JOURNAL
OF GEOPHYSICAL
RESEARCH,
VOL. 96, NO. C8, PAGES 14,885-14,907, AUGUST
15, 1991
Structure and Dynamics of a Coastal Filament
RICHARD K. DEWEY, 1 JAMES N. MOUM, CLAYTON A. PAULSON, DOUGLAS R. CALDWELL,
AND STEPHEN D. PIERCE
College of Oceanography, Oregon State University, Corvallis
Repeated microstructure transects across filaments in the coastal transition zone (CTZ) have
revealedfundamentalstructureand dynamicsof the complicatedfeatures.The measurements
allow
detailed momentum and vorticity analyses and provide a possible explanations for structural
asymmetry of the fronts. Observations made between July 2 and July 23, 1988, along the central
meridional CTZ survey line were used to estimate terms in the meridional momentum equation. The
analysisindicatesgeostrophicflow along the axes of the fronts with the acrosg-fr0ntpressuregradient
explaining as much as 87% of the variance in the balance. Significant ageostrophicflow in the
across-front
coordinatewasfound,with the along-frontpressuregradientexplainingonly 7!% of the
variance in the momentum balance. The fronts were found to be asymmetric in relative vorticity, with
stronger positive vorticity on the cooler side of the front and weaker negative vorticity on the warm
side. Mean vertical velocities were estimatedfrom the repeated transectsof acousticDoppler current
profiles and the rapid samplingvertical profiler hydrographicand turbulence measurements.Regions
of upwelling
anddownwelling
arelikelyassociated
withadjustments
in therelativevorticity,resulting
in maximum
verticalvelocities
of 40 m d-l . Asymmetry
in thenear-surface
temperature
andsalinity
extremaare explainedby cross-frontalexchang
e. This cross-frontalexchangemodifiesthe relative
rolesof salinityand temperaturein determiningthe densityaway from the coastalupwellingregion,a
dynamically
importantcharacteristic
not revealedby advancedvery highresolutionradiometer
imagery.
1.
"Squirtlike"
measurements,and hourly meteorologicalmeasurements.
The microstructuresurveywas conductedbetweenJuly 2
INTRODUCTION
structures extend hundreds of kilometers
seawardof the C•iliforniacontinentalshelf. In late spring
and July 23, 1988.
Results from the microstructure pilot cruises in 1986
(April-June) alongshore southward winds over the Oregon
and northern California shelf regions induce coastal upwelling that introduces a significant tilt in the isopycnal
indicated that strong turbulent activity is limited to the
surface mixing layer, driven by surface wind stresses.For
[Mourn
et al., 1988]and1987[Dewey
andMourn,1990]
slopesoverthe continental
shelf[Huyerand Kosro,1987]. windspeeds
greaterthan6 m s-l , DeweyandMourn[1990]
find that the integrateddissipationrates over the surface
to as the CaliforniaCurrent.Satelliteimages(e.g., Flarnent mixinglayeraresignificantly
correlated
withthewindpower
The alongshore southward Current that develops is referred
et al., 1985; Abbott and Barksdale, this issue; Strub et al.,
this issue] reveal that the fronts associated with the Califor-
nia Current are not confined to the shelf and upwelling
region. Between the central •California regions of Cape
Mendocino and Point Reyes the fronts undergo large displacements from the continental shelf and often extend
hundreds of kilometers seaward of the upwelling region.
Processeswithin this transition zone, bounded by the continental slopeand the deep ocean, determinethe exchangeof
properties between coastal upwelling and mid-ocean environments.
(poU,3).They alsofind a significant
trendbetweenthe
inefficiencyof wiiid-forcedmixingin raisingthe mixedlayer
potentialenergy and the depth of the pycnocline.In both
pilot studies,the cool, salinecore of the meanderlikestructures were characterized by a shallow pycnocline that acted
to impedethe surface-generatedturbulencefrom penetrating
to middepths(>40 m). Near-surface (<200 m) currents were
found to be well explained (80%) by the geopotentialanomalies induced by the slopingisopycnals.
The dynamics governing the formation, maintenance, and
modification of these Complicated features are not completely Understood.The importance of cyclostrophiccontributions and the distribution of relative vorticity are exam-
Microstructure measurements were collected along the
central "D line" of the coastal transition zone (CTZ) hydrographic survey grid [Huyer et al., this issue], west of Point
plesof importantdynamicalprocesses
that canbe resolved
Arena, California. The grid was made up of six alongshore
only by observations densely sampled both in time and
lines (A-F) extending from the shelf break to 100 km
space. A description of the microstructure observations
seaward of the shelf region. Microstructure measurements
includedthermistorchain, rapid samplingvertical profiler
from July 1988and the analysispresentedhere will attempt
to address some of the fundamental questions related to the
structure and dynamics of these upwelled filaments. In
particular, the following analysis evaluates a full momentum
equation for two orientations corresponding to acrossINow at ScienceApplications
International
Corporation,
Belle- filament and along-filamentcoordinates. Estimates are made
vue, Washington.
of the ageostrophic contributions, with attempts to deterCopyright 1991 by the American Geophysical Union.
mine their significanceand the resulting degree of geostrophy. Estimates of the relative vorticity reveal considerable
Paper number 91JC00944.
0148-0227/91/91 JC-00944505.00
spatial and temporal variability.
(RSVP) and acoustic Doppler current profiler (ADCP) profiles, continuous sea surface temperature and conductivity
14,885
14,886
DEWEY ET AL ' STRUCTUREAND DYNAMICSOF A COASTALFILAMENT
2.
DATA
Typical momentumanalysesfrom current meter and hydrographicobservationscompareestimatesof two or three
A total of 12 RSVP and 26 shipboardADCP sectionswere
terms in the momentum equations[Flament et al., 1985; collected on the R/V Wecorna during July 1988. In addition,
Huyer and Kosro, 1987; McWilliarns, 1976; Nishida and four currentmetermooringswere deployedbetweenJune22
White, 1982; Fofonoff and Hall, 1983]. A high correlation and July 23, 1988,2 km east of the D line, centeredaboutthe
between the Coriolis acceleration (i.e., fU) and the corre- core of the filament. Two of the moorings were equipped
spondingpressuregradient[- 1/poOP/Oy]
is often assumedto with upward-projectingADCPs measuringcurrentsin the
be sufi%ientin determining the degree of geostrophy. Ageo-
upper 110 m.
strophiccontributions(i.e., OV/Ot and UOV/Ox) are often
omitted because they are assumed to be small and are
typically difi%ultto measureand requirerepeatedobservations. Although they are typically smaller than the two
"geostrophic" contributions, ageostrophicterms may con-•
tribute significantlyto the momentumbalance.To determine
the degree of geostrophy, each term in the momentum
The RSVP systemprovidesverticalprofilesof temperature T, salinityS, deriveddensityanomaly•rt, and the rate
of viscousdissipationof turbulent kinetic energy (e) [Caldwell et al., 1985]. Horizontal profile separationrangedbetween 0.6 and 1.5 kin, with maximum profile depths of
250-160 m, both dependenton the ship speed (1.2-2.5 m
s-1). RSVPdatawerecollectedduringthenorthward
head-
equationsshouldbe estimated.Only when it has been ing transectsonly, while steaminginto the prevailingwinds.
establishedthat the ageostrophicterms are in fact insignifi- The shipboard300-kHz ADCP data consistof 15-rainaverageprofilesof U andV in 4-mverticalbinsoverthedepth
cant can it be stated that the flow is geostrophic.
range15-250m. ShipboardADCP data were recordedwhile
Previous studies in the area [Flament et al., 1985; Kosro
and Huyer, 1986;Huyer and Kosro, 1987;$trub et al., 1987; steamingboth northward and southwardalong the D line.
RSVP temperature,salinity, and •rt data were averaged
Mourn et al., 1988;Dewey and Mourn, 1990]find reasonable
into
profileswith vertical spacingof 2.5 m and horizontal
Correlationsbetween geostrophic and measuredvelocities,
spacing
of 1.8 kin. The shipboardADCP data and the RSVP
but synopticityand poor temporal resolutiongive no indication of the magnitude or the net contribution from ageo- dissipationrate (e) measurementswere averagedintø prostrophicdynamics. In the following analysis,the data col- files with vertical and horizontal spacingof 5.0 m and 1.8 kin,
lectedalongthe central "D.7,'line of the hydrographicsurvey respectively.Continuoussamplingalongthe D line resulted
grid [Huyer et al., this issue]will be used to estimate seven in repeatedtransectsof RSVP data approximatelyevery 2
days and in almost daily ADCP transects (sampledwhile
terms in the meridional momentum equation.
ADCPobservations,
bothshipboard
andmoored,
areused headingboth northwardand southward).A total of 12RSVP
to estimate the relative vorticity at two locations. Temporal
changes,tilting and stretchingof vorticity are also estimated
in a limited vorticity analysis.Advection of relative vorticity
and 24 ADCP
transects across the filament were collected
during the 21-day cruise. These uniformly spaced,gridded
data (U(y, zs, t2), V(y, zs, t2), T(y, z2.5, tl), S(y, z2.5,
is found to result in regions within the filament of both tl), err(y, z2.5, tl), and e(y, zs, t•)) are used in the
following analysisto estimate terms in the meridionalmoupwelling and downwelling.
mentumequation(t• indicatesRSVP data collectedwhile
The finely spaced sampling provided by the microstrucheading northward only, a total of 12 transects, and t2
ture profiler reveals an asymmetric structure in the nearindicates ADCP data collected while heading both northsurface temperature and salinity distributionsthat can be
ward and southwardfor a total of 26 transects;z 2.5indicates
explainedby cross-frontalexchange.Strub et al. [this issue]
data averagedinto vertical bins of 2.5 m (T, S, crt), and z5
summarizethe complicatedwater massstructuresfound in indicates 5-m bins (U, V, e)).
the surfacelayers acrossa variety of upwelledfilamentsand
Four current meter moorings were deployed approxiidentify possiblesourceregionsfor the water masses.Steep mately 2 km east of, and parallel to, the D line. Three of
isopycnalslopesin the frontal regionforce cross-frontalflow these moorings contained upward-projecting 300-kHz
to have vertical componentsof velocity. This cross-frontal ADCPs. Two ADCP moorings, referred to as D2 (latitude
exchange
stirstogetherconsiderably
differentwatermasses. 38.1873,longitude125.0442)and D3 (latitude 37.8323,longi-
As part of the momentumanalysis,the mean vertical veloc- tude 124.7781), sampled the upper 110 m (15 to 110 m
ity structurewithin the filament is estimated,and the implied depths).The mooredADCP data consideredin the following
divergencesand convergencesprovide a possibleexplana- analysesconsistsof 10-min-averagedprofiles with 4-m vertion for the observed temperature-salinity structure.
tical bins. Both shipboardand mooredADCP velocitycomThe microstructure measurements were collected along a ponents have been rotated 30ø counterclockwise into
singlemeridionalsurvey line (D line). The filamentbisecting "along" (V) and "across" (U) componentsrelative to the
the D line in July 1988 underwent a considerablereorienta- hydrographicsurvey grid.
tion between two stable and almost perpendicular aligned
Errors in the ADCP measurements come from a number of
phases. During the first phase (phase 1, July 2-16, 1988; sources[Kosro, 1985]. The three most significantsourcesof
Figure l a) the filament axis (as determinedby the maximum error are the near-random fluctuations in the velocity estiADCP velocity vectors) crossed the D line at nearly fight mates between individual acoustic transmissions caused by
angles.After the reorientation (which occurredduring strong varying levels in the acousticbackscatterintensity, varianortherly winds between July 16 and 19), the filament axis tions due to rapid accelerationsof the ship (e.g., as a result
was directed southward, crossing the D line at approxi- of surface waves) and errors in the estimated mean ship
mately 30ø (phase 2, July 20-23, 1988; Figure lb). Micro- velocity. The moored data are subject to only the first of
structure measurements were made during both filament these errors. Temporal averaging of consecutiveprofiles
reduces the errors caused by backscatter intensity fluctuaphases.
