2016 
Akuetevi, C. Q. C., Barnier, B., Verron, J., Molines, J. M., & Lecointre, A. (2016). Interactions between the Somali Current eddies during the summer monsoon: insights from a numerical study. Ocean Science, 12(1), 185–205.
Abstract: Three hindcast simulations of the global ocean circulation differing by resolution (1/4 or 1/12 degrees) or parametrization or atmospheric forcing are used to describe the interactions between the large anticyclonic eddies generated by the Somali Current system during the Southwest Monsoon. The present investigation of the Somalian coherent eddy structures allows us to identify the origin and the subsequent development of the cyclones flanked upon the Great Whirl (GW) previously identified by Beal and Donohue (2013) in satellite observations and to establish that similar cyclones are also flanked upon the Southern Gyre (SG). These cyclones are identified as potential actors in mixing water masses within the large eddies and offshore the coast of Somalia. All three simulations bring to light that during the period when the Southwest Monsoon is well established, the SG moves northward along the Somali coast and encounters the GW. The interaction between the SG and the GW is a collision without merging, in a way that has not been described in observations up to now. During the collision the GW is pushed to the east of Socotra Island, sheds several smaller patches of anticyclonic vorticity, and often reforms into the Socotra Eddy, thus proposing a formation mechanism for that eddy. During this process the GW gives up its place to the SG. This process is robust throughout the three simulations.


Carton, X., Ciani, D., Verron, J., Reinaud, J., & Sokolovskiy, M. (2016). Vortex merger in surface quasigeostrophy. Geophysical And Astrophysical Fluid Dynamics, 110(1), 1–22.
Abstract: The merger of two identical surface temperature vortices is studied in the surface quasigeostrophic model. The motivation for this study is the observation of the merger of submesoscale vortices in the ocean. Firstly, the interaction between two point vortices, in the absence or in the presence of an external deformation field, is investigated. The rotation rate of the vortices, their stationary positions and the stability of these positions are determined. Then, a numerical model provides the steady states of two finitearea, constanttemperature, vortices. Such states are less deformed than their counterparts in twodimensional incompressible flows. Finally, numerical simulations of the nonlinear surface quasigeostrophic equations are used to investigate the finitetime evolution of initially identical and symmetric, constant temperature vortices. The critical merger distance is obtained and the deformation of the vortices before or after merger is determined. The addition of external deformation is shown to favor or to oppose merger depending on the orientation of the vortex pair with respect to the strain axes. An explanation for this observation is proposed. Conclusions are drawn towards an application of this study to oceanic vortices.


Ciani, D., Carton, X., & Verron, J. (2016). On the merger of subsurface isolated vortices. Geophysical And Astrophysical Fluid Dynamics, 110(1), 23–49.
Abstract: Vortex merger is a phenomenon characterizing the whole class of geophysical vortices, from atmospheric storms and large oceanic eddies up to small scale turbulence. Here we focus on the merger of subsurface oceanic anticyclones in an idealized primitive equations model. This study has been motivated by past and recent observations of colliding lenslike anticyclones off of Gibraltar Strait. The critical conditions for merger (critical merger distance and time needed for merger) are determined. We will show that the predictions of classical twodimensional merger are not verified for subsurface isolated vortices. For instance, critical merger distances will be reduced because of the vortex potential vorticity (PV) structure. The postmerger characteristics of the vortex (radius, extension and PV), are also determined. Mergerrelated effects, like production of peripheral filaments and smallscale eddies are also investigated and suggest the contribution of merger in both direct and inverse energy cascades.


2015 
Brankart, J. M., Candille, G., Garnier, F., Calone, C., Melet, A., Bouttier, P. A., et al. (2015). A generic approach to explicit simulation of uncertainty in the NEMO ocean model. Geoscientific Model Development, 8(5), 1285–1297.
Abstract: In this paper, a generic implementation approach is presented, with the aim of transforming a deterministic ocean model (like NEMO) into a probabilistic model. With this approach, several kinds of stochastic parameterizations are implemented to simulate the nondeterministic effect of unresolved processes, unresolved scales and unresolved diversity. The method is illustrated with three applications, showing that uncertainties can produce a major effect in the circulation model, in the ecosystem model, and in the sea ice model. These examples show that uncertainties can produce an important effect in the simulations, strongly modifying the dynamical behaviour of these three components of ocean systems.


Ruggiero, G. A., Ourmieres, Y., Cosme, E., Blum, J., Auroux, D., & Verron, J. (2015). Data assimilation experiments using diffusive backandforth nudging for the NEMO ocean model. Nonlinear Processes In Geophysics, 22(2), 233–248.
Abstract: The diffusive backandforth nudging (DBFN) is an easytoimplement iterative data assimilation method based on the wellknown nudging method. It consists of a sequence of forward and backward model integrations, within a given time window, both of them using a feedback term to the observations. Therefore, in the DBFN, the nudging asymptotic behaviour is translated into an infinite number of iterations within a bounded time domain. In this method, the backward integration is carried out thanks to what is called backward model, which is basically the forward model with reversed time step sign. To maintain numeral stability, the diffusion terms also have their sign reversed, giving a diffusive character to the algorithm. In this article the DBFN performance to control a primitive equation ocean model is investigated. In this kind of model nonresolved scales are modelled by diffusion operators which dissipate energy that cascade from large to small scales. Thus, in this article, the DBFN approximations and their consequences for the data assimilation system setup are analysed. Our main result is that the DBFN may provide results which are comparable to those produced by a 4Dvar implementation with a much simpler implementation and a shorter CPU time for convergence. The conducted sensitivity tests show that the 4Dvar profits of long assimilation windows to propagate surface information downwards, and that for the DBFN, it is worth using short assimilation windows to reduce the impact of diffusioninduced errors. Moreover, the DBFN is less sensitive to the first guess than the 4Dvar.


Verron, J., Sengenes, P., Lambin, J., Noubel, J., Steunou, N., Guillot, A., et al. (2015). The SARAL/AltiKa Altimetry Satellite Mission. Marine Geodesy, 38, 2–21.
Abstract: The IndiaFrance SARAL/AltiKa mission is the first Kaband altimetric mission dedicated to oceanography. The mission objectives are primarily the observation of the oceanic mesoscales but also include coastal oceanography, global and regional sea level monitoring, data assimilation, and operational oceanography. Secondary objectives include ice sheet and inland waters monitoring. One year after launch, the results widely confirm the nominal expectations in terms of accuracy, data quality and data availability in general.Today's performances are compliant with specifications with an overall observed performance for the Sea Surface Height RMS of 3.4cm to be compared to a 4cm requirement. Some scientific examples are provided that illustrate some salient features of today's SARAL/AltiKa data with regard to standard altimetry: data availability, data accuracy at the mesoscales, data usefulness in costal area, over ice sheet, and for inland waters.


