VOL. 85, NO. C1
JOURNAL
OF GEOPHYSICAL
RESEARCH
JANUARY
20, 1980
Ocean Transientsas Observedby Geos 3 Coincident Orbits
A.
L.
GORDON
AND
T.
N.
BAKER
Lamont-Doherty GeologicalObservatoryof Columbia University
Palisades, New York 10964
Ocean mesoscaletransientsare revealed in Gees 3 altimeter data. The transientsare brought out by
inspectionof the differenceswithin groupsof coincidentorbits in the westernsubtropicalNorth Atlantic
Ocean. Each of the five groups,used in the study, is composedof three individual Gees 3 orbits, lying
within 2 km of the mean orbit of the group. The differenceof each orbit from the group mean contains
sea level transientsand instrumentalnoise;the steady stategeoid is removed.The noise dominates the
spectrumbelow 200 km wavelength,whereasoceanmesoscale
transientfeaturesdominateabove200 km.
At the low frequencyend of the spectrathe time separationof the individual orbits may attenuate the
signalof the long wavelengthtransients.
The total relief of the mean climatic sea level is approximately 2.0 m (relative to 1000 dbar [Storereel,1965]). Superimposedon mean sealevel, which definesthe mean horizontal
currentsby the geostrophicrelation, are tidesand more slowly
varying sea level transients,which may be conceptualizedas
eddies [Mode Group, 1978; Dtiing, 1978]. The non-tidal sea
level features with spatial scalesfrom the Rossby radius to a
scale small compared to the large scale gyre circulation
(roughly 100-1000 kin) are consideredthe mesoscale.
The associatedmesoscalecirculation is also in near geostrophicbalance. Some mesoscalefeatures may be in steady state, so are
not necessarilytransients, nor are all transientsmesoscale,in
that the seasonalvariation of the large gyresare not mesoscale
in size. In this study we are concerned with transient mesoscale features.
Wyrtki [1975] showsthe fluctuationsin dynamic height of
the sea surface relative to 500 dbar, superimposedon the seasonal scale variations, are typically 10 dynamic centimeters
(dy cm) or more in the western North Pacific, dropping to
about 6 dy cm in the east. Using Ocean Station time series
data, Wyrtki shows standard deviation in the monthly dynamic height in the western North Pacific at Victor (34øN,
164øE)varies between 10 and 20 dy cm, while further east at
November (30øN, 140øW) standard deviation drops to less
than 5 dy cm.
Bernsteinand White [1974, 1977], Dantzler [1976, 1977], and
Roden[1977] also showthe transientsin the westernregion of
the subtropicalgyre to be more energeticthan those of the
east. Kim and Rossby[1979] suggestthat the higher transient
level in the west may be associatedwith spin-off eddies of the
western boundary current, superimposedon the mesoscale
transients characteristic
of the ocean interior.
Analysisof ship drift data from merchantshipsby Wyrtki et
al. [1976] indicatesthe mean kinetic energyis about equal to
the eddy kinetic energy in the western margins of the subtropical gyres, but lessthan one tenth of the eddy kinetic energy in the central and easternregionsof the subtropicalgyre.
This is similar to the resultsof Roden [1977]. Roden, using
hydrographicdata in the North Pacific, showsthe transient
baroclinic
flow relative to 1500 dbar is about 10 times that of
by expendable bathythermograph traces, find the predominant
horizontal
scale west of 170øW in the North
Pacific
is near 900 kin, closer to 600 km in the east.
The dynamic height range and horizontal scale associated
with the Mode mesoscalefeature observedduring the Mode
projectis about 20-30 dy cm and between400 and 500 kin, respectively(Mode-I Atlas Group[ 1977],Figure 2.7--sea surface
dynamictopographyrelative to 1500dbar; alsosee Voorhiset
al. [ 1976] and Dantzler [1976]--note the structurefunction
peak at 200-250 km in Dantzler's Figure 7 correspondsto half
of the predominant length scaleand apparently drifted westward at typical velocitiesof 2-3 kin?day [Mode Group, 1978]).
The objectof this studyis to determineif the satelliteradar
altimeter of Geos 3 can be used to study the statisticsof sea
level mesoscaletransients.Huang et al. [1978] have shown the
Geos 3 altimeter detectsGulfstream spin-offeddies.
