Journal of Marine Systems 55 (2005) 177 – 203
www.elsevier.com/locate/jmarsys
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
a
University of Liège, Dep. Oceanology, Sart-Tilman B6c, B- 4000 Liège, Belgium
Modélisation et Methodes Mathématiques, Sart-Tilman B37, B- 4000 Liège, Belgium
c
Netherlands Institute of Ecology, Centre for Estuarine and Coastal Ecology, P.O. Box 140,4400 AC-Yerseke, The Netherlands
b
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 the University of Liège. The ecosystem model 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 by Kriest 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’AzurQ
Meteorological 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 agreement with observations and differences observed can be explained with 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 ecosystem has experienced changes in biodiversity due to the
* Corresponding author.
E-mail address: C.Raick@ulg.ac.be (C. Raick).
0924-7963/$ - see front matter D 2004 Elsevier B.V. All rights reserved.
doi:10.1016/j.jmarsys.2004.09.005
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 phytoplanktonic community. According to Bethoux et al.
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C. Raick et al. / Journal of Marine Systems 55 (2005) 177–203
(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 determination 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 bbiological
pumpQ (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 largescale 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 AQUAPHY (Lancelot et al., 1991a) describes phytoplankton
C. Raick et al. / Journal of Marine Systems 55 (2005) 177–203
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 initialization, calibration, and validation were performed with
the FRONTAL campaign (1984–1988). Mémery et al.
(2002) proposed a NPZD-DOM biogeochemical
model [including Nitrate, Ammonium, Phytoplankton, 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 representation 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 ecosystem. It is a size-based ecosystem model describing the
nitrogen and carbon cycles and considering silicate as
179
a potential limiting nutrient of diatoms growth.
Nineteen state variables are considered: three sizedgroups 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 Plimitation 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 phosphorus 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 hydrodynamic and biogeochemical models. The hydrodynamic and ecosystem models are described in Section 3
as well as the numerical methods and boundary conditions used to force the model. Section 4 presents and
analyzes hydrodynamic and biogeochemical model
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C. Raick et al. / Journal of Marine Systems 55 (2005) 177–203
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) in
the 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
Marty et al. (2002). Abundance and biomass of freeliving bacteria, heterotrophic nanoflagellates, and ciliates are described in Tanaka and Rassoulzadegan
(2002) and Tamburini et al. (2002). Particulate organic
matter in carbon and nitrogen has also been measured at
the DYFAMED station from May 1997. A range of
plankton pigments has been detected, in order to
characterize different phytoplankton groups (e.g., Vidussi et al., 2000, 2001, Marty et al., 2002; Marty and
Chiaverini, 2002). Fucoxanthin is the marker of diatoms and corresponds to the microphytoplankton
group. Nano- and pico-flagellates containing chlorophyll c are characterized by 19V-hexanoyloxyfucoxanthin (19V-HF) and by 19V-butanoyloxyfucoxanthin (19VBF). 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 phytoplankton community composition. The biomass proportion
Fig. 2. Meteorological conditions for year 2000: (a) Insolation (Wm2): the mean of 5 years FRONTAL data measurements (1984–1988) and
the sinusoid reconstructed from the punctual data. (b) Air temperature (8C). (c) Wind speed at the surface water (ms1) from the bCôte d’AzurQ
Meteorological Buoy (DYFAMED site).
C. Raick et al. / Journal of Marine Systems 55 (2005) 177–203
(BP) associated with each size class is further defined
as:
BPpico=(Zea+Tchlb)/DP
BPnano=(Allo+19VHF+19VBF)/DP
BPmicro=Fuco/DP
w i t h D P= Z e a + Tc h l b + A l l o + 1 9VH F + 1 9 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’AzurQ
Meteorological 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 measurements 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
181
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 GeoHydrodynamics 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-, microphytoplankton) 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 composition 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 environmental conditions prevailing (e.g., Soetaert et al., 2001;
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C. Raick et al. / Journal of Marine Systems 55 (2005) 177–203
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 represents 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-
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 Q 10 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 assimilations 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 contents are considered as independent state variables for
each phytoplankton group. Phytoplankton N:C ratios
Fig. 3. Representation of the ecosystem model. Each style of lines represent different flux of matter: plain arrows for organic matter flows,
dashed arrows for inorganic matter flows, and dotted arrows for gas flows. Double arrows represent sinking. Dissolved Inorganic Carbon (DIC)
is considered as a pool.
