s 64 (2007) 89–109www.elsevier.com/locate/jmarsys

Journal of Marine System

A generalized model of pelagic biogeochemistryfor the global ocean ecosystem. Part I: Theory

M. Vichi a,⁎, N. Pinardi b, S. Masina a

a Istituto Nazionale di Geofisica e Vulcanologia, Sezione di Bologna, V. Creti 12, 40128 Bologna, Italyb Alma Mater Studiorum Università di Bologna, Centro Interdipartimentale per la Ricerca sulle Scienze Ambientali, Ravenna, Italy

Received 3 November 2005; received in revised form 1 March 2006; accepted 12 March 2006Available online 3 July 2006

Abstract

The set of equations for global ocean biogeochemistry deterministic models have been formulated in a comprehensive andunified form in order to use them in numerical simulations of the marine ecosystem for climate change studies (PELAGOS,PELAgic biogeochemistry for Global Ocean Simulations). The fundamental approach stems from the representation of marinetrophic interactions and major biogeochemical cycles introduced in the European Regional Seas Ecosystem Model (ERSEM). Ourtheoretical formulation revisits and generalizes the stoichiometric approach of ERSEM by defining the state variables as ChemicalFunctional Families (CFF). CFFs are further subdivided into living, non-living and inorganic components. Living CFFs are thebasis for the definition of Living Functional Groups, the biomass-based functional prototype of the real organisms. Both CFFs andLFGs are theoretical constructs which allow us to relate measurable properties of marine biogeochemistry to the state variablesused in deterministic models. This approach is sufficiently generic that may be used to describe other existing biomass-basedecosystem model.© 2006 Elsevier B.V. All rights reserved.

Keywords: Marine biogeochemistry; Biomass-based ecosystem model; Ecological stoichiometry; ERSEM; PELAGOS; BFM

1. Introduction

Biogeochemical models representing trophic andchemical interactions in the marine system have beendiscussed largely in the past 20 years (see reviews byHofmann and Lascara, 1998; McCarthy et al., 2002;Denman, 2003), particularly focusing on a biomass-based description of the pelagic system. Nevertheless, atheoretical formulation of the basic equations in terms ofpartial differential equations (pde) of key biogeochem-ical constituents and associated rates has not been

⁎ Corresponding author. Tel.: +39 051 4151 456; fax: +39 051 4151499.

E-mail address: vichi@bo.ingv.it (M. Vichi).

0924-7963/$ - see front matter © 2006 Elsevier B.V. All rights reserved.doi:10.1016/j.jmarsys.2006.03.006

published yet in the scientific literature. This kind ofapproach helps to define the numerical implementationof marine biogeochemistry coupled with physicalcirculation models at all spatial and temporal scales.

The aim of this paper is to formulate a set of equationsdescribing the pelagic biogeochemistry coupled to phy-sical processes of importance. We call this a generalizedmodel of pelagic biogeochemistry, meaning the mathe-matical representation, by means of partial differentialequations of biogeochemical processes. In general thepdes contain the divergence of material fluxes that deter-mine the rate of change of the ecosystem state variables.

The biogeochemical rates of change are outlinedstarting from the parameterizations of the EuropeanRegional Seas Ecosystem Model (Baretta et al., 1995;

90 M. Vichi et al. / Journal of Marine Systems 64 (2007) 89–109

Baretta-Bekker et al., 1997, ERSEM I and ERSEM II),which was the first comprehensive ecosystem model toinclude physiological considerations in the definition ofthe divergence of material fluxes. However, in theoriginal ERSEM papers (Baretta et al., 1995; Baretta-Bekker et al., 1997, and other papers in the two specialissues), the biogeochemical process formulations weregiven in a finite difference form, and a generalformalism of pdes was actually lacking.

On the other hand several implementations of thismodel have shown the skill of this approach, both incoastal areas with large land-derived inputs but also inthe oligotrophic Mediterranean regions and in thesubtropical Atlantic Ocean (Ruardij et al., 1997; Allenet al., 1998; Vichi et al., 1998; Zavatarelli et al., 2000;Obernosterer et al., 2001; Allen et al., 2001; Petihakis etal., 2002; Vichi et al., 2004; Raick et al., 2005). Thesame approach has also been used in the context ofclimate studies, particularly to capture and analyzeclimate variability in the North Sea and in the AdriaticSea (Taylor et al., 2002; Vichi et al., 2003a). A directdescendant of ERSEM, the Biogeochemical Flux Model(BFM), is now being developed in the framework of theEU project MFSTEP (Mediterranean Forecasting Sys-tem Toward Environmental Predictions, http://www.bo.ingv.it/bfm) and applied to the whole Mediterraneanbasin and subregional seas. Finally, a recent publication(Blackford et al., 2004) has shown that the ERSEMapproach to pelagic biogeochemistry was able to adaptto contrasting sites in the world ocean making itappealing for applications in the global ocean.

In this paper we present the pde formulation ofpelagic biogeochemistry in a general framework. Asrecently stated by Anderson (2005), the continuedarticulation of details in ecosystem models needs to bepursued with due care and attention to the formula-tions employed, and therefore a common unifiedformalism is necessary. Our aim is to generalize thebiogeochemical concepts developed in ERSEM be-yond their original implementation in coastal ecosys-tems. We do that elucidating the basic constituents andintroducing a clear definition of the ecosystem statevariables that may be further generalized to includemore processes if needed. Particularly, our equationsare different from ERSEM for the addition ofimportant biogeochemical constituents such as ironand chlorophyll which are relevant for global oceanbiogeochemistry.

We propose a new nomenclature and formalismwhich highlight the general concepts behind the biomassapproach to marine biogeochemistry. We also formalizethe definition and grouping of model state variables and

interactions, which helps to understand the basic modelhypotheses and assumptions. A companion paper (Vichiet al., 2006-this issue) presents the numerical imple-mentation of this revised model to the global oceanecosystem with a direct coupling to a general circulationmodel, and a comparison with the distribution andseasonal variability of bulk properties (nutrients andsatellite chlorophyll) and the different phytoplanktongroups.

The paper is organized as follows. In Section 2 wegive an overview of the theoretical approach and thebasic equations describing the pelagic biogeochemicalprocesses. In Section 3 we illustrate the basic formalismand nomenclature used throughout the paper. Section 4presents the physical parameters that affect pelagicbiogeochemistry. In Section 5 the biogeochemicalequations are written in all details for the pelagic statevariables and Section 6 offers a discussion.

2. Towards a generic formalism for pelagicbiogeochemistry

The ERSEM view of the marine ecosystem wasbased upon the recognition that the major ecologicalfunctions of producers, decomposers and consumers andtheir specific trophic interactions can be expressed interms of material flows of basic elements (C, N, P, etc.).The concentration and characteristics of organic andinorganic compounds in the water were thus seen undera stoichiometrical perspective as the final result of thedirect uptake and release by producers, decomposers,heterotrophic consumers of these constituents. Thecentral role was thus not played by single species butby the total biomass of a collection of species sharingthe same functional behavior.

This functional approach is rewritten here with a newformalism which is based on the definition of ChemicalFunctional Families (CFF) and Living FunctionalGroups (LFG). The core components of the formalismare the CFFs (Fig. 1) which are theoretical constructsthat are useful to describe the way materials areexchanged in marine biogeochemistry. CFFs can besometimes identified as specific compounds such asdissolved inorganic nutrients, but in most of the casesare defined as the inventory of a certain biogeochemicalelement contained in more complex living and non-living components of marine biogeochemical cycles. Atypical example is the total C content in phytoplanktonor bacteria and N content in dissolved or particulateorganic matter. CFFs can be described in terms ofconcentrations and the choice of CFFs as the basic statevariables is natural since they are measurable quantities

Fig. 1. Scheme of the various types of Chemical Functional Families (CFF) expressed in terms of basic biogeochemical elements. Hydrogen is notconsidered a basic constituent in the model but is indicated for completeness of the chemical compound formulations. Living organic CFFs are thebasis for the modelling of Living Functional Groups (LFGs).

91M. Vichi et al. / Journal of Marine Systems 64 (2007) 89–109

in the limits of laboratory or in situ experiments. CFFsare divided in inorganic, non-living organic and livingorganic compounds (Fig. 1) and they are measured inequivalents of major chemical elements (C, N, P, Si, O,Fe) or in molecular weight units as in the case ofchlorophyll. Their type and number cannot be fixed apriori and it is mostly linked to the degree of knowledgeof the relevant biogeochemical processes.

The concept of LFG is more familiar, and has beenfrequently used in marine and terrestrial ecosystemmodelling (Baretta and Ruardij, 1988; Smith et al.,1997; Le Quéré et al., 2005). Producers, consumers anddecomposers are broad LFGs, and several criteria can bedefined for further distinguishing assemblages of organ-isms that have an explicit biogeochemical role in marineecosystems (Le Quéré et al., 2005). In the pelagic domain,the term LFG is equivalent to Plankton Functional Type(PFT Le Quéré et al., 2005; Anderson, 2005). However,aiming at a more generalized approach, LFG is preferable

because it allows to include other functional groups whichare not planktonic, such as benthic organisms or anypossible biomass-based representation of fish.

Members of one LFG are represented by the pro-totype of a standard organism as in Fig. 2 (modified afterBlackford and Radford, 1995). As well as CFFs, also thestandard organism is a theoretical construct, whichshould not be identified with the real organism. Thestandard organism is thus the model of the LFGs, whosetotal biomass is composed of living CFFs and interactswith other (living and non-living) CFFs by means ofuniversal physiological and ecological processes such asphotosynthesis, excretion, grazing, etc. The paramete-rization of the physiological and trophic dynamicsconsidered are generally limited to interactions at themembrane level, which also implies neglecting thedetails of ingestion mechanisms in metazoans. It isimportant to notice that this approach does not excludethe further implementation ofmore detailed formulations

Fig. 2. Scheme of the standard organism, which is the prototype of anyLiving Functional Group (LFG), and the physiological/trophicrelationships among the Chemical Functional Families and majorenvironmental forcings. The standard organism is a theoreticalrepresentation of the real organisms and can describe both anautotroph, a heterotroph or a mixotroph, depending on the choice ofthe (internal) living CFFs and the process equations that link them.

92 M. Vichi et al. / Journal of Marine Systems 64 (2007) 89–109

which mechanistically resolve the intracellular transportof nutrients and carbon (e.g. Flynn, 2001) or paramete-rizations of the feeding behavior of zooplankton.

Table 1List of the Chemical Functional Family state variables (CFF, for a total of 44 ppublications

Variable Type Components # of CFFs Description

N(1) IO P 1 Phosphate (mmolN(3) IO N 1 Nitrate (mmol N mN(4) IO N 1 Ammonium (mmoN(5) IO Si 1 Silicate (mmol SiN(6) IO R 1 Reduction equivalN(7) IO Fe 1 Dissolved iron (μmO(2) IO O 1 Dissolved oxygenO(3) IO C 1 Carbon dioxide (mPi(1) LO C N P Si Fe Chl 6 Diatoms (mg C m−

μmol Fe m−3 andPi(2) LO C N P Fe Chl 5 Flagellates (")

Pi(3) LO C N P Fe Chl 5 Picophytoplankton

Bi LO C N P 3 Pelagic bacteria ("

Zi(4) LO C N P 3 Omnivorous meso

Zi(5) LO C N P 3 Microzooplankton

Zi(6) LO C N P 3 Heterotrophic Flag

Ri(1) NO C N P 3 Dissolved organic

Ri(6) NO C N P Si Fe 5 Particulate organic

Type legend: IO = Inorganic; LO = Living organic; NO = Non-living organic.

Pi(1)≡ (Pc

(1); Pn(1); Pp

(1); Ps(1); Pl

(1); Pf(1)).