THE
DATA
Geos 3, launched in April 1975in an orbit carrying it to 62ø
latitude, possesses
a radar altimeter [Leitao et al., 1975]. The
altimeter pulse, emitted by the satellite each 0.1 s (intensive
mode), is reflectedfrom the oceansurfaceback to the satellite.
The return pulse,elongatedby the varied surfaceshapedue to
waveswithin the 4 km footprint of the pulse, is usedto obtain
the altitude
of the satellite above the local mean ocean sur-
face.
Knowledgeof the distancebetweenthe orbit and the earth's
reference spheroid, determined independently, allows determination of the difference between sea surfaceand spheroid.
Removal of geoid determinesthe sealevel height. Variation in
the sea level relative to the geoid includesmean and transient
circulation, tides, and atmosphericeffects.
The uncertainty in the geoid shapeand orbital errors (distance above the spheroid) are larger than the variations in sea
level; in addition, the random pulse by pulse noiseof the Geos
3 altimeter is about 72 cm [Martin and Butler, 1977]. Hence it
is not possibleto useGeos 3 to directly determinethe sealevel
shape relative to the geoid to high enough accuracyto study
specifictransientevents.As shownbelow the statisticalcharacteristicsof the larger transients are revealed when differ-
the mean flow. The dynamic height expressionof the tran- ences of coincident orbits are considered.
sients,describedby Roden [1977], peak to trough, range from
DATA PROCESSING METHODS
10 to 30 dy cm, with a wave length of 400-600 kin. Bernstein
Orbits were selectedthat were nearly coincidentin position.
and White [1974], studyingthe isothermtopographyobserved
In each group all of the orbits are lessthan 2 kin. from the
mean orbit for the group. The groups used in this study are
Copyright¸ 1979by the American GeophysicalUnion.
Paper number 9C 1356.
0148-0227/79/129C-
1356501.00
502
GORDON
41•BO
-75
AND BAKER: BRIEF REPORT
-6o42
-70
503
60
a5•.(201
•
•
r•
em(2o)
40
A..•(20)
"•
•(19)_••
•
z
+
t•9{19)
•(I)
+x•U8)
•(9)
2 0
•(,9)
•
• •
+.7(9)
•+
/•
'•(•)
+•(T8)
••
+
+•(I)•
o.o
o'.s
,'.o
,'.s
a'.o
DISTANCE FROM MEAN OR•IT
Fig. 2. Total spectralenergyfor each orbit of each of the five groups
as function of distan• from the mean position of the group.
i
i
;:)3-E!O
i
i
!
-7S
i
i
i
-70
i
i
!
!
geoid from the data sincevariationsin the geoid on a scaleof
2-4 km are minor. This is supportedby Figure 2, which is a
plot of the total energy in the spectrum of each orbit versus
distance of each orbit from the mean orbit position for that
group. This figure showsno systematicincreasein energy with
increasing distance from the mean orbit position, which
I
Fig. 1. Positionof the fivegroupsof orbits,eachcomposed
of three
individual orbits (see Table 1), used in this study.
given in Figure I and Table 1. All groupshave 3 orbits. The
raw data contained spikes(more than 2 m differencefrom the
previous good point, spikes are generally composed of 5
points or less)which were removedby linear interpolation between the good data points immediately adjacent to the spike.
All orbits usedwere sampledwith the satelliteoperatingin the
intensive mode, which collecteddata at the rate of one sample
every 0.1 s. That resulted in a spacingof data points slightly
greater than 0.69 km. Each raw orbit was then low-pass filtered using an Ormsby [1961] convolution filter designed to
passwavelengthsgreater than 10 kin. The low-passedorbits
for each group were then averaged to produce a mean orbit
for that group. This mean orbit was then subtractedfrom each
low-passedindividual orbit in the group to produce residuals
which would contain only ocean transients and instrumental
noise.We believe that this method removesvirtually all of the
TABLE I.
would
have been the case if the differences
odic fluctuations.
Possible sources of trends in the sea level re-
siduals are the long wavelength variations introduced by
tracking errors,tides and atmosphericweather systems.These
have been removed to enable inspectionof quasi-geostrophic
mesoscaletransients of sea level. In the wavenumber domain,
spectra were smoothed with a Hanning spectral window
[Blackman and Tukey, 1958, p. 98].
