Interactive comment on “ Carbon fixation prediction during a bloom of Emiliania huxleyi is highly sensitive to the assumed regulation mechanism ” by O

In this paper the authors used a model to test different scenarios concerning the regulation of calcification and photosynthesis in Emilliania huxleyi. They considered either carbon dioxide, bicarbonate, carbonate or the calcite saturation state to be a regulating factor. They run the models at three different concentrations of atmospheric carbon dioxide and compared the carbon dynamics, including export within and between the models. The qualitative results of this paper directly follow


Introduction
Coccolithophorids play an important role in CO 2 trapping (Frankignoulle et al., 1994), since they transform dissolved inorganic carbon (DIC) into respectively particulate organic and inorganic matter which, being denser than seawater, sink towards the ocean floor. (1) Such export of both particulate organic carbon (POC) (equation ( 1)) and particulate inorganic carbon (PIC) (equation (2)), operated by the biological pump from the surface ocean layers, constitutes a carbon sink to the deep ocean on a geological scale (Klepper et al., 1994;Falkowski, 1997).
Coccoliths formation thus accounts for nearly 70% of the biogenic carbonate precipitation in the oceans (Houghton et al., 1996).Yet, such structures are relatively sensitive to pH and tend to dissolve when the water becomes too acidic.It is expected that a doubling in partial pressure of atmospheric CO 2 (pCO 2 ) will have direct consequences on the ability of these organisms to maintain their growth rate (Riebesell et al., 2000;Sciandra et al., 2003).As a corollary, acidification of the oceans due to increase in atmospheric pCO 2 (Orr et al., 2005) could jeopardize their role as a CO 2 pump.
Hence, how coccolithophorids may respond to shifts in global pCO 2 is a critical question to be addressed.However, sell (2004), carbonate saturation state may exert a stronger control on calcification than any of the other possible candidates, e.g.pH, CO 2 , or CO 2− 3 concentrations.Therefore, we considered that calcite saturation state Ω might also drive the calcification rate, and we introduced a new model, with Ω acting as a regulating factor.The underlying phytoplankton growth model, based on the representation of a cell quota, is a Droop-like model (Droop, 1968;Burmaster, 1979;Droop, 1983) in which we added the dependence to both inorganic carbon and light.
Our goal was to point out how the generic model of (Bernard et al., 2008), successively run with the different regulating factors, predicts significantly different amounts and fluxes of carbon.We simulated the typical situation of an Emiliania huxleyi late-Spring bloom, following a diatom bloom which depleted the inorganic carbon stock (Riebesell et al., 1993).The four versions of the model only differ by their assumption on the factor regulating the inorganic carbon uptake of photosynthesis and calcification.In this simplified model, we assume that all the chemical and biological concentrations are homogeneous in the mixed layer.The main idea developed throughout this paper is that some transient phenomena can lead to paradoxical effects on the predicted carbon fluxes.We stress that, depending on the supposed regulating factor, the exported carbon can vary twofold.Results also reveal that the variability of the fluxes, both due to the assumed regulating factor and to parameter uncertainty, is higher than the influence of a pCO 2 increase.
In the following section, we present the biological model of photosynthesis and calcification and describe its variants, according to the chemical species regulating the inorganic carbon compartment.We then recall classical modelling theories of the carbonate system dynamics in seawater.The hydrodynamical structure of the water column, in the considered typical situation, is exposed in section 2. Section 3 is devoted to Monte Carlo model simulations under two environmental conditions, represented by the current pCO 2 and that expected in the end of the 21 st century, after a pCO 2 doubling.The results are then discussed in section 5.
2 Modelling a bloom of E. huxleyi in a mixed layer 2.1 Growth in conditions of nitrogen limitation: extension of the Bernard et al. (2008) modelling framework In this section we briefly recall the fundamentals of the modelling framework developed in Bernard et al. (2008) for the biological kinetics.In the present work, these biological models are improved and further included in a simple physical framework representing a mixed layer.The principle of the model development is to account for the process uncertainty, and thus decline a modelling framework into various, structurally identical models to test alternative hypotheses.Uptake of inorganic nitrogen (nitrate, denoted S 1 (mmol.L −1 )) by the coccolithophorid biomass (whose particulate nitrogen concentration is denoted N (mmol.L −1 )), is represented by the following mass flow, where ρ(S 1 ) is the nitrate absorption rate: Generally, nitrate uptake is assumed to depend on external nitrate concentration NO 3 , following a Michaelis-Menten type equation (Dugdale, 1967): where ρ m and k N are the maximum uptake rate and the halfsaturation constant, respectively.The flux of inorganic carbon into organic biomass X (mmolC.L −1 ) and coccoliths C (mmolC.L −1 ) is associated to a flux of calcium (Ca 2+ , denoted S 2 (mmol.L −1 )) and of dissolved inorganic carbon (D ,(mmolC.L −1 ): Where µ is the photosynthesis rate.Here, for sake of simplicity, we assume that photosynthesis and calcification are coupled (see Bernard et al. (2008) for models where these processes are uncoupled).This coupling underlies the fact that the CO 2 released during calcification can be used as a substrate for photosynthesis.The constant α represents the proportion of the total up taken DIC which is allocated to photosynthesis.
The expression of the rate of inorganic carbon acquisition is more tricky; as shown by Droop (1968Droop ( , 1983)), this rate depends on the internal nitrogen quota Q, where Q = N/X is the ratio of particulate phytoplanktonic nitrogen to particulate organic carbon.However, coccolithophorids photosynthesis and calcification are also sensitive to the DIC concentration, and there is a consensus to admit that CO 2 would eventually be the substrate for photosynthesis while