The mathematical relationships between the CFFs(i.e. the LFG's internal content of C, N, P, etc., Fig. 2)and the LFG functionalities are defined following thestoichiometrical requirements of basic elements. Theserequirements can be both dynamically varying betweengiven maximum and minimum values of element ratiosor constant. This makes the definition of LFGs verygeneral and can be also applied, for instance, to otherexisting biogeochemical models which use one singlenutrient as currency. If it is assumed that the standardorganism has fixed stoichiometry (e.g., Redfield ratiosin phytoplankton), then the dynamics of the LFG canbe formulated with one single CFF, and the time rate ofchange of the others are derived from the constantratios.

Starting from the theoretical assumption that the eco-system can be basically described by concentrations ofCFFs in living and non-living components, we can writethe conservation equation for an infinitesimal volume offluid. Here we make again the continuum hypothesis(Batchelor, 1967), i.e., if Ci indicates a given CFFconcentration, the values of Ci is a continuous functionof space and time. The basic equation in a fluid is thus:

ACi

At¼ −jYdYF; ð1Þ

where FY is a generalized flux of Ci through and withinthe basic infinitesimal element of mass of the fluid. This

rognostic equations) for the pelagic model and references to the original

Reference

P m−3) Baretta et al., 1995−3) “l N m−3) “m−3) “ents, HS− (mmol S m−3) Vichi et al., 2004ol Fe m−3) this work(mmol O2 m

−3) Baretta et al., 1995g C m−3) –3, mmol N–P–Si m−3,mg Chl-a m−3)

Varela et al., 1995; Ebenhöh et al., 1997;Baretta-Bekker et al., 1997; this work“

(") “) Baretta-Bekker et al., 1995;

Baretta-Bekker et al., 1997zooplankton (") Broekhuizen et al., 1995; this work(") Baretta-Bekker et al., 1995, 1997;

this workellates (") “detritus (") Baretta et al., 1995; Vichi et al., 2003adetritus (") “

The subscript i indicates the basic components (if any) of the CFF, e.g.

93M. Vichi et al. / Journal of Marine Systems 64 (2007) 89–109

flux can be further separated in a physical part and abiological reaction term

ACi

At¼ −jYdF

Yphys−j

YdFY

bio: ð2Þ

The second term on the right hand side of Eq. (2)cannot be measured directly and therefore weassume that it can be approximated in the followingway:

jY

dFY

bio ¼ −wBACi

Azþ ACi

At

�����bio

: ð3Þ

Both terms in Eq. (4) represent the biogeoche-mical divergence flux and parameterize the sin-king of biological particulate matter and the localtime rate of change due to biogeochemical trans-formation processes. The sinking velocity wB is intro-duced for those state variables that have a distinc-tive vertical velocity with respect to fluid verticalvelocity.

Fig. 3. Scheme of the state variables and pelagic interactions of the biogeochemindicated with bold-line square boxes, non-living organic CFFs with thin-lineBlackford and Radford, 1995).

This approximation brings us to the well-known formof an advection–diffusion-reaction equation in a movingocean:

ACi

At¼ −jdðuCiÞ þjH dðAHjHCiÞ þ A

AzAV

ACi

Az

−wBACi

Azþ ACi

At

����bio

ð4Þ

where u≡ (u, v, w) is the three-dimensional currentvelocity and (AH, AV) are the turbulent diffusivitycoefficients.

The primitive form (4) is at the basis of biomass-based ecosystem modelling in the ocean (e.g. Hofmannand Lascara, 1998). Our model starts from theseassumptions trying to identify the most completeformulation of the biological rate term in Eq. (3) forthe different CFF state variables listed in Table 1. Wewrite here the equations for this term building on theERSEM approach, somewhat following the originalnotation (Blackford and Radford, 1995) but upgrading itfor the definition of state variables and rates of change.As shown in Table 1, each LFG is mathematically

istry model. Living (organic) Chemical Functional Families (CFF) aresquare boxes and inorganic CFFs with rounded boxes (modified after

94 M. Vichi et al. / Journal of Marine Systems 64 (2007) 89–109

expressed by a multi-dimensional array that contains theconcentrations of the living CFF based upon thebiogeochemical elements. We use a superscript indicat-ing the CFF for a specific living functional group and asubscript for the basic constituent. For instance, diatomsare LFG of producers and comprise 6 living CFFswritten as Pi

(1)≡ (Pc(1), Pn

(1), Pp(1), Ps

(1), Pf(1), Pl

(1)) for theC, N, P, Si, Fe and chlorophyll content; particulateorganic detritus is composed of 5 non-living CFFs asRi(6)≡ (Rc

(6), Rn(6), Rp

(6), Rs(6), Rf

(6)).The particular configuration of 44 CFF state

variables shown in Fig. 3 was chosen for testing in aglobal ocean coupled physical–biogeochemical numer-ical application named PELAGOS (PELAgic biogeo-chemistry model for Global Ocean Simulations), whichis fully presented in the companion paper (Vichi et al.,2006-this issue). The model resolves 3 different LFGsfor phytoplankton P(j), j=1, 2, 3 (diatoms, autotrophicnanoflagellates and picophytoplankton), 3 for zooplank-ton Z(j), j=4, 5, 6 (omnivorous mesozooplankton,microzooplankton and heterotrophic nanoflagellates),1 LFG for bacteria, 8 inorganic CFFs for nutrients andgases (phosphate, nitrate, ammonium, silicate, dissolvediron, reduction equivalents, oxygen, carbon dioxide)and 8 organic non-living CFFs for dissolved andparticulate detritus (cf. Table 1 and Fig. 3). The statevariable nitrate is assumed here to be the sum of bothnitrate and nitrite. Reduction equivalents represent allthe reduced ions produced under anaerobic conditions.This variable was originally used only in the benthicnutrient regeneration module of ERSEM (Ruardij andVan Raaphorst, 1995) but was extended to the watercolumn in Vichi et al. (2004).

With this kind of approach, all the nutrient:carbonratios in chemical organic and living functional groupsare allowed to vary within their given ranges and eachcomponent has a distinct biological time rate of change.This kind of parameterizations are meant to mimic theadaptation of organisms to the diverse availability ofnutrients and light observed in the world ocean, and alsoallow to recycle organic matter along the water columndepending on the actual nutrient content (Baretta et al.,1995; Vichi et al., 2003b; Polimene et al., in press).

3. The basic formalism of the biological rate term

Each state variable interacts with the others throughthe universal physiological and ecological processesdepicted in Fig. 3, which are mostly derived from theoriginal ERSEM scheme (Baretta et al., 1995). Thebiological reaction term in Eq. (4) is generally written inecological modelling as an ordinary differential equation

holding the primitive biogeochemical processes on theright hand side. For a generic phytoplankton state varia-bles P, for instance, the biological term is indicated as:

dPdt

¼ Uptake−Exudation−Lysis−Respiration−Grazing

On the other hand, for a generic Z state variable ofmesozooplankton, the reaction term is composed of thefollowing processes:

dZdt

¼ Ingestion−Egestion−Respiration−Predation

A generic B state variable for bacteria has a reactionterm written as:

dBdt

¼ Uptake−Remineralization−Respiration−Predation

The terms for the inorganic and organic componentsare eventually derived from the relations above usingconservation principles. This kind of notation is used inthe scientific literature and is meant to emphasize thezero-dimensional biological interactions shown in Fig.3. However, it can hardly be generalized in mathemat-ical terms and at any spatial scale and therefore a pdeform is preferable. We use here two different interpre-tation levels: (1) rates of change form; and (2) explicitfunctional form. In “rates of change form”, thebiogeochemical reaction term in (4) for the CFF statevariable C is written as:

ACAt

����bio

¼Xi¼1;n

Xj¼1;m

ACAt

����ej

Vi

; ð5Þ

where the right hand side contains the terms represent-ing significant processes for each living or non-livingCFF. The superscripts ej are the abbreviations indicatingthe process which determines the variation. In Table 2we report the acronyms of the processes used in thesuperscripts. The subscripts Vi is the CFF state variableinvolved in the process. If V=C, we refer to intra-groupinteractions such as cannibalism.

When a term is present as a source in one equationand as a sink in another, we refer to it following thisequivalent notation:

ACAt

����e

V

¼ −AVAt

����e

C

: ð6Þ

In “functional process form”, the formulation of thedynamic dependencies on other variables is made explicit,i.e.: all the rates of change in Eq. (5) are given in thecomplete functional parameterization. Although this is the

Table 2List of all the abbreviations used to indicate the physiological andecological processes in Eq. (5)

Abbreviation Comment

gpp Gross primary productionrsp Respirationprd Predationrel Biological release: egestion, excretionexu Exudationlys Lysissyn Biochemical synthesisnit/denit Nitrification, denitrificationscv Scavengingrmn Biochemical remineralizationupt Uptake

95M. Vichi et al. / Journal of Marine Systems 64 (2007) 89–109

more complete mathematical form, it is more difficult toread and interpret at a glance, especially when trying todistinguish which processes affect which variable dynam-ics. Thus, in our description, we will write the equationsboth in rate of change and in functional process forms.

4. The environmental parameters affectingbiological rates

Before starting with the model equations in their fullformwe describe the dependencies of the biogeochemicalprocesses from the physical environment. In Eq. (4) thecoupling between physics and biogeochemistry is realizedexplicitly through the advecting velocity field and thediffusion coefficients. There is another implicit couplingwhich affects the biological reaction term through surfaceirradiance and temperature that are also provided by thephysical model. Temperature regulates several physio-logical processes in the model and its effect, denoted byf T, is parameterized in this non-dimensional form

f T ¼ QT−101010 ð7Þ

where the Q10 coefficient is different for each functionalprocess considered (see Appendix).

Light is fundamental for primary producers and theenergy source for photosynthesis is the underwatertransmitted amount of the incident solar radiation at thesea surface. We assume that the PhotosyntheticAvailable Radiation (PAR) EPAR (the notation ofSakshaug et al., 1997, is used here) is parameterizedaccording to the Lambert–Beer formulation with depth-dependent extinction coefficients

EPARðzÞ ¼ ePARQSekwzþ

R 0

zkbioðz VÞdz V ð8Þ

The short-wave surface irradiance flux QS is obtainedgenerally from an atmospheric radiative transfer model

and is converted fromWm−2 to the units of μE m−2 s−1

with the constant factor 1/0.215 (Reinart et al., 1998).εPAR is the coefficient determining the portion of PAR inQS. Light propagation takes into account the extinctiondue to suspended particles, λbio, and λw as thebackground extinction of water. The biological extinc-tion is written as

kbio ¼X3j¼1

cPðjÞPðjÞl þ cRð6ÞRð6Þ

c ð9Þ

where the extinctions due to the concentration ofphytoplankton chlorophyll and particulate detritus areconsidered. Extinction due to dissolved substances andinorganic suspended matter is currently not consideredfor global ocean applications. The c constants are thespecific absorption coefficients of each suspendedsubstance (see Appendix).

5. The biogeochemical equations

In this section we write the reaction terms for the 44state variables both in the rates of change and in theexplicit functional forms. We group them into theclassical ERSEM subdivision of LFGs (phytoplankton,zooplankton and bacteria) and we add the equations forall the CFFs.

