JOURNAL OF GEOPHYSICAL
A new
method
RESEARCH, VOL. 103, NO. CI, PAGES 1343-1362, JANUARY
to determine
the
mean
15, 1998
sea surface
dynamic topography from satellite altimeter
observations
R. C. V. Feron,• W. P.M. De Ruijter, and P. J. van Leeuwen
Institute for Marine and Atmospheric Research, Utrecht University, Utrecht, Netherlands
Abstract. A method is presentedto calculatemean seasurfacedynamic topography
from satellite altimeter observationsof its temporal variability. Time averagingof a
simplifiedversionof the quasi-geostrophic
potential vorticity equation for the upper
ocean layer results in a differential equation for the averagedrelative vorticity in
which the mean divergenceof the eddy vorticity fluxes acts as a sourceor sink.
The essentialpart is that these eddy fluxes can be determined from the altimeter
observations.Consequently,no parameterisationsappear in the averagedvorticity
equation. From the averagevorticity field, surfacegeostrophicvelocitiesand related
mean dynamic sea surfacetopographycan then simply be derived. The usefulness
of the method is establishedusing "perfect" data, namely numerical output from
the United Kingdom Fine Resolution Antarctic Model. The method appears
applicable to areas of the ocean with strong enough mesoscalevariability such as
the major western boundary currents and their extensionsand to frontal regionsof
the Antarctic Circumpolar Current. Quite realistic results are presentedfor active
regionsof the world ocean. Results are comparedwith hydrographicobservations
for the major westernboundary current extensionsof the Southern Ocean. An
important application is to combinethe newly derived averagedflow field with the
observededdy field to derive the total time-varying geostrophicsurfacevelocity
field. As a striking example this is applied to the Agulhas Current retrofiection,
where the repeated sheddingof large rings can now be synoptically reconstructed
as a continuous process.
1. Introduction
pographyr/•. Assuminggeostrophy,r/• can only be used
to computethe time-variable surfacevelocity field. The
The expected accuracyof recent marine geoid mod- possibilityof accuratelyobservingocean variability in
els at scales shorter than about 4000 km is still at the
the mesoscalerange (10-100 days, 50-500 km) has led
decimeter level. This is not adequate for determination
to progressin understanding and mapping the ocean
of the mean global ocean circulation at these length
eddy field [e.g., Cheneyet al., 1983; Wakker et al.,
scales[Chelton,1988; Nerem et al., 1990; Fu et al., 1990; Tai and White, 1988; $hum et al., 1990; Gor1996]. The only direct way to use satellitealtimeter don and Haxby, 1990; Feron et al., 1992]. However,
observationsfor determining the mean global ocean cir- the inability to determine the MSSDT, and thus the
culation is to combine the altimeter observations with
mean flow field, makes interpretation of altimeter oba geoid model with centimeter precisionat all wave- servations very difficult. For instance, it is impossilengths.
ble to distinguish between ring formations and current
A direct consequence
of the inability to extract the meanders, and ring trajectories are hard to study in
MSSDT, r/, is that the high measurementprecisionand regions with strong mean currents. Methods to imaccuracy(3-5 cm) of altimeterscan only be optimally prove interpretation of altimeter time seriesare based
exploited to determine the time-variable sea surface to- on additional information, e.g., other independent ob-
servations. Vazquezet al.
• Now at
Survey Department, Rijkswaterstaat, Delft,
Netherlands
[1990] combinedGeosat
data with observationsof seasurfacetemperature in the
Gulf Stream area. Other studies[e.g., Tai and White,
1988; Willebrand et al., 1990; Gordon and Haxby, 1990;
Copyright 1998 by the American Geophysical Union.
Ichikawa and Imawaki, 1994] combinedhydrographic
data and/or surfacedrifter buoyswith Geosat data to
study rings detached from the mean flow. Kelly and
Paper number 97JC00389.
0148-0227/98/97JC-00389509.00
1343
1344
FERON ET AL'
MEAN SEA SURFACE TOPOGRAPHY
Gille [1990]and Qiu et al. [1991]investigated
the mean cluding sectionthe method, its results, and limitations
flow in the Gulf Stream and Kuroshio Extension, re- are summarized and discussed.
spectively,by fitting a synthetic current's height profile
to Geosat residualheight data along individual tracks. 2. Data
Their resultswere found to be in remarkableagreement
with hydrographic and acoustic Doppler current proThe geostrophicsurfaceflow and seasurfacedynamic
files[e.g.,Kelly et al., 1991; Teageet al., 1990]. More topography,•7, can be decomposedin a time-averaged
recently,Gille [1994]usedthe sametechniquefor map- mostly large-scalepart (• and 5) and a time-variable
ping the Antarctic CircumpolarCurrent. Both the Sub- mesoscale
part (u• and v•),
antarctic
Front and the Polar Front could be determined
and analyzed from Geosat altimeter data.
Another way to improveinterpretation is application
of statistical techniquesthat analyse decorrelationin
time and space[e.g.,Feronet al., 1992].
v
=•+v
•
Two methods are presently in use to estimate the
long wavelengthpart of the MSSDT from altimeter obIf the observedtime series(•'(x, y, t)) are sufficiently
servations. The first method simultaneouslyadjuststhe
long in time, realistic estimates of the time-variable vegravity field and determinesthe MSSDT. This so-called
locity (cross)covariances,
u•u•, v•v•, and u•v•, can be
integrated least squaresapproachis successfulfor wave-
computed(Plate 1). The overbarindicatestime averaglengthslargerthan roughly4000km [e.g.,Marsh et al., ing, in this study over 3 years,e.g., the completeGeosat
1990; Engelis and Knudsen, 1989; Nerem et al., 1990;
Exact Repeat Mission(ERM) data set. Geosatsuffered
Visser,1992].The secondmethodhasbecomeincreas- from data lossin certain regionsduring the third year,
ingly more interestingdue to the very accuratelyknown
orbit of the recentTOPEX/POSEIDON satellitemission. Due to that high precision(3-5 cm in radial position), height observationscan simply be subtracted
from the best availablegeoidmodelto give an estimate
of MSSDT [e.g.,Minsteret al., 1993;Naeijeet al., 1993;
Fu et al., 1996]. This approachis beginningto work
becauseof improvementsin the accuracyof the latest
geoid models. A limiting factor in both approachesis
that the errorsin the gravity model are largerthan the
MSSDT signal for wavelengthssmaller than approximately 4000 km. The short wavelengthpart of the
MSSDT canthereforenot be separatedfrom the gravity
field.