HCO −
3 would be the substrate for calcification Berry et al. (2002).Therefore the regulation of photosynthesis and calcification could theoretically be triggered by CO 2 or HCO − 3 .In addition, Bernard et al. (2008) examined the possibility that CO 2− 3 was involved in the regulation of inorganic carbon acquisition, as suggested by recent works Merico et al. (2006).Here, we also consider that availability of calcium can potentially regulate calcification.With this last hypothesis, µ is a function of Ω, the saturation state of calcite (CaCO 3 ): where the solubility constant yields k sp = 5.15 10 −7 mol 2 .L −2 .
As a consequence, in the sequel we examine four possible models that only differ by the regulation mechanism of inorganic carbon acquisition: -CO 2 is the regulating species, and thus µ(Q, CO 2 ) is an increasing function of both Q and CO 2 .
-HCO − 3 is the regulating species, and thus µ(Q, HCO − 3 ) is an increasing function of both Q and HCO − 3 .-CO 2− 3 is the regulating species, and thus µ(Q, CO 2− 3 ) is an increasing function of both Q and CO 2− 3 .
-Ω is the regulating factor, and thus µ(Q, Ω) is an increasing function of both Q and Ω.To keep a general denomination, we denote µ p (Q, D p ) the growth rate, where, depending on the model M p , D p is chosen among CO 2 , HCO − 3 , CO 2− 3 and Ω.The first three models were mathematically studied in Bernard et al. (2008), where the authors analysed qualitative responses to in vitro shifts in pCO 2 .Results demonstrated that models (M p ) where D p was either CO 2 or HCO − 3 supported the results of Iglesias-Rodriguez et al. (2008b), while models where CO 2− 3 was the regulating factor supported the results obtained by Sciandra et al. (2003).
These biological models are modified here to reproduce more realistic environmental conditions.They now account for light distribution and are used to simulate a more complex in situ bloom of E.huxleyi in a mixed layer.

