Impact of exchange flows on wetland flushing
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Andradottir, Hrund O., and Heidi M. Nepf. “Impact of exchange
flows on wetland flushing.” Water Resources Research 37.12
(2001) ©2001 American Geophysical Union
As Published
http://dx.doi.org/10.1029/2001WR000257
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American Geophysical Union
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WATER RESOURCES RESEARCH, VOL. 37, NO. 12, PAGES 3265-3273, DECEMBER
2001
Impact of exchange flows on wetland flushing
Hrund(3.Andrad6ttir
• andHeidiM. Ncpf
Ralph M. ParsonsLaboratory,Department of Civil and EnvironmentalEngineering
Massachusetts
Institute of Technology,Cambridge,Massachusetts,
USA
Abstract. The flushingof littoral regionsis governedby barotropicriver flows,QR, and
baroclinicexchangeflows,AQ. This note presentsfield observationsof two different
flushingregimesin a shallowwetlandthat bordersa lake. In spring,when river flowsarc
high, the wetland circulationis river- or jet-dominated,AQ/QR < 1, and the river shortcircuitsthroughthe wetland in a much shortertime than the nominal residencetime.
During summerlow flows,however,the wetlandcirculationis dominatedby exchange
flows,AQ/Q• > 1, that vary both on diurnal and synoptic(10-20 days)timescalesin
responseto differentialheatingand coolingbetweenthe wetland and lake and to wind.
These exchangeflowscan enhancewetlandflushingby a factor of 10 relativeto river
flushing.A one-dimensionald½couplcd
heat and flow model representsdiurnal exchange
flowsin this systemwell and may be usedto assess
the importanceof exchangeflowsin
other systems.
exchangeflowsbetweena shallowwetland and a lake, (2)
characterizethe timescalesand magnitudesof the driving
Littoral regionsplay an importantrole in lake water quality. forcesproducingthe exchangeflows, and (3) evaluatethe
They receive,transform,and conductnutrientsand anthropo- relativeimportanceof exchangeflowsto river flowson wetland
genicchemicals
from terrestrialsystems
to lakes.The transport flushingover the courseof a year. The site and studymethods
of materialthroughtheseshallowregionsis governedby two are introduced in section 2. The field observations of the memajor mechanisms:
barotropicriver flows and baroclinicex- teorologicalconditions,exchangeflows,and wetland circulachangeflows(Figure1). The exchange
flowsare generatedby tion are summarizedin section3. Finally, section4 introduces
differentialheating and coolingbetweenregionsof different a simpleanalyticaltool that maybe usedto assess
the impordepth or opticalclarity and can thereforebe highlytemporal tanceof exchangeflowsin other shallowsidearmsystems.
[Monismithet al., 1990].Wind can either surpressor promote
theseflowsdependingupon the wind direction.For example,
winds have been found to increasethe flushingof shallow 2. Methods
estuariesby a factorof 3 [Geyer,1997].
2.1.
Site
To date,freshwaterexchangeflowshavebeenmostlystudied
TheUpperMysticLakeisa small(509,000
m2)dimictic
lake
in the lab or throughnumericalmodeling.The earlier studies
focuson the steadybarocliniccirculationin sidearmsof cool- located at the base of a contaminated watershed in suburban
(Figure2a). The AberjonaRiver deliving lakesand its role in improvingheat dissipation[e.g.,Bro- Boston,Massachusetts
card and Harleman, 1980]. More recent work considersthe ers nutrientsand heavymetalssuchas arsenicand lead from
exchangeflows in natural sidearmsand characterizestheir the watershedto the lake [Solo-Gabrieleand Perkins,1997].
temporalvariabilityand mixingproperties[Farrowand Patter- Beforeenteringthe lake, the river flowsthroughtwowetlands,
son, 1993;Sturmanet al., 1996;Sturmanand Ivey, 1998]. De- first,the largerupperforebay(140,000m2) and then the
are
spite their variabilitytheseflowshave been found to signifi- smallerlowerforebay(51,600m2).The lakeandforebays
cantlyenhancesidearmflushing[Sturmanet al., 1999;Horsch surroundedby treesand housesand a hill to the northwest.In
and Stefan,1988] and to contributeto lake nutrient budgets this note, we investigatethe exchangeflow betweenthe lower
[Jamesand Barko, 1991].Still onlyvery few field observations forebayand the lake that occursthrougha 60-m-widechannel
are availableto describetheseflows,especiallyfor wide and whichwe call the inlet. The lower forebayhasa generallyflat
shallow(<2 m deep)naturalsidearmssuchaswetlands.More bathymetry,exceptfor a 2- to 2.4-m-deepchannelthat runs
importantly,to the authors'knowledge,no studyhascompared from the necktowardthe lake inlet (dashedline on Figure2b).
the long-termimpactof exchangeflowson sidearmflushingto Owing to sailingactivitiesthe wetland is treated with herbithat of river flows.For example,there may be time periods cideseveryyear, leavingonly its borderand easternlobe denduringthe year when exchangeflowsare presentbut provide sily vegetatedwith water lilies and coontail in the summer
no additionalflushingbecausethe ratio of exchangeflow to months.The mean water depth in the wetland rangesfrom
river flow is much less than 1.