5.1. Phytoplankton

The dispute about the number of phytoplanktonfunctional groups to be represented in ecosystem modelsis still open, but there is some consensus on about 5distinct types (Le Quéré et al., 2005): siliceous andcalcareous autotrophs, autotrophic nanoflagellates(chlorophytes), cyanobacteria and picophytoplankton.The original ERSEM II structure already comprisedsome of these groups (Baretta-Bekker et al., 1997). Inthis formulation we decided to leave out largedinoflagellates because they are assumed to be oflimited importance in open ocean waters. There arethree functional subgroups (Table 1 and Fig. 3): diatoms,autotrophic nanoflagellates, and picophytoplankton.Diatoms (Pi

(1) in the model) have an EquivalentSpherical Diameter (ESD) of 20–200 μm, preyed uponby adult mesozooplankton (>200 μm, Zi

(4)) and partiallyby microzooplankton of larger dimensions (20–200 μm,Zi(5)). They are the main source of biogenic silica in the

model and differ from the other groups because theirgrowth is limited by dissolved silicate. Flagellates Pi

(2),ESD=2–20 μm (nanoplankton), are mainly preyed bymicrozooplankton. Picophytoplankton Pi

(3) has a

96 M. Vichi et al. / Journal of Marine Systems 64 (2007) 89–109

nominal ESD of 0.2–2 μm. In a global ocean context,our picophytoplankton represents procaryotic organismgenerally indicated as non-diazotrophic autotrophicbacteria such as Prochlorococcus and Synechococcus,but can also include eucaryotic species (Worden et al.,2004). Picophytoplankton have an important ecologicalrole because they are the main sources of carbontogether with bacteria for heterotrophic nanoflagellates.

The processes parameterized in the biological sourceterm of Eq. (4) are gross primary production (gpp),respiration (rsp), exudation (exu), cell lysis (lys),nutrient uptake (upt), predation (prd) and biochemicalsynthesis (syn). All the phytoplankton groups share thesame form of primitive equations, but are differentiatedin terms of the values of the physiological parameters(see Appendix for a table of the values). There are 6living CFFs that describes the constituents of phyto-plankton (C, N, P, Si, Fe and Chl) and thus for eachgroup we have 5 or 6 equations:

APc

At

����bio

¼ APc

At

����gpp

Oð3Þ−APc

At

����exu

Rð1Þc

−APc

At

����rsp

Oð3Þ−Xj¼1;6

APc

At

����lys

RðjÞc

−X

k¼4;5;6

APc

At

����prd

ZðkÞc

ð10Þ

APn

At

����bio

¼Xi¼3;4

APn

At

����upt

N ðiÞ−Xj¼1;6

APn

At

����lys

RðjÞn

−Pn

Pc

Xk¼4;5;6

APc

At

����prd

ZðkÞc

ð11Þ

APp

At

����bio

¼ APp

At

����upt

N ð1Þ−Xj¼1;6

APp

At

����lys

RðiÞp

−Pp

Pc

Xk¼4;5;6

APc

At

����prd

ZðkÞc

ð12Þ

APs

At

����bio

¼ APs

At

����upt

N ð5Þ−APs

At

����lys

Rð6Þs

−Ps

Pc

Xk¼4;5;6

APc

At

����prd

ZðkÞc

ð13Þ

if Ps=Ps(1), otherwise APs

At jbio ¼ 0

APl

At

����bio

¼ APl

At

����syn

−Pl

Pc

Xj

APc

At

����prd

ZðjÞc

ð14Þ

APf

At

����bio

¼ APf

At

����upt

N ð7Þ−APf

At

����lys

Rð6Þf

−Pf

Pc

Xk¼4;5;6

APc

At

����prd

ZðkÞc

ð15Þ

Most of the terms in Eqs. (10)–(13) have alreadybeen described in ERSEM II (Baretta-Bekker et al.,

1997). Eqs. (14) and (15) are new instead, and will beexplained in details below. The predation terms aredescribed in Section 5.2 when discussing zooplanktondynamics since they are conversion terms in thenotation (6).

5.1.1. Carbon and nutrient dynamicsGross primary production in Eq. (10) is the rate of

change of phytoplankton carbon Pc due to photosyn-thesis that involves an uptake of dissolved carbondioxide O(3). This term is written as:

APc

At

����gpp

Oð3Þ¼ f TP f EP f

fP f

sPr

0PPc; ð16Þ

where rP0 is the maximum specific photosynthetic rate

under nutrient-replete, light-saturated conditions, andthe f functions are multiplicative, non-dimensional regu-lating factors for temperature, light, iron and silicate,respectively.

This functional form comes from the originalERSEM parameterization of photosynthesis (Baretta-Bekker et al., 1997; Ebenhöh et al., 1997; Vichi, 2002)and has been modified here according to the notationsuggested in Sakshaug et al. (1997). The non-dimen-sional light regulating factor is rewritten from the Webbet al. (1974) or Platt et al. (1980) formulation (withoutconsidering photoinhibition) as:

f EP ¼ 1−exp −EPAR

EK

� �ð17Þ

where EPAR is the available light and EK the lightsaturation parameter, which corresponds to the variableIopt in the original ERSEM formulation (Ebenhöh et al.,1997). According to the Sakshaug et al. (1997)notation, Ek is the ratio between the maximum chl-specific photosynthetic rate and the maximum lightutilization coefficient, Ek=Pm⁎ /α⁎ (the ⁎ superscriptindicates an instantaneous value). Based on the recentwork by Behrenfeld et al. (2004), we assume that

P⁎m ¼ f TP f fP fsPr

0PPc=Pl

and

α⁎ ¼ f TP f fP fsPα

0chl;

where αchl0 is the maximum slope of the production–

irradiance curve at optimal conditions. This parameter-ization implies that variations due to environmentalfactors other than light acclimation in the parameters ofthe production–irradiance curve are correlated (i.e. Ek-independent, according to Behrenfeld et al., 2004). The

97M. Vichi et al. / Journal of Marine Systems 64 (2007) 89–109

non-dimensional regulating factor for light (17) takesthus the form:

f EP ¼ 1−exp −a0chlEPARPl

r0PPc

� �: ð18Þ

Temperature dependence f PT in Eq. (16) takes the

form written in Eq. (7), silicate regulation is parameter-ized as an external limiting factor with a Michaelis–Menten form f s ¼ N ð5Þ

N ð5Þþhs( f s=1 for the groups other

than diatoms), and iron limitation f f is described belowin Section 5.1.3. All the nutrient regulating factors fapart from temperature have non-dimensional valuesbetween 0 and 1.

The activity exudation rate in Eq. (10) is written as:

APc

At

����exu

Rð1Þc

¼ ½bP þ ð1−bPÞð1−f n;pP Þ�APc

At

����gpp

Oð3Þð19Þ

and is composed of a constant fraction of carbon uptake(βP) and a nutrient-related complementary fraction,which is controlled by the internal nutrient ratiosaccording to the following Liebig-like regulating factor(always constrained between 0 and 1):

f n;pP ¼ minPn=Pc−nmin

P

noptP −nminP

;Pp=Pc−pmin

P

poptP −pminP

!ð20Þ

The optimal (Redfield-like) and minimum nutrientquota are indicated as nP

opt, nPmin for nitrogen and pP

opt,pPmin for phosphorus, respectively. Respiration is written

as:

APc

At

����rsp

Oð3Þ¼ f T bPPc þ gP

APc

At

����gpp

Oð3Þ−APc

At

����exu

Rð1Þc

( )ð21Þ

and is composed of a temperature-regulated meta-bolic part (with constant specific rate bP) and afraction γP of the assimilated production. The lysisproducts are a function of the intracellular nutrient-stress, and are partitioned into particulate anddissolved detritus according to a variable fractionen;pP ¼ min 1; pmin

PPp=Pc

;nminP

Pn=Pc

� �, which forces the release to

be particulate when nutrients are at the minimum value.The total carbon release through lysis is written as:

Xj¼1;6

APc

At

����lys

RðjÞc

¼ 1f p;nP þ hp;nP

d 0PPc ð22Þ

The uptake of nutrients is regulated by a Droopkinetic as detailed in Baretta-Bekker et al. (1997) andVichi (2002):

Xi¼3;4

APn

At

����upt

N ðiÞ¼ min

�ða3PN ð3Þþa4pN

ð4ÞÞPc; noptP GP

þ f TP r0P nmaxP −

Pn

Pc

� �Pc

�ð23Þ

APp

At

����upt

N ð1Þ¼min a1PN

ð1ÞPc; poptP GPþ f TP r0P pmax

P −Pp

Pc

� �Pc

� �ð24Þ

where GP is the net production, the algebraic sum of thefirst 4 terms on the right hand side of Eq. (10) and the aconstants are the membrane affinity for nitrate, ammo-nium and phosphate (see Appendix). If the nitrogenuptake rate (23) is positive, then the partitioningbetween N(3) and N(4) uptake is done using the ratios

a3PNð3Þ

a3PNð3Þ þ a4PN

ð4Þ

and

a4PNð4Þ

a3PNð3Þ þ a4PN

ð4Þ ;

respectively.The lysis process affects phytoplankton nutrient

content proportionally to the total carbon loss in Eq.(22) with the exception that the particulate fractionhas always the minimum allowed N:C or P:C ratios.For phosphorus in phytoplankton, the equations are:

APp

At

����lys

Rð6Þp

¼ pminP

APc

At

����lys

Rð6Þc

ð25Þ

APp

At

����lys

Rð1Þp

¼ Pp

Pc

Xj¼1;6

APc

At

����lys

RðjÞc

−APp

At

����lys

Rð6Þp

ð26Þ

The equations for N can be derived likewise.For the silicate dynamics (13) there is no storage in

the cytoplasm (but only in the exostructure) and silicateis released only in particulate form proportionally to thecarbon lysis:

APð1Þs

At

����upt

N ð5Þ¼ smax

Pð1ÞGPð1Þ ð27Þ

98 M. Vichi et al. / Journal of Marine Systems 64 (2007) 89–109

APð1Þs

At

����lys

Rð6Þs

¼ Pð1Þs

Pð1Þc

APð1Þc

At

����lys

Rð6Þc

: ð28Þ

5.1.2. Chlorophyll dynamicsThe chl equation written in Eq. (14) is composed of

two terms. The first one is chlorophyll synthesis, whichis mostly derived from Geider et al. (1996, 1997) withsome adaptations to the ERSEM features, and thesecond one represents the losses due to grazing.

Net chl synthesis is a complicated function ofacclimation to light conditions, nutrient availability(mainly N and Fe) and turnover rate. The former processis taken into account by Geider's parameterization, whilethe latter is generally parameterized with differentformulations, for instance by assuming a dependenceon gross carbon uptake (Geider et al., 1997; Blackford etal., 2004) and/or on nitrogen assimilation (Geider et al.,1998; Flynn et al., 2001). To integrate these processesinto the ERSEM formulation, it is assumed that nutrient-stressed cells that release substantial amount of DOCtend to regulate their internal chl:C ratio as well,therefore we write net synthesis as a direct function ofnet carbon assimilation:

APl

At

����syn

¼qchlAPc

At

����gpp

Oð3Þ−APc

At

����exu

RðiÞc

−APc

At

����rsp

Oð3Þ−APc

At

����lys

RðiÞc

!:

ð29Þ

This rate is primarily controlled by the dynamicalchl:C ratio ρchl proposed by Geider et al. (1997) whichregulates the amount of chl in the cell according to anon-dimensional ratio between the realized photosyn-thetic rate in Eq. (16) and the maximum potentialphotosynthesis:

qchl ¼ h0chl

APcAt jgppOð3Þ

a*EPARPlð30Þ

and multiplying by a maximum potential chl:C ratioθchl0 different for each phytoplankton functional group

(see Appendix).According to the notation shown in the previous

section, the original Geider's formulation is rewrittenafter some algebra as:

qchl ¼ h0chlf EP r

0PPc

a0chlEPARPlð31Þ

The ratio is down-regulated when the rate of lightabsorption (governed by the quantum efficiency and the

amount of pigments themselves) exceeds the rate ofutilization of photons for carbon fixation, as explainedin detail in Geider et al. (1996).

The losses of chl are not explicitly taken into accountin the model because we have currently not implemen-ted a chl component in detritus and dissolved organicmatter. The same consideration applies to the ingestedchl fraction in zooplankton. All these terms are presentlycollected into a generic sink term that is used for massconservation purposes, but can be easily split into itsmajor components once it is seen necessary to follow thedegradation products of chl (e.g. phaeopigments) in aglobal context.