Net carbon fixation rate modelling in a light gradient
As in Bernard et al. (2008), we consider an analytical expression of µ p (Q, D p ) based on the Droop model (Droop, 1968(Droop, , 1983)).However, here, the carbon fixation kinetics is completed by two phenomena which cannot be neglected when considering the natural environment: exponential attenuation of light (I) in the seawater and mortality (including respiration and grazing losses).The net growth is now represented by the following function, depending on the the incident irradiance I 0 : where Q 0 and k Dp are respectively the subsistence quota and the half-saturation constant for the chosen regulating species.
The mortality rate m is supposed constant during the short period of time considered for the bloom simulation (typically one month).
The averaged maximal hypothetical growth rate at incident light I 0 , denoted μ(I 0 ), is the mean value of the maximum hypothetical growth rate for a light intensity I(z) (denoted μ(I(z))) exponentially decreasing along the depth z.We use the following expression, supported e.g. by Nimer and Merrett (1993): To compute the maximum hypothetical growth rate averaged on the mixed layer, μ(I 0 ), we take into account the exponential decrease of light with depth.We use the model of Oguz and Merico (2006) assuming that light extinction rate is the sum of a constant rate k 1 (due to the background and suspended material extinction) and, because of the phytoplankton-specific extinction, a rate proportional (with a coefficient k 2 ) to phytoplanktonic nitrogen N .
We denote μ(I 0 ) the average value of μ I(z) I(z)+k I in the mixed layer of depth L. It can then be computed as follows: a straightforward computation leads to:
Dissolved inorganic carbon (denoted D) is defined as the sum of the various inorganic carbon species: The carbonate alkalinity (CA) represents the sum of the electric charges carried in the carbonate system: An approximation of the total alkalinity (TA) can be obtained using the expression (see Zeebe and Wolf-Gladrow (2003) for more details) : To a first approximation, the ions that most contribute to λ depend on the salinity and remain constant.It is worth noting that total alkalinity is affected by calcification, and must be recomputed at each time point taking into account the calcium: To compute inorganic carbon speciation and pH, once dissolved inorganic carbon and calcium are known, a system of equations must be considered on the basis of equations ( 12) to ( 14) and of the equilibrium constants of the involved acid/base couples (Zeebe and Wolf-Gladrow, 2003).To solve this system, we used the Matlab code (supplement to Zeebe and Wolf-Gladrow (2003)), which was modified to account for the effects of changes in calcium concentration on the computation of total alkalinity (equation 15).

Considered simplified physics
In summer, density gradients generated by increasing temperatures lead to water stratification.The surface layer remains mixed over a generally shallow depth.Here we considered a mixed layer depth L of 15m, and to keep the model as simple as possible we assumed, as in Tyrell and Taylor (1996), an homogeneous distribution.We simulated the growth of coccolithophorids in this mixed layer, as represented in Fig. 1.CO 2 concentration in the water equilibrates with that in the atmosphere, following the difference in concentration between the two compartments and according to the diffusion coefficient k L .
In the water, CO 2 equilibrates with HCO − 3 and CO 2− 3 .The CO 2 pool is also affected by the coccolithophorids activity, being fueled by respiration and consumed through the processes of photosynthesis and calcification (see ( 5)).The model simulates a nitrate uptake limited by the availability in the mixed water are replenished from the deeper waters (with an exchange rate k d ) whose concentration are respectively S 1,0 , D 0 and S 2,0 .As water acidity affects the coccoliths persistence, we accounted for a possible dissolution of coccoliths whose rate is dependent on pH through the calcite saturation state.We assume that this rate can be written as where k diss is the dissolution rate when Ω = 1.Settlement of organic and inorganic particulate carbon is represented through a sinking process below the mixed layer with a sedimentation rate k sed .

Model equations
The resulting model equations, when considering the presented extension of the models from Bernard et al. (2008) embedded in the simplified considered physics, can now be written as: D p is the regulating factor (among CO 2 , HCO − 3 , CO 2− 3 and Ω) assumed to control both photosynthesis and calcification.
The initial conditions have been chosen assuming that coccolithophorids bloom right after a large diatom bloom which reduced the nitrate and inorganic carbon concentrations in the mixed layer (Riebesell et al., 1993).According to real pCO 2 data observed during in situ bloom experiments (Keeling et al., 1996;Benthien et al., 2007), we consider that 0.2 mmol.L −1 of total inorganic carbon was consumed by the previous bloom.The reference (i.e.before the diatom bloom) dissolved inorganic carbon concentration was computed assuming an equilibrium with the atmosphere (see Table 3).

