Diagnosis of physical and biological controls on ...
Transcript of Diagnosis of physical and biological controls on ...
Diagnosisof physical and biological controls on
phyoplankton distribution in the Gulf of
Maine-Georges Bank regionby
Caixia WangB.S.in Applied Mathematics,OceanUniversity of Qingdao1993
M.S. in PhysicalOceanography,OceanUniversity of Qingdao,Qingdao,China 1996
Submittedto the Joint Programin PhysicalOceanographyin partial fulfillment of the requirementsfor the degreeof
Masterof Science
at the
MASSACHUSETTSINSTITUTE OF TECHNOLOGY
June1999
© CaixiaWang 1999. All rights reserved.
Theauthorherebygrantsto MIT permissionto reproduceanddistributepublicly paperand electroniccopiesof this thesisdocument
in whole or in part.
Author1rogram in PhysicalOceagraphy
Certified byPaolaMalanotte-Rizzoli
ProfessorThesisS ervisor
AcceptedbyBrechnerW. Owens
Chairman,Joint Committeefor PhysicalOceanographyMassachusettsInstitute of Technology
Woods Hole OceanographicInstitution
Diagnosisof physical and biological controls onphytoplankton distribution in the Gulf of
Maine-Georges Bank regionby
Caixia Wang
Submittedto the Joint Programin PhysicalOceanographyon May 7, 1999, in partial fulfillment of the
requirementsfor the degreeofMasterof Science
AbstractThe linkage betweenphysics and biology is studied by applying a one-dimensionalmodel and a two-dimensionalmodel to the SargassoSea and the Gulf of Maine-GeorgesBank region, respectively. The first model investigatesthe annualcycles ofproductionand the responseof the annua]cyclesto externalforcing. The computedseasonalcyclescomparereasonablywell with thedata. Thespring bloomoccursafterthe winter mixing weakensandbeforethe establishmentof thesummerstratification.Sensitivity experimentsare also carried out, which basically provide information ofhow the internal bio-chemicalparametersaffect the biological system. The secondmodel investigatesthe effect of the circulationfield on thedistribution of phytoplankton, andthe relativeimportanceof physicalcirculationand biological sourcesby usinga dataassimilationapproach.The model resultsrevealseasonaland geographicvariations of phytoplanktonconcentration,which comparewell with data. The resultsverify that the seasonalcyclesof phytoplanktonarecontrolledby both the biologicalsourceand the physicaladvection,which themselvesare functions of spaceandtime.The biological sourceandthe physicaladvectionbasicallycounterbalanceeachother.Advection controls the tendencyof the phytoplanktonconcentrationmore often inthe coastal region of the western Gulf of Maine than on GeorgesBank, due to thesmall magnitudeof the biological sourcein the former region, although the advection flux divergenceshavegreatermagnitudeson GeorgesBank than in the coastalregion of the western Gulf of Maine. It is also suggestedby the model results thatthe two separatedpopulationsin the coastalregion of the westernGulf of Maine andon GeorgesBank are self-sustaining.
ThesisSupervisor: PaolaMalanotte-RizzoliTitle: Professor
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Contents
Abstract 2
1 Introduction 9
2 Applications of a one-dimensional physical-biological model to Sar
gassoSea 13
2.1 The model 13
2.1.1 The physicalmodel 13
2.1.2 The biological model 15
2.2 The seasonalvariability of the upper layer physics and biology of the
SargassoSea: responseto physicalforcings in the default case . . . . 21
2.2.1 The upperlayer physical structure 24
2.2.2 The upperlayer biological structure 25
2.2.3 Dynamicsof the phytoplanktonblooms 28
2.3 Sensitivity experimentsof biochemicalparameters 31
2.4 Comparisonof model resultswith BATS observations 37
3 Observation of phytoplankton Chlorophyll a in the Gulf of Maine -
GeorgesBank region 40
3.1 Methods 40
3
3.1.1 Studyareaand datasource 40
3.1.2 OAX - optimal linear estimation 46
3.2 Results 49
3.2.1 Annual cycle of Chl 50
3.2.2 Comparisionwith maps from the monographyof O’Reilly and
Zetlin 1996 55
3.3 Sensitivitytests 57
4 An adjoint data assimilation approach to diagnosis of physical and
biological controls on phytoplankton in the Gulf of Maine - Georges
Bank region 63
4.1 Methods 63
4.1.1 Circulation field 63
4.1.2 An adjoint dataassimilationtechnique 65
4.2 Results 68
4.3 Discussion 82
5 Conclusions 87
Appendix 90
A Computation and mapping of the water column mean distribution
of Chlorophyll a 90
Bibliography 92
4
List of Figures
2-1 Schematicof the five-compartmentbiological model showingthe flow
pathwaysfor nitrogen 16
2-2 The annualvariationsof the surfaceboundaryconditions used in the
model 22
2-3 The initial conditionsusedin the model 23
2-4 The depthand time variationsof the a temperature°C, bsalinity
ppt and c eddy diffusion coefficient cm2/s 25
2-5 Thedepthandtimevariationsof theanitrate, bammonium,cphytoplankton,
d zooplanktonand e detritus 27
2-6 The depthand time variationsof the anondimensionalnutrient lim
itation function, bnondimensionalnutrient limitation function and
cthe net limitation functionwithin the year 29
2-7 The depth and time variationsof the a new production, b regen
erated production, c zooplanktongrazingand d time changeof
phytoplankton 30
2-8 The depth and time variations in Case Cl of the alight limitation
function,bthe netlimitation function, c phytoplanktonandd zooplankton
within the year 33
5
2-9 The depth and time variations in Case C2 of the alight limitation
function, bthenetlimitation function, cphytoplanktonand dzooplankton
within the year 34
2-10 Thedepthandtimevariationsof theaphytoplanktonand bzooplankton
of CaseFl; aphytoplanktonand bzooplanktonof CaseF2 36
2-11 Thedepthandtimevariationsof theaphytoplanktonand bzooplankton
of Case01; cphytoplanktonand dzooplanktonof Case02 37
2-12 Climatological 1961-1970seasonablecycles of a temperature°C
and b salinity for HydrostationS 38
2-13 Climatologicalseasonalecycle of nitrate for the first 4 years 1988-1992
of the BATS record Knap et al., 1991, 1992, 1993 39
3-1 NortheastU.S. continentalshelf reproducedfrom O’Reilly and Zetlin,
1996 42
3-2 Bottom topographyof the shelf reproducedfrom O’Reilly and Zetlin,
1996 43
3-3 Stationsand subdivisionsof the shelf reproducedfrom O’Reilly and
Zetlin, 1996 . . . . . . . . 44
3-4 Map of Tiles reproducedfrom O’Reilly and Zetlin, 1996 45
3-5 Jan-Febmapof Chl of default case 50
3-6 Mar-Apr mapof Chl of default case 51
3-7 May-Junmapof Chl of default case 51
3-8 Jul-Augmapof Chl of default case 52
3-9 Sep-Octmapof Chl of default case 52
3-10 Nov-Decmapof Chl of default case 53
3-11 Mapsof Chl reproducedfrom O’Reilly and Zetlin, 1996 56
3-12 Jan-Febmapof Chl of caseAl 58
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3-13 Jan-Feberror mapof Chl of caseAl 59
3-14 Jan-Feberror mapof Chl of default case 60
3-15 Jan-Febmap of Chl of caseA2 61
3-16 Jan-Feberror mapof Chl of caseA2 61
4-1 The generalcirculation in the Gulf of Maine during stratified season
Beardsleyet al., 1997. This picture is reproducedfrom McGillicuddy
et a!., 1998 65
4-2 Thefirst setof controlvolume experimentreproducedfrom McGillicuddy
et al., 1998 which definesthe "region of interest" 70
4-3 Thesecondsetof controlvolumeexperimentreproducedfrom McGillicuddy
et al., 1998: initial conditions a and the resultsafter two monthsof
integrationusing the flow field of periodJan-Febb, May-Junc, and
Sep-Octd 71
4-4 The inversion resultsfor the period from Jan-Febto Mar-Apr 73
4-5 The inversion resultsfor the period from Mar-Apr to May-Jun 75
4-6 The inversion resultsfor the period from May-Junto Jul-Aug 76
4-7 The inversionresultsfor the period from Jul-Aug to Sep-Oct 78
4-8 The inversionresultsfor the period from Sep-Octto Nov-Dec 80
4-9 The inversionresultsfor the period from Nov-Dec to Jan-Feb 81
4-10 The predicteddistribution of periodMar-Apr from periodJan-Feb. . 83
4-11 The cost function for eachof the six assimilationexperimentsnormal
ized to the initial value in eachcase 83
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List of Tables
2.1 Parameterdefinitions and values for the default case. References:
Wroblewiski et. al., 1988; Scott C. Doney et a!, 1996; G. C. Hurtt
et a!, 1996; Oguzet al, 1996 18
2.2 Climatologicalphysicalforcing functions for referencecase 21
2.3 Parametervaluesfor the sensitivityexperiments.The line "df" stands
for thedeafult values. If the value is not defiled it is the sameasthe
default 32
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Chapter 1
Introduction
Photosynthesis,the conversionof solar energyto chemicalenergy, is a fundamental
stepby which inorganiccarbonis fixed by algaeand convertedinto primaryproduc
tion. Significant ratesof primary productioncan occur only in the well-lit euphotic
zone. Hence, the animalswhich feed on the primary productioncansurvive mostly
within the mixed layer where thereare high levels of food for them. Physical pro
cessesplay an importantrole in marineecosystemdynamicsMann and Lazier, 1991
andcanmodify or limit biological productionthroughthe nutrientssupply and mean
irradiancefield e.g. McClain et al., 1990; Mitchell et al., 1991. This thesisstudies
the linkage betweenphysicsand biology via the applicationof two physical-biological
coupledmodels. Thefirst model is one-dimensional,designedto investigatethe verti
cal structureof a simple biochemicalmodel coupledto a physicalmodelof the upper
oceanmixed layer, with an applicationto the SargassoSea. The secondmodel is a
two-dimensionaladvection-diffusion-reactionequationfor biology concentration,with
a sourceor sink term determinedthroughanassimilationapproach.The model is de
signedto investigatethe effect of thehorizontalcirculation on thebiology distribution
and is appliedto the Gulf of Maine-GeorgesBank region.
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The depthof the mixed layer, the intensity of the solar radiationpenetratinginto
the watercolumn and the distribution of the dissolvednutrientswith depthare some
of the major factors regulatingthe biosystemof the sea. The seasonalvariation in
the atmosphere-oceanheat flux imparts a seasonalcycle to the depth of the mixed
layer Sverdrupet al., 1942; Menzel and Ryther, 1960. Thevariationof wind stress
also affectsthe depth of the mixed layer. According to Menzel and Ryther 1960,
productionin theSargassoSeaoff Bermudais closelydependentuponverticalmixing,
high levels occurringwhenthe water is isothermaland mixed to or nearthe depth of
the permanentthermocline400 m, low levels beingassociatedwith the presenceof
a seasonalthermoclinein the upper100 m.
The goal of Chapter2 is to investigateand understandthe interplayingand rel
ative importanceof the physical vertical processesoccurring in the euphotic zone
in determiningthe vertical distribution of nutrients and biology. The biochemical
part comprisesfive components,i.e. nitrate, ammonium,phytoplankton,zooplank
ton and detritus Oguz et al., 1996. A case-studyis carried out by applying the
model to the SargassoSea oligotrophic region, using the U. S. Joint Global Ocean
Flux Study JGOFS BermudaAtlantic Time-seriesStudy BATS site data. The
coupling betweenthe biological and physical model is accomplishedby vertical mix
ing coefficients. In this chapter,we first study the seasonalresponseof the mixed
layerphysics and biology to the externalforcing wind-stress,heatflux, and surface
salinity. Successivelywe perform a sensitivity analysisof the model components
to the biochemicalparameters.The details of the impact of nutrients, light avail
ability, and the interactionbetweenthe biochemicalsand productionare examined
throughthe sensitivity experiments.Ecosystemmodelshave now widespreadappli
cationsfor different oceanicconditions e.g., Varela et al., 1992; Radachand Moil,
1993; Sharplesand rfett 1994. Another more recentapplicationof a similar coupled
physical-biologicalmodel to the BATS dataDoneyet a!., 1996 was very successful
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in reproducingthe seasonalcycles of the upper watercolumn temperaturefield, as
well asof the chlorophyll andprimary production.