5.1.3. Iron dynamicsIt is currently recognized that iron in the ocean is a

crucial regulator of the productive phase of marinephytoplankton. In the past 15 years, the “ironhypothesis” (Martin et al., 1991) has been verified bymeans of open ocean iron fertilization experiments(Martin et al., 1994; Boyd et al., 2000) and experimen-tal studies of iron chemistry and bioavailability (Coaleet al., 1996; Sunda and Huntsman, 1997; Price, 2005). Itis however still unclear how much of the actual carbonexport depends on the iron availability and whichmechanisms control the supply of iron to the euphoticzones from the major geochemical sources (Johnson etal., 1997; Fung et al., 2000). Iron is included in themodel (Fig. 3 and Table 1) as an inorganic CFFrepresenting dissolved form N(7), as a living organicCFF of phytoplankton and a non-living organic CFF forparticulate detritus (units are μmol m−3). Iron in thewater is thought to be almost entirely bound in complexmolecules by means of organic ligands (Johnson et al.,1997) and the concentration of dissolved inorganic iron[Fe′] has a very small solubility limit (∼0.75 nM at20 °C and pH=8.1–8.2) over which hydroxides areformed and adsorbed onto sinking particles. Recentstudies (Kraemer, 2004) have shown that bacteriaproduce molecules called siderophores to whichdissolved Fe(III) binds. The photochemical reactionhelps to transform the iron complexes into a Fe(II)-based form that enables other marine organisms toacquire it. Since these processes are still beinginvestigated, the effect of iron ligands and bacterialcomplexation is currently neglected. State variable N(7)

thus represents all the bioavailable iron [Fe′] but sinceiron is considered an internal component of all thefunctional groups, the model can be easily expanded tointroduce new important concepts.

Eq. (15) for iron in phytoplankton Pf contains a termfor the uptake of [Fe′], a loss term related to turnover/cell

99M. Vichi et al. / Journal of Marine Systems 64 (2007) 89–109

lysis and a predation term. In most models, it is assumedthat cellular Fe is in constant proportion with C.However, by linearly interpolating culture data underdifferent [Fe′], Sunda and Huntsman (1997) found thatthe Fe:C ratio needed for cell maintenance at zero growthrate is close to 3 μmol Fe:mol C (∼330,000 mol C:molFe) and phytoplankton linearly increase the intracellularFe:C ratio as a function of external [Fe′] for saturatinglight conditions (Sunda and Huntsman, 1995, see theirFig. 3). Therefore a value of 2–3 represents the minimuminternal ratio for cell survival, but it is not simple to findone single constant value representative of the optimalcellular requirement (Sunda, 1997). Ho et al. (2003)derived an optimal value of 60 for the averagestoichiometry of the soft tissues of some marinephytoplankton species cultivated in non–limitingmedia ((C124)1000Fe7.5). Data from Sunda and Huntsman(1995) show that saturation of growth rate is achievedwhen the intracellular ratio is above 20, depending onlight conditions. The prescribed value of the optimalratio is ϕP

opt =6 μmol Fe:mol C, closer to the constantratios assumed by other authors in their models (Leonardet al., 1999; Aumont et al., 2003). Similarly to N and Pcontent, intracellular Fe:C quota are allowed to varybetween a maximum and a minimum thresholds (ϕP

max

and ϕPmin, see values in Appendix), and the realized

quotum is used to derive a non-dimensional regulatingfactor as in Eq. (20):

f fP ¼ Pf =Pc−/minP

/optP −/min

P

ð32Þ

The allowed minimum ratio ϕPmin represents the

evolutive adaptation of each functional group at theprevailing iron concentrations, and the optimal valueϕPopt indicates the cellular requirement for optimal

growth. Minimum values are smaller for picophyto-plankton and higher for diatoms, according to observa-tions and surface: volume ratio considerations (Strzepekand Harrison, 2004; Timmermans et al., 2004, 2005).This regulating factor modulates the actual photosyn-thetic rate in Eq. (16) since there is a clear decrease in theactivity of PSUs due to insufficient cellular Fe (Sundaand Huntsman, 1997).

The regulating factor inhibits carbon fixation, butiron can still be uptaken in the cell, progressivelyincreasing the internal quotum. Iron uptake fromdissolved pools is computed according to Droopkinetics by taking the minimum of two rates, a linearfunction of the ambient concentration simulating themembrane through-flow at low external Fe concentra-tion, and the balancing flux according to the carbon

assimilation as in the case of N and P macronutrients(Eqs. (23)–(24)):

APf

At

����upt

N ð7Þ¼ min

�a7PN

ð7ÞPc;/optP GP

þ f TP r0P /maxP −

Pf

Pc

� �Pc

�ð33Þ

Direct iron excretion from phytoplankton is still anunknown biochemical pathway, therefore we assumethat the only physiological iron loss from phytoplanktonis linked to cell disruption, computed according tocarbon lysis and assuming that particulate material hasthe minimum structural Fe:C ratio:

APf

At

����lys

Rð6Þf

¼ /minP

APc

At

����lys

Rð6Þc

: ð34Þ

5.2. Zooplankton

The zooplankton LFGs in the model are: omnivorousmesozooplankton Zi

(4), comprising any permanentmember of the zooplankton community which isbetween 200 μm and 3 to 4 cm long as an adult;microzooplankton Zi

(5), representing the biomass con-centration of microzooplankton with a ESD in the range20–200 μm, and heterotrophic nanoflagellates, statevariable Zi

(6), which are protozoa with dimensionsbetween 2 and 20 μm, mainly grazing upon picophy-toplankton and bacteria. These latter groups alsoembrace many mesozooplankton species that aretraditionally considered part of the microzooplanktonwhen in juveniles stages (Broekhuizen et al., 1995).

Zooplankton parameterization is derived fromBaretta-Bekker et al. (1995) and Broekhuizen et al. (1995). Bothmicro- and mesozooplankton groups also indulge in“cannibalism”, preying on other members of their ownfunctional group. The zooplankton equations parameter-ize the processes of growth due to ingestion and the lossterms due to excretion/egestion, mortality, respiration andpredation due to other zooplankters. Each zooplanktonLFG comprises 3 CFFs for C, N and P content:

AZcAt

����bio

¼XX¼P;Z

AZcAt

����prd

Xc

−Xj¼1;6

AZcAt

����rel

RðjÞc

−AZcAt

����rsp

Oð3Þ

−X

k¼4;5;6

AZcAt

����prd

ZðkÞc

ð35Þ

100 M. Vichi et al. / Journal of Marine Systems 64 (2007) 89–109

AZnAt

����bio

¼ Fn

Fc

XX¼P;Z

AZcAt

����prd

Xc

−Xj¼1;6

AZnAt

����rel

RðjÞn

−AZnAt

����rel

N ð4Þ

−ZnZc

Xk¼4;5;6

AZcAt

����prd

ZðkÞc

ð36Þ

AZpAt

����bio

¼ Fp

Fc

XX¼P;Z

AZcAt

����prd

Xc

−Xj¼1;6

AZpAt

����rel

RðjÞp

−AZpAt

����rel

N ð1Þ

−ZpZc

Xk¼4;5;6

AZcAt

����prd

ZðkÞc

ð37Þ

We currently do not consider Si, Fe and chl as livingCFFs for zooplankton. This is a reasonable approxima-tion for Si, because biogenic silica in the form offrustiles is directly egested by zooplankters. Chl is anegligible part of C and N in the total biomass of preys,but the absence of internal Fe dynamics implies that theiron content of ingested food does not affect zooplank-ton net growth as instead occurs for N and P. In addition,we neglect the explicit recycling pathways of Fe throughzooplankton activity (Schmidt et al., 1999) which areinstead parameterized implicitly as shown below in Eq.(69).

The total amount of food available to zooplankton iscomputed considering the set of possible preysXi∈{Pi

(j), Bi, Zi(j)} as the vector Fi=∑XδZ,XeZ,XXi,

where δZ,X is the availability of prey Xi to predator Zand eZ,X is the capture efficiency. The product of thelatter terms gives the total preference. There are manydefinitions of preference in the literature, and we haveused concepts from Gentleman et al. (2003) and Gibsonet al. (2005) to combine together the parameterizationsdescribed in Baretta-Bekker et al. (1995) for micro-zooplankton and in Broekhuizen et al. (1995) formesozooplankton. Availability represents the qualityof the prey and is assumed to be mostly dependent onthe prey nominal dimensions (see Appendix). Captureefficiency (or relative preference) is also a non-dimensional factor which is set to 1 for mesozooplank-ton and is density-dependent in microzooplankton,eZ;X ¼ Xc

XcþlZ, according to the threshold half-saturation

density μZ (μZ=0 for mesozooplankton).The first term on the right hand side of Eq. (35) is the

total carbon ingestion, which corresponds to the sum ofall the predation loss terms in the carbon equations ofthe other functional groups preyed by zooplankton.Applying the inter-functional group conversion definedin Eq. (6), the rate term for each predation processes is

parameterized with a Type 2 formulation (Gentleman etal., 2003),

AZcAt

����prd

Xc

¼ −AXc

At

����prd

Zc

¼ f TZ r0ZdZ;X eZ;XXc

Fc

Fc

Fc þ hFZZc ð38Þ

which is traditionally rewritten in terms of the specificsearch volume in the case of mesozooplankton hFZ ¼ r0Z

mZ,

because this parameter is generally available in theliterature. For brevity, in the zooplankton equations wewill use the following notation to indicate the totalingestion rate in units of the chemical constituents:

Ii ¼XX

AZiAt

����prd

Xi

i ¼ c; n; p: ð39Þ

Metabolic rates in zooplankton are assumed to beclosely coupled to growth, therefore total ingested carbonis used part for net production, part for respiration and theremainder is egested/excreted. The parameters that can bemeasured in laboratory experiments are net growthefficiency ηZ (the ratio between net secondary productionand the sum of net production and activity respiration) andthe egested portion of ingested material βZ (also takinginto account sloppy feeding). From the point of view ofstoichiometric ecology, we notice here that the ingestionrate in Eq. (39) is not directly affected by prey quality inour present formulation (Mitra and Flynn, 2005).Nevertheless, the definition of constant optimal nutrientquota in zooplankton (Baretta-Bekker et al., 1997),equivalent to the Threshold Elemental Ratios of Andersenet al. (2004, TER), implies that the ingestion of low-quality (i.e. nutrient-poor) food lead to the disposal of theingested carbon in excess, thus effectively limitingbiomass growth.

On the other hand, an excess of nutrients, as forinstance due to the ingestion of phytoplankton under“luxury uptake” conditions, leads to an increase of thenutrient remineralization rates as shown below in Eqs.(45) and (46). The release of extra C is parameterized as anincrease of the egestion rates of organic carbon com-pounds or, in alternative, by increasing the respirationrates. Both processes are well documented in freshwaterzooplankton (Frost et al., 2004; Anderson, 2005) and wehave decided to parameterize the increase of excretionrates. The two pathways are equivalent from the point ofview of internal element regulation in zooplankton, butthe consequences of one choice or another on thebiogeochemical cycling of carbon are still to beinvestigated both experimentally and in model studies.