--•1.5 m in late summerto 1.9 m in early spring.The Upper
The goalsof thisnoteareto (1) providefieldobservations
of Mystic Lake beginsto stratify in April and remainsstratified
until it overturnsin November[Aurilioet al., 1994]. During
peak summerstratificationthe 22ø-27øCsurfacewater is sep•Nowat Mars& Company,
Greenwich,
Connecticut,
USA.
arated from the 4ø-7øChypolimneticwater by a 5-m-thick
Copyright2001 by the AmericanGeophysicalUnion.
thermoclinetypicallystartingat 5-6 m depth.A 1- to 1.5-mthick diurnalsurfaceheatinglayer can developin the lake on
Paper number 2001WR000257.
1.
Introduction
0043-1397/01/2001WR000257509.00
warm, calm afternoons.
3265
3266
ANDRADOTTIR
AND NEPF: TECHNICAL NOTE
a)
•i•(•)_Nec••.•.•.•'FoUrP•
Aberjon
River
q>w
I•"
./•'h'[,Lower
Wetland/Sidearm
rmoc,
L
Lake
Figure 1. Sidearmflushingis governedby river flows,QR,
andexchange
flows,,
AQ. The exchange
flowsare generated
becauseof differentialheatingand coolingbetweena sidearm
andlake (Tw 4: Tz.) andare modifiedbywindshearstress,rw.
•
2.2.
/,
,metres,,
Observations and Analysis
Two 4-dayfield studieswereconductedin 1997,the firstone
on April 14-17 duringhigh river flowsand the secondone at
the end of Julyduringlow river flows.Water speedand direction were sampledat the inlet at 10- to 30-cmdepthintervals
(5-7 pointsin the vertical) three to four times during each
studyusinga Sontekacousticdopplervelocimeter(ADV) with
a resolutionof 0.1 mm/s.The ADV wasdeployedfrom a boat
anchoredon both endsin April and from a free-standingrod
stuckinto the wetlandsediments
in July.The water speedwas
recordedat eachdepthfor 3-7 min at 12-15 Hz, a longenough
recordto unambiguously
removesurfacewaveor boat swaying
motions.The mobile ADV systemwas also usedto measure
the water speedsand directionsalongthe trajectoryfrom the
neck to lake inlet (Figure 2b) on April 17 and July 30-31.
Hourly Aberjona River flow was measuredby the U.S. GeologicalSurvey(USGS) approximately
800 m upstreamof the
entranceto the upper forebay.A flow rate factor of 1.06 was
applied to accountfor the additionaldrainagearea between
the USGS station and the lower forebay.Two independent
estimatesfor the exchangeflow rate, AQ • and AQ2, were
derivedfrom eachvelocityprofileat the inletby calculatingthe
flow rate in the upper and lower layers,Q • and Q2, and then
subtractingthe river flow rate, QR, from the outflowinglayer
(seeFigure 1). The cross-sectional
areasof the two layers,A •
andA 2, and the width of the interfacebetweenthe layers,w,
were estimatedfrom a traverseof depthmeasurements
made
acrossthe inlet at 3- to 5-m intervals.The relativemagnitude
of inertial and buoyantforceswas assessed
by calculatingthe
compositeinternal Froude number,G,
//
Neck
tDy
e ADV
/•r. •
ßCTDand
{ ' . O/.•X'X•'• Fvle;ø•t•t•t•
r
,,
ß•
100m
Figure 2. (a) The Upper MysticLake systemfield site and
monitoringprogram. Exchangeflows occur at the inlet betweenthe lower forebayand lake. Locationsof water temperatureprobesare denotedby T, anemometeris denotedby W,
andthe weatherstationis denotedby S. (b) A close-upon the
lowerforebay,with locationsof the acousticdopplervelocimeter (ADV) andconductivity-temperature-depth
(CTD) vertical profiles(Julystudy).
conductivity-temperature-depth
(CTD) profilesweretakeninsidethe wetlandand the lake on April 16 (9:00-10:00A.M.,
11:00A.M. to 1:00P.M.), April 17 (9:00-10:00A.M.), July30
(1:00-2:00 P.M., 3:00 P.M., and 6:00 P.M.), July 31 (11:30
G2= g 'A•/w -•g 'A2/w'
(1) A.M. to 1:00 P.M., 5:30-6:30 P.M.) and August(4:00-5:00
P.M.). A map of typicalfluorometerand CTD measurement
where u = Q/A is the meanwater velocityin eachlayer and locationsis portrayed on Figure 2b. A Differential Global
g' = gig2- P•l/P is the reducedgravitybaseduponthe PositioningSystemprovided 3- to 5-m accuracyon spatial
densityin the upperandlowerlayers,p• andP2[Dalziel,1992]. position.
