Study of the seasonal cycle of the biogeochemical processes in the Ligurian …doga.ogs.trieste.it/doga/echo/eo/pdf/2005Raick_Delhez_al.pdf · 2006. 1. 12. · Study of the seasonal

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Journal of Marine System

Study of the seasonal cycle of the biogeochemical processes in the

Ligurian Sea using a 1D interdisciplinary model

C. Raicka,*, E.J.M. Delhezb, K. Soetaertc, M. Grégoirea,c

aUniversity of Liège, Dep. Oceanology, Sart-Tilman B6c, B- 4000 Liège, BelgiumbModélisation et Methodes Mathématiques, Sart-Tilman B37, B- 4000 Liège, Belgium

cNetherlands Institute of Ecology, Centre for Estuarine and Coastal Ecology, P.O. Box 140,4400 AC-Yerseke, The Netherlands

Received 20 December 2003; accepted 30 September 2004

Available online 2 December 2004

Abstract

A one-dimensional coupled physical–biogeochemical model has been built to study the pelagic food web of the Ligurian Sea

(NW Mediterranean Sea). The physical model is the turbulent closure model (version 1D) developed at the GeoHydrodynamics

and Environmental Laboratory (GHER) of theUniversity of Liège. The ecosystemmodel contains 19 state variables describing the

carbon and nitrogen cycles of the pelagic food web. Phytoplankton and zooplankton are both divided in three size-based

compartments and the model includes an explicit representation of the microbial loop including bacteria, dissolved organic matter,

nano-, and microzooplankton. The internal carbon/nitrogen ratio is assumed variable for phytoplankton and detritus, and constant

for zooplankton and bacteria. Silicate is considered as a potential limiting nutrient of phytoplankton’s growth. The aggregation

model described byKriest and Evans in (Proc. Ind. Acad. Sci., Earth Planet. Sci. 109 (4) (2000) 453) is used to evaluate the sinking

rate of particulate detritus. The model is forced at the air–sea interface by meteorological data coming from the bCôte d’AzurQMeteorological Buoy. The dynamics of atmospheric fluxes in the Mediterranean Sea (DYFAMED) time-series data obtained

during the year 2000 are used to calibrate and validate the biological model. The comparison of model results within in situ

DYFAMED data shows that although some processes are not represented by the model, such as horizontal and vertical advections,

model results are overall in agreementwith observations and differences observed can be explainedwith environmental conditions.

D 2004 Elsevier B.V. All rights reserved.

Keywords: Ecosystem–hydrodynamic interactions; Biogeochemical cycles; Mathematical model; Ligurian Sea

1. Introduction

In the last few decades, the Mediterranean ecosys-

tem has experienced changes in biodiversity due to the

0924-7963/$ - see front matter D 2004 Elsevier B.V. All rights reserved.

doi:10.1016/j.jmarsys.2004.09.005

* Corresponding author.

E-mail address: [email protected] (C. Raick).

effect of human activity. In the Western Mediterranean

Sea, from 1960 to 1994, phosphate and nitrate

concentrations in deep waters increased (Bethoux et

al., 1998), leading to changes in N:Si and Si:P ratios.

Changes in these nutrient ratios are chemical evidence

of changes in surface inputs, but also in the phyto-

planktonic community. According to Bethoux et al.

s 55 (2005) 177–203

C. Raick et al. / Journal of Marine Systems 55 (2005) 177–203178

(2002), the most probable change is a shift from an

ecosystem dominated by siliceous species (diatoms) to

assemblages dominated by nonsiliceous species, such

as flagellates.

A thorough understanding of the Mediterranean

Sea ecosystem functioning and evolution requires the

development of dynamic biogeochemical models

coupled with the physical environment to determine

the spatio-temporal evolution of the biological

production and the influence of environmental

factors on its intensity and distribution. The deter-

mination of the primary production is essential for

the assessment of the carbon transfer rate from the

superficial toward the deeper layers. A part of the

carbon consumed during photosynthesis is recycled

directly within the euphotic layer, the part left is

remineralized in subsurface and deep waters, which

are therefore richer in inorganic carbon than the

surface waters. It corresponds to the bbiologicalpumpQ (Copin-Montégut, 2000).

The Ligurian Sea (in Fig. 1) is a semi-enclosed

area located in the NW part of the Mediterranean

Sea. The Liguro–Provenal current is the main large-

scale hydrodynamics feature of the region: two

strong and variable currents, the Western Corsican

Current and the Eastern Corsican Current enter the

domain of the Ligurian Sea. Both advect the

Modified Atlantic Water at the surface, and the

Eastern Corsican Current also transports the denser

Fig. 1. Location of the Ligurian Sea and the DYFAMED station

(Marty and Chiaverini, 2002).

Levantine Intermediate Water. These currents join

and give birth to the Northern Current, flowing along

the French coast. Northern and Western Corsican

Currents describe a cyclonic circulation along the

Liguro–Provenal front.

The seasonal cycle of the biological productivity

is characterized by the presence of a winter–early

spring bloom starting in February after the winter

mixing, and usually followed by a secondary bloom

in April–May depending on the spring vertical

mixing. Oligotrophy prevails in summer due to the

depletion in nutrients in the water column. Another

bloom occurs in fall due to the enrichment in

nutrients of the surface layers by vertical mixing

induced by strong wind events. Marty et al. (2002)

report a significant interannual variability with a

general increase in the phytoplankton biomass during

a 9-year study (1991–1999), mainly due to the

lengthening of the summer stratification period,

favouring the growth of the small-size species

supporting the regenerated production.

A large data base, including biological, physical,

chemical, and meteorological data, is available for the

Ligurian Sea. From 1984 to 1988, the FRONTAL

campaign has provided basic informations on spatial

structure and temporal evolution of the superficial

layer. Since 1991, the time-series program dynamics

of atmospheric fluxes in the Mediterranean Sea

(DYFAMED) records measurements in a selected site

in the central part of the Ligurian Sea (in Fig. 1) in

order to study the response of the ecosystem to

climate variability and anthropogenic inputs. The

DYFAMED program has been organized in the scope

of the French-Joint Global Ocean Flux Studies

(JGOFS) program (Marty, 2002).

The existence of this large data base and the

particular hydrodynamics conditions with moderate

horizontal advection make the DYFAMED site and

the offshore FRONTAL station ideal test areas for

performing 1D modelling studies. 1D models have

been applied in the area in order to simulate the

variability of biological processes at different levels of

complexity in relation to the hydrodynamics of the

mixed layer. For instance, Tusseau et al. (1997)

proposed a biogeochemical model that describes the

C, N, and Si cycles through the pelagic food web as

represented by 13 state variables: the module AQUA-

PHY (Lancelot et al., 1991a) describes phytoplankton

C. Raick et al. / Journal of Marine Systems 55 (2005) 177–203 179

dynamics, based on the concept of energy storage and

the module HSB (Billen and Servais, 1989) describes

organic matter microbial degradation. The model has

been calibrated on the FRONTAL 1986 data. Chifflet

et al. (2001) applied a coupled model in order to

interpret short-time changes of the ecosystem in the

open NW Mediterranean Sea during the DYNAPROC

cruise (May 1995) devoted to the study of the

DYNAmics of the rapid PROCess of the water

column. The biological model based on the previous

models of Andersen et al. (1987) and Andersen and

Nival (1988, 1989) describes the nitrogen cycles

through eight state variables (three phytoplankton,

one zooplankton, two nutrients, and two sized-groups

of particulate organic matter). The 1D MODECOGeL

model (Lacroix, 1998; Lacroix and Nival, 1998;

Lacroix and Grégoire, 2002) studies the Ligurian

Sea ecosystem response to the seasonal variability of

the upper layer dynamics. The biological model

represents the nitrogen cycle of the pelagic food

web through 12 biological state variables, including

the microbial loop. It allows to describe the ecosystem

dynamics and to point out marked seasonal cycle

attributed to atmospheric conditions. Model initializa-

tion, calibration, and validation were performed with

the FRONTAL campaign (1984–1988). Mémery et al.

(2002) proposed a NPZD-DOM biogeochemical

model [including Nitrate, Ammonium, Phytoplank-

ton, Zooplankton, Detritus, and Dissolved Organic

Matter (DOM)] with the aim of representing at first

order the basic biogeochemical fluxes. The model is

embedded in a 1D physical model and qualitatively

validated with DYFAMED data, using nitrate and

chlorophyll profiles of years 1995, 1996, and 1997.

Bahamon and Cruzado (2003) proposed a representa-

tion of the nitrogen cycle through five state variables

in the pelagic environment (three nitrogen nutrients,

one phytoplankton, and one zooplankton) to compare

two oligotrophic environments: the Catalan Sea (NW

Mediterranean) and the subtropical northeast Atlantic

Ocean, with emphasis in nitrogen fluxes and primary

production.

The model described in this paper has been

defined in order to incorporate most state variables

and processes we can think of importance to obtain an

accurate representation of the Ligurian Sea ecosys-

tem. It is a size-based ecosystem model describing the

nitrogen and carbon cycles and considering silicate as

a potential limiting nutrient of diatoms growth.

