Phytoplankton Functional Type Algorithm Theoretical Basis Document Ver.0 (2012.3.30)
PI No. 134 Takafumi Hirata (GCOM-C/SGLI Ocean Team)
CIs: Nick Hardman-Mountford, Tim Smyth, Shubha Sathyendranath, Trevor Platt, Akio Ishida,
Yasuhiro Yamanaka

1. Introduction
This document describes algorithms that retrieve several Phytoplankton Functional Types (PFTs)
as a satellite observation. PFTs may be defined in terms of a role of phytoplankton on
biogeochemical cycles in the oceans or size of the phytoplankton cell which is an useful parameter inecosystem analysis. In general, the agreement between functional- and taxonomic- or size-basedclassiﬁcation, while far from universal, is adequate, therefore we use the term “phytoplankton
functional types (PFTs)” to mean different groups of phytoplankton. This document provides (1)background of the algorithm (e.g. definition of PFTs), (2) in situ data used for the algorithm
development, (3) algorithm equations, (4) operation procedure and (5) algorithm testing including
uncertainty estimation.

2. Background of the algorithm
The PFT algorithms shown here are empirical algorithms. In the following, theoretical basis for‘empirical-based algorithm’ is described.
Figure 1 shows in situ measurement of the total Chlorophyll-a concentration (TChla in [mg/m3])
against a percentage contribution of different PFTs [%] to TChla: a)Picoplankton, b) Nanoplankton,c) Microplankton, d) Pico-Eukaryote, e) Prymnesiophyte (Haptophyte), f) Diatom, g) Prokaryote, h)Green Algae, i) Dinoflagellates, j) Prochlorococcus sp. It is clear that there are well definedrelationships between TChla and PFTs, which implies that a percentage contribution of PFTs toTChla can be estimated (or “inverted”) using TChla, if the relationships are quantified between them.
TChla is a standard product of SGLI/ GCOM-C1, therefore it should be possible to derive thepercentage contribution of PFTs to TChla. A practical issue in the estimation of PFTs by means ofsuch approach is collection of in situ data to develop the empirical algorithms. It will be described inSection 3.
Relationships between TChla and PFTs observed in situ can be quantified by regression
analysis. Non-linear regression was done by using Nelder-Mead method. However, the logistic
function is applied here as a base function for the fitting, since ecological theory describes population
dynamics by the equation; i.e. Y=A / [1-m * exp (-k*x)], where Y is a fractional contribution [0-1] of PFT
to TChla, so that A=1, and m and k are fitting parameters. Finally, x is TChla if it is in linear or logspace).

Figure 1. Observed relationship between TChla and PFTs.

3. In situ data set
The PFT algorithms are developed based on existing in situ data by seeking relationships
between TChla and PFTs. Thus, the algorithms are empirical algorithms. To obtain PFTs from in situ
observation, the following in situ data sets of HPLC are used: NERC AMT (Aiken et al., 2009),
JAMSTEC BEAGLE (Barlow et al., 2007), NASA NOMAD and SeaBASS (Werdell and Bailey,2005), University of Tokyo SEEDSII experiments (Suzuki et al., 2005), Fisheries Research Agencyof Japan A-line cruise (Isada, 2009), Hokkaido University Oshoro-maru cruise (Howell et al.,personal communication). These individual dataset was re-compiled to generate a global dataset
which consists of 3966 data point after quality control. Fig. 2 shows spatial distribution of thesedataset.

Figure 2. Distribution of phytoplankton pigment data used in this study; blue dot: the NERC AMT
cruise (Aiken et al., 2009), black triangle: the JAMSTEC BEAGLE cruise (Barlow et al., 2007),
cyan diamond: the NASA NOMAD (Werdell and Bailey, 2005), magenta cross: the NASA SeaBASS,
brown star: the SEEDS II cruise (Suzuki et al., 2005) + A-line stations (Isada et al., 2009), green
square: the HU Oshoro-maru cruise.