2014 
Djath, B., Melet, A., Verron, J., Molines, J. M., Barnier, B., Gourdeau, L., et al. (2014). A 1/36 degrees model of the Solomon Sea embedded into a global ocean model: On the setting up of an interactive open boundary nested model system. Journal Of Operational Oceanography, 7(1), 34–46.
Abstract: The implementation of a regional 1/36 degrees numerical model of a key sub region of the southwestern Pacific Ocean: the Solomon Sea is discussed.This model is twoway embedded into a 1/12 degrees resolution basinscale model, itself oneway nested in a global 1/12 degrees resolution ocean model.The three main questions discussed in this study concern (i) the bathymetry, (ii) the setting up of adequate forcing functions, especially regarding the wind stress parameterization, and (iii) the strategy used to embed and conned the model configurations together Such a system, exemplified here for the Solomon Sea, represents a prototype of embedded model systems that are considered in operational oceanography.


Djath, B., Verron, J., Melet, A., Gourdeau, L., Barnier, B., & Molines, J. M. (2014). Multiscale dynamical analysis of a highresolution numerical model simulation of the Solomon Sea circulation. Journal Of Geophysical ResearchOceans, 119(9), 6286–6304.
Abstract: A high 1/36 degrees resolution numerical model is used to study the ocean circulation in the Solomon Sea. An evaluation of the model with (the few) available observation shows that the 1/36 degrees resolution model realistically simulates the Solomon Sea circulations. The model notably reproduces the high levels of mesoscale eddy activity observed in the Solomon Sea. With regard to previous simulations at 1/12 degrees resolution, the average eddy kinetic energy levels are increased by up to approximate to 3040% in the present 1/36 degrees simulation, and the enhancement extends at depth. At the surface, the eddy kinetic energy level is maximum in MarchAprilMay and is minimum in DecemberJanuaryFebruary. The high subsurface variability is related to the variability of the western boundary current (New Guinea Coastal Undercurrent). Moreover, the emergence of submesoscales is clearly apparent in the present simulations. A spectral analysis is conducted in order to evidence and characterize the modeled submesoscale dynamics and to provide a spectral view of scales interactions. The corresponding spectral slopes show a strong consistency with the Surface QuasiGeostrophic turbulence theory.


Ganachaud, A., Cravatte, S., Melet, A., Schiller, A., Holbrook, N. J., Sloyan, B. M., et al. (2014). The Southwest Pacific Ocean circulation and climate experiment (SPICE). Journal Of Geophysical ResearchOceans, 119(11), 7660–7686.
Abstract: The Southwest Pacific Ocean Circulation and Climate Experiment (SPICE) is an international research program under the auspices of CLIVAR. The key objectives are to understand the Southwest Pacific Ocean circulation and the South Pacific Convergence Zone (SPCZ) dynamics, as well as their influence on regional and basinscale climate patterns. South Pacific thermocline waters are transported in the westward flowing South Equatorial Current (SEC) toward Australia and PapuaNew Guinea. On its way, the SEC encounters the numerous islands and straits of the Southwest Pacific and forms boundary currents and jets that eventually redistribute water to the equator and high latitudes. The transit in the Coral, Solomon, and Tasman Seas is of great importance to the climate system because changes in either the temperature or the amount of water arriving at the equator have the capability to modulate the El NinoSouthern Oscillation, while the southward transports influence the climate and biodiversity in the Tasman Sea. After 7 years of substantial in situ oceanic observational and modeling efforts, our understanding of the region has much improved. We have a refined description of the SPCZ behavior, boundary currents, pathways, and water mass transformation, including the previously undocumented Solomon Sea. The transports are large and vary substantially in a counterintuitive way, with asymmetries and gating effects that depend on time scales. This paper provides a review of recent advancements and discusses our current knowledge gaps and important emerging research directions. Key Points <list id=“jgrc20950list0001” listtype=“bulleted”> <listitem id=“jgrc20950li0001”>Southwest Pacific WBCs transport large volumes toward the equator and the pole <listitem id=“jgrc20950li0002”>Pathways are complex; water properties tend to erode during the transit <listitem id=“jgrc20950li0003”>Variations due to seasons, ENSO and the SPCZ modulate the relative WBC strengths


Gaultier, L., Djath, B., Verron, J., Brankart, J. M., Brasseur, P., & Melet, A. (2014). Inversion of submesoscale patterns from a highresolution Solomon Sea model: Feasibility assessment. Journal Of Geophysical ResearchOceans, 119(7), 4520–4541.
Abstract: A highresolution realistic numerical model of the Solomon Sea, which exhibits a high level of variability at mesoscales and submesoscales, is used to explore new avenues for data assimilation. Image data assimilation represents a powerful methodology to integrate information from highresolution observations such as satellite sea surface temperature or chlorophyll, or highresolution altimetric sea surface height that will be observed in the forthcoming SWOT mission. The present study investigates the feasibility and accuracy of the inversion of the dynamical submesoscale information contained in highresolution images of sea surface temperature (SST) or salinity (SSS) to improve the estimation of oceanic surface currents. The inversion method is tested in the context of twin experiments, with SST and SSS data provided by a model of the Solomon Sea. For that purpose, synthetic tracer images are built by binarizing the norm of the gradient of SST, SSS or spiciness. The binarized tracer images are compared to the dynamical image which is derived from the FiniteSize Lyapunov Exponents. The adjustment of the dynamical image to the tracer image provides the optimal correction to be applied on the surface velocity field. The method is evaluated by comparing the result of the inversion to the reference model solution. The feasibility of the inversion of various images (SST, SSS, both SST and SSS or spiciness) is explored on two small areas of the Solomon Sea. We show that errors in the surface velocity field can be substantially reduced through the inversion of tracer images.


