Introduction
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
e.g..
Many laboratory experiments are performed with monocultures, with the advantage that physiological responses
may then become well expressed in measurements while variability between replicates or even between repeated
experiments should remain low. In this context a series of laboratory studies with monocultures of calcifying
coccolithophores were conducted to investigate responses
in calcification to variations in carbonate chemistry, often with Emiliania huxleyi,
e.g..
These studies were motivated by the expectation that the observed trend in ocean acidification (OA) will
affect calcifying algae and that their physiology is likely sensitive to the seawater's calcite saturation state
.
The repeated laboratory OA experiments showed ambiguous responses in calcification to variations in
carbon dioxide (CO2) concentrations and pointed out that differences
in laboratory methodology, but also details in experimental design, are likely the reason for the large observed
variability in E. huxleyi responses to changes in carbonate chemistry. Similarly, stressed
that variations in the observed ratio between particulate inorganic carbon and particulate organic carbon (PIC : POC ratio)
increase with the decrease of measured relative growth rates, depending on whether “low” growth conditions were
balanced (as achieved with chemostats) or resulted from unresolved transient nutrient-limitation effects in batch cultures.
This ongoing discussion is accompanied by the question of how representative the outcomes of monoculture laboratory
experiments are, to allow for reliable future projections of OA effects on oceanic calcification rates of coccolithophores
and on possible climate feedbacks.
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 Emiliania huxleyi. A series of studies were conducted to investigate effects of OA on
plankton dynamics. Among those were experiments with tanks or bags called mesocosms, with some enclosed water volume that typically comprised
a natural plankton community. These mesocosms were typically perturbed and exposed to different CO2 concentrations,
e.g. Pelagic Ecosystem CO2 Enrichment (PeECE) studies .
Few studies focused on the impact of OA on growth of E. huxleyi.
In contrast to monoculture laboratory experiments, CO2 perturbation mesocosm experiments yield “net” community
response signals that are anticipated to be more indicative for possible future changes in oceanic calcification of coccolithophores.
Replicate mesocosms with similar initial nutrients, as well as initial dissolved inorganic carbon (DIC) concentrations typically show
comparable temporal response patterns, i.e. an exponential growth phase until nutrients become depleted and a post-bloom
period where chlorophyll a concentrations decline. However, replicate mesocosms that all included E. huxleyi
exhibited large deviations in calcification responses, thereby altering carbonate chemistry.
Such variability was well reflected in total alkalinity (TA) measurements of the PeECE-I experiment .
Furthermore, during PeECE-I it happened that mesocosms with high and low calcification rates were revealed
among replicates in all three CO2 treatments. To find enhanced variability in calcification in mesocosm experiments is
comprehensible and can be attributed to the likely mixture of superimposed responses of multiple plankton species even
within replicates of similar CO2 perturbation.
Thus, small deviations in the initial relative mass distribution of photoautotrophs, zooplankton, and detritus between replicate
mesocosms can translate into some pronounced variability in measurements even under similar environmental
conditions e.g..
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 and in . presented a dynamical
model to simulate the mass flux of carbon (C), nitrogen (N), and phosphorus (P) for the same PeECE-I experiment. Their model resolves
growth and losses of E. huxleyi together with interdependencies between bacteria, viruses, detritus, and dissolved organic
matter (DOM). The model of also features the exudation and coagulation process of dissolved polysaccharides
(here referred to as dissolved combined carbohydrates, dCCHO) to form transparent exopolymer particles (TEP).
In the study of some emphasis is put on the enhanced mortality of E. huxleyi due to viral lysis
and on the variable stoichiometry (C : N ratio) of the particulate organic matter (POC : PON ratio). They did not attempt to resolve a dependency
between calcification and CO2 concentration and therefore restricted their simulations to one treatment with three replicate mesocosms
that were exposed to present-day CO2 concentrations.
The focus of our model approach is different in that we distinguish between two phytoplankton functional types, calcifying algae
(e.g. E. Huxleyi) and bulk non-calcifying algae, i.e. an unresolved combination of picoplankton, dinoflagellates, and diatoms.
We assume a CO2 sensitivity for the ratio of calcification to net carbon fixation (photosynthesis minus respiration), based on results from
the meta-analysis of . In our data–model synthesis we concentrate on the initialisation (initial filling) of the mesocosms,
with possible variations in the relative distribution of plankton and detritus resolved in our model. A data assimilation (DA) method is employed
for the estimation of parameter values, which helps to disentangle and understand some of the differences and commonalities seen in observations,
in particular in TA and PIC data, but also in measurements of dissolved inorganic nitrogen (DIN) and DIC, chlorophyll a, as well as in
particulate organic nitrogen (PON) and particulate organic carbon (POC).
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 .
Thereafter, the data assimilation method for parameter estimation will be briefly explained. Specific details of the model and of the
data assimilation method are given in the Appendix. Ensembles of three distinct model solutions will be presented together with their mass
flux estimates of C and N. We will discuss the problem of
identifying initial conditions in combination with important model parameters. We will also address the problem of resolving the variability observed
in the accumulation of PIC and how this variability is related to the expression of the CO2 effect introduced to the model.
Material and methods
For our analysis we consider the setup and data of the PeECE-I experiment, a study conducted at the Marine Biological Field Station
(Raunefjorden, 60.3∘ N, 5.2∘ E) of the University of Bergen, Norway between 31 May and 25 June 2001
.
The objective of this study was to investigate OA effects on marine calcifying algae (coccolithophores) captured in polyethylene bags of enclosed water
volumes (mesocosms) and perturbed by different levels of CO2 concentrations. A dynamical plankton ecosystem model is used for simulations of
N and carbon C flux within each mesocosm. We apply a data assimilation method to identify best estimates of model
parameter values together with initial conditions
for model simulations.
Experimental data
Nine mesocosms of 2 m diameter and 11 m3 volume were filled with unfiltered, post-bloom, nutrient-depleted water from the fjord.
After the filling of the mesocosms, nutrients were added so that all mesocosms had similar initial nutrient concentrations,
approximately 15 mmol m-3 of nitrate together with nitrite and 0.5 mmol m-3 of phosphate. Like the nutrients, the initial
TA in all nine bags was 2146 mmol m-3 approximately (or if normalised to unit
mass ≈2200 µmol kg-1). The bags were covered with air-tight tents of tetra-fluoroethylene foil that
allowed 95 % of photosynthetically active radiation (PAR) to pass through. The mesocosm bags were subject to three different levels of
perturbation of partial pressure of CO2: (a) mesocosms 1–3, referred to as M1, M2, and M3, were exposed to similarly high DIC levels
(initial DIC = 2119, 2119, 2122 mmol m-3) with 700 ppmV of initial
pCO2; (b) M4, M5, and M6 started from DIC = 2048, 2056, 2040 mmol m-3 with a
corresponding pCO2= 370 ppmV; and treatment (c) with initial DIC = 1919 mmol m-3, 1929 m-3, 1927 m-3
with 180 ppmV pCO2 in mesocosms M7, M8, and M9. Thus, data from three replicate mesocosms are available for each of the
three CO2 treatments. For each mesocosm the partial pressure of atmospheric CO2 above the surfaces was largely controlled by a
continuous injection of gas with a treatment-specific, individually prescribed CO2 content. Because there was an open space between
surface of mesocosms and the tents, we assumed the pCO2 in the air above the mesocosms' surfaces to be a mixture of 90 % of
the perturbed pCO2 inside a mesocosm and 10 % of the actual atmospheric pCO2 (340 ppm) in all replicates.
