Journal of Marine Systems 78 (2009) 18–27

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Journal of Marine Systems

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Estimation of global zooplankton biomass from satellite ocean colour

K.H. Patrik Strömberg a,⁎, Timothy J. Smyth a, J. Icarus Allen a, Sophie Pitois b, Todd D. O'Brien c

a Plymouth Marine Laboratory, Prospect Place, PL1 3DH, Plymouth, UKb The Centre for Environment, Fisheries and Aquaculture Science, Pakefield Road, Lowestoft, NR33 OHT, Suffolk, UKc National Marine Fisheries Service-NOAA, Silver Spring, Maryland, USA

⁎ Corresponding author. Tel.: +44 1752 633466; fax:E-mail address: psto@pml.ac.uk (K.H.P. Strömberg).

0924-7963/$ – see front matter © 2009 Elsevier B.V. Adoi:10.1016/j.jmarsys.2009.02.004

a b s t r a c t

a r t i c l e i n f o

Article history:

A changing Earth System Received 31 July 2008Received in revised form 24 January 2009Accepted 3 February 2009Available online 15 February 2009

Keywords:Zooplankton biomassPrimary productionGlobal modelTrophic efficiencySatellite data

requires knowledge on a global scale. The only way of obtaining detailedinformation at these scales is by using satellite remote sensing and/or modeling. In the marine environment,information on primary production (PP) is derivable from satellite data, whereas datasets of higher trophiclevels are sparse. The challenge is to combine these two sources. A model relating the flow of energy from PPto zooplankton biomass, was used to address this problem. The model was parameterised with PP from theSeaWiFS satellite ocean colour record and a subset of a global dataset of zooplankton biomass. The model wasthen validated with the remaining zooplankton data. The model was used to: produce a map of annualglobal, zooplankton biomass, quantify the flow of carbon from PP to zooplankton and investigate the spatialvariability of this flow. One of the more notable findings is that more energy is transferred to zooplanktonwhen PP is low.

© 2009 Elsevier B.V. All rights reserved.

1. Introduction

A fundamental challenge in Earth System science is the responseof the marine ecosystem to changes in climatic forcing. In particularhow will it affect ecosystem functioning and the sustainability ofbio-resources. Datasets which allow us to map the distribution ofmarine biota are sparse. Satellite remote sensing can provide detailedinformation on a global scale for several bio-physical parameters, suchas temperature and chlorophyll (Robinson, 2004). The challenge is tocombine satellite data with the sparse in-situ datasets to generateglobal distributions of higher trophic levels. Models relating oceancolour to primary production arewell documented (Eppley et al.,1985;Behrenfeld and Falkowski, 1997; O'Reilly et al., 1998; Joint et al., 2002;Smyth et al., 2005; Carr et al., 2006). However, the flow of energy fromlower to higher trophic levels is less understood. The macroecologicaltheory developed by Jennings and Blanchard (2004) provides away ofaddressing this problem. The algorithm relates the flowof energy fromone trophic level, TL, to another using allometric scaling laws (Brownet al., 2004). Allometric scaling in biology (a variable raised to thepower≠1, autonym: isometric), was first documented by Kleiber(1932), in this case it refers to the scaling of metabolic rate, with bodymass, M, usually as M−0.75 (Brown et al., 2004). In a size structuredfoodweb where organisms share a common energy source the higherlevels will be constrained by inefficient transfer of energy, generallythought to be ≈10% between each level (Lindeman, 1942; Brown andGillooly, 2003). This loss of energy is referred to as the trophicefficiency, TE (predator production/prey production). To estimate the

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energy, E, of a chosen TL the decrease of E from TL0 to TLn, scales asEn=E0×TETLn−1 (Jennings andBlanchard, 2004). The attraction of thistheory is that it provides a simple set of relationships which relatesflow of energy through the marine foodweb. In order to demonstratethe applicability of this methodology the focus in this study is ongenerating a global climatology of zooplankton biomass. We combinethe primary production information from the SeaWiFS record (1998–20051) with a subset of the NMFS Coastal and Oceanic PlanktonEcology, Production and Observation Database, COPEPOD (O'Brien,2005), in order to parameterise themodel.We then ran themodel overthe global datasets and validated it with the remaining COPEPOD datanot used for the parametrisation.

It has been debated, in the literature, whether or not TE shouldvary with the availability of nutrients or PP, e.g. TE is higher in regionswith high PP and lower in regions with low PP (Sprules andMunawar,1986; Ahrens and Peters, 1991). This can be compared with analternative finding of higher grazing pressure in oligotrophic regions(Calbet, 2001). A study in the Atlantic ocean shows that high TE is notcoupled with high PP (San Martin et al., 2006). TE was thereforeinvestigated separately: I. on each grid point; and II. on regionssubdivided based on levels of primary productivity.

The overall aims of this study are: I. to provide a way of usingsatellite data to supplement otherwise sparse in situ data types (i.e.produce a global map of zooplankton biomass) II. to quantify theflow of energy to zooplankton biomass from primary production

1 ⁎(SeaWiFS data are currently available up to 2007, but COPEPOD data were up toand including 2005 and the aim here is annual biomass, hence the selection ofSeaWiFS data).