In the next section the observations are described. In
this paper a method is proposedto estimate MSSDT
from satellite altimeter observations of sea surface vari-
ability (section3). It is basedon time averagingof a
simplifiedvorticityequationin whichseasurfacetopography is separatedin a mean and a time-varyingpart
(section2).
The approximationis valid only for oceanareaswith
strong mesoscalevariability such as the major western boundary currentsand the jets within the Antarctic Circumpolar Current. Application of this method
showssurprisinglypromisingresults(section4) ascomparedto hydrographicobservations
in three major western boundary currentsof the SouthernOcean. A more
detailed comparisonbetweenclimatologyand the new
MSSDT fieldsis achievedby comparingmeridionalsections (section6). Section7 showshowmeanand time-
somethingthat should be kept in mind when looking
at the results. These eddy stressterms can be derived
from satellite altimeter anomaliesunder the assumption of geostrophy(Plate 1) and are computedat an
equidistantAx -- Ay -- 0.5ø grid. They hold statistical information
of the mesoscale turbulence
over the
total averagingperiod[e.g.,Hollowayand Kristmannsson,1984;Holopainen,1978;Hoskinset al., 1983].
Gridding has been done with a 1ø decorrelationdistance. Obviously,the 0.5ø grid oversampledthe spatial
scalesGeosat is able to resolve. This oversamplingis
chosenfor computationalpurposes.The spatial derivatives, necessaryto compute the above mentioned eddy
stressterms, are derived over a 1ø spatial distance both
in longitudinal and latitudinal direction. Let • be the
time-variable relative vorticity:
•' =
Ov'
Ou'
Ox
Oy
(1)
The geostrophictime-variable flow is divergencefree.
This allows the relative vorticity eddy flux terms u• •
and v• • to be expressedin terms of the eddy stresses:
=
v,½,
-
-
Oy
-
Ox
+Ou,v,
(2)
Ox
O,v,
Oy
(3)
Computingu'•' and v'•' from (2) and (3) is very efficient and less sensitive to measurement
noise because
variable flow can be combined to determine absolute
the gradients are computed from the time-averaged
time-varying sea surfacetopographyfieldsfrom the al- eddy stress terms. The spatial distribution of these
timetry time series. This is applied to determine ring meanrelativevorticityeddyflux terms(Plate 2, top two
sheddingin the AgulhasRetrofiectionarea. In the con- panels)showsclear inhomogeneities.In such regions
FERON
ET AL.' MEAN
SEA SURFACE
TOPOGRAPHY
1345
30 S
'i..•
360
40S
330
300
50 s
10
o
20
30
50
40
60
70 E
270
UtV•
240
•1o
180
150
-150
-100
-50
0
50
100
150
120
9O
VtV•
30 $
6O
units:
cm2 s-2
50 S
0
10
20
30
40
50
60
70 E
Plate 1. Horizontal eddy stressterms in the Southern Ocean computed from almost 3
yearsof Geosataltimeter data. Oceanregionswith strong mesoscaleactivity correlatewith
largeeddystresses
(unitsarecm2 s-2).
the divergenceof these averageeddy fluxes is nonzero, this Rossby number is of order 1. An estimate of the
so it can act to modify the meanflow (Plate 2, bottom relative importance of stretching is obtained by conpanel).
sideringthe potential vorticity equation for the upper
ocean layer
3.
The
Method
3.1. The Vorticity
Balance
Areas with larger eddy variability are the separation
regions of the major western boundary currents and
their extensions(Plate 1). There the divergenceof the
mean relative vorticity eddy flux has values of order
10-12 s-2 (Plate2, bottompanel).Thisis an orderof
magnitudelarger than vorticity input at the surfaceby
the wind (0 (10-13S
-2) [e.g.,HellermannandRosenstein,1983])and of the sameorderas the advectionof
dt
h
where • is relative vorticity, f is the Coriolis parameter,
and h is the upper layer thickness.If lower layer velocities are relatively small, than it can be shownthat in the
time-averagedform of the potential vorticity equation,
an estimate of the stretchingis given by
p ½,ov
-5p
at _½,ov
at
values: • - 103 m, the density,
planetaryvorticity(/3• = 1.6x 10-12 s-2 for• = 0.1 m for characteristic
s-1 and fi = 1.6 x 10-11 m-1 s-1 is the variationwith p- 103 kg m-3, densitydifference
betweenupperand
the effectof
latitude of the Coriolisparameter). A measurefor the lowerlayer,Ap -- 1 kg m-3. Consequently,
relative importance of advection of relative vorticity is
stretchingcan be estimated from the data. In the areas
the fi Rossbynumber•/l•L 2. With the abovecharac- with large eddy variability this term appears to be of
teristicvaluefor fi and• anda lengthscaleL = l0 s m, order10-14 s-2 (Plate3 andTable1), soit isat leastan
1346
FERON
ET AL'
MEAN
SEA SURFACE
u'zeta'
TOPOGRAPHY
(units:
x 10'9tn/ s2)
30 S
a
..:;•
60
-." 50
40S
40
30
50 S
,,
30
lO
0
40
50
60
70 E
ßx 10'9m/s 2)
(units
v' zeta'
3O S
b
40 S
-10
50 S •
-EO
10
0
20
30
40
50
60
70 E
x 104•s-2)
divergenceof eddystresses (units:
30 S
-30
c
-40
40S
-50
-60
50 S '
10
0
20
30
40
50
60
70 E
Plate 2. The vorticityeddyfluxstress
termsu'•' andv'•' (x 10-9ms-2) in the Southern
Ocean computed from almost 3 years of Geosat altimeter data. The bottom panel shows
the divergenceof these eddy flux stressterms, i.e., (O(u'•')/Ox + O(v'•')/Oy) (units are
X10-14 S-2).
order of magnitudesmallerthan the above-mentioned
processes.
• -
g o•/
g o•/
•, =
f Oy'
f Ox
(8)
Obviously,the above assumptionsare only approxiAveraging(6) in time gives
mately valid in the areaswe consider.It shouldbe consideredas a first step in the developmentof a method,
where the questionto be addressedhere is whether it
leads to reasonableresults. If that is already the casein
o½
•-•
+_o½
v•-•y
+•/3- - ffz
u•7- •ov,•' (9)
this simplecontext,than it isworthwhileto developand In this balance between mean relative vorticity advecrefine further the method and include a more complete tion by the mean flow, planetaryvorticity advection,
of the averageeddy fluxesof relamodel. So the starting point is the vorticity equation and the divergence
tive
vorticity,
the
latter
term isestimatedby satellitealfor the upper layer:
timetry(Plate2, bottompanel).So,withinthismodel
,•(C+ ½'+ f)
dt
=0
(6)
where
d
0
dt -
Ot
0
0
(7)
context a solution can be determined without parameterizing the eddy fluxes.
