SGLI/GCOM-C1
Algorithm Theoretical Basic Document
Phytoplankton functional type (PHFT)

Version 331 March 2016

PI: Toru Hirawake1*
Co-I: Amane Fujiwara2, Tomonori Isada3 and Sei-ichi Saitoh1, 41

Faculty of Fisheries Sciences, Hokkaido University
2
JAMSTEC
3Field Science Center, Hokkaido University
4
Arctic Research Center, Hokkaido University*PI: hirawake@salmon.fish.hokudai.ac.jp

Contributors
Hisatomo Waga, Faculty of Fisheries Sciences, Hokkaido University
Koji Suzuki, Faculty of Environmental Earth Sciences, Hokkaido University
This ATBD is based on Waga et al. " Distributional shifts in size structure ofphytoplankton community" preparing to submit to Remote Sensing.

1. Algorithm outline
1.1 Algorithm CodePHFT_V3.f95
1.2 Product Code
PHFT (Phytoplankton functional type, research level product)
1.3 PI
Toru Hirawake (GCOM-C1 2nd RA 133, 4th RA 304)
1.4 Overview of algorithm
Phytoplankton functional types (PFTs) are phytoplankton groups classified basedon their biogeochemical and ecological functions. Size distribution of phytoplankton
is one of the PFTs and important factor to determine the structure of ecology,
particularly a number of trophic levels in the ocean. This algorithm estimatesabundance of each phytoplankton size classes (micro-, nano- and picoplankton) in
their ratio and chlorophyll a (Chl a) concentration.
Phytoplankton size class has been modeled using one of inherent optical properties(IOPs) in the past studies; light absorption of phytoplankton [e.g. Fishwick et al.,2006; Hirata et al., 2008] and backscattering coefficient [e.g. Montes-Hugo et al.,2008; Vaillancourt et al., 2004]. While ratio of the absorption coefficient,aph(λ1)/aph(λ2), tends to express pigment composition and packaging, spectral slope ofthe scattering coefficient, γ, is controlled by geometry of phytoplankton cell. To takethe advantage of these IOPs, the size deriving model (SDM) using both the absorption
ratio and γ was established in the Arctic Ocean and estimated the abundance ofultraplankton (< 5µm) [Fujiwara et al., 2011].
In the previous RA (RA2), the SDM had been improved to estimate three sizeclasses. However, dataset is quite limited because of difference in filter pore size
among cruises and lack of backscattering data. Therefore, we applied the theory ofparticle size distribution [Junge, 1963] and estimated slope of chlorophyll size
distribution (CSD) using only absorption coefficient of phytoplankton in the RA4.
The data set used in this study were obtained from a wide range of the North
Pacific Ocean and the Western Arctic through fifteen cruises over a 9-year period(Figure 1). At each station, size fractionated Chla (Chlasize), light absorption
coefficient and spectral radiation were measured. Seawater samples were collected

from the sea surface using a clean platic bucket. Seventy percent of in situ data (N =180) were used for model development and the rest (N = 78) was reserved for modelvalidation.

Figure 1. Map of sampling stations.

2. Theoretical Description
2.1. Basic of algorithm
Assuming that the PSD follows the Junge-type [Junge, 1963] power law size
distribution [Bader, 1970], the number concentration of particles (N) of particles perunit volume of seawater normalized by the size bin diameter (D) can be expressed asfollows:
𝐷𝐷𝑁𝑁(𝐷𝐷) = 𝑁𝑁0 (𝐷𝐷 )−𝜉𝜉 ,0(1)where ξ is the Junge slope of PSD, and D0 is a reference diameter at which N0=N(D0).
Therefore, the total number of particles in a given size range can be derived asintegrating Eq. (1) from the minimum diameter (Dmin) to the maximum diameter(Dmax) enabling the PSD to be partitioned into distinct classes, described by

𝐷𝐷

𝐷𝐷

𝑁𝑁 = ∫𝐷𝐷 max 𝑁𝑁0 (𝐷𝐷 )−𝜉𝜉 𝑑𝑑𝑑𝑑.
mix

(2)

