Ocean Acidification Perturbation Experiments Perturbation Experiments to Investigate the Impact of Ocean Acidification: Approaches and Software Tools Bgd Ocean Acidification Perturbation Experiments

Introduction Conclusions References Tables Figures Back Close Full Screen / Esc Abstract Introduction Conclusions References Tables Figures Back Close Full Screen / Esc Abstract Although future changes in the seawater carbonate chemistry are well constrained, their impact on marine organisms and ecosystems remains poorly known. The biological response to ocean acidification is a recent field of research as most purposeful experiments have only been carried out in the late 1990s. The potentially dire conse-5 quences of ocean acidification attract scientists and students with a limited knowledge of the carbonate chemistry and its experimental manipulation. Hence, some guidelines on carbonate chemistry manipulations may be helpful for the growing ocean acidifica-tion community to maintain comparability. Perturbation experiments are one of the key approaches used to investigate the biological response to elevated pCO 2. They are 10 based on measurements of physiological or metabolic processes in organisms and communities exposed to seawater with normal or altered carbonate chemistry. Seawater chemistry can be manipulated in different ways depending on the facilities available and on the question being addressed. The goal of this paper is (1) to examine the benefits and drawbacks of various manipulation techniques and (2) to describe a new 15 version of the R software package seacarb which includes new functions aimed at assisting the design of ocean acidification perturbation experiments. Three approaches closely mimic the ongoing and future changes in the seawater carbonate chemistry: gas bubbling, addition of high-CO 2 seawater as well as combined additions of acid and bicarbonate and/or carbonate.


Introduction
Ocean acidification refers to the on-going decrease in ocean pH as a result of the uptake of anthropogenic carbon dioxide (CO 2 ) in the ocean.The partial pressure of CO 2 (pCO 2 ) increases in the atmosphere due to anthropogenic inputs.It has increased by more than 35% since the beginning of the industrial revolution leading to changes in the Earth's climate and in the functioning of terrestrial ecosystems.The world's oceans expression "ocean acidification" refers to the decrease in pH but does not imply that the pH of surface ocean waters will become acidic (below 7.0) any time soon.
Although the chemistry of ocean acidification is very well known, the associated impacts on marine organisms and ecosystems remain poorly known.The impact of low pH on marine organisms started to be investigated several decades ago (e.g.Bouxin, 1926), yet research into the biological response to ocean acidification is still in its infancy: the first purposeful manipulative experiment was carried out only in the 1980s (Agegian, 1985) and others began only in the late 1990s.The potentially dire consequences of ocean acidification have attracted the interest of scientists and students with a limited knowledge of the carbonate chemistry and its experimental manipulation.
Hence, some guidelines on carbonate chemistry and its manipulation may be helpful for the growing ocean acidification community in order to ensure that the most adequate approaches are used and that results and subsequent analyses are comparable.The need to standardize measurement of parameters of the carbonate system has been identified (Kleypas et al., 2006), a gap which was recently filled (Dickson et al., 2007).
Perturbation experiments are one of the key approaches used to investigate the biological response to elevated pCO 2 .They are based on measurements of physiological or metabolic processes in organisms and communities exposed to seawater with normal or altered chemistry.Seawater chemistry can be manipulated using different ways 4415 Introduction

Conclusions References
Tables Figures

Back Close
Full depending on the facilities available and on the question being addressed.Langdon (2000) summarized the state-of-the-art techniques used with reef builders.Here we examine the benefits and drawbacks of current methods and provide a software package to assist the design of perturbation experiments.

Method
Detailed information on the carbonate chemistry, including the merit of units and scales, as well as on the measurement methods can be found in Dickson et al. (2007), Zeebe and Wolf-Gladrow (2001) and in the Guide for Best Practices in Ocean Acidification Research and Data Reporting in preparation (see http://www.epoca-project.eu).
The R package seacarb was used to calculate the carbonate chemistry parameters.R is a free cross-platform language and environment for statistical computing and graphics (R Development Core Team, 2008).The previous version, seacarb 1.2.3 (Proye and Gattuso, 2003) is superseded by version 2.0 which was recently released (Lavigne et al., 2008).The new version has been updated in order to be fully consistent with the most recent guidelines to best practices for ocean CO 2 measurements (Dickson et al., 2007), and five new functions have been added to assist the design of ocean acidification perturbation experiments.These new functions are described in the present paper.

