Table Of ContentProcess-based approach on tidal inlet evolution – Part 1
D.M.P.K.Dissanayake&J.A.Roelvink
UNESCO-IHE,Delft,TheNetherlands
ABSTRACT: Thelong-termaimofthisstudyistounderstandandmodelthebehaviouroftidalinletswhich
arefacingrelativesealevelriseandclimaticchanges.Thepresentworkisfocusedonthetidalinletevolution
drivenbytidalforcing.Thisusesaschematizedapproachwitha2Dprocess-basedmodel(Delft3D)torepresent
themorphologicalevolutionoftheAmelandinletintheDutchWaddensea.Themaximummorphologicalperiod
sofarextendsupto50years.Theresultsqualitativelycorrespondwiththeobserveddata.Finalbedevolution
agreeswiththeempiricalrelationbetweentidalprismandminimumcrosssectionalareaofthegorge.Flood-or
ebb-dominantsituationofthemodeldependsontheinitialdepthatbasin.Nomodelhasreachedtoanequilibrium
conditionbasedontheresidualtransportpatterns.Theresultsshowtheapplicabilityoftheprocess-basedmodel
inthelong-termmorphologicalstudyintidalinlets.Themorphologicaldevelopmentsappeartobeoverestimated,
whichmaybeduetoinitialconditions,transportformulationsusedandwaveeffectswhichwerenotincludedyet.
1 INTRODUCTION that the equilibrium exists between the morphologi-
calelements:cross-sectionandtidalprism(O’Brien,
1.1 General 1969andJarret,1976),volumeoftidalchannelsand
tidalprism(Eysink,1990),cross-sectionanddischarge
Barriertidalinletsystemsaretypicallyfoundinsandy
(Kraus,1998),ebbdeltavolumeandtidalprism(Wal-
coastal planes world-wide.A series of barrier inlets
ton andAdams, 1976). Eysink (1990) describes the
formtheentrancestotheDutchWaddensea.Channels,
morphological adaptation of tidal inlets due to sud-
shoals,tidalflatsandbarrierislandsarethemainmor-
denchanges(closureorreclamationwork).Acriterion
phologicalelementsofabarriertidalinlet.Theyhave
has been developed by Wang et al. (1999) to deter-
a high ecological value (feeding grounds for birds,
mine the flood- and ebb-dominancy of a tidal inlet.
breedingareasforfishandtheenvironmentforflora
They use the ratios of shoal volume to channel vol-
and fauna) and an economic value (tourism, fishing
ume (Vs/Vc) and tidal amplitude to mean channel
andnavigation).Thepresentstudyisfocusedonthe
depth(a/h).DeVriendetal.(1993)andLatteux(1995)
AmelandinletintheDutchWaddensea.
describethereductiontechniquesandselectingrepre-
TheAmelandinletislocatedbetweenAmelandand
sentativeconditionsrespectivelytoobservelong-term
Terschelling barrier islands.The morphological pro-
morphologicalchanges.VanLeeuwenetal.(2003)use
cesses in this area are governed by tidal force.This
aschematizedapproachtoinvestigatetheconceptof
causes residual current leading to a strong sediment
downstreamaccretionofatidalinlet(Sha,1989).A
transportbetweenthebarrierislands.Theinlethasa
recentapproachisfoundinRoelvink(2006)tomodel
uniquemorphologyinthesensethatitismodulating
thecoastalevolution:“onlinemorphology”.Thebed
betweenaone-channelandatwo-channelsystemdur-
levelupdateoccursineachhydrodynamictimestep,
ing a period of approximately 50 years (De Grimal,
but the morphological changes are accelerated by a
1998).Theebbdeltahasacyclicbarbehaviourwith
constantfactor.
barsmigratingtoeastwardandattachingtothecoast
ofSchiremonnikoog(DeSwart,2004;Ehlers,1988).
1.3 Objective
The objective of the present work is to observe
1.2 Relevantstudies
the influence of initial conditions and tidal motion
Different approaches are found in the literature to on morphological evolution using 2D process-based
understandthephysicalprocessesandthelong-term model(Delft3D).However,thelong-termaimofthis
behaviouroftidalinlets.Empiricalrelationshipsshow study is to understand and model the behaviour of
3
© 2008 Taylor & Francis Group, London, UK
tidal inlets which are facing relative sea level rise describedinLesseretal.(2004)isapproximatedby
and climatic changes. Morphodynamic evolution of thedepth-integratedadvection-diffusionequation:
atidalinletinvolvesawiderangeoftimeandspace
scales.Therefore,wefocusonmeso-andmacro-scale
morphodynamicevolutionoftidalinlets.
