The effect of ocean acidification on growth and calcification of the marine algae

Much knowledge about growth and mortality of phytoplankton has been inferred from experiments where
environmental factors like light, temperature, and nutrient availability have been predominantly controlled,
e.g. in laboratory experiments with batch cultures or with chemostats. Typically, these experiments
are designed to determine a physiological response to variations of a single factor,
e.g. explaining changes in photosynthetic rate when exposed to different light conditions

The repeated laboratory OA experiments showed ambiguous responses in calcification to variations in
carbon dioxide (CO

If we seek to make inferences about future changes in calcification under oceanic conditions, experimental data are needed
that consider more realistic environmental conditions with a natural phytoplankton community that may include calcifying
algae like

Here we investigate data and their variability of replicate mesocosms during the PeECE-I experiment.
For this we take a modelling approach to simulate environmental conditions and the predominant dynamics of nine individual
mesocosms as described in

The focus of our model approach is different in that we distinguish between two phytoplankton functional types, calcifying algae
(e.g.

First we will briefly provide some background information about the experimental setup of PeECE-I, including irradiance, temperature, and salinity,
as these environmental factors enter our model simulations. This will be followed by a description of the model equations that include components
of the optimality-based approach to simulate algal growth, using parameterisations proposed by

For our analysis we consider the setup and data of the PeECE-I experiment, a study conducted at the Marine Biological Field Station
(Raunefjorden,

Nine mesocosms of 2 m diameter and 11 m

Daily samples were collected and measured over a period of 23 days. For every mesocosm, temperature and salinity data were interpolated to
hourly values for direct use as environmental input for model simulations (Fig.

Forcing variables for all nine mesocosms:

For model simulations we assume that all mesocosms are homogeneously mixed,
as we neglect an explicit representation of vertical turbulent mixing
(0-D-model approach). Furthermore, we assume no light gradient in mesocosms
and use depth integrated hourly irradiance data to force the model. The
applied model equations describe mass exchange rates of N and C between
compartments of (1) dissolved inorganic nitrogen and carbon (DIN and DIC),
(2) N and C biomass of coccolithophores and other phytoplankton (CoccoN and
CoccoC , PhyN and PhyC), (3) zooplankton (ZooN and ZooC), (4) detritus (DetN
and DetC), and (5) labile dissolved organic N and C (DON and DOC),
Fig.

Initial conditions and model parameters that are subject to optimisation.

Schematic representation of the model: boxes characterise individual compartments that are represented by one or more model state variables.
The arrows represent key biogeochemical processes (named in red) between compartments.
One compartment includes dissolved inorganic carbon and nitrogen (DIC and DIN). This compartment also embeds total alkalinity (TA).
Biomass and chlorophyll concentrations of photoautotrophs are resolved with respect to
carbon and nitrogen explicitly (referred to as PhyC and CoccoC, PhyN and CoccoN, and Chl

In our model we distinguish between calcifying and non-calcifying photoautotrophs, coccolithophores (Cocco), and other bulk
phytoplankton (Phy). Respective net photoautotrophic growth rates (

The biomass build-up (net growth) of photoautotrophs depends on the amount of N and C assimilated by the algae minus losses because of
aggregation, grazing by zooplankton, and exudation or leakage of organic matter.
The sources minus sinks (sms) terms of the photoautotrophs' biomass are as follows:

The synthesis of chlorophyll

The respective differential equations for chlorophyll

The process of calcification in our model depends on the amount of energy
provided through photosynthesis and is simply expressed by a ratio of PIC formation per carbon fixed (

The grazing losses of the photoautotrophs are resolved with an explicit representation of zooplankton biomass.
With our grazing approach (Holling type III) no distinctions are made between micro- and meso-zooplankton or between different feeding types.
Changes in zooplankton biomass are subject to a mortality (

The differential equation for zooplankton biomass and grazing function are given in Appendix

Detritus comprises a variety of components with particles of different sizes and sinking rates

The DIN pool represents the total concentration of nitrate, nitrite, and ammonium.
Nitrogen utilisation by phytoplankton and coccolithophores is a sink of DIN, whereas heterotrophic excretion and remineralisation
of

The DIC pool combines CO

Temporal changes in TA in our model are due to the sinks and sources of DIN and DIP
(

Dissolved organic matter (DOM) is produced by exudation of the photoautotrophs and by hydrolysis of detrital matter.
The DOM is subject to remineralisation, being the source of DIN and DIC.
The applied model distinguishes between dCCHOs and a residual fraction of