Quality control was undertaken by the procedure described by Hirata et al. 2008: A linear
regression analysis of TChla vs accessory pigments was made to exclude ‘outlier’ data, which wasdefined as any data larger than 2x standard deviation around the regression line. This was repeatedthree times.
Within the quality controlled dataset, 70% were sub-sampled to find relationships between
TChla and PFTs, and 30% were reserved for algorithm testing. The 30% dataset was obtained insuch a way that 30% of individual dataset was sub-sampled using a random selection to ensure thateach individual dataset evenly contribute to the 30% dataset.
PFTs were classified based on Diagnostic Pigment Analysis (Viddussi et al., 2001) which
deﬁnes a suite of Diagnostic Pigments (DP) for speciﬁc PFTs that can be quantiﬁed towards

estimation of the relative abundance of a speciﬁc PFT (Table 1). The DPA was subsequently reﬁnedby Uitz et al. (2006) to scale DPs to TChla, permitting the application of DPA-based approaches tosatellite-derived TChla. In addition, Hirata et al. (2008) used the reﬁned DPA to separate
pico-eukaryotes from nano-eukaryotes, and Brewin et al. (2010) developed a method to quantify therelationship, which is used in the present work. Here, DPA is further reﬁned to account for ambiguityof the fucoxanthin (Fuco) signal. Fuco is deﬁned as a DP for Diatoms by Vidussi et al. (2001).
However, Fuco is also a precursor pigment of 19’-Hexanoyloxyfucoxanthin (Hex), the DP for
prymnesiophytes (haptophytes), and can co-occur in this group. Fuco is also contained in the otherheterokonts (e.g. chrysophytes, bolidophytes) and dinoﬂagellates, which are relatively abundant incoastal environments (Wright and Jeffrey, 2006). Thus, diatoms could be overestimated in DPA.
Hirata et al. (2008) found a non-negligible proportion of Fuco within the oligotrophic gyres of thesubtropical Atlantic, where small prokaryotes (predominantly Prochlorococcus sp. andSynechococcus sp.) and pico-eukaryotes (which can partly belong to the prymnesiophytes(haptophytes) so may also contain Hex) usually dominate the phytoplankton community (Zubkov etal., 1998; Tarran et al., 2006). In these oligotrophic waters, TChla is low (<0.25 mg m−3, Aiken et al.,2009), therefore, it is more reasonable to assume that the background level of Fuco detected resultsfrom smaller prymnesiophytes (haptophytes) rather than diatoms which are more prevalent ineutrophic waters. Therefore, we calculated a baseline for the Fuco/Hex ratio, (Fuco/Hex)baseline, using
Fuco and Hex in the Chl-a range less than 0.25 mg m−3 in the original data set (denoted as Fucooriginaland Hexoriginal, respectively). The proportion of Fuco as a diatom biomarker is then corrected so that
Fucocorrected = Fucooriginal − (Fuco/Hex)baseline× Hexoriginal.
The Fuco conversion is only signiﬁcant in the lower Chl-a range (<0.5 mg m−3) and isnegligible for higher Chl-a values. Using these HPLC pigment signals, PSCs and PFTs are deﬁned
and classiﬁed as in Table 1.
Micro-, Nano- and Picophytoplakton are based on size-based classification, which may be
defined, according to Sieburth et al. (1978), by microplankton >20 µm, nanoplankton 20–2 µm,picoplankton <2 µm in physical cell size. Although the DPA described above do not specify the sizeclasses directly, outputs of the DPA are assumed to follow the size classification definition bySieburth, since an agreement between taxonomic and size classification is generally accepted.
However, a user must be aware this assumption in use of the present algorithms for micro-, nanoand picoplankton.