Nineteen state variables are considered: three sized-

groups of primary producers, three sized-groups of

zooplankton, heterotrophic bacteria, two classes of

detritic matter, three inorganic nutrients, and the

number of aggregates formed by sinking detritus.

N:C ratios of primary producers and detritic organic

matter (dissolved and particulate) are variable, all

other ratios are maintained constant. During the

bibliographic research, phosphorus has also been

noted as an important element in the control of the

Mediterranean biological productivity (e.g., Thingstad

and Rassoulzadegan, 1999; Moutin and Raimbault,

2002). The choice of considering in a first time

nitrogen only (instead of phosphorus) as the major

limiting nutrient has been decided by inspecting

publications of measurements data at the DYFAMED

station. Marty et al. (2002) present a 9-year study

(1991–1999) of seasonal and interannual dynamics of

nutrients and phytoplankton pigments that indicates

that the N:P ratio in surface is always higher than 20

during the oligotrophic period and generally lower

than 20 during the rest of the year, which indicates a

probable shift from N-limitation in winter to P-

limitation in summer. Making the choice of one main

limiting element in order to limit the complexity of

the model, we have chosen nitrogen in order to

represent correctly the first winter–early spring

phytoplankton bloom. For the first time, it was

reasonable to take one nutrient only into account

because adding another nutrient, such as phosphorus,

in the model requires three additional states variables

(inorganic phosphorus, dissolved and particulate

organic phosphorus) if the phytoplankton’s phospho-

rus uptake in fully coupled to its nitrogen uptake, and

a lot of parameters to calibrate.

The initialization, the calibration, and the validation

of the model results are made with the physical and

biogeochemical data coming from the DYFAMED

time-series station.

The paper is organized as follows: Section 2

describes the data used to perform the initialization,

the calibration, and the validation of the hydrody-

namic and biogeochemical models. The hydrodyna-

mic and ecosystem models are described in Section 3

as well as the numerical methods and boundary con-

ditions used to force the model. Section 4 presents and

analyzes hydrodynamic and biogeochemical model


results. In Section 5, models’ results are compared

with measurement data.

2. Data

2.1. Hydrobiological data

Physical, biological, and chemical data have been

collected since 1991 at the DYFAMED station,

located 52 km off Cap–Ferrat (43825VN, 07852VE) inthe central zone of the Ligurian Sea (in Fig. 1). These

data have been measured monthly, with a vertical

resolution of about 10 m, from the surface to 200 m

and about 100 m, in the 200–2000 m depth depending

on the measured variable.

Nutrients (nitrite, nitrate, silicate, and phosphate)

profiles are described in details in Bethoux et al. (1998,

2002). Temperature and salinity data are presented in

Fig. 2. Meteorological conditions for year 2000: (a) Insolation (Wm�2): th

the sinusoid reconstructed from the punctual data. (b) Air temperature (8C)Meteorological Buoy (DYFAMED site).

Marty et al. (2002). Abundance and biomass of free-

living bacteria, heterotrophic nanoflagellates, and ci-

liates are described in Tanaka and Rassoulzadegan

(2002) and Tamburini et al. (2002). Particulate organic

matter in carbon and nitrogen has also beenmeasured at

the DYFAMED station from May 1997. A range of

plankton pigments has been detected, in order to

characterize different phytoplankton groups (e.g., Vi-

dussi et al., 2000, 2001, Marty et al., 2002; Marty and

Chiaverini, 2002). Fucoxanthin is the marker of dia-

toms and corresponds to the microphytoplankton

group. Nano- and pico-flagellates containing chloro-

phyll c are characterized by 19V-hexanoyloxyfucoxan-thin (19V-HF) and by 19V-butanoyloxyfucoxanthin (19V-BF). Zeaxanthin (Zea) is the marker of cyanobacteria

but is also present in prochlorophytes. Vidussi et al.

(2001) used chemotaxonomic correspondence of

HPLC-determined pigments to study the phytoplank-

ton community composition. The biomass proportion

e mean of 5 years FRONTAL data measurements (1984–1988) and

. (c) Wind speed at the surface water (ms�1) from the bCôte d’AzurQ


(BP) associated with each size class is further defined

as:

BPpico=(Zea+Tchlb)/DP

BPnano=(Allo+19V�HF+19V�BF)/DPBPmicro=Fuco/DP

with DP=Zea+Tchlb+Allo+19 V�HF+19 V�BF+Fuco

where the subscripts pico, nano, and micro refer to the

size classification. DP is the diagnostic pigment (in

mgChl m�3) is a valid estimator of the total

Chlorophyll a.

All data are available through the DYFAMED

Observatory data base http://www.obs-vlfr.fr/jgofs2/

sody/home.htm.

2.2. Meteorological data

The meteorological data used to force the model at

the air–sea interface come from the bCôte d’AzurQMeteorological Buoy, located at the DYFAMED site.

Measurements are available nearly every hour since

March 1999 for the wind speed and direction, the air

and surface water temperatures, the atmospheric

pressure, and the relative humidity. Air temperature

and wind speed used to force the model at the air–sea

interface are presented in Fig. 2b and c. Insolation,

precipitations, and cloudiness were not available: a

mean of these data over the 5 years of the FRONTAL

campaign (1984–1988) have been imposed to the

hydrodynamic model. Fig. 2a shows the isolation

curve used to force the model and obtained by fitting

a classic sinusoidal function with insolation measure-

ments performed during the FRONTAL experiments

(mean values for the period 1984–1988). Date recorded

during the FRONTAL campaign came from the Nice

Airport and the Cap–Ferrat. In this paper, the model has

been used to simulate the year 2000 due to the large

amount of data collected during this year, that can be

used to callibrate, initialize, and validate the model.

3. Models

3.1. The hydrodynamic model

The G.H.E.R. primitive equations hydrodynamic

model is a nonlinear, baroclinic model using a turbulent

closure scheme based on the turbulent kinetic energy

and on an algebraic mixing length taking the intensity

of both stratification and surface mixing into account

(e.g., Nihoul and Djenidi, 1987; Delhez et al., 1999). It

has been successfully applied in many marine areas

around the world: the Bering Sea (e.g., Deleersnijder

and Nihoul, 1988), the North Sea (e.g., Martin and

Delhez, 1994), the Mediterranean Sea (e.g., Beckers,

1991), and the Black Sea (e.g., Grégoire et al., 1998),

demonstrating the generality of the approach. Reduced

to its vertical dimension, it contains five state variables:

two components of horizontal velocity, temperature,

salinity, and turbulent kinetic energy. The GeoHydro-

dynamics and Environmental Laboratory (GHER) 1D

hydrodynamic model has been applied in the Ligurian

Sea to simulate the FRONTAL experiments (Lacroix

and Nival, 1998; Lacroix and Grégoire, 2002). Model

description and equations are described in Lacroix and

Nival (1998).

3.2. The ecosystem model ecosystem model

The state variables and processes described in the

ecosystem model have been defined after a thorough

study of the Ligurian Sea ecosystem obtained from the

inspection of the available literature and from

previous modelling studies performed in the region

as well as in the Mediterranean Sea in general (e.g.,

Andersen et al., 1987; Andersen and Nival, 1988,

1989; Andersen and Rassoulzadegan, 1991; Baretta et

al., 1995; Baretta-Bekker et al., 1997; Ebenhöh et al.,

1997; Gattuso et al., 1998; Levy et al., 1998; Crise et

al., 1999; Crispi et al., 1999a,b; Allen et al., 2002).

The size-based ecosystem model represents the

partly decoupled carbon, nitrogen, and silicium cycles

of the Ligurian Sea pelagic zone. It is defined by three

groups of autotrophs (i.e., pico-, nano-, microphyto-

plankton) and three groups of heterotrophs (i.e., nano-,

micro-, mesozooplankton) divided according to their

size, heterotrophic bacteria, three inorganic nutrients

(nitrate, ammonium, silicate), particulate and dissolved

organic matter, detrital silicate, and the number of

aggregates formed by the particulate organic matter.

It is well known that the relative internal composi-

tion of phytoplankton in carbon and nitrogen is highly

variable over the whole year. The N:C internal ratio

may vary up to a factor of 4, according to environ-

mental conditions prevailing (e.g., Soetaert et al., 2001;

http://www.obs-vlfr.fr/jgofs2/sody/home.htmhttp://www.obs-vlfr.fr/jgofs2/sody/home.htm


Vichi et al., 2003a,b). In addition, it is usually a rough

assumption to consider the N:C internal ratio of

phytoplankton constant equals to the Redfield ratio.