0

If assuming that the Chla is particle and thus the Chla size distribution (CSD) also
follows the Junge-type power law distribution, the total Chla (Chlatotal) and Chlasize ina given size range from D1 to D2 can be expressed with Eq. (3) and (4) as follows:
𝐷𝐷𝐷𝐷

Chl𝑎𝑎total = ∫𝐷𝐷 max Chl𝑎𝑎0 (𝐷𝐷 )−𝜂𝜂 𝑑𝑑𝑑𝑑,
𝐷𝐷min𝐷𝐷(3)0Chl𝑎𝑎size = ∫𝐷𝐷 2 Chl𝑎𝑎0 (𝐷𝐷 )−𝜂𝜂 𝑑𝑑𝑑𝑑,1(4)0where Chla0 is the reference Chla at D0 (here, 0.7 μm), and η is the exponent of Chlasize spectrum (hereafter CSD slope). The strong magnitude of the CSD slope
indicates the large proportion of smaller phytoplankton, while that of low magnitude
suggests the larger phytoplankton dominant condition. In this study, we assumed Dmin
and Dmax as the pore size of GF/F filter (i.e. 0.7 μm) and 200 μm [Dussart, 1965],
respectively. The CSD slope is derived as the slope of linear regression in log-space
between the inverse log-transformed median diameters from log-transformed D1 to D2
and Chlasize normalized by the size bin width.
Note that the Chla fraction of arbitrarily defined size range (Fsize) can be derived
using the CSD slope as follows:
Chl𝑎𝑎size

𝐹𝐹size = 100× Chl𝑎𝑎total= 100×𝐷𝐷
𝐷𝐷10200𝐷𝐷∫0.7 Chl𝑎𝑎0 (𝐷𝐷 )−𝜂𝜂 𝑑𝑑𝑑𝑑0∫𝐷𝐷 2 Chl𝑎𝑎0 (𝐷𝐷 )−𝜂𝜂 𝑑𝑑𝑑𝑑

𝐷𝐷1−𝜂𝜂

−𝐷𝐷1−𝜂𝜂

1= 100× 20021−𝜂𝜂 −0.71−𝜂𝜂 ,(5)where the constants Chla0 and D0 no longer exist in Eq. (6), so that only the CSDslope and diameter range are required for estimating the each fraction ofphytoplankton size classes.

2. 2. Quantification of CSD slope using phytoplankton absorption spectra
To quantify the CSD slope using the spectral shape of aph(λ), we applied PCA tonormalized aph(λ) following the method of Wang et al. [2015]. In brief, normalizedaph(λ) (aphstd(λ)) was derived from its wavelength mean and the standard deviation.
The formula for aphstd(λ) is shown as below:std𝑎𝑎ph(λ) = �𝑎𝑎ph (𝜆𝜆) − mean �𝑎𝑎ph (𝜆𝜆)�� /std(𝑎𝑎ph (𝜆𝜆)),(6)where mean(aph(λ)) and std(aph(λ)) are the wavelength mean and standard deviationof aph(λ), respectively.
PCA was then applied to aphstd(λ) to capture spectral feature of phytoplankton
absorption property. The input values for PCA was a matrix (m × N) constituted ofaphstd(λ), where m and N were the number of wavelengths and samples, respectively.
The resulting PC scores were assumed to correlate with the CSD slope, and hence theCSD slope was quantified as the logistic-type regression model using ith PC score (Si)and regression coefficients between the CSD slope and PC scores (β0 and βi) as
below:−1𝜂𝜂 = �𝛽𝛽0 + exp ∑𝑘𝑘𝑖𝑖=1 𝛽𝛽𝑖𝑖 𝑆𝑆𝑖𝑖 � ,(7)where k is the number of PCs. Here, Si can also be express as follows:
std𝑆𝑆𝑖𝑖 = ∑𝑚𝑚𝑗𝑗=1 𝑤𝑤𝑖𝑖,𝑗𝑗 𝑎𝑎ph (𝜆𝜆𝑗𝑗 ),(8)where wi,j and aphstd(λj) are the loading factor for the ith PC and aphstd(λ) value atwavelength j, respectively. Therefore, we obtained an equation by substituting for
calculation of Si in Eq. (7):−1std𝜂𝜂 = �𝛽𝛽0 + exp ∑𝑚𝑚
𝑗𝑗=1 𝐶𝐶𝑗𝑗 𝑎𝑎ph (𝜆𝜆𝑗𝑗 )� ,𝐶𝐶𝑗𝑗 = ∑𝑘𝑘𝑖𝑖=1 𝛽𝛽𝑖𝑖 𝑤𝑤𝑖𝑖,𝑗𝑗 .