DEWEY ET AL.' STRUCTURE AND DYNAMICS
128 ø
127 ø
i
i
126 ø
i
OF A COASTAL FILAMENT
14 887
12 4 ø
125 ø
i
12 3 o
I
!
ß
'"ß.:
41 ø
+
+
1 6-.Tu
1--,_-,"",-,""
_
'.•'::4 ,.-"'-"'
_._
,.'
+
+
+
1ø
16
-I'e rnpe t-',_•.t.
u t--e
1-'4
Cape Mendocino
1¸
1L.--'1
40 ø
+
+
+
i_!
::
.:
39 ø
-+
+
+
-' Pt Arena
,.,. , '.',
ß
ß
ß
.-
,
:•:.:.:
Pt Reyes
•8 ø
+
+
+
ß
i.
37 ø
+
+
+
..
+
Fig. la. Advanced very high resolution radiometer (AVHRR) satellite image taken on July 16, 1988, showing the
sea surface temperature gradients east of the California coast. The cooler, upwelled water is represented by the lighter
shading. The central D line along which the microstructure data were collected is shown, at an angle of 30øfrom north
to south. The maximum current vectors associated with the offshore flow of the filament crossed the D line at right
anglesfor a period of nearly two weeks (July 2-16, 1988).Also shown are the two ADCP mooring locations, D2 to the
north
and D3 to the south.
tions and waves. Errors in the ship velocity are minimized
by careful examination of the navigation data. For this
study, LORAN-C navigation was used, lane jumping being
the largest source of navigation error. Verification with
periodic GPS coverage provided a cross-reference which
indicated no major errors or "jumps" had permeated
through the analysis. Uncertainty in the 15-min-averaged
semidiurnalM 2 tides. Tidal (M2) ellipseswere alignedin the
alongshore(D line) direction with major and minor axes of
shipboardADCP velocitiesis estimatedto be +-8cm s-l.
leading the northern (D2) by approximately 30øin the surface
values (over a separation of 46 km). This phase shift decreased with depth. The results of the tidal analysis agree
with the findings of Munk et al., [1970].
Local accelerations (i.e., OV/Ot) have been calculated by
Uncertainty in the 10-min-averaged moored ADCP velocities is estimated to be +-5 cm s -l.
Tidal analysis of the moored ADCP data, using the programs of Foreman [1978], indicates significant signal in the
approximately
9 and 5 cm s-l respectively.
This wasthe
only tidal component with associated velocity vectors larger
than the estimated uncertainty in the ADCP measurements.
The precessionof the M 2 tidal vector was clockwise, with a
slight phase shift in latitude, the southern mooring (D3)
14,888
DEWEY ET AL.: STRUCTUREAND DYNAMICS OF A COASTAL FILAMENT
128 ø
I
127 ø
12B ø
I
125 ø
I
124 ø
I
12• ø
I
.
.:.:
I
..
•i--
•
-"'
41 ø
+
._1
'•%-
::•. +
+
-
,.-'4 '4Z
+
...
1_
.?..
•:•i ']'e rC•F,
e t-'o.t:.u t-'e
•"•'
ß
14
Cape Mendocino
1'2
10
40 ø
+
+
+
39 ø
+
+
+
+ .,,'•'
";'"
PtArena
??
:-.?-.--
.'{ -.•:::
r
....
•i'.-•:
,
.....
ß
• .:... •..
,
....
.?.•...:.: • .•:.'..-.•.
•:::
•,
•
.•• .•
-.if,''-: 'Pt Reyes
....
•
,.• .
..•.:..
..-
.
i.
37 ø
+
+
+
•;• v
•
.
.
-
-..'•.¾:,:,-:
.,.
.
Fig. Ib. AVHRR satellite image taken on July 23, 1988, showing the sea surface temperature gradients east of the
California coast. The cooler, upwelled water is represented by the light shading. The central D line along which the
microstructure data were collected is shown at an angle of 30øfrom north to south. During this orientation, the current
at the D line is due south (July 19-23, 1988).
taking first differences between consecutive transects of the
shipboardADCP velocity estimates(Appendix A). The M2
tidal componentof the flow was removedfrom the shipboard
ADCP before the differencing in order to reduce the effects
of aliasingand tidal accelerations.This was accomplishedby
linear extrapolation of the tidal ellipses along the entire D
line. The local tidal vectors (both in time and space) were
then predicted and subtractedfrom the ship ADCP observations. Maximum
tidal velocities
were of the order of 10 cm
s-1 with approximate
uncertainties
of +5 cm s-1 Had
these components not been removed, tidal accelerationsas
large as one-fifth the Coriolis acceleration would have contaminated the local acceleration estimates. Apart from a
regional tidal model [Foreman and Freeland, 1991], the
authors are unaware of other attempts to remove tides from
shipboard ADCP data.
The multiple transects of microstructure and shipboard
ADCP measurements represent a time series of the acrossfilament
structure.
The measurements
indicate
two reason-
ably stable filament orientations. During phase 1 (July 2-16,
1988)the velocity vectors were approximately perpendicular
to the ship tracks (Figure 2a). Eight complete RSVP
transects, one partial RSVP transect, and 18 shipboard
ADCP transects were made across the filament during this
phase. On or about July 18 the filament underwent a rapid,
barotropic reorientation. During the second phase (July
DEWEY ET AL ' STRUCTUREAND DYNAMICSOF A COASTALFILAMENT
16
km
Vector
cm/s
Average
"along" the ship track, the 60øveering of the current will be
consideredsufficientto investigatethe relative importanceof
meridionalgeostrophybetween the two phases.
Shown in Figures 3a and 3b are the temperature, salinity,
%, and U (perpendicularto the D line) valuesat 25 and 125m
depth, respectively,duringphase 1. The surface(25 m) structure is less stationarythan the deeper (125 m) structure.The
northernsurfacesignatureof the filamentgraduallyprogresses
southwardduring the 2-week observationperiod (July 2-16,
1988). Shown in Figures 4a and 4b are the temperature,
salinity,%, and U valuesat 25 and 125m depthfor phase2.
Temporalaveragesof temperature,salinity, %, U, and V
for Phase 1 are shown in Figure 5. The averagesfor Phase 1
were calculated from nine RSVP (northward heading only)
and eighteen ADCP (northward and southward heading)
25.0 m
Latitude
Fig. 2. Average velocity vectorsfrom the shipboardADCP, for
the periods(a) July 2-16 and (b) July 20-23, 1988.The shiptrack (D
line) is orientedat 30ø from true north. Approximately18 transects
(not all were completefrom end to end) were averagedduringPhase
1, and six transects were averaged for Phase 2. The locations of the
two ADCP mooringsare also shown, displacedapproximately4 km
to the northeast of the D line. The latitude scalefor all figuresis the
projection of latitude onto the D line, with 1ø = 128 km.
20-23, 1988) the maximum velocity vectors associatedwith
the filament were due south(Figure 2b). Three RSVP and six
ADCP transects were made during the phase 2 orientation.
Although the current vectors duringphase2 are not exactly
/
.........
..-
..:,:"V'<'---:.':.
•'.-.r'
...............
:...................
•::..':.::..
.'_..'.•V
.........
'
(averagedfrom three RSVP and six ADCP transects,respectively). The average sectionsfor Phase 2 have larger variances, as they are constructed from fewer observations. The
effects of small-scale fluctuations, such as internal waves,
have not been as greatly reduced in the phase 2 averages.
During the entire period of the microstructure cruise the
location of the two ADCP current meter mooringsbounded
the core of the velocity jet (Figure 2). The northern mooring
(D2) remained within the negative relative vorticity, and the
southernmooring (D3) remainedwithin the positive relative
vorticity. The ship tracks (along the D line) passed the
,,,..-..::•:::.,. •
",. '":'.::::'•.'.-,:,
,,.
,
ß
•
transects. Figure 6 shows the same fields for Phase 2
,.:•.'tj:'........
;:?'-',:•.::::'-.::?::,
..... ".
.::?::,,,-......., ...,'.'.•.,'•q:.,':'
........:, ,,•.....
....'.'"':•:•::-d':;..'•.:'i,f,'--:':::'
.......-,,.i/ ........ ,
--:,............
,
14,889
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.,.
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...........
,,,'-,,
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::•,k•::?.?.'..:•:'":'.-c-....... •--.•-•-'-••:•:•.-.•!111:!:•!!:::::
...................
i
37,2
:37,:3
:37.4
:37•$
37.•
:37.7
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38.•
La[i[ude
i
:38.:3
:38.4
:38.,5
38.•
:38,7
:38.8
:38,9
:39.0
Depth: 25 m
Fig. 3a
Fig. 3. Temperature,salinity,%, and U at (a) 25 m and(b) 125m depthfrom eachtransectrepresenting
phase1
(July 2-16, 1988). Maximum variabilityis near the surfaceand the northernsignatureof the front. With depth,
variability is reduced, and the front becomes more "one sided."
14,890
DEWEYETAL ' STRUCTURE
ANDDYNAMICS
OFA COASTAL
FILAMENT
[
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,
,
[
[
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i
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38.Z
38.3
38.4
38.5
i
38.6
38.7
38.8
Latitude
38.9
39.0
Depth: 125 m
Fig. 3b
mooringsat between 2 and 8 km to the southwest.This av
•+
combinationof ship and moored ADCP data allows an at
analysisof vorticity at two locationseither sideof thejet.
In the followinganalyses,verticalgradientsare estimated
by differencingthe griddeddata over 10 m. Althoughdifferencingunderestimatesa differential, we make no attemptto
av
u•+
ax
av
v•+
ay
av
w•+
fu
1 oP
1
az
--•Po •+
•Po •7'Wy
i + //•72V, (lb)
ay
correct for this underestimate in our calculations. The RSVP
wherethe termsrepresentlocal acceleration,rate of change
data (T, S, o't, and e) are independentat vertical length of momentum due to advection, Coriolis acceleration, presscales shorter than 10 m, while our ADCP estimates of U
sure gradient, submesoscale
flux divergence(where the
and V are independentat separationsof 16m. This is a result stressfor eachcomponent
n is •'ni= (•'nx,•'ny,•nz)),and
of the acousticpulselength,the gatingand filteringusedin viscous diffusion. The central two terms for each component
processingthe ADCP data. As a result, 12-m (three bin) representthe well-knowngeostrophicequations.For this
separationsin the originalADCP data are nearly indepen- reasonthe termsfU and(- 1/po)(OP/Oy)
will be referredto as
dent, and 16-m (four bin) separationsare completelyinde- the geostrophicterms, without implyingthat the flow is
pendent.
purely "geostrophic."Data collectedalong the "northsouth" D line can be used to estimate terms in the meridional
3.
