Potential sources of variability in mesocosm experiments ... · sition succeeded in the experiments (Emiliania huxleyi was the major contributor to POC in PeECE II (Engel et al.,2008)

Biogeosciences 14 1883ndash1901 2017wwwbiogeosciencesnet1418832017doi105194bg-14-1883-2017copy Author(s) 2017 CC Attribution 30 License

Potential sources of variability in mesocosm experiments on theresponse of phytoplankton to ocean acidificationMaria Moreno de Castro1 Markus Schartau2 and Kai Wirtz1

1Helmholtz-Zentrum Geesthacht Centre for Materials and Coastal Research Geesthacht Germany2GEOMAR Helmholtz Centre for Ocean Research Kiel Kiel Germany

Correspondence to Maria Moreno de Castro (mariamorenodecastrooutlookcom)

Received 9 March 2016 ndash Discussion started 8 April 2016Revised 6 March 2017 ndash Accepted 13 March 2017 ndash Published 6 April 2017

Abstract Mesocosm experiments on phytoplankton dynam-ics under high CO2 concentrations mimic the response ofmarine primary producers to future ocean acidification How-ever potential acidification effects can be hindered by thehigh standard deviation typically found in the replicates ofthe same CO2 treatment level In experiments with multipleunresolved factors and a sub-optimal number of replicatespost-processing statistical inference tools might fail to de-tect an effect that is present We propose that in such casesdata-based model analyses might be suitable tools to unearthpotential responses to the treatment and identify the uncer-tainties that could produce the observed variability As testcases we used data from two independent mesocosm ex-periments Both experiments showed high standard devia-tions and according to statistical inference tools biomass ap-peared insensitive to changing CO2 conditions Converselyour simulations showed earlier and more intense phytoplank-ton blooms in modeled replicates at high CO2 concentrationsand suggested that uncertainties in average cell size phyto-plankton biomass losses and initial nutrient concentrationpotentially outweigh acidification effects by triggering strongvariability during the bloom phase We also estimated thethresholds below which uncertainties do not escalate to highvariability This information might help in designing futuremesocosm experiments and interpreting controversial resultson the effect of acidification or other pressures on ecosystemfunctions

1 Introduction

Oceans are a sink for about 30 of the excess atmosphericCO2 generated by human activities (Sabine et al 2004) In-creasing carbon dioxide concentration in aquatic environ-ments alters the balance of chemical reactions and therebyproduces acidity which is known as ocean acidification (OA)(Caldeira and Wickett 2003) Interestingly the sensitivityof photoautotrophic production of particulate organic carbon(POC) to OA is less pronounced than previously thoughtSeveral studies on CO2 enrichment revealed an overall in-crease in POC (eg Schluter et al 2014 Eggers et al 2014Zondervan et al 2001 Riebesell et al 2000) but other stud-ies did not detect CO2 effects on POC concentration (egJones et al 2014 Engel et al 2014) or primary produc-tion (Nagelkerken and Connell 2015) General compilationstudies that document controversial results are eg Riebe-sell and Tortell (2011) and Gao et al (2012)

In some experiments the different treatment levels iedifferent CO2 concentrations have been applied in parallelrepetitions also known as replicates or sample units Thiswas the case in several CO2 perturbation experiments withmesocosms (Riebesell et al 2008) Often high variances arefound in measurements among replicates of similar CO2 lev-els (Paul et al 2015 Schulz et al 2008 Engel et al 2008Kim et al 2006 Engel et al 2005) It is this variance in datathat reflects system variability thereby introducing a severereduction in the ratio between a true acidification responsesignal and the variability in observations Ultimately the ex-perimental data exhibit a low signal-to-noise ratio

Mesocosms typically enclose natural plankton communi-ties which is a more realistic experimental setup compared to

Published by Copernicus Publications on behalf of the European Geosciences Union

1884 M Moreno de Castro et al Potential sources of variability in mesocosm experiments

batch or chemostat experiments with monocultures (Riebe-sell et al 2008) Along with this mesocosms allow for alarger number of possible planktonic interactions that pro-vide opportunities for the spread of uncontrolled heterogene-ity Moreover physiological states vary for different phyto-plankton cells and environmental conditions For this reasonindependent experimental studies at similar but not identi-cal conditions might yield divergent results The variabil-ity in data of mesocosm experiments is thus generated byvariations of ecological details ie small differences amongreplicates of the same sample such as in species abundancenutrient concentration and metabolic states of the algae atthe initial setup of the experiments Differences of these fac-tors often remain unresolved and might therefore be treatedas uncertainties in a probabilistic approach

To account for all possible factors that determine all differ-ences in plankton dynamics is practically infeasible whichalso impedes a retrospective statistical analysis of the ex-perimental data However since unresolved ecological de-tails might propagate over the course of the experiment it ismeaningful to consider a dynamical model approach to up-grade the data analysis From a modeling perspective someimportant unresolved factors translate into (i) uncertainties inspecifying initial conditions (of the state variables) and (ii)uncertainties in identifying model parameter values Herewe apply a dynamical model to estimate the effects of eco-physiological uncertainties on the variability in POC concen-tration of two mesocosm experiments Our model describesplankton growth in conjunction with a dependency betweenCO2 utilization and mean logarithmic cell size (Wirtz 2011)The structure of our model is kept simple thereby reducingthe possibility of overparameterizing the mesocosms dynam-ics The model is applied to examine how uncertainties inindividual factors namely initial conditions and parameterscan produce the standard deviation of the distribution of ob-served replicate data Our main working hypotheses on theorigins of variability in mesocosm experiments are the fol-lowing

ndash Differences among replicates of the same sample canbe interpreted as unresolved random variations (nameduncertainties hereafter)

ndash Uncertainties can amplify during the experiment andgenerate considerable variability in the response to agiven treatment level

ndash Which uncertainties are more relevant can be estimatedby the decomposition of the variability in the experi-mental data

For our data-supported model analysis of variability de-composition we consider the propagation of distributions(JCGM 2008b) to seek potential treatment responses thatare masked by the variability in observations of two indepen-dent OA mesocosm experiments namely the Pelagic Enrich-ment CO2 Experiment (PeECE II and III) The central idea

is to produce ensembles of model simulations starting froma range of values for selected factors The range of valuesfor these selected factors is determined so as the variabilityin model outputs does not exceed variability in observationsover the course of the experiment The margins of the varia-tional range of each factor were thus confined by the abilityof the dynamical model to reproduce the magnitude of thevariability observed in POC These confidence intervals de-scribe the tolerance thresholds below which uncertainties donot escalate to high variability in the modeled replicates andcan serve as an estimator of the tolerance of experimentalreplicates to such uncertainties This information can be im-portant to ensure reproducibility allowing for a comparisonbetween the results of different independent experiments andincreasing confidence regarding the effects of OA on phyto-plankton (Broadgate et al 2013)

2 Method

Potential sources of variability are estimated following a pro-cedure already applied in system dynamics experimentalphysics and engineering (JCGM 2008b) The basic princi-ples of uncertainty propagation are summarized here usinga six-step method (see Fig 1) Steps 1 and 2 are describedin Sect 21 and comprise a classical model calibration (us-ing experimental data of biomass and nutrients) to obtain thereference run representing the mean dynamics of each treat-ment level In this way we found the reference value for themodel factors ie parameters and initial conditions Steps 3and 4 described in Sect 22 include the tracked propagationof uncertainties by systematically creating model trajectoriesfor POC each one with a slightly different value of a modelfactor In steps 5 and 6 we estimated the thresholds of themodel-generated variability and the effect of the uncertaintypropagation (also explained in Sect 22)

21 Model setup data integration and description ofthe reference run

In this section we describe the biological state that was usedas reference dynamics Our model resolves a minimal set ofstate variables insofar monitored during experiments that areassumed to be key agents of the biological dynamics Modelequations are shown in Table 1 Reference values of the pa-rameters are shown in Table 2 An exhaustive model docu-mentation is given in Appendix A The model simulates ex-perimental data from the Pelagic Enrichment CO2 Experi-ment (PeECE) a set of nine outdoor mesocosms placed incoastal waters close to Bergen (Norway) during the springseasons of 2003 (PeECE II) and 2005 (PeECE III) In boththe experiments blooms of the natural phytoplankton com-munity were induced and treated in three replicates for thefuture present and past CO2 conditions (Engel et al 2008Schulz et al 2008 Riebesell et al 2007 2008) Experimen-

Biogeosciences 14 1883ndash1901 2017 wwwbiogeosciencesnet1418832017

M Moreno de Castro et al Potential sources of variability in mesocosm experiments 1885

Table 1 States variables and their dynamics

State variable Dynamical equation Ini cond Units

Phytoplankton carbon dPhyCdt = (P minusRminusL) middotPhyC 25 micromol-CLminus1

Phytoplankton nitrogen dPhyNdt = V middotPhyCminusL middotPhyN 04 micromol-NLminus1

Nutrient concentration dDINdt = r middotDHNminusV middotPhyC 8plusmn 05lowast micromol-NLminus1

14plusmn 2lowastlowast micromol-NLminus1

Detritus and heterotrophs C dDHCdt = L middotPhyCminus (s middotDHC+ r) middotDHC 01 micromol-CLminus1

Detritus and heterotrophs N dDHNdt = L middotPhyNminus (s middotDHN+ r) middotDHN 001 micromol-NLminus1

lowast PeECE II lowastlowast PeECE III

Table 2 Parameter values used for the reference run 〈φi〉 All values are common to both PeECE II and III experiments only the meantemperature (determined by environmental forcing) and the averaged cell size in the community are different since different species compo-sition succeeded in the experiments (Emiliania huxleyi was the major contributor to POC in PeECE II (Engel et al 2008) but also diatomssignificantly bloomed during PeECE III (Schulz et al 2008)

Parameter Value Units Variable Reference

aCO2 carbon acquisition 015 (micromol-C)minus1 L PhyC this studyaPAR light absorption 07 micromolphotminus1 m2 PhyC this studyalowast carboxylation depletion 015 micromminus1 PhyC this studyPmax max photosyn rate 12 dminus1 PhyC this studyQlowastsubs subsist quota offset 033 mol-N (mol-C)minus1 PhyC this studyαQ Qsubs allometry 04 ndash PhyC this studyζ costs of N assimil 2 mol-C (mol-N)minus1 PhyC Raven (1980)` mean size Ln(ESD1 microm) 16 ndash PhyC PhyN DIN PeECE II data

18 ndash PeECE III datafp fraction of protein in 04 ndash PhyC PhyN DIN this study

photosyn machineryV lowastmax max nutrients uptake 05 mol-N (mol-Cd)minus1 PhyC PhyN DIN this studyAff nutrient affinity 02 (micromol-Cd)minus1L PhyC PhyN DIN this studyαV Vmax allometry 045 ndash PhyC PhyN DIN Edwards et al (2012)Llowast photosyn losses coeff 11times 10minus3 (micromol-Cd)minus1 PhyC PhyN and this study

DHC DHNrlowast DIN remin amp excret 15 dminus1 DHC DHN this studys DH sinking 10 L(micromol-Cd)minus1 DHC DHN this studyTref reference temperature 83 Celsius PhyC PhyN and PeECE II data

101 Celsius DIN DHC DHN PeECE III data

tal data are available via the data portal Pangaea (PeECE IIteam 2003 PeECE III team 2005)

Field data of aquatic CO2 concentration temperature andlight were used as direct model inputs (see Appendix B)Measurements of POC particulate organic nitrogen (PON)and dissolved inorganic nitrogen (DIN) were used for modelcalibration Although both the experiments differ in theirspecies composition environmental conditions and nutri-ent supply the same parameter set was used to fit PONPOC and DIN from PeECE II and III (ie a total of 54series of repeated measures over more than two weeks) afeature indicating the model skills In addition the model

was validated with another 36 series of biomass and nutri-ents data from an independent mesocosm experiment ((Paulet al 2014) data not shown) The experimental POC andPON data were redefined for a direct comparison with modelresults (see Appendix C) since some contributions (egpolysaccharides and transparent exopolymer particles) re-main unresolved by our dynamical equations State variablesof our model comprise carbon and nitrogen contents of phy-toplankton PhyC and PhyN and DIN as representative forall nutrients The dynamics of non-phytoplanktonic compo-nents ie detritus and heterotrophs (DH) are distinguished

wwwbiogeosciencesnet1418832017 Biogeosciences 14 1883ndash1901 2017

Factor mean (from ref run)