Main approaches
The seawater chemistry can be manipulated in various ways in order to alter parameters of the carbonate system.The following sections examine the five techniques that are most useful in the context of ocean acidification.Calculations were carried out using the first and second dissociation constants of carbonic acid given by Lueker et al. (2000).In systems open to the atmosphere, it is assumed that the seawater Introduction

Conclusions References
Tables Figures

Back Close
Full and atmosphere are in equilibrium with respect to CO 2 .It must be pointed out that the methods described below enable to set the carbonate chemistry at the beginning of a perturbation experiment.However, initial values can be altered by biological (e.g.photosynthesis, respiration and calcification) and physical processes (e.g.air-seawater exchange of CO 2 and temperature changes), which must also be taken into account in the experimental design.

Gas bubbling
Bubbling seawater with gases is an efficient way to manipulate its carbonate chemistry.
The seacarb function pgas estimates the changes in the carbonate chemistry resulting from changes in pCO 2 generated by bubbling gases.The syntax is (more information is available in the help files of the seacarb package): pgas(flag, var1, var2, pCO 2 g, S, T, P, Sit, Pt) The input parameters below are required: flag: a number (1 to 24) indicating which couple of parameters of the carbonate system are known.For example, flag is 8 when pH T and total alkalinity are known.
-var1 and var2: the values of the two parameters of the carbonate system prior to the perturbation which are known (pH and alkalinity in the example above).See the seacarb manual for more detail, especially regarding the units.
-pCO2g is the CO 2 partial pressure (in µatm) of the gas used to bubble the medium.
Example: Seawater with a pCO 2 of 384 µatm and TA of 2325 µmol kg −1 is bubbled with a mixture of CO 2 and air with a pCO 2 of 793 µatm.Salinity is 34.9, temperature is 18.9 • C and calculations are made for surface waters.The command needed is: pgas(flag = 24, var1 = 384, var2 = 2325e−6, pCO 2 g = 793, S = 34.9,T = 18.9) This approach exactly reproduces the changes of all parameters of the carbonate system expected in the year 2100 (Fig. 1 and Table 2).Smith and Roth (1979) is perhaps the first publication which manipulated the carbonate chemistry via gas bubbling within a range compatible with that of the on-going ocean acidification.
Two techniques have been used in the context of ocean acidification: pH-stat and bubbling with premixed gases.In pH-stat systems, pH is monitored continuously and a controller opens or closes valves when pH goes above or below a set value.Gases are then delivered until pH reaches the set value again.Different combination of gases have been used: (1) air and pure CO 2 , (2) CO 2 -free air and pure CO 2 , and (3) air, CO 2free air and pure CO 2 .CO 2 -free air can be produced easily using CO 2 scrubbers such as soda lime or NaOH and Ca(OH) 2 in low concentrations (Hintz, personal communication).The pH threshold is calculated using the desired pCO 2 and total alkalinity which must either be constant or frequently measured.This method allows one to compensate for any change in the carbonate chemistry due to photosynthesis and respiration or, in the case of open culture systems, to changes in the source water.However, it does not compensate for changes in total alkalinity that would result from precipitation and dissolution of CaCO 3 which could occur between measurements of total alkalinity.Hence, the carbonate chemistry can be maintained with good efficiency in the culture vessel, e.g. with variability of pCO 2 better than ±10 µatm.The main drawback of this technique is that the pH electrode must be frequently calibrated in order to avoid drift.Hence, the other technique of bubbling with premixed gases may be attractive.Air with Introduction

