Journal of Marine Systems 94 (2012) S23–S33

Contents lists available at SciVerse ScienceDirect

Journal of Marine Systems

j ourna l homepage: www.e lsev ie r .com/ locate / jmarsys

Is it relevant to explicitly parameterize chlorophyll synthesis in marineecological models?

M. Mateus a,⁎, P.C. Leitão b, H. de Pablo a, R. Neves a

a MARETEC, Instituto Superior Técnico, Universidade Técnica de Lisboa, Av. Rovisco Pais, 1049-001, Lisboa, Portugalb Rua Rui Teles Palhinha, nº4 - 1º, Leião, 2740-278 Porto Salvo, Portugal

⁎ Corresponding author. Tel.: +351 21 8419436; fax:E-mail address: mmateus.maretec@ist.utl.pt (M. Ma

0924-7963/$ – see front matter © 2011 Elsevier B.V. Alldoi:10.1016/j.jmarsys.2011.11.007

a b s t r a c t

a r t i c l e i n f o

Available online 12 November 2011

Keywords:Chlorophyll aEcological modelingCarbon-to-chlorophyll ratioPrimary productionRemote sensingTagus estuary

Oceanographers and modelers often relate chlorophyll concentrations with phytoplankton carbon invoking asuitable C:Chla ratio. However C:Chl ratios are not constant in natural systems, thus making chlorophyll a de-ceptive measure of true biomass.In this paper we report on the adaptation of an algorithm for chlorophyll synthesis to a complex ecologicalmodel for the marine environment. Based on this model we have developed several simulation experimentsto assess the performance of the chlorophyll synthesis and the phytoplankton photoadaptation strategy. Themodel was applied to three distinct settings, comprising distinctive model geometries and ambient condi-tions: a schematic setting corresponding to a virtual mesocosmwithout any transport scheme (0D), a 1D ver-tical open-ocean application to a 150 m deep water-column, and an application to an estuary using a 2Dconfiguration. Conditions vary from spatially stable in the first case to a strong spatial and temporal hetero-geneity in the case of the estuary. Our results fall within the range and reproduce some of the trends found inpublished data, supporting the idea that when conditions have strong changes of nutrient availability andlight conditions, a photoacclimation mechanism becomes an essential requirement for reliable chlorophyllbiomass estimates. This is particularly relevant if model simulations are to be used to study natural systemscomplemented by data retrieved from direct measurements.

© 2011 Elsevier B.V. All rights reserved.

1. Introduction

Ecological models are expected to be as simple as possible and yetconvey the complexity of living systems. A challenge inmarine ecologicalmodeling has been to identify which processes must be included inmodel simulations to address this complexity in a realistic way. The ex-plicit inclusion of chlorophyll dynamics in models is a common exampleof this challenge. Chlorophyll a (named Chl, hereafter) has been used forlong time as a measure of algal biomass, especially for its measurementsimplicity and because it is a common pigment to all phytoplankton spe-cies. Oceanographers and modelers often relate Chl concentrations tophytoplankton biomass by means of empirical factors, using it as aproxy to carbon biomass. The canonical C:Chl of 60 is commonly usedin estimations of C biomass from Chl readings (Cloern et al., 1995).But because this ratio can change in time (see Domingues et al., 2008and references therein), chlorophyll is a deceptive measure of true bio-mass, and so this procedure has been recognized to be doubtful giventhe lack of precision of these empirical factors.

This limitation hinders the use of spatial chlorophyll mapsobtained by remote sensing techniques to estimate biomass. Similar

+351 21 8419423.teus).

rights reserved.

drawbacks are expected from ecological models that do not addresschlorophyll synthesis and calculate this index from fixed C:Chl ratios.In these cases, light is used to calculate a limitative factor to produc-tion and chlorophyll does not play any role in the model performance.This has been the paradigm of marine ecological models for long time(Fasham et al., 1990).

Photosynthesis is broadly described as the carbon fixation mediatedby Chl, a pigment that is common to all planktonic autotrophs. The fun-damental relationship governing the photosynthetic process is usuallyexpressed by the following equation:

nCO2 þ 2nH2O →light

n CH2Oð Þ þ nO2 þ nH2O

However, the whole photosynthetic process is not a single reac-tion, but rather the result of distinct steps. These can be broadly sum-marized as: (i) capturing and transferring light energy into chemicalforms, (ii) further changes in the chemical forms into a suitablechemical form for biochemical reactions, and (iii) fixing carbonusing the energy produced by the former steps (Parsons et al., 1984).

Mechanisticmodels account formuch of the details of the photosyn-thesis process, modeling the Photosynthetically Available Radiation(PAR), i.e., the wavelength spectra used by chlorophyll and pigmentsduring photosynthesis, and the different chemical compounds

S24 M. Mateus et al. / Journal of Marine Systems 94 (2012) S23–S33

produced in the process. Yet, this level of details is not suitable for eco-logical models because they add complexity in the parameterizationand require more computer power. Several approaches have beenused to simulate the role of photosynthesis and account for primaryproduction in phytoplankton (Behrenfeld and Falkowski, 1997). Inmost models, primary production is generally summarized as a relation-ship between carbon assimilation and incident light intensity by assum-ing that the rate of photosynthesis P(t) is directly proportional to theavailable light energy I(t). These relationships aremainly derived empir-ically, although some may have a physiological background (Eilers andPeeters, 1988; Megard et al., 1984). Basically this means that primaryproduction is modeled by converting the absorbed radiation into netphotosynthesis, either by using light as a forcing function that drivesthe C-fixation or in a stoichiometric conversion of the flux of light intochemical compounds (Kooijman, 2000).

The trend has been to increase the degree of sophistication inmodels, merging biological, physical and chemical processes, toopen their scope of simulation purposes. Chl has become a standardfeature in more recent marine ecological models incorporation. How-ever, degree of sophistication in models dealing with chlorophyll dy-namics vary significantly, frommore detailed mechanistic approaches(Baird and Emsley, 1999) to chlorophyll assessment using diagnosticmethods (Ebenhoh et al., 1997). With the increase complexity of eco-logical models during the last decades, much as a reflex of the naturalincrease in experimental knowledge, particular attention has beendevoted to the explicit parameterization of intracellular Chl produc-tion and variable Carbon to Chl quotas (expressed as C:Chl ratios, orsimply, C:Chl).

The knowledge that the C:Chl ratio is not constant but varies in re-sponse to light levels and cell physiological state, has paved the wayto the incorporation of acclimation mechanisms into the modeledprocesses of phytoplankton dynamics (Behrenfeld et al., 2005;Faugeras et al., 2004). This acclimation of the photosynthetic appa-ratus, expressed not only in the variability of C:Chl but also of Nitro-gen:Chl (N:Chl), is a physiological response to external conditions,namely the variations in irradiance and nutrient availability(Domingues et al., 2008). In addition, phytoplankton specific com-position is also a relevant driver of C:Chl ratios (Chan, 1980). In re-sponse to the growing awareness of photo adaptation importance,over the past decade a number of models have been developed toaccount for variable chlorophyll content in algae (Sathyendranathet al., 2009; Wang et al., 2009). Light history is reflected in C:Chlfluctuations in these models, which in turn affects the instanta-neous photosynthesis-light response (C-fixation).