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(i.e. determine TE); and III. to investigate the spatial variability of thetransfer efficiency of this flow (i.e. determine how TE varies).

2. Methods

2.1. Model theory

The production, P, at a trophic level, TL, can be expressed as:

PTL = PP × TETL−1 ð1Þ

where TE = trophic transfer efficiency (TE = predator production/prey production), PP = primary production and TL = trophic level(Jennings and Blanchard, 2004).

In this study the trophic level of zooplankton is set to 2 (i.e. not 15Nbased (Owens, 1987) because: I. choosing a different TL(s) will notaffect the outcome (model is tuned to a ratio TE/PBR, as explainedbelow, TL falls out of the caluclation); II. data was not available on thespecies level; III. it keeps the model simple; IV. it is standard practice(Lindeman, 1942; Jennings and Blanchard, 2004; Gascuel, 2005).TL=2 reduces Eq. (1) to:

SP = PP × TE ð2Þ

where SP is secondary production.TE can be set to a fixed number because even if secondary

production is higher in areas of high primary production, (for exampleupwelling areas compared with oligotrophic areas) the higher SP isnot the result of higher TE per se (San Martin et al., 2006) but mostlikely the higher PP. To support this statement TE was investigatedseparately.

In order to make the comparison of model and data from thedatabase it was necessary to convert SP to biomass, B. An empiricallyderived P:B ratio (PBRe) was originally (i.e. Jennings and Blanchard(2004) used for this purpose:

PBRe = 10TL− 3:471

0:386 ð3Þ

Eq. (3) was specifically determined for higher trophic levels (e.g.fish) (Simon Jennings, pers. comm.) and is not applicable for thisstudy. Therefore we have a parametrisation problem of one equationand two unknowns; TE and PBR. A Monte Carlo randomisationapproach with PBR and TE as variables was used to solve this problem.The PBR is added to the model resulting in:

B =PP × TE

PBRð4Þ

The model (Eq. (4)) was tuned and validated with observationaldata. Half the data was randomly selected for the parametrisation ofthe model (i.e. the data were indexed using random numbers drawnfrom a uniform distribution to ensure that all values were equallylikely to be selected). The remaining half was retained for modelvalidation purposes. This division of the data set enables a moreindependent way of tuning and then assessing the model.

Satellite derived PP (details in next section)was extracted from thesame geographical position as the COPEPOD data (n=4843). TE forzooplankton can vary between 10–20% (Lindeman, 1942; Kiorboe andNielsen, 1994; Jennings and Blanchard, 2004; Gascuel, 2005). Hence,random values (20000) of TE were drawn from a uniform distribution(all values are equally likely to occur) between 0.1–0.2 and secondaryproduction was calculated using Eq. (2). Simultaneously, randomvalues (20000) of PBR from a uniform distribution between 0.05 to 1,were used to scale secondary production to biomass. This PBR rangewas selected based on observations: copepodites, 0.14 d− 1

(McClatchie et al., 2004); generic zooplankton (excluding Larvaceansand Thaliaceans), 0.06–1.6 d−1 (Hirst et al., 2003). The broad range of

PBR ensures that all possible values are tested and is narrowed downin the tuning process. The combination of TE and PBR that gave thebest goodness of fit (minimised RMSE) between modelled andobserved biomass was then saved for further analysis.

2.2. Satellite data

Satellite derived maps of ocean colour (O'Reilly et al., 1998) wereused to produce monthly averaged values of PP using the methodol-ogy of Smyth et al. (2005); these were then composited into a meanannual field, at a nominal resolution of 18 km, for the period between1998 and 2005.

The units for satellite derived PP are in mg C m−2 d−1. To make adirect comparison with the in-situ biomass, the units need to beconverted to mg C m−3 d−1. This is achieved by dividing by theeuphotic depth, Ze: (mg C m−2 d−1×m−1=mg C m−3 d−1). To dothis maps of Zewere produced using a similar technique as for PP (i.e.composited into annual mean). Ze, (m) was estimated fromchlorophyll-a, as (Morel and Berthon, 1989):

Ze = 200:0C−0:293tot ; if Ze b 102 Z Ze¼568:2C−0:746

tot ð5Þ

where the total pigment content, Ctot, (mg m−2) from the sea surfacedown to D is expressed as a function of pigment concentration in thesurface layer, Cs, (mg m−3);

Ctot = 40:2C0:507s ; if Cs b 1Z Ctot = 38C0:425

s ð6Þ

2.3. COPEPOD database

The COPEPOD database (O'Brien, 2005, http://www.st.nmfs.noaa.gov/plankton), is comprised of zooplankton biomass and abundancedata from four general sources: I. National Marine Fisheries ServicesEcosystem surveys; II. historical plankton data; III. data centres,institutions, and project data; and IV. direct investigator submissions.While the abundance data are sparse for many regions of the globe,COPEPOD does achieve near global coverage of zooplankton biomassdata. Most of these data are located in the northern Hemisphere andaround North America, with lesser amounts available for the southernPacific and the south Atlantic.