Factor values

Step 4POC

standard deviation

Frequency

POC at a given dayDay

Step 1model

calibration

Model-data fit using biomass and nutrients data (POC PON and DIN) from 2 mesocosm experiments with

3 treatment levels times 3 replicates

Step 2reference run per treatment

Parameter set minimizing model-data residualsDINPOC

Step 3factor

standard deviation

Step 5 tolerance of

mesocosms to uncertainty

Step 6 sensitivity coefficient

Estimated by the uncertainty such that simulated POC standard deviation do not exceed experimental POC standard deviation

dayCon

For each factor

Virtual replicates for that factor

Uncertainty

Variability

Residuals

Model ref run Sample mean

=UncertaintyVariability

Figure 1 Variability decomposition method based on uncertaintypropagation (summary of the basic principles given in Sect 511and 562 and Annex B in JCGM 2008b)

by DHC and DHN Thus in our study POC= PhyC+DHCand PON= PhyN+DHN

The mean cell size in the community represented as thelogarithm of the mean equivalent spherical diameter (ESD)was used as a model parameter It determines specific eco-physiological features by using allometric relations that arerelevant for the computation of subsistence quota as well asnutrient and carbon uptake rates Regarding the latter to re-solve sensitivities to different DIC conditions we used a rela-tively accurate description of carbon acquisition as a functionof DIC and size It has been suggested by previous observa-tions and models that ambient DIC concentration increasesprimary production (eg Schluter et al 2014 Rost et al2003 Zondervan et al 2001 Riebesell et al 2000 Chen1994 Riebesell et al 1993 Riebesell and Tortell 2011) andmean cell size in the community (Sommer et al 2015 Eg-gers et al 2014 Tortell et al 2008) While state-of-the-artmodels such as Artioli et al (2014) used empirical biomassincrease to describe OA effects we adopted and simplifieda biophysically explicit description for carbon uptake fromWirtz (2011) where the efficiency of intracellular DIC trans-port has been derived as a function of the mean cell size`= ln(ESD1microm) and CO2 concentration For very large

cells the formulation converges to the surface to volumeratio which in our notation reads eminus` In contrast the de-pendence of primary production on CO2 vanishes for (doesnot apply to) picophytoplankton the rate limitation by sub-optimal carboxylation then reads

fCO2 =

(1minus eminusaCO2 middotCO2

1+ alowast middot e(`minusaCO2 middotCO2)

The specific carbon absorption coefficient aCO2 reflects size-independent features of the DIC acquisition machinery (forinstance the carbon concentration mechanisms Raven andBeardall 2003) The coefficient alowast represents carboxylationdepletion

22 Uncertainty propagation

We considered that uncertainties were only present in theinitial setup of the system this allowed us to perform adeterministic non-intrusive forward propagation of uncer-tainty which neglects the possible coupling between uncer-tainties and temporal dynamics unlike in intrusive methods(Chantrasmi and Iaccarino 2012) involving stochastic dy-namical equations with time-varying uncertainties (Toral andColet 2014 de Castro 2017 Forward refers to the fact thatunresolved differences among replicates simulated as vari-ations of the model control factors are propagated throughthe model to project the overall variability in the system re-sponse in contrast to backward methods of parameter esti-mation where the likelihood of input values is conditionedby the prior knowledge of the output distribution (as for in-stance in Larssen et al 2006)

Our approach is based on a Monte Carlo method for thepropagation of distributions It is based on the repeated sam-pling from the distribution for possible inputs and the evalu-ation of the model output in each case (JCGM 2008b) Nextthe overall simulated POC variability is compared with thatin POC experimental data (ie the mean trends of the treat-ment levels as well as the standard deviations are comparedthe former for the calculation of the reference run and the lat-ter for the uncertainty propagation) Among the available ex-perimental data we favored POC over PON and DIN in theuncertainty propagation analysis since it is usually the tar-get variable of OA effects and shows the highest variabilityA variability decomposition with more than one dependentvariable (equivalent to a multivariate ANOVA design for in-stance) is beyond of the scope of the study The comparisonbetween simulated and experimental variability in POC helpsin the identification of the changes in physiological state andcommunity structure that are the main potential contributorsto the variability

We considered model factors φi with i = 1 N = 19consisting of 14 process parameters and 5 initial conditionsfor the state variables Their reference values 〈φi〉 wereadjusted to yield model solutions reproducing the mean of

each treatment level (steps 1 and 2 Tables 1 and 2) Totest our first hypothesis factor variations representing poten-tial uncertainties are introduced as random values distributedaround 〈φi〉 with standard deviation 4φi To calculate 4φi we first generate 104 simulations each one with a differentfactor value φi (steps 3 and 4) The ensemble of model so-lutions for each factor and treatment level simulates the po-tential experimental outcomes hereafter referred to as ldquovir-tual replicatesrdquo (see Appendix D) The factor value for eachPOC trajectory is randomly drawn from a normal distribu-tion around the factor reference value 〈φi〉 (same distributionis assumed by popular parametric statistical inference toolssuch as regressions and ANOVA Field et al 2008) For ev-ery treatment level and at every time step we calculated theensemble average of the virtual replicates 〈POCmod

i 〉 and thestandard deviation 4POCmod

i Thus 4φi is the standard de-viation of the distribution of factor values such as4POCmod

i which do not exceed the standard deviation of the experimen-tal POC data4POCexp for any mesocosm at any given time(step 5) The effect of variations of φi on the variability (step6) is given as follows

εi =4POCmod

4φi (2)

This ratio expresses the maximum variability a factor cangenerate 4POCmod

i relative to the associated range of thatfactor variations 4φi to ensure that 4POCmod

i is the closestto 4POCexp at any time In general εi defines how much ofthe uncertainty of a dependent variable Y (here Y = POC)is explained by and the uncertainty of the input factors φi a proxy of which is known as the sensitivity coefficientci =

partYpartφi

in the widespread formula to calculate error prop-agation (Ellison and Williams 2012) also known as law ofpropagation of uncertainty (JCGM 2008a)

(4Y )2 =

Nsumi=1

c2i middot (4φi)

This expression is based on the assumption that changesin Y in response to variations in one factor φi are inde-pendent from those owing to changes in another factor φj and that all changes are small (thus cross-terms and higher-order derivatives are neglected) Where no reliable mathe-matical description of the relationship Y (φi) exists (in ourcase only an expression for the rate equation dPOCdt isknown (see Table 1) but not its analytical solution ie POC)ci can be evaluated experimentally (Ellison and Williams2012 JCGM 2008a) As mentioned in the Introduction andAppendix A such high-dimensional multi-factorial measure-ments are costly in mesocosm experiments Therefore weobtained equivalent information by numerically calculatingεi Such approximations to sensitivity coefficients calculatedby our Monte Carlo method of uncertainty propagation cor-respond to taking all higher-order terms in the Taylor se-ries expansion into account since no linearization is required

(see Sect 510 and 511 and Annex B in JCGM 2008b) Astraightforward extension including the cross-terms showingsynergistic uncertainties effects as in an experimental multi-way ANOVA design requires the assumption of joint distri-butions for the uncertainty of factors and the calculation ofcovariance matrices a considerable effort that is beyond ofthe scope of this paper

Hereafter the standard deviation of any given factor iefactor uncertainty will be given as percentage of the refer-ence values and will be called 48i The actual factor rangeis given as4φi =

48i middotφi100 Strong irregularities in the standard

deviations of experimental POC data (for instance small4POCexp at day 8 in Fig 2p) translates to remarkably en-hanced or reduced sensitivity coefficients if the modelndashdatacomparison would be performed at a daily basis Thereforewe considered the temporal mean of the standard deviationper phase ie prebloom bloom and postbloom We inferredphases for PeECE II from Engel et al (2008) and for PeECEIII from Schulz et al (2008) and Tanaka et al (2008)

To numerically calculate the ensemble of 104 POC tra-jectories per factor (ie the virtual replicates see Fig 8)we applied the Heun integration method with a time step of4times 10minus4 (about 35 s of experimental time) The number ofsimulated POC time series is chosen such as a higher num-ber of model realizations ie a higher number of virtualreplicates will produce the same results (see Adaptive MonteCarlo procedure Sect 79 in JCGM 2008b) We dismissedthe negative values that randomly appeared when drawing104 values from the normal distribution of factor values thisreduction in the number of trajectories did not affect the re-sults

Environmental data showed low variability among simi-lar treatment replicates (see Fig 9) suggesting a non-directrelation between variations in environmental factors amongreplicates and the observed biomass variability Thereforewe focused on uncertainties in ecophysiology and commu-nity composition and used environmental data as forcingPerturbations of the similarity among replicates producedby strong changes in environmental conditions (storms dys-functional devices etc) or by errors in manipulation or sam-pling procedures are not within the scope of this work Af-ter a few decades the current state-of-the-art of experimentaltechniques for running plankton mesocosms is advanced Webelieve such differences are of low impact or well understoodin terms of their consequences for final outcomes (Riebesellet al 2010 Cornwall and Hurd 2015)

Notably our analysis suggested sufficient (but not neces-sary Brennan 2012) causes of uncertainties in mesocosmexperiments Variations in model characterization includingstructural variability (Adamson and Morozov 2014 Fuss-mann and Blasius 2005) or uncertainties in model parame-terization (Kennedy and OrsquoHagan 2001) or comparisons todifferent uncertainty propagation methods (de Castro 2017)require further extensive analyses which is beyond the scopeof this study However we performed a series of preceding

PON (micromolminusN Lminus1

POC (micromolminusC Lminus1

DIN (micromolminusN Lminus1

(c) F uture CO (aq)2

(f) Present CO (aq)2

2 4 6 8 10 12 14 16 18

(i) Past CO (aq)2

Figure 2 Solid lines show reference runs for POC PON and DIN simulating the mean of the replicates per treatment level with differentcolors for the three experimental CO2 setups Dots are replicated data from the Pelagic Enrichment CO2 Experiment (PeECE II) for newlyproduced POC and PON ie starting values at day 2 were subtracted from subsequent measurements as in Riebesell et al (2007)

model analyses (including uncertainty propagation) by usingslightly different model formulations (data not shown) Fromthese preceding analyses we found that different model for-mulations can lead to quantitatively different confidence in-tervals but leave the final results qualitatively unchanged

3 Results

31 CO2 effect on POC dynamics

Our model reproduces the means of PON POC and DINexperimental data per treatment level ie for the futurepresent and past CO2 conditions in two independent PeECEexperiments (Figs 2 and 3) For PeECE II PON is moder-ately overestimated and postbloom POC is slightly underes-timated Nonetheless the model represents the experimentaldata with similar precision than the means of experimentalreplicates (see Appendix E) The means of the same treat-ment replicates and their associated standard deviations aretypically used to represent experimental data (see Fig 1b inEngel et al 2008 for PeECE II or Fig 8a in Schulz et al2008 for PeECE III) The means are in the foundations ofthe statistical inference tools that did not detect acidificationresponses for PeECE II and III However with our mechanis-tic model-based analysis phytoplankton growth in the futureCO2 conditions showed an earlier and elevated bloom withrespect to past CO2 conditions The future and past referencetrajectories limit the range of the CO2 enrichment effect as

shown by the dark gray area in Fig 4 POC variability owingto variations in model factors simulating experimental uncer-tainties is plotted as the light gray area in the figure Our re-sults suggest that avoiding high POC standard deviations thatpotentially mask OA effects in experimental data requires thereduction of the factor variations triggering variability duringthe bloom