The focus of Chapter2 is on the vertical physical and biochemicalprocesses.
However, the horizontal flow field doesaffect the biological system e.g. Campbell,
1986; CampbellandWroblewski, 1985; Flierl andDavis, 1993; Franksand Chen, 1996;
McGillicuddy et al., 1998. Therefore, the goal of Chapter3 and 4 is to investigate
and understandhow advectionand diffusion processesdeterminedby the horizontal
circulation affect the horizontal distribution of phytoplanktonwith relationshipto
growth versusmortality region. An applicationis carriedout for the Gulf of Maine-
GeorgesBank region.
GeorgesBank is oneof themostproductiveshelfecosystemsin the world O’Reilly
et a!., 1987; Cohenand Grosslein,1987, havingan annualarea-weightedproduction
two-to-threetimes that of the world’s averagefor continentalshelves. Interdiscipla
nary field programsexaminingthe physicsand biology of the regionhaveshownthe
high ratesof productionto be strongly linked to the unusualcirculation dynamicson
theBank e.g.,Riley, 1941; Cohenet al., 1982; Home et a!., 1989. A two-dimensional
x, z coupledphysical-biologicalmodel of the planktonon GeorgesBank during the
summerwas developedby Franksand Chen in 1996. In their study, the physically
forced vertically integratedfluxes of phytoplankton, zooplankton,and nutrients on
and off the Bank were quantified, with the biological variablesbehavingas conser
vative, passivetracers.Their study showedthat the largestchangesoccurredwithin
thefronts,wherebiochemicalswere transportedfrom deepwaters toward the shallow
watersof the Bank. The phytoplanktonfield becamevertically homogeneouson the
top of the Bank, with slightly decreasingconcentrationsfrom southto north. A patch
of high phytopianktonbiomassformed in the northerntidal front.
The geomorphological,physical, chemical, and biological characteristicsof the
Gulf of Maine are reasonablyconsistentwith the current concept of an estuary
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Campbell, 1986. A prominent characteristicof estuariesis that the import and
exportof materialsand organismsplay importantroles in controlling biological pro
duction within the system Margalef, 1967. Riley 1967 a modeledthe effects of
shorewardnutrient transporton the productivity of coastalwaters off southernNew
England. He concludedthat nutrient transportwas an importantfactor explaining
the distribution of biological productivity acrossthe continentalshelf.
In the Gulf of Maine-GeorgesBank region, McGillicuddy et al. 1998 utilized an
adjoint dataassimilationmethodto determinethe mechanismsthat control seasonal
variations in the abundanceof Pseudocalanusspp. It was postulatedin his model
that theobserveddistributionsresult from theinteractionof thepopulationdynamics
with the climatologicalcirculation. The problemwas posedmathematicallyasa 2-D
x, y advection-diffusion-reactionequationfor a scalarvariable.
The secondpart of this thesis appliesthe above model of McGillicuddy et al.
1998 to the Gulf of Maine-GeorgesBank region, with the Chlorophyll a datafrom
the Marine ResourcesMonitoring, Assessmentand PredictionprogramMARMAP
of the National OceanographicandAtmosphericAdministration,NortheastFisheries
ScienceCenterbetween1977 and1988 O’Reilly and Zetlin, 1996. In Chapter3, the
OAX - optimal linearestimationpackageis usedto map and analysethe observation
of phytoplanktonChlorophyll a in the Gulf of Maine-Georgesregion. Experimentsare
also carriedout to testthesensitivityof the mappingresultsto themodelparameters.
Chapter4 focuseson the adjoint dataassimilationapproachand the analysisof the
modelresults. The investigationis separatedinto six bi-monthly periodsand confined
to the "regionof interest",asdefinedin McGillicuddy et a!., 1998, aregionnot affected
by boundaryconditionsand wheredataare available.
The future of this study lies in the combinationof the above two types of models,
i.e. a full three-dimensionalapproachthat allows to accesstherelativeimportanceof
vertical versushorizontalprocessesin the dynamicsof the ecosystem.
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Chapter 2
Applications of a one-dimensional
physical-biological model to
SargassoSea
2.1 The model
The completemodel includesthe physicaland biological submodels. The model is
restrictedto two dimensionstime anddepth, in which the vertical mixing processis
parameterizedby the level 2.5 Mellor and Yarnada1982 turbulenceclosurescheme.
It involves afairly sophisticatedmixed layerdynamics.Its biologyis kept intentionally
simpleto understandand explore the basicbiological interactionsand mechanisms.
2.1.1 The physical model
The physical model is the one-dimemsionalversion of the PrincetonOceanModel
BlumbergandMellor, 1987. For ahorizontallyhomogeneous,incompressible,Boussi
nesqandhydrostaticseawithout anyverticalwatermotion, thehorizontalmomentum
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equationis expressedas
-‘ a- fk X ‘U = Km + Vm 2.1.1
wheret is time, z is the verticalcoordinate,iZ is thehorizontalvelocity of the mean
flow with the componentsu, v, Ic is the unit vectorin thevertical direction,and f is
the Coriolis parameter.Km denotesthe coefficient for the verticalturbulentdiffusion
of momentum,and ‘1m representsits backgroundvalueassociatedwith internal wave
mixing and other small-scalemixing processes.
The temperatureT andsalinity S aredeterminedfrom transportequationsof the
form
ac a ac--=- Kh+vh--- 2.1.2
where C denoteseither T or 5, Kh is the coefficient for the vertical turbulent
heatand salt diffusions, and Vh is its backgroundvalue. For simplicity, the solar
irradiancewhich penetratesinto the watercolumnis not parameterizedseparatelyin
the temperatureequation. It is respresentedthroughthe surfaceboundarycondition
given in 1.2.4 togetherwith other componentsof the total heat flux. The density
is functions of the potential temperature,salinity and pressure,p = pT, 5, p using
a non-linearequationof stateMellor, 1990.
The vertical mixing coefficientsare determinedfrom
Km, Kh = lqSm,Sh 2.1.3
where 1 andq are the turbulent length scaleand turbulentvelocity, respectively.
Sm and Sh are the stability factors expressedby Mellor and Yamada 1982. In
the level 2.5 turbulenceclosure, 1 and q are computedfrom the turbulent kinetic
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energy, q2, and the turbulent macroscaleequations. The turbulent buoyancyand
shearproductionsarecalculatedby the vertical shearof the horizontalvelocity and
the vertical density gradient of the meanflow. Kh is assumedto representthe eddy
coefficient for vertical turbulentdiffusion of the biological variableaswell.
The boundaryconditionsat the seasurfacez=0 are
p0Km = 2.1.4
= 2.1.5az P0Cp
S = S 2.1.6
where‘ is thewind stressvectorat the seasurface,QH is the net seasurfaceheat
flux, S is the sea surfacesalinity, Po is the referencedensity and c is the specific
heatof water. The bottom of the model is takenat 400 meter. No stress,no-heat
and no-salt flux conditions are specifiedat the bottom
poKm = 0 2.1.7
Kh- = 0 2.1.8
where C againdenoteseitherT or S.
2.1.2 The biological model
Biological constituentsin the coupled modelare treatedasequivalentscalarconcen
trationsof nitrogen mmolNm3. Nitrogen plays a critical role in oceanbiology as
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an importantlimiting nutrient, particularlyin subtropicalgyres,andis a naturalcur
rency for studyingbiological flows Fashamet al., 1990. The biological scalarsadvect
and diffuse following the physicalrulesoutlined aboveand the biological interactions
aremodeledas flows of nitrogenbetweencompartments.The art in ecosystemmod
elling lies in identifying the appropriatetypes of compartmentsand their linkages.
Detailedmodelsmay lead to better,more realistic simulations,but at the expenseof
addedcomplexity, less interpratablesolutionsand increasingnumberof free parame
tersthat must be specifiedand for which we havefew reliableestimates.Therefore,in
our model, an attempthasbeenmadeto keepthe model assimple aspossiblewith
out eliminatingessentialdynamicsof the system.Thesimple, five-componentsystem
- phytoplanktonP, zooplanktonZ, nitrate N, ammoniumA and detritus D
is outlined schematicallyin Figure 2-1.
Figure 2-1: Schematicof the five-compartmentbiological model showing the flowpathwaysfor nitrogen.
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The local changesof the biochemicalvariablesaredescribedby
= [Kh + Vh-_] + FB 2.1.9
whereB representsany of the five biological variableswith P for phytoplankton
biomass,H for herbivorouszooplanktonbiomass,D for pelagicdetritus,N for nitrate
andA for ammoniumconcentrations.FB signifies the biological interactiontermsfor
the equationsof the five biological variablese.g., Wroblewski, 1977; Fashamet aL,
1990
F = I, N, AP - CPH - mP 2.1.10
FH = ‘yGPH - mhH - /hH 2.1.11
FD = 1- GPH + mP + mhH - ED + w5 2.1.12
FA = 4aI, AP + /LhH + ED - A 2.1.13
FN = -I,NP+QA 2.1.14
where the definitions of the parametersand their default valuesare given in Table
2.1.
The total productionof phytoplankton,I, N, A, is defined by
I, N, A = ammin[a’I, /3N, A] 2.1.15
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Definition Value Unites
f Coriolis parameter l0 sg gravitationalacceleration 9.81 ms2Po referencedensity 1000 kgm3cv specificheatof water 4e3 JIcg’c’/c Von Karmanconstant 0.4 -
Urn maximumphytop!anktongrowth rate 0.75 day’k light extinction coefficient for PAR 0.03 m’k phytoplanktonself-shadingcoefficient 0.03 m2mmolN1R nitratehalf-saturationconstant 1 mmolNm3Ra ammoniumhalf-saturationconstant 0.8 mmolNm3Rg herbivorehalf-saturationconstant 0.3 mmolNm3a photosynthesisefficiency parameter 0.05 wm21
m phytoplanktondeathrate 0.05 day’Tg herbivoremaximumgrazingrate 0.21 day1mh herbivoredeath rate 0.01 day1bth herbivoreexcretionrate 0.05 day1
E detrital remineralizationrate 0.05 day1Q ammoniumoxidation rate 0.03 day1w8 detrital sinking rate 0.5 mday’
‘yh herbivoreassimilationefficiency 0.8P0 initial phytoplanktonconcentration 0.05 mmolNm3H0 initial herbivoreconcentration 0.1 mmolNm3D0 initial detritusconcentration 0.05 mmolNm3A0 initial ammoniumconcentration 0.1 mmolNm3
Table 2.1: Parameterdefinitions and valuesfor the default case. References:Wroblewiski et. al., 1988; Scott C. Doney et a!, 1996; G. C. Hurtt et al, 1996; Oguz et al,1996.
18
wheremm refers to the minimumof eitheraI or jN, A representingthe light
limitation function and the total nitrogen limitation function of the phytoplankton
uptake,respectively.Here i3N, A is given in the form
A = N + aA 2.1.16
with 13aA and/3N signifying thecontributionsof theammoniumand nitratelimi
tations, respectively.They areexpressedby theMichaelis-Mentenuptakeformulation
aA= Ra+ A
2.1.17
= R+N2.1.18
where R and Ra are the half-saturationconstantsfor nitrate and ammonium,re
spectively. The exponentialterm in the last of the aboveequationsrepresentsthe
inhibiting effect of ammoniumconcentrationon nitrateuptake,with b signifying the
inhibition parameterWroblewski, 1977.