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. ). Hourly photosynthetic available radiation (PAR)
data were derived from meteorological global irradiance measurements of the Geophysical Institute at Bergen .
Figure shows that temperature increased by approximately 3 ∘C during the experiment and variations between
the different mesocosms remained small. Small but noticeable differences exist between mesocosms with respect to salinity. In all mesocosms a
gradual decrease in salinity was observed, from S= 31.3 to approximately S= 30.8. The PAR data exhibit variations on an hourly scale, due to
changes in cloud cover.
Forcing variables for all nine mesocosms: (a) shows temperature, linearly
interpolated to hourly values between daily observations.
(b) Displays hourly interpolated salinity values, and (c) reveals the
irradiance data with hourly temporal variations resolved.
Modelling approach
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. . Due to the design of the PeECE-I experiment, our
model includes some additional features. The first is that we consider an
explicit representation of dissolved combined carbohydrates (dCCHO) that act
as precursors for carbon content of transparent exopolymer particles (TEPC),
similar to and . Since
our model resolves changes in TA along with DIC so that we can also derive pH
values and the corresponding partial pressure of CO2 (pCO2). We
resolve neither viral infections nor bacterial biomass explicitly, as done in
. Microbial activity is implicitly considered by
parameterisations of hydrolysis and remineralisation. Both processes are
assumed to be temperature-dependent but are independent of changes in
bacteria biomass. Instead, hydrolysis and remineralisation rates are
calculated as
being proportional to substrate
availability only. Likewise, any effects by viral lysis remain unspecified and are an integral part of a single total mortality that is assigned
to phytoplankton and coccolithophores. In the following, the general model equations of mass flux of C and N are described as sources
and sinks, inducing changes in the mass concentration of the respective state variables.
Initial conditions and model parameters that are subject to optimisation.
Initial conditions &
Description
Unit
parameters for optimisation
1. PON0
Initial concentration of particulate organic nitrogen
mmol N m-3
2. fdet
Fraction of PON0 assigned to non-living detritus
–
3. fzoo
Fraction of living PON0 assigned to zooplankton
–
4. fcocco
Initial coccolithophore fraction of photoautotrophs
–
5. Q0
Subsistence quota (minimum cellular N : C ratio)
mol mol-1
6. αcocco
Photosynthetic efficiency of coccolithophores
mol C (g Chl a)-1 m2 W-1 d-1
7. αphy
Photosynthetic efficiency of non-calcifying phytoplankton
mol C (g Chl a)-1 m2 W-1 d-1
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 Chlphy and Chlcocco respectively).
Variations in carbon and nitrogen biomass are also resolved for zooplankton (ZooC and ZooN) and for detritus (DetC and DetN). Dissolved combined
carbohydrates (dCCHO) are distinguished from other labile
dissolved organic matter, described as LDOC and LDON. Only dCCHO are assumed to act as precursor for the formation of transparent exopolymer particles,
whose carbon content is explicitly resolved (TEPC). One compartment represents the formation and dissolution of particulate inorganic carbon (PIC), affecting
DIC as well as TA.
Photoautotrophs
In our model we distinguish between calcifying and non-calcifying photoautotrophs, coccolithophores (Cocco), and other bulk
phytoplankton (Phy). Respective net photoautotrophic growth rates (μcocco/phy) are described as rates of
gross carbon fixation (VC) minus some corresponding sum of respiration costs (rC) due to
the synthesis of chlorophyll a, nutrient assimilation, and maintenance: μcocco/phy = VC-rC.
The proportions of VC and rC are determined by optimal resource allocation while energetic
trade-offs are imposed, as described in . These physiological equations of
optimal allocation have been shown to be well applicable for a series of different conditions (e.g. including diazotrophy)
and scales e.g..
Here we neglect diazotrophy as well as the effect of phosphorus availability
on nitrogen uptake and thus on algal growth. From the data we could not infer any phosphorus limitation of growth prior to nitrogen
depletion and we assume that cellular nitrogen (N) directly limits the net growth rate of photoautotrophs (μcocco/phy).
Nitrogen is generally necessary for synthesising enzymes. According to the model approach of ,
the major metabolic pathways within the algae are regulated by the resources allocated to produce these enzymes.
Thus, key processes like photosynthesis, chlorophyll a synthesis, and net carbon fixation become affected by internal resource
allocation. The model maximises the photoautotrophic growth rates by optimising the allocation of resources to nutrient acquisition
sites and to the light-harvesting complex (LHC). The auxiliary variables mentioned above are described in Table
in Appendix . The detailed equations are given in Appendix .
Biomass concentrations of photoautotrophs
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:
sms of photoautotroph biomass=C and N uptake-exudation/leakage-aggregation-grazing.
The corresponding sms differential equations of C and N biomass for phytoplankton and coccolithophores are given in
Appendix .
Chlorophyll a concentrations
The synthesis of chlorophyll a (Chl) is represented by an optimal trade-off between photosynthesis and respiratory
costs in the chloroplast of a cell. The synthesis rate depends on the degree of light saturation (SI),
on the amount of net carbon fixed inside chloroplasts, and on the chlorophyll-to-carbon ratio (θ).
Also, the chlorophyll synthesis rate is sensitive to changes in the cellular nitrogen-to-carbon ratio (N : C), QN.
The descriptions of the above-introduced auxiliary variables are given in Table .
Like for biomass, the parameterisations for chlorophyll a are identical for the calcifying and non-calcifying phytoplankton
in our model:
sms of chlorophylla=synthesis of chlorophylla-aggregation-grazing.
The respective differential equations for chlorophyll a of non-calcifying phytoplankton (with subscripts phy) and coccolithophores (cocco)
are listed in Appendix .
Formation of particulate inorganic carbon (PIC)
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 (fPIC, Eq. ).
The differential equation of PIC describes a net accumulation rate (formation minus dissolution) and no explicit distinctions can be made with
respect to how PIC becomes eventually distributed between algal biomass, detritus, or zooplankton:
sms of PIC=calcification by coccolithophores-dissolution of
coccoliths (calcite).