Using geostrophy,this equation can be written as
a third-order nonlineardifferentialequationin r/ (the
MSSDT):
FERON
ET AL-
MEAN
SEA SURFACE
TOPOGRAPHY
1347
3O S
50S
0
10
-6
-5
20
-4
-3
30
-2
-1
40
0
50
1
2
60
3
4
70 E
5
6
units:
x 10-15tns-2
Plate 3. The •'Orl'/Ot derivedfrom almost 3 yearsof Geosat altimeter data (units are
x 10-ls m s-2).
wherethe two underlinedtermswill be regardedas unknownsthat can be approximatedvia a leastsquares
roy Ox+fOx Oy+/30xprocedure.tiere ,•., •., O•./Ox, and O•./Oy are inig Or/OAr/
g Or/OAr/
tially estimatedfromthe Levitus[1982]climatology.
By
f Oy Ox
f Ox Oy
adding(12) and (13) to (9), the systembecomes
overdeapproximation
forO•/Ox
Instead of directly solving this nonlinear equation, we terminedandtheleastsquares
and
O•/Oy
can
be
determined.
follow an iterative two-step approachwhich first solves
Because
the vorticityequationhasbeenderivedusing
( and than •.
important simplificationsand the climatologyis known
3.2. The Approximate
Solution for the Mean
to be uncertain,wegiveequalweightsto all threeequaDynamic Topography
tions. Solvingthe above set of equationsresults in
new estimatesfor the unknownsconsistingof an optiEquation (9) can be usedto form the followingset of
mal
combination
of the vorticitybalance(whichinclude
equations:
g00A
g00A
the altimeterobservations
of horizontal
eddyvorticity
fluxes)and climatology.
Oncenewvalues
forO•/OxandO•/Oyhavebeendetermined,they are differentiated
with respectto x and
y, respectively,and summedto find Q'
O(j_ O(•.
Ox
(12)
O•
O(•,
Oy
Oy
(13)fromwhich(
Ox
Q- OxOx
t OyOy
can be solvedstraightforwardly
using,
e.g.,iterativemultigridmethods
[e.g.,Wesseling,
1992].
Table 1. Estimated Maximum and Minimum for Different Terms in the Potential Vorticity
Equation
Variable
Low/Noise High/Maximum
Units
u' • v' • • • •
0.05
0.5
m s-1
O-•/Ox,-.,O•/Oy ,.,00•/Ox,.,00•/Oy
•'• •
O•/Ox • O•/Oy • O•'/Ox • O•'/Oy
1 x 10-7
1 x 10-7
1 x 10-•2
2 x 10-•
2 x 10-•
2 x 10-•
s-•
s-•
s-• m-•
1.6 X 10-11
m-• s-•
1 x 10-8
1 x 10-7
ms -2
I x 10-•6
i x 10-•4
I x 10-14
i x 10-•2
m s-2
s-2
•
u• •v•
•
•Ov•/Ot
• o(•'½,)/oy
(14)
FERON
1348
ET AL.- MEAN
SEA SURFACE
TOPOGRAPHY
,
Smoothed initial field (FRAM)
A
30 S
ß'
E60
•50
•40
405
•
-
230
•
220
.....
20
B
30
40
50
210
60E
........ E00
Divergenceof eddy stresses
.•190
160
170
160
150
Cl•
140
130
I1O
c
Best
•,.,•,
1oo
solut, ion
•t.•-
-•....
•
-
. -
oo
30 S
6o
7o
6o
40S
6o
-..
4o
20
30
40
50
60 E
Plate 4. (a) Smoothedinitial field (FRAM) derivedfrom a 2-yearaveragedFRAM dynamic
topography.
(b) The divergence
of FRAM eddyflux stresses
(unitsare x 10-•3 s-2). (c)
New MSSDT solutionfrom the potential vorticky approach(units, seeright-handside fo
vertical colorbar).
The horizontalresolutionis chosenaccordingto the ob- geostrophicflow field in terms of the mean sea surface
servations,e.g., Ax = Ay = 0.5ø. Necessarybound- dynamic topography,we can write
ary conditionsfor this elliptic differential equation are
taken from climatology and prescribedon closedconf OxOx f OyOy
tours wherethe seasurfacevariability equals7 cm. Results of changingthis boundary condition showedmore from which • can be easily solved. The boundary consensitivity to the smoothnessof the contour than to the ditionsfor (16) alsoneedto be givenon the 7-cmvarimagnitude of variability. Those contoursencloseocean ability contour:
regionswhere the oceansignal is large comparedto the
altimeter noiselevel which means that the right-hand
•bound
-- •Lev [variability=7
cm
(1T)
sideof (9) can be determinedwith confidence.
So at the boundarieswe prescribed• derivedfrom the
+g
•bound: •Lev
Ivariability=7
cm
Levitus[1982]climatology.Followingthis two-stepap(15) proach the mean sea surface dynamic topography, •,
The secondstep in the procedureis to derive • from can be estimated as a function of the horizontal coorthe improvedtime-averagedrelative vorticity •. Using dinates z and y. To find • that fulfills both equations
the definitionof the relative vorticity of the stationary (11)-(la) and (10) the above-described
procedurehas
FERON
ET AL.: MEAN
SEA SURFACE
TOPOGRAPHY
1349
OriginalField (FRAM)
A
30 S
"
260
"250
_ .., _..._-----../-'
..
ß
'.
20
30
40
50
60 E
200
Absolute error
B
210
ß
ß----
190
........ IS0
170
160
1150 CM
140
130
o
2
4
0
i
2
6
8
120
3
4
It0
Relative error
c
too
30 S
9O
,..
8O
7O
6O
40S
.
20
30
40
50
40
60 E
Plate 15. (a) Original2-yearaveraged
FRAM dynamic
topography.
(b) Absolute
error
definedas the differencebetweenthe best solutionand the original dynamictopography.
(c)Relative
errordefined
asv/u2+ v2,where
u andv arethegeostrophic
surface
velocities
derivedfrom the absoluteerror in the dynamictopography.
to be repeatedby computinga new•,, •,, O•,/Ox, and
O•,/Oy and followingthe samesolvingstrategy.After
eachiterationthe new• fieldis regardedasthe new (improved)climatologyuntil the solutionhasconverged
to
an • fieldthat in very goodapproximationfulfills(10).
3.3.Testing the Method
purposes. Two years of FRAM surface pressurefields
have been usedto derive eddy statistics, namely the divergenceof the averageeddy fluxesof relative vorticity.