32 CO2 effect on uncertainty propagation

The estimation of the tolerance thresholds of the dynamicsto uncertainty propagation for the two test-case experimentsper acidification levels and per factor uncertainty are listedin Table 3 We investigated the potential interaction of thetreatment and the uncertainty effects on the tolerance by alinear mixed-effects model with φi as the random factor (RCore Team 2016) The synergistic effect between the factoruncertainty and the treatment levels was found to be non-significant (F = 29 with p = 006) Therefore the thresh-olds do not appear to statistically depend on the treatmentlevel even when the standard deviation of the measured POCdata 4POCexp for the future and past acidification condi-tions were on average about 70 larger than the standarddeviation of the present conditions (POC experimental datain Figs 2 and 3 are more spread in the future and past concen-trations than in the present concentration) Despite the lowstatistical power of this test (only data from two indepen-dent samples the two PeECE experiments were available)

Table 3 Tolerance of mesocosms experiments to differences among replicates given as a percentage of the reference factor value listedin Tables 1 and 2 According to our model projections above these thresholds the simulated variability 4POCmod

i exceeds the observed

variability 4POCexp Main contributors to the simulated variability during the bloom are highlighted in bold (see Sect 3)

Factor φi 48i () AveragedPeECE II PeECE III tolerance

Future Present Past Future Present Past ()

PhyC(0) initial phyto C biomass 68 49 46 78 60 100 67plusmn 6PhyN(0) initial phyto N biomass 26 19 22 21 16 29 22plusmn 4DIN(0) initial DIN 20 28 29 17 11 18 20plusmn6aCO2 carbon acquisition 89 46 23 86 63 46 59plusmn 23aPAR light absorption gt100 gt100 98 gt100 gt100 92 gt 100Pmax maximum photosyn rate 27 18 16 22 16 28 21plusmn 5Qlowastsubs subsistence quota offset 6 5 6 5 4 9 6plusmn 1αQ Qsubs allometry 9 7 8 7 5 10 8plusmn 2` size Ln(ESD1microm) 25 20 29 19 14 22 22plusmn5fp fraction of protein in 92 75 44 36 17 38 50plusmn 25

photosyn machineryV lowastmax maximum nutrient uptake 13 11 14 10 8 14 12plusmn 2Aff nutrients affinity 39 31 42 38 36 55 40plusmn 7αV Vmax allometry 14 11 15 10 8 14 12plusmn 2L lowast phytoplankton losses 22 30 28 12 10 15 20plusmn8rlowast DIN remineralization 73 99 98 128 37 52 81plusmn 31s DH sinking gt 100 gt 100 96 gt 100 61 79 gt100Tref reference temperature 17 12 14 9 7 14 12plusmn 3

DIN (micromolminusN kgminus1

(l) future CO2(aq)

(o) present CO2(aq)

2 5 8 11 14 170

2 5 8 11 14 17

(r) past CO2(aq)

Figure 3 As in Fig 2 for PeECE III

Figure 4 Reference simulations of POC for high CO2 (red) and lowCO2 (blue) conditions bind the range of acidification effect (darkgray) according to our model projections Light gray area shows thelimits of the overall simulated POC variability 4POCmod Inlaygraph display the signal-to-noise ration (black solid lines) ie theratio between the variance of the acidification effect and the vari-ance of the overall variability

we still considered the potential lack of CO2 effect on theuncertainty propagation as sufficient justification to simplifyfurther analysis on variability decomposition by averagingthe thresholds and the sensitivity coefficients over treatmentlevels (see last column in Table 3 and Fig 7)

33 Variability decomposition

Our method allows for decomposition of POC variability infactor-specific components 4POCmod

i The effect of factorvariations simulating experimental differences among repli-cates is classified depending on its nature intensity and tim-ing (Figs 5 6 and 7)

POC variability during the prebloom phase can be ex-plained mainly by the differences of factors related to sub-sistence quota ie Qlowastsubs and αQ in both PeECE II and IIIexperiments (left column in Figs 5 and 6) This suggests thatthe differences in subsistence quota first intensify the diver-gence of POC trajectories and then weaken a few days laterbecause of the system dynamics These subsistence param-eters only need to vary about 6 and 8 among replicates(see Table 3) to maximize their contribution to the4POCexpthus their sensitivity coefficients are the highest (see Fig 7)

Differences in the initial nutrient concentration DIN(0)mean cell size ` and phytoplankton biomass loss coeffi-cient Llowast generate the modeled variability mainly during thebloom (with just about 20 differences among replicatessee Table 3 and second column in Fig 5) showing high val-ues of the sensitivity coefficient (highlighted in Fig 7)

Amplified variability in the postbloom phase (third col-umn in Figs 5 and 6) can be attributed to the uncertainties

in the reference temperature Tref for the Arrhenius equationEq (A4) in sinking loss or export flux s and in remineral-ization and excretion rlowast The sensitivity coefficient of Trefis high with just about 12 variation Therefore even ifdifferences in ambient temperature among replicates of thesame sample are negligible (see the low standard deviationsin the temperature Fig 9) differences in the metabolic de-pendence on that ambient temperature seems to be relevant inthe decay phase Interestingly variations among replicates inthe physiological dependence on other environmental factorsdo not show the same relevance (the sensitivity coefficientεi is low for carbon acquisition aCO2 and light absorptionaPAR) Generating high divergence during the postbloom re-quires a strong perturbation of parameters for the descriptionof the non-phytoplanktonic biomass (about 81 of the ref-erence value for sinking and 96 for remineralization andexcretion see Table 3) which translates to a relatively lowsensitivity coefficient

Perturbations of the initial detritus concentration DHC(0)and DHN(0) have no impact on the dynamics provided thatthey remain within reasonable ranges (48i lt 100) In factmore than 10-fold difference among replicates in such non-relevant factors were necessary to achieve a perceptible vari-ability 4POCmod

i POC variability throughout the bloom phases (right col-

umn in Figs 5 and 6) can be attributed to the varying car-bon and nitrogen initial conditions PhyC and PhyN nutrientuptake-related factors V lowastmax αV and Aff and protein allo-cation for photosynthetic machinery fp With regard to thelatter high standard deviations of the tolerance (see Table 3)suggest non-conclusive results

4 Discussion

We used the uncertainty quantification method to decom-pose POC variability by using a low-complexity model thatdescribes the major features of phytoplankton growth dy-namics The model fits the mean of mesocosm experimentalPeECE II and III data with high accuracy for all CO2 treat-ment levels We confirmed the working hypotheses (Figs 5ndash7) in particular we showed that small differences in ini-tial nutrient concentration mean cell size and phytoplanktonbiomass losses are sufficient to generate the experimentallyobserved bloom variability 4POCexp that potentially maskacidification effects as discussed in the following subsec-tions

The results of our analyses are conditioned by the dynami-cal model equations imposed Deliberately the modelrsquos com-plexity is kept low mainly to limit the generation of struc-tural errors with respect to model design At the same timethe level of complexity resolved by the model suffices toexplain POC measurements of two independent mesocosmexperiments with identical parameter values (see Table 2)which highlights model skill The used equations comply

F uture CO (aq)2

microm

olminus

minus1)

Present CO (aq)2

2 6 10 14 180

Past CO (aq)2

2 6 10 14 18D ay

Postbloom

2 6 10 14 18D ay

variability variabiliy variabilityIrregularvariability

BloomPrebloom

Figure 5 POC variability decomposition per factor 4POCmodi

for PeECE II Shaded areas are limited by the standard deviation of 104

simulated POC time series (see Sect 2) around the mean trajectory of the ensemble (solid line) The timing of the amplification of thevariability determines four separated kinds of behavior factor uncertainties generating variability during the prebloom bloom postbloomor at irregular phase (see Sect 3)

with theories of phytoplankton growth (eg Droop 1973Aksnes and Egge 1991 Pahlow 2005 Edwards et al 2012Litchman et al 2007 Wirtz 2011) The uncertainty propa-gation employed here can be applied to any model As longas the model features a similar structural complexity and isalso able to reproduce POC with sufficient accuracy we ex-pect similar qualitative findings with respect to the factors(8i) and similar identification of the major contributors tothe variability However we would not expect other modelsto reveal exactly similar values in the ratio εi which wouldlikely depend on the equations used to resolve some of theecophysiological details

41 Nutrient concentration

Differences among replicates in the initial nutrient concen-tration substantially contribute to POC variability a sensi-tivity that is interestingly not well expressed when varyingthe initial cellular carbon or nitrogen content of the algaePhyC(0) and PhyN(0) The relevance of accuracy for the ini-tial nutrient concentration in replicated mesocosms has al-ready been pointed out in Riebesell et al (2008) Under aconstant growth rate DIN(0) determines the timing of nu-

trient depletion therefore differences in the initial nutrientconcentration might also translate into temporal variations inthe succession of species We showed that such dependenceis noted even in more general dynamics and that our methodcan also estimate the variational range for differences in theinitial DIN concentration for experiments with a low numberof replicates The standard deviation of DIN(0) in the exper-imental setup for PeECE III was 50 of the mean which issignificantly above our tolerance threshold (see Table 3 forinitial DIN concentration) Following Riebesell et al (2007)we considered day 2 as the initial condition when the mea-sured DIN was 14plusmn2 micromol-CLminus1 as shown in Table 1 Since2 micromol-CLminus1 is approximately 14 of 14 micromol-CLminus1 thevariability of replicates at day 2 was about 14 Thereforeexperimental differences in the initial nutrient concentrationwere similar to the tolerance threshold for the initial DIN es-tablished to avoid high variability ((20plusmn 6) in Table 3)which represents an explanation for the high divergence ob-served in POC measurements

For PeECE II experimentally measured DIN concentra-tion at day 0 was 107plusmn 08 micromol-CLminus1 suggesting a 75difference among replicates which was below our projectedtolerance level (75 is out of the range [1426]) The same

F uture CO (aq)2

microm

olminus

minus1)

Present CO (aq)2

2 6 10 140

Past CO (aq)2

2 6 10 14D ay

Figure 6 As Fig 5 for PeECE III

0 5 10 15 20 25 30 35 40 45

PeECE III PeECE II

Pre- bloom post-

Figure 7 Sensitivity coefficients (εi Eq 2) of factors φi listed inTables 1 and 2 for different bloom phases in two OA-independentmesocosm experiments Factors whose uncertainties potentiallymask acidification effects (Fig 4) by triggering variability duringthe bloom (Figs 5 and 6) are highlighted

was noted for day 2 with DIN concentration equal to 8plusmn05 micromol-CLminus1 (Table 1) Our approach showed that dif-ferences in initial nutrient concentration in PeECE II werenot sufficiently high to trigger the experimentally observedPOC variability Incidentally phosphate re-addition on day8 of the experiment established new initial nutrient concen-

tration for the subsequent days When the dynamics in onereplicate significantly diverges from the mean dynamics ofthe treatment even if the re-addition occurs at the same timeand at the same concentration in all the replicates the meso-cosm with the outlier trajectory will not respond as the oth-ers do and with the addition of a new nutrient condition thedivergence might be further amplified In this case nutrientre-addition has the same impact on the systems as variationsin the initial conditions of nutrient concentration Also forPeECE II variability in POC is about 30 higher than thatfor PON as shown in Fig 2 We attribute the temporal de-coupling between C and N dynamics to the break of symme-try among replicates by the nutrient re-addition owing to thestrong sensitivity of the system to initial nutrient concentra-tions and a concomitant change in subsistence N C quotawhich is a sensitive parameter especially during the pre-bloom phase (Figs 5 6 and 7) Increase of POC PON ratiosunder nitrogen deficiency has been observed frequently dur-ing experimental studies (eg Antia et al 1963 Biddandaand Benner 1997) and has been attributed to preferentialPON degradation and to intracellular decrease of the N Cratio (Schartau et al 2007) Hence we confirmed that nutri-ent re-addition during the course of the experiments resultsin a significant disturbance as has been previously reported(Riebesell et al 2008) although a complete analysis wouldrequire a model that explicitly accounts for other nutrients

