Seasonal and geographic variations in phytoplankton losses from the mixed layer on the Northwest Atlantic Shelf

Journal of Marine Systems 80 (2010) 36–46

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Journal of Marine Systems

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Seasonal and geographic variations in phytoplankton losses from the mixed layer onthe Northwest Atlantic Shelf

Li Zhai a,b,⁎, Trevor Platt a,c, Charles Tang a, Shubha Sathyendranath b,c, César Fuentes-Yaco a,b,Emmanuel Devred a,b, Yongsheng Wu a

a Bedford Institute of Oceanography, Dartmouth, Nova Scotia, Canada B2Y4A2b Department of Oceanography, Dalhousie University, Halifax, Nova Scotia, Canada B3H4J1c Plymouth Marine Laboratory, Prospect Place, The Hoe, Plymouth, PL13DH, UK

⁎ Corresponding author. Bedford Institute of OceanogCanada B2Y4A2.

E-mail address: [email protected] (L. Zhai).

0924-7963/$ – see front matter © 2009 Elsevier B.V. Adoi:10.1016/j.jmarsys.2009.09.005

a b s t r a c t

Article history:Received 1 December 2008Received in revised form 6 July 2009Accepted 25 September 2009Available online 12 October 2009

Keywords:Phytoplankton lossesMixed layerPrimary productionSeaWiFS, AVHRR

The total daily phytoplankton loss from the mixed layer is estimated as the difference between the primaryproduction and the realized change of phytoplankton carbon biomass. A Monte Carlo procedure is used torecover the total loss rates for ten geographic locations on the Northwest Atlantic continental shelf. Thestrong seasonal and geographic variations in mixed-layer loss rates of phytoplankton are tied closely to theprimary production. The daily, mixed-layer, total loss ranges from 50 to 1000 mgCm−2d−1, which iscompared with the output of process models, the closure error being generally less than 10% of the total loss.The model results show that the annual respiration is generally greater than losses due to zooplanktongrazing and sinking, except that zooplankton grazing dominates other loss terms on the west Greenlandshelf.

raphy, Dartmouth, Nova Scotia,

ll rights reserved.

© 2009 Elsevier B.V. All rights reserved.

1. Introduction

Quantifying the carbon cycling through marine phytoplankton isimportant for understanding the impact and feedback of climatechange on ocean ecosystems (Emerson and Hedges, 2008; Koelleret al., 2009). Until recently, we lacked the tools to study the problemon synoptic scales. Fortunately, the SeaWiFS ocean-colour data havebeen available since 1997, and are invaluable for determiningabundance, growth and loss of phytoplankton (Platt et al., 2009a). Itis straightforward to estimate photosynthetic rate and the change ofphytoplankton carbon with time from serial composite images ofchlorophyll concentration (Platt et al., 2008). The difference betweenthem is defined as the phytoplankton total loss. The total loss includesphysical (advection and mixing) and biological (respiration, grazing,sinking and natural mortality) losses. Every one of the biologicalcomponents is difficult to measure, either in the laboratory or in thefield.

The oceanic mixed layer has an ecological as well as a physicalsignificance because it generally encompasses much, or all, of thelayer in which photoautotrophic production can occur in theNorthwest Atlantic Ocean. The phytoplankton total loss from themixed layer is an informative indicator of the pelagic ecosystem status

(Platt and Sathyendranath, 2008; Platt et al., 2009b), and is a key termin models of the ocean carbon cycle (Fasham et al., 1990; Antoine andMorel, 1995; D'Ortenzio et al., 2008). Also, as a check on the output ofecosystemmodels, we need to know the time-varying phytoplanktontotal loss from the mixed layer. Although measurements of phyto-plankton losses have been collected in the sea (Deuser and Ross, 1980;Lampitt et al., 1993; Francois et al., 2002; Suttle, 2005), the under-sampling poses a significant challenge for estimation of the mixed-layer phytoplankton total loss at large temporal and spatial scales(Walsh, 1983). Given the limitations of sampling, there has been littlepreviouswork to determine this important quantity over a wide rangeof physical and biological regimes. Siegel et al. (2002) used a remote-sensing method to estimate the loss terms, but their method isapplicable only at the time of spring bloom initiation.

Here, we develop an approach to provide estimates of theseasonally and geographically varying phytoplankton total loss fromthemixed layer using eight-day composite images of remotely-sensedocean-colour data. We quantify mixed-layer total loss for thecontinental shelf of the Northwest Atlantic Ocean (Fig. 1), where thephysical and biological processes are highly dynamic. Our resultsshould be of interest to those studying the biologically-mediated oceancarbon cycle, ecosystem models, physical and biological interactions,and to those measuring phytoplankton losses at sea in general.

The paper is structured as follows. Section 2 introduces themethodand discusses the observations and parameters. Section 3 presentsseasonal and geographic variations in the estimated phytoplanktontotal loss. In Section 4, the total loss is used to check the closure of

Fig. 1. The study region with ten geographic locations on the Northwest Atlantic Shelf(square boxes). Bathymetric contours are labeled in meters. The locations of theobserved photosynthetic parameters are marked by the solid circles. Abbreviationsused: Nova Scotia (N.S.) and Newfoundland (Nfld).

Fig. 2. The function f (I⁎m) calculated from the fifth-order polynomial approximations forthe range 0.2≤ I⁎

m≤20.

37L. Zhai et al. / Journal of Marine Systems 80 (2010) 36–46

process models, and to compare with the sum of losses resulting fromrespiration, excretion, zooplankton grazing, sinking and mixing.Summary and conclusions are given in Section 5.