By introducing dCCHO we account for an additional sink of DOC other than
microbial degradation, which is the physical-chemical transformation of
dissolved to particulate matter, here resolved as the coagulation of dCCHO to
form transparent exopolymer particles (TEP) of carbon. This transformation is
parameterised as an aggregation process, as proposed in

The carbon content of TEP is explicitly resolved because it can be a significant constituent of POC measurements

Out of 33 model parameters, 26 parameters are fixed and the remaining 7 parameters (4 initial condition parameters
(

Initial condition values for some of the state variables in the model are computed by initial condition parameters, given in fractions.
The initial biomass during the start of the experiments, specified by PON

A peculiarity of the PeECE-I experiment is that high and low changes in TA were found in all three CO

In our data assimilation approach we consider data from the three cases (LC, MC, and HC) separately, but we make identical statistical assumptions.
The observation vector (

dissolved inorganic carbon (DIC, mmol m

dissolved inorganic nitrogen (DIN) (nitrate + nitrite, mmol m

chlorophyll

particulate organic nitrogen (PON, mmol m

particular organic carbon (POC, mmol m

particulate inorganic carbon (PIC, mmol m

total alkalinity (TA, mmol m

For the cases LC, MC, and HC we calculated daily residual standard errors (

The time-varying covariance matrices

A maximum likelihood (ML) estimator is applied, meaning that no explicit prior information is considered
for the estimation of parameter values.
Eventually, we use three similar cost functions but with data (

Maximum likelihood parameter estimates of three model solutions: low, medium, and high calcification (LC, MC, and HC).

Probability distributions of the initial condition and physiological model parameters: the cumulative sum of non-parametric probability densities (CDF) were derived from the posteriors of the Markov Chain Monte Carlo (MCMC) approach. The bars on the bottom of each panel show respective 95 % credible (uncertainty) ranges of the parameter estimates.

The same seven model parameters (Table

Credible interval limits for each parameter were derived from nonparametric probability densities of the MCMC estimates.
Figure

Correlation coefficients of parameter estimates of low, medium, and high calcification model solutions (LC, MC, and HC).
Correlation coefficients

During the post-bloom period, the mesocosms pooled in HC reveal TA changes that are consistently higher than in the LC mesocosms.
In fact, these differences become well reflected in our parameter estimates. Thus, our optimised ensemble model solutions are providing
the statistical evidence that HC and LC are significantly different.
With respect to the mesocosms assigned to the MC case we see in our parameter estimates and ensemble model solutions
that they are rather close to conditions also met by the HC mesocosms. In this case the differences in parameter estimates (between MC and HC) are
small, although we find significantly different estimates for

Full variational range of model outputs due to uncertainties in parameter estimates. Model ensembles of high, medium, and low calcification solutions compared with observations.

The variational range of parameter estimates (Fig.

The ensembles reflect uncertainty ranges in model solutions, which correspond nicely with most of the variability in observations.
Almost the entire range of variability in TA is recovered with our three distinct solutions of calcification. The observed variability in POC is captured
with the optimal ensemble model solutions. Only few maximum values seen in POC data remain unresolved, likely because we have optimised parameters
that hardly introduce changes in the solution of TEPC concentrations.
The model solutions exhibit some faster increase in the accumulation of PON during the exponential growth phase, in spite of the fact that DIN data are well
matched. Although this systematic model offset (bias) is pronounced, it does not correspond with any similar model bias in POC. Another general
offset can be seen for simulated Chl

According to our model approach we resolve changes in the rate of calcification relative to the carbon that is assimilated for growth of the coccolithophores.
For the period of nutrient repletion the values of the molar calcification-to-C-assimilation ratio (

Mean initial values of PON (PON

Molar calcification-to-C-fixation ratio compared to net growth rate of coccos (

Optimised model results of LC yield the highest TA values of all mesocosms, being in accordance with the TA data.
DIN concentrations are well resolved by the model, and variations of the ensemble DIN simulations are similarly low to in observations.
The previously mentioned biases in PON and Chl

DIN is well resolved in the HC solutions (Fig.

Low calcification solution. The coloured bands represent ensemble of model results according to the posterior and symbols show observations.

High calcification solution. The coloured bands represent ensemble of model results according to the posterior and symbols show observations.