C. Raick et al. / Journal of Marine Systems 55 (2005) 177–203
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 minimum (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)PHY
ratios (Eq. (A.19)) as in Soetaert et al., (2001).
Light availability for the photosynthesis of phytoplanktonic 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 k water(z) (in m1) 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 (k Chl) 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 respiration 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)PHY
ratios, nitrate is not assimilated and ammonium is
183
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
c 1 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 and Williams
(1998), and Anderson and Pondaven (2003). Moreover, 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 c 2 of growth
flux, that is the first formulation described in Anderson
and Williams (1998).
Mortality of phytoplanktonic groups is represented 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 stoichiometry (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 consumers 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
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C. Raick et al. / Journal of Marine Systems 55 (2005) 177–203
requirements, bacteria consumes ammonium to completely 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 Q 10 law (Eq. (A.45)). Bacteria mortality flux
supplies the DOM box.
3.2.3. Zooplankton modelling
Zooplankton ingests phytoplankton, bacteria, detritus, 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 (Ba c and Ba n , in mmolC m3 and
mmolN m3, 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 is
the zooplankton intake of carbon and nitrogen
(respectively, I C and I N) given in Eq. (A.28). A
constant fraction b of these intakes (b C and b N) is
assimilated by zooplankton. The fraction left, (1b c )
and (1b n ) is released by egestion, that supplies the
particulate 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 k c 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 temperature (Eq. (A.33)) is used for nano- and microzooplankton 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 process of detrital silicate dissolution into mineral silicate
is also formulated by a constant dissolution rate. The
nitrification process is represented as a direct oxydation 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
C. Raick et al. / Journal of Marine Systems 55 (2005) 177–203
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(d i ) of size d i follows a power
law: n(d i )=Ade
where A and e are variable in time.
i
The mass m(d i ) of a particle of size d i is also assumed
to be described by a two-parameter function:
m(d i )=Cdfi , the distribution of mass is then represented by m(d i )=ACdfe
. This size distribution is
i
modified by two processes: aggregation and sedimentation. 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(d i ) is also assumed
to be represented by a power law: w(d i )=Bdgi . 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 in
Eqs. (A.10) and (A.11)), calculated by an integral over
the size range of particles. The aggregation rate n is a
function 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 can
be 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 oligotrophy 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.
185
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 implemented 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 system, we use the subroutines library Flexible Environment 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 FORTRAN 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.
186
C. Raick et al. / Journal of Marine Systems 55 (2005) 177–203
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 of
individual 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.
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 dextraexcretionT of carbon (parameter c 2 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, respectively. 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
Fig. 4. Contours of hydrodynamic results: (a) temperature; (b) the mixing layer depth computed by the hydrodynamic model for the year 2000.
C. Raick et al. / Journal of Marine Systems 55 (2005) 177–203
low in March, but the thermocline only appears in midApril 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 and
insolation 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.
187
4.2.1. Seasonal plankton dynamics
Fig. 5 shows the seasonal evolution of the autotrophs 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 phytoplankton 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
Fig. 5. Integration of phytoplankton (mgChl m2) and zooplankton (mmolC m2) biomass over 200 m depth. Phy1: picophytoplankton [0.2, 2]
Am; Phy2: nanophytoplankton [2, 20] Am; Phy3: microphytoplankton [20, 200] Am; Zoo1: nanozooplankton [2, 20] Am; Zoo2:
microzooplankton [20, 200] Am; Zoo3: mesozooplankton [0.2, 2] mm.
188
C. Raick et al. / Journal of Marine Systems 55 (2005) 177–203
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
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 microphytoplankton 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 m3, 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 m3 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
Fig. 6. Evolution in time and in the 100 upper meters of the six plankton groups. (a,b,c) Phytoplankton in mgChl m3; (d,e,f) zooplankton in
mmolC m3. (a) Phy1: picophytoplankton; (b) Phy2: nanophytoplankton; (c) Phy3: microphytoplankton; (d) Zoo1: nanozooplankton; (e) Zoo2:
microzooplankton; (f ) Zoo3: mesozooplankton.