In this paper we report on the adaptation of an algorithm for chloro-phyll synthesis to a complex ecological model for the marine environ-ment. Based on this model we have developed several simulationexperiments to assess the performance of the chlorophyll synthesis andthe phytoplankton photoadaptation strategy. This work was developedin the context of EU project Data Integration System for EutrophicationAssessment in CoastalWaters (INSEA), a collaborative project to developa coastalmanagement systembased on the efficient integration of obser-vations and biophysical models. Since many ecosystem models are notbased on Chl, but on carbon, a suitable C:Chl ratio has is usually invokedto estimate Chl for comparison with remote sensing data. In the contextof the project this work is a contribution to understand the factors thatinfluence C:Chl ratios, thus providing relevant insights on the choice ofadequate ratios.

2. Material and methods

2.1. Chlorophyll synthesis formulation

The chlorophyll synthesis algorithm (Geider et al., 1996, 1997,1998) was adapted to fit an ecological model made from scratch(Mateus, 2012-this issue) inside the MOHID modeling system

(Leitão et al., 2008), a community model shared by a large usergroup around the world. The ecological model reflect the currenttrends and paradigms of marine ecological models (Baretta-Bekkeret al., 1997), with explicit modeling of carbon and nutrient cycles,variable stoichiometry in organism and organic matter components,and different phytoplankton groups. With this formulation, chloro-phyll is explicitly modeled allowing the adaptation to different ambi-ent light, temperature and nutrient conditions. This adaptation isexpressed in variable C:Chl ratios. Unless stated otherwise, parametervalues have been taken from Mateus et al. (2012-this issue).

Phytoplankton growth rates (C-fixation) are determined by avail-able light and nutrients using a modified form of a growth modeltaken from the literature (Geider et al., 1996, 1997, 1998). Themodel parameterization includes the following regulatory features:(a) Chl synthesis requires N assimilation, (b) the carbon-specific,light-saturated photosynthetic rate depends on the internal nitrogenstatus of the cell, (c) the carbon-specific, light-limited photosyntheticrate depends on the C:Chl ratio, and (d) Chl synthesis is downregu-lated when the rate of light absorption exceeds the rate of utilizationof photons for carbon fixation, with the extent of downregulationbeing governed by the imbalance between rates of light absorptionand photosynthesis.

The actual specific assimilation/photosynthesis rate is describedby:

Pphotc ¼ Pmax

c 1− exp−αchl⋅X�

chl⋅I0Pmaxc

!" #ð1Þ

where αchl is the chlorophyll light absorption coefficient, Xchl* thechlorophyll cell quota or Chl:C, and I0 the available irradiance in thecell. Pcmax, the maximum rate of C-specific photosynthesis is a functionof temperature ΩT, a dimensionless function that can have differentforms (Arrhenius, Q10, optimal interval, etc.), ranging between0 (total limitation) and 1 (no limitation), and the maximum daily as-similation rate r at a reference temperature:

Pmaxc ¼ r⋅ΩT ð2Þ

Allowing for phytoplankton acclimation to light and nutrients, thelight history is reflected on growth by the variation of the Chl:C. Tokeep the nomenclature of the original model the Chl:C ratio (Xchl*)is used in the equations, but the inverse C:Chl ratio (Xchl) is used else-where since it is the most common ratio found in the literature(Domingues et al., 2008; Sathyendranath et al., 2009; Wang et al.,2009). A short description of all parameters and their units is provid-ed in Table 1.

Themodel of phytoplankton growth and physiological acclimationtreats nutrient uptake and photosynthesis rates as functions of bothenvironmental factors and cellular chemical compositions (Chl:Cand N:C). Chl synthesis, Pac, is regulated by the balance between pho-tosynthetic carbon fixation and light absorption (the ratio of energyassimilated to energy absorbed). This regulation term, ρchl, is formu-lated as:

ρchl ¼ Xmaxchl:n

Pphotc

αchl⋅X�chl⋅Io

ð3Þ

whereXchl:nmax is themaximumvalue of Chl:N ratio. The remaining variableshave already been defined for Eq. (1). The Chl synthesis parameterizationis then:

Pac ¼ρChl:νn

X�chl

−ϕchl ð4Þ

Chl synthesis is assumed to be proportional to nitrogen uptake,νn, reflecting the need for the synthesis of proteins used in light

Table 1Parameter list with respective description and units.

Parameter Meaning Units

I0 Available irradiance μmol photons m−2s−1

Xchl* Chlorophyll cell quota or Chl:C mgChl(mgC)−1

αchl Initial slope of the photosynthesis-lightcurve

mgCm2(mgChl μmol photons)−1

r Maximum daily assimilation rate d−1

Xchl:nmax maximum value of Chl:N ratio mgChl(mmolN)−1

ρchl Chl synthesis regulation term mgChl(mmolN)−1

Pcmax Maximum rate of C-specific

photosynthesisd−1

Pcphot Specific assimilation/photosynthesis

rated−1

νn Total Nitrogen uptake mmolN(mgC)−1d−1

ϕchl Chl degradation rate d−1

S25M. Mateus et al. / Journal of Marine Systems 94 (2012) S23–S33

harvesting complexes and elsewhere in the photosynthetic system.A Chl degradation rate is also considered in the formulation, ϕchl.Besides this potential loss term, Chl can also be lost by phytoplank-ton mortality and so this has to be considered in the mass balanceequation. According to this parameterization the instantaneousrates of light utilization, carbon assimilation, Chl synthesis, and nu-trient assimilation are determined by environmental variables. Thisway the instantaneous rates can change in time due to the effects ofpast environmental conditions by including intracellular variablesChl:C and N:C.

All processes and state variables of the model are calculated for acontrol-volume, regardless of any transport scheme. This makes themodel generic by enabling its application to different geometric set-tings and transportation schemes. The control-volume approach con-sists of dividing the water body into finite segments or “controlvolumes” (Chapra, 1997). For each control volume, a system of linearequations is solved resolving the interdependence of different prop-erties, calculating the mass balances taking into account the transportin the interfaces between volumes as well as sources and sinks withineach control volume.

2.2. Model simulations

The basic characteristics of light that have significant biologicalimportance are quantity and quality. Light intensity and spectralcomposition varies in marine environments, sometimes in great mag-nitude, depending on time (i.e. daily, seasonally, and annually), space(different location, depth), weather conditions, suspended particulatematter, colored dissolved organic matter, etc. In order to test the per-formance of the Chl synthesis algorithm in a complex ecologicalmodel under a wide range of conditions, we have applied the modelto three distinct scenarios comprising distinctive model geometriesand ambient settings: a schematic setting corresponding to a virtualmesocosmwithout any transport scheme (0D), an 1D open-ocean ap-plication to a 150 m deep water-column with vertical diffusion, andto an estuary using a 2D approach. Conditions vary from spatially sta-ble in the first case to a strong spatial and temporal heterogeneity inthe case of the estuary.