The individual contributionsof the nitrateand ammoniumuptakesto the phyto
planktonproductionare representedby, respectively,c.f. Varelaet al., 1992
N = crmmin[aI, /3N, A] /3n//3t 2.1.19
a1, A = ammzm[aI,,13N,A] ,8a/t 2.1.20
The light limitation is parameterizedaccordingto Jassbyand Platt 1976 by
IEI = tamh[aIz,t] 2.1.21
Iz,t = Iexp[-k + kPz] 2.1.22
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where a denotesphotosynthesisefficiency parametercontrolling the slope of aI
versusthe irradiancecurve at low valuesof the photosyntheticallyactive irradiance
PAR. I denotesthe surface intensity of the PAR which is taken as 0.45 of the
climatologicalincomingsolar radiationfrom the data.
The zooplanktongrazingability is representedby the Michaelis-Mentenformula
tionP
GP = °g R9 + P2.1.23
For phytoplankton,zooplankton,nitrateand ammoniumtheboundaryconditions
at the surfaceandbottom are given by an equationof the form
Kh+vh=0 at z=0,z=-D 2.1.24
For the detritus equationthe surfaceboundarycondition is modified to include
the downwardsinking flux
Kh+vh+w8D=0 at z=0 2.1.25
The samecondition is also prescribedat the lower boundaryof the model which
is takenat 400 m depth, well below the euphotic zone. Our choice of the sinking
rate is relatively low w = 0.5 rn/day, Table 2.1. The advantageof locating the
bottomboundaryat considerabledistanceawayfrom theeuphoticlayeris to allow the
completeremineralizationof the detrital materialuntil it reachesthe lower bounday
of the model and the vertically integratedbiological model is fully conservative.
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2.2 The seasonalvariability of the upperlayerphysics
and biology of the SargassoSea: response to
physical forcings in the default case
The annualvariationsof the wind stressand heatflux componentsare expressedby
smooth,climatologicalsurfaceforcing functions Doneyet al., 1996
F = Mean+ Amplitude.cos27rg - phase 2.2.26
where time, t, is given in days. The annualmeans, seasonalamplitudes,and
phasesas shown in Table 2.2 are computedfrom climatologicaldatasets Esbensen
andKushnir, 1981; Isemerand Hasse,1985 for the regionof the BATS site 31°50’N
and 64°10’W.
Units Annual Mean ] Amplitude Phase°Wind stress N/m2 0.081 0.040 60
Net longwave W/m2 -60.0 5.0 70Sensibleheat W/m2 -26.0 22.0 170Latent heat W/m2 -162.5 90.0 170
Solar W/m2 198.7 - -
Table 2.2: Climatologicalphysicalforcing functionsfor referencecase
The surfacewind stressFig. 2-2 c peaksat 1.2 dyncrn2 in March, and the
annualmeanheatloss from the non-solartermsis 248.5 wm2 with a maximum of
365.5 wrn2 in late December. Solar radiation is computedwith a constantcloud
fraction of 0.75, which leadsto an annual meansolar heating rate 01 198.7 ‘w’rrr2
that is within the reportedclimatological rangeof 180 - 200 wm2 Esbensenand
Knshnir, 1981. The requiredcloud fraction, however, is slightly higher than the
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climatological value of approximatly0.6 near BermudaWarren et aL, 1988. The
annualheatbudgetat Bermudais not closedlocally by air-seaexchangethe dashed
line in Fig. 2-2 a, therefore,an excessheat flux at the surfaceis addedin our
model in order to run stable,multi-year integrations.The surfaceheatflux function
we usedto force the model is the solid line in Figure 2-2 a.
a Surface Heat Flux b Salinity
___
36
-150SONDJ FMAMJ J A
3635S 0 N D J F MA M J J A
c Wind Stress d Photosynthetic Available Irradiance110
SONDJ FMAMJ J A 40SONDJ FMAMJ J A
Figure 2-2: The annualvariationsof the surfaceboundaryconditions used i.n themodel.
The surfacesalinity valueswere derived by the linear interpolationof the mean
monthly CTD dataover the upper 8 meter of the oceanLevitus, 1994. As shown
in Figure 2-2 b, it has greatestvaluesduring the winter and early spring with a
maximumvalue of 36.7, andlowest valuesduring the summerwith a minimum value
of 36.4. ThephotosyntheticAvailableIrradiancePAR variationsFig. 2-2 d were
the climatologicaldatafrom Word OceanAtlas 1994. The PAR is expresselasa
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harmonicfunction with amplitude 30 wrn2 and centeredat 70 wrn2 on February
28.
The model temperatureand salinity profiles are initialized with the Levitus 94
datain Septemberas shown in Figure 2-3 a and b, respectively. The biological
simulationsareinitialized with auniform nitrateconcentrationof 0.3 mmolNm3over
the mixed layer 0-150 m, increasinglinearly below that depth to 6.0 mrnolNm3
at 400 m Fig. 2-3 c.
a Temperature b Salinity
Figure 2-3: The initial conditionsusedin the model.
The model equationsare solved usingthe finite differenceproceduredecribedby
Mellor 1990. A total of 27 vertical levels are usedfor the watercolumn of 400 m
depth. The grid spacingis compressedslightly toward the surfaceto increasethe
resolution within the uppermostlevels. The numericalschemeis implicit to avoid
100
E200
300
15 20 25 30
Temperatureec
c Nitrate
36.6Salinityppt
Nitrate mmot/m3
23
computationalinstabilities associatedwith the small vertical grid spacing. Aselin
filter 1972 is applied at every time stepto avoid time splitting due to the leapfrog
time scheme. A time step of 10 minutesis usedin the numericalintegrationof the
equations.
First, the physicalmodel is integratedfor 5 years. An steadystatewith repeating
yearly cycle of the dynamicsis obtainedafter 3 years of integrationin this system.
Then using the fifth year solution of the physical model, the biological model is
integratedfor 4 yearsto obtain the repetitiveyearly cyclesof the biological variables.
The depthintegratedtotal nitrogencontent,N = N+A+P+Z+D, should remain
a constantvalueover the annualcycle when the equilibrium stateis obtained.
2.2.1 The upper layer physical structure
The yearly responseof the upper layer physical structureto the forcing functionsis
shownin Figure 2-4. Thewinter is characterizedwith strongcooling and deepmixed
layer, especiallyin Februaryand March, the mixed layer depth exceeds220 rn and
the mixed layer temperatureis about 19.5°C. Accordingly, there are high valuesof
eddy diffusivity during the sameperiod Fig. 2-4 c. After mid-April, as thewater
column warmsup gradually, the mixed layer depth decreases.During the summer,
due to the weak mixing associatedwith the weak wind stressforcing and the strong
heating,the surfacetemperatureincreasesuptoa maximumvalueof 27°C, the mixed
layershoalsto less than 10 m deep, and a sharpseasonalthermoclinesystemat the
baseof the mixed layer is developed. The wind-induced,weak and shallow mixed
layer characteristicsare consistentwith the low valuesof eddy diffusity shown in
Figure 2-4 c. The autumn period is characteristicwith mixed layer depth of 50-75
m and temperatureof around22°C, salanityaround36.575. This is then followed by
the deeperpenetrationof the mixed layer andsubsequentcold watermassformation
24
a Temperature eC
J F M A M J J Ac Eddy Diffusion Coefficient cm2/s
S 0 N D
‘"J F M A M J J A S 0 N D
Figure 2-4: The depth and time variationsof the a temperature°C, bsalinityppt andc eddy diffusion coefficient crn2/s.
asa result of the strongcooling in Januaryand February.
2.2.2 The upper layer biological structure
The temporal and vertical distributions of the five biochemicalvariablesare shown
in Figure 2-5. In agreementwith the physicalstructureof the upperocean,thereare
severalphasesof thebiological structurewithin the year. Due to thedeepconvection
in the winter, the surfacelayer is enrichedwith nutrientsentrainedfrom below. The
mixed layer nitrogenconcentrationthen increasesgradually to its maximumvalues
in April. The phytoplanktonbloom startsto develop asa result of nutrient enrich-
Salinity ppt
-100E
--2000
-"UI.,
-100E
-2000
_______
-6.65 ------36.65 :36. 36.6 : 36.6
Rci i -36.55
.11
25
ment and sufficient light availability during Januaryand reachesthe maximumlevel
in March and April. In this period, as a result of strongvertical mixing generatedby
the winter convectiveoverturningmechanism,the water column is overturnedcom
pletely and the deepestand coolestmixed layerformation is established.The spring
phytoplanktongrowth processtakesplaceduring March and April and remainsuntil
June. The summerand fall periodsare characterisedby the nutrient depletionand
low phytoplanktonproduction in the mixed layer. The phytoplanktonbiomass is
low because,with weak convection,the nutrient supply from the nutrient rich water
below the mixed layer is no longer possibleand the phytoplanktonbiomass is con
sumedby the herbivorein the surfacewaters. In the summer,the stratification and
the subsequentformationof the strongseasonalthermoclineinhibit nutrientflux into
the shallow mixed layerfrom below, so nutrient limitation prohibits the development
of bloom during the summerseason.The nitrate concentrationsbelow the seasonal
thermoclineincreaseand togetherwith sufficient light availability, leadto the surface
maximum of phytoplanktonbiomassin the layer betweenthe seasonalthermocline
and the baseof the euphotic zone during July and August. Remineralizationof the
particulateorganicmaterial following degradationof the springbloom producesam
monium. A part of the ammoniumis usedin the regeneratedproductionandthe rest
is convertedto the nitrate throughthe nitrification process.Theyearly distributions
of zooplanktonand detritus follow closely that of phytoplanktonwith a time lag of
approximatelytwo weeks. Themaximumzooplanktonconcentrationsoccur following
the phytoplanktonspring bloomsaswell asthe periodof summersubsurfacephyto
planktonmaximum,respectively.
26
a Nitrate mmol/m3 Default
-100
. -2000
F MA MJ JASON DC Phytoplanktonmmol/m3 Default
FMAMJ J ASONDe Detritus mmol/m3 Default
:":‘......L
flT5: ü05
FMAMJ J ASOND
ciciE
-200
b Arnmonium mmoVm3 Default
ASOND dZoopla nktonmmol/ m3Defau lt-100
.-20
0 D‘
JFM A MJ JA S O ND
Figure 2-5: The depth and time variations of the anitrate, bammonium,cphytoplankton,dzooplanktonand edetritus.
-100
-2000
V-100
. -200
27
2.2.3 Dynamics of the phytoplankton blooms.
In this section, we describebriefly the main mechanismscontrolling the initiation,
developmentanddegradationof the bloom, aswell asthe subsurfacemaximumof the
summerseason.First, we considerthe relative roles of light and nutrient uptakein
the primary productionprocess.The control of the phytoplanktongrowth by either
light or nutrient limitation during the year is shown in Figures 2-6 a and b. In
Figure 2-6 b relatively high gradient regionat about 50-100 m deepseparatesthe
low nitrogen limitation region nearthe surfacefrom the regionof high valuesbelow
during the summer. The light limitation function has the oppositestructurewith
decreasingvaluestowardsthe deeperlevels Fig. 2-6 a. Therefore,the net growth
function Fig. 2-6 c, which is the minimum of thesetwo, is generallygovernedby
the nitrogenlimitation near the surfaceand by the light limitation at deeperlevels.
A subsurfacemaximumis presentat the depthsof about 50-100 m wherethey both
have the moderatevalues. During the summerseason,this is responsiblefor the
subsurfacephytoplanktonproduction.
From Figure 2-6 c we note that the highestvaluesof the net growth function
within the upper 50 m layer occur during Januaryand February. But the bloom
developsat a later time, at the end of March Fig. 2-5 c. There are two dy
namical reasonsfor the absenceof the b]oom generationin the midwinter period.