COPEPODoffers standardisedmean zooplankton biomass values ona global one degree longitude–latitude spatial grid. Per O'Brien (2005),this compilation consists of total sampled biomass data (e.g., wetmass,dry mass) and/or biovolume data (e.g., displacement volume, settledvolume), standardised to a common depth interval (0–200 m) and acommon mesh size (i.e. samples with mesh size 150–200 µm whereconverted to 330 µm). These biomass and biovolume values areavailable as carbon mass, converted to carbon (mg C m−3) using thepublished conversions of Wiebe (1988) and others (O'Brien, 2005).

The COPEPOD carbon mass fields are available by seasons and as asingle annualfield. The seasons aredefinedas themeteorological seasonsof the northern hemisphere: winter (Dec.–Feb.); 3650 values, spring(Mar.–May); 3792 values, summer (Jun.–Aug.); 4484 values, autumn(Sep.–Nov.); 3501 values (total of 15427 data values). The annual field iscreated from the average of the four seasonal fields (O'Brien, 2005). Thisstudy used the annual zooplankton carbon mass field, which wascomprised of 9687 zooplankton carbon mass (mg C m−3) values.

2.4. CPR data set

In addition to COPEPOD we also used the Continuous PlanktonRecorder (CPR) data set as an independent validation and parame-trisation source. The CPR survey has now been running for more than70 years, and provides one of the longest and most extensive marine

Fig. 1. Regions used. A. As defined by the Rutgers basin mask; 1. Atlantic, 2. Pacific, 3. Indian ocean, 4. Arctic, 5. Antarctic, and 6. Mediterranean. B. Location of the regions of theCOPEPOD database (approximate boundaries).

2 Provided by David Antoine at the Observatoire Oceanologique Laboratoire dePhysique et Chimie Marines, France. WWW Page, http://marine.rutgers.edu/opp/Mask/MASK1.html.

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ecological time-series in the world (Beare et al., 2003; Reid et al.,2003).

Information on the abundance of copepods and cladocerans(a total of 60 taxa) was extracted from the CPR database for theperiod 1998–2005 and covering the area delimited by latitudes 45°Nto 63°N and longitude 15°W to 10°E. Copepods and cladocerans wereselected because identification in CPR samples is generally carried outto species or genus level for these groups (in some other taxonomicgroups, identification is limited to family or higher categories). Out ofthe original 60 species, only those contributing at least 0.1% of totalbiomass in at least one of the five sub areas were kept, resulting indata on 29 key species being retained, accounting for N99% of totalbiomass.

The CPR survey collects samples at different times of day and atlocations that do not follow a regular grid. The data therefore need tobe spatially interpolated and regularised in time and space beforebeing subjected to numerical analyses (Beare et al., 2003). This wasundertaken on a 50×50 nautical mile (92.6×92.6 km) grid usingInverse Distance Interpolation (Lam, 1983; Legendre and Legendre,1998). A search radius of 150 miles (i.e. 277.8 km), and a minimum offive miles, and maximum of 100 neighbours were used, respectively.These values were chosen as a compromise between numericalefficiency and the need to keep the number of missing values in theinterpolated grid to a minimum. Average monthly abundances forindividual species were calculated taking diel variability of the CPRdata into account (Beaugrand et al., 2003).

Unfortunately the CPR is known to under-estimate zooplanktonabundance when compared with other datasets (John et al., 2001). Tocompensate for this, and to convert abundance values to biomass as mgdrymass m−3, the datawas corrected for under-sampling by usingWP-2(200 µm)/CPR (270 µm) ratios as described in Pitois and Fox (2006).The biomass values were converted from mg dry weight, (DW) m−3 tomg C m−3 using the method of O'Brien (2005) for conversion of theCOPEPOD zooplankton biomass data: log10(C)=(log10(DW)−0.499)/0.991 (Wiebe, 1988). This method of conversionwas selected to enable abetter comparison of CPR data and COPEPOD data.

The resulting data set, comprising matrices of CPR biomass, wasprocessed to condense the values for each year, 1998 to 2005, into asingle value at each grid point (by combining all the matrices). Thiscreated a total of 328 annualmean biomass values. Half of these valueswere randomly selected to tune themodel, and the remaining half wasused to assess the skill (to decrease the dependence on data).

2.5. Definition of regions

In the different analysis carried out different regions are analysed.These regions are: A. defined by the Rutger's basin mask2 and B.regions of the COPEPOD database. These regions are shown in Fig. 1.

2.6. Statistical methods

The following criteria were used to evaluate model skill.The percentage model bias is defined as:

kbias =

PM − Dð ÞP

D× 100 ð7Þ

where D represents the observations and M the model predictedvalues. Values were categorised as b10% excellent; 10 to 20% verygood; 20 to 40% good; N40% poor (Marechal and Holman, 2005). Anegative value indicates a tendency to underestimate.

The Root Mean Square Error (RMSE) was used for the modelparametrisation:

RMSE =

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiPD−Mð Þ2n

sð8Þ

RMSE can be used as a basic cost function (measure of goodness offit); the closer to zero, the better the fit.