Gourdeau, L., Verron, J., Melet, A., Kessler, W., Marin, F., & Djath, B. (2014). Exploring the mesoscale activity in the Solomon Sea: A complementary approach with a numerical model and altimetric data. Journal Of Geophysical ResearchOceans, 119(4), 2290–2311.
Abstract: The Solomon Sea is an area of high level of eddy kinetic energy (EKE), and represents a transit area for the lowlatitude western boundary currents (LLWBCs) connecting the subtropics to the equatorial Pacific and playing a major role in ENSO dynamics. This study aims at documenting the surface mesoscale activity in the Solomon Sea for the first time. Our analysis is based on the joint analysis of altimetric data and outputs from a 1/12 degrees model simulation. The highest surface EKE is observed in the northern part of the basin and extends southward to the central basin. An eddy tracking algorithm is used to document the characteristics and trajectories of coherent mesoscale vortices. Cyclonic eddies, generated in the south basin, are advected to the north by the LLWBCs before merging with stationary mesoscale structures present in the mean circulation. Anticyclonic eddies are less numerous. They are generated in the southeastern basin, propagate westward, reach the LLWBCs, and dissipate. The seasonal and interannual modulations of the mesoscale activity are well marked. At seasonal time scale, maximum (minimum) activity is in MayJune (September). At interannual time scale, the mesoscale activity is particularly enhanced during La Nina conditions. If instabilities of the regional circulations seem to explain the generation of mesoscale features, the modulation of the mesoscale activity seems to be rather related with the intrusion at Solomon Strait of the surface South Equatorial Current, rather than to the LLWBCs, by modulating the horizontal and vertical shears suitable for instabilities. Key Points <list id=“jgrc20632list0001” listtype=“bulleted”> <listitem id=“jgrc20632li0001”>A first analysis of the surface mesoscale activity in the Solomon Sea <listitem id=“jgrc20632li0002”>Mesoscale is related with the SEC inflow at Solomon Strait rather than to LLWBC <listitem id=“jgrc20632li0003”>Maximum activity is in MayJune, it is enhanced during La Nina conditions


Remy, F., Flament, T., Michel, A., & Verron, J. (2014). Ice sheet survey over Antarctica using satellite altimetry: ERS2, Envisat, SARAL/AltiKa, the key importance of continuous observations along the same repeat orbit. International Journal Of Remote Sensing, 35(14), 5497–5512.
Abstract: From September 2002 to October 2010, the Envisat radar altimeter surveyed Greenland and Antarctica ice sheets on a 35 day repeat orbit, providing a unique data set for ice sheet mass balance studies. Up to 85 repeat cycles are available and the whole Envisat data set may be alongtrack processed in order to provide height variability and trend with a good spatial resolution for the objectives of ice sheet survey. Soon, a joint Centre National d'Etudes Spatiales/Indian Space Research Organisation mission, SARAL (Satellite with Argos and AltiKa), with the AltiKa payload on board, will be launched on exactly the same orbit (less than 1 km of the nomimal orbit in the acrosstrack direction). This will allow an extension of previous European Remote Sensing (ERS) satellite, ERS1 and ERS2, and Envisat missions of the European Space Agency (ESA), in particular from the point of view of ice altimetry. However, AltiKa operates in the Ka band (36.8 GHz), a higher frequency than the classical Ku band (13.6 GHz), leading to important modifications and potential improvements in the interactions between radar wave and snowpack. In this paper, a synthesis is presented of all available information relevant to ice altimetry scientific purposes as derived from the Envisat mission: mean and temporal derivatives of the height but also of the backscatter and of the two waveform parameters snowpack change corrections, acrosstrack surface slope at 1 km scale, etc. The spatial and temporal variability of ice sheet surface elevation is investigated with the help of the highresolution Envisat alongtrack observations. We show that at least 50 repeat cycles are needed to reach the required accuracy for the elevation trend. It is thus advocated as potentially highly beneficial for SARAL/AltiKa as a followon mission. Moreover, the novel characteristics of SARAL/AltiKa are promising in improving our understanding of snow penetration impact.


2013 
Gaultier, L., Verron, J., Brankart, J. M., Titaud, O., & Brasseur, P. (2013). On the inversion of submesoscale tracer fields to estimate the surface ocean circulation. Journal Of Marine Systems, 126, 33–42.
Abstract: In this paper, we demonstrate the feasibility of inverting the information contained in oceanic submesoscales, such as the ones evidenced in tracer observations of sea surface temperature (SST), to improve the description of mesoscale dynamics provided by altimetric observations. A small region of the Western Mediterranean Sea is chosen as a test case. From a SST snapshot of the region in July 2004, information is extracted to improve the velocity field as computed by geostrophy from the AVISO altimetric data at the same location and time. Image information is extracted from SST using a binarization of the SST gradients. Similarly, image information is extracted from the dynamic topography using finite size Lyapunov exponents (FSLE). The inverse problem is formulated in a Bayesian framework and expressed in terms of a cost function measuring the misfits between the two images. The large amount of information which is already available from ocean color satellites or which will be available from highresolution altimetric satellites such as SWOT, is a strong motivation for this work. Moreover, the image data assimilation approach which is explored here, is a possible strategy for handling the huge amount of satellite data imprinted by small scale information. (c) 2012 Elsevier B.V. All rights reserved.


Koshel, K. V., Sokolovskiy, M. A., & Verron, J. (2013). Threevortex quasigeostrophic dynamics in a twolayer fluid. Part2. Regular and chaotic advection around the perturbed steady states. Journal Of Fluid Mechanics, 717, 255–280.
Abstract: We study fluidparticle motion in the velocity field induced by a quasistationary point vortex structure consisting of one upperlayer vortex and two identical vortices in the bottom layer of a rotating twolayer fluid. The regular regimes are investigated, and the possibility of chaotic regimes (chaotic advection) under the effect of quite small nonstationary disturbances of stationary configurations has been shown. Examples of different scenarios are given for the origin and development of chaos. We analyse the role played by the stochastic layer in the processes of mixing and in the capture of fluid particles within a vortex area. We also study the influence of stratification on these effects. It is shown that regular and chaotic advection situations exhibit significant differences in the two layers.


Meinvielle, M., Brankart, J. M., Brasseur, P., Barnier, B., Dussin, R., & Verron, J. (2013). Optimal adjustment of the atmospheric forcing parameters of ocean models using sea surface temperature data assimilation. Ocean Science, 9(5), 867–883.
Abstract: In ocean general circulation models, nearsurface atmospheric variables used to specify the atmospheric boundary condition remain one of the main sources of error. The objective of this research is to constrain the surface forcing function of an ocean model by sea surface temperature (SST) data assimilation. For that purpose, a set of corrections for ERAinterim (hereafter ERAi) reanalysis data is estimated for the period of 19892007, using a sequential assimilation method, with ensemble experiments to evaluate the impact of uncertain atmospheric forcing on the ocean state. The control vector of the assimilation method is extended to atmospheric variables to obtain monthly mean parameter corrections by assimilating monthly SST and sea surface salinity (SSS) climatological data in a low resolution global configuration of the NEMO model. In this context, the careful determination of the prior probability distribution of the parameters is an important matter. This paper demonstrates the importance of isolating the impact of forcing errors in the model to perform relevant ensemble experiments. The results obtained for every month of the period between 1989 and 2007 show that the estimated parameters produce the same kind of impact on the SST as the analysis itself. The objective is then to evaluate the longterm time series of the forcing parameters focusing on trends and mean error corrections of airsea fluxes. Our corrections tend to equilibrate the net heatflux balance at the global scale (highly positive in ERAi database), and to remove the potentially unrealistic negative trend (leading to ocean cooling) in the ERAi net heat flux over the whole time period. More specifically in the intertropical band, we reduce the warm bias of ERAi data by mostly modifying the latent heat flux by wind speed intensification. Consistently, when used to force the model, the corrected parameters lead to a better agreement between the mean SST produced by the model and mean SST observations over the period of 19892007 in the intertropical band.