Here h is the water depth, u¯ and v¯ are the depth-
2 MODELCONFIGURATION averagedvelocitycomponentsinx-andy-directions,
D is the horizontal dispersion coefficient, c¯ is
H
2.1 Hydrodynamics thedepth-averagedsedimentconcentration,c¯ isthe
eq
depth-averagedequilibriumconcentrationandT isan
Themodelusestheunsteadyshallowwaterequations s
adaptationtime-scale.
intwo-dimensions(depthaveraged).Theapplication
Thedepth-averagedequilibriumconcentration c¯
of these equations in DELFT3D-FLOW module is eq
isdefinedas:
extensivelydescribedbyLesseretal.(2004).
Neglecting the evaporation and precipitation, the
depth-averagedcontinuityequationisreducedto,
Here, S is the depth-integrated suspended sed-
sus,eq
iment transport for steady and uniform conditions.
Therearetwowaysofspecifyingthistransportrate,
Neglecting the influence of Coriolis’ force, den-
dependingonthetypeofformulationused.
sitydifferences,windandwaves,thedepth-averaged
In using a formulation developed for depth-
momentumequationsarereducedto,
averagedsimulations,theexistingalgorithmsprovide
S directly and no further action is required. For
sus,eq
formulations developed for 3D simulations, such as
VanRijn1993or2004,S hastobedeterminedby
sus,eq
(1DV)numericalintegration:
The equilibrium velocity profile is assumed to be
logarithmic:
where,ζ=waterlevel
h=waterdepth
u¯=depthaveragedvelocityinxdirection
v¯=depthaveragedvelocityinydirection
Theequilibriumconcentrationprofileiscomputedby
g=gravitationalaccelerationfactor
numericallyintegratingSchmidt’sequation:
c =frictioncoefficient
f
ν=eddyviscosity
C=Chezycoefficient
The constant factors, g, ν and C are taken as
Here D (z) is the vertical dispersion coefficient as
9.81m/s2, 1m2/s and 60m1/2/s (in both directions) v
prescribed byVan Rijn (1993); the boundary condi-
respectively.
tion is taken as c (z )=c , where the reference
eq ref ref
2.2 Sedimenttransport concentrationisafunctionofthelocalbedshearstress.
Theadaptationtimeisafunctionofwaterdepth,fall
Sediment transport field is calculated following the velocityandshearvelocity,accordingtotheGalappatti
approachofVanRijn(1993).Hecalculatedthetotal (1983)formulations.
transportasthesumofsuspendedloadtransportand
the bed load transport based on a reference height
whichisdefinedbythebedroughness.Weselectedthis
transportformulationasweexpecttoincludewaves
in the next series of simulations. In depth-averaged HereT isananalyticalfunctionofshearvelocityand
sd
simulations, the 3D advection-diffusion equation as fallvelocity.
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© 2008 Taylor & Francis Group, London, UK
The bed load sediment transport can be found by
applyingthefollowingrelation,
S =bedloadtransportrate(kg/m/s)
b
f =calibrationfactor(1.0)
bed
u(cid:1) =effectivebedshearvelocity
∗
D∗=dimensionlessparticlediameter
ρ =densityofsediment
s
η=relativeavailabilityofsandatbottom
Ta=dimensionlessbedshearstress Figure1. Schematizedmodelareaandcross-section.
Thed valueisapplied200µminthisstudy.The
50
lateralbedslopeandtransversebedslopeareselected Table1. Modelswithdifferentinitialbathymetries.
as50and1respectively.Theinfluenceofbedslopes
are considered at two stages.The first follows Bag- Model Inletwidth(km) Basindepth(m)
nold (1966). The magnitude of sediment transport
1 1.0 2
is adjusted according to the slope along the sedi-
2 3.5 2
ment transport vector which defines by the velocity
3 1.0 3
field.ThesecondfollowsIkeda(1982).Thedirection
4 1.0 4
of sediment transport is adjusted based on the slope 5 3.5 4
perpendiculartothesedimenttransportvectorwhich
definesbythevelocityfield.
2.4 Modelset-up
2.3 Morphodynamicupdating
Theschematizedmodelset-upconsistsofthreeareas:
Thebedlevelisupdatedateachcomputationaltime
backbarrierbasin,inletgorgeandopenseaarea.The
stepbymultiplyingtheerosionanddepositionfluxes backbarrierbasinhasdimensionsof24km×13km
fromthebedtotheflowandviceversa,byaconstant while the open sea area has 60km×25km. The
factor:‘MorphologicalScaleFactor’.
inlet gorge is 6km in width and 3km in length.
These dimensions are based on Admiralty Chart,
1993.