The differential equations for precipitation and dissolution of PIC are given in Appendix .
Zooplankton
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 (Mzoo; e.g. losses to higher trophic levels). Other loss terms represent
respiratory costs (rzoo) as well as excretion (γzoo).
Zooplankton restore C and N towards a constant N : C ratio (Qconstzoo) of 0.19. The restoring time (τ)
in our model is equal to 1 day.
It mimics an increase in respiration (rzoo) if the N : C ratio falls below Qconstzoo and an increase
in excretion (γzooN)
if N : C is above Qconstzoo. Details of auxiliary variables related to the zooplankton compartment of the model are given in
Table .
The buildup of zooplankton biomass depends on the total prey concentrations (phytoplankton and coccolithophores):
sms of zooplankton biomass=grazing on phytoplankton+grazing on coccolithophore-respiration (or excretion)-mortality.
The differential equation for zooplankton biomass and grazing function are given in Appendix .
Detritus
Detritus comprises a variety of components with particles of different sizes and sinking rates .
The detritus resolved by our model simply combines dead plankton biomass and fecal pellets.
Sources of detrital C and N mass are given in terms of phytoplankton aggregation and mortality of zooplankton.
Aggregation is parameterised with quadratic loss terms of the photoautotrophs. These aggregation equations resolve interactions between
two types of particles (small cells of photoautotrophs and large aggregates of detritus):
(a) aggregation of cells of photoautrophs and (b) aggregation of small photoautotrophs with larger detritus – see details in the Appendix .
The two-particle-type approach allows a trade-off between accuracy of estimated mass flux and the resolution of particle size .
We assume that hydrolysis is temperature-dependent and that it is responsible for the degradation of detritus, acting as a source for
(labile) LDON and LDOC. The equations of detrital C and N can thus be described as follows:
sms of detritus=aggregation of phytoplankton+aggregation of coccolithophore+zooplankton mortality-hydrolysis.
The respective differential equations of detrital C and N mass are given in the Appendix .
Dissolved inorganic compounds (DIN, DIC) and total alkalinity (TA)
Dissolved inorganic nitrogen (DIN)
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 LDON are the major sources:
sms of DIN=-N uptake by phytoplankton-N uptake by coccolithophores +excretion by zooplankton+remineralisation.
The sms differential equation for DIN is given in Appendix .
Dissolved inorganic carbon (DIC)
The DIC pool combines CO2, bicarbonate, and carbonate.
The primary sinks of DIC are net carbon fixation to support photoautotrophic growth (μcocco/phy) and calcification of coccolithophores.
We do not differentiate between the utilisation of CO2 and bicarbonate for algal growth and calcification. Note that
net carbon fixation (μcocco/phy) in our model becomes slightly negative in the absence of light (dark respiration
of the photoautotrophs). Total heterotrophic respiration acts as major DIC source and is expressed by zooplankton respiration and
by the remineralisation of dissolved organic carbon (LDOC + dCCHO):
sms of DIC=-net C uptake by phytoplankton-net C uptake by coccolithophores-calcification + dissolution of PIC+zooplankton respiration+remineralisation + gas exchange.
The corresponding differential equation for DIC is listed in Appendix .
Total alkalinity (TA)
Temporal changes in TA in our model are due to the sinks and sources of DIN and DIP
(ΔDIP=116×ΔDIN), a process of precipitation and dissolution of calcite plates
produced by the calcifying algae. We follow the nutrient-H+ compensation principle described in .
In our model we are resolving the nitrogen flux of zooplankton excretion but we are eventually not resolving any associated net
change in TA. This is because we cannot differentiate between the excretion of ammonium (NH4+) and of nitrate (NO3-)
and nitrite (NO2-). The excretion of 1 mole NH4+ would increase TA by 1 mole, whereas the excretion of
1 mole NO3- or NO2- would decrease TA by 1 mole . In other words, we indirectly impose that half of
the N excretion by zooplankton is NH4+ and the other half is NO3- and NO2-, which would introduce a net TA change of zero.
Measured values of DIN, TA, and DIC on day one of the experiment were taken as initial conditions for respective mesocosms.
sms of total alkalinity=N and P uptake by phytoplankton+N and P uptake by coccolithophores-calcification by coccolithophores + dissolution of calcite-remineralisation of dissolved organic N and P.
The differential equation for TA is given in the Appendix .
Dissolved labile organic matter and transparent exoplymer particles
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 LDOC and LDON. This distinction is made because only dCCHOs are simulated to act as precursors for the formation of
TEPs. In our model the DOM's primary source is freshly exuded and leaked organic matter from photoautotrophs.
An additional source of DOM is due to degradation of detrital matter (hydrolysis and microbial exudation) in response to bacterial activity.
The fraction of exudates that enter the dCCHO pool may vary between the exponential growth phase and during periods of nutrient limited
growth, described as two modes of exudation in . We therefore introduced a parameterisation
(fdCCHOcocco/phy, Eq. ) that simulates such a shift in quality of the exudates, depending on
the respective cell quota of the coccolithophores and of the other phytoplankton (Qcocco/phyN).
Remineralisation and microbial respiration are respective sinks of LDOC and LDON.
Table lists all associated auxiliary variables.
The equations for labile DOC and DON are described as follows (with details given in Appendix ):
sms ofLDON=exudation by photoautotrophs+hydrolysis/degradation of detritus+hydrolysis/degradation of gels- remineralisation/respiration of dissolved organic matter.
Dissolved combined carbohydrates (dCCHO)
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
and effectually applied in
and in (see details in
Appendix ):
sms of dCCHO=exudation-coagulation of dCCHO-aggregation of dCCHO with TEPC-remineralisation of dCCHO.
Transparent exopolymer particles (TEP)
The carbon content of TEP is explicitly resolved because it can be a significant constituent of POC measurements .
This consideration is important for our data–model synthesis, in particular because it affects the stoichiometric C : N ratio of particulate organic matter.
The sink terms of dCCHO, described before, are the only sources for TEPC in our model approach. The degradation of TEPC is parameterised similarly to
the hydrolysis of detritus:
sms of TEPC=coagulation of dCCHO+aggregation of dCCHOwith TEPC-degradation.
The corresponding differential equation for TEPC production is listed in the Appendix .
Model parameters and initial conditions
Out of 33 model parameters, 26 parameters are fixed and the remaining 7 parameters (4 initial condition parameters
(fcocco, fzoo, fdet. PON0) and 3 ecological parameters (αphy,
αcocco, Q0) enter the
optimisation procedure.
The decision on which parameters should become subject to optimisation is based on a series of preceding parameter optimisations
and subsequent sensitivity analyses. A major objective is to reduce the number of parameters for optimisation to a meaningful minimum.