MOMENTUM
momentumequations(lb) only. Apart from the viscous
term, which is very small and can be omitted from the
BALANCE
The primitivezonal and meridionalmomentumequations analysiswithoutconsequence,
we have been able to esti-
can be written [Pedlosky, 1978],
au
--+
at
au
au
u--+v--+w---fv
ax
ay
mate the remaining seventerms in (lb).
Details on the estimation of each term in the meridional
au
momentumequation(lb) from the measuredquantitiesare
presentedin AppendixA. The technicaldetails of the
az
1 aP
P0 ax
1
F• V.'rxi + uV2U,
P0
(la)
calculationshave been separatedfrom the present discussionof dynamicsin orderto keep the focuson the physics.
The dominantterms in (lb) are the two geostrophicterms.
DEWEYET AL.' STRUCTURE
ANDDYNAMICS
OFA COASTAL
FILAMENT
14,891
ß,........
::,•,:,,
.....,,:::•.::::::?..•
..........
i
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i
37,23 37.3 37.4 37.5 37.6 37.7 37.8 37.9 38.0 38.1 38.E 38.3 38.4 38.5 38.6 38.7 38.8 38,9 39,0
Latitude
Depth: 25rn
Fig. 4a
Fig. 4. Temperature,
salinity,o-t andU at (a) 25m and(b) 125m depthfromeachtransect
representing
Phase2
(July20-23,1988).Maximumvariability
is nearthe surface
andthe northernsignature
of the front.With depth
variability is reduced, and the front becomes more "one-sided."
The Coriolisterm is simplythe zonalvelocityU asmeasured zero at the 95% confidencelevel (summed confidenceinterby the ADCP, multipliedby the localmeanCorioliscompo- vals) along the entire D line.
•
nent of rotationf(=8.98 x 10-5 s-I). The meridional A linear regressionbetween the two geostrophicterms
pressuregradient-(1/p0)0P/0y was calculatedfrom horizon- (Figure8) indicates
an.offset.of-.6.3 (cms-i), a regression
tal differences
in the geopotential
anomalyf g 8dp,where8 coefficientof 1.03, 'ahda correlation coefficient of r = 0.94
is the specific volume anomaly determined from RSVP witha 95%bootstrap
confidence.interval
of 0,02' (The95%
profilesof T, S, andp. A level (pressure)of knownmotion confidence
interval
foreach
coefficient
i•si•dicated
inFigure
wastakento be 150m, the geopotential
anomalygradientset 8.)Fromthecombined
ninetransect%
a totaiof89indepenequal to the ADCP-measuredCoriolis term (fU) at this dentobservations
are estimated,by dividingthe total record
depth.Measurement
errorsin ADCP velocityestimatesby the observedintegrallengthscaleas determinedfrom the
increasewith depthbelow 150 m. By settingtheseterms autocorrelation.Thereforebasedon the numberof indepenequal at 150 m depth, we recover only differencesin mea- dent observations,
a correlationIr > 0.21 is significantly
sured and geostrophicshear between 150 rn and the surface different
fromzeroat the95%confidence
level[Bendatand
and thereforedo not recoverall of the ageostrophy
in the Piersol,1986].Theresidual
difference
[PrieStley,
1989]beflow. Velocitieswithin the jet are still considerableat 150m
tween the geostrophic terms (Figure 7b) indicates that
(---20-30
cms-I), andageostrophy
remains
unresolved.
(o-.•
U - o'i½s)/O'fu
2 2 = 89% of the observedVariancein the
Coriolis
acceleration
•r•uis explained
by thegeopotential
Shownin Figure 7a are the mean geostrophictermsfor
phase 1 (July 2-16), (fU) (solid) and (-(1/po)OP/Oy) anomaly.
(dashed),eachscaledby 100/f,sothe valuesare equivalent Withoutestimatingageostrophic
contributions,one might
to zonal flow in centimetersper second.The anglebrackets concludethat the residualof the geostrophic
terms,with a
represent a temporal average from consecutive transects.
variance
of O'r2es
•' 66cm2 s-2, represents
thefullcontribu-
The geostrophicresidualis shownin Figure7b. Each mean tion from ageostrophic
dynamics,plus any noisein the two
valuein the momentumanalysishas alsobeendepthaver- geostrophicestimates,representingonly 5.6% of the accuagedbetween20 and 30 m. Confidenceintervals(95%)have mulated
variance.
It ispossible,
ontheotherhand,thatlocal
beenestimatedusinga bootstrap(Monte Carlo)technique accelerations
(oV/ot) are balancedentirelyby cyclostrophic
[Efron, 1987].The residualis not significantly
differentfrom adjustments
(UOV/Ox, VOV/Oy). In sucha case,determining
14,892
DEWEYET AL.' STRUCTURE
ANDDYNAMICS
OFA COASTAL
FILAMENT
i
:87.•
87.8
87.4
87.$
87.8
87.?
87.B
87,9
i
8B.O
i
8B.•
i
8B.•
:lB.8
i
i
i
i
:]8.4
8B.$
8B.8
8B.?
i
8B.B
:SB.•
J
89.0
Fig. 4b
a balancebetweenfU and -(1/po)OP/Oywould be insuffi- Coriolis accelerationfU is explained by the meridional
cientforassessing
thegeostrophic
character
oftheflow.A gradientof the geopotentialanomaly(Figure9). The linear
betweenthe two geostrophic
terms(Figure 10)
geostrophicflow must have insignificantageostrophic
con- regression
tributions, regardlessof the correlation between the two indicates a correlation of r = 0.87, with a 95% bootstrap
"geostrophic" terms. Any conclusionon the degree of confidence interval of 0.05. From the combined three
geostrophymust includean evaluationof the ageostrophic transectsof phase2, a total of 24 independentobservations
terms.
During phase 1, mean current vectors (Figure 2a) were
perpendicular to the D line. The mean density section
therefore resolved the maximum pressuregradient and thus
representsa good test for geostrophy.Simple scalingargumentspredict [Pond and Pickard, 1978]a maximum degree
of geostrophy across a strong mean current. Similarly,
geostrophyis not expectedto be as dominantin the momentum component aligned parallel to the axis of a strong
current. Although a very high degreeof correlationis found
between the geostrciphicterms, there is no a priori reasonto
expect each ageostrophicterm to be negligible,althoughwe
may expect them to have a small net contributionto the
are estimated,and thereforea correlationIrl > 0.41 is
significantly
differentfrom zero at the 95% confidencelevel.
The linearregressionbetweenthe two geostrophictermsfor
phase
2 (Figure
10)indicates
anoffset
of0.33(cms-1)anda
regressioncoefficientof 1.05. Again, if the geostrophic
residual,
witha variance
of O're
2s= 76cm2 S-2, representsall
the ageostrophic
dynamicsplusany noisein the geostrophic
terms,the ageostrophic
varianceaccountsfor a maximumof
13% of the total meridional momentum variance.
The difference between the "geostrophic" correlation
coefficients
for phase1 andphase2 is Ar = 0.07 with a 95%
uncertaintyof ___0.05.
The differenceis significantlydifferent
from zero, and the correlationsare therefore significantly
balancesincethe unexplained
residualis alreadysmall. different at the 95% confidencelevel. Although the correlaDuring phase 2, mean current vectors crossedthe D line
much more obliquely, at 30ø from meridional (Figure 2b).
These observationsprovide a reasonabletest of the hypothesis that the ageostrophic components of the momentum
equationwill have increasedimportancealongthe axis of the
tion for phase2 suggests
a lower degreeof geostrophy,the
confidenceintervals are larger owing to the much lower
number of obõervations (three versus nine RSVP transects,
and 24 versus89 independent"observations"). At this stage
of the analysisit is not clearwhethera true decreasein the
meridionalgeostrophyhasbeenrevealed,and in particular,
Duringphase2, only76%of the observedvariancein the what physicsmay be causingthe ageostrophy,or whether
"jet."
DEWEY E'• AL.' STRUCTUREAND DYNAMICS OF A COASTALFILAMENT
0
i "'
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L•TITUDE
(degrees)
Fig. 5.
(continued)
consecutive transects during phase 1 will provide some
,oo
indicationof the variability due to the decreasein the
number of observationsand therefore thi• apparent "signal
C
250
37.50
3 75
38.00
38.25
38.50
38.75
39.00
LATITUDE (degrees)
Fig. 5. Contourplots of the average(a) temperature,(b) salinity, and (c) o-t structureas revealed by RSVP measurementsand of
the averageADCP velocity structure(d) U and (e) V alongthe D
to noise" during phase 2, Since the momei•tum equations are
always obeyed, the goal is to show that our observationsand
calculations represent significant estimates of both the geostrophie and ageostrophiccontributions.
The details of estimating each ageostrophicterm detract
somewhat from the present discussion, and therefore have
been relegated to Appendix A. In arriving at an estimate of
the mean vertical advection of meridional momentum,
W(OV/Oz), a calculation for mean vertical velocities W is
presentedin Appendix B.
Duringphase1, no ageostrophic
contributionwas significantlydifferentfrom zero at the 95-%confidencelevel. Zonal
km resolutionin the horizontaland verticaldirections,respectively. advection.southOf the filamentcore was the largestage0-
linefoi•July2-17, 1988.The datain Figures5a, 5b, and5chavebeen
averaged
ontoa fixedlatiiudegridwithapproximately
1.8kmby2.5
A total of nine RSVP transectsmake up the averages,with fewer
Samplesnear the northern;southern,and deeperboundaries.Maxi-
mumisopiethdisplacement
acrossthe frontis --•100m. The daiain
strophie component during phase 1, with a magnitude
(scaledby 100/f)of (U/f)oV/Ox = 10 cm s-•. Despitethis
Figures5d and 5e have been averagedonto a fixed latitudegrid with relatively large mean contribution, considerablevariability
approximately
1.8 km by 5 m resolutionin the horizontalandvertical in UOV/Ox resultsin a large confidenceinterval, rendering
directions,
respectively.
Thecoordinate
system
isrotated30øfromtrue the mean insignificantly(at 95%) different from zero. During
north;u istherefore
periaendicular
totheD lineandV isparallel
tothe phase2, both the acceleration(0 V/Ot) and meridional advection (VOV/Oy) terms indicate regionssignificantlydifferent
D line. A total of 18ADCP transectsmakeup the ave?hges,
with fewer
samplesnear the northern,southern,and deeperboundaries.
from zero, with scaled magnitudes as large as 5 and 10 cm
s-i respectively.
thereis simplya reducedsignalto noiselevelduringphase2.
After adding the estimated ageostrophic terms to the
Estimationof the ageostrophic
termsin (lb) will attemptto geostrophic residual, we can reevaluate the total level of
addressthesepointsand determinewhethertrue balances geostrophy of the meridional momentum balances. During
have been obtained. Also, a momentum balance from three
phase 1 the mean pressuregradient -(1/po)OP/Oy explained
14,894
DEWEYETAL.' STRUCTURE
ANDDYNAMICS
OFA COASTAL
FILAMENT
o
ß
.
/•6
'
/4.7..
50
150
200
TEMPERATURE
(C)I
I
i
250
i
I
I
a
0
5O
5O
•
•oo
E
I-
•_ 15o
200
200
-
250
t SALINITY
(psu)
I
i
i
I
_
b
•
DOPPLER
VELOCITY
V (cm/s) :';
250
39.00
LATITUDE (degrees)
Fig. 6.