2. Methods and sources

The principle for calculation of the generalized loss rates ofphytoplankton was proposed by Cushing (1992) and Platt andSathyendranath (2008), and developed by Zhai et al. (2008) whopresented an algorithm, based on a Monte Carlo procedure, to recovertotal loss rates of phytoplankton at the sea surface from time series ofthe marine chlorophyll a field, as determined by remote-sensing ofocean-colour. One advantage of the Monte Carlo procedure is that itprovides a quantitative assessment of the uncertainty estimates onthe calculation. In this study, we apply the algorithm to estimate thephytoplankton total loss from the entire mixed-layer using 8-daycomposite images of phytoplankton biomass fields (indexed asconcentration of chlorophyll a) and an analytical model for daily,mixed-layer primary production. The calculation was done for 10representative 1°×1° squares located on the continental shelf of theNorthwest Atlantic Ocean (Fig. 1). In principle, we could apply thealgorithm at the global scale, given remotely-sensed biomass fieldsand the necessary information on parameters of the photosyntheticresponse of phytoplankton.

2.1. Method

Over a given interval of time, the net change of phytoplanktoncarbon biomass for the mixed layer is the difference between the

mixed-layer primary production and the phytoplankton total lossfrom the mixed layer. It might be formulated simply as

∫ZmðtÞ0

∂ðχBðz; tÞÞ∂t dz = ∫ZmðtÞ

0 ½Pðz; tÞ−Lðz; tÞ�dz; ð1Þ

where z is depth (positive downward), Zm is the mixed layer, t is time,χ=79B−0.35 is the ratio of phytoplankton carbon to chlorophyll asgiven by Sathyendranath et al. (2009), B is the phytoplankton biomass(chlorophyll concentration), and P and L are the rates of productionand total loss in carbon units. The vertical distribution of biomasswithin the surface mixed layer of the ocean may be assumed to beuniform. This assumption allows us to simplify Eq. (1) (see AppendixA) and to write the daily phytoplankton production in themixed layerin the canonical form given by Platt and Sathyendranath (1993). Thedaily phytoplankton total loss from the mixed layer can then beexpressed as

LZm ;T = PZm ;T−ZmΔðχBÞΔt

; ð2Þ

where PZm,T and LZm,T are the daily mixed-layer primary productionand loss, Δt is the time interval (about 8 days) between twoconsecutive 8-day composite images in the ocean-colour time series,and Δ(χB) is the net change of phytoplankton carbon biomass duringthe time interval Δt. The daily phytoplankton production in the mixedlayer (Platt and Sathyendranath, 1993) is given as

PZm ;T = A × f ðIm⁎ Þ−A × f ðIm⁎ e−KZm Þ; ð3Þ

where A=PmB DB/K, PmB is the assimilation number, D is the day length,

K is the vertical diffuse attenuation coefficient (Sathyendranath andPlatt, 1988), I⁎

m= I0m/Ik is the dimensionless, surface irradiance at local

noon, I0m is the maximum surface irradiance at local noon, Ik is theadaptation parameter, and f (.) is a known function (Fig. 2) that can beapproximated, for example, by a fifth-order polynomial function onthe interval 0.2≤qI⁎

m≤20 (all variables and parameters are summa-rized in Table 1).

There are manymodels available for estimating primary productionfrom ocean-colour data (Platt and Sathyendranath, 1988; Morel, 1991;Behrenfeld and Falkowski, 1997). Carr et al. (2006) and Friedrichs et al.(2009) comparedmore than twentymodels of primary production, andreported that model performance is affected mainly by uncertainties inparameters and in input variables. In this study, photosynthesis–irradiance parameters are assigned to each pixel from a data base,including more than a thousand 14C measurements in the NorthwestAtlantic (Fig. 1), using a Nearest-Neighbourhood Method that has beentested against direct observations of the parameters (Platt et al., 2008).

Table 1Glossary of mathematical notation.

Notation Quantity and description Typical units

A Scale factor in expression for daily, watercolumn production

mgCm−2d−1

B Biomass, as concentration of chlorophyll a mgChlm−3

D Daylength hEZm,T Daily excretion loss from the mixed layer mgCm−2d−1

g Micro-zooplankton grazing rate d−1

GZm,Tmicro Daily micro-zooplankton grazing loss from

the mixed layermgCm−2d−1

GZm,Tmacro Daily macro-zooplankton grazing loss from

the mixed layermgCm−2d−1

H Heaviside step function DimensionlessI Irradiance in the Photosynthetically Active

Range (PAR)Wm−2

I0 Irradiance at the surface (z=0) Wm−2

I0m Maximum surface irradiance at local noon Wm−2

Ik=PmB /αB Adaptation parameter of the PB–I curve Wm−2

I⁎m= I0

m/Ik Dimensionless irradiance at local noon DimensionlessK Vertical attenuation coefficient for irradiance m−1

L Total loss rate per unit volume mgCm−3h−1

LZm,T Daily phytoplankton total loss from the mixedlayer

mgCm−2d−1

MZm,T Daily phytoplankton loss from the mixedlayer resulting from deepening of mixed layer

mgCm−2d−1

P Primary production rate per unit volume mgCm−3h−1

PZm,T Daily primary production in the mixed layer mgCm−2d−1

⟨PB⟩Zm ;T Daily primary production in the mixed layernormalized to biomass, averaged over depth

mgC(mg Chl)−1d− 1

PmB Assimilation number mgC(mg Chl)−1h−1

R0B Maintenance respiration mgC(mgChl)−1d−1

RD Coefficient of respiration in the dark DimensionlessRL Coefficient of respiration in the light DimensionlessRZm,T Daily respiration loss from the mixed layer mgCm−2d−1

SZm,T Daily sedimentation loss from the mixedlayer

mgCm−2d−1

w Sinking velocity md−1

Zm Mixed-layer depth mαB Initial slope of the PB–I curve mgC(mg Chl)−1h−1

(W m−2)−1

a⁎B Specific absorption coefficient for chlorophyll m2(mgChl)−1

ϕm Maximum realizable quantum mgCh−1W−1

χ Phytoplankton carbon-to-chlorophyll ratio mgC(mg Chl)−1

38 L. Zhai et al. / Journal of Marine Systems 80 (2010) 36–46

The uncertainties in input variables and parameters are taken intoaccount by a Monte Carlo procedure. The Monte Carlo method,described in Zhai et al. (2008) is used to solve Eq. (2) and calculatesan ensemble of phytoplankton losses. The procedure is to repeat thecomputation 1000 times with randomly selected input variables andparameters from the ensemble of observations. The probabilitydistribution of the ensemble (based on many pixels in a given box,and on variations between years) is estimated from the kernel density, a

Fig. 3. The seasonal and geographic variations of median values of (a) phytoplan

smoothed version of the histogram. The width of the envelope of thekernel density represents the spatial and interannual variabilityobserved in this study. The shape of the kernel density indicatespossible deviations of the probability distribution from a normaldistribution.