First, although the net growth function hashigh values, the amountof phytoplank
ton biomassat that time is not sufficient to initiate the bloom. Second,the surface
layer has relatively strong downwarddiffusion seeFig. 2-4 c, which counteracts
againsttheprimary productionand thereforepreventsthe bloom development.How
ever,assoonastheintensity of thevertical mixing diminishesin April, a newbalance
is established.The time changeterm Fig. 2-7 d reachesmaximum at the surface
at the beginningof April andsubsurfacemaximumin the latehalf of April. This new
28
a Light Limitation Case Default b Nitrogen Limitation Case Default
-100 ‘c’ -100
-250 -250 : :
.,0-300 -300
JFMAMJJASOND JFMAMJJASOND
c Net Limitation case Default
F50 05’
o -200
-250
J F MA MJ JASON D
Figure 2-6: The depthand time variationsof the anondimensionalnutrient limitation function, bnondimensionalnutrient limitation function and cthe net limitation function within the year.
balanceleadsto an exponentialgrowth of the phytoplanktonconcentrationin the
mixed layer. Soonafter the initiation phase,the zooplanktongrazingFig. 2-7 c
startsdominatingthe systemand balancesthe primary production. This continues
until the nitrate stocks in the mixed layer are depletedand the nitrate-basedpri
mary production new production Fig. 2-7 a weakens.At the sametime, rapid
recyclingof theparticulatematerialallows for the ammonium-basedregeneratedpro
duction Fig. 2-7 b, which also contributesto the bloom development.The bloom
terminatesabruptly towardsthe end of May whenthe ammoniumstocksare also no
longer enoughfor the regeneratedproduction.
The downward diffusion processmentionedabove is evident in the period from
29
Januaryto April with valuesof Kh greaterthan 2 crn2/s in the mixed layer seeFig. 2-
4 c. Theterminationof theconvectivemixing processin lateApril is implied in Fig.
2-4 c by a suddenan order of maginitudereductionin theKh values. Shownfurther
in Figures 2-4 a and 2-5 c is that the periodof high K,?, values is identified with
the vertically uniform temperaturestructureof about 19.5°Cand thephytoplankton
structureof approximately0.3 mmolNrn3. Following the terminationof convective
overturning, the subsurfacestratification beginsestabilishing. As the mixed layer
temperatureincreasesby about0.5°C from 19.5 to 20°C, the phytoplanktonbloom
attains its peakamplitude 3.5 mmolNrn3 within the next half month.
a New Production mmollm3day b Regenerated Production mmol/m3day
-100 .-100
a a
-150 -150
-200JFMAMJJASOND JFMAMJJASOND
c Grazing mmollm3day d Time Change mmollm3day
-50
aa,,-100
a
-150
-2CC -‘--‘-‘
___________________________
J F MAMJ J ASOND J F MAMJ J ASOND
Figure 2-7: Thedepthandtime variationsof thea new production,b regeneratedproduction,c zoop!anktongrazingand d time changeof phytoplankton
LJ t
-50
aa,--100-c
a
-150 IytLr1Irt30
2.3 Sensitivity experimentsof biochemicalparam
eters.
A series of experimentsare carried out to analysethe sensitivity of the model to
the externallyspecified parametersseeTable 2.1. The experimentsand the pa
rametervalues,which arechangedfor eachexperiment,are listed in Table 2.3. The
experimentsshow that if the variation of one parameteraffects the distribution of
phytoplankton, it affects phytoplanktoneven more drastically. The important pa
rametersthat affect the structureof phytoplankton,and thereforezooplankton,are
phytoplanktonmaximumgrowth rateUrn, phytoplanktondeathratenip, light extinc
tion coefficient for PAR k, nitratehalf-saturationconstantR, herbivoremaximum
grazingraterg, herbivoredeathraternh, herbivoreexcretionrate.th, herbivoreassim
ilation efficiency ‘Yh, herbivorehalf-saturationconstantR9, detrital remineralization
rateE, and detrital sinkingratew8. The bloom structuredoesnot changemuch when
the values of phytop!anktonself-shadingcoefficient k, ammoniumhalf-saturation
constantRa, photosynthesisefficiency parametera, and ammoniumoxidation rate
vary. A few examplesare presentedto give an idea of how the settingsof the
biological parametersaffect phytoplanktonand zooplankton.
Tests of the extinction coefficient of PAR default value k = 0.03 m1.
As shown in Table 2.3, two experimentswere carried out accordingto this pa
rameter. We ran the model with the value of k = 0.06 m1 in experimentCl and
k = 0.015 m1 in experimentC2. An increaseto the default value of k intensifies
the distribution of phytoplanktonand zoop!anktontowardsthe seasurfaceFig. 2-8
c and d. Loweringits value,the distributionsof phytoplanktonand zooplankton
arestretchedinto the deeperwater Fig. 2-9 c andd. In our model, phytoplank
31
UrnHmpId.f .75 .05Al 1.5
A2H375
k1 k arj mh[ [ {.03 .03 .05 .21___ ,oi .o5 T .05 .O31
_ .1 - - - -___-___
.02501 .06
r-_ .015 1Dl .06
J D2 .015
E2____
1 1 T-
1
-
1__cG2
H?____-
___
r-__I____
J_5
u T T .42I?
___ H05
J2II!_I___ .02
.005 ___
_T___
2____{__ .1
{,025_I .____- -_- ______
Ml I .1M2 1.025
f1iN?
01
-__-
..
- - --- I_ .06
.015
öT____ - .05
Table 2.3: Parametervaluesfor the sensitivity experiments.The line "dl" standsforthe deafult values. If the value is not defined it is the sameas the default.
32
Figure 2-8: The depth and time variations in Case Cl of the alight limitationfunction, bthe net limitation function, cphytoplanktonanddzooplanktonwithinthe year.
ton growth rate dependson the minimumof nutrient limitation and light limitation.
As decribedin section1.3.3, it is governedby thenitrogenlimitation nearthe surface
and by the light limitation at deeperlevels. Comparingthe light limitation in Figure
2-8 a with Figure 2-6 a, we see that the light limitation in caseCl decreases
except in the very near surfaceregion. The most striking difference is that in the
deafult case, the 0.05 contour of light limitation rangesfrom 100 to 150 meter in
depth, while in case Cl, it is between66 and 84 meter. The subsurfacemaximum
of net limitation decreasesand shifts towardsthe sea surfaceexcept in the winter.
Therefore,the distribution of phyoplanktonis squeezedtowardsthe seasurfacewhen
it is not in the winter. Zooplankton,which feeds on phytoplankton,also moves its
33
a Light Limitation Case Cl b Net Limitation case Cl
.......
-,----.G .o6-----50
.,-100aa
.,-l50
a -200
-250
-o
aa
.,-1500.ao -200
-250
-300
-50
..-100aa
-150C.a
-200
-250
-300
J F M A M J J A S 0 N D J F M A M J J A S 0 N D
Phytoplankton mmol/m3 Case Cl d Zooplankton mmol/m3 Case Cl
-50
-100aa
.-150C.a -200
-250
-300.JFMAMJJASOND JFMAMJJASOND
-50
‘c-l00aa
.-l50C.a -200
-250
-300
-50
‘c-l00aa
-l50C.a- -200
-250
-300.
Figure 2-9: The depth and time variations in Case C2 of the alight limitationfunction, bthe net limitation function, cphytoplanktonand dzooplanktonwithinthe year.
distribution about 50 meter closerto the seasurfacethan in the default case. The
dynamics in caseC2 is oppositeto that in caseCl.
Testsofthe nitrate half saturation coefficient default R = 1 rnrnrnolNm3.
If algaeareplacedin a nutrient medium, the concentrationof nutrientsdecreases
over time in the mediumas they are incorporatedinto the plant cells. The velocity
at which algaeuptake removesnutrients dependson the nutrient concentrationin
the mediumValiela, 1995. Uptakeratesof nitrateor ammoniumby phytoplankton
give hyperbolaswhengraphedagainstthe nitrateor ammoniumconcentrationin the
environmentEppley, 1969. In the Michaelis-Mentenequation,the half saturation
34
a Light Limitation Case C2
-50
‘-l00aa
C.a-o -200
-250
b Net Limitation case C2
0
-50
-100aa
.-l50
C.a-o -200
-250
JFMAMJJASOND JFMAMJJASOND
c Phytoplanlcton mmollm3 Case C2 d Zooplankton mmollm3 Case C2
. .
JFMAMJJASOND JFMAMJJASOND
constantreflects therelativeability of phytoplanktonto uselow levelsof nutrientsand
thusmay beof ecologicalsignificance. In thecaseof nitrate,nutrient uptakeoccursin
two steps:first, nutrientsaretaken into the phytoplanktoncell at a rate determined
by the ambient nutrient concentration;then, as the concentrationinside of the cell
increases,the nutrient is utilized in proportionto the internal cellular concentration
and not the externalambientconcentration. If the nitrateuptakerate is measured
when ammoniumis present, the uptake of nitrate maybeseverelyunderestimated
becauseof the preferencefor ammoniumby manyalgae. The half saturationconstant
is high in more euphoticand nutrient-richwater andlow in oligotrophicwaters.
Two experimentswere carriedout: R = 2 rnrnrnolNm3 in caseFl andR = 0.5
mmmolNrn3 in caseF2. Increasingthe value of R in caseFl increasesthe values
and elongatesthe duranceof the phytoplanktonspring bloom Fig. 2-10 a and
b. The subsurfacemaximumof phytoplanktonnow extendsinto July, while in the
default caseit extendsinto June. However,zooplanktonhas only weak distribution
which spansfrom July to Novemberin the upper 120 meter. Oppositeresultswere
obtainedwhenthe valueof R was decreasedin caseF2 Fig. 2-10 c and d.
Tests of the detrital sinking rate default w = 0.5 rnday’.
The sinking rateof the particulateorganicmatter,w8, is one of the most critical
parametersin the model. The valueof w, appropriatefor the modelsimulationsis 0.5
mday’, which impliesthat thefastersinking, largerparticlesdo not contributeto the
processestaking placewithin the euphoticzone. The choiceof greatervaluescauses
faster sinking of the detrital material toward the deeperlevels, therebydecreasing
the detritus and subsquent!ythe nitrogenconcentrationsin the euphotic layer. The
sinking material thus effectively becomeslost from the euphotic zone. Figure 2-11
a and b show the resultsof the model run when the sinking velocity is taken
as 3 rnday1, and c and d show the resultswhen the sinking velocity is 0.025
35
a Phytoplankton mmol/m3 Case Fl b Zooplankton mmol/m3 Case Fl
-50 - L-4i100
E
-250 -250
300J FMAMJ J ASOND J FMAMJ J ASOND
C Phytoplankton mmol/m3 Case F2 d Zooplankton mmol/m3 Case F2
..-150 .-iso
-200 -200
-250 -250
-300J FMAMJ J ASOND J FMAMJ J ASOND
Figure 2-10: The depth and time variations of the aphytoplankton andbzooplanktonof CaseFl; aphytoplanktonand bzooplanktonof CaseF2.
mday’. Thechangein the valueof w3 altersthewhole biological systemdrastically.
In case01 w3 = 3 mday1, thereexists only a weak bloom in April and May Fig.
2-11 a, with almost no zooplanktonbiomassand detritus in the study area. The
euphotic layer is depletedin both ammoniumand nitrate, which are, accumulated
at deeperlevels. The case with w. = 0.025 mday’ allows a more than complete
remineralizationof the detrital materialbefore it reachesthe lower bounday of the
model. Upon the decreaseof the value of w, the concentrationsof phytoplankton
and zooplanktonarehigher than in the default caseasshownin Figure 2-11 c and
d, especiallyduring the winter whenthe completeoverturningof the watercolumn
36
provides richer supply of nutrients in the euphoticzone.
b Zooplankton mmol!m Case 01
-30CJ F MA MJ J A SON D
d Zooplankton mmol/m3 Case 02
Figure 2-11: The depth and time variations of the aphytoplankton andbzoop!anktonof Case01; cphytop!anktonand dzooplanktonof Case02.
2.4 Comparison of model results with BATS oh
servations.
The mode! solutions of temperatureand salinity Fig. 2-4 correspondwell with
the climatologicaldata1961-1970in Figure 2-12 from HydrostationS WHOI and
BBSR, 1988; Musgraveet al., 1988. They also comparequite well with the model
results of Doney et al., 1996. The model simulationsexhibit the characteristicdeep
winter convectivedepth,shallow summermixed layerand sharpseasonalthermocline
-50
..-100aa
.-l50C.ao -200
-250
a Phytoplankton mmolfm3 Case 01
;.-. .