Alldepthvaluesareappliedwithrespecttomean
This allows accelerated bed level changes to be sealevel(MSL).Theopenseaareahasaconcavebed
dynamicallycoupledwiththeflowcomputations.This profileinthefirst9kmbyvaryingdepthfrom0mto
‘Online morphology’ approach is described exten- 20m(Figure1).Ithasaconstantdepthof20matoff-
sively by Roelvink (2006). Sensitivity analysis is shorearea.Thebackbarrierbasinandinletgorgehave
carriedoutbyapplyingdifferentmorphologicalfac- initiallyaflatbed(Table1).Theshadedareainfigure1
tors(50,117,235and353).Theresultsshowthatthe indicatestheerodiblebanksinthemodel.Thebank-
bedlevelupdatesareintherangeof1–5%ofthelocal elevationissetto+5m.Onecanobservethewidening
water depth. However, there are points which rarely oftheinletintemporalscalebasedonthisapproach.
exceedthisrange.Onemorphologicalfactor(235)is Further, this allows to observe whether back-barrier
selectedforthisstudybasedonthepercentageofbed basin attempts to widen with longer morphological
levelupdate,thecomputationaltimeandtherequired periods.
accuracy. The model has three open boundaries: north, east
Themodelconsistsofdrycellsaroundthebackbar- andwest.Theseawardboundary(north)isdefinedby
rierbasinandalongthegorge(Figure01).Thedrycell aM tidewhichhasamplitudeof0.8m.Thetidalwave
2
erosionfactorinthemodelissetto1.Thismeansthat ispropagatingfromwesttoeastparalleltothecoast
theamountoferosionthatoccursattheadjacentwet withaphasedifferenceof37◦.
celliscompletelyassignedtothedrycell.Thiscontin- Thecross-shoredirectionhasafinergridsizecom-
uesuntilthedrycellbecomesawetcellandcontributes paredtoalongshoredirection.Thesmallestgridsize
tothehydrodynamicprocess.Detaileddescriptionon (60m×125m)isfoundatinletgorgewhilethemax-
drycellerosionprocessisfoundinLesseretal.(2004) imum grid size (1000m×1000m) is found at open
andRoelvink(2006). sea area. This gives rise to form accurate channel
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© 2008 Taylor & Francis Group, London, UK
Figure 2. 50-year morphological evolution with different
initialbathymetry(modelnumbersarereferredtotable1).
andshoalpatterns.Thetime-stepis1minuteforthe
hydrodynamiccomputations.
A few models are selected to discuss in this
paper. Table 1 shows the models with different ini-
tialbathymetry.Thesearesimulatedwiththeselected
Figure 3. Comparison of model hypsometries with
morphological scale factor (section 2.2) in order to
observeddata(modelnumbersarereferredtotable1).
observe50-yearmorphologicalevolution.
Theresultsofthesemodelsarediscussedinthenext
section.
The hypsometry shows the water surface area at
a given water depth. Therefore, this measures the
amount of channels and shoals in a tidal basin. Fig-
3 RESULTS
ure3showsthehypsometryfortheselectedmodels
andfortheobserveddata.
3.1 Qualitativeanalysis
Both models 1 and 2 have similar hypsometry
A qualitative analysis of each result is carried out because they have initial water depth of 2m in the
beforeanalyzingtheresultsindetail.Thisisbasedon basin.Ontheotherhand,models4and5behavesimi-
theebbdeltaconfigurationandchannel/shoalpatterns. larly as both models have the water depth of 4m in
Thus,thisisagoodestimatortodecidethevalidityof the basin. The data are in good agreement in deep
the outcomes.The results show that a large amount water(waterdepthgreaterthan10m).However,our
ofpatternformation(shoalsandchannels)occursdur- flat bathymetry has a constant depth everywhere in
ingthefirstdecadeofthemorphologicalperiod.Finer the basin, which is not the case of observed data.
adjustments of these patterns are found in the next Therefore, model results show little deviation in the
decades.However,majorchangesareagainobserved shallow water.The model 1 which has the shallow-
afterseveraldecades.Figure2showstheevolutionof est bathymetry, gives the best agreement with the
channelandshoalpatternfordifferentmodelsatthe data.The morphological characteristics of our mod-
endof50-yearperiod. elstendtobehaveasobserveddataaccordingtothe
Final pattern formation has an asymmetric ebb- hypsometry.