2.2. Biomass, diatom occurrence and C:Chl ratio

The 8-day climatological chlorophyll was created from the 10-year(1998 to 2007) time series of 8-day SeaWiFS chlorophyll composites,which were processed using SeaDAS software and the OC4 (v4.3)algorithm and have a resolution of 1.5 km. The 8-day climatology foreach 1°×1° square includes a large number of pixels (≤3×104), andcontains information on statistical modes and probability distribu-tions (see Zhai et al., 2008 for details). The median values of biomassdistribution for the ten boxes (Fig. 3a) exhibit strong seasonal andlatitudinal variation. Thewinter biomass concentration varies from0.2to 0.7 mg Chl m−3 from boxes 1 to 10. During the spring bloom, thebiomass is highly variable and ranges from 0.5 to 4 mg Chl m−3,whereas during the fall bloom, the biomass is less variable and rangesfrom 0.5 to 1.5 mg Chlm−3. The biomass concentration in the summerhas values ranging from 0.3 to 1.0 mg Chl m−3.

The phenology of spring and fall blooms (Platt et al., 2009a) varieswith latitude (Fig. 3a). The timing of spring blooms is later frommiddleto high latitudes, whereas the timing of fall blooms occurs earlier athigher latitudes. These observational features are consistent with thecaricature presented by Cushing (1959), in which the seasonal cycleincluded spring andautumnblooms in temperate latitudes, but only onebloom per year in the Arctic. These features have been captured in aperiodically-forced phytoplankton-nutrient model (Platt et al., 2009b).

There are local effects (e.g. mixed-layer depth) that modify thegeneral latitudinal trend of spring blooms. For example, spring blooms(Fig. 3a) start earlier in box 1 (Western Greenland, 61.5° N) than inbox 3 (Labrador Shelf, 54.25° N) (Wu et al., 2008). The spring bloomsalso occur earlier in box 8 (Middle Scotian Shelf) compared with box10 (Gulf of Maine). Spring blooms start when the depth-averagedirradiance in the Photosynthetically Active Range (PAR) in the mixedlayer reaches at least 13 Wm−2 (Platt et al., 2009a).

Wehaveapplied the algorithmof Sathyendranath et al. (2004) to thetime series of remotely-sensed ocean colour data in the ten boxes todetermine whether the phytoplankton community is dominated bydiatoms. In general, the diatom climatology (Fig. 3b) demonstratessimilar seasonal and geographic variation to that of chlorophyll. Thehigher probabilities of occurrence of diatoms coincide with spring andfall blooms,whereas the probability of occurrenceof diatoms falls below0.2 when biomass is low. The probability of occurrence of diatom is anindex of the probability that the phytoplankton community at a givenpixel and time is dominated by diatoms. It is not equal to the percentage

kton biomass and (b) probability of occurrence of diatoms for the ten boxes.

39L. Zhai et al. / Journal of Marine Systems 80 (2010) 36–46

of total chlorophyll contained in diatoms, although the two are looselycorrelated. It is note-worthy that diatoms dominate the fall bloommorethan they do the spring bloom for boxes 7 to 10.

It is known that χ varies with the trophic status of the ecosystemand the associated community structure of phytoplankton. Sathyen-dranath et al. (2009) derived the relationship for phytoplanktoncarbon-to-chlorophyll ratio from more than 800 field and laboratorymeasurements of particulate carbon and chlorophyll a. The phyto-plankton carbon is assumed to be the left-hand tail of probabilitydistribution of an ensemble of particulate carbon at a given chlo-rophyll a concentration. We have applied the empirical relationshipbetween phytoplankton carbon and chlorophyll of Sathyendranathet al. (2009) to the time series of remotely-sensed ocean-colour datain the ten boxes to determine the carbon-to-chlorophyll ratio. Themedian values of C:Chl ratio (Fig. 4) range from 47 to 110 throughoutthe year for the ten boxes. During spring blooms, the C:Chl ratio isconsistently low, ranging from 47 to 60, associated with thedominance of diatoms. After the bloom, the C:Chl ratio increases to90, as the species composition of the phytoplankton communitybecomes dominated by flagellates (Forget et al., 2007). The increasedC:Chl ratio for boxes 1 to 6 in the winter and summer, also suggeststhat the phytoplankton communities in that period are different fromthose found during the spring bloom.

2.3. SST and mixed-layer depth

The sea surface temperature (SST) is used (with chlorophyll) asinput to the assignment of photosynthetic parameters using theNearest-Neighbour Method (Platt et al., 2008). The 8-day climatolog-ical SST is constructed using the 10-year time series (from 1998 to2007) of 8-day AVHRR SST composites in each of the 10 boxes. SSTvaries from −2 to 20 °C, with seasonal cycles being stronger intemperate latitudes and weaker in higher latitudes (Fig. 5a). Theseasonal variation of SST is affected mainly by net sea surface heatflux, however ocean circulation and mixing also influence thetemporal and spatial variations of SST. For example, the winter SSTin box 4 (Flemish Cap) is above 3 °C on average and is affected by theNorth Atlantic Drift carrying warm Gulf Stream water (Petrie et al.,2003). The winter SST in box 8 (Middle Scotian Shelf) is warmer thanboxes 7 and 9 and probably associated with the onshore heat flux ofslope water through the Scotian Gulf to Emerald Basin (Smith, 1978;Smith and Petrie, 1982).