This facilitates the identification of those parameter values that are of primary concern. Since we address differences in initial conditions in our study,
we consider four parameters that determine these differences, and they need to become subject to optimisation. The additionally selected three growth
parameters are amongst those to which the model solution is most sensitive. The model solutions are also highly sensitive to variations of the maximum
potential nitrogen uptake rate (V0N). This parameter is excluded from optimisation, because it is not possible to obtain estimates of (V0N) that
are independent of estimates of the photosynthetic efficiency. Therefore, a value is assigned to V0N that is typical and was used for simulations of
other experiments (e.g. Pahlow et al., 2013), ensuring credible estimates of those parameters that are optimised in our study. The mesocosm experiment
covers only a short post-bloom period and we found other parameters, like maximum grazing rates and the aggregation parameters, to be weakly constrained
by the available data. Their consideration for optimisation would impede the identification of the other more important parameters. Values assigned to those
parameters that are excluded from optimisation are adapted from other studies (e.g. Pahlow et al., 2013; Schartau et al., 2007).
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 PON0, is distributed between living and non-living biomass, which is
determined by the parameter of the initial detritus fraction (fdet). The living biomass is further distributed between photoautotrophs
and zooplankton, specified by the initial zooplankton fraction parameter (fzoo).
Finally, the remaining relative distribution of photoautotrophic biomass is set by fcocco. For example, a value of fcocco = 1 would
mean that all photoautotrophic biomass is associated with the presence of coccolithophores exclusively.
PON0=DetN0+ZooN0+CoccoN0+PhyN0with the individual fractions:DetN0=fdet⋅PON0ZooN0=fzoo⋅(PON0-DetN0)CoccoN0fcocco⋅(PON0-DetN0-ZooN0)PhyN0=(1-fcocco)⋅(PON0-DetN0-ZooN0)
For initial zooplankton, coccolithophore, and phytoplankton biomass we apply a constant C : N ratio of 6.625.
We consider a higher C : N ratio (= 2 × 6.625) only for initial detritus. Since the mesocosms were filled with post-bloom,
nutrient-depleted water masses, we assume that all dead particulate organic matter has a C : N ratio that is rather typical for such post-bloom conditions.
Initial conditions of PIC, DIC, and TA are taken from the data for respective mesocosms, whereas we assume same small fixed values
(e.g. DON = 0.05, DOC = 102.5, dCCHO = 1.0 and TEPC = 3.5 mmol m-3)
as initial conditions for all mesocosms.
(a) shows three distinct calcification patterns, reflected in total alkalinity
(TA) data. Those mesocosms that exhibit high TA values (a reduced drawdown during the bloom and post-bloom period)
feature rates of low calcification (LC, in blue colour). Mesocosms with low TA values (a strong reduction of TA)
reveal rates of high calcification (HC, marked red). Rates of medium calcification (MC) are assigned to the
remaining mesocosms (with intermediate TA values, marked black). (b) shows the respective different
CO2 treatments in the same colours as for LC, MC, and HC. The figure shows that each calcification case
(LC, MC, and HC) includes mesocosm of all three CO2 treatments.
Design of data assimilation (DA) approach
A peculiarity of the PeECE-I experiment is that high and low changes in TA were found in all three CO2 treatments,
in response to differences in
calcification . Because the three distinct patterns in calcification (Fig. )
are attributable to all three treatments, a factor other than the CO2 perturbations induced variations between the individual mesocosms.
For all other observations no such clear pattern could be
identified. We designed our data assimilation approach according to this finding and therefore investigate three possible situations (model solutions)
that differ in their
TA response: low, medium, and high calcification (referred to as LC, MC, and HC respectively). Thus, for each of these three (LC, MC, and HC)
situations we find three mesocosms that were subject to three different CO2 levels (initial 700, 370, and 180 ppmV).
By adapting the same nomenclature as in and in , we can assign the mesocosms M1, M6, and M8 to those
with low calcification rates (highest TA), M2, M5, and M7 to the ones with medium
calcification, and finally M3, M4, and M9 to mesocosms with high calcification rates (lowest TA).
Definition of cost function (data–model misfit)
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 (yi) contains daily means of three mesocosms of the following measurements:
dissolved inorganic carbon (DIC, mmol m-3),
dissolved inorganic nitrogen (DIN) (nitrate + nitrite, mmol m-3),
chlorophyll a (Chl a, mg m-3),
particulate organic nitrogen (PON, mmol m-3),
particular organic carbon (POC, mmol m-3),
particulate inorganic carbon (PIC, mmol m-3),
total alkalinity (TA, mmol m-3).
Like the data vector yi, the vector Hix represents mean values
of three simulated mesocosms for each calcification case (LC, MC, and HC). It combines results of model states:
C and N biomass concentrations of the photoautotrophs (PhyN & PhyC and CoccoN & CoccoC),
of zooplankton (ZooN & ZooC), of detritus (DetN & DetC), and carbon concentration
of transparent exopolymers particles (TEPC).
The vector of differences (di) between observation (yi) and model results Hix is given as
follows.
di=yi-Hix=DICi(NO3-+NO2-)iChlaiPONiPOCiPICiTAi︸data
-DICiDINi(Chlphy+Chlcocco)i(PhyN+CoccoN+ZooN+DetN)i(PhyC+CoccoC+ZooC+DetC+TEPC)iPICiTAi︸model results
For the cases LC, MC, and HC we calculated daily residual standard errors (σi) based on the measurements.
Unlike other variables, the estimation of the standard errors for DIC is not straightforward because of the different CO2 levels.
For the derivation of the standard errors we considered the differences (offsets) of the mean initial DIC concentrations between the different
CO2 treatments. DIC concentrations of those mesocosms that were initially exposed to high-CO2 (DIC) concentrations are “offset” – corrected so
that their initial mean DIC matches the initial mean of the present-day DIC concentrations. Mesocosms of the low-CO2 treatment were adjusted likewise.
In this manner, all initial mean DIC concentrations have become identical, but changes and variations (between the mesocosms) with respect to
these mean values remain. Thus, variances of the respective LC, MC, and HC mesocosms can be calculated after applying these (two) offset
corrections to all DIC data of the high- and low-CO2 treatments. Eventually, individual standard errors for the LC, MC, and HC
mesocosms are derived for all sampling dates.
The time-varying covariance matrices Ri are constructed with Si (with diagonal elements of standard errors,
see Eq. in Appendix ) together with some correlation matrices (C(y)). Correlations between
measurements were computed based on data of all nine mesocosms.
Two matrices C(y) have been derived from data for two distinct periods:
(1) the exponential growth phase and (2) the post-bloom period.