deltaineachmodel.Theebbdeltaisorientedtothe Volume change in ebb delta, inlet and back bar-
direction where the tidal wave comes from. Further, rier basin are calculated based on the initial flat
mainchannelintheebbdeltashowssimilarasymme- bathymetry.Positivevolumechangegivesrisetosedi-
tryexceptinthemodel2and5.Thelattertwomodels mentationwhilethenegativevolumechangeindicates
hbaavsienwshiodwersiannitaiaslyminmleetstri(c3c.5hkanmn)e.lTphaettebranctkoob.aTrhrieeyr emroosdieoln(.FTighuerein4l)e.tItaecxtspoarstsasesdeidmimenetnitnstoouthrceeebinbdeealctha
areorientedtothedirectionoftidalwavepropagation. andbackbarrierbasinsimultaneouslyorimportsedi-
TheAmelandinletshowsthesametypeofasymmetry mentfrombackbarrierbasinandexportintotheebb
initsmajormorphologicalelements. delta.Thesedimentexportingcapacityoftheinletis
largerwhenithasasmallerinitialinletwidth(larger
amount of sediment from erodible banks). The ebb
3.2 Quantitativeanalysis
deltavolumealwayskeepsonincreasingthroughout
The quantitative analysis helps to understand the themorphologicalperiod.However,thedeeperinitial
macro-scale morphological changes. Several param- bathymetries (model 4 and 5) show that they reach
eters are used in this analysis: hypsometry, change nearlyaconstantvolumechangesafterabout25-year
of sediment volume, cross-section width at inlet, morphologicalperiod.Ontheotherhand,theyimport
seaward extension of ebb delta, flat- and channel- sandintothebackbarrierbasin.Thesmallertheinitial
characteristics.Thefollowingparagraphsdescribethe waterdepth,thelargerthesedimentexportfromthe
outcomesoftheseparameters. basin.
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© 2008 Taylor & Francis Group, London, UK
Figure4. Volumechangeinebbdelta,inletandbackbarrier
basinwithrespecttoinitialbathymetry(modelnumbersare
referredtotable1).
Figure 6. Behaviour of model results according to the
relationproposedbyWangetal.(1999).
temporal)toestimatetheseparametersareseparately
calculatedusingtherespectivebathymetryatdecadal
time intervals. The analysis shows the variation of
channelarea,channelvolume,basinarea,tidalprism,
flatareaandshoalvolumeduringthemorphological
evolution.
The results show that the large amount of evolu-
tionhasoccurredduringthefirstdecade.Thereafter,
theevolutionisobservedinrelativelylowerrate.The
shallow bathymetry takes a longer period to adjust
themorphologicalparameters.Thisanalysisgavethe
insightofmorphologicalevolutionalongthe50-year
period.Nextsectionshowsthecomparisonofresults
withtwoempiricalrelations.
Figure 5. Seaward protrusion of ebb delta and mean
cross-sectionwidth(modelnumbersarereferredtotable1). 3.3 Comparisonwithempiricalrelations
The model results are compared with two empirical
Volume changes in these three elements are not relations.ThefirstrelationisproposedbyWangetal.,
equaltozero.Thelossorgainsedimentamountcan (1999) with the ratio of offshore tidal amplitude to
bedescribedbymeansofopenboundary(north,west meanchanneldepth(a/h)andtheratioofshoalvol-
andeast)sedimentloss. umetochannelvolume(V/V ).Accordingly,theright
s c
The maximum seaward protrusion of ebb delta is side of the curve is defined as flood dominant and
about10kmaccordingtothemodelresults.Theshal- theleftsideisdefinedasebbdominant.Ourmodels
lowbathymetryreachesaconstantprotrusionatlower extendto50-yearmorphologicalperiod.However,the
morphologicalperiods.TheobserveddataatAmeland resultsshowthattheytendmovetowardstherelation
inlet show that the seaward protrusion of ebb delta (Figure6).Theshallowbathymetryshowsmoreflood
is about 6–8km.The larger ebb delta extension can dominantsituationcomparedtodeeperbathymetries.
beexpectedasthepresentmodelshavenotincluded
wavesandwind.Further,wehaveconsideredonlyM
2
tidalcomponenttodrivethemodel.Themeancross
section width increases all along the morphological
periodandreachesabout3.5km.Infact,themodels
with wider inlets (3.5km) show that the cross sec-
tionwidthremainconstant(3.8km)afterafewyears Vs–shoalvolume
(Figure5). Vc–channelvolume
Next,thechannel-andflat-relatedparametersare a–offshoretidalamplitude
computed.Thehydrodynamicconditions(spatialand h–meanchanneldepthinthebasin
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© 2008 Taylor & Francis Group, London, UK
theebbdeltabecomesscatterafterseveraldecadesof
morphology.Additionally,sandbarsareformedinthe
openseaarea.Therefore,wehavetolimitthemorpho-
logicalperiodto50-yearinordertocarryonthestudy
withtidalforceonly.However,futurestudytakesinto
accountlongermorphologicalperiodsafterincluding
wavesandwinds.