C. Raick et al. / Journal of Marine Systems 55 (2005) 177–203
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 ammonium 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 m3 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 m3, respectively, for pico- and
nanophytoplankton.
The model simulates a variation of the phytoplankton N:C ratios by a factor 4 around the Redfield ratio ((N:C)PHY varies between (N:C)PHY,min
and (N:C)PHY,max), which emphasizes the importance of the variability of this ratio. Because all
phytoplankton N:C ratios follow the same trend, Fig.
7 shows the seasonal variability of the nanophytoplankton 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
189
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 microphytoplankton, which highlights the nanophytoplankton 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 zooplankton 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 ammonium concentration, the DOC concentration, and the
(N:C)DOM. The development of bacteria is conditioned 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
Fig. 7. Evolution in time and space (over the 100 upper meters) of the nanophytoplankton N:C ratio.
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C. Raick et al. / Journal of Marine Systems 55 (2005) 177–203
Fig. 8. Seasonal evolution of the microbial loop over the 200 upper meters. (a) Bacteria biomass in mmolC m3, (b) excretion of ammonium in
mmolN m3 d1, (c) ammonium concentration in mmolN m3, (d) dissolved organic matter in mmolC m3, (e) (N:C)DOM in molN molC1.
(N:C)DOM ratio varies between 0.02 and 0.14 molN
molC1. 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.
C. Raick et al. / Journal of Marine Systems 55 (2005) 177–203
191
Fig. 9. Temperature (in 8C) and salinity profiles at different periods of the year. In continuous line: model results, dotted line: data measurement
obtained 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 midMay 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 nitracline. The depth of the maximum of phytoplankton
biomasses and their intensities are correctly reproduced. 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
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C. Raick et al. / Journal of Marine Systems 55 (2005) 177–203
Fig. 10. Living organisms vertical profiles. Chl: Chlorophyll a; Phy1: picophytoplankton; Phy2: nanophytoplankton; Phy3: microphytoplankton; 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 attributed 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 diatomdominated 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 overestimated 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-
C. Raick et al. / Journal of Marine Systems 55 (2005) 177–203
193
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 limitation 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 nitrogen 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, silicate never limits diatoms growth in our simulations.
Fig. 12 presents the particulate organic matter computed 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–hydrodynamical 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, temperature, 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 conceptualization 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
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C. Raick et al. / Journal of Marine Systems 55 (2005) 177–203
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 variables with monthly measurement data coming from the
DYFAMED station in the central zone of the Ligurian
Sea have shown a rather good qualitative and quantitative agreement (Section 5.2). The vertical distribution, 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
C. Raick et al. / Journal of Marine Systems 55 (2005) 177–203
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.
Table A.2
List of variables used in Tables A.3 and A.4
Variables
Description
Units
k̃
Turbulent diffusion
coefficient
Temperature factor
Light intensity
Light extinction coefficient
Chlorophyll at depth z time t
Phytoplankton i growth flux
Phytoplankton i chlorophyll:
carbon ratio
Phytoplankton i nitrogen:
carbon ratio
Phytoplankton i nitrate
uptake
Phytoplankton i ammonium
uptake
Phytoplankton i
ammonium excretion
Phytoplankton 3 silicate
uptake
Phytoplankton i mortality
flux in carbon
Phytoplankton i mortality
flux in nitrogen
Grazing flux of zooplankton
i in carbon
Grazing flux of zooplankton
i in nitrogen
Grazing flux of prey i by
all its predators
Zooplankton i intake
of carbon
Zooplankton i intake
of nitrogen
Zooplankton i growth flux
in carbon
Zooplankton i growth flux
in nitrogen
Zooplankton i excretion flux
of ammonium
Zooplankton i respiration flux
Zooplankton j mortality flux,
j=1, 2
Closure term applied to
zooplankton 3
Bacteria uptake of DOC
Bacteria uptake of DON
Bacteria potential uptake
of ammonium
Bacteria uptake
of ammonium
Bacteria growth flux
m2s1
f(T)
I(z)
k ext
Chl(z,t)
GrowthPHYi
(Chl:C)PHYi
(N:C)PHYi
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 NICOKNAW Netherlands Institute of Ecology contribution
no. 3439.