The mixed-layer depth is defined as the depth at which densitychanges by 0.1 kg m−3 from the sea surface density. The density iscalculated from the monthly climatology of temperature and salinity(Tang, 2007). In this study, the 8-day climatology of the mixed-layer

Fig. 4. The seasonal and geographic variations of median values of the carbon-to-chlorophyll ratio for the ten boxes.

depth is acquired through the linear interpolation of the monthlyclimatology. The median values of the mixed-layer depth lie in therange from 2 to 150 m (Fig. 5b), showing a strong seasonal cycle andgeographic differences between the ten regions. The seasonal cycle ofmixed-layer depth is determined by both meteorological andoceanographic conditions (Tang et al., 1999; Wu et al., 2007). Surfacecooling and high winds cause the mixed layer to deepen through thelate fall and winter. From early April to early fall, the mixed layershallows due mainly to solar heating and fresh water flux. The wintermixed-layer depth generally increases with latitude, but it is relativelydeeper than expected in Gulf of Maine (box 10), because of strongtidal mixing in the Bay of Fundy and southwest Nova Scotia. Theduration of the shallow (<10 m) mixed-layer phase in the summerdecreases from low to high latitude, associated with the decreasingsolar heating with latitude, but the duration is relatively long on thewestern Greenland shelf, likely associated with the northwardadvection of the low-salinity water of Irminger Sea carried by theWestern Greenland Current.

The shallowing of the mixed-layer depth in spring is important forthe initiation of spring blooms. The conventional theory is still that ofSverdrup (1953), which tells us that the incipient shallowing ofmixed-layer depth in spring, associated with the increase in solarradiation, promotes the rapid growth of phytoplankton in the layer.Platt et al. (1991) refined the Sverdrup theory and gave a sufficientcondition for the occurrence of a bloom, which is that the time scalefor bloom development should be small compared with the timeinterval between storms. Any deepening of the mixed-layer depthdilutes and redistributes the biomass in the mixed layer. We discussthis further in Section 3.

2.4. Daily photosynthesis

A key step in computing themixed-layer primary production is theobjective assignment, on a pixel-by-pixel basis (1.5×1.5 resolution),of the photosynthetic parameters. Here we use the Nearest-Neighbour Method (NNM) (Platt et al., 2008). For each pixel, theassignment is made on the basis of its chlorophyll and temperature bysearching in an archive of photosynthetic parameters arrangedaccording to chlorophyll, SST and the time of the year. Fig. 1 showsthe spatial distribution of our archived photosynthetic parameters forthe Northwest Atlantic.

The 10-year time series of the assimilation number PmB and initialslope αB of the P–I curve were obtained using the NNM, andwere thengrouped in the same way as the satellite chlorophyll to create 8-dayclimatological fields for the ten boxes. The median values of assignedPmB andαB (Fig. 6) show a seasonal cycle and a variationwith latitude, a

consequence of the dependence of photosynthetic parameters on SSTand chlorophyll (Platt et al., 2008). The assigned assimilation numberPmB ranges from1.5 to 5.5 mgC(mg Chl)−1h−1, and the assigned initial

slope varies between 0.04 and 0.18 mgC(mg Chl)−1h−1(Wm−2)−1.During spring blooms, PmB and αB are consistently low, associated withhigh biomass concentration and the dominance of diatoms (Platt et al.,2008). Themaximum Pm

B occurs between August and October and lagsthemaximumSST by about one to twomonths,whereas themaximumαB occurs around June when the solar irradiance is highest.

From the assigned PmB and αB we can derive another important

quantity, namely the photoadaptation parameter Ik=PmB /αB. The

median values of Ik (Fig. 6c) range from 18 to 58 Wm−2, rising tomaxima in March and early fall and dropping to a minimum in June.There is a general tendency for Ik to decrease with increasing latitude(Platt et al., 1994). The changes in Ik appear to be duemore to changesin αB rather than to those in Pm

B . Since αB=a⁎Bϕm (Platt and Jassby,

1976), where a⁎B is the specific absorption coefficient for chlorophyll

and ϕm is the maximum realizable quantum yield (Table 1), thesechanges could be due to an increase (decrease) in the average specificabsorption coefficient per unit chlorophyll associated with a decrease

Fig. 5. The seasonal and geographic variations of median values of (a) the AVHRR sea surface temperature and (b) the mixed-layer depth for the ten boxes.

40 L. Zhai et al. / Journal of Marine Systems 80 (2010) 36–46

(increase) in the cellular chlorophyll content at higher (lower) lightintensity (Platt and Jassby, 1976; Kirk, 1994).

To generalize the analytical model of daily water column primaryproduction, Platt et al. (1991) defined a normalized irradiance at localnoon I⁎

m, obtained by scaling noon irradiance to Ik. The noon irradiance isderived from an empirical relationship between the SeaWiFS total dailyPARclimatology, daylengthand latitude (Platt et al., 2009b). Themedianvalues of I⁎

m (Fig. 6d) range from 2.5 to 17.5. The quantity I⁎m reaches a

maximum in the summer and a minimum in the winter, and decreaseswith latitude. The function f (I⁎

m) in the production model (Eq. (3)) isdimensionless and accounts for all the variability in primary productiondue to changes in PAR forcing. Values of f (I⁎

m) over the typical range of I⁎m

(Fig. 2) vary from 0 to 3.The calculation of daily primary production in the mixed layer is

obtained as the difference between the production of the entire water

Fig. 6. The seasonal and geographic variations of median values of (a) assimilation numbercurve, (c) adaptation parameter (Wm−2) of the P–I curve, and (d) dimensionless irradianc

column and that below mixed layer Zm (Platt and Sathyendranath,1993). The daily production for thewholewater column is forcedwiththe surface light intensity, and the production below the mixed layercan be thought of as that for another infinite column, but forced by thereduced light I0 exp(−KZM). The advantage of the above interpreta-tion is the mathematical similarity for the two terms on the right sideof Eq. (3).