ThismodelusesVanRijn(1993)transportformulas.
The model results show that these formulas accel-
erate the morphological changes compared to other
transportformula(EngelundandHansen).Therefore,
itisworthwhiletoobservetheinfluenceofdifferent
transportformulasinmorphologicalevolution.
The erodible banks, located at inlet, consist of a
large amount of sediment. Therefore, they have a
remarkable influence on the ebb delta as well as in
thebasinchannel/shoalpattern.Theinletalwaysacts
asasedimentsourceforebbdelta.Ontheotherhand,
Figure 7. Behaviour of model results with the relation
proposedbyJarret(1976)forsinglejettyorno-jettyscenario. itactsasasediment-sourceor-sinktothebackbarrier
basindependingonitsinitialdepth.
Further,theresultsshowtheinfluenceofinitialinlet
width.Thelargerthewidth,thecloserthepointtothe 5 CONCLUSIONS
relation.Therefore,thisrelationindicateswhetherthe
systemisinflood/ebbdominantsituation.However,it Thisstudyshowstheapplicabilityof2Dprocessbased
isrecommendedtocarryoutfurtheranalysistoesti- modelinlong-termmorphologicalstudyofthistidal
mate the flood/ebb flow condition.According to the inlet.Theschematizedapproachgivesfeasibleresults
results,themodelsarerequiredtosimulatealonger which can be compared with the observed data and
periodtoreachthisempiricalrelation. physical processes. Therefore, this approach can be
Thesecondempiricalrelationshipdealswithtidal used to observe the morphological changes in tidal
prism and minimum cross section area at inlet (Jar- inletindifferentdecadalscales.
ret,1976).Therelationshipforsingle-jettyorno-jetty The results suggest that large morphological
scenarioreadsas, changesoccurduringthefirstdecadeofthemorpho-
logicalperiod.Then,fineadjustmentsofthesechanges
are observed in the next decades. However, major
changes in morphology can be observed again after
A – minimumcrosssectionareabelowMSL(m2) severaldecadeslater.
P – tidalprism(m3) Thepresentstudyisentirelycarriedoutusingtidal
Our model results are moving towards the rela- forcing(M )conditiononly.Nowavesandwindsare
2
tionwhenthemorphologicalperiodbecomeslonger. considered.However,theresultsarealreadyinsome
Though initial flat bathymetries are scattered in the agreementwiththeobserveddata.Therefore,onecan
figure,theyaregettingcloserwhenthemorphologi- understandtheimportanceoftidalforceinthemodel.
calperiodishigher.Thisrelationshipfurtherconfirms This reveals that the tidal force is the main driving
thevalidityourmodelresults. forceofamorphologicalmodelinourstudyarea.
Anotherremarkableconclusionisontheinfluence
of initial condition at back barrier basin.The model
4 DISCUSSION resultswiththepresentforcingshowthatthevolumeof
backbarrierbasinisclosetotheequilibriumfortheini-
Thepresentstudyusesonlythetidalforcing(M )con- tialdepthof3m.However,itisimportingsedimentfor
2
dition.Further,nowavesandwindareincludedyet. theinitialdepthof4mwhileitisexportingsediment
Thus,itisdifficulttoexpectactualconfigurationsof fortheinitialdepthof2m.Theshallowestmodel(2m)
theAmelandinletwiththepresentmodelset-up.How- exportsabout180Mm3in50years.Accordingly,this
ever,themodelresultsshowthattheorientationofebb wouldtakealongerperiodtoreachtheequilibrium.
deltaandthechannelpatternsarequalitativelyagreed Though the model of 3m initial depth reaches to
withtheobserveddata. equilibrium,itistoodeepaccordingtothehypsomet-
Ourmainconcernonthemodelresultsistoobserve ric curves (Figure 3). This implies the fact that the
thefeasibleebbdeltaconfiguration.Theearlysimu- modeldoesnotincludeanimportingmechanism,such
lationswithlongermorphologicalperiodsshowthat asM /M asymmetryorwaveforcing.
2 4
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© 2008 Taylor & Francis Group, London, UK
Finally,themodelresultsshowthattheyaremov- Latteux,B.1995.Techniquesforlong-termmorphological
ing towards the empirical relationship. Thus, it is simulationundertidalaction,MarineGeology126,pp.
necessary to carry out longer period of morpho- 129–141.
logical simulations in order to compare with these O’Brien, M.P., 1969. Equilibrium flow areas of inlets on
sandy coasts, Journal of the Waterways and Harbors
relationships.
division,Proc.ASCE,pp.43–52.