Formal significance tests for differences between regions wereconducted using Analysis of Similarities, ANOSIM. The ANOSIMstatistic, R, contrasts the ranks of resemblances within groups andthose between groups, and is scaled to vary between −1 and +1(although values less than −0.1 are rarely achieved in practice). Ifgroups are perfectly separated then all ranks within groups will be lessthan all ranks between groups, and R=1. The null hypothesis of “nodifferences” between groups is addressed by randomisation. Multiplerandom rearrangements of the labels in the resemblance matrix areused to build up the distribution of R under the null hypothesis,

Fig. 3. Histograms showing the model tuned to a randomly selected 50% of the COPEPOD. The remaining half is plotted as ‘data’ and used for model — data comparisons (location ofthe regions shown in Fig. 1B). For statistics see Table 1. The data have been binned with bin size 4 (e.g. “0” on x-axis is the range 0–4, etc). Values over 100 are set to 100 (max of data).

Fig. 2. Annual (1998–2005) zooplankton biomass [mgCm−3] from themodel (TE≈0.16, PBR≈0.3). The biomass spatial distribution is the same as theunderlying PP asmapped from space.Thequantities are similar to the COPEPOD (% bias ~1%, Fig. 3).Most values are below10mgCm−3, hence the plot is in log space. Values over 100 are removed (set to 100, i.e. appears in black).

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Fig. 4.Mean zooplankton biomass [mg Cm−3], when the model is tuned to regions (Fig. 1a), compared with the model tuned on global scale. Error bars are the standard deviation ofthe mean [mg C m−3].

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against which the observed value is compared (P. Somerfield, personalcommunication). Tests were conducted in Primer v6 (Clarke andGorley, 2006).

2.7. The variability of trophic transfer efficiency

2.7.1. Trophic transfer efficiency on each grid pointTE was estimated at each grid point (i.e. lat/lon position),

where data were available (e.g. COPEPOD annual zooplanktonbiomass). A map of TE was then plotted to visualise any patterns(e.g. higher in upwelling regions and lower in oligotrophicregions). PBR was again allowed to vary 0.05–1. TE was allowedto vary between 0.1 to 0.2 and 20000 TE values were randomised(using uniform distribution) at each grid point, a total of 9686000(4843×20000) randomisations. The resulting matrix of TE valueswas globally mapped. Additionally, the resulting TE versus PPrelationship was tested for any correlation. This experiment wasrepeated with a fixed PBR.

2.7.2. Trophic transfer efficiency in regions defined by levels of PPThe global oceanwas divided into six basins (Fig. 1A); (1) Atlantic;

(2) Pacific; (3) Indian Ocean; (4) Antarctic; (5) Arctic; and (6)Mediterranean. These regions were then subdivided based on levels of

Table 1Statistics for histogram in Fig. 3.

Region n % bias RMSE r 2

Global 4533 −0.89 4.24 0.33North Atlantic 456 −4.55 10.84South Atlantic 371 31.91 7.71North Pacific 1526 −28.1 15.58South Pacific 1263 40.29 10.5Indian ocean 743 53.01 11.04Arctic 163 −36.81 15.77Antarctic 83 −44.92 13.5Bering–Chukchi 391 −68.49 21.49Gulf–Caribbean 206 −28.33 11.42Mediterranean 33 193.2 27.98Indonesia 304 8.18 15.18CPR 164 2.68 1.37

The RMSE and % bias is the goodness of fit between the model and the remaining datanot used for tuning. r 2 from data used for tuning (because there is no correlationbetween data for tuning and data for assessing skill) is shown for regions which themodel is tuned to. The regions are from the COPEPOD database definitions (Fig. 1B).

PP, which where low (PPb100.5 (~3.2) mg C m−3 d−1), medium(PPN100.5b101.5 (~32) mg C m−3 d−1 and high (PPN101.5 mg C m−3

d−1. The model was then tuned to the data in the regions to elucidateany patters related to levels of PP.

3. Results

3.1. Global map of zooplankton

Fig. 2, shows the global map of annual zooplankton biomass, withclear featues such as higher biomass in uppwelling regions and on thecontinental shelves, compared to e.g. the oligotrophic gyres. Anotherfeature is the stable patchiness of the Antarctic waters (annual scale).Fig. 3 illustrates one of the more important findings; that thedistributions of biomass are consistently lognormal (i.e. normal inlogspace).

The randomisation of TE and PBR, that gave the best goodness of fit(minimises RMSE), are: TE≈0.16, with a PBR≈0.30, at RMSEb0.01.(TEmodel/PBRmodel≈0.53). The skill (assessed with data not used fortuning) of this fit is RMSE≈4.24, % bias≈−0.89. Mean globalzooplankton biomass is 5.52 mg C m−3 (SD=8.94, n=4843).

These statistics indicate that the map of zooplankton biomass(Fig. 2) is accurate on the global scale, but less accurate on the regionalscale (Figs. 3, 4, Table 1 and Table A.1). Fig. 3 is showing thedistributions of biomass, withmost of the values in the lower bins. Thedistributions of data are similar for all regions except for one that willbe addressed separately in the discussion. The results agree broadlywith literature (Fig. 4, Table A.1).

