JOURNAL
JOURNAL OF
OF GEOPHYSICAL
GEOPHYSICAL RESEARCH,
RESEARCH, VOL
VOL.102,
102,NO.
NO. C6,
C6,PAGES
PAGES12,727-12,748,
12,727-12,748, JUNE
JUNE 15,
15,1997
1997
Altimeter-derived
in the
Altimeter-derived variability
variability of
of surface
surfacevelocities
velocitiesin
the
California
California Current
Current System
System
1.
Evaluation
of
TOPEX
1. Evaluation of TOPEX altimeter
altimeter velocity
velocity resolution
resolution
P. Ted
Ted Strub
Strub
College
and
Sciences,
Oregon
State
University,
Corvallis,
Oregon
Collegeof
of Oceanic
Oceanic
andAtmospheric
Atmospheric
Sciences,
Oregon
State
University,
Corvallis,
Oregon
Teresa
Teresa K.
K. Chereskin
Chereskin and
and Pearn
Peam P.
P. Niiler
Niiler
Scripps
Institution
of
La
Scripps
Institution
ofOceanography,
Oceanography,
LaJolla,
Jolla,California
California
Corinne
CorinneJames
Jamesand
andMurray
Murray D.
D. Levine
Levine
College
and
Sciences,
Oregon
State
University,
Corvallis,
Oregon
Collegeof
ofOceanic
Oceanic
andAtmospheric
Atmospheric
Sciences,
Oregon
State
University,
Corvallis,
Oregon
Abstract.
InInthis
paper,
we
evaluate
the
temporal
and
horizontal
resolution
of
Abstract.
this
paper,
we
evaluate
the
temporal
and
horizontal
resolution
ofgeostrophic
geostrophic
surface
velocities
calculated
from
TOPEX
satellite
altimeter
heights.
Moored
surfacevelocitiescalculatedfrom TOPEX satellitealtimeterheights.Mooredvelocities
velocities
(from
vector-averaging current
current meters
meters and
and an
an acoustic
acoustic Doppler
Doppler current
current profiler)
profiler) at
at depths
(fromvector-averaging
depths
below
the
Ekman
layer
are
used
to
estimate
the
temporal
evolution
and
accuracy
of
belowthe Ekmanlayerare usedto estimatethe temporalevolutionand accuracy
of
altimeter
geostrophic
surface
velocities
at
a
point.
Surface
temperature
gradients
from
altimetergeostrophic
surface
velocities
at a point. Surfacetemperature
gradients
from
satellite fields are used
used to determine the
the altimeter's horizontal resolution of
of features
features in
in the
velocity
field.
The
results
indicate
that
the
altimeter
resolves
horizontal
scales
of
50-80
velocityfield. The resultsindicatethatthealtimeter
resolves
horizontal
scalesof 50-80
km
direction.
between
km in
in the
thealong-track
along-track
direction.The
Therms
rmsdifferences
differences
betweenthe
thealtimeter
altimeterand
andcurrent
current
meters
are 7-8 cm
ofofwhich
comes
from
variability
metersare
cms1,
s-•,much
much
which
comes
fromsmall-scale
small-scale
variabilityin
inthe
theoceanic
oceanic
currents.
to have
currents.We
We estimate
estimatethe
the error
errorin
in the
thealtimeter
altimetervelocities
velocitiesto
havean
an rms
rmsmagnitude
magnitudeof
of
3-5 cm
s1
or
less.
Uncertainties
in
the
eddy
momentum
fluxes
at
crossovers
are
more
cm s-• or less.Uncertainties
in the eddymomentum
fluxesat crossovers
are more
difficult to
to evaluate
with
difficult
evaluateand
andmay
maybe
be affected
affectedby
by aliasing
aliasingof
of fluctuations
fluctuations
withfrequencies
frequencies
higher than
than the
the altimeter's
altimeter's Nyquist
Nyquist frequency
frequencyof
of0.05
0.05cycles
cyclesdd1,
by
higher
-•, as
asindicated
indicated
byspectra
spectra
from
subsampled
current
meter
data.
The
eddy
statistics
that
are
in
best
agreement
are
fromsubsampled
currentmeterdata.The eddystatistics
thatarein bestagreement
are
the
velocity
variances,
eddy
kinetic
energy
and
the
major
axis
of
the
variance
ellipses.
thevelocityvariances,
eddykineticenergyandthemajoraxisof thevariance
ellipses.
Spatial averaging
of
meter
produces
greater
agreement
with
Spatial
averaging
of the
thecurrent
current
metervelocities
velocities
produces
greater
agreement
withall
all
altimeter statistics
statistics and
and increases
our confidence that
that the altimeter's
increases our
altimeter's momentum
momentum fluxes
and
of
differing
andthe
theorientation
orientation
of its
itsvariance
varianceellipses
ellipses(the
(thestatistics
statistics
differingthe
themost
mostwith
withsingle
single
moorings)
represent
well
the
statistics
of
spatially
averaged
currents
(scales
of 50-100
50-100
moorings)
represent
well thestatistics
of spatially
averaged
currents
(scales
of
km) in
Besides
evaluating
altimeter
performance,
the
several
km)
in the
theocean.
ocean.
Besides
evaluating
altimeter
performance,
thestudy
studyreveals
reveals
several
properties
of
the
circulation
in
the
California
Current
System:
(1)
velocity
components
properties
of thecirculation
in theCaliforniaCurrentSystem:(1) velocitycomponents
are
but
strongly
so
(2)
arenot
notisotropic
isotropic
butare
arepolarized,
polarized,
strongly
soat
atsome
somelocations,
locations,
(2) there
thereare
areinstances
instances
of
strong
and
persistent
small-scale
variability
in
the
velocity,
and
(3)
the
energetic
region
of strong
andpersistent
small-scale
variability
in thevelocity,
and(3) theenergetic
region
of the
by
theCalifornia
CaliforniaCurrent
Currentis
isisolated
isolatedand
andsurrounded
surrounded
by aaregion
regionof
oflower
lowerenergy
energystarting
starting
500-700 km
that
within 500
500
500-700
km offshore.
offshore.This
Thissuggests
suggests
thatthe
thesource
sourceof
of the
thehigh
higheddy
eddyenergy
energywithin
km
of
the
coast
is
the
seasonal
jet
that
develops
each
spring
and
moves
offshore
to
the
km of the coastis the seasonal
jet thatdevelops
eachspringandmovesoffshoreto the
central region
region of
of the
Current, rather
rather than
than aa deep-ocean
eddy field
field approaching
central
theCalifornia
California
Current,
deep-ocean
eddy
approaching
the coast from
the
from farther
farther offshore.
offshore.
1. Introduction
1.
Introduction
cam'
et al.,
caut et
al., 1995].
1995]. Velocities
Velocitiescalculated
calculatedfrom
from the
thealtimeter
altimeter
heights
have
also
been
evaluated
over
the
equatorial
Pacific
heights
have
also
been
evaluated
over
the
equatorial
Pacific
In
the
In previous
previousstudies,
studies,
theTOPEX
TOPEX satellite
satellitealtimeter
altimeterheight
height Ocean by comparisons to current meters [Menkes et al.,
Ocean
by
comparisons
to
current
meters
[Menkes
et al.,
data
have
been
verified
at
their
most
basic
level,
in
tenns
of
data have been verified at their most basic level, in terms of
1995]
and surface
surface drifters
drifters [Yu
[Vuetetal.,
al., 1995].
1995]. In
In this
paper
1995]
and
this
paper
errors
in
the
various
range
calculations,
environmental
and
errorsin the variousrangecalculations,environmentaland
we
examine
the
ability
of
the
TOPEX
altimeter
to
resolve
we
examine
the
ability
of
the
TOPEX
altimeter
to
resolve
orbital
height
errors
[Fu
et
al.,
1994;
Katz
et
al.,
1995;
Piorbitalheighterrors[Fu et al., 1994;Katz et al., 1995;Pi- the principal spacescales and timescales of surface velocithe principal spacescales
and timescalesof surfacevelocities (beneath
ties
(beneaththe
the wind-driven
wind-drivensurface
surfaceEkman
Ekman layer)
layer) over
over the
the
Copyright
1997
by
the
American
Geophysical
Union.
Copyright1997 by the AmericanGeophysical
Union.
midlatitude California
velocmidlatitude
CaliforniaCurrent
CurrentSystem.
System.Higher-order
Higher-order
velocity statistics
fluxes, and
ity
statistics(spectra,
(spectra,momentum
momentumfluxes,
and principal
principal axis
axis
Paper
Papernumber
number97JC00448.
97JC00448.
ellipses) are
0148-0227/97/97JC-00448$09.00
0148-0227/97/97 JC-00448509.00
ellipses)
are also
alsoevaluated.
evaluated.
12,727
12,728
12,728
STRUB ET AL.:
AL.: TOPEX
TOPEX VELOCITIES-ACCURACY
VELOCITIES-ACCURACY AND
AND ALONG-TRACK
ALONG-TRACK RESOLUTION
RESOLUTION
Ideally,
we would
Ideally, we
wouldlike
like to
to estimate
estimateboth
boththe
theerror
errorvariance
variance
and
and signal
signalvariance
variancespectra,
spectra,as
asaafunction
functionof
ofwavenumber
wavenumber
and
and frequency.
frequency.In
In practice,
practice,the
the"ground
"groundtruth"
truth"time
timeseries
series
of
two-dimensional
surface
velocity
fields
necessary
to
of two-dimensionalsurfacevelocity fields necessary
to do
do
this
are
lacking.
As
an
alternative,
we
evaluate
two
aspects
this are lacking. As an alternative,we evaluatetwo aspects
of
velocities
of the
theresolution
resolutioncapabilities
capabilitiesof
ofgeostrophic
geostrophic
velocitiescalcalculated
culatedfrom
from the
the TOPEX
TOPEX height
heightdata:
data: (1)
(1) the
themagnitude
magnitude
of
currents
of the
thedifference
differencebetween
betweengeostrophic
geostrophic
currentscalculated
calculated
from
measured
by
from TOPEX
TOPEX heights
heightsand
andcurrents
currents
measured
byan
anacoustic
acoustic
Doppler
current
Dopplercurrent
currentprofiler
profiler(ADCP)
(ADCP) and
andconventional
conventional
current
meters
below
the
depth
of
the
wind's
influence
and
metersbelow the depthof the wind's influenceand(2)
(2) the
the
along-track
spatial
scales
of
velocity
resolved
by
the
sensor.
along-trackspatialscalesof velocityresolvedby the sensor.
The
surface
The accuracy
accuracyof
ofthe
thealtimeter-derived
altimeter-derived
surfacevelocity
velocity
velocity field
field that
that are
velocity
areresolved
resolvedby
by the
theactual
actualmeasurements
measurements
along ground
along
groundtracks.
tracks.
In
In the
the next
next section
section we
we describe
describe the
the data
data and
and methods
methods
used in
in the
the study.
study. In
with
used
In section
section3,
3, the
theresults
resultsare
arepresented
presented
with
respect
to
the
accuracy
of
the
velocity,
temporal,
and
spatial
respectto the accuracyof the velocity,temporal,andspatial
resolution
velocity statistics.
statistics. In
resolutionand
and higher-order
higher-ordervelocity
In section
section44
we summarize
summarize and
and discuss
The
we
discussour
our conclusions.
conclusions.
TheAppendix
Appendix
gives details
details of
of the
velocity
calculation and
and the
the
gives
the geostrophic
geostrophic
velocitycalculation
effects
effectscaused
causedby
by changing
changingthose
thosedetails.
details.
2.
2. Data
Data and
and Methods
Methods
2.1.
and In
2.1. Sateffite
Satellite and
In Situ
Situ Data
Data
statistics and
The satellite
data are
of the
the
statistics
andthe
thetemporal
temporalresolution
resolutionat
ataa point
pointare
areaddressed
addressed The
satellitealtimeter
altimeterdata
arefrom
from cycles
cycles1-111
1-111of
by
to
of
measurements
at
TOPEX geophysical
data
records
(GDRs),
obtained
from
by comparison
comparison
to13-18
13-18months
months
ofvelocity
velocity
measurements
at TOPEX
geophysicaldata records(GDRs), obtainedfrom
a satellite
point (the
the Jet
data are
are
a
satellitealtimeter
altimetercrossover
crossoverpoint
(the location
locationwhere
whereasas- the
JetPropulsion
PropulsionLaboratory
Laboratory(JPL).
(JPL). POSEIDON
POSEIDON data
cending
tracks
using
used.
These
data
cover
a
period
of
3
years
(September
cendingand
anddescending
descending
trackscross),
cross),
usingmeasurements
measurements not
notused.Thesedatacovera periodof 3 years(September
from
to September
correcfrom 50-100
50-100 m
m of
ofdepth.
depth.This
Thisgives
givesthe
themost
mostdirect
directestiesti- 1992
1992 to
September1995).
1995). Standard
Standardenvironmental
environmental
correcmate
mate of
of the
the "errors"
"errors" inincross-track
cross-trackvelocities
velocities and
andmomenmomentions are
tions
are applied
applied[Callahan,
[Callahan,1993],
1993],including
includingthe
thedry
drytrotrotum
posphere correction,
correction, solid
solid Earth,
Earth, and
and pole
pole tides
tides from
the
tum fluxes
fluxescalculated
calculatedat
at aapoint
pointalong
alongan
analtimeter
altimetertrack.
track. posphere
from the
We
place
"errors"
in
quotes
to
remind
the
reader
that
meaGDR.
The
sea
surface
height,
mean
sea
surface,
dry
troWe place"errors"in quotesto remindthe readerthatmea- GDR. The seasurfaceheight,meanseasurface,dry trosured ocean
components
and
posphere, solid
solid earth
earth and
and pole
to the
the
sured
oceancurrents
currentsinclude
includeageostrophic
ageostrophic
components
and posphere,
poletides
fidesare
areinterpolated
interpolated
to
small-scale variability
variability that
that are
Ziotnicki-Fu along-track
along-track grid
grid with
with 6.2-km
6.2-km spacing,
spacing, and
and the
the
small-scale
are not
notresolved
resolvedby
by the
thealtimealtime- Zlotnicki-Fu
ter' s geostrophic
geostrophic velocities,
velocities, as
as we
further
corrections are
are then
subtracted
from
the
sea
surface
height.
ter's
we discuss
discuss
furtherbelow.
below. corrections
thensubtracted
fromthe seasurfaceheight.
The
The ocean
tide is
at the
The hourly
hourlycurrent
currentmeter
metervelocity
velocitydata
dataalso
alsoallow
allowcomparcompar- The
oceantide
is calculated
calculatedat
the grid
gridpoints
pointsand
andsubsub-
isons of
tracted from
from the
the s6a
sa surface
height
using
the
of
isons
of the
the full
full variance
varianceand
andcovariance
covariance(u'v')
(u%•)frequency
frequency tracted
surface
height
using
thetide
tidemodel
model
of
spectra from
from the
velocities
by
spectra
the measured
measured
velocitiesto
to those
thoseobtained
obtainedby
subsampling
the
current
meters
at
the
10-day
TOPEX
samsubsampling
the currentmetersat the 10-dayTOPEX sampling period,
period, demonstrating
the
to the
the
pling
demonstrating
thedegree
degreeof
of aliasing
aliasingdue
dueto
TOPEX
sampling
pattern.
The
covariance
statistics
repreTOPEX samplingpattern. The covariancestatisticsrepresent
by eddies
eddies in
in the
the upper
upper
sentmomentum
momentumfluxes
fluxesaccomplished
accomplished
by
ocean
oceanand
and are
arean
animportant
importantdynamic
dynamicquantity
quantitywhich
which can
can
be calculated
points
be
calculatedonly
only at
at the
thecrossover
crossover
points[Morrow
[Morrowet
et al.,
al.,
1994],
1994], since
sincethese
theseare
arethe
theonly
onlylocations
locationswhere
whereboth
bothcomcomponents of
velocity
ponents
of horizontal
horizontalgeostrophic
geostrophic
velocitycan
canbe
becomputed
computed
from
the
along-track
altimeter
height
gradients.
from the along-trackaltimeterheightgradients.
To
To determine
determinehow
how well
well the
thealtimeter
altimeterresolves
resolvesthe
the spaspatial
scales
of
velocity
variability
along
the
altimeter
tial scalesof velocityvariabilityalongthe altimetertracks,
tracks,
we
we use
usealong-track
along-trackspatial
spatialgradients
gradientsof
of sea
seasurface
surfacetemtemperature (SST)
very
raperature
(SST) from
fromthe
theadvanced
advanced
veryhigh
highresolution
resolution
radiometer
satellite sensor.
diometer(AVHRR)
(AVHRR) satellite
sensor.In
In regions
regionswhere
wheresalinsalinities
(or
ities are
arewell
well correlated
correlatedwith
with temperatures
temperatures
(or unimportant)
unimportant)
and
where
surface
temperatures
are
representative
of
andwheresurfacetemperatures
are representative
of deeper
deeper
temperature
features,
spatial
gradients
of
SST
are
temperature
features,spatialgradientsof SST arerelated
related
to horizontal
to
horizontalvelocities
velocitiesthrough
throughthe
thethermal
thermalwind
windrelation.
relation.
These
conditions
hold
well
enough
for
given
times
These conditionshold well enoughfor given timesand
andrere-
Egbert
signal
Egbertet
et al.
al. [1994].
[1994]. The
Theresulting
resulting
signalisisthe
thedynamidynamically important
important variable
variable and
and is
is referred
referred to
to as
cally
as the
the "corrected
"corrected
sea surface
height." No
are
sea
surfaceheight."
No residual
residualorbit
orbiterror
errorcorrections
corrections
are
removed,
since
they
are
expected
to
be
small
and
to
have
removed,sincethey are expectedto be small and to have
large spatial
spatial scales,
large
scales,producing
producinglittle
little effect
effecton
onthe
thevelocities
velocities
calculated
from
the
along-track
gradient
of
height.
calculatedfrom the along-trackgradientof height.CrossCrosstrack geostrophic
velocities are
are calculated
calculated from
track
geostrophic
velocities
fromthe
thealongalong-
track
difference
with
trackgradient
gradientof
of the
theheight
heightusing
usingaacentered
centered
difference
with
aa span
Details
spanof
of 62
62 km
km(10
(10grid
gridspacings).
spacings).
Detailsof
ofthe
thecalculacalculation
tion are
arepresented
presentedin
in the
theAppendix.
Appendix.
The
SST
gradients
come
containing
The SSTgradients
comefrom
fromAVHRR
AVHRRimages
images
containing
cloud-free
regions
during
periods
within
several
days
cloud-free
regionsduringperiodswithinseveraldaysof
ofthe
the
altimeter
overpasses.
Temperature
gradients
are
calculated
altimeteroverpasses.
Temperature
gradientsare calculated
from channel
channel 44 alone
from
alone(11.5
(11.5 nm),
p,m),with
with no
nomultichannel
multichannelatatmospheric correction
correction (since
(since this
this introduces
introduces additional
additional noise
noise
mospheric
into the
the SST
mean
from
into
SST field).
field). AAlong-term
long-term
meanisissubtracted
subtracted
from
the SST
SST data
data along
gradients and
and
the
alongeach
eachtrack
trackbefore
beforeforming
forminggradients
low-pass filtering
filtering the
the along-track
along-track temperature
temperature gradients
gradients with
with
low-pass
the
cross-track
vethe same
sameoperators
operatorsused
usedin
in the
thegeostrophic
geostrophic
cross-track
velocity
calculation
(see
Appendix).
Thus
the
temperature
and
locitycalculation(seeAppendix).Thusthetemperature
and
gions
are
as
gions of
of the
the California
California Current
Currentto
to allow
allowaatest
testof
ofthe
thehorhor- height
heightgradients
gradients
areprocessed
processed
assimilarly
similarlyas
aspossible.
possible.
izontal
resolved by
by the
the altimeter.
Independent
velocity
estimates
come
from
izontal scales
scalesresolved
altimeter. In
In the
theCalifornia
California
Independent
velocityestimates
comefromfive
five moorings
moorings
Current
located near
near the
Current System
Systemduring
during late
late summer
summerand
andfall,
fall, the
theseasonal
seasonal located
the altimeter
altimetercrossover
crossoverat
at 37.1°N,
37.1øN, 127.6°W.
127.6øW.
The mooring
are located
located in
in
The
mooringarray
array and
and altimeter
altimetercrossover
crossoverare
water approximately
approximately4800
4800 m
m in
in depth,
depth, more
than 400
water
more than
400 km
km
offshore of
of the
the continental
offshore
continentalshelf
shelfand
andslope.
slope.Neither
Neitherbottom
bottom
topography nor
nor amplified
amplified shallow-water
shallow-water tides
tides are
are a
a problem
problem
topography
1991].
at this
this location.
location.
1991]. Thus
Thus we
we use
usedata
datafrom
from faIl
fall 1992
1992 and
andwinter
winter 1993
1993 at
to evaluate
to
evaluate the
the TOPEX
TOPEX altimeter's
altimeter's horizontal
horizontal resolution.
resolution. It
It
On
the
esOn themooring
mooringdirectly
directlyunder
underthe
thealtimeter
altimetercrossover,
crossover,
esis
the
of
horizontal
velocity
are
available
from
a
downward
is important
importantto
to note
notethat
thatwe
weare
arenot
notaddressing
addressing
thequestion
question timates
timatesof horizontalvelocityareavailablefroma downward
of
in
looking ADCP
ADCP mounted
mounted in
in the
the bridle
bridle of
of a
a surface
surface buoy.
buoy. DeDeof what
what scales
scalesmay
maybe
bewell
well represented
represented
in two-dimensional
two-dimensional looking
fields
and
are
fields constructed
constructed from
from the
the altimeter
altimeter data,
data,which
whichinvolve
involve tails
tailsof
of the
thedeployment
deployment
andprocessing
processing
aregiven
givenby
byChereCherethe
interpolation.
the
a year
the use
useof
ofspace-time
space-time
interpolation.We
Weare
areaddressing
addressing
the skin
skin[1995].
[1995]. This
This record
recordprovides
providesapproximately
approximately
a
year
more
more fundamental
fundamentalquestion
questionof
of the
the horizontal
horizontalscales
scalesof
of the
the of
of overlap
overlapwith
with the
theTOPEX
TOPEX altimeter,
altimeter,from
fromlate
lateSeptember
September
jet
jet moves
movesfar
farenough
enoughoffshore
offshoreto
tobe
beseen
seenover
overlarge
largeportions
portions
of
of the
thecoarsely
coarselyspaced
spacedaltimeter
altimetertracks,
tracks,while
whilestill
stillcarrying
carrying
the temperature
signal
the
temperature
signalfrom
fromupwelled
upwelledwater
waterand
andgeostrophic
geostrophic
adjustments
associated
with
the
meandering
jet [Strub
[Strub et
etal.,
adjustments
associated
with the meandering
jet
al.,
STRUB
Er AL:
STRUB ET
AL.:TOPEX
TOPEXVELOCfl1ESACCURACY
VELOCITIES-ACCURACYAND
ANDALONG-TRACK
ALONG-TRACKRESOLUTION
RESOLUTION
1992
to mid-October
1993. Range
1992 to
mid-October 1993.
Rangegating
gatingthe
the signal
signalpropro-
Vcd = u cos
0 ++ vv sin
cos 0
sin 0
0
duces aa vertical
profile of
velocity at
at 44 m
m intervals,
intervals, with
with the
the
duces
verticalprofile
of velocity
shallowest
depth
centered
at
8
m
and
the
deepest
centered
shallowestdepthcenteredat 8 m and the deepestcentered
at
at 164
164 m.
m. The
Thesample
samplerate
ratewas
was11Hz
Hzfor
fora a5-mm
5-min interinterval
every
20
mm,
which
reduced
velocity
aliasing
val every20 min, which reducedvelocityaliasingand
and filter
filter
skew
bias due
surface waves
waves to
to less
less than
than
skewbias
due to
to high-frequency
high-frequencysurface
11 cm
cm s
s1-• inineach
5-mm
ensemble
average
[Chereskin
etetal.,
each
5-min
ensemble
average
[Chereskin
al.,
1989;
1989; Chereskin
Chereskinand
and Harding,
Harding,1993;
1993;Chereskin,
Chereskin,1995].
1995].
In addition
In
additionto
to the
thedownward
downwardlooking
lookingADCP,
ADCP, currents
currentsare
are
also available
also
availablefrom
from four
four conventional
conventionalvector
vectoraveraging
averagingcurcurrent
rent meters
meters(VACMs)
(VACMs) at
at approximately
approximately100-rn
100-m depth
depthover
over
periods
of 18-24
periodsof
18-24 months.
months.One
Onemooring
mooringwas
waslocated
located2.2
2.2
km
east
of
the
crossover
and
ADCP
mooring,
km east of the crossoverand ADCP mooring,while
while the
the
other
otherthree
threewere
werelocated
locatedapproximately
approximately15
15 km
km north,
north,west,
west,
and
and south
southof
of the
thecentral
centralADCP
ADCP mooring.
mooring.Positions
Positionsof
of the
the
moorings
relative to
mooringsrelative
to the
thealtimeter
altimetertracks
tracksare
areshown
shownbelow.
below.