Factor levels

x nreplicates

Experimental approach Model approach

x 19 factorsx 3 acidification levels

x N factorsx 3 acidification levels

Low HighLow

104 virtual replicates

2 6 10 14 D ay

104 factor values

Variability decomposition

Figure 8 The exploration of the sources of variability in an ex-periment with a multi-way repeated measures ANOVA design with3 acidification levels requires a multi-factorial high-dimensionalsetup (left panel) Alternately we numerically simulate the biomassdynamics with 104 virtual replicates each one with a different nor-mally distributed factor value (right panel) Uncertainty propagationrelates the dispersion of the factor values with the dispersion of thePOC trajectories As an example we plot results of POC variabilityin 50 virtual replicates of PeECE III at low acidification with un-certainty in initial nutrient concentration Mesocosm drawing fromScheinin et al (2015)

42 Mean cell size as a proxy for community structure

We found a limited tolerance to variations in the mean cellsize of the community ` which has a threshold of about 22variation (see Table 3) If we consider the averaged meancell size of PeECE II 〈`〉 = 16 and III 〈`〉 = 18 from Ta-ble 2 we obtain 〈`〉 = 17 Then the absolute standard de-viation is 4`= 22 middot 17

100 sim 04 Therefore our methodologyshows that variations within the range limited by 〈`〉plusmn4`ie [1321] are sufficient to reproduce the observed ex-perimental POC variability during the bloom Since ` is inthe log scale the corresponding ESD increment is within thevariational range 〈ESD〉plusmn4ESD that is [3781]microm (or[25285]microm3 in volume) These values are easily reached inthe course of species succession This supports studies show-ing that community composition outweighs ocean acidifica-tion (Eggers et al 2014 Kroeker et al 2013 Kim et al2006)

43 Phytoplankton loss

Another major contributor to POC variability during thebloom phase is phytoplankton biomass loss Llowast With a stan-dard deviation of about 20 (Table 3) uncertainties in Llowast

generate variability larger than the model response to OA inparticular at the end of the growth phase and the beginning

of the decay phase Unresolved details in phytoplankton lossrate include among others replicate differences in cell ag-gregation or damage by collisions mortality by virus par-asites and morphologic malformations or grazing by non-filtered mixotrotophs or micro-zooplankton

44 Inference from summary statistics on mesocosmdata with low number of replicates

To test the hypotheses outlined in the Introduction entailstwo important aspects First heuristic exploration of vari-ability would require experiments designed to quantify thesensitivity of mesocosms to variations in potentially rele-vant factors that specify uncertainties in environmental con-ditions cell physiology and community structure Howeverthis would require high-dimensional multi-factorial setups(see Appendix D) which would be difficult to handle if atall even for low number of replicates Second standard sta-tistical inference tools might come to their limitations in esti-mating treatment effects Repeated measures of relevant eco-physiological data (eg POC) are collected from mesocosmexperiments that span a few weeks If the differences amongtreatment levels are smaller than those among replicates ofthe same treatment level post-processing statistical analy-ses might conclude that there are no detectable effects (Fieldet al 2008)

In many cases the mean and the variance of the sampleare taken as a fair statistical representation of the effect of thetreatment level and its variability However summary statis-tics such as the mean and the variance might fail to describedistributions that do not cluster around a central value iewhen the data are not normally distributed in the sampleThis is because a feature of normally distributed ensemblesis that the mean represents the most typical value and de-viations from that main trend (caused by unresolved factorsnot directly related to the treatment) might cancel out in thecalculation of the ensemble average Actually this cancel-lation is the reason for using replicates (Ruxton and Cole-grave 2006) but many circumstances can remarkably lowerthe likelihood for cancellation for instance (i) effects thatare sensitive to initial conditions (thus small initial differ-ences in the replicates of a given sample might become am-plified and produce departures that enlarge over the courseof the experiment) (ii) non-symmetrically distributed initialconditions in the sample (that might lead to non-symmetricaldistribution of the results) and (iii) a low number of repli-cates ie a sample size not adapted to the intensity of thetreatment effect the sensitivity of all effects to initial condi-tions and the intended accuracy of the experiment Each inci-dent decreases the statistical power and therefore misleadingconclusions might be inferred (Miller 1988 Cohen 1988Peterman 1990 Cottingham et al 2005)

(microm

minus1)

PeECE II

F uture CO (aq)

Present CO (aq)2

Past CO (aq)2

0 2 4 6 8 10 12 14 16 18 200

(microm

minus2s

minus1)

50PeECE III

0 2 4 6 8 10 12 14 16 18 200

Figure 9 Environmental data from PeECE II and III are taken as model inputs Error bars denote the standard deviation of the same treatmentreplicates

45 Consequences for the design of mesocosmexperiments

In our simulations the CO2 level affected the intensity andtiming of the bloom (Fig 4) Thus the slope of the growthphase can be regarded as a suitable target variable to de-tect OA effects Moreover our model analysis revealed a lowsignal-to-noise ratio The ability to distinguish the treatmenteffect from noise depends on the experimental design thestrength of the treatment and the variability that it is notexplained by the treatment When the signal-to-noise ratiois as low as it is shown by our simulations a large exper-imental sample size is needed to avoid incurring a type IIerror (Field et al 2008) In particular we can assume a twosample two-sided balanced t test with two treatment levelsas in Fig 4 ie the maximum difference between meansequal to approximately 5 micromol-CLminus1 (see ie PeECE III atday 10) and the variability4POCmod approximately equal to4 micromol-CLminus1 If we aim for a statistical power of 08 iea 80 chance of observing a statistically significant resultwith that experimental design the required number of repli-cates per treatment level would be 11 (R Core Team 2016)which is unpractical in mesocosm experiments With n= 3replicates the chance declines to only 20

We provided an estimation for the uncertainty thresh-olds that can be used for improving future sampling strate-gies with a low number of replicates ie n= 3 Tolerancesshown in Table 3 can be used to quantify how much repli-cates similarity can be compromised before the variability ofthe outcomes outweighs potential acidification effects Some

tolerances indicate maximal variations in observable quanti-ties such as nutrient concentration and community compo-sition These model results suggest that a better control ofsuch dissimilarities among replicates can help maintain thevariability below the range of the acidification effect espe-cially during the bloom

Strategies to reduce 4POCmod should similarly apply tolower 4POCexp For example model results turned out tobe very sensitive to variations in mean logarithmic cell sizeVariations of this factor during the initial filling of the meso-cosms may already generate divergent responses in POC sothat a potential CO2 signal becomes difficult to detect if atall To determine spectra of cell sizes (or mean of logarithmiccell size) of the initial plankton community prior to CO2 per-turbation would be a possibility to countervail this difficultyThe decision of which mesocosm to select for which kind(ie intensity) of perturbation may then be adjusted accord-ing to similarities in initial plankton community structureFor example we may consider some number of availablemesocosms that should become subject to two different CO2perturbation levels We may first select two mesocosms thatreveal the greatest similarity with respect to their initial sizespectra and assign them to the two different CO2 treatmentlevels Likewise from the remaining mesocosms we againchose those two mesocosms that show the closest similaritybetween their size spectra Those two are chosen to becomesubject to the two different CO2 perturbations The selectionprocedure could be repeated until all mesocosms have beenassigned to either of the two CO2 treatments Thus meso-cosms with similar initial conditions are assured to become

subjected to different CO2 perturbations This reduces a mix-ture of random effects due to variations in experiment initial-ization and CO2 effect and it will likely facilitate data anal-ysis in experimental setups with low number of replicateswhere sample randomization (Ruxton and Colegrave 2006)might not be effective see Sect 44 Mesocosms may thenbe first analyzed pairwise (similar initial setup) with respectto differences in CO2 response

In addition our analysis results help interpreting non-conclusive results and provide plausible explanations for thenegative results for the detection of potential acidificationeffects (Paul et al 2015 Schulz et al 2008 Engel et al2008 Kim et al 2006 Engel et al 2005) Thus our studyalso suggests the limitation of the statistical inference toolscommonly used to assess the statistical significance of effectdetectability

Finally we found the same main contributors to POC vari-ability for all the treatment levels even if experimental vari-ability is about 70 higher in the mesocosms where thecarbon chemistry was manipulated In particular the hetero-geneity of variance measured in future levels is larger thanunder the other acidification conditions (see fluctuations ofthe standard deviations of CO2 concentrations Fig 9) Thesedifferences in biomass variability among treatment levels arenot explained by uncertainties in our model factors Theymight have been originated by the irregularities in the CO2aeration (Riebesell et al 2008 Cornwall and Hurd 2015)however further analyses need to be conducted to determinepotential sources of differences in variability

5 Conclusions

Our model projections indicated that phytoplankton re-sponses to OA were mainly expected to occur during thebloom phase presenting a higher and earlier bloom underacidification conditions Moreover we found that amplifiedPOC variability during the bloom that potentially reduces thelow signal-to-noise ratio can be explained by small variationsin the initial DIN concentration mean cell size and phyto-plankton loss rate

The results of the model-based analysis can be used forrefinements of experimental design and sampling strategiesWe identified specific ecophysiologial factors that need to beconfined in order to ensure that acidification responses do notbecome masked by variability in POC

With our approach we reverse the question of how experi-mental data can constrain model parameter estimates and in-stead determine the range of variability in experimental datathat can be explained by modeling with variational rangesbounding uncertainties of specific control factors We testedthe hypothesis of whether small differences among replicateshave the potential to generate higher variability in biomasstime series than the response that can be attributed to the ef-fect of CO2 Therefore we conclude that modeling studiesthat integrate data from acidification experiments should re-solve physiological regulation capacities at cellular and com-munity levels In fact modeling the propagation of uncertain-ties revealed cell size to be a major contributor to phytoplank-ton biomass variability This suggests the use of adaptivesize-trait-based dynamics since such approaches allow forthe resolution of ecophysiologial trait shifts in non-stationaryscenarios (Wirtz 2013) The role of intracellular protein al-location can also be clarified by using a trait-based approachsince our results about the impact of its variations were non-conclusive

In this study we established a foundation for furthermodel-based analysis for uncertainty propagation that can begeneralized to any kind of experiments in biogeosciencesExtensions comprising time-varying uncertainties by intro-ducing a new random value for parameters at every time stepor including covariance matrices showing the simultaneousinteraction of variations in two factors can be straightfor-ward implemented (de Castro 2017) Finally we believe thatan explicit description of uncertainty quantification is essen-tial for the interpretation and generalization of experimentalresults

Data availability Experimental data are available via the data por-tal Pangaea (PeECE II team 2003 PeECE III team 2005 Paulet al 2014)

Appendix A Definition of relative growth rate

Relative growth rate micro is calculated from the primary pro-duction rate by subtracting respiration and mortality lossesas follows micro= P minusRminusL

A1 Primary production

Primary production rate reflects the limiting effects of lightdissolved inorganic carbon (DIC) temperature and nutrientinternal quota as follows

P = Pmax middot fPAR middot fCO2 middot fT middot fQ middot fp (A1)

Pmax is the maximum primary production rate (Table 2)Specific light limitation fPAR depends on light and CO2 Forthe attenuation coefficient az we consider that in coastal re-gions light intensity is typically reduced to 1 of its surfacevalue at 5 m (Denman and Gargett 1983) and we obtainedaz = 075mminus1 Next PAR experienced by cells at mixedlayer depth (MLD= 45 m Engel et al 2008) was calcu-lated from the level of radiation at the water surface PAR0(see Appendix B) following an exponential decay describedby the LambertndashBeer law

PAR= PAR0

MLDint0

eminusazmiddotzdz (A2)