Exactly the sametechniqueswere usedas those usedfor
computingthe eddy statisticsfrom Geosat data. Taking
a smoothedversion of the 2-year averagedFRAM dy-
namictopographyasinitial field (Plate 4a), the solution
strategy as describedabove is applied to the Agulhas
for improvingthe smoothclimatology(suchas Levitus Current Region. Plates 4a-4c showthe smoothedinitial
[1982]),we appliedthe methodto output of the Fine FRAM field, the FRAM eddy divergence,and the final
ResolutionAntarctic Model (FRAM) [FRAM group, solution after applying the method, respectively. Plate
1991]. Severalearlierstudieshaveshownthat FRAM 5 showsthe original FRAM field together with the absoresultscomparewith altimeterdata [e.g.,Feron,1995; lute and relative error. The absolute error is defined as
Lutjeharmsand Webb,1995]. The resultsof suchan the differencebetweenthe original field and the best soeddy-resolvingmodel supply a perfect test for control lution. The relativeerror is definedas x/u2 + v2, where
To test the applicability of the proposed method
1350
FERON
ET AL.:
A
SEA SURFACE
Levitus
20
B
MEAN
30
40
50
60
70
80
90
100
110
120
TOPOGRAPHY
MSSDT
130
140150160170 180 19(•200el0 220230•40 eS0cm
Improved MSSDT (GEOSAT)
Plate 6. (a) The MSSDTfromLevitusrelativeto 1000dbar. (b) NewMSSDTsolution
fromthe potential
vorticityapproach.
Differences
onlyoccurin oceanareaswithstrong
variability,i.e., the westernboundarycurrents.
u and v are the geostrophicsurfacevelocities derived From this test an upper bound of 8-10 cm could be
derived for active ocean regions.
from the absolute error in the solution.
3.4.Measurement
Error
Propagation 4. Application
toWestern
Boundary
An errorof 0.05 m in the altimeterobservations
of Currents
V' will be propagatedto the surfacevelocity fieldsu•
and v•; eddy stresstermsu•u•, v•v•, and u•v•; and mean
In thissectionthe iterativesolvingstrategydescribed
relative vorticity eddy flux terms u• • and v• •. Error abovefor obtainingan approximate
meansurfacedypropagationrules result in 0.07 m s-1 for u• and v•; namictopographyfrom the observededdy fluxesis ap8.1 x 10-s m2 s-2 for u•u•, vtv•, and u•vt;and 1.0 x plied to the most eddy-activeareasof the world ocean.
10-s m s-2 for u• • andvt••. TheseerrorpropagationAfter 30 iterations,wherethe new• is repeatedlyused
estimates are based on computing spatial derivatives to derivea new•, and•, field,the solutionconverges
over 1ø spatial distancesat 45ø latitude. To get some to • as shownin Plate 6b. The climatologic
field from
insight in how these errors translate into errors in the Levitus[1982],whichis usedasboundaryconditionand
final MSSDT, a sensitivitytest wasperformedby using initial field, is shown in Plate 6a
the solutionstrategy describedin the previoussection. In ocean regionswhere strongeddy activity is ob-
FERON
ET AL.- MEAN
A
Levitus
SEA SURFACE
TOPOGRAPHY
1351
MSSDT
".'•
•5o
5O N
.
.- ....
240
230
40N
220
210
200
30 N
-60
-70
-80
B
Divergence
-lO
-20
-30
-50
190
180
of eddy stresses
170
7
160
150
140
130 CM
-6
-5
-4
-3
-2
-1
0
I
2
3
4
5
6
11o
lOO
90
c
Improved MSSDT(GEOSAT)
80
50 N
7O
6O
x..
._
.-
5O
40N
4O
3O
30 N
•o
-80
-70
-60
-50
-40
-30
-20
- 10
Plate 7. (a) The MSSDT in the Gulf Streamareain dynamiccentimeters
fromthe Levitus,
[1982]climatology,relativeto 1000 dbar. (b) The divergence
of the eddyflux stressterms
enlargedfromthe bottompanelof Plate I (unitsare x10-13 s-2); the 7-cmvariability
contouris shownon whichthe boundaryconditionsare prescribed.(c) New MSSDT solution
from the conservation
of potentialvorticity approach(section3); the contourintervalis 10
cm.
served(Plates 1 and 2), the gradientsin the solution Because the method only applies for certain regions
for •, correspondingto surfacegeostrophicvelocities, in the ocean, the major western boundary currents will
are increased. In other ocean areas the eddy vortic-
be studied in more detail. To achieve better compari-
ity fluxesare too small (Plates 7b-11b), and the new son betweenthe climatologyand the improved MSSDT
solution is forced to and thus equivalent to the clima- fields, the Gulf Stream (GS), the KuroshioExtension
tology. Those regionswhere the method appliescorre- (KE), the Brazil/MalvinasConfluence(BMC), the Agspondto the westernboundarycurrentsand their ex- ulhasExtension(AE), and the East AustralianCurrent
tensions and frontal areas in the Antarctic Circumpolar (EAC) are shoxvnseparatelyand enlargedin Plates 7Current. The relevanceof the new results(Plate 6b) 11.
The Gulf Stream is probably the best investigated
comparedto MSSDT fieldsdeterminedfrom simultaneousapproximationof the gravity field and the MSSDT westernboundarycurrentof the world ocean[e.g.,Fois that they containthe total variety of spatial scales, fonoff, 1981; Watts, 1983]. Gulf Stream meandering
from 200 km to the very large scales.
including warm and cold core ring formation has been
1352
FERON
ET AL.-
A
MEAN
Levitus
SEA SURFACE
TOPOGRAPHY
MSSDT
25O
*'
40 N
240
230
220
30 N
---{200
210
11o
120
130
B
140
150
160
170
190
180 E
Divergence of eddy stresses
170
t 160
' -
150
140
130
-6
-5
-4
-3
-2
-1
0
I
2
3
4
5
6
CM
IlO
10o
9o
C
8O
ImprovedMSSDT
(GEOSAT)
7O
•
4ON
6o
5O
4O
30 N
:-'-
"" ø
3O
,.
ß
2O
110
120
130
140
150
160
170
180 E
Plate 8. (a) The MSSDT in the KuroshioExtension
in dynamiccentimeters
fromthe
Levitus[1982]climatology,
relativeto 1000dbar. (b) The divergence
of the eddyflux stress
termsenlarged
fromthebottompanelofPlateI (unitsarex10-la s-2); the7-cmvariability
contouris shownon whichthe boundaryconditionsareprescribed.(c) New MSSDT solution
from the conservation
of potentialvorticity approach(section3); the contourintervalis 10
cm.
studiedextensivelyby hydrography,
drifters,satellite The Gulf Streampathseemsto be stationaryuntil the
imagery,and altimeter observations
of the seasurface current reaches65øW, whereafterthe standarddevia[e.g.,Olsonet al., 1983;Halliwelland Mooers,1983; tion (Figurela) increases
significantly.