(continued)
•oo
tion, was not significantlydifferent from zero. Therefore
1.50
geostrophic
balanceto withinthe accuracyof the present
during
phase
1 thezonalor along-filament
current
wasin
measurements and the observed noise variance.
Phase2, representing
an approximation
to across-filament
dynamics,indicatesa significantdecreasein the level of
geostrophy.
Themeanmeridional
pressure
gradientexplains
200
250
76% of the variancein (fU), and 70% of the variancein the
total balance.The ageostrophiccomponentswere occasion-
37150
LATITUDE (degrees)
ally significantly
differentfrom zero at the 95% level; however,theyfail to reducetherelativevarianceaccumulated
in
Fig. 6. Contourplotsof the average(a) temperature,(b) salinity, and(c) •rt structureasrevealedby the RSVP andof the average
ADCP velocity structure(d) U and (e) V alongthe D line for July
20-23, 1988.The data in Figures6a, 6b, and 6c havebeenaveraged
onto a fixed latitude grid with approximately 1.8 km by 2.5 m
the residual,indicatingseparateregionsof coherentincrease
resolution in the horizontal and vertical directions, respectively. A
total of three RSVP transects make up the averages, with fewer
2 than in the perpendicularcaserepresentedby phase1.
and decrease in the balance residual. Nonetheless, the mean
pressuregradient,the secondlargestterm in the balance,
contributes 9% less to the momentum balance during phase
In order to estimate the relative change in the signal to
samplesnear the northern,southern,and deeperboundaries.The noiselevel duringphase2, introducedby the fewer number
data in Figures6d and 6e have beenaveragedonto a fixed latitude
gridwith approximately1.8 km by 5 m resolutionin the horizontal of observations, a series of three consecutive transects
and vertical directions, respectively, and rotated through 30ø into duringphase1 are analyzed.It will be assumedthat noise
the D line coordinates. A total of six ADCP transects make up the
averages,with fewer samplesnear the northern, southern,and
deeper boundaries.
sourcesduringthe two phasesare similarand that a change
in the signalto noiserepresents
a decreasein the signal.This
may not be the case, but our observationsprovide no
indicationthat the noise (e.g., internal wave displacements
of isopycnals)is differentbetweenphases1 and 2. The
geostrophic
momentumtermsfor thisthree:transect
phase1
strophiccontributions
wereneversignificantly
differentfrom balanceare shown in Figure 11. During this 4-day period
zero and show little coherent structure. Even the mean zonal
(July10-13)the meanpressure
gradientaccounts
for 88%of
89% of the variancein (fU) and 87% of the variancefrom all
contributions to the meridional momentum equation. Ageo-
advectionterm (UOV/Ox), the largestageostrophiccontribu-
the variancein the observedvelocityfield, and an unchanged
DEWEYET AL ' STRUCTURE
AND DYNAMICSOF A COASTALFILAMENT
14,895
-2]
On-shore
r=0.94
,./.--...-'...'
',.
,../.,,.
x',,
+/-0.02
..
.-,...x-• ...............
..
o
"" .....,.'
.....
ß'/'"'
' •
,,.,
g)
' 5;/ .,.'
';,"..........................
",,, x 5':::::-,.,..,...... ?' .•'?" ", ":
• .-•• %*,•_-•.-':'-' ' •..;- - V
• -'......
." '.._."'
..'2 ..... •'.X"..
.,
Off-shore
."-,,----"•
,,, ,,,
..,'
ß
'•,._ T.].::
.......,
%
I
,,.,
\
.......
''...........
L"'
/
609.1
Geostrophic
511.1
66.3
b) r
•
+
+
•J'7.2
3'•.33'•.43'•,53'•.63'•.73'•.83'•.93d.O3d.13d.23d.33•.4 3d.53d,63d.73d.83d.93c•.0
LATITUDE
DEPTH 25 rn
Fig. 7. (a) Temporalaverages
of the ADCP zonalvelocityU (solidline) andthe negativegeostrophic
velocity
(1/fpo)OP/Oy
(longed-line
dash)in centimeters
per secondfor the firstfilamentorientation(phase1), eachshownwith
95% confidence
intervals.A 10-mverticalaveragehasalsobeenapplied,centeredat a depthof 25 m. A total of 500
bootstrapiterationswere performed,with 95% confidencelimits calculatedfrom the resultingdistributions.The
correlationbetweentheobserved(ADCP)andthegeostrophic
currentsis r = 0.94 with a bootstrapconfidence
interval
(95%)of0.02.To therightofthelabelsarethevariances
ofthetwoseries
(incm2 s-2). (b)The"geostrophic"
residual
in centimetersper second,simplythe differencebetweenthe seriesshownin Figure7a. The confidence
intervalis the
sumof the two individual95%intervals.The varianceof the residualis indicatedat the right.The two symbolsat the
bottom indicate the location of the moored ADCPs.
88% of the variance in the total balance. The correlation
coefficientbetweenthe geostrophicterms is r = 0.94 with a
(We have also assumedhere that the viscousterms in (1) can
be ignored.)After somealgebrathe vorticity equationcanbe
95% confidence interval of 0.02. Based on the number of
written,
independentobservations(15), a coefficientIrl > 0.51 is
significantlydifferent from zero at the 95% confidencelevel.
These results are nearly identical to the total balance for
phase 1 estimated by including all nine transects. The
0•
--+
Ot
0•
U--+
Ox
0•
V--+
Oy
0•
W--
Oz
+ V/3 cos (30ø) + U/3 sin (30ø)
variances of the estimated ageostrophiccomponentsare
below the noise levels, and the final residual indicates that
ageostrophydoes not significantlycontribute to the balance.
The increased variability in the ageostrophicterms and
reducedcorrelationbetweenthe two geostrophicterms for
phase 2 is therefore not due to the analysis of fewer
observationsbut likely representsa true decreasein the level
of geostrophy.
4.
VORTICITY
-f-j-if- SC•x
+ r/--•-y
+ •'
(2)
where the velocity componentsare in the D line coordinates.
(This coordinatetransformationresultsin both components
of flow in the D line systemcontributingto the advectionof
planetary vorticity, thus the /3 cos and /3 sin in (2).) The
three-dimensionalrelative vorticity is given by
ANALYSIS
The location of the ADCP mooringsis such that between
July 2 and 16 the northern mooring (D2) remained north of
thejet core and the southernmooring(D3) remainedsouthof
the jet core (Figure 2). Across a uniform jet the relative
=0,
OU
[= (•, rl,i')=
•
.
Oz'Oz Ox'Ox 3• '
(3)
Terms in the vorticity equation (2) represent the rate of
changeof relative vorticity, advectionof relative vorticity,
vorticity changesfrom positiveto negative.The following advection of planetary vorticity, stretching of planetary
analysisis intendedto reveal the magnitude,structure,and vorticity, and tilting and stretchingof relative vorticity.
variability of the vorticity field acrossthe observedfilament.
At each mooringlocation (D2 -• 38.27øand D3 = 37.9ø)the
The vorticity equation is derived by simply cross differ- total relative vorticity • was estimatedby first differencing
entiating and subtractingthe linear momentumequations ADCP velocity estimates between the mooring and ship
(la) and (lb), thus eliminatingthe pressuregradientterms. track locations and along the ship track. For differences
DEWEY
14,896
ET AL.' STRUCTURE AND DYNAMICS
I
OF A COASTAL FILAMENT
Both northward and southward transects were used, the ship
//
speeddoubling
(ranging
from1.2-2.5m s- • to 4.0-6.0m s- •)
between northward- and southward-heading transects, respectively. The averagingperiod varied similarly, from --•1.5
'•"•r
,' /
hours for the northward (slower) transects to -<1 hour for the
• o.•4 (+/- o.o• )
•
'•.•
southward (faster) transects.
_ ..................
- _.
The zonal gradient in relative vorticity (O•'/Ox)cannot be
estimated from our meridional transects, and 0•/0y can be
evaluated only between the two mooring sites, acrossthe jet.
Temporal changescan be estimated from the time seriesof •
•
// '
,
provided by the repeated transects. All other terms are
estimated directly from the ADCP-measured U and V ve,
locities and W estimated from the first term in (B4).
Figure 12 showsthe relative vorticity at a depth of 25 m for
/
both
the northern (D2) and southern (D3) locations (scaled
•I // •'
by I/f). The large negative value during Julian day 190 (D2,
July 8, 1988), • = -0.95f, is the result of significantOV/Ox
•
/
shear between the ship and moored ADCP data at D2. Poor
•-80
•0
-40
-•0
0
•0•
',•,
•
•
4•0 ship navigation is believed to have caused this "error,"
although there is not discernible reason for rejecting the
navigation data used (P.M. Kosro, personal communica•ig. 8. An [inea• •eg•es•ion (solid line) between the average
ADC• zonal cu•ent (U) and the scaled average pressuregradient tion, 1990) and the subsequentship velocity vectors. None(l//•o)•P/•
duffng •hase I. •he uncertainty for each regression theless, this vorticity value is in question. Such large negacoe•cient
is
tive vorticities are unlikely, since instabilities in potential
vorticity dynamics (proportional to [1/(f + •)]) act to
between the mooring locations and the ship track velocities, diffuse momentum in regions of strong negative vorticity
the shipboardADCP data were averagedinto 12-kin bins and [Hoskins, 1974, 1982].The large positive vorticity duringday
the mooring data were averaged temporally for periods 188 (D3, July 6) is believed to be real, indicating relative
equivalent to the spatial averages based on the ship speed. vorticity equal to planetary vorticity.
/
/
-2]
On-shore
r=0.87
---
Off-shore
+/-0.05
Doppler
316.1
Geostrophic 219.7
75.9
b)
•
+
+
137.23'•.3 3'•.4 3'•.5 3'•.6 3'•.? 3'•.8 3'•.9 3•.0 38.1 3•.2 31•.331•.431•.53•.6 3•.7 3•.8 3•.9
•TITUDE
DEPTH 25.
m
Fig. 9. (a) Temporal averages of the ADCP zonal velocity U (solid line) and the negative geostrophic velocity
(l/fpo)OP/Oy
(long-dashed
line)in centimeters
per secondfor phase2, eachshownwith 95%confidence
intervals.The values
have also been vertically averagedover 10 m, centeredat a depth of 25 m. The correlationbetween the observed(ADCP)
and the geostrophiccurrentsis r = 0.87 with a bootstrapconfidenceinterval(95%) of 0.05. To the right of the labelsare the
variances
of thetwoseries
(incm2 s-:). (b)The"geostrophic"
residual
in centimeters
persecond,
simplythedifference
betweenthe seriesshownin Figure9a. The confidenceintervalis the sumof the two individual95% intervals.The variance
of the residual is indicated at the right. The two symbolsat the bottom indicate the location of the moored ADCPs.
DEWEY ET AL.: STRUCTUREAND DYNAMICS OF n COASTAL FILAMENT
14,897
error bars of 1 standard deviation. The temporal mean
relative vorticities are approximately (•) = -0.16f and
(•) = 0.25f for the northern and southernmooring locations,
respectively (not including the erroneous low value on Julian
day 1990). This assymetry in the shear can be seen in the
mean current vectors (Figure 2a). Considerable asymmetry
o was also observed by Kosro and Huyer [ 1986] during a 1982
survey of a similar filament. As was indicated above, instabilities that work preferentially in regions of large negative
relative vorticity act to "diffuse" momentum (vorticity),
thus spreading the shear and perhaps contributing to the
current asymmetry observed [Hoskins, 1974; Haidvogel et
al., this issue; Huyer et al., this issue].