VACM
velocities were
VACM velocities
were vector
vectoraveraged
averagedover
overevery
every30
30 mm.
min.
Chereskin [1995]
[1995] used
used these
Chereskin
these same
same ADCP
ADCP velocities
velocities to
to
look
lookat
at wind-driven
wind-drivenEkman-like
Ekman-likecurrents
currentsabove
above48-rn
48-m depth.
depth.
She found
48 m,
She
found most
most of
of the
the wind-driven
wind-driven shear
shear above
above 48
m,
little
48 and
little shear
shearbetween
between48
and60
60 m,
m,and
andsomewhat
somewhatgreater
greater
geostrophic shear
shear below
below that.
that. Correlations
with
geostrophic
Correlations
with the
thealtimealtimeter
ter velocities
velocitiesare
arealso
alsogreatest
greatestfor
for ADCP
ADCP velocities
velocitiesbetween
between
48
the best
best represenrepresen48 and
and60
60 m
m and
andwe
weuse
usethe
the48-rn
48-m depth
depthas
asthe
tation of
the geostrophic
velocities,
beneath the
the wind-driven
tation
of the
geostrophic
velocities,beneath
wind-driven
Ekman layer.
layer. Although
Ekman
Althoughthe
the 100-rn
100-m depths
depthsof
of the
theVACMs
VACMs
are
greater
than
this
optimal
depth,
the
mean
shear
are greaterthanthis optimaldepth,the meanshearbetween
between
the 48-m and
and 100-m
100-rnADCP
ADCPbins
binsisisless
lessthan
than22cm
cms-•,
s1, and
the
and
the
rms
difference
between
these
depths
is
5
cm
s.
These
thermsdifference
between
thesedepths
is 5 cms-•. These
measurements from
from 100-rn
depth are
measurements
100-m depth
are useful
usefulin
in demonstratdemonstrating the
in the
ing
the small-scale
small-scalevariability
variabilityin
the currents
currentsthat
thataccounts
accounts
for much
for
much of the
the difference
difference between
between the altimeter
altimeter and
and meameasured
sured velocities.
velocities.
u --
V-
Vca +
q-Vcd
Vcd
2cos0
2 cos 0
Vd - Vca
sin 0
v-- 22sin0
12,729
(lb)
(lc)
(ld)
where
where00 is
is the
theangle
anglebetween
betweenthe
theground
groundtrack
trackand
andthe
thenorth
north
meridian (symmetric
for ascending
and
orbits)
meridian
(symmetricfor
ascending
anddescending
descending
orbits)
and
are defined
defined positive
positive if
if they
andboth
bothVea
Vca and
andVcd
V•d are
theyhave
havean
an
eastward component.
component. See
See Figure
Figure 11 of
eastward
of Mesias
Mesias and
and Strub
Strub
[1995]
for
a
picture
of
the
geometry.
[1995] for a pictureof the geometry.
Assuming the
the error
Assuming
errorvariances
variancesfor
for the
thecross-track
cross-trackvelocivelocities
at
the
crossover
are
uncorrelated
and
equal
tiesat thecrossover
areuncorrelated
andequalfor
forascending
ascending
and
tracks and
the error
varianddescending
descending
tracks
andare
aregiven
givenby
by rr•, the
error
variances
for the
the uu and
calculated
from (lc)
(ic) and
ancesfor
andvv components
components
calculatedfrom
and
(Id)
are
of
(ld) at
ataacrossover
crossover
are(using
(usingsimple
simplepropagation
propagation
of error)
error)
2
2
O'vc
0.63a
u = 0.80cr
a•, = 2cos
2cos
200 m0.63av2•a•,-- 0.80aw
(2a)
(2a)
2
2
O'vc
v -= 1.54a
av = 2sin
• 2.36a
2.36a•2cav
1.54aw
2 sin200
(2b)
(2b)
The numerical
values on
on the
The
numericalvalues
the right
rightare
arefor
for0=27.4°,
0=27.4ø, which
which
applies
to the
orbit at
at 37.1°N.
applies to
the TOPEX/POSEIDON
TOPEX/POSEIDON orbit
37.1øN. The
The
point of
is
error
point
of this
thiscalculation
calculation
is the
thefact
factthat
thatthe
theexpected
expected
error
variances
are
different
for
the
two
orthogonal
components,
variances
aredifferentfor thetwo orthogonal
components,
due
and
dueto
tothe
thegeometry,
geometry,
andthat
thatthese
thesechange
changeas
asaa function
functionof
of
latitude.
Ideally,
we
would
like
to
first
estimate
by findfindOijc
latitude.Ideally,we wouldliketo firstestimate
aw by
ing
between
the
velocity
estiingthe
therms
rmsdifference
difference
between
thecross-track
cross-track
velocity
estimated
from the
the altimeter
altimeter (see
(see (A1))
(Al)) and
matedfrom
andthe
thecoincident
coincidentvalue
value
from
the current
current meters
meters as
as calculated
calculatedby
by(la)
(la) or
or (lb).
(ib). This
fromthe
This
allows estimates
estimates of the
the uncertainties
uncertainties in
in altimeter-derived
altimeter-derived u
and
to
Although the
andvv values
valuesaccording
according
to (2a)
(2a)and
and(2b).
(2b). Although
the
time
difference
between
ascending
and
descending
tracks
is
time
difference
between
ascending
and
descending
tracks
is
2.2.
at aa
2.2. Methods:
Methods: Accuracy
Accuracyand
andTemporal
Temporal Resolution
Resolution at
negligible
for
the
crossover
point
at
37.1
°N,
127.6°W
(the
negligiblefor the crossover
pointat 37.1øN,127.6øW(the
Point
Point
ascending
track 69
track
ascending
track
69 follows
followsthe
thedescending
descending
track54
54 by
by 14.5
14.5
The
point at
hours), we
linearly
interpolate
the
cross-track
velocities
The ADCP
ADCP and
andaltimeter
altimeterdata
datafrom
fromthe
thecrossover
crossover
point
at hours),
we linearlyinterpolatethe cross-track
velocitiesto
to
37.
10°N, 1127.56øW
27.56°W are
are used
used to
to estimate
estimate the
of
them to
37.10øN,
theaccuracy
accuracy
of the
the aa common
commontime
time before
beforecombining
combiningthem
to form
formthe
thevector
vector
altimeter's
velocities.
altimeter'svelocity
velocitycalculation
calculationand
andits
itstemporal
temporalresolution
resolution velocities.
at
a
fixed
point.
The
long-term
temporal
In comparing
the
estimates
of
surat a fixedpoint. The long-termtemporalmeans
meansof
ofall
allvelocvelocIn
comparing
thealtimeter
altimeter
estimates
ofgeostrophic
geostrophic
surity
"anomalies" for
face velocity
ity time
time series
seriesare
areremoved
removedto
to form
form velocity
velocity"anomalies"
for face
velocityanomalies
anomalieswith
with the
theADCP
ADCP and
andVACM
VACM subsursubsurall
reported below.
below. Comparisons
of
face measurements,
we need
several
processes
all comparisons
comparisons
reported
Comparisons
of ADCP
ADCP and
and face
measurements,
we
needto
toevaluate
evaluate
several
processes
altimeter-derived
velocities are
are most
most directly
in the
the upper
upper ocean
which
produce
real
variability
in
the curcuraltimeter-derived
velocities
directlyaccomplished
accomplished in
oceanwhichproduce
realvariabilityin the
by projecting
dithat
geostrophic
calculations
(altimeter
or
otherwise)
by
projectingthe
the ADCP
ADCP velocities
velocitiesonto
ontothe
thecross-track
cross-track
di- rents
rentsthat geostrophic
calculations
(altimeteror otherwise)
rection
altimeter tracks.
tracks. Alrectionof
of ascending
ascendingand
and descending
descendingaltimeter
Al- cannot
cannotresolve.
resolve.Geostrophic
Geostrophicvertical
verticalshears
shearswill
will be
be created
created
ternatively, estimation
estimation of
of the
the orthogonal
east-west (u)
(u) and
the surface and the current meters at 48 and
between the
and 100
100
ternatively,
orthogonaleast-west
and between
north-south (v)
(v) components
of velocity
from the
the two
density
gradients in
in the
the upper
upper 5050north-south
componentsof
velocity from
two alal- m
m if
if there
thereare
arehorizontal
horizontal
densitygradients
timeter
with
m of
the
jet
timetertracks
tracksis
is possible
possibleat
atthe
thecrossover,
crossover,
withadditional
additional 100
100 m
of the
thewater
watercolumn.
column.Although
Although
themeandering
meandering
jet
uncertainty introduced
by
and
that develops
in this
this region
region [Huyer
et al.,
uncertainty
introduced
bythe
thefact
factthat
thatthe
theascending
ascending
anddede- and
andeddy
eddysystem
systemthat
developsin
[Huyeret
al.,
scending tracks
tracks are
are not
et al.,
al., 1994].
1991; Paduan
Paduan and
scending
not orthogonal
orthogonal[Morrow
[Morrow et
1994]. 1991;
and Nii!er
Niiler, 1990]
1990]do
doinclude
includehorizontal
horizontaldendenThe
gradients,
Kosro
et
al.
[19911
estimate
The prograde
progradegeometry
geometryof
of the
theTOPEXIPOSEIDON
TOPEX/POSEIDON orbit
orbit sity
sity gradients,Kosroet al. [1991] estimatemixed
mixedlayer
layer
has ascending
has
ascendingtracks
tracksmoving
movingfrom
from southwest
southwestto
to northeast
northeast depths
depthsto
to be
be 60-90
60-90 m
min
inwinter
winterand
and20-60
20-60mmininsummer.
summer.
and
tracks
density
gradients
are
weak
in
the
upper 40-60
40-60 m
m of
anddescending
descending
tracksmoving
movingfrom
from northwest
northwestto
to southeast,
southeast, Thus
Thusdensitygradientsare weak in the upper
of
opposite to
to those
those from
from Geosat.
Geosat. Given
the the
opposite
Given this
thisgeometry,
geometry,the
thewater
watercolumn
columnfor
formuch
muchof
ofthe
theyear.
year.
relationships
between
the
of
Another source of unresolved vertical
vertical shear is the windwindrelation^ships^
between
thecomponents
components
ofthe
thetrue
truevelocity
velocity Another
(il
=
ui
+
vj)
at
a
crossover
and
the
cross-track
velocity
of driven
[1995]
(i• = ui + vj) at a crossoverand the cross-track
velocityof
drivenEkman
Ekmancurrent
currentin
in the
theupper
upperocean.
ocean.Chereskin
Chereskin
[ 1995]
the
and descending
descending (V•a)
(Vd) tracks
analyzes the
the "defect"
48 m
theascending
ascending(Vca)
(V•.) and
tracksare
are
analyzes
"defect" of
of velocities
velocitiesabove
above 48
m and
andshows
shows
that
most
of
the
observed
wind-driven
velocity
occurs
above
thatmostof theobserved
wind-drivenvelocityoccurs
above
Vca = u cos
U-- vv sin
(la) this
depth.
Any
residual
wind-driven
Ekman
flow
at
cos0
sin 0
0
(la)
this depth. Any residualwind-drivenEkman flow at 48
48 m
m
12,730
12,730
STRUB
AND
RESOLUTION
STRUBET
ET AL.:
AL.:TOPEX
TOPEXVELOCITIESACCURACY
VELOCITIES-ACCURACY
ANDALONG-TRACK
ALONG-TRACK
RESOLUTION
will
than
3. Results
will be
bemuch
muchlower
lowerin
inmagnitude
magnitude
thanthe
themaximum
maximumvalue
value 3.
Results
of 5 cm s's-•that
Chereskin
found
that
Chereskin
foundnear
nearthe
thesurface.
surface.NearNear-
3.1. Regional Circulation Characteristics
inertial
inertialmotions
motionsare
areanother
anotherpotential
potentialsource
sourceof
of error,
error,since
since 3.1. Regional Circulation Characteristics
the
of
will
Figure 11 shows
field of
of SST
thesurface
surfaceheight
heightsignature
signature
ofthese
thesemotions
motions
will remain
remainin
in
Figure
showsthe
the horizontal
horizontalfield
SST from
from an
an
the
AVHRR image
image on
on October
October 9,
9, 1992
day 283),
thealtimeter
altimeterheights
heightsbut
butwill
will be
beremoved
removedfrom
fromthe
theADCP
ADCP AVHRR
1992 (year
(yearday
283), overlain
overlain
data
40-hour filter.
filter. D'Asaro
D'Asaro et
by TOPEX
velocity
from aa 7-day
7-day pepedataby
by the
the40-hour
et al.
al. [1995]
[1995]report
reportspaspa- by
TOPEX cross-track
cross-track
velocityanomalies
anomaliesfrom
tially
varying
inertial
currents
in
the
eastern
North
riod during
tially varyinginertialcurrents
in the easternNorthPacific
Pacific riod
duringcycle
cycle 2
2 (year
(yeardays
days279-285).
279-285). The
TheADCP
ADCP data
data
with
changes
over
of
with10
10cm
cms1
s-•horizontal
horizontal
changes
overdistances
distances
of50
50 km.
km. used
usedin this
thissection
sectioncome
comefrom
from the
themooring
mooringunder
underthe
the crosscrossWe
with
of
ascending
track
69
and
descending
track
54. The
We estimate
estimatemaximum
maximumsurface
surfaceslopes
slopesassociated
associated
withthese
these ing
ing of ascendingtrack 69 and descending
track 54.
The
ageostrophic
motions to
to be
be a
a change
of 1-2
cm over
the 50
50 long-term
(1-2 year)
ageostrophic
motions
change
of
1-2cm
overthe
long-term(1-2
year) means
meanswhich
whichare
areremoved
removedfrom
fromthe
the
km distance,
equivalentto
to 2-4
2-4 cm
cm ss-• in
ADCP
km
distance,
equivalent
inthe
thegeostrophic
geostrophic
ADCP and
and VACM
VACM data
data to
to form
formvelocity
velocityanomalies
anomaliesare
are of
of
calculation.
Finally,
with
3-4
cm
s1,
whereas
daily
velocities
have
magnitudes
calculation.
Finally,internal
internalwave
wavevelocities
velocities
withperiods
periods order
order3-4 cms-•, whereas
dailyvelocities
havemagnitudes
of
by
of
velocity
anomalies
and
of 5-40
5-40 mm
minmay
maybe
bealiased
aliased
bythe
theburst
burstsampling
sampling
of the
the of
of up
upto
to30
30cm
cmsE.
s-•.Thus
Thus
velocity
anomalies
andabsolute
absolute
ADCP
ADCP but will
will not
not affect
affect the
the VACMs.
VACMs. Differences
Differences between
velocities
are nearly
with an
velocitiesare
nearly identical,
identical,with
an offset
offsetequal
equalto
to apapthe
of
velocities
from
inproximately 10%
10% of
of the
and we
thespectra
spectra
ofunfiltered
unfiltered
velocities
fromthe
thetwo
twosensors
sensors
in- proximately
the maximum
maximum velocities,
velocities,and
we use
use
dicate
less
dicatethat
thataliasing
aliasingdoes
doesoccur
occurbut
butcontributes
contributes
lessthan
thanaa the
the terms
termsvelocity
velocityand
andvelocity
velocityanomaly
anomalyinterchangeably.
interchangeably.
few
centimeters
per
second
to
the
unfiltered
ADCP
data.
This
figure
and
other
fields
of
few centimeters
per secondto the unfilteredADCP data.
This figure and otherfields of TOPEX
TOPEX cross-track
cross-trackvelocvelocThe
The 40-hour
40-hour filter
filter reduces
reducesthe
the effects
effectsof
of this
thisaliasing
aliasingfurfur- ities
and
AVHRR
SST
patterns
are
similar
ities and AVHRR SST patternsare similarto
tothe
thesummer
summer
ther. Thus
ther.
Thus we
we assume
assumethat
thatthe
the48-rn
48-m velocity
velocityis
is as
asclose
closeto
to patterns
by
surveys
durpatternsdocumented
documented
byhydrographic/ADCP
hydrographic/ADCP
surveys
durgeostrophic as
as we
the
1987-1988
coastal
transition
zone
(CTZ)
experiment
geostrophic
we can
canexpect
expectto
tofind
findand
andthat
thatageostrophic
ageostrophicing
ing the 1987-1988coastaltransitionzone(CTZ) experiment
velocity components
componentswill
willcause
causedifferences
differencesofof4 4cm
cms-•
s1 or
or in
a surface
equatorward
velocity
in the
thesame
sameregion:
region: a
surfacejet
jet meanders
meanders
equatorward
less between
between the altimeter
altimeter and
and filtered
filtered ADCP
ADCP velocities.
velocities.
on
on the
the offshore
offshoreside
sideof
of colder
colderwater,
water,with
with less
lessorganized
organized
flow
inshore of
of this
this jet.
jet. Altimeter
flow and
and SST
SST patterns
patternsfarther
fartherinshore
Altimeter
2.3. Methods:
2.3.
Methods: Horizontal
Horizontal Resolution
Resolution
cross-track
alternate in
in sign
sign on
on scales
of 100-300
cross-trackvelocities
velocitiesalternate
scalesof
100-300
km,
jet and
To check
km, as
asthe
thealtimeter
altimetertracks
trackscross
crossthe
themeandering
meanderingjet
and
To
check the
the horizontal
horizontal resolution
resolution of
of the
the altimeter,
altimeter, we
we
eddy
system.
One
must
remember
that
only
the
flow
estimate the
scales
of
using
in
estimate
thealong-track
along-track
scales
ofvelocity
velocityfeatures
features
usingthe
the eddy system. One must rememberthat only the flow in
to
along-track
AVHRR
temperature gradients
gradients and
and the
the thermal
the direction
directionperpendicular
perpendicular
to the
thealtimeter
altimetertrack
trackcan
canbe
bererealong-track
AVHRR temperature
thermal the
calculation,
wind
persistence
in
solvedby
by the
thegeostrophic
geostrophic
calculation,except
exceptat
atcrossovers.
crossovers.
wind relation.
relation.We
Wealso
alsouse
usecycle-to-cycle
cycle-to-cycle
persistence
in the
the solved
At
the
crossover
at
37.1°N,
127.6°W
(the
ADCP
mooring
horizontal
structure
of
the
altimeter's
cross-track
velocity
At
the
crossover
at
37.1øN,
127.6øW
(the
ADCP
mooring
horizontal structureof the altimeter's cross-trackvelocity
components
The location),
features
location),the
the addition
additionof
of the
thetwo
twocross-track
cross-track
components
features to
to indicate
indicate features
features that
that are
arewell
well resolved.
resolved. The
produces aa velocity
thermal
velocityanomaly
anomalythat
thatis
isdirected
directedapproximately
approximately
thermal wind
wind relation
relationrelates
relatesthe
thevertical
verticalshear
shearof
ofvelocity
velocity produces
toward
the
east
at
30
cm
s*
toward
the
east
at
30
cm
s
-•.
in
one
direction
to
the
horizontal
gradient
of
density
in
a
in one directionto the horizontalgradientof densityin a
The
jet on
The equatorward
equatorwardjet
onthe
theoffshore
offshoreside
sideof
of colder
colderwater
water
direction
to
directionperpendicular
perpendicular
to the
thevelocity:
velocity:
satisfies
the
thermal
wind
relation.
Surveys
from
satisfiesthe thermalwind relation. Surveysfrom1987
1987and
and
gg Op
0V
1988
show uplifted
uplifted isopycnals
and
isotherms
under colder
OV•
op
1988
show
isopycnals
and
isotherms
under
colder
(3a)
=
(3a)
SSTs
on the
Oz
SSTs on
the inshore
inshoresides
sidesof
of the
thecyclonic
cyclonicmeanders
meandersand
and
Oz - p1
p.fOs
Os
deepened
isotherms
under
warmer
SSTs
on
deepenedisothermsunder warmer SSTs on the
theoffshore
offshore
go
g 0
--{p[1
+ a(S
- S0)
- fl(T - -T0)]}
+ .(s
- So)
to)I)
sides
sides of
of the
theanticyclonic
anticyclonicmeanders
meanders[Kosro
[Kosro et
et al.,
al., 1991;
1991;
Huyer et
of
Huyer
et al.,
al., 19911.
1991]. The
Thecorrespondence
correspondence
ofthe
thedeeper
deepertherthermal structure
to
the
SST
patterns
is
confirmed
by
Ramp
et
mal
structure
to
the
SST
patterns
is
confirmed
by
Ramp
et
OVc
.qfi' OT
(3c) al.
in the
m
(3c)
al. [1991],
[1991], who
who find
find significant
significantcorrelations
correlationsin
the same
same
Oz
I Os
.f
Os
region between
between surface
(down
to
region
surfaceand
anddeeper
deepertemperatures
temperatures
(down to
at
least
100-rn
depth).
This
correspondence
between
SST
betweenSST
where zz is
S and
where
is the
the vertical
vertical dimension,
dimension,S
and T
T are
aresalinity
salinityand
and at least 100-m depth). This correspondence
and
justifies our
andthe
thedeeper
deeperthermal
thermalstructure
structure
justifies
ouruse
useof
of the
thetherthertemperature,
and
p
is
the
density,
represented
as
a
linear
temperature,
and p is the density,represented
as a linear mal wind relation in the upper 100 rn of this region
of
the
mal
wind
relation
in
the
upper
100
m
of
this
region
of
the
function
of
salinity
and
temperature
around
some
reference
functionof salinityand temperature
aroundsomereference
California
Current
System.
California
Current
System.
S0 and T0. The parameter, /3, is the coefficient of thermal
0vC
OV•
0z
Oz
_i
pf
p.f Os
Os
(3b)
So and To. The parameter,
•, is the coefficientof thermal
expansion of
of salt
salt water
water and
and c•
a is
of
expansion
isthe
thecoefficient
coefficient
of expansion
expansion 3.2.
3.2. Temporal
Temporal Resolution
Resolutionand
andAccuracy
Accuracyof
of the
theVelocity
Velocity
due to
to salinity.
isisobtained
by
due
salinity.The
Thefinal
finalexpression
expression
obtained
byassuming
assuming Statistics
Statistics
that salinity
inindetermining
density
that
salinityis
iseither
eitherinsignificant
insignificant
determining
density
Stick
(/3'
with
(3'
/3,
Stick plots
plotsof
of the
thedaily
dailyADCP
ADCP velocity
velocityanomalies
anomaliesfrom
from
(•= = /3)
•) or
oris
iscorrelated
correlated
withtemperature
temperature
(• combines
combines
•,
the
mooring
are
presented
in
Figure
2a,
after
removing
tidal
a,
and
the
regression
coefficient
between
temperature
and
the
mooring
are
presented
in
Figure
2a,
after
removing
tidal
c•, and the regression
coefficientbetweentemperature
and
and
inertial
motions
with
the
low-pass
filter
(40-hour
half
salinity).
If
the
value
of
the
velocity
is
V,
at
the
surface
and
and
inertial
motions
with
the
low-pass
filter
(40-hour
half
salinity).If thevalueof thevelocityis Vcat thesurfaceand
power)
and
the
mean
velocity
from
the
period
(approxigoes
to
zero
at
some
reference
depth
(level
of
no
motion)
power)
and
the
mean
velocity
from
the
period
(approxigoesto zero at somereferencedepth(levelof no motion)
mately
cm ss1
InInFigure
2b,
mately44 cm
-• totothe
thesouth).
south).
Figure
2b,the
thesame
samedata
data
Zr,
Z,.,then
then•Oz • Vc/Zr
Vc/Z,.and
and
are
shown
subsampled
to
the
TOPEX
days,
for
comparison
are shownsubsampled
to the TOPEX days,for comparison
Zgf3'
to
Zrg•' AT
to the
the daily
daily ADCP
ADCP data
data in
in Figure
Figure 2a
2a and
and to
to the
theTOPEX
TOPEX
4
vV•C -m Zrg•' OT
()
-- -•AT
(4)
data
in
Figure
2c.
The
TOPEX
vectors
are
reconstructed
f2nAs
Os
data in Figure 2c. The TOPEX vectorsare reconstructed
ff Os
.f2nAs
from
the cross-track
cross-track velocity
velocity anomalies
anomaliesusing
using(lc)
(Ic) and
and (1
(ld).
from the
d).
where
is the
the half
half span
gradient
calculation
Thesedata
dataqualitatively
qualitativelyreveal
revealthe
thetemporal
temporalaspects
aspectsof
of the
the
wheren.
n is
spanof
of the
thecentered
centered
gradient
calculation These
(we
use 2n
2n =- 10
2nAs =- 62
AT is
data,especially
especiallythe
the long
longtimescales
timescalesof
of the
theprimary
primarymodes
modes
(we use
10grid
gridintervals,
intervals,2hAs
62 km)
km) and
andAT
is data,
of
variability,
consisting
of
alternating
currents
the
along-track
temperature
increase
over
the
62
km.
of variability,consistingof alternatingcurrentswith
with periods
periods
the along-tracktemperature
increaseoverthe 62 km.