In this coupled biological–physical simulations, irradiance or lightavailability is determined by known laws of physics. The short-wavesurface irradiance flux used for atmospheric forcing is converted fromWm−2 to the units of μmol photons m−2 s−1 with the constant factor1/0.215 (Reinart et al., 1998).We assume that the Photosynthetic Avail-able Radiation is parameterized according to the Lambert–Beer formu-lation with depth-dependent extinction coefficients. Light propagationtakes into account the extinction due to suspended particles, concentra-tion of chlorophyll and the background extinction of water. Extinctiondue to dissolved substances is not considered.

In all applications the model runs with a time step of 60 s for thehydrodynamic and a time step of 3600 for the ecology. Simulations

running period were one and a half years in all cases, with a 6-month spin up period. Real data were used as environmental forcing(temperature and radiation). Solar radiation data has enough resolu-tion to reproduce both the diel cycle and the seasonal variation (in-tensity and light period). The model has several types ofphytoplankton groups and multiple limiting nutrients (N, P, Si).Here we focus on the Chl dynamics in each system for a period ofone year to account for seasonal fluctuations. Only relevant detailsare provided like the information on the model application and re-sults that may help to understand the performance of the Chldynamics.

2.3. Virtual mesocosm (0D)

In this simplified 0D scheme without any physical transport pro-cesses (simulating a tank with a simple square geometry and one ver-tical 5 m layer), the sources and sinks terms of each property are afunction of chemical and biological processes occurring inside theecological model alone. This approach enables a detailed study ofmodel performance independently from any transport scheme.Values for surface forcing of temperature and radiation were takenfrom field data time-series (measured at 38°49′N, 09°05′W), withranges and marked seasonal fluctuations typical for mid-latitudezones. Initial conditions for nutrient concentrations have been de-fined as 10 mmol N m−3 for nitrate, 1 mmol P m−3 for phosphateand 6 mmol Si m−3 for silicate, and a spin-up period of four yearwas used.

2.4. Water column (1D)

This model simulation consists of a 1D vertical geometry with 1 mlayers from the surface down to a depth of 150 m. Advection fluxesare not modeled (vertical transport) and vertical mixing is achievedby turbulent diffusion (sub-grid scale mixing processes). To repro-duce open-ocean conditions, data from Papa Station (Station P) inthe Gulf of Alaska (50°N, 145°W), was used as forcing conditions inthe simulation (temperature, radiation levels and wind) and for theinitial values for nutrients (profiles of nitrate, phosphate and silicateconcentrations).

2.5. Tagus estuary (2D)

The model was used to simulate the dynamics of the Tagus estuary,Portugal (located at 38°49′N, 09°05′W) for the year of 2004, followingthemethodology proposed byMateus et al. (2012-this issue). Themod-eled domain is characterized by a variable square grid with 73×94computation points, with higher resolution inside the estuary withcells covering ~3.72 km². Meteorological forcing, boundary conditions,and river discharges are explicitly imposed, all with temporal variabili-ty. The tide was imposed with tide-gauge elevations at the openboundary. Atmosphere–water interactions (e.g., heat fluxes, windstress, solar radiation) and the interaction between the bottomand water column (e.g., cohesive sediments resuspension and de-position) are handled by the model. Known values were used forthe forcing conditions such as surface radiation and temperature,river and Waste Water Treatment Plant flow and loads, and tidalconditions. All data sets correspond to the year of 2004.

3. Results

3.1. Analysis of model formulation

The influence of different parameter values on the photosynthesisrate (C-fixation) (Eq. (1)) is presented in Fig. 1. Assuming all other ki-netic parameters constant, photosynthesis rate Pc

phot increases linear-ly with the increase of temperature dependence ΩT, as shown in

Fig. 1. Plots of photosynthesis rate values as a function of different ranges of (A) temperaturedependence (B) irradiance, and (C) C:Chl. Values used: r=2.5 d−1, I0=200 W m−2,Xchl=100 and αchl=3.0025 mg C m2(mg Chl W d)−1.

Fig. 2. Variation of factors influencing Chl production dynamics: (A) Chl synthesisregulation as a function of light intensity; (B) Chl synthesis rate dependence ontotal nitrogen uptake; and (C) Chl synthesis regulation and synthesis rate for arange of C:Chl . Values used: Pc

phot=2.5 d− 1, Xchl : nmax =3 mg Chl(mmol N)− 1,

Xchl=50 and αchl=3.0025 mg C m2(mg Chl W d)− 1.

S26 M. Mateus et al. / Journal of Marine Systems 94 (2012) S23–S33

Fig. 1A. This reflects the influence of temperature in photosynthesismaximum rate calculation, Pcmax=r⋅ΩT. When there is no limitationfrom temperature, Pcphot is regulated by other processes and parame-ters like light I0, C:Chl Xchl and the Chl light absorption coefficient αchl.

The direct influence of Xchl and I0 on photosynthesis can be seen inFig. 1B and C, respectively. By assuming that photosynthesis rate isproportional to chlorophyll amount in the cell, expressed by Xchl,the model estimates a faster increase in photosynthesis rate as C:Chlbecomes lower (Fig. 1B). This simulates a simple functional responsedetermined by the higher amount of photosynthetically active pig-ments. When C:Chl is high, more radiation is necessary to achievethe maximum photosynthesis rate Pc

max. Conversely, this rate isachieved at lower radiation levels when C:Chl is low. Eventually, pho-tosynthesis rate will stabilize, constrained by its parameterization,

even if radiation continues to increase, leading to Pcphot=Pc

max. Thesame principle is illustrated in Fig. 1C, allowing to conclude thatwhen light radiation is sufficiently high, Pcphot tends to Pc

max, even athigh Xchl. Another relevant aspect is that the model is more sensitiveto Xchl at low radiation regimes.

The Chl molecule is responsible for the conversion of radiant energyinto chemical energy and so chlorophyll content per cell determinesphotosynthesis. For this reason photosynthesis is closely coupled to C:Chl and therefore dependent on Chl synthesis. Chl production Pac is me-diated by the regulation term ρChl which in turn is controlled by thelight intensity I0, the photosynthesis rate Pc

phot, and C:Chl Xchl. The Chlregulation dependency on irradiation is shown in Fig. 2A, where the

S27M. Mateus et al. / Journal of Marine Systems 94 (2012) S23–S33

sharp decrease with increasing light intensity is evident. The regulationis also influences by C:Chl but in a linear way (Fig. 2B). This adaptationmechanism of Chl synthesis regulation allows Chl production duringphotosynthesis while C-fixation occurs, but slows down Chl synthesisas Xchl increases, thus acting as a control on Xchl variation. Another rele-vant feature is the inverse response to light availability, leading tohigher Chl production (imposed by lower values of Xchl) to compensatefor lower light levels. At high light intensity levels, less Chl is needed toconvert the same amount of energy, and the regulation term becomeslow reducing Chl production.