Not all terms in (2) can be estimated, and a vorticity
balance will not be attempted, although the available terms
can be compared in a limited vorticity analysis. Shown in
Figure 13 are the significanttime series and temporal means
for
four terms in the vorticity equations (scaled by 1//3) at
1-80
-60
-40
-20
0
20
40
both mooring locations (D2 in Figure 13a, D3 in Figure 13b)
• O• •___•0
[ms-2 ]
and the residual (plot 5) of the six estimated terms. The
Fig. 10. A linear regression (solid line) between the average dominant terms are the observed temporal changes (O•/Ot)
ADCP zonal current (U) and the scaled average pressure gradient (plot 1) and the stretchingof planetary vorticity (fOW/Oz)
(1/fpo)OP/Oyduring phase 2. The uncertaintyfor each regression (plot 3). Tilting and stretching of relative vorticity (plot 4)
coefficient is 95%.
contributes significantly only during a 1-day period at location D2 (Figure 13b; July 14; Julian day 196). Advection of
The northern mooring location is a site of consistent planetary vorticity is smaller than all other terms by more
negative relative vorticity and the southern mooring a loca- than 2 orders of magnitude (not shown). Vertical advection
tion of positive vorticity (Figure 12). The time-averaged of relative vorticity is never significantly different from zero
means for the two periods are also shown (Figure 12) with (plot 2). At times the residuals(plot 5) are considerable, and
/
/
/
/
/
/
/
/
/
/
/
/
/
/
ß
Meridional
Momentum
Balance
(X1--•}[!TZ
$-2]
On-shore
r--0.94
+/-0.02
Doppler
610.4
Geostrophic 501.4
Off-shore
70.9
b) ?
•7.2 3'•.3 3'•.4 3'•.5 3'•.6 3'•.7 3'•.8 3'•.9 31•.031•.131•.231•.331•.431•.531•.63fi.7 3fi.8 31•.93•.0
LATITUDE
DEPTH 25.
m
Fig. 11. (a) Mean zonal velocitiesand estimatedmeridionalpressuregradient(geostrophicvelocities)from three
consecutive transects (between July 10 and 14) during Phase 1 indicating the possible ageostrophy implied by a
reduction in the number of observations. The mean ADCP velocity U (solid line) and the negative "geostrophic"
velocity -U = (1/fpo)OP/Oy(long-dashedline) are each shownwith 95% confidenceintervals. (b) The geostrophic
residual(differenceof seriesin Figure 1la) with the summed95% confidenceinterval. The correlationis r = 0.94 with
a 95%confidence
intervalof 0.02.An estimated15independent
observations
implya correlationIrl > 0.51, significantly
different
fromzeroat the95%level.At therightof thelabelsandtheresidual
aretheseries
variances
in cm2 s-2.
14,898
DEWEY ET AL.' STRUCTUREAND DYNAMICS OF A COASTAL FILAMENT
1.00
• = -0.4f), but the rate of change O•/Otis no larger than that
observed at other times (Figure 13b; July 5, Julian day 187).
Despite the density of observations resulting from the repeated transects (estimatesevery 1-2 days), the variability in
the vorticity appears to be undersampled (Figure 13b, plot
1). Within the core of the filament, maximum surface speeds
D3South
(37.9
ø)
0 75
40.50
•
0.00 ........ •,_c
•
.......
wereof theorderof 1m s-1 or --•80kmd-1 whichsuggests
• -0.50
0
• -0.75
- 1.00
,
•
i
D2North
(38.27
ø)
i
Time (Julian day)
Fig. 12. Time series of the relative vorticity • calculated from
the ship and moored ADCP velocity vectors and scaledby 1/f. The
northern location (D2, dashed line) shows consistent negative vorticity, the southern location (D3, solid line) shows consistentpositive vorticity. The very large negativevalue duringJulian day 190 at
D2 is believed to be a result of poor ship navigation. Averages for
each location and filament orientation
intervals of 1 standard deviation.
tions, we are unable to close the balance or estimate our
"noise" residual. Even without the two advection terms, the
variability in the observed contributionsresults in temporal
mean and residuals insignificantly different from zero.
During the transition from phase 1 to phase 2 (on or about
(-+2 days) July 18, Julian Day 200) the relative vorticity south
(D2) of the filament core (Figure 12) remained near • = 0.5f.
North (D3) of the core the vorticity decreased(from • = 0 to
/
15o•
at
5Oql
/
/
5.
DISCUSSION
are shown with confidence
the horizontal advection terms (UO•/Ox), (VO•/Oy), not
estimated, are expected to contribute significantly to the
dynamics in reducing this residual. Without these contribu-
as0q •_•
that mesoscale structures could easily have been advected
by the observation sites between transects, aliasing the daily
estimates. Drifter data provide a Lagrangian perspective of
vorticity [Paduan and Niiler, 1990; M. Swenson et al.,
Drifter observations of the dynamical and thermodynamical
structures in a cold filament off Point Arena, California, in
July 1988, submitted to Journal of Geophysical Research,
1990, hereinafter referred to as Swenson et al., submitted)
that at first seemsmore stable, but drifter groups are selected
subjectively and tend to accumulate in regions of convergence, again aliasing the vorticity field.
The analysis of the meridional component of momentum
indicates two levels of geostrophy, corresponding to two
components in the filament coordinates (across and approximately along filament). During phase 1 the hydrographic
sections resolved the maximum pressure gradient. The average meridional momentum field was found to be highly
geostrophic. Ageostrophic contributions to the momentum
balance
were determined
to be below
the noise level of the
measurements, with only 6.5% of the variance in the meridional momentum equation unexplained. The meridional momentum analysisduring phase2, representingapproximately
the along-filament component, indicates a significant increase in the level of ageostrophy. The residual during phase
2 represents 15% of the total variance.
25oa-1•
15o--[•t,
.....
•-250•2
•
aso
3 0W
-250
•50 -250J
2 •
•
• -so
-150
--•
•250
150
. ..........
150
50
•50
-150
-250
Residual
•
..........
-
250
-•5o•,
•.VW
-250 4
•o
_
50
250•
150q
-50
-150
•____
- __
--•
50 5
-50
-50•
-250
-50
L_250
4
-150
I50
250•-•
-250
--250150•
Residual
•
•
Time (Julian day)
Fig. 13a
Da(38.a7
ø)
Time (Julian day)
D3(37.9
•)
Fig. 13b
Fig. 13. Estimatedterms in the vorticity equationscaledby 1//3for (a) the northernlocation (D2) and (b) the
southernlocation (D3). In order, they are (1) the observedrate of changeO•/Ot,(2) vertical advection WO•/Oz, (3) the
stretchingof planetaryvorticityf0 W/Oz, (4) the tiltingand stretchingof relativevorticity (•OW/Ox+ •qO
W/Oy+ •0 W/Oz),
and (5) the sumof all estimatedtermsrepresentingthe residual(lessthe meanhorizontaladvectionof relative vorticity).
Also shownare two temporal averagesof the residualterm for phases1 and 2 with uncertaintiesof 1 standarddeviation.
DEWEY ET AL ' STRUCTUREAND DYNAMICS OF A COASTAL FILAMENT
CTZ
1988
14,899
W
Phase
1
LATITUDE (degrees)
37.25
37 50
37 75
38.00
38.25
38.50
38.75
39 O0
1::-,,',,
:,")'",,,
,,•,',,",,
....
,',,,• •
•g
[:'.',,,
E•
',,:'
•
,
•g
:
',,,,
, ',
o
o
•
Vertical Velocity W (m/day)
Fig. 14. Mean vertical velocities(in metersper day) duringphase1 calculatedusing(B4). Solid contoursindicate
positive(upward) velocities,dashedcontoursnegative(downward)velocities.Maximum ve•ical velocitiesare •40 m
d-• . The surfaceregionnorthof 38.4ølatitudehasbeenblankedbecause
of the deepsurfacemixedlayerthatexists
there,resulting
in verylowbuoyancy
frequencies
(N2) andinaccurate
W estimates.
Uncertainties
derivedfromthe
variationsin individualcontributionsto W are of the order of • 10 m d -• .
The only significant feature revealed by the vorticity
analysis is the persistent asymmetry of the filament. Ship
and moored ADCP
observations
were used to estimate
the
total relative vorticity on either side of the filament core.
Larger (magnitude) positive relative vorticity was consistently observed on the south (cool) side of the front.
An interesting result of the momentum analysis is the
estimation of the mean vertical velocity section across the
filament (Appendix B). Because of their small magnitude,
vertical velocitiesare difficult to measureand estimate, yet
may play important roles in many aspectsof the physicsand
biology associatedwith fronts. The subductionof nutrient
rich coastal water (recently upwelled), along the filament
[Washburn et al., this issue; B. Jones et al., Chemical and
biological structure of a cool filament observed off northern
California in July 1986, submitted to Journal and Geophysical Research, 1990) and the divergence and convergence
implied by drifter groups (Swenson et al., submitted) are
examplesof studiesdirectly dependenton the distribution of
vertical
velocities
within
the filament.
The estimated vertical motions were mostly driven by
adjustmentsin the relative vorticity (Appendix B) and simply represent the vertical component of near-geostrophic
flow along sloping isopycnal surfaces. Within the central
region of the filament, where the data density (temporal) is
highest and the estimates are significantly different from
zero, three dominant regions of W exist (Figure 14). Coinciding with a horizontal velocity maximum (Figure 5d, 38.1ø)
in the filament models [e.g., Walstad et al., this issue;
Haidvogel et al., this issue], but poor spatial resolution in
the models limits a direct comparison with our estimates.
Individualwater packetsdo not remain in these high
vertical velocity regionsfor long periods and only "slide" up
(or down) for several hours, resulting in vertical excursions
of perhaps10-20m (D. Haidvogel,personalcommunication,
1990). These regions of vertical motion are typically tens of
meters (20-100 m) thick and tens of kilometers wide. They
appear consistentlyin the repeated sections (although they
vary in magnitudeand shape), indicating persistentunderlying recirCulations,due mostly to adjustmentsin vorticity.
Individual sections of W, T, and S often have high correlations between interleaving temperature-salinity intrusions
and implied regionsof upwelling and downwelling, an inde-
pendent indication that (B4) predicts real vertical velocity
structure. A separate study of the intrusive activity will
follow in a future paper.
One feature revealed by the multiple transects across the
filament is the position of the surface temperature minimum
relative to the salinity minimum and maximum. During
phase 1 the maximum mean zonal velocity at a depth of 25 m
occurredat approximately 38.1ølatitude (Figure 15a), with a
magnitude
of =-65 cm s-•. This locationcorresponds
exactly with the maximum meridional density gradient, in
accordance with geostrophy. On closer inspection, the po-
sitionand relativeshapeof the temperature
and salinity
extrema reveal important characteristics that can be exis a regionof upwelling(10-40m d-i), boundedon either plained through cross-frontal exchange.