Roelvink, J.A., 2006. Coastal morphodynamic evolution
techniques,CoastalEngineering53,pp.277–287.
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Fluids.Proc.RoyalSoc.Philos.Trans.,London,Vol.249. VanLeeuwen,S.M.,VanderVegt,M.andDeSwart,H.E.,
DeGrimal,V.R.,1998.Long-termmorphologicalprediction, 2003. Morphodynamics of ebb-tidal deltas: a model
Bonrif,DelftHydraulicsReport,H2284/Z2474 approach, Estuarine, Coastal and Shelf Science 57, pp.
De Swart, H.E., Schuttelaars, H.M. and Bonekamp, J.G., 1–9.
2004. Dynamics of channels and shoals on ebb-tidal Van Rijn, L.C., (1993) Principles of sediment transport in
deltas:theroleofwavesandtides,PECS,Mexico. rivers,estuariesandcoastalseas.AQUAPublications,the
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Latteux,B.andStive,M.J.F.,1993a.Approachestolong- Walton,T.L.andAdams,W.D.,1976.Capacityofinletouter
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Engineering,21,pp.225–269. Honolulu,ASCE,NewYork,Vol.II,pp.1919–1937.
Ehlers,J.,1988.ThemorphodynamicsoftheWaddenSea, Wang, Z.B., C. Jeuken and H.J. De Vriend., 1999. Tidal
Balkema,Rotterdam. assymetry and residual sediment transport in estuar-
Eysink,W.D.,1990.Morphologicresponseoftidalbasinsto ies. A literature study and applications to the Western
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Ikeda,S.,1982.LateralBed-LoadTransportonSideSlopes. Netherlands.
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3278.
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© 2008 Taylor & Francis Group, London, UK
Sensitivity analysis of a morphodynamic modeling system
applied to a Portuguese tidal inlet
X.Bertin,A.B.Fortunato&A.Oliveira
EstuariesandCoastalZonesDivision,NationalCivilEngineeringLaboratory,Lisbon,Portugal
ABSTRACT: Coastalareamorphodynamicmodelsarepronetosevereerrorsarisingfromvarioussources,
including: (1) the use of empirical sediment transport formulae (Pinto et al., 2006); (2) the reliability of the
datausedtofeedthemodels;(3)theuseofsimplifyingphysicalassumptions;(4)theerrorpropagationbetween
thevariousmodules.Sincetheseerrorscanbesignificant,theusefulnessandcredibilityofmorphodynamic
simulationsrequireathoroughunderstandingoftheiruncertainty.Thispaperaddressesthepracticalimplications
oftheseinputparametersonthedevelopmentofatidalinlet.Asensitivityanalysisisperformedthroughthe
applicationofthemorphodynamicmodelingsystemMORSYS2D(FortunatoandOliveira,2004)totheÓbidos
lagoon(Oliveiraetal.,2005),asmallbutveryrapidlyevolvingcoastalsystemlocatedinwesternPortugal.The
influencesof:(1)sedimentcharacteristics;(2)thechoiceoftheforcingtideand(3)thesedimenttransportformula
areanalysed,namelythroughtheinletcross-sectionevolutionandtheebb-deltadevelopment.Thechoiceofthe
forcingtideappearsimportant,sincetheuseofarealtide,ratherthanarepresentativetide,induces:(1)faster
morphologicalchanges;(2)15-daycyclicevolutions(spring-neaptidalcycle);(3)largerebb-deltasandinlet
cross-sections.Sedimentgrainsizeandempiricaltransportformulaeratheraffecttherapidityofmorphological
changes,sinceequilibriumisreachedafter3monthsofsimulationsandfinalinletmorphologiesarenoticeably
comparable.Nevertheless,thegoodagreementoftheresultsafterthreemonthsofsimulationdemonstratesthe
reliabilityofthemodellingsystemonthetimescalesofmonths.
1 INTRODUCTION sedimenttransportandbottomevolution.Thestrongly
non-linear coupling between these modules gen-
Theeconomicalandenvironmentalimportanceoftidal erate numerical oscillations and instabilities, that
inletshasbeengrowingworldwideforthelastdecades. have started to be addressed in the last years, by
Themanagementofthesecoastalsystemsisnolonger usingnumericalfilters(JohnsonandZiserman,2002;
restricted to the maintenance of navigation channels Callaghanetal.,2006),byintroducingartificialdif-
but also addresses new challenges such as adjacent fusion in the Exner equation (Cayocca, 2001) or by
shoreline stabilization or water renewal in the back improving time-marshing schemes (Thanguy et al.,
barrierlagoonswhichareoftenusedforaquaculture. 1993). In addition to these numerical problems, the
Portuguese inlets illustrate this fact very well, since computationofsandfluxesitselfhaslimitationsdue
theyoftencombine:(1)constructiondevelopmenton toerrorsoftheempiricaltransportformulae,thedata
the barrier islands, (2) aquaculture and fishing; (3) usedtofeedtheseformulae(Pintoetal.,2006),and
commercial maritime traffic; (4) tourism and recre- the propagation of these errors through the various
ational activities. Because of the combination of a modules(Fortunato,2007).
