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College of Marine Science
12-15-2001
West Florida Shelf Response to Local Wind
Forcing: April 1998
Robert H. Weisberg
University of South Florida St. Petersburg, [email protected]
Zhenjiang Li
University of South Florida St. Petersburg
Frank E. Muller-Karger
University of South Florida St. Petersburg, [email protected]
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Scholar Commons Citation
Weisberg, Robert H.; Li, Zhenjiang; and Muller-Karger, Frank E., "West Florida Shelf Response to Local Wind Forcing: April 1998"
(2001). Marine Science Faculty Publications. 55.
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JOURNAL
OF GEOPHYSICAL
RESEARCH,
VOL. 106, NO. C12, PAGES 31,239-31,262, DECEMBER
2001
West Florida shelf response to local wind forcing: April 1998
Robert H. Weisberg,Zhenjiang Li, and Frank Muller-Karger
College of Marine Science,Universityof South Florida, St. Petersburg,Florida, USA
Abstract. We comparewest Florida shelf velocityand sea level data with a model
simulationfor April 1998. Responsesfor three upwellingand three downwellingfavorable
wind eventsare documented.Along-shelfjets accompaniedby oppositelydirected upper
and lower layer across-shelf
flows(with connectingverticalvelocity)comprisethe fully
three-dimensionalinner shelf responses,which are sensitiveto stratification.With an
initial densityfield representativeof April 1998 the model simulatesvelocityand sea level
variationsin general agreementwith the observations,whereassubstantialmismatches
occurwithout stratification.Despite the winds being the primary motive agent for the
inner shelf the stratificationdependencerequiresthat model densityfieldsbe maintained
through a combinationof adequateinitial conditions;surface,offshore,and land-derived
buoyancyinputs;and data assimilation.Dynamical analysesdefine the inner shelf as the
region where the surfaceand bottom boundarylayers are important in the momentum
balance.Kinematically,this is where surfaceEkman layer divergence,fed by the bottom
Ekman layer convergence,or conversely,setsup the across-shelfpressuregradient.
Stratificationcausesa responseasymmetrywherein the offshorescaleand magnitudeof
the upwellingresponsesare larger than thosefor the downwellingresponses.This
asymmetryis attributed to thermal wind effects acrossthe bottom Ekman layer. Buoyancy
torque by isopycnalsbendinginto the bottom addsconstructively(destructively)with
planetaryvorticitytilting under upwelling(downwelling)favorablewinds,and this may
have important implicationsfor nutrientsand other material property distributionson the
shelf.
shore and local buoyancyforcing, all such factors must be
treated in order to produce useful model products.
Continental
shelf circulation
results from both local and
The paper is organized as follows. Section 2 reviewsbackoffshoreforcing. Local forcing is by momentum and buoyancy ground materials on the responseof a continental shelf to
input at the seasurfaceand buoyancyinput at the land bound- synopticwind forcing.Section3 introducesthe in situ data and
ary. Offshore forcing is by momentum and buoyancyinput at the model used to simulate these data. Section 4 compares
the shelfbreak. The partition of influencebetweenthese con- model resultsand data. Motivated by thesecomparisons,
albeit
tributingfactorsvarieswith shelf location and geometry,and at limited observationallocations,section5, where fully threenowhere is this partition quantitativelyaccountedfor. How dimensional structuresare shown, expandsupon the model
continental
shelves are forced thus remains a fundamental
flow field kinematics.For brevity we emphasizeone complete
questionfor both the circulationand for the biological,chem- cycle of responsesto successivedownwellingand upwelling
ical, and geologicalconsequences
of the circulation.
favorable winds, and an asymmetrybetween upwelling and
The west Florida shelf (WFS) is an end-memberin the downwellingresponsesis noted. Section 6 then exploits the
ensembleof continentalshelvesfor which local forcing may be model fields to developthe momentumand vorticitybalances
presumedto be of primary importance.This is becausethe that help to define the inner shelf separate from the shelf
WFS iswide enoughfor its inner shelfto be distinguishedfrom break. Section7 summarizesthe results,where, discussingthe
the shelf break. Given the complex nature of continental asymmetry,it is recognizedthat the synopticand seasonalscale
shelvesand the limitations of both in situ data and models, it variability cannotbe fully separatedsincethe responsesof one
is usefulto simplifythe circulationproblemby isolatingfactors dependsupon the densityfield providedby the other. This is
and questioninghow well a givendata set can be explainedby true for sea level and more so for currents.
thesefactors.Along thisvein we ask how well coastalsealevel
and inner shelf currentscan be explained by the influence of
local wind forcing alone. We comparein situ data from April
2. Background
1998with a numericalmodel drivenby observedtime varying,
Continental shelvesare dynamicallycomplex.In relatively
but spatially uniform, winds. Our results suggestthat inner
deep
water the surfaceand bottom boundarylayersare sepashelf currents may be accountedfor by local wind forcing,
rated
by a bottom slope-constrainedgeostrophicflow. As the
given an appropriatelyspecifiedinitial densityfield. The denwater
depth decreasestoward the coast,the surfaceand botsity field, however, is shown to play an important role, and
sincethe densityfield is determinedby a combinationof off- tom boundary layers tend to merge acrossthe geostrophic
1.
Introduction
interior.
Copyright2001 by the American GeophysicalUnion.
Paper number 2000JC000529.
0148-0227/01/2000J C000529509.00
Here
we define
the inner
shelf as the near-coastal
regionwhere the surfaceand bottom boundarylayersare dynamically important. Our definition is somewhat different
from that given by Lentz [1994], and this difference will be
31,239
31,240
WEISBERG
ET AL.: WEST FLORIDA
SHELF RESPONSE TO LOCAL WIND
clarifiedin section6. Theseboundarylayerinfluences,coupled
with the coastlineconstraint,resultin kinematicaland dynamical characteristics
of the inner shelfthat may differ markedly
from thoseoccurringfarther offshore.Generally,for synopticscalevariabilitywherewind stressis the principalmotiveagent,
the inner shelfreactsto the presenceof the coastthroughthe
establishmentof a surface pressure gradient. This occurs
through divergencebrought about by surfaceand bottom Ekman layer transports[e.g., Gill, 1982, p. 394], and recent evidence for such adjustmenton the WFS is given by the upwellingcasestudyof Weisberg
et al. [2000].Regularlyoccurring
subtidalsealevelvariationsshowthis adjustmentto be a common feature
of all shelves.
FORCING
Florid
•___.1
27
•
Oharlot•arb
25
Descriptionsof inner shelfvariabilityhave emergedlargely
from observations
on the continental
shelves and Great Lakes
of North America. Csanady[1982], Walsh [1988], and Brink
[1998] provide overviews,and recent representativeworks
from different regionsinclude those of Lentz [1994], Smith
[1995], Weisberget al. [1996], Weatherlyand Thistle [1997],
Yankovskyand Garvine[1998],Lentz et al. [1999], and Munchowand Chant [2000]. Insightson the dynamicsof the inner
shelf are found in the analyticaltreatment of Mitchurn and
Clarke [1986a]. The complex nature of turbulent boundary
layers,however,limitsthe useof analyticaltechniques,
andthis
has led to numerical
model studies of inner shelf turbulence
that
each individual
continental
shelf environment
C
-•e••85
87
- 83
81
Longitude
29
in
simulationsof one or two dimensions[e.g.,Weatherly
andMartin, 1978; Allen et al., 1995; Lentz, 1995]. Two dimensions,
however,excludethe interactionsthat may occurbetweenlocal
and large-scaleprocesses
andthe possibilitythat the dynamical
interactionscontrollingdivergenceand vertical motion may
vary in the along-shelfdirection.For example,in contrastwith
the two-dimensionalcirculationpattern of equal and opposite
upper and lower layer flowsreportedby Lentz [1994] for the
northernCaliforniacoast,Munchowand Chant[2000]report a
fully three-dimensional
flow with a net across-shelf
transport
for the New Jerseycoast.Three dimensionalitythere is attributed to an along-shelfpressuregradient force due to coastal
geometryand baroclinicity.Long-wavemodelsthat assumea
boundary condition of no net across-shelfflow at some distancefrom the coast[e.g.,Clarkeand Van Gorder,1986;Lopez
and Clarke,1989]are to someextentcontraryto thesefindings,
and additional sensitivitystudiessuch as that by Samelson
[1997] are warranted.While the generalphysicalconceptsespousedin all of thesestudiesapply,it is becomingincreasingly
clear
23
• 27
25
23
87
85
83
81
Longitude
Figure 1. (top) West Florida shelfbathymetryandthe measurementlocationsand (bottom) numericalmodel domain
with coordinate systemdescriptionas applied herein. The
model seawardboundariesare open exceptfor the southeast
cornerwhere the solid line representsclosureby the Florida
Keys.The solidline offshorefrom Sarasotadenotesthe section
sampledfor kinematicaland dynamicalanalyses.
is
somewhatuniqueand that the regionof the inner shelf,where
importantacross-shelf
transportsoccur,requiresbetter understanding.
located at the 50 m isobath. These measurement
locations are
shown in Figure 1. The data collection effort was initially
unsupportedby hydrographicdata. Through efforts by the
Mote Marine Laboratory(G. Kirkpatrick,personalcommunication, 1998) and the Universityof South Florida, monthly
3.