Conclusions References
Tables Figures

Back Close
Full the desired pCO 2 can be produced using gas mixing pumps or purchased.Another technique would be to control atmospheric pCO 2 to the desired level in the laboratory or growth cabinet in which the experiments are carried out.A simple air pump can then be used to bubble the experimental seawater.To the best of our knowledge, this technique has yet to be used in the context of ocean acidification.
Seawater aeration by bubbling may lead to difficulties in phytoplankton cultures Shi et al. (2009).It may also enhance the coagulation of organic matter (Engel et al., 2004).This coagulation may be critical for studies investigating the response of microbial communities because their metabolism depends on the respective abundance of dissolved and particulate organic matter.This drawback may be avoided by enclosing the community in a dialysis bag, which is itself enclosed in a container bubbled with a gas having the desired pCO 2 (Weinbauer, personal communication).Such bags are permeable to gases and small molecules in solution but impermeable to larger molecules and particles.

Addition of high-CO 2 sea water
DIC and TA are conservative quantities with respect to mixing (Wolf-Gladrow et al., 2007).Hence, when two water parcels are mixed, the amount of a solute in the mixture equals the sum of the amounts of this solute in the two initial water parcels.Hence: Where the subscripts "sw" and "high CO 2 ", respectively indicate concentrations in the normal and high CO 2 seawater.Concentrations are in µmol kg −1 and M is the mass in kg.The seacarb function pmix estimates the carbonate chemistry after mixing of two water samples.Its syntax is: pmix(flag, var1, var2, pCO 2 s, wf, S, T, P, Pt, Sit) Introduction

Conclusions References
Tables Figures

Back Close
Full -pCO 2 s: pCO 2 of the high-CO 2 water in µatm wf: weight fraction of the high-CO 2 seawater vs. final weight Example: One mixes, in a closed system, 0.99623 kg of seawater having a TA of 2325 µmol kg −1 , and pCO 2 of 384 µatm with 0.00377 kg of seawater having TA of 2325 µmol kg −1 and saturated with CO 2 (pCO 2 =1×10 6 µatm).The weight fraction, wf is 3.77e-3.Salinity is 34.9, temperature is 18.9 • C and calculations are made for surface waters.The command needed is: pmix(flag = 24, var1 = 384, var2 = 2325e−6, pCO 2 s = 1e6, wf = 3.77e − 3, S = 34.9,T = 18.9) This produces seawater with a final pCO 2 of 793 µatm and all parameters of the carbonate chemistry in 2100 are perfectly reproduced.To the best of our knowledge, this approach has only been used in the context of CO 2 perturbation experiments carried out in mesocosms (Schulz et al., unpubl.).The seacarb function pTA computes the changes in the carbonate chemistry due to addition of CO 2− 3 or HCO − 3 .Its syntax is: pTA(flag, sys, var1, var2, pCO2a, co3, hco3, S, T, P, Sit, Pt) flag, var1, var2, S, T, P, Sit and Pt where defined in the previous sections.The other input parameters below are required:

Addition of CO
sys: 0 if the manipulation is carried out in a system closed to the atmosphere or 1 if its is carried out in a system open to the atmosphere (in the later case, full equilibrium between air and water is assumed).

Conclusions References
Tables Figures

Back Close
Full Screen / Esc Printer-friendly Version

Interactive Discussion
Results are shown in Fig. 3 and Table 2.In a closed system, the target pCO 2 of 793 µatm is reached but all other parameters of the carbonate system are very different from their values expected in 2100.pH is higher than it should be (7.993instead of 7.941) and TA, DIC, [CO 2− 3 ], Ω a , and Ω c are higher than the target values.They are even higher than the values of the initial seawater.Those differences are magnified in open systems.
Manipulation of total alkalinity has often been used to investigated the physiological response to changes in the carbonate chemistry (e.g.Swift and Taylor, 1966).Marubini and Thake (1999) used bicarbonate additions to test the hypothesis that the supply of DIC in seawater limits coral calcification.Langdon et al. (2000) used this approach in the Biosphere 2 coral reef mesocosm.They used additions NaHCO 3 and Na 2 CO 3 to increase the CaCO 3 saturation state.Since the experiment lasted several months, additions of CaCl 2 were used to restore a normal Ca 2+ concentration.The manipulations of the CaCl 2 concentration is described in Sect.3.6.

