compute cross‐scale energy transfers in general settings, allowing for arbitrary flow structure, anisotropy, and inhomogeneity. We employ Green's function approach to the kinetic energy equation to relate kinetic energy at a point to its Lagrangian history. A spatial filtering of the resulting equation naturally decomposes kinetic energy into length‐scale‐dependent contributions and describes how the transfer of energy between those scalestakes place. The method is applied to a doubly periodic simulation of vortex merger, resulting in the demonstration of the expected upscale energy cascade. Somewhat novel results are that the energy transfers are dominated by pressure work, rather than kinetic energy exchange, and dissipation is a noticeable influence on the larger scale energy budgets. We also describe, but do not employ here, a technique for developing filters to use in complex domains. Key Points: A method for computing cross‐scale energy transfers for general settings is developedPotential to kinetic energy cross‐scale exchanges are dominantDissipation is surprisingly strong as an effect on large scales [ABSTRACT FROM AUTHOR]

Accurate predictions of scalar fields advected by a turbulent flow is needed for various industrial and geophysical applications. In the framework of large-eddy simulation (LES), a subgrid-scale (SGS) model for the subgrid-scale scalar flux has to be used. The gradient model (GM), which is derived from a Taylor series expansions of the filtering operation, is a well-known approach to model SGS scalar fluxes. This model is known to lead to high correlation level with the SGS scalar flux. However, this type of model cannot be used in practical LES because it does not lead to enough global scalar variance transfer from the large to the small scales. In this work, a regularization of the GM is proposed based on a physical interpretation of this model. The impact of the resolved velocity field on the resolved scalar gradient is decomposed into compressional, stretching, and rotational effects. It is shown that rotational effect is not associated with transfers of variance across scales. Conversely, the compressional effect is shown to lead to forward transfer, whereas the stretching effect leads to back-scatter of scalar variance. The proposed regularization is to neglect the stretching effect in the model formulation. The accuracy of this regularized gradient model (RGM) is tested in comparison with direct numerical simulations and compared with other classic SGS models. The accuracy of the RGM is evaluated in term of structural and functional performances, i.e., the model ability to locally approximate the SGS unknown term and to reproduce its global effect on tracer variance, respectively. It is found that the RGM associated with a dynamic procedure exhibits good performances in comparison with the standard dynamic eddy diffusivity model and the standard gradient model. In particular, the dynamic regularized gradient model (DRGM) provides a better prediction of scalar variance transfers than the standard gradient model. The DRGM is then evaluated in a series of large-eddy simulations. This shows a substantial improvement for various scalar statistics predictions. [ABSTRACT FROM AUTHOR]

An established iceberg module, ICB, is used interactively with the Nucleus for European Modelling of the Ocean (NEMO) ocean model in a new implementation, NEMO-ICB (v1.0). A 30-year hindcast (1976-2005) simulation with an eddy-permitting (0.25°) global configuration of NEMO-ICB is undertaken to evaluate the influence of icebergs on sea ice, hydrography, mixed layer depths (MLDs), and ocean currents, through comparison with a control simulation in which the equivalent iceberg mass flux is applied as coastal runoff, a common forcing in ocean models. In the Southern Hemisphere (SH), drift and melting of icebergs are in balance after around 5 years, whereas the equilibration timescale for the Northern Hemisphere (NH) is 15-20 years. Iceberg drift patterns, and Southern Ocean iceberg mass, compare favourably with available observations. Freshwater forcing due to iceberg melting is most pronounced very locally, in the coastal zone around much of Antarctica, where it often exceeds in magnitude and opposes the negative freshwater fluxes associated with sea ice freezing. However, at most locations in the polar Southern Ocean, the annual-mean freshwater flux due to icebergs, if present, is typically an order of magnitude smaller than the contribution of sea ice melting and precipitation. A notable exception is the southwest Atlantic sector of the Southern Ocean, where iceberg melting reaches around 50% of net precipitation over a large area. Including icebergs in place of coastal runoff, sea ice concentration and thickness are notably decreased at most locations around Antarctica, by up to ∼20% in the eastern Weddell Sea, with more limited increases, of up to ∼10% in the Bellingshausen Sea. Antarctic sea ice mass decreases by 2.9 %, overall. As a consequence of changes in net freshwater forcing and sea ice, salinity and temperature distributions are also substantially altered. Surface salinity increases by ∼0.1 psu around much of Antarctica, due to suppressed coastal runoff, with extensive freshening at depth, extending to the greatest depths in the polar Southern Ocean where discernible effects on both salinity and temperature reach 2500m in the Weddell Sea by the last pentad of the simulation. Substantial physical and dynamical responses to icebergs, throughout the global ocean, are explained by rapid propagation of density anomalies from high-to-low latitudes. Complementary to the baseline model used here, three prototype modifications to NEMO-ICB are also introduced and discussed. [ABSTRACT FROM AUTHOR]