The Observations
and the Model
hydrographicsectionswere initiated in March 1998.
3.1.
Observations
Covariationsin winds,sealevel, and currentsoccurthroughExploratorymeasurements
of inner shelfvelocityprofileson out the record,as expectedfrom previousWFS shelfobservathe WFS wereinitiatedin November1996with the deployment tions [e.g.,Mitchum and Sturges,1982]. A new finding is the
on the 20 m isobathoffshoreof Sarasota,Florida, of a bottom- variability in the relative turning of the velocityvectorswith
mounted300 kHz acousticDoppler currentprofiler (ADCP) depthfor eachsynopticweatherevent.Responses
to upwelling
manufacturedby RD Instruments,Inc. Using 0.5 m bin spac- favorablewindsgenerallyshowonshoreflow near the bottom
ing, and after editing surfaceeffects,the data setyieldedhor- and offshore flow near the surface and show the converse for
izontal velocityprofilesbetweendepthsof 2.5 and 16 m. An- responsesto downwellingfavorablewinds. These responses
cillary data setsinclude sea level from the National Oceanic are oftentimesaccompaniedby bottom temperaturechanges.
and AtmosphericAdministration(NOAA) tide gaugeat St. Once the supportivehydrographicsectionscommenced,it bePetersburg,Florida, surfacewinds from NOAA buoy 42036 came clear that the velocityvector turning is related to the
located at midshelf, and velocity profile data from a buoy densitystratification.April 1998 is a particularlyinteresting
WEISBERG ET AL.: WEST FLORIDA
a.
SHELF RESPONSE TO LOCAL WIND FORCING
31,241
Across-shelfVelocityComponent
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C.
St. PetersburgSea Level
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April 1998 (day)
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[,,,,,,,,
.....................
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..........
3
5
7
9
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13
15
'.................
...........
17
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25
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29
April 1998 (day)
Figure2. April1998measurements
of (a) across-shelf
and(b) along-shelf
velocity
components
sampled
at
the 20 m isobathoffshoreof Sarasota,
Florida,(c) sealevelat St. Petersburg,
(d) windvelocitysampledat
NOAAbuoy42036,and(e) windstress.
Thecontour
intervals
are0.05m s-• forthevelocity
components,
northisupandeastisto therightforthewindvectors,
andalldataarelow-pass
filteredto exclude
oscillations
at timescales shorter than 36 hours.
to eachof these.In the along-shelf
directioneach
monthwith a succession
of synopticweathereventsand large responds
velocityvectorturning.We focusour attentionon thismonth windchangegivesriseto a coastaljet of varyingverticalstrucfor a comparison
betweenthe in situ data and a numerical ture; that is, someshowsubsurfacemaximawhile othersshow
model simulation.
surfacemaxima.Accompanying
the coastaljets are opposing
The April 1998dataare shownin Figure2. With emphasis onshoreand offshoreflowsoverthe upperand lowerportions
on the timescales
of the synopticweathervariations,all of the of the water column.The mostpronouncedresponseoccurson
data are low-passfilteredto removeoscillations
at timescales April 12whenthe upwellingfavorablewindsare largest,causjet of magnitude
0.6 m s-• withonshore
(offshorterthan36 hours(subsequent
modelresultsare alsolow- ing a coastal
shore)
flow
in
the
bottom
(surface)
Ekman
layer
exceeding
passfiltered).Providedarevelocitycomponent
isotachs
for the
do not differ
along-shelf
and across-shelf
directions,
coastalsealevel,wind 0.2 m s-•. Althoughthe wind stressmagnitudes
to upwellingevents(April 12beingan
velocityvectors,andwindstress
vectors.Alongshelfis defined muchfromdownwelling
the responses
in the currentsto the upwelling
as 333ø relative to the true north. Open contoursare in this exception),
to the
upcoastdirection,and shadedcontoursare in the reciprocal windsare largerin all three casesthan the responses
winds.A response
asymmetry
on theWFS is thus
downcoastdirection. For the across-shelfcomponent, open downwelling
(shaded)contoursare directedonshore(offshore).The wind observed.Asymmetricbehaviorin bottom boundarylayer
hasbeenreportedelsewhere(e.g., Trowbridge
and
velocity(stress)variations
for April 1998are primarilyin the thickness
Lentz
[1991]
and
Lentz
and
Trowbridge
[1991]
for
the
northern
along-shelfdirection.Upwellingand downwellingfavorable
or stabilizing
influences
windsare observedoverthreedistinctiveperiods,and sealevel Californiacoast),andthe destabilizing
31,242
WEISBERG
ET AL.' WEST FLORIDA
SHELF RESPONSE TO LOCAL WIND
FORCING
Constant Density Case
0.2
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-0.4
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Stratified Case
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21
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April 1998 (day)
Figure 3. Modeled(dash-dotted
lines)and observed(solidlines)sealevelvariabilityfor the (a) constant
densityand (b) stratifiedcases,alongwith the (c) and (d) April 1998wind vectors.
of eitherdownslopeor upslopedensitytransports,respectively,
has been offered in explanation.As we will discuss,however,
theseboundarylayer turbulenceargumentsdo not explainthe
responseasymmetryreported here.
3.2.
Model
We employthe PrincetonOcean Model (POM) [Blumberg
andMellor, 1987]on the basisof the followingattributes.As a
primitive equationmodel, it allowsus to diagnosedynamical
balances.Its verticalsigmacoordinatehelpsto resolvethe flow
structureson a gentlyslopingshelf,and its horizontalorthogonal curvilinearcoordinateallowsthe model grid to conform
to topography.By parameterizingfriction with an embedded
Sixteensigmalevelsare usedin the vertical,distributedlogarithmicallyabout the middle to achievefiner resolutionof the
surfaceand bottom boundarylayers relative to the interior.
Other WFS applicationsof this model grid, alongwith discussionsof the openboundaryconditions,are givenby Li [1998]
and Li and Weisberg
[1999a,1999b].