101M. Vichi et al. / Journal of Marine Systems 64 (2007) 89–109

The carbon loss term in Eq. (35) thus represents thesum of the activity excretion/egestion (higher formesozooplankton because of sloppy feeding), themortality rates and the nutrient-limited excretion oforganic carbon:

Xj¼1;6

AZcAt

����rel

RðjÞc

¼ bZIc þ d0Z fTZ Zc þ ddnsZ ZgZ

c þ QcZ ð40Þ

The released fraction is further divided intoparticulate (faecal pellets) and dissolved organicforms using a constant percentage εZ

c (mesozooplank-ton is assumed to have no dissolved products).Mortality is parameterized as senescence with a first-order constant rate dZ

0 and a grazing closure by highertrophic levels not resolved in the model, which is apower function of density valid only for mesozoo-plankton (dZ

dns =0 for microzooplankton).The balancing flow of C, QZ

c, is computed from theactual elemental ratios of ingested material:

CiZ ¼ ð1−bZÞIc

gZIc; i ¼ n; p ð41Þ

which are cross-compared with the optimal (constant)TERs, nZ

opt and pZopt. If nitrogen is limiting (ΓZ

n<nZopt),

and/or phosphorus is limiting (ΓZp<pZ

opt), then

QcZ ¼ gZIc−

ð1−bZÞnoptZ

In−ð1−bZÞpoptZ

Ip; ð42Þ

otherwise QZc =0.

Taking into account the activity excretion in Eq. (40)and after some algebra, the total respiration rate can bewritten as:

AZcAt

����rsp

Oð3Þ¼ ð1−bZÞð1−gZÞIc þ bZf

TZ Zc ð43Þ

where the constant body-respiration rate bZ is alsoconsidered.

The nutrient dynamics for zooplankton given in Eqs.(36) and (37) are mainly derived from carbon dynamicstaking into account the nutrient content of the total fooduptake. The excretion/egestion rate of organic nutrientsis obtained from Eq. (40) as:

Xj¼1;6

AZiAt

����rel

RðjÞi

¼ ZiZc

ðbZIc þ d0Z fTZ Zc þ ddnsZ ZgZ

c Þ;

i ¼ n; p ð44Þ

and is subsequently partitioned between particulateand dissolved according to the non-dimensionalfraction εZ

i which parameterizes the different distribu-tion of nutrients between structural parts and cyto-plasm (see values in Appendix).

The third terms on the right hand side of Eqs. (36)and (37) parameterize the zooplankton excretion ofinorganic nutrients, which occur only when the internalnutrient quota exceed the optimal quota for P and N, pZ

opt

and nZopt, respectively. The following formulations allow

organisms to have temporary imbalance in their nutrientcontent:

AZpAt

����rel

N ð1Þ¼ mpZmax 0;

ZpZc

−poptZ

� �Zp ð45Þ

AZnAt

����rel

N ð4Þ¼ mnZmax 0;

ZnZc

−noptZ

� �Zn ð46Þ

and the time scales of excretion are controlled by thespecific constant rates νZ

p and νZn (see Appendix). The

excretion is in the form of phosphate and urea, but thelatter in the model is assumed to be as labile as theammonium, therefore the rate is directed to theN(4) pool.

5.3. Bacterioplankton

The equations for bacterioplankton are written in asimilar manner to the ones for P and Z living functionalgroups. The bacteria LFG comprises 3 CFFs for the C, Nand P content, with 3 dynamical equations that havebeen recently formulated by (Vichi et al., 2003b) andextended to include denitrification and anaerobicprocesses in Vichi et al. (2004). Bacteria are hetero-trophs and their production rates depend directly on theavailability of organic substrate. The original ERSEMpapers did not include any prognostic variable fordissolved organic matter (DOM), which was assumed tobe directly available to bacteria within the same day ofproduction. The CFFs representing organic matter aredivided into a particulate and a dissolved fractionwritten in terms of C, N, P and Si content (the latter forparticulate only, cf. Table 1 and Section 5.4.3). Asshown in the previous sections, the nutrient content offreshly-produced DOM and detritus is set by the otherLFGs according to their internal nutrient quota.

Bacterial physiological processes are the uptake oforganic substrate (upt) and the uptake or remineraliza-tion of inorganic nutrients (upt, rel). They are currentlynot assumed to release organic matter (e.g. capsular

102 M. Vichi et al. / Journal of Marine Systems 64 (2007) 89–109

material), therefore their loss terms are limited torespiration and predation:

ABc

At

����bio

¼Xj¼1;6

ABc

At

����upt

RðjÞc

−ABc

At

����rsp

Oð3Þ−Xk¼5;6

ABc

At

����prd

ZðkÞc

ð47Þ

ABn

At

����bio

¼Xj¼1;6

RðjÞn

RðjÞc

ABc

At

����upt

RðjÞc

þ f nBABn

At

����upt;rel

N ð4Þ

−Bn

Bc

Xk¼5;6

ABc

At

����prd

ZðkÞc

ð48Þ

ABp

At

����bio

¼Xj¼1;6

RðjÞp

RðjÞc

ABc

At

����upt

RðjÞc

þ f pBABp

At

����upt;rel

N ð1Þ

−Bp

Bc

Xk¼5;6

ABc

At

����prd

ZðkÞc

ð49Þ

The realized total carbon uptake rate of organicsubstrate in Eq. (47) is regulated by environmentalfactors and substrate availability in a Liebig-likeformulation:

Xj¼1;6

ABc

At

����upt

RðjÞc

¼ min

�f n;pB Q

T−101010 r0BBc; mRð6Þ f n;pRð6ÞR

ð6Þc

þ mRð1Þ f n;pRð1ÞRð1Þc

�; ð50Þ

where the first term between brackets is the bacterialgrowth at a given temperature, rB

0 is the maximumpotential growth rate (see value in Appendix) and f B

n,p isthe non-dimensional regulating factor parameterizingthe internal nutritional status of bacteria:

f n;pB ¼ minBp=Bc

popt;Bn=Bc

nopt

� �: ð51Þ

The second term is the availability of substrate,parameterized by a regulating factor linked to the“quality” of organic matter, i.e. the nutrient content,which can be used as a proxy for the degree of lability(Ogawa and Tanoue, 2003):

f n;pRðjÞ ¼ min

RðjÞp =RðjÞ

c

popt;RðjÞp =RðjÞ

c

nopt

!j ¼ 1; 6 ð52Þ

The constant parameters νR(j) in Eq. (50) mark thenominal degree of lability of detritus and DOM, whichis further modulated by their nutrient content.

Bacterial respiration is a measure of remineralizationactivity, and is written to take into account chemotrophic

processes such as denitrification and sulphate reduction.Respiration comprises basal and activity rates as:

ABc

At

����rsp

Oð3Þ¼ bBf

TB Bc þ ½1−gB þ goBð1−f oB Þ�

Xj¼1;6

ABc

At

����upt

RðjÞc

ð53Þ

The potential bacterial growth efficiency ηBcontrols the quota of carbon that is respired formetabolic processes and this portion increases of aquantity ηB

o as a steep sigmoidal function of theambient oxygen concentration

f oB ¼ ðOð2ÞÞ3ðOð2ÞÞ3 þ ðhoBÞ3

ð54Þ

to parameterize the lower efficiency of anaerobicmetabolism (see Appendix for a list of parametervalues and description). Eqs. (53) and (54) are usedbelow to derive the bacterial oxygen demand and/orthe demand of other oxidized inorganic species suchas nitrate (Section 5.4.2) and sulphate.

Depending on their internal nutrient:carbon ratios,bacteria can behave as remineralizers or as competitorswith phytoplankton, taking up inorganic nutrientsdirectly from the water. The optimal nutrient quota forP and N, pB

opt and nBopt, regulate the intensity of this

process:

ABp

At

����upt;rel

N ð1Þ¼ f pB m

pB

Bp

Bc−poptB

� �Bc ð55Þ

ABn

At

����upt;rel

N ð4Þ¼ f nB m

nB

Bn

Bc−noptB

� �Bc ð56Þ

and the sign is controlled by the non-dimensional factorsf Bp and f B

n and by the specific constant rates νBp and νB

n. Inthe case of phosphorus, for instance, if Bp

Bc−poptB > 0

(excretion of nutrients) the non-dimensional parameterf Bp =−1, and if Bp

Bc−poptB < 0 there is direct uptake from

the water as a function of the nutrient concentration in aMichaelis–Menten form, f pB ¼ N ð1Þ

N ð1ÞþhpB.

5.4. Chemical functional families

5.4.1. Oxygen, carbon dioxide and anoxic processesThe dynamics of dissolved oxygen and carbon

dioxide are important closures of global biogeochem-ical cycles. We do not describe here the exchange ofgases at the air sea interface which is assumed to be apurely physical process and has been thoroughly

103M. Vichi et al. / Journal of Marine Systems 64 (2007) 89–109

investigated elsewhere, especially for CO2 (Olsen etal., 2005).

Anaerobic processes and denitrification dynamics area consequence of oxygen dynamics and are describedhere for completeness, although they are of limitedimpact in the well-oxygenated euphotic zones of theopen ocean. Nevertheless, these processes are importantfor the sulfur cycle and for the fate of exported carbon inthe meso- and bathypelagic layers of the ocean wherebacteria are the major drivers of these processes. Toaccount for hypoxic and anoxic remineralization in thewater, the original ERSEM parameterization of anaer-obic processes in the sediments proposed by Ruardij andVan Raaphorst (1995) was extended to the pelagicsystem by Vichi et al. (2004). The state variable“reduction equivalents” N(6) (Table 1 and Fig. 3) is aninorganic CFF state variable containing all the reducedchemical species and assumed to be chemicallyequivalent to the sulphide ion HS−. The basicconstituent is indicated with the letter R because thisvariable account for all the reduced biochemicalproducts, although it should be mostly regarded assulphur S. Reduction equivalents are produced as aresult of bacterial anoxic respiration and are partly usedfor the parameterization of denitrification processes andpartly for direct sulphide production. We refer to Vichiet al. (2004) for major details on the parameterizationand for an application to the Baltic Sea.

The pelagic net production of oxygen is derived fromthe sum of gross primary production and communityrespiration rates from phytoplankton, zooplankton andbacteria, also subtracting the losses due to pelagicchemical reactions:

AOð2Þ

At

����bio

¼ Xoc

X3j¼1

APðjÞc

At

����gpp

Oð3Þ−APðjÞ

c

At

����rsp

Oð3Þ

!

−Xoc f

oB

ABc

At

����rsp

Oð3Þ−Xo

c

X6j¼4

AZðjÞc

At

����rsp

Oð3Þ

−XonAN ð4Þ

At

����nit

N ð3Þ−

1Xr

o

AN ð6Þ

At

����reox

sinkr

ð57Þ

All the rates are converted into oxygen units bymeans of constant stoichiometric coefficients (seeAppendix). Since bacteria are active both under aerobicand anaerobic conditions the bacterial oxygen demandEq. (53) is partitioned into oxygen consumption andreduction equivalent production by using the oxygenregulating factor f B

o in Eq. (54). The nitrification rate isa source term of the nitrate Eq. (64), and a sink term forammonium (65) and oxygen (57). Nitrification is not

explicitly resolved but parameterized with a simplefirst-order dependence on ammonium and oxygenconcentrations:

AN ð4Þ

At

����nit

N ð3Þ¼ Knit

N ð4Þ f TN ð4ÞOð2Þ

Oð2Þ þ hoN ð4Þ

N ð4Þ ð58Þ

where ΛN4nit is the constant specific nitrification rate and

f T a temperature regulating factor with the Q10

formulation shown in Eq. (7).The formation of reduction equivalents is parame-

terized converting the biological oxygen demand ofbacteria (under low oxygen conditions) into sulphideions by using the stoichiometric coefficient Ωo

r (seeAppendix) as:

AN ð6Þ

At

����bio

¼ XroX

ocð1−f oB1Þ

ABc

At

����rsp

Oð3Þ−Xr

oX̃on

AN ð3Þ

At

����denit

sinkn

−AN ð6Þ

At

����reox

sinkr

ð59Þ

The utilization of nitrate as an electron acceptor inmicrobial metabolic reactions is parameterized in anindirect way. Firstly, when the oxygen level fallsbelow the threshold level and f B1

o <1 (Eq. (54)), themetabolic formation of reduction equivalents beginsaccording to the carbon mineralization rate (53). Thedenitrification reaction is favored with respect to thepure anaerobic sulpho-reduction, therefore a portion ofthis oxygen demand is redirected towards thedenitrification process. In order to achieve this neteffect, the changes in the redox conditions enhance thedenitrification flux in the following way:

AN ð3Þ

At

����denit

¼ KdenitN ð3Þ

1

M∗o

Xocð1−f oB Þ

ABc

AtjrspOð3Þ

" #N ð3Þ:

ð60Þ

where ΛN(3)denit is the specific denitrification rate at a

reference anoxic mineralization M∗o (see Appendix

for a list of parameter values). If nitrate is still presentin the water, the bacterial rate of production ofreduction equivalents N(6) is converted to nitrateconsumption, mimicking the bacteria-mediated deni-trification reactions. Note that this chemical rate doesnot lead to a direct production of gaseous N2 in thewater, because this variable is not currently defined inthe model.