The ensemble model solutions for LC and HC constitute two extremes and we therefore concentrate on the C and N budgets of these two cases.
Carbon and N flux estimates were computed as integrals over the entire 23-day period.
Figure

Carbon and nitrogen fluxes estimated by the model in mesocosms with low observed calcification but different CO

Carbon and nitrogen fluxes estimated by the model in mesocosms with high observed calcification but different CO

The data assimilation approach applied in this study was designed to resolve differences in TA and thus in calcification, while variations in other
data (e.g. DIN, PON, and POC) should also be explained with our model. We distinguished between mesocosms with high, medium, and
low calcification rates (HC, MC, and LC) and their respective data were used to come up with optimal estimates of initial conditions and of
some important physiological model parameters. Ideally, we would have identified similar optimal values of the physiological parameters
and would have obtained different estimates of the initial conditions for all three cases, HC, MC, and LC. However, our results
reflect a more complex picture and our optimised values for the initial conditions also depend on the best estimates for the model parameters.
The initial conditions could not be constrained independently and model solutions of the HC case do not automatically imply a higher initial
abundance of coccolithophores relative to the other, non-calcifying, phytoplankton. Likewise, the LC solution does not require a lower initial
biomass of calcifying algae. Instead of differences in relative species abundance, the initial physiological conditioning, e.g. acclimation states
of the algae, seems relevant as well, which is in the end reflected in the estimates of the physiological parameters

Large variations can be seen in the data of PIC, reflecting the variability measured in TA. Since optimal ensembles of model solutions were
derived for three distinct cases of calcification (LC, MC, and HC), we automatically capture most of the observed variability in PIC with our
simulations. The spread of the ensemble solutions for TA and PIC is smaller in each of the three cases relative to the observed total range.
This means that the respective uncertainties in our parameter estimates are small enough to obtain three distinctive ensembles of model solutions.
However, as discussed before, it is not possible to identify optimal values of the initial condition
parameter

Ratios of [POC] : [PON] and [DIC] : [DIN] determined from daily sampled noon values of model results.
Filled circles represent log

The posterior uncertainties in the estimates of the subsistence quota, (

Variability in POC is much more pronounced than in PON. All three model solutions show a steep increase in the POC : PON ratio as soon as
algal growth becomes nutrient-limited (Fig.

Simulated nitrogen biomass concentrations of photoautotrophs and zooplankton in high and low calcification solutions.

Our results show an increase in molar

The optimised model solutions for HC and LC reveal significant differences in the development of coccolithophore biomass.
As discussed before, these differences are not solely attributable to differences in the relative proportions of initial biomass concentrations.
In fact, the optimisations yielded estimates that suggest fairly similar initial coccolithophore biomass concentrations between all nine mesocosms.

From a modelling perspective it is helpful to know about the initial individual mass contributions to PON

For now we are interested in the question: what induces the different model solutions for LC and HC, in spite of similar initial conditions
in the concentrations of coccolithophores and phytoplankton? First of all, we have some differences between the relative proportions
of initial detrital, zooplankton, and photoautotrophic biomass (e.g. DetN : ZooN : (PhyN

Bar plots depicting cumulative sum of PIC residual (model–data misfit) from day 13 to day 18 of the experiment for three replicates
in mean solution of HC, MC, and LC ensembles. First row shows mesocosms with high CO

Full spread of model solutions according to credible range in parameter estimates, including ensemble solutions
of high, medium, and low calcification (light brown shaded area). Symbols represent observations of all mesocosms.
Khaki shaded bands show CO

Differences in photosynthetic efficiency estimates for the LC and HC cases could possibly be invoked for two
reasons: (a) because of unresolved differences in initial photo-acclimation states (e.g. different light history during the filling period),
since we assume identical initial Chl : N (

Model biases disclose systematic deviations of simulation results from observations, which may point towards (i) erroneous model counterparts to
observations (definition of

With our model we do not distinguish between growth of picoplankton and the other non-calcifying phytoplankton during the initial
bloom phase. The initial abundance of picoplankton (mainly

Results of our data–model synthesis also exhibit a small but distinctive
bias in the calcification response to elevated CO

We considered a simple CO

The advantage of resolving LC, MC, and HC solutions separately is that for each case we can compare data with model results of
mesocosms individually, of low- (glacial), medium- (present), and high- (future) CO

Figure (

An analysis of data of a mesocosm experiment is often approached by first grouping individual mesocosms according to the level of perturbation (e.g. the level of DIC added). In some cases, such an apparently self-evident approach may not help to reveal some basic phenomenon in mesocosm experiments. For a meaningful data analysis the mesocosms need not be exclusively differentiated by the different levels of perturbation but may first be sorted by major differences between relevant response signals, as done with respect to the magnitude of calcification in our study (by differentiating between LC, MC, and HC). In mesocosm experiments these differences in responses are likely associated with variations in initial conditions.