The modelis forcedfrom mid-MarchthroughApril 1998by
a spatiallyuniform, time-dependentwind stress.The wind
stresscomponentsare computedfrom the in situwind velocity
vectorsobservedat the NOAA buoy using a wind speeddependentdrag coefficient[Wu, 1980]. Forcingsby surface
heat andcoastalbuoyancyfluxesare excludedbecauseof a lack
of data.
turbulenceclosuresubmodel[Mellorand Yamada,1982] the
To initialize the densityfield, we use hydrographicsections
frictionalforcesevolvewith the flow and densityfields.
from
March and May 1998; April 1998 hydrographyis not
The model domain(Figure 1) extendsabout750 km along
shelf from the Florida Panhandleto the Florida Keys and available.Each sectionshowsa well-definedpycnocline.On
this basiswe initialize the model densityfield with a 4 o-t
about 400 km offshore from the coast. It covers the entire WFS
and part of the easternGulf of Mexico so that the shelfbreak densitychangethat spans20 m in the vertical, centeredon
region is resolved.Realistic shelf bathymetryfrom the Na- 20 m depth. To avoid speciousbaroclinicadjustments,this
tional Center for Atmospheric Researchis usedwith 1500 m initial densityfield is input without horizontalgradient.Subbeing the maximumdepth beyondthe shelf break and 5 m sequentdensityfield evolutionoccursin dynamicalbalance
beingthe minimumdepthat the coastline.The horizontalgrids with the appliedforcing.A twin experimentwith densityset
range in size from 6.5 to 15 km, with an averageof 9 km. constant
at 1023kg m-3 is alsoperformed
to comparethe
WEISBERGET AL.: WESTFLORIDA SHELFRESPONSETO LOCAL WIND FORCING
31,243
Across-shelf Velocity Component
a i i ßi .j • i i i j i i
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Along-shelfVelocityComponent
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Time (day)
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April 1998 (day)
•isure 4. April•998stratified
modelsimulations
of (a) across-shelf
and(b) alone-shelf
vclocJ•components
and(c)isopycnal
variations
sampled
atthe20misobath
offshore
ofSarasota,
Florida,
a]on•with(d)thewind
vectorsusedto drivethemodel(withnorthup andeastto thed•ht). The contourJntc•alsare0.05m s- • for
the vdocJtycomponents
and0.5 sigmaunitsfor the
responsesunder stratified and unstratified conditions. Clarke stratifiedcases,respectively,
and Figures3c and 3d showthe
and Brink [1985],throughscaleanalysisof the shallowwater windstress
vectortime seriesusedto forcethe model.Agreeequations,
showthat the response
of a wide shelf(with small mentisverygoodfor the stratifiedcase;it isnot asgoodfor the
Burgernumber(L•/L) •, whereL• is the Rossby
radiusof constantdensitycase.While the generalpatternsof sealevel
deformation
at the shelfbreakandL is the shelfwidth) to responsesto upwellingand downwellingfavorablewinds are
synoptic
wind fluctuations
shouldbe barotropic.Mitchurn,and replicatedin both cases,considerable
quantitativemismatch
Clarke[1986b]suggest
that(L•/L) 2 < 10-: fortheWFS,and existsbetweenin the modelresponses
andthe observations
for
this magnitudeis consistentwith the stratificationused here. the constantdensitycase.In particular,the overestimatefor
The stratifiedand constantdensityexperiments
providean the upwellingresponsearoundday 23 impliesan excessive
opportunity
to examinethisbarotropicresponse
conceptwith across-shelf
volumetransportoverthe innershelfregiondura primitiveequationmodel.Fifteendaysof modelstartup are ingthisevent.Sincea verticallyintegratedacross-shelf
volume
performedusingobservedwindsprior to samplingthe model transportin excessof the volumetricrate of sealevel change
resultsforApril 1998.Sincewe findthepressure
fieldresponse canonlyoccurin a three-dimensional
flow,suchdisparityon
to be largelybarotropic,consistent
with the Burgernumber agreementswith in situ data between the stratified and conargument,the spin-uptime is on the orderof a pendulumday stantdensitymodelsimulations
impliesthat stratification
sigand muchlessthan the 15 daysthat we used.
nificantlyaffectsthe three-dimensionalflow field.
4.
Comparison Between the in Situ Data
and the Model
4.1.
Sea Level
Results
4.2.
Currents
Modeledalong-shelfand across-shelf
components
of velocity from the 20 m isobathoff Sarasota,Florida, are shownin
Figure4. As is the casefor sealevelunderstratifiedconditions,
Comparisonsbetweensealevel observedand modeled at St. the model reproducesthe generalpattern evolutionof the
Petersburg,
Florida,for the monthof April 1998are shownin observed
velocitycomponent
variations(Figure2). All three
Figure3. Figures3a and3b are for the constantdensityand upwellingfavorablewindeventsdrivedowncoast
jetswithver-
31,244
WEISBERG
ET AL.: WEST FLORIDA
•a I •
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9
SHELF RESPONSE TO LOCAL WIND FORCING
Across-shelf Velocity Component
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Velocity
Component
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20
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c
_
ß-- -lO
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13
April 1998 (day)
Figure 5. April 1998 constantdensitymodel simulationsof (a) across-shelf
and (b) along-shelfvelocity
componentssampledat the 20 m isobathoffshoreof Sarasota,Florida, alongwith the wind vectorsusedto
drivethe model(withnorthup andeastto theright).The contourintervals
are0.05m s-• for thevelocity
components.
tical structuressimilar to those observed,somewith subsurface
locityare the primarycontributors.Across-shelfadvectionover
and otherswith near-surfacemaxima.Thesedowncoast
jets are the lower portion of the water columnoccursas a boundary
accompanied
by onshore(offshore)flow over the lower (up- layer responseto the coastaljet. Sincethe coastaljet tendsto
per) portion of the water column.Similarstatementsapplyfor be maximumwhen the sealevel responseis maximum,acrossthe responsesto the downwellingfavorablewind events,i.e., shelf and vertical advection are also maxima at that time. Thus
upcoastjets and across-shelf
flow reversalswith depth.While upwellingand downwellingisopycnaldisplacement
maximaocthe pattern evolutionsfor the modeledand observedcurrents cur at the transitionsbetweenupwellingand downwellingfaare generallysimilar, differencesin details exist for several vorablewinds, accountingfor the lag between the isopycnal
reasons.First, the model simulationsare highly dependent displacementsand sea level. This phaserelationshipcontrasts
upon stratification,and our initial stratificationis merely a that of an inviscid,standingbaroclinic mode for which the
guessbasedupon limited measurements.
Second,no provision isopycnaland sea level responsesoccur in an antiphaserelais made for (unknown)surfaceheat fluxesor for correcting tionship, demonstrating the importance of the frictional
inevitabledeparturesof the model stratificationfrom nature boundarylayers.By not imposinga surfaceheat flux the isopyover the courseof the 45 day integration.Third, we use spacnalsalsotend to slopeup with time, reducingthe stratificatiallyuniformwindswhenthe spatialstructureof eachsynoptic tion.
weather systemmay be different. Despite theseshortcomings
As with sealevel, the twin experimentwithout stratification
the quantitative agreementsare surprisinglygood, with the
yieldsresultsfor the currents(Figure5) that are both qualitabest agreementsoccurringduring the downwelling/upwelling
tively and quantitativelydifferent from the observations.
For
sequenceof April 7-13. Here the model underestimatesthe
the along-shelfcomponentthe vertical shear is much more
magnitudeof the along-and across-shelf
componentsby about
20%. For other sequencesthis magnitudemismatchis either uniformwith depth,but the more interestingcontrastis in the
component.Without stratificationthere is very
larger or smaller,and for the reasonsstatedabovethere is little across-shelf
gained by more detailed comparisons.One clear deficiency little turning in the surfaceand bottom boundarylayers,and
circulationrelativeto the
comparingthe modelwith the data lieswithin the upper3 m of hencethere is very little across-shelf
results with stratification.
This behavior
for the across-shelf
the water columnwherethere are no data.The modelpurports
large vertical shear over the upper few meters becauseits componentmimicsthe longer-termobservationalrecord that
turbulenceclosureroutine yieldssmall eddyviscosity(turbu- showspronouncedvelocityvectorturningduringtimesof anlencelengthscaleis zero at the surface).Whether or not such ticipated stratificationversuslittle turning during timeswhen
near-surface shear is realistic remains to be determined.
the water columnis expectedto be well mixed.On the basisof
betweenthe in situdata andthe stratAlso depictedin Figure 4a are the modeledisopycnalvari- the generalagreements
ations. Relative maxima in isopycnal displacementsoccur ified model results we now use the model to discuss the flow
when the across-shelfcomponentis zero, suggestingthat ad- field kinematicsand dynamicswith emphasison the downvectivechangesthroughhorizontaldivergenceand verticalve- welling/upwelling
responsesequencefrom April 7 to 14.
WEISBERG ET AL.: WEST FLORIDA SHELF RESPONSE TO LOCAL WIND FORCING
(-0.55-0.23)
m'• . •
ß
day12
day 8
•
(-0.11-0.18) m
day 9
day 13
(-0.3-0.12)
(-0.11-0.32) m
day10
• _•
1
m
day 14
(-0.25-0.14)
,
,
,
,
3
5
7
9
m
, - ,
11
13
15
17
19
21
23
25
27
29
April 1998 (day)
Figure 6a. Daily snapshots
of the stratifiedmodel-simulated
WFS sea surfacetopographyspanningthe
periodof downwelling
andupwellingbetweendays7 and 14. The contourintervalis 0.02m, andthe ranges
for sea level are given in parentheses.