Ri=Si⋅C(y)⋅Si
Equation () is applied because correlations between observations can change from pre-bloom
period to post-bloom period. For example, PON and DIC are strongly negatively correlated during the exponential growth
phase but become weakly positively correlated during the post-bloom period, when both DIC and PON decrease.
The correlation matrices, C(y), for the two respective periods are also given in the Appendix .
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 (y) and covariances (R) from the respective three mesocosms of each case.
These daily data (yi) are available for a period of Nt=23 days, with subscript i indicating the day when measurements were made.
The elements of the parameter vector of interest (Θ) are those parameters listed in Table , including the initial value of
PON0 and initial condition parameters that further specify how PON0 is distributed between detritus, zooplankton,
coccolithophores, and the remaining photoautotrophs.
For a ML estimation of the parameters (including the initial conditions) we maximise the conditional
probability of explaining the data, given our model, together with a set of values assigned to the parameters (to each element of Θ):
p(y|Θ)=constant⋅exp[-12∑i=1NtdiTRi-1di]∝exp[-12J(Θ)].
The ML estimate of parameter values can be found by actually identifying the minimum of the exponent of p(y|Θ) of
Eq. (), since the constant term is independent of Θ. We thus compute and minimise the following cost function
J(Θ):
J(Θ)=∑i=1Ntyi-HixTRi-1yi-Hix.
We not only wish to identify the minimum of J(Θ) that corresponds with one best estimate of parameter values
(Θ^) but also confine a credible region of parameter estimates. This credible region tells us how reliable the
parameter estimates are (yielding lower and upper credibility limits) and resolves correlations (collinearities) between the parameters.
The parameter optimisation procedure implemented in this study is described in detail in the Appendix .
Maximum likelihood parameter estimates of three model solutions: low, medium, and high calcification (LC, MC, and HC).
Parameter
Description
LC
MC
HC
Units
PON0
Parameter of initial PON concentration
1.25
1.90
1.61
mmol N m-3
fdet
Parameter of initial detritus fraction
0.89
0.89
0.89
–
fzoo
Parameter of initial zoopl. fraction
0.72
0.63
0.88
–
fcocco
Parameter of initial coccolithophore fraction
0.39
0.88
0.40
–
Q0
Subsistence N : C ratio
5.5 ×10-2
4.2 ×10-2
4.2 ×10-2
–
αcocco
Photosynth. light absorpt. coeff. of coccolithoph.
1.40
0.50
1.66
mol C (g Chl a)-1 m2 W-1 d-1
αphy
Photosynth. light absorpt. coeff. of non-calcifiers
1.73
3.10
1.71
mol C (g Chl a)-1 m2 W-1 d-1
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.
Results
Parameter estimates for specific mesocosms with low, medium, and high calcification
The same seven model parameters (Table )
were optimised for all three calcification cases (LC, MC, and HC) independently, using data from respective mesocosms.
With our data assimilation approach we can thus specify commonalities and differences between model solutions for mesocosms with LC, MC, and HC.
Table lists all ML estimates, which correspond with the best model solutions obtained with the
Markov Chain Monte Carlo (MCMC) method.
Collinearities are expressed by the correlation coefficients of two parameter combinations, which we have also calculated based on results of
the MCMC method (Table ).
Credible interval limits for each parameter were derived from nonparametric probability densities of the MCMC estimates.
Figure shows cumulative density function (CDF) for corresponding posterior probability distributions.
The steeper the CDF increase is, the narrower the 95 % credible interval of the parameter estimate.
According to the width of credible intervals we find uncertainty ranges of initial conditions parameters fdet, fzoo, and PON0 to
be generally small for all three cases of calcification respectively. The initial condition
parameters are best constrained for the solution of medium calcification (MC). The parameter fcocco shows the largest
uncertainty for the HC case. A large fraction (≈ 90 %) of initial biomass comprises of detrital matter in all three solutions.
Table shows mean concentration values of PON0, DetN0, ZooN0,
CoccoN0,
and PhyN0 along with their uncertainties according to respective MCMC estimates.
Initial zooplankton concentration is highest in HC solutions. Thus, more photoautotrophic biomass is lost due to grazing by zooplankton and less by aggregation in model solutions for HC, which is reflected by the negative correlation between initial condition parameters fzoo and fdet.
For those parameters that do not specify the initial conditions we hoped to find that all credible intervals overlap, which would have suggested
insignificant differences between the estimates. A single set of values of these parameters could then be unambiguously used for simulations of
all nine mesocosms, independently of how the values of the initial conditions turned out to be. This is not the case, as can be seen in
Fig. and in the correlation coefficients
(Table ). Estimates of the subsistence quota (Q0) are lower for the mesocosms with high and medium calcification rates.
Apparently, lower Q0 and higher αcocco values are required to build up high coccolithophores biomass in mesocosms with
high calcification rates as initial coccolithophores concentration is low and grazing pressure is high.
Correlation coefficients of parameter estimates of low, medium, and high calcification model solutions (LC, MC, and HC).
Correlation coefficients ≥ 0.6 are marked bold face.
fdet
fzoo
fcocco
Q0
αcocco
αphy
PON0
-0.03/0.03/-0.30
0.57/0.48/0.51
-0.10/0.29/0.66
0.05/-0.20/-0.34
0.11/0.03/-0.56
-0.10/0.19/0.60
fdet
1
-0.51/-0.33/-0.92
0.13/0.01/-0.28
0.23/0.25/0.11
-0.15/-0.10/0.10
0.13/0.03/-0.40
fzoo
1
-0.47/0.24 / 0.5
-0.11/-0.30/-0.16
0.50/0.52/-0.38
-0.42/0.22/0.63
fcocco
1
0.10/-0.12/-0.25
-0.99/-0.15/-0.95
0.99/0.93/0.93
Q0
1
-0.10/-0.25/ 0.18
0.13/0.10/-0.26
αcocco
1
-0.97/-0.18/ -0.87
αphy
1
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 αcocco and for fzoo between MC and HC (see Fig. ).
Thus, we may have one or two out of the three MC mesocosms that might have been better assigned to the HC case. However, this is reflected in our
data assimilation results and we are primarily concerned with the upper and lower extremes in calcification, as resolved by the six mesocosms in the LC and HC cases.
Full variational range of model outputs due to uncertainties in parameter estimates.
Model ensembles of high, medium, and low calcification solutions compared with observations.
Data–model comparison
The variational range of parameter estimates (Fig. )
induce ensembles of model trajectories (model results) that are statistically indistinguishable (or equivalent).
Based on these posterior ensemble parameter estimates of all three calcification solutions we find a general good agreement between model
results and the data (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 a concentrations during the post-bloom period. Our model shows sharp draw down
in Chl a in all three solutions (HC, MC, and LC) during the post-bloom period, whereas observed Chl a values are more variable.