This indicates
Maul et al., 1978; Cornilion, 1985; Kelly and Gille, an north-southincreaseof the envelopeof Gulf Stream
1990; Zlotnicki,1991]. From the Florida Straitspast positions.Thesemodelresultssomewhatcontradicta
CapeHatterasthe Gulf Streamentersdeepwaters.At studyof Cornilion[1985],whofoundfromsatellitetemapproximately70øW the meandersof the Gulf Stream
start to increasein amplitude. After 62øW, where the
Gulf Stream reachesthe New England Seamounts,the
meanderingcontinuesto increase.Figure l a showsthe
1-yearmeanpositionof the Gulf Streamasderivedfrom
a high-resolution quasi-geostrophicnumerical model
whichhas beenassimilated
with TOPEX/POSEIDON
perature imagesthat the envelopewhich constrainsthe
Gulf Stream positionsdid not increasebetween68ø and
58øW. Relevantfor our study is that the cross-frontal
lengthscaleof the envelopedefineshow strongthe instantaneous
Gulf Streampositionwill be smoothedby
averagingover a long time interval. The new approxi-
mationfor • (Plate 7c) showsa moreor lesszonalGulf
altimeterdata (formoredetails,seeBlayoet al. [1994]). StreamfromCapeHatterasto 63øW.At this pointthe
FERON
ET AL-
MEAN
SEA SURFACE
Levitus
TOPOGRAPHY
1353
MSSDT
260
30 S
•40
•os
•oo
50S
190
-60
-70
-50
-40
-30
-20
-10
0
180
B
Divergence of eddy stresses
170
160
150
140
130
CM
120
11o
3
4
5
6
9O
8O
c
Improved MSSDT((IEOSAT)
30 S
7O
.,
.
-
.
.
..,
5O
40S
4O
3O
20
50S
-70
-60
-50
-40
-30
-20
-10
0
Plate 9. (a) The MSSDT in the Brazil/MalvinasConfluencein dynamiccentimetersfrom
the Levitus[1982]climatology,
relativeto 1000dbar. (b) The divergence
of the eddyflux
stresstermsenlarged
fromthe bottompanelof Plate 1 (unitsare x10-•3 s-2); the 7-cm
variability contouris shownon which the boundaryconditionsare prescribed. (c) New
MSSDT solutionfrom the conservationof potential vorticity approach(section3), the
contour
mean Gulf Stream
interval
is 10 cm.
bends a few hundred
kilometers
to
the north whereafter it follows a zonal path to the east
along the 40øN latitude band. This Gulf Stream pattern is in remarkablegood agreementwith the findings
of recent other studies designedto determine the mean
and White, 1990; Qiu et al., 1991]. Annual and interannual variability appears to be a prominent element of the KE and was found in temperature data
[e.g., Mizuno and White, 1983], direct current measurementsaccompaniedwith hydrographicobservations
Gulf Streamposition[e.g.,Kelly and Gille, 1990; Glenn [e.g.,Schmitzet al., 1987]and satellitealtimeterdata
et al., 1991;Blayo et al., 1994](Figurela).
[e.g., Tai and White, 1988; Qiu et al., 1991]. Figure
The KuroshioCurrent separatesthe southerncoastof
lb showsthe Kuroshio mean position derived from 2.5
Japanat 140øEand 35øN.After separationit is named years of Geosat altimeter data. The position is digthe Kuroshio Extension, which is characterized, as the itized from Quiet al. [1991],who fitted a synthetic
Gulf Stream east of approximately 70øW, as an east- current's height profile to independentsatellite tracks.
ward flowinginertial jet with large amplitude meanders The Kuroshio Extension differs from the other western
and warm and cold core ring formations. Mesoscale boundary currents in the sensethat it has two modes
perturbationsgenerallypropagatewestward[e.g., Tai between which the Kuroshio can switch, one with a
1354
FERON ET AL- MEAN SEA SURFACE TOPOGRAPHY
Levitus
MSSDT
30 $
24O
220
40S
•1o
,,
•oo
50S
10
20
30
40
5o
70 E
190
160
B
Divergence of eddy sireases
170
160
150
140
...
130 CM
1180
-6
-5
-4
-3
-2
-1
0
I
2
rio
5
3
6
IOO
9o
8O
c
Improved MSSDT (GEOSAT)
7O
3O S
6O
5O
40S
4O
3O
50 $
•
0
10
20
30
40
50
60
2O
70 E
Plate 10. (a) The MSSDT in the AgulhasExtensionin dynamiccentimetersfrom the
Levitus[1982]climatology,
relativeto 1000dbar. (b) The divergence
of the eddyfluxstress
termsenlarged
fromthe bottompanelofPlateI (unitsare x10-13 s-2); the7-cmvariability
contourisshownonwhichthe boundaryconditions
areprescribed.(c) New MSSDT solution
fromthe conservation
of potentialvorticityapproach(section3); the contourintervalis 10
cm.
more northern trajectory than the other. This bimodal- pal Investigators,1990]. An exampleof hydrographic
ity diffusesthe definitionof a long-termmean current observationsfrom the Brazil/Malvinas Confluencecan
position; that is, the climatologywill be a smoothed be found in Figure le. The new approximation(Plate
representation of the two Kuroshio modes. The new 9c) for • revealsa well definedconfluence
positionbeapproximationfor • (Plate 8c) revealsthe KuroshioEx- tween 39ø and 42øS with a quasi-stationarywave-like
tensionhas its maximumnorthwardpositionat approx- pattern. It compareswell with resultsfound in hydroimately 150øE,whereafteris slightlyturns to the south. graphicobservations
for Brazil Currentextension[e.g.,
Surfacecurrentsare clearlyenhancedcomparedto the Confluence
Principal Investigators,1990]. The waveLevitus climatology.
like pattern seemsa realistic phenomenonand is also
In the Brazil/Malvinas Confluenceregionthe Brazil observedin other western boundary regions. Compar-
Current and the Malvinas Current convergeand form ing the Levitus[1982]climatology(Plate 9a) with the
newapproximation(Plate 9c) showsthe increaseof hortween38ø and 46øS [e.g., Legeckisand Gordon,1982; izontal resolution in the MSSDT field.