31,245
31,246
WEISBERGET AL.: WESTFLORIDA SHELFRESPONSETO LOCALWIND FORCING
(-0.17~0.07)
m
•
ß
day
8
(-0.11~0.26)
m
(-0.59~0.17)
m
ß
,,
day
9
day
10 day
'=•
(-0.1~0.13)
m
5
7
9
11
13
15
17
19
21
23
25
i
i
27
29
April 1998 (day)
Figure6b. Dailysnapshots
of theconstant
density
model-simulated
WFSseasurface
topography
spanning
theperiodof downwelling
andupwelling
between
days7 and14.Thecontour
intervalis0.02m,andtheranges
for sealevel are givenin parentheses.
WEISBERGET AL.: WEST FLORIDA SHELF RESPONSETO LOCAL WIND FORCING
Along-shelfVelocity Across-shelfVelocity
VerticalVelocity
31,247
Density
o
log
J::
50
,
•o•
-=
50
J::
50
r-
50
I•
day11
lOO
0
.
day 12
day 12
lOoO
50
day 13
lOO
200
300
400
200
Distance(km)
-10 I-
1
I
3
I
5
I
7
300
400
200
Distance(km)
I
9
I -
11
I
13
300
400
200
Distance(km)
I
15
I
17
I
19
I
21
300
400
Distance(km)
I
23
I
25
I
27
-,
29
April 1998 (day)
Figure7a. Dailysnapshots
of the along-shelf,
across-shelL
andverticalvelocitycomponents
anddensity
sampled
alonga cross
section
offshore
ofSarasota,
Florida,spanning
theperiodofdownwelling
andupwelling
between
days7 and13.Thecontour
intervals
are0.05m s-1 forthehorizontal
velocity
components,
10-5 m
s-• forthevertical
velocity
component,
and0.5sigma
unitsfordensity.
5.
Model
Flow Field Kinematics
The orderof presentation
includesplanarviewsof sealevel,
crosssectionsof velocityand densityat the Sarasotatransect,
andplanarviewsof currents.
We beginwithdailysnapshots
of
sealevelfrom day7 throughday14 (Figure6a) for the stratifiedexperiment.
Peakdownwelling
andupwelling
responses
in
the sealevelfields(aswith all otherfields)appearon days9
and 12, respectively.
During thesepeaksthe setdownat the
coastfor the upwellingresponsein generalis more than a
factor of 2 larger than the setupat the coastfor the downwellingresponse.Moreover,the offshorescalefor the upwellingresponselargelyexceedsthat for the downwelling
re-
31,248
WEISBERG
ET AL.: WEST FLORIDA
SHELF RESPONSE TO LOCAL WIND
Along-shelfVelocity Across-shelfVelocity
ay
•
FORCING
VerticalVelocity
ay
OoO
.c:
50
ay
OoO
.c:
50
•
ay
ay
OoO
.c:
50
•
10g
.c:
'
y o
ay'0
a'
ay11
ay1,1•
50
•'
•
lOO
,•. 0
•
ayo
ay1
,.....
50
•
day 12
day 12
day 12
lOO
ay 13
ay 13
lOO
200
300
Distance(km)
400
200
300
Distance(km)
400
200
300
400
Distance (km)
Figure 7b. Daily snapshots
of thealong-shelf,
across-shelL
andverticalvelocitycomponents
for theconstant
densitycasesampledalonga crosssectionoffshoreof Sarasota,Florida,spanningthe periodof downwelling
and upwelling
betweendays7 and 13. The contourintervalsare 0.05m s-• for the horizontalvelocity
components
and10-5 m s-• for theverticalvelocity
component.
sponse.The transitionsto thesepeak responsesshowalongand across-shelf
surfaceheightgradientsof comparablemagnitude. While no clear senseof propagationemerges,it does
appearthat the along-shelfvariationsin geometry,particularly
the relativelynarrowshelfin the north and the partial closure
by the Florida Keysin the south,play rolesin determiningthe
sealevel adjustments.The end resultsare monotonicsealevel
slopeswith coastalmaxima, but the transitionsto these end
statesare more convoluted,suggestiveof complicatedflow
6a (in bothmagnitudeandoffshorescale),the constantdensity
experimentyieldssea level displacementmagnitudesthat are
nearlyproportionatewith the wind stressand that have comparableoffshorescalesfor either upwellingor downwelling.
Crosssectionsfor the along-shelf,across-shelf,
and vertical
velocitycomponents
and densityoffshoreof Sarasota,Florida,
are shownin Figure7a. Our focusis againon the day9 andday
12 peak responses.On day 9 we see an upcoastjet in the
along-shelf
component,
with onshoreflow overthe upperhalf
patterns.
and offshore flow over the lower half of the water column in
Similarplotsfor the constantdensityexperimentare givenin
Figure6b. Contrastedwith the asymmetric
responses
of Figure
the across-shelf
componentand with downwellingoccurring
synchronously
with the offshoreflow.In a parallelbut opposite
WEISBERG ET AL.' WEST FLORIDA
a.
SHELF RESPONSE TO LOCAL WIND FORCING
31,249
Across-shelfVelocityComponent(data)
I
I
I
I
I
I
I
I
J
I
11
13
15
17
19
21
4
7
10
13
16
19
•E22
.c 25
e 28
31
34
37
40
43
1
3
b.
23
Along-shelfVelocityComponent(data)
I
I
I
I
I
3
5
'
7
'
9
I
I
I
I
I
I
'
17
'
19
21
23
i
i
25
27
29
i
I.
i
i
4
7
10
13
16
19
,[E22
-'= 25
ß 28
31
34
37
4O
43
1
----
ß-: -10
•
• 1'1 13'
15
'
25
27
29
27
29
C
1
•
3
•
5
7
•
•
• 11
I 23
• 25
•
9 11 13 1•5 17
9 21
April 1998 (day)
Figure 8. April 1998measurements
of (a) across-shelf
and (b) along-shelfvelocitycomponentssampledat
the 50 m isobathoffshore
of TampaBay.The contourintervalsare0.05m s-• for thevelocitycomponents,
north is up and eastis to the right for the wind vectors,and all data are low-passfilteredto excludeoscillations
at timescales
shorter than 36 hours.
sense,on day 12 we see a downcoastjet in the along-shelf lower portion of water occurover the entire offshoreextentof
component,with offshoreflow overthe upperhalf and onshore the coastaljet for either upwellingor downwellingsituations.
flow over the lower half of the water column in the across-shelf
Sincethe upwellingresponseexistsover a largeroffshorescale
componentand with upwellingoccurringsynchronously
with than the downwellingresponse,the across-shelf
transportsof
the onshore flow. Because of the frictional
effects of the
water for upwellingoccurover larger distancesthan for downboundarylayers,the coastaljet has a vertical shear structure welling.
with isotachsbendingoffshorewith depth. This accountsfor
Similarplotsfor the constantdensityexperimentare givenin
the subsurface maxima that occur in both the in situ data and
Figure 7b. As found for sea level, the asymmetryin the curthe model simulation. In summingthe geostrophicinterior rentsunder stratifiedconditionsis replacedby a more proporwith the frictional boundary layer flows the velocity vector tionate responseunder constantdensity.With the offshore
turns counterclockwise over most of the water column. This is
scalesof the coastaljet, the surfacedisplacementbeing equal,
shownfor the WFS by Weisberg
et al. [2000] and for the New the differencein scalesfor the upwellingand downwelling
Jerseyshelfby Munchowand Chant [2000].As is the casefor responses
understratifiedand constantdensityconditionsparsealevel, the magnitudesand offshorescalefor the peak up- allels that in Figures6a and 6b.