Fig. 5.Model tuned to a randomly selected 50% of the CPR data set. The data plotted arethe remaining half of the CPR data set.

Fig. 6. Annual (1998–2005) zooplankton biomass [mg C m−3] from the model tuned to the regions: 1. Atlantic 2. Pacific 3. Indian Ocean 4. Arctic 5. Antarctic 6. Mediterranean(Fig. 1a). (Values over 100 set to 100, i.e. black in the plot).

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3.2. Comparison with CPR data

When the model is tuned to and compared with CPR data theresult is similar, but the average biomass is lower (Fig. 5).

TE was ≈0.16 when PBR≈0.25, (i.e. TEmodel/PBRmodel≈0.63). Thegoodness of fit was RMSEb0.01. This TE and PBR results in a meanbiomass of ≈4.1 mg C m−3 (SD=1.34, n=164). When the model isassessed, with the remaining data, the goodness of fit was; RMSE≈1.37% bias≈2.7% (indicating a total overestimation by ~2.7%, Table 1).

3.3. Tuning to regions

Model performance is excellent when assessed globally (%bias~1), but the model underestimates the lowest values (Fig. 3).When the model is compared to data on a regional basis (still tuned tothe global) the trend is similar, with underestimation of the lowervalues (Fig. 3), but a poorer overall fit with is indicated by the % bias(Table 1).

To investigate if a better fit could be obtained, for data in the basins,the model was also tuned to regions defined by Rutger's basin mask(Fig. 1a).

Fig. 7. The total proportion (TE/PBR) of primary production required to reproduce the zoopla

The basins contain enough data tomake such a tuning and to assessit. The outcome of this exercise was that model performance was stillgood in terms of goodness of fit, but the r2 was very poor (~0.09). Thissupports the feasibility of the original approach of usingone value of TEand PBR globaly. It alsomeans that themodel is still able to extrapolatethe zooplankton biomass from using the PP (e.g. reproduce the meanand standard deviation), but the trends (peaks) in the data are lost. Thereason for the low r 2 could be that there are outliers, so the modelbecomes skewed to higher values and hence the mismatch (Table 1).Some effects on the plot of global zooplankton biomass (e.g.differences in Figs. 2 and 6) are: 1. lower values for Mediterranean;2. the gyres are more clearly visible; 3. the low biomass region in theIndian Ocean is expanded; and 4. the biomass of the Arctic is higher.

3.4. The variability of trophic transfer efficiency

3.4.1. Trophic transfer efficiency on each grid pointNo spatial patterns were evident (hence plot not included) and

there was no relationship between PP and TE (ρ2b0.003, Spearman'srank correlation). This supports the finding of Gaudy et al. (2003) thathigh PP does not lead to higher ecological efficiency. It also supportsSan Martin et al. (2006) who showed that TE is not related to trophic

nkton biomass of the COPEPOD database for three different levels of primary production.

Fig. 8. Thefitted linearmodel for COPEPODbiomass vs PPwas: log10 (biomass)≈0.98×log10(PP) − 0.37, r 2≈0.36, pb0.001). CPR biomass is marked as red squares in the plot. Theregression for CPR biomass vs PP: log10 (CPR biomass)≈0.20×log10 (PP)−0.39, r 2≈0.01,p≈0.027(no linewasplotted). ThePPdataare fromthe samegeographical coordinates as thebiomass data.

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conditions. This assumes that nutrients are coupled with PP (e.g. highnutrients leads to high sea surface chlorophyll).

3.4.2. Trophic transfer efficiency in regions defined by the basin mask andlevels of production

Patterns become clearer when TE and PBR are examined in regionssubdivided on levels of primary production, e.g. a higher TE/PBR ratiowhen PP is low, indicating that more carbon needs to be transferredfrom PP to reproduce the zooplankton biomass reported in COPEPOD(Fig. 7, Table A.3). The PP levels in Fig. 7 are: high; N101.5 (~32),medium; N100.5b101.5, and low; b100.5 (~3.2) [mgCm−3 d−1]. Except:Mediterranean high; N101 (10), medium; N101b100.8, and low; b100.8

(~6.3). North Indian medium; N100.8b101.5, low; b100.8. South Indianhigh; N101.2 (~16) medium; N100.5 b101.2. Arctic medium; N100.9 (~8)b101.5, low; b100.9 (these exceptions are indicated by ⁎ in Table A.3).The differences between the regions are statistically significant whentested with ANOSIM (described in the method section).

(Global R≈0.35, p≈0.001. High vs medium; R≈0.45, p≈0.001.High vs low; R≈0.50, p≈0.001. Medium vs low; R≈0.18, p≈0.017.)

4. Discussion

An implication of simultaneously varying TE and PBR is tuning to theratio TE/PBR (the fraction of PP transferred to zooplankton biomass).Thismeans that TEandPBRare not independent. AnyTEandPBR,withinthe given limits, results in the ratio that maximises the RMSE goodnessof fit, hence the TE/PBR ratio is given in Fig. 7, Tables A.2 and A.3.However it is clear that TE is often higher then the commonly used valueof 10% but falls well within the range reported in the literature(Lindeman, 1942; Ikeda and Motoda, 1977; Kiorboe and Nielsen, 1994;Jennings and Blanchard, 2004; Gascuel, 2005). Furthermore this meansthat choosing a different TL in themodel will only change PBRwhile theresulting TE/PBR ratio (amount of carbon required fromPP to reproducethe biomass of COPEPOD) will remain the same (Table 2).