uptake
NO3,i
uptake
NH4,i
excr
NH4,i
uptake
SiOsPhy3
MortPHYC,i
MortPHYN,i
GrazCI
GrazNI
Appendix A. Mathematical formulation of the
model
GrazPreyi
I C,I
Table A.1
List of biogeochemical state variables, description, and units
I N,I
State variables
Description
Units
GrowthZOOC,i
NOs, NHs
SiOs
NPhy1, NPhy2,
NPhy3
Nitrate NO3, Ammonium NH4
Silicate SiO2
Pico-, nano-,
microphytoplankton in
nitrogen
Pico-, nano-,
microphytoplankton
in carbon
Nano-, micro-,
mesozooplankton
Bacteria
Dissolved organic carbon
and nitrogen
Particulate organic carbon
and nitrogen
Detrital particulate silicate
Aggregates number
mmolN m3
mmolSi m3
mmolN m3
GrowthZOON,i
mmolC m3
RespZOOi
MortZOOj
mmolC m3
ClosureZOO3
mmolC m3
mmol m3
Uc
Un
U*A
CPhy1, CPhy2,
CPhy3
CZoo1, CZoo2,
CZoo3
CBac
DOC, DON
POC, PON
SiDet
AggNum
mmol m3
ExcrZOOi
UA
3
mmolSi m
m3
195
GrowthBAC
–
Wm2
m1
mgChl m3
mmolC m3 d1
gChl molC1
molN molC1
mmolN m3 d1
mmolN m3 d1
mmolN m3 d1
mmolSi m3 d1
mmolC m3 d1
mmolN m3 d1
mmolC m3 d1
mmolN m3 d1
mmol m3 d1
mmolC m3 d1
mmolN m3 d1
mmolC m3 d1
mmolN m3 d1
mmolN m3 d1
mmolC m3 d1
mmolC m3 d1
mmolC m3 d1
mmolC m3 d1
mmolN m3 d1
mmolN m3 d1
mmolN m3 d1
mmolC m3 d1
(continued on next page)
196
C. Raick et al. / Journal of Marine Systems 55 (2005) 177–203
Table A.2 (continued)
Variables
Description
Units
RespBAC
ExcrBAC
Bacteria respiration flux
Bacteria excretion flux
of ammonium
intermediary variable
Bacteria mortality flux
mmolC m3 d1
mmolN m3 d1
TestBAC
MortBAC
mmolN m3 d1
mmolC m3 d1
Table A.3
The biogeochemical model state equations
B vPhy CPHY3
dCPHYi B
BCPHYi
k̃
k
þ ð1 c1 c2 ÞGrowthPHYi MortPHYC;i GrazCPHYi
¼
di;3
Bz
Bz
dt
Bz
i ¼ 1; 2; 3
dNPHYi
B
BNPHYi
BðvPHY NPHY3 Þ
excr
k̃
k
Mort PHYN;i GrazNPHYi þ ð1 ci Þ NOuptake
¼
di;3
þ NHexcr
4;i NH4;i
3;i
Bz
Bz
dt
Bz
ðA:1Þ
i ¼ 1; 2; 3
ðA:2Þ
dCZOOi
B
BCZOOi
k̃
k
¼
þ GrowthZOOC;i di;1 þ di;2 MortZOOi di;3 ClosureZOO3 GrazCZOOi