Therefore, in the model, the nitrogen and carbon

internal contents of the three groups of autotrophs vary

independently. The microphytoplankton box repre-

sents essentially diatoms whose growth can be limited

by silicate availability. The internal N:Si ratio of

diatoms is constant and equals to 1 as suggested by

Redfield et al. (1963), Brzezinski (1985), and Leblanc

et al. (2003). For zooplankton and bacteria, several

studies have shown their capacity to maintain constant

their element composition, despite the variable quality

of their growth substrates (e.g., Goldman et al., 1987;

Moloney and Field, 1991; Anderson, 1992; Sterner and

Robinson, 1994; Touratier et al., 2001). For instance,

homeostatic regulation of element composition has

been demonstrated for cladocerans and copepods living

at low and middle latitudes where accumulation of

lipids is small or never occurs (Hessen, 1990; Urabe

and Watanabe, 1992; Sterner et al., 1993; Touratier et

al., 2001). In addition, in the model, the internal N:C

ratio of bacteria and of the three sized-groups of

zooplankton is maintained constant.

A schematic representation of the ecosystem model

showing the interactions between the different com-

Fig. 3. Representation of the ecosystem model. Each style of lines repres

dashed arrows for inorganic matter flows, and dotted arrows for gas flows.

is considered as a pool.

partments is shown in Fig. 3. The model state

variables are listed in Table A.1. The state equations

of the biogeochemical model are given in Table A.3,

and most biogeochemical processes are summarized

in Table A.4. Table A.2 defines the variables used in

Tables A.3 and A.4. The parameters used in these

formulations are listed in Table A.5. A size adaptation

of parameters is made, accounting for a faster

metabolism for smaller species. All tables and

equations are given in Appendix A.

Most processes are assumed to depend on the

temperature, according to a Q10 law (Eq. (A.14); e.g.,

Oguz et al., 2000; Flynn, 2001; Gregoire, 1998;

Soetaert et al., 2001; Vichi et al., 2003b).

3.2.1. Phytoplankton modelling

The basis of the pelagic biogeochemical model is a

model of unbalanced phytoplankton growth (Tett,

1998; Smith and Tett, 2000) already implemented in

Soetaert et al. (2001). Carbon and nitrogen assimila-

tions are decoupled in time and space. Nitrogen

assimilation is made in the form of ammonium and

nitrate, whereas carbon assimilation (photosynthesis) is

synonymous with growth. Nitrogen and carbon con-

tents are considered as independent state variables for

each phytoplankton group. Phytoplankton N:C ratios

ent different flux of matter: plain arrows for organic matter flows,

Double arrows represent sinking. Dissolved Inorganic Carbon (DIC)


vary around the Redfield ratio, between the limits

(N:C)PHY,min and (N:C)PHY,max. Nitrogen uptake

increases at low (N:C)PHY and remains unaffected by

light intensity. The phytoplankton growth flux (Eq.

(A.17)) depends on the light and the availability in

nutrients according to the Liebig’s law of the mi-

nimum (e.g., Parsons et al., 1984; Dippner, 1998; Tett,

1998). Light limited carbon assimilation (Eq. (A.18))

is formulated by a quantum efficiency formulation,

such as in Sharples and Tett (1994). The quantum

yield (Quant) represents the transfer of energy from

pigments to photosynthetic systems: it expresses how

many moles of CO2 are fixed when one unit of

chlorophyll absorbs one unit of energy (Parsons et al.,

1984). The chlorophyll to carbon ratio of each

phytoplankton group depends on their internal N:C

ratio and on the minimal and maximal (Chl:N)PHYratios (Eq. (A.19)) as in Soetaert et al., (2001).

Light availability for the photosynthesis of phyto-

planktonic organisms is calculated according to Eq.

(A.15). The solar radiation at the air–sea interface

[I(z=0)] is illustrated in Fig. 2a. The extinction

coefficient of water kwater(z) (in m�1) of Eq. (A.16)

is estimated from the measurements of Ivanoff (1977)

and can be found in Lacroix and Grégoire (2002). The

light extinction coefficient due to the self-shading of

phytoplankton cells (kChl) has been chosen as in

Fasham et al. (1990) and Lacroix and Grégoire

(2002).

Phytoplankton respiration assumes a basal rate

(Resp), (e.g., Vichi et al., 2003b) and a production

dependent term (ProdResp). According to Parsons et

al. (1984), respiration takes place both in the light

and in the dark, and the basic dark respiration of

algae obtained from many different species and

growth conditions will be around 10% of maximum

gross photosynthesis. High respiration rates are

attributed to phytoflagellates (35–60%) due to the

motility of these organisms. Therefore, sinking

diatoms (PHY3) are characterized by smaller respi-

ration rates.

Nitrogen uptake in the form of nitrate and

ammonium is described by Eqs. (A.20) and (A.21).

Nitrogen assimilation increases at low (N:C)PHY ratios

and remains unaffected by light intensity. The

inhibition of nitrate uptake by the presence of

ammonium is taken into account. At high (N:C)PHYratios, nitrate is not assimilated and ammonium is

excreted according to Eq. (A.21). Diatoms need

silicate to construct their frustule. Silicate uptake is

calculated as the nitrogen uptake, assuming a constant

N:Si ratio for the uptake.

A constant fraction of growth and uptake of nutrient

c1 is released in the form of Dissolved Organic Matter(DOM) by leakage (i.e., passive diffusion of molecules

through the cellular membrane) as in Fasham et al.

(1990), Lancelot et al. (1991b), Anderson andWilliams

(1998), and Anderson and Pondaven (2003). More-

over, as in Anderson and Williams (1998) and

Anderson and Pondaven (2003), an additional release

of carbon occurs: the extra photosynthetic carbon, due

to metabolic instabilities. The production of this extra

carbon is calculated by a constant fraction c2 of growthflux, that is the first formulation described in Anderson

and Williams (1998).

Mortality of phytoplanktonic groups is repre-

sented by a constant mortality rate affected by the

temperature regulating factor of Eq. (A.14) (e.g.,

Soetaert et al., 2001). The mortality rates are referred

to the value of Jorgensen et al. (1991). This mortality

flux is divided into the dissolved and particulate

organic matter compartments according to a constant

fraction e as in Anderson and Williams (1998),Anderson and Pondaven (2003), and Vichi et al.

(2003b). When diatoms die or are grazed, the silicate

frustule goes immediately to the silicate detritus

compartment.

3.2.2. Bacteria modelling

The nitrogen–carbon balanced model described in

Anderson and Pondaven (2003) is used to model

bacteria. In this model, bacteria growth, excretion, and

respiration are calculated from elemental stoichiom-

etry (Anderson, 1992; Anderson and Williams, 1998).

This method assumes that labile DOC and DON are

the primary growth substrates, with ammonium

supplementing DOM when the C:N of DOM is high.

In addition, bacteria act as remineralizers or consum-

ers of ammonium depending on the relative imbalance

in the C:N ratio of the DOM they consume compared

to their C:N ratio. The model assumes a complete

utilization of the DOM. If the C:N ratio of the DOM is

lower than the C:N ratio of bacteria, bacteria are

carbon limited and will act as a remineralizers through

the excretion of ammonium. Otherwise, when the

DOM is poor in nitrogen compared to bacterial


requirements, bacteria consumes ammonium to com-

pletely utilize the DOM. In the event that this potential

ammonium uptake is insufficient to meet the bacterial

nitrogen requirements, bacteria will regule their C:N

ratio through respiration. The mortality of bacteria is

described by a linear function of their biomass with a

mortality rate dependent on the temperature according

to a Q10 law (Eq. (A.45)). Bacteria mortality flux

supplies the DOM box.

3.2.3. Zooplankton modelling

Zooplankton ingests phytoplankton, bacteria, detri-

tus, and is also cannibal. According to Parsons et al.

(1984), the size of prey items is probably the single

most important factor governing prey selection among

various organisms in the zooplankton community. This

size-selection hypothesis has two properties: these are

firstly that predators are generally larger than their prey

and secondly, within the prey size range of a particular

predator, the largest prey items will be selected when

available. In this paper, one assumes that zooplankton

feeds on preys whose size is equal and lower by one or

two orders of magnitude, with different capture

efficiencies as in Vichi et al. (2003a) (Table A.5 in

Appendix A). For the three sized-groups, a classic

Michaelis–Menten law has been used to simulated

zooplankton grazing (Eq. (A.23)), accounting for all

available preys (Bac and Ban, in mmolC m�3 and

mmolN m�3, respectively, Eq. (A.26)). A fraction /of the food grazed by zooplankton is directly released

in the form of dissolved organic matter and constitutes

the messy feeding as in Anderson and Williams

(1998, 1999), Anderson and Ducklow (2001), and

Anderson and Pondaven (2003). The messy feeding is

associated to the breakage of prey items before

consumption. Measurements made on copepods

report a value of 0.1–0.3 for / (Parsons et al.,1984). The fraction left (1�/) of the food grazed isthe zooplankton intake of carbon and nitrogen

(respectively, IC and IN) given in Eq. (A.28). A

constant fraction b of these intakes (bC and bN) isassimilated by zooplankton. The fraction left, (1�bc)and (1�bn) is released by egestion, that supplies theparticulate organic matter compartment, respectively

in carbon and nitrogen.