Olsonet al., 1988; Gordon,1989; ConfluencePrinciWhen the Agulhas Current runs out of western
a strong thermal front which has been observed be-
FERON ET AL.- MEAN SEA SURFACE TOPOGRAPHY
Levitus
1355
MSSDT
•o
•40
30 S
•30
40S
200
12o
11o
13o
14o
15o
16o
17o
18o E
190
180
Divergence
of eddy stresses
170
•
•)
160
150
140
130
CM
120
11o
-6
-5
-4
-3
-2
-1
0
I
2
3
4
5
6
9O
Improved
M$SDT
(GEOSAT)
c
8o
70
30 S
õo
ß
/
40
z[OS
c
30
2O
110
120
130
140
150
160
170
180 E
Plate 11. (a) The MSSDT in the East AustralianCurrent in dynamiccentimetersfrom the
Levitus[1982]climatology,relativeto1000dbar. (b) The divergence
of the eddyflux stress
termsenlarged
fromthebottompanelofPlateI (unitsare x10-la s-2); the 7-cmvariability
contouris shownon whichthe boundaryconditionsare prescribed.(c) New solutionfrom
the conservation
of potentialvorticity approach(section3), the contourintervalis 10 cm.
from the AgulhasCurrent (compareFigboundary, it separates and makes a large almost 180ø measurements
anticyclonic turn which is generally referred to as the ure lc). Also,the path of the AgulhasCurrent is clearly
AgulhasRetrofiection[e.g., Ou and De Ruijter, 1986; visible. Someevidencefor a large meander (wave-like
Boudra and Chassignet,1988; Lutjeharms and van Bal- pattern whichmay be relatedto bottom topography)in
legooyen,1988]. The AgulhasReturn Current carries the Agulhas Extension downstreamfrom the retroflecmost of the Agulhas water back into the Indian Ocean
(seeFigure lc). In the AgulhasExtensionthe new ap-
tion can be observed
in Plate
10c.
The East AustralianCurrent (Plate 11) is a relatively
weak surface current. It flows southward along the contration of the AgulhasCurrent (Plate 10c) in the region tinental slope and usually separatesfrom the coast bewhereit retrofiects[e.g.,Harris et al., 1978;Gordonet tween 31ø and 33øS and forms a large anticyclonic me-
proximation for • revealsa more intensewestward pene-
al., 1987;Lutjeharmsand van Ballegooyen,
1988]. The
Agulhas Retrofiection, which is totally absent in the
Levitus climatologic fields, is clearly present in the new
solution between 20ø and 25øE. This position for the
Agulhas Retrofiection is also observedin hydrographic
anderwhichmay extendsouthwardasfar as 38øS[e.g.,
Mulhearn,1987](seeFigure ld). The new approximation evidently has more structure in the time-averaged
flow pattern. The results shown in Plate 1l c agree with
the most likely position of the East Australian Current
1356
FERON ET AL' MEAN SEA SURFACE TOPOGRAPHY
140
10oE
30
E
150E
15 ø
20 ø
160
25 ø
30 ø
E
35 ø
ø
OOE ....
'
•5 o
'
'
'
,
'
'
::iii!111iiiiii
.......
2e
aa..
ZOø
'
'
40
ø
,
d
2.1o
[.:.o:.:.•:.!•:.
31' - Smoky Ca•:'•:':•':'i•
..;:•:•:•:•:;:;:•:;::
,
'
ø
2.40
% .....
Cape
,
35
-
60øW
1.90
'
2.30
•_•.__••oO
.55 ø
50 ø
'...............
'•:?ii?,111
................
_
'• ' ,.,;,• e
.o..f
t
•b.w
......
•
....
sb
....
Figure1. (a)GulfStream
climatology
[Levitus,
1982]
withitsmean
position
(thickline),
derivedfroma high-resolution
quasi-geostrophic
modelwhichhasbeenassimilated
with
TOPEX/POSEIDON
data,superimposed.
(b)Kuroshio
Current
climatology
[Levitus,
1982]
withitsmeanposition
(thickline),derived
byfittinga synthetic
Gaussian-shaped
velocity
profile
though
2.5yearsofGeosat
altimeter
data(digitized
fromQiuet al. [1991]),
superimposed.
(c) Theseasurface
dynamic
topography
in theAgulhas
Current
relative
to the
1500-dbar
surface
[afterGordon
et al.,1987].(d) Theseasurface
dynamic
topography
in
the East AustralianCurrentrelativeto the 1300-dbarsurface[afterBolandand Church,
1981].(e)Theseasurface
dynamic
topography
intheBrazil/Malvinas
Confluence
relative
to the 1500-dbar
surface
[afterGordon,
1989].All heights
aregivenin dynamic
meters
FERON
ET AL.: MEAN
250 ,I,..I.,.I,.,I,.,I,..I,..
I,,.
,
SEA SURFACE TOPOGRAPHY
300
I,
,..I,.,I,,.I.,,
:
ß
250 ...............
I..,
:
!
,
,
,
200- ...... }............ C............ {............ -:............. •'............ •............ {............ 4......
1357
I...
I,.,
b
,
Ku.:roshio
Ektension
i153øE).'"
i .............. i.............. i............... • .............. • .............. •..............
,
,
:
:
.
.
GuifStrea•.':
(62øW."
)
,
,
,
.
.,• 15o•
200
....
•.............
T..............
[..............
tOO.
ß
50....... •............•............'..............:..............'"
,
'
ß
.
|
ß
ß
ß
:
0- -........ LevitusMSSDT
•
..................................................
•......
ImprovedMSSDT
-50 ' i ' ' ' i ' ' ' i ' ' I i ' '' • ' ' ' • '' ' • ' '' • '
I
26
30
I
34
I
501.
t• Levitus
Imprøved
MSSDT
II..........
t[ .........
MSSDT
I
•
38
I
I
I
I
I
I
I
I
30
32
34
36
38
40
42
44
Latitude
Latitude
200 ' ' X•h•s
{ ....
] ....
Retroflectioh
[
- - Improved
MSSDT
Ic
150-
2øø/
I Ocean
.... I .... I .... I .... I .... /
4 ....
Indiafi
ACC
• 150
.•................
i.................
:• lOO
• too.
ß
50
50
-35
-40
-45
-50
-25
-30
-35
-40
Latitude
•8o
....
I ....
I ....
Bi'azii Malvilias
-45
-50
-55
Latitude
I ....
I ....
'
:
•
t60
.........
• ....
i..Confluenœ:o
................
]
Improved
MSSDT
200]
, , , /•a•t•u•t;alia,
•u;re•t
.........
[f
:
180
i....................
i....................
i.....................