Evidencefor this model-basedassertionof asymmetryexists
welling responseare substantiallylarger than for the peak
downwellingresponse.Since the bottom Ekman layer is a in simultaneous in situ data that were collected on the 50 m
responseto the coastaljet, across-shelftransportsover the isobath(Figure 8). The samecoastaljets as seenin shallower
31,250
WEISBERG ET AL.: WEST FLORIDA SHELF RESPONSETO LOCAL WIND FORCING
(a)depth-averaged
(day9).max:
0.34mffI
(b)subsurface
(day9).max:0.53m,.•
1
(c)mid-level
(day9).max:0.36m,.•
1
(d)near-bottom
(day9).max:0.09ms
-1
Figure9. Horizontalvelocityvectorfields(a) depth-averaged,
(b) near-surface,
(c) midwater,and (d)
near-bottom,
sampled
duringthe peakdownwelling
eventon day9. Vectorsare shownfor everyothergrid
pointwith the maximumvaluefor eachpanelgivenin the panellegend.The near-bottom
vectorsare
magnifiedby a factorof 2 relativeto the otherpanels.
water(Figure2) appearhere,butwithlessverticalstructure,as Horizontalvelocityvectormapsfor the depth average,nearin the model. For each wind-driven flow reversal we see that
surface,middepth,and near-bottomfieldsare shownin the
for the day 9 peak downwelling
the near-surfaceEkman layer response(extendingdown to Figures9a-9d, respectively,
The depth-averaged
flowisthe simplest
of thefields.
about20 m depth)is largerthanthe near-bottom
Ekmanlayer response.
directed
jet, confined
to theproximityof theshore,
response,alsoconsistent
with the model.Moreover,for the An upcoast
peak downwelling
responsearoundday 9 we seenearlyzero is seenwith maximumspeedsoccurringwherethe seasurface
across-shelfflow in the bottom Ekman layer versus about heightgradientis maximum.The jet is fed by surfaceEkman
that are onlypartiallyoffsetbybottomEkman
0.05 m s-• onshoreflow in the bottomEkman layerfor the layertransports
sincethe bottomEkmanlayeris effectedonly
peak upwellingresponsearoundday 12. Theseobservations layertransports
are consistentwith larger offshore extentsfor the surface where the surfaceheight gradientand coastaljet are estabdownstream.
The charheight field and the coastaljet under upwellingfavorable lished.Thusthe coastaljet accelerates
winds.
acterof the near-bottomflowalsochangesfrom the innershelf
jet, to the shelfbreak
The horizontalstructureof the velocityfield is complex. region,whereit is relatedto the coastal
WEISBERG ET AL.: WEST FLORIDA
SHELF RESPONSE TO LOCAL WIND FORCING
(a)depth-averaged
(day12).max:0.42m•1
(b)subsurface
(day12).max:0.59m• 1
(c)mid-level
(day12).max:0.59m•1
(d)near-bottom
(day12).max:0.13ms
-1
31,251
Figure 10. Horizontal velocityvector fields (a) depth-averaged,(b) near-surface,(c) midwater,and (d)
near-bottom,sampledduringthe peakupwellingeventon day12.Vectorsare shownfor everyothergridpoint
with the maximumvaluefor eachpanelgivenin the panellegend.The near-bottomvectorsare magnifiedby
a factor of 2 relative to the other panels.
region, where it arisesby topographicwave variability. The
origin of these near-bottomflow variationswill be evident in
the section6 dynamicalanalyses.The middepth vectorslook
verysimilarto the depthaveragevectorssincethere the acrossshelf flows due to the opposingsurfaceand bottom Ekman
layer flows are minimal.
A parallel set of velocitymapsare givenin Figure 10 for the
day 12 peak upwellingresponse.Similaritiesexistwith Figure
9 (albeit with oppositesign). ContrastingFigures9 and 10,
however,is the larger offshorescalefor the upwellingfields.
Strongonshoreflows in the bottom Ekman layer exist out to
about the 100 m isobath,particularlyin the northern part of
the domainwhere the magnitudeof the coastaljet is largest.
Bottom Ekman layer flows in the southern portion of the
domain are reducedby the adversepressuregradient due to
the partial closureby the Florida Keys.Stratificationalsotends
to promote regionsof flow field confluenceas seen at middepth.
A resultof the flow field kinematicsin switchingfrom downwelling to upwellingfavorablewindsis manifestin sea surface
temperature(SST). Platesla and lb showsatelliteadvanced
very high resolutionradiometer (AVHRR) SST imageson
April 10 and 13 when the downwellingand upwellingcirculations, respectively,culminate in isopycnaldisplacementmaxima. The month of April, in general,showsa cold tonguethat
extends downcoastat midshelf from a region of seasonally
31,252
WEISBERG ET AL.: WEST FLORIDA
SHELF RESPONSE TO LOCAL WIND FORCING
x 10-4
Along-shelf
Direction
i
i
i
i
i
i
1
I
I
i
•' •-Pressure
gradient
0.5
0
:'
Tendency
terrn-•",...,"
.T'.
Wind
....
•......
•'""-""""•0•-'/'•
•'•..•••,'i-.
-o.5
-1
-1.5
x 10-4
4
Across-shelf
Direction
i
i
i
I
i
i
I
1
3
,
5
,
7
i
i
i
i
1•I
•
,
/.
o
•
9
i
./' \ '.
i
i
•
/•-Coriolis
,
13
•
15
,
17
,
19
i
i
i
i
i
!/
b
i
, 2•1 23'
i
x<--Lower
column
transport
\
•'""•.
i
• oT_•-•,-•//-<••
%•
••-1 I
Upper
columntranavia./
•
i
i
25
,
27
•
29
,
i
i
i
•-•-
.• I•Expected
Ek•ntransport
-2
I
I
I
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I
I
I
I
I
I
I
I
I
I
I
1
3
5
7
9
11
13
15
17
19
21
23
25
27
29
/
I
I
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I
I
/
:•:•'
3
i
'• %' •
•.
11
i
•-Pressure
gradient
,•,' • t '•
,•
i
AgeostrophicField
I/
I
I
I
I
I
•:.•:':•'• .•4..'i•.,-" .::.'ii•;•:•:•}
.....•......
,:.•i,,:::'
•'•....,.•.•••'
.•- ß....
;•.... •...............
ß
.... ß
ß
..........
<•
....• •'.•'.•'.•:•'"•:•
.....................
...-"
• ' .•'.-'•:'
..,'...'.,'::.•.•r•:•
...............
...........
,...•"'"":
.v::"'":•:.
,•
•:'•'•"'-•-•*•:•-•:•'"-•>'•5;•t•'.•:,•
.......
•......
"•.... •g'
•14
17
20
1
3
5
7
9
11
13
15
17
19
21
23
25
27
29
Time (day)
Figure 11. Time seriesof the verticallyintegrated(a) along-shelfand (b) across-shelf
momentumbalance
termsand (c) the across-shelf
transports,alongwith (d) the across-shelf
ageostrophic
momentumresidual,all
sampledat the 20 m isobathoffshoreof Sarasota,Florida, from the stratifiedmodel simulation.
coldest
SST in the northeastern
Gulf
of Mexico.
Associated
with this boreal spring cold tongue is a chlorophyllplume,
referredto asthe "greenriver"by Gilbeset al. [1996].Thiscold
tongueis evidenton April 10 with warmerwatersboth inshore
and offshore. Transitioningfrom downwellingto upwelling
winds,the cold tongueon April 13 is greatlyamplifiedand the
inshorewaters are severaldegreescolder than on April 10. A
regionof locallycoldestSST is alsoseensouthof Tampa Bay
on about the 25 m isobathconsistentboth with the region of
maximumverticalvelocityin Figure 7a and with the upwelling
casestudyresultsof Weisberg
et al. [2000].Farther southis a
imply that surfaceheat flux is not a contributingfactor, these
SST changesare consistent
with the kinematicalfeaturesof the
numerical
6.
6.1.
model
simulation
described
in this section.
Model Flow Field Dynamics
Momentum
Balances
We begin with vertically integratedmomentumand mass
balances(Figure 11) calculatedat the 20 m isobathoffshore
from Sarasota, Florida. The wind stressis the lead term in the
along-shelfdirection(Figure 11a).This causesa localacceleration as the currentstend to adjustto the time-varyingwinds,
layer inhibitionby adversepressuregradientshownin Figure followedby an along-shelfpressuregradient,a bottom stress,
10. Right at the shorelinein the Florida Big Bend regionand and a Coriolis acceleration,with all of these responseterms
alongthe Florida Panhandlewestof ApalachicolaBay,we also beingof comparablemagnitude(althoughthe along-shelf
pressee eruptionsof cold water to the surface.While we do not sure gradientis generallythe largestof these). In a purely
diminution
of cold SST consistent
with
the bottom
Ekman
WEISBERG ET AL.: WEST FLORIDA
SHELF RESPONSE TO LOCAL WIND FORCING
31,253
f
10 April 1998
i
dq
'
i
.
i ,a
1
".?'
r
ss?