The randomisation method for conversion of production tobiomass (using the PBR variable) was selected over alternativemethods because the COPEPOD data used are not at a species- orindividual level but only bulk biomass. Alternative methods to convertproduction into biomass could involve individual growth rates (e.g.Huntley and Lopez,1992; Hirst et al., 2003). Thesemethods, especiallythose of Hirst et al. (2003), are excellent for use in a finer scale model(i.e. not bulk biomass but species or individual level).

The main reason for choosing the simple model is that it suits thepurpose of producing the global map of annual biomass. We are notneglecting the fact that the pelagic foodweb is highly complex withmany factors at play. Some factors which potentially affect theproduction of zooplankton (and hence biomass), are; ontogenetic dietshifts (e.g. the juveniles are herbivorous and the adults are carni-vorous and therefore at different TL); community structure andphysics (e.g. turbulence, turbidity, temperature, density, and entrain-ment). On the smaller scale most of these factors are feasible to beincluded in a model (subject to computational power). This isprobably also possible on the global scale, however there are nodata available to thoroughly assess such a model.

The fact that the model performs less well on the regional scale(Fig. 3, Table 1) is not surprising since it is tuned to the global scale.

Table 2The effect of different TLs on the model parameters is that PBR will be lower as TL ishigher, while the TETL−1/PBR ratio remains the same.

TL TETL−1 PBR TETL−1/PBR

2 0.108 0.196 0.5492.5 0.054 0.098 0.5493 0.018 0.032 0.5493.5 0.003 0.006 0.5494 0.002 0.003 0.549

One aim of this study was to produce a map of zooplankton biomass,given the data available. The RMSE used (as a cost function) to tunethe model is optimal to obtain a good fit. Furthermore, because thenumber of tunable parameters in this model are only two (TE andPBR) themodel ability to generalise is not affected asmuch as if a lot ofparameters would have been used (i.e. less dependant on data). Tofurther examine the relation between PP and the zooplanktonbiomass data from COPEPOD, the data were fitted to a linear model.A log transformation of the datawas applied tomake the data closer tonormal distribution (improve homogeneity of variances), reduceinfluence of outliers and improve linearity. The relation between log10biomass and log10 primary production (PP) was investigated in aregression: log10(biomass)=k×log10 (PP)+m, for both data sets(Fig. 8). This makes evident that the amount of variance that can beexplained by regressing these two variables is r 2~0.36.

The low correlation betweenmodel and data, r~0.33 (Table A.1), isnot surprising considering that the correlation between PP and data(COPEPOD) is also low; r~0.36 (Fig. 8).

The histogram plots of the different regions (Fig. 3) show generallysimilar distributions of the data, with the exception of Bering–Chuckhi.The Bering–Chukchi region has almost no biomass data for winter andautumn seasons (due to ice) and it is dominated by data from a regularsurvey that only samples in the summer. Hence the lower values fromother seasons are less dominant compared with the other regions.

The ecological explanation for the varying TE and PBR for thedifferent regions is uncertain. But interestingly the TE/PBR ratio (i.e.amount of carbon transferred from PP to zooplankton biomass) ismore or less the same for the Indian Ocean, Mediterranean and theAtlantic (Table A.2). This supports the initially proposed theory thatfixing TE and PBR to produce a global map gives a good estimate of thebiomass in those regions. The high TE/PBR in the Arctic could be aresult of underestimated primary production. For example if most ofthe zooplankton were sampled in the summer, then the proportion ofannual PP (which is lower than during summer, defined as themeteorological season of the northern hemisphere (O'Brien, 2005))that needs to be utilized to result in the SP biomass of COPEPOD willbe high. The same could be true for the Pacific and Antarctic region,but with a less dramatic effect (Table A.2). However it could also besome other factor such as low chlorophyll maxima (production not‘seen’ by satellite) or importance of the microbial loop. In the case ofthe microbial loop it again means that the assumed direct grazing on

Table A.1Model (M) tuned to global, data (D) and literature (L) on zooplankton biomass[mg C m−3] from different regions as defined by the Rutgers basin mask (Fig. 1A).Ref. 1. Piontkovski et al. (2003), 2. Pitois and Fox (2006), 3. Olli et al. (2007)([g DW m−2] converted by using sample depth (0–200 m) and the method ofO'Brien (2005), 4. Pakhomov and Froneman (2004) (2.69 mg C m−3 is at “spring iceedge ~60°S 6°E” and 12.32 mg C m−3 is at “Antarctic polar front ~50°S 6°E” during“Austral summer”), 5. Rakhesh et al. (2006) (“shelf, bay of Bengal”), 6. Batten andWelch (2004) (estimated from diagram. The data were from a cruise track ~35 N120 W to 60 N 145 W. Annual estimates from three years; 1997, 2000 and 2001), and7. Gaudy et al. (2003) (NW Mediterranean, mean of two investigations).