Also controlling Chl synthesis is the nitrogen uptake (Fig. 2C). Asmentioned before, this simulates the need for this element in the pro-duction of proteins in the light harvesting complexes in the Chlmolecule.

3.2. Model simulations

3.2.1. Virtual mesocosm (0D)Phytoplankton dynamics is mostly shaped by temperature, exter-

nal nutrient concentrations (Fig. 3A and B) and available light. Part ofthis control is exerted through the influence on the chlorophyll syn-thesis and on the photosynthetic process. Model results (Fig. 3C)shows a seasonal cycle with higher autotrophic flagellates Chl valuesin spring–summer when light availability is higher. Diatoms appar-ently become limited by silica during this time of year. The model isable to simulate a physiological response by phytoplankton to sea-sonal changes, expressed in the C:Chl and consisting of lower valuesin autumn and winter and higher values during spring and summer(Fig. 3D).

Nitrate concentrations detected between May and July (around2 mmol N m−3, Fig. 3B) are very close to classic Ks values for DIN(see Dortch and Whitledge, 1992; Justic et al., 1995) and even lower

Fig. 3. Chl concentration and C:Chl variation for a one-year simulation in a virtual mesocosm.(black) and autotrophic flagellates (blue).

than some Ks values previously reported in the literature (Carpenterand Guillard, 1970; Sarthou et al., 2005). However, nitrogen is neverlimiting because during the entire simulation the intracellular C:Nratio is always equal or lower than the Redfield ratio (results notshown), defined in the model as the threshold above which limitationoccurs. As such, the seasonal fluctuation on the C:Chl can beexplained by the seasonal temperature signal and light availability.As light availability decreases, producers compensate by synthesizingmore Chl. Another relevant result is the fact that, while C:Chl tempo-ral pattern is similar among groups (Fig. 3D), it differs in values,denoting the capacity of the model to reproduce inter-specificvariations.

The simulation also reveals that along with the adaptation to envi-ronmental conditions on a seasonal scale, some adaptation also oc-curs on a diurnal scale. This daily variation is exemplified in Fig. 4for two phytoplankton groups and also illustrates different Chl behav-ior among groups. Lower values occur during night time and, conse-quently, higher values during day time, as a response to irradiationlevels. Diel oscillations are known for rates of photosynthesis andchlorophyll synthesis, leading inevitably to fluctuations of C:Chl ona daily basis. In addition, the balance between assimilation and respi-ration also contributes to this pattern. These results show that the ad-aptation mechanism can be sensitive enough to adapt to diel cycles.

3.2.2. Water column (1D)Simulated Chl concentrations reproduce a typical seasonal dissimi-

larity and vertical profile for this latitude and location (Fig. 5A). Highervalues are observed in the spring and near the surface where radiationis higher. In winter, with low radiation levels and strong vertical diffu-sion induced by thewind at the surface, Chl concentration is vertical ho-mogeneous and extremely low. For this reason, nitrogen availability israther uniform in depth and higher at the mixed layer (~30 m,

Lines with different colors denote results for different groups of phytoplankton: diatoms

Fig. 4. Dynamics of C:Chl over a two-day period in a virtual 5 m mesocosm. Resultsfor two groups of phytoplankton: diatoms (black) and autotrophic flagellates (blue).

S28 M. Mateus et al. / Journal of Marine Systems 94 (2012) S23–S33

Fig. 5B), when compared with the spring scenario when it drops as aconsequence of phytoplankton uptake. Higher values of total nitrogenin spring below 10 m (compared to winter) is a consequence of biologi-cal activity products that sink from the surface in the form of particulateorganic nitrogen and are mineralized to ammonium in the process.

The distinct seasonal and spatial conditions that shape the Chl dis-tribution also control the variation of the C:Chl, either by inducing thesynthesis of Chl to compensate for low exposure to light, by limitingthe synthesis lowering the C:N because of decreasing in N availability,or by promoting photosynthesis (C-fixation) when both light and nu-trients are adequate. The result of these interacting factors is seen inthe vertical profile of C:Chl portrayed in Fig. 5C. While the relativelysimilar vertical conditions in winter result in the same approximateC:Chl at all depths (~24), the increase in light availability in spring in-duces photosynthesis slightly rising the ratio to ~28.

C:Chl is always low throughout the simulated year (Fig. 6), usuallybellow 40, which can be explained by the phytoplankton adaptationto low light levels all year around typical from these latitude. Thesharp decrease in C:Chl noticed around Julian day 240 is associatedwith the thermocline erosion induced by the wind regime that in-creases during the summer–autumn transition. The mixing in theupper water column causes the producers to be exposed to lesslight. The functional response will be an increase in the respiration:production ratio and a compensation by synthesizing more Chl.Both will lower the C:Chl ratio. Also in Fig. 6 it is possible to noticethe differences in C:Chl among phytoplankton groups, with diatomshaving systematically higher values. The similar pattern between

Fig. 5. Depth profiles of Chl concentration (picophytoplankton), total nitrogen (ammoniu(1D vertical) model simulation.

the two groups show the same basic response to environmental fac-tors, with the difference in values explained by different parametervalues like the maximum daily assimilation rate r and distinct nutri-ent uptake dynamics.

3.2.3. Tagus estuary (2D)This is a dynamic simulation with a horizontal transport scheme to

account for the advection of properties. Being influence by rivers dis-charges, winds and tidal cycles, among other factors, environmentalconditions go through strong seasonal changes, especially for tempera-ture, nutrient availability and light conditions.

As a dynamic system, ambient factors in the estuary vary widelyspatially and over time. Radiation levels vary seasonally and also spa-tially in the water column as a result of light attenuation by sus-pended particulate matter and depth. Nutrient concentrations alsochange as a consequence of river discharges and biological activity.These changes are expected to exert some effect on the phytoplank-ton dynamics, noticed in C:Chl fluctuations. Phytoplankton Chl distri-bution in the estuary reveals a typical mid-latitude seasonal cycle,with higher values in spring–summer and lower concentrations inthe remaining of the year (Fig. 7). There is a clear seasonal fluctuationin C:Chl ratio consisting of lower values of C:Chl during autumn/wintermonths and higher values in Spring/Summer. The conspicuous 15-dayvariation noticed in Fig. 7 corresponds to the tidal regime shaped byfortnightly spring–neap tide cycles. These variations are related withthe control of light availability shaped by the dynamics of suspendedparticulate matter (Valente and da Silva, 2009; Vaz et al., 2011).Model results show that higher Chl concentrations and lower C:Chloccur during neap tides when suspended matter concentrations arelower.

The values for C:Chl vary around a minimum of ~46 and a maxi-mum of ~114. This seasonal tendency reflects seasonal changes ofthe system, expressed in the yearly cycle of radiation and nutrientavailability as a function of river discharges. The combination of lowradiation and high nitrogen availability in winter months increasesChl synthesis, thus lowering the C:Chl. In spring–summer months,the increase in temperature increases photosynthesis (C-fixation)raising the C:Chl. Also during this period the light ambient in thewater is most favorable because radiation reaching the surface ishigher and that daylight period longer. Another putative environ-mental driver for the increase in C:Chl during spring–summer is re-duced nutrient availability.