The daily primary production in the mixed layer is estimated usingthe NNM for parameter assignment. The NNM method has beenvalidated in various aquatic systems and leads to good estimates ofprimary production in regions where the available data on photosyn-thetic parameters are sufficient (Forget et al., 2007; Platt et al., 2008).The median values of the primary production (Fig. 7a) vary from 40 to860 mgCm−2day−1, with maximum values during the spring bloomandminimumvalues in thewinter and summer. The standard deviation

(mgC(mgChl)−1h−1), (b) initial slope (mgC(mgChl)−1h−1 (Wm−2)−1) of the P–Ie at local noon for the ten boxes.

Fig. 7. The seasonal and geographic variations of median values of (a) primary production (mgCm−2day−1) and (b) phytoplankton total loss (mgCm−2day−1) from the mixedlayer for the ten boxes.

41L. Zhai et al. / Journal of Marine Systems 80 (2010) 36–46

is about 38% of the median value. During spring blooms, the primaryproduction exceeds 600 mgCm−2d−1. The low production in thewinter is limited by low surface irradiance, whereas in summer the lowintegrated production is due to the shallow mixed-layer depth. Duringfall blooms the mixed-layer production is about 300 mgCm−2d−1 andreaches tomore than 600 mgCm−2d−1 in the Gulf ofMaine and on theeastern Scotian Shelf, consistent with the high biomass in these areas.

3. Phytoplankton total loss

The phytoplankton total loss is retrieved from the remotely-sensedocean-colour data using a Monte Carlo procedure. The Monte Carlomethod is ideally suitable for nonlinear dynamic systems and for non-Gaussian observations (Dowd, 2006), which are two of the maincharacteristics of the phytoplankton total loss in this study. First, Zhaiet al. (2008) demonstrated that theprobability distributionsof observedbiomass are asymmetric, with heavy tails and large variance at highbiomass, indicative of the non-Gaussian characteristic of biomassdistribution. Second, the phytoplankton total loss is a nonlinear functionof biomass (Eq. (2)), since f (.) and χ depend nonlinearly on thebiomass. Therefore, the Monte Carlo procedure is appropriate toestimate the time-varying phytoplankton total loss in this study.

Themedian values of phytoplankton total loss rates from themixedlayer (Fig. 7b) show similar seasonal and latitudinal variations to thoseof themixed-layer production throughoutmost of the year, suggestingthat to first order, phytoplankton photosynthesis is balanced by thetotal loss. However, during spring and autumn blooms the timing ofthemaximumtotal loss occurs later than that of themaximumprimaryproduction, indicating that during these periods the balance is tempo-rarily perturbed. Our results are consistent with those of Cushing(1992),who re-examined thework of Peinert et al. (1982) and showedthat there is a strong coupling between the primary production andthe total loss in winter, spring and early summer in the Kieler Bucht.

The median values of estimated total loss rates in the ten boxes aremostly positive and range from 50 to 1000 mgCm−2day−1 duringmost of the year (Fig. 7b). The standard deviation is about 63% of themedian value, and is higher than that of primary production. Duringthe rapidly-increasing phase of spring bloom in the second and thirdweeks of April, the median value of total loss in box 1 is negativebecause of the heavy-tailed kernel density distribution. Negative lossmeans that the increase of local biomass with time is faster than thepredicted primary production, and may arise from three possiblesources: an underestimation of the primary production, the advectionof high-biomass water into the study box 1, or the vertical mixing ofthe subsurface chlorophyll maximum. To test the second possibility,we examined the horizontal biomass flux on the western Greenlandshelf. At the time of the bloom, the biomass increases along the shelf

in the direction of the West Greenland Current flowing northward(Wu et al., 2007). In other words, the West Greenland Current carrieswater of relatively low biomass northwestward, such that in earlyApril the horizontal biomass flux acts as a sink of biomass for box 1.Hence, the advection hypothesis must be discarded. The subsurfacechlorophyll maximum is usually not present in the spring: it istypically a summer phenomenon. The explanation for the negativeloss is then most likely related to under-sampling of photosyntheticparameters in this region (Fig. 1), leading to bias in the estimatedphotosynthetic parameters and resulting underestimation of produc-tion (Platt et al., 2008).

We also calculated the median values of the total loss ratenormalized to chlorophyll and carbon-to-chlorophyll ratio, and aver-aged over mixed layer. It ranges from 0.1 to 0.6 d−1 for the ten boxes(Fig. 8). The dependence of normalized loss rates on SST and biomasspresented in Fig. 8 is similar to the dependence of photosynthesis on SSTand biomass (Bouman et al., 2005; Platt et al., 2008). There is a positivecorrelation (r2=0.83, p<0.05) between the normalized total loss andSST (Fig. 8a). In the laboratorymeasurements, phytoplankton losses areoften expressed as a function of temperature (Langdon, 1988), which issupported by our results. There is no significant correlation between thenormalized total loss and chlorophyll. According to Fig. 8b, low loss ratesare found at high-chlorophyll concentrations, whereas at intermediateand low chlorophyll concentrations loss rates are highly variable.