Region Source Min Median Mean SD Max Ref. Comment

Global M 0.53 3.32 5.52 8.94 271.5D 0.02 4.18 7.35 8.62 99.00

Atlantic M 0.96 4.71 7.98 13.12 271.5D 0.02 5.03 6.94 6.67 67.68 See also

CPRL 0.7 – – – +40 1 S.Atlantic

CPR M 1.91 4.13 4.10 1.34 9.78 N.AtlanticD 0.78 3.37 4.00 2.41 13.6 2

Arctic M 0.89 11.34 17.24 17.45 158.19D 0.02 2.91 6.45 8.78 55.53L – – ~3.20 – – 3 Converted

DWAntarctic M 0.72 2.79 3.87 3.97 108.06

D 0.2 6.71 8.41 8.02 59.73L 0.44 – 2.69–

12.32– 20.88 4 Converted

DWIndian Ocean M 1.03 3.45 5.4 8.48 269.86

D 0.02 2.44 4.81 6.82 59.07L – – 5.02 4.69 – 5 Converted

DWPacific M 0.53 3.09 4.53 6.78 191.33

D 0.04 5.03 8.61 9.74 99.00L 1.55 2.57 2.83 1.06 4.6 6 Converted

DWMediterranean M 1.22 3.66 6.77 10.72 156.07

D 0.67 1.46 2.53 2.72 13.51L 2.28 1.15 7 Converted

DW

25K.H.P. Strömberg et al. / Journal of Marine Systems 78 (2009) 18–27

the PP is not applicable or less dominant. The reason is that a largeportion of carbon could originate from DOM (dissolved organicmatter) via bacteria and not directly from PP.

4.1. Some possible sources of uncertainty

4.1.1. Tuning methodThemethod of tuning themodel using RMSE goodness of fit clearly

produce a model that reproduces the mean and standard deviation(low % bias and RMSE) correctly but fails to reproduce the trends(low r) of the data (Fig. 3, Table 1).

4.1.2. Zooplankton biomass dataThis could be a potential bias because the chosen TL=2 should

ideally only include organisms that feed directly on PP (TL=1). Thefact is thatwhat is referred to here as TL=2 is really TL=2 to ~3.5. TheCOPEPOD annual carbon mass fields, however, cannot be convertedback to individual zooplankton groups. This makes it impossible toassess and tune the model at each (TL) step. There are also areas(datasets) in the COPEPODwhere data are perhaps not as reliable as inothers, for example some data in the North Pacific. The choice oftemporal resolution (annual) could possibly contribute to this bias. Forexample there was little sampling in the northern Pacific during thewinter. However this should probably be of little concern because PPdata were also calculated as annual (eight years 1998 to 2005) meanbiomass.

Both the COPEPOD and the CPR data have beenprocessed in variousdifferent ways (explained in the method section). The COPEPOD datahasmany different origins. The zooplankton from COPEPOD have beensampled using changing techniques by different investigators and wasthen processed as described by O'Brien (2005) to produce the annualmean biomassfields. The CPR data have then been corrected for under-sampling, interpolated to a regular grid (to enable comparisons fromyear to year) and converted from abundance to dry weight and finallyto biomass. Both these data sources still give a good qualitativeindication to of the steady state annual standing stock zooplanktonbiomass.

4.1.3. PP estimatesPP may be underestimated as the Smyth et al. (2005) model only

uses surface values of chlorophyll. For example the deep chlorophyllmaxima could be higher (more important) than estimated in the PPmodel in some regions. The PP estimates are accurate on the globalscale (Smyth et al., 2005). Also some regions where the PP algorithmsare known to perform less well, for example the polar regions, theequatorial, northern Indian Ocean and in case II waters (affected byriverine output) (e.g. Carr et al., 2006). All of these issues affect theaccuracy of the main result in this study; the map of zooplanktonbiomass.

4.1.4. A large proportion of the energy is re-circulatedThe importance of energy from themicrobial loop and protozoa could

be underestimated. The approach of setting the trophic level, TL=2means that it is assumed that all energy (carbon) comes directly from PP.There is also the issue of ontogenetic diet shifts. In other words; allzooplankton are present in the carbon mass data fields, but only a smallproportion feeds directly on PP. This could explain the fact that lowprimary production yields a high proportion of energy transferred tozooplankton biomass (Fig. 7, Table A.3). However, if the model wasmodified, using adifferent TL (or TL's), theproportionTE/PBRwhich givesthe final result of zooplankton biomass, would remain the same (Table 2).

5. Conclusions

The map of annual zooplankton biomass is accurate (low RMSEand % bias) when assessed with the data available. It provides

information that is useful for comparisons with any future or pastchange in biomass. Furthermore, it demonstrates the feasibility ofcombining sparse in situ data with the data rich satellite remotesensing products.

This study also has shown that proportionally less energy (carbon)is transferred from PP when PP is high then when PP is low. Thespatial variability of transfer efficiency is important and cannot beignored if accurate zooplankton biomass is to be extrapolated on theglobe.