Z3'
STRUB ET
ET AL.:
AL.: TOPEX
AND
STRUB
TOPEXVELOCITIESACCURACY
VELOCITIES-ACCURACY
ANDALONG-TRACK
ALONG-TRACKRESOLUTION
RESOLUTION
12,731
12,731
41
E
U
;•::.•
.....
25
cm
s- 1T7•.
4o.••.:•
•:•..•'""• + '•':%••
+ •'":'
I
+
40
1
:.:.:,•
....
•:,...
...........
.?-....:::;.:•:;•:
........
':-::.::•
..:..•:.......•:2•:.--.:::::-•:•:•:•::::•:•
...... ::;•'•
•;•{;.:.:•:.;•:•:•::::::::;:
..........
-.:•:.:.-.:;$•-•:.
.......
•.
I
I
39
;.....
+
I
38
ß
"'::
•."-"'.
"-'.z
.....
•:•:.
:.•.•.:
,;•..-...,•
•.•.
..................
:.:?:::•.
•.• .
ß....
...:'..::'-•:.-.
'••.•
'' '•"' ":
-•
•.•
I
I
37
r
36
• • .•'
;. ,••.
.
•/•'•.... ..-•>
'•'
35
?:•:•:•.,•
. .•
129
-129
•-.
128
-128
•:• ...+.•.•.:•,:•.,:•..
127
-127
'•:::
..
. ./.::.•..
,•. •"...?
:.•..
.....
•.;•.
•..•.:.:-•-:
.............
126
-126
125
-125
124
-124
;.......:".....,::.,::..•,
........
•:.,.:•:•,,•
z:•:::•::?
:,..:::.:
.....
123
-125
122
-122
Topex cycle
cycle 002
002 (( October
5-11, 1992
Topex
October5-11,
1992 )
AVHRR
date
AVHRR dote
Oct
Oct
1992
9
9 1992
Figure
velocities
01
Figure 1.
l. AAfield
fieldofofTOPEX
TOPEXcross-track
cross-track
velocitiesfrom
fromcycle
cycle22 (October
(October5-11,
5-l l, 1992),
1992),characteristic
characteristicot
late
and fall,
denote
late summer
summerand
fall, overlain
overlainon
on an
an SST
SST image
imagefrom
fromOctober
October9,
9, 1992.
1992.Lighter
Lightershades
shades
denotecolder
colder
temperatures. The
The current
are located
located under
under the
the crossover
crossover of
of tracks
tracks 54
54 and
and 69.
temperatures.
currentmeter
metermoorings
mooringsare
69.
ADCPotat 48
48 m
ADCP
m
30 •
.0 --=
>..
0
0
v
10
-10
20
o -•o
30
0
Sep92
Sep
92
-20
•
Nov 9f11
I
Jen'
93 ....
Met93
Jan 93
Mar 93
•-
3C
30
>'
>,
ic
10
b.
•o 2C
20
0
0
'9
o
1C
e
'• -10
2C
-20
Jul
Jul93
93
Sep 93
Sep
93
Nov
Nov 93
93
Moy
93
Jul 93
Jul
93
Sep 93
93
Sep
Nov 93
Sep
Sep 93
93
Nov 95
93
Nov
,
/
C
J
Moy
93
May 93
ADCP
Topex times
times (aye)
ADCP•tat Topex
(•ve)
G9
30
•0 -•o
Sep92
'•0 Sep
92
o
Nov 92
Nov
92
Jon
93
Jon
93
30
20
2O
/
10
10
0
10
•-•o
20
-20
30
-30
0
Mot
93
Mar 93
'- Sep92
Sep 92
Nov
Nov92
92
Jan
den93
95
May 93
Topex
using inverse
To
ex using
inverse model
model tide
tide
/
Mar 93
Mot
95
-
May 93
Moy
93
•
/
Nov
93
-
Jul
dul93
95
Figure 2.
from
Figure
2. Stick
Stickplots
plotsofofvelocity
•clocityanomalies
anomalies
f[omthe
theADCP
ADCPmooring
mooting(48-rn
(4g-mbin)
bin) and
andTOPEX
TOPEX crossover
at 37.1
°N, ]27.6øW,
1 27.6°W,from
fromSeptember
September1992
1992thiough
throughOctober
October1993.
1993.(a)
(a) Daily
Daily low-pass
low-pass filtc[cd
filtered (40-hou[
(40-hour
at
37.]øN,
half
power)
ADCP
data;
(b)
10-day
subsampled
low-pass
ADCP
data;
(c)
TOPEX
geostrophic
velocities.
halfpowc[)ADCPdata;(b) ] 0-daysubsampled
low-pass
ADCPdata;(c) TOPEXgcost[ophic
velocities.
12,732
12,732
STRUB ET AL:
AL.' TOPEX
TOPEXVELOCITIES-ACCURACY
VELOCITIES-ACCURACY AND
AND ALONG-TRACK
ALONG-TRACK RESOLUTION
RESOLUTION
of
2-4 months.
variability
of approximately
approximately2-4
months.This
Thislong-period
long-period
variability
is
is associated
associatedwith
with the
theslow
slowmovement
movementof
of the
thejet
jet meanders
meanders
and
point.
andeddy
eddyfield
field(Figure
(Figure1)
1)past
pastthe
thefixed
fixedmeasurement
measurement
point.
Shorter
are also
Shorterfluctuations
fluctuationsare
also apparent
apparentin
in the
the daily
daily ADCP
ADCP
data.
of
data.The
The10-day
10-daysubsampling
subsampling
of the
theADCP
ADCP data
dataindicates
indicates
TOPEX
that
the
sampling
is
capable
of
resolving
that the TOPEX samplingis capableof resolvingthe
thedomdominant
inant temporal
temporalscales,
scales,while
while missing
missingsome
someof
of the
theshorter
shorter
period
periodvariability.
variability.
Statistics of
of the
the ADCP
velocity variability
Statistics
ADCP and
and TOPEX
TOPEX velocity
variability
at
point
in
at the
themooring/crossover
mooring/crossover
pointare
arepresented
presented
inTables
Tables1l aa
and
are the
Vca and
Vd are
and lb.
lb. The
Thecomponents
componentsV•
and V•a
the cross-track
cross-track
velocity
on
(69)
velocityanomaly
anomalycomponents
components
on the
theascending
ascending
(69) and
anddedescending
(54)
altimeter
tracks,
respectively,
while
the
scending(54) altimetertracks,respectively,while the uu and
and
v
are in
in the
v components
componentsare
the nonnal
normaleast
eastand
andnorth
northdirections.
directions.
EKE
is
eddy
kinetic
energy
and
is
simply
O.5(u'2
EKE is eddykineticenergyand is simply0.5(u
•2 +
+ v'2).
v•2).
The
The major
major and
andminor
minor principal
principal axes
axesand
andthe
thedirection
directionof
of
the
the major
majoraxis
axis(here
(herereported
reportedclockwise
clockwisefrom
from north)
north)are
are calcalculated
Morrow et
et al.
al. [1994]
culatedfollowing
following Morrow
[1994] and
andPreisendorfer
Preisendorfer
00
-o
00
Th
-ciocn
a cn rn
i
0
i
N
I-
0
o
b0'
i
'
N
rd
CfC 0'. 0 CI'. 00
O CI'.
("I CfC
cn 00 CSI
N
C,,
000 CI'.
[1988]:
[1988]:
00
00
N
C.)
an = i{u/2+vF2+[(u12
I {•t,
t2 vt2 •
2)2+46?7)2]}
(5a)
+ 4(u'v')2]
«} (5a)
a1
+ v'2)
a22 -= (u"2
0'22
('ut2-3Vt2)--- 0.11
tanO'
0 ==
tan
all
0.11-- 'tt't2
00 -= -(0'
- (0'++90°)
90ø)
'4-.
N
b0
I.,'
0
N
E
C.)
(5b)
(5b)
(5c)
(5c)
'-;C-;'
i
i
i
i
i
N
3c,) 0
C
N
N 0'. CI'.
N
.
0000
E
U
(Sd)
(5d)
where 0.•
a and
where
and a22
0.22are
arethe
thevariances
variancesalong
alongthe
the major
majorand
and
minor
axes,
0'
is
the
direction
of
the
major
axis
as
minoraxes,0• is thedirectionof themajoraxisasmeasured
measured
N
I:,
counterclockwisefrom
fromeast,
east, and
and 00 is
counterclockwise
is the
the direction
direction of
of the
the
major
axis
as
measured
clockwise
from
north,
which
major axis as measuredclockwise from north, which we
we
find a more
find
more natural
natural orientation.
orientation.
The
in Table
Table llaa show
The variance
variance and
and covariance
covariance statistics
statistics in
show
aa drop
dropin
in ADCP
ADCP variances
variancesof
of approximately
approximately30-40%
30-40% when
when
the
the time
time series
seriesare
arefiltered
filtered(40-hour
(40-hourhalf
half power)
power)to
to remove
remove
tidal
the hourly
tidal and
andinertial
inertialperiod
periodenergy.
energy. Subsampling
Subsampling
the
hourly
ADCP
data at
10-day period
period results
results in
in only
ADCP data
at the
the TOPEX
TOPEX 10-day
only
slight
but
slightchanges
changesin
in the
thevariances
variances
butreduces
reducesthe
thealready
alreadylow
low
value
u'v')•) even
value of
of eddy
eddymomentum
momentumflux
flux (covariance,
(covariance,u•v
evenfurfurther.
EKE
ther. Using
Usingmonthly
monthlymeans
meansreduces
reducesthe
thevariances
variancesand
and EKE
another
30-40%.
Variances
of TOPEX
the 10-day
crossanother30-40%.
Variances
of the 10-day
TOPEX
crosstrack velocities
are within
20-30% of
track
velocities are
within 20-30%
of the
the ADCP
ADCP variances
variances
N0
N
N
E
C.)
N
N
N
for
for the
thetwo
two tracks,
tracks,with
withmuch
muchsmaller
smaller(less
(lessthan
than10%)
10%)differdiffer-
ences in
in the
in uu and
ences
the variances
variances in
and v.
v. Both
Both ADCP
ADCP and TOPEX
TOPEX
data
data show
showaa moderate
moderatepolarization
polarizationin
in the
thenorth-south
north-southdirecdirection
during
the
common
1-year
ADCP
period.
tion during the common1-yearADCP period.The
Themagmagnitude
momentumflux
fluxisis40
40cm
cm2
-2
nitudeof
of the
theTOPEX
TOPEXeddy
eddymomentum
2 s-2
compared
to
the
ADCP
value
of
only
6
cm2
-2
(both
negcompared
to theADCPvalueof only6 cm2 s-2 (bothnegative).
ative). The
The TOPEX
TOPEX and
andADCP
ADCP principal
principalaxis
axisstatistics
statisticsfor
for
the same
the
sameperiod
periodboth
bothshow
showpolarization
polarization(ratios
(ratiosof
of 2:1
2:1 and
and
1.5:1 between
between major
major and
and minor
minor axes)
axes) but
but differ
differ in
in the
the didi1.5:1
rection
of
the
major
axes
by
about
20°.
The
ADCP
major
rectionof the major axesby about20ø. The ADCP major
axis
from
axis is
is nearly
nearlydue
duenorth
north(7°counterclockwise
(7øcounterclockwise
from north),
north),
while
the
TOPEX
major
axis
about
30°counterclockwise
while the TOPEX major axis about 30øcounterclockwise
from north
from
north (the
(the difference
differencecaused
causedmostly
mostlyby
by the
thedifferent
different
magnitudes
of
magnitudes
of the
theeddy
eddymomentum
momentumflux).
flux). Overall,
Overall,the
theeddy
eddy
momentum flux
flux and
momentum
and the
the angle
angleshow
showthe
thegreatest
greatestdifference
difference
between
and 48-rn
between the
the TOPEX
TOPEX
and
48-m ADCP
ADCP data.
data.
o•
o
STRUB
ET AL.:
STRUB ET
AL.: TOPEX
TOPEX VELOCITIESACCURACY
VELOCITIES-ACCURACY AND
AND ALONG-TRACK
ALONG-TRACK RESOLUTION
RESOLUTION
12,733
12,733
Table lb.
Table
lb. TOPEX
TOPEX Crossover
Crossover and
and 48-rn
48-m ADCP
ADCP Statistics:
Statistics' RMS
RMS DifferDifferences
encesin
in Velocity
Velocity at
at the
theCrossover
CrossoverFrom
FromCross-Track
Cross-Trackand
andOrthogonal
Orthogonal
Components
Components
vc',,
'Vca,
Vd,
'Vcd,
cm
cm
ss1
cm
cm
ss1
cm
cm
ss1
77
77
5
7
8
4
5
--1
10-day TOPEX-ADCP
TOPEX-ADCP rms
10-day
rms
30-day
30-dayTOPEX-ADCP
TOPEX-ADCP rms
rms
33
Statistics
from the
the full
full 33 years
years of
of TOPEX
TOPEX data
data
Statisticscomputed
computedfrom
are
than those
are more
moreenergetic
energeticthan
thosefrom
from the
the 1-year
1-yearperiod
period(EKE
(EKE
and
and variances)
variances)but
but have
have lower
lower covariances.
covariances.The
Thedirection
direction
of
the
TOPEX
major
axis
is
stable
around
-30°over
of .theTOPEX major axis is stablearound-30øoverall
all peperiods.
The
degree
of
polarization
of
the
variance
ellipse
is
riods. The degreeof polarizationof the varianceellipse is
more like
like the
the ADCP
ADCP data
more
data (ratio
(ratio of
of 1.5:1).
1.5:1). These
Thesedifferences
differences
between statistics
that
between
statisticscalculated
calculatedover
over 11 and
and 3
3 years
yearsindicate
indicatethat
the eddy
momentum flux
flux is
is the
the most
the
eddymomentum
mostunstable.
unstable.Because
Becausethe
the
temporal scales
scales of
of variability
are long
temporal
variability are
long (2-4
(2-4 months),
months),the
the
number
of eddies
eddies sampled
sampled at
at aa single
in aa year
numberof
singlelocation
locationin
year is
is
small.
small. Even
Evenif
if there
thereis
isno
nointerannual
interannualvariability
variabilityin
in the
theeddy
eddy
field,
field, there
there are
are only
only aa few
few degrees
degreesof
of freedom
freedomfor
for records
records
less
than
3
or
more
years.
less than 3 or more years.
--1
v,,
•I
U,
71•,
--1
cm ss --1
cm
cross-track
from the
the same
same time.
time. These
cross-trackvelocity
velocity anomalies
anomaliesfrom
These
show the
the mooring
to the
show
mooringlocations
locationsrelative
relative to
the altimeter
altimetertracks
tracks
and
one instance
instance of
andone
of aa persistent
persistentsmall-scale
small-scaleanticyclonic
anticyclonicfeafeature, discussed
ture,
discussed below.
below.
Data from
Data
from the
the common
common18-month
18-monthperiod
periodof
of VACM
VACM moormooring data,
data, decimated
TOPEX times,
times, are
used to
to
ing
decimatedto
to the
the 10-day
10-dayTOPEX
are used
calculate the
in
calculate
the statistics
statisticspresented
presented
in Tables
Tables2a
2a and
and2b.
2b. StatisStatistics from
from the
the 13-month
ADCP bins
bins at 48
48 and
m are also
tics
13-month ADCP
and 100
100 m
also
presented (the
(the 48-rn
ADCP statistics
presented
48-m ADCP
statisticsare
are repeated
repeatedfrom
from TaTable la).
ble
l a). The
Therms
rmsdifferences
differencesbetween
between48
48 and
and 100
100 m
m are
are 55
cm s
s1,
decrease
ininenergy
with
cm
-• with
witha a20-30%
20-30%
decrease
energy
withdepth,
depth,as
as
reflected
in
lower
values
of
EKE,
variances,
and
reflectedin lower valuesof EKE, variances,andprincipal
principal
axis
ellipses. The
is
axisellipses.
Themean
meanshear
shear
isless
lessthan
than22 cm
cmss-• between
between
these depths,
these
depths,partly
partlybecause
becausesome
someeddies
eddiesappear
appearto
to be
bedepth
depth
intensified. The
flux at
at 100
intensified.
The eddy
eddymomentum
momentumflux
100 m
m is
islarger
larger
in
than at
in magnitude
magnitudethan
at 48
48 m
m and
andthe
theprincipal
principalaxis
axisellipse
ellipse
orientation
is
more
counterclockwise
(24°versus
7°). The
orientation is more counterclockwise(24øversus7ø).
The
100-rn
ADCP velocities
velocities are
are also
also lower
100-m ADCP
lower in
in energy
energythan
than the
the
central
but are
centralVACM
VACM but
are more
moresimilar
similarto
to the
thespatial
spatialaverage
average
of
of the
the four
fourVACM
VACM currents.
currents.Comparing
Comparingthe
thefour
fourVACMs
VACMs
to each
to
eachother,
other,the
the energy
energylevels
levels are
are similar,
similar, while
while the
the eddy
eddy
momentum fluxes
momentum
fluxesand
andprincipal
principalaxis
axisdirections
directionscan
candiffer
differby
by
factors
of 3-5.
from
factorsof
3-5. Statistics
Statistics
fromthe
thewestern
westernmooring
mooringare
are the
the
most different
most
different of
of the
the group,
group,with
with aaprincipal
principalaxis
axisorientaorientation more
more counterclockwise
counterclockwise (-34ø),
(-34°), similar
the altimeter's
tion
similar to
to the
altimeter's
orientation
-30°.
orientationof
of approximately
approximately-30
ø.
An
examination
of
the
velocity
records in
in Figure
Figure 4a
4a and
An examinationof the velocity records
and
4b shows
at
4b
showsexamples
examplesof
of velocities
velocitiesin
in opposite
oppositedirections
directionsat
the northern
(15 km
km apart)
for periods
periods
the
northernand
andcentral
centralmoorings
moorings(15
apart)for
of
(May 1993).
of several
severalweeks
weeks (May
1993). In
In Figure
Figure 4e,
4e, the
the data
datafrom
from
The rms
The
rms differences
differences between
between altimeter
altimeter and
and ADCP
ADCP vevelocity
anomaly components
components are
are shown
shown in
in Table
Table lb
lb for
locity anomaly
for the
the
data
datafrom
from 10-day
10-daycycles
cyclesand
andfrom
from monthly
monthlyaverages.
averages.These
These
indicate
indicate aa basic
basicdifference
differencein
in cross-track
cross-trackvelocities
velocitiesof
of apapto
proximately
7-8 cm
proximately
7-8
cmss-• for
for10-day
10-daydata,
data,which
whichdrops
drops
to
approximately
3-5
cm
s1
for
the
monthly
means.
Figure
approximately
3-5 cm s-1 for themonthlymeans.Figure
33 shows
showsscatterplots
scatterplotsfor
for each
eachof
ofthe
the10-day
10-daycomponents,
components,
48-rn ADCP
ADCP versus
48-m
versusTOPEX,
TOPEX, with
with the
thevalues
valuesof
ofthe
thecorrelacorrelation
indicated.
tion between
betweenthe
theADCP
ADCP and
andTOPEX
TOPEX components
components
indicated.
These
values are
are significant
at the
These correlation
correlationvalues
significantat
the 95%
95% level
level
for
for 5-10
5-10 degrees
degreesof
of freedom.
freedom.Given
Giventhe
thelong
longtimescales
timescalesof
of
the
the dominant
dominantvelocity
velocityfluctuations,
fluctuations,the
the number
numberof
of degrees
degrees
of
less than
than 10
of freedom
freedomare
are probably
probablyless
10 for
for the
theI-year
1-yearrecord.
record.
Figure
2
makes
it
clear,
however,
that
the
altimeter
capFigure 2 makes it clear, however,that the altimeter
captures
this
long-period
variability.
The
differences
between
turesthis long-periodvariability. The differencesbetween
the
48 m
m below
the surface
the ADCP
ADCP velocities
velocities(measured
(measured48
below the
surfaceat
at aa
single
point)
and
the
geostrophic
cross-track
velocities
(calsinglepoint)andthe geostrophic
cross-track
velocities(caland the
the altimeter
on May
May 1I depict
culated
on
all five
five moorings
moorings and
altimeter on
depictan
an
culatedusing
usingaa62-km
62-kmsurface
surfaceheight
heightdifference
differencecentered
centered
on all
the array
that
anticycloniceddy
eddythat
that moved
movedover
overthe
arrayand
andcaused
causedthis
this
that point)
point) are
are not
notonly
only due
dueto
to errors
errorsand
andnoise
noisein
in the
thealal- anticyclonic
horizontal variability.
velocities
timeter
by
horizontal
variability. The
The altimeter's
altimeter'scross-track
cross-track
velocities
timeterdata.
data.They
Theyare
arealso
alsocaused
caused
bysmall-scale,
small-scale,
horizontal horizontal
capture
the
anticyclonic
sense
and
the
position
of
the
differences
in
measured
point
velocities
that
the
geostrophic
feature
differencesin measuredpoint velocitiesthat the geostrophic capturethe anticyclonicsenseandthepositionof thefeature
calculation
calculation does
does not
not resolve,
resolve, as
as well
well as
asvertical
vertical shears
shearsbebe- but
but fail
fail to
to represent
representthe
thesmall-scale
small-scalenature
natureof
of the
the feature
featureand
and
tween
velocities
the true
true velocity
velocityat
at the
thecrossover.
crossover.
tweenthe
thesurface
surfacegeostrophic
geostrophic
velocities(estimated
(estimatedby
by the
the the
By averaging
altimeter)
By
averagingthe
the velocities
velocitiesfrom
from the
the four
four moorings
mooringsfor
for
altimeter)and
and measured
measuredvelocities
velocitiesat
at 48
48 m.
m.
each hour,
hour, an
The
each
an estimate
estimateof
of aa spatially
spatiallyaveraged
averagedvelocity
velocitycan
can
The effects
effects of
of small-scale
small-scale vertical
vertical and
andhorizontal
horizontal varivaribe formed over a region approximately 30 km across. Alability can
can be
be evaluated
ability
evaluatedby
by statistics
statisticsfrom
from the
the4848- and
and100100- be formed over a region approximately30 km across.Although this
this spatial
is over
m
spatialaveraging
averagingis
over aa smaller
smallerregion
regionthan
than
m ADCP
ADCP bins
bins and
andthe
theVACMs
VACMs from
from 100-m
100-m depth
depth at
at four
four though
the
60-80
km
smoothing
inherent
in
the
altimeter
moorings
the
velocity
mooringssurrounding
surrounding
theADCP
ADCP mooring,
mooring,with
with separations
separations the 60-80 km smoothinginherentin the altimetervelocity
it is
calculation, it
is more
more like
like the
the altimeter
altimeter estimate
estimate than
than curcurof
of 15
15 km.
km. Daily
Dailyfiltered
filteredvelocity
velocityanomalies
anomaliesfrom
from two
two of
of calculation,
rents
from
the
individual
moorings.
The
averaging
causes
the
moorings
are
shown
in
Figures
4a
and
4b
(located
15
rents
from
the
individual
moorings.
The
averaging
causes
the mooringsare shownin Figures4a and 4b (located15
velocities,
km north
dropof
of 17%
17%in
inEKE
EKE for
forthe
thespatially
spatiallyaveraged
averaged
velocities,
km
northand
and 22 km
km east
eastof
of the
theADCP
ADCP mooring),
mooring),along
alongwith
with aa drop
as
compared
with
the
central
mooring
(Table
2a),
with aa
the
spatially
averaged
velocity
from
all
four
100-rn
mooras
compared
with
the
central
mooring
(Table
2a),
with
the spatiallyaveragedvelocityfrom all four 100-m moor•2
•2
reduction in
in ,u
u'2
(25%)
than vv'2
(13%).
ings,
10-day
(Figure
greaterreduction
(25%) than
(13%). The
The value
value
ings,decimated
decimatedto
to the
thealtimeter's
altimeter's
10-daysampling
sampling
(Figure greater
averaged
eddy
flux
4c) and
of the
thespatially
spatially
averaged
eddymomentum
momentum
fluxisis-34
-34cm2
cm2
4c)
andthe
the10-day
10-dayaltimeter
altimeterdata
data(Figure
(Figure4d).
4d). A
A horizontal
horizontal of
this
18-month
period,
more
like
value
snapshot
s-2for
for
this
18-month
period,
more
likethe
thealtimeter's
altimeter's
value
snapshotof
of velocity
velocityanomalies
anomaliesfrom
from all
all five
five moorings
mooringson
on s2
rather than
than the
May
-36 cm2
of-36
cm2 s-22 for
forthe
thesame
sameperiod,
period,rather
the48
48 and
and
May 1,
1, 1993,
1993, is
isshown
shownin
inFigure
Figure4e,
4e,along
alongwith
withTOPEX
TOPEX of
STRUB
ET AL.:
AL.:
TOPEX
VELOCmESACCURACY AND
STRUB ET
TOPEX
VELOCITIES-ACCURACY
AND ALONG-TRACK
ALONG-TRACK RESOLUTION
RESOLUTION
12,734
12,734
30
3O
___________
30
3O
a.
r=0.70
r = 0.65
r'=
0.65
20
2O
>'
+
+
0
o
-
+p+
+
10
+
0
+
20
2O
+
10
lO
IJ
,[,,,,,,,l,,,,,,,],[,,,,,,,,
b.
