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The Time-Mean Circulation in the Agulhas Region Determined with the Ensemble Smoother

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The Time-Mean Circulation in the Agulhas Region Determined with the Ensemble Smoother JOURNAL OF GEOPHYSICAL RESEARCH, VOL. 104, NO. C1, PAGES 1393-1404, JANUARY 15, 1999 The time-mean circulation in the Agulhas region determined with the ensemble smoother Peter Jan Van Leeuwen Institute for Marine and Atmospheric Research Utrecht, Utrecht, Netherlands Abstract. The time-mean circulation in the Agulhas Retroflection area is deter- mined by combiningTOPEX/POSEIDON data and a two-layerquasi-geostrophic model using the ensemblesmoother. By taking the time-mean circulation as the unknown in the data assimilation procedure, the time-varying altimeter signal is used to constrain the time-mean field. The quasi-geostrophicmodel is applied as a strong constraint, with only the time-mean circulation containing errors. Inspection of the posterior penalty function showedthat the inversionwas successful.The errors in the time-mean sea surface topography reduced from about 10 to about 3 cm. A cyclonicrecirculation cell over the AgulhasPlateau was found, related to the northward meander of the Agulhas Return Current. Another cyclonicrecirculation cell was found west of Africa, probably related to the passageof anticyclonic Agulhas Rings south of it. The new field is compared with advancedvery high resolution radiometer infrared satellite data, confirming the northward meander of the Agulhas Return Current. 1. Introduction The time-mean circulation cannot be directly deter- mined with accuracy. Clearly, this is an important Satellite observations are becoming more and more quantity, to study quantitatively, for instance, trans- important for our understanding and monitoring of the ports such as interocean exchanges or ring-shedding world oceans. A serious drawback of this kind of obser- processes(meanders cannot be separatedfrom eddies). vations is the fact that they measure only at the surface To solve these problems, different methods can be used. of the ocean. Satellite infrared images measure the skin One way to improve interpretation is application of temperature, while optical sensorscan reach depths of statistical techniques that analyze decorrelation in time about 50 m in clear-water conditions. So these measure- and space.For instance,Feron et al., [1992]were able to ments contain only information of the mixed layer and determine the instancesof ring sheddingfrom the time- the air- sea interaction. Satellite altimeters and also varying signal only. Another approach is to combine syntheticapperture radar (SAR) imagescontain infor- the altimeter signal with other independent observa- mation on the shape of the water surface, so they mea- tionsof the circulation. Vazquezet al., [1990]combined sure an integrated quantity. This is the reasonwhy al- Geosat data with observationsof sea surface tempera- timetry, in particular, has been usedto study mesoscale ture in the Gulf Stream area. Other studies[e.g. Tai ocean dynamics. and White, 1988; Willebrand et al., 1990;Gordon et al., A seriousproblem with altimetry is that the shape of 1990; Ichikawa and Imawaki, 1994] combinedhydro- '•i• ocean surface as dictated by gravity is not known graphicdata and/or surfacedrifter buoyswith Geosat with high accuracy. So although the measurements data to study rings detached from the mean flow. themselves have an accuracy of 2 to 5 cm, it is im- Two methods are presently in use to estimate the possible to distinguish the geoid from the time-mean long-wavelengthpart of the time-mean circulation from circulationsignal [Chelton, 1988; Nerern et al., 1990;Fu altimeter observations. The first method simultane- et al., 1996]. Of course,the geoidis to a large extent ously adjusts the gravity field and this circulation. This time invariant, so the time-varying part of the altime- so-calledintegrated least squaresapproach is successful ter signal can be used to observethe mesoscaleactivity for wavelengthslarger than roughly 1400 km by using of the oceanvery accurately[e.g. Cheneyet al., 1993; a priori information on the time-mean circulation from Wakker et al., 1990; Tai and White, 1988; $hum et al., other measurements[e.g. Marsh et al., 1990; Engelis 1990;Gordonand Haxby,1990; Feron et al., 1992]. and Knudsen,1989;Nerem et al., 1990;Visser, 1992]. In the secondmethod the geoid is determined more accu- Copyright1999 by the AmericanGeophysical Union. rately from the orbit of the satellite. The geoid reflects , the shape of the gravity field, which influencesthe orbit Papernumber 1998JC900012. of the satellite. The very high precisionof the height 0148-0227/99/1998JC900012509.00 measurementstogether with the very accurately known 1393 1394 VAN LEEUWEN: TIME-MEAN CIRCULATION IN AGULHAS REGION satelliteorbit allowthe geoidto