The respiration and excretion fluxes are computed in

order to maintain constant the internal N:C ratio of each

zooplankton. We use the model described in Anderson

and Hessen (1995) and Anderson and Pondaven

(2003). In this model, the N:C ratio of the ingested

food of the zooplankton is compared to a theoretical

N:C ratio given in Eq. (A.29). If the ingested food has

a lower N:C ratio than this theoretical ratio, we are in

the case of nitrogen limitation: growth is calculated by

Eq. (A.30) and no excretion of ammonium occurs. In

case of carbon limitation, the growth and excretion

fluxes are computed according to Eq. (A.31). In both

cases, respiration is given by Eq. (A.32).

A basal respiration as in Anderson and Hessen

(1995) representing unavoidable metabolic losses is

considered instead of using a feeding threshold in the

calculation of the grazing. Indeed, a fraction kc of the

assimilated food is used for the growth and the

remaining part is respired to compensate the costs

associated to the maintenance, the activity, and the

transformation of matter (Parsons et al., 1984).

A second-order mortality rate controlled by temper-

ature (Eq. (A.33)) is used for nano- and micro-

zooplankton as in Soetaert et al. (2001) and

Bahamon and Cruzado (2003). Predators of the

mesozooplankton (e.g., salps, chetognaths) are not

explicitly included in the model. Therefore, a closure

term in the equation of mesozooplankton is used to

represent natural mortality and predation by higher

trophic levels (Eq. (A.34)). It has been parameterized

as in Anderson and Pondaven (2003). It is assumed

that this flux is divided into the detritic organic matter

(dissolved and particulate) and the inorganic matter,

according to constant fractions X given in Table A.5.

3.2.4. Detritus and inorganic nutrients

Degradation of particulate organic matter into

dissolved organic matter is controlled by constant

degradation rates with a higher rate for PON as in

Anderson and Pondaven (2003). The chemical proc-

ess of detrital silicate dissolution into mineral silicate

is also formulated by a constant dissolution rate. The

nitrification process is represented as a direct oxy-

dation of ammonium into nitrate.

A lot of papers emphasize the importance of the

export of organic matter through the water column

and the subsequent importance of the evaluation of

sinking rates (e.g., Alldredge and Gotshalk, 1989;

Passow et al., 1994; Kriest and Evans, 1999, 2000;

Kriest, 2002; Jackson, 1995, 2001; Boyd and Stevens,

2002). The sinking velocity of POM has been


implemented according to the aggregation model

developed in Kriest and Evans (2000) and Kriest

(2002). This model needs to consider as an additional

state variable the number of aggregates (AggNum)

whose evolution is calculated by Eq. (A.13). These

aggregates are formed when particles move relative to

each other, collide, and stick together. Mechanisms

that are responsible for collision are differential

settlement and turbulent shear. The main assumption

of the aggregation model is that the distribution of the

number of aggregates n(di) of size di follows a power

law: n(di)=Adi�e where A and e are variable in time.

The mass m(di) of a particle of size di is also assumed

to be described by a two-parameter function:

m(di)=Cdif, the distribution of mass is then repre-

sented by m(di)=ACdif�e. This size distribution is

modified by two processes: aggregation and sedimen-

tation. Sinking preferentially removes large particles

and leaves behind the smaller ones. Aggregation

creates large particles: it affects only the number,

but not the mass of the particles.

The sinking speed of particles w(di) is also assumed

to be represented by a power law: w(di)=Bdig. Sinking

rates attributed to the number of aggregates and to the

mass of aggregates (formed with particulate organic

matter) are average sinking rates (U in Eq. (A.13); C inEqs. (A.10) and (A.11)), calculated by an integral over

the size range of particles. The aggregation rate n is afunction of the number of particles, their size,

turbulent shear rate, settling speed, and the stickiness,

i.e., the probability that two particles stick together

after contact. Analytic evaluations of U, C, and n canbe found in Kriest and Evans (2000) and Kriest

(2002).

3.3. Implementation

3.3.1. Models

The physical and biological models are coupled

off-line. The main impact of the biology on the

physics would be the shading caused by the amount

of chlorophyll in the expression of the attenuation of

light coefficient in the water column. In an oligo-

trophy region, the poor amount of chlorophyll does

not influence the light intensity of the water column

in a great way. By neglecting the shading caused by

chlorophyll, the physics is totally independent of the

biology and both models can be coupled off-line.

Simulations with the hydrodynamic model are

performed, storing the temperature and turbulent

diffusion coefficient profiles. Then, the biological

model is integrated using hydrodynamic model

results.

The 1D hydrodynamic model has been imple-

mented by Lacroix and Nival (1998). The model runs

in FORTRAN on a personal computer. The model is

integrated over 1 year with a time step of 15 min and a

vertical mesh size of 2 m.

To integrate our partial differential equations sys-

tem, we use the subroutines library Flexible Environ-

ment for Mathematically Modelling the Environment

(FEMME) developed by Soetaert et al. (2002) and

designed for implementing, solving, and analyzing

mathematical models in ecology. The depth of the

vertical domain has been set to 400 m, in order to be

sure that all the organic matter produced in the euphotic

layer by primary production is remineralized in the

modelled domain. In this way, the model is fully

conservative: no matter is lost and we do not need to

add nutrient fluxes at the bottom of the domain. The

vertical mesh size is constant and equals to 1 m. All

scalars and vectors are defined in the center of each

box. The constant time step used is about 2 h. Time

stepping is done using explicit Euler integration, except

for turbulent mixing which is solved with an implicit

method. The model has been implemented in FOR-

TRAN on a personal computer. Contours maps have

been obtained using Matlab 5.3 program.

3.3.2. Initial conditions

The simulation starts on January 1st, 2000 during a

period of high mixing. Homogeneous profiles of both

the hydrodynamic and biological variables are

imposed. The spinup time of the hydrodynamic model

is of 6 years. Using the results of the sixth year of

simulation of the physical model, the biological model

is then integrated to obtain almost repetitive yearly

cycles of the biogeochemical variables (this is the case

after 2 years).

3.3.3. Boundary conditions

At the air–sea interface, the hydrodynamic model

is forced by meteorological conditions described in

Section 2.2.

A zero flux condition is imposed at the bottom and

at the surface for each ecosystem state variable.


3.3.4. Sensitivity and identifiability of parameters

Large environmental simulation models are usually

overparameterized with respect to given sets of

observations. Not all of their parameters can be

identifiable from the measured profiles. It raises the

question of how to select a subset of model parameters

to be included in a formal parameter estimation

process. The problem of parameter identifiability of a

given model structure is then crucial, especially when

working with large environmental simulation models

(Brun et al., 2001; Omlin et al., 2001). The systematic

approach to tackle this problem is described in Brun et

al. (2001). Omlin et al. (2001) give an application of

this approach for a biogeochemical model of Lake

Zqrich. The first tool used is a sensitivity analysis ofindividual parameters to model outputs. In order to

assess the identifiability of a subset K of k parameters,

we have to consider the joint influence of the subset

parameters on the model output. It may happen that a

change in the model output caused by a change in a

model parameter in K can be (nearly) compensated by

appropriate changes in the other parameters’ values. An

analysis of the approximate linear dependence of

sensitivity functions of parameter subsets is performed.

The results of the analysis are used to select a parameter

subset for a fit with measured data. Implemented in the

library of subroutines FEMME (Soetaert et al., 2003),

we used this method to determine the list of parameters

that are worth to be estimated together.

Fig. 4. Contours of hydrodynamic results: (a) temperature; (b) the mixing l

Most sensitive parameters that had been detected

are: the mortality rates of all living organisms,

parameters associated with the closure of the model,

maximal growth rates of phytoplankton groups,

maximal ingestion rates of zooplankton groups,

parameters associated to light, and the fraction of

primary production which is released by dextra-excretionT of carbon (parameter c2 in Section 3.2.1).Capture efficiencies play also an important role in the

repartition of plankton species.

4. Models result

4.1. Hydrodynamic model

The seasonal evolution of the temperature and the

mixing layer depth, i.e., the depth range through which

surface fluxes are being actively mixed by turbulent

process (explained in Brainerd and Gregg, 1995),

simulated by the model are presented in Fig. 4. The

mixing layer depth has been estimated from kinetic

turbulent energy profiles. In January, the vertical

mixing is intense and mixes the 200 upper meters of

the water column. Temperature and salinity profiles are

homogeneous with values of 13 8C and 38.5, respec-tively. In February, the vertical mixing is lower due to

reduced winds, except at the end of the month because

of strong wind events (in Fig. 2). The vertical mixing is

ayer depth computed by the hydrodynamic model for the year 2000.


low in March, but the thermocline only appears in mid-

April when the air temperature significantly increases.

The mixing layer depth reaches 40–50 m in April, and

20–30 m in May. In mid-July, meteorological events

occur, that will have an influence on the biology as we

will see later: strong wind events occur (in Fig. 2c)

producing an intense mixing in the upper 20 m and a

decrease in the air temperature (in Fig. 2b) partly erodes

the thermocline (in Fig. 4). The temperature increases

to 24 8C in August, due to high air temperature andinsolation values. The thermocline is located near 50 m

depth. The intensity of the vertical mixing at the end of

October due to increased wind stress progressively

destroys the vertical stratification. The thermocline

completely disappears in December.

