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Fabien Roquet

Abstract

The concept of available potential energy is supposed to indicate which part of the potential energy is available to transform into kinetic energy. Yet it is impossible to obtain a unique definition of available potential energy for the real ocean because of nonlinearities of the equation of state, rendering its usefulness largely hypothetical. In this paper, the conservation of energy is first reformulated in terms of horizontal anomalies of density and pressure for a simplified ocean model using the Boussinesq and hydrostatic approximations. This framework introduces the concept of “dynamical potential energy,” defined as the horizontal anomaly of potential energy, to replace available potential energy. Modified conservation equations are derived that make it much simpler to identify oceanic power input by buoyancy and mechanical forces. Closed budgets of energy are presented for idealized circulations obtained with a general circulation model, comparing spatial patterns of power inputs generated by wind and thermal forcings. Finally, a generalization of the framework to compressible fluids is presented, opening the way to applications in atmosphere energetics.

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Friederike Pollmann, Fabien Roquet, and Gurvan Madec

Abstract

Large-scale overturning cells in the ocean typically combine an essentially horizontal surface branch and an interior branch below, where the circulation spans both horizontal and vertical scales. The aim of this study is to analyze the impact of this asymmetry between the two branches by “folding” a one-dimensional thermohaline loop, such that its lower part remains vertical while its upper part is folded down into the horizontal plane. It is found that both the transitory response and the distribution of thermohaline properties are modified significantly when the loop is folded. In some cases, velocity oscillations are induced during the spinup that were not seen in the unfolded case. This is because a circular loop allows for compensations between the density torques produced above and below the heat forcing level, while such compensations are not possible in the folded loop because of the horizontal direction of the surface circulation. Furthermore, the dynamical effects associated with nonlinearities of the equation of state are significantly altered by the folding. Cabbeling tends to decelerate the flow in the folded loop, instead of accelerating it as in the circular case, and can also act to dampen velocity oscillations. Thermobaricity also alters the loop circulation, although comparatively less.

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Fabien Roquet, Carl Wunsch, and Gurvan Madec

Abstract

Pathways of wind-power input into the ocean general circulation are analyzed using Ekman theory. Direct rates of wind work can be calculated through the wind stress acting on the surface geostrophic flow. However, because that energy is transported laterally in the Ekman layer, the injection into the geostrophic interior is actually controlled by Ekman pumping, with a pattern determined by the wind curl rather than the wind itself. Regions of power injection into the geostrophic interior are thus generally shifted poleward compared to regions of direct wind-power input, most notably in the Southern Ocean, where on average energy enters the interior 10° south of the Antarctic Circumpolar Current core. An interpretation of the wind-power input to the interior is proposed, expressed as a downward flux of pressure work. This energy flux is a measure of the work done by the Ekman pumping against the surface elevation pressure, helping to maintain the observed anomaly of sea surface height relative to the global-mean sea level.

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Etienne Pauthenet, Fabien Roquet, Gurvan Madec, and David Nerini

Abstract

The thermohaline structure of the Southern Ocean is deeply influenced by the presence of the Antarctic Circumpolar Current (ACC), where water masses of the World Ocean are advected, transformed, and redistributed to the other basins. It remains a challenge to describe and visualize the complex 3D pattern of this circulation and its associated tracer distribution. Here, a simple framework is presented to analyze the Southern Ocean thermohaline structure. A functional principal component analysis (PCA) is applied to temperature θ and salinity S profiles to determine the main spatial patterns of their variations. Using the Southern Ocean State Estimate (SOSE), this study determines the vertical modes describing the Southern Ocean thermohaline structure between 5 and 2000 m. The first two modes explain 92% of the combined θS variance, thus providing a surprisingly good approximation of the thermohaline properties in the Southern Ocean. The first mode (72% of total variance) accurately describes the north–south property gradients. The second mode (20%) mostly describes salinity at 500 m in the region of Antarctic Intermediate Water formation. These two modes present circumpolar patterns that can be closely related with standard frontal definitions. By projecting any given hydrographic profile onto the SOSE-based modes, it is possible to determine its position relative to the fronts. The projection is successfully applied on the hydrographic profiles of the WOCE SR3 section. The Southern Ocean thermohaline decomposition provides an objective way to define water mass boundaries and their spatial variability and has useful application for comparing model output with observations.

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Saeed Falahat, Jonas Nycander, Fabien Roquet, and Moundheur Zarroug

Abstract

A direct calculation of the tidal generation of internal waves over the global ocean is presented. The calculation is based on a semianalytical model, assuming that the internal tide characteristic slope exceeds the bathymetric slope (subcritical slope) and the bathymetric height is small relative to the vertical scale of the wave, as well as that the horizontal tidal excursion is smaller than the horizontal topographic scale. The calculation is performed for the M2 tidal constituent. In contrast to previous similar computations, the internal tide is projected onto vertical eigenmodes, which gives two advantages. First, the vertical density profile and the finite ocean depth are taken into account in a fully consistent way, in contrast to earlier work based on the WKB approximation. Nevertheless, the WKB-based total global conversion follows closely that obtained using the eigenmode decomposition in each of the latitudinal and vertical distributions. Second, the information about the distribution of the conversion energy over different vertical modes is valuable, since the lowest modes can propagate over long distances, while high modes are more likely to dissipate locally, near the generation site. It is found that the difference between the vertical distributions of the tidal conversion into the vertical modes is smaller for the case of very deep ocean than the shallow-ocean depth. The results of the present work pave the way for future work on the vertical and horizontal distribution of the mixing caused by internal tides.

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Fabien Roquet, Gurvan Madec, Laurent Brodeau, and J. Nycander

Abstract

There is a growing realization that the nonlinear nature of the equation of state has a deep impact on the global ocean circulation; however, the understanding of the global effects of these nonlinearities remains elusive. This is partly because of the complicated formulation of the seawater equation of state making it difficult to handle in theoretical studies. In this paper, a hierarchy of polynomial equations of state of increasing complexity, optimal in a least squares sense, is presented. These different simplified equations of state are then used to simulate the ocean circulation in a global 2°-resolution configuration. Comparisons between simulated ocean circulations confirm that nonlinear effects are of major importance, in particular influencing the circulation through determination of the static stability below the mixed layer, thus controlling rates of exchange between the atmosphere and the ocean interior. It is found that a simple polynomial equation of state, with a quadratic term in temperature (for cabbeling), a temperature–pressure product term (for thermobaricity), and a linear term in salinity, that is, only four tuning parameters, is enough to simulate a reasonably realistic global circulation. The best simulation is obtained when the simplified equation of state is forced to have an accurate thermal expansion coefficient near the freezing point, highlighting the importance of polar regions for the global stratification. It is argued that this simplified equation of state will be of great value for theoretical studies and pedagogical purposes.

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Etienne Pauthenet, Fabien Roquet, Gurvan Madec, Jean-Baptiste Sallée, and David Nerini

Abstract

The first 2000 m of the global thermohaline structure of the ocean are statistically decomposed into vertical thermohaline modes, using a multivariate functional principal component analysis (FPCA). This method is applied on the Monthly Isopycnal and Mixed-Layer Ocean Climatology (MIMOC). The first three modes account for 92% of the joint temperature and salinity (TS) variance, which yields a surprisingly good reduction of dimensionality. The first mode (69% of the variance) is related to the thermocline depth and delineates the subtropical gyres. The second mode (18%) is mostly driven by salinity and mainly displays the asymmetry between the North Pacific and Atlantic basins and the salty circumpolar deep waters in the Southern Ocean. The third mode (5%) identifies the low- and high-salinity intermediate waters, covarying with the freshwater inputs of the upper ocean. The representation of the ocean in the space defined by the first three modes offers a simple visualization of the global thermohaline structure that strikingly emphasizes the role of the Southern Ocean in linking and distributing water masses to the other basins. The vertical thermohaline modes offer a convenient framework for model and observation data comparison. This is illustrated by projecting the repeated Pacific section P16 together with profiles from the Array for Real-Time Geostrophic Oceanography (ARGO) global array of profiling floats on the modes defined with the climatology MIMOC. These thermohaline modes have a potential for water mass identification and robust analysis of heat and salt content.

Open access
Fabien Roquet, Jean-Benoit Charrassin, Stephane Marchand, Lars Boehme, Mike Fedak, Gilles Reverdin, and Christophe Guinet

Abstract

A delayed-mode calibration procedure is presented to improve the quality of hydrographic data from CTD–Satellite Relay Data Loggers (CTD–SRDL) deployed on elephant seals. This procedure is applied on a dataset obtained with 10 CTD–SRDLs deployed at Kerguelen Islands in 2007. A comparison of CTD–SRDLs with a ship-based CTD system is first presented. A pressure-effect correction, linear with pressure, is deduced for both temperature and salinity measurements. An external field effect on the conductivity sensor is also detected, inducing an additional salinity offset. The salinity offset cannot be estimated directly from the ship-based CTD comparisons, because the attachment of the CTD–SRDL on the seal head modifies the magnitude of the external field effect. Two methods are proposed for estimating a posteriori the salinity offset. The first method uses the stable salinity maximum characterizing the Lower Circumpolar Deep Water (LCDW), sampled by seals foraging south of the Southern Antarctic Circumpolar Current Front. Where this approach is not possible, a statistical method of cross-comparison of CTD–SRDLs surface salinity measurements is used over the sluggish Northern Kerguelen Plateau. Accuracies are respectively estimated as ±0.02°C for temperature and ±0.1 for derived salinity without corrections. The delayed-mode calibration significantly improves the CTD–SRDL data, improving accuracies to ±0.01°C and ±0.03, respectively. A better salinity accuracy of ±0.02 is achieved when the LCDW method can be used. For CTD–SRDLs where ship-based CTD comparisons are not available, the expected accuracy would be ±0.02°C for temperature and ±0.04 for the derived salinity.

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Lia Siegelman, Fabien Roquet, Vigan Mensah, Pascal Rivière, Etienne Pauthenet, Baptiste Picard, and Christophe Guinet

Abstract

Most available CTD Satellite Relay Data Logger (CTD-SRDL) profiles are heavily compressed before satellite transmission. High-resolution profiles recorded at the sampling frequency of 0.5 Hz are, however, available upon physical retrieval of the logger. Between 2014 and 2018, several loggers deployed on elephant seals in the Southern Ocean have been set in continuous recording mode, capturing both the ascent and descent for over 60 profiles per day during several months, opening new horizons for the physical oceanography community. Taking advantage of a new dataset made of seven such loggers, a postprocessing procedure is proposed and validated to improve the quality of all CTD-SRDL data: that is, both high-resolution profiles and compressed low-resolution ones. First, temperature and conductivity are corrected for a thermal mass effect. Then salinity spiking and density inversion are removed by adjusting salinity while leaving temperature unchanged. This method, applied here to more than 50 000 profiles, yields significant and systematic improvements in both temperature and salinity, particularly in regions of rapid temperature variation. The continuous high-resolution dataset is then used to provide updated accuracy estimates of CTD-SRDL data. For high-resolution data, accuracies are estimated to be of ±0.02°C for temperature and ±0.03 g kg−1 for salinity. For low-resolution data, transmitted data points have similar accuracies; however, reconstructed temperature profiles have a reduced accuracy associated with the vertical interpolation of ±0.04°C and a nearly unchanged salinity accuracy of ±0.03 g kg−1.

Open access
Vigan Mensah, Fabien Roquet, Lia Siegelman-Charbit, Baptiste Picard, Etienne Pauthenet, and Christophe Guinet

Abstract

The effect of thermal mass on the salinity estimate from conductivity–temperature–depth (CTD) tags sensor mounted on marine mammals is documented, and a correction scheme is proposed to mitigate its impact. The algorithm developed here allows for a direct correction of the salinity data, rather than a correction of the sample’s conductivity and temperature. The amplitude of the thermal mass–induced error on salinity and its correction are evaluated via comparison between data from CTD tags and from Sea-Bird Scientific CTD used as a reference. Thermal mass error on salinity appears to be generally O(10−2) g kg−1, it may reach O(10−1) g kg−1, and it tends to increase together with the magnitude of the cumulated temperature gradient (T HP) within the water column. The correction we propose yields an error decrease of up to ~60% if correction coefficients specific to a certain tag or environment are calculated, and up to 50% if a default value for the coefficients is provided. The correction with the default coefficients was also evaluated using over 22 000 in situ dive data from five tags deployed in the Southern Ocean and is found to yield significant and systematic improvements on the salinity data, including for profiles whose T HP was weak and the error small. The correction proposed here yields substantial improvements in the density estimates, although a thermal mass–induced error in temperature measurements exists for very large T HP and has yet to be corrected.

Open access