The relationship between photosynthesis and irradiance canbe formulated by referring to a cumulative one-hit Pois-son distribution (Ley and Mauzerall 1982 Dubinsky et al1986) With the temperature and carbon acquisition depen-dence it yields

fPAR =

(1minus e

minusaPARmiddotPAR

PmaxmiddotfCO2middotfT

) (A3)

where aPAR is the effective absorption related to the chloro-plast cross section and saturation response time for receptors(Geider et al 1998a Wirtz and Pahlow 2010) the carbonacquisition term fCO2 is described in Sect 21 Eq ()fT is the temperature dependence We considered that all

metabolic rates depend on protein folding that increases withrising temperature following the Arrhenius equation (Scalleyand Baker 1997) as described in Geider et al (1998b) orSchartau et al (2007)

fT = eminusEamiddot

(1Tminus

) (A4)

with activation energyEa =T 2

ref10 middotlog(Q10) as in Wirtz (2013)

where we usedQ10 = 188 for phytoplankton (Eppley 1972Brush et al 2002) and Tref was the mean measured temper-ature (see Appendix B)

The allometric factor αQ quantifies the scaling relation ofsubsistence quota and cell size We used the Droop depen-dency on nutrient N C ratio (Droop 1973) which has beenrecently mechanistically derived (Wirtz and Pahlow 2010Pahlow and Oschlies 2013)

(1minus

) (A5)

where Q= PhyNPhyC

Its lower reference the subsistence quota

Qsubs =Qlowast

subs middot eminusαQmiddot` is considered size-dependent and re-

flects a lower protein demand for uptake mechanisms in largecells (Litchman et al 2007)

The last term in Eq (A1) accounts for an energy alloca-tion trade-off in phytoplankton cells protein allocation forphotosynthetic compounds such as RuBisCo and pigmentsfp versus allocation for nutrient uptake fv expressed byfp+ fv = 1 (Wirtz and Pahlow 2010 Pahlow and Oschlies2013) We simplified the detailed partition models by settingthe trait fractions as constant

A2 Respiratory cost and nutrient uptake rates

Efforts related to nutrient uptake V are represented by a res-piration term Other expenses such as biosynthetic costs areneglected (Pahlow 2005) The respiration rate is then cal-culated as R = ζ middotV where ζ expresses the specific respira-tory cost of nitrogen assimilation (Raven 1980 Aksnes andEgge 1991 Pahlow 2005) For simplicity our model mergesthe set of potentially limiting nutrients (eg P Si and N) to asingle resource only ie DIN We follow Aksnes and Egge(1991) as described in Pahlow (2005) for the maximum up-take rate

Vmax =1

1V lowastmaxmiddotfT

AffmiddotDIN

comprising the maximum uptake coefficient V lowastmax and nu-trient affinity Aff In addition to a temperature dependenceof nutrient uptake as reported by Schartau et al (2007) weassumed that respiratory costs decrease with increasing cellsize (Edwards et al 2012) which leads to an allometric scal-ing in nutrient uptake (Wirtz 2013) with exponent αV Wealso accounted for the static proteins allocation trade-offsbetween photosynthetic machinery fp and nutrients uptakefv = 1minus fp Thus the nutrient uptake term yields

V = (1minus fp) middotVmax middot eminusαV middot` (A7)

A3 Loss rates

To describe the loss rate of phytoplankton biomass we useda density-dependent term

L= Llowast middot (PhyC+DHC) (A8)

The resulting matter flux increases the biomass of detritusand heterotrophs (DH) and a fraction of it becomes a part of

the remineralizable pool A temperature-dependent reminer-alization term (Schartau et al 2007)

r = rlowast middot fT (A9)

describes any kind of DIN production such as hydrolysisand remineralization of organic matter excretion of ammo-nia directly by zooplankton and rapid remineralization offecal pellets produced also by the zooplankton The otherfraction of the non-phytoplanktonic biomass is removed bysettling with a rate related to the sinking coefficient sshown in Tables 1 and 2 Our model was calibrated with ex-perimental data from enclosed mesocosms where aquariumpumps ensured mixing Therefore we assumed that suffi-ciently wealthy organisms could achieve neutral buoyancy(Boyd and Gradmann 2002) and thus sinking might nothave directly affected the phytoplankton biomass

Appendix B Forcings

We used measured aquatic CO2 and temperature per meso-cosm and ambient PAR as model inputs (see Fig 9) Forthe two PeECE experiments the photon flux density wasmeasured by the Geophysical Institute of the University ofBergen To calculate the surface radiation inside the meso-cosms PAR0 we followed (Schulz et al 2008) and consid-ered that 80 of incident PAR passed through the gas tighttents of which up to 15 penetrated to approximately 25 mdepth the center of the mixed surface layer in PeECE III Thedaily carbon dioxide data were interpolated and PAR signalwas filtered by singular spectrum analysis to avoid suddenchanges that could be detrimental to the performance of thenumerical calculation since the Heun method requires dif-ferentiable functions

Appendix C Definition of POC

The applied model equations attribute phytoplankton detri-tus and herbivorous heterotrophs to particulate organic mat-ter Measurements of particulate organic carbon also includesome fractions of large bacterioplankton carnivorous zoo-plankton as well as extracellular gel particles such as trans-parent exopolymer particles These additional organic con-tributions to POC measurements are not explicitly resolvedin our model Therefore for comparisons between simula-tion results and observations we redefine the raw data fromPANGAEA named POCprime hereafter (dots in Figs 2 3 and5 represent the already modified POC data) We used dataof transparent exopolymer particles TEP from Egge et al(2009) for PeECE III such as here POC = POCprime minus TEPFor PeECE II TEP data were not available We used POC =POCprime minus POCprimeprime where POCprimeprime is the difference between parti-cle abundance PA of the Coulter counter measurements andthe flow cytometry data in Engel et al (2008)

POCprimeprime = β middot (PA Coulter counterminusPA flow cytometry) (C1)

The scaling parameter β = 0000065 micromol-CLminus1 was tunedto provide reductions between 40 and 50 from total POCin agreement with the adjustments of PeECE III

Appendix D Model representation of replicates

Heuristic exploration of the potential origins of the observedvariability uses statistical inference tools such as a multi-way repeated measures ANOVA exploring which indepen-dent factors are contributing the most to the standard devia-tions Such approaches have the advantage of accounting forinteracting effects between combinations of factors (and notonly for the synergistic effects of each factor and acidifica-tion as in our model-based approach see Sect 3) Howeverthe realization through an experimental setup would make ahigh-dimensional multi-factorial experiment extremely dif-ficult to perform (Fig 8) For three acidification levels theminimum number of factor levels (ie high and low) mini-mum number of sample units (ie duplicates) and the samenumber of factors we analyze here (ie N = 19) the totalnumber of mesocosms would be 3times 2times 2times 19= 228 Thepossibility of simulating a high number of replicates is one ofthe unique strengths of modeling For each factor we simu-late possible realizations of the same acidification level withslight variations of the factor reference value (simulating dif-ferences in physiological states and community structure)We generated model solutions for 104 normally distributedfactor values ie in total 3 acidification levels times 19 factorstimes 104 virtual replicates for PeECE II and III experimentsExamples of 50 virtual replicates with uncertainty in initialnutrient concentration are shown in Fig 8 and examples of 10virtual replicates with uncertainty in phytoplankton biomasslosses are shown in Fig 1 both numerically calculated forlow CO2 conditions in PeECE III

Appendix E Residuals of the modelndashdata fit

For the modelndashdata fit shown in Figs 2 and 3 we calculatedthe cumulative residuals E and M (Table E1) with respect tothe mean of experimental replicates per treatment time andmesocosm For experimental data residuals E were calcu-lated as follows

E =sum

treatrepday|Y

exptreatrepdayminus〈Y

exptreatday〉|η (E1)

and for model results residuals M were calculated as fol-lows

M =sum

treatrepday|Ymod

treatrepdayminus〈Yexptreatday〉|η (E2)

with η = 9 being the total number of mesocosms High resid-uals entail high deviation from the trend In the case of Ethis is the deviation from the mean of the treatment (typi-cally used in statistical inference tools) and in the case ofM the deviation from the model reference run When bothE andM values are comparable we can infer that the qualityof both representations is similar (see Table E1) Thus con-clusions inferred from both approaches are based on equallyvalid assumptions

Table E1 Cumulative residuals for PeECE III

Y E M units

POC 351 374 micromol-CLminus1

PON 60 91 micromol-NLminus1

DIN 67 92 micromol-NLminus1

Author contributions Kai Wirtz Markus Schartau and MariaMoreno de Castro developed the model code Maria Moreno deCastro performed the simulations and prepared the manuscriptwhich was revised by Kai Wirtz and Markus Schartau

Competing interests The authors declare that they have no conflictof interest

Acknowledgements We thank Sabine Mathesius for the PAR andtemperature data for both the PeECE II and III experiments andKaela Slavik for the English edition of the preliminary version ofthe manuscript We acknowledge our two anonymous reviewersfor their helpful comments and suggestions This work is acontribution to the National German project Biological Impacts ofOcean Acidification (BIOACID) and it is also supported by theHelmholtz society via the program PACES

The article processing charges for this open-accesspublication were covered by a ResearchCentre of the Helmholtz Association

Edited by M GreacutegoireReviewed by two anonymous referees

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Broadgate W Riebesell U Armstrong C Brewer P DenmanK Feely R Gao K Gatusso J P Isensee K Kleypas J

Laffoley D Orr J Poumletner H O de Rezende C E SchimdtD Urban E Waite A and Valdeacutes L Ocean acidificationsummary for policymakers ndash Third Symposium on the oceanin a high-CO2 world International Geosphere-Biosphere Pro-gramme Sweden p 26 2013

Brush M Brawley J Nixon S and Kremer J Modeling phy-toplankton production problems with the Eppley curve andan empirical alternative Mar Ecol Prog Ser 238 31ndash45doi103354meps238031 2002

Caldeira K and Wickett M E Oceanography Anthropogenic car-bon and ocean pH Nature 425 365ndash365 doi101038425365a2003

Chantrasmi T and Iaccarino G Forward and backward uncer-tainty propagation for discontinuous system response using thePade-Legendre method International Journal for UncertaintyQuantification 2 125ndash143 2012

Chen C Y Effect of pH on the growth and carbon uptake of marinephytoplankton Mar Ecol Prog Ser 109 83ndash94 1994

Cohen J Statistical Power Analysis for the Behavioral SciencesLawrence Erlbaum Associates Hillsdale NJ 2nd edn 1988

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Cottingham K L Lennon J T and Brown B L Know-ing when to draw the line designing more informative eco-logical experiments Front Ecol Environ doi1018901540-9295(2005)003[0145KWTDTL]20CO2 2005

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Dubinsky Z Falkowski P G and Wyman K Light harvestingand utilization by phytoplankton Plant Cell Physiol 21 1335ndash1349 1986

Edwards K Klausmeier C A and Litchman E Allometric scal-ing and taxonomic variation in nutrient utilization traits andmaximum growth rate of phytoplankton Limnol Oceanogr 57554ndash556 2012

Egge J K Thingstad T F Larsen A Engel A Wohlers JBellerby R G J and Riebesell U Primary production duringnutrient-induced blooms at elevated CO2 concentrations Bio-geosciences 6 877ndash885 doi105194bg-6-877-2009 2009

Eggers S L Lewandowska A M Barcelos e Ramos J Blanco-Ameijeiras S Gallo F and Matthiessen B Community com-position has greater impact on the functioning of marine phy-toplankton communities than ocean acidification Glob ChangeBiol 20 713ndash723 doi101111gcb12421 2014

Ellison S L R and Williams A EurachemCITAC guide Quan-tifying Uncertainty in Analytical Measurement third edn p 262012

Engel A Schulz K G Riebesell U Bellerby R Delille Band Schartau M Effects of CO2 on particle size distribution andphytoplankton abundance during a mesocosm bloom experiment(PeECE II) Biogeosciences 5 509ndash521 doi105194bg-5-509-2008 2008

Engel A Cisternas Novoa C Wurst M Endres S Tang TSchartau M and Lee C No detectable effect of CO2 on el-

emental stoichiometry of Emiliania huxleyi in nutrient-limitedacclimated continuous cultures Mar Ecol Prog Ser 507 15ndash30 2014