104 M. Vichi et al. / Journal of Marine Systems 64 (2007) 89–109

Furthermore, as long as there is some oxygen left,reduction equivalents are also quickly reoxidized at thefollowing rate:

AN ð6Þ

At

����reox

sinkr

¼ KreoxN ð6Þ f TN ð6Þ

Oð2Þ

Oð2Þ þ hoN ð6Þ

N ð6Þ ð61Þ

where ΛN(6)reox is the (constant) specific daily reoxidation

rate, f N(6)T is the temperature regulating factor given in

Eq. (7) and hN(6)o is the half-saturation concentration (see

Appendix). When oxygen and nitrate are completelydepleted the last two terms in Eq. (59) become zero andthe process turns to a strict anaerobic formation ofsulphide ions coupled to the availability of the organicsubstrate.

In the current implementation of the model thereis no explicit resolution of all the carbon dioxidedynamics, because CO2 is assumed to be infinitelyavailable in the waters and only the biologicalinteractions are resolved. The aquatic chemistry ofCO2 and carbonates is a further extension to theoriginal ERSEM formulation previously published inBlackford and Burkill (2002), and the theory of itschemical reactions is well understood (Zeebe andWolf-Gladrow, 2001). Carbonate dynamics andsurface exchange processes are currently beingincluded in PELAGOS, particularly taking intoaccount the works done in the Ocean CarbonModel Intercomparison Project (Doney et al., 2004).The biological production and consumption of CO2

presently considered in the model can be easilyderived by collecting the first 4 terms on the righthand side of Eq. (57) without considering thestoichiometric factor Ωc

o and taking the total bacterialrespiration as

AOð3Þ

At

����bio

¼X3j¼1

APðjÞc

At

����gpp

Oð3Þ−APðjÞ

c

At

����rsp

Oð3Þ

!−ABc

At

����rsp

Oð3Þ

−X

k¼4;5;6

AZðkÞc

At

����rsp

Oð3Þ: ð62Þ

5.4.2. Dissolved inorganic nutrientsThe pelagic cycles of dissolved inorganic nutrients

are an essential component of any biogeochemicalmodel of the marine ecosystem. Five inorganic CFFs fordissolved compounds are considered here (Fig. 3)):

phosphate, nitrate (nitrate+nitrite), ammonium, silicateand bioavailable iron with the following equations

AN ð1Þ

At

����bio

¼ −X3j¼1

APðjÞp

At

����upt

N ð1Þþ f pB

ABp

At

����upt;rel

N ð1Þ

þX

k¼4;5;6

AZðkÞp

At

����rel

N ð1Þð63Þ

AN ð3Þ

At

����bio

¼ −X3j¼1

APðjÞn

At

����upt

N ð3Þþ AN ð3Þ

At

����nit

N ð4Þ−AN ð3Þ

At

����denit

sinkn

ð64Þ

AN ð4Þ

At

����bio

¼ −X3j¼1

APðjÞn

At

����upt

N ð4Þþ f pB

ABn

At

����upt;rel

N ð4Þ

þX

k¼4;5;6

AZðkÞn

At

����rel

N ð4Þ−AN ð4Þ

At

����nit

N3

ð65Þ

AN ð5Þ

At

����bio

¼ −APð1Þ

s

At

����upt

N ð5Þþ ARð6Þ

s

At

����rmn

N ð5Þð66Þ

AN ð7Þ

At

����bio

¼ −APf

At

����upt

N ð7Þþ ARð6Þ

f

At

����rmn

N ð7Þþ AN ð7Þ

At

����scv

sinkf

ð67Þ

Most of the rates in the equations above have alreadybeen described in previous sections and will be brieflyrecalled here.

The pelagic cycle of phosphate N(1) in Eq. (63) isaffected by phytoplankton uptake (23), bacterialuptake/release (55) and excretion from zooplanktongroups (45).

The pelagic processes for nitrate N(3) shown in (64),involve phytoplankton uptake described in Eq. (11) andthe nitrification and denitrification process parameter-izations described in Eqs. (58) and (60), respectively.

Ammonium (Eq. (65)) is consumed by phytoplank-ton as described in Eq. (23) and remineralized (orutilized) by bacteria according to the quality of thesubstrate and their internal content of nitrogen accordingto Eq. (56). Zooplankton participates to the ammoniumdynamics through the excretion of urea, which isassumed to be directly available in the form of ammo-nium, as shown in Eq. (46).

The pelagic cycle of silicate is quite simple in themodel because of the many uncertainties linked to thecomplex dynamics of this element in the water. Silicate

105M. Vichi et al. / Journal of Marine Systems 64 (2007) 89–109

concentration was originally only affected by diatomuptake (27), but a simple first-order reaction parame-terizing bacterial dissolution (e.g. Bidle and Azam,2001) have been introduced accounting for the disso-lution of silicate frustules as:

ARð6Þs

At

����rmn

N ð5Þ¼ Krmn

s f TRð6ÞRð6Þs ð68Þ

where Λsrmn is the constant specific dissolution rate and

f R(6)T is the temperature regulating factor as in Eq. (7),

mimicking bacterial activity enhancement at highertemperatures.

Iron is made available in dissolved form throughremineralization of biogenic particles produced byphytoplankton and zooplankton. As described inSection 5.1.3, the biochemical pathways of the reminer-alization process are not completely clear and involveboth syderophores and photochemical reactions. Sinceall these processes are primarily bacterial-mediated, it ispreliminary assumed that dissolved Fe is released fromdetritus according to a first-order relationship as forsilicate (68):

ARð6Þf

At

����rmn

N ð5Þ¼ Krmn

f f TRð6ÞRð6Þf ð69Þ

where Λfrmn is a constant specific dissolution rate and

f R(6)T is the temperature dependence. Both numbers are

currently unknown, and therefore they need to beadjusted numerically for balancing the iron cycle inthe ocean. The further inclusion of iron as an explicitcomponent of zooplankton and bacteria may link thisprocess to the direct excretion of organisms andbacterial regeneration activity, once the importantpathways and time-scales have been properly assessedby laboratory and in situ experiments.

Dissolved inorganic iron species are scavenged ontoparticle surfaces owing to hydroxide precipitation. Sincethe concentration of iron ligands is about 0.6 nM in thedeep ocean, Johnson et al. (1997) suggested that ironscavenging can be parameterized with a constant ratewhen the [Fe′] is above this threshold. Ligandsdynamics have been further investigated by Archerand Johnson (2000), Parekh et al. (2004), Lefevre andWatson (1999), but the simplest approach proposed byJohnson et al. (1997) and Aumont et al. (2003) has beenused here:

AN ð7Þ

At

����scv

sinkf

¼ Kscvf minð0;N ð7Þ−0:6Þ ð70Þ

with a given time constant Kscvf ¼ 1

40 years−1 and with

the further assumption that scavenging results intodefinitive adsorption onto sinking particles and seques-tration in the deeper layers.

5.4.3. Dissolved and particulate organic matterThe equations for dissolved organic matter (DOM,

Rj(1)) is linked to 3 biogeochemical basic constituents C,

N and P and is thus described by 3 equations:

ARð1Þc

At

����bio

¼X3j¼1

APðjÞc

At

����exu

Rð1Þc

−ABc

At

����upt

Rð1Þc

þXk¼5;6

AZðkÞc

At

����rel

Rð1Þc

ð71Þ

ARð1Þi

At

����bio

¼X3j¼1

APðjÞi

At

����exu

Rð1Þi

−Rð1Þi

Rð1Þc

ABc

At

����upt

Rð1Þc

þXk¼5;6

ZðkÞi

ZðkÞc

AZðkÞc

At

����rel

Rð1Þc

i ¼ n; p ð72Þ

which show that DOM is produced by phytoplankton,bacteria and microzooplankton and used as organicsubstrate by bacteria. The different degrees of lability ofDOM are reflected in the nutrient content of R(i)

(1), whichregulates bacterial uptake as shown in Eq. (50).Refractory organic matter is not considered in thismodel, because it is considered to be a background valuewhich is constantly maintained at the global scale(Ogawa and Tanoue, 2003).

Particulate detritus is instead described by 5equations, one for each biogeochemical basic constitu-ent C, N, P, Si and Fe as:

ARð6Þc

At

����bio

¼X3j¼1

APðjÞc

At

����lys

Rð6Þc

−ABc

At

����upt

Rð6Þc

þX6k¼4

AZðkÞc

At

����rel

Rð6Þc

ð73Þ

ARð6Þi

At

����bio

¼X3j¼1

APðjÞi

At

����lys

Rð6Þi

−Rð6Þi

Rð6Þc

ABc

At

����upt

Rð6Þc

þX6k¼4

ZðkÞi

ZðkÞc

AZðkÞc

At

����rel

Rð6Þc

i ¼ n; p ð74Þ

ARð6Þs

At

����bio

¼ APð1Þs

At

����lys

Rð6Þs

þ Pð1Þs

Pð1Þc

X6j¼4

APð1Þc

At

����prd

ZðjÞc

−ARð6Þ

s

At

����rmn

N ð5Þ

ð75Þ

106 M. Vichi et al. / Journal of Marine Systems 64 (2007) 89–109

ARð6Þf

At

����bio

¼ APf

At

����lys

Rð6Þf

þ Pf

Pc

X6k¼4

APc

At

����prd

ZðkÞc

−ARð6Þ

f

At

����rmn

N ð7Þ

ð76Þ

The carbon, nitrogen and phosphorus component ofparticulate detritus in Eqs. (73) and (74) respectively)are produced by all the members of the planktoniccommunity except bacteria, which are the only utilizersof this component according to Eq. (50). The pelagiccycle of biogenic silica is instead restricted to the releaseof diatom frustules through mortality and other lysisprocesses as in Eq. (27) and via micro/mesozooplanktonpredation (including sloppy feeding) with the additionof the chemical dissolution shown in Eq. (68).

Particulate iron dynamics are the consequence ofprocesses described in Eqs. (34), (69) and (70).Particulate organic Fe is also derived from zooplanktonegestion and mortality. It is assumed that zooplankton isnever iron-limited and the iron fraction of the ingestedphytoplankton is directly egested as particulate detritus.

5.5. Active sinking of biological state variables

The sinking of biogenic material is a fundamentalprocess for the simulation of carbon sequestration in theinterior of the ocean. However, the estimation of thesinking velocity wB in Eq. (4) is still parameterized in avery simplified way in the model. Only organic detritusRi(6) and diatoms are allowed to sink, the former with a

constant velocity that does not take into account anyaggregation mechanism, and the latter is parameterizedwith the original ERSEM formulation (Varela et al.,1995). Diatoms reach their maximum velocity ωsink as afunction of the total nutrient stress f P(1)

nut =min (fP(1)n,p, f P(1)

f ,f P(1)s ) as follows:

wPð1Þ ¼ xsinkmaxð0; lsink−f nutPð1Þ Þ ð77Þ

where lsink is the nutrient regulating factor value belowwhich the mechanism is effective.