With our data assimilation approach we could disentangle three distinctive ensembles of model solutions that represent mesocosms with high,
medium,
and low calcification rates. The results of our data–model synthesis show that the initial relative abundance of coccolithophores and the
prevailing physiological acclimation states drive the bloom development and determine the amount of calcification in the mesocosms.
Small variations of these two initial factors between the mesocosms can generate differences in calcification that are larger than the
change in calcification induced by OA. In spite of this difficulty, a CO

An alternative approach to setting up mesocosms is to gradually increase the level of perturbation for a series of mesocosms. This way a gradient of different perturbation levels is introduced. The advantage then is that mesocosms that have been collated according to, for example, the lowest and highest response signals (or likewise according to similarities in initial conditions) may then be separately analysed with respect to their responses to the individual levels of perturbation.

From this modelling study we infer that collinearities exist between estimates of initial conditions and physiological model parameters,
in particular for the photosynthetic efficiencies

The results presented are made available by the authors. The model output data are centrally stored. Please send requests to skrishna@geomar.de or to mschartau@geomar.de.

The effect of temperature on the metabolic rates and biological activities of the vast majority of organisms
is given by the Arrhenius relationship

The resource allocation depends on the cellular nitrogen-to-carbon (N : C) ratio, expressed by the cell quota (

In the model, the optimal allocation factor for the LHC in an algal cell is calculated from

The total N uptake rate of photoautotrophs is calculated from the local N uptake rate

The gross carbon fixation rate of calcifiers and non-calcifiers is calculated from day length, degree of light
saturation,

where

The differential equations of C and N biomass for phytoplankton and coccolithophores are as
follows.

The differential equations for chlorophyll

The regulation term for chlorophyll

Total respiration cost in a cell includes costs due to chlorophyll synthesis, nutrient acquisition, and cell maintenance.

PIC formation can be written as a single differential equation:

A reference rate of PIC formation under nutrient-replete and light-saturated conditions
is prescribed as a molar ratio of

The sms differential equations for zooplankton carbon and nitrogen biomass
are as follows:

Equations below represent Holling type 3 grazing dynamics.

Respiration is parameterized as a function of respiration maintenance rate coefficient, temperature-dependent
metabolic rates, and carbon concentration of heterotroph.

The corresponding differential equations of detrital C and N mass are as
follows.

Aggregation equations for bulk phytoplankton and coccolithophores are given below.

Auxiliary model variables and model parameters.

The nitrogen uptake (

The sms differential equation for DIC is given below.

The differential equation listed below accounts for TA in the system.

The differential equations for dissolved organic matter are given below.

The differential equation for dissolved combined carbohydrates (dCCHO) is given
as follows.

Given below is the parameterisation to estimate the fraction of phytoplankton exudates that become available to be part of
dCCHO during two distinct modes of carbon overconsumption described in

The differential equation for formation of TEPC is shown below.

The entire optimisation procedure of each (LC, MC, and HC) case is subject to five consecutive analysis steps:

adjustment of parameters while considering
published typical values

application of simulated annealing algorithm (SANN) (see

local refinement of the parameter estimate, using the Broyden–Fletcher–Goldfarb–Shanno (BFGS)
algorithm

calculation of the inverse of second derivatives of

application of a Markov Chain Monte Carlo (MCMC) method, using the marginal error information of item 4 above to
confine credible range of optimal parameter values

Correlations during pre-bloom (

The authors declare that they have no conflict of interest.

The development of the modelling framework for mesocosm simulations and data assimilation was supported by the large integrated project Surface Ocean Processes in the Anthropocene (SOPRAN, 03F0662A), funded by the German Federal Ministry of Education and Research (BMBF). This study is a contribution to the BMBF-funded BIOACID (03F0728A) project. We gratefully acknowledge support by Markus Pahlow, who helped to refine equations in our model. We also like to acknowledge support given by Andreas Oschlies and by the GEOMAR data management team. We thank Sabine Mathesius for the compilation and inclusion of the forcing data into the mesocosm modelling setup. We thank Yonss Jose and Hadi Bordbar for helpful and constructive comments. The article processing charges for this open-access publication were covered by a Research Centre of the Helmholtz Association. Edited by: J. Middelburg Reviewed by: two anonymous referees