RESULTS
The residualsof the individual orbits from the group mean
for Group One (Figure 3) show high frequency variation su-
Groups Used in This Study
Time of
Latest Orbit
Minus
Time
Group Number
Orbit Number
1
1188
1
1583
2204
1063
0709
2744
1382
1059
1061
1793
0889
1599
0851
0883
1592
1
9
9
9
18
18
18
19
19
19
20
20
20
are due to residual
geoid effects.
Spectra were calculated from the residualsby a version of
the Cooleyand Tukey [1965] fast Fourier transform algorithm.
Before transforming, the mean and linear trend were removed
from each set of residualsby a least squaresstraight line fit. A
linear trend in the data (if present)can add unwanted energy
to the low wavenumber portion of the spectrain addition to
the energy occurring at low wavenumbersdue to truly peri-
Date
Oct. 8, 1975
Nov. 14, 1975
Aug. 24, 1976
Sept. 29, 1975
Spacing,days
Time
37
320
37
320
37
75
37
112
37
75
Nov. 5, 1975
Aug. 15, 1975
Aug. 14, 1975
Sept. 21, 1975
Oct. 28, 1975
Aug. 18, 1975
Nov. 1, 1975
Dec. 8, 1975
Sept. 6, 1975
Oct. 14, 1975
Nov. 20, 1975
of
Earliest Orbit,
days
504
GORDON
AND BAKER:
BRIEF REPORT
W^¾B_ITH
26
28
30
32
LATITUDE
0
500
34
36
(tiM)
38
(DEG NORTH)
KILOMETERS
I000
150•
'øø1
-I00
•
Ei•. 3½. S•a 1•1 diE•r•nc• of eachorbit of Group I from the mean
of Group 1.
perimposedover long wave length variations in sea level.
Peak to trough sealevel variation is about 40 cm.
The averagedspectrafor three setsof groups(Figure 4) are
determined:
1. The longestcommon length of the sectionsof the five
groupsseawardof the Gulf Stream. The very long Group 19
is divided into two sub groups. Set A representsconditions
within the westernregion of the subtropicalgyre.
2. The longestcommon length of the five groups.Again
Group 19 is divided into two sub groups.The variation in
Gulf Stream positionand someslopewater regionis included
Fig. 3b. Spectrafor Group I differences.
INTERPRETATION
in this set.
3. A long section composed of the two longest groups.
This setis dominatedby the subtropicalgyre region.
The spectracharacteristicsshow a nearly flat spectrumat
wave lengthsabove 500 km, a nearly -2 power slopebetween
200 and 500 km wave lengths,a peak and trough near 100 and
200 km, respectively,with a flat spectrumat wavelengthsbelow 100 km. The filter cut off at 10 km is clearly shown.
WAVELENGTH
a
io%ø
10 a
i
1•0
•
10•
10a
I""'
'
•11lll
2IIIIirl
rill111
•I lnllll
ff-_=•-.10
.•
LJ
10
9O%
t ---
10•
ld •
id a
ld •
•AVEN•M•ER
, •x•l
18 SPECTRA FROM GRIPS 1,9,18,
19 (2 F• EACH ORBIT) & 20
I0 km CUTOFF
km
10•
10
i
4
10-•
l•O
( KM )
3
10
10
10
1
10-1
J_O
II111
, ,,,1,
'i 1,11,
........
11
I pl,,,,
,
'"""
' I'""•'
' .---.
_
.x•
,OJ
_
90%
t
, ,•
i
10
( CPKM}
1050 POINTS= 755
WAVELEN5 T H
WAVELBNGI H t KM)
( KM )
10
The significanceof the spectra(Figure 5) can be discussed
in terms of available 'ground truth' data. The -2 slope from
200 to 500 km is similar to the spectraof isothermtopography
found in the Pacific by Bernsteinand White [1974]. This portion of the spectrais taken as representingreal ocean signal.