I,,,,{,,,,{
1
Plate la. SatelliteAVHRR temperatureimagefor April 10, the time of warmestSST associated
with the
peak downwellingof day 9.
two-dimensionalflow the bottom stresswould be comparable 11e). The four time seriesare (1) the Ekman transport assoto the surface stress,whereas in this three-dimensional result ciatedwith the wind stress,(2) the verticallyintegratedupper
the bottom stressis no larger than the other secondaryterms. and (3) the lower layer transportsdirectedeither onshoreor
The verticallyintegratedacross-shelf
momentumbalance(Fig- offshoredependingon wind stress,and (4) the total vertically
ure lib) is much simpler(note the scalechangebetweenFig- integrated transport. The Ekman transport is computed as
ures 11a and lib). Here the verticallyintegratedflow is essen- Ue = rW/(pof, where r w is the along-shelfcomponentof the
tially geostrophicsincethe ageostrophic
contributionsfrom the wind stress.The upper and lower layer transportsare defined
surfaceand bottom Ekman layerstend to cancel.The magni- asUupper
= fC•r
uupper
dz, Utower
= fdrH Utower
dz,where
u
tudes of the terms in the across-shelf momentum
balance are
is the velocitycomponentin the across-shelf
direction,dr is the
about a factor of 4 larger than those in the along-shelfmo- depthat whichthe across-shelf
flowreversesdirection,r/is the
mentum balance.
free surfaceelevation,andH is the meanwater depth.The net
The three-dimensionalityof the flow field is also evidentin across-shelf
transportis Unet•- f•H U dz. The upper layer
the vertically integrated across-shelfmasstransport (Figure transportis alwayslessthan the Ekman transportbecausethe
31,254
WEISBERG
ET AL.' WEST FLORIDA
SHELF RESPONSE TO LOCAL WIND
FORCING
i
ß
i
ß
SST
20
i.
30
Plate lb. Satellite AVHRR temperatureimage for April 13, the time of coldestSST associatedwith the
peak upwellingof day 12.
20 m isobath is within
the inner shelf where there occurs an
upper layer across-shelf
transportdivergencealongwith the
surfaceslopesetup.Seawardof the innershelf,the upperlayer
transportis comparableto the Ekman transport.The upper
layertransportat thisparticularlocationis generallyovercompensatedfor by the lower-layertransport.A contributingfactor
is the along-shelfpressuregradient that supportsan acrossshelfgeostrophictransport.The along-shelfpressuregradient
appearsto be larger for upwellingfavorablewinds than for
downwellingfavorablewinds(Figure 11a). With massconvergence/divergenceinferred in the across-shelfdirection there
must be a massdivergence/convergence
in the along-shelfdirection to maintain continuity.The coastaljets offshore of
Sarasota,Florida, are thereforespatiallyacceleratingjets, and
a consequenceof this for upwellingfavorablewinds is an increase in the intensity of upwelling over what would occur
without the spatial acceleration.This is consistentwith the
region of maximumsurfacecoolingshownin Plate lb.
An asymmetryin across-shelftransportbetweenupwelling
and downwellingis alsoevidentin Figure 1l c. This asymmetry
arisesfrom the bottom Ekman layer as demonstratedby the
ageostrophicportion of the across-shelfmomentumbalance
(Figure 11d). The ageostrophic
part is definedas the residual
after addingthe Coriolisand pressuregradientterms.Both the
magnitudeandverticalextentof the ageostrophicresidualthat
comprisesthe bottom Ekman layer at this locationare larger
WEISBERG ET AL.: WEST FLORIDA
SHELF RESPONSE TO LOCAL WIND FORCING
31,255
0
PG
L• day
9
100
5O
./
50
Cl:5x10
-7ms
-2
h
5O
lOO
200
300
400
Distance (km)
:•!iili•;•
'•
C':5x10-?
ms-2
200
300
400
Distance (km)
Figure 12. The across-shelfmomentum balance during the peak downwellingevent on day 9 sampled
offshorefrom Sarasota,Florida,from the stratifiedmodelsimulation.The panelsare (a) Coriolis;(b) pressure
gradient;(c) their sum,or the ageostrophic
residual;(d) friction (primarilyvertical);(e) the sum of the
Coriolis,pressuregradient,andfrictionterms;(f) advectiveacceleration;
(g) the sumof Figures12e and 12f;
and (h) the localacceleration.
Contourintervalsare givenin eachpanel,and shadedregionsare negative.
for thethreeupwellingeventsthanfor the downwelling
events(in
particular,comparethe April 9 and 12 patterns).This findingis
oppositeto whatis expectedfrom stabilityarguments
for upslope
and downslopeflowsin a stratifiedfluid [Trowbridge
and Lentz,
1991].Here the bottomboundarylayeris consistently
largerfor
upwellingthan for downwelling
conditions!
To exploretheseissuesfurther,we analyzethe across-shelf
momentum balance over the Sarasota,Florida, transect.Fig-
ure 12 showsthe resultsfor the peak downwellingevent of
April 9. Figures12a-12h providethe sequentialorder of terms
that comprisethe momentumbalancein thiscoordinatedirection. Figures12a and 12b are the Coriolisand pressuregradient terms. Their sum (the ageostrophicresidual)is given in
Figure 12cfor comparisonwith the frictionaltermsof Figure
12d (wherefrictionis almostentirelyof verticalorigin). The
sumof Figures12c and 12d, in Figure 12e, is for comparison
31,256
WEISBERG
ET AL.: WEST FLORIDA
SHELF RESPONSE TO LOCAL WIND FORCING
0
b
1000
d
50
108
50
1000
h
so
I
200
300
400
Distance (krn)
7 I //
C':5x10-Zms-2
200
300
400
Distance (krn)
Figure 13. The across-shelf
momentumbalanceduringthe peakupwellingeventon day12sampledoffshore
from Sarasota,Florida, from the stratifiedmodel simulation.The panelsare (a) Coriolis;(b) pressure
gradient;(c) their sum,or the ageostrophic
residual;(d) friction(primarilyvertical);(e) the sumof the
Coriolis,pressure
gradient,andfrictionterms;(f) advective
acceleration;
(g) the sumof Figures13eand13f;
and (h) the localacceleration.
Contourintervalsare givenin eachpanel,andshadedregionsare negative.
with the advectiveaccelerationtermsin Figure12f.Finally,the
sumof Figures12e and 12f, in Figure 12g,is for comparison
with the onlyremainingterm, the localacceleration,
in Figure
12h. Closureis observedshowingthat the calculationis performedcorrectly.The lead termsare the Coriolisandpressure
gradient terms. The ageostrophicresidualis accountedfor
primarilyby the surfaceand bottom Ekman layers,and the
only other term of substanceis the local acceleration. The
pressure gradient is maximum near the coast, and it de-
creasesto zero by about the 50 m isobath. Modified by
surfaceand bottom friction, the coastaljet seenin the Coriolis term followsthe pressuregradient.The pressuregradient is relativelydepth independent;that is, it is primarily
barotropic,consistentwith the Burgernumberargumentsof
ClarkeandBrink [1985].The pressuregradient,however,does
decreaseacrossthebottomEkmanlayerbecauseof the sloping
isopycnalsthere.
The comparableanalysisfor the peakupwellingeventof day
WEISBERG ET AL.: WEST FLORIDA
SHELF RESPONSE TO LOCAL WIND FORCING
x 10-9
i
31,257
a
i
i
i
i
i
i
i
i
i
i
i
i
i
,.
'..<--Bottom
pressure
torque
ß
ß
.
Bottom
stress
torqu
.•• '
.
/-'r• '..
3,
•."-'/ "''" ".
'.,...•Q•
.(...•
/ i51/
./3
•'--'(--•ur•ce
st)?Ching•
"....