4. Closure of the system

4.1. Contributions from respiration, excretion, grazing, sinking andmixing

The estimated phytoplankton total loss from the mixed layer canbe used to check the cumulative loss estimated as the sum ofcontributions to total loss by individual processes calculated sepa-rately from process models. Phytoplankton total loss comprises lossesfrom biological and physical processes, including respiration (RZm,T),excretion (EZm,T), grazing (GZm,T), sinking (SZm,T) and mixing (MZm,T):

LZm ;T = RZm ;T+ EZm ;T + GZm ;T

+ SZm ;T + MZm ;T+ ε ð4Þ

where ε is the closure error. Based on the results of available mea-surements in the laboratory and in the field, Platt et al. (1991) gaveparametrizations for algal respiration, excretion, grazingbymicro- andmacro-zooplankton, and sedimentation, which may be expressed as,

RZm ;T= ½RB

0 + ðRD + RLÞ⟨PB⟩Zm ;T �ZmB; ð5Þ

EZm ;T = ð0:05⟨PB⟩Zm ;T ÞZmB; ð6Þ

Fig. 8. Themedian values of daily normalized loss rate of phytoplankton LZm,T/χZmB (d−1) plotted as a function of (a) SST and (b) biomass for the ten boxes. The linear regression fit toSST is LZm,T/χZmB=0.026*SST+0.12 (r2=0.83) and is statistically significant (p<0.05). There is no significant correlation between loss and chlorophyll.

42 L. Zhai et al. / Journal of Marine Systems 80 (2010) 36–46

GmicroZm ;T

= gχZmB; ð7Þ

GmacroZm ;T

= ð0:04⟨PB⟩Zm ;T ÞZmB; and ð8Þ

SZm ;T = ðwχ= ZmÞZmB; ð9Þ

where

⟨PB⟩Zm ;T = PZm ;T = ðZmBÞ ð10Þ

is the daily primary production normalized to biomass and averagedover the mixed layer (mgC(mgChl)−1day−1), R0B is maintenancerespiration of 0.09 mgC(mgChl)−1d−1 (Geider and Osborne, 1989),

Fig. 9. The seasonal and geographic variations of median values of (a) respiration rate (mgCloss (mgCm−2day−1) and (d) macro-zooplankton grazing loss (mgCm−2day−1) for the t

RD and RL are the dimensionless coefficients of increase in respirationin the dark and light respectively and set to be 0.175 (Langdon, 1988;Weger et al., 1989), g is the removal rate of phytoplankton, about0.05 d−1 and w is the sinking velocity, set at 1 md−1.

The median values of respiration losses in a seasonally-varyingmixed layer (Fig. 9a) range from 20 to 300 mgCm−2day−1 for the tenboxes, and the standard deviation is about 37% of the median value.Excretion losses EZm,T are estimated from laboratory experiments(Williams and Yentsch, 1976; Sharp, 1977; Smith et al., 1977), andconventionally parameterized to be 5% of daily primary production forhealthy cells. The median values of excretion in the mixed layer(Fig. 9b) are between 3 and 45 mgCm−2day−1 for the ten boxes, thestandard deviation being 37% of the median value. It is expected fromthe model parametrization that both respiration and excretion losses

m−2day−1) and (b) excretion rate (mgCm−2day−1), (c) micro-zooplankton grazingen boxes.

43L. Zhai et al. / Journal of Marine Systems 80 (2010) 36–46

follow the seasonal and geographic variations of the primary pro-duction in the mixed layer, with highest losses during spring bloomsand lowest losses in the summer.

Micro-zooplankton grazing losses are assumed to be 5% of thestanding stock of phytoplankton carbon in themixed layer (Burkill et al.,1987;Paranjape, 1990). Themedianvaluesofmicro-zooplanktongrazingin the mixed layer (Fig. 9c) vary from 10 to 450 mgCm−2day−1, thestandard deviation being 28% of the median value. We can set an upperbound on phytoplankton removal rate by micro-zooplankton grazingimplied by our results, if we make the (temporary) assumption that alllosses (LZm,T/(χZmB)) are due to this process. We find that the maximumremoval rate lies in the range from 0.1 to 0.7 d−1, which agrees with theobserved values of the Northwest Atlantic Ocean (Paranjape et al., 1985;Paranjape, 1990).Macro-zooplanktongrazing losses are approximated tobe 4% of primary production (Walsh et al., 1987), and themedian valuesrange from 1 to 35 mgCm−2day−1 (Fig. 9d).

Sedimentation losses aremodelled as the reciprocal ofmixed-layerdepth given a sinking rate of 1 mday−1 (Fasham et al., 1990). Themedian values of sedimentation losses from themixed layer vary from20 to 200 mgCm−2day−1 (Fig. 10a), and the standard deviation isabout 28% of the median value. Comparing Figs. 3b and 10a, we findthat the sinking losses are positively associated with the probability ofdiatomoccurrence, with a correlation coefficient of 0.62 (p<0.05).Wecan determine the maximum sinking velocity implied by our results ifwe assume temporally that all losses are due to this cause.We find thatthe maximum sinking velocity (LZm,T/(χB)) lies in the range from 1 to10 md−1 with relatively large values (N6 md−1) during the springbloom and small values (<4 md−1) in the summer. These rangesmayprovide useful bounds for inputs to ecosystem models.

The phytoplankton virtual loss associated with the deepening ofthe mixed layer can be parameterized (Denman, 1973; Niiler andKraus, 1977; Fasham et al., 1990; Tang et al., 2002; Platt et al., 2003a;see Appendix B) as

MZm ;T= HχB

ΔZmΔt

ð11Þ

where H is the Heaviside step function having the properties:

H =1; if

ΔZmΔt

N 0

0; ifΔZmΔt

< 0:

8>><>>:

ð12Þ

An increase in mixed-layer depth tends to dilute the biomass overa wider interval of depth, whereas a decrease in mixer-layer depthdoes not affect the biomass accumulated at the surface. The medianvalues of MZm,T (Fig. 10b) are relatively small in comparison withthe other loss terms, and range from 0 to 40 mgCm−2day−1, the

Fig. 10. The seasonal and geographic variations of median values of (a) sinking loss (mgCm−

ten boxes.

standard deviation being 26% of the median value. The virtual lossesare non-zero only in the late fall and winter, associated with thedeepening of the mixed layer. Although deep chlorophyll maxima areoften observed in the summer (Greenan et al., 2004), the virtual lossof biomass from the mixed layer is zero because the mixed-layerdepth is shoaling under the influence of solar heating.