-
-50
-100a
C.aD -200
-250
-50
‘-l00
.-l50C.ao -200
-250
-300
J F MA MJ JASON D
c Phytoplankton mmollm3 Case 02
J F MA MJ JASON D
-50
-100aa
.-l50C.av -200
-250
-300
05
J F MA MJ JASON D
37
found in the data. The seasonalsalinity cycle also generallyagreeswith climatology,
showingthe greatestsalinitiesduring the winter convectionperiodandthe formation
of a freshsurfacelayer over the summer.A sub-surfacesalinity maximum5> 36.6
appearsin both the model solutionand the observation.
0.
SC’.
00.C
150.C.
200.
2.50
300.
a
0.
50.
- 00.C- 5o.C.aC
20D.
250.
300.
b
Figure 2-12: Climatological 1961-1970seasonableand b salinity for HydrostationS.
cycles of a temperature°C
Our model is driven with a uniform nitrateconcentrationof 0.3 rnrnolNrn3 over
the mixed layer 0 - 150 m, increasinglinearly below that depthto 6.0 mrnolNm3
at 400 m. A directcomparisionof thecoupledmodel and thedatais difficult because
40 8.0Time mcnths
Temperature
-4.Ci 0.0 40 8.0 12.0 16.0flme. months
Sc Unity
38
the BATS datacontainsconsiderableinterannualvariability and is currently of in
sufficient length to generatea true biological climatology. The smoothclimatological
forcing hasthe likely effect on the model solutions of reducingvariability of deep
convectionduring the winter, causinggreaterhomogenizationof propertiesover the
winter mixed layer depth, and weakeningindividual bloom eventsdriven by short-
term variability. The monthly climatologiesin Figure 2-13 of nitrate was created
from the first four yearsof BATS 1988-1992Knap et a!., 1991, 1992, 1993. The
climatologiesare useful for judging the generalcharacterof the model solutions,but
quantitativecomparisonshould be limited to more robust featuresof the biological
seasonalcycle. The model nitrate field agreesreasonabllywell with the BATS field
data. The surfacewinter concentrationsare about 0.2 mrnolNm3 and the depth
of the summernitracline is about 100-125m. The approximatelyuniform concen
trations in the deepwinter mixed-layergradually increaseover the summerdue to
the remineralizationof detritus. However, in the model result the nitratevaluesare
generallylower thanthat observed.
0.
-?00.
5 -150.
-200.
-250.
Figure 2-13: Climatologicalseasonalecycle of nitrate for the first 4 years 1988-1992of the BATS record Knap et al., 1991, 1992, 1993
NJutrenth mmot/m3
39
Chapter 3
Observation of phytoplankton
Chlorophyll a in the Gulf of Maine
- GeorgesBank region
3.1 Methods
3.1.1 Study area and data source
Our study areaincludesthe Gulf of Maine, GeorgesBank and a small part of the
Middle Atlantic Bight that is north of 39°N Fig. 3-1, O’Reilly and Zetlin, 1996.
In this thesis, the expression"North Middle Atlantic Bight" will be used to refer
to the small areanorth of 39°N on the Middle Atlantic Bight. The Gulf of Maine,
GeorgesBank andthe Middle Atlantic Bight constitutethe threemajor subdivisions
of the NortheastU.S. continentalshelf, with different bottom topographiesFig. 3-2,
O’Reilly and Zetlin, 1996. The Gulf of Maine, a semi-enclosedcontinentalshelf sea,
is boundedby the northeastU.S. and Nova Scotia coastsand includeswaterswest
of longitude 66°W betweenGeorgesBank and the entranceof the Bay of Fundy.
40
The bottom depth throughout much of the Gulf of Maine is greater than 100 m
and averages150 m Uchupi and Austin, 1987. There are three large basins, the
GeorgesBasin, Wilkinson Basin and JordanBasin andseveralsmallerones. Shallow
water of depthless than60 m is mostly confined to a relatively narrowband along
the coastand on StellwagenBank which is west of the JordanBasin and north of
Cape Cod. GeorgesBank is generally limited by the 200 m isobathexcept in the
west and northwest. From GeorgesBasin to GeorgesBank the water shoalsquickly
from 200 m to 60 m within a relatively short distance,less than 30 km. The eastern
and southernextent aredefined by the NortheastChannelandthe shelf-break.The
Middle Atlantic Bight includesthe shelf areabetweenCapeHatterasand the Great
South Channel. The shelf here slopesgently offshoreand is shallow comparedwith
the Gulf of Maine and GeorgesBank.
The concentrationof Chlorophyll a, the dominantphotosyntheticpigment in phy
toplankton, is widely usedby biological oceanographersasa proxy for phytoplankton
biomass.The dataof concentrationof Chlorophyll a were collectedfrom the Marine
ResourcesMonitoring, Assessmentand PredictionprogramMAPMAP of the Na
tional Oceanographicand AtmosphericAdministration, NortheastFisheriesScience
Centerbetween1977 and 1988. Most of the Chlorophyll a datawere obtainedfrom
more than five thousandhydrocastsprofiles of the upper100 m of the watercolumn.
The MARMAP surveysoccupied up to 193 standardsites. In our study areawe
usedstations64 to 193. The station locations are shown in Figure 3-3 O’Reilly and
Zetlin, 1996. The coordinatesof the 193 MARMAP stationswereusedto definethe
standardlocations. Tiles Greenand Sibson, 1978 or Dirichiet cells Ripley, 1981
were constructedaroundeachstandardlocationasshownin Figure3-4 O’Reilly and
Zetlin, 1996. The averagedistancebetweenthe standardMARMAP coordinates
defining the 193 tiles is of 42 km.
The dataare themeanChlorophyll a concentrationsover a 2-monthperiod from
41
44°
3-1: NortheastU.S. continentalshelf reproducedfrom O’Reilly and Zetlin,
4C
400
38°
36°
Figure1996
42
44
NortheastU.S. ContinentalShell
Depth m-1 -0
214040-51604080.100100.2002’0 100000020002002 30003002.4000-4000
Figure 3-2: Bottom topographyof the shelf reproducedfrom O’Reilly and Zetlin,1996 43
420
4cr.
3801
36°
750
Figure 3-3: Stationsand subdivisions of the shelf reproducedfrom O’Reilly andZethin, 1996
44
9661 ‘UThZ pu AJli-JO moij poonpoidoisrj, jo dij, :J7- JniJ
4,99
1 1 0
Lt
89 00L t’L G9L
do[S u1q1;o
tU00 V‘I.L
IUI.j ?j1n0 1i
10ri:. I01t 1U’1S0.4 V13 10Z/y
s10qS10fM11U0J
S1104 P.-W’. yU3flJ0 .
‘lUt1 S02J00
X or 21vl4 U2Ll1flO4jptc fl 0.Lt71J0N
,Xti0 JP’IS .L0rk UJ11FZ
O9-O’ ji:1cp’J%: Wfl ?0
‘9-0t J,41.tSPF’4 D0i?7 Jp4spu’iuntpr.,s +ot-c °0’N p ZU2
‘{‘t U? rrkS X210r1 1110 jtJ0p?11-j V
1U1?.J L.it’5j01 2W1141 ‘‘IT
ue idj Itisru nurtt PPU
II
V
000 *_0 0 0 e.J
‘‘ 0 *-0 /
o 0 fiO
aa
/t
+1+/ / ‘4
+
oU 110+
U 00
o.t 0H a
110 0
o00 0
00
.1 -Oo
OOZC4.11..9
.,104r-; L1i’.i au:rt] ?opic#f 0
S25100. QLl0 it.LVfl? V Q
UW4ifl14N *
Uiu qid’
V
VT4v‘1’
80aaa
00.
0a 0a *c 0
aa0
00t7
Jan-Febto Nov-Dee,by tile, andby depthfor theGulf of Maine-GeorgesBank region.
3.1.2 OAX - optimal linear estimation
Since the dataset is not uniform neitherin spatial nor in temporalcoverage,it is
necessaryto interpolate the irregular databoth in spaceand in time. The OAX
software packageseehttp:/ /aimsirl. bio.dfo. ca/channah/oax.demo.html,by Charles
Hannah, Mary Jo Gracaand John Loder, 1995 is used for the optimal linear es
timation. Distant spaceor time observationshave little influence on an estimate
when comparedto nearbypoints and we chooseonly the best subsetof datapoints
that havethe highestcorrelation,i.e. lowest error with the interpolationpoint. So
OAX optimal linear estimationis a correlationweightedlinearcombinationof a finite
number nu’m_closestof nearestdatapoints.
We supposethat at a datapoint X themeasuredvalueçb1. is the truevalue9X
plus some randomnoise :
q=9X+e n=l,2 ,num_closest 3.1.1
And the linear estimateat grid point X is a sum of the weightedmeasuredvalues
at num_closestdatapoints:
nurn_closest
= I 3.1.2
The coefficientscç- are determinedsuch that the expectedvalue of the sum of
the squarederrors is minimized. Two different estimatesare possibledependingon
the treatmentof the meanvalue of 0x*
46
ANOMALY METHOD
Assumptions:
1. zero mean
= 0 3.1.3
2. known correlationfunction
9X0X-l-oX = FSX 3.1.4
hereF is the correlationmatrix which is the covariancenormalizedby thecovariance
at zero separation.The specific covariancemodel implementedin this packageis:
covariancer = e’1 + r + r2/3 3.1.5
wherer is a pseudo-distancecalculatedas
3.1.6
where
a is the local scalefactor of the i" independentcoordinate,
x and y, are the componentsof x and y respectively.
This pseudo-distancecontrolsthe selectionof nearestneighboursand the genera
tion of weights.
3. errorsareuncorrelatedwith one anotherand with the field
rnn = 0 mOn = U m n 3.1.7
47
4. known errorvarianceE
rnn = E 711 = n 3.1.8
The optimal linear estimationis:
nurn_closest
Ox = > Cxn>Aqrn 3.1.9n=1 rn
where
Anrn = nm = FX - Xrn + ESnrn 3.1.10
is the covariancematrix and
= q5nqx = FX - X 3.1.11
is the covariancevector.
The estimatederror varianceis
Ox - 9x2 = - CnCrnA 3.1.12m,n
The first term is the naturalvariation in the absenceof any dataand the second
term measuresthe informationprovided by the data. Therefore,only the locationof
the datapoints, the knowledgeof the covariancefunction and noise level determine
the error. The error output in the OAX programis
- 23.1.13
The noise level E is assignedthe samevalue 0.1 for all the locations in this project.
48
ESTIMATED MEAN METHOD
For our case actually for generalcasesthe meanof 9x is not known and the
ANOMALY METHOD doesnot apply. A revisedestimateis:
= 0+ Cxn>Acbrn - 0 3.1.14n m
where0 is the estimatedmeanvalue
= rn,nAnrnm3.1.15
rn,n nm
The error varianceis
Ox - Ox2 = Cxx - CnxACxrn +1 - m,nCxrn’n2
3.1.16m,n rn,n nm
The lastterm is the error associatedwith the uncertaintiesof the estimatedmean
and the first two termsare as alreadyexplainedin the ANOMALY METHOD. The
dimensionalerrorscanbe calculatedby multiplying the outputerror by the standard
deviation of the dependentvariable.
3.2 Results
The resultingestimatesof thedistribution of Chl are illustratedin mapsfrom Figure
3-5 to Figure 3-10for the six periods: Jan-Feb,Mar-Apr, May-Jun,Jul-Aug, Sep-Oct
and Nov-Dec respectively. As defined in the Appendix A, Chl is the upper 75 m
water column meanof the 11-year1977-1988averagedphytoplanktonChlorophyll
a concentration.In order to comparewith the mapsfrom O’Reilly and Zetlin 1996,
we usedexactly the samecolormapsasthey used. The colormapfor Chl is [0 .125
49
4 - 8p/l in the CentralShoals,the EasternOuter Shoalsand the NantucketShoals
seeFig. 3-3. Except in the NantuchetShoalsand on the SouthernFlank the con
centrationof Chl decreasesafterthe WS bloom andthe decreasingtrend continues
until the end of the year. When the Chl decreasesafter the WS bloom, the Chl
in southernwatersdecreasesfaster than that in northernwaters. In the Nantucket
Shoalsafter the WS bloom in April, Chl reachesits minimum in Jul-Aug andthen
it increasesagainto reachanotherbloom in Sep-Oct.The maximumof Chl in Sep
Oct has lower magnitudethan that in April and it is called the Fall bloom. On the
SouthernFlank thereappearto be two blooms, theWinter-Springbloom in May-Jun
and the Fall bloom in Sep-Oct, though thesetwo blooms are smaller in magnitude
and not very evident. The Winter-Springbloom starts from Mar-Apr and reaches
bloom level in May-Jun. The Fall bloom occurs in Sep-Octwith lower concentration
thanthe Winter-Springbloom.