Export computation
The exported carbon flux is computed at two different times.First, during the bloom, equations ( 16) to ( 22) are numerically integrated using the Matlab solver ode15s (Shampine and Reichelt, 1997).The flux follows the material export to the deep layer, through the processes of sedimentation and exchange through the thermocline.The end of the bloom occurs after 20 days; in this second phase, we assume that an unmodelled process, i.e. a high cell lysis or a strong predation event, makes E. huxleyi disappear within ten days, concomitantly to a high transparent exopolymer particles (TEP) production (Engel et al., 2004;Harlay et al., 2009).The dynamics of this process is not represented, but from a macroscopic point of view we assume that it leads to the transformation of the PIC and POC reached at the end of the bloom into settling particles.We estimated the fraction of exported carbon from studies on the link between primary production and organic export (De La Rocha and Passow, 2007;Boyd and Trull, 2007).Last, representing the export of coccoliths is far from trivial, as this complex phenomenon is neither clearly understood nor quantitatively described yet.The main export mechanism would be related to particles aggregation, mainly fecal pellets, which is also enhanced with TEP abundance (De La Rocha and Passow, 2007;Boyd and Trull, 2007;Harlay et al., 2009) and can be enhanced in conditions of nitrate limitation (Corzo et al., 2000;Engel et al., 2004).Let us keep in mind that our goal is not to provide an exhaustive description of this mechanism, but to catch a realistic range of magnitude with our simplified model.

Export carbon computation during the bloom
During E.huxleyi growth, the carbon flux is proportional to the material exported to the deep layer.The average exported POC during the 20 days of the bloom can thus be computed as follows: where η 1 is the fraction of POC non locally degraded (De La Rocha and Passow, 2007).
To compute the exported PIC, we refer to the estimate proposed by Ridgwell et al. (2007), assuming that it is related to the POC flux with a carrying capacity of organic aggregates for minerals (Passow and De la Rocha, 2006), and that a fraction, depending on Ω, may be dissolved.The mean flux during the 20 days of the bloom then reads (with parameters as in Ridgwell et al. (2007)):

Export carbon computation after the bloom
As the coccolithophorid bloom declines, a high quantity of TEP is produced (Engel et al., 2004;Harlay et al., 2009), which triggers the efficiency of particle coagulation and formation of macroscopic aggregates (Logan et al., 1995;De La Rocha and Passow, 2007;Kahl et al., 2008).We assume that TEP is related to the remaining POC at the final time of the simulation (i.e. when the bloom starts to decline).
The average daily POC flux during the ten days following the bloom is assumed to be a fraction η 2 of the remaining primary production at the end of the bloom: The same expression as equation ( 24) based on the formulation of Ridgwell et al. (2007) is used to compute the exported PIC: 3 Model simulation

Model calibration
Depending on the choice of the regulating inorganic carbon variable D p , four different models result from the different hypotheses as for the mechanisms driving both photosynthesis and calcification.Even if the objective is to sketch a generic bloom of E.huxleyi, the models were carefully calibrated using realistic parameter values, as detailed in the following.
Temperature and salinity are 15 • C and 35g/kg −1 , respectively.The residence time in the mixed layer is assumed to be 20 days (Schmidt et al., 2002), while the sedimentation rate k sed was computed using an average coccolith sedimentation rate of 0.75m/day (Gregg and Casey, 2007).The dissolution constant k diss was computed so that the calcite dissolution rate in standard pCO 2 conditions is 0.75d −1 (Oguz and Merico, 2006).The DIC deep concentration is assumed to be related to atmospheric pCO 2 , and depending on the considered pCO 2 scenario, three values will be considered, denoted D 0,380 , D 0,760 and D 0,1140 .The fraction of POC exported to the deep layer during the bloom (η 1 = 0.3) and the fraction of the remaining POC exported during the declining phase (η 2 = 0.1) have been calibrated using ranges provided by Honjo et al. (2008).
The nitrogen uptake rate is derived from Bernard et al. (2008), together with the values of the half saturation constants k Dp (according to Rost and Riebesell (2004), see Table 4).The light extinction coefficients are computed from Oguz and Merico (2006).The values for the half saturation constants k Dp are taken from Bernard et al. (2008).
The maximum exponential growth rate under non limiting conditions can be computed from the maximum hypothetical growth rate (Bernard and Gouzé, 1995): and thus we can get μ(I) from µ max (I): The values for µ max (I, D p ) are taken from Gregg and Casey (2007), using our values of temperature and half saturation constant for light intensity.We assume that this growth rate is obtained under nowaydays pCO 2 (380ppm) associated to standard CO 2 , HCO − 3 , CO 2− 3 and Ω computed using standard seawater values (Zeebe and Wolf-Gladrow, 2003).This provides the values of μ(I) for each of the four proposed models.
Finally, the set of nominal parameter values are presented in Tables 2 and 4. The considered seawater composition is presented in Table 3.
At this stage, we can remark that models regulated by CO 2− 3 and Ω present similar behaviours (data not shown).Indeed the simulations show very close predictions that always differ by less than 1%.This fact is consequent to the stability of Ca 2+ concentration in surface seawater, which makes Ω proportional to CO 2− 3 along the simulation.Note that this property is not straightforward for in vitro experiments (especially in batch conditions) where the high biomass level may affect the Ca 2+ stock, and thus more drastically influence Ω.
In the sequel we will therefore only consider the model in which the calcite saturation state is the regulating factor.