A spatial pattern in C:Chl is also observed with systematicallylower values in inner areas when compared with values at the rivermouth (Fig. 8) for summer conditions. Again, the spatial pattern is

m+nitrate) and C:Chl for spring and winter conditions. Results for the open-ocean

Fig. 6. Time series for C:Chl at the surface in two phytoplankton groups: diatoms and picophytoplankton. Results for the 1D vertical model over a simulated period of one year.

S29M. Mateus et al. / Journal of Marine Systems 94 (2012) S23–S33

the result of a combination of light and nitrate availability. The C:Chlspatial pattern reflects the simultaneous control on Chl synthesis ofthe light ambient in the water column and the uptake of nitrogen reg-ulated by its availability. Model results for these properties showhigher radiation values (Fig. 9A) and nitrogen concentration(Fig. 9B) in upper and shallower estuarine areas. Light is controlledto some extent by the shading effect of suspended particulate matter,a common feature in estuaries (Cloern, 2001). In some mixed transi-tional systems (e.g. Kocum et al., 2002), mean light intensity in themixed layer is higher in the more turbid, shallower inner locationsthan at the clearer, deeper outer locations. Also, in the case of shallowestuarine ecosystems, bottom topography is also a relevant driver oflight availability, as it can be noticed in Fig. 9A where lower level ofradiation occur in the deeper channels inside the estuary. As a conse-quence, higher chlorophyll synthesis production rates are expected tocompensate for the low levels of light. Together with the hydrody-namics and nutrient availability, these factors shape the chlorophylla distribution in the system (Fig. 9C) and exert a strong control onthe dynamics of chlorophyll synthesis.

4. Discussion

4.1. The Chl synthesis algorithm

Some of the model biases in chlorophyll distributions have beenattributed to inadequate parameterization of important physiologicalmechanisms such as light acclimation (Vichi et al., 2007b). This limi-tation emphasizes the need to choose robust algorithms to simulatethis process in marine ecological models. Smith and Yamanaka(2007) have recently compared two such algorithms, the Geider

Fig. 7. Chlorophyll a concentration and C:Chl for diatoms at two stations: inside the estuaryreference.

et al. (1998) dynamic regulatory model of acclimation to light, andPahlow's (2005) model of optimal phytoplankton growth. These au-thors show that both models were able to reproduce experimentaldata, thus simulating adequately functional response of phytoplank-ton to changing ambient conditions.

We have adopted Geider et al. (1998) model because it is formulatedin terms of instantaneous rates (which varywith light, temperature, etc.),and not in terms of daily mean net rates like Pahlow's model. The advan-tage of thismodel is that it resolves differences in the assimilation of nitro-gen and accounts for the effect of respiration rate in light versus darkness,unlike Pahlow's model that cannot resolve day–night differences. Thischaracteristicmay explain the interest inGeider et al.model and its recentinclusion in complex ecological models (Allen et al., 2007; Holt et al.,2005; Vichi et al., 2007a, 2007b).

4.2. Fluctuations in the C:Chl

In phytoplankton cultures C:Chl ratios varies from b10 to>100 mg C(mg Chl)−1 (Geider, 1987), a range that is also expectedto occur in natural systems. For this reason, chlorophyll is a poor mea-sure of phytoplankton biomass (Cullen, 1982; Mateus and Neves,2008). Consequently, addressing the factors and mechanisms thatshape C:Chl ratios in natural systems is essential in improvingmodel estimations and usefulness. Of great significance is the physio-logical response of phytoplankton to environmental conditions (suchas light regime and nutrient availability) expressed in the photoadap-tation or light adaptation mechanism, i.e., a physiological adjustmentto surrounding conditions which, among others, involve the followingmorphological or biochemical changes within the cell: (i) changes intotal photosynthetic pigment content (Geider et al., 1996; Geider

(black) and at the estuary mouth (blue). The canonical C:Chl=60 ratio is marked for

Fig. 8. C:Chl for diatoms in the Tagus estuary under two distinct environmental conditions: early spring (Julian day 90) and early summer (Julian day 180).

S30 M. Mateus et al. / Journal of Marine Systems 94 (2012) S23–S33

et al., 1997; Geider et al., 1998), (ii) change in the ratio of photosyn-thetic pigments (Ansotegui et al., 2003; Putland and Iverson, 2007;Sathyendranath et al., 2009). This process is expressed in the adjust-ment of pigment synthesis to irradiance levels, temperature and nu-trient availability (Figs. 1 and 2). This is a universal feature of algalphysiology, known to differ among phytoplankton groups (Geideret al., 1997). Our experiments show that this variation can be capturedin model simulations and partly explained. The results show a variation

Fig. 9. Mean light intensity (A), total nitrogen (ammonium+nitrate) (B) and diatoms'Chl concentration (C) in the Tagus estuary for Julian day 180 of simulation.

in the C:Chl in all modeled groups of producers ranging from ~20 to~120 (see Figs. 3–8). In addition, themodel is also able to reproduce dif-ferences in photoadaptation among the groups (see Figs. 3, 6, and 8).

Overall, the values of C:Chl obtained in this study fall within therange of values found in the literature and reported in other systems(Chan, 1980; Putland and Iverson, 2007 and references therein;Sathyendranath et al., 2009; Wang et al., 2009). Also, the model wasable to reproduce seasonal patterns such as lower C:Chl ratios in win-ter and higher in summer, as well as lower values associated withlower salinity (Fig. 8) in the estuary (see Putland and Iverson, 2007).

The results shed some light on the dynamics of phytoplankton innatural systems. The opposing effects of nutrients and light on photo-synthesis and Chl synthesis (expressed in C:Chl) seems to sharpen upgrowth events, allowing models to better simulate both temporal andspatial gradients of carbon and chlorophyll in natural systems(Chapra, 1997). This is particularly evident in the results for the estu-ary simulation (Fig. 7). Typically, it is assumed that acclimation servesto increase growth rates under suboptimal ambient conditions overthe value that would be achieved if cellular chemical compositionwere static (Behrenfeld et al., 2002; Geider et al., 1997, 1998;MacIntyre et al., 2002).

The down-regulation of pigment synthesis at high irradiance hasbeen well documented in both prokaryotic and eucaryotic phyto-plankton (Falkowski and Laroche, 1991; Falkowski and Owens,1980; Falkowski et al., 1985), along with its reflex on C:Chl ratios.Our model simulations show that there is a strong influence of exter-nal conditions on photosynthesis, expressed on marked fluctuationsin C:Chl. Even in the schematic simulation without any transportscheme and with homogenous underwater light environment, simpletemporal variations of nutrient abundance, temperature and irradia-tion affect the chlorophyll synthesis (see Fig. 3). This modeling ap-proach renders more realism to simulations of natural systems andconfirms the inadequacy of using fixed C:Chl ratios.