4.2. Biogeochemical results

In this section, we present the seasonal evolution of

the biological variables over one year of simulation,

computed by the ecosystem model.

Fig. 5. Integration of phytoplankton (mgChl m�2) and zooplankton (mmolC

Am; Phy2: nanophytoplankton [2, 20] Am; Phy3: microphytoplanktomicrozooplankton [20, 200] Am; Zoo3: mesozooplankton [0.2, 2] mm.

4.2.1. Seasonal plankton dynamics

Fig. 5 shows the seasonal evolution of the auto-

trophs and zooplankton fields, integrated over 200 m

depth. Chlorophyll evolution clearly follows the

hydrographic structure of the water column: the intense

winter vertical mixing in January (in Fig. 4) does not

allow the development of a bloom because phyto-

plankton spends too much time in low light conditions.

From early February, the mixing layer depth is reduced

to 20–40 m. Despite the low water temperature (13 8C)and insolation, primary production is enhanced and

reaches its maximum in mid-March, feeding on nitrate

brought by the winter vertical mixing of January. In

addition, the model simulates a winter–early spring

bloom starting in February and reaching its peak in

mid-March. Then, waters become nutrient-depleted

and zooplankton exerts a non-negligible pressure on

phytoplankton which causes chlorophyll concentration

to decrease. In mid-April, environmental conditions

enhance primary production again: temperature and

insolation increase in surface waters, and nutrients have

m�2) biomass over 200 m depth. Phy1: picophytoplankton [0.2, 2]

n [20, 200] Am; Zoo1: nanozooplankton [2, 20] Am; Zoo2:


been brought back in the surface layer due to the

mixing of the end of March (in Figs. 2 and 4). The

model then simulates a bloom starting in mid-April and

reaching its peak in mid-May. Another bloom is

simulated in June–July thanks to the feeding on

regenerated nutrients accumulated below the nitracline,

as we will see later. At the end of October, the

intensification of the mixing caused by strong wind

events (in Fig. 2) enriches the surface layer in nutrients,

causing a new phytoplankton bloom. In December,

insolation and temperature are low, and mixing is

intense (the mixing layer depth reaches 100 m):

primary production is reduced.

Fig. 6a,b,c shows the evolution in time and depth of

the three modelled phytoplankton groups. The seasonal

variations of the three groups of phytoplankton are

roughly similar, due to the availability in nutrients in

the water column. The winter–early spring bloom

starting at the end of February is composed of the three

Fig. 6. Evolution in time and in the 100 upper meters of the six plankton

mmolC m�3. (a) Phy1: picophytoplankton; (b) Phy2: nanophytoplankton; (

microzooplankton; (f ) Zoo3: mesozooplankton.

phytoplankton groups as shown in Figs. 5a, and 6a, b

and c. The pico- and nanophytoplankton reach their

peak of biomass at the surface while the micro-

phytoplankton composed of diatoms reaches its peak

of development at 25 m depth due to its sedimentation

and its better adaptation to low insolation values. The

maximum concentrations reached in March are of 0.3,

1, and 0.4 mgChl m�3, respectively, for pico-, nano-,

and microphytoplankton. The following depletion of

nutrients in the upper layers limits all phytoplankton

groups production and a decrease in all phytoplankton

concentrations is observed. In May, environmental

conditions enhance a new phytoplankton bloom.

Maximal concentrations reach 0.35, 1.2, and 0.6

mgChl m�3 in mid-May, respectively, for pico-,

nano-, and microphytoplankton. These peaks are

simulated at the surface for the first two groups while

the maximum development of microphytoplankton

occurs at 30–40 m depth. From May to October, the

groups. (a,b,c) Phytoplankton in mgChl m�3; (d,e,f) zooplankton in

c) Phy3: microphytoplankton; (d) Zoo1: nanozooplankton; (e) Zoo2:


thermocline prevents the vertical diffusion in the

surface layer of regenerated nutrients accumulated

below the nitracline. When all the nutrients of the

surface layer are consumed, primary production occurs

at a depth below the seasonal thermocline feeding on

regenerated nutrients (in Fig. 8c showing the ammo-

nium evolution in time and depth). A bloom of

nanophytoplankton then occurs at 30–40 m depth in

June and July, reaching its peak of 1.5 mgChl m�3 in

mid-July. At this period, meteorological events (strong

wind events and a decrease in the air temperature, in

Fig. 2) perturb the two smaller phytoplankton groups,

still present in the surface waters. Phytoplankton is then

mixed through the 40 upper meters and disappears

after, because of the lack of nutrients. In early October,

a third phytoplankton bloom occurs for the two smaller

phytoplankton groups due to the nitrogen brought in

upper layers by mixing. Maximal concentration reach

0.15 and 0.4 mgChl m�3, respectively, for pico- and

nanophytoplankton.

The model simulates a variation of the phyto-

plankton N:C ratios by a factor 4 around the Red-

field ratio ((N:C)PHY varies between (N:C)PHY,minand (N:C)PHY,max), which emphasizes the impor-

tance of the variability of this ratio. Because all

phytoplankton N:C ratios follow the same trend, Fig.

7 shows the seasonal variability of the nanophyto-

plankton N:C ratio over the 100 upper meters.

Analyzing the contribution of each phytoplankton

group to chlorophyll, we note that the dominant group

is the nanophytoplankton group all along the year (in

Fig. 5a). A mean over the whole year shows that

Fig. 7. Evolution in time and space (over the 100 upp

nanophytoplankton represents 68.3% of chlorophyll a

while the mean contribution of microphytoplankton is

of 20.4%. In addition, primary production results

show the following contribution to total primary

production: 13.8% for the picophytoplankton, 72.3%

for the nanophytoplankton, and 13.9% for micro-

phytoplankton, which highlights the nanophytoplank-

ton dominance.

Zooplankton clearly follows the phytoplankton

repartition (in Figs. 5b and 6d,e,f), but is always

present in the first 200 m through the year, because it

also feeds on particulate detritus too and does not

need light to perform assimilation. Maximal zoo-

plankton biomasses are found as a consequence of

phytoplankton blooms, except for mesozooplankton

which is characterized by a slower metabolism

compared to two others zooplankton groups. It does

not grow during the first phytoplankton bloom but

significantly develops from May to mid-July when it

reaches its peak of development, due to the high

biomass of the nanophytoplankton and the subsequent

concentration of particulate detritus.

4.2.2. Bacteria dynamics

Fig. 8 shows the annual evolution of the bacteria

biomass, the excretion of ammonium by bacteria (i.e.,

the intensity of the remineralization flux), the ammo-

nium concentration, the DOC concentration, and the

(N:C)DOM. The development of bacteria is condi-

tioned by DOC availability as shown by comparing

Fig. 8a and d. Remineralization occurs mainly in the

first 100 upper meters as shown in Fig. 8b. The

er meters) of the nanophytoplankton N:C ratio.

Fig. 8. Seasonal evolution of the microbial loop over the 200 upper meters. (a) Bacteria biomass in mmolC m�3, (b) excretion of ammonium in

mmolN m�3 d�1, (c) ammonium concentration in mmolN m�3, (d) dissolved organic matter in mmolC m�3, (e) (N:C)DOM in molN molC�1.


(N:C)DOM ratio varies between 0.02 and 0.14 molN

molC�1. Its minimal value is reached in February–

March through the 20 upper meters, with the

consequence of a nitrogen limitation for bacterial

production and an uptake of ammonium, that can be

seen in Fig. 8b where the excretion of ammonium by

bacteria reaches zero. Then bacteria are nearly all the

year limited by the carbon content of the organic

substrate, depending on the variability of the

(N:C)DOM ratio, and then act as remineralizers.

5. Discussion

In this section, model results are compared with

measurements data collected in the year 2000 at the

DYFAMED station and described in Section 2.

5.1. Hydrodynamic model results

Fig. 9 compares the temperature and salinity

profiles simulated by the model and reconstructed

from in situ data for each month. The temperature

and the thermocline depth are correctly reproduced

by the hydrodynamic model, except between 20

and 50 m depth in the end of September, where

temperature simulated by the model is too high.

The model overestimates salinity in fall. As it has

been explained in Section 2.2, precipitations

imposed in the model come from the FRONTAL

mission (mean values for the period 1984–1988).

It may happen that real precipitations were more

important in the year 2000. The difference observed

in fall may be attributed to an another cause: the past

studies indicate that the site is generally not perturbed,

although exceptional intrusions of waters coming

from the Ligurian current are possible during the cold

season (Taupier-Letage and Millot, 1986; Marty et al.,

2002; Barth et al., in press). Advection of the

Northern Current (in Fig. 1) can reach important

values, transporting Atlantic water, with a salinity

of 38.1–38.2, values observed at the DYFAMED

station. A 1D model is not able to represent this

observation.

Fig. 9. Temperature (in 8C) and salinity profiles at different periods of the year. In continuous line: model results, dotted line: data measurementobtained at the DYFAMED site for the year 2000.