4.2. Annual-integrated production and losses

The annual-integrated primary production and total phytoplank-ton losses are also calculated, and their probability distributions(basedonmanypixels in a givenbox, andonvariations betweenyears)are estimated from the kernel density, a smoothed version of thehistogram. Fig. 11a shows the normalized-kernel density estimates ofthe annually-integrated primary production for ten boxes. It should benoted that boxes 2 to 3 are covered by sea ice during the winter time,and themixed-layer primary production is low or negligible due to thelow light. There is a generally-decreasing trend of annual primaryproduction with increasing latitude due to the trend in PAR forcing.The median values of the annual primary production (Fig. 11a) rangefrom 80 to 90 gCm−2y−1 for boxes 5, 6, 8 and 9, and are greater than100 gCm−2y−1 for boxes 4, 7 and 10. The standard deviation of theannual primary production is about 6% of the median value.

The ten boxes do not all lie in the same biogeochemical province(Longhurst, 1995). Moreover, we know that the boundaries of theprovinces in this area vary dynamically with season (Devred et al.,2007). The biogeochemical province assignment for box 4 is highlyvariable, and switches between three provinces: the NorthwestAtlantic Shelf province, North Atlantic Drift province and Arcticprovince (Platt et al., 2009a), due to its position near the intersectionof these provinces in the Longhurst scheme. Although boxes 7 and 10lie in the same province of the Northwest Atlantic Shelf, their regionalphysical forcings are quite different. Box 7 is strongly affected by freshwater runoff from St. Lawrence River, whereas box 10 is affected bystrong tidally-induced mixing.

The normalized-kernel-density estimates of the annually-inte-grated total loss (Fig. 11b) show larger variance than those of theprimary production, as a result of the large variability of local changeof biomass. The median values of the annual phytoplankton loss(Fig. 11b) are similar to those of production, ranging from 80 to90 gCm−2year−1 for boxes 5, 6, 8 and 9, and being greater than100 gCm−2year−1 for boxes 4, 7 and 10. The standard deviation ofthe annual total loss is about 15% of themedian value. The annual totalloss shows similar geographic distributions to those of primaryproduction, again indicating that phytoplankton total loss estimatedby the Monte Carlo method is strongly coherent with the production.Note that this is not an assumption of the method. However, whenindividual loss terms are compared, it emerges that respiration, which

2day−1) and (b) loss due to the deepening of the mixed layer (mgCm−2day−1) for the

Fig. 11. The kernel density estimates (KDE) of (a) the annually-integrated primary production from the mixed layer (gCm−2y−1) and (b) the phytoplankton total loss from themixed layer (gCm−2y−1) for the ten boxes. The median values of KDEs are marked by the white dashed line.

44 L. Zhai et al. / Journal of Marine Systems 80 (2010) 36–46

is a function of primary production, generally dominates the total loss,and may explain the result from the Monte Carlo method to someextent. Contributions from (micro- and macro-) zooplankton grazingand sinking losses rank second and third respectively in importanceamong the loss terms for boxes 2 to 10 (Table 2). However, thezooplankton grazing is the largest loss term for box 1.

Fig. 12 shows the closure error normalized to the annual phyto-plankton total loss. The closure error ε in Eq. (4) is the annually-integrated difference between the total loss estimated from ocean-colour data and the model output of all loss terms from processmodels. That is, ε includes the effect of errors and also of otherunspecified loss processes. On an annual basis, the median values ofthe closure error range from−11 to+6 gCm−2y−1 for boxes 2 to 10,and may be related to the total effect of vertical and horizontaladvection of biomass. A positive (negative) closure error may beinterpreted as evidence that the advection acts to decrease (increase)the biomass. The closure error (Table 2) is less than 10% of the total lossfor boxes 2 to 10, suggesting that the system is approximately closed.The relatively large discrepancy for box 1 is about −27 gCm−2y−1,due probably to the underestimation of primary production, and to thestrong advection of biomass by currents on the west Greenland shelf.

5. Concluding remarks

We have presented here the estimate of phytoplankton total lossfrom the mixed layer on the Northwest Atlantic shelf. Oneachievement of the study is to illustrate the principle for the losscalculation proposed by Platt and Sathyendranath (2008) and place it

Table 2The ratio (in percentage) between annual individual loss terms and annual total loss forten boxes.

Box RZm ;T

LZm ;T

EZm ;T

LZm ;T

GmicroZm ;T

LZm ;T

GmacroZm ;T

LZm ;T

SZm ;T

LZm ;T

MZm ;T

LZm ;Tε

1 38 5.2 46 5.2 30 1.8 −272 34 4.9 22 4.9 26 5.0 3.03 36 5.1 27 5.1 26 3.4 −3.24 37 5.2 32 5.2 20 2.0 −0.95 36 5.1 38 5.1 23 2.9 −116 36 5.1 30 5.1 21 1.9 1.37 36 5.0 25 5.0 25 3.3 1.28 35 5.0 23 5.0 25 1.2 5.99 36 5.0 22 5.0 28 2.4 1.810 36 5.1 32 5.1 24 3.6 −7.1

The individual loss terms are calculated independently using standard equations asgiven in the text. The last column (ε) shows the ratio (in percentage) between theclosure error and the total loss. The positive (negative) ε means that the total lossestimated from the satellite data is greater (less) than the sum of the individual lossestimates.

on a firm basis by combining satellite observations, a data base ofphysiological parameters and an analytical production model. Thecombination of these elements into a Monte Carlo procedure hasproduced a robust picture of phytoplankton total loss, which may noteasily be achieved on the same temporal and spatial scale by othermethods. This study provides a benchmark for future studies of theprocesses that are responsible for phytoplankton losses.