The variation of the C:Chl is also particularly relevant during thespring bloom because changes in the light and nutrient environmentcan be dramatic. In addition, an highly variable mixing depththroughout the diel cycle can occur (Barkmann and Woods, 1996),causing the intermittent exposure of phytoplankton to limiting andsaturating irradiances during the bloom event. Under such conditionsit is expected a physiological adjustment of C:Chl ratios, with conse-quent effects on phytoplankton growth. As seen in the results fromthe schematic case (Fig. 4), the algorithm is adequate to simulatethese scenarios given its sensitivity to fluctuations in conditions onthe scale of hours.

4.3. Initial conditions

The increase in the number of parameters in amodelmay hinder themodeling exercise by adding (sometimes unnecessary) complexity tosimulations. Of particular relevance is the need for initial conditionsthat are difficult, if not impossible, to retrieve from typical data sets

S31M. Mateus et al. / Journal of Marine Systems 94 (2012) S23–S33

and field observations. This is usually the case of data on C:Chl thatrequires both values of C-content and Chl for phytoplankton. Inthe absence of this information, one has to make an estimatedguess. A frequent alternative is to assume the canonical value of60 (Cloern et al., 1995).

To evaluate the effect of the initial condition of C:Cha we have per-formed a simple test in the Tagus estuary by repeating the same simu-lation under two distinct scenarios: one with initial C:Chl=60 andother with C:Chl=100. Despite some minor fluctuations in the C:Chlthroughout the simulated period, this variation does not produce anysignificant change in the overall trend of Chl concentrations(Fig. 10A). During summer, when chlorophyll values are higher, the re-sults converge to almost identical C:Chl ratios (Fig. 10B). Taking as anexample the diatoms chlorophyll concentration shown in Fig. 10, onecan assume that the model was not much sensitive to the initial C:Chlin this kind of scenarios.

4.4. Variable vs. static C:Chl ratios

Since Chl is the most widespread index of phytoplankton abun-dance in water (Cullen, 1982), its explicit inclusion in productionmodels has become an important aspect of model development. C:Chl ratios have clear implications on model estimates. As an example,in one study where different fixed ratios have been used to determinethe fluxes of produced material, a change from a C:Chl ratio of 50 to35 resulted in a decrease of 17 t/year and a net transport loss increaseof 2 t/year (Jassby et al., 2002).

Fixed C:Chl used in conversion to estimate Chl concentrations inmodels may produce good results when conditions are more stable,whether from nutrient availability or light climate, but will eventuallyfail to correctly depict the evolution of a system with a strong season-al and spatial heterogeneity, or when seasonal changes in phyto-plankton composition occur along with significant inter-specific C:Chl variability (Chan, 1980; Domingues et al., 2008; Putland and

Fig. 10.Model outcome for two initial and forcing C:Chl ratio conditions: (A) diatoms chlorothe estuary. The canonical C:Chl=60 ratio is marked with a dashed line for reference.

Iverson, 2007). Moreover, there is always the problem of which con-version ratio to choose in a simulation, considering the variation thatis known to occur (Chapra, 1997; Geider, 1987; Parsons et al., 1984).Also, while there is a similar photosynthetic behavior of organismswithin each taxonomic group, there is a rather striking difference be-tween those of different groups, because of different Pcmax and nutri-ent uptake dynamics, among other factors (Behrenfeld et al., 2002;Geider et al., 1996, 1998; Sathyendranath et al., 2009).

The results highlight the difference between groups (see Fig. 3Dand 6) with diatoms systematically having higher C:Chl ratios. Forthe mesocosm scenario the model shows diatoms C:Chl ranging be-tween 70 and 100, while for autotrophic flagellates it ranges between60 and 80. The same pattern is repeated in the 1D application withdiatoms having higher ratios, between 20 and 50, and autotrophicflagellates between 20 and 40. The laboratory measurements ofChan (1980) contradict these results by providing evidences thatdiatoms are characterized by lower C:Chl values (32.9 and 35.2 fortwo distinct species) when compared to dinoflagellates (92.6 and120.0 also for two distinct species). It must be stressed that thesemeasurements have been undertaken under the same light andtemperature conditions and without nutrient limitations, thus fail-ing to account for the effect of environmental variability and cellu-lar response. From a modeling perspective, this disparity points tothe need of assessing the adequacy of a more adequate parameter-ization for both primary producers' functional groups.

Using model results for the inner station in the Tagus case as a ref-erence, we have compared the difference in chlorophyll concentra-tions between model results (with variable C:Chl ratios) with Chlvalues derived from model results for diatom carbon biomass usingfixed ratios (Fig. 11). It is possible to notice that there is a striking dif-ference between winter and summer. While a C:Chl=100 is bettersuited to estimate chlorophyll content in summer conditions(expressed in a better adjustment with the variable C:Chl results),the lower ratio (C:Chl=60) is more adequate for winter conditions.

phyll concentration, and (B) C:Chl evolution in time. Model results for the station inside

Fig. 11. Chl concentrations obtained by the model (variable C:Chl) and calculated from diatoms carbon biomass using fixed C:Chl ratios. C:Chl ratios of 60 (top) and 100 (bottom)were used as reference values. Inset plot shows the actual C:Chl at each time instant calculated by the model based on diatoms C and Chl content.

S32 M. Mateus et al. / Journal of Marine Systems 94 (2012) S23–S33

Diatoms (especially Bacillariophyceae) dominate phytoplanktonin the estuary, but other groups such as Chlorophyceae and Dinophy-ceae are also part of the phytoplankton communities (Cabeçadaset al., 1999; Cabrita et al., 1999; Gameiro et al., 2004). The composi-tion of these communities changes seasonally and also spatially, asreported by Cabrita et al. (1999) that shows a growing contributionin the percentage of dinoflagellates in the total producers populationfrom mid estuary to lower estuary (between 5 and 16% of the totalphytoplankton populations at the estuary mouth). These spatial andtemporal variations in the composition of phytoplankton communi-ties are a common feature in estuaries and coastal areas. As such,based on the differences found in the C:Chl ratios of distinct phyto-plankton groups independently of environmental conditions (Chan,1980; Domingues et al., 2008), it is expected this ratio to vary as afunction of phytoplankton composition. Again, this emphasizes theadequateness of having dynamic C:Chl ratios in models.

Curiously, besides the seasonal difference, there are also spatialdifferences (Fig. 8), denoting the limitation of a fixed ratio. These ob-servations suggest that when conditions are stable, whether from nu-trient availability or light climate, a fixed rate might be a reasonablechoice. However, when conditions have strong changes of nutrientavailability and light conditions, and marked annual phytoplanktonsuccession is likely to occur or a spatial pattern in the compositionof phytoplankton communities, a photoacclimation mechanism is anessential choice for reliable chlorophyll biomass estimates.

In systems like estuaries or coastal zones, light is a key limitingfactor for pelagic primary production (Cloern, 1999). In turbid sys-tems or well mixed vertically, phytoplankton populations have toadapt to continuously changing irradiance conditions ranging fromcomplete darkness to saturating light. Under such conditions, aphoto-adaptation mechanism like the production of chlorophyll in re-sponse to environment optical conditions enables a better approxi-mation to the estimation of chlorophyll than the use of fixed C:Chlratios.