Addition of strong acids and bases
The carbonate chemistry can be manipulated by addition a strong acid or a strong base, such as HCl and NaOH, which dissociate fully in seawater.The addition of a strong acid or base in a system closed to the atmosphere does not alter the concentration of dissolved inorganic carbon (DIC) but modifies total alkalinity (TA).TA decreases following addition of acid and increases following addition of a base.
The change of total alkalinity after addition of a strong acid or base in a system open to the atmosphere is identical to that described above for a closed system.However, the concentration of DIC is modified through CO 2 exchange at the air-water interface in order to equilibrate the partial pressure of CO 2 in the atmosphere and seawater.
The seacarb function ppH calculates the changes in the carbonate chemistry during pH manipulations.The change in salinity due to the addition of acid or base is vol: the volume of acid or base added in liter.By convention, it is given a negative sign for acid additions and a positive sign for base additions.
-N: the normality of the acid or base (mol kg −1 ).
Example: A volume of 14.18 ml of 0.01 N HCl is added to 1 kg of seawater having a known pCO 2 (384 µatm) and TA (2325×10 −6 mol kg −1 ).The atmospheric pCO 2 is 384 µatm, salinity is 34.9 and temperature is 18.9 • C. Calculations are made for surface waters.The command needed in a closed and open system are: ppH(flag=24, sys=0, var1=384, var2=2325e-6, pCO 2 a=384, vol=-0.1418e-3,N=0.01, S=34.9, T=18.9) ppH(flag=24, sys=1, var1=384, var2=2325e-6, pCO 2 a=384, vol=-0.1418e-3,N=0.01, S=34.9, T=18.9) Results are shown in Fig. 4 and Table 2.The target pCO 2 of 793 µatm is reached in a closed system but pH is lower than the value expected in 2100 (7.768 instead of 7.993, corresponding to a 5.6% increase in [H + ] that results from the decrease in total alkalinity generated by acid addition).This is an undesirable effect of the direct manipulation of pH as TA will not change significantly during the course of this century (Table 1).As a result, DIC, HCO − 3 , CO 2− 3 and the CaCO 3 saturation states are lower than their target values.However, it is possible to restore TA to its initial level by adding of CO 2− 3 and HCO − 3 , an approach that is described in Sect.3.5.Obviously, due to gas exchange at the air-water interface, pCO 2 and other parameters of the carbonate chemistry cannot be successfully adjusted by a one-time acid addition in an open system.Introduction

Conclusions References
Tables Figures

Addition of strong acid as well as CO
Results are shown in Table 2.The first addition raises DIC to the desired level of 2190×10 −6 mol kg −1 but increases TA to a value higher than target (2467 vs. 2325 ×10 −6 mol kg −1 ).The subsequent addition of HCl restores TA to the desired value without affecting DIC.All carbonate parameters after both additions are on the target values (Table 2).Introduction

Conclusions References
Tables Figures

Back Close
Full Screen / Esc

Printer-friendly Version
Interactive Discussion To our knowledge, the first paper which used addition of acid, base and NaHCO 3 to manipulate the carbonate chemistry within a range compatible with ocean acidification is that of Borowitzka (1981) who investigated, in the laboratory, the response of photosynthesis and calcification of an articulated coralline red algae.

