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

2

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

6

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

7

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

8

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.

9

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

10

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

11

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.

12

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

13

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

14

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

15

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.

16

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

17

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

19

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.

20

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

21

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

22

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


c Phytoplanlcton mmollm3 Case C2 d Zooplankton mmollm3 Case C2

. .


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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