Gulf of Maine
TheGulf of Maine, beingdeeperand locatedat higher latitudesthantheMiddle
Atlantic Bight and GeorgesBank, has lower valuesof Chl than the North Middle
Atlantic Bight and GeorgesBank throughout the year. The lowest concentrations
of Chl, less than 0.5 p/l, occur in a largeareaof the GeorgesBasin, JordanBasin
and Scotian Shelf. The nearshorewaters of the WesternGulf of Maine, especially
the isolated areabetweenCape Cod and the PenobscotBay, has generally higher
phytoplankton concentration2 - 4,u/l than the rest of the Gulf of Maine. The
Winter-Spring bloom startshere in Jan-Feb. The bloom level occurs in Mar-Apr
with larger area of values between2 and 4 j..t/l and the Chl valuesare relatively
higher than thoseof Jan-Feb.The areawith valueslower than .5 ,u/l shrinksfrom
the period Jan-Febto the period Mar-Apr. In May-Jun, the westernGulf of Maine
haslower Chl concentrationsthan in Mar-Apr while thenortheasternGulf of Maine
54
hasvalueshigher than thoseobservedin Mar-Apr. In Jul-Aug, the areawith values
lower than .5 /l of Chl in the Gulf of Maine decreasesfurther. Theareawith values
lower than 0.5 i/l reachesits minimumin the period Sep-Oct. The high values in
Nov-Decnearthe ScotianShelf in the northeasternGulf of Maine arenot asreliable
sincethe observationswere poor.
3.2.2 Comparision with maps from the monography of O’Reilly
and Zetlin 1996
Our resultscomparequite well with thoseof O’Reilly and Zetlin. Our maps Fig.
3-5 to Fig. 3-10 andtheir mapsFig. 3-11 look very similar. Thesimilarities listed
below are only some examples.
a. Chl contoursareparallel to isobaths.
b. Theshallowerand/orsouthernregionshaverelatively higherdistributionsthan
the deeperand/ornorthernregions.
c. The high values 2-4 p/l of Jan-Febare in the shallow nearshorewaters on
the NorthernMidshelf of the Middle Atlantic Bight and in the isolatedregionof the
WesternGulf of Maine betweenCapeCod and the PenobscotBay.
d. TheWinter-Springbloomcommencesearlierin Jan-Febin theshallownearshore
waterson the North Middle Atlantic Bight and in the isolated regionof the Western
Gulf of Maine betweenCapeCod and the PenobscotBay, and it commenceslater in
March on GeorgesBank.
Thereare severalmajor differences. Firstly, the minimal Chl in O’Reilly and
Zetlin’s results is during the periodof Jul-Aug while accordingto our results it hap
pensin Sep-Oct. Secondly,thereare no estimatesaroundthe two islandsMartha’s
Vineyard and Nantucketsouthof CapeCod in O’Reilly and Zetlin’s maps,but the
concentrationof Chl thereturns out to be relatively high accordingto our estima
55
Figure 3-11: Mapsof Ch1 reproducedfrom O’Reilly and Zetlin, 1996
Chlorophylla
mean,upper75 n
19774988
Jan4eh
/
MarApr
Miy-Jun
-.
7
JulAug
SepOct NovDec
4
56
tion. Lastly, therearemore small scalevariations in O’Reilly and Zetlin’s contours
than in ours. The abovediscrepanciesmay dependon the very different approaches
we used.
1. Mapping
O’Reilly and Zetlin usedLambert’sconicconformalmapprojectionUchupi, 1965;
Snyder, 1987 to transformfrom the latitude and longitude coordinatesto map co
ordinates. They usedsurface III Sampson,1988 to generatecontoureddistribu
tions, and PcxMapsupplementedby their own Fortran graphicsprogramto shade
and transformthe output from SurfaceIII into a PcPaintbrushbinary graphicsfile
Zsoft, 1990. Our mappingapproachis very different asdetailedin the AppendixA.
2. Estimation
We usedcorrelationasthe weight to estimatethe grid valueswhile O’Reilly and
Zetlin usedthe inversesquaredistancedjstnce2 The numberof nearestdatapoints
we usedto estimatea grid value is 50 while they used8. This is wherewe think the
most significant difference lies. More neighbourdatapoints averageout smal] scale
variationsand thereforereducethe maximumand increasethe minimum.
3.3 Sensitivity tests
We also did sensitivity experimentswith regardsto the interpolation/extrapolation
parametersnum_closestand global_scalesand the estimationmethodbasedon the
Jan-Febperiod. Global_scalesare correlationsused in determiningthe underlying
datastructureseeAppendix A.
Test A: experiments with num_closestwhich has default value 50.
CaseAl: Double num_closestnum..closest= 100.
Only a slight difference is observedbetweenresults of case Al and the default
57
separatedthe datainto six two-monthperiods.
Test C: optimal interpolation with the ANOMALY METHOD.
The meanof Chlorophyll a is substractedfirst to get the anomalydataand the
anomalydatais fed into OAXS for interpolation. Thenthemeanvalue is addedback
to the results. Since the meanof Chlorophyll a is about1.02 .t/l, the distribution of
Chl of this experimentis alwaysand everywherehigher than 1 p/l, which is not rea
sonable.This verifies that for our casethe ESTIMATED MEAN METHOD should
be used insteadof the ANOMALY METHOD.
62
Chapter 4
An adjoint data assimilation
approach to diagnosis of physical
and biological controls on
phytoplankton in the Gulf of
Maine - GeorgesBank region
4.1 Methods
4.1.1 Circulation field
The circulation field of the Gulf of Maine-GeorgesBank region is depicted in Figure
4-1 Beardsleyet al., 1997. The generalcirculation in the Gulf of Maine is cyclonic
Biglow, 1927; Beardsleyet al., 1997 and Lhat on GeorgesBank is anticyclonic.
Thereare two primary and distinct inflows into this region,one is the Scotian Shelf
63
freshwaterthroughtheNorthernChannelnorth of Browns Bank, anotheroneis the
slopewaterthroughthe NortheastChannel. Otherminor sourcesare St. JohnRiver,
St. Croix River, PenobscotRiver etc.. Outflows go to the west mainly along the 60
m and 100 m isobathssouthof GeorgesBank and the Nantucket Shoals. The inflow
from the Scotian Shelf continuespast the mouth of the Bay of Fundy and joins the
Maine CoastalCurrent, togetherwith the input from the St. John River and other
sources.TheMaine CoastalCurrentseparatesinto two branchesnearPenobscotBay,
with one branchflowing seawardsand feedingthe JordanBasin cyclonic gyre. The
otherbranchcontinuesalong the coastand bifurcateswhenit gets to CapeCod, with
a portion branchingseawardsandjoining the clockwise circulationon GeorgesBank
andanotherbranchcontinuingsouthwards,beforeturning westwardandjoining the
outflow alongthe 60 m isobath. Before the bifurcationat CapeCod, a subbranch
feeds into the circulation of MassachusettsBay and CapeCod Bay from the point
of CapeAnn. The Great South Channelsill depth70 m, the NortheastChannel
sill depth 230 m, and the Northern Channel140 m connectthe Gulf with the
adjacentwaters on the continentalslope. Exchangeof seawaterbetweenthe Gulf
and North Atlantic is fairly restricted,occuringmostly through the deepNortheast
ChannelRampet al., 1985; Mountainand Jessen,1987.
Intensemodeling activities have been carried out in the Gulf of Maine-Georges
Bank region. Lynch et al. 1996 employeda finite elementapproachto facilitate
realistic representationof the complex geometryin this area. The model is three
dimensional,hydrostatic,fully nonlinearand it incorporatesa level 2.5 turbulence
closureschemeMellor andYamada,1982 to representthevertical mixing of momen
tum, heatand mass. The climatologicalmeancirculationhasbeenshownto compare
well with availableobservationsNaimie, 1996; Lynch et al., 1997. Thesolutionsare
separatedinto six bi-monthlyperiodsand are theinputs to the two-dimensionalADR
advection-diffusion-reactionequationon the samegrid. Boundary conditions used
64
of dataDickey, 1991 and mathematicalmodelsare frequentlyused,dataassimila
tion is becomingan importanttopic. Thereexistsa varietyof assimilationtechniques
including successivecorrection Cressman,1959; Bratseth,1986, optimal interpo
lation Gandin, 1963; Lorenc, 1981, Kalmnan filtering Kalman, 1960; Kalmanand
Bucy, 1961; Ghil et al., 1981 and the variationalmethod Lewis and Derber, 1985;
Derber, 1985; Le Dimet and Talagrand,1986; Lorenc, 1988 a, b. The dataassimila
tion techniqueusedin this study is the variational, or adjoint method. The adjoint
methodhasbeenusedfor parameterestimation in a variety of oceanographicsystems
Panchangand O’Brien, 1989; Lardner amid Das, 1994. More recently, it hasbeen
usedwith simplebiological modelsLawsonet al., 1995. In the model McGillicuddy
et al., 1998 we use, the computercodefor the adjoint is constructeddirectly from
the model computercode. This techniqueis straightforwardand reducesthe chance
of introducingerrors in the constructionof the adjoint code.
The coupled model we use to study our problem is from McGillicuddy et al.
1998. The two-dimensionaladvection-diffusion-reactionequationfor the positive
definite depth-averagedbiology concentrationBx, y, t is expressedas:
+ VB - V. HKVB = Rx, y 4.1.1
where H is the bottom depth. The reactiontermRx, y variesin spaceonly, and
servesas a highly idealized parameterizationof population dynamics. PositiveR
implies net growth and negativeR implies net mortality.
In order to measurethe misfit betweenpredictedB and observedconcentration
B0b5, a cost functionJ is defined:
rL tL5 pt1J
= j J J 8MB - B0b52dxdydt 4.1.2L2 L t5
66
where L and L2 representthe extent of the horizontal domain of interest, and
M hasvalue of one whereverobservationis available in spaceand time, anl zero
otherwise.
Given initial conditions B05x,y, t0, the output from the fprward model is the
value of the cost function, which gives a measureof the misfit betweenthe model-
derivedconcentrationB and the measuredB0b5x,y, t1 whenthe next set of obser
vation is availableat t1. Integrationof the adjoint equationthen transformsthese
measuresof misfit into the gradient of the cost function with respectto the control
variable in thsi case,R. The gradient is then usedto find the direction in which
the valueof R is adjustedin order to decreasethe differencebetweenthe model out
put and the data. However, the cost function is typically not expressedexplicitly in
termsof R and in order to avoid the difficulty of the gradientcalculation,Lagrange
multipliers are introducedand the Lagrangefunction, L, is definedas
L L0 t1 1L = +
f_Lx f_L9 L A-- + . VB - V. HKVB - Rdxdydt 4.1.3
where A = Ax, y, t is the unknownLagrangemultiplier.
The model equations,the adjoint equationsand the gradient of the costfunction
areobtainedby finding a saddlepoint of the Lagrangefunction, that is, a point in B,
R, A spacewherethe partialderivativesof L vanishsimultaneously, = = - =
0. The R that minimizes L at the saddlepoint is to be obtained. The requirement
of = 0 returnsthe model equation. The adjoint model is an advection-diffusion
reactionequationfor theLagrangemultiplier forcedby themisfit betweenthemodeled
and observedvaluesof B
-
- V A7- V. HKVA = -2MB - B0b5 4.1.4
67
with homogeneousboundaryconditions.