Manipulation of the Ca 2+ concentration
Although manipulating the calcium concentration is not technically altering the carbonate chemistry per se, this approach has been used in the context of ocean acidification.The reason is that some calcifying organisms, such as corals, respond to the calcium carbonate saturation state of seawater (Ω) which is expressed as: 3 ] sw are the concentrations of calcium and carbonate in seawater, respectively, and K * sp is the solubility product at the in situ conditions of temperature, salinity and pressure (Zeebe and Wolf-Gladrow, 2001).It can readily be appreciated that the changes in Ω resulting from decrease in [CO 2− 3 ] driven by ocean acidification can be mimicked by altering [Ca  2+ ] sw .This approach involves the use of artificial seawater (Gattuso et al., 1998).It is recommended to use the simplied synthetic sea water recipe described by Gattuso et al. (1998) and based on DOE (1994) because it is the basis of the synthetic seawater that has been used to determine a variety of equilibrium constants for use in seawater.
The seacarb function pCa estimates the changes in Ω c and Ω a resulting from the manipulation of the Ca 2+ sw concentration.Note that this function does not account for the effect of the changes in the calcium concentration of the dissociation constants of carbonic acid and on the solubility product of CaCO 3 (Ben-Yaakov and Goldhaber, 1973).The syntax is: pCa(flag, sys, var1, var2, Ca, S, T, P, Sit, Pt) Introduction

Conclusions References
Tables Figures
This approach has been used to investigate the response of corals (Gattuso et al., 1998) and coccolithophores (Trimborn et al., 2007) to changes in the saturation state of calcium carbonate.It has also been used to replenish calcium when its concentration decreases below its natural levels during long-term experiments with calcifiers (e.g.Langdon et al., 2000).

Discussion and conclusion
Three approaches closely mimic the on-going and future changes in the seawater carbonate chemistry: gas bubbling, addition of high-CO 2 seawater, and combined addition of acid and bicarbonate and/or carbonate.All three methods increase dissolved inorganic carbon at constant total alkalinity, a situation that closely resembles the changes in the carbonate chemistry that have occurred during the last 200 years and are expected to continue during the next few hundreds years.All three approaches therefore offer precise control of carbonate chemistry variables, which reach target values at the beginning of a perturbation experiment.Gas bubbling is the easiest to implement and can be used to maintain constant conditions over long periods of time.However, during bubbling, biological processes (e.g., calcification, dissolution of CaCO 3 , nutrient uptake and release) can alter the carbonate chemistry by changing total alkalinity even though Introduction

Conclusions References
Tables Figures

Back Close
Full the concentration of dissolved inorganic carbon remains constant.Also, in all three approaches, calcification can deplete the concentration of Ca 2+ when the organism to volume ratio is high or the incubation time long.The approach that adds CO 2− 3 and/or HCO − 3 appears of limited practical because most carbonate chemistry variables reach values that far from target values.Several studies have used acid addition to manipulate the carbonate chemistry.Although this technique offers precise control of pCO 2 in systems closed to the atmosphere, it also alters total alkalinity which drives other carbonate system variables to levels far from those expected in the future.That is, pH is lower than its target value, DIC remains unchanged (whereas it increases under natural ocean acidification), and the CaCO 3 saturation state) as well as the concentrations of bicarbonate and carbonate.To avoid this drawback, it is recommended to first add bicarbonate or carbonate or both, to increase DIC, before adding acid.Iglesias-Rodriguez et al. (2008a) have recently reported that, in contrast to previous reports, calcification of the coccolithophore Emiliania huxleyi increases at elevated pCO 2 .They argued that this is due to the different approaches used to manipulate the carbonate chemistry and that the approach of gas bubbling (changing DIC at constant TA) is superior to the approach of acid addition (changing TA at constant DIC) (Iglesias-Rodriguez et al., 2008a,b).The argument is that acid addition does not reproduce the increase in the HCO − 3 concentration generated by natural ocean acidification whereas gas bubbling does reproduce it.The authors claim that HCO − 3 may stimulate photosynthesis and, in turn, calcification.They conclude that experiments which used acid addition and demonstrated that calcification declines at lower pH, confounded the issue.This statement is misleading, although there is no doubt that gas bubbling better mimics the future carbonate chemistry (see above as well as Table 2).In contrast to the claims by (Iglesias-Rodriguez et al., 2008a,b), several previous perturbation experiments were also carried out with gas bubbling.They also reported lower rates of calcification of coccolithophores at lower pH and higher pCO 2 (Sciandra et al., 2003;Delille et al., 2005;Feng et al., 2008).Second, the concentrations of CO 2 , HCO 3 , and H + all change in the same direction with both approaches: gas bubbling and acid addition (compare Fig. 1a-c with Fig. 4a-c; Table 2).Hence, the magnitude of biological responses may be different, but should at least tend in the same direction.Differences in the two approaches cannot explain the opposite directions of the biological responses.Finally, perturbation experiments carried out using gas bubbling can also lead to poor control of the carbonate chemistry, for example when the experiments last too long or when the biomass to volume ratio is too large (see above).Although the cause of the discrepancy in the response of calcification by the coccolithophore E. huxleyi to ocean acidification remains a matter of debate (e.g., Riebesell et al., 2008;Shi et al., 2009), it does not appear to be related to the approach used to perform the manipulation of the carbonate chemistry in perturbation experiments.
Fortunately, the situation is clearer in zooxanthellate scleractinian corals.Schneider and Erez (2006) measured the rate of calcification under constant DIC, constant pH and constant pCO 2 and showed that calcification is controlled by the concentration of CO 2− 3 , the future value of which is relatively well mimicked by acid addition.
Our goal here has been to provide the appropriate computational tools and to highlight the positive and negative aspects of the different approaches that are used to investigate ocean acidification by perturbing the carbonate chemistry.We have not addressed practical issues that must be taken into account to design and conduct perturbation experiments.To mention just a few: response time, bubbling rate, impact of autoclaving, evaporation, heat flux, impact of nutrients and temperature.These issues, as well as others, will be covered in a Guide for Best Practices in Ocean Acidification Research and Data Reporting in preparation (see http://epoca-project.eu).Introduction