Engel A Zondervan I Aerts K Beaufort L Benthien AChou L Belille B Gattuso J-P Harlay J Heemann CHoffmann L Jacquet s Nejstgaard J Pizay M -D Rochelle-Newall E Scheider U Terbrueggen A and Riebesell UTesting the direct effect of CO2 concentration on a bloom of thecoccolithophorid Emiliania huxleyi in mesocosm experimentsLimnol Oceanogr 50 493ndash507 2005

Eppley R W Temperature and phytoplankton growth in the seaFishery Bulletin 1972

Field A Miles J and Field Z Discovering statistics using RSAGE Publications Ltd 2008

Fussmann G F and Blasius B Community response to enrich-ment is highly sensitive to model structure Biol Lett 1 9ndash12doi101098rsbl20040246 2005

Gao K Helbling E W Haumlder D P and Hutchins D A Re-sponses of marine primary producers to interactions betweenocean acidification solar radiation and warming Mar EcolProg Ser 470 167ndash189 doi103354meps10043 2012

Geider R Macintyre Graziano L and McKay R M Re-sponses of the photosynthetic apparatus of Dunaliellatertiolecta (Chlorophyceae) to nitrogen and phosphoruslimitation European Journal of Phycology 33 315ndash332doi10108009670269810001736813 1998a

Geider R J Maclntyre H L and Kana T M A dynamicregulatory model of phytoplanktonic acclimation to light nu-trients and temperature Limnol Oceanogr 43 679ndash694doi104319lo19984340679 1998b

JCGM Guide to the Expression of Uncertainty in Measure-ment (GUM 1995 with minor corrections) by a Joint Com-mittee for Guides in Metrology (JCGM 1002008) availableat httpwwwbipmorgutilscommondocumentsjcgmJCGM_100_2008_Epdf 2008a

JCGM Supplement 1 to the rsquoGuide to the Expression of Un-certainty in Measurement ndash Propagation of distributions us-ing a Monte Carlo method (JCGM 1012008) availableat httpwwwbipmorgutilscommondocumentsjcgmJCGM_101_2008_Epdf 2008b

Jones B M Iglesias-Rodriguez M D Skipp P J Ed-wards R J Greaves M J Jeremy R Y Elderfield Hand OrsquoConnor D Responses of the Emiliania huxleyi Pro-teome to Ocean Acidification PLoS ONE 8 2857ndash2869doi101371journalpone0061868 2014

Kennedy M C and OrsquoHagan A Bayesian Calibration of Com-puter Models Journal of the Royal Statistical Society Series B63 425ndash464 2001

Kim J-M Lee K Shin K Kang J-H Lee H-W Kim MJang P-G and Jang M-C The effect of seawater CO2 con-centration on growth of a natural phytoplankton assemblage in acontrolled mesocosm experiment Limnol Oceanogr 51 1629ndash1636 2006

Kroeker K J Kordas R L Crim R Hendriks I E Ramajo LSingh G S Duarte C M and Gattuso J-P Impacts of oceanacidification on marine organisms quantifying sensitivities andinteraction with warming Glob Change Biol 19 1884ndash1896doi101111gcb12179 2013

Larssen T Huseby R B Cosby B J Hoslashst G Hoslashgaringsen Tand Aldrin M Forecasting acidification effects using a Bayesiancalibration and uncertainty propagation approach Environ SciTechnol 40 7841ndash7847 2006

Ley A C and Mauzerall D C Absolute absorption cross-sectionsfor photosystem II and the minmum quantum requirement forphotosynthesis in chlorella vulgaris Biochimica et BiophysicaActa 680 95ndash106 1982

Litchman E Klausmeier C A Schofield O and Falkowski PThe role of functional traits and trade-offs in structuring phyto-plankton communities scaling from cellular to ecosystem levelEcol Lett 10 1170ndash1181 2007

Miller R G J Beyond ANOVA Basics of Applied Statistics Wi-ley New York ndash Chichester ndash Brisbane ndash Toronto ndash Singapore1988

Moreno de Castro M Tolerance of mesocosm experiments to time-varying uncertainties in preparation 2017

Nagelkerken I and Connell S D Global alteration ofocean ecosystem functioning due to increasing humanCO2 emissions P Natl Acad Sci 112 13272ndash13277doi101073pnas1510856112 2015

Pahlow M Linking chlorophyllndashnutrient dynamics to the RedfieldNC ratio with a model of optimal phytoplankton growth MarEcol Prog Ser 287 33ndash43 2005

Pahlow M and Oschlies A Optimal allocation backs Drooprsquoscell-quota model Mar Ecol Prog Ser 473 1ndash5 2013

PeECE II team PeECE II ndash Pelagic Ecosystem CO2 EnrichmentStudy Raunefjord Bergen Norway 2003 PANGAEA availableat doi101594PANGAEA723045 2003

PeECE III team PeECE II ndash Pelagic Ecosystem CO2 EnrichmentStudy Raunefjord Bergen Norway 2005 PANGAEA availableat doidoi101594PANGAEA726955 2005

Paul C Matthiessen B and Sommer U Warming but not en-hanced CO2 concentration quantitatively and qualitatively af-fects phytoplankton biomass Mar Ecol Prog Ser 528 39ndash51doi103354meps11264 2015

Peterman R M The importance of reporting statistical power theforest decline and acidic deposition example Ecology 71 2024ndash2027 1990

R Core Team R A Language and Environment for Statistical Com-puting R Foundation for Statistical Computing Vienna Aus-tria available at httpswwwR-projectorg (last access 3 April2017) 2016

Raven J and Beardall J Carbon Acquisition Mechanisms of Al-gae Carbon Dioxide Diffusion and Carbon Dioxide Concen-trating Mechanisms in Photosynthesis in Algae edited byLarkum A Douglas S and Raven J vol 14 of Advances inPhotosynthesis and Respiration 225ndash244 Springer Netherlandsdoi101007978-94-007-1038-2_11 2003

Raven J A Nutrient transport in microalgae Adv Microb Phys-iol 21 47ndash226 1980

Riebesell U and Tortell P D Effects of Ocean Acidificationon Pelagic Organisms and Ecosystems in Ocean Acidificationedited by Gattuso J-P and Hansson L 99ndash121 Oxford Uni-versity Press Oxford UK 2011

Riebesell U Wolf-Gladrow D A and Smetacek V Carbon diox-ide limitation of marine phytoplankton growth rates Nature 361249ndash251 doi101038361249a0 1993

Riebesell U Zondervan I Rost B Tortell P D Zeebe R Eand Morel F M M Reduced calcification of marine plank-ton in response to increased atmospheric Nature 407 364ndash367doi10103835030078 2000

Riebesell U Schulz K G Bellerby R G J Botros MFritsche P Meyerhofer M Neill C Nondal G OschliesA Wohlers J and Zollner E Enhanced biological carbonconsumption in a high CO2 ocean Nature 450 545ndash548doi101038nature06267 2007

Riebesell U Bellerby R G J Grossart H-P and ThingstadF Mesocosm CO2 perturbation studies from organism to com-munity level Biogeosciences 5 1157ndash1164 doi105194bg-5-1157-2008 2008

Riebesell U Fabry V J Hansson L and Gattuso J P Guide tobest practices for ocean acidification research and data reportingPublications Office of the European Union 2010

Rost B Riebesell U Burkhardt S and Sueltemeyer D Car-bon acquisition of bloom-forming marine phytoplankton Lim-nol Oceanogr 48 55ndash67 2003

Ruxton G D and Colegrave N Experimental design for the lifesciences Oxford Oxford University Press 2006

Sabine C L Feely R A Gruber N Key R M Lee K Bullis-ter J L Wanninkhof R Wong C S Wallace D W RTilbrook B Millero F J Peng T-H Kozyr A Ono T andRios A F The Oceanic Sink for Anthropogenic CO2 Science305 367ndash371 doi101126science1097403 2004

Scalley M L and Baker D Protein folding kinetics exhibit anArrhenius temperature dependence when corrected for the tem-perature dependence of protein stability P Natl Acad Sci 9410636ndash10640 doi101073pnas942010636 1997

Schartau M Engel A Schroumlter J Thoms S Voumllker C andWolf-Gladrow D Modelling carbon overconsumption and theformation of extracellular particulate organic carbon Biogeo-sciences 4 433ndash454 doi105194bg-4-433-2007 2007

Scheinin M Riebesell U Rynearson T A Lohnbeck K T andCollins S Experimental evolution gone wild J R Soc Inter-face 12 doi101098rsif20150056 2015

Schluter L Lohbeck K T Gutowska M A Groger J A Riebe-sell U and Reusch T B H Adaptation of a globally importantcoccolithophore to ocean warming and acidification Nature Cli-mate Change 4 1024ndash1030 doi101038nclimate2379 2014

Schulz K G Riebesell U Bellerby R G J Biswas H Meyer-houmlfer M Muumlller M N Egge J K Nejstgaard J C NeillC Wohlers J and Zoumlllner E Build-up and decline of or-ganic matter during PeECE III Biogeosciences 5 707ndash718doi105194bg-5-707-2008 2008

Sommer U Paul C and Moustaka-Gouni M Warming andOcean Acidification Effects on Phytoplankton ndash From SpeciesShifts to Size Shifts within Species in a Mesocosm ExperimentPLOS ONE 10 39ndash51 doi101371journalpone01252392015

Tanaka T Thingstad T F Loslashvdal T Grossart H-P Larsen AAllgaier M Meyerhoumlfer M Schulz K G Wohlers J Zoumlll-ner E and Riebesell U Availability of phosphate for phyto-plankton and bacteria and of glucose for bacteria at differentpCO2 levels in a mesocosm study Biogeosciences 5 669ndash678doi105194bg-5-669-2008 2008

Toral R and Colet P Stochastic Numerical Methods Wiley-VCH2014

Tortell P D Payne C D Li Y Trimborn S Rost B SmithW O Riesselman C Dunbar R B Sedwick P and DiTullioG R CO2 sensitivity of Southern Ocean phytoplankton Geo-phys Res Lett 35 l04605 doi1010292007GL032583 2008

Wirtz K W Non-uniform scaling in phytoplankton growth ratedue to intracellular light and CO2 decline J Plankton Res 331325ndash1341 2011

Wirtz K W Mechanistic origins of variability in phytoplanktondynamics Part I Niche formation revealed by a Size-BasedModel Mar Biol 160 2319ndash2335 2013

Wirtz K W and Pahlow M Dynamic chlorophyll and nitro-gencarbon regulation in algae optimizes instantaneous growthrate Mar Ecol Prog Ser 402 81ndash96 2010

Zondervan I Zeebe R E Rost B and Riebesell U Decreas-ing marine biogenic calcification A negative feedback on ris-ing atmospheric pCO2 Global Biogeochem Cy 15 507ndash516doi1010292000GB001321 2001

Abstract

Introduction

Method

Model setup data integration and description of the reference run
Uncertainty propagation
Results
CO2 effect on POC dynamics
CO2 effect on uncertainty propagation
Discussion
Nutrient concentration
Mean cell size as a proxy for community structure
Phytoplankton loss
Inference from summary statistics on mesocosm data with low number of replicates
Consequences for the design of mesocosm experiments
Conclusions
Data availability
Appendix A1 Primary production
Appendix A2 Respiratory cost and nutrient uptake rates
Appendix A3 Loss rates
Appendix B Forcings
Appendix E Residuals of the model--data fit
Author contributions
Competing interests
Acknowledgements
References

batch or chemostat experiments with monocultures (Riebe-sell et al 2008) Along with this mesocosms allow for alarger number of possible planktonic interactions that pro-vide opportunities for the spread of uncontrolled heterogene-ity Moreover physiological states vary for different phyto-plankton cells and environmental conditions For this reasonindependent experimental studies at similar but not identi-cal conditions might yield divergent results The variabil-ity in data of mesocosm experiments is thus generated byvariations of ecological details ie small differences amongreplicates of the same sample such as in species abundancenutrient concentration and metabolic states of the algae atthe initial setup of the experiments Differences of these fac-tors often remain unresolved and might therefore be treatedas uncertainties in a probabilistic approach