5.2. Ecosystem model results

Fig. 10 compares the living organisms’ vertical

profiles simulated by the model and reconstructed from

in situ observations. It shows that the model is able to

reproduce the main features of the annual cycle of the

biological productivity. The duration of the different

blooms, their vertical distribution, and composition are

in a quite good agreement with the observations.

5.2.1. Autotrophs

In January, the model is not able to simulate a bloom

at 50 m depth. It can be explained as follows.

DYFAMED data reveal that in 1999, the fall bloom

occurred only in December due to the absence of

vertical mixing at the end of October to bring nutrients

in the upper layers. We suspect that the bloom revealed

by the data in January 2000 is the continuation of the

late fall bloom of the year 1999. The first winter–early

spring bloom occurring in February to late March and

the second spring bloom occurring in mid-April to mid-

May are correctly reproduced although the measure-

ments frequency does not allow to observe them

separately. The repartition of phytoplankton groups

during these blooms are also in a good agreement with

observations. From May to September, surface waters

are nutrient-depleted and autotrophs follow the nitra-

cline. The depth of the maximum of phytoplankton

biomasses and their intensities are correctly repro-

duced. A period of several days of intense vertical

mixing beginning in mid-July over 30–40 m depth

causes primary production to decrease because

nutrients have not been brought to the upper layers

during this mixing. This effect had already been noted

in Fig. 6. In fall, pico- and nanophytoplankton develop

above 50 m depth, thanks to the nutrients brought by

the deep vertical mixing.

As has been observed in Section 4.2.1, the model

reveals a nanophytoplankton-dominated ecosystem

for the year 2000, because of its higher contribution

to the total primary production (72.3%) and to

chlorophyll (68.3%). This conclusion is in agreement

with Marty et al. (2002) when analyzing seasonal

patterns of phytoplankton biomass from pigments data

Fig. 10. Living organisms vertical profiles. Chl: Chlorophyll a; Phy1: picophytoplankton; Phy2: nanophytoplankton; Phy3: micro-

phytoplankton; Bac: bacteria; Zoo1: nanozooplankton; Zoo2: microzooplankton. Continuous lines: model results. Dotted lines: profiles

reconstructed from DYFAMED data of year 2000.


measured at the DYFAMED station between 1991 and

1999: they note an apparent increase of total

phytolankton biomass which could be mainly attrib-

uted to nano- and picophytoplankton. This apparent

shift of phytoplankton populations towards a

decreased importance of diatoms in phytoplankton

biomass is also consistent with the data of Bethoux et

al. (2002), which suggest that the increase of nutrients

and changes in N:P:Si ratios since the early 1960s

could lead to a shift of phytoplankton from diatom-

dominated ecosystem towards a nonsiliceous one.

This 1-year simulation does not represent this shift,

but models a nanoflagellates-dominant ecosystem, the

new trend of the Ligurian Sea ecosystem.

5.2.2. Heterotrophs

The model seems able to reproduce the bacteria,

the nano-, and the microzooplankton profiles

observed during the first 3 months of year 2000 (in

Fig. 10). Zooplankton is however slightly overesti-

mated in late March due to the slight overestimation

of the pico- and the nanophytoplankton at this period.

Bacteria, nano- and microzooplankton have been

measured at the DYFAMED station between May

1999 and March 2000 (Tanaka and Rassoulzadegan,

2002). Mean over depth mesozooplankton values

have been measured in 2001 and 2002 by Gasparini

and Mousseau (http://www.obs-vlfr.fr/jgofs2/sody/

home.htm). For a comparison, the Fig. 11 presents

vertically integrated values (between 5 and 110 m

depth) of nano-, microzooplankton, and bacteria with

available DYFAMED data. Mean mesozooplankton

values are also presented. We note a high variability in

the mesozooplankton observed values. The computed

variables are shown to have the same range of

variations as the observed variables.

5.2.3. Nutrients and detritic matter

Simulated nitracline depth (in Fig. 12) is in a good

agreement with observations, except in late September,

where mixing has been overestimated, what we have

already noted in Fig. 9 showing temperature and sa-

http://www.obs-vlfr.fr/jgofs2/sody/home.htmhttp://www.obs-vlfr.fr/jgofs2/sody/home.htm

Fig. 11. Comparison of zooplankton and bacteria biomass with available data at the DYFAMED station from 1999 to 2002. The model simulates

the year 2000. Zoo1: nanozooplankton; Zoo2: microzooplankton; Zoo3: mesozooplankton; Bac: bacteria.


linity results. In early December, the model represents a

supply of upper waters in nitrogen due to mixing,

which is not observed at the DYFAMED station. In the

background literature, silicate has not been always

reported as a limiting nutrient in the Mediterranean Sea

(Marty et al., 2002). Silicate has been introduced as a

potential limiting element for diatoms growth. The

numerical simulations have shown that the nitrate li-

mitation occurs before the silicate limitation. Upper

waters are completely depleted in nitrate from May to

December, unlike silicate, which is still present at these

depths (in Fig. 12). One of the aims of this paper was to

test the potential silicate limitation on diatoms primary

production. When analyzing nutrients uptake in nitro-

gen and silicate, we obtain smaller values for nitrogen

uptake all along the year. Although the model is able to

represent correctly the year 2000 silicate profiles, si-

licate never limits diatoms growth in our simulations.

Fig. 12 presents the particulate organic matter com-

puted profiles and profiles reconstructed from in situ

DYFAMED data of year 2000. Although the model

computes too small particulate organic matter concen-

trations at the beginning of the year, the range of

variations and the depth of the maximum are correct.

6. Conclusions

In this paper, a 1D coupled biogeochemical–hydro-

dynamical model has been built to study the seasonal

cycle of the biogeochemical processes in the Ligurian

Sea (NW Mediterranean Sea). The hydrodynamical

model is able to reproduce the main features of the

Ligurian Sea hydrodynamics: thermocline depth, tem-

perature, and salinity evolutions. The results of the

biogeochemical model illustrate the spatial (vertical)

and temporal variability of the lower trophic levels and

confirm the necessity of choices of variables and

processes that have been made during the conceptual-

ization of the model, such as the variability of the

phytoplankton N:C ratio. The two possible behaviors

of bacteria, remineralizers or consumers of ammonium,

have been simulated thanks to the variability of the

organic substrate N:C ratio, the case of carbon

Fig. 12. Inorganic nutrients and particulate organic matter vertical profiles. Continuous lines: model results. Dotted lines: DYFAMED data of

the year 2000.


limitation being the most frequent: bacteria act nearly

all the year as remineralizers. Phytoplankton is known

to be limited by nutrient availability but never by

inorganic carbon availability. Therefore, carbon and

nitrogen have to be considered together because of the

strong and nonlinear coupling between phytoplankton,

zooplankton, and bacteria dynamics. The potential

silicate limitation of diatoms growth has been studied:

although the model is able to represent correctly the

silicate profiles for year 2000, silicate never limits

diatoms growth in our simulations.

The comparison of the simulated biological varia-

bles with monthly measurement data coming from the

DYFAMED station in the central zone of the Ligurian

Sea have shown a rather good qualitative and quanti-

tative agreement (Section 5.2). The vertical distribu-

tion, the duration, and the composition of the different

blooms are correctly reproduced. The model simulates

a nanoflagellates-dominant ecosystem in agreement

with Marty et al. (2002). Zooplankton, bacteria, and

the particulate organic matter are shown to be in the

correct range of variations.

For several years, measurements in the Western

Mediterranean Sea have proved phosphorus to be an

important limiting nutrient for phytoplankton and

bacteria growth (e.g., Zweifel et al., 1993; Egge,

1998; Mostajir et al., 1998; Guerzoni et al., 1999;

Thingstad and Rassoulzadegan, 1999; Benitez-Nelson,

2000; John and Flynn, 2000; Turley et al., 2000; Crise

et al., 1999; Crispi et al., 1999a,b, 2001, 2002; Diaz et

al., 2001; Touratier et al., 2001; Allen et al., 2002;

Marty et al., 2002; Moutin and Raimbault, 2002;

Tanaka and Rassoulzadegan, 2002; Van Wambeke et

al., 2002). The choice of considering nitrogen (instead

of phosphorus) as the major limiting nutrient has been

decided by inspecting publications of measurement

data at the DYFAMED station. In their 1991–1999

study of the dynamics of nutrients and phytoplankton

pigments, Marty et al. (2002) indicate a probable shift

from N-limitation in winter to P-limitation in summer.

Making the choice of one main limiting element in

order to limit the complexity of the model, we have

chosen nitrogen in order to represent correctly the first

winter–early spring phytoplankton bloom. Without

Variables Description Units

k̃ Turbulent diffusioncoefficient

m2s�1

f(T) Temperature factor –

I(z) Light intensity Wm�2

kext Light extinction coefficient m�1

Chl(z,t) Chlorophyll at depth z time t mgChl m�3

GrowthPHYi Phytoplankton i growth flux mmolC m�3 d�1


considering phosphorus, the model results have been

shown to be close to the in situ measurements and the

nitrate measurement data show a complete utilisation of

nitrate in surface waters. If a limitation by phosphorus

would occur in summer, a nitrate limitation occurs

simultaneously and the phytoplankton nutrient uptake

stops because of the use of a minimum formulation for

the uptake rates. A summer phosphorus limitation will

probably not change our model results.