5. Conclusion

Photoacclimation is one of the physiological processes that regu-late phytoplankton by imposing a down regulation of pigment con-tent under high irradiance regimes, but also implicitly allowingphytoplankton to maximize growth under unfavorable conditionslike low irradiance. The fact that photosynthetic organisms have thisregulatory mechanism of adaptation to environmental conditions jus-tifies its inclusion in models.

From the simulations here presented it is apparent that adaptivechanges in photosynthesis expected to occur in natural system canbe reproduced by the model through diel fluctuations, seasonal

differences, spatial variations (vertically and horizontally) of C:Chl,and interspecific physiological responses to light and nutrientavailability.

Our results suggest that Chl synthesis must be a standard featureof marine ecological models considering the wide range of conditionsfound in this ecosystem, mostly involving light, nutrient availabilityand temperature. Unlike models that assume static C:Chl (usuallywith no parameterization for Chl), this approach to Chl cell variablecontent enables the model to respond to different conditions, render-ing the model more versatile and generic. Our results support the ideathat when ambient conditions (nutrients and light availability)change significantly, a photoacclimation mechanism becomes an es-sential requirement for reliable chlorophyll biomass estimates. Thisis particularly relevant if model simulations are to be used to studynatural systems complemented by data retrieved from direct mea-surements, using optical instruments like remote sensing of Chl con-centration from satellites and aircraft, or by continuous measurementsuch as in vivo fluorescence in ship-based or moored instruments.

To conclude, and to answer the question that drove this study, itcan be said that because of the intrinsic nature of most marine sys-tems, with high spatial–temporal variability in physical and chemicalconditions, marine ecological models must consider the explicit pa-rameterization of chlorophyll.

Acknowledgments

We are grateful to 2 anonymous reviewers for their useful sug-gestions and comments. The present study was partly supportedby the project INSEA (Contract SST4-CT-2005-012336). The first au-thor is supported by the Portuguese Science Foundation programCiência2008.

References

Allen, J.I., Holt, J.T., Blackford, J., Proctor, R., 2007. Error quantification of a high-resolution coupled hydrodynamic-ecosystem coastal-ocean model: Part 2.Chlorophyll-a, nutrients and SPM. Journal of Marine Systems 68 (3–4), 381–404.

Ansotegui, A., Sarobe, A., Trigueros, J.M., Urrutxurtu, I., Orive, E., 2003. Size distribution ofalgal pigments and phytoplankton assemblages in a coastal–estuarine environment:contribution of small eukaryotic algae. Journal of Plankton Research 25, 341–355.

Baird, M.E., Emsley, S.M., 1999. Towards a mechanistic model of plankton populationdynamics. Journal of Plankton Research 21 (1), 85–126.

Baretta-Bekker, J.G., Baretta, J.W., Ebenhoh, W., 1997. Microbial dynamics in the marineecosystem model ERSEM II with decoupled carbon assimilation and nutrient uptake.Journal of Sea Research 38 (3–4), 195–211.

Barkmann, W., Woods, J.D., 1996. On using a Lagrangian model to calibrate primaryproduction determined from in vitro incubation measurements. Journal of PlanktonResearch 18, 767–788.

Behrenfeld, M.J., Falkowski, P.G., 1997. A consumer's guide to phytoplankton primaryproductivity models. Limnology and Oceanography 42 (7), 1479–1491.

S33M. Mateus et al. / Journal of Marine Systems 94 (2012) S23–S33

Behrenfeld, M.J., Marañón, E., Siegel, D.A., Hooker, S.B., 2002. A photoacclimation andnutrient based model of light-saturated photo-synthesis for quantifying oceanicprimary production. Marine Ecology Progress Series 228, 103–117.

Behrenfeld, M.J., Boss, E., Siegel, D.A., Shea, D.M., 2005. Carbon-based ocean productivityand phytoplankton physiology from space. Global Biogeochemical Cycles 19 (1).

Cabeçadas, L., Brogueira, M.J., Cabeçadas, G., 1999. Phytoplankton spring bloom in theTagus coastal waters: hydrological and chemical conditions. Aquatic Ecology 33,243–250.

Cabrita,M.T., Catarino, F., Slawyk, G., 1999. Interactions of light, temperature and inorganicnitrogen in controlling planktonic nitrogen utilisation in the Tagus estuary. AquaticEcology 33, 251–261.

Carpenter, E., Guillard, R.R., 1970. Intraspecific differences in nitrate half-saturationconstants for 3 species of marine phytoplankton. Ecology 52 (1) (183–&).

Chan, A.T., 1980. Comparative physiological study of marine diatoms and dinoflagellatesin relation to irradiance and cell-size.2. Relationship betweenphotosynthesis, growth,and carbon-chlorophyll a-ratio. Journal of Phycology 16 (3), 428–432.

Chapra, S., 1997. Surface Water-Quality Modeling. Civil Engineering Series, McGraw-Hill,New York. (844 pp).

Cloern, J.E., 1999. The relative importance of light and nutrient. Aquatic Ecology 33, 3–15.Cloern, J.E., 2001. Our evolving conceptual model of the coastal eutrophication problem.

Marine Ecology Progress Series 210, 223–253.Cloern, J.E., Grenz, C., Vidergar-Lucas, L., 1995. An empirical model of the phytoplankton

chlorophyll : carbon ratio — the conversion factor between productivity and growthrate. Limnology and Oceanography 40 (7), 1313–1321.

Cullen, J.J., 1982. The deep chlorophyll maximum — comparing vertical profiles ofchlorophyll-a. Canadian Journal of Fisheries and Aquatic Sciences 39 (5), 791–803.

Domingues, R.B., Barbosa, A., Galvao, H., 2008. Constraints on the use of phytoplankton as abiological quality elementwithin theWater FrameworkDirective in Portuguesewaters.Marine Pollution Bulletin 56 (8), 1389–1395.

Dortch, Q., Whitledge, T.E., 1992. Does nitrogen or silicon limit phytoplankton productionin theMississippi River plume and nearby regions. Continental Shelf Research 12 (11),1293–1309.

Ebenhoh, W., Baretta-Bekker, J.G., Baretta, J.W., 1997. The primary production module inthe marine ecosystem model ERSEM II, with emphasis on the light forcing. Journalof Sea Research 38 (3–4), 173–193.

Eilers, P.H.C., Peeters, J.C.H., 1988. Amodel for the relationship between light-intensity andthe rate of photosynthesis in phytoplankton. Ecological Modelling 42 (3–4), 199–215.

Falkowski, P.G., Laroche, J., 1991. Acclimation to spectral irradiance in algae. Journal ofPhycology 27 (1), 8–14.

Falkowski, P.G., Owens, T.G., 1980. Light-shade adaptation — 2. Strategies in marine-phytoplankton. Plant Physiology 66 (4), 592–595.