The gradientof the cost function with respectto the control variableR can also
be derivedthrough the integrationof the adjoint model
a tti
-=j Ax,y,tdt 4.1.5
Oncethedirectionto adjustR is found, the stepsize, that is the sizeof thechange
in that particulardirection, must be determined.After the variablesareadjustedby
the calculatedstep size and direction, the model is again applied and the process
repeated.Hence, by repeatingthe iterative procedurewhich includesa model run,
an adjoint run and a step size calculation,convergenceis reachedon the valuesof
Rx, y that minimize thecost function. This alsoprovidesthebestfit of B to the ob
servationB0b5 underthe constraintthat the forwardmodel equationis satisfied. The
optimal stepsizeis determinedusingthe steepestdescentmethodasin Derber:1985.
4.2 Results
The interpretationof the effect of the circulation on passivelydrifting biology is con
fined to theregionwhich is not affectedby theboundaryeffects, sincethe distribution
of phytoplanktonis not very well sampledin some of the inflow regions asshown in
chapter3. For this purpose,McGilhicuddy et al. 1998 carriedout a seriesof control
volume simulations. In the experiments,the concentrationis assignedwith valueone
uniformly in the domain and zero at inflow. After two monthsof forward integra
tion fbr eachof the six bi-monthly periods, a substantialregionof the domain not
affected by boundaryeffects is found, although the details are slightly different for
different periods. The "region of interest" as definedin McGilicuddy et al. 1998 is
68
the intersectionof the areasin which 1 observationsareavailableand2 boundary
effects are minimal on bi-monthly time scalesFig. 4-2, McGillicuddy et al., 1998.
Our study will be confinedinside of the "region of interest".
As we seein Figure 4-1, thereare flows onto and away from GeorgesBank. The
questionsof interestarewherethetransportpathwaysareand how much thecircula
tion retainsthepopulationon the Bank undertheinfluenceof theflows. Therefore,a
secondset of control volume two-monthintegrationswereperformedin McGillicuddy
et al. 1998 for eachof the bi-monthly periods, with the initial conditions set to
one on the Bank and zero elsewhereFig. 4-3 a. The initial conditonsand in
tegration results for periods January-February,May-Juneand September-October
are illustrated in Figure 4-3 McGillicuddy et aL, 1998. In the period of January-
February Fig. 4-3 b the high concentrationon GeorgesBank is diluted by the
zero-concentrationinflow from the Gulf of Maine. A pathwayto the southwestbrings
the high concentrationfrom the crest of the Bank to the Great South Channeland
continuesto the westuntil it is out of thedomain. Theconcentrationcenteris shifted
to the southwestedgefrom the centerof the Bank. Duringspringtime Fig. 4-3 c
thedilution causedby theinflow from theGulf of Maineandthesouthwestwardtrans
port from the Bank crest still exist, however the establishedseasonalstratification
enablesthe clockwisecirculation to be more retentive. Although the concentration
centeris shifteda little bit to theweston theBank, theorganismsaremostlyconfined
insideof the 60 m isobathandthe concentrationin the GreatSouthChannelis lower
thanits winter values. The influenceof the southwestwardflow off the Bank crestis
still evident, but the concentrationcenter is moved to the west insteadof southwest,
which servesasanotherpieceof evidencefor the moreretentiveclockwiseflow pattern
on the Bank. When the seasonalstratificationis the strongestduring summertime,
the retentivecharacterof the GeorgesBank circulation systemreachesits peak Fig.
4-3. The distribution remainscenteredon the Bank as in the initial condition and
69
3.5 4 8] ,u/l finer than in Chapter3 for the conveniencein analysingtheinversionre
sults. Theinversionresultsaremapsof the sourceterm, theadvectiveflux divergence
term, thediffusive flux divergenceterm and thetendencyterm in the ADR equation.
The tendencyterm is calculatedas the sum of the other threeterms. The modeled
concentrationsof the last forward model run all very much resemblethe correspond
ing observationsand so only that from the first period which is initialized with the
January-Februaryobservationis shown in Figure 4-10 asan exampleto be compared
with the March-April dataof Figure 4-4 and 4-5. The cost function valuesare re
ducedapproximatelyan order of magnitudeafter 50 iterationswith the exceptionof
the periodsfrom July-Augustto September-Octoberand from September-Octoberto
November-DecemberFig. 4-il. In theselast two periods, the cost functionvalues
are reducedapproximatelyan order of magnitudeafter 200 iterations.
January-February to March-April
The sourceterm mapshows stronggrowth red shadingon the crest of Georges
Bank, moderategrowth yellow shading in the coastalareaof MassachusettsBay
andweak growth greenshadingin most of theareaof the Gulf of Maine, especially
in the western Gulf. On GeorgesBank, a balanceexistsbetweenthe advectionand
the sourceterm. Flow onto the crest acrossthe miorthern flank of the Bank iniports
low concentrationsof phytoplanktonfrom the Gulf of Maine. The positive advec
tive flux divergenceon the southernpart of the Bank transportshigh concentration
fluid from the crest towards the Great South Channelon the southwest see Fig.
4b, McGillicuddy et al., 1998. However,the net growth and net mortality coincide
with the negativeand positive advectiveflux divergencein space,respectively. The
net growth has larger magnitudethan the iiegative advectiveflux divergenceand
the net mortality hassmallermagnitudethan the positive advectiveflux divergence,
thereforethe overall tendencyon GeorgesBank is for the concentrationto increase
72
from January-Februaryto March-April. In the coastalregion of MassachusettsBay,
the negativecontributionfrom advectionis weakerthanthat from the net moderate
growth. The tendencyis then largely controlled by the net moderategrowth. The
concentrationin this region increasesslightly. In the Gulf of Maine, the tendencyof
phytoplanktonvaries with space. Only someregions in the interior of the Gulf and
the westerncoasthavepositive tendencies.
March-April to May-June
In the coastalregion of CapeAnn and MassachusettsBay, the positive source
term hasgreatermagnitudethan in the previousperiod. However,strong negative
divergenceof advectiveflux brings low-concentrationwaterherefrom the interior of
the Gulf of Maine. The net tendencyof this region is that concentrationdecreases
from March-April to May-June, with the negativecontribution from the advective
flux divergenceovershadowingthe growth. On GeorgesBank, comparedwith the
previousperiod,the sourceterm decreaseswith smaller positivevalues in the center
and the northernpart of the Bank. Due to the strongerstratificationcomparedwith
the previousperiod, the clockwiseflow patternon the Bank is more retentive. The
position of the dipole structureof advectiveflux divergencered and blue on the
Bank rotatesslightly clockwiseandthe negativecontributionfrom the Gulf of Maine
decreasesin magnitude.The combinedinfluenceon GeorgesBank is that the concen
tration over most of the regiondecreases,exceptfor a small areaof thewesternBank
where the concentrationincreasesa little bit. In the Gulf of Maine, the tendencyis
negativeand relatively small.
May-Juneto July-August
In the coastalregionof CapeAnn, MasschusettsBay and CapeCod Bay, the mag
nitude of net growth is smallerthan that from March-April to May-June. Because
74
the flow field still brings low concentrationfrom the Gulf of Maine into this region
and this influence overweighsthe weak growth, the overall tendencyof this region
is negativeand hasa magnitudesimilar to the previousperiod. On GeorgesBank,
the dipole structureof the advectiveflux divergencerotatesclockwisefurtherand the
magnitudesare smallerthan that in the precedingperiod. On GeorgesBank, the
sourceterm hasnegativecontribution except in a small region on the northeastern
edge. With the small areaof net growth overshadowedby the negativeadvectiveflux
divergencefrom the Gulf and the net mortality exceedingthe positive advectiveflux
divergencefrom the crestto the GreatSouthChannel,theconcentrationin thewhole
region of GeorgesBank hasa tendencyto decrease.Except in the coastalregion of
CapeAnn, MassachusettsBay and CapeCod Bay, thetendencyin the Gulf of Maine
is for the concentrationto increaseslightly.
July-August to September-October
On GeorgesBank, the sourceterm and the advectiveflux divergencetermmirror
eachother in spacealmost exactly. On the southernand northernBank, the source
termis positiveandtheadvectiontermis negative.On theeasternand westernBank,
the sourceterm is negativeand the advectionterm is positive. Except in a small area
on the northernand southernedge,the tendencyis to decreasewith the net mortal
ity overcomingthe positive advectionand the net growth overcomeby the negative
advection. On the southernand northern edge, there is small-areavery weak in
crease.In the Gulf of Maine, the situationin thewesterncoastdoesnot changemuch
from the previousperiod. Inside of the Gulf of Maine the tendencyof increasefrom
May-Juneto July-August is substitutedby a trendthat is partial increaseand par
tial decline, with the westernpart havingmore tendencyto decreaseand the eastern
part havingmoretendencyto increase.Theincreaseanddecreasearebothvery weak.
77
September-October to November-December
The source term shows moderategrowth on northernand northeasternGeorges
Bank and net mortality on rest of the Bank. Although the strong seasonalstratifi
cation in summertime from September-OctoberenablesGeorgesBank to be sort of
resistantto the influence from the Gulf of Maine, the negativeadvectiveflux diver
gencecontributionto the Bank still persistson the north flank. The dipole structure
of advectiveflux divergenceon the Bank is not shifted clockwise as much as in the
precedingperiod, which suggeststhat the circulation on the Bank is not so retentive
as in the precedingperiod. On the northern Bank, the net growth is overshadowed
by the low concentrationinflow from the Gulf of Maine or from the westernpart of
the Bank and the tendency is for the concentrationto decrease. On the southern
Bank, there is a regionwherethe positive concentrationinput from the Bank crest
counteractsthe mortality and the tendencyis slightly positive. In rest of the areaon
the Bank, the net mortality hasa largermagnitudethanthe positive advectiveflux
divergence,and the concentrationtends to decrease. In the coastalregion of Mas
sachusettsBay and CapeCod Bay, becauseof the impact of the low concentration
inflow from the Gulf of Maine at Cape Ann and the weak mortality, declineis the
overall trend. In the Gulf of Maine, the tendencystill varies with space,but in this
periodthe leadingtrend is to decrease.
November-December to January-February
In this period, the growth in the coastalareaof CapeAnn is comparablewith
that in the period from January-Februaryto March-April and is thesecondstrongest
of all thesix periodssecondaryto that from March-April to May-June.The growth
on GeorgesBank is weakerthanthat in thecoastalregionof CapeAnn. Theinflow at
CapeAnn brings low-concentrationwaterfrom theinterior of the Gulf of Maine. The
combinedeffect of the growth andthe inflows enablestheconcentrationin this coastal
79
region to increase,so asto acceleratethe arrival of the spring bloom. On Georges
Bank, with the declining seasonalstratification, the circulation on the Bank is less
retentivethan in the summerseason.The negativeadvectiveflux divergenceacross
the north flank overshadowsthe net growth. The positive advectiveflux divergence
from the Bankcrestto the GreatSouthChannelhasasmallermagnitudethanthe net
mortality in most of the placeswherethey intersect.Therefore,the concentrationon
GeorgesBank decreasesexcept over a limited areain the southwest,which is Ofl the
pathwayof the outflow from thecrest to thesouthwest.On thenortheasternBank, in
a small region, the decreasingtrend reachesits peaki.e. the negativetendencyhas
its maximum magnitude.The concentrationin the westernGulf of Maine increases
and that in the easternGulf of Maine decreases.
Diffusion doesnot havea systematicimpact on the biology distribution,because
the diffusive flux divergenceterm generallyhasa smallermagnitudethanthe source
term and the advectiveflux divergenceterm. Sometimesit does have comparable
magnitude,suchas in the period from January-Februaryto March-April on Georges
Bank, but it is rather noisy and organizedin small patchesthat do not affect the
main featuresof the biology distribution. The only possibleeffect of diffusion is to
smoothout the biology concentration.