. ,':
,
.
/<--Dto/Dt
' '" '...'
,.
-2
1
3
5
7
9
11
13
15
17
19
21
23
25
27
29
Time (day)
•--
•
b
1
,
3
,
5
,
7
,
9
,
,
,
,
,
,
,
,
,
11 13 15 17 19 21 23 25 27 29
Time (day)
Figure 14. Time seriesof the vertically integrated vorticity balance terms sampled at the 20 m isobath
offshore of Sarasota, Florida, from the stratified model simulation.
12 is shownin Figure 13. The orderingof termsis the sameas
in Figure 12. The differenceis in the magnitudeand the offshorescaleof the Coriolis and pressuregradientterms. Here
the pressuregradient nodal line extends out to the 100 m
isobath,the coastaljet is muchstronger,and hencethe bottom
Ekman layer is much more developed.Oppositeto the downwellingcase,the pressuregradientincreasesacrossthe bottom
Ekman layer becauseof the slopeof the isopycnals
there. We
will return to this point in section7.
during the transitionswhen the sea surfaceslope is rapidly
changingand the coastaljets are weak. Sincethesetime series
are spatiallydependent,their horizontalfieldshelp to define
the inner shelf.
Figure 15 showsthe four fields for the day 9 peak downwelling response.Once the pressurefield and coastaljets are
established,the inner shelf is the region where the primary
vorticity balance is between the bottom stress and bottom
pressuretorques.At this time the stretchingof planetaryvorticity by free surfacedeformation is small everywhereexcept
6.2. ¾orticity Balance
for regionsof strongeddiesthat form along the shelf break.
Our analysisof the verticallyintegratedvertical component The bottom pressuretorque is large everywhere,but this tenof vorticityis similarto that of Ezer and Mellor [1994].Taking dencyto inducerelativevorticitycan onlybe offsetwherelarge
the curl of the verticallyintegratedmomentumequations,we near-bottom currentsare capable of producinglarge bottom
discussthe vorticitybalancewith respectto four terms: (1) stresses,i.e., only in the inner shelfregionfor this local windstresstorque, (2) bottom pressuretorque, (3) stretchingof forced experiment.Elsewhere,the imbalancein thesevorticity
planetaryvorticityby free surfacedeformation(plusthe plan- tendencyterms leads to a large material rate of change of
etarybeta effect), and (4) the materialrate of changeof rela- relativevorticity.Thus the primarybalancefor the inner shelf
tivevorticity(plusthe stretchingandtiltingof relativevorticity is between the bottom stressand bottom pressuretorques,
by the flow field). Sincewe employeda spatiallyuniformwind whereasthe primarybalancefor the shelfbreak is betweenthe
stress,the stresstorque is entirely due to bottom stress.The bottompressuretorque and material rate of changeof relative
bottompressuretorque,throughthe bottom kinematicbound- vorticity. Similar field representationsfor the day 12 peak
ary condition,is the stretchingof planetaryvorticityby geostro- upwellingresponseare shownin Figure 16. The conclusions
phic flow acrossthe slopingbottom. This is generallymuch are the same aswith Figure 15 with the added point of asymlarger than the stretchingby free surfacedeformation(or by metry. The offshorescaleof the inner shelfis larger for the day
the planetary beta effect that we lumped together with free 12 upwellingresponsethan it is for the day 9 downwelling
surfaceterm). The residualof thesetendenciesis the variation response.
in relativevorticity (that we lumped togetherwith the kinematical
terms associated with the flow field deformations
of
relativevorticityandwith the relativelyinsignificanthorizontal
diffusionterms).
7.
Summary and Discussion
How water movesacrossthe shelfis the underlyingphysical
These four terms calculated at the 20 m isobath offshore of
oceanographicquestionpertinent to multidisciplinarycontiSarasota,Florida, for April 1998 are given in Figure 14. The nental shelf studies.Boundary layer and eddy transportprobottom stressand bottom pressuretorquesare the lead terms, cessesare involvedbecauseof the vorticity constraintby the
althoughthe other two termsmaybe of comparablemagnitude slopingbottom. Understandingthese processespresupposes
31,258
WEISBERG ET AL.: WEST FLORIDA SHELF RESPONSE TO LOCAL WIND FORCING
;!1D1.•5_D:
8.9,:
1x10_9ms_2
\•'('/•'(•• •!3C•)_r'971•;
1x10_9
m
s_2
• ottom
stress
torque
Figure 15. Horizontaldistributionfieldsfor the verticallyintegratedvorticitybalancetermsduringthe peak
downwelling
eventon day9: (a) the materialrate of change,plustiltingandstretching
of relativevorticity;(b)
the stretchingof planetaryvorticityby changesin the free surface,plus the planetarybeta terms;(c) the
bottompressuretorque;and (d) the bottomstresstorque.Contourintervalsand rangesare givenwith each
panel, and shadedregionsare negative.
an understandingof the shelfresponses
to its variousforcing
agents:momentuminputat the seasurfaceandshelfbreakand
buoyancyinput at the seasurface,shelfbreak,andland. Since
eachcontinentalshelfis different, and sincesomanyprocesses
are involved,it is useful to isolate regionsand forcing conditionsto answersmallersubsetsof questions.Along thisveinwe
focuson the WFS, which is wide enoughfor its inner shelf to
be distinguished
from the shelfbreak. Using in situ data and a
ing the sealevel and circulationof the inner shelfwhen forced
by localwindsonly. We concludethat local windsare a major
driver of the inner shelf circulation. However, stratification
impactsthe natureof the circulationand the across-shelf
transports, and it doesthis by affectingturbulenceand hencethe
verticalscalesof the surfaceand bottom Ekman layers.When
theselayersare verticallyconstrained,throughthe suppression
of turbulence by stratification,the velocity vector turning
numerical model simulation, we ask how well the currents over within the boundarylayers increasesover that for constant
the inner shelfare accountedfor by localwind forcingalone.In density.Stratification,in thisway,largelyincreasesacross-shelf
doingthiswe describethe boundarylayer effectsthat account masstransportin responseto localwind forcing.
Flow field kinematicsand dynamicsanalysesshowthe WFS
for the transportsacrossthe inner shelf,providea dynamical
definitionof the inner shelf,and describean asymmetryin the circulationto be fully three dimensional(along-shorevariainner shelf responsesto upwellingversusdownwellingfavor- tionsare significant).These analysesdefinethe inner shelfas
able winds.
the regionwherethe surfaceandbottomEkmanlayersplayan
The model and in situ data comparisonshowsthat a prim- importantrole in the momentumbalance.Kinematically,the
itive equationmodel (in this casethe sigmacoordinatePOM inner shelf is where the Ekman layers induce a sea surface
With respectto verticallyintegrated
with Mellor/Yamadaturbulenceclosure)is effectiveat describ- slopethroughdivergence.
WEISBERG
ET AL.: WEST FLORIDA
SHELF RESPONSE TO LOCAL WIND FORCING
31,259
a) Do)/Dt
(-14-12.2):lxl 0-9ms
-2
ottom stress torque
(-14.2-20.7):
lxlO-9ms
-2
(-16
86)lx10-9ms
-2
Figure 16. Horizontal distributionfieldsfor the verticallyintegratedvorticitybalanceterms duringthe peak
upwellingeventon day 12: (a) the materialrate of change,plustilting and stretchingof relativevorticity;(b)
the stretchingof planetaryvorticityby changesin the free surface,plus the planetarybeta terms; (c) the
bottom pressuretorque;and (d) the bottom stresstorque. Contour intervalsand rangesare givenwith each
panel, and shadedregionsare negative.
vorticitythe inner shelfis the regionwhere the primary balance
is betweenbottom stressand bottom pressuretorques,as contrastedwith the shelf break where the primary balance is between the bottom pressuretorque and the material rate of
changeof relative vorticity.
An asymmetryis found in the WFS responseto upwelling
and downwellingfavorablewinds,wherein the magnitudeand
offshoreextent of the responsesto upwellingfavorablewinds
exceedthosefor downwellingfavorablewinds under stratified
conditions.While this asymmetryappearsin all of the dynamical analyses,theseanalysesalone do not provide an explanation. The asymmetryis due to stratificationas demonstratedby
comparingmodel twin experiments,one with and the other
without stratification.Asymmetryonly occursin the stratified
experiment.