Melet, A., Gourdeau, L., Verron, J., & Djath, B. (2013). Solomon Sea circulation and water mass modifications: response at ENSO timescales. Ocean Dynamics, 63(1), 1–19.
Abstract: The South Pacific low latitude western boundary currents (LLWBCs) carry waters of subtropical origin through the Solomon Sea before joining the equatorial Pacific. Changes in their properties or transport are assumed to impact El Nino Southern Oscillation (ENSO) dynamics. At ENSO timescales, the LLWBCs transport tends to counterbalance the interior geostrophic one. When transiting through the complex geography of the Solomon Sea, the main LLWBC, the New Guinea Coastal Undercurrent, cannot follow a unique simple route to the equator. Instead, its routes and water mass properties are influenced by the circulation occurring in the Solomon Sea. In this study, the response of the Solomon Sea circulation to ENSO is investigated based on a numerical simulation. The transport anomalies entering the Solomon Sea from the south are confined to the top 250 m of the water column, where they represent 7.5 Sv (based on ENSO composites) for a mean transport of 10 Sv. The induced circulation anomalies in the Solomon Sea are not symmetric between the two ENSO states because of (1) a bathymetric control at Vitiaz Strait, which plays a stronger role during El Nino, and (2) an additional inflow through Solomon Strait during La Nina events. In terms of temperature and salinity, modifications are particularly notable for the thermocline water during El Nino conditions, with cooler and fresher waters compared to the climatological mean. The surface water at Vitiaz Strait and the upper thermocline water at Solomon Strait, feeding respectively the equatorial Pacific warm pool and the Equatorial Undercurrent, particularly affect the heat and salt fluxes. These fluxes can change by up to a factor of 2 between extreme El Nino and La Nina conditions.


Sokolovskiy, M. A., Koshel, K. V., & Verron, J. (2013). Threevortex quasigeostrophic dynamics in a twolayer fluid. Part 1. Analysis of relative and absolute motions. Journal Of Fluid Mechanics, 717, 232–254.
Abstract: The results presented here examine the quasigeostrophic dynamics of a point vortex structure with one upperlayer vortex and two identical bottomlayer vortices in a twolayer fluid. The problem of three vortices in a barotropic fluid is known to be integrable. This fundamental result is also valid in a stratified fluid, in particular a twolayer one. In this case, unlike the barotropic situation, vortices belonging to the same layer or to different layers interact according to different formulae. Previously, this occurrence has been poorly investigated. In the present work, the existence conditions for stable stationary (translational and rotational) collinear twolayer configurations of three vortices are obtained. Small disturbances of stationary configurations lead to periodic oscillations of the vortices about their undisturbed shapes. These oscillations occur along elliptical orbits up to the second order of the Hamiltonian expansion. Analytical expressions for the parameters of the corresponding ellipses and for oscillation frequencies are obtained. In the case of finite disturbances, vortex motion becomes more complicated. In this case we have made a classification of all possible movements, by analysing phase portraits in trilinear coordinates and by computing numerically the characteristic trajectories of the absolute and relative vortex motions.


2012 
Brankart, J. M., Testut, C. E., Beal, D., Doron, M., Fontana, C., Meinvielle, M., et al. (2012). Towards an improved description of ocean uncertainties: effect of local anamorphic transformations on spatial correlations. Ocean Science, 8(2), 121–142.
Abstract: The objective of this paper is to investigate if the description of ocean uncertainties can be significantly improved by applying a local anamorphic transformation to each model variable, and by making the assumption of joint Gaussianity for the transformed variables, rather than for the original variables. For that purpose, it is first argued that a significant improvement can already be obtained by deriving the local transformations from a simple histogram description of the marginal distributions. Two distinctive advantages of this solution for large size applications are the conciseness and the numerical efficiency of the description. Second, various oceanographic examples are used to evaluate the effect of the resulting piecewise linear local anamorphic transformations on the spatial correlation structure. These examples include (i) stochastic ensemble descriptions of the effect of atmospheric uncertainties on the ocean mixed layer, and of wind uncertainties or parameter uncertainties on the ecosystem, and (ii) nonstochastic ensemble descriptions of forecast uncertainties in current sea ice and ecosystem preoperational developments. The results indicate that (i) the transformation is accurate enough to faithfully preserve the correlation structure if the joint distribution is already close to Gaussian, and (ii) the transformation has the general tendency of increasing the correlation radius as soon as the spatial dependence between random variables becomes nonlinear, with the important consequence of reducing the number of degrees of freedom in the uncertainties, and thus increasing the benefit that can be expected from a given observation network.


Cosme, E., Verron, J., Brasseur, P., Blum, J., & Auroux, D. (2012). Smoothing Problems in a Bayesian Framework and Their Linear Gaussian Solutions. Monthly Weather Review, 140(2), 683–695.
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 filterbased 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.


Duchez, A., Verron, J., Brankart, J. M., Ourmieres, Y., & Fraunie, P. (2012). Monitoring the Northern Current in the Gulf of Lions with an observing system simulation experiment. Scientia Marina, 76(3), 441–453.
Abstract: The coastal circulation in the Gulf of Lions (GoL) is influenced by the Northern Current (NC), forced by a complex wind system and also affected by important river discharges from the Rhone River. Correct modelling of this current is therefore important for obtaining a good representation of the gulf circulation. An observing system simulation experiment using the SEEK filter data assimilation method was used in a regional 1/16 degrees configuration of the GoL in the NEMO model. The synthetic observation database used for the experiment comprised altimetric data in addition to insitu temperature and salinity profiles. Statistical diagnostics and other physical criteria based on the improvement of NC representation were set up in order to assess the quality of this experiment. Comparisons between the free 1/16 degrees simulation and the experience with assimilation show that data assimilation significantly improved the description of the characteristics of the NC as well as its seasonal and mesoscale variability, which in turn improved the description of the water exchanges between the coastal region and the open sea.