Conclusions References
Tables Figures

Back Close
Full

BGD Introduction Conclusions References
Tables Figures

Back Close
Full Table 1.Changes in the carbonate chemistry of surface seawater from the Last Glacial Maximum (LGM; 18 ky B.P.) to 2100.Total alkalinity, CO 2 partial pressure (pCO 2 ), salinity and temperature were fixed and used to derive all other parameters using the seacarb software (Lavigne et al., 2008) and the dissociation constant of carbonic acid of Lueker et al. (2000).
It is assumed that the ocean and atmosphere are in equilibrium with respect to CO 2 .Values of temperature, salinity, total alkalinity and total phosphate in 1766, 2007 and 2100 are from Plattner et al. (2001) prescribing historical CO 2 records and non-CO 2 radiative forcing from 1766 to 1990 and using the A2 IPCC SRES emissions scenario (Nakićenović and Swart, 2000) thereafter.Temperature during the LGM was set 1.9 • C colder than in 2007 (MARGO Project Members, 2009).The LGM salinity was set 1.07 higher than during pre-industrial time (Paul and Sch äfer-Neth, 2003).Total alkalinity in the LGM was scaled to salinity while the total phosphate concentration was assumed to be the same as in 1766.pCO 2 in 1766 and 2100 are from Plattner et al. (2001), while values in the LGM and 2007 are, respectively from Petit et al. (2001) and Keeling et al. (2008).The concentration of total silicate is assumed to have remained constant from the LGM to 2100.It was calculated using the gridded data reported by Garcia et al. (2006) between 0 and 10 m and weighing the averages using the surface area of each grid cell.pH is expressed on the total scale.Table 2. Seawater carbonate chemistry in 2007, in 2100, and after perturbation.Total alkalinity (TA), partial pressure of CO 2 in seawater (pCO 2 sw ), salinity and temperature were used to derive all other parameters using the seacarb package (Lavigne et al., 2008) except for manipulations of the calcium concentration for which DIC was used rather than pCO 2 sw .For the sake of simplicity, it is assumed that temperature, salinity and total alkalinity in 2100 are identical to their 2007 values, respectively 18.9 • C, 34.9 and 2325×10 −6 mol kg −1 .The concentrations of total phosphate and silicate were set to 0.63×10 −6 0.55×10 −6 , respectively.The seawater pCO 2 was set at 384 in 2007 (Keeling et al., 2008) and 793 µatm in 2100 (according to the A2 SRES emission scenario; Plattner et al., 2001).The main body of the text provides further information.(a): ×10 Full   Fig. 2. Effect of mixing with high-pCO 2 seawater in a closed system as computed with the seacarb function pmix.The letters "i" and "f" are, respectively, the value of a parameter before and after perturbation for the example described in the text.ter in a closed system as computed with the seacarb function the value of a parameter before and after perturbation for the Fig. 2. Effect of mixing with high-pCO 2 seawater in a closed system as computed with the seacarb function pmix.The letters "i" and "f" are, respectively, the value of a parameter before and after perturbation for the example described in the text.as computed with the seacarb function pTA.The letters "i" and "f" are, respectively, the value of a parameter before and after perturbation for the example described in the text.as computed with the seacarb function pgas.By convention, addition of acid is negative whereas addition of base is positive.The letters "i" and "f" are, respectively, the value of a parameter before and after perturbation for the example described in the text.The letters "i" and "f" are, respectively, the value of Calcium carbonate saturation state before and after perturbation for the example described in the text.
, var2, S, T and P where defined in Sect.3.1.The other input parameters required are: Screen / EscPrinter-friendly Version Interactive Discussion