Variations in calcification in response to growth conditions
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 (ΔPIC : ΔC ≈ 0.5)
are smaller than the values under nutrient-depleted growth conditions. All ensembles of model solutions (LC, MC, and HC) reveal a similar behaviour,
with variations in ΔPIC : ΔC greater than 0.5 (up to 2.2) for growth rates between 0 and 0.3 d-1.
These variations depend on the light-acclimation state (e.g. θcocco), fluctuations in irradiance, and cell quota (QcoccoN).
The variations in ΔPIC : ΔC during the nutrient-depleted period can be attributed to fluctuations in carbon assimilation due to production
of TEPC .
Mean initial values of PON (PON0), detritus (DetN0), zooplankton (ZooN0), coccolithophores
(CoccoN0),
and bulk phytoplankton (PhyN0) according to posterior of the (initial condition) parameter estimates of three solutions:
low, medium, and high calcification (LC, MC, and HC).
State variable
LC/mmol N m-3
MC
HC
name
PON0
1.2 ± 0.01
1.9 ± 0.01
1.7 ± 0.1
DetN0
1.1 ± 4 × 10-4
1.7 ± 1 × 10-3
1.6 ± 0.01
ZooN0
0.1 ± 1 × 10-3
0.1 ± 1 × 10-3
0.2 ± 0.01
CoccoN0
0.02 ± 2 × 10-3
0.06 ± 1 × 10-3
0.01 ± 2 × 10-3
PhyN0
0.02 ± 2 × 10-3
0.01 ± 4 × 10-4
0.01 ± 3 × 10-3
Molar calcification-to-C-fixation ratio compared to net growth rate of coccos (μcocco)
in high and low calcification solutions.
Distinctions between model results of low and high calcification (LC and HC)
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 a are most conspicuous in this LC ensemble of optimal model results. Variability in the POC data of
the LC mesocosms is not captured by the model ensemble.
But simulation results (solid lines in Fig. )
match the POC mean of the three mesocosms. For PIC we also find a good agreement between model
ensemble results and data. However, a noticeable potential bias exists for the PIC response in the high-CO2 treatment (M1), where model
results overestimate PIC data during the maximum bloom period and shortly after nutrient depletion. This overestimation is more pronounced
in mesocosms with high CO2 treatment. The LC ensemble successfully reproduces amplitude of Chl a peak seen in data; this is
also the case in the solutions of HC mesocosms.
DIN is well resolved in the HC solutions (Fig. ).
Simulated Chl a also fits well to observations. HC solutions yield the largest variability in DIC, TA, and PIC amongst all optimised solutions,
which we mainly attribute to the large uncertainty ranges of the model parameters fcocco and αcocco. The HC solutions show
sharp drawdown in DIC during the bloom period compared to other solution (LC).
This can be explained by an enhanced calcification activity due to high growth rates of coccolithophores in HC during the bloom period.
Again, model overestimates observed PIC values (M3) under high-CO2 conditions shortly after the maximum of bloom.
PON is best reproduced in this HC case in comparison to LC. Although model HC solutions reproduce the entire variability in
observed PIC, the corresponding best fits (to M3, M4, and M9) underestimate PIC data.
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.
Integrated flux estimates of carbon and nitrogen (C and N budgets of mesocosms)
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
shows mean C and N flux estimates and their standard
errors of the LC solutions of the low- and high-CO2 treatments.
Figure shows the corresponding flux estimates for the HC solution. We learn from these flux estimates that the
simulated C and N mass flux estimates differ more between the mesocosms with different calcification rates than between the mesocosms
exposed to different CO2 levels.
In both cases (LC and HC), most inorganic carbon and nitrogen (DIC and DIN) are utilised by non-calcifiers
(≈ 56 % in case of HC and ≈ 64 % in the LC solution), despite the differences between LC and HC.
Generally, more carbon fixation (with C : N uptake ratio of 168:10 ≈ 17) occurs in the HC than in the LC
mesocosms (C : N uptake ratio ≈ 13). Flux budgets show that non-calcifiers clearly dominate in mesocosms with low calcification rates,
and in HC mesocosms coccolithophores and bulk phytoplankton biomasses are comparable
(Figs. and ).
Although grazing, in general, is high in HC mesocosms (Table ), there is a trend of higher grazing pressure on bulk phytoplankton
than on coccolithophores. This is shown by N flux estimates, where zooplankton gain nearly 57 % of their total biomass through grazing on
non-calcifiers in HC and LC. According to our model solutions, the coccolithophores are always less vulnerable
to grazing than the bulk phytoplankton. This model behaviour may not be fully conclusive, because we have no information about
the actual grazing rates or about grazing preferences.
A noticeable difference between high and low calcification model ensembles is in terms of mortality of zooplankton.
Higher mortality is seen in HC solutions. Since the carbon fixation in HC is high, exudation and leakage rates are also higher.
Accordingly, TEPC production is enhanced in HC solutions.
Unlike estimates of C flux, the N fluxes in HC and LC ensembles are similar, e.g. aggregation losses of phytoplankton and
of coccolithophores are 3 ± 0.4 and 2 ± 0.4 mmol N m-3 in HC, and 3.4 ± 2 × 10-3
and 1.5 ± 2 × 10-3 mmol N m-3 in LC respectively. Similarly, flux estimates of all mesocosms
show almost the same rates of DIN utilisation, excretion, exudation, and remineralisation.
Carbon and nitrogen fluxes estimated by the model in mesocosms with low observed calcification but different CO2
treatment, high (a) and low (b).
All the arrows that point downwards show flux estimates from the respective compartment on the right hand side,
whereas arrows pointing upwards show values on the left hand side.
Carbon and nitrogen fluxes estimated by the model in mesocosms with high observed calcification but different CO2
treatment, high (a) and low (b).
All the arrows that point downwards show flux estimates from the respective compartment on the right hand side,
whereas arrows pointing upwards show values on the left hand side.
Discussion
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
Q0, αcocco, and αphy).
An alternative data assimilation approach would be to optimise the physiological model parameters (Q0, αcocco, and αphy)
together with the initial conditions (PON0, fdet, fzoo, and fcocco) for mesocosms of one calcification case in a first step,
e.g. the MC case (using data of mesocosms M2, M5, and M7). In a second step we could have fixed the optimised physiological model parameters
Q0, αcocco, and αphy (as identified with data of, for example, the MC case) and would have then estimated only the
initial condition parameters for the other mesocosms, e.g. low and high calcification (LC and HC). This alternative approach does work (not shown),
but we learned that we may then put too much confidence into those estimates of Q0, αcocco, and αphy obtained
first, e.g. estimates for the MC mesocosms. It can even obscure the fact that collinearities exist between some initial condition estimates and
the other model parameters. Furthermore, with such an alternative approach we could end up with different estimates of the initial conditions,
if we would have started with data of either the HC or LC mesocosms first instead. The design of our data assimilation approach is more challenging but it is
better suited to disclose major uncertainties and collinearities in estimating initial conditions together with model parameters of algal growth.