Melet, A., Verron, J., & Brankart, J. M. (2012). Potential outcomes of glider data assimilation in the Solomon Sea: Control of the water mass properties and parameter estimation. Journal Of Marine Systems, 94, 232–246.
Abstract: Steerable underwater gliders are a recent addition to ocean observing systems. Gliders were deployed in the Solomon Sea to improve our knowledge of this potentially important region for Pacific climate. In this study, we explore the potential use of glider data assimilation to control some properties of the ocean state estimation, chosen here to be Solomon Sea thermohaline misfits due to an erroneous tidalmixing parameterization. Ocean observing system simulation experiments involving several scenarios of glider deployment show that the fleet design can strongly impact the control efficiency. A fairly good control of the Solomon Sea mass field can be achieved with a somewhat unrealistic fleet of 50 gliders. With a more realistic configuration of 10 gliders, the performance depends on the space and time distribution of the vehicles. Substantial control is achieved when glider trajectories are coordinated to collect informationrich data. As a complement, glider data assimilation was used to directly correct the model: the uncertain tidal mixing parameter is estimated through assimilation of data provided by the 10 coordinated gliders using an ensemble simulation method. This promising strategy allows an accurate estimation of the parameter and therefore yields an efficient correction of the errors in Solomon Sea thermohaline properties. (C) 2011 Elsevier B.V. All rights reserved.


Ubelmann, C., Verron, J., Brankart, J. M., Brasseur, P., & Cosme, E. (2012). Assimilating altimetric data to control the tropical instability waves: an observing system simulation experiment study. Ocean Dynamics, 62(6), 867–880.
Abstract: Tropical instability waves (TIWs) are not easily simulated by ocean circulation models primarily because such waves are very sensitive to wind forcing. In this study, we investigate the impact of assimilating sea surface height (SSH) observations on the control of TIWs in an observing system simulation experiment (OSSE) context based on a regional model configuration of the tropical Atlantic. A Kalman filtering method with suitable adaptations is found to be successful when altimetric data are assimilated in conjunction with sea surface temperature and some in situ temperature/salinity profiles. In this rather realistic system, the TIW phase is roughly controlled with a single nadir observing satellite. However, a right correction of the TIW structure and amplitude requires at least two nadir observing satellites or a wide swath observing satellite. The significant impact of orbital parameters is also demonstrated: in particular, the Jason or GFO satellite orbits are found to be more suitable than the ENVISAT orbit. More generally, it is found that as soon as adequate subsampling exists (with periods of 510 days), the length of the repetitivity cycle of orbits does not have a significant impact.


2011 
Brankart, J. M., Cosme, E., Testut, C. E., Brasseur, P., & Verron, J. (2011). Efficient Local Error Parameterizations for Square Root or Ensemble Kalman Filters: Application to a BasinScale Ocean Turbulent Flow. Monthly Weather Review, 139(2), 474–493.
Abstract: In largesized atmospheric or oceanic applications of square root or ensemble Kalman filters, it is often necessary to introduce the prior assumption that longrange correlations are negligible and force them to zero using a local parameterization, supplementing the ensemble or reducedrank representation of the covariance. One classic algorithm to perform this operation consists of taking the Schur product of the ensemble covariance matrix by a local support correlation matrix. However, with this parameterization, the square root of the forecast error covariance matrix is no more directly available, so that any observational update algorithm requiring this square root must include an additional step to compute local square roots from the Schur product. This computation generates an additional numerical cost or produces highrank square roots, which may deprive the observational update from its original efficiency. In this paper, it is shown how efficient local square root parameterizations can be obtained, for use with a specific square root formulation (i.e., eigenbasis algorithm) of the observational update. Comparisons with the classic algorithm are provided, mainly in terms of consistency, accuracy, and computational complexity. As an application, the resulting parameterization is used to estimate maps of dynamic topography characterizing a basinscale ocean turbulent flow. Even with this moderatesized system (a 2200kmwide square basin with 100kmwide mesoscale eddies), it is observed that more than 1000 ensemble members are necessary to faithfully represent the global correlation patterns, and that a local parameterization is needed to produce correct covariances with moderatesized ensembles. Comparisons with the exact solution show that the use of local square roots is able to improve the accuracy of the updated ensemble mean and the consistency of the updated ensemble variance. With the eigenbasis algorithm. optimal adaptive estimates of scaling factors for the forecast and observation error covariance matrix can also be obtained locally at negligible additional numerical cost. Finally, a comparison of the overall computational cost illustrates the decisive advantage that efficient local square root parameterizations may have to deal simultaneously with a larger number of observations and avoid data thinning as much as possible.


Krysta, M., Blayo, E., Cosme, E., & Verron, J. (2011). A Consistent Hybrid VariationalSmoothing Data Assimilation Method: Application to a Simple ShallowWater Model of the Turbulent Midlatitude Ocean. Monthly Weather Review, 139(11), 3333–3347.
Abstract: In the standard fourdimensional variational data assimilation (4DVar) algorithm the background error covariance matrix B 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 variationalsmoothing algorithm is based on a reducedrank incremental 4DVar. Its consistent coupling to a singular evolutive extended Kalman (SEEK) smoother ensures the evolution of the B matrix. In the analysis step, a lowdimensional 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 shallowwater 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 B 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 4DVar are described and an explanation of the possible reasons for this is proposed.


Melet, A., Verron, J., Gourdeau, L., & KochLarrouy, A. (2011). Equatorward Pathways of Solomon Sea Water Masses and Their Modifications. Journal Of Physical Oceanography, 41(4), 810–826.
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 lowfrequency modulation of El NinoSouthern Oscillation, modifications to water masses in the Solomon Sea have never been analyzed to our knowledge. A highresolution 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 degrees0.3 degrees 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 (approximate to 60%) by strong diapycnal mixing in the Solomon Sea. As for STMW, about a third of this mixing is due to tidal mixing.


Titaud, O., Brankart, J. M., & Verron, J. (2011). On the use of FiniteTime Lyapunov Exponents and Vectors for direct assimilation of tracer images into ocean models. Tellus Series ADynamic Meteorology And Oceanography, 63(5), 1038–1051.
Abstract: Satellite ocean tracer images, of sea surface temperature (SST) and ocean colour images, for example, show patterns like fronts and filaments that characterize the flow dynamics. These patterns can be described using Lagrangian tools such as FiniteTime Lyapunov Exponents (FTLE) or FiniteTime Lyapunov Vectors (FTLV). In recent years, several studies have investigated the possibility of directly assimilating structured data from satellite images into numerical models. In this paper, we exploit specific properties of FTLE and FTLV to define observation operators that can be used in a direct ocean tracer image assimilation scheme. In an idealized context, we show that highresolution SST and ocean colour images can be exploited to correct velocity fields using FTLE or FTLV.