'
'5•....••..
: .........
Levitus
MSSDT
............................................................
140
............
"at20
..............
:::.,.;i[
:...-:51•
i....................
i....................
{.....................
•too
.....................
ii..........
:::
......•-----• ...........
i.....................
::71
40 I
-35
-40
,
,
•
'
-45
-50
-55
-60
Latitude
tOO
-25
-30
-35
-40
-45
Latitude
Figure 2. Meridionalsectionof (a) the Gulf StreamMSSDT at 62.0øW and (b) of the
KuroshioExtensionat 153.0øE.The dashedand solidlinesshowthe Levitus[1982]climatologyand the new solutionfrom the potentialvorticity approach(section3), respectively.
Meridionalsectionof the AgulhasCurrent system(c) at 24.5øE and (d) at 54.5øE. (e)
Meridionalsectionof the Brazil/Malvinas Confluenceat 50.0øW. (f) Meridionalsectionof
the East Australian
Current
at 157.5øE.
-50
1358
FER.¸N
ET
AL.-
MEAN
SEA
SURFACE
TOPOGRAPHY
totalseasurfacetopography
(week29)
250
•40
"230
220
ElO
totalseasurfacetopography(week 30)
•
2oo
-
150
140
totalseasurface
topogra...phy
(week31)
t 3o
CM
120
11o
100
90
80
70
total
sea
surface
to.o_,po,.graphy•(week
32)
'30S •0 C.3k-.•
, •._' .
60
50
40
30
20
50 S
....
0
10
20
30
40
50
60
70 E
Plate 12. A time sequence
of the absolutedynamicheightin the AgulhasRetroflectionat
weeklyintervalsdetermined
by applyingthe proposed
methodto Geosataltimeterheight
observations.
Ring sheddingcan be observed.Analysisof the 3-yearobservational
period
shows
that 12 similarring-shedding
eventsoccurred.Time is relativeto November
8, 1986,
and the contour interval is 10 cm.
derivedfromsatelliteinfraredimagery[Mulhearn,1987] Streamandthe KuroshioExtension,two in the Agulhas
andhydrography
[BolandandChurch,
1981].
Extension,
andoneeachin theBrazil/Malvinas
Conflu-
5. Meridional
enceand East AustralianCurrent (Figure 2). The new
MSSDT fieldsare calculatedover the total ERM period
of Geosat(fromNovember1986to September1989).
Cross
Sections
The meridional
section in the Gulf Stream is chosen
A more detailed comparison can be made between at 62øW (Figure 2a). The mean Gulf Streamlatitude
climatology and the improved MSSDT fields by analyz- derivedfrom Blayo et al. [1994]is markedin the plot,
ing meridional sectionsof dynamic topography. For this which is the position where the MSSDT gradient has
purpose, six sectionswere chosen,one each in the Gulf its maximum.
FERON
ET AL.: MEAN
SEA SURFACE TOPOGRAPHY
Figure 2b shows the meridional section though the
Kuroshio
Extension
at 153øW.
The mean Kuroshio
lat-
events could be determined
1359
of which Plate 12 shows one
example. Thesesheddingeventscorrespondto the dom-
itude from Qiu et al. [1991]is markedin the plot. The inant EOF modesas analyzedby Feron et al., [1992].
Besides 12 ring-sheddingevents the following picture
of what happensin the Agulhas Retrofiection emerges:
The Agulhas Current occasionally interacts with rethe AgulhasRetrofiection(Figure 2c) the new method cently formed rings. Over the 3-year observationalpeshowsa realistic more westward penetration of the Ag- riod this strong interaction resultedin severalreabsorpulhas Current which is not present in the Levitus cli- tion events(we countedsix of them) whichmeansthat
one ring is in fact sheddedtwice. Also, smallerrings are
matology.
Improvements in the MSSDT at the 54.5øE section occasionallyformed. The observedtranslation speedof
shownin Figure 2d are clearly confinedto the Antarctic largeAgulhasringsis typically 8 cm/s just after separaCircumpolar Current, roughly between 37ø and 44øS. tion. Their characteristicspatial scaleis approximately
The north-south gradient of the heights is increased 300 km.
with an approximate factor of 2. Maximum surface
new MSSDT solution suggestsa slightly more north-
ward front position.
In the crosssection at 24.5øE which is right through
geostrophicvelocityis 8 cm/s and 20 cm/s in the cli-
7. Summary
and Discussion
matology and new solution, respectively. Such a result could be expected as the Levitus climatology is
In this study we proposed, applied, and analyzed
a mean over unevenly distributed samples and spread
a simple method to improve the smooth climatologic
over more than 50 years in time. Climatology over the
mean sea surfacedynamic topography with satellite almuch shorter Geosat period determined by our method timeter observations. We have shown that in areas with
shouldlead to sharpermean jets, given the (in situ)
large eddy variability, vorticity input by the wind and
observedjet like nature of the ACC in this area [e.g.,
stretching are small compared to the divergenceof the
Olberset al., 1992].
Compared to the Levitus climatology the center of
the ACC (or its front) is shifted to the north by approximately 100 kin. This is also observed in spatial
fieldsof'the MSSDT (Plate 10).
The
meridional
section
in the
BMC
is chosen
at
50.0øW (Figure 2e). In the improved MSSDT the
Brazil/Malvinas Extensionis locatedat approximately
40ø-42øS,which is in agreementwith hydrographicdata
[e.g.,Confluence
PrincipalInvestigators,
1990].Trans-
relative vorticity stress and advection of relative and
planetary vorticity. Starting from a simplified vorticity
equation, we have presenteda method to better approximate the time-averagedflow field in areas with large
enough mesoscalevariability. The model includes di-
vergenceof the relative vorticity stress(measuredby
altimeter), advectionof relative vorticity, and advec-
tion of planetary vorticity. The proposedmethod only
applies to ocean regionswith strong mean currents and
sufficienttemporal variability suchas the major western
lated into surfacegeostrophicflow the climatology of 7
boundary currents and their extensions.
cm/s is increasedto 15 cm/s for the potentialvorticity
Application of the method to the five major westapproach(Figure 2e).