++
ci,
>
+
/4•+
0
0
o -10
10
+
o
-lo
20
-2O
20
-20
30
-3O
30
-50
300 20
10
-20
-10
30 20
10
-20
-10
-30
0
20
20
10
10
30
30
30
3O
d.
EH.
rr == 0.73
0.73
20
2O
+
+
++
0' 'U
/
0
0
>..
10
t
!
-o
20
20
10
10
20
20
30
30
+++
(I)
ci,
e
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+
r=0.59
+
++.• ++
++
(-I
+
+
0.59
10
C
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+
0
>'
+• •+ +
o_
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+++/2 L+ +
++
0
0
C
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++
10
10
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0
0
ci,
>
o
0
+
0
0
(I,
•o
0
30
30
C.
..E
iii1[11111
iiil[1111ltll
Topex velocity
velocity N/S
N/s
Topex
Topex velocity
velocity E/W
Topex
E/W
•
+
0
-
o'U -10
ß
>
ß
ci
<
• 20
20
30
30
nmn ..
,
300 20
10
-20
-10
0
0
10
10
20
20
30
30
Topex
velocity ascending
Topex velocity
ascending track
track
0
•
20
-20
30
30
20
10
-30
-20
-10
-30
0
0
10
10
20
20
30
50
Topex
velocity descending
Topex velocity
descending track
track
Figure 3.
of
for the
the 13
13 months
months of
of data:
data: (a)
(a) u,
Figure
3. Scatterplots
Scatterplots
ofADCP
ADCP versus
versusTOPEX
TOPEX velocity
velocitycomponents
components
for
,u,,
areinincentimeters
centimeters
second.
Correlations
are shown
in theleft
upper
Vca, (d) Vd.
(b) v,
v, (c) Vca,
Vca. Units
Units are
perper
second.
Correlations
are shown
in the upper
for left for
the data
data in
the
in each
eachpanel.
panel.
100-rn
ADCP values
values of
100-mADCP
of -6
-6 and
and-17
- 17 cm2
cm2 ss2
-2for
forthe
the1-year
1-year
period
(the
altimeter's
value
changes
very
little
between
the
period(the altimeter'svaluechangesverylittle betweenthe
1-year
and
18-month
period).
This
provides
evidence
that
1-yearand 18-monthperiod). This providesevidencethat
the
of
the TOPEX
TOPEX velocities
velocitiesare
aremore
morerepresentative
representative
ofspatially
spatially
averaged
currents,
eliminating
small-scale
variability.
averagedcurrents,eliminatingsmall-scalevariability.
The
The rms
rmsdifferences
differencesbetween
betweenTOPEX
TOPEX velocity
velocityanomalies
anomalies
and those from
and
from the
the individual
individual 100-rn
100-m central
central and
and southern
southern
mooring
velocities are
are 7-8
7-8 cm
cm s
s1
2b),
to
mooring
velocities
-1(Table
(Table
2b),similar
similar
tothe
the
difference between
between TOPEX
TOPEX and
and ADCP
ADCP (48
difference
(48 and
and 100
100 m)
m) vevelocity anomalies.
locity
anomalies.Velocities
Velocitiesfrom
fromthe
thenorthern
northernand
andwestern
western
TOPEX and
and ADCP
ADCP velocities.
TOPEX
velocities. On
On the
the smallest
smallestscales,
scales,the
the
rms
the 100-rn
ADCP bin
bin and
rms difference
difference between
between the
100-m ADCP
and the cencentral
(separatedby
by22km)
km)isis3-4
3-4cm
cmss1.
tral VACM
VACM (separated
-1. We
Wetake
take
this
to
be
the
level
of
measured
velocity
"noise",
caused
by
thisto be the level of measured
velocity"noise",causedby
aliasing
of
internal
waves
by
the
ADCP's
burst
sampling,
aliasingof internalwavesby the ADCP's burstsampling,
very
very small-scale
small-scalecurrents,
currents,etc.
etc.
ences between
from
ences
betweenthe
the velocity
velocityanomaly
anomalycomponents
components
from the
the
central
mooring
and
the
surrounding
moorings,
separated
by
centralmooringandthe surrounding
moorings,separated
by
from other
other unresolved
unresolved sources
sources and
and current
current meter
meter noise.
noise. This
This
from
As
we attribute
the 77As aa result
resultof
of these
thesecomparisons,
comparisons,we
attributethe
8 cm
differences
between
cm s1
s-1rms
rms
differences
betweenthe
thealtimeter
altimeterand
and the
the
ADCP
(at both
both 48
48 and
ADCP velocities
velocities(at
and 100
100 m)
m) to
tocontributions
contributions
of 5-7 cm
s1
rms
from
natural,
small-scale,
horizontal
cm s-1 rms from natural,small-scale,
horizontal
mooring
produce
slightly
higher
values.
The
rms
differvariability,
5
cm
s1
from
vertical
shears,
and
3-4
mooringproduceslightly higher values. The rms differ- variability,
5 cm s-1 fromverticalshears,
and3-4 cm
cmss-1
apportioning
accounts for
for the
the complete
of the
apportioningaccounts
completemagnitude
magnitudeof
the
(Table 2c),
2c), revealing
revealing that
that the
the degree
degree difference
15 km,
km, are
are 5-7
5-7 cm
difference between
between the altimeter
altimeter and
and current
current measurements
measurements
15
cmss-• (Table
of small-scale
and suggests
that the
error is
is no
than the
the
of
small-scalevariability
variabilityin
in the
theoceanic
oceanicvelocity
velocityfield
field at
atthis
this and
suggeststhat
the altimeter
altimetererror
no greater
greaterthan
between
current
meters
separated
by
location is
is nearly
the 3-4
location
nearlyas
aslarge
largeas
asthe
therms
rmsdifference
differencebetween
betweenthe
3-4 cm
cmss-1 difference
difference
between
current
meters
separated
by
STRUB ET
ET AL:
STRUB
AL.: TOPEX
TOPEXVELOCITIES-ACCURACY
VELOCITIES-ACCURACY AND
AND ALONG-TRACK
ALONG-TRACK RESOLUTION
RESOLUTION
12,735
12,735
at 102.m
( 37.215,-127.618
37.215,-127.618 )) at
102.m (North)
(North)
2
i
oire
.........................
'
E
-20
Sep
Sep 92
92
Nov
Nov 92
92
Jon 93
Jan
93
Nor 93
Mar'
93
Jul
Jul 93
93
May
May 93
93
Nov 93
93
Nov
Sep
Sep 93
93
Jan 94
Jan
94.
Nor
Mar'94
94.
Jul
Jul 94
94.
May 94.
94
May
Sep 94
Sep
94.
37.1 12,-127.535 )) at
( 37.112,-127.535
ot 98.m
98.m (Center)
(Center)
ß
,
Nov 92
Nov
92
Sep
Sep 92
92
30
30
20
Jon
Jan 93
93
Nor
Mar 93
93
Jul 93
Jul
93
May
May 93
93
Nov
Nov 93
9•
Sep 93
Sep
9•
Jon
Jan 94
94
Mar 94
Mar
94
May
May 94
94
,
,
Jul
Jul 94
94
Sep
Sep 94
94
Average
at 100.
Averoge ot
100. m
rn
.
c'10
E
...
10
Eø-10
20
-20
-30
30
...................
Nov
Nov 92
92
Sep 92
Sep
92
30
30
20
20
Jon 93
Jan
9,3
Mar 93
Mar
9,3
Jul
Jul 93
9,3
May
May 93
9,3
Jan 94
Jan
94
Mar 94
94
Mar
Jar( 9
Mar
Mar 94
94
May 94
94
May
Jul 94
Jul
94
Sep 94
94
Sep
Jul
Jul 94
94
Sep
Sep 94
94
'N//
10
10
0
0
10
20
-20
30
-50
Nov 93
Nov
9,3
Topex velocity
Topex
velocity
.
(4)
E
Sep 93
93
Sep
,
,
Sep
Sep 92
92
Nov
Nov 92
92
Jan
Jan 93
9,3
Mar
Mar 93
9,3
Jul 93
Jul
95
May 9,3
93
May
,
,
Sep
Sep 93
93
i
,
Nov
Nov 93
93
,
,
May
May 94
94
38.0
38.0
37.5
57.5
7
'7 L
L
L
>
I
37.0
57.0
36.5
56.5
Figure 4.
of
Figure
4. Comparison
Comparison
ofvelocities
velocitiesfrom
from100-rn
100-m deep
deepcurcurrent
the
point,
rentmeters
metersfrom
frommoorings
mooringssurrounding
surrounding
thecrossover
crossover
point,
August
August1992-September
1992-September1994.
1994. Mean
Meanvelocities
velocitieshave
havebeen
been
'7
25
25 cm/sec
cm/sec
T
V
, -i•' ....
-128.
-128.
i , , •',/,
-127.5
-127.5
I ,
-127.
-127.
Topexcycle
cycle02,3
023(9,3121
(93121 -- 93121)
Topex
9,3121)
removed from
from the
the records
removed
records for
for the
the display
displayperiods.
periods. (a)
(a)
Daily low-pass
low-pass filtered
filtered velocities
velocities from
from 15
15 km
km north
north of
of the
the
Daily
crossover. (b)
from 22 km
crossover.
(b) Daily
Daily low-pass
low-passfiltered
filtered velocities
velocitiesfrom
km
northeast of
the crossover
(central
northeast
of the
crossover
(centralmooring).
mooring).(c)
(c)Ten-day
Ten-dayvevelocities from
from the
locities
the average
averageof
of the
thefour
fourmoorings
moorings(the
(thecentral
central
mooring and
and moorings
moorings located
located 15
km to
to the
the north,
north, west,
mooring
15 km
west,and
and
south of
south
of the
the crossover),
crossover),subsampled
subsampledat
at the
the altimeter
altimetertimes.
times.
(d)
Ten-day velocities
velocities from
from the
the altimeter.
altimeter. (e)
(e) TOPEX
TOPEX crosscross(d) Ten-day
track velocities
track
velocitiesand
and 100-rn
100-m ADCP
ADCP (center)
(center)and
andVACM
VACM vevelocities for
for May
May 1,
locities
1, 1993.
1993. This
Thisshows
showsthe
theposition
positionof
of the
the
current meter
relative to
to the
current
meter moorings
mooringsrelative
the altimeter
altimeter tracks
tracks and
and
demonstrates the
the degree
demonstrates
degreeof
of small-scale
small-scalevariability
variability that
that can
can
be
caused
by
eddies
in
the
region.
be causedby eddiesin the region.
STRUB ET
ET AL:
STRUB
AL.' TOPEX
TOPEXVELOCITIESACCURACY
VELOCITIES-ACCURACY AND
ANDALONG-TRACK
ALONG-TRACK RESOLUTION
RESOLUTION
12,736
12,736
Table
From
10-Day
Table 2a.
2a. Statistics
Statistics
FromNearby
NearbyMoorings:
Moorings:Filtered
Filteredand
andSubsampled
Subsampled
10-DayCurrent
CurrentMeter
Meter Data
Data
Major
Major
Axis
Axis
0'•,,
cm2
s22
cm
2 s-
0¾,
cm2
s22
cm2 s-
u'v',
U'V',
cm2
cm
2 s-s22
EKE,
EKE,
cm2
s2
cm2 s-
81
77
77
92
92
73
146
146
136
136
128
128
144
144
113
107
107
110
110
108
108
55
55
78
125
125
-14
-14
-72
-72
-17
- 17
-19
- 19
-34
-34
-17
-17
-6
2
North
North
West
West
South
South
Center
Center
VACM
VACM average
average
100-rn ADCP
ADCP
100-m
48-rn
48-m ADCP
ADCP
2
110
110
149
101
90
90
94
94
125
Minor
Minor
Axis
Axis
9, deg
0,
deg
011,
0'11,
022,
0'22,
cm2
s2
cm2 s-2
cm2
s22
cm2 s-
148
184
184
134
134
149
149
139
139
78
29
85
85
68
41
41
-12
-12
-34
-34
-21
-21
--14
14
117
150
71
100
-24
-24
-7
-22
-22
As
As in
in Table
Table la.
l a.
2-km.
be conservative,
conservative,we
weuse
usevalues
valuesofof3-5
3-5cm
cms-•s' for
2-km. To be
for These
Thesehourly
hourlytime
time series
serieswere
weredecimated
decimatedto
to the
the TOPEX
TOPEX1010day
spectra
day sampling
samplingtimes
timesto
to produce
producesubsampled
subsampled
spectra(dashed
(dashed
velocities
TOPEX geostrophic
lines) for
for the
(Figure 5a)
5a) and
Although
the spatially
spatiallyaveraged
averagedvelocities
velocities(Figure
and
Althoughthe
the TOPEX
geostrophic
velocitiesappear
appearacac- lines)
the
individual
northern
mooring
(Figure
5b).
The
curate,
the
10-day
sampling
creates
a
Nyquist
period
of
20
dashed
curate,the 10-daysamplingcreatesa Nyquistperiodof 20 the individual northernmooring(Figure 5b). The dashed
calculated
days.
to
TOPEX
line in
in Figure
Figure5c
5c is
isthe
thespectrum
spectrum
calculatedfrom
from TOPEX
days.The
The ability
ability of
of the
the TOPEX
TOPEX data
dataat
at crossovers
crossovers
to corcor- line
data
from
the
2-year
period
coincident
with th
rectly
represent
frequency
spectra
of
velocities
is
thus
subdata
from
the
2-year
period
coincident
with
the
northern
rectlyrepresentfrequencyspectraof velocitiesis thussubmooring deployment
deployment times.
times. In
are
ject
higher
In Figure
Figure5d,
5d,spectra
spectra
areprepreject to
toaliasing
aliasingof
ofenergy
energywith
withfrequencies
frequencies
higherthan
than0.05
0.05 mooring
cycle
d'.
data
from
thethe
current
meters
provide
estisentedfrom
from the
thespatially
spatiallyaveraged
averaged100-rn
100-mmooring
mooringdata,
data,subsubcycled
-•.The
The
data
from
current
meters
provide
esti- sented
TOPEX 10-day
times (solid
(solid line),
line), from
TOPEX
mates
sampledto
to TOPEX
10-day times
from TOPEX
matesof
of the
thecomplete
completespectra
spectraof
of currents
currents(over
(over1-2
1-2 years).
years). sampled
data from
Subsampling
of the
from the
thesame
same18-month
18-monthperiod
periodas
ascovered
coveredby
by the
thespaspaSubsamplingof
the current
currentmeters
metersat
atthe
the10-day
10-dayTOPEX
TOPEX data
sampling
times
indicates
that
aliasing
is
indeed
a
problem,
tially
averaged
mooring
data
(dashed
line)
and
from
thefull
full
samplingtimesindicatesthat aliasingis indeeda problem, tially averagedmooringdata (dashedline) and from the
although
currents.
3 years
yearsof
of TOPEX
TOPEX data
data(dotted
(dottedline).
line).
althoughnot
notas
assevere
severefor
forthe
thespatially
spatiallyaveraged
averaged
currents. 3
mooring
Figures
(in
It can
canbe
beseen
seenthat
thatsubsampled
subsampled
mooringdata
dataproduce
produce
Figures5a
5a and
and5b
5bpresent
presentthe
thespectra
spectra
(in energy-preserving
energy-preserving It
form)
components
of
spectra with
at low
form) for
for the
thecross-track
cross-track
components
ofvelocity
velocityanomalies
anomalies spectra
with artificially
artificiallyenhanced
enhancedenergy
energyat
low frequenfrequencies, especially
from
from the
the 100-m
100-mVACM
VACM on
on the
thenorthern
northernmooring
mooring(15
(15 km
km cies,
especiallyfor
for the
theindividual
individualnorthern
northernmooring
mooring(Figure
(Figure
5b). The
ADCP
to
point),
to the
thenorth
northof
ofthe
thecrossover
crossover
point),which
whichhas
hasthe
thelongest
longest 5b).
Thesame
sameis
istrue
trueof
ofthe
theshorter
shorter
ADCP record
record(not
(notpicpicrecord
of all
tured). When
When the
thehourly
hourlycurrent
currentmeter
meterdata
dataare
arefirst
firstfiltered
filtered
record(2
(2 years),
years),and
andfrom
from the
thespatial
spatialaverage
averageof
all four
four tured).
with aa half
100-m
VACMs over
over their
their common
period. The
100-m VACMs
common18-month
18-monthperiod.
The with
half power
power of
of 20
20 days,
days,the
thesubsampled
subsampleddata
data do
do not
not
produce
the
higher
low-frequency
spectra,
indicating
velocities
used
are
the
components
in
the
cross-track
dithat
velocitiesused are the components
in the cross-trackdi- producethe higher low-frequencyspectra,indicatingthat
crossover. The
the problem
problem is
rection
for the two
rection for
two tracks
tracks at the
the TOPEX
TOPEX crossover.
The
the
is aliased
aliasedenergy
energywith
with periods
periodsshorter
shorterthan
than20
20
individual
spectra
from
the
two
tracks
are
averaged
in
each
days.
It
appears
to
be
less
severe
of
a
problem
for
the
spaindividualspectrafrom the two tracksareaveraged
in each days. It appearsto be lesssevereof a problemfor thespacase. The
tially averaged
averaged currents
currents (Figure
(Figure 5a),
5a), for
for which
case.
The hourly
hourlycurrent
currentmeter
meterdata
data(after
(afterapplying
applyingthe
the 4040- tially
which the
the spectral
spectral
hour
the
slopes at
at low
correct. This
low frequency
frequencyare
are approximately
approximatelycorrect.
This is
is
hourhalf
halfpower
powerfilter)
filter)are
areused
usedto
tocalculate
calculate
thefull
fullspectra,
spectra, slopes
which are
in
which
arepresented
presented
in the
thefirst
firstthree
threepanels
panelsfor
forthe
thenorthern
northern consistent
consistentwith
with the
thefact
factthat
thatthere
thereis
isless
lessenergy
energyat
atfrequenfrequenmooring
(dotted
greater than
than 0.05
0.05cycle
cycledd'
of
mooring(solid
(solidlines)
lines)and
andthe
thespatial
spatialaverage
average
(dottedlines).
lines). cies
ciesgreater
-• ininthe
thefull
fullspectrum
spectrum
ofthe
the
spatially
averaged
data
(Figure
5a)
than
in
the
individual
spatially averageddata (Figure 5a) than in the individual
mooring
energy
mooring(less
(lesshigh-frequency
high-frequency
energyto
to be
be aliased).
aliased).
Therefore
it
seems
likely
that
the
TOPEX
Table 2b.
mis
Thereforeit seemslikely that the TOPEX spectra
spectrain
in FigFigTable
2b. Statistics
StatisticsFrom
FromNearby
NearbyMoorings:
Moorings: 10-day
10-day rms
Difference
ures
Sc
and
Sd
contain
aliased
high-frequency
energy,
Difference from
from TOPEX
TOPEX
ures5c and5d containaliasedhigh-frequency
energy,which
which
the altimeter
the
altimetervelocity
velocityuncertainty.
uncertainty.
Vca,
Vca •
cm
North
North
West
West
South
South
Center
Center
Average
Average
100-rn
ADCP
100-m ADCP
48-rn
48-m ADCP
ADCP
As
As in
in Table
Table lb.
lb.
s
--1 1
Vd,
Vcd•
rm
cm
s
--1 1
U,
71,•
cm s'
cmv;_1
--1
9
9
8
9
10
8
cm
s
--1
cm
s
8
8
8
7
10
10
9
7
8
7
7
77
7
7
7
7
6
7
66
8
8
7
7
8
8
7
Table
Statistics From
From Nearby
Nearby Moorings:
Moorings: 10-day
Table 2c.
2c. Statistics
10-dayrms
rms
Difference Between
Between the
the Central
Moorings
Difference
Centraland
andSurrounding
Surrounding
Moorings
U,
--1
cm
cm s
s
North
North
West
South
100-rn
ADCP
100-m ADCP
7
7
7
4
4
v,
--1
cm
cm ss
5
6
5
3
STRUB ET AL:
AL.:TOPEX
TOPEXVELOCITIES-ACCURACY
VELOCITIES-ACCURACY AND
AND ALONG-TRACK
ALONG-TRACK RESOLUTION
RESOLUTION
60
6O
200 10 5033 20
60
ib
200 lt0 5033 20
?
•,
-
10
- 2 yr
North
2 yr
Northhourly
hourly
a - 2 yr2 North
yr Northhourly
hourly
50
5O
12,737
12,737
1.5 yr
yr average
...... 1.5
overoge hourly
hourly
yr average
...... 1
1.5.5 yr
overoge hourly
hourly
- - 1010day
-doyoverage
overoge
--- - 1010day
doyNorth
North
.
40
40
.
40
E
U
**
30
30
\
>..
-
o
0
ß
20
_.e 20
.
20
10
lO
0
i
i
i
,
i
0.10
O. lO
cycles/day
cycles/doy
60
6O
2
200 10 5033 20
'•
'
40
40
E
0
60
ib
d
''I
'I
1.00
1.00
200 10 5033 20
10-day
10-doyspatial
spotiol
o.
-
--2
Il
0.10
0.10
0.01
0.01
hourly
hourly
yr
jA --2
yr Topex
Topex
x
?
•
i
cycles/day
cycles/doy
2 yr
yr North
North
hourly
hourly
1.5
yr
.... 1.5 yr average
overoge
50
5O
i
1.00
1.0o
0.01
0.01
-
average
overoge
- -1.5 yrs
--1.5
yrsofofTopex
Topex
..... 3
5 yrs
yrs of
of Topex
Topex
'
II
40
!
U
!
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>'
0
30
50
!
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!
_e 20
t.
20
'I'
\%
ß
I I
I
10
10
0
0
,,,,
0.10
0.10
cycles/day
cycles/doy
0.01
0.01
1.00
1.00
0.001
0.001
I
I
0.010
0.100
0.010
0.100
cycles/day
cycles/doy
1.000
1.000
Figure
autospectra
for
of
velocities. Low-pass
Low-pass (40-hour
(40-hour half
half power)
power)
Figure5.
5.Frequency
Frequency
autospectra
forvariances
variances
of cross-track
cross-track
velocities.
filtered
at
filteredmeasured
measuredcurrents
currentsfrom
from 100
100 m,
m, measured
measuredcurrents
currentssubsampled
subsampled
at the
the10-day
10-dayTOPEX
TOPEX crossover
crossover
current estimates.
estimates. All
times,
times,and
and TOPEX current
All spectra
spectraare
areaverages
averagesof
of the
thetwo
two individual
individualspectra
spectrafrom
from the
the
ascending
and
descending
cross-track
components.
Spectra
are
presented
in
energy-preserving
form.
ascending
anddescending
cross-track
components.
Spectraarepresented
in energy-preserving
form.(a)
(a)
Spectra
currents from
from the
the mooring
mooring 15
15 km
km north
Spectrafrom
from 24
24 months
monthsof
of hourly
hourlymeasured
measuredcurrents
northof
of the
thecrossover
crossover
(solid
hourly
currents
(solidline)
line) and
andfrom
from18
18months
monthsof
ofspatially
spatiallyaveraged
averaged
hourlymeasured
measured
currentsfrom
fromthe
thefour
fourmoorings
moorings
times
(dotted
currents
subsampled
at
(dottedline),
line), and
andthe
thesame
samespatially
spatiallyaveraged
averaged
currents
subsampled
atthe
the10-day
10-dayTOPEX
TOPEX crossover
crossover
times
(dashed
(dashedline).
line). (b)
(b) As
As in
in Figure
Figure5a,
5a, except
exceptfor
for the
thedashed
dashedline,
line, which
whichis
is now
nowthe
the10-day
10-daysubsampled
subsampled
data
mooring. (c)
(c) As
data from
from the
the northern
northernmooring.
As in
in Figure
Figure5a,
5a, except
exceptfor
for the
the dashed
dashedline,
line, which
which is
is now
now the
the
over the
the same
same 24
24 months
months used
used for
for the
the northern
mooring. (d)
10-day
10-dayTOPEX
TOPEX velocities,
velocities,over
northernmooring.
(d) Spectra
Spectrafor
for the
the
using the
the same
subsampled,
spatially
measured currents
currents (solid
(solid line),
line), from
subsampled,
spatiallyaveraged
averaged
measured
fromTOPEX
TOPEX using
same18
18months
months
record
as
measured
currents
line), and
asfor
for the
thespatially
spatiallyaveraged
averaged
measured
currents(dashed
(dashedline),
andfrom
fromthe
thefull
full 3-year
3-yearTOPEX
TOPEX record
(dotted
(dottedline).
line).
STRUB ET AL.:
STRUB
AL.: TOPEX
TOPEX VELOCITIES-ACCURACY
VELOCITIES-ACCURACY AND
AND ALONG-TRACK
ALONG-TRACK RESOLUTION
RESOLUTION
12,738
12,738
100 50
50
?
20
20
lOO
1.4x104 a
10
lO
5
2
100
10050
5'0
- 1.4x104
b
-10 10
dayday
ADCP
ß
ADCP
-filtered
redhourly
hourlyADCP
ADCP
--filtered
filtered hourly
hourlyNorth
North
1.2x104
.... filtered
filtered hourly
hourlyCenter
Center
- 10 day North
- 1.2x104 ' - 10 day North
...... 10
10 day
day Center
Center
1.0x104
- 1.0x104
_
E
o
v 8.0xl 03
o
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-6.Ox 10
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2.0x103
' 5'! ....
0
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0.00
o.ool
0
0.010
0.100
0.010
O.
1 O0
cycles/day
cycles/day
1
200
200 100
100 50
50
1.4x
1.4x104 CC
20
20
10
10
1.000
1.000
!
I
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1.000
1.000
cycles/day
cycles/day
55
2
2
200100
200
1O050
5'0
-
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1.4
-filtered
hrlyhrly
spatial
average
ß
filtered
spatial
overage
10
day
spatial
average
1.2
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1.2x104
' - 10dayspatial
overage
iveroge
day
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spatial .everage
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Figure
spectra
for
presented
ininenergy-preserving
form.
filtered
Figure6.6.Frequency
Frequency
spectra
forcovariances,
covariances,
presented
energy-preserving
form.(a)
(a)Low-pass
Low-pass
filtered
hourly measured
currents
from
at
(solid
line),
mooring
hourly
measured
currents
fromthe
theADCP
ADCPvelocity
velocity
at48-rn
48-mdepth
depth
(solid
line),from
fromthe
thenorthern
northern
mooring
at
line),
mooring
at
line).
filtered
at 100
100m
m(dashed
(dashed
line),and
andfrom
fromthe
thecentral
central
mooring
at100
100m
m(dotted
(dotted
line). (b)
(b) Low-pass
Low-pass
filtered
measured currents
currents subsampled
at the
times for
for the
the ADCP
measured
subsampled
at
the10-day
10-dayTOPEX
TOPEXcrossover
crossover
times
ADCPvelocity
velocityat
at 48-rn
48-m
depth (solid
mooring
at 100
line), and
mooring
at
depth
(solidline),
line),from
fromthe
thenorthern
northern
mooring
at
100rn
m (dashed
(dashed
line),
andfrom
fromthe
thecentral
central
mooring
at
100 m
m (dotted
(dotted line).
line). (c)
filtered,
averaged measured
measured currents
currentsat
at 100
100 m
m (solid
(solid
100
(c)Low-pass
Low-pass
filtered,hourly,
hourly,spatially
spatially
averaged
line) and
and the
the same
at the
the 10-day
crossover times
times (dashed
(dashed line).
line). (d)
line)
samedata,
data,subsampled
subsampled
at
10-dayTOPEX
TOPEXcrossover
(d)Covariance
Covariance
spectra from
from the
of
averaged
measured
currents,
subsampled at
at the
the 10-day
TOPEX
spectra
the18
18months
months
ofspatially
spatially
averaged
measured
currents,
subsampled
10-dayTOPEX
crossover
times
data over
the same
period (dashed
line), and
crossover
times(solid
(solidline),
line),from
fromTOPEX
TOPEXdata
overthe
same18-month
18-month
period
(dashed
line),
andfrom
from
TOPEX
TOPEX data
dataover
overthe
thefull
full3-year
3-yearperiod
period(dotted
(dottedline).
line).
cannot
of
in
cannotbe
be removed.
removed.What
Whataspects
aspects
of the
theTOPEX
TOPEX spectra
spectra
in
Figure
5d
are
realistic?
The
18-month
TOPEX
data
proFigure5d are realistic?The 18-monthTOPEX dataproduce
with
duceaa spectrum
spectrum
withsimilar
similarshape
shapearound
aroundperiods
periodsof
of 100
100
days
100-rn
daysto
to the
thespatially
spatiallyaveraged
averaged
100-mcurrent
currentmeter
meterrecord,
record,
although
with
The
energy is
although
withhigher
higherenergy.
energy.
Thehigher
higherTOPEX
TOPEXenergy
is
consistent
with
the
fact
that
it
represents
surface
currents,
consistent
with the fact thatit represents
surface
currents,
given the
the decrease
in energy
the 48
48 and
given
decreasein
energybetween
betweenthe
and100-rn
100-m
ADCP currents.
currents. When
ADCP
Whenthe
thefull
full 33 years
yearsof
ofTOPEX
TOPEXdata
dataare
are
STRUB ET
ET AL.:
AL.: TOPEX
STRUB
TOPEX VELOCITIESACCURACY
VELOCITIES-ACCURACYAND
ANDALONG-TRACK
ALONG-TRACKRESOLUTION
RESOLUTION
used,
peak is
with periods
periods around
around 100-150
used,aa peak
is observed
observedwith
100-150 days.
days.
This
peak
is
consistent
with
previous
measurements
in
This peak is consistent
with previousmeasurements
in the
the
same
sameregion
region[Stabeno
[Stabenoand
andSmith,
Smith,1987]
1987]and
andwith
withthe
thevisual
visual
interpretation
of dominant
dominant time
time scales
scales in
in Figures
Figures 22 and
interpretationof
and4.
4.
Thus
TOPEX time
Thus although
althoughaliased,
aliased,the
thethree-year
three-yearTOPEX
time series
series
appears
appearsto
to resolve
resolvethe
the100-150
100-150day
dayperiodicity
periodicityevident
evidentin
in
TOPEX
Figures
2
and
4.
and
current
meter
records
Figures2 and 4. TOPEX and currentmeterrecordsshow
show
that
that22 years
yearsof
of data
dataare
arenot
notlong
longenough
enoughto
to resolve
resolvethis
thispeak.
peak.
The
spectra
calculated
from
the
covariances
(u'v',
The spectracalculatedfrom the covariances
(u•v•, Figure
Figure
6a)
6a) are
areeven
evenmore
moredifficult
difficult to
to interpret.
interpret.The
TheADCP
ADCP currents
currents
from
48-rn
depth
produce
a
broad
peak
of
energy
with
from 48-m depthproducea broadpeak of energy
withpeperiods
riods between
between2
2 and
and10
10 days.
days.ADCP
ADCP currents
currentsfrom
from100-rn
100-m
depth
depthproduce
produceaa less
lessenergetic
energeticpeak
peakat
atthe
thesame
sameperiods
periods(not
(not
shown).
shown).The
The individual
individualVACM
VACM data
data (Figure
(Figure 6a)
6a) and
andtheir
their
12,739
12,739
6c).
6c). The
The full
full 33 years
yearsof
of TOPEX
TOPEX data
dataproduce
produceaa covariance
covariance
spectrum
that
is
even
higher
in
energy
and blue.
blue. Given
spectrumthat is even higherin energyand
Given the
the
uncertainty
currents,
uncertaintycaused
causedby
by the
thealiasing
aliasingof
of the
themeasured
measured
currents,
we
in the
TOPEX covariwe place
place no
no confidence
confidencein
the shape
shapeof
of TOPEX
covariance
spectra
may
ancespectra.
spectra.This
Thisaliasing
aliasingof
ofthe
thecovariance
covariance
spectra
may
explain
explainwhy
why the
the momentum
momentumflux
flux statistics
statisticsare
are the
the most
mostvarivariable
characteristics
ablewhen
whenthe
therecord
recordlength
lengthand
andsubsampling
subsampling
characteristics
are
changed.
are changed.
3.3.
3.3. Horizontal
Horizontal Resolution
Resolution
Tracks
the
Tracks130
130 and
and69
69 (Figure
(Figure1)
1) are
areused
usedto
tocompare
compare
the
spatial
structure
of
the
cross-track
velocities
to
the
spaspatialstructureof the cross-track
velocitiesto the spatial
in the
tial structure
structurein
the SST
SST fields.
fields.We
Wehave
havealready
alreadynoted
noted
the
general
sense
in
which
the
cross-track
velocities
the general sense in which the cross-trackvelocitiesand
and
SST
SST patterns
patternsin
in Figure
Figure 11 are
areconsistent
consistentwith
with the
the thermal
thermal
wind
relation. In
of
wind relation.
In Figure
Figure77 we
weshow
showlinear
linearregressions
regressions
of
spatial
(Figure 6c)
6c) do
do not
not produce
produce this
this peak.
peak. As
spatial average
average(Figure
As
noted
notedabove,
above,the
theburst
burstsampling
samplingof
ofthe
theADCP
ADCPdata
data(5(5mm
min
of
T during
cycle
2 for
these
two
of 11 Hz
Hz data
dataevery
every20
20 mm)
min) was
wasdesigned
designedto
to reduce
reducethe
the inin- V
Vcagainst
against-AT
during
cycle
2 for
these
twotracks,
tracks,i.e.,
i.e.,
fluence
of
surface
waves
(and
conserve
battery
power)
- A1T. WeWe
define
14V•totobebepositive
fluenceof surfacewaves(and conservebatterypower)but
but V
Vc== Ao
Ao-A•AT.
define
positiveif
if itit is
is
allows
with periods
periods of
of 5-40
5-40 mm.
directed toward
toward the
the east
T to
ififtemperallowsaliasing
aliasingof
of internal
internalwaves
waveswith
min. directed
eastand
andAT
tobe
bepositive
positive
temperThese
by
ature increases
toward the
the north.
Thesewaves
waveswould
wouldnot
notbe
bealiased
aliased
bythe
theVACM
VACM30-mm
30-min ature
increasestoward
north.Thus
Thuspositive
positivevelocities
velocities
vector
correspond
to
temperatures
and
surface
heights
vector averages.
averages.
correspond
to temperatures
and surfaceheightsdecreasing
decreasing
Using
the
toward the
the north,
north, ifif the
wind relation
relation holds.
holds. The
The
the thermal
thermal wind
Using only
only the
theVACM
VACM data,
data,subsampling
subsampling
theindividual
individual toward
TOPEX 10-day
100-rn
current meter
meter data
data at
quantify
the
agreement
between
the
two
sides
of
100-m current
at the
the TOPEX
10-daysampling
sampling regressions
regressions
quantifythe agreementbetweenthe two sidesof
rate produces
spectra that
that do
(4), keeping
keeping Z,.
Zr constant
within
each
track
but
allowing
rate
producescovariance
covariancespectra
do not
not capture
capturethe
the (4),
constant
withineachtrackbut allowingit
it
mildly
red nature
separations
between
mildly red
natureof
of the
thehourly
hourlycovariance
covariancespectra
spectra(Figure
(Figure to
to vary
varybetween
betweentracks.
tracks.The
Thetemporal
temporal
separations
between
6b).
the spatial
data are
are 22 and
6b). Subsampling
Subsamplingthe
spatialaverage
averageof
of the
thecurrent
currentmeme- altimeter
altimeterand
andAVHRR
AVHRR data
and44 days
daysfor
fortracks
tracks130
130
ter
data
also
fails
to
capture
the
shape
of
the
Considering
all
ter data also fails to capturethe shapeof thecovariance
covariance and
and69
69 during
duringcycle
cycle2,
2,respectively.
respectively.
Considering
all of
ofthe
the
spectrum
(Figure 6c),
6c), although
the area
we
between
temporal
sepaspectrum(Figure
althoughthe
area under
underthe
the curve
curveis
is data
dataexamined,
examined,
wefind
findno
norelation
relation
between
temporal
sepanot
between
not greatly
greatlyin
in error.
error.Covariance
Covariancespectra
spectrafrom
from 18
18 months
monthsof
of rations
rationsof
of up
upto
to55 days
daysand
andthe
theagreement
agreement
betweenaltimeter
altimeter
TOPEX
AVHRR
data
(other
factors
are
more
important
than the
the
TOPEX data
dataare
aremore
moreenergetic
energeticthan
thanthe
thecovariance
covariancespecspec- and
andAVHRR data(otherfactorsaremoreimportantthan
trum
spatially
trum from
from the
thesubsampled
subsampled
spatiallyaveraged
averagedl00-m
100-mdata,
data, offset
offset in
in time).
time).
with
current
In
plots
with peaks
peaksand
andtroughs
troughssimilar
similarto
tothe
thesubsampled
subsampled
current
In Figure
Figure88 we
we show
showalong-track
along-track
plotsof
of V.
V• for
forthe
thesame
same
meter data
and
meter
data (Figure
(Figure 6d)
6d) but
butdifferent
differentfrom
fromthe
thecovariance
covariance tracks
tracksduring
duringcycles
cycles11 and
and22 (late
(lateSeptember
September
andOctober),
October),
spectrum
to -A
A1iT
where
the
AVHRR
spectrumfrom
from the
thefull
full record
recordof
of filtered
filteredhourly
hourlydata
data(Figure
(Figure compared
comparedto
•ATin regions
in regions
where
the
AVHRRimage
image
0.4
0.4
.........
I .........
I .........
• .........
0.2
0.4
0.4
I .........
F+
4:
0.2
••+
o.o
0.2
0.2
+-
E
•o.o
•++
-0.2
-0.4
-0.•
• .........
.........
• .........
3 2
-2
-0.2
0.2
• .........
1
• .........
• .........
0
0
T ( °C )
130
TOPEX
track 130
TOPEX frack
00.•4
• .........
2
3
3 2
-2
0
2
T ( °C )
TOPEX
track
TOPEX frack
Figure 7.
TOPEX
•i•ure
?. Linear
•in•ar regression
m•ssien scatterplot,
scatm•plet,cycle
c•cl• 2,
•, tracks
tracks130
l•O and
and69:
6•: TO•EX
3
69
6g
versus ST. The
AVHRR image is from October 9, 1992. The TOPEX tracks are from October 8 (track 130) and
October 5, 1992 (track 69).
STRUB ET AL.:
AL.: TOPEX
TOPEXVELOCITIES-ACCURACY
VELOCITIES-ACCURACY AND
AND ALONG-TRACK
ALONG-TRACK RESOLUTION
RESOLUTION
12,740
12,740
Track
Track 130
130
'""'
0.30
0.30
0.20
0.20
Track
Track 69
69
_
- 0.30
0.30
0.30
0.30
- 0.30
0.30
ß
0.20
0.20
ß ß
0.20
0.20
....
•
0.20
0.20
ß ß
ß
I
c'.1
U)
oo 0.10
0.10
0.10
E
0.00
x
-0.10
-0.10
0
0o
F•-
"'
\.:
0.10
0.10
.... .
r*:c
c'.1
0.00
0.00
U)
-0.20
-0.30
37
37
38
38
39
39
40
40
0.30
0.30
0.20
0.20
-0.20
:..'
-0.30
ß
0.00
o.oo
•u-
-0.10
-O. lO
Q-U,
..........
-0.20
-0.20
-0.30
-0.30
'..:
ß
35
35
0.20
0.20
0)
0)
m
ß
!
41
- 0.30
0.30
0.10
0.10
•--
.
-0.10
-o.o
-0.20
ßi-0.20
-0.30
-0.30
36
36
'.
ß
-0.10
-o.o
"
c.'1
.o
ß
ß
0.00
o.oo
-0.20
-0.20
-0.30
-0.30
35
35
"-"
0)
ß
,,
v
>
0)
'.' ...........................................
36
36
37
37
38
38
39
39
40
40
,
41
0.30
0.30
0.30
- 0.30
0.20
0.20
0.20
0.20
0.10
:O.
lO
0)
0)
•
0.10
O.
lO
0.10
0.10
0.00
o.oo
•
0.00
o.oo
0.00
0.00
CN
0.10
0.10
0.00
0.00
-0.10
-o.o
-O. lO-•
-0.20
-0.20
o
-0.30
.• -0.30
36
36
35
37
37
38
39
39
40
0)
0)
-0.10
-0.1o
--0.10
-O. lO -
-0.20
-0.20
-0.30
-0.30
- -0.20
-0.20
-0.30
ß -0.50
35
35
41
0
.
36
36
37
37
38
38
39
39
40
40
41
Figure
plots of
ofTOPEX
TOPEXVc
V (dotted
(dottedline)
line)and
and-A
-A1T
line)
(top)
and
Figure8.
8. Along-track
Along-track
plots
•AT(solid
(solid
line)for
forcycles
cycles
(top)11 and
(bottom)
2
for
tracks
130
and
69
(dates
of
tracks
to
the
right
of
each
panel).
The
SST
gradients
come
(bottom)
2 for tracks130and69 (dates
of tracksto therightof eachpanel).TheSSTgradients
come
from
images on
on September
24, 1992
9,
fromAVHRR
AVHRRimages
September
24,
1992(cycle
(cycle1),
1),and
andOctober
October
9,1992
1992(cycle
(cycle2).
2).
was
are the
regressions in
in Figure
Figure 7;
7; and
was judged
judged to
to be
beclear.
clear. These
These are
the data
data used
used in
in the
the regressions
andby
by the
thescales
scalesof
of the
thefeatures
features
Figure
7
regressions.
Figures
1,
7,
and
8
allow
several
in altimeter
velocities
that
persistent
from
Figure 7 regressions.Figures 1, 7, and 8 allow several in
altimeter
velocities
thatwere
weretemporally
temporally
persistent
from
kinds
of
kindsof
of qualitative,
qualitative,visual
visualdeterminations
determinations
of the
thehorizontal
horizontal
scales
resolved
by
the
altimeter:
by
comparison
of Vc
V to
scalesresolvedby the altimeter:by comparison
of
tothe
the
pattern
of
SST
gradients
(Figures
1
and
8)
in
regions
where
patternof SST gradients(Figures1 and8) in regionswhere
the
thethermal
thermalwind
windrelation
relationappears
appearsvalid,
valid,as
asjudged
judgedby
bythe
the
cycle
cycleto
to cycle.
cycle.
Table
the
of
coefficient,
Table33 presents
presents
thevalues
values
ofthe
theregression
regression
coefficient,
A1,
the
correlation
coefficient,
r,
r2
(as
the
percent
of
A•, thecorrelation
coefficient,
r, r 2 (asthepercent
ofvarivariance
explained),
and
the
temporal
separation
between
anceexplained),and the temporalseparation
betweenalal-
Table
of
Velocity
SST Gradient
Table3.
3. Regressions
Regressions
ofCross-Track
Cross-Track
Velocityand
andAlong-Track
Along-Track
SST
Gradient
TOPEX
TOPEX Cycle
Cycle
AVHRR Date
Date
A'
A•
r
re x 100
100
Temporal
TemporalSeparation
Separation
65.7%
50.5%
50.5%
37.3%
37.3%
24.8%
39.5%
40.4%
33.5%
31.3%
77.0%
33 days,
days,66 hours
hours
-1 days,
-1
days,21
21 hours
hours
22 days,
days,33 hours
hours
33 days,
days,13
13 hours
hours
22 days,
days,11
11 hours
hours
57.2%
76.6%
70.1%
37.8%
22.9%
18 hours
hours
18
-4
-4 days,
days,55 hours
hours
-7
-7 hours
hours
3 hours
3
hours
2 hours
2
hours
TOPEX
TOPEX Track
Track 130
130
1
22
88
9
9
10
10
15
15
17
17
23
23
29
9-24-92
10-9-92
12-4-92
12-4-92
12- 13-92
12-13-92
12-23-92
12-23-92
2-13-93
3-3-93
4-29-93
4-29-93
6-29-93
0.158
0.158
0.114
0.098
0.117
0.145
0.145
0.191
0.191
0.160
0.125
0.161
0.161
0.811
0.811
0.711
0.711
0.610
0.498
0.628
0.635
0.635
0.579
0.560
0.878
2 hours
2
hours
22 days,
days,55 hours
hours
55 days,
days,55 hours
hours
2 days,
2
days,21
21 hours
hours
TOPEX Track
Track 69
TOPEX
69
1
22
88
99
10
10
9-24-92
9-24-92
10-9-92
12-4-92
12-13-92
12-13-92
12-23-92
0.162
0.195
0.115
0.134
0.134
0.073
0.073
0.756
0.875
0.837
0.615
0.479
STRUB
AND
STRUBET AL.:
AL.:TOPEX
TOPEXVELOCITIES-ACCURACY
VELOCITIES-ACCURACY
ANDALONG-TRACK
ALONG-TRACKRESOLUTION
RESOLUTION
12,741
12,741
tures.
feature
around 40øN,
40°N,
tures.A
A warm
warmanticyclonic
anticyclonic
featureis
iscentered
centered
around
126.2°W.
The
colder
water
farther
offshore
of
this
feature
126.2øW.
The
colder
water
farther
offshore
of
this
feature
sented
only
for
the
regressions
along
the
two
longer
tracks
sented
onlyfor theregressions
alongthetwolongertracks
of
meander
found
of interest
interest during
during cycles
cycles where
where the
the record
record of
of AT
AT was
judged may
maybe
beaa remnant
remnant
ofthe
thecyclonic
cyclonic
meander
foundin
inFigure
Figure
of
wasjudged
1
around
40.2°N,
127°-128°W.
Likewise,
the
cold
cyclonic
to
be
cloud-free
along
a
path
of
approximately
300
km
or
1
around
40.2øN,
127ø-128øW.
Likewise,
the
cold
cyclonic
to be cloud-freealonga pathof approximately
300 km or
and 39øN,
39°N, 126°
and 127°W
scales are
are 50-80
50-80 km
km and
meanderbetween
between37°
37øand
126øand
127øW in
in Figure
Figure
more.
more. Spatial
Spatialdecorrelation
decorrelation
scales
andrere- meander
I
may
have
evolved
into
the
cool
feature
with
cyclonic
flow
sult
in
approximately
4-10
degrees
of
freedom
for
records
1
may
have
evolved
into
the
cool
feature
with
cyclonic
flow
sultin approximately
4-10 degrees
of freedom
for records
found
between
36°and
38°N,
127°and
129°W
in
Figure
9,
found
between
36øand
38øN,
127øand
129øW
in
Figure
9,
of
300-500
km
in
length,
with
corresponding
95%
signifiof 300-500km in length,with corresponding
95% signifiwith
a
separate
cool
feature
found
inshore
of
this
between
cance
primarcoolfeaturefoundinshoreof thisbetween
cancelevels
levelsof 0.75
0.75 to
to 0.58.
0.58. We
Weuse
usethese
thesestatistics
statistics
primar- with a separate
36°and 38°N,
ily
where
gradient
patterns
may
38øN, 124.5°and
124.5øandl26.5°W.
126.5øW.The
Thelinear
linearregressions
regressions
ily to
toindicate
indicate
wherethe
thetemperature
temperature
gradient
patterns
may 36øand
for
cycles
13
or
14,
plotted
in
Figure
10,
be
better
or
worse
indicators
of
the
velocity
patterns.
for cycles13 or 14, plottedin Figure10,show
showthe
thegenergenerbe better or worse indicatorsof the velocity patterns.
ally
smaller
range
of
AT
values
that
exist
in
winter.
During
cycles
1
and
2,
for
example,
the
temperature
graThe
Duringcycles1 and2, for example,
thetemperature
gra- ally smallerrangeof AT valuesthatexistin winter.The
regressions explain
explain less
less of
of the
dients
appear
to
good
of
thevariance
variance(27%-46%)
(27%-46%)than
than
dients
appear
togive
giveaarelatively
relatively
goodpicture
picture
ofthe
thevelocity
velocity regressions
those from
from early
early fall.
fall. As
structure along
along tracks
tracks 130
51 to
Asin
inFigure
Figure7,
7, many
manyof
ofthe
thepoints
points
structure
130and
and69
69 (explaining
(explaining
51
to 77%
77%of
of those
which
do
not
fit
the
regressions
of
Figure
10
are
for
values
the
variance),
with
correlations
that
are
significant.
Altimewhich
do
not
fit
the
regressions
of
Figure
10
are
for
values
thevariance),
withcorrelations
thataresignificant.
Altime(0.5°øtoto1.0°C).
of Vc
V and
ter velocities
in Figures
picture
of ATI
I/XTI<_<
1.0øC).Plots
Plotsof
and-A1AT
-AxAT for
for
ter
velocities
in
Figures11 and
and88 depict
depictaaconsistent
consistent
picture of
of
(negative) flow
flow north
north of
of 40.0ø-40.5øN,
40.0°-40.5°N, onshore
cycles14
14 and
and15
15are
areshown
shownin
in Figure
Figure11.
11.The
Theanticyclonic
anticyclonic
of offshore
offshore
(negative)
onshore cycles
featurebetween
between39°and
39øand41°N,
41øN, 126°and
126øand127°W,
127øW,and
andthe
thecycyflow between
between39°and
39øand40°N,
40øN,offshore
offshoreflow
flow between
between38°and
38øand feature
clonic
feature
between
36°and
38°,
127°and
129°W
N
between
36øand
38
ø,
127øand
129øW
N can
can
39°N,
flow
36.5°and
37.5°N,
39øN,and
andonshore
onshore
flowbetween
between
36.5øand
37.5øN,which
which
and in
in some
is
along tracks
tracks 145
and 54
54 in
in Figure
Figure 1.
be seen
seenin
in the
thealtimeter
altimetersignals
signalsand
someof
of the
the SST
SST
is also
alsoindicated
indicated
along
145and
1. The
The be
gradients.
The
persistence
of
the
larger
signals
in
poorest
agreement
between
SST
gradients
and
TOPEX
veof the largersignalsin the
thealalpoorest
agreement
between
SSTgradients
andTOPEXve- gradients.The persistence
gives
that
locities
timetervelocities
velocities
givesthe
theoverall
overallimpression
impression
thatalthough
although
locitiesoccurs
occursin
in the
theSE
SEpart
partof
ofthe
theregion
regionduring
duringcycle
cycle2,
2, timeter
the structure
seems less
less organized
organized in
in Figure
Figure 9,
9, there
there is
is still
still
where
part
structure
seems
wherethe
thesouthern
southern
partof
of track
track130
130lies
liesin
inaaregion
regionof
oflowlow- the
agreement
between
the
strongest
features
in
the
SST
patterns
temperature
gradients
(as
indicated
by
Figure
1).
In
Figure
agreement
between
the
strongest
features
in
the
SST
patterns
temperature
gradients
(asindicated
byFigure1). In Figure
the altimeter
which still
resolve features
features with
with
and the
altimetervelocities,
velocities,which
still resolve
7,
contribute
to the
of
7, these
theseregions
regions
contribute
to
thelarge
largenumber
number
of points
points and
scales
of
80
km
and
greater
in
winter.
lines
with AT m 00 which
whichlie
lie off
offthe
theregression
regression
linesfor
for track
track scalesof 80 km and greaterin winter.
One
with
the comparison
between the
the cross-track
cross-track
130.
clouds
to
Oneproblem
problem
withthe
comparison
between
130.Undetected
Undetected
cloudsand
andmist
mistmay
maycontribute
contribute
to the
thelack
lack
velocity
and
along-track
temperature
gradient
is
the
fact that
that
of
SST
features,
as
may
subduction
of
the
colder
jet
water
temperature
gradient
is thefact
of SST features,as may subduction
of the colderjet water velocityandalong-track
the
"long-term"
mean
temperature
that
is
removed
at
each
in
this
region
[Brink
and
Cowles,
1991].
The
persistence
meantemperature
thatis removedat each
in thisregion[Brinkand Cowles,1991]. The persistencethe "long-term"
number
of
at
of the
velocity
pointmay
mayhave
haveaa different
different
number
ofrealizations
realizations
atdifferent
different
thealtimeter
altimetercross-track
cross-track
velocityfeatures
featuresduring
duringsequensequen- point
spatial
points
along
the
track,
which
can
create
unrealistic
tial
cycles
1-2
(with
some
strengthening,
weakening,
and
spatial
points
along
the
track,
which
can
create
unrealistic
tial cycles1-2 (withsomestrengthening,
weakening,
and
occur in
in the
features in the
shift
argues
for
of
features.
thegradients.
gradients.Similar
Similarproblems
problemsoccur
the
shiftin
inposition)
position)
argues
forthe
thevalidity
validity
ofthose
those
features. features
TOPEX
data
but
are
far
fewer
due
to
the
smaller
number
are
due the smaller number of
In
8,
in
with
In the
thetop
topleft
leftpanel
panelof
ofFigure
Figure
8,oscillations
oscillations
invelocity
velocity
with TOPEX data
missing data.
data. We
the
wavelengths of
of approximately
approximately 30
30 km
km are
are seen
Wecan
canavoid
avoidthis
thisby
byforming
forming
thedifference
difference
wavelengths
seenalong
alongtrack
track missing
between
two
individual
cycles
(along
a
given
track),
130
in
cycle
1
between
36°and
37°N,
which
cannot
be
diswithout
130in cycle1 between
36øand37øN,whichcannot
bedis- betweentwoindividualcycles(alonga giventrack),without
mean.
represents
the
tinguished from
from noise
noise due
due to
to their
and
takingout
outaalong-term
long-term
mean.This
Thisdifference
difference
represents
the
tinguished
theirlack
lackof
ofpersistence
persistence
and taking
change
in
cross-track
velocity
at
each
point.
This
removes
correspondence
to
the
SST
gradients.
In
contrast,
the
oscilvelocityat eachpoint.Thisremoves
correspondence
totheSSTgradients.
In contrast,
theoscil- changein cross-track
lations
over
theartificial
artificialvelocities
velocitiescaused
causedby
by the
thegeoid
geoid(which
(whichshould
should
lationswith
with scales
scalesof
of 50-80
50-80 km
kmare
arepersistent
persistent
overpairs
pairsof
of the
be
the
same
for
the
two
altimeter
records),
uses
data
only
cycles
and
assumed
valid.
Overall,
the
figures
suggest
that
be
the
same
for
the
two
altimeter
records),
uses
data
only
cycles
andassumed
valid.Overall,
thefigures
suggest
that
where
there
are
good
data
during
both
cycles,
and
creates
velocity
structures
with
scales
of
50-80
km
and
larger
are
where
there
are
good
data
during
both
cycles,
and
creates
velocitystructures
with scalesof 50-80 km andlargerare
no artificial
Comparison
of
between
11
resolved by
no
artificialsignals.
signals.
Comparison
ofdifferences
differences
between
11
resolved
by the
thealtimeter.
altimeter.
pairs
of
cycles
along
track
130
and
four
pairs
along
track
Values of
of A
A1
Values
• in Table
Table3 are
aremost
mostoften
oftenbetween
between0.1
0.1 and
and pairsof cyclesalongtrack130andfourpairsalongtrack
mean
results in
in similar
0.2.
values
for
g, f,
/3 (assuming
69, with
withno
nolong-term
long-term
meanremoved,
removed,results
similaror
or
0.2.Using
Using(4)
(4)and
andtypical
typical
values
forg,
f, and
and/•
(assuming69,
better
agreement
between
A(V)
and
A(-A1AT))
as
implied
by
no
influence
of
salt
on
density),
the
value
of
Zr
better
agreement
between
A(Vc)
and
A(-A•AT))
asthe
the
no influence salton density),thevalue Z,. impliedby
comparisons between
between Vc
V and
these
values of
of A
A1• is
is approximately
approximately 300-600
300-600 m.
m. These
andAT
AT during
duringindividual
individualcycles
cycles
thesevalues
Thesevalval- comparisons
Plots
of
A(V)
and
depth
(with
the
long-term
mean
extracted).
ues
are
of
the
same
order
of
magnitude
as
the
600-m
(with
the
long-term
mean
extracted).
Plots
of
A(V•)
and
uesareof the sameorderof magnitude
asthe600-mdepth
pairs
in
of the "level
"level of
of no
nomotion"
motion"which
which Waistad
Walstadet al.
al. [1991]
[1991] A(-A1AT))
A(-A•AT)) for
forfour
fourofofthe
thecycle
cycle
pairsare
arepresented
presented
in
Figure 12.
show
resolving
found to
to give
between
geostrophic
cal12.These
Thesegenerally
generally
showgood
goodagreement,
agreement,
resolving
found
givethe
thebest
bestagreement
agreement
between
geostrophic
cal- Figure
the features
with scales
scales of
of 50-80
50-80 km.
features with
km.
culations and
and ADCP
ADCP fields
Waistad
culations
fieldsin
in this
thisregion,
region,although
although
Walstad the
et al.
al. make
"level
is
et
makethe
thepoint
pointthat
thatno
nosingle
single
"levelof
ofno
nomotion"
motion"
is
optimum
for aa regional
velocity
4. Discussion
4.
Discussion and
and Conclusions
Conclusions
optimumfor
regional
velocityfield.
field.
During
in
of
Duringwinter,
winter,the
thecirculation
circulation
in this
thisregion
regionconsists
consists
of
Below
and
Below we
we give
givethe
themajor
majormethodological
methodological
andoceanooceanoa poleward
Davidson
Current next
next to
to the
carrying
a
poleward
Davidson
Current
thecoast,
coast,
carrying graphic
conclusions,
along
with
a
discussion
of
points
which
alongwitha discussion
of pointswhich
warmer water
water to the
the north.
north. In the
the field
field graphicconclusions,
warmer
theoffshore
offshoreregion,
region,the
need
elaboration
or
clarification.
The
Appendix
includes
aa
need
elaboration
or
clarification.
The
Appendix
includes
of eddies
of
eddies from summer and fall continues
continues to evolve
evolve and
discussion
of
how
details
of
the
geostrophic
calculation
indiscussion
of
how
details
of
the
geostrophic
calculation
indissipate. The
picture
dissipate.
Thelate
lateJanuary
January
pictureof
of SST
SSTand
andcycle
cycle14
14 fluence
fluence the scales of
of circulation
circulation features
features that are
are resolved.
resolved.
altimeter velocities
velocities shown
shown in
in Figure
altimeter
Figure99 depicts
depictsthe
thewarmer
warmer
band
of
poleward
flow
next
to
the
coast.
SST
gradients
bandof polewardflow nextto the coast.SST gradients4.1.
4.1. Methodological
MethodologicalConclusions
Conclusions
of offare
more
pattern
areweaker,
weaker,with
withaa somewhat
somewhat
moreconfused
confused
patternof
offaccuracy,
the
shore
and
velocities
than
1. Considering
Considering
accuracy,
thelevel
levelof
of noise
noisein
in the
thealtimealtimeshoreSST
SSTpatterns
patterns
andcross-track
cross-track
velocities
thanfound
found 1.
or
less,
corresponding
to
noise
ter
velocities
is
cm
s
Close
inspection,
however,
reter
velocities
is
3-5
cm
s
-1
or
less,
corresponding
to
noise
in late
summer
and
fall.
late summerand fall. Close inspection,however,rein
the
altimeter
heights
of
approximately
2
cm.
Results
of
veals
a
continued
correspondence
of
SST
and
velocity
feain
the
altimeter
heights
of
approximately
2
cm.
Results
of
vealsa continued
correspondence
of SST andvelocityfea-
timeter tracks
tracks and
and the
are
timeter
the SST
SST image.
image.These
Thesestatistics
statistics
areprepre-
STRUB
ET AL.:
STRUB ET
AL.: TOPEX
TOPEX VELOCITIESACCURACY
VELOCITIES-ACCURACY AND
ANDALONG-TRACK
ALONG-TRACKRESOLUTION
RESOLUTION
12,742
12,742
41
40
39
38
37
36
36
35
55
129
-129
127
128
-128
-127
125
126
-126
-125
124
123
-123
-124
122
-122
Topex
cycle014
014 (( Febrary
Febrary 2-7,
2-7, 1993
Topexcycle
199.3 )
AVHRR
date Jan
Jon 29
AVHRR date
29 1993
199.3
Figure
winter
velocities
Figure 9.
9. AAcharacteristic
characteristic
winterfield
fieldof
ofTOPEX
TOPEX cross-track
cross-track
velocities(cycle
(cycle 14)
14) overlain
overlainon
on an
an SST
SST
image
(January
29,
1993).
As
in
Figure
1.
image(January29, 1993). As in Figure 1.
0.4
0.4
0.4
0.2
0.2
0.2
In
E
E
>
>
>1
0)
'1)
I-
I-0
0
0
0
0.2
0.2.2
-0.2
321
0.4
-2
-1
04
0
0
11
AT ((øC)
°C )
-AT
TOPEXtrack
track 130
TOPEX
130
2
33
32
-3
-2
1
-1
00
1
1
2
3
AT ((øC)
°C )
-AT
TOPEX
track
TOPEX track
69
69
Figure
as
cycles (left)
Figure 10.
10. Linear
Linearregressions
regressions
asin
in Figure
Figure7,
7, for
for'cycles
(left) 13
13 and
and(right)
(right) 14.
14. The
TheAVHRR
AVHRR image
image
is
is from
from January
January29,
29, 1993.
1993. The
TheTOPEX
TOPEX tracks
tracksare
arefrom
fromJanuary
January25,
25, 1993
1993(track
(track130),
130),and
andFebruary
February1,1,
1993 (track
(track 69).
1993
69).
12,743
12,743
STRUB ET
HI'AL.:
AL.:
TOPEX
VELOCmES-ACCURACY AND
AND ALONG-TRACK
ALONG-TRACK RESOLUTION
RESOLUTION
STRUB
TOPEX
VELOCITIES-ACCURACY
Track
Track 69
69
Track 130
1,30
- 0.30
0.30
0.30
0.30 -0.20
0.20 -
0.20
0.20
.:;
0.00'"
oo
.
0.10
0.10
0.10
0.00
o.oo
....
ß
'/
0.00
0.00
:'
ß
.....
....
0.20
0.20
.
0.00
-0.10-O. lO
0.20
0.20
N)
0.10
; .. 0.10
.'
- 0.30
0.30
14)
ß
0.100.10
0.30
0.30
ß
-o.•o •
ß
-0.10
-O. lO
0.00
0.00
-0.10
-0.10
.
ß
o
40
40
39
39
38
38
37
37
36
36
ß
36
36
35
5
- 0.30
0.30
0.20
0.20
0.20
0.20
- -0.20
-0.20
-0.30
-0.30
-0.20
41
-
ß
ß:
-0.20 .:
...........................................................
-0.30
-0.30
- -0.20
-0.20
, -0.30
-0.30
ß ,.
35
35
37
37
38
38
40
40
39
39
41
41
0.30
0.30
- 0.30
0.30
0.20
0.20
0.20
0.20
0.10
0.10
N)
N)
•
0.10
0.10
0.10
O.lO •
0.10
O.
lO
0.00
0.00
0.00
0.00
0.00
0.00
E
o
-0.20
-0.20
-0.30
-0.30
35
,35
•-
•
-0.10-•
-0.10
1.
-0.10
-0.10
x
"'
11
-0.20
-0.20
-0.30
-0.30
•-'
0
0'10
ø"
ß
0.30
0.30
0
.....
....i
.........
i .........
37
,37
36
,36
i .........
i .........
i ........
40
40
39
,39
38
,38
Latitude
Latitude
---
-."
0
0)
0.00
0.00
-0.10
-O. lO
-0.10
.
-0.20
-0.20
...........................................................
-0.30
-0.30
37
38
39
36
35
,35 ,36
,37 ,38
,39
Latitude
Latitude
- -0.20
-0.20
ß -0.30
-0.50
41
.. ..
40
40
- -0.20
-0.20
-0.30
-0.30
41
41
(solid line) for cycles (top) 14
Figure 11.
plotsof
ofTOPEX
TOPEXVc
V(dotted
(dottedline)
line)and
and
-A 1T (solid
Figure
11.Along-track
Along-track
plots
-AzAT
line)The
forcycles
(top)14
panel).
SST
gradients
and
15 for
for tracks
tracks 130
130 and
and 69
69 (dates
(dates of
of tracks
tracks to
to the
the right
right of
of each
and(bottom)
(bottom)
15
each
panel).
The
SST
gradients
(cycle 14), and February 13, 1993 (cycle 15).
come from
from AVHRR
images on
on January
January 29,
come
AVHRRimages
29,1993
1993(cycle14),andFebruary
13,1993(cycle15).
N)
N)
0
: :0.4
0.4 ? • 0.4
0.4
0
0.2
- 0.2
o.•• ?
.-
0.4 =
0)
-
I
:'
03
0.2
0,2 -
o•
0.0-;."
0.0
-r
0"
o•
..
....
....
-
•
-0.4
•
-0.6
!
0
14)
0)
ß -0.6 o.
0
35363738394041
.........
, .........
35
36
i .........
i .........
37
i .........
38
! ........
39
40
o
'" -0.6
i-
35
,35
41
36
,36
37
,37
38
,38
39
,39
40
40
ß -0.6 o
41
4)
0.4=
0.4 0.2
0.2
.
-
.
ß
:
:
..
.
.
:
.
.
-:0.4
0.4 0? •
0.4:
0.4
:0.2
0.2 '- g
>.
0.2
0.2
-
0
-.0.4-o.4
to
:
-
--0.2.
N)
•:
\.:'
..
.
.
.
-
o
-0.2-
4.)
•
35
,35
36
,36
37
,37
U
>'
U
40
o.o g
0
''
-.0.4•-o.•
-o.4 o
- ...........................................................
U.Q o
Q
-0.6
to -0.6
0_
C1
0.0
ß
--0.4 •
..................... '" ...................................
41
40
39
37
38
36
35
35
36
37
38
39
40
41
1J.0
0.2
-0.2• • -0.2
I
::.../
:0.4
to •0 0.0
0.0 ..
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-0.4 x
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39
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40
40
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•
-o.4,,x,
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41
between -A1T for the same
Figure 12.
between
V for
of
and
Figure
12.Differences
Differences
between
Vc
forpairs
pairs
ofcycles
cycles
anddifferences
differences
between
-Azthe
AT forthesame
pairs of
AVHRR
dates are
are to
to the
the left
panel
and
numbers are
are to
to theright.
pairs
ofcycles.
cycles.
AVHRR
dates
leftof
ofeach
each
panel
andcycle
cycle
numbers
right.
12,744
STRUB
FT AL:
STRUB ET
AL.:TOPEX
TOPEXVELOCITIESACCURACY
VELOCITIES-ACCURACY AND
ANDALONG-TRACK
ALONG-TRACK RESOLUTION
RESOLUTION
comparisons
comparisonsbetween
betweenaltimeter
altimetergeostrophic
geostrophicvelocities
velocitiesand
and Stammer
Stammer[1995],
[ 1995],seems
seemslikely
likelyto
toreduce
reduceeffects
effectsof
of aliasing
aliasing
velocities
measured
beneath
the
Ekman
layer
depend
on
dein
their
frequency
spectra
of
height
variance.
velocitiesmeasuredbeneaththe Ekman layerdependon de- in their frequencyspectraof heightvariance.
tails
calculation,
in
Regarding spatial
spatial resolution,
the TOPEX
3. Regarding
resolution,the
TOPEX cross-track
cross-track
tails of
of the
thegeostrophic
geostrophic
calculation,as
asdescribed
described
inthe
theApAppendix.
For
a
62-km
finite
difference,
followed
by
a
50-km
velocities
can
repeatedly
resolve
features
pendix. For a 62-km finite difference,followedby a 50-km velocitiescan repeatedlyresolvefeatureswith
withhorizontal
horizontal
spatial
filter,the
thetotal
totalrms
rmsdifference
difference
7-8
cm
by
bespatialfilter,
is is
7-8
cm
s-•.s. This
This scales
scalesof
of 50-80
50-80 km,
km,asasdemonstrated
demonstrated
bycomparisons
comparisons
beimproves
tween the
improvesslightly
slightlywhen
whenthe
themeasured
measuredvelocities
velocitiesare
arespatially
spatially tween
the along-track
along-trackgradients
gradientsof
of SST
SST and
andthe
thecross-track
cross-track
averaged
velocity from
from the
the altimeter.
altimeter. Given
averagedover
over aa 30-km
30-km region,
region,showing
showingthat
thatthe
thealtimeter
altimeter geostrophic
geostrophicvelocity
Given the
the 62-km
62-km
measurement
of
horizontal spacing
in
and
measurementis
is representative
representative
of spatially
spatiallyaveraged
averagedvelociveloci- horizontal
spacingof
of the
thefinite
finitedifference
difference
in heights
heights
andthe
the
ties
Of
50-km spatial
the
veloctiesrather
ratherthan
thanpoint
pointmeasurements.
measurements.
Of this
thisrms
rmsdifference,
difference, 50-km
spatialfilter
filterused
usedto
tocalculate
calculate
thegeostrophic
geostrophic
velocsmall-scale
ities, this
this agreement
is as
as good
good as
as can
can be
be expected.
small-scale horizontal
horizontal circulation
circulation features
features in
in the
the ocean
ocean cause
ities,
agreement
is
expected.This
This
rms
differences
between
current
meters
separaises
the
question
of
whether
shorter
finite
differences
5-7 cm
s
cm s-• rmsdifferences
between
currentmeterssepa- raisesthe questionof whethershorterfinite differencesand
and
spatial filters
filters could
could be
be used
the resolution.
rated by
by 15-30
55 cm
rms difference
exists
rated
15-30km.
km.Another
Another
cmss-• rms
difference
exists spatial
usedto
to improve
improvethe
resolution.In
In
between
current meters
meters at
at 48
48 and
and l00-m
the the
the Appendix
Appendix we
we show
showthat
thatshorter
shorterfinite
finitedifferences,
differences,folfolbetweencurrent
100-mdepth,
depth,showing
showingthe
effects
(shear). Thus
lowed by
by the
the 50-km
50-km loess
bess filter,
the
filter,increase
increase
therms
rmsdifferences
differences
effectsof
of vertical
verticalspatial
spatialvariability
variability(shear).
Thusof
of the
thetoto- lowed
tal
rms difference,
difference, less
less than
than 3-5
3-5 cm
cm ss1
to
measured velocities
velocities and
and TOPEX
TOPEXfrom
from 8-9
8-9 cm s-•
tal rms
-• can
canbe
beattributed
attributed
to between measured
noise
(span of
of 50
50 km)
km) to
to 14-17
14-17 cm
cm ss1
of
noise in
in the
the altimeter
altimeter calculation,
calculation, similar
similar to
to the
thedifference
difference (span
-• (span
(span
of12.4
12.4km).
km).Use
Use
between
the 100-rn
by the
the ADCP
of shorter
the
between the
100-m currents
currentsmeasured
measuredby
ADCP and
and of
shorterspans
spanswith
with no
nofilter
filterincreases
increases
therrns
rmsdifferences
differences
VACM when
when separated
separated by
by 22 km.
km. This
from 88 cm
cmss1
of
to 20-30
20-30 cm
cmss1
of
VACM
This shows
showsaa greater
greateracac- from
-• (span
(span
of62
62 km)
km)to
-1 (span
(span
of
curacy
than
previous
estimates
of
10-17
cm
s1
by
Menkes
12.4
km).
The
50-km
filter
is
less
important
for
the
longer
curacythanprevious
estimates
of 10-17 cms-• byMenkes 12.4 km). The 50-km filter is lessimportantfor the longer
et
current meters
meters at
at the
the equator.
spans, but
but it
with spans
spans of
of
et al.
al. [1995],
[ 1995], using
using current
equator. In
In the
the spans,
it appears
appearsthat
thatgradient
gradientoperators
operatorswith
Appendix
it is
7.6 cm
cm 50-60
50-60 km
are
necessary
to
achieve
the
lower
rms
differAppendixit
is shown
shownthat
thatthe
thefull
full rms
rmsdifference
differenceof
of 7.6
km are necessaryto achievethe lower rms differs1
totoheight
errors
of
a 3-5
3-5 ences
ences of
of 7-8
7-8 cm
between altimeter
altimeter and
and measured
curcm ss -• 1 between
measuredcurs-•corresponds
corresponds
height
errors
of3.3
3.3cm
cmrms,
rms,while
whilea
corresponds
to
of
cm
rents. Error
with
cmss-• difference
difference
corresponds
toheight
heighterrors
errors
ofapproxiapproxi- rents.
Errorlevels
levelsassociated
associated
withother
othergradient
gradientoperators
operators
mately
2 cm
are discussed
further
mately 2
cm and
and less.
less.These
Thesevalues
valuesare
aresimilar
similarto
to the
the rms
rms are
discussed
furtherin
in the
theAppendix.
Appendix.
height
errors found
found by
by Katz
Katz et
et al.
al. [1995]
4. Eddy
Eddy statistics
statisticsare
aremore
moreproblematic.
problematic.The
The most
mostrobust
robust
heighterrors
[ 1995]and
andPicaut
Picautet
etal.
al.
[1995],
based
on
temperature
and
conductivity
moorings
in
eddy
statistics
are
the
values
of
EKE,
the
velocity
[1995], basedon temperatureand conductivitymooringsin eddystatistics
arethevaluesof EKE, thevelocityvariances,
variances,
the equatorial
equatorial Pacific.
and the
the
Pacific.
and
the lengths
lengthsof
of the
themajor
majoraxes
axesof
of the
theprincipal
principalaxis
axiselellipses.
The
magnitude
of
the
momentum
fluxes
and
2.
With
respect
to
temporal
resolution,
the
altimeter
10the
2. With respectto temporalresolution,the altimeter10- lipses. The magnitudeof the momentumfluxes and the
orientation of
of the
the principal
principal axis
axis of
day
day sampling
samplingappears
appearscapable
capableof
of resolving
resolvingthe
thedominant
dominant orientation
of the
the TOPEX
TOPEX data
datashow
show
with those
those of
of the
the in
100-150
greaterdisagreement
disagreementwith
in situ
situ current
currentmeamea100-150 day
day periods
periodsof
ofvariability
variabilityin
inthe
theoffshore
offshoreregion
region greater
but the
is
of the
of
the California
California Current,
Current,as
asseen
seenby
byvisual
visualcomparisons
comparisons surements,
surements,
but
theagreement
agreement
is much
muchgreater
greaterwith
withthe
thespaspaof the
Thus, aa good
part
of altimeter
and current
of
altimeter and
current meter
meter data
data (Figures
(Figures22 and
and 4)
4) and
and tial
tial average
average
of
thein
in situ
situmeasurements.
measurements.
Thus,
goodpart
of
the
differences
is
due
to
real
variability
between
surface
by
spectral
analysis
of
the
3-year
TOPEX
record
(Figure
by spectralanalysisof the 3-year TOPEX record (Figure of thedifferences
is dueto real variabilitybetweensurface
5d),
energy
and deeper
deeperfeatures
featuresand
andreal,
real, small-scale
small-scalehorizontal
horizontalvariabilvariabil5d), although
althoughaliasing
aliasingof
ofhigher-frequency
higher-frequency
energydoes
doesafaf- and
fect
spectral
calculations
of
the
TOPEX
data.
The
measured
ity
in
the
measured
currents.
We
feel
that
of the
fect spectralcalculationsof the TOPEX data. The measured ity in the measured
currents.We feel thatanalyses
analyses
of
the
velocities are
are used
used to
to calculate
calculate full
(after
the 4040- spatial
spatial and
temporal
fields
of
EKE
and
velocity
variance
velocities
full autospectra
autospectra
(afterthe
and temporalfieldsof EKE and velocityvariance
hour
after
the
will produce
results similar
hourfilter)
filter) and
andautospectra
autospectra
aftersubsampling
subsampling
thesame
samedata
data will
produceresults
similarto
to that
thatwhich
whichwould
wouldhave
havebeen
been
at
below
obtained by
by an
an array
at the
theTOPEX
TOPEX 10-day
10-dayperiod.
period.Energy
Energyat
atfrequencies
frequencies
below obtained
arrayof
of current
currentmeters.
meters.
the
frequency(0.05
(0.05cycles
cyclesdd')
for
Principal
theNyquist
Nyquistfrequency
-1)increases
increases
forthe
the
Principalaxis
axisellipses
ellipsesare
aremore
morecomplex
complexthan
thanthe
thescalar
scalar
subsampled
spectra,
although
less
so
when
the
spatial
of EKE
EKE and
velocity variance.
variance. Morrow
Morrow et
et al.
al. [1994]
subsampledspectra,althoughless so when the spatialavav- values
valuesof
andvelocity
[ 1994]
erage
velocities
to
the
erage(over
(over aa 30-km
30-km region)
region)of
ofthe
themeasured
measured
velocitiesis
is use
useaa simple
simpleapproach
approach
toestimate
estimate
theoverall
overalluncertainty
uncertainty
used.
TOPEX
data
represent
averages
over
longer
spatial
in
the
principal
axis
ellipses,
which
rejects
used. TOPEX data representaveragesover longerspatial in the principalaxis ellipses,whichrejectsellipses
ellipseswith
with
scales
in slope
major axes
than
variance
scalesand
and their
their autospectra
autospectraappear
appearsimilar
similar in
slopeto
to the
the major
axesof
of less
lessmagnitude
magnitude
thanthe
thelargest
largesterror
errorvariance
full
measured
velocities
expected at
at that
full spectra
spectrafrom
fromthe
thespatially
spatiallyaveraged
averaged
measured
velocities expected
that latitude.
latitude. We
We use
use this
this method
methodwith
with our
our
over
estimates of
rms cross-track
velocity
over an
an 18-month
18-monthcommon
commonperiod,
period,giving
givingsome
someconfidence
confidence estimates
of the
therms
cross-track
velocityerrors,
errors,as
ascalculated
calculated
in
calculated
from (2a)
in the
thespectral
spectralcharacteristics
characteristics
calculatedfrom
fromTOPEX
TOPEX data.
data. from
(2a) and
and(2b).
(2b). In
In Figure
Figure13,
13,principal
principalaxes
axesellipses
ellipses
Over
a
3-year
period,
the
TOPEX
autospectra
resolve
are shown
as calculated
from the
the 33 years
data
Overa 3-yearperiod,theTOPEX autospectra
resolveaapeak
peak are
shownas
calculatedfrom
yearsof
of TOPEX
TOPEX data
with
a
100-150
day
period,
similar
to
the
visual
interpretaover
the
large-scale
California
Current
regime.
The
error
with a 100-150 day period,similarto the visualinterpreta- over the large-scaleCaliforniaCurrentregime. The error
tion of
in
peak
calculated
from
tion
of timescales
timescales
in all
all of
of the
thevelocity
velocitydata.
data.A
A spectral
spectral
peak variances
variances
calculated
from(2a)
(2a)and
and(2b),
(2b),using
usinguave== 50
50cm2
cm2
at
70-100
days
has
been
found
in
deeper
(1250
m)
meas2
are
shown
on
the
right
axis
for
reference,
adopting
aa
at 70-100 days has been found in deeper(1250 m) mea- s-2, areshown
ontherightaxisforreference,
adopting
sured
estimate
of
altimeter
noise
as
7
cm
s1.
Using
suredvelocities
velocitiesat
at aa nearby
nearbydeep
deepocean
oceanlocation
locationby
byStabeno
Stabeno conservative
conservative
estimate
of altimeter
noiseas7 cms-•. Using
and
result
ininerror
ellipses
half
and Smith
Smith[1987],
[1987], giving
givingfurther
furtherconfidence
confidencein
in the
thepeak
peak 5
5 cm
cms1
s-•would
would
result
error
ellipses
halfas
aslarge.
large.All
All
resolved
principal
(with
resolvedby
by the
the longer
longerrecord.
record.The
The2-year
2-yearrecords
recordsof
ofmeamea- "significant"
"significant"
principalaxis
axisellipses
ellipses
(withmajor
majoraxis
axisgreater
greater
sured
than the
are
by
suredand
andTOPEX
TOPEX velocities
velocitiesare
arenot
notlong
longenough
enoughto
toresolve
resolve than
thelarger
largererror
errorvariance)
variance)
areindicated
indicated
bydark
darkshading.
shading.
this
peak.
The
fact
that
the
spatially
averaged
measured
aa number
of
this peak. The fact that the spatiallyaveragedmeasured Figure
Figure13
13 demonstrates
demonstrates
numberof
of aspects
aspects
ofthe
thevelocvelocvelocities
exhibited less
less severe
argues for
for the
the use
ity statistics
in this
velocitiesexhibited
severealiasing
aliasingargues
use ity
statistics
in
thisregion.
region.The
Thelargest
largestellipses
ellipsesare
arefound
foundat
at
of
100
km) in
in making
making the
closest
to
of larger
largerspatial
spatialfiltering
filtering(approximately
(approximately
100 km)
theone
oneor
ortwo
twocrossovers
crossovers
closest
tothe
thecoast
coast(within
(withinapproxapproxthe
velocity
i.e.,
thegeostrophic
geostrophic
velocitycalculation
calculationfrom
fromTOPEX
TOPEXheights,
heights, imately
imately500
500km
kmof
ofthe
thecoast),
coast),
i.e.,the
theregion
regionof
ofthe
theenergetic
energetic
prior
of aljet
found
in
numerous
surveys
and
in
drifter
priorto
to spectral
spectralanalysis.
analysis.Similarly,
Similarly,spatial
spatialaveraging
averagingof
al- seasonal
seasonal
jet foundin.•numerous
surveysandin driftertracks
tracks
timeter
used
and
[Brink and
and Cowles,
Brink et
et al.,
al., 1991].
timeterheights,
heights,such
suchas
asthe
the2°
2øaverages
averages
usedby
byWunsch
Wunsch
and [Brink
Cowles, 1991;
1991; Brink
1991]. Offshore
Offshoreof
of
STRUB
STRUB ET
ET AL:
AL.'TOPEX
TOPEXVELOCITIES-ACCURACY
VELOCITIES-ACCURACYAND
ANDALONG-TRACK
ALONG-TRACKRESOLUTION
RESOLUTION
Topex
ellipsesof
of variance
varioncefor
for Sep
Sep92
92 -- Sep
Topex ellipses
Sep 95
95
50
I
0
I
0
0
-
12,745
12,745
0o
•
_
-o
_o
45
0
o
•0
- 0
0
O
0
0
0
-o
-o
•
0
(•
-
/
0
0
¸
major
axis
-- 100(cm/sec)
2
_
(cm/sec)22
minor axis
axis == 50
minor
50 (cm/sec)
_
40
4O
I
00 I
51
0
35
-135
-135
0
0
0
0
o
0
0 Sill
I
-130
-130
0o
o
0I ii
0 0
I
I
0
o
0
o
25
theta =
= 0.
O.
theta
o
0
0
-_
..
00 101%
-oo
0
o
major axis = 100 (cm/sec)2
0
0
-
I
I
-125
-125
I
I
-120
-120
-115
-115
-110
0
Figure 13.
in the
Figure
13. Principal
Principalaxis
axisellipses
ellipsesfor
forall
allTOPEX
TOPEX crossover
crossoverpoints
pointsin
the region
regionof
of interest,
interest,using
using all
all
33 years
of
TOPEX
data.
Uncertainty
variance
ellipses
are
drawn
along
the
right
axis,
showing
years of TOPEX data. Uncertaintyvarianceellipsesare drawn along the right axis, showingthe
the
v (vertical
uncertainty in
in uu (horizontal
axis)
axis), as
as calculated
from (2a)
(2a) and
uncertainty
(horizontal
axis)and
andv
(verticalaxis),
calculated
from
and(2b),
(2b),using
using e _
50.0 cm
cm2
to an
an rms
rms uncertainty
uncertaintyofof77cm
cms-1.
s. Ellipses
with
axes
than
50.0
e s_2,
-z, corresponding
corresponding
to
Ellipses
withmajor
major
axesgreater
greater
than
the uncertainty
the
uncertaintyare
are shown
showndarkened.
darkened.
this region,
region, the
the variances
are low.
low. This
This is
this
variancesare
is the
the"eddy
"eddydesert"
desert"
pointed
out
by
numerous
analyses
of
altimeter
pointedout by numerousanalysesof altimeterand
andother
other
data as
data
astypical
typicalof
of eastern
easternboundary
boundarycurrents.
currents.Considering
Considering
the smaller
smaller ellipses,
ellipses, south
south of
of 35ø-45øN
35°-45°N the
pothe
thenorth-south
north-south
polarization becomes
becomes more
more pronounced,
pronounced, similar
similar to
to the
larization
theerror
error
variance ellipses.
ellipses. These
ellipses in
in the
the offshore
variance
Theselow-energy
low-energyellipses
offshore
region
regionprovide,
provide,in
in effect,
effect,an
anempirical
empiricalestimate
estimateof
of principal
principal
axis
values
axis ellipses
ellipsesdue
dueto
to altimeter
altimeternoise,
noise,supporting
supporting
valuesless
less
than
7
cm
s1.
The
lower
values
offshore
also
highlight
the
than cms-1 . Thelowervaluesoffshore
alsohighlight
the
more
energetic
region
of
the
California
Current.
Thus
more energeticregion of the California Current. Thus the
the
evaluation
of altimeter
error is
is helpful
evaluationof
altimetervelocity
velocityerror
helpfulin
in defining
defining
the
signal
of
interest
in
the
region,
which
is
the
the signalof interestin the region,which is the subject
subjectof
of
subsequent
papers.
subsequent
papers.
Turning
to the
eddy statistics,
statistics, the
the valTurningto
the more
moreproblematic
problematiceddy
values
uesof
of eddy
eddymomentum
momentumflux
flux (u'v')
(u•v•)vary
varybetween
betweenTOPEX
TOPEX
and
by aa factor
and ADCP
ADCP velocities
velocitiesby
factorof
of 66and
andvary
varybetween
between
100-m-deep
VACMs separated
separatedby
by 15-30
15-30 km
km by
by a
a factor
100-m-deepVACMs
factorof
of
5.
Spectra
of
(u'v')
indicate
that
one
problem
is
5. Spectraof (u•v•) indicatethat one problemisaliasing
aliasing
of
variability, and
and at
at present
of higher-frequency
higher-frequency
variability,
presentwe
we have
haveno
no
confidence
in
these
covarance
spectra.
The
agreement
beconfidencein thesecovariancespectra.The agreement
between
valuesof
ofTOPEX
TOPEXu•v
u'v'
(-40 to
to -24
-24 cm
cm2
tweenvalues
• (-40
e ss2
-e for
forI1and
and3-year
3-yearrecords)
records)and
andthe
the100-rn
100-mVACMs
VACMs is
is improved
improvedby
by
using
averaged VACM
VACMvelocities
velocities(-34
(-34cm
cm2
s2).
usingspatially
spatiallyaveraged
e s-Z).
These numbers
numberssuggest
suggestan
anestimate
estimateof-30
of -30q-±10
10cm
cm2
These
e ss2
-e
at
estimate
of the
at this
this location
locationas
asaarepresentative
representative
estimateof
the mean
mean
eddy
momentum
flux.
The
analysis
also
indicates
eddy momentumflux. The analysisalso indicatesthat
that the
the
geostrophic
velocity calculations
calculations should
should use
use gradient
geostrophicvelocity
gradientoperoperators
atorswith
with larger
largerspatial
spatialdifferences
differencesand
and cover
coverthe
the longest
longest
period available
available to
to try
try to
to stabilize
stabilize the
the statistics.
statistics. The
period
The orientaorientation of
of the
the principal
principal axis
measured
tion
axisfor
for the
the spatially
spatiallyaveraged
averagedmeasured
12,746
12,746
STRIJB ET AL.:
AND
RESOLUTION
STRUB
AL.: TOPEX
TOPEXVELOCITIESACCURACY
VELOCITIES-ACCURACY
ANDALONG-TRACK
ALONG-TRACK
RESOLUTION
currents (-22°)
estimate (-30ø).
(-30°). ter
ter with
a bess
filter
currents
(-22ø) is
isalso
alsomore
morelike
like the
theTOPEX
TOPEX estimate
witha
loess
filterwith
withaahalf
halfspan
spanof
of50
50km,
km,as
asgiven
given
We
thus
end
with
greater
confidence
in
the
TOPEX
by Chelton
et al.
al. [1990].
is aa highWe thusend with greaterconfidence
in the TOPEXeddy
eddy by
Chelton
et
[1990].The
The62-km
62-kmdifference
difference
is
highstatistics (other
spectra)
as
statistics
(otherthan
thanthe
thecovariance
covariance
spectra)
asrepresentarepresenta- pass
passfilter,
filter,reducing
reducingthe
theenergy
energyby
by half
half for
for scales
scalesof
of motion
motion
tive
currents
when
over
filter
tiveof
of oceanic
oceanic
currents
whenaveraged
averaged
overspatial
spatialscales
scales greater
greaterthan
thanapproximately
approximately250
250 km.
km. The
Thebess
loess
filterelimielimiof
nates
energy
by
a
factor
of
2
for
scales
of
motion
of approximately
approximately50-100
50-100 km.
km.
natesenergyby a factor of 2 for scalesof motion less
lessthan
than
80 km,
eliminating
the
minor
effects
of
the
high-frequency
80
km,
eliminating
the
minor
effects
of
the
high-frequency
4.2.
4.2. Oceanographic
OceanographicConclusions
Conclusions
sidebobes
of the
the difference
difference operator.
operator. The
of
sidelobes
of
Thecombination
combination
of
the
two
filters
reduces
the
energy
of
signals
by
an
order
of
The
velocity
components
in
the
California
Current
are
the
two
filters
reduces
the
energy
of
signals
by
an
order
of
1. The velocitycomponents
in the CaliforniaCurrentare
outside
of
between
approximately
60
anisotropic
and
magnitude
outside
of the
therange
range
between
approximately
60
anisotropic
andmay
maybe
bestrongly
stronglypolarized,
polarized,even
evenat
atlocations
locations magnitude
and
625
km.
At
the
edges
of
tracks
or
around
missing
data
400
km
from
the
shelf
break
over
the
deep
ocean.
The
and
625
km.
At
the
edges
of
tracks
or
around
missing
data
400 km from the shelf break over the deepocean. The
points,
the number
statistics
in Tables
points,where
wherethe
numberof
of points
pointsis
is less
lessthan
thanneeded
neededfor
for
statistics in
Tables la
l a and
and 2a
2a indicate
indicate that
that the
the minor
minor axes
axes
the
bess
filter,
we
substitute
a
simple
three-point
running
of
than
a simplethree-point
running
of the
theprincipal
principalaxis
axisellipses
ellipsesare
aresmaller
smallerin
inmagnitude
magnitude
than theloessfilter,we substitute
filter
of
the major
to mean.
mean.This
Thisis
isaalow-pass
low-pass
filterwith
withaa half
halfpower
powerpoint
pointof
the
majoraxes
axesby
by factors
factorsof
of 1.5
1.5(hourly
(hourlyfiltered
filteredADCP)
ADCP) to
approximately
30-40
km.
Although
the
running
mean
has
4
(spatial
average
of
100-rn
VACMs).
TOPEX
at
the
same
30-40 km. Althoughtherunningmeanhasaa
4 (spatial averageof 100-m VACMs). TOPEX at the same approximately
less
aesthetically
pleasing
set
sidelobes,
location
shows
a
factor
of
1.25
to
2,
depending
on
the
period
less
aesthetically
pleasing
setof
ofhigh-frequency
high-frequency
sidelobes,
locationshowsa factorof 1.25to 2, depending
ontheperiod
there
is
almost
no
difference
between
statistics
calculated
there
almost
no
difference
between
statistics
calculated
used.
Figure
13
shows
a
similar
level
of
polarization
in
the
used.Figure13 showsa similarlevelof polarization
in the
using the
ellipses judged
judged significant.
significant. Thus
the running
runningmean
meaneverywhere
everywhereand
andthose
thosecalculated
calculated
ellipses
Thusestimates
estimatesof
of EKE
EKE based
based using
using
the
bess
filter.
In
fact,
neither
the
bess
filter
nor
using
the
loess
filter.
In
fact,
neither
the
loess
filter
nor the
the
on
cross-track
velocity
variances
that
assume
isotropy
are
on cross-trackvelocityvariancesthat assumeisotropyare
three-point
running
mean
change
the
statistics
of
the
in error
in
error in
in some
some locations.
locations.
three-pointrunningmeanchangethe statistics
of thecomcomto
meters
substantially,
although
they
variability occurs
occurs in
in the
parison
tocurrent
current
meters
substantially,
although
theymake
make
2. Persistent,
Persistent,small-scale
small-scalevariability
the offoff- parison
the
along-track
velocity
fields
look
smoother.
shore region
region of
with
shore
of the
theCalifornia
CaliforniaCurrent
CurrentSystem,
System,
withopposoppos- the along-trackvelocityfieldslook smoother.
The
parameters
is
on
ing velocities
velocities(4(± 20 cm s_1)
of 15-30
Thechoice
choiceof
ofthese
these
parameters
isbased
based
onexperience
experience
-•) found
foundat
atdistances
distances
15-30
with
Geosat
data
and
further
tests
with
TOPEX
data.
Geosat
data
and
further
tests
TOPEX
data. DurDurkm,
lasting
several
weeks.
Figure
4e
demonstrates
this
at
km, lastingseveralweeks. Figure 4e demonstrates
this at
ing
the
Geosat
Exact
Repeat
Mission,
hydrographic
surthe
mooring
sites
from
measured
currents
at
100-m
depth.
ing
the
Geosat
Exact
Repeat
Mission,
hydrographic
surthe mooringsitesfrommeasured
currents
at 100-mdepth.
veys
were
conducted
off
northern
California
in
spring
and
An
anticyclonic
eddy
appears
to
have
drifted
over
the
moorveys
were
conducted
off
northern
California
in
spring
and
An anticycloniceddyappearsto havedriftedoverthemoorof 1987
and 1988
ing
velocity
differences. The
summerof
1987 and
1988 as
as part
partof
of the
theOffice
Officeof
of Naval
Naval
ing site,
site,creating
creatingthese
thesesmall-scale
small-scale
velocitydifferences.
The summer
coastal
Research-sponsored
coastaltransition
transitionzone
zoneinitiative.
initiative. SurSurchoice
operators
used
altimeter
choiceof
of numerical
numerical
operators
usedin
incalculating
calculating
altimeter Research-sponsored
veys
in
MayJune
1987
were
coincident
with
Geosatdata
data
velocities
should take
variability
velocitiesshould
take this
thissmall-scale
small-scale
variabilityinto
into acac- veys in May-June 1987 were coincidentwithGeosat
along
tracks which
apcount.
count.
alongascending
ascending
tracks
whichran
ranparallel
parallelto
tothe
thecoast
coast
approximately
100
and
250
km
offshore.
Use
of
these
data
proximately
100
and
250
km
offshore.
Use
of
these
data
Small
principal
axis
ellipses
indicate
low
eddy
en3. Small principalaxis ellipsesindicatelow eddyenAVHRR
gradients
(tests
andcoincident
coincident
AVHRR temperature
temperature
gradients
(testssimilar
similar
ergy
levels at crossovers
ergy levels
crossoverslocated
located700 km and
and more
more from the
the and
to
those
reported in
in section
3)
gave
an initial
initial indication
that
to
those
reported
section
3)
gave
an
indication
that
coast,
isolating
the
more
energetic
region
within
approxicoast,isolatingthe moreenergeticregionwithinapproxithe
altimeter
could
resolve
mesoscale
features
of
50-100
altimeter
resolve
mesoscale
50-100
mately
500
km
of
the
coast.
Surface
drifters
and
field
surmately 500 km of the coast. Surfacedrifters and field surkm. The
data
more
tests
veys
jets within
Thehydrographic
hydrographic
dataallowed
allowed
morequantitative
quantitative
tests
veysalso
alsofind
find energetic
energeticeddies
eddiesand
andmeandering
meandering
jets
within km.
of
various
methods
of
calculating
the
along-track
height
gra500 km
of
methods
of calculating
thealong-track
height
gra500
km of
of the
thecoast.
coast.The
Theisolation
isolation
ofthis
thisregion
regionsupports
supports of various
These tests
testsresulted
resulted in the
the use
useof
of aacentered
centereddifferdifferthe hypothesis
that
eddies
the
hypothesis
thatthe
theobserved
observed
eddiesare
arederived
derivedfrom
fromthe
the dients. These
followed
by
running
California Current,
that ence
encewith
withaa63-km
63-kmspan,
span,
followed
byaathree-point
three-point
running
California
Current,rather
ratherthan
thanbeing
beingdeep
deepocean
oceaneddies
eddiesthat
mean.
With
TOPEX
data,
10
grid
intervals
on
the
tracks
move
onshore
into
the
California
Current
System.
mean.
With
TOPEX
data,
10
grid
intervals
on
the
tracks
move onshoreinto the CaliforniaCurrentSystem.
produced by JPL
JPL produce
and we
we have
have
produced
produceaa 62-km
62-kmdifference,
difference,and
replaced the
the running
running mean
mean with
with the
the loess
bess filter
where
replaced
filterexcept
except
where
the number
the
numberof
of points
pointsis
islimited.
limited.
Appendix:
Appendix- Geostrophic
GeostrophicCalculations
Calculations
The
effects
of
varying
the
and
Theeffects
of varying
thefinite
finitedifference
difference
andsmoothing
smoothing
operators
were
further
tested
during
the
present
study,
based
Our
velocity
werefurthertestedduringthepresent
study,
based
Our calculation
calculationof
ofthe
thegeostrophic
geostrophic
velocityfrom
fromalongalong- operators
on
changes
in
the
rms
difference
between
the
TOPEX
veon
changes
in
the
rms
difference
between
the
TOPEX
vetrack
trackgradients
gradientsof
of altimeter
altimeterheights
heightsbegins
beginswith
with aa centered,
centered,
locities at
at the
the crossover
crossover and
the
spatially
averaged 18-month
finite
difference
form
of
the
geostrophic
calculation.
locities
and
the
spatially
averaged
18-month
finite differenceform of the geostrophic
calculation.
record of 100-rn
under
record
100-m current
currentmeasurements
measurements
underthe
thecrossover.
crossover.
the
filter
while
the
g h(j+n)h(jn) (Al) Eliminating
Eliminating
thespatial
spatial
filterentirely,
entirely,
whilekeeping
keeping
the6262km
finite
difference,
had
little
effect,
increasing
the
rms
km
finite
difference,
had
little
effect,
increasing
the
rms
lOs
2n,Ls
f
Vc(.j)-.fOs=-.'•
2r•.
As ] (A1)difference from 7 to 8 cm s1 for the cross-track compo-
gO/i
where
surface
velocity
(positive
to
whereV
Vcisisthe
thecross-track
cross-track
surface
velocity
(positive
tothe
the
right
rightof
of the
thetrack,
track,when
whenlooking
lookingalong
alongthe
thetrack
trackfrom
fromsouth
south
to
is the
of gravity,
to north),
north),gg is
theacceleration
acceleration
of
gravity,.ff is
isthe
theCoriolis
Coriolis
parameter,
h isisthe
sea
height,
s is
is the
parameter,h.
thecorrected
corrected
seasurface
surface
height,s
the
along-track
coordinate,
j isisthe
grid
along-track
coordinate,
.j
theindex
indexof
ofthe
thealong-track
along-track
grid
point,
from
and
n is
point,numbered
numbered
fromsouth-to-north,
south-to-north,
andr•.
isthe
thehalf
halfspan
span
of
the
centered
difference.
The
resulting
velocities
are
of thecentered
difference.The resultingvelocities
arethen
then
smoothed
with aa spatial
smoothed
with
spatialfilter
filterand
andthe
themean
meanvelocity
velocityfrom
from
the
at
thetotal
totalperiod
periodis
isremoved
removed
ateach
eachgrid
gridpoint
pointto
toeliminate
eliminate
the
the influence
influenceof
of the
themarine
marinegeoid.
geoid.