2010 
Beal, D., Brasseur, P., Brankart, J. M., Ourmieres, Y., & Verron, J. (2010). Characterization of mixing errors in a coupled physical biogeochemical model of the North Atlantic: implications for nonlinear estimation using Gaussian anamorphosis. Ocean Science, 6(1), 247–262.
Abstract: In biogeochemical models coupled to ocean circulation models, vertical mixing is an important physical process which governs the nutrient supply and the plankton residence in the euphotic layer. However, vertical mixing is often poorly represented in numerical simulations because of approximate parameterizations of subgrid scale turbulence, wind forcing errors and other misrepresented processes such as restratification by mesoscale eddies. Getting a sufficient knowledge of the nature and structure of these errors is necessary to implement appropriate data assimilation methods and to evaluate if they can be controlled by a given observation system. In this paper, Monte Carlo simulations are conducted to study mixing errors induced by approximate wind forcings in a threedimensional coupled physicalbiogeochemical model of the North Atlantic with a 1/4 degrees horizontal resolution. An ensemble forecast involving 200 members is performed during the 1998 spring bloom, by prescribing perturbations of the wind forcing to generate mixing errors. The biogeochemical response is shown to be rather complex because of nonlinearities and threshold effects in the coupled model. The response of the surface phytoplankton depends on the region of interest and is particularly sensitive to the local stratification. In addition, the statistical relationships computed between the various physical and biogeochemical variables reflect the signature of the nonGaussian behaviour of the system. It is shown that significant information on the ecosystem can be retrieved from observations of chlorophyll concentration or sea surface temperature if a simple nonlinear change of variables (anamorphosis) is performed by mapping separately and locally the ensemble percentiles of the distributions of each state variable on the Gaussian percentiles. The results of idealized observational updates (performed with perfect observations and neglecting horizontal correlations) indicate that the implementation of this anamorphosis method into sequential assimilation schemes can substantially improve the accuracy of the estimation with respect to classical computations based on the Gaussian assumption.


Brankart, J. M., Cosme, E., Testut, C. E., Brasseur, P., & Verron, J. (2010). Efficient Adaptive Error Parameterizations for Square Root or Ensemble Kalman Filters: Application to the Control of Ocean Mesoscale Signals. Monthly Weather Review, 138(3), 932–950.
Abstract: In Kalman filter applications, an adaptive parameterization of the error statistics is often necessary to avoid filter divergence, and prevent error estimates from becoming grossly inconsistent with the real error. With the classic formulation of the Kalman filter observational update, optimal estimates of general adaptive parameters can only be obtained at a numerical cost that is several times larger than the cost of the state observational update. In this paper, it is shown that there exists a few types of important parameters for which optimal estimates can be computed at a negligible numerical cost, as soon as the computation is performed using a transformed algorithm that works in the reduced control space defined by the square root or ensemble representation of the forecast error covariance matrix. The set of parameters that can be efficiently controlled includes scaling factors for the forecast error covariance matrix, scaling factors for the observation error covariance matrix, or even a scaling factor for the observation error correlation length scale. As an application, the resulting adaptive filter is used to estimate the time evolution of ocean mesoscale signals using observations of the ocean dynamic topography. To check the behavior of the adaptive mechanism, this is done in the context of idealized experiments, in which model error and observation error statistics are known. This ideal framework is particularly appropriate to explore the illconditioned situations (inadequate prior assumptions or uncontrollability of the parameters) in which adaptivity can be misleading. Overall, the experiments show that, if used correctly, the efficient optimal adaptive algorithm proposed in this paper introduces useful supplementary degrees of freedom in the estimation problem, and that the direct control of these statistical parameters by the observations increases the robustness of the error estimates and thus the optimality of the resulting Kalman filter.


Cosme, E., Brankart, J. M., Verron, J., Brasseur, P., & Krysta, M. (2010). Implementation of a reduced rank squareroot smoother for high resolution ocean data assimilation. Ocean Modelling, 33(12), 87–100.
Abstract: Optimal smoothers enable the use of future observations to estimate the state of a dynamical system. In this paper, a squareroot smoother algorithm is presented, extended from the Singular Evolutive Extended Kalman (SEEK) filter, a squareroot Kalman filter routinely used for ocean data assimilation. With this filter algorithm, the smoother extension appears almost costfree. A modified algorithm implementing a particular parameterization of model error is also described. The smoother is applied with an ocean circulation model in a doublegyre, 1/4 degrees configuration, able to represent midlatitude mesoscale dynamics. Twin experiments are performed: the true fields are drawn from a simulation at a 1/6 degrees resolution, and noised. Then, altimetric satellite tracks and sparse vertical profiles of temperature are extracted to form the observations. The smoother is efficient in reducing errors, particularly in the regions poorly covered by the observations at the filter analysis time. It results in a significant reduction of the global error: the Root Mean Square Error in Sea Surface Height from the filter is further reduced by 20% by the smoother. The actual smoothing of the global error through time is also verified. Three essential issues are then investigated: (i) the time distance within which observations may be favourably used to correct the state estimates is found to be 8 days with our system. (ii) The impact of the model error parameterization is stressed. When this parameterization is spuriously neglected, the smoother can deteriorate the state estimates. (iii) Iterations of the smoother over a fixed time interval are tested. Although this procedure improves the state estimates over the assimilation window, it also makes the subsequent forecast worse than the filter in our experiment. (C) 2009 Elsevier Ltd. All rights reserved.


Laanaia, N., Wirth, A., Molines, J. M., Barnier, B., & Verron, J. (2010). On the numerical resolution of the bottom layer in simulations of oceanic gravity currents. Ocean Science, 6(2), 563–572.
Abstract: The role of an increased numerical vertical resolution, leading to an explicit resolution of the bottom Ekman layer dynamics, is investigated. Using the hydrostatic ocean model NEMOOPA9, we demonstrate that the dynamics of an idealised gravity current (on an inclined plane), is well captured when a few (around five) sigmacoordinate levels are added near the ocean floor. Such resolution allows to considerably improve the representation of the descent and transport of the gravity current and the Ekman dynamics near the ocean floor, including the important effect of Ekman veering, which is usually neglected in today's simulations of the ocean dynamics. Results from high resolution simulations (with Sigma and zcoordinates) are compared to simulations with a vertical resolution commonly employed in today's ocean models. The latter show a downslope transport that is reduced by almost an order of magnitude and the decrease in the along slope transport is reduced sixfold. We strongly advocate for an increase of the numerical resolution at the ocean floor, similar to the way it is done at the ocean surface and at the lower boundary in atmospheric models.