The salinity maximum is slightly offset to the south of the
side (and below) by regions of downwelling. Broad regions
of relativelyhighverticalvelocities
(40m d-1) arepredicted velocity core, a region between 37.75ø and 38.0ø latitude
14,900
DEWEYET AL ' STRUCTURE
ANDDYNAMICS
OFA COASTAL
FILAMENT
b)
...........
:'...................
t•
:".................' •--"
....
,'....'.., ......
','""?•--/
.,/' I ""• .,,/'"'/ •-'
•
Temperature
•x '", ......
\ '"',,.,
t
\
Maximum
/•
".
T
\
........
\
......'.........
\
.....,,
-.......
.......'
.........
/
38,8
38.9
......
i
i
!
37.2
37.3
J,
37.4
i
37.5
i
37.6
37.7
i
37.8
i
37.9
i
38,0
i
38.1
i
t
38.2
Latitude
38.3
i
38.4
i
38.5
i
38.6
i
38.7
Depth:
39.0
75 m
Fig. 15. Spatialseriesof the averagetemperature
(T), salinity(S), •rt, andthe zonalvelocity(U) at (a) 25 m and
(b) 75 m depthsfor phaseI (July2-16, 1988)•
alongtheD line.Thetemperature
andsalinityscales
havebeenchosen
tø representequalcontributions
to variations
in the density(or •rt). Of specialinterestare the relativepositions
and
shapesof the salinitymaximumandtemperature
minimumto the southand the salinityminimumjust northof the
maximum zonal velocity.
(Figure15a).Similarly,
thetemperature
minimum
issouth
of smalltemperaturemaximumwithin the northernextremeof
the maximum current, but sigtlificantly broader (37.75ø to
38.1ølatitude) than the salinity maximum. To the north of the
current maximum there is a local salinity minimum, between
the offshore flow (38.4ø to 38.6ø latitude).
Coastalupwellingis believedto be the main sourceof
potential
energy
for thesefilaments,
bringing
cool,saline
38.1øand 38.45ø latitude.Fresher•urfacewa•eris therefore water to the surface over the continental shelf. Once sepabeing transportedon the north (negativerelative vorticity)
side of the filament, while the colder, more saline surface
water is confinedto the south (positive vorticity) side of the
filament. This asymmetricstructureappearsto be a persistent feature of the upwelled fronts in this region and is
discussedfurther by $trub et al [this issue].
rated from the shelf, coastal (Ekman) upwelling ceases.
During coastal upwelling, temperature-salinityextrema are
highlycorrelated[Huyer and Kosro, 1987],asthey are in the
mean structure at 125 m (Figure 3b). The near-surface
distributionof temperature and salinity (Figure 15a) has
apparently
undergone
a transformation
sincethewaterwas
The mean structureat 75 m depth (Figure 15b) is signifi- upwellednearthe coast.The salinitymaximum,southof the
cantly different than the surface structure, and the three current maximum, is considerably narrower than the assolocal extrerna are less identifiable; yet the overall range of ciated temperatureminimum (Figure 15a), indicatingthe
temperature, salinity, and trt across the filament remain mixing of different water masses. Local upwelling/
is a candidatefor
similar(Figure 15a). In the deepersection(Figure 15b)the downwelling(divergence/convergence)
only anomalousfeature distinct from the main front is a bringing different water masses together (stirring); near-
DEWEY ET AL ' STRUCTURE AND DYNAMICS OF A COASTAL FILAMENT
14,901
LATITUDE (degrees)
37 25
37 50
37 75
38 O0
38.25
38.50
38.75
39.00
ß
$IGMA-t
Fig. 16. Contours of the mean density (as in Figure 5c) during phase I (July 2-16, 1988) along the D line.
Superimposedare vectorsrepresentingthe possible"isopycnal" flow suggestedby the meridionalADCP velocity
sections and the estimated vertical velocities (Figure 14). The vectors have been drawn parallel to the isopycnal
surfaces and scaled so that the vertical component representsthe daily vertical displacement centered at the mark on
each vector.
surface, wind-driven turbulence is likely the only available
mechanism for the mixing [Mourn et al., 1988; Dewey and
Mourn• 1990]. The estimatedmean vertical velocity W
(Figure 14) and the implied cross-frontal circulation, can
explain some of the structure in the observed surface distributions.
The mean crt structure for phase 1 is shown in Figure 16.
Superimposedare conceptualvelocity vectors showingflow
the mixing of the cooler (subsurface)part of the fresh pool
from the north side, with the shallower water found on the
upwelled side (south) of the filament. Observations(Figure
15a, also Hayward and Mantyla [ 1990] and Strub et al., [this
issue])indicatethe presenceof a pool of fresher,cool water
on the seawardside of upwelledfronts alongthe California
coast. This po01 is typically confined to the upper 60 m and
is 20-30 km wide. It is believed this fresher water may
alongisppycnalsurfaces•
as indicatedby the meanestimates originate at the Columbia river mouth (some 1000 km to the
of V a.nd W (Figures 5e and 14 respectively). The arrows north), where it is ejected onto the continental shelf and then
(Figure 16) were not measured directly, but are estimates flows southward, remaining on the outer edge of the upscaledso tha.tthe verticalcomponentrepresentsthe daily welling (divergent) region and the subsequentfront that is
vertical displacement.
formed by the upwelling.
Zonal isopycnal slopes (not resolved by the meridional
If the internal upwelling region near the zonal velocity
transects) may contribute significantlyto W, and the regions maximumin Figure 16were to bringfresherand cooler water
of estimatedupwelling(downwelling)havebeeninterpreted from the north, up along isopycnals to the surface on the
simply as flow along the resolvedisopycnalsurfaces(Figure south side of the velocity maximum, wind-induced turbulent
16). Nonetheless, for a descriptive explanation we require mixing could then produce the observed temperatureonlya conceptual
pictureof the possible
flow. In the depth salinity distributions. Observed turbulent dissipation rates
range 25-100 m, three regions of upwelling are evident havebeenlow withintheseupwelled
filaments,
belowthe
(Figure16).Nearthecentralregionof thefront(50-125m, wind driven surface layer [Mourn et al., 1988; Dewey and
37.90-38.3ølatitude) is a downwelling region, narrower at 50 Mourn, 1990]. The only persistentturbulentregion is the
m, expanding to a wider region at depth (100 m, Figures I4 near surface mixing layer driven by wind stresses. The
and 16). A second, s.maller dOwnwelling region is evident fresher water found at the surface, north of the velocity
north of the strongest upwelling. The central upwelling maximum (Figure 15a) may be maintained by the converregion (Figure 16) implies cross-frontal flow from the north genceimplied by the region of local down-welling(Figure 14)
sideof thevelocitymaximum(38.1ølatitude)alongisopycnal between 38.3ø and 38.4ø latitude. The local temperature
surfacestowards the uplifted dense core of the filament to maximumat depth(75 m, Figure 15b)may originatenearer
the south (37.85o-38.0ø)
the surface on the south side of the velocity maximum,
A possible mechanism responsible for causing the ob- where it is then advecteddownwardalongi•opycnalsin the
served asymmetric temperature minimum and salinity max- downwelling
regionind,
icatedin Figures14and16.
imum on the south side of the filament core (Figure 15a) is
The asymmetryin the temperature-salinity
distributions
ß
14,902
DEWEY ET AL..' STRUCTURE AND DYNAMICS OF A COASTAL FILAMENT
north and southof the current maximum indicatethat temperature measurementsalone are insufficientin determiningthe
density structure. Salinity variations play a crucial role in
determining the local density structure and therefore the dynamicheightfields.Thermal satelliteimages,revealingonly the
surfacetemperaturestructure, may be less representativeof
the density structure away from the coastalupwelling region,
where internal circulations within the filament-current system
can redistributeand mix water types, modifying the relative
rolesof temperatureand salinityin governingthe local density.
6.
CONCLUSIONS
narrow, near surface (<50 m) salinity maximum embedded
in a broader temperature minimum, both confined to the
region south of the current maximum. Confined to a region
north of the current maximum was a "pool" of less saline
water. The influence of the observed salinity structure on the
density field (and therefore the pressure and dynamic height
fields) cannot be revealed by thermal remote sensing (advanced very high resolution radiometer).
APPENDIX
A: CALCULATIONS
FOR MOMENTUM
ANALYSIS
Our coordinate system is right-hand Cartesian, aligned
with the hydrographic survey grid. It is a simple rotation of
standard linear Earth coordinates (x = east, y = north) by
30ø counterclockwise. In this system, x = east-northeast,
perpendicularto the D line, and y - north-northwest, along
During July 2-23, 1988, a significantupwelled filament was
observed in two substantially different orientations. The
observations during each filament orientation have been
from measured "Earth"
used to estimate average terms in the meridional momentum the D line. The transformation
coordinate
velocities
(Ue,
Ve)
is
then
balance. During phase 1 the current componentperpendicular to the transect line was found to be in geostrophic
U = Ue cos (30ø) + Ve sin (30ø),
(Ala)
balance. During phase 2 the meridional data closely represent a coordinate system along the axis of the filament, and
V- Ve cos (30ø) - Ue sin (30ø).
(Alb)
the meridional momentum balance was found to be significantly more ageostrophic. Observed acceleration and cy- Under this transformation, the momentum equations (1) are
unchanged, and "meridional" will now refer to the new y
clostrophic contributions to the momentum balance (i.e.,
OV/Ot and VOVG/Oy) were significantlyabove the estimated direction. As a result of this rotation, D line latitude is slightly
stretched from normal latitude such that 1.0 ø "latitude" = 128
noise levels at a number of locations during phase 2.
Although it appears that a considerableeffort has been km. During phase 1 the orientation of the filament is suchthat
exerted to show the near-surface (< 150 m) currents associated water "north" of the velocity maximum representswarmer,
with thesefronts are highly geostrophic,the resultsare by no offshore,nonupwelledwater, and water "south" of the velocmeans serendipitous.The strongcurrents, narrow structure, ity maximum representscooler, coastal upwelled water.