Falkowski, P.G., Dubinsky, Z., Wyman, K., 1985. Growth–irradiance relationships inphytoplankton. Limnology and Oceanography 30 (2), 311–321.

Fasham, M.J.R., Ducklow, H.W., Mckelvie, S.M., 1990. A nitrogen-based model of planktondynamics in the oceanic mixed layer. Journal of Marine Research 48 (3), 591–639.

Faugeras, B., Bernard, O., Sciandra, A., Lévy,M., 2004. Amechanisticmodelling and data as-similation approach to estimate the carbon/chlorophyll and carbon/nitrogen ratiosin a coupled hydrodynamical–biological model. Nonlinear Processes in Geophysics11 (4), 515–533.

Gameiro, C., Cartaxana, P., Cabrita, M.T., Brotas, V., 2004. Variability in chlorophyll and phy-toplankton composition in an estuarine system. Hydrobiologia 525 (1–3), 113–124.

Geider, R.J., 1987. Light and temperature-dependence of the carbon to chlorophyll-aratio in microalgae and cyanobacteria — implications for physiology and growthof phytoplankton. New Phytologist 106 (1), 1–34.

Geider, R.J., MacIntyre, H.L., Kana, T.M., 1996. A dynamic model of photoadaptation inphytoplankton. Limnology and Oceanography 41 (1), 1–15.

Geider, R.J., MacIntyre, H.L., Kana, T.M., 1997. Dynamic model of phytoplankton growthand acclimation: responses of the balanced growth rate and the chlorophyll a:car-bon ratio to light, nutrient-limitation and temperature. Marine Ecology ProgressSeries 148 (1–3), 187–200.

Geider, R.J.,MacIntyre, H.L., Kana, T.M., 1998. A dynamic regulatorymodel of phytoplanktonicacclimation to light, nutrients, and temperature. Limnology and Oceanography 43 (4),679–694.

Holt, J.T., Allen, J.I., Proctor, R., Gilbert, F., 2005. Error quantification of a high-resolutioncoupled hydrodynamic-ecosystem coastal–ocean model: Part 1. Model overviewand assessment of the hydrodynamics. Journal of Marine Systems 57 (1–2),167–188.

Jassby, A.D., Cloern, J.E., Cole, B.E., 2002. Annual primary production: patterns andmecha-nisms of change in a nutrient-rich tidal ecosystem. Limnology and Oceanography47 (3), 698–712.

Justic, D., Rabalais, N.N., Turner, R.E., Dortch, Q., 1995. Changes in nutrient structure ofriver-dominated coastal waters — stoichiometric nutrient balance and its conse-quences. Estuarine, Coastal and Shelf Science 40 (3), 339–356.

Kocum, E., Nedwell, D.B., Underwood, G.J.C., 2002. Regulation of phytoplankton primaryproduction along a hypernutrified estuary. Marine Ecology Progress Series 231,13–22.

Kooijman, S.A.L.M., 2000. Dynamic Energy and Mass Budgets in Biological Systems.Cambridge University Press, Cambridge. (424 pp.).

Leitão, P.C., Mateus, M., Braunschweig, F., Fenandes, L., Neves, R., 2008. Modellingcoastal systems: the MOHID Water numerical lab. In: Neves, R., Baretta, J., Mateus,M. (Eds.), Perspectives on Integrated Coastal Zone Management in South America.IST Press, Lisboa, pp. 77–88.

MacIntyre, H.L., Kana, T.M., Anning, T., Geider, R.J., 2002. Photoacclimation of photosyn-thesis irradiance response curves and photosynthetic pigments in microalgae andcyanobacteria. Journal of Phycology 38, 17–38.

Mateus, M., 2012. A process-oriented model of pelagic biogeochemistry for marine sys-tems. Part I: Model description. Journal of Marine Systems 94, S78–S89 (this issue).

Mateus, M., Neves, R., 2008. Using a process-oriented ecological model to evaluate lightlimitation and nutrient limitation in the Tagus estuary. Journal of Marine Engineeringand Technology 12, 43–54.

Mateus, M., Vaz, N., Neves, R., 2012. A process-oriented model of pelagic biogeochem-istry for marine systems. Part II: Application to a mesotidal estuary. Journal ofMarine Systems 94, S90–S101 (this issue).

Megard, R.O., Tonkyn, D.W., Senft, W.H., 1984. Kinetics of oxygenic photosynthesis inplanktonic algae. Journal of Plankton Research 6 (2), 325–337.

Pahlow, M., 2005. Linking chlorophyll-nutrient dynamics to the Redfield N:C ratio witha model of optimal phytoplankton growth. Marine Ecology Progress Series 287,33–43.

Parsons, T., Takahashi, M., Hargrave, G., 1984. Biological Oceanographic Processes. PergamonPress, New York.

Putland, R., Iverson, J., 2007. Phytoplankton biomass in a subtropical estuary: distribution,size composition, and carbon:chlorophyll ratios. Estuaries and coasts 30 (5), 878–885.

Reinart, A., Arst, H., Blanco-Sequeiros, A., Herlevi, A., 1998. Relation between underwaterirradiance and quantum irradiance in dependence onwater transparency at differentdepths in the water bodies. Journal of Geophysical Research-Oceans 103 (C4),7749–7752.

Sarthou, G., Timmermans, K.R., Blain, S., Treguer, P., 2005. Growth physiology and fateof diatoms in the ocean: a review. Journal of Sea Research 53 (1–2), 25–42.

Sathyendranath, S., et al., 2009. Carbon-to-chlorophyll ratio and growth rate of phyto-plankton in the sea. Marine Ecology Progress Series 383, 73–84.

Smith, S.L., Yamanaka, Y., 2007. Quantitative comparison of photoacclimation modelsfor marine phytoplankton. Ecological Modelling 201 (3–4), 547–552.

Valente, A.S., da Silva, J.C.B., 2009. On the observability of the fortnightly cycle of theTagus estuary turbid plume using MODIS ocean colour images. Journal of MarineSystems 75 (1–2), 131–137.

Vaz, N., Mateus, M., Dias, J.A., 2011. Semidiurnal and spring – neap variations in theTagus Estuary: application of a process-oriented hydro-biogeochemical model.Journal of Coastal Research 64, 1619–1623 (SI).

Vichi, M.,Masina, S., Navarra, A., 2007a. A generalizedmodel of pelagic biogeochemistry forthe global ocean ecosystem. Part II: Numerical simulations. Journal of Marine Systems64 (1–4), 110–134.

Vichi, M., Pinardi, N., Masina, S., 2007b. A generalized model of pelagic biogeochemistry.forthe global ocean ecosystem. Part I: Theory. Journal ofMarine Systems64 (1–4), 89–109.

Wang, X.J., Behrenfeld, M., Le Borgne, R., Murtugudde, R., Boss, E., 2009. Regulation ofphytoplankton carbon to chlorophyll ratio by light, nutrients and temperature inthe Equatorial Pacific Ocean: a basin-scale model. Biogeosciences 6 (3), 391–404.