Tracer experimentswere also conducted,in which 25 g and
In additionto the two field experiments,air temperature,
39 g of RhodamineWT dyewere releasedacrossthe width of relativehumidity,and solarradiationwere monitoredevery5
the neckover a 20-minintervalon April 17 (10:20A.M.) and min in the lower forebayfrom April throughNovember1997.
on July 30 (12:35 P.M.), respectively.The dye leaving the Simultaneously,
wind speed,W•o, and direction,0, were meawetlandwas monitoredover the first severalhoursfollowing sured10 m abovegroundat an unobstructedlocationat the
the releaseby measuringverticalprofilesof dye and temper- southern end of the lake at 10-min intervals. The measured
ature with vertical resolution of 2-5 cm at three different
windrepresents
well the conditions
overthe lake.The inlet and
locations across the lake inlet. In addition, fluorometer and wetland,however,may experiencesignificantwind sheltering
ANDRADOTTIR
AND NEPF: TECHNICAL NOTE
relative to the lake becauseof a nearbyhill and surrounding
houses and trees. The net heat fluxes over the lake were calculated from these measurements
3
/•,,
and cloud cover monitored
at the BostonLogan Airport (15 km east of the studysite)
using establishedempirical relationships[e.g.,Fisher et al.,
1979, p. 163]. Continuousrecordsof water temperaturewere
alsotakenat 5-min intervalsduringthe fall of 1997in the lower
forebayboth 10-20 cm belowthe surfaceand 10-20 cm above
the bed usingOnsettemperatureloggerswith 0.2øCresolution
and at 1-m intervalsin the shallowernorthern region of the
lake usingthermistorchainswith 0.1øCresolution[Frickerand
Nepf,2000](T on Figure2a). On the basisof verticaltemperature profilesin this systemthe depth-averaged
wetlandtemperaturewas found to be best representedas the weighted
averageof the continuoussurface(67%) and near-bed(33%)
temperatures.Similarly,the water temperaturerecordedcontinuouslyat 1.8 m depthwas found to most closelyrepresent
the depth-averagedwater temperaturein the lake epilimnion
(top 5 m). The longitudinaldensitygradientfrom the wetland
into the lake, Op/Ox,was calculatedbasedupon the depthaveragedtemperaturedifferencebetweenthe lake surfaceand
wetland
waters,
Ap=
a)
3267
-- 1997.
Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec
Sep 15
Nov 1
b) 500
-500
I
I
I
I
I
260
270
280
290
300
c)
• i , , ,
- plr•, andthelength
scale
forthe
longitudinaltemperaturegradient,Ax. Detailed CTD profiling
alongthe transectfrom the wetlandinto the lake indicatedthat
80-90% of the temperaturedrop occurredwithin 100 _+30 m
of the inlet, so Ax was chosenas 100 m. The longitudinal
gradientWedderburnnumber,
I
I
I
,.
I
I
260
270
280
290
300
260
270
280
290
300
260
270
280
290
300
E 5
ap
a /-/2max
Weg=
Tw
,
(2)
•'• 0
o
wasusedto estimatethe relativeimportanceof buoyancyand
wind stressin generatingthe exchangeflowswithin the inlet
channelwith maximumdepth,Hmax.The meanwind stress,*w,
alongthe directionof the flow axis(wetlandto lake), Ox,was
estimated
as
-5
e)
102
3'w-- parlOW•OcOS
(0 -- Ox)
,
(3)
wherePais the air density
andCso= 10-3 is thewinddrag
coefficient[Hickset al., 1974].Last,an opposingwindbalances
the buoyantforcingand producesminimum steadyexchange
flowswhenWea• - (7-9) [Andrad6ttir,
2000].On thisbasis
the criterionfor whichthe wind dominatesbuoyancywastaken
100
Julian Days
as
Figure 3. Meteorological conditionsin the Upper Mystic
Lake system.(a) AberjonaRiver flowrates.(b) Instantaneous
[Wel 8.
(4) (solidlines)and daily(circles)net surfaceheat fluxesper unit
The signof the Wea wasusedto determine
whetherthewind area. (c) Differencebetweenthe weightedaverageof surface
and near-bedwater temperaturein the wetland, Tw, and the
promoted
(Wea > 0) or surpressed
(Wea < 0) the density- temperatureat 1.8 m depth in the lake, T/•. (d) Mean wind
driven circulation.
speedsalonginlet axis(positivewind is into lake). (e) Wedderburnnumbers.For clarity,the recordshavebeen low-pass
filtered using a second-orderButterworth filter with cutoff
3.
Results
frequencyof 0.1 cpd and 0.5 cph.
3.1. Meteorological Conditions
As discussed
in section1, the two major flushingmechanismsin lake sidearmsare river throughflowsand exchange
flowsdrivenby differentialheatingand coolingand modified
by winds.Figure 3 summarizesthe variationin the meteorologicalconditionscontrollingtheseflushingmechanisms
in the
Upper MysticLake wetlandsystem.First, considerthe 10-day
averageAberjona River flow rate. Figure 3a showsthat the
river flow changesdrasticallyoverthe courseof the year from
meltto 0.1m3/sandlessduringthedrysummer.
Thisstrong
seasonalvariationin the AberjonaRiver flowis typicalof many
riversin temperateregions.