Table 1. Diagnostic Pigments and PSCs/PFTs
Size Classes/PFTs

Diagnostic Pigments

Estimation Formula

Microplankton (>20μm)*1

Fucoxanthin (Fuco), Peridinin (Perid)

1.41(Fuco+Perid) / ΣDP*1

Diatoms

Fuco

1.41Fuco / ΣDP*2

Dinoflagellates

Perid

1.41Perid / ΣDP*2

Nanoplankton (2-20μm)*119’-Hexanoyloxyfucoxanthin(Hex)(Xn*1.27Hex+1.01Chlb+0.35But+0.60Allo)/ΣDP*3

Chlorophyll-b (Chlb)
Butanoyloxyfucoxanthin (But)Alloxanthin (Allo)
Green algae

Chlb

1.01Chlb / ΣDP*2

Prymnesiophytes*4Hex, But(Haptophytes)
Picoplankton (0.2-2μm)*1Zeaxanthin(Zea), Hex, Chlb

(0.86Zea+Yp1.27Hex)/ΣDP*3

Prokaryotes

Zea

0.86Zea / ΣDP*2

Pico-eukaryotes*5Hex, Chlb

Prochlorococcus sp.

Divinyl Chlorophyll-a (DVChla)

0.74DVChla / Chla

*1Sieburth et al., (1978)*2ΣDP= 1.41Fuco+1.41Perid+1.27Hex+0.6Allo+0.35But+1.01Chlb+0.86Zea=Chla (Uitz et al, 2006)*3X indicates a proportion of nanoplankton contribution in Hex, respectively. Similarly Y indicates a proportion ofnppicoplankton in Hex, respectively (Brewin et al., 2010)*4 Given that contributions of Alloto nanoplankton were only a few percent in our data set, haptophytes wereapproximated to Nano minus Green Algae*5 Pico-eukaryotes can be determined from picoplankton minus prokaryotes (see also Fig. 2 caption)

4. Algorithm Equations
The PFT algorithms use the following equations to estimate nine PFTs (i.e. Microplankton, Diatom,Nanoplankton,GreenAlgae,Prymnesiophyte,

Picoplankton,

Prokaryote,Pico-Eukaryote,

Prochlorococcus sp.). The algorithms return a fraction [0-1] of a specified PFT relative to TChla[mg/m3].

Microplankton = 1 / [ 0.9117+exp(-2.7330 *log10(TChla) + 0.4003) ]Eq. (1)

Diatom = 1 / [ 1.3272 + exp(-3.9828 *log10(TChla) + 0.1953) ]Eq. (2)

Nanoplankton = 1- Microplankton – Picoplankton

Eq. (3)

Green Algae = (0.2490/TChla) * exp ( -1.2621 * ( log10(TChla)-0.5523 )2

Eq. (4)Prymnesiophyte ≓ Nano-Green Algae

Eq. (5)

Picoplankton =- (1 / [0.1529+exp(1.0306*log10(TChla) – 1.5576)])+ 1.8597 + 2.9954

Eq.(6)

Prokaryotes = (0.0067/0.6154/TChla) * exp( -19.519 * (log10(TChla)+0.9643 )2 / 0.00672 )+ 0.1027*[log10(TChla)]2 - 0.1189*log10(TChla) + 0.0626

Eq.(7)

Pico-Eukaryote = Picoplankton – Prokaryote
Prochlorococcus sp. = (0.0099/0.6808/TChla) * exp( -8.6276*(log10(TChla) + 0.9668)2 / 0.00992 )+0.0074*[log10(TChla)]2 -0.1621*log10(TChla) + 0.0436

Eq.(8)

5. Operation Procedure
The PFT algorithms assume that total TChla are obtained in prior to their implementation.
Thus, it is important to note that (a) TChla must be obtained by any mean (e.g. GCOM-C1Chlorophyll-a algorithm) prior to implementation of the present PFT algorithms. Without TChla,PFTs cannot be estimated. Once TChla is prepared, the following PFTs must be estimated first:
Microplankton, Diatom, Green Algae, Picoplankton, Prokaryote and Prochlorococcus sp (thesePFTs can be estimated in any order). Secondly, Nanoplankton (=1-Mircoplankton-Picoplankton)
and Pico-eukaryote (=Picoplankton-Prokaryote) can be derived. Finally, Prymnesiophyte can be
estimated from Nanoplankton-GreenAlgae. Figure 3 visually summarizes the operation flow.