meso-tidal range with a severe wave climate, Por- Given these various potential error sources, per-
tuguesetidalinletsareoftencharacterizedbyfastand forming a sensitivity analysis when using a given
complexdynamics.Therefore,itappearsessentialto morphodynamic modeling system appears essential
understandandtopredictbathymetricchangesofthese before envisaging obtaining reliable morphological
coastalsystemsintheperspectiveoftheirsustainable predictions.Itisthepurposeofthispapertoperform
development. such a sensitivity analysis, through the application
To reach this goal, the development of reliable oftheMORSYS2Dmodelingsystem(Fortunatoand
morphodynamic modeling systems appears one of Oliveira, 2004, 2007a) to the very rapidly evolv-
themostpromisingavenues.Thesemodelingsystems ing Óbidos Lagoon, located on the western Coast
are typically composed of different coupled mod- of Portugal. This coastal system will be briefly
ules,whichreproducewaterflows,wavepropagation, described in the following section. The modeling
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© 2008 Taylor & Francis Group, London, UK
Figure1. GenerallocationofthestudyareaandbathymetryoftheÓbidoslagooninJuly2001,whichistheinitialbathymetry
fornumericalsimulations.
systemMORSYS2Dispresentedinthethirdsection,
with a detailed description of several improvements
sincethefirstversionofFortunatoandOliveira(2004).
Thesensitivityanalysisofthismodelingsystemwill
betheninvestigatedinthefourthsection,throughthe
influence of the model settings on the development
ofthetidalinlet.Thepertinenceofmodelpredictions
comparingtoclassicaltheoreticalknowledgeontidal
inletstabilityisalsodiscussedinthislastsection.
Figure2. DiagramofMORSYS2Dprocedure.
2 THESTUDYAREA
permanentmutation,withmeandersthatform,grow
TheÓbidoslagoonisasmallcoastalsystemlocated
anddisappearinafewmonths(Oliveiraetal.,2006).
on the western Portuguese coast (Figure 1). This
In this study, the bathymetry measured in July 2001
areaissubjectedtosemi-diurnaltides,rangingfrom
willbeconsideredastheinitialcondition(Figure1).
1m to 4m (meso-tidal). The oceanic wave regime
is very energetic during the winter months, during
which waves of significant height exceeding 6m
3 THEMORPHODYNAMICMODELING
were already recorded in front of the inlet (Oliveira
etal.,2006). SYSTEMMORSYS2D
The lower lagoon is characterized by a tidal inlet
3.1 Modeldescriptionandlatestdevelopments
connected to a web of narrow channels and large
sand banks, where velocities are very large. The The modeling system MORSYS2D simulates the
upperlagoonhassmallvelocitiesandmuddybottom non-cohesive sediment dynamics in estuaries, tidal
(Oliveira et al., 2006) and thus this study will focus inlets and coastal regions, driven by tides, wind,
on the lower lagoon (figure 1). The morphological river flows and waves (Figure 2). It integrates
evolutionofthelowerlagoonisdrivenessentiallyby hydrodynamic models (ADCIRC, Luettich et al.
tidalcurrentswhiletheoceanicpartofthetidalinletis 1991 – www.adcirc.org, and ELCIRC, Zhang et al.
alsoinfluencedbywaves.Thelowerlagoonchannels 2004–www.ccalmr.ogi.edu/CORIE/modeling/elcirc/
evolverapidly,withdisplacementsofthechannelson index.html), a wave model (REF/DIF1, Kirby and
theorderoftenmetersinasingletidalcycle. Dalrymple, 1994 – http://chinacat.coastal.udel.edu/
Aerialphotosofthelastdecadesshowthattheposi- programs/refdif/refdif.html),asandtransportmodel
tion and number of channels and sand banks is in andabottomupdatemodel(SAND2D,Fortunatoand
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© 2008 Taylor & Francis Group, London, UK
Oliveira2004).ThesystemconsistsofaC-Shellscript constantCu.TheCuatthetimestepn+1isestimated
that runs independent models, manages the transfer fromthepreviousCu,usingalog-linearextrapolation:
of information between them and performs control
checks.