ern boundary current systems, the Gulf Stream,
Figure 2f showsthe sectionthrough the EAC which
the Kuroshio Current, the Agulhas Current, the
is chosen at 157.5øE. The current is located between
32ø and 34øS with a surfacegeostrophicvelocity of 11
Brazil/Malvinas Confluence,and the East Australian
Current, showspromising results. The new results con-
cm/s. Climatologygivesa surfacevelocity of only 5
tain the total variety of spatial scales, from 200 km
cm/s. The resultscomparewell with the averageposito the very large scales. On averagethe new solution
tion of the TasmanFront, derivedby Mulhearn[1987],
from satellite thermal imagery between 1982 and 1985. results in geostrophicsurfacecurrents which are more
narrow and a factor of 2 strongerthan Levitus climatol-
6. Combining Mean and Time-Varying
Flow Fields: With Application to
Agulhas Ring Shedding
Adding the computed MSSDT to the observedrelative sea heights gives absolute dynamic sea surface
heightsat every desiredtime. A very striking application can be shownthe Agulhas Current Retrofiection
region. Plate 12 showsa time sequenceof sea surface heights in the Agulhas Retrofiection. It reveals
the formation of a large Agulhas ring. From applying
our method to the 3-year Geosat observationalperiod
in the Agulhas Retrofiection, 12 major ring-shedding
ogy. To what degreethe new resultsare affectedby the
boundary conditionstaken from the climatology, which
includesthe assumptionof a level of no motion, is under
investigation.
Application of the method to the Agulhas Current
retrofiection region revealedfor the first time a full sequenceof actual ring-sheddingevents over the Geosat
period. So far, the lack of a mean current field precluded
suchan analysis(e.g., Plate 12). It revealedthat rings
are regularly reabsorbed and then shed again. Over
the period from November 1986 to September 1989 a
net amount of 12 Agulhasringswas pinchedoff, which
is 30% lessthan earlier estimates[Gordonand Haxby,
1990;Feron et al., 1992].
1360
FERON
ET AL.: MEAN
SEA SURFACE
TOPOGRAPHY
The purpose of the present study was to investigate Boudra, D.B., and E.P. Chassignet, Dynamics of Agulhas retrofiection and ring formation in a numerical
whether the simplifiedvorticity equation could be used
model, 1, The vorticity balance, J. Phys. Oceanogr.,
to obtain reasonableand possiblysurprisingresults in
18, 280-303, 1988.
large parts of the SouthernOcean. By comparingthe
resultwith hydrographicobservations
we concludethat Chelton, D.B., WOCE/NASA altimeter algorithm
workshop, U.S. WOCE Tech. Rep. 2, 70 pp., U.S.
indeedthe vorticity-basedmethodgivesrealisticresults.
Moreover, the method was tested by applying it to out-
Planning Off. for WOCE, CollegeStation, Tex., 1988.
J.G. Marsh, and B.D. Beckley,
Global mesoscalevariability from collinear tracks of
SEASAT altimeter data, J. Geophys.Res., 88, 4343-
put of the United KingdomFine ResolutionAntarctic Cheney, R.E.,
Model [FRAM Group,1991].
In this study,eddy stresseshavebeen determinedby
4354, 1983.
averagingover 3 years, i.e., the completeGeosatExact Repeat Mission data set. If averagingover, say, Confluence Principal Investigators, CONFLUENCE
I year would be sufficientto determineeddy stresses 1988-1990: An intensive study of the Southwestern
accurately,for every separateyear a MSSDT can be
Atlantic, Eos Trans.AGU, 71(41), 1131-1133,1137,
1990.
determined. Then it allowsthe investigationof interannual (long-term)changes
in the flowfield. Furthermore, Cornilion, P., The effectof the New England Seamounts
usingthe samemethodwith TOPEX/POSEIDON obon Gulf Stream meanderingas observedfrom satellite
servationswill give insight in the solution'ssensitivity
IR imagery, J. Phys. Oceanogr.,16, 386-389, 1985.
to the eddy stressterms derivedby different satellites Engelis, T., and P. Knudsen, Orbit improvement and
averagedover different years.
determination of the ocean geoid and topography
Given a density profile, geostrophicvelocities may
from 17 days of SEASAT data, Dep. of Geod. Sci.
now be computed at every depth. The classicproband Surv., Ohio State Univ., Columbus, 1989.
lem of assuminga level of no motion, at great depth, Feron, R.C.V., The Southern Ocean westernboundary
maythereforebe no longernecessary.
The newMSSDT
currents: Comparison of Fine Resolution Antarctic
improvesthe difficult interpretationof sealevel anomaModel results with Geosat-altimeter data, J. Geolies alone. The exchangeand redistributionof momenphys. Res., 100, 4959-4975, 1995.
tum and energybetweeneddiesand the mean flow may Feron, R.C.V., W.P.M. De Ruijter, and D. Osbe studiedin detail (Plate 12). Fluxesand transports kam, Ring-sheddingin the Agulhas Current System,
acrossthe Antarctic CircumpolarCurrent (of whichthe
J. Geophys.Res., 97, 9467-9477, 1992.
meanpositionis determinedby this method)maybe es- Fine Resolution Antarctic Model (FRAM) Group,
timated particularly if the surfacefieldsare coupledto a
An eddy-resolvingmodel of the Southern Ocean,
diagnostic,multilayer, eddy-resolvingnu•nericalmodel.
Eos Trans.AGU, 72(15), 169, 174-175,1991.
The expected accuracyof the marine geoid at scales
Fofonoff,N.P., The Gulf Streamsystem,in Evolutionof
shorter than about 1400 km is not adequate for deterPhysicalOceanography,
editedby B.A. Warrenand C.
mination of the mean global ocean circulation at these
Wunsch,.,pp. 112-139, MIT press,Cambridge,1981.
lengthscales[Chelton,1988;Neremet al., 1990]. The Fu, L-L., C.J. Koblinsky, J-F. Minster, and J.
only direct way to use satellite altimeter observations
Picaut, Reflecting on the first three years of
for determining the mean global oceancirculation is to
TOPEX/POSEIDON, Eos Trans.AGU, 77(12),109,
combine the altimeter observationswith a geoid model
111,117, 1996.
with centimeter precisionat all wavelengths. Thus, as Gille, S.T., Mean sea surface height of the Antarclong asthere is no accurategeoiddownto the mesoscale, tic Circumpolar Current from Geosat data: Method
the resultspresentedin this study may be a good alterand application,J. Geophys.Res., 99, 18,255-18,273,
native.
Acknowledgments.
We like to thank Roger Haagmans for preprocessingthe altimeter data at Delft University of Technology. This investigation was partly funded by
the SpaceResearchOrganizationNetherlands(SRON) and
NOPII.
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[email protected])
W. P.M.
De Ruijter and P. J. van Leeuwen, Institute
for Marine and AtmosphericResearch,Utrecht University,
Princetonplein 5, NL-3584 CC Utrecht, Netherlands.
(ReceivedFebruary13, 1995;revisedAugust 12, 1996;
acceptedNovember7, 1996.)