While we are not aware of such downwelling/upwelling
asymmetrybeing reported elsewhere,MacCreadyand Rhines
[1991] and Garrettet al. [1993] provide a conceptualand ana-
lyticalbasisfor it. Their argumentis that stratificationimpedes
across-shelftransport in the bottom Ekman layer on a slope
when the buoyancyforce tendsto balancethe Coriolis force of
the along-shelfvelocitycomponent.We diagnosethis concept
from both momentumand vorticityperspectives.
With respect
to momentum the sea level responseto downwellingwinds
results in an offshore-directedpressure gradient force that
drivesthe offshore-directedflow in the bottom Ekman layer.
Isopycnalsbendinginto the bottom result in a buoyancyforce
that opposesthis (Figure 12). In contrastto downwellingthe
sea level responseto upwellingwinds resultsin an onshoredirected pressure gradient force that drives an onshoredirectedflow in the bottom Ekman layer. Isopycnalsbending
into the bottom now result in a buoyancyforce that enhances
this (Figure 13). Granted,fewer isopycnals
bend into the bottom; nevertheless,the ones that do act constructivelyrather
than destructively.
The simplestexplanationfor the asymmetryderivesfrom the
31,260
WEISBERG
ET AL.: WEST FLORIDA
Tilting
•
SHELF RESPONSE TO LOCAL WIND FORCING
Buoyancytorque
Dissipation
Otherterms
50
lOO
lOO
200
300
Distance(km)
200
300
Distance(km)
200
300
Distance(km)
200
300
Distance(km)
Figure 17. An analysisof the along-shelfcomponentof vorticityduringthe peak downwellingandupwelling
responses
on (a) day 9 and (b) day 12, respectively.
From left to right in eachpanel are (1) the tilting of
planetaryvorticityfilamentsby the shearedalong-shelfjet, (2) the buoyancytorque, (3) the dissipationof
relativevorticityby the shearedacross-shelf
flow,and(4) the localrate of changeof relativevorticity,plusthe
remainder of other omitted terms. The contour interval is 10-7 s-2.
streamwisecomponent of vorticity. For a stratified Ekman
layer we considerthe balance between the tendenciesto in-
interferencebetweenplanetaryvorticity tilting and buoyancy
torque is observedfor downwelling,versusconstructiveinterducerelativevorticityby (1) the tiltingof planetaryvorticityby ferencefor upwelling.Similarresults(not shown)arefoundfor
the verticallyshearedalong-shelf
jet, (2) the buoyancytorque the other two downwellingand upwellingpairs.The buoyancy
by the slopingisopycnals,
and (3) the dissipationof relative torque(byisopycnals
bendinginto the slopingbottom)hasthe
vorticityby the verticallyshearedacross-shelf
flow. Equation same signfor downwellingand upwelling,whereasthe tilting
(1) expresses
thisbalance,with terms1-3 on the left-handside term reversessign.
and the local rate of change of relative vorticity, plus the
A corollaryaffect, expandedon by Garrettet al. [1993] in
omitted residualterms on the right-handside:
relationshipto the Lentzand Trowbridge
[1991]and Trowbridge
and Lentz [1991] findings,is an asymmetryin the bottom
(1) boundarylayerverticalscaledue to the stabilizing/destabilizing
+
g
=
influencesof upslopeand downslopeflows.While related,this
where u and v are the across-shelfand along-shelfvelocity is a differentphenomenonthat appearsto be contraryto our
components,respectively,p is density,K is the vertical eddy finding(in Figure 11) that the bottomboundarylayerscaleis
by
coefficient,and R is the residual.For downwelling,planetary actuallylarger for upwelling.We reconcilethis discrepancy
vorticitytilting tendsto be balancedby buoyancytorque, re- noting that our larger boundarylayer scalefor upwellingfolquiring less relative vorticity dissipation.For upwelling the lows from the larger upwellingresponse.Had the upwelling
buoyancytorque,while reducedin magnitudefrom the down- and downwellingresponseson the WFS been of equal magniwelling case,adds to the planetaryvorticity tilting, requiring tude with regard to the interior along-shelfflows, as in the
increasedrelativevorticitydissipation.We demonstratethese numericalexperimentsreported by Garrettet al. [1993], then
effectsin Figure 17 by comparingthe peak downwellingand we wouldhaveexpectedresultssimilarto theirs.Asymmetryin
upwellingresponses
on days9 and 12, respectively.
Destructive the bottom boundarylayer is important in nature for the rea-
WEISBERG ET AL.: WEST FLORIDA
SHELF RESPONSE TO LOCAL WIND FORCING
sonsespousedin theseearlier papers,includingWeatherlyand
Martin [1978].
The inner shelf providesadded importance to these stratified boundarylayer conceptson a slope. For the inner shelf
the surfacepressuregradient set up by surfaceEkman layer
divergence,the geostrophicinterior flow adjustment to the
pressuregradient, and the bottom Ekman layer reaction to
the interior flow all occur nearly in unison. Anything that
impedesone of these three stepswill impede all of them.
Thus, by inhibiting (or promoting)the bottom Ekman layer,
thereby reducing (or increasing) the near-bottom divergencethat is necessaryto feed the near-surfacedivergence,
stratificationproducesthe asymmetryin the magnitude and
offshoreextentof the responses
to downwellingand upwelling
favorable
winds.
A physicalconsequenceof asymmetryis the rectificationof
the shelfresponseto oscillatorywinds.This providesa possible
explanationof why the region southof Tampa Bay was found
by Yang et al. [1999] to be devoid of surface drifter tracks
during a year long set of deployments.Stratification-induced
asymmetrymay alsohave importantbiological,chemical,and
geologicalconsequences.
In analogyto a flapper valve, with
upwelling responsesfavored over downwelling responses,
near-bottommaterial propertiesare more readily transferred
into, than away from, the near-shorezone. Support for this
comesfrom unpublishedhydrographicdata (G. Vargo, personalcommunication,2000) that showlarge chlorophyllfluorescenceextendingacrossthe shelfin the bottom Ekman layer.
In the along-shelfdirectionthe rectificationof material property transportsby the coastaljets may alsobe important,impacting, for instance,long-term sedimenttransport. Further
theoreticaland observational
studiesare neededto explorethe
ramificationsof stratification-induced
asymmetryon the continental
31,261
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Gill, A. E., Atmosphere-Ocean
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northern California shelf,J. Phys.Oceanogr.,21, 1186-1202, 1991.
Lentz, S. J., R. T. Guza, S. Elgar, F. Feddersen,and T. H. C. Herbers,
Momentum balanceson the North Carolina inner shelf,J. Geophys.
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Ph.D. thesis,309 pp., Univ. of South Fla., St. Petersburg,1998.
Li, Z., and R. H. Weisberg,WFS responseto upwellingfavorablewind
forcing:Kinematics,J. Geophys.Res.,104, 13,507-13,527, 1999a.
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MacCready, P., and P. B. Rhines, Buoyantinhibition of Ekman transport on a slope and its effect on stratifiedspin-up,J. Fluid Mech.,
A related conclusionis that the seasonaland synopticscales
cannotbe fully separated.With synoptic-scale
wind-forcedresponsesdependent on stratificationit is necessaryeither to
assimilatedensity data into a model or to simulate density
changesthrougha combinationof surfacebuoyancyfluxesand
activeoffshoreboundaryconditions.In our casea 45 day (15
daysof startupand 30 daysof analysis)simulationworkedwell,
whereasattemptsto carry the model integrationlonger met
with increasingdeviationsfrom the in situ data because of
densityfield changes.Nowcastingand forecastingof the inner
shelfmustbe supportedby sufficientin situ data for density
field assimilationand boundaryconditions.
Acknowledgments. Support for this work derived from the Office
of Naval Research,grantN00014-98-1-0158;the National Oceanicand
AtmosphericAdministration, grant NA76RG0463; and the Minerals
Management Service,contract MMS 14-35-0001-30804.G. Mitchum
offered helpful discussions;R. Cole, J. Donovan, R. He, and W.
Hemme assistedwith the data collectionand analyses.
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