Monte Carlo simulations
In order to assess the effect of the parameter uncertainty and their possible variations during the bloom, Monte Carlo simulations are performed from randomly parameter values.The probability distribution of the parameters is supposed to be Gaussian, centered on the nominal value (See Tables 2 and  4), and with a standard deviation of 10% of the nominal value (i.e.95% of the parameter values are in the interval ±20% of their nominal value).1000 random parameter sets are chosen, and for each set a simulation is run.The average prediction together with its standard deviation is then computed.

Simulation at nowadays pCO 2
We used each of the three models to simulate a large bloom of Emiliania huxleyi.Phytoplankton cells are assumed to grow in a homogeneous layer, where aqueous CO 2 equilibrates with the atmosphere.It takes several weeks to supply inorganic carbon from both atmosphere and the deeper ocean to the cells in the whole mixed layer, and to reconstitute the   stock of inorganic carbon depleted by the previous bloom (Figures 3 and 4).The inorganic carbon stock reconstitution is slowed down by the consumption of inorganic carbon by the E. huxleyi bloom.As a consequence, during the simulation, CO 2− 3 and Ω show higher values, while CO 2 and HCO − 3 are lower compared to their respective steady state value.This fact can explain the significantly different behaviours observed between the 3 models (Figure 4).Indeed, it turns out that because of the high consumption of CO 2 by the blooming biomass, the progressive depletion of inorganic carbon results in a stronger down regulation of photosynthesis and calcification in models controlled by CO 2 or HCO − 3 .On the contrary, the models regulated by CO 2− 3 or Ω are enhanced by the depletion in inorganic carbon.It results that the predicted, fixed carbon during the bloom formation is twofold in the CO 2− 3 and Ω models compared to the CO 2 model (Figure 2).

Simulation with doubled pCO 2
Based on the accumulation rate of CO 2 observed in the atmosphere from the beginning of the industrial era, current models roughly predict a pCO 2 doubling.Since the atmosphere tends to be in equilibrium with the superficial oceanic layers, changes in atmospheric CO 2 directly affect the CO 2 seawater concentration, and consequently the carbonate system speciation.
Under such conditions of elevated pCO 2 , the initial condition of depleted inorganic carbon concentration in the water column, due to the development of the previous bloom, is transiently observed and still appears more favorable to the  CO 2− 3 and Ω models (data not shown).However this tendency does not last, since inorganic carbon rapidly increases as CO 2 in the water equilibrates with the elevated values of both atmosphere and deep layer (see Figure 5).After one week, ambient conditions are back to high CO 2 concentrations and then prove to be much more favorable to the CO 2 and HCO − 3 models which induce stimulated inorganic carbon uptake and rapidly recover.Yet, important differences appear in the final PIC and POC concentrations, with higher predicted values in the CO 2 model (see Table 5).