Thebottomupdatemodelsimulatessandtransport
duetowavesandcurrentsusingsemi-empiricalformu-
Thenthepredictedtimestepisdefinedas:
laeandcomputestheresultingbedchangesthroughthe
Exner equation (Fortunato and Oliveira, 2004).This
equationissolvedwithanode-centeredfinitevolume
techniquebasedonanunstructuredtriangulargrid:
Toavoidoscillationsofthepredicted(cid:6)t,arelaxation
factorisused,accordingto:
whereQisthesedimentfluxintegratedoverthemor-
Whereαisauser-specifiedconstanttypicallybetween
phologicaltimestep,λistheporosityandhisdepth
0.6to0.9.Theimplementationofthisadaptativetime-
relativetothemeanwaterlevel.
stepleadsto(cid:6)tvaluesofabout5minuteswhensand
Intheoriginalformulation,velocitiesandwaterlev-
fluxesaremaximum(typicallybetween1and2hours
elswerefedintoSAND2Dinthefrequencydomain
beforeandafterlowtide)and45minuteswhensand
(i.e.,throughtidalamplitudesandphases,ratherthan
fluxesareminimum(aroundhighandlowtide).
time series). In order to compute the harmonic con-
stants, a hydrodynamic simulation for at least a full
3.2 Simulationsettingsandanalysisstrategy
tidalcyclewasrequiredforeachmorphologicalstep,
independently of the time step. While this method MORSYS2D simulations were conducted for 90
has revealed to be efficient for slowly evolving sys- days (180 tidal cycles), starting from the July 2001
tems, its application to the very dynamic Óbidos bathymetry(figure1),afterarepositioninganddredg-
lagoon required the use of the morphological factor ing of the mouth (Fortunato and Oliveira, 2007b).
method(Roelvink,2006)withmorphologicalfactors Thesesimulationswereforcedbytidesalone,ignoring
wellbelowunity(typically0.1,FortunatoandOliveira, riverflowinputs(whicharenegligibleintheabsence
2007) to prevent large Courant numbers and sub- offloods)andwaveaction(whichisnotthedominant
sequent numerical oscillations. Besides being very process during the summer months). Boundary con-
time-consuming,thismethodimpliedtousearepre- ditionsforthehydrodynamicmodelweretakenfrom
sentativetide(M2only),whichcouldbeproblematic theregionaltidalmodelofFortunatoetal.(2002).
whentryingtoreproducenaturalbehaviorofacoastal Sincebathymetricdatacouldnotbecollectedwithin
system.Finally,Oliveiraetal.(2007)showedthatsolv- the surf zone during the hydrographic surveys, the
ingeq.(1)withtidally-averagedfluxeswasinadequate morphodynamicsimulationsstartedwithoutebbdelta
in areas where the tidal excursion is larger than the atthetidalinlet.Resultanalyseswerefocusedonthe
spatialscaleofvariabilityoftidalhydrodynamics. inletmoutharea,wheremeshsizewasrefinedupto
Hence,itwasdecidedtomodifytheinitialcodeby 10m.Inadditiontoqualitativeobservations,thesen-
feeding SAND2D with hydrodynamic results in the sitivityanalysisofthemodelwasperformedthrough
timedomain.Thestabilityofthesystemdependson thetemporalevolutionoftwokeyparametersintidal
themaximumCourantnumberCuateachmorphody- inletdynamics:theinletcrosssection(O’Brien,1931;
namictimestep,sincenumericaloscillationstendto Jarrett, 1976; FitzGerald, 1996) and the volume of
appearforvaluessignificantlylargerthan1: theebbdelta(WaltonandAdams,1976;FitzGerald,
1996).Threeparametersweretested:(1)thesediment
grainsize;(2)theempiricaltransportformula;(3)the
forcingtide(representative/real)(Table1).
where q is the sand flux over the element, h is the
s 4 RESULTSANDDISCUSSION
waterdepth,(cid:6)xistheelementsize,(cid:6)t themorpho-
dynamic time step and b the velocity power in the
4.1 InfluenceofsedimentgrainsizeontheÓbidos
transportformulae(typicallybetween3and5,depend-
Inletdevelopment
ingonthespecificformulation).Usingaconstanttime
step(cid:6)t,maximumvaluesofCuvaryovermorethan Sedimentgrainsizearoundtheinletmouthtypically
threeordersofmagnitudewithinatidalcycle,thereby ranges from 0.5 to 0.6 mm but then decrease land-
imposingverysmalltimesteps.Toimproveefficiency, wardandseaward(Oliveiraetal.,2006).Theinfluence
an adaptative time step was implemented, aiming at ofsedimentgrainsizeontheinletdevelopmentwas
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