Bz
dt
Bz
i ¼ 1; 2; 3
ðA:3Þ
dCBAC
B
BCBAC
¼
k̃
k
þ GrowthBAC MortBAC GrazCBAC
dt
Bz
Bz
ðA:4Þ
X
3
dNOs
B
BNOs
k̃
k
¼
NOuptake
þ nitrif NHs
3;j
Bz
dt
Bz
j¼1
ðA:5Þ
X
3 dNHs
B
BNHs
k̃
k
¼
þ
þ NHexcr
ExcrZOOj NHuptake
4;j Þ nitrif NHs þ XNH4 ClosureZOO3 UA þ ExcrBAC
4;j
Bz
dt
Bz
j¼1
ðA:6Þ
dSiOs
B
¼
¼
Bz
dt
BSiOs
k
k̃
SiOsuptake
Phy3 þ dissSiDet SiDet
Bz
ðA:7Þ
3 X
dDOC
B
BDOC
ðc1 þ c2 ÞGrowthPHYj þ MortPHYC;j þ /GrazCj þ MortBAC
¼
k̃
k
Uc þ degradPOC POC þ
dt
Bz
Bz
j¼1
þ XDOM ClosureZOO3
ðA:8Þ
3 h i
X
dDON
B
BDON
¼
k̃
k
Un þ degradPON PON þ
þ MortPHYN;j þ /GrazNj þ XDOM ClosureZOO3
c1 NOuptake
þ NHuptake
3;j
4;j
dt
Bz
Bz
j¼1
ðN : CÞz þ MortBACðN : CÞB
ðA:9Þ
3 X
dPOC
B
BPOC
BðWPOCÞ
¼
k̃
k
þ ð1 bC ÞIC degradPOC POC GrazPOC þ
ð1 ÞMortPHYC;j þ dj;1 þ dj;2 ÞMortZOOj dt
Bz
Bz
Bz
j¼1
þ XPOC ClosureZOO3
ðA:10Þ
C. Raick et al. / Journal of Marine Systems 55 (2005) 177–203
197
Table A.3 (continued)
3 X
dPON
B
BPON
BðWPONÞ
ðN : CÞz dj;1 þ dj;2 MortZOOj þ dj;3 XPON ClosureZOO3 ¼
k
k̃
þ ð1 bN ÞIN GrazPON þ
dt
Bz
Bz
Bz
j¼1
þ ð1 ÞMortPHYN;j g degradPON PON
ðA:11Þ
dSiDet
B
BSiDet
BðvSiDet SiDetÞ
¼
k̃
k
dissDetSi DetSi þ MortPHYN;3 þ GrazNHPY3 ðSi : NÞPHY3
dt
Bz
Bz
Bz
ðA:12Þ
dAggNum
B
BAggNum
BðUAggNumÞ BPON bio AggNum
¼
k̃
k
þ
n
dt
Bz
Bz
Bz
Bt PON
ðA:13Þ
Note:
–
–
d i,j is the Knonecker symbol, equals to 1 if i=j, 0 else.
BPON bio
Bt j is
calculated by Eq. (A.11) except the transport and the sedimentation terms.
Table A.4
Mathematical formulation of biogeochemical fluxes
T 20
f T ¼ Q1010
ðA:14Þ
"
I ð zÞ ¼ I ð z ¼ 0Þð1 albedoÞexp Z
#
z
kext ðzÞdz
ðA:15Þ
0
kext ðzÞ ¼ kwater ð zÞ þ kChl Chlðz; tÞ
ðA:16Þ
Phytoplankton, (i=1, 2, 3)
GrowthPHYi ¼ CPHYi f T min limnut;i ; limlight;i
h
i
limlight;i ¼ Quanti LightðChl : CÞPHYi Respi ð1ProdRespi Þ
with
ðN : CÞPHYi ;min
limnut;i ¼ lmax;i 1 ðN : CÞPHi
(
ðA:17Þ
f
ðA:18Þ
ðChl : CÞPHYi ¼ ðN : CÞPHYi ðChl : NÞPHYi ;min þ ½ðChl : NÞPHYi ; max . . .
. . . ðChl : NÞPHYi ;min for (N:C)PHYi V (N:C)PHYi,
max
ðN : CÞPHYi ðN : CÞPHYi ;min
ðN : CÞPHYi ;max ðN : CÞPHYi ;min
)
ðN : CÞPHYi
NOs
kin
CPHYi
ðN : CÞPHYi ;max NOs þ kNOsi kin þ NHs
ðN : CÞPHYi
NHs
NHuptake
¼NHumax i f T 1 CPHYi
4;i
ðN : CÞPHYi;max NHs þ kNHsi
excr
NH4;i ¼ 0
NOuptake
3;i
¼ NOumax i f
for (N:C)PHYi N (N:C)PHYi,
T
ðA:19Þ
1
ðA:20Þ
max
NOuptake
¼ NHuptake
¼0
3;i
4;i
ðN : CÞPHYi
excr
T
NH4;i ¼ NHumax i f 1 CPHYi
ðN : CÞPHYi ;max
MortPHYX ;i ¼ mortPHY i f T X PHYi ; X ¼ C; N
ðA:21Þ
ðA:22Þ
Zooplankton, (i=1, 2, 3)
Bac;i
CZOOi
Bac;i þ ksat;i
GrazNi ¼ GrazCi ðN : CÞfood;i
GrazCi ¼ f T maxGrazi
ðA:23Þ
ðA:24Þ
(continued on next page)
198
C. Raick et al. / Journal of Marine Systems 55 (2005) 177–203
Table A.4 (continued)
3
X
GrazX Preyi ¼
GrazXj eX Preyi ;Zooj X Preyi =Bax;j ;
X
Bax;i ¼
X ¼ C; N
ðA:25Þ
j¼1
eprey; Zooi X Prey;
X ¼ C; N
ðA:26Þ
preys
ðN : CÞfood;i ¼ Ban;i =Bac;i
ðA:27Þ
IX ;i ¼ ð1 /i ÞGrazXi ;
ðA:28Þ
X ¼ C; N
(
ðN : CÞfood;i b ðN : CÞ4i Z N limitation
kc;i bC;i
Y
ðN : CÞ4i ¼ ðN : CÞz
ðN : CÞfood;i NðN : CÞ4i Z C limitation
bN;i
ðA:29Þ
(
GrowthZOON;i ¼ bN;i IN;i
GrowthZOOC;i ¼GrowthZOON;i =ðN : CÞZ
Excr ZOOi ¼ 0
( GrowthZOO ¼ k b I
C;i
c;i C;i C;i
If C limits GrowthZOON;i ¼ GrowthZOOC;i ðN : CÞZ
Excr ZOOi ¼ bN;i IN;i GrowthZOON;i
If N limits :
ðA:30Þ
ðA:31Þ
RespZOOi ¼ bC;i IC;i GrowthZOOC;i
ðA:32Þ
M ortZOOj ¼ f T mZ;j CZOOj2 j ¼ 1; 2
ðA:33Þ
ClosureZOO3 ¼ f T
mZ;3 CZOO23
kClos þ CZOO3
ðA:34Þ
Bacteria
Uc ¼ lB CBAC
DOC
;
kDOM þ DOC
UA4 ¼ lB CBACðN : CÞB
Un ¼ Uc ðN : CÞDOM
NHs
kA þ NHs
ðA:35Þ
ðA:36Þ
GrowthBAC ¼ xB Uc
ðA:37Þ
RespBAC ¼ ð1 xB ÞUc
ðA:38Þ
TestBAC ¼ Un GrowthBACðN : CÞB
ðA:39Þ
if TestBAC N0 Y C limitation case:
ðA:40Þ
UA ¼ 0
ExcrBAC ¼ TestBAC
ðA:41Þ
if TestBACb0YN limitation case:
if jTestBACjV UA4 Z UA ¼ ½Un GrowthBACðN : CÞB ExcrBAC ¼ 0
ðA:42Þ
if j TestBACjNUA4 Z UA ¼ UA4
GrowthBAC ¼ ðUn þ UA Þ=ðN : CÞB
RespBAC ¼ GrowthBACð1=xB 1Þ
ExcrBAC ¼ 0
ðA:43Þ
MortBAC ¼ f T mortB CBAC
ðA:44Þ
C. Raick et al. / Journal of Marine Systems 55 (2005) 177–203
199
Table A.5
Parameter values for biological processes
Par.
Units
Value
Description
Ref.
Q 10
k Chl
Albedo
–
(mgChl m2)1
–
2
0.02
0.085
temperature coefficient
self-shading extinct. coeff.
surface albedo
(1)
(2)
(2)
Phytoplankton
(N:C)Red
(N:C)PHY,min
(N:C)PHY,max
(N:Si)
(Chl:C)min
(Chl:C)max
Quant
PHY1
0.15
0.05
0.2
–
1
2
0.4
PHY1
0.15
0.05
0.2
–
1
2
0.4
PHY1
0.15
0.05
0.2
1
1
2
0.55
Redfield ratio (16:106)
minimal N:C ratio
maximal N:C ratio
N:Si ratio
min. Chl:C ratio
max. Chl:C ratio
Max. Quantum yield
0.05
0.25
3
0.4
1
0
0.5
0.3
0.5
–
0.05
0.65
0.12
0.34
0
0.05
0.25
2.5
0.4
1
0
0.7
0.5
0.5
–
0.05
0.65
0.1
0.34
0
0.03
0.15
2
0.4
1
1
1
0.7
0.5
1
0.05
0.65
0.07
0.34
0.865
Respiration rate
frac. of pp used for resp.
Max. spec. growth rate
Max. NO3 uptake rate
Max. NH4 uptake rate
Max. SiO2 uptake rate
half-sat. cst
half-sat. cst
inhibition coefficient
half-sat. cst
leakage fraction
extra excretion fraction
mortality rate
mort. fraction to DOM
sinking rate
(c,1,5)
(c,1,5)
(2)
(1)
(1)
(c)
(2)
(2)
(1)
(4)
(3)
(c)
(6)
(3)
(c,2)
bacteria internal ratio
Max. uptake rate
half-sat. for DOC uptake
half-sat. for NH 4 uptake
gross growth efficiency
mortality rate
(7)
(3)
(3)
(3)
(3)
(2)
internal ratio
max. grazing rate
half-sat cst
Assimilation N effic.
Assimilation C effic.
net growth effic.
messy feeding frac.
max zoo mort
max zoo3 loss
half-sat for closure
frac of loss. to DOM
frac of loss. to NH 4
frac of loss. to PON
frac of loss. to DIC
frac of loss. to POC
(3)
(c)
(2)
(3)
(3)
(3)
(3)
(c)
(3)
(3)
(3)
(3)
(3)
(3)
(3)
Resp
ProdResp
Amax
NOumax
NHumax
Siumax
k NOs
k NHs
k in
k SiOs
c1
c2
mortphy
e
v PHY
molN molC1
molN molC1
molN molC1
molN molSi1
gChl molC1
gChl molC1
((molC m2)/
(gChldW))
d1
d1
molN molC1d1
molN molC1d1
molSi molC1d1
mmolN m3
mmolN m3
mmolN m3
mmolSi m3
–
–
d1
–
m d1
Bacteria
(N:C)B
lB
k DOC
kA
xB
mortB
molN molC1
d1
mmolC m3
mmolN m3
–
d1
9:50
13.3
25
0.5
0.14
0.06
Zooplankton
(C:N)Z
MaxGraz
k sat
bN
bC
kc
/
mZ
mZ3
k Clos
X DOM
X NH4
X PON
X DIC
X POC
molC molN1
d1
mmolC m3
–
–
–
–
(mmolC m3d)1
d1
mmolC m3
–
–
–
–
–
ZOO1
5.5
4.5
2.75
0.77
0.64
0.8
0.23
1.2
–
–
–
–
–
–
–
ZOO2
5.5
2.7
4.125
0.77
0.64
0.8
0.23
0.5
–
–
–
–
–
–
–
ZOO3
5.5
1.2
5.5
0.77
0.64
0.8
0.23
–
0.3
1.1
0.38
0.33
0.29
0.16
0.46
(1)
(1)
(1)
(1)
(c,1)
(continued on next page)
200
C. Raick et al. / Journal of Marine Systems 55 (2005) 177–203
Table A.5 (continued)
Par.
Units
X:
e X,Zoo1
e X,Zoo2
e X,Zoo3
Phy1
1
0.25
0
Value
Phy2
0.25
1
0.15
Phy3
0
0.8
1
Zoo1
0.5
1
0
Zoo2
0
0.5
1
Bac
1
0.3
0
POM
0
0.2
0.2
Description
Ref.
Capture eff.
(c,9)
Non-living matter
nitrif
d1
degradPOC
d1
degradPON
d1
dissSiDet
d1
m d1
v SiDet
0.03
0.045
0.055
0.01
1
nitrification rate
degrad. rate of POC
degrad. rate of PON
diss. rate of SiDet
sinking rate of SiDet
(2)
(3)
(3)
(c)
(c)
Aggregation
Shear
g
B
Stick
S
L
f
C
75168
0.62
1700
0.08
2.d5
0. 01
1.62
0.4744
shear rate
sinking exponent
sinking factor
stickiness
minimal cell size
maximal cell size
N content exponent
N content coefficient
(8)
(8)
(c,8)
(c,8)
(8)
d1
–
mg d1
–
m
m
–
mmolN mf
(8)
(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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