To minimize and quantify errors, the repeated transects
relatively large Rossby number (U/Lf = 0.3), and temporal
variability of these upwelled fronts suggeststhat quasi- during each phasewere used to provide multiple estimatesof
geostrophicdynamicsmay play a significantrole. Despitethese each momentum term from which mean values were calcustructural characteristics, the present analysis indicates a lated. Simple statistical analysis was used to estimate the
highly geostrophicflow. The measurementsanalyzed here variabilities and uncertainties. The estimated mean of each
representa uniqueset of observations,ideal for examiningthe term for each filament phase is bounded by an uncertainty
dynamics of fronts. To our knowledge, the present analysis derived from the variability of the individual estimates. A
also representsa unique attempt to complete a momentum full meridional momentum balance [i.e., (lb)] can be estibalance.
mated from a minimum of two transects (in order to estimate
Mean vertical velocities are estimated from the multiple OV/Ot); however, no statistical confidence can be assignedto
transects using ship ADCP and RSVP hydrographic and the terms in a two-transect balance. Including more
turbulence data (Appendix B). The calculation is made transectsin the analysisincreasesthe co.nfidence,at the
possible by the temporal resolution of observations in a expense of resolving variability on short time scales.
near-geostrophicflow field. Previous estimates of W utilized
Since the number of independent observationsis limited,
only moored current measurements. The estimated vertical
error statistics are calculated using a bootstrap technique
velocities from the ship observationsare in agreementwith [Efron and Gong, 1983, Elton, 1987]. The procedure simply
model predictions.
calculatesthe mean of n estimatesof the appropriatestatistic
Relative vorticity is estimated from moored and ship (i.e., mean, variance, or correlation coefficient) calculated
ADCP measurements.During the microstructure survey, the from i random selections from the original ensemble of i
northern mooring location is found to remain in the negative estimates. A bootstrap iteration of 500 was found to give
relative vorticity shear:of the filament, while the southern stable results. In other words, to estimate the confidence
mooringremains in the positive relative vorticity. The mean interval for the mean of a quantity at a fixed location from i
magnitude of the positive vorticity (0.25f) is larger than the transects, 500 (=n estimates of the mean were calculated
mean magnitude of the negative vorticity (-0.16f), a possi- from 500 ensemblesof i random selectionsfrom the original
ble consequenceof instabilities that work preferentially in i estimates. The final mean is then the mean of the 500
regions of negative vorticity.
estimated means (insignificantly different from the sample
Finally, the repeat.edtransects of high-resolutionhydrog- mean), and confidence limits (95%) can be selected directly
raphy reveal temperature and salinity distributions that from the bootstrap distribution of means.
suggest considerable recirculation within and across the
When estimating statistics for terms in the momentum
filament. Local adjustments in the relative vorticity may balance from multiple transects it is assumed that the dycause submesoscaledivergences and convergences that re- namics are reasonably stationary during that period and that
sult in upwellingand downwellingalongisopycnalsurfaces. the variability of the estimates reflects natural uncertainty
The resulting redistribution of water massesmay form the rather than a trend about the mean. To test the validity of
DEWEY ET AL.' STRUCTUREAND DYNAMICS OF A COASTAL FILAMENT
this presumption for phase 1 (July 2-16), three momentum
analyses were performed on successive groups of four
consecutive transects. No trend was found, and the inclu-
sion of all nine transects in a single momentum analysis was
deemed justifiable.
One final note about the analysis to follow. Some of the
terms in the momentum equation (lb) were calculated using
both RSVP (hydrographic) and ADCP (velocity) data
(WOV/Ozand(1/O0)Vß•yi), onetermfromRSVPdataonly
(-(1/po)OP/Oy), and some terms from ADCP data only
(OV/Ot, UOV/Ox, VOV/Oy, fU). Therefore althoughwe have
nearly twice the density (in time) of ADCP observations to
RSVP observations (northward and southward transects as
opposed to northward only), we use only coincident data
(collected simultaneously during the northward-heading
transects). This assures that the estimated contributions to
the momentum balance represent observations of the same
14,903
easily differenced to estimate 0V/Oy. Estimates of the mean
gradient across both three and five consecutive 15-minaverage profiles were compared and the gradient across
three was used, as it was insignificantly different from the
broader gradient estimate.
The flux divergence term represents turbulentlike (eddy)
processes that act to redistribute momentum. Here it is
parameterized through the gradient of the Reynolds stressx.
This is an important term when wind forcing directly influences the near-surface flow, as the surface stress (momentum flux) is translated to the flow through turbulent diffusion.
This term also represents the momentum flux from submesoscaleeddies. Although such contributions may be significant, we have no means of accurately estimating them for
the limited period of our measurements.
A useful parameterization of Reynolds stresses is to
assume that the momentum
flux at turbulent
scales acts like
"field."
molecular diffusion, and the stress components can be
There were 10 northward heading RSVP/ADCP transects approximated by eddy viscosities working on local velocity
attempted during Phase 1 (July 2-16). Of these, one was gradients. As a consequence of this parameterization, the
aborted prematurely (transect4, after only 30 km) and during horizontal eddy viscositiesare much larger than the vertical
the eighthtransect, instrumentproblemskept the RSVP out of equivalent because of the much weaker horizontal shears.
the water. Therefore in the momentumanalysis,eightcomplete Although oceanic models often require adjustable horizontal
transectsand one shorttransectmake up the data duringphase viscositiesto match observed flux rates, applicable parameterizations for measuredoceanic shears(horizontal) have yet
1; three completetransectsmake up phase2 (July 20-23).
The first ageostrophicterm in (lb) is the net acceleration, to be verified and are typically ignored [Gregg, 1987].
OV/Ot. By repeating transects every -•1-2 days we estimate
Parameterizing a vertical eddy viscosity is more common,
the acceleration by first-differencingADCP estimatesof V at wherethe verticalturbulentmomentum
flux(•yz -pv'w') is
each position (y) between consecutivetransects(•it). During approximatedby pKm(OV/Oz), where K m is the vertical
the northward-heading transects, when both RSVP and eddy viscosity and the angle brackets denote an appropriate
ADCP data were collected, the ship speed ranged between averagingprocessthat eliminatesshort time scalefluctuations
2.5 and 5 knots(-1.2-2.5 m s-l). At thesespeeds,the in the mean shear (internal waves, noise) but not general
averaged (gridded) ADCP profiles have separations of 1.8 trends. An estimateof K m is obtained from the steady state
km horizontally and are equivalent to 15-min averages. turbulent kinetic energy equation, where turbulence producAlthough the estimateduncertainty in 15-minADCP velocity tion is assumedto be balancedby viscousdissipation[Osborn,
averages
is about8 cm s-1 first-differencing
thesevelocity 1980; Crawford, 1982;Dillon et al., 1989],
estimates over periods of 1-2 days results in relatively larger
uncertainties in the acceleration (small differences between
large quantities). The errors are reduced by averaging several estimates, each obtained from a first difference between
2 + (OV/Oz)
2 is the totalvertical
consecutive transects. Of the nine transects during Phase 1, where(0U/0z)2 = (OU/Oz)
eight were complete, resulting in seven estimates of 0V/Ot at shear variance. Dissipation rate estimates from the RSVP
each location (both in y and z). Had the M2 tide not been profiles and shear estimates from the ADCP measurements
removed from the shipboard ADCP data, aliasing would are combined to give estimates of the ve•ical eddy viscosity.
The full flux divergence in (lb) is approximated by the
have contributed fictitious accelerations (tidal) as large as
ve•ical flux divergence of small-scale meridional momentum
(OV/Ot)/f-• 10cm s-• .
The second ageostrophic term in (lb) represents zonal given by
advection of meridional momentum (UO V/Ox). The meridional transectsdo not provide direct information on the zonal
gradients. Only at the two ADCP mooring locations do we Po
Po
have zonal gradient information on U and V. Therefore for
each transect and each mooring location, an estimate of This formulation has been used in the analysis of equatorial
UOV/Ox is made from the mean U between mooringand the dynamics, where the flow is not constrained by Coriolis
ship track and the first-difference gradient OV/Ox between accelerations [Crawford, 1982; Gregg et al., 1985; Dillon et
the two locations. The moored ADCP velocities were averal., 1989]. Here, the individual sections of e and ADCP shear
aged over 1.5-hour periods centered when the ship passed are combined and the flux divergence estimated.
The final ageostrophic term in the meridional momentum
the y location of the mooring. The spatial (ship) ADCP data
was averaged over the same interval, representing approxi- equation (lb) to be estimated is the vertical advection of
mately - 12 km of ship track. The averageminimum distance mefidional momentum, (W) (OV/Oz). The ve•ical shear in V
is obtained by d•erencing the ADCP measurements, as was
between the ship track and the moorings was -•4.6 km.
The ageostrophiccomponentof the meridionalmomentum described above The ve•ical velocity W is not measured,
balance VOV/Oy is estimated directly from the shipboard but a mean value can be estimated using both the RSVP
ADCP measurements.Measured V along the ship track (y) is hydrographic data [•z)] and the ADCP velocity (U, V)
m•
c)Z
/ • (E),
1
-
(t2)
10•yz
0( (•)(OV/Oz)
).
-
14,904
DEWEY ET AL.' STRUCTURE AND DYNAMICS OF A COASTAL FILAMENT
Meridional
Momentum
Balance
X•-
]
0.8
i
o
d)
:a,.,
•
......
v'
"'
......
"'""......
'--• .......:'"" """"': •
•_
....
•
/'•
"" .......' •"
!
\ •,
--- 104
'
e):•
iJ ../
........
.....
...•.......
---}'-'-"----'-"'-":-....
•-"-'
....
•--•r•'.-•X
- :':,,,,•,,•
'""""
•......" '""......
"'+-
LATITUDE
'".+ ,'"
"',,. ,,.....v"",,,'", :'
ß
• 104
DEPTH 25. m
Fig. 17. Temporallyaveragedageostrophic
contributions(in centimetersper second)to the meridionalmomentum
balance
at 25m duringphase1, with95%bootstrap
confidence
limits.To therightaretheseriesvariances
(incm2 s-2).
(a) The averageaccelerationOV/Ot,not significantly
differentfrom zero. (b) MeridionaladvectionVOV/Oy,showing
narrowregionsof significance.
(c) VerticaladvectionWOV/Oz,with two regionsof highvariability,but insignificantly
differentfrom zero. (d) Vertical mixing,almostalwayspositive(deceleration),yet never significantly
differentfrom
zero. (e) "Geostrophic"residual(solid)from Figure7b, and total residual(dashed)after includingthe ageostrophic
contributions.Shown above the two mooringlocationsare the estimatesof zonal advection UOV/Ox, with 95%
confidence
intervals.At bothlocationsthezonaladvection
actsto reducethefinalresidual.Alsoshownat the rightare
the rms values for the geostrophicand final residuals.
measurements.
Since this calculation has not been verified
the error variance for any particular measurement will
by in situ measurements
of W and may not be universally simply
be (re
2 = (e/2)2 wheree is anestimate
of measureaccepted(or known), AppendixB is dedicatedto a thorough ment uncertainty. For example, given that the ship ADCP
description of the formulation and calculation.
Unique in the presentanalysisof the meridionalmomentum terms, the vertical advection term is calculated once for
each filamentorientation.This is due to the temporalmean
required in estimatingreliable vertical velocities. The temporal means, (W) and (OV/Oz), are then multiplied and
confidencelimits are determinedfrom the uncertaintyof
individualconstituentsleadingto the final product. It is
acknowledgedthat (W)(OV/Oz) is not equivalentto (W(OV/
Oz)). Becauseof the temporalaveragingrequiredto estimate
reliablevertical velocities(AppendixB), the productof the
mean values is deemed a reasonableapproximationto the
meanof the productin light of the stationarycharacterof the
filament duringthe two phases.
Before looking at the estimatedageostrophiccontributions, we shouldestablishthe expectederror level for each
term due simplyto measurementuncertainty.Assumingthat
measurement errors are random and normally distributed,
velocitieshave a uncertaintyof _+8cm s-• the error
variancefor U is approximately
16cm2 s-2. Therefore,an
estimated
variancelessthan--16 cm2 s-2 for a scaled
fU
term is at or below the expected measurementnoise level.
The multiple transects and observations are treated as an
ensemble and an uncertainty in a mean estimate from N
transects
willbereduced
by(N - 1)- •/2.Forcertainproduct
terms(i.e., UOV/Ox),the errorscanbe assumedto be independent and the error variance is then the sum of the individual
variances
divided
by 22/2.Consequently,
theestimated
variance noise levels for the remaining meridional momentum
terms
are(afterscaling
by 1001f)
12cm2 s-2 for-(1/p0)OP/Oy,
18cm2 s-2 for OV/Ot,
24cm2 s-2 for UOV/Ox,
30for VOV/Oy
(this variance, and others with similar products, is larger
because
V andOVaredependent
andnotrandom),
26cm2 s-2
forWOV/Oz,
and24cm2s-2for(1/po)O•yz/OZ.