In contrastto the river flow, differentialheatingand cooling
betweena wetlandand lake occurspredominantlyon shorter
timescalesthan a year [Andrad6ttirand Nepf, 2000]. This is
particularlythe casefor wetlandsthat exchangewith a lake
approximately
2 m3/sduringspringsurface
runoffandsnow- much faster than annually and thus mimic the lake annual
ANDRADOTTIR
3268
AND NEPF: TECHNICAL NOTE
b)
April
a)
July
H
4/15 AM
-0.5
-0.5
I 4/14 PM
7/3O AM
I----I 7/30 PM
-1.5
-1.5
-2
Wetland
-2.5
-6
Lake
I
I
-4
-2
0
U (cm/s)
-2
I
I
2
4
6
-6
Lake
Wetland
I
I
-4
-2
I
I
0
U (cm/s)
Figure 4. Averagewater speedsbasedon 3- to 7-min recordsat the centerof the inlet betweenthe wetland
andlake in (a) April and (b) July1997.The horizontalbarsrepresent1 standarddeviationaroundthe mean
speed,after removingmotionsassociated
with boat sway,and are mostlyan indicationof water turbulence
levels.
heatingcycle.The close-upin Figure 3b showsthe net surface speedsare fairly constantthroughoutthe year in this system,
heat fluxesover the Upper MysticLake duringa typicallow windsare expectedto play an equallysignificantrole in modflowperiodin fall, whenQ/• < 0.4 m3/s.The surfaceheat ifyingthe barocliniccirculationduringotherseasons
not shown
fluxesvary considerablyover the courseof the day and from in Figure 3e.
dayto day as shownby the net dailyheat fluxes(circles).This
3.2.
Inlet Flow Characteristics
producesboth diurnaland synoptic(10-20 days)differential
heatingand cooling,where the wetlandwater oscillatesfrom
As shownin Figure 3, river flows vary predominantlyon
being 1ø-2øCwarmer to 1ø-2øCcolder than the lake surface seasonaltimescales,whereasfreshwaterexchangeflows are
waters (Figure 3c). Notice that the synopticvariationscan largelyforcedon synopticand diurnaltimescales.
This section
exceedthe diurnalvariations,for example,duringJ.D. = 280- provideswater current observations
that supportthesetime300. This strongsynopticcomponent,to the authors'knowl- scalesof variabilityand indicatehowimportantexchangeflows
edge,has not been previouslyreported in sidearmliterature. canbe relativeto river flowsfor wetlandflushing.
Last,windsoverthe Upper MysticLake blowpredominantly
Figures4a and 4b illustratemorning(dashedlines) and
from the south at 1.4-2 m/s in summer and from the north at
afternoon(solidlines)water speedprofilesat the centerof the
1.8-3 m/s in springand fall. A close-upon a 1.5-monthfall inlet duringthe spring(highriverflow) andsummer(low river
period(Figure3d) revealsthat the wind componentalongthe flow) studies,respectively.These centerlineflow speedsare
inlet from the wetlandinto the lake typicallychangesdirection representativeof the flow acrossthe entire crosssectionbased
every1-3 daysand canvary in speedanywherefrom 0-6 m/s on additionalprofilestaken to the left andrightof the centerover the course of one to several days. Therefore, as with line. In the April studythe wetland and lake water are both
differentialheatingand cooling,windsvary mostlyon synoptic
warming,and the wetlandis persistently1ø-1.7øC
warmerthan
and diurnal timescales.The influence of wind on density- the lake surface water. Consistent with this, a sustainedtwodriven flowscan be evaluatedwith a time seriesof the longilayeredflowis observedin the afternoonof April 14 (solidline
tudinal
Wedderburn
number,
Wea.Figure
3eillustrates
IWeal on Figure4a), with the warmerwetlandwater movingtoward
derivedfrom the wind and temperaturemeasurements
in Figthe lake at the surfaceat 4 cm/s and bottom water entering
ures3cand3d.Theelongated
timeperiods
forwhichIWeal< from the lake at 3 cm/s.Duringthe followingmorning(dashed
8 indicatethat the wind is an important mechanismin modiline on Figure4a) the sameflow patternis maintainedduring
fying baroclinicexchangeflows in this system.During these
slightlylesswindy conditions.Again 2 dayslater, this flow
timeperiodsthe signof the Wea variesmostlyon 1- to 3-day
pattern
is observedboth at the westernand easternsideof the
timescales,
as a resultof changingwind directions(Figure3d)
giventhe strongsynopticvariabilityin temperaturevariations inlet (not shownon Figure4a). In July,however,the flowalong
(Figure3c).Accounting
for thisvariability
in thesignof Wea, the inlet variessignificantlyoverthe courseof the day.Specif(4) suggests
that the wind suppresses
the density-driven
circu- ically,Figure 4b showsthat at 10:00A.M. in the morningon
lation 10-25% of the time and promotesit 5-12% of the time July 30, when the wetland bottom water is 0.2øCcolder than
during this fall period. These percentagerangeswere calcu- the lake surfacelayer, a weak (<1.5 cm/s) two-layeredflow
lated by consideringthe uncertaintyin the Wedderburnnum- occurs,with bottom outflow from the wetland and a surface
ber, originatingboth from the uncertaintyin estimatingthe intrusionfrom the lake. In the midafternoonof that sameday,
densitygradients(33%) and the local wind stressalongthe by which time the wetland water has become0.8øCwarmer
lake inlet into the wetland (20%). The latter uncertaintyis than the lake water, the flow has reversed direction and belargelyassociated
with projectingthe wind from the southern comemuchstronger(>4 cm/s)sincethe morning.A similar
end of the lake to the lake inlet. The formulation(3) doesnot afternoonvelocityprofile was observedat three differentloaccountfor wind sheltering,suchthat northerlywinds(short cationsacrossthe lake inlet the followingday (not shownon
fetch)maybe overestimated.
Last,sincemonthlyaveragewind Figure4b). The diurnalflow reversalin Julyandthe sustained
ANDRAD(STTIR
AND NEPF: TECHNICAL NOTE
3269
Table 1. ExchangeFlow Characteristics
at Lake Inlet and Daily Wind During the 1997April and July Studiesa
Time,
AQ/
Date
LT
W•o, m/s
April 14
April 15
April 17
July 25
July30
July30
July 31
2:00P.M.
10:00A.M.
1:30P.M.
12:40P.M.
10:20A.M.
3:40P.M.
2:20 P.M.
5.3 _+2.1
2.7 _+1.6
0.8 + 0.5
5.1 _+1.3
2.9 _+1.1
2.9 _+1.1
1.7 _+0.8
WindDirection Q•, m3/s Q2, m3/s AQ•, m3/s AQ2, m3/s QR, m3/s
NW
NW
S
NE
N
N
NW
2.4
2.2
1.5
-0.2
-0.1
0.6
0.9
-0.4
-0.3
-0.1
0.3
0.2
-0.9
-0.8
0.2
0.4
0
0.2
0.1
0.5
0.8
0.4
0.3
0.1
0.2
0.1
0.9
0.8
2.2
1.8
1.5
0.09
0.06
0.06
0.06
Q,•
G2
0.1-0.2
0.2
0.1
2
2
8-15
13
3
3
6
0.3
0.0
0.7
0.7
aThepositivesigncorresponds
to the wetlandoutflowto the lake, and the negativesigncorresponds
to the return flow from the lake into the
wetland.The accuracyof the flow rate estimatesis 25%, whichincorporatesa 10% uncertaintyin cross-sectional
area, a 10%-15% uncertainty
in the meanof the verticalspeedprofile,and a 6-10% uncertaintyin the expansionof this profile acrossthe crosssection.
April flowsreflect the diurnal and synoptictimescalesfor differential heatingand coolingdiscussed
in section3.1.
Let us now take a closerlook at the magnitudeof the two
majorflushingmechanisms
in the wetland.Table 1 summarizes
both the measuredAberjona River flow rates, QR, and the
estimatedexchangeflow rates,AQ•,2 (see section2.2), at
varioustimesduringthe two studyperiods.Table 1 showsthat
the exchangeflowsare of the sameorder of magnitudeduring
both studies,consistentwith the observationthat the driving
forces,buoyancyand wind, do not vary significantly
with season(section3.1). The goodagreementbetweenthe two independentestimatesof the exchange
flows,AQ • and AQ2, is an
indication of measurementaccuracy.The Aberjona River
flows,however,are -20 times larger during the springstudy
thanthe summerstudy.This leadsto a shiftin wetlandflushing
regime.In springthe river is the dominantflushingmechanism,
/XQ/QR <0.2, whereasin summerthe exchangeflowsbecome
the dominantflushingmechanism,/X
Q/Q• = 2-15. Sections
3.3 and 3.4 consider how this shift affects wetland
circulation
and flushingtimescales.
3.3.
Wetland
Circulation
A changein AQ/Q• impliesa shiftin wetlandcirculation.In
spring,whenthe circulationis river-dominated,/XQ/Q•< 1,
flow ratesseverelyconstrainor evenfully arrestthe exchange
flow.In July,however,the wetlandsurfaceand bottomcurrent
speedsincreasetowardthe inlet (Figure5d). Sincethe water
depth is also increasing,this accelerationsuggeststhat the
wetlandinflow and outfloware tunneledfrom a wide portion
of the wetland through the narrow channel to the lake as
schematically
illustratedon Figure5b. At the inlet constriction
the flow is subcritical,
G2 < i (Table 1), suggesting
that
summerexchangeflows in the Upper Mystic Lake are submaximal.This is alsoconsistent
with Dalziel's[1992]hydraulic
control theory,which predictsmaximalflow rates of 0.6-1.2
m3/sthatgenerally
exceedthe observed
flowratesat the lake
inlet (Q• and Q2 in Table 1). Figure 5d alsoshowsthat the
exchangeflow extendsfrom the lake acrossthe wetland and
evenup into the upper forebay,as displayedby the upstream
bed velocitymeasurednear the neck.The surfacewater temperaturesare graduallycoolingfrom 27øCat the neck to 25øC
at the lake inlet. This suggestsa continuousentrainment of
colderwater from the lower layer, similar to the sidearmcirculationobservedbyAdamsand Wells[1984]and modeled,for
example,by Jain [1980].
3.4. Wetland Flushing
In the previoussectionthe wetlandcirculationwasshownto
change
fromjet flowin spring(Figure5a) to pointsinkflowin
the flowat the lakeinletis supercritical
basedon G2 ) i in
the summerand fall (Figure5b). This changealsoaffectsthe
Table 1. The dominance of inertial forces causes the river to
behavelike a jet, whichindependentof the wind and buoyancy flushingdynamicsof the wetland. To evaluate the flushing
takes the shortestpath acrossthe wetland (Figure 5a). In timescalesand provide additionalsupportto the circulation
summer, however, the wetland circulation is exchange- describedabove,a slugof dyewasreleasedat the neck,andthe
were monitoredat the lake inlet. The redominated,/XQ/Q• • 1, with buoyancyandwind asthe main dye concentrations
drivingforces.Sincethe buoyancyforcingresultsfrom differ- sultsare shownon Figures5e and 5f.
In April a substantial
portion(20%) of the dyemassexitsthe
entialheat absorptionbetweenthe wetlandand lake, it actson
wetland
in
only
2.5
+_
0.3 hours (Figure 5e). This is much
the whole wetland. Consequently,this forcingis expectedto
shorter than the nominal residencetime of 18 hours, defined as
producea point sink at the lake inlet, with water drawnfrom
all directions,as illustratedon the schematicFigure 5b. In the
caseof nonuniformlyvegetatedwetlandsthe flow will draw
preferentiallyfrom sparsely
vegetatedareasthat offer the least
flow resistance.
the ratio between the wetland volume and total flow
AH
tnøm
= QR+ AQ'
(5)
This short circuitingis consistentwith a jet-dominatedcirculation (Figure5a). Furthermore,the observedshort-circuiting
timescaleof 2.5 hourscorrespondscloselywith what shallow
jet theorypredictsfor the Upper Mystic Lake site configuration [Chu and Baines,1989].Also note that duringthe shortcircuitingperiod,higherdye concentrations
occurat the western sideof the inlet (circleson Figure 5e) than at the center
and easternside (solid lines and crosses),consistentwith a
wetland,
consistent
withW2 ) i (Table1),andDalziel's
[1992] linearjet trajectorybetweenthe wetlandentranceand the lake
hydrauliccontrol theory,which predictsthat the high spring (Figure5a).
Water speedand temperaturemeasurements
in the wetland
supportthe differentcirculationpatternsdescribedabove.Figure 5c showsthat in April the currentspeedsslowlydecrease
alongthe trajectoryfrom the neckto the lake inlet, consistent
with a river jet entrainingwater while it crossesthe wetland.
Towardthe neck(x < 100 m) the warm riverjet occupiesall
of the water column,as seenby the unidirectionalflow. The
cold return flow from the lake is arrested halfway into the
3270
ANDRADOTTIR
a)
AND NEPF: TECHNICAL NOTE
b)
APRILAQ/QR< !
Circulation
Zone
lOO m
100 m
Inlet
Neck
c)
o
Neck
d)
Inlet
o
11 øC
-50
-lOO
-lOO
E
•' -150
N
N -200
•o -200
-300
-250
-3OO
-400.
0
5O
100
150
250
2OO
50
100
x (m)
e)
0.2
!
O
150
200
25O
x (m)
,
t
norn
f)
o.1
!
tnora •, 1 day
• tR• 18hrs
tR= 13days
0.08
0.15
0.06
o0.1
'"•0.04
x
x
0.05
0.02
x ,x
0
0
1
2
3
:
4
t (hrs)
•
2
0 0
4
x
6
t (hrs)
Figure 5. Wetlandcirculationandflushingregimes.Schematic
of the (a) jet-dominatedcirculationin spring
and (b) point sink circulationin summer(and fall). Longitudinaltemperatureand speedtransectfrom the
neck to the lake inlet (c) on April 16 (11:00A.M. to 1:00 P.M.) and April 17 (8:00 A.M. to 2:00 P.M.),
respectively,
and (d) on July30 (noonto 1:00P.M.) and July31 (11:00A.M. to 4:00 P.M.), respectively.
Maximumdyeconcentrations
measured
overdepthat thewest(circles),center(solidlines),andeast(crosses)
sideof the inlet normalizedby the injectedmass,Mo, followingthe slugreleaseson (e) April 17 (10:20A.M.
to 3:20 P.M.) and (f) July30 (12:30-8:30 P.M.).
In July,however,Figure5f showsthat it takesapproximately
3 timesas long (8 hours)for a similarportion (30%) of the
injecteddyemassto leavethe wetland.In addition,the highest
dyeconcentrations
occurpersistentlyat the centerand eastern
side of the lake inlet. Both of these observations
are consistent
with the point sink circulationdepictedin Figure 5b. Unlike
April, the nominalflushingtimescaleof the wetlandcannotbe
estimatedfrom (5) becauseAQ varieswith time duringthe
summerstudy,often reversingat night as discussed
in section
3.2. During suchunsteadyflow conditionsthe nominalflushing
timescale,t.... or the timescalefor net transportof material
through the wetland to the lake, can be assessed
from the
ANDRADOTTIR
AND NEPF: TECHNICAL NOTE
4.
1.2
3271
Discussion
The observations
in the Upper MysticLake systemdemonstratetwo differentcirculationand flushingregimes.In spring,
when river flow rates are high, the circulation is river- or
0.8
jet-dominated,whereasin summerthe circulationis exchangedominated.Many wetland-lakesystemsfollow similarseasonal
0.6
trendsin atmosphericheating and river flow rates as the one
0.4
studiedin this note and couldgo througha similartransition.
Thereforeit is usefulto derivean expression
for the magnitude
0.2
of the exchangeflowsbasedon readily availableinformation
suchas site geometryand meteorologicalconditions.This al0
lowsus to assess
the potentialimportanceof exchangeflows
0
10
20
30
40
50
prior to undertakingfield experimentsand can help guide
futurestudies.Buildingupontheworkof FarrowandPatterson
Figure 6. Fraction of massretained in the wetland after the
to find an
July30 dyerelease,basedon dyeandflowmeasurements
at the [1993],we will make severalsimplifyingassumptions
analytical
solution
for
the
exchange
flow
rates
and
later
discuss
lake inlet (t < 8 hours),and dyeconcentration
measurements
the limitationsof thoseassumptions.
Let us start by considerat 6-15 locationsin the wetland(t > 8 hours).
ing the heat budget.The one-dimensional
governingequation
for the mean water temperature,T, can be written as
OT
decayof dyemassleft in the wetland,Mleft(t), relativeto the
injected
mass,
Mo,
f• mleft(t)
d! ZmleftA!
/nom
=
M0
•
M0 '
(6)
Figure 6 displaysthe massof dye left in the wetlandfollowing
the July slugrelease,estimatedfrom cumulativeoutflow(for
t < 8 hours)andfrom concentration
measurements
withinthe
wetland(for t > 8 hrs).For thesemeasurements,
(6) yieldsan
effectivewetland flushingtimescaleof 1.0 _+0.1 days.Alternatively,assuminga stirred reactor and fitting the measure-
mentson Figure6 to an exponential
decaycurvegives7 =
1.2 +_0.1 days,whichcompareswithin the uncertaintyto the
previousestimate.Equating(5) with the resultsof (6) indicates
that the unsteadyexchangeflow producesflushingequivalent
to aneffective
steadyexchange
flowrate,AQ, of 0.6m3/s.This
valuecorresponds
closelyto the maximumexchangeflow observedduring this study (Table 1), suggestingthat the exchangeflow contributesefficientlyto the net flushingof the
wetland,with little massreturningwhen the flow reverses.
The significance
of the exchangeflowson wetlandflushingis
shownby comparingthe observednominal flushingtimescale
(6) to the nominalflushingtimescaledue to river flowsonly
((5) with AQ = 0 and QR from Table 1), that is,
OT
0
0--•+u0x pCph'
(7)
where u(z) is the water speedassociated
with the exchange
flows, 0 is the net heat flux per surfacearea assumedto be
uniformilydistributed
overdepthh, and p and Cp are the
densityand specificheat of water,respectively.
Note that h is
typicallylimitedby the water depthin shallowsidearmsand the
light absorptiondepth (Secchidepth)in deeperlakes.To decouple the thermal and momentum equations,we start by
settingasidethe advectiveheat flux term u 0T/Ox. Differentiatingthe simplifiedversionof (7) alongtheflowaxis,x, yields
the followinggoverningequationfor the longitudinaltemperature gradient:
O00W•o
O0
OS)h020x'
Oh
OW•o
Ox 1-•-•-•
(8)
The first term on the right-handside of (8) representsthe
feedback
ofthetempera.
turegradient
onSurface
heating
which
is generallyneglected.The next two termscorrespondto wind
shelteringandsunshading,bothof whichcanbe importantin
smalllittoralwetlandssurrounded
byobstructions
suchashills,
trees, and buildings.In practice,however,estimatingthese
termsis difficultasit requiresdetailedspatialmeasurements
of
both wind speeds,W•o, and incomingsolarradiation,S. The
tR= Q-•-= 0.06m3/s - 13_+1days.
remainingterm describesdifferential heat absorptionand is
typicallythe biggestcontributorto differential heating and
That tnom<< tR demonstrates
that exchangeflowscan signifcooling.Therefore it is the sole term that will be kept in the
icantlyenhancewetlandflushing,specifically
in this systemby
following analysis.Assumingthat the net surface heat flux
a factor of 10. With this dramaticallyenhancedflushingthe
variessinusoidally
with period,P, and amplitude,A0,
capacityof the wetlandto removecontaminantsand thermally
mediate the temperatureof the lake inflow is impaired. Con0 = AOei2=t/P,
(9)
sequently,wetlandsthat exchangewith lakesplay a very different role in lake water quality than wetlands that do not andplugging(9) into (8) givesan estimatefor the temperature
exchangewith lakes.Specifically,insteadof being considered gradientamplitudeas
as transformers,they need to be consideredas "communicators" in the sensethat they communicatepropertiesfrom the
•
:2 '•- ß
shoreline(e.g., watershedrunoffs)to the lake interior. This
communication
capacitywill be reducedif theselittoral regions
are verydenselyvegetated,becauseof the dragimposedon the
Similarly,but not shown,assumingthat the flow is viscousflow by the plants.
dominatedand at a quasisteadystatewith the pressuregra-
AH
51,600 x 1.3 m3
OT AOPoh
3272
ANDRADOTTIR
AND NEPF: TECHNICAL NOTE
dient,the exchangeflow ratesassociated
with differentialheating and coolingcan be derivedas
AQ=5.4x
10-3
•-•l
gal
OTAH3
Imz,
where# istheacceleration
of gravity,
a = (1-2)10-4/øC
isthe
thermal expansivity,
Kmz is the vertical diffusivityof momentum, andA andH are the cross-sectional
area and depthat the
sidearm/wetland
entrance,respectively
[Andrad6ttir,2000].Replacinga OT/Oxwith Op/Ox,this solutioncorresponds
to the
widelyusedHansenandRattay[1965]andOfficer[1976,p. 118]
model for estuarinebarocliniccirculation.Incorporating(10)
into (11), the magnitudeof the exchangeflowscan be compared to the river flowsto determinewhether and when density-drivenexchangeflowscontributesignificantlyto sidearm
flushing.Similarly,plugging(10) into the Wedderburnnumber
(2) determinesthe potential effects of winds in modifying
freshwaterexchangeflows.
For validation this analysisis used to predict the diurnal
temperaturegradient and exchangeflow rates in the Upper
MysticLake system.During summerand fall, Figure3b shows
daily (P = 1 day) heat flux variationswith amplitudeA4>=
sitygradientassociated
with synoptic(P = 10-20 days)heating/cooling.Therefore(10) and (11) are not representative
for
the synopticflow variabilityat that site, and to predictthose
flows,the coupledthermal and flow equationsmustbe solved
numerically.The modelalsoassumes
that the flow is at quasi
steadystateand is viscous-dominated.
Both assumptions
hold
reasonably
well in shallowsidearmswith a mild densitygradientsuchaswetlands(basedonFarrowandPatterson
[1993]and
Monismithet al. [1990]).Also note that the modelpresented
here dependsstronglyon Kmz, which may vary duringthe day
as the exchangeflow progresses
and with variablewind conditions. To the authors'knowledge,no work has been done to
parameterizeKmz in terms of the flow conditionsin shallow
freshwatersystems,so Kmz may ultimately need to be measuredat eachsiteusing,for example,a microstructuretemperature profiler. Last, our model does not accountfor bed friction and thus will overestimateflows in denselyvegetated
systems.
To conclude,this note presentsfield observations
in a wetland-lake systemthat highlight the importanceof exchange
flows to wetland flushingand the seasonalvariation of their
importance.Specifically,during high spring flows the river
dominatesthe wetland flushing,whereasin the dry summer,
exchangeflowscan enhancewetlandflushingby a factorof 10
300-400 W/m2. Recallfrom section2.2 that A(b canbe esti- relative to river flushing.A one-dimensionaldecoupledheat
mated basedon solar radiation,wind speed,cloud cover, air and flow model is found to predict well the magnitude of
temperature,relative humidity and water temperaturemea- diurnal exchangeflows in the Upper Mystic Lake sidearm
surements,the majority of which are available from local system,indicatingthat it can be a valuabletool for first-order
weatherservices.
The heat absorption
gradient,Ioh/oxl, is assessment
of the importanceof exchangeflowsin other shal0.04 m/m basedon the bottom slopealongthe lake inlet with low freshwater sidearms.
60-70 m2 cross-sectional
areaand2.5m maximum
depth.The
samegradientcanbe derivedfrom the differencebetweenthe
Acknowledgments.This work wasfundedby the NationalInstitute
meanwetlandwater depth(1.5 m) and lake epilimniondepth
of EnvironmentalHealth Sciences,SuperfundBasic ResearchPro(5 m) over the inlet length (-100 m). With this input, (10) gram, grant P42-ES04675.The authorswould like to thank Rocky
yieldsIoT/oxl • o.007øC/mwhichcompares
within10-20% Geyer for hisvaluableinsight;David Senn,Harry Hemond, and Terry
to our observedamplitude of diurnal temperaturevariations Donohue for their help in designingthe field studies;David Senn,
(-IøC on Figure3c) overa lengthof 100 +_30 m. On the basis Wendy Pabich, Katja Knauer, Jenny Jay, Dan Brabander,Carolyn
of microstructure
temperaturemeasurements
at thissite [Nepf Oldham, Kathryn Linge, ChrissyReilly, Marnie Bell, Shu-FenYun,
and Oldham,1997],Kmz -- O(10-4 m2/s),for which(11)
yieldsan exchangeflow rate of
collection.
9.8 x 1.5 x 10-4X
AQ • 5.4 x 10-3
andDaniel Feller for their fieldworkparticipation.Specialthanksgo to
the Winchesterand Medford boat clubsfor facilitatingour field data
0.007 x 65 x 2.5 3
10-4
• 0.6 m3/s,
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(10) and (11) representwell the diurnalexchangeflow in the Upper MysticLake
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made to
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(10) and (11). For a
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