Acknowledgements

This research was funded by the EU Marie Curie EST projectMETAOCEANS (MEST-CT-2005-019678). Roger Harris–for constructivecomments on the manuscript. SAHFOS – for consistently maintainingone of the longest plankton time series database in the world. Allindividual investigators and institutions who have contributed toCOPEPOD. Simon Jennings for suggesting a different P:B-ratio approach.All statistical testing was performed using the R language andenvironment for statistical computing (http://CRAN.R-project.org).Satellite data was prepared in IDL. Ocean color data used in this studywere produced by the SeaWiFS Project at Goddard Space Flight Center.The data were obtained from the Goddard Earth Sciences DistributedActive Archive Center under the auspices of the National Aeronauticsand Space Administration. Use of this data is in accordwith the SeaWiFSResearch Data Use Terms and Conditions Agreement.

Appendix A

Table A.2Model (Mg) tuned to global, Model (Mr) tuned to region (Fig. 1A) and data (D).Zooplankton biomass [mg Cm−3]. TE and PBR tuned to region. The over all (global)modelperformance after this tuning is % bias≈−0.81, RMSE≈5.84, r2≈0.09. The TE and PBRvary on regions and “Global Mr” is the summary of all regions (⁎).

Region Source Min Median Mean SD Max TE PBR TE/PBR

Global Mg 0.53 3.32 5.52 8.94 271.5 0.16 0.30 0.53Mr 0 4.97 7.29 9.90 155.4 ⁎ ⁎ –

D 0.02 4.18 7.35 8.62 99.00Pacific Mg 0.53 3.09 4.53 6.78 191.33

Mr 0.71 4.16 6.09 9.12 257.3 0.10 0.14 0.71D 0.04 5.03 8.61 9.74 99.00

Atlantic Mg 0.96 4.71 7.98 13.12 271.5Mr 0.81 3.94 6.68 10.99 227.34 0.16 0.35 0.46D 0.02 5.03 6.94 6.67 67.68

Indian Ocean Mg 1.03 3.45 5.4 8.48 269.86Mr 0.77 2.58 4.03 6.33 201.38 0.16 0.40 0.40D 0.02 2.44 4.81 6.82 59.07

Arctic Mg 0.89 11.34 17.24 17.45 158.19Mr 1.2 4.66 6.46 6.61 180.14 0.16 0.17 0.94D 0.02 2.91 6.45 8.78 55.53

Antarctic Mg 0.72 2.79 3.87 3.97 108.06Mr 0.0 9.41 8.41 8.35 47.91 0.16 0.25 0.64D 0.2 6.71 8.41 8.02 59.73

Mediterranean Mg 1.22 3.66 6.77 10.72 156.07Mr 0.9 2.69 4.97 7.88 114.68 0.18 0.44 0.41D 0.67 1.46 2.53 2.72 13.51

Table A.3Model tuned to basin (Fig. 1A. North and South are separated at the equator) and levelof primary production. ⁎ indicates different bin sizes.

Region PP level Mean PP SD PP n TE PBR TE/PBR

Global High 59 43 549 0.16 0.63 0.25Medium 10 6.3 7880 0.16 0.24 0.67Low 2.7 0.36 637 0.19 0.34 0.56

North Pacific High 51.73 29.1 225 0.14 0.38 0.36Medium 10.21 6.35 2948 0.18 0.21 0.88Low 1.75 1.34 534 0.17 0.05 3.2

South Pacific High 66.45 37.65 53 0.13 0.9 0.14Medium 9.79 5.02 678 0.19 0.28 0.68Low 1.57 1.26 108 0.2 0.07 2.81

North Atlantic High 78.83 71.94 92 0.12 0.75 0.16Medium 13.43 6.62 1426 0.1 0.2 0.52Low 2.83 0.23 26 0.19 0.08 2.31

South Atlantic High 91.4 56.6 20 0.16 0.96 0.16Medium 10.14 5.89 354 0.2 0.49 0.41Low 2.48 0.37 89 0.16 0.15 1.07

North Indian Ocean High 52.8 34.98 84 0.17 0.56 0.3Medium⁎ 13.77 6.21 569 0.16 0.34 0.47Low⁎ 5.91 0.71 14 0.15 0.07 2.15

South Indian Ocean High⁎ 42.33 2.01 2 0.14 0.82 0.17Medium⁎ 6.72 2.67 683 0.18 0.72 0.26Low 2.51 0.33 44 0.14 0.33 0.42

Antarctic High 55.92 23.87 26 0.18 0.7 0.25Medium 6.53 4.11 986 0.11 0.13 0.88Low 2.91 0.17 68 0.16 0.04 4.25

Arctic High 36.38 8.18 25 0.13 0.76 0.17Medium⁎ 19.34 5.25 126 0.16 0.28 0.56Low⁎ 7.28 0.82 2 0.12 0.13 0.92

Mediterranean High 11.64 1.93 13 0.14 0.48 0.28Medium⁎ 7.72 0.89 27 0.12 0.54 0.23Low⁎ 5.57 0.44 12 0.11 0.19 0.59

26 K.H.P. Strömberg et al. / Journal of Marine Systems 78 (2009) 18–27

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