Surprisingly,
the
ageostrophicterms do not have significantlylarger measurement error variancethan the geostrophicterms; however, no
DEWEY ET AL.' STRUCTUREAND DYNAMICS OF A COASTAL FILAMENT
14,905
1.9
b)
16.2
Fig. 18. Temporally averagedageostrophiccontributions(in centimetersper second)to the meridional momentum
balance
at 25m duringphase2, with95%bootstrap
confidence
limits.To therightaretheseriesvariances
(incm2 s-2).
(a) The averageaccelerationOV/Ot, now with a singleregion significantlydifferent from zero. (b) Meridional advection
VOV/Oy, showing narrow regions of significanceand a greatly increased variability. (c) Vertical advection WOV/Oz,
nowhere significantly different from zero. (d) Vertical mixing, clearly a very small ageostrophic component,
insignificantlydifferent from zero. (e) "Geostrophic" residual (solid line) from Figure 9b, and total residual (dashed)
after including the ageostrophiccontributions. Shown above the two mooring locations are the estimates of zonal
advection UOV/Ox, with 95% confidenceintervals. During phase 2 the zonal advection contributesvery little to the
meridional momentum balance. Also shown at the right are the rms values for the geostrophic and final residuals,
showinga significantincreasein the variability, a result of the fewer observationsduring phase2 as well as the influence
of more variable ageostrophiccontributions.
additionalerror has been added for the assumptionsused in
arriving at the terms. Bootstrappingmultipletransectsof each
term also providesconfidencelimits representingthe variability in the observations.
Mean values for the five ageostrophicterms for phase 1
(July 2-16) are shown in Figure 17. The stationarity of the
filament over this two week period is reflected by the low
estimatesin the mean accelerationOV/Ot (Figure 17a). The
highest variability (widest confidence interval) occurs near
the center of the jet. The meridional advection term (Figure
17b) VOV/Oy is rarely significantlydifferent from zero, with
maximum magnitudeswithin the core of the jet. (Note that at
the endsof certain momentumcontributions(e.g., VOWay),
the bootstrap confidence intervals collapse, indicating regions sampled only once.)
Both vertical advection and turbulent diffusion (Figures
17c and 17d, respectively) are negligible over most of the
region, with maximum magnitudes to the north. This is a
result of the deep mixed layer in the northern extent of the
sections (Figure 5c). Large temporal changes in density
(Op/Ot)and weak stratification
(low N 2) resultin larger
estimates of W and e. Below 50 m, within the pycnocline,
these terms are negligible. At both mooring locations the
mean contributions from UOV/Ox are positive but are not
significantly different from zero at a 95% level.
Root-mean-square values for the geostrophic and total
residuals respectively are shown to the right in Figure 17e.
The variance and rms for the geostrophic residual are 66.3
(cm2 s-2) and10.4(cms-•), respectively,
andthevariance
andrmsforthetotalresidualare78.3(cm2s-2) and10.4(cm
s-•), respectively.
The additional
four completeandtwo
mooring location ageostrophic terms have not reduced the
variance
or rms of the momentum
balance residual.
The fact
that the rms values are larger than the square root of the
variances indicates a nonzero mean. If the individual ageostrophic terms represent random noise, the total variance
would simply be the sum of the individual variances (66.3 +
9.8 = 76.1 cm2 s-2). The total residualvariance(78.3cm2
14,906
DEWEY ET AL.: STRUCTURE AND DYNAMICS OF A COASTAL FILAMENT
S-2)is insignificantly
different
fromthesumof theindividual
variances that are below the estimated noise levels, indicating that the ageostrophic contributions to the meridional
momentum equation are indistinguishable from random
noise and below the noise level of calculation (measurement). Some variance (perhaps a considerable amount) is
omitted by estimating the zonal advection at only two
locations, although the indication (Figure 17e) is that this
contribution may still be insufficient to balance the "noise"
summed
in the final residual.
Mean values for the five ageostrophic terms for phase 2
(July 20-23) are shown in Figure 18. During phase 2, the
meridional advection term has considerably more variance
(Figure 18b), a result of the filament turning more northsouth and increased V (Figure 2b). The total residual (Figure
Rearranging the terms in (B 1) and assumingthat we can
approximateO(pe)/Oz -• pOe/Oz,we get an equation for W,
Op/Ox
Op/Oy
I •-•/•zz
Op/Op
0.2
0e
W=- (UOp/Oz
Op/Oz/
N
20z
+ V
-
+
.
(B3)
The three main componentsof (B3) represent horizontal flow
along sloping isopycnal surfaces, vertical displacement of
isopycnals, and diapycnal mixing. From the RSVP and
ADCP sections we can directly estimate all terms in (B3)
except the zonal density gradient Op/Ox.To this end, we use
the thermal wind equations to equate horizontal isopycnal
slopes in terms of vertical velocity gradients. The multiple
transects result in temporal resolution sufficient to recover
the mean flow and justify the use of the thermal wind
18e)hasa variance
of 99.4cm2 s-2, againnearlyequalto the approximation.Upon substitution((#/po)Op/Ox= -f OV/Oz,
sum of the individual ageostrophic variances. The increase
in residual variance is greater than the sum of the individual
noise variances, indicating that certain ageostrophicterms
are contributing significant variance but not consistently
reducing the rms of the final residual. Both the mean
acceleration(Figure 18a) and the meridional advection (Figure 18b) have regions significantly different from zero at the
95% level, and yet they are not always of the right sign to
reduce the residual. In particular, the magnitude of the total
residual is smaller than the geostrophic residual in the
southern section (37.9ø-38.15ø) but larger to the north (38.2ø38.4ø).The variance of the final residual now represents 18%
of the observed variance. Again, the total variance is still
missing some contributions from the zonal advection, sampled only at two locations.
APPENDIX
B: ESTIMATING
VERTICAL
VELOCITY
THE MEAN
W
The following technique for estimating the mean vertical
velocity W was first reported by Bryden [1976] and was
subsequentlyused in vorticity analyses by Bryden [1980],
Hall [1986], and Freeland and Mcintosh [1989]. The formulation is extended here by including contributions to the
mean vertical velocity due to vertical mixing.
Vertical velocities can be estimated by considering the
conservation
of mass in an Eulerian
reference
frame.
The
conservation of mass can be written,
(g/po)Op/Oy= fOU/Oz), we find
f
OV
Op
+N20z'
W=-•-• UOzV•' _Op
Ot/Oz
where the thermal
wind substitution
(B4)
assumes that the mean
velocity estimates U and V are in near geostrophicbalance.
We have already found that the mean zonal velocity field is
reasonablyexplained by a simple geostrophicbalance (for
phase1), and that the combinedthermal wind approximations
probablyintroduce a maximum error of only ---30% in W.
In the Bryden [1980] derivation a transformation of coor-
dinates is made, and the current components (U, V) are
representedin polar coordinates, say, R for current speed
and 0 for current direction. The first term in (B4) is then
rewrittenas -(f/N2)R200/Oz,whereR is theaveragecurrent speed over the depth interval Oz. Thus W is shown to be
proportional to current veering with depth. Brydens' notation is no more intuitive than that shown in (B3) and (B4),
component flow along appropriate isopycnal slope. In fact
the present notation (B4) shows directly that the vertical
velocities are a consequence of adjustments in the local
vorticity field. The vertical shears OV/Oz and OU/Oz are the
major contributionsto the horizontal componentsof vorticity, sc = (OW/Oy - OV/Oz)and r/ = (OU/Oz - OW/Ox)
respectively. Therefore, the vertical velocities represented
by the first term in (B4) result from horizontal advection of
relative vorticity, namely (UOV/Oz - VOU/Oz) = -(U• +
Vr/), if IoU/ozl >> IoW/oxl and Iov/ozl >> IoW/oyl. A
similar result is obtained by consideringpotential vorticity
OpOpOpOp
0( O•_Zp
)
--+
Ot
U--+
Ox
V m+
Oy
W--=-K
Oz Oz
P
'
(B1)
dynamics [Levine et al., 1986].
The second and third terms in (B4) represent vertical
displacement of isopycnals and the net vertical velocity
where p is the densityand turbulentdiffusionhasbeenapproxresultingfrom turbulent diapycnal mixing. Vertical displaceimated by the divergenceof the local vertical turbulent diffuments of isopycnal surfacesmay compensatefor horizontal
sioncoefficientworkingon the local verticaldensitygradient.
advection of tilted isopycnals but also represents locally
Following Osborn [1980], we approximate an upper limit
forced upwelling and downwelling. The diapycnal mixing
to the turbulent diffusion coefficient by
term does not model vertical turbulent velocities (w'), but
0.2e
representsthe net raising of potential energy accomplished
Kp-<N2,
(B2) by turbulent mixing. Both of these contributions to W are
estimatedfrom the RSVP sections.The contribution(OtYOt)/
whereN 2 = -(9/po)Op/Oz
andtheconstant
0.2isa resultof (OtiOz)is estimatedby first-differencingthe density sections
a constant
fluxRichardson
number
Rif = O.15in thesteady betweenconsecutivetransects,thereforeobtainingsevenand
state turbulent kinetic energy equation where production is two estimatesfor phases1 and 2, respectively.The diapycnal
balanced by dissipation and buoyancy flux. Rohr and Van mixingtermis estimated
for eachRSVPsectionof e andN 2.
Atta [1987] indicate that laboratory studies show 0.2 is a
The first term in (B4) is calculated directly from the
resonable approximation in stratified flows with Richardson individualRSVP and ADCP sections
of N 2, U, V, OU/Oz,
numbersRi • 0.1.
and OV/Oz. Averaging this contribution over several realiza-
DEWEY ET AL..' STRUCTURE AND DYNAMICS OF A COASTAL FILAMENT
tions (transects) justifies the use of the thermal wind equations. Instantaneous estimates of W using (B4) have large
nongeostrophic contributions to U and V resulting from
noise like processes(e.g., inertial waves). Shown in Figure
14 is the mean W structure (in meters per day) for phase 1,
formed by summing the three mean contributions. On average, the final contributions to (W) are represented by 8090% from the flow along sloping isopycnals, 10-20% from
isopycnaldisplacements
and0-10% from diapycnalmixing.
Acknowledgments. The authors would like to thank all those
who assisted in data acquisition: Mike Neeley-Brown, Jose Baer,
Ray Kreth, Terry Sullivan, Mark Willis, Pat Collier, Jane Huyer and
Rich Schramm. Mike Kosro processedthe shipboard ADCP data,
Mark Abbott processed the AVHRR images, and Dave Reinert
drafted several figures.The mooringdata was provided courtesyof
Bob Smith and Mike Kosro. Fruitful discussions with Dave Hebert,
Jane Huyer, Mike Kosro, and Bob Smith greatly assistedin formulating ideas. The authors thank the reviewers for their helpful
comments. The authors would also like to extend special thanks to
the editors (K. Brink and T. Cowles) of this special issue for their
commentsand uncompensatedtime. This project was supportedby
the Office of Naval Researchthrough the Coastal Sciencesprogram
(T. Kinder) under contract N00014-90-J-1215.
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