At lesserwave lengths the spectrumis nearly white, whereas
the isopycnalstructureobservedby Katz [1973, 1975]suggests
10 •
WAVEN•M•R
( CPNM}
•8 SPECTRA FROM G•
1,9,•8,
19(2 FOR EACH ORBIT) • •
•544
POINTS=lOS0
k•
•
a
i tillIll
i
WAVENUMbER (OPKM)
6 SPECTRA, GROUPS I& 19
2048
POINTS=1430
km
I0 km CUTOFF
I0 km CUTOFF
Fig. 4. Spectrafor threesetsof group.In setsA and B the long orbitsof Group 19 are dividedinto 2 segmentsto increasestatisticalsignificance.Set A is entirely in the subtropicalgyre. Set B crossesthe Gulf Stream.Set C representsthe
longestsignificantgrouping.
I I IllIll
1o
GORDON AND BAKER: BRIEF REPORT
WAVELENGTH
505
(KM)
for a lateral shift of a half wavelengthof the transientfeature
is given in Figure 6 as function of transient spatial scale.Using 3 cm/s (about 2.5 km/day) as characteristic,half of the
maximum sea level expressionof a 200 km transient would be
seenby coincidentorbits of slightlylessthan 1 month separation, but a 500 km transientrequiresorbit separationof about
3 months and a 1000 km transient requires separation of
slightly lessthan 6 months.
Therefore detection of transientsby coincident orbits dependsnot only on measurementprecisionof the altimeter and
S•gnal
transientamplitude, but also on the time separationof orbits;
it is possiblethat the drop off in energy above 500 km tranId'
•sientsmay be due to non-independentorbits for theselarger
transientsrather than a real drop off in energy. However, set
C (Figure 4), which is composedof two groups,each with at
10-2/I 11111111
I l illllll I I II'•111/I III1
i6"
163
i62
i61
i
leastone orbit pair separationof over 3.73 months,showssigWAVENUMBER (CPKM)
nificantslopechangenear 500 km. Group one spectrum(Figure 3b), which has maximum separation in .time of the five
Fig. 5. Interpretationof setC spectra.
groups,displaysthe maximum drop off above 500 km. In addition, the 500 km peak is the same as observedfor the Mode
continuationat somewhatlessthan -2 slopeinto this region eddy scale.The slopechangenear 500 km is believedto be
of the spectrum.Henceinstrumentnoiseis responsible
for the real, though the actual drop off may not be as large as inwhite spectrum.
dicated by the spectra.
The peakat 100km and troughat 200 km is probablynoise,
CONCLUSION
though the high frequency end of the Bernsteinand White
[ 1974] isotherm spectrum shows a similar structure. In addiIt is concluded that the Gees 3 altimeter can reveal mesotion, the width of the 100km peak is surprisinglybroad, even scale transient featuresin energy spectrafor wavelengths
consideringthe logarithmic wavenumber scale. While noise above 200 km. Mode scale transients are indicated.
seemsto be the most likely explanation,further consideration
The Gees 3 data may be usedto investigatethe spatialvarimay be warranted.
ation of sea level transientsfor the world ocean.The energy
The flat spectrumabove 500 km may not be entirely real, variationsof the transientsdescribedfor the subtropicalgyre
sincethe orbits may not be truly independentfor the low fre- of the North Atlantic and North Pacific by Bernsteinand
quency transients. The time separation of the orbits varies White [1974, 1977],Roden[1977], and Dantzler [1976, 1977]
10
3I0" 10
3 10
2 I0
I'HIIII
II Illlll•(,•jI
II IIIIIII
II IIII111
II
from 37 days to nearly 1 year (Table 1). Transientfeatures may be tested and expandedfor southernhemispheresubwith very long time scalesmay appearsteadystateto coinci- tropical gyresin addition to equatorialand more polar latident orbitsseparatedby shortertime. Assumingdrift ratesof tudes.
transientsof 1-5 cm/s (0.86-4.3 km/day), the time required
Preliminary inspection of the Seasat A altimeter reveals
that it has much higher precisionthan doesthe Gees 3 altimeWAVELENGTH
I0'•
I03
I02
(KM)
I0
ter. It is expectedthat SeasatA will allow for improvedstudy
I
I0-I
of sea level transients.
We feel certain that satellite altimetry will becomean important tool for physicaleceanegraphers.
I0 •
I
I
Acknowledgments.Supportfor this work is providedby Office of
Naval Research contract NOD014-75-C-0210 Scope C2. The com-
-
mentsof variouspeopleat the 1979AGU SpringMeeting,wherethis
materialwas presentedin a postersession,are greatlyappreciated.