6. Discussion and final remarks

The representation of the biogeochemical processes ofpelagic ecosystem presented here emphasizes the flows ofthe major biogeochemical elements from the (in)organicpelagic pools through the food web as a function oforganisms' demand and trophic relationships. The basicconcepts of modelling pelagic ecosystem functions orprocesses through the exchange of multiple biogeochem-ical elements incidentally originated from Redfield's

consideration that different organisms interact differentlywith their environment, and modify the external condi-tions likewise. This concept is now being re-formalized ina new branch of science called “ecological stoichiometry”(Sterner and Elser, 2002) and ERSEM incorporated fromthe beginning a large portion of the fundamentals of thisdiscipline. A recent paper by Elser and Hessen (2005)illustrates well this representation by defining the conceptof “biosimplicity” via stoichiometry. Complexity inmarine food webs is described in terms of organismfunctionalities and not by species and populationdynamics. Stemming from the original ERSEM ap-proach, in this paper we wrote the practical implemen-tation of these concepts in partial differential equationswhich represent the rates of change of the major ChemicalFunctional Families in the pelagic ecosystem.

The degree of approximation of this approach withrespect to the real system is large and there will alwaysbe a strong debate on the number and kind ofcomponents that can provide a sufficient degree ofconnectivity with the observed functioning of marineecosystems. We have proposed here a formal method torevisit and extend ERSEM – one of the most complexexisting ecosystem models – by defining the biogeo-chemical components as Chemical Functional Familiesand Living Functional Groups. CFFs and LFGs aretheoretical constructs which allow us to relate measur-able properties of marine biogeochemistry to the statevariables used in deterministic models. This approach issufficiently generic that may be used to describe otherexisting biomass-based ecosystem model.

In a companion paper (Vichi et al., 2006-this issue)we present an application of this approach to thesimulation of the major global biogeochemical process-es. A global implementation implies the choice of givenvalues for the many parameters discussed in this paper,which have to be valid in all the regions of the globalocean. We see the inclusion of physiological regulationfactors and stoichiometrical considerations in the modelequation as a way to simulate the adaptation mechan-isms of plankton components. However, this approachincreases the number of parameters, and it is thereforeimportant that a clear definition and formalism isestablished to promote the exchange of informationbetween modelers and experimentalists.

In an even wider perspective, it might also bepossible to build a unified theory that link togetherdifferent type of ecosystem models, as recentlyproposed by Fennel and Osborn (2005) for individuals,population and biomass-based models.

Currently, the various parameters are derived fromtheoretical allometric considerations on the average

107M. Vichi et al. / Journal of Marine Systems 64 (2007) 89–109

dimension of the population or from laboratoryexperiments on selected single species. The highvariability of natural assemblages and the difficulty ofmeasuring the important rates of change makes thederivation of a unique set of parameters hard,especially when moving from unicellular organismsto metazoans. This is a possible limitation of thisapproach for the future challenge of extending the foodweb in order to include a detailed description ofzooplankton dynamics (deYoung et al., 2004). All theCFFs are treated as bulk biomass quantities, which isan approximation that generally holds for dissolvedsubstances and unicellular organisms in the limits ofthe continuum analysis. Intermediate and higher trophiclevels, from small metazoans to fish, have distinct ageclasses and cease to behave as “functional clouds”,generally showing individual differences which resultsin selective feeding behaviors and a wide range ofecological strategies.

Biomass-based models, by construction, neglect thediversity of zooplankton populations. It is thereforeneeded to implement nesting approaches of pelagicbiogeochemistry models like the one presented here withother models that are capable of simulating thefunctional complexity of zooplankton and fish (deYounget al., 2004). Higher trophic levels can be key indicatorsof climate changes, nevertheless they are not consideredin global ocean applications of pelagic biogeochemistrymodels. We suggest that the concepts of ecologicalstoichiometry can be the linkage between the differenttrophic levels of the global ocean ecosystem. A cleardefinition of the mathematical formalism used todescribe the pelagic biogeochemical processes imple-mented in ecosystem models is thus seen as a necessarystep for making this linkage effective.

Acknowledgements

We are grateful to all the members of the ERSEMteam, and particularly to J.W. Baretta, H. Baretta-Bekker, W. Ebenhoeh and P. Ruardij. We wish to thankM. Zavatarelli and J.I. Allen for their helpful commentson the manuscript. This work has been partially fundedby the EU projects DYNAMITE [project no. 00393(GOCE)] for MV and SM, and MFSTEP [project no.EVK3-CT-2002-00075] for NP.

Appendix A

Tables with the parameter units and description andthe values used in the companion paper (Vichi et al.,

2006-this issue) are available as on-line supplementalmaterial at http://www.bo.ingv.it/∼vichi/PELAGOS/tables_vichi_et_al_2006.pdf.

References

Allen, J., Blackford, J., Radford, P., 1998. A 1-D vertically resolvedmodelling study of the ecosystem dynamics of the Middle andSouthern Adriatic Sea. J. Mar. Syst. 18, 265–286.

Allen, J., Blackford, J., Holt, J., Proctor, R., Ashworth, M., Siddorn, J.,2001. A highly spatially resolved ecosystem model for the NorthWest European Continental Shelf. Sarsia 86, 423–440.

Andersen, T., Elser, J.J., Hessen, D.O., 2004. Stoichiometry andpopulation dynamics. Ecol. Lett. 7, 884–900.

Anderson, T.R., 2005. Plankton functional type modelling: runningbefore we can walk? J. Plankton. Res. 27, 1073–1081.

Archer, D.E., Johnson, K.S., 2000. A model of the iron cycle in theocean. Glob. Biogeochem. Cycles 14, 269–279.

Aumont, O., Maier-Reimer, E., Monfray, P., Blain, S., 2003. Anecosystem model of the global ocean including Fe, Si, P co-limitations. Glob. Biogeochem. Cycles 17 (2), 1060.

Baretta, J., Ruardij, P., 1988. Tidal Flat Estuaries: Simulation andAnalysis of the Ems Estuary. Vol. 71 of Ecol. Studies. SpringerVerlag, Heidelberg.

Baretta, J., Ebenhöh, W., Ruardij, P., 1995. The European RegionalSeas EcosystemModel, a complex marine ecosystemmodel. J. SeaRes. 33 (3–4), 233–246.

Baretta-Bekker, J., Baretta, J., Rasmussen, E., 1995. The microbialfood web in the European Regional Seas Ecosystem Model. J. SeaRes. 33 (3–4), 363–379.

Baretta-Bekker, J., Baretta, J., Ebenhoeh, W., 1997. Microbialdynamics in the marine ecosystem model ERSEM II withdecoupled carbon assimilation and nutrient uptake. J. Sea Res.38 (3/4), 195–212.

Batchelor, G., 1967. An Introduction to Fluid Dynamics. CambridgeUniversity Press, Cambridge.

Behrenfeld, M.J., Prasil, O., Babin, M., Bruyant, F., 2004. In search ofa physiological basis for covariations in light-limited and light-saturated photosynthesis. J. Phycol. 40, 4–25.

Bidle, K.D., Azam, F., 2001. Bacterial control of silicon regenerationfrom diatom detritus: significance of bacterial ectohydrolases andspecies identity. Limnol. Oceanogr. 46 (7), 1606–1623.

Blackford, J.C., Burkill, P.H., 2002. Planktonic community structureand carbon cycling in the Arabian Sea as a result of monsoonalforcing: the application of a generic model. J. Mar. Syst. 36 (3),239–267.

Blackford, J., Radford, P., 1995. A structure and methodology formarine ecosystem modelling. J. Sea Res. 33 (3–4), 247–260.

Blackford, J.C., Allen, J.I., Gilbert, F.J., 2004. Ecosystem dynamics atsix contrasting sites: a generic modelling study. J. Mar. Syst. 52,191–215.

Boyd, P.W., Watson, A.J., Law, C.S., Abraham, E.R., Trull, T.,Murdoch, R., Bakker, D.C.E., Bowie, A.R., Buesseler, K.O.,Chang, H., Charette, M., Croot, P., Downing, K., Frew, R., Gall,M., Hadfield, M., Hall, J., Harvey, M., Jameson, G., LaRoche,J., Liddicoat, M., Ling, R., Maldonado, M.T., McKay, R.M.,Nodder, S., Pickmere, S., Pridmore, R., Rintoul, S., Safi, K.,Sutton, P., Strzepek, R., Tanneberger, K., Turner, S., Waite, A.,Zeldis, J., 2000. A mesoscale phytoplankton bloom in the polarSouthern Ocean stimulated by iron fertilization. Nature 407,695–702.

108 M. Vichi et al. / Journal of Marine Systems 64 (2007) 89–109

Broekhuizen, N., Heath, M., Hay, S., Gurney, W., 1995. Modelling thedynamics of the North Sea's mesozooplankton. J. Sea Res. 33 (3–4), 381–406.

Coale, K.H., Fitzwater, S.E., Gordon, R.M., Johnson, K.S., Barber, R.T., 1996. Control of community growth and export production byupwelled iron in the equatorial Pacific ocean. Nature 379,621–624.

Denman, K.L., 2003. Modelling planktonic ecosystems: parameteriz-ing complexity. Prog. Oceanogr. 57, 429–452.

deYoung, B., Heath, M., Werner, F., Chai, F., Megrey, B., Monfray, P.,2004. Challenges of modeling ocean basin ecosystems. Science304, 1463–1466.

Doney, S.C., Lindsay, K., Caldeira, K., Campin, J.M., Drange, H.,Dutay, J.C., Follows, M., Gao, Y., Gnanadesikan, A., Gruber, N.,Ishida, A., Joos, F., Madec, G., Maier-reimer, E., Marshall, J.C.,Matear, R.J., Monfray, P., Mouchet, A., Najjar, R., Orr, J.C.,Plattner, G.K., Sarmiento, J., Schlitzer, R., Slater, R., Totterdell, I.J., Weirig, M.F., Yamanaka, Y., Yool, A., 2004. Evaluating globalocean carbon models: the importance of realistic physics. Glob.Biogeochem. Cycles 18, 3017.

Ebenhöh, W., Baretta-Bekker, J., Baretta, J., 1997. The primaryproduction module in the marine ecosystem model ERSEM II withemphasis on the light forcing. J. Sea Res. 38, 173–193.

Elser, J.J., Hessen, D.O., 2005. Biosimplicity via stoichiometry: theevolution of food-web structure and processes. In: Belgrano, A.,Scharler, D., Ulanowicz, U. (Eds.), Aquatic Food Webs: AnEcosystem Approach. Oxford University Press, Oxford, UK,pp. 7–18.

Fennel, W., Osborn, T., 2005. A unifying framework for marineecological model comparison. Deep-Sea Res., Part 2, Top. Stud.Oceanogr. 52, 1344–1357.

Flynn, K.J., 2001. A mechanistic model for describing dynamic multi-nutrient, light, temperature interactions in phytoplankton. J.Plankton. Res. 23, 977–997.

Flynn, K.J., Marshall, H., Geider, R.J., 2001. A comparison of two N-irradiance interaction models of phytoplankton growth. Limnol.Oceanogr. 46, 1794–1802.

Frost, P.C., Xenopoulos, M.A., Larson, J.H., 2004. The stoichiometryof dissolved organic carbon, nitrogen, and phosphorus release by aplanktonic grazer, Daphnia. Limnol. Oceanogr. 49, 1802–1808.

Fung, I.Y., Meyn, S.K., Tegen, I., Doney, S.C., John, J.G., Bishop, J.K.B., 2000. Iron supply and demand in the upper ocean. Glob.Biogeochem. Cycles 14, 281–295.

Geider, R., MacIntyre, H., Kana, T., 1996. A dynamic model ofphotoadaptation in phytoplankton. Limnol. Oceanogr. 41 (1), 1–15.