In the
we
In
thepresent
presentcalculations,
calculations,
weuse
useaaspan
spanof
of10
10TOPEX
TOPEX
intervals
(n=5)
to
produce
a
62-km
difference
and
intervals(r•,=5)to producea 62-km differenceandthen
thenfilill-
difference
from7 to 8 cms-• forthecross-track
components of
of velocity.
Retaining
the
reducing
nents
velocity.
Retaining
the50-km
50-kmfilter
filterwhile
whilereducing
the span
the
spanof
of the
thefinite
finitedifference
differencehad
had aa much
muchmore
moredrastic
drastic
effect.
of
by
effect.Spans
Spans
of50,
50,37,
37,25,
25,and
and12.5
12.5km,
km,followed
followed
by the
the
50-km
resulted in
of 8,
50-kmfilter,
filter,resulted
in rms
rmsdifferences
differences
of
8, 10,
10,13
13and
and15
15
cm
s,-•respectively,
compared
to
cms
respectively,
compared
to77cm
cmss-• for
forthe
the62-km
62-km
span.
span.
An
to
operators
isis
An alternative
alternative
tothe
theuse
useof
offinite
finitedifference
difference
operators
to
fit
linear
regressions
to
a
span
of
points.
Morrow
et
al.
to fit linearregressions
to a spanof points.Morrowet al.
[1994]
for
[1994] used
usedaa 25-point
25-pointlinear
linearregression
regression
forGeosat
Geosatdata,
data,
which
removed
most
variability
with
scales
less
than 100
whichremovedmostvariabilitywith scaleslessthan
100
km. Given
level
km.
Giventhe
thelower
lowernoise
noise
levelin
inTOPEX
TOPEXdata,
data,present
present
calculations
are
being made
made with
with 12-20
calculations
arebeing
12-20point
pointlinear
linearregresregres-
STRUB
STRUB ET
ET AL.:
AL.' TOPEX
TOPEX VELOCITIESACCURACY
VELOCITIES-ACCURACYAND
ANDALONG-TRACK
ALONG-TRACKRESOLUTION
RESOLUTION
12,747
12,747
sions
sions[D.
[D. Chelton,
Chelton,personal
personalcommunication,
communication,1996].
1996]. For
For the
the References
References
crossover
considered
here,
use
of
a
ten-point
linear
regrescrossoverconsideredhere, use of a ten-pointlinear regression
sion(to
(to compare
compareto
to the
theten-point
ten-pointdifference)
difference)results
resultsin
in rms
rms
Brink, K.H.,
K.H., and
and T.J.
Ti. Cowles,
transition
zone
program,
Cowles,The
Thecoastal
coastal
transition
zoneprogram,
differences
of9-11
9-11 cm
cm ss'-1between
TOPEX
differences
of
between
TOPEXand
andthe
thespaspa- Brink,
J.
Geophys.
Res.,
96,
14,637-14,647,
1991.
J.
Geophys.
Res.,
96,
14,637-14,647,
1991.
tially
components
of
tially averaged
averaged100-rn
100-mcross-track
cross-track
components
ofvelocity.
velocity. Brink, K.H., R.C. Beardsley, P.R Niiler, M. Abbott, A. Huyer,
Brink, K.H., R.C. Beardsley,P.P.Niiler, M. Abbott,A. Huyer,
This
than the
the 7-8
7-8 cm
crn ss1
using
Thisis
is larger
largerthan
-• obtained
obtained
usingthe
the1010S. Ramp, T. Stanton, and D. Stuart, Statistical properties of
point
difference, with
with or
or without
without the
the 50-km
50-km loess
bess spapointfinite
finite difference,
spatial
in
of
tial filter,
filter, due
dueto
to the
thedecrease
decrease
inthe
thesrnoothing
smoothing
of the
thelinear
linear
fit
and Chelton,
fit [Schiax
[Schlaxand
Chelton,1992].
1992]. Use
Use of
of aa 12-16
12-16 point
pointlinear
linear
fit
approximately
reproduces
the
results
using
the
fit approximatelyreproducesthe resultsusingthe ten-point
ten-point
difference
and the
differenceand
the 50-km
50-km bess
loessspatial
spatialfilter.
filter.
Our
Our conclusion
conclusionis
is that
thatthe
the10-point
10-pointfinite
finitedifference
differenceopoperator,
followed by
by the
the 50-km
50-km loess
bess filter,
erator,followed
filter, is
is as
asreasonable
reasonableaa
choice
choiceof
of gradient
gradientoperator
operatoras
asany
anyother
othersimple
simpleoption
optionin
in this
this
region
the ocean.
using
regionof
of the
ocean.A
A linear
linearregression
regression
using12-16
12-16 points
points
would
scale
would work
work as
aswell.
well. The
Theappropriate
appropriate
scaleof
ofthe
thegradient
gradient
operator
may
differ
in
other
regions.
For
global
operatormay differ in other regions. For globalapplicaapplications,
spans of
of 16-20
tions, more
more conservative
conservativespans
16-20 points
pointsmight
mightbe
be
advised.
advised.Decreasing
Decreasingthe
the scale
scaleof
of the
theoperator
operatorbelow
below50
50 km
km
rapidly
requiring
adrapidlyamplifies
amplifiesthe
thenoise
noisein
inthe
thecalculation,
calculation,
requiring
additional
when
ditionalsmoothing.
smoothing.There
Theremay
maybe
bespecific
specificinstances
instances
when
itit is
isworth
worthpushing
pushingthe
thespatial
spatialresolution
resolutionto
to smaller
smallerscales,
scales,
but
butonly
onlyif
if the
thesignal
signalisisstrong
strongenough
enoughto
tostand
standout
outabove
above
the increased
increased noise.
noise.
Finally, how
how do
Finally,
do these
theselevels
levelsof
of velocity
velocityuncertainty
uncertaintyrelate
relate
to
the
expected
levels
of
uncertainty
in
altimeter
to the expectedlevels of uncertaintyin altimeterheights?
heights?
As aa first
As
first estimate
estimatewe
we assume
assumethat
that errors
errorsin
in height
heightare
are
S. Ramp, T. Stanton,and D. Stuart,Statisticalpropertiesof
near-surface flow
flow in
in the
near-surface
the California
California coastal
coastaltransition
transitionzone,
zone, J.
J.
Geophys. Res.,
Res., 96,
96, 14693-14,706,
Geophys.
14693-14,706,1991.
1991.
Callahan,
S., TOPEX/POSEIDON
Project GDR
GDR User's
Callahan,P.
P.S.,
TOPEX/POSEIDON Project
User'sHandHandhood,
Pub!. JPL
bood,Publ.
JPLD-8944,
D-8944, rev.
rev.A.,
A., Jet
JetPropul.
Propul.Lab.,
Lab.,Pasadena,
Pasadena,
Calif.,
Calif., 1993.
1993.
Chelton,
Chelton, D.B.,
D.B., M.G.
M.G. Schlax,
Schlax, D.L.
D.L. Witter,
Witter, and
andJ.G.
J.G.Richman,
Richman,
Geosat
of the
the surface
of the
Geosat altimeter
altimeter observations
observations of
surface circulation
circulation of
the
Southern Ocean,
Ocean, J.
Southern
J. Geophys.
Geophys.Res.,
Res.,95,
95, 17,877-17,903,
17,877-17,903,1990.
1990.
Chereskin,
T.K., Direct
for an
Chereskin, T.K.,
Direct evidence
evidence for
an Ekman
Ekman balance
balance in
in the
the
California
CaliforniaCurrent,
Current,J.
J. Geophys.
Geophys.Res.,
Res.,100,
TO0,18,261-18,271,
18,261-18,271,1995.
1995.
Chereskin,
T. K.,
K., and
of
Chereskin,T.
andA.
A. J.
J.Harding,
Harding,Modeling
Modelingthe
theperformance
performance
of
an acoustic
an
acousticDoppler
Dopplercurrent
currentprofiler,
profiler,J.
J.Atmos.
Atmos.Oceanic
OceanicTechTechnol., 10,
TO,41-63,
41-63, 1993.
1993.
Chereskin
T. K.,
K., E.
ChereskinT.
E. Firing,
Firing, and
andJ.
J.A.
A.Gast,
Gast,On
Onidentifying
identifyingand
and
screening filter
filter skew
skew and
and noise
noise bias
bias in
in acoustic
Doppler current
current
screening
acousticDoppler
profiler
J. Atmos.
Atinos. Oceanic
6, 1040profiler measurements,
measurements,J.
OceanicTechnol.,
Technol.,6,
10401054, 1989.
1989.
D'Asaro,
D' Asaro,E.A.,
E.A.,C.C.
C.C.Eriksen,
Eriksen,M.D.
M.D.Levine,
Levine,P.
P.Niiler,
Niiler,C.A.
C.A. Paulson,
Paulson,
and
P.
Van
Meurs,
Upper-Ocean
inertial
currents
forced
andP. Van Meurs,Upper-Ocean
inertialcurrents
forcedby
byaa
strong
with
strongstorm,
storm,I,
I, Data
Dataand
andcomparisons
comparisons
with linear
lineartheory,
theory,J.
J.
Phys.
Phys.Oceanogr.,
Oceanogr.,25,
25, 2909-2936,
2909-2936,1995.
1995.
Egbert, G.D.,
Egbert,
G.D., A.F. Bennett,
Bennett,and
andM.G.G.
M.G.G. Foreman,
Foreman,TOPEXTOPEX- POSEIDON
tides estimated
using aa global
J. GeoSEIDON tides
estimatedusing
globalinverse
inversemodel,
model,J.
Geophys.
phys.Res.,
Res.,99,
99, 24,821-24,852,
24,821-24,852, 1994.
1994.
uncorrelated
the error
Fu, L.-L.,
uncorrelatedand
and propagate
propagatethe
errorin
in height
heightthrough
throughthe
the Fu,
L.-L., E.J.
E.J. Christensen,
Christensen,C.A.
C.A. Yamarone
YamaroneJr.,
Jr., M.
M. Lefebvre,
Lefebvre, Y.
Y.
Ménard, M.
geostrophic
calculation
MCnard,
M. Dorrer,
Dorrer, and
and P.
P. Escudier,
Escudier,TOPEX/POSEIDON
TOPEX/POSEIDON mismisgeostrophic
calculationusing
usingthe
the'simple
•imple finite
finite difference
differenceof
of
sion
J. Geophys.
sionoverview,
overview,J.
Geophys.Res.,
Res.,99,
99, 24,369-24,382,
24,369-24,382,1994.
1994.
62 km
filter):
62
km (without
(withoutaa subsequent
subsequent
filter):
Huyer, A.
A. P.M.
S.R.
Huyer,
P.M. Kosro,
Kosro,J.
J.Fleischbein,
Fleischbein,
S.R.Ramp,
Ramp,T.
T. Stanton,
Stanton,
Washburn, F.P.
ER Chavez,
T.J.
Cowles,
S.D.
Pierce,
and
L.
Washburn,
Chavez,
T.J.
Cowles,
S.D.
Pierce,
and R.L.
R.L.
(A2)
Smith, Currents and water masses
massesof the
the coastal
coastal transition
transition zone
zone
off northern
northern California,
California, June
June to
Res.,
off
to August
August1988,
1988,J.
J.Geophys.
Geophys.
Res.,
where L
L is
is the
the span
96, 14,809-14,831,
where
spanof
of the
the finite
finite difference.
difference.For
For normal
normalvalval96,
14,809-14,831, 1991.
1991.
ues of
of gg and
and .f
f atatmidlatitudes
Katz, E.J.,
E.J., A.
ues
midlatitudesand
andfor
for L
L == 62
62 km,
km, an
anunceruncer- Katz,
A. Busalacchi,
Busalacchi,M.
M. Bushnell,
Bushnell,F.
F. Gonzalez,
Gonzalez,L.
L. Gourdeau,
Gourdeau,
McPhaden, and
and J.
J. Picaut,
of
coincidental time
time
tainty of 7.6
7.6 cm
in cross-track
velocity
to
M. McPhaden,
Picaut,A
A comparison
comparison
of coincidental
tainty
cmss-• in
cross-track
velocitycorresponds
corresponds
to
series
of
the
ocean
surface
height
by
satellite
altimeter,
moorseries
of
the
ocean
surface
height
by
satellite
altimeter,
mooran
rms
uncertainty
in
height
of
3.3
cm.
Uncertainties
of
3-5
an rms uncertaintyin heightof 3.3 cm. Uncertaintiesof 3-5
ing, and
J. Geophys.
andinverted
invertedecho
echosounder,
sounder,
J.
Geophys.Res.,
Res.,100,
TOO,25,10125,101cm
totorms
height
uncertainties
of
cms1
s-•correspond
correspond
rms
height
uncertainties
ofapproxapprox- ing,
25,108, 1995.
25,108,
1995.
imately
2
cm.
These
uncertainties
in
height
compare
very
imately 2 cm. These uncertaintiesin height comparevery Kosro,
Kosro, P.M.,
P.M., et
et al.,
al., The
The structure
structureof
of the
thetransition
transitionzone
zone between
between
well to
to previous
previous estimates
estimates of
of 2.7-3.3
2.7-3.3 cm
cm [Katz
et al.,
al., 1995]
well
[Katz et
1995]
coastal
California, winter
coastalwaters
watersand
andthe
theopen
openocean
oceanoff
off northern
northernCalifornia,
winter
1995], from
from inverted
and
and
and 3.3-3.7
3.3-3.7 cm
cm [Picaut
[Picaut et
et al.,
al., 1995],
inverted echo
echo
andspring,
spring,1987,
1987, J.
J. Geophys.
Geophys.Res.,
Res.,96,
96, 14,707-14,731,
14,707-14,731,1991.
1991.
sounders
and A.
A. J.
Menkes,C.,
C., J.-P.
J.-P.Boulanger,
Boulanger,and
J. Busalacchi,
Busalacchi,Evaluation
Evaluationof
of
soundersand
andfrom
from moorings
mooringsin
in deep
deepwater
wateron
on which
whichstrings
strings Menkes,
TOPEX
Tropical
Atmosphereof temperature
temperature and
and conductivity
conductivity sensors
sensors allow
allow calculation
calculation of
of
TOPEX and
andbasin-wide
basin-wide
TropicalOcean
Oceanand
andGlobal
GlobalAtmosphereof
Tropical
Ocean
topographies
and
TropicalAtmosphere
Atmosphere
Oceansea
seasurface
surface
topographies
anddedecontinuous
time
continuous
timeseries
seriesof
ofdynamic
dynamicheight.
height.
rived
currents,
100, 25,087rived geostrophic
geostrophic
currents,.1.
J. Geophys.
Geophys.Res.,
Res., TOO,
25,087Acknowledgments.
Support for
S and
and CJ
CJ was
was provided
provided by
25,099,
25,099, 1995.
1995.
Acknowledgments. Support
for PT
PTS
by
JPL
958128, ONR
Mesias, J.M.,
J.M., and
and P.T.
P.T. Strub,
Strub, An
An inversion
inversion method
method to
to determine
determine
JPL grant
grant958128,
ONR grant
grantN0014-92-J-1631
N0014-92-J-1631and
andNASA
NASA grants
grants Mesias,
NAGW-2475
and NAF-5-30553.
ocean
data,
NAGW-2475 and
NAF-5-30553. Support
Supportfor
for MDL
MDL was
wasprovided
provided
oceansurface
surfacecurrents
currentsusing
usingirregularly
irregularlysampled
sampledaltimetry
altimetrydata,
by
J.
12, 830-849,
J. Atmos.
Atmos. Oceanic
OceanicTechnoL,
Technol., 12,
830-849, 1995.
1995.
by JPL
JPL grant
grant958128.
958128. Support
Supportfor
forTKC
TKC was
wasprovided
providedby
byONR
ONR
S2 2SH2()2 = 2S2(_-)2
$w2_
25H2(•_ff)2
_ 2SH2()2
(A2)
grant
and NSF
grant 14-92-J-1584
14-92-J-1584 and
NSF grant
grantOCE-9216411.
OCE-9216411. Support
Supportfor
for
PPN
by ONR
PPN was
was provided
providedby
ONR grant
grantN0014-91-J-1016.
N0014-91-J-1016. The
The ONR
ONR
support
was part
supportwas
part of
of the
theEastern
EasternBoundary
BoundaryCurrent
CurrentARI
ARI (Code
(Code
322,
322, Physical
PhysicalOceanography).
Oceanography).TOPEX
TOPEX data
datawere
wereprovided
providedby
by
the
Laboratory.
Tidal corrections
the Jet
JetPropulsion
Propulsion
Laboratory. Tidal
correctionswere
were provided
provided
by
by Gary
Gary Egbert
Egbert and
and Andrew
Andrew Bennett.
Bennett.The
Themooring
mooringdesign,
design,dedeployment,
and recovery
were made
by technical
ployment,and
recoverywere
madepossible
possibleby
technicalsupport
support
from
from Oregon
OregonState
StateUniversity's
University'sBuoy
BuoyGroup,
Group,Scripps
ScrippsInstitution
Institution
of
Instrument
of Oceanography's
Oceanography's
InstrumentDevelopment
DevelopmentGroup,
Group,Woods
WoodsHole
Hole
Oceanographic
Institution's Buoy
Oceanographic
Institution's
Buoy Group,
Group,University
Universityof
of Miami's
Miami's
Buoy
Group, and
and the
the captain
captain and
and crew
crew of
of the
the R/V
RN Point
BuoyGroup,
PointSur.
Sur.DisDiscussions
cussionswith
with Dudley
Dudley Chelton,
Chelton,Michael
Michael Kosro,
Kosro,Michael
Michael Freilich,
Freilich,
Morrow, R.,
R., R.
R. Coleman,
I. Church,
Morrow,
Coleman, J.
Church, and
and D.
D. Chelton,
Chelton, Surface
Surface
eddy
flux and
eddy momentum
momentumflux
andvelocity
velocityvariances
variancesin
in the
theSouthern
Southern
Ocean
.1. Phys.
Phys. Oceanogr.,
Oceanogr., 24,
24, 20502050Oceanfrom
from Geosat
Geosataltimetry,
altimetry,J.
2071,
2071, 1994.
1994.
Paduan, J.D.,
J.D., and
description
of
Paduan,
andPP.
P.P.Niiler,
Niiler,A
A Lagrangian
Lagrangian
description
of motion
motion
in Northern
filaments,
in
NorthernCalifornia
Californiacoastal
coastaltransition
transition
filaments,J.
J.Geophys.
Geophys.
Res., 95,
95, 18,095-18,109,
Res.,
18,095-18,109, 1990.
1990.
Picaut,
Picaut, J.,
J., A.J.
A.J.Busalacchi,
Busalacchi,M.J.
M.J. McPhaden,
McPhaden,L.
L. Gourdeau,
Gourdeau,F.I.
F.I.
Gonzalez, and
validation
TOPEXGonzalez,
andE.C.
E.C. Hackert,
Hackert,Open-ocean
Open-ocean
validationof
of TOPEXPOSEIDON sea
equatorial
Pacific,
POSEIDON
sealevel
levelin
inthe
thewestern
western
equatorial
Pacific,.1.
J. GeoGeophys. Res.,
phys.
Res., 100,
TOO,25,109-25,129,
25,109-25,129, 1995.
1995.
Preisendorfer,
R. W.,
Analysis
Preisendorfer,
R.
W., Principal
PrincipalComponent
Component
Analysisin
inMeteorolMeteoroland
ogy and
and Oceanography,
425
andKathie
KathieKelly
Kelly were
wereuseful
usefulduring
duringthe
the analysis.
analysis.Careful
Carefulreviews
reviews
ogy
Oceanography,
425 pp.,
pp.,Elsevier,
Elsevier,New
New York,
York, 1988.
1988.
by
reviewers
K.H.
by Fabrice
FabriceHernandez
Hernandezand
andtwo
two anonymous
anonymous
reviewersresulted
resultedin
in aa Ramp,
Ramp, S.R.,
S.R., P.R
P.F.Jessen,
Jessen,
K.H. Brink,
Brink,P.P.
P.P.Niiler,
Niiler, EL.
F.L.Daggett,
Daggett,
clearer
and J.S.
clearerand
andmore
moreconcise
concisepaper.
paper.
and
J.S. Best,
Best,The
The physical
physicalstructure
structureof
of cold
coldfilaments
filamentsnear
near
12,748
12,748
STRUB ET
iff AL:
AL.:TOPEX
TOPEXVELOCITIESACCURACY
VELOCITIES-ACCURACY AND
ANDALONG-TRACK
ALONG-TRACK RESOLUTION
RESOLUTION
Point
Res.,
Point Arena,
Arena, California,
California,during
duringJune
June1987,
1987,J.J.Geophys.
Geophys.
Res., Yu,
Yu, Y.,
Y., W.
W. J.
J. Emery,
Emery, and
andR.
R. R.
R.Leben,
Leben,Satellite
Satellitealtimeter
altimeterdede96,
rived geostrophic
geostrophic currents
currents in
tropical
Pacific
96, 14,859-14,884,
14,859-14,884, 1991.
1991.
rived
in the
thewestern
western
tropical
Pacificduring
during
Schiax,
Frequency
domain
1992-1993
and their
with
Schlax,M.G.,
M.G., and
andD.B.
D.B.Chelton,
Chelton,
Frequency
domaindiagnostics
diagnostics
1992-1993and
theirvalidation
validation
withdrifting
driftingbuoy
buoytrajectories,
trajectories,
for linears
.1.
Geophys. Res.,
Res., 100,
100, 25,069-25,085,
for
linears smoothers,
smoothers, J.
J. Am.
Am. Stat.
Stat. Assoc.,
Assoc., 87,
87, 1070-1081,
1070-1081,
J. Geophys.
25,069-25,085,1995.
1995.
1992.
1992.
Stabeno,
Stabeno,P.J.,
P.J.,and
andR.L.
R.L. Smith,
Smith,Deep-sea
Deep-seacurrents
currentsoff
off northern
northernCalCalifornia,
P.
ifornia, J.
J. Geophys.
Geophys.Res.,
Res.,92,
92, 755-771,
755-771, 1987.
1987.
Strub, C.
C. James,
D. Levine,
P. T.
T. Strub,
James,and
andM.
M.D.
Levine,College
Collegeof
of
Strub,
Strub, P.T.,
P.T., P.M.
P.M. Kosro,
Kosro, A.
A. Huyer,
Huyer,and
andCTZ
CTZ Collaborators,
Collaborators,The
The
Oceanic
and
Atmospheric
Sciences,
Oregon
State
University,
Oceanic
and
Atmospheric
Sciences,
Oregon
State
University,
nature of
of the
nature
the cold
coldfilaments
filamentsin
inthe
theCalifornia
CaliforniaCurrent
CurrentSystem,
System, 104
Building,
1104 Ocean
OceanAdministration
Administration
Building, Corvallis,
Corvallis,OR
OR9733
97331J.
J. Geophys.
Geophys.Res.,
Res.,96,
96, 14,743-14,768,
14,743-14,768,1991.
1991.
5503.
(email:
5503.
(email: tstrub@oce.orst.edu;
tstrub@oce.
orst.edu; corinne@oce.orst.edu;
corinne
@oce.orst.edu;
Walstad,
L.J., J.S.
of mlevine@oce.orst.edu)
Walstad,L.J.,
J.S.Allen,
Allen, P.M.
P.M. Kosro,
Kosro,and
andA.
A. Huyer,
Huyer,Dynamics
Dynamicsof
mlevine@oce.orst.edu)
the
the coastal
coastaltransition
transitionzone
zonethrough
throughdata
dataassimilation
assimilationstudies,
studies,J.
J.
T.
and
Institution
of
T. K.
K. Chereskin
Chereskin
andP.
P.P.
P.Niiler,
Niiler,Scripps
Scripps
Institution
ofOceanogOceanogGeophys. Res.,
Res., 96,
96, 14,959-14,979,
Geophys.
14,959-14,979, 1991.
1991.
raphy,
raphy,9500
9500 Gilman
Gilman Drive,
Drive, La
La Jolla,
Jolla,CA
CA92093-0230.
92093-0230. (email:
(email:
Wunsch,
C.,
and
D.
Stammer,
The
global
frequency-wavenumber
Wunsch,C., and D. Stammer,The global frequency-wavenumber tchereskin@ucsd.edu;
pniiler@ucsd.edu)
tchereskin@ucsd.edu;
pniiler@ucsd.edu)
spectrum of
spectrum
of oceanic
oceanicvariability
variabilityfrom
fromTOPEX/POSEIDON
TOPEX/POSEIDON alaltimetric
J.
Res.,
May 7,
7, 1996;
timetricmeasurements,
measurements,
J.Geophys.
Geophys.
Res.,100,
100,24,895-24,910,
24,895-24,910, (Received
(ReceivedMay
1996; revised
revisedOctober
October23,
23,1996;
1996;
1995.
1995.
accepted
January 3,
acceptedJanuary
3, 1997.)
1997.)