Lamont-DohertyGeologicalObservatorycontribution2920.
REFERENCES
WEEK
5
Bernstein,R. L., and W. B. White, Time and lengthscalesof baroIO
cliniceddiesin thecentralNorthPacificOcean,J. Phys.Oceanogr.,
4, 613-624, 1974.
•AY
I
I•"
, ,,.,,I
, ,
16•
•,, ,
16•
WAVENuMBER
I
I0
16'
I
0
(CPKM)
Fig. 6. Time (hours) requiredfor one half wavelengthtranslation
of transients for 1-5 cm/s translation rates, as a function of transient
wavelength.
Bernstein,
R. L., and W. B. White,Zonal variabilityin the distribution of eddy energyin the mid-latitudeNorth PacificOcean,J.
Phys. Oceanogr.,7, 123-126, 1977.
Blackman,R. B., and J. W. Tukey, The Measurement
of Power
Spectra, 190 pp., Dover, New York, 1958.
Cooley,J. W., and J. W. Tukey, An algorithmfor the machinecalculationof complexFourierseries,Math. Cornput.,
19, 297-301, 1965.
Dantzler,H. L., Jr., Geographic
variations
in intensityof the North
AtlanticandNorthPacificoceaniceddyfields,DeepSeaRes.,23,
783-794, 1976.
Dantzler,H. L., Jr.,Potential
energymaximain thetropicalandsubtropicalNorth Atlantic,J. Phys.Oceanogr.,7, 512-519, 1977.
DQing,W., Spatialand temporalvariabilityof majoroceancurrents
and mesoscale
eddies,BoundaryLayerMeteorol.,13, 7-22, 1978.
506
GORDON
AND BAKER:
Huang, N. E., C. D. Leitao,and C. G. Parra,Large-scaleGulf Stream
frontal study using Geos 3 radar altimeter data, J. Geophys.Res.,
83, 4673-4682, 1978.
Katz, E. J., Profile of an isopycnalsurfacein the main thermoclineof
the SargassoSea,J. Phys.Oceanogr.,3, 448-457, 1973.
Katz, E. J., Tow spectrafrom Mode, J. Geophys.
Res.,80, 1163-1167,
1975.
Kim, K., and R. Rossby,On the eddy statisticsin a ring-rich area: A
hypothesisofbimodal structure,J. Mar. Res.,37, 201-213, 1979.
Leitao, C. D., C. I. Purdy, and R. L. Brooks,Wallops Geos-C altimeter preprocessing
report,NASA Tech.Memo.X-69357,68, 1975.
Martin, C. F., and M. L. Butler, Calibration results for the Geos-3 al-
timeter,NASA Contract.Rep.CR-141430,85, 1977.
Mode Group, The Mid-Ocean DynamicsExperiment,DeepSea Res.,
BRIEF REPORT
Roden, G. I., On long-wave disturbancesof dynamic height in the
North Pacific,J. Phys.Oceanogr.,7, 41-49, 1977.
Stommel, H., Summary chartsof the mean dynamic topographyand
current field at the surface of the ocean, and related functions of the
mean wind stress,in Studieson Oceanography,edited by K, Yoshida,pp..53-58, Universityof WashingtonPress,Seattle,1965.
Voorhis, A.D.,
E. H. Schroeder, and A. Leetmaa, The influence of
deepmesoscale
eddieson seasurfacetemperature
in the North Atlantic subtropical convergence,J. Phys. Oceanogr., 6, 953-961,
1976.
Wyrtki, K., Fluctuations of the dynamic topographyin the Pacific
Ocean, J. Phys. Oceanogr.,5, 450-459, 1975.
Wyrtki, K., L. Magaard, and J. Hager, Eddy energyin the oceans,J.
Geophys.Res.,81, 2641-2646, 1976.
25, 859-910, 1978.
Mode-I Atlas Group, Atlas of the Mid-Ocean DynamicsExperiment
(Mode-I), editedby ¾. Lee and C. Wunsch,MIT Press,Cambridge,
Mass., 1977.
'
Ormsby, J. F. A., Design of numerical filters with applicationsto a
missiledata processing,J. Ass. Comput.Machin., 8, 440-466, 1961.
(Received June 23, 1979;
revisedSeptember 13, 1979;
acceptedSeptember20, 1979.)