Uncertainty ranges in parameter estimates and variability in model solutions
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 fcocco independently from estimates of the other physiological model parameters. This situation is aggravating but
not unusual . For instance, in a sensitivity study with a regional marine ecosystem model, stressed that
collinearities exist between initial conditions and the values assigned to the biological parameters.
Ratios of [POC] : [PON] and [DIC] : [DIN] determined from daily sampled noon values of model results.
Filled circles represent log10 (DIC : DIN) ratios.
Asterisk symbols represent POC : PON ratio over the duration of the experiment.
The posterior uncertainties in the estimates of the subsistence quota, (Q0), are rather small, if compared with the uncertainty ranges of the
other parameter estimates. Likewise, parameter estimates of the initial condition parameters PON0, fdet, and fzoo are fairly confined.
The variational range that we see in our model solutions is mainly induced by uncertainties in estimates of the
photosynthesis parameters αcocco and αphy and of fcocco.
The combination of these three parameters mainly determine the spread in model solutions with respect to the amount of C-fixation and
also calcification. This also explains why the ensemble model solutions exhibit only small variations in DIN and PON concentrations and
thus in our N-flux estimates.
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. ). The variability seen in the POC : PON ratio is thus mainly due to a
temporal variation in QN (N : C ratio of both photoautotrophs) and thus of the algal growth conditions.
The temporal variations in QN eventually disperse into zooplankton biomass and detritus,
inducing elevations of their respective C : N ratios during the post-bloom period. Another contribution to the elevation of POC : PON ratios is also
related to changes in POC because it constitutes concentrations of TEPC, which is explicitly resolved in our model.
Simulated nitrogen biomass concentrations of photoautotrophs and zooplankton in high and low calcification solutions.
Our results show an increase in molar ΔPIC : ΔC-assimilation at low net growth rates (μcocco) under
nutrient-limited conditions (Fig. ) in both HC and LC cases.
These variations are translated into some variability seen in the PIC : POC ratio. Variability in PIC : POC is discussed in
, where they collected and analysed data of diverse experiments and documented an increase (up to fourfold)
in values of cellular PIC : POC at relative growth rate (RGR) ≈ 0.2 d-1 and below in various CO2 treatments.
The reason for a sharp increase in the molar ΔPIC : ΔC-assimilation ratio at
low growth rates in our model is because of a down regulation of LHC. Such model behaviour
is in agreement with the interpretation of , who describe calcification as a process into which
the coccolithophores can channel excess energy. In order to maximise (optimise) growth rate under nutrient-depleted and high-light conditions, the model allocates more resources and energy to support nutrient acquisition than to the
LHC (indicated by low f0coccoLHC values). Since ΔPIC : ΔC-assimilation is inversely
related to f0coccoLHC in our model, an increase in calcification (relative to C-fixation) is obtained at low growth rates.
The maximum of ΔPIC : ΔC-assimilation ratio in our simulations are in accordance with those found
in .
Differences between high and low calcification solutions (HC and LC)
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.
stressed that variations in initial plankton composition can be responsible for large differences in the responses observed
on community level, thereby masking any possible CO2 effect on photosynthesis or calcification. Briefly, our results not only support the findings
of , they provide additional insight to the problem of resolving a CO2 response in the presence of variability in
measurements. One added message compared to is that our mass flux estimates are shown to differ more between
the different calcification solutions than between the different CO2 treatments. This situation exemplifies that simulation results
(e.g. future model projections) may involve uncertainties in flux estimates that are larger than the CO2 effect introduced to the model
(e.g. by following Findlay et al., 2011). Another added message is that initial conditions may not be independently estimated from estimates
of phytoplankton growth parameters, like αphy and αcocco. This is particularly relevant for model assessment and model
analyses of mesocosm experiments. We stress that the original design of the experiment was meaningful, in particular with respect to the initial
filling of the mesocosms in the PeECE-1 experiment. The retrospective separation of the CO2 response signal from the system's
variability was only possible because mesocosms with similar initial conditions were subject to different CO2 concentrations. Such separation
would be more difficult, in retrospect, if mesocosms with similar initial conditions would have been (by chance) exposed to similar CO2 levels.
From a modelling perspective it is helpful to know about the initial individual mass contributions to PON0, including details in the initial
composition of the plankton. But the level of compositional detail remains unclear, since these variations in individual plankton composition
will in the end always translate into some variational (uncertainty) range in, for example, the initial photo-acclimation state, since our model approach
only distinguishes between calcifiers and all other, non-calcifying, phytoplankton.
These considerations were disregarded when we designed this study and we originally thought of the importance of the
relative mass distributions between the state variables resolved by our model, while imposing fixed initial stoichiometric
ratios (C : N and Chl a : N). It seems plausible to allow for some variations of the initial stoichiometric ratios as well.
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 + CoccoN) = 80:10:1 for HC and 28:3:1 for LC).
The difference between these ratios point towards net photoautotrophic growth rates that are higher in the LC case than in the HC case,
since losses due to grazing and aggregation must be lower in the LC case. However, the initial conditions in mesocosms of the LC case do
not automatically yield model solutions of the highest photoautotrophic growth. Instead we find overall reduced growth rates but some
pronounced differences in the relative proportions of biomass between the coccolithophores and the non-calcifying phytoplankton
(Fig. ).
The reason for these differences lies primarily in the relative differences between the estimates of the physiological parameters,
with estimates of αcocco always being smaller than of αphy. The photosynthetic
efficiency of the coccolithophores remains clearly smaller (LC case) or can become similar (HC case) relative
to the other, non-calcifying, phytoplankton. Major differences between the LC and HC solutions can thus be attributed to
higher αcocco values (median αcocco = 1.7 mol C (g Chl a)-1 m2 W-1 d-1) in
HC posterior distribution compared to LC (median αcocco = 1.4 mol C (g Chl a)-1 m2 W-1 d-1).
The estimates of αcocco are negatively correlated with the estimates of fcocco (Table 4) and
we may therefore look on the combination of the two parameters. To do so we compare two extreme solutions, selected from the ensemble
solutions of LC and HC respectively. One extreme solution yields the lowest calcification among all HC solutions, based on the parameter
combination (αcocco = 1.84 mol C (g Chl a)-1 m2 W-1 d-1 , fcocco = 0.34).
The other selected solution represents the highest calcification of all LC solutions, which corresponds with
(αcocco = 1.59 mol C (g Chl a)-1 m2 W-1 d-1 , fcocco = 0.35).
Thus, it is mainly the photosynthetic efficiency αcocco to which the model solution is highly sensitive.