To account for all possible factors that determine all differ-ences in plankton dynamics is practically infeasible whichalso impedes a retrospective statistical analysis of the ex-perimental data However since unresolved ecological de-tails might propagate over the course of the experiment it ismeaningful to consider a dynamical model approach to up-grade the data analysis From a modeling perspective someimportant unresolved factors translate into (i) uncertainties inspecifying initial conditions (of the state variables) and (ii)uncertainties in identifying model parameter values Herewe apply a dynamical model to estimate the effects of eco-physiological uncertainties on the variability in POC concen-tration of two mesocosm experiments Our model describesplankton growth in conjunction with a dependency betweenCO2 utilization and mean logarithmic cell size (Wirtz 2011)The structure of our model is kept simple thereby reducingthe possibility of overparameterizing the mesocosms dynam-ics The model is applied to examine how uncertainties inindividual factors namely initial conditions and parameterscan produce the standard deviation of the distribution of ob-served replicate data Our main working hypotheses on theorigins of variability in mesocosm experiments are the fol-lowing

ndash Differences among replicates of the same sample canbe interpreted as unresolved random variations (nameduncertainties hereafter)

ndash Uncertainties can amplify during the experiment andgenerate considerable variability in the response to agiven treatment level

ndash Which uncertainties are more relevant can be estimatedby the decomposition of the variability in the experi-mental data

For our data-supported model analysis of variability de-composition we consider the propagation of distributions(JCGM 2008b) to seek potential treatment responses thatare masked by the variability in observations of two indepen-dent OA mesocosm experiments namely the Pelagic Enrich-ment CO2 Experiment (PeECE II and III) The central idea

is to produce ensembles of model simulations starting froma range of values for selected factors The range of valuesfor these selected factors is determined so as the variabilityin model outputs does not exceed variability in observationsover the course of the experiment The margins of the varia-tional range of each factor were thus confined by the abilityof the dynamical model to reproduce the magnitude of thevariability observed in POC These confidence intervals de-scribe the tolerance thresholds below which uncertainties donot escalate to high variability in the modeled replicates andcan serve as an estimator of the tolerance of experimentalreplicates to such uncertainties This information can be im-portant to ensure reproducibility allowing for a comparisonbetween the results of different independent experiments andincreasing confidence regarding the effects of OA on phyto-plankton (Broadgate et al 2013)

2 Method

Potential sources of variability are estimated following a pro-cedure already applied in system dynamics experimentalphysics and engineering (JCGM 2008b) The basic princi-ples of uncertainty propagation are summarized here usinga six-step method (see Fig 1) Steps 1 and 2 are describedin Sect 21 and comprise a classical model calibration (us-ing experimental data of biomass and nutrients) to obtain thereference run representing the mean dynamics of each treat-ment level In this way we found the reference value for themodel factors ie parameters and initial conditions Steps 3and 4 described in Sect 22 include the tracked propagationof uncertainties by systematically creating model trajectoriesfor POC each one with a slightly different value of a modelfactor In steps 5 and 6 we estimated the thresholds of themodel-generated variability and the effect of the uncertaintypropagation (also explained in Sect 22)

21 Model setup data integration and description ofthe reference run

In this section we describe the biological state that was usedas reference dynamics Our model resolves a minimal set ofstate variables insofar monitored during experiments that areassumed to be key agents of the biological dynamics Modelequations are shown in Table 1 Reference values of the pa-rameters are shown in Table 2 An exhaustive model docu-mentation is given in Appendix A The model simulates ex-perimental data from the Pelagic Enrichment CO2 Experi-ment (PeECE) a set of nine outdoor mesocosms placed incoastal waters close to Bergen (Norway) during the springseasons of 2003 (PeECE II) and 2005 (PeECE III) In boththe experiments blooms of the natural phytoplankton com-munity were induced and treated in three replicates for thefuture present and past CO2 conditions (Engel et al 2008Schulz et al 2008 Riebesell et al 2007 2008) Experimen-

Factor values

Step 4POC

standard deviation

Frequency

Step 1model

calibration

Step 3factor

standard deviation

Step 5 tolerance of

dayCon

For each factor

Uncertainty

Variability

Residuals

fCO2 =

εi =4POCmod

4φi (2)

partYpartφi

(4Y )2 =

Nsumi=1

c2i middot (4φi)

2 4 6 8 10 12 14 16 18

(i) Past CO (aq)2

3 Results

(l) future CO2(aq)

(o) present CO2(aq)

2 5 8 11 14 170

2 5 8 11 14 17

(r) past CO2(aq)

4 Discussion

F uture CO (aq)2

microm

olminus

minus1)

Present CO (aq)2

2 6 10 14 180

Past CO (aq)2

2 6 10 14 18D ay

Postbloom

2 6 10 14 18D ay

BloomPrebloom

F uture CO (aq)2

microm

olminus

minus1)

Present CO (aq)2

2 6 10 140

Past CO (aq)2

2 6 10 14D ay

0 5 10 15 20 25 30 35 40 45

PeECE III PeECE II

Pre- bloom post-

Factor levels

x nreplicates

Low HighLow

2 6 10 14 D ay

104 factor values

(microm

minus1)

PeECE II

F uture CO (aq)

Present CO (aq)2

Past CO (aq)2

0 2 4 6 8 10 12 14 16 18 200

(microm

minus2s

minus1)

50PeECE III

0 2 4 6 8 10 12 14 16 18 200

5 Conclusions

PAR= PAR0

MLDint0

fPAR =

(1minus e

minusaPARmiddotPAR

) (A3)

fT = eminusEamiddot

(1Tminus

) (A4)

(1minus

) (A5)

where Q= PhyNPhyC

Qsubs =Qlowast

Vmax =1

AffmiddotDIN

A3 Loss rates

Appendix B Forcings

E =sum

treatrepday|Y

M =sum

treatrepday|Ymod

Y E M units

References

Abstract

Introduction

Method

Results
Discussion
Phytoplankton loss
Conclusions
Data availability
Appendix B Forcings
Competing interests
Acknowledgements
References

Factor values

Step 4POC

standard deviation

Frequency

Step 1model

calibration

Step 3factor

standard deviation

Step 5 tolerance of

dayCon

For each factor

Uncertainty

Variability

Residuals

fCO2 =

εi =4POCmod

4φi (2)

partYpartφi

(4Y )2 =

Nsumi=1

c2i middot (4φi)

2 4 6 8 10 12 14 16 18

(i) Past CO (aq)2

3 Results

(l) future CO2(aq)

(o) present CO2(aq)

2 5 8 11 14 170

2 5 8 11 14 17

(r) past CO2(aq)

4 Discussion

F uture CO (aq)2

microm

olminus

minus1)

Present CO (aq)2

2 6 10 14 180

Past CO (aq)2

2 6 10 14 18D ay

Postbloom

2 6 10 14 18D ay

BloomPrebloom

F uture CO (aq)2

microm

olminus

minus1)

Present CO (aq)2

2 6 10 140

Past CO (aq)2

2 6 10 14D ay

0 5 10 15 20 25 30 35 40 45

PeECE III PeECE II

Pre- bloom post-

Factor levels

x nreplicates

Low HighLow

2 6 10 14 D ay

104 factor values

(microm

minus1)

PeECE II

F uture CO (aq)

Present CO (aq)2

Past CO (aq)2

0 2 4 6 8 10 12 14 16 18 200

(microm

minus2s

minus1)

50PeECE III

0 2 4 6 8 10 12 14 16 18 200

5 Conclusions

PAR= PAR0

MLDint0

fPAR =

(1minus e

minusaPARmiddotPAR

) (A3)

fT = eminusEamiddot

(1Tminus

) (A4)

(1minus

) (A5)

where Q= PhyNPhyC

Qsubs =Qlowast

Vmax =1

AffmiddotDIN

A3 Loss rates

Appendix B Forcings

E =sum

treatrepday|Y

M =sum

treatrepday|Ymod

Y E M units

References

Abstract

Introduction

Method

Results
Discussion
Phytoplankton loss
Conclusions
Data availability
Appendix B Forcings
Competing interests
Acknowledgements
References

Factor values

Step 4POC

standard deviation

Frequency

Step 1model

calibration

Step 3factor

standard deviation

Step 5 tolerance of

dayCon

For each factor

Uncertainty

Variability

Residuals

fCO2 =

εi =4POCmod

4φi (2)

partYpartφi

(4Y )2 =

Nsumi=1

c2i middot (4φi)

2 4 6 8 10 12 14 16 18

(i) Past CO (aq)2

3 Results

(l) future CO2(aq)

(o) present CO2(aq)

2 5 8 11 14 170

2 5 8 11 14 17

(r) past CO2(aq)

4 Discussion

F uture CO (aq)2

microm

olminus

minus1)

Present CO (aq)2

2 6 10 14 180

Past CO (aq)2

2 6 10 14 18D ay

Postbloom

2 6 10 14 18D ay

BloomPrebloom

F uture CO (aq)2

microm

olminus

minus1)

Present CO (aq)2

2 6 10 140

Past CO (aq)2

2 6 10 14D ay

0 5 10 15 20 25 30 35 40 45

PeECE III PeECE II

Pre- bloom post-

Factor levels

x nreplicates

Low HighLow

2 6 10 14 D ay

104 factor values

(microm

minus1)

PeECE II

F uture CO (aq)

Present CO (aq)2

Past CO (aq)2

0 2 4 6 8 10 12 14 16 18 200

(microm

minus2s

minus1)

50PeECE III

0 2 4 6 8 10 12 14 16 18 200

5 Conclusions

PAR= PAR0

MLDint0

fPAR =

(1minus e

minusaPARmiddotPAR

) (A3)

fT = eminusEamiddot

(1Tminus

) (A4)

(1minus

) (A5)

where Q= PhyNPhyC

Qsubs =Qlowast

Vmax =1

AffmiddotDIN

A3 Loss rates

Appendix B Forcings

E =sum

treatrepday|Y

M =sum

treatrepday|Ymod

Y E M units

References

Abstract

Introduction

Method

Results
Discussion
Phytoplankton loss
Conclusions
Data availability
Appendix B Forcings
Competing interests
Acknowledgements
References

εi =4POCmod

4φi (2)

partYpartφi

(4Y )2 =

Nsumi=1

c2i middot (4φi)

2 4 6 8 10 12 14 16 18

(i) Past CO (aq)2

3 Results

(l) future CO2(aq)

(o) present CO2(aq)

2 5 8 11 14 170

2 5 8 11 14 17

(r) past CO2(aq)

4 Discussion

F uture CO (aq)2

microm

olminus

minus1)

Present CO (aq)2

2 6 10 14 180

Past CO (aq)2

2 6 10 14 18D ay

Postbloom

2 6 10 14 18D ay

BloomPrebloom

F uture CO (aq)2

microm

olminus

minus1)

Present CO (aq)2

2 6 10 140

Past CO (aq)2

2 6 10 14D ay

0 5 10 15 20 25 30 35 40 45

PeECE III PeECE II

Pre- bloom post-

Factor levels

x nreplicates

Low HighLow

2 6 10 14 D ay

104 factor values

(microm

minus1)

PeECE II

F uture CO (aq)

Present CO (aq)2

Past CO (aq)2

0 2 4 6 8 10 12 14 16 18 200

(microm

minus2s

minus1)

50PeECE III

0 2 4 6 8 10 12 14 16 18 200

5 Conclusions

PAR= PAR0

MLDint0

fPAR =

(1minus e

minusaPARmiddotPAR

) (A3)

fT = eminusEamiddot

(1Tminus

) (A4)

(1minus

) (A5)

where Q= PhyNPhyC

Qsubs =Qlowast

Vmax =1

AffmiddotDIN

A3 Loss rates

Appendix B Forcings

E =sum

treatrepday|Y

M =sum

treatrepday|Ymod

Y E M units

References

Abstract

Introduction

Method

Results
Discussion
Phytoplankton loss
Conclusions
Data availability
Appendix B Forcings
Competing interests
Acknowledgements
References