(Chl:C)PHYi Phytoplankton i chlorophyll:

carbon ratio

gChl molC�1

(N:C)PHYi Phytoplankton i nitrogen:

carbon ratio

molN molC�1

NO3,iuptake Phytoplankton i nitrate

uptake

mmolN m�3 d�1

NH4,iuptake Phytoplankton i ammonium

uptake

mmolN m�3 d�1

NH4,iexcr Phytoplankton i

ammonium excretion

mmolN m�3 d�1

SiOsPhy3uptake Phytoplankton 3 silicate

uptake

mmolSi m�3 d�1

MortPHYC,i Phytoplankton i mortality

flux in carbon

mmolC m�3 d�1

MortPHYN,i Phytoplankton i mortality

flux in nitrogen

mmolN m�3 d�1

GrazCI Grazing flux of zooplankton

i in carbon

mmolC m�3 d�1

Acknowledgments

This work was supported by the Fonds pour la

Formation la Recherche dans l’Industrie (FRIA,

Belgium). We would like to thank J.-C. Marty for

the hydrodynamic and biological data coming from

the DYFAMED station and METEO France for the

meteorological data. We are very grateful to Dr. G.

Lacroix and J. Walmag for providing the 1D version

of the GHER hydrodynamic model. This paper is the

MARE publication no. MARE055, and the NICO-

KNAW Netherlands Institute of Ecology contribution

no. 3439.

GrazNI Grazing flux of zooplankton

i in nitrogen

mmolN m�3 d�1

GrazPreyi Grazing flux of prey i by

all its predators

mmol m�3 d�1

Appendix A. Mathematical formulation of the

model

IC,I Zooplankton i intake

of carbon

mmolC m�3 d�1

IN,I Zooplankton i intake

of nitrogen

mmolN m�3 d�1
Table A.1
List of biogeochemical state variables, description, and units

State variables Description Units

NOs, NHs Nitrate NO3, Ammonium NH4 mmolN m�3

SiOs Silicate SiO2 mmolSi m�3

NPhy1, NPhy2,

NPhy3

Pico-, nano-,

microphytoplankton in

nitrogen

mmolN m�3

CPhy1, CPhy2,

CPhy3

Pico-, nano-,

microphytoplankton

in carbon

mmolC m�3

CZoo1, CZoo2,

CZoo3

Nano-, micro-,

mesozooplankton

mmolC m�3

CBac Bacteria mmolC m�3

DOC, DON Dissolved organic carbon

and nitrogen

mmol m�3

POC, PON Particulate organic carbon

and nitrogen

mmol m�3

SiDet Detrital particulate silicate mmolSi m�3

AggNum Aggregates number m�3

Table A.2

List of variables used in Tables A.3 and A.4

GrowthZOOC,i Zooplankton i growth flux

in carbon

mmolC m�3 d�1

GrowthZOON,i Zooplankton i growth flux

in nitrogen

mmolN m�3 d�1

ExcrZOOi Zooplankton i excretion flux

of ammonium

mmolN m�3 d�1

RespZOOi Zooplankton i respiration flux mmolC m�3 d�1

MortZOOj Zooplankton j mortality flux,

j=1, 2

mmolC m�3 d�1

ClosureZOO3 Closure term applied to

zooplankton 3

mmolC m�3 d�1

Uc Bacteria uptake of DOC mmolC m�3 d�1

Un Bacteria uptake of DON mmolN m�3 d�1

UA* Bacteria potential uptake

of ammonium

mmolN m�3 d�1

UA Bacteria uptake

of ammonium

mmolN m�3 d�1

GrowthBAC Bacteria growth flux mmolC m�3 d�1

(continued on next page)

Variables Description Units

RespBAC Bacteria respiration flux mmolC m�3 d�1

ExcrBAC Bacteria excretion flux

of ammonium

mmolN m�3 d�1

TestBAC intermediary variable mmolN m�3 d�1

MortBAC Bacteria mortality flux mmolC m�3 d�1

Table A.2 (continued)

Table A.3

The biogeochemical model state equations

dCPHYi

dt¼ BBz

�k̃kBCPHYi

Bz

�� di;3

B vPhyCPHY3� �

Bzþ 1� c1 � c2ð ÞGrowthPHYi�MortPHYC;i�GrazCPHYi i ¼ 1; 2; 3 ðA:1Þ

dNPHYi

dt¼ B

Bz

�k̃kBNPHYi

Bz

�� di;3

B vPHYNPHY3ð ÞBz

�Mort PHYN;i � GrazNPHYi þ 1� cið Þ NOuptake3;i þ NHexcr4;i � NHexcr4;i

� �i ¼ 1; 2; 3

ðA:2Þ

dCZOOi

dt¼ B

Bz

�k̃kBCZOOi

Bz

�þ GrowthZOOC;i � di;1 þ di;2

� �MortZOOi � di;3ClosureZOO3 � GrazCZOOi i ¼ 1; 2; 3 ðA:3Þ

dCBAC

dt¼ B

Bz

�k̃kBCBAC

Bz

�þ GrowthBAC�MortBAC� GrazCBAC ðA:4Þ

dNOs

dt¼ B

Bz

�k̃kBNOs

Bz

��X3j¼1

NOuptake3;j þ nitrif NHs ðA:5Þ

dNHs

dt¼ B

Bz

�k̃kBNHs

Bz

�þ

X3j¼1

�ExcrZOOj � NHuptake4;j þ NHexcr4;j Þ � nitrif NHsþ XNH4ClosureZOO3 � UA þ ExcrBAC ðA:6Þ

dSiOs

dt¼ B

Bz¼

�k̃kBSiOs

Bz

�� SiOsuptakePhy3 þ dissSiDetSiDet ðA:7Þ

dDOC

dt¼ B

Bz

�k̃kBDOC

Bz

�� Uc þ degradPOCPOCþ

X3j¼1

c1 þ c2ð ÞGrowthPHYj þ �MortPHYC;j þ /GrazCj�

þMortBAC

þ XDOMClosureZOO3 ðA:8Þ

dDON

dt¼ B

Bz

�k̃kBDON

Bz

�� Un þ degradPONPONþ

X3j¼1

c1 NOuptake3;j þ NH

uptake4;j

� �þ �MortPHYN;j þ /GrazNj

h iþ XDOMClosureZOO3

� N : Cð Þz þMortBAC N : Cð ÞB ðA:9Þ

dPOC

dt¼ B

Bz

�k̃kBPOC

Bz

�� B WPOCð Þ

Bzþ 1� bCð ÞIC � degradPOCPOC� GrazPOC þ

X3j¼1

1� �ð ÞMortPHYC;j�

þ dj;1 þ dj;2ÞMortZOOj��

þ XPOCClosureZOO3 ðA:10Þ


dPON

dt¼ B

Bz

�k̃kBPON

Bz

�� B WPONð Þ

Bzþ ð1� bNÞIN � GrazPON þ

X3j¼1

N : Cð Þz dj;1 þ dj;2� �

MortZOOj þ dj;3XPON��

ClosureZOO3 �

þ 1� �ð ÞMortPHYN;jg � degradPONPON ðA:11Þ

dSiDet

dt¼ B

Bz

�k̃kBSiDet

Bz

�� B vSiDetSiDetð Þ

Bz� dissDetSiDetSiþ MortPHYN;3 þ GrazNHPY3

� �Si : Nð ÞPHY3 ðA:12Þ

dAggNum

dt¼ B

Bz

�k̃kBAggNum

Bz

�� B UAggNumð Þ

Bzþ BPON

Bt

bio

AggNum

PON� n ðA:13Þ

Note:–

d i ,j is the Knonecker symbol, equals to 1 if i=j, 0 else.– BPON

Btjbiois calculated by Eq. (A.11) except the transport and the sedimentation terms.


Table A.4

Mathematical formulation of biogeochemical fluxes

f T ¼ QT�2010

10 ðA:14Þ

I zð Þ ¼ I z ¼ 0ð Þ 1� albedoð Þexp"�Z z0

kext zð Þdz#

ðA:15Þ

kext zð Þ ¼ kwater zð Þ þ kChlChl z; tð Þ ðA:16ÞPhytoplankton, (i=1, 2, 3)

GrowthPHYi ¼ CPHYi f Tmin limnut;i ; limlight;i� �

ðA:17Þ

with f limlight;i¼ QuantiLight Chl : Cð ÞPHYi�Respih i 1�ProdRespið Þlimnut;i¼ lmax;i

�1�

N : Cð ÞPHYi ;minN : Cð ÞPHi

�ðA:18Þ

Chl : Cð ÞPHYi ¼ N : Cð ÞPHYi

(Chl : Nð ÞPHYi ;min þ Chl : Nð ÞPHYi;max½ . . .