Modelling choices
The objective of this work was to explore the effect of the dynamical nature of the considered processes on the carbon fluxes predictions.A a consequence, this work does not assume a constant pCO 2 in the seawater, contrary to most of the studies dealing with the impact of pCO 2 increase.Indeed, our models represent the pCO 2 variation due the coc-  Table 5. Final values of and POC at t=20 days, and average daily exported carbon during the bloom, in mgC.m −2 .d−1 with respect to the considered model and pCO2 .In brackets: CV (Coefficient of variation), expressed in %.
colithophorid bloom which consumes both inorganic carbon and alkalinity.We have thus chosen to detail the phenomena within the time scale of the bloom, and especially those which are likely to vary with respect to a pCO 2 change.As a consequence, we have assumed that mortality (due to predation (Garcia et al., 2008), viruses (Jacquet et al., 2002), ... ) was constant during 20 days, and that Emiliania huxleyi was dominating the phytoplankton community during this period.The important point is that these phenomena of slower dynamics are not directly influenced by the pCO 2 and can therefore reasonably be considered to be of similar intensities for various pCO 2 scenarii.Focusing on the pCO 2 dependent biological and chemical processes, we can thus compare different pCO 2 situations under the hypotheses that they are comparable since the non represented phenomena have a similar effect.In the same spirit, we have not represented the strong mechanisms (predation or viruses) that transform, within 10 days, the living cells of E.huxleyi into settling organic and inorganic matter.We assume therefore that the predation process will be rather unaffected by the pCO 2 , so that that its global efficiency to transform biomass into exported material is only impacted by the saturation state of calcite Ω through inorganic carbon export expressions ( 24) and ( 26) (Ridgwell et al., 2007).It is however likely that this assumption introduces a bias since the link between POC concentration and TEP production is probably pCO 2 dependent (Engel, 2002;Engel et al., 2004;Riebesell et al., 2007), and thus parameters η 2 should be an increasing function of TEP.However, in the models where photosynthesis and calcification are stimulated by an increase in pCO 2 , even if this effect is not represented, a higher POC is produced leading to higher carbon export.

Hypothesis of a regulation based on calcite saturation state
The new biological model that we introduced, in which the calcite saturation state drives calcification, turns out to be an alternative explanation to the CO 2− 3 model.This model assumes that the calcite saturation state, even when higher than 1 (meaning that dissolution rate is low), strongly influences the calcification rate.The simulations illustrate a property that could have been shown analytically, using similar principles than in Bernard et al. (2008): the Ω follows the CO 2− 3 model.This model can thus explain the experimental results obtained by Sciandra et al. (2003).In the hypothesis of uncoupled calcification and photosynthesis, if Ω is used to control the calcification rate while the photosynthesis rate is driven by CO 2 , then the experimental results of Riebesell et al. ( 2000) can be reproduced.This results holds for in situ considerations since calcium in the mixed layer is only marginally affected by the bloom.However, this conclusion may not hold for the high biomasses reached in in vitro experiments.
It is worth remarking that the models only focus on the factor impacting growth and calcification.They do not assume any hypothesis on the nature of the inorganic carbon species which is consumed.Indeed, the models globally represent the uptake in the inorganic carbon D compartment.When a mole of inorganic carbon is consumed (whatever the species), the chemical equilibria are displaced.As a consequence, in this approach, only the regulating factor nature is uncertain.
O.Bernard, A.Sciandra and S.Rabouille: Prediction of E.huxleyi carbon fixation