Melet, A., Gourdeau, L., Kessler, W. S., Verron, J., & Molines, J. M. (2010). Thermocline Circulation in the Solomon Sea: A Modeling Study. Journal Of Physical Oceanography, 40(6), 1302–1319.
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 lowfrequency modulation of ENSO, the circulation inside the Solomon Sea is poorly documented. A 1/12 degrees 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 degrees S, and the spinup and spindown of the subtropical gyre as a response of Rossby waves forced south of 10 degrees S.


Melet, A., Gourdeau, L., & Verron, J. (2010). Variability in Solomon Sea circulation derived from altimeter sea level data. Ocean Dynamics, 60(4), 883–900.
Abstract: The Solomon Sea is a key region in the Pacific Ocean where equatorial and subtropical circulations are connected. The region exhibits the highest levels in sea level variability in the entire south tropical Pacific Ocean. Altimeter data was utilized to explore sea level and western boundary currents in this poorly understood portion of the ocean. Since the geography of the region is extremely intricate, with numerous islands and complex bathymetry, specifically reprocessed alongtrack data in addition to standard gridded data were utilized in this study. Sea level anomalies (SLA) in the Solomon Sea principally evolve at seasonal and interannual time scales. The annual cycle is phased by Rossby waves arriving in the Solomon Strait, whereas the interannual signature corresponds to the basinscale ENSO mode. The highest SLA variability are concentrated in the eastern Solomon Sea, particularly at the mouth of the Solomon Strait, where they are associated with a high eddy kinetic energy signal that was particularly active during the phase transition during the 19971998 ENSO event. Track data appear especially helpful for documenting the fine structure of surface coastal currents. The annual variability of the boundary currents that emerged from altimetry compared quite well with the variability seen at the thermocline level, as based on numerical simulations. At interannual time scales, western boundary current transport anomalies counterbalance changes in western equatorial Pacific warm water volume, confirming the phasing of South Pacific western boundary currents to ENSO. Altimetry appears to be a valuable source of information for variability in low latitude western boundary currents and their associated transport in the South Pacific.


Sokolovskiy, M., Verron, J., Carton, X., & Gryanik, V. (2010). On instability of elliptical hetons. Theoretical And Computational Fluid Dynamics, 24(14), 117–123.
Abstract: Using the method of contour surgery, we examine the evolution of an initially vertically aligned elliptical heton. A classification of quasistable and unstable regimes for the case of twolayered vortex structure is suggested.


2009 
Brankart, J. M., Ubelmann, C., Testut, C. E., Cosme, E., Brasseur, P., & Verron, J. (2009). Efficient Parameterization of the Observation Error Covariance Matrix for Square Root or Ensemble Kalman Filters: Application to Ocean Altimetry. Monthly Weather Review, 137(6), 1908–1927.
Abstract: In the Kalman filter standard algorithm, the computational complexity of the observational update is proportional to the cube of the number y of observations (leading behavior for large y). In realistic atmospheric or oceanic applications, involving an increasing quantity of available observations, this often leads to a prohibitive cost and to the necessity of simplifying the problem by aggregating or dropping observations. If the filter error covariance matrices are in square root form, as in square root or ensemble Kalman filters, the standard algorithm can be transformed to be linear in y, providing that the observation error covariance matrix is diagonal. This is a significant drawback of this transformed algorithm and often leads to an assumption of uncorrelated observation errors for the sake of numerical efficiency. In this paper, it is shown that the linearity of the transformed algorithm in y can be preserved for other forms of the observation error covariance matrix. In particular, quite general correlation structures (with analytic asymptotic expressions) can be simulated simply by augmenting the observation vector with differences of the original observations, such as their discrete gradients. Errors in ocean altimetric observations are spatially correlated, as for instance orbit or atmospheric errors along the satellite track. Adequately parameterizing these correlations can directly improve the quality of observational updates and the accuracy of the associated error estimates. In this paper, the example of the North Brazil Current circulation is used to demonstrate the importance of this effect, which is especially significant in that region of moderate ratio between signal amplitude and observation noise, and to show that the efficient parameterization that is proposed for the observation error correlations is appropriate to take it into account. Adding explicit gradient observations also receives a physical justification. This parameterization is thus proved to be useful to ocean data assimilation systems that are based on square root or ensemble Kalman filters, as soon as the number of observations becomes penalizing, and if a sophisticated parameterization of the observation error correlations is required.


Cummings, J., Bertino, L., Brasseur, P., Fukumori, I., Kamachi, M., Martin, M. J., et al. (2009). Ocean Data Assimilation Systems For Godae. Oceanography, 22(3), 96–109.
Abstract: Ocean data assimilation has matured to the point that observations are now routinely combined with model forecasts to produce a variety of ocean products. Approaches to ocean data assimilation vary widely both in terms of the sophistication of the method and the observations assimilated, and also in terms of specification of the forecast error covariances, model biases, observation errors, and qualitycontrol procedures. In this paper, we describe some of the ocean data assimilation systems that have been developed within the Global Ocean Data Assimilation Experiment (GODAE) community. We discuss assimilation methods, observations assimilated, and techniques used to specify error covariances. In addition, we describe practical implementation aspects and present analysis performance results for some of the analysis systems. Finally, we describe plans for improving the assimilation systems in the postGODAE time period beyond 2008.


Lauvernet, C., Brankart, J. M., Castruccio, F., Broquet, G., Brasseur, P., & Verron, J. (2009). A truncated Gaussian filter for data assimilation with inequality constraints: Application to the hydrostatic stability condition in ocean models. Ocean Modelling, 27(12), 1–17.
Abstract: In many data assimilation problems, the state variables are subjected to inequality constraints. These constraints often contain valuable information that must be taken into account in the estimation process. However, with linear estimation methods (like the Kalman filter), there is no way to incorporate optimally that kind of additional information. In this study, it is shown that an optimal filter dealing with inequality constraints can be formulated under the assumption that the probability distributions are truncated Gaussian distributions. The statistical tools needed to implement this truncated Gaussian filter are described. It is also shown how the filter can be adapted to work in a reduced dimension space, and flow it can be simplified following several additional hypotheses. As an application, the truncated Gaussian assumption is shown to be adequate to deal with the condition of hydrostatic stability in ocean analyses. First, a detailed evaluation of the method is made using a onedimensional zcoordinate model of the mixed layer: particular attention is paid to the parameterization of the probability distribution, the accuracy of the estimation and the sensitivity to the observation system. In a second step, the method is applied to a threedimensional hybrid coordinate ocean model (HYCOM) of the Bay of Biscay (at a 1/15 degrees resolution), to show that it is efficient enough to be applied to real size problems. These examples also demonstrate that the algorithm can deal with the hydrostatic stability condition in isopycnic coordinates as well as in zcoordinates. (C) 2008 Elsevier Ltd. All rights reserved.


Ourmieres, Y., Brasseur, P., Levy, M., Brankart, J. M., & Verron, J. (2009). On the key role of nutrient data to constrain a coupled physicalbiogeochemical assimilative model of the North Atlantic Ocean. Journal Of Marine Systems, 75(12), 100–115.
Abstract: A sequential assimilative system has been implemented into a coupled physicalbiogeochemical model (CPBM)of the North Atlantic basin at eddypermitting resolution (1/4 degrees), with the longterm goal of estimating the basin scale patterns of the oceanic primary production and their seasonal variability. The assimilation system, which is based on the SEEK filter [Brasseur, P., Verron, J., 2006. The SEEK filter method for data assimilation in oceanography: a synthesis. Ocean Dynamics. doi: 10.1007/s1023600600803], has been adapted to this CPBM in order to control the physical and biogeochemical components of the coupled model separately or in combination. The assimilated data are the satellite Topex/Poseidon and ERS altimetric data, the AVHRR Sea Surface Temperature observations, and the Levitus climatology for salinity, temperature and nitrate. In the present study, different assimilation experiments are conducted to assess the relative usefulness of the assimilated data to improve the representation of the primary production by the CPBM. Consistently with the results obtained by Berline et al. [Berline, L, Brankart, JM., Brasseur, P., Ourmieres, Y., Verron, J., 2007. Improving the physics of a coupled physicalbiogeochemical model of the North Atlantic through data assimilation: impact on the ecosystem. J. Mar. Syst. 64 (14),153172] with a comparable assimilative model, it is shown that the assimilation of physical data alone can improve the representation of the mixed layer depth, but the impact on the ecosystem is rather weak. In some situations, the physical data assimilation can even worsen the ecosystem response for areas where the prior nutrient distribution is significantly incorrect. However, these experiments also show that the combined assimilation of physical and nutrient data has a positive impact on the phytoplankton patterns by comparison with SeaWiFS ocean colour data, demonstrating the good complementarity between SST, altimetry and in situ nutrient data. These results suggest that more intensive in situ measurements of biogeochemical nutrients are urgently needed at basin scale to initiate a permanent monitoring of oceanic ecosystems. (c) 2008 Elsevier B.V. All rights reserved.


Skachko, S., Brankart, J. M., Castruccio, B. F., Brasseur, P., & Verron, J. (2009). Improved Turbulent AirSea Flux Bulk Parameters for Controlling the Response of the Ocean Mixed Layer: A Sequential Data Assimilation Approach. Journal Of Atmospheric And Oceanic Technology, 26(3), 538–555.
Abstract: Bulk formulations parameterizing turbulent airsea fluxes remain among the main sources of error in presentday ocean models. The objective of this study is to investigate the possibility of estimating the turbulent bulk exchange coefficients using sequential data assimilation. It is expected that existing ocean assimilation systems can use this method to improve the airsea fluxes and produce more realistic forecasts of the thermohaline characteristics of the mixed layer. The method involves augmenting the control vector of the assimilation scheme using the model parameters that are to be controlled. The focus of this research is on estimating two bulk coefficients that drive the sensible heat flux, the latent heat flux, and the evaporation flux of a global ocean model, by assimilating temperature and salinity profiles using horizontal and temporal samplings similar to those to be provided by the Argo float system. The results of twin experiments show that the method is able to correctly estimate the largescale variations in the bulk parameters, leading to a significant improvement in the atmospheric forcing applied to the ocean model.


Skandrani, C., Brankart, J. M., Ferry, N., Verron, J., Brasseur, P., & Barnier, B. (2009). Controlling atmospheric forcing parameters of global ocean models: sequential assimilation of sea surface MercatorOcean reanalysis data. Ocean Science, 5(4), 403–419.
Abstract: In the context of stand alone ocean models, the atmospheric forcing is generally computed using atmospheric parameters that are derived from atmospheric reanalysis data and/or satellite products. With such a forcing, the sea surface temperature that is simulated by the ocean model is usually significantly less accurate than the synoptic maps that can be obtained from the satellite observations. This not only penalizes the realism of the ocean longterm simulations, but also the accuracy of the reanalyses or the usefulness of the shortterm operational forecasts (which are key GODAE and MERSEA objectives). In order to improve the situation, partly resulting from inaccuracies in the atmospheric forcing parameters, the purpose of this paper is to investigate a way of further adjusting the state of the atmosphere (within appropriate error bars), so that an explicit ocean model can produce a sea surface temperature that better fits the available observations. This is done by performing idealized assimilation experiments in which MercatorOcean reanalysis data are considered as a reference simulation describing the true state of the ocean. Synthetic observation datasets for sea surface temperature and salinity are extracted from the reanalysis to be assimilated in a low resolution global ocean model. The results of these experiments show that it is possible to compute piecewise constant parameter corrections, with predefined amplitude limitations, so that longterm free model simulations become much closer to the reanalysis data, with misfit variance typically divided by a factor 3. These results are obtained by applying a Monte Carlo method to simulate the joint parameter/state prior probability distribution. A truncated Gaussian assumption is used to avoid the most extreme and nonphysical parameter corrections. The general lesson of our experiments is indeed that a careful specification of the prior information on the parameters and on their associated uncertainties is a key element in the computation of realistic parameter estimates, especially if the system is affected by other potential sources of model errors.


Ubelmann, C., Verron, J., Brankart, J. M., Cosme, E., & Brasseur, P. (2009). Impact of data from upcoming altimetric missions on the prediction of the threedimensional circulation in the tropical Atlantic Ocean. Journal Of Operational Oceanography, 2(1), 3–14.
Abstract: The use of Sea Surface Height (SSH) satellite measurements in ocean models is a key element the efficient control of the threedimensional circulation through data assimilation and therefore in the quality of operational oceanography products. This paper attempts to evaluate the impact of future satellite data, particularly from the upcoming JASON2, SARAL and SWOT missions, introduced into a model through a sophisticated data assimilation procedure. For this purpose, Observing System Simulation Experiments (OSSEs) are performed in the tropical Atlantic Ocean. The NEMO model is used (at a 1/4 degrees resolution) in a configuration covering the tropical Atlantic from 15 degrees S to 17 degrees N, and the assimilation scheme is a reducedorder Kalman (SEEK) filter. The study focuses principally on controlling of the circulation of the North Brazil Current and the propagation of Tropical Instability Waves (TIW). Among the orbits tested for altimetric satellites, the JASON2 orbit (10day repeat period) is found to give the best single satellite sampling for data assimilation. The addition of a second or third satellite to JASON2 is particularly useful in the TIW region and is even required to properly control the Brazil rings. A SWOT satellite would provide benefits that are equivalent to the contribution of two or three satellites, depending on the case.