Geider, R., MacIntyre, H., Kana, T., 1997. A dynamic model ofphytoplankton growth and acclimation: responses of the balancedgrowth rate and chlorophyll a:carbon ratio to light, nutrientlimitation and temperature. Mar. Ecol. Prog. Ser. 148, 187–200.

Geider, R., MacIntyre, H., Kana, T., 1998. A dynamic regulatorymodel of phytoplanktonic acclimation to light, nutrients, andtemperature. Limnol. Oceanogr. 43 (3), 679–694.

Gentleman, W., Leising, A., Frost, B., Strom, S., Murray, J., 2003.Functional responses for zooplankton feeding on multipleresources: a review of assumptions and biological dynamics.Deep-Sea Res., Part 2, Top. Stud. Oceanogr. 50, 2847–2875.

Gibson, G.A., Musgrave, D.L., Hinckley, S., 2005. Non-lineardynamics of a pelagic ecosystem model with multiple predatorand prey types. J. Plankton. Res. 27, 427–447.

Ho, T.Y., Quigg, A., Finkel, Z.V., Milligan, A.J., Wyman, K.,Falkowski, P.G., Morel, F.M.M., 2003. The elemental compositionof some marine phytoplankton. J. Phycol. 39, 1145–1159.

Hofmann, E., Lascara, C., 1998. Overview of InterdisciplinaryModeling for Marine Ecosystems. In: Brink, K.H., Robinson, A.R. (Eds.), The Sea, vol. 10. John Wiley & Sons, Inc., New York,pp. 507–540.

Johnson, K.S., Gordon, R.M., Coale, K.H., 1997. What controlsdissolved iron concentrations in the world ocean? Mar. Chem. 57,137–161.

Kraemer, S.M., 2004. Iron oxide dissolution and solubility in thepresence of siderophores. Aquat. Sci. 66, 3–18.

Le Quéré, C., Harrison, S., Prentice, I., Buitenhuis, E., Aumont, O.,Bopp, L., Claustre, H., da Cunha, L.C., Geider, R., Giraud, X.,Klaas, C., Kohfeld, K., Legendre, L., Manizza, M., Platt, T.,Rivkin, R., Sathyendranath, S., Uitz, J., Watson, A., Wolf-Gladrow, D., 2005. Ecosystem dynamics based on planktonfunctional types for global ocean biogeochemistry models. Glob.Chang. Biol. 11, 2016–2040.

Lefevre, N., Watson, A.J., 1999. Modeling the geochemical cycle ofiron in the oceans and its impact on atmospheric CO2 concentra-tions. Glob. Biogeochem. Cycles 13, 727–736.

Leonard, C.L., Mcclain, C.R., Murtugudde, R., Hofmann, E.E.,Harding, L.W., 1999. An iron-based ecosystem model of thecentral equatorial Pacific. J. Geophys. Res. 104, 1325–1341.

Martin, J.H., Gordon, R.M., Fitzwater, S.E., 1991. The case for iron.Limnol. Oceanogr. 36, 1793–1802.

Martin, J.H., Coale, K.H., Johnson, K.S., Fitzwater, S.E., Gordon, R.M., Tanner, S.J., Hunter, C.N., Elrod, V.A., Nowicki, J.L., Coley,T.L., Barber, R.T., Lindley, S., Watson, A.J., Vanscoy, K., Law, C.S., Liddicoat, M.I., Ling, R., Stanton, T., Stockel, J., Collins, C.,Anderson, A., Bidigare, R., Ondrusek, M., Latasa, M., Millero, F.J., Lee, K., Yao, W., Zhang, J.Z., Friederich, G., Sakamoto, C.,Chavez, F., Buck, K., Kolber, Z., Greene, R., Falkowski, P.,Chisholm, S.W., Hoge, F., Swift, R., Yungel, J., Turner, S.,Nightingale, P., Hatton, A., Liss, P., Tindale, N.W., 1994. Testingthe iron hypothesis in ecosystems of the equatorial Pacific Ocean.Nature 371, 123–129.

McCarthy, J., Robinson, A., Rothschild, B., 2002. Biological–physical interactions in the sea: emergent findings and newdirections. In: Robinson, A., McCarthy, J., Rothschild, B. (Eds.),The Sea, vol. 12. John Wiley & Sons, Inc., New York, pp. 1–17.Ch. 1.

Mitra, A., Flynn, K.J., 2005. Predator–prey interactions: is ‘ecologicalstoichiometry’ sufficient when good food goes bad? J. Plankton.Res. 27, 393–399.

Obernosterer, I., Ruardij, P., Herndl, G., 2001. Spatial and diurnaldynamics of dissolved organic matter (DOM) fluorescence andH2O2 and the photochemical oxygen demand of surface waterDOM across the subtropical Atlantic Ocean. Lymnol. Oceanogr.46 (3), 632–643.

Ogawa, H., Tanoue, E., 2003. Dissolved organic matter in oceanicwaters. J. Oceanogr. 59, 129–147.

Olsen, A., Wanninkhof, R., Trinanes, J.A., Johannessen, T., 2005. Theeffect of wind speed products and wind speed–gas exchangerelationships on interannual variability of the air–sea CO2 gastransfer velocity. Tellus B 57, 95–106.

Parekh, P., Follows, M.J., Boyle, E., 2004. Modeling the global oceaniron cycle. Glob. Biogeochem. Cycles 18, GB1002.

Petihakis, G., Triantafyllou, G., Allen, I.J., Hoteit, I., Dounas, C.,2002. Modelling the spatial and temporal variability of the CretanSea ecosystem. J. Mar. Syst. 36, 173–196.

Platt, T., Gallegos, C.L., Harrison, W.G., 1980. Photoinhibition ofphotosynthesis in natural assemblages of marine phytoplankton. J.Mar. Res. 38, 687–701.

109M. Vichi et al. / Journal of Marine Systems 64 (2007) 89–109

Polimene, L., Allen, J.I., Zavatarelli, M., in press. Dissolved OrganicCarbon–bacteria interactions in marine systems: a theoreticalmodelling study. Aquat. Microb. Ecol.

Price, N.M., 2005. The elemental stoichiometry and composition of aniron-limited diatom. Limnol. Oceanogr. 50, 1159–1171.

Raick, C., Delhez, E.J.M., Soetaert, K., Gregoire, M., 2005. Studyof the seasonal cycle of the biogeochemical processes in theLigurian Sea using a ID interdisciplinary model. J. Mar. Syst.55, 177–203.

Reinart, A., Arst, H., Blanco-Sequeiros, A., Herlevi, A., 1998.Relation between underwater irradiance and quantum irradiancein dependence on water transparency at different depths in thewater bodies. J. Geophys. Res. 103 (C4), 7749–7752.

Ruardij, P., Van Raaphorst, W., 1995. Benthic nutrient regeneration inthe ERSEM ecosystem model of the North Sea. J. Sea Res. 33 (3–4), 453–483.

Ruardij, P., Haren, H.V., Ridderinkhof, H., 1997. The impact ofthermal stratification on phytoplankton and nutrient dynamics inshelf seas: a model study. J. Sea Res. 38 (3–4), 311–331.

Sakshaug, E., Bricaud, A., Dandonneau, Y., Falkowski, P.G., Kiefer,D.A., Legendre, L., Morel, A., Parslow, J., Takahashi, M., 1997.Parameters of photosynthesis: definitions, theory and interpreta-tion of results. J. Plankton. Res. 19, 1637–1670.

Schmidt, M.A., Zhang, Y.H., Hutchins, D.A., 1999. Assimilation of Feand carbon by marine copepods from Fe-limited and Fe-repletediatom prey. J. Plankton. Res. 21, 1753–1764.

Smith, T., Shugart, H.H., Woodward, F.I., 1997. Plant FunctionalTypes: Their Relevance to Ecosystem Properties and ClimateChange. Cambridge University Press, Cambridge.

Sterner, R.W., Elser, J.J., 2002. Ecological Stoichiometry: The Biologyof Elements from Molecules to the Biosphere. PrincetonUniversity Press, Princeton, NJ.

Strzepek, R.F., Harrison, P.J., 2004. Photosynthetic architecture differsin coastal and oceanic diatoms. Nature 431, 689–692.

Sunda, W.G., 1997. Control of dissolved iron concentrations in theworld ocean: a comment. Mar. Chem. 57, 169–172.

Sunda, W.G., Huntsman, S.A., 1995. Iron uptake and growthlimitation in oceanic and coastal phytoplankton. Mar. Chem. 50,189–206.

Sunda, W.G., Huntsman, S.A., 1997. Interrelated influence of iron,light and cell size on marine phytoplankton growth. Nature 390,389–392.

Taylor, A.H., Allen, J.I., Clark, P.A., 2002. Extraction of a weakclimatic signal by an ecosystem. Nature 416, 629–632.

Timmermans, K.R., van der Wagt, B., de Baar, H.J.W., 2004. Growthrates, half-saturation constants, and silicate, nitrate, and phosphate

depletion in relation to iron availability of four large, open-oceandiatoms from the Southern ocean. Limnol. Oceanogr. 49,2141–2151.

Timmermans, K.R., van der Wagt, B., Veldhuis, M.J.W., Maatman, A.,de Baar, H.J.W., 2005. Physiological responses of three species ofmarine picophytoplankton to ammonium, phosphate, iron and lightlimitation. J. Sea Res. 53, 109–120.

Varela, R., Cruzado, A., Gabaldon, J., 1995. Modelling primaryproduction in the North Sea using the European Regional SeasEcosystem Model. J. Sea Res. 33 (3–4), 337–361.

Vichi, M., 2002. Predictability studies of coastal marine ecosystembehavior. Ph.D. thesis, University ofOldenburg,Oldenburg,Germany.URL http://docserver.bis.uni-oldenburg.de/publikationen/dissertation/2002/vicpre02/vicpre02.html.

Vichi, M., Zavatarelli, M., Pinardi, N., 1998. Seasonal modulation ofmicrobial-mediated carbon fluxes in the Northern Adriatic Sea.Fisheries Oceanogr. 7 (3/4), 182–190.

Vichi, M., May, W., Navarra, A., 2003a. Response of a complexecosystem model of the northern Adriatic Sea to a regional climatechange scenario. Clim. Res. 24, 141–159.

Vichi, M., Oddo, P., Zavatarelli, M., Coluccelli, A., Coppini, G., Celio,M., Fonda Umani, S., Pinardi, N., 2003b. Calibration andvalidation of a one-dimensional complex marine biogeochemicalfluxes model in different areas of the northern Adriatic shelf. Ann.Geophys. 21, 413–436.

Vichi, M., Ruardij, P., Baretta, J.W., 2004. Link or sink: a modellinginterpretation of the open Baltic biogeochemistry. Biogeosciences1, 79–100.

Vichi, M., Masina, S., Navarra, A. 2006-this isssue. A generalizedmodel of pelagic biogeochemistry for the global oceanecosystem: Part II. Numerical simulations. J. Mar. Syst. 64,110–134, doi:10.1016/j.jmarsys.2006.03.014.

Webb, W., Newton, M., Starr, D., 1974. Carbon dioxide exchange ofAlnus rubra: a mathematical model. Ecologia 17, 281–291.

Worden, A.Z., Nolan, J.K., Palenik, B., 2004. Assessing the dynamicsand ecology of marine picophytoplankton: the importance of theeukaryotic component. Limnol. Oceanogr. 49, 168–179.

Zavatarelli, M., Baretta, J., Baretta-Bekker, J., Pinardi, N., 2000. Thedynamics of the Adriatic Sea ecosystem; an idealized model study.Deep-Sea Res., Part 1, Oceanogr. Res. Pap. 47, 937–970.

Zeebe, R.E., Wolf-Gladrow, D.A., 2001. CO2 in Seawater: Equilib-rium, Kinetics, Isotopes. Vol. 65 of Oceanography Book Series.Elsevier, Amsterdam.