(9)

(10)

Finally, the CSD slope is derived from Eq. (9) using the model parameters of β0and Cj.
The resulting model parameter β0 was -0.221 and Cj for each wavelengths at 412,443, 469, 488, 531, 547 and 555 nm were -0.222 and 0.314, 0.021, -0.780, 0.243,1.714, -0.189 and -1.305, respectively.

2. 3. Evaluation of estimate accuracy
The root-mean square error (RMSE) was adopted when we validated the agreementof two values such as measured and estimated CSD slope. The RMSEs werecomputed as relative values so as to give equal weights to all samples, and expressedas percentages [Ciotti et al., 2006], described by1

𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑖𝑖 −𝑀𝑀𝑀𝑀𝑀𝑀𝑖𝑖 2𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅(%) = 100×�𝑁𝑁 ∑𝑁𝑁
𝑖𝑖=1 �

𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑖𝑖

� ,(11)

where and Measi and Modi are ith measured and modelled values, respectively.

3 Validation
The performance of CSD model was examined by comparing measured CSD slope
determined from in situ Chlasize and modeled CSD slope estimated from in situ
Rrs(λ). The resulting RMSE between measured and modeled CSD slope was 25.9%(Figure 2). Since CSD model relies on the spectrum shape of aph(λ), the accuracy ofestimated CSD slope strongly depends on the robustness of IOP algorithms. Thesatellite product accuracy goal for Chla has been delimited the ± 35% of agreementwith respect to actual value measured in the field [Hooker and McClain, 2000], andother products such as primary production were also evaluated based on this range.
Moreover, the existing methods to derive phytoplankton size structure often use Chlaas an input data [Devred et al., 2011; Hirata et al., 2011; Brewin et al., 2010] and areexpected to contribute for understanding the biogeochemical process [McClain, 2009].
Therefore, the CSD model enabled to retrieve size structure of phytoplankton
community with the same or better accuracy when comparing to Chla and otherproducts came from Chla.

Figure 2. Comparison of in situ CSD slope determined from in situ Chlasize andmodelled CSD slope derived from estimated aphstd(λ) through QAA-v5 using in situ
PRR data. Solid and dashed lined represent the 1:1 agreements and regression lines,respectively.

4. References
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Brewin, R. J. W., Sathyendranath, S., Hirata, T., Lavender, S. J., Barciela, R. M.,
Hardman-Mountford, N. J. A (2010), Three-component model of phytoplankton
size class for the Atlantic Ocean, Ecol. Model., 221, 1472–1483.
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SeaWiFS channels in a continental shelf region off Brazil, Limnol. Oceanogr.
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Dussart, B. H. (1965), Les différentes catégories de plancton, Hydrobiologia, 26, 72–74.
Devred, E., Sathyendranath, S., Stuart, V., Platt, T. (2011), A three component
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Hirata, T., J. Aiken, N. Hardman-Mountford, T. J. Smyth, and R. G. Barlow (2008), An
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Hooker, S. B., McClain, C. R. (2000), The calibration and validation of SeaWiFS data.
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Junge, C. E. (1963), Air chemistry and radioactivity. New York and London: AcademicPress Inc., 382
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