be found[e.g., Minster It has been applied successfullyin the Agulhas area et al., 1993; Naeije et al., 1993; Fu et al., 1996]. Both to study the shedding of large Agulhas Rings that methods still lack accuracyfor wavelengthsshorter than transport heat, salt, vorticity, and energy from the In- about 1400 km. dian to the south Atlantic Ocean as part of the Indian One can also try to determinethe mean flow directly SouthAtlantic supergym[VanBallegooijen et al., 1994; from the altimeter signal by assuminga certain shape Byrne et al., 1995]. In the study by Van Leeuwen, of the current. Kelly and Gille, [1990]and Qiu et al. [1998]the time-meancirculation of the GordonSouth- [1991]investigated the mean flow in the Gulf Stream ern OceanAtlas [Gordon,1982] was added to TOPEX/- and Kuroshio Extension respectively by fitting a syn- POSEIDON gridded altimeter fields, and this combina- thetic current's height profile to Geosat residualheight tion was assimilated in a two-layer quasi-geostrophic data along individual tracks. Their resultswere found model. to be in remarkable agreementwith hydrographicand In the ensemble smoother a Bayesian view is taken in acousticDoppler current profiles [e.g., Kelly et al., 1991; which the prior probability densityof the model and the Teagueet al., 1990]. More recently,Gille, [1994]used probability density of the data are combinedto form a the same techniquefor mapping the Antarctic Circum- posterior density. The mean and the covarianceof this polar Current. Both the Sub-Antarcticfront and the density give the optimal model evolution and its errors. Polar front could be determined and analyzed from The advantage of this smoother over all others is that Geosat altimeter data. no adjoint equations need to be integrated and error All of the methods given above lack a very valu- estimates are easily obtained. able piece of information: the dynamicsof the water. This paper is organizedas follows. First, the data as- Obviously, the time-mean and the time-varying parts similation method is described in some detail. Then the of the ocean circulation are dynamically coupled. Re- data treatment is explained and the model is outlined. cently,Feron et al., [1998]used this dynamicalcoupling. In section 4, results from the inversion are given and a Time averagingof the potential vorticity equation for comparison is made with infrared satellite images. A the upper ocean layer, in which stretchingwas shown summary with conclusionscloses the paper. to be negligible, results in a differential equation for the averagedrelative vorticity in whichthe mean diver- 2. The Ensemble Smoother gence of the eddy vorticity fluxes acts as a sourceor sink. The essential part is that these eddy fluxes can The determination of the generalized inverse can be be determined from the altimeter observations. Con- considered as the estimation of the unknown true model sequently,no parameterizationsappear in the averaged variables •, given the data and the model estimates, vorticity equation. From the averagevorticity field sur- with information about their prior error statistics. In- face geostrophicvelocities and related mean dynamic tuitively, it is clear that the probability density of the seasurface topography can then be simplyderived. The model and the probability density of the data contain utility of the method is establishedusing 'perfect' data, all information needed to calculate the inverse estimate. namely numerical output from the U.K. Fine- Resolu- Using Bayesian statisticsi, one can considerthe proba- tion Antarctic Model. The method appears applica- bility density of the model forecast as prior information, ble to areas of the ocean with strong enoughmesoscale which is 'updated' by the data. This results in a new variability suchas the major westernboundary currents probability density of the model, given the data. The and their extensionsand frontal regionsof the Antarc- procedureis describedin detail by VanLeeuwen, [1998]. tic Circumpolar Current. Quite realistic results were In the context of time-independent problems this idea reported for active regions of the world ocean, using has beenused by Tarantola,[1987] (but slightlymodi- comparisonswith hydrographicobservations. Also, an fied) and Lorenc,[1988]. error estimate could be attached to the new time-mean The unknown state vector • is viewed as the value circulation, so it can be used for quantitative studies. of a random variable •, and the probability density of Feron et al., [1998]showed that the repeatedshedding the data d is interpreted as the conditionalprobability of large rings can now be synopticallyreconstructed as densityf(d[O) of __dassuming • - •. The modelwith a continuous process, by combining the new time-mean its error estimates is regarded as a priori information, signal with the time-varying altimeter signal. and it is usedto assigna densityf(O) to
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