Hence, a difference of ≈ 0.3 mol C (g Chl a)-1 m2 W-1 d-1 can effectively determine the
differences in our simulations with respect to rates of carbon fixation and calcification.
The build-up of comparable nitrogen biomass of coccolithophores and bulk
phytoplankton in HC solutions are achieved with identical Q0 values and only nuanced differences in values
between αcocco and αphy. In contrast, bulk phytoplankton (non-calcifiers) out-compete coccolithophores
during the bloom period in the LC solutions (Fig. ).
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 CO2 treatment (future), second row medium CO2
treatment (present), and third row low CO2 treatment (glacial).
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 CO2 effect in the model, for solutions with lowest, medium, and highest calcification rates.
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 (θcoccoN = θphyN) and N : C
(Qcocco = Qphy) ratios for all nine
mesocosms (and thus for LC, MC, and HC), or (b) because of unresolved varying conditions in irradiance.
To impose identical surface PAR forcing on all nine mesocosms might not be appropriate, and the arrangement of neighbouring
mesocosms may have caused some shading effects. From the available data and with our model approach it is not possible to resolve
such varying conditions afterwards.
Model biases
Model biases disclose systematic deviations of simulation results from observations, which may point towards (i) erroneous model counterparts to
observations (definition of H(x) in Eq. ) or (ii) deficiencies in model dynamics (errors in x).
Some bias is related to the increase in PON concentration during the late phase of exponential growth
(between days 10 and 12, Fig. ).
The noticeable bias (temporal offset) in simulated PON concentrations can be explained with an apparent overestimation of initial coccolithophore
biomass. The estimates of fcocco turned out to be highest, if compared with the estimates for the low and high calcification (LC and HC)
model solutions. Furthermore, the range of credible values for fcocco is small (Fig. ). Both estimates of fcocco
and of PON0 lead to an initial biomass concentration of coccolithophores that is approximately three times higher than in the LC case
and even six times the initial concentration of the model solutions for HC.
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 Micromonas spp.) and their decline was observed during the
early pre-bloom period of the PeECE-I experiment .
This explains why our simulated Chl a and PON concentrations are lower compared to observations between day 1 and day 4.
Another discrepancy between simulated and observed Chl a exists during the post-bloom period.
We assume that this bias is mainly because we do not account for detrital chlorophyll pigments (presumably of inactive or destroyed cells)
in our model. Formation of detritus is associated with the aggregation of coccolithophores and of the other phytoplankton to form
detritus (simulated as a transfer of algal biomass into detritus) in our model, and the fate of Chl a within the detritus compartment
remains unresolved. Once N and C biomass of the photoautotrophs are transformed to detritus, an associated flux of
Chl a is disregarded. An explicit consideration of the fate of Chl a would likely improve model performance
and some refinements in this respect are recommended for the future.
Results of our data–model synthesis also exhibit a small but distinctive
bias in the calcification response to elevated CO2 levels. The
distinctions we made with respect to mesocosms of LC, MC, and HC helped us to
identify such bias. This bias implies that the CO2 effect on
calcification, as introduced to our model, is slightly smaller than in the
observations, which will be discussed in detail hereafter.
Disentangling CO2 effect from the observed variability in PIC
We considered a simple CO2 relationship that mimics only OA effects on calcification. It is a dependency that was adopted from the meta-analysis
of . With this CO2 dependence we can already capture differences in PIC formation. The CO2 sensitivity that we introduced to
our model is only effective with respect to the ratio of calcification versus C-fixation, thereby reducing the overall calcification rate under high-CO2
conditions. This effect turned out to be small compared to the total variability seen in PIC data.
According to our model setup we do not consider any potential changes in vulnerability to predation (or edibility) of the coccolithophores
due to elevated CO2. Likewise, any additional CO2 effects, e.g. on the rate of aggregation, are not accounted for.
Such effects remain unresolved, and therefore the comparison of our budget calculations yield only small differences between high
and low CO2 levels, in particular with respect to nitrogen flux estimates. Thus, differences in C and N budgets between the two
extreme calcification cases, LC and HC, are more pronounced than between different levels of CO2. To resolve consecutive ecological
effects in response to a reduction of the relative calcification rate we would have needed explicit data, i.e. revealing differences in grazing
and aggregation rates between the individual mesocosms. With the PON and POC data used in our data assimilation approach it is not possible to
distinguish between different coccolithophore loss terms like grazing and aggregation, since detritus and zooplankton are both constituents
of the same PON and POC measurements.
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) CO2 treatments. In other words, for every LC, MC, and HC case we
resolve three mesocosms, of which each was subject to different CO2 levels. This way we have separated differences between
LC, MC, and HC from variations induced by a CO2 effect.
Doing so reveals PIC formation to be systematically overestimated by the model for all
mesocosms of the future treatment (Figs. and , MC case not shown).
In contrast to , our results show an early onset of calcification in mesocosms of the high-CO2 treatment
between day 10 and day 15. It indicates that the CO2 effect introduced to our model is likely too weak.
This becomes evident according to positive model–data residuals in PIC between day 13 and day 18
for those mesocosms with future treatment (Fig. ). It is not evident for the
glacial and present-day CO2 treatments, where the corresponding residuals do not show a systematic positive offset.
Figure () shows the total variability seen in PIC data together with the full variational range of all ensemble model solutions.
In addition, we depict those ranges in simulated PIC that are solely due to the CO2 effect, based on the two extreme calcification solutions
(lowest and highest simulated PIC) and the best model solution (according to the lowest cost function values) for the MC mesocosms. If we compare the
simulated CO2 response signal on calcification with the total variability in PIC (in Fig. ), we find that the CO2 effect remains small.
This situation demonstrates the difficulty in isolating a distinctive CO2 signal from the total variability seen in PIC observations.
However, with our model-based analysis approach this CO2 signal becomes detectable.
Conclusions
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 CO2 response signal may still be identifiable, as long as mesocosms
that reveal the strongest similarities (with respect to initial composition of plankton and their physiological state) are not used as replicates
for similar CO2 conditions (perturbations). Instead, mesocosms with similar initial conditions should be exposed to different levels of OA.
Such favourable starting conditions were met in the mesocosm experiment described in and ,
as well as in the experiment of .
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 αphy and αcocco and the initial fraction of coccolithophores determined
by fcocco. Therefore, it is not possible to identify initial concentration of photoautotrophs independently of parameters responsible
for phytoplankton growth in HC, MC, and LC model solutions.
This was only found because we optimised initial conditions together with physiological parameters for HC, MC, and LC mesocosms separately.
By this separation we could better specify the CO2 effect on PIC formation.
In doing so, we could identify a systematic overestimation of calcification in our model and we conclude
that our simulated CO2 effect on PIC formation is even too weak.