4.3 Discussion
The resultsrevealsignificant seasonalandgeographicvariationof phytoplanktoncon
centration,which is compatiblewith the climatologicaldistribution patternsderived
from the MARMAP dataand theflow field. Two populationcentersare found in the
GeorgesBank-Gulfof Maineregion, one is on GeorgesBank itself and the other is in
the westerncoastalregionof the Gulf of Maine i.e. the coastalregionof CapeAnn,
82
MassachusettsBay and CapeCod Bay. During the periodof January-Februaryto
March-April, it is a time of growthfor both GeorgesBank and thewesterncoastalre
gion of the Gulf of Maine and thegrowth is strongeron GeorgesBank. Therefore,we
definethis periodasa time of stronggrowth on GeorgesBankand a time of moderate
growthin the westerncoastalregionof theGulf of Maine. After thespringbloom peak
in March-April, comesthe time of declinefrom March-April to November-December.
March-April to July-August is a period of faster decline, while from July-August
until the end of the year, the concentrationdecreasesslightly and is an interval of
slight decline or relative stability. The changingtrend from November-Decemberto
January-Februaryon GeorgesBank is oppositeto that in the coastalregion of the
westernGulf of Maine. Phytoplanktonabundanceincreasesin the coastalregion of
the westernGulf of Maine anddecreaseson GeorgesBank in the meantime. The de
cline on GeorgesBank is evenstrongerthanthat during the periodfrom July-August
to November-December.
Themostimportantandinterestingresultsarethat the seasonalcyclesof thephy
toplanktondistribution are controlledby both the biological sourceandthe physical
advectionwhich basically balanceseach other, and their relative significancevaries
with spaceand time. On GeorgesBank, net growth negativeadvectiveflux diver
gencealways lies north of the net mortality positive advectiveflux divergenceand
net growth net mortality mirrors negativeadvectiveflux divergencepositive ad
vective flux divergencein space. Net growth and net mortality thus respectively
counterbalancenegativeand positive advectiveinfluencethroughoutthe yeardespite
the seasonalor spatialvariability.
As we haveshown in Chapter2, the phytoplanktongrowth or mortality is very
closelyrelatedto the availability of nutrientsand sunlight in the mixed layer. During
winter, strong mixing continuouslyimports into the euphotic layer nutrients from
below. While in summer, the stratification inhibits nutrient flux from below the
84
shallow mixed layer and so the nutrient supply is limited. Therefore, on Georges
Bank, most of the biological growth occurs during the interval betweenJanuaryand
April, when there is sufficient nutrientsand light availability aswell, while in other
months the dominant source is weak growth or net mortality due to the lack of
nutrientsand/orlight. In the coastalregionof the westernGulf of Maine, the source
term is positive throughoutthe year except from September-Octoberto November-
December.Onepossiblereasonis the availability of both nutrientsand light resulting
from theshallow depthandthe consequentcompletevertical mixing in this particular
region.
The value of advectiveflux divergenceis also a function of vertical mixing or
stratification,especiallyon GeorgesBank. During winter whenthereis deepmixing,
the circulationpatternon GeorgesBank is less retentive,and hencethe distribution
on the Bank is moresusceptibleto the influence of the flow from the Gulf of Maine
thanduringsummerwhenthereis strongstratification. Theadvectiveflux divergence
termincluding both the advectionfrom the Gulf of Maine on thenorth flank andthe
advectionfrom the crest to the southwesthasthe largestmagnitudein the period
of January-Februaryto March-April. Its magnitudedecreaseswith the arrival of
summer.Thespatialvariationofthe influenceof advectionon biologyis quite notable,
too. Generallyspeaking,themagnitudeof thenegativeadvectiveflux divergencefrom
the Gulf of Maine is larger in magnitudeon the north flank of GeorgesBank than
in the coastalregion of the westernGulf of Maine. However, it is importantto note
that, advectionis the controllingfactorof temidencymoreoften in the coastalregion
of the westernGulf thanon the Bank, becauseof the small magnitudeof the source
term in the formerregion.
In the coastal region of the western Gulf of Maine, the tendency is generally
controlled by the negativeadvectiveflux divergence,with the exceptionthat from
November-Decemberto March-April, the contribution from advection is overshad
85
owedby themoderatelyhigh netgrowth. Thecaseon GeorgesBank is quite different.
The only time whenthe negativeinfluence by the advectionfrom the Gulf of Maine
plays a controlling part togetherwith the net mortality is the declineinterval from
March-April to May-June. During the seasonof increasefrom January-Februaryto
March-April, the advectionfrom the Gulf of Maine is overshadowedby the positive
sourceterm. It is thenet growth and the positive advectiontogetherthat causesthe
increaseof the phytoplanktonconcentration.From May-Juneto January-February,
the declinetrend is determinedby the net mortality and also by the negativecontri
bution from the Gulf of Maine. In this period, while the low concentrationfrom the
Gulf of Maine doeshelp to overcomethe net growth on the north flank, the major
factoris the net mortality that overbalancesthe advectionfrom the crest.
86
Chapter 5
Conclusions
In this thesis, we studiedthe interactionbetweenphysicaland biological dynamics
with two approaches.Firstly, in the SargassoSea,we looked into the responseof a
five-componentecosystemto the externalforcing heat flux, wind stressand surface
salinity, investigatingthe sensitivity of the ecosystemto biochemicalparameters.
Secondly, in the Gulf of Maine-GeorgesBank region, we exploredthe effect of the
circulation field on the distribution of phytoplankton,and the relative importanceof
physical circulation and biological sourceto the concentrationof phytoplanktonas
well.
In the researchof the SargassoSea, the model results comparequite successfully
with the observatiomiandthe model resultsof Doneyet al., 1996. The default model
resultsand the sensitivityexperimentsshoweda seasonalcycle of physicsandbiology.
In summer,the shallow seasonalthermoclinedepthand the weakconvectioninhibits
the nutrientssupply from below the mixed layer, thereforethe concentrationsof all
the biochemicalvariablesare low and limited to a shallow surfacelayer. In winter,
the strong vertical convectionand deepmixing make it possiblefor more nutrients
to enrichthe euphotic zone. Hence,right after the winter time, in March and April,
87
phytoplanktonfeedingupon nutrients reachesits spring bloom level. The bloom of
zooplankton,which feeds on phytoplankton, follows that of phytoplanktonwith a
time lag of about two weeks. The resultsof the sensitivity experimentsshow that
zooplanktonis usuallymoresensitiveto the variationof biochemicalparametersthan
phytoplankton. The systemis sensitiveto all the parametersexcept for the phyto
planktonself-shadingcoefficient, ammoniumhalf-saturationconstant,photosynthesis
efficiency parameter,and ammoniumoxidation rate. For example,smaller detrital
sinkingrateandhigherdetrital reninerahizationrateprovidehighernutrientsconcen
tration in the euphotic zone, while a smaller light extinction coefficient gives more
and deepersolar radiationin the watercolumn. Both circumstancesallow theblooms
to be more intense,deeper,and longer in time.
The researchin the Gulf of Maine-GeorgesBank region revealsseasonalandge
ographicvariations of phytoplanktonconcentration,which are consistentwith the
MARMAP data. In this region, thereare two populationcenters,one on the Georges
Bank, and the other in the coastalregion of the westernGulf of Maine. January-
February to March-April shows a strong growth on GeorgesBank and a medium
growth in the coastalregion of the western Gulf of Maine. March-April to July-
August is the declinetime for both of the two population centers. July-August to
November-Decembershows a slight declinelimited to relative stability period both
on the Bank and in the coastal region of the western Gulf. November-December
to January-Februaryis a growth period in the coastalregionof the westernGulf of
Maine and a decline period on GeorgesBank. The inversion results verify that the
seasonalcyclesof the phytoplanktondistributionarecontrolledby both thebiological
sourcenet growth or mortality andthe physicaladvectionby the circulation. Both
the biological sourceand the physicaladvectionare functionsof spaceand time. The
relative importanceof them also varies with spaceand time. The seasonalcycles
of the magnitudeof net growth mortality approximatelycoincide with that of the
88
magnitudeof thenegativeadvectionpositiveadvection,especiallyon GeorgesBank.
Therefore,net growth and net mortality basically counterbalancenegativeand pos
itive advectiveflux divergencesthroughoutthe year, despitethe seasonalor spatial
variability. The magnitudeof the negativeadvectiveflux divergencefrom the Gulf of
Maine is larger on the north flank of GeorgesBank than in the coastalregion of the
western Gulf of Maine. However, advectionis the controlling factor of the tendency
more often in the coastalregionof the westernGulf of Mainethan on GeorgesBank,
becauseof the small magnitudeof the sourceterm in the former region. This part
of researchalso suggeststhat the two separatedpopulationsin the coastalarea of
the westernGulf of Maine and on GeorgesBank are self-sustaining,and that Gulf of
Maine is not the sourcefor them.
In the two-dimensionalmodel, the source term Rx,y is a function of space
only, thus not representingthe underlyingbiological processesrealisticlly enough. A
morerealisticrepresentationof thesourcetermis needed.Forthe generaltopic of the
interactionof biology andphysics,a full three-dimensionalbiological-physicalcoupled
modelwould undoubtedlyprovidebetterunderstandingand more realisticresults. A
majorfocusof future researchis thereforeto combinethe aboveone-dimensionaland
two dimensionalmodelsusedin this research,i.e. to build up afull three-dimensional
biological-physicalcoupledmodelwith a moresophisticatedbiological reactionterm,
andto investigatethe responseof the biological dynamicsto the externalforcing and
the horizontal circulation.
89
Appendix A
Computation and mapping of the
water column mean distribution of
Chlorophyll a
Step1: Coordinate transformation.
Latitude and lomigitude coordinatesof eachstationare transformedinto map co
ordinatesusing a Fortranprogramwrittemi by ChristopherE. Naimie of Dartmouth
College 1996.
Step2: Select tile-averaged Chlorophyll a data for interpolation.
We first separatethe data into the six two-month periods: Jan-Feb,Mar-Apr,
May-Jun, Jul-Aug, Sep-OctandNov-Dec. For instance,in order to interpolatein the
Jan-Febperiodonly the datameasuredin the first two-monthperiodfor all theyears
1977-1988are extracted.
Step3: Compute bathymetric gradient file.
Step4: Prepare the OAX grid files.
The estimationis centeredin themiddle of eachtwo-monthperiodwith time scale
90
30 day andhorizontalbasescale30 km. The horizontalcorrelationscalesare specified
in termsof the local cross-isobathand along-isobathdirectionswhich are defined by
the bathymetricgradient vector.
Step5: Run OAX.
For our casethe optimalestimationmethod "ESTIMATED MEAN" is usedsince
it doesnot makethe knownzero meanassumption,unlike the "ANOMALY" method.
The OAX model parametersincluding global_scalesand num_closestare definedin
a deck file. Global_scalesare correlationsusedin determiningthe structureof the
underlyingdatastructureCharlesHannah,1995.
Step6: Extract level surface files.
In this step elevenfiles for depthlevels 1 m, 5 m, 10 m, 15 m, 20 m, 25 m, 30 m,
35 m, 50 m, 75 m and 100 m areobtained.
Step7: Calculate the water column mean of Chlorophyll a.
We integrateChlorophyll a over the upper 75 m of the water column and divide
theintegral by 75 m to get the mean.This two-monthmeanof the upper75 m water
column is calledChl.
Step8: Produce .s2r file with the Chl,4, data.
The .s2rfile is the FEM filetype, asdetailedin thedatafile standardsfor the Gulf
of Maine Project from the Numerical Methods Laboratoryat DartmouthCollege.
This documentis locatedin the OPNML notebookunderExternal Documents. In
the .s2r file thereare two columns, the first of which is the node numberand the
secondcolumn is floating point.
Step9: Read and map the .s2r file.
Two matlabtools "read_s2r.m"and "coiormesh2d.m"areusedto readandplot the
.s2rfiles. In order to facilitatecomparisonwith the mapsfrom the reportof O’Reilly
and Zetlin 1996, the colormapswe useare exactly the sameas thoseO’Reilly and
Zetlin used.The colormapfor Chl is [0 0.125 0.25 0.5 1 2 4 8] j.t/l.
91
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