2 4 6 8 10 12 14 16 18

(i) Past CO (aq)2

3 Results

(l) future CO2(aq)

(o) present CO2(aq)

2 5 8 11 14 170

2 5 8 11 14 17

(r) past CO2(aq)

4 Discussion

F uture CO (aq)2

microm

olminus

minus1)

Present CO (aq)2

2 6 10 14 180

Past CO (aq)2

2 6 10 14 18D ay

Postbloom

2 6 10 14 18D ay

BloomPrebloom

F uture CO (aq)2

microm

olminus

minus1)

Present CO (aq)2

2 6 10 140

Past CO (aq)2

2 6 10 14D ay

0 5 10 15 20 25 30 35 40 45

PeECE III PeECE II

Pre- bloom post-

Factor levels

x nreplicates

Low HighLow

2 6 10 14 D ay

104 factor values

(microm

minus1)

PeECE II

F uture CO (aq)

Present CO (aq)2

Past CO (aq)2

0 2 4 6 8 10 12 14 16 18 200

(microm

minus2s

minus1)

50PeECE III

0 2 4 6 8 10 12 14 16 18 200

5 Conclusions

PAR= PAR0

MLDint0

fPAR =

(1minus e

minusaPARmiddotPAR

) (A3)

fT = eminusEamiddot

(1Tminus

) (A4)

(1minus

) (A5)

where Q= PhyNPhyC

Qsubs =Qlowast

Vmax =1

AffmiddotDIN

A3 Loss rates

Appendix B Forcings

E =sum

treatrepday|Y

M =sum

treatrepday|Ymod

Y E M units

References

Abstract

Introduction

Method

Results
Discussion
Phytoplankton loss
Conclusions
Data availability
Appendix B Forcings
Competing interests
Acknowledgements
References

(l) future CO2(aq)

(o) present CO2(aq)

2 5 8 11 14 170

2 5 8 11 14 17

(r) past CO2(aq)

4 Discussion

F uture CO (aq)2

microm

olminus

minus1)

Present CO (aq)2

2 6 10 14 180

Past CO (aq)2

2 6 10 14 18D ay

Postbloom

2 6 10 14 18D ay

BloomPrebloom

F uture CO (aq)2

microm

olminus

minus1)

Present CO (aq)2

2 6 10 140

Past CO (aq)2

2 6 10 14D ay

0 5 10 15 20 25 30 35 40 45

PeECE III PeECE II

Pre- bloom post-

Factor levels

x nreplicates

Low HighLow

2 6 10 14 D ay

104 factor values

(microm

minus1)

PeECE II

F uture CO (aq)

Present CO (aq)2

Past CO (aq)2

0 2 4 6 8 10 12 14 16 18 200

(microm

minus2s

minus1)

50PeECE III

0 2 4 6 8 10 12 14 16 18 200

5 Conclusions

PAR= PAR0

MLDint0

fPAR =

(1minus e

minusaPARmiddotPAR

) (A3)

fT = eminusEamiddot

(1Tminus

) (A4)

(1minus

) (A5)

where Q= PhyNPhyC

Qsubs =Qlowast

Vmax =1

AffmiddotDIN

A3 Loss rates

Appendix B Forcings

E =sum

treatrepday|Y

M =sum

treatrepday|Ymod

Y E M units

References

Abstract

Introduction

Method

Results
Discussion
Phytoplankton loss
Conclusions
Data availability
Appendix B Forcings
Competing interests
Acknowledgements
References

4 Discussion

F uture CO (aq)2

microm

olminus

minus1)

Present CO (aq)2

2 6 10 14 180

Past CO (aq)2

2 6 10 14 18D ay

Postbloom

2 6 10 14 18D ay

BloomPrebloom

F uture CO (aq)2

microm

olminus

minus1)

Present CO (aq)2

2 6 10 140

Past CO (aq)2

2 6 10 14D ay

0 5 10 15 20 25 30 35 40 45

PeECE III PeECE II

Pre- bloom post-

Factor levels

x nreplicates

Low HighLow

2 6 10 14 D ay

104 factor values

(microm

minus1)

PeECE II

F uture CO (aq)

Present CO (aq)2

Past CO (aq)2

0 2 4 6 8 10 12 14 16 18 200

(microm

minus2s

minus1)

50PeECE III

0 2 4 6 8 10 12 14 16 18 200

5 Conclusions

PAR= PAR0

MLDint0

fPAR =

(1minus e

minusaPARmiddotPAR

) (A3)

fT = eminusEamiddot

(1Tminus

) (A4)

(1minus

) (A5)

where Q= PhyNPhyC

Qsubs =Qlowast

Vmax =1

AffmiddotDIN

A3 Loss rates

Appendix B Forcings

E =sum

treatrepday|Y

M =sum

treatrepday|Ymod

Y E M units

References

Abstract

Introduction

Method

Results
Discussion
Phytoplankton loss
Conclusions
Data availability
Appendix B Forcings
Competing interests
Acknowledgements
References

F uture CO (aq)2

microm

olminus

minus1)

Present CO (aq)2

2 6 10 14 180

Past CO (aq)2

2 6 10 14 18D ay

Postbloom

2 6 10 14 18D ay

BloomPrebloom

F uture CO (aq)2

microm

olminus

minus1)

Present CO (aq)2

2 6 10 140

Past CO (aq)2

2 6 10 14D ay

0 5 10 15 20 25 30 35 40 45

PeECE III PeECE II

Pre- bloom post-

Factor levels

x nreplicates

Low HighLow

2 6 10 14 D ay

104 factor values

(microm

minus1)

PeECE II

F uture CO (aq)

Present CO (aq)2

Past CO (aq)2

0 2 4 6 8 10 12 14 16 18 200

(microm

minus2s

minus1)

50PeECE III

0 2 4 6 8 10 12 14 16 18 200

5 Conclusions

PAR= PAR0

MLDint0

fPAR =

(1minus e

minusaPARmiddotPAR

) (A3)

fT = eminusEamiddot

(1Tminus

) (A4)

(1minus

) (A5)

where Q= PhyNPhyC

Qsubs =Qlowast

Vmax =1

AffmiddotDIN

A3 Loss rates

Appendix B Forcings

E =sum

treatrepday|Y

M =sum

treatrepday|Ymod

Y E M units

References

Abstract

Introduction

Method

Results
Discussion
Phytoplankton loss
Conclusions
Data availability
Appendix B Forcings
Competing interests
Acknowledgements
References

F uture CO (aq)2

microm

olminus

minus1)

Present CO (aq)2

2 6 10 140

Past CO (aq)2

2 6 10 14D ay

0 5 10 15 20 25 30 35 40 45

PeECE III PeECE II

Pre- bloom post-

Factor levels

x nreplicates

Low HighLow

2 6 10 14 D ay

104 factor values

(microm

minus1)

PeECE II

F uture CO (aq)

Present CO (aq)2

Past CO (aq)2

0 2 4 6 8 10 12 14 16 18 200

(microm

minus2s

minus1)

50PeECE III

0 2 4 6 8 10 12 14 16 18 200

5 Conclusions

PAR= PAR0

MLDint0

fPAR =

(1minus e

minusaPARmiddotPAR

) (A3)

fT = eminusEamiddot

(1Tminus

) (A4)

(1minus

) (A5)

where Q= PhyNPhyC

Qsubs =Qlowast

Vmax =1

AffmiddotDIN

A3 Loss rates

Appendix B Forcings

E =sum

treatrepday|Y

M =sum

treatrepday|Ymod

Y E M units

References

Abstract

Introduction

Method

Results
Discussion
Phytoplankton loss
Conclusions
Data availability
Appendix B Forcings
Competing interests
Acknowledgements
References

Factor levels

x nreplicates

Low HighLow

2 6 10 14 D ay

104 factor values

(microm

minus1)

PeECE II

F uture CO (aq)

Present CO (aq)2

Past CO (aq)2

0 2 4 6 8 10 12 14 16 18 200

(microm

minus2s

minus1)

50PeECE III

0 2 4 6 8 10 12 14 16 18 200

5 Conclusions

PAR= PAR0

MLDint0

fPAR =

(1minus e

minusaPARmiddotPAR

) (A3)

fT = eminusEamiddot

(1Tminus

) (A4)

(1minus

) (A5)

where Q= PhyNPhyC

Qsubs =Qlowast

Vmax =1

AffmiddotDIN

A3 Loss rates

Appendix B Forcings

E =sum

treatrepday|Y

M =sum

treatrepday|Ymod

Y E M units

References

Abstract

Introduction

Method

Results
Discussion
Phytoplankton loss
Conclusions
Data availability
Appendix B Forcings
Competing interests
Acknowledgements
References

(microm

minus1)

PeECE II

F uture CO (aq)

Present CO (aq)2

Past CO (aq)2

0 2 4 6 8 10 12 14 16 18 200

(microm

minus2s

minus1)

50PeECE III

0 2 4 6 8 10 12 14 16 18 200

5 Conclusions

PAR= PAR0

MLDint0

fPAR =

(1minus e

minusaPARmiddotPAR

) (A3)

fT = eminusEamiddot

(1Tminus

) (A4)

(1minus

) (A5)

where Q= PhyNPhyC

Qsubs =Qlowast

Vmax =1

AffmiddotDIN

A3 Loss rates

Appendix B Forcings

E =sum

treatrepday|Y

M =sum

treatrepday|Ymod

Y E M units

References

Abstract

Introduction

Method

Results
Discussion
Phytoplankton loss
Conclusions
Data availability
Appendix B Forcings
Competing interests
Acknowledgements
References

5 Conclusions

PAR= PAR0

MLDint0

fPAR =

(1minus e

minusaPARmiddotPAR

) (A3)

fT = eminusEamiddot

(1Tminus

) (A4)

(1minus

) (A5)

where Q= PhyNPhyC

Qsubs =Qlowast

Vmax =1

AffmiddotDIN

A3 Loss rates

Appendix B Forcings

E =sum

treatrepday|Y

M =sum

treatrepday|Ymod

Y E M units

References

Abstract

Introduction

Method

Results
Discussion
Phytoplankton loss
Conclusions
Data availability
Appendix B Forcings
Competing interests
Acknowledgements
References

PAR= PAR0

MLDint0

fPAR =

(1minus e

minusaPARmiddotPAR

) (A3)

fT = eminusEamiddot

(1Tminus

) (A4)

(1minus

) (A5)

where Q= PhyNPhyC

Qsubs =Qlowast

Vmax =1

AffmiddotDIN

A3 Loss rates

Appendix B Forcings

E =sum

treatrepday|Y

M =sum

treatrepday|Ymod

Y E M units

References

Abstract

Introduction

Method

Results
Discussion
Phytoplankton loss
Conclusions
Data availability
Appendix B Forcings
Competing interests
Acknowledgements
References

Appendix B Forcings

E =sum

treatrepday|Y

M =sum

treatrepday|Ymod

Y E M units

References

Abstract

Introduction

Method

Results
Discussion
Phytoplankton loss
Conclusions
Data availability
Appendix B Forcings
Competing interests
Acknowledgements
References

Y E M units

References

Abstract

Introduction

Method

Results
Discussion
Phytoplankton loss
Conclusions
Data availability
Appendix B Forcings
Competing interests
Acknowledgements
References

References

Abstract

Introduction

Method

Results
Discussion
Phytoplankton loss
Conclusions
Data availability
Appendix B Forcings
Competing interests
Acknowledgements
References

Abstract

Introduction

Method

Results
Discussion
Phytoplankton loss
Conclusions
Data availability
Appendix B Forcings
Competing interests
Acknowledgements
References

Abstract

Introduction

Method

Results
Discussion
Phytoplankton loss
Conclusions
Data availability
Appendix B Forcings
Competing interests
Acknowledgements
References

Potential sources of variability in mesocosm experiments ... · sition succeeded in the experiments (Emiliania huxleyi was the major contributor to POC in PeECE II (Engel et al.,2008)

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