Figure 3. Flow chart of PFTs estimation. A step estimation is necessary to derive all nine PFTs.

6. Algorithm testing
Figure 4 shows residual between PFTs derived from the algorithms and in situ HPLC data used
for the development of the algorithms. Ideally, the residual is zero, however, variable residual isfound over the TChla range as well as over the PFTs. This residual may be assumed to represent
uncertainty of the present algorithms, given that in situ data of PFTs for all location and time
period is unavailable. Table 2 summarizes the mean and maximum residual for the nine PFTs.

Figure 4. Residual between PFTs derived from in situ HPLC data and its best fit curve. Note that
Dinoflagellate algorithm is not a deliverable.

Fig.5 shows PFTs derived from Eqs. 1-8 against another subset of NOMAD data (Werdell and Bailey,2005) which was not used for algorithm development. Statistics are summarized in Table 3.
Picoplankton is retrieved with the regression slope 1.00, although some scatters are found. While
there is more scatter in Prochlorococcus sp. than Pico assembles, the regression slopes for bothphytoplankton types are similarly good (1.0 for Pico and 0.982 for Prochlorococcus). Prokaryotes

and Pico-Eukaryotes have scatter (7.71%, 5.25%) and the regression slope is 0.864 and 0.801,
respectively. Nanoplankton have relatively larger RMSE (8.55%) compared to other PFTs. However,Prymnesiophytes, which may be considered as nanoplankton fraction, has an increased RMSE andintercept (10.0 and -9.721, respectively) than Nanoplankton assembles. Microplankton and Diatoms
show similar results. Note that Dinoflagellate algorithm is not a deliverable.
Since the algorithms were developed based on the global climatology of the PFTs derived
from in situ observations, a check is need to ensure whether the temporal variation of PFTs is also
retrieved from the present algorithms. Figure 6 shows power spectra of three phytoplankton types(Micro, Nano and Pico) for different ocean basins derived from the existing satellite data as anexample. One of the significant variability of phytoplankton dynamics is known as seasonality (i.e.
365 day cycle). The seasonality is clearly seen in all basins under the present algorithms.

Table 2. Mean and Maximum ResidualPFTs

Residual [%]Maximum Residual [%]Microplankton

6.7

31.1

Diatom6.3

31.8

Nanoplankton

7.6

27.6

Green Algae

4.2

17.8

Prymnesiophyte

8.4

29.5

Picoplankton

6.1

23.8

Prokaryote

7.1

25.2

PicoEukaryote

4.6

16.6

Prochlorococcus sp.

6.1

21.4

Table 3. Statistical results of the PFT algorithms against in situ data
Slope

InterceptRMSE

Micro1.109

1.073

8.28

Diatom

1.115

1.732

7.98

Nano

1.168

3.055

8.55

Prymnesiophyte

1.218-9.721

10.0

Green Algae

0.809

2.035

4.71

Pico

1.000-8.093

7.12

Pico-Eukaryotes

0.801

2.564

5.25

Prokaryotes

0.864

3.712

7.71

Prochlorococcus sp.

0.982

0.353

6.25

Figure 5. Comparison between in situ PFTs and those derived from the present PFT algorithms. Notethat in situ data used for the algorithm evaluation is a subset of the original data set, which was not
used for algorithm development.

Figure 6. Power spectra for Pico, Nano and Microplankton for different ocean basins (NAT: NorthAtlantic, SAT: South Atlantic, NPC: North Pacific, SPC: South Pacific, IND: Indian Ocean, Glb:Global Oceans).

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