Outcome of two opposite effects
The simulations turn out to show that the production and export predictions are the consequence of two antagonist effects.
The first effect is related to the fact that, at higher pCO 2 , the HCO − 3 and CO 2 models predict an enhanced uptake of dissolved inorganic carbon, compared to the model regulated through Ω.From a quantitative point of view, the magnitude of this phenomenon relies on the way models are calibrated.They all predict the same photosynthesis and calcification rates for 380 ppm and standard alkalinity.This reference situation, for which many data are available, was used to calibrate most of the parameters.The second effect turns out to be the opposite of the direct effect: for pCO 2 lower than 380, i.e. right after the diatom bloom, the photosynthesis and calcification rates of the HCO − 3 and CO 2 models is lower because of the inorganic carbon depletion in the water column.On the contrary, for the model enhanced by Ω, the first ten days of the bloom are in highly favorable conditions and thus both POC and PIC production are enhanced.Finally, whatever the considered model, the first ten days of the bloom and the last ten days lead to opposite inorganic carbon uptake conditions.This compensation phenomenon is probably the key reason why, in the end, the prediction difference between the models is strongly reduced.Despite this effect due to depletion of the inorganic carbon when the bloom takes place, as indicated by the figures in Table 5, the CO 2 and Ω models predict a two-fold difference in the final PIC and POC concentrations under a doubled pCO 2 .
4.4 Can we predict the effect of a pCO 2 increase ?
Here, simulations suggest that a change in pCO 2 will impact coccolithophorid bloom formation.Yet, depending on the model, this variation is an increase (see the doubling in PIC in the CO 2 model) or a decrease (see the 50 % PIC drop in the Ω model).Hence, simulations also point out two-fold differences in these predicted concentrations, depending on the considered regulating factor.That is, the variability in the predicted values, observed between the models, equals or even exceeds that due to the rise in pCO 2 .This statement is reinforced when considering a tripling of pCO 2 (see Table 5).This point is absolutely critical as it demonstrates the strong dependence of the model outcome on the initial hypotheses made as for the regulation of photosynthesis and calcification.
Figures 6 and 7 present the averaged simulations of the three different models (each curve thus corresponds to 3000 simulations) as a response to pCO 2 .It is remarkable that the average predictions seem to be rather unaffected by the pCO 2 value: without a firm hypothesis on the regulation mechanisms, no effect of a pCO 2 shift can be estimated.When considering Figure 7, the only prediction that seems to hold for the whole set of models is the decrease of the PIC:POC ratio when increasing the pCO 2 , which is a direct consequence of increased coccolith dissolution.
The phenomena, revealed by our short time scale approach, are likely to appear when dealing with models designed to simulate longer terms dynamics, including more accurate interactions with the whole ecosystem.The tight dependence of the stock and flux predictions on the underlying regulation mechanisms and the paradoxical effect due to the inorganic carbon depletion after the diatom bloom may both strongly affect any modelling prediction.So far, to our knowledge, none of the complex models dealing with coccolithophorids (Tyrell and Taylor, 1996;Merico et al.;Oguz and Merico, 2006;Gregg and Casey, 2007) accurately represent inorganic carbon dynamics and its impact on the biological kinetics.As stated by Riebesell (2004), it seems impossible at this point to provide any reliable forecast of largescale and long-term biological responses to global environmental change.Our study should therefore be considered as a methodological approach on a bench model to highlight a phenomenon that will take place in more detailed models (including food web interactions).As more experimental works are needed to unravel the carbon acquisition modes and their regulation in coccolithophorids, prediction statements should be made with caution and discussed in regard to the plausible hypotheses.
Last, another hypothesis was recently brought forward by several authors: the calcification mechanisms also seems to be highly strain dependent (Fabry, 2008;Langer et al., 2009).As an assemblage of various strains (with different carbon acquisition regulation mechanisms), a natural population would then show a range of different responses to increases in pCO 2 .To provide an accurate, simulated response to pCO 2 change, a model should then represent each subpopulation, with various responses to carbonate chemistry, so that the resulting overall response reveals to be a combination of the subpopulation behaviours.Our Monte Carlo simulation approach can also be interpreted as a way to reproduce this natural variability.It then shows that this variability also induces large uncertainties in the flux predictions.We considered parameter variability with a 10% variation coefficient, and it resulted in more than 100% variability in the predictions of particulate stocks and fluxes.

Conclusions
The originality of this work is to consider the dynamics of both carbonate system and inorganic carbon uptake and their coupling.As a consequence, our models point out the transient periods during which the inorganic carbon is much lower than its value at equilibrium with atmosphere.During these transient phases, the scenarii in which CO 2− 3 or Ω regulate calcification and photosynthesis may be strongly advantaged, leading thus to an unexpected effect which highly attenuates the direct effect of pCO 2 increase.
This study stresses how correct identification of the chemical species that drive calcification and photosynthesis processes is critical for accurate predictions of coccolithophorid blooms and for the estimation of the consequent amount of carbon withdrawn from the atmosphere and trapped into the deep ocean.Model results reveal a striking difference in the predicted biomass increase when the saturation state Ω (or equivalently CO 2− 3 ) is the regulating factor compared to the CO 2 model.
A detailed validated model including interactions with a trophic network may allow predictions at larger time scale, especially for carbon export, but it may also be affected by the same uncertainties that our bench model, thus resulting in highly uncertain predictions of carbon fluxes in the situations of large blooms of coccolithophorids.
Results thus strongly call for further experimental approaches to more accurately identify the chemical species that primarily regulate photosynthesis and calcification.

Fig. 1 .
Fig. 1.Schematic diagram of the well mixed upper ocean represented by the model.

Table 1 .
Definition of variables and fluxes for the four considered models.

Table 2 .
Definitions and values of the model parameters. 1 : depends on the model type, see Table4.† : unitless for Ω.

Table 3 .
Composition of deep seawater.

Table 4 .
Kinetics parameters depending on the chosen model.( † unitless for kΩ)