. . . � Chl : Nð ÞPHYi ;min� �N : Cð ÞPHYi � N : Cð ÞPHYi ;min

N : Cð ÞPHYi ;max � N : Cð ÞPHYi ;min

)ðA:19Þ

for (N:C)PHYi V (N:C)PHYi , max

NOuptake3;i ¼ NOumax i f T

�1�

N : Cð ÞPHYiN : Cð ÞPHYi ;max

�NOs

NOs þ kNOsikin

kin þ NHsCPHYi

NHuptake4;i ¼NHumax i f T

�1�

N : Cð ÞPHYiN : Cð ÞPHYi;max

�NHs

NHs þ kNHsiCPHYi

NHexcr4;i ¼ 0 ðA:20Þ

for (N:C)PHYi N (N:C)PHYi , max

NOuptake3;i ¼ NH

uptake4;i ¼ 0

NHexcr4;i ¼ NHumax i f T�1�

N : Cð ÞPHYiN : Cð ÞPHYi ;max

�CPHYi ðA:21Þ

MortPHYX ;i ¼ mortPHY i f TXPHYi; X ¼ C;N ðA:22Þ

Zooplankton, (i=1, 2, 3)

GrazCi ¼ f TmaxGraziBac;i

Bac;i þ ksat;iCZOOi ðA:23Þ

GrazNi ¼ GrazCi N : Cð Þfood;i ðA:24Þ




GrazXPreyi ¼X3j¼1

GrazXjeXPreyi ;Zooj XPreyi=Bax;j; X ¼ C;N ðA:25Þ

Bax;i ¼Xpreys

eprey; Zooi XPrey; X ¼ C;N ðA:26Þ

N : Cð Þfood;i ¼ Ban;i=Bac;i ðA:27Þ

IX ;i ¼ 1� /ið ÞGrazXi; X ¼ C;N ðA:28Þ

N : Cð Þi4 ¼ N : Cð Þzkc;ibC;ibN;i

Y

(N : Cð Þfood;ib N : Cð Þi4ZN limitationN : Cð Þfood;iN N : Cð Þi4Z C limitation

ðA:29Þ

If N limits :

(GrowthZOON;i ¼ bN;iIN;iGrowthZOOC;i¼GrowthZOON;i= N : Cð ÞZExcrZOOi ¼ 0

ðA:30Þ

If C limits

(GrowthZOOC;i ¼ kc;ibC;iIC;iGrowthZOON;i ¼ GrowthZOOC;i N : Cð ÞZExcrZOOi ¼ bN;iIN;i � GrowthZOON;i

ðA:31Þ

RespZOOi ¼ bC;iIC;i � GrowthZOOC;i ðA:32Þ

MortZOOj ¼ f TmZ;jCZOO 2j j ¼ 1; 2 ðA:33Þ

ClosureZOO3 ¼ f TmZ;3CZOO

23

kClos þ CZOO3ðA:34Þ

Bacteria

Uc ¼ lBCBACDOC

kDOM þ DOC; Un ¼ Uc N : Cð ÞDOM ðA:35Þ

UA4 ¼ lBCBAC N : Cð ÞBNHs

kA þ NHsðA:36Þ

GrowthBAC ¼ xBUc ðA:37Þ

RespBAC ¼ 1� xBÞUc ðA:38Þð

TestBAC ¼ Un � GrowthBAC N : Cð ÞB ðA:39Þ

ðA:40Þif TestBACN0YC limitation case:UA ¼ 0

ExcrBAC ¼ TestBAC ðA:41Þ

if TestBACb0YN limitation case:

if jTestBAC jVUA4 Z UA ¼ � ½Un � GrowthBAC N : Cð ÞB�ExcrBAC ¼ 0 ðA:42Þ

if jTestBAC jNUA4 Z UA ¼ UA4GrowthBAC ¼ ðUn þ UAÞ= N : Cð ÞBRespBAC ¼ GrowthBACð1=xB � 1ÞExcrBAC ¼ 0

ðA:43Þ

MortBAC ¼ f TmortBCBAC ðA:44Þ


Par. Units Value Description Ref.

Q10 – 2 temperature coefficient (1)

kChl (mgChl m2)�1 0.02 self-shading extinct. coeff. (2)

Albedo – 0.085 surface albedo (2)

Phytoplankton PHY1 PHY1 PHY1(N:C)Red molN molC

�1 0.15 0.15 0.15 Redfield ratio (16:106)

(N:C)PHY,min molN molC�1 0.05 0.05 0.05 minimal N:C ratio (1)

(N:C)PHY,max molN molC�1 0.2 0.2 0.2 maximal N:C ratio (1)

(N:Si) molN molSi�1 – – 1 N:Si ratio

(Chl:C)min gChl molC�1 1 1 1 min. Chl:C ratio (1)

(Chl:C)max gChl molC�1 2 2 2 max. Chl:C ratio (1)

Quant ((molC m2)/

(gChldW))

0.4 0.4 0.55 Max. Quantum yield (c,1)

Resp d�1 0.05 0.05 0.03 Respiration rate (c,1,5)

ProdResp � 0.25 0.25 0.15 frac. of pp used for resp. (c,1,5)Amax d

�1 3 2.5 2 Max. spec. growth rate (2)

NOumax molN molC�1d�1 0.4 0.4 0.4 Max. NO3 uptake rate (1)

NHumax molN molC�1d�1 1 1 1 Max. NH4 uptake rate (1)

Siumax molSi molC�1d�1 0 0 1 Max. SiO2 uptake rate (c)

kNOs mmolN m�3 0.5 0.7 1 half-sat. cst (2)

kNHs mmolN m�3 0.3 0.5 0.7 half-sat. cst (2)

kin mmolN m�3 0.5 0.5 0.5 inhibition coefficient (1)

kSiOs mmolSi m�3 – – 1 half-sat. cst (4)

c1 – 0.05 0.05 0.05 leakage fraction (3)c2 – 0.65 0.65 0.65 extra excretion fraction (c)mortphy d

�1 0.12 0.1 0.07 mortality rate (6)

e – 0.34 0.34 0.34 mort. fraction to DOM (3)vPHY m d

�1 0 0 0.865 sinking rate (c,2)

Bacteria

(N:C)B molN molC�1 9:50 bacteria internal ratio (7)

lB d�1 13.3 Max. uptake rate (3)

kDOC mmolC m�3 25 half-sat. for DOC uptake (3)

kA mmolN m�3 0.5 half-sat. for NH4 uptake (3)

xB – 0.14 gross growth efficiency (3)mortB d

�1 0.06 mortality rate (2)

Zooplankton ZOO1 ZOO2 ZOO3(C:N)Z molC molN

�1 5.5 5.5 5.5 internal ratio (3)

MaxGraz d�1 4.5 2.7 1.2 max. grazing rate (c)

ksat mmolC m�3 2.75 4.125 5.5 half-sat cst (2)

bN – 0.77 0.77 0.77 Assimilation N effic. (3)bC – 0.64 0.64 0.64 Assimilation C effic. (3)kc – 0.8 0.8 0.8 net growth effic. (3)

/ – 0.23 0.23 0.23 messy feeding frac. (3)mZ (mmolC m

�3d)�1 1.2 0.5 – max zoo mort (c)

mZ3 d�1 – – 0.3 max zoo3 loss (3)

kClos mmolC m�3 – – 1.1 half-sat for closure (3)

XDOM – – – 0.38 frac of loss. to DOM (3)XNH4 – – – 0.33 frac of loss. to NH4 (3)XPON – – – 0.29 frac of loss. to PON (3)XDIC – – – 0.16 frac of loss. to DIC (3)XPOC – – – 0.46 frac of loss. to POC (3)

Table A.5

Parameter values for biological processes




Par. Units Value Description Ref.

X: Phy1 Phy2 Phy3 Zoo1 Zoo2 Bac POM

eX ,Zoo1 1 0.25 0 0.5 0 1 0 Capture eff. (c,9)

eX ,Zoo2 0.25 1 0.8 1 0.5 0.3 0.2

eX ,Zoo3 0 0.15 1 0 1 0 0.2

Non-living matter

nitrif d�1 0.03 nitrification rate (2)

degradPOC d�1 0.045 degrad. rate of POC (3)

degradPON d�1 0.055 degrad. rate of PON (3)

dissSiDet d�1 0.01 diss. rate of SiDet (c)

vSiDet m d�1 1 sinking rate of SiDet (c)

Aggregation

Shear d�1 75168 shear rate (8)

g – 0.62 sinking exponent (8)B m�g d�1 1700 sinking factor (c,8)

Stick – 0.08 stickiness (c,8)

S m 2.d�5 minimal cell size (8)L m 0. 01 maximal cell size

f – 1.62 N content exponent (8)C mmolN m�f 0.4744 N content coefficient (8)

(c) after calibration. References: (1) Soetaert et al., 2001. (2) Lacroix and Grégoire, 2002.; (3) Anderson and Pondaven, 2003. (4) Tusseau, 1996.

(5) Parsons et al., 1984. (6) Jorgensen et al., 1991. (7) Goldman et al., 1987. (8) Kriest, 2002. (9) Vichi et al. (2003a).


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