The total loss estimated in this study allows us to check whetherproduction and loss of phytoplankton are balanced or unbalanced on aseasonal and an annual basis. First, the total loss from themixed layer isbalanced by the production to first order, and the balance is perturbedduring blooms. Second, the annual total loss is roughly equal to theannual primary production.

The estimated total loss in ten study regions demonstrated seasonaland geographic variations across and within biogeochemical provinces,resulting from large-scale and regional-scale variations in physicalforcings. In addition, there are also strong spatial and interannualvariationswithin every 1°×1° box, indicated by the greaterwidth of theenvelope of kernel density estimates. The interannual variations couldbe useful indicators of ecosystem change (Platt and Sathyendranath,2008) in response to environmental perturbation, for example tounderstand fluctuations in fish stocks (Platt et al., 2003b; Fuentes-Yacoet al., 2007), and to provide information relevant to ecosystem-basedmanagement of the pelagic zone.

The phytoplankton total loss estimated from ocean-colour datawas used to check the cumulative losses calculated separately fromprocessmodels for each component of losses, which include biological

Fig. 12. The kernel density estimates (KDE) of the closure error normalized to theannual phytoplankton total loss. The median values of KDEs are marked by the whitedashed line.

45L. Zhai et al. / Journal of Marine Systems 80 (2010) 36–46

loss terms parameterized by Platt et al. (1991) and virtual loss due tovertical mixing. However, there may be other loss terms such asbiomass fluxes and viral infection, also playing a role in shaping thebiomass distribution. The annual discrepancy between the estimatesof two losses is largest on the west Greenland shelf. One of the uses ofthe model presented here is to identify priority areas that need moreobservations to improve model parametrization, and the west Green-land shelf emerges as one such area from these results. Directquantification of advection requires information on the gradient ofbiomass and the ocean currents. In fact, this information can nowbe diagnosed from composite images of the biomass fields, fromhydrographic and current measurements and from coupled physical–biologicalmodels. The effect of physical forcing on phytoplanktonmayalso be revealed by comparing the spatial and temporal variability inthe physical forcing and in the biomass fields. The benefits ofquantifying the advection of biomass may include: further reducingthe error between the two methods for estimation of total losses,refining the parametrization of individual loss terms, improving ourunderstanding of the biophysical interaction in phytoplankton.

Acknowledgments

Wearegrateful toG.N.White III for providing the totaldaily PARdata.The authors would like to thank two anonymous reviewers, P. Smith, B.Greenan, M. Dowd, V. Stuart, M.-H. Forget, H. A. Bouman and S. Roy fortheir useful comments and suggestions to improve the manuscript. Thisstudy was funded by the Canadian Space Agency (GRIP program). Thiswork is a contribution to the NCEO and Oceans2025 projects of NERC(UK).

Appendix A

The term on the left-hand side of Eq. (1) can be written as

∫ZmðtÞ0

∂χBðz; tÞ∂t dz =

∂∂t ∫ZMðtÞ

0 χBðtÞdzh i

−χBðtÞ ∂ZmðtÞ∂t : ðA1Þ

Since the biomass is distributed uniformly within the mixed layer,Eq. (A1) can be reduced to

∫ZmðtÞ0

∂χBðz; tÞ∂t dz =

∂ðχBðtÞZmðtÞÞ∂t −χBðtÞ ∂ZmðtÞ∂t

= ZmðtÞ∂ðχBðtÞÞ

∂t + χBðtÞ ∂ZmðtÞ∂t −χBðtÞ ∂ZmðtÞ∂t

= ZmðtÞ∂ðχBðtÞÞ

∂t : ðA2Þ

The discrete form of Eq. (1) now can be written as

ZmðtÞΔðχBÞΔt

= PZm ;T−LZm ;T : ðA3Þ

We rearrange Eq. (A3) to put

LZm ;T = PZm ;T−ZmΔðχBÞΔt

: ðA4Þ

Appendix B

To derive Eq. (11), we start with a one-dimensional model ofbiomass, following the concept of the one-dimensional heat conser-vation equation (Denman, 1973; Niiler and Kraus, 1977)

∂B∂t +

∂∂z ð w′B′―Þ = Growth−Loss ðB1Þ

where B and B′ are the time mean and fluctuating components ofbiomass, Growth is the primary production, Loss is the sum ofbiological losses, and the term ∂ðw′B′

―Þ= ∂z represents the localdivergence of the turbulent flux of biomass. Integration of theEq. (B1) over the mixed layer (of uniform biomass) leads to

Zm∂B∂t + ð w′B′

―Þ jZm = ∫Zm0 ðGrowth−LossÞdz: ðB2Þ

If the turbulent mixing is assumed to be zero at the bottom of themixed layer z=Zm, then Eq. (B1) can be integrated between z=Zm−Δhand z=Zm (to first order in Δh):

∂∂t ð∫

ZmZm−ΔhBdzÞ + B jZm−Δh

∂ðZm−ΔhÞ∂t −B jZm

∂Zm∂t − w′B′

― jZm−Δh

= ΔhðGrowth−LossÞ ðB3Þ

where Δh is the thickness of the interface at the bottom of the mixedlayer. In the limit as Δh→0, and the assumption of biomass to be zeroat z=Zm, Eq. (B2) reduces to the following expression for the mixingentrainment at the bottom of the mixed layer:

w′B′― jZm = HB

∂Zm∂t : ðB4Þ

where H is the Heaviside step function having the properties

H =1; if

∂Zm∂t N 0; entrainment mixing at z = Zm

0; if∂Zm∂t < 0; no entrainment mixing:

8>><>>:

ðB5Þ

We substitute Eq. (B4) into (B2):

Zm∂B∂t = ∫Zm

0 ðGrowth−LossÞdz−HB∂Zm∂t : ðB6Þ

The discrete form of HB∂Zm∂t is expressed as MZm,T/χ in Eq. (11).

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