3
As mentioned in Sect.3.4, the addition of acid does not enable to fully mimic the changes in carbonate chemistry expected during the present century but the addition of acid circumvents this problem.The first addition elevates DIC to the desired level and the acid addition (at constant DIC) precisely cancels the increase in TA resulting from the addition of CO 2− 3 and/or HCO − 3 There is no specific seacarb function to handle this approach.The changes in the carbonate chemistry can be calculated by using successively the pTA and ppH functions.
, var1, var2, S, T, P, Sit and Pt where defined in the previous sections.Ca is the calcium concentration in mol kg −1 .

Fig. 1 .
Fig.1.Effect of bubbling seawater with gases of varying pCO 2 on the carbonate chemistry of seawater as computed with the seacarb function pgas.The letters "i" and "f" are, respectively, the value of a parameter before and after perturbation for the example described in the text.
pCO 2 on the carbonate chemistry of seawater as letters "i" and "f" are, respectively, the value of a parameter cribed in the text.

Fig. 1 .
Fig.1.Effect of bubbling seawater with gases of varying pCO 2 on the carbonate chemistry of seawater as computed with the seacarb function pgas.The letters "i" and "f" are, respectively, the value of a parameter before and after perturbation for the example described in the text.

Fig. 3 .
Fig. 3. Effect of CO 2− 3 and HCO − 3 addition in a closed (A, B and C) and open system (Dand E) as computed with the seacarb function pT A. The letters "i" and "f" are, respectively, the value of a parameter before and after perturbation for the example described in the text.

Fig
Fig. 3. Effect of CO 2− 3 and HCO − 3 addition in a closed (A, B and C) and open system (Dand E) as computed with the seacarb function pTA.The letters "i" and "f" are, respectively, the value of a parameter before and after perturbation for the example described in the text.

FFig. 4 .
Fig. 4. Effect of addition of a strong acid or a strong base in closed (A, B and C) and open systems (D, E and F)

Fig. 4 .Fig. 5 .
Fig. 4. Effect of addition of a strong acid or a strong base in closed (A, B and C) and open systems (D, E and F) as computed with the seacarb function pgas.By convention, addition of acid is negative whereas addition of base is positive.The letters "i" and "f" are, respectively, the value of a parameter before and after perturbation for the example described in the text.

Fig. 5 .
Fig.5.Calcium carbonate saturation state as a function of the calcium concentration as computed with the seacarb function pCa.The letters "i" and "f" are, respectively, the value of Calcium carbonate saturation state before and after perturbation for the example described in the text.
pCO 2 a, S, T, P, Sit and Pt where defined in sections above.The other input parameters required are: