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Evguéni Kazantsev, Joël Sommeria, and Jacques Verron

Abstract

The feasibility of using a subgrid-scale eddy parameterization, based on statistical mechanics of potential vorticity, is investigated. A specific implementation is derived for the somewhat classic barotropic vorticity equation in the case of a fully eddy-active, wind-driven, midlatitude ocean on the β plane.

The subgrid-scale eddy fluxes are determined by a principle of maximum entropy production so that these fluxes always efficiently drive the system toward statistical equilibrium. In the absence of forcing and friction, the system then reaches this equilibrium, while conserving all the constants of motion of the inviscid barotropic equations. It is shown that this equilibrium is close to a Fofonoff flow, like that obtained with truncated spectral models, although the statistical approach is different.

The subgrid-scale model is then validated in a more realistic case, with wind forcing and friction. The results of this model at a coarse resolution are compared with reference simulations at a resolution four times higher. The mean flow is correctly recovered, as well as the variability properties, such as the kinetic energy fields and the eddy flux of potential vorticity. Although only the barotropic dynamics of a homogeneous wind-driven ocean flow has been considered at this stage, there is no formal obstacle for a generalization to multilayer baroclinic flows.

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Jacques Verron, Linda Cloutier, and Philippe Gaspar

Abstract

This article looks at the problem of optimizing spatiotemporal sampling of the ocean circulation using single- or twin-satellite missions. A review of the basic orbital constraints is first presented and this, together with some elementary sampling considerations, provides a solid foundation for choosing satellite orbital parameters. A modeling and assimilation approach enables even further progress to be made by simulating the dynamic features of the ocean fields that are to be measured; it also enables the process of integrating data into models to be simulated.

Several scenarios for two altimetric satellites flying simultaneously are evaluated with respect to their ability to monitor oceanic circulation as simulated with a numerical model. The twin-experiment approach is used: simulated data are assimilated into the numerical model, while a benchmark experiment provides the necessary dataset for validation and intercomparison. The model is quasigeostrophic and multilayered. The ocean model domain is at basin scale, centered on the midlatitudes. Model resolution (20 km) is fine enough to exhibit the intense mesoscale nonlinear variability typical of the midlatitudes. The assimilation technique used is sequential nudging of sea surface height applied to along-track data.

Dual scenarios are built consisting of all possible combinations of satellites having 3-, 10- (Topex-Poseidon), 17- (Geosat) and 30-day orbital repeat periods. In the specific context of our modeling and assimilation approach, improved scenarios with respect to Topex-Poseidon, and a fortiori Geosat, appear to be those that favor improving temporal rather than spatial resolution. This unexpected result would, for example, suggest that a Topex-Poseidon- or Geosat-type satellite is satisfactory with regard to the spatial sampling of oceanic mesoscales. But any further gain would be acquired mostly by increasing temporal sampling, for example, by flying another Topex-Poseidon- or Geosat-type satellite offset in time by a typical half-period. Investigations of ground-track inclination effects are also presented.

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Emmanuel Cosme, Jacques Verron, Pierre Brasseur, Jacques Blum, and Didier Auroux

Abstract

Smoothers are increasingly used in geophysics. Several linear Gaussian algorithms exist, and the general picture may appear somewhat confusing. This paper attempts to stand back a little, in order to clarify this picture by providing a concise overview of what the different smoothers really solve, and how. The authors begin addressing this issue from a Bayesian viewpoint. The filtering problem consists in finding the probability of a system state at a given time, conditioned to some past and present observations (if the present observations are not included, it is a forecast problem). This formulation is unique: any different formulation is a smoothing problem. The two main formulations of smoothing are tackled here: the joint estimation problem (fixed lag or fixed interval), where the probability of a series of system states conditioned to observations is to be found, and the marginal estimation problem, which deals with the probability of only one system state, conditioned to past, present, and future observations. The various strategies to solve these problems in the Bayesian framework are introduced, along with their deriving linear Gaussian, Kalman filter-based algorithms. Their ensemble formulations are also presented. This results in a classification and a possible comparison of the most common smoothers used in geophysics. It should provide a good basis to help the reader find the most appropriate algorithm for his/her own smoothing problem.

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Jacques Verron, Christian Le Provost, and William R. Holland

Abstract

High resolution ocean general circulation model experiments were carried out to investigate the effects of a midocean ridge on the eddy field and the mean circulation on the basin scale. A quasigeostrphic two-layer model was used. Long term statistics were computed for a detailed comparison with the flat bottom case. An eddy-driven anticyclonic gyre, locked over the topography, appears as a new feature of the deep circulation pattern. The eddy energy radiation in both layers is strongly constrained by the topography. Insofar as surface currents are concerned, the ridge acts, to a limited extent, as a new western boundary for the eastern basin.

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Monika Krysta, Eric Blayo, Emmanuel Cosme, and Jacques Verron

Abstract

In the standard four-dimensional variational data assimilation (4D-Var) algorithm the background error covariance matrix remains static over time. It may therefore be unable to correctly take into account the information accumulated by a system into which data are gradually being assimilated.

A possible method for remedying this flaw is presented and tested in this paper. A hybrid variational-smoothing algorithm is based on a reduced-rank incremental 4D-Var. Its consistent coupling to a singular evolutive extended Kalman (SEEK) smoother ensures the evolution of the matrix. In the analysis step, a low-dimensional error covariance matrix is updated so as to take into account the increased confidence level in the state vector it describes, once the observations have been introduced into the system. In the forecast step, the basis spanning the corresponding control subspace is propagated via the tangent linear model.

The hybrid method is implemented and tested in twin experiments employing a shallow-water model. The background error covariance matrix is initialized using an EOF decomposition of a sample of model states. The quality of the analyses and the information content in the bases spanning control subspaces are also assessed. Several numerical experiments are conducted that differ with regard to the initialization of the matrix. The feasibility of the method is illustrated. Since improvement due to the hybrid method is not universal, configurations that benefit from employing it instead of the standard 4D-Var are described and an explanation of the possible reasons for this is proposed.

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Angélique Melet, Jacques Verron, Lionel Gourdeau, and Ariane Koch-Larrouy

Abstract

The Solomon Sea is a key region of the southwest Pacific Ocean, connecting the thermocline subtropics to the equator via western boundary currents (WBCs). Modifications to water masses are thought to occur in this region because of the significant mixing induced by internal tides, eddies, and the WBCs. Despite their potential influence on the equatorial Pacific thermocline temperature and salinity and their related impact on the low-frequency modulation of El Niño–Southern Oscillation, modifications to water masses in the Solomon Sea have never been analyzed to our knowledge. A high-resolution model incorporating a tidal mixing parameterization was implemented to depict and analyze water mass modifications and the Solomon Sea pathways to the equator in a Lagrangian quantitative framework. The main routes from the Solomon Sea to the equatorial Pacific occur through the Vitiaz and Solomon straits, in the thermocline and intermediate layers, and mainly originate from the Solomon Sea south inflow and from the Solomon Strait itself. Water mass modifications in the model are characterized by a reduction of the vertical temperature and salinity gradients over the water column: the high salinity of upper thermocline water [Subtropical Mode Water (STMW)] is eroded and exported toward surface and deeper layers, whereas a downward heat transfer occurs over the water column. Consequently, the thermocline water temperature is cooled by 0.15°–0.3°C from the Solomon Sea inflows to the equatorward outflows. This temperature modification could weaken the STMW anomalies advected by the subtropical cell and thereby diminish the potential influence of these anomalies on the tropical climate. The Solomon Sea water mass modifications can be partially explained (≈60%) by strong diapycnal mixing in the Solomon Sea. As for STMW, about a third of this mixing is due to tidal mixing.

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Thierry Penduff, Bernard Barnier, Marie-Aurélie Kerbiriou, and Jacques Verron

Abstract

The characteristics of the mesoscale turbulence simulated at a resolution of ⅓° by a sigma-coordinate model (SPEM) and a geopotential-coordinate model (OPA) of the South Atlantic differ significantly. These two types of models differ with respect to not only their numerical formulation, but also their topography (smoothed in SPEM, as in every sigma-coordinate application). In this paper, the authors examine how these topographic differences result in eddy flows that are different in the two models. When the topography of the Agulhas region is smoothed locally in OPA, as is done routinely in SPEM, the production mechanism of the Agulhas rings, their characteristics, and their subsequent drift in the subtropical gyre, are found to converge toward those in SPEM. Furthermore, the vertical distribution of eddy kinetic energy (EKE) everywhere in the basin interior becomes similar in SPEM and OPA and, according to some current meter data, becomes more realistic when mesoscale topographic roughness is removed from the OPA bathymetry (as in SPEM). As expected from previous process studies, this treatment also makes the sensitivity of the Agulhas rings to the Walvis Ridge become similar in SPEM and OPA. These findings demonstrate that many properties of the eddies produced by sigma- and geopotential-coordinate models are, to a significant extent, due to the use of different topographies, and are not intrinsic to the use of different vertical coordinates. Other dynamical differences, such as the separation of western boundary currents from the shelf or the interaction of the flow with the Zapiola Ridge, are attributed to intrinsic differences between both models. More generally, it is believed that, in the absence of a correct parameterization of current–topography interactions, a certain amount of topographic smoothing may have a beneficial impact on geopotential coordinate model solutions.

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Don L. Boyer, Gabriel Chabert d'Hieres, Henri Didelle, Jacques Verron, Rui-Rong Chen, and Lijun Tao

Abstract

The problem of the oscillatory motion of a homogeneous, rotating fluid in the vicinity of an isolated topographic feature is investigated in the laboratory and numerically. The laboratory experiments are conducted by fixing a cosine-squared body of revolution near the outer boundary of a circular tank rotating about a vertical axis with an angular velocity Ω(t)=Ω01sinωt, where Ω0 is the mean background rotation and Ω0 and ω are the magnitude and frequency of an oscillatory component. Experiments with an oscillatory flow show clearly that a mean anticyclonic vortex is formed in the vicinity of the topographic feature. Surface floats are used to determine typical particle paths for various flow conditions and these are shown to vary markedly with the Rossby and temporal Rossby numbers of the background flow. Eulerian velocity profiles along and normal to the streamwise axis are used to quantify the anticyclonic vortex. A scaling analysis is advanced to show how the strength and distribution of the anticyclonic current varies with the various system parameters. The laboratory findings are in good agreement with the scaling analysis and with the theoretical model of Wright and Loder.

A nonlinear numerical model, using the quasi-geostrophic potential vorticity equation, is considered; the results correlate well with the scaling analysis and the laboratory experiments. The laboratory and numerical experiments are used to estimate the magnitude of the mean anticyclonic motion that might be expected in the vicinity of Fieberling Guyot. Future laboratory and numerical experiments will consider the additional feature of background stratification.

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Angélique Melet, Lionel Gourdeau, William S. Kessler, Jacques Verron, and Jean-Marc Molines

Abstract

In the southwest Pacific, thermocline waters connecting the tropics to the equator via western boundary currents (WBCs) transit through the Solomon Sea. Despite its importance in feeding the Equatorial Undercurrent (EUC) and its related potential influence on the low-frequency modulation of ENSO, the circulation inside the Solomon Sea is poorly documented. A model has been implemented to analyze the mean and the seasonal variability of the Solomon Sea thermocline circulation. The circulation involves an inflow from the open southern Solomon Sea, which is distributed via WBCs between the three north exiting straits of the semiclosed Solomon Sea. The system of WBCs is found to be complex. Its main feature, the New Guinea Coastal Undercurrent, splits in two branches: one flowing through Vitiaz Strait and the other one, the New Britain Coastal Undercurrent (NBCU), exiting at Solomon Strait. East of the Solomon Sea, the encounter of the South Equatorial Current (SEC) with the Solomon Islands forms a previously unknown current, which the authors call the Solomon Islands Coastal Undercurrent (SICU). The NBCU, SEC, and SICU participate in the feeding of the New Ireland Coastal Undercurrent (NICU), which retroflects to the Equatorial Undercurrent, providing the most direct western boundary EUC connection, which is particularly active in June–August. The Solomon Sea WBC seasonal variability results from the combination of equatorial dynamics, remotely forced Rossby waves north of 10°S, and the spinup and spindown of the subtropical gyre as a response of Rossby waves forced south of 10°S.

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Jacques Verron, Dominique Renouard, Gabriel Chabert D'Hieres, Thong Nguyen, Henri Didelle, and Don L. Boyer

Abstract

Alongshore oscillatory flows over an elongated topographic feature next to a vertical wall for a homogeneous, rotating fluid were investigated by means of numerical and laboratory experiments. The physical experiments were conducted in the Grenoble 13-m diameter rotating tank, in which an elongated obstacle of limited longitudinal extent was placed along the vertical sidewall. The background oscillating motion was obtained by periodically varying the platform angular velocity. Fluid motions were visualized and quantified by direct velocity measurements and particle tracking. The numerical model employed was a tridimensional model developed by Haidvogel et al. It consists of the traditional primitive equations, that is, the Navier-Stokes equations for a rotating fluid with the addition of the hydrostatic, Boussinesq, and incompressibility approximations. (The experiments described here employ the homogeneous version.) The numerical formulation uses finite differences in the horizontal and spectral representation in the vertical dimensions.

Both the laboratory and numerical experiments show that in the range of dimensionless parameters considered, two distinct flow regimes, based on general properties of the rectified flow patterns observed, can be defined. It is further shown that the flow regime designation depends principally on the magnitude of the temporal Rossby number, Rot, defined as the ratio of the flow oscillation to the background rotation frequency. Good qualitative and quantitative agreement is found between the laboratory experiments and the numerical model for such observables as the spatial distribution of rectified flow patterns. Several other flow observables are defined and their relation with the system parameters delineated.

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