Novel method for quantifying the cell size of
marine phytoplankton based on
optical measurements
Junfang Lin,1,2 Wenxi Cao,2,* Wen Zhou,2 Zhaohua Sun,2 Zhantang Xu,2 Guifen Wang,2
and Shuibo Hu1,2
2
1
University of Chinese Academy of Sciences, Beijing 100049, China
State Key Laboratory of Tropical Oceanography, South China Sea Institute of Oceanology, Chinese Academy of
Sciences, Guangzhou 510301,China
*
[email protected]
Abstract: Phytoplankton size is important for the pelagic food web and
oceanic ecosystems. However, the size of phytoplankton is difficult to
quantify because of methodological constraints. To address this limitation,
we have exploited the phytoplankton package effect to develop a new
method for estimating the mean cell size of individual phytoplankton
populations. This method was validated using a data set that contained
simultaneous measurements of phytoplankton absorption and cell size
distributions from 13 phytoplankton species. Comparing with existing
methods, our method is more efficient with good accuracy, and it could
potentially be applied in current in situ optical instruments.
©2014 Optical Society of America
OCIS codes: (010.4450) Oceanic optics; (010.1030) Absorption.
References and links
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
13.
P. Boyd and P. Newton, “Evidence of the potential influence of planktonic community structure on the
interannual variability of particulate organic carbon flux,” Deep Sea Res. Part I Oceanogr. Res. Pap. 42(5), 619–
639 (1995).
L. Guidi, L. Stemmann, G. A. Jackson, F. Ibanez, H. Claustre, L. Legendre, M. Picheral, and G. Gorsky, “Effects
of phytoplankton community on production, size and export of large aggregates: A world-ocean analysis,”
Limnol. Oceanogr. 54(6), 1951–1963 (2009).
A. M. Waite and P. S. Hill, “Flocculation and phytoplankton cell size can alter 234Th-based estimates of the
vertical flux of particulate organic carbon in the sea,” Mar. Chem. 100(3-4), 366–375 (2006).
T. L. Richardson and G. A. Jackson, “Small phytoplankton and carbon export from the surface ocean,” Science
315(5813), 838–840 (2007).
P. M. Holligan, R. P. Harris, R. C. Newell, D. S. Harbour, R. N. Head, E. A. S. Lindley, M. I. Lucas, P. R. G.
Tranter, and C. M. Weekley, “Vertical distribution and partitioning of organic carbon in mixed, frontal and
stratified waters of the English Channel,” Mar. Ecol. Prog. Ser. 14, 111–127 (1984).
M. V. Zubkov, M. A. Sleigh, G. A. Tarran, P. H. Burkill, and R. J. Leakey, “Picoplanktonic community structure
on an Atlantic transect from 50 N to 50 S,” Deep Sea Res. Part I Oceanogr. Res. Pap. 45(8), 1339–1355 (1998).
J. Uitz, H. Claustre, A. Morel, and S. B. Hooker, “Vertical distribution of phytoplankton communities in open
ocean: An assessment based on surface chlorophyll,” J. Geophys. Res. 111, C08005 (2006).
F. Vidussi, H. Claustre, B. B. Manca, A. Luchetta, and J. C. Marty, “Phytoplankton pigment distribution in
relation to upper thermocline circulation in the eastern Mediterranean Sea during winter,” J. Geophys. Res.
106(C9), 19939–19956 (2001).
T. Hirata, J. Aiken, N. Hardman-Mountford, T. Smyth, and R. Barlow, “An absorption model to determine
phytoplankton size classes from satellite ocean colour,” Remote Sens. Environ. 112(6), 3153–3159 (2008).
J. Ras, H. Claustre, and J. Uitz, “Spatial variability of phytoplankton pigment distributions in the Subtropical
South Pacific Ocean: comparison between in situ and predicted data,” Biogeosciences 5(2), 353–369 (2008).
E. Devred, S. Sathyendranath, V. Stuart, H. Maass, O. Ulloa, and T. Platt, “A two-component model of
phytoplankton absorption in the open ocean: Theory and applications,” J. Geophys. Res. 111, C03011 (2006).
J. Lin, W. Cao, W. Zhou, S. Hu, G. Wang, Z. Sun, Z. Xu, and Q. Song, “A bio-optical inversion model to
retrieve absorption contributions and phytoplankton size structure from total minus water spectral absorption
using genetic algorithm,” Chin. J. Oceanology Limnol. 31(5), 970–978 (2013).
E. Organelli, A. Bricaud, D. Antoine, and J. Uitz, “Multivariate approach for the retrieval of phytoplankton size
structure from measured light absorption spectra in the Mediterranean Sea (BOUSSOLE site),” Appl. Opt.
52(11), 2257–2273 (2013).
#207741 - $15.00 USD
(C) 2014 OSA
Received 5 Mar 2014; revised 3 Apr 2014; accepted 4 Apr 2014; published 23 Apr 2014
5 May 2014 | Vol. 22, No. 9 | DOI:10.1364/OE.22.010467 | OPTICS EXPRESS 10467
14. A. M. Ciotti, M. R. Lewis, and J. J. Cullen, “Assessment of the relationships between dominant cell size in
natural phytoplankton communities and the spectral shape of the absorption coefficient,” Limnol. Oceanogr.
47(2), 404–417 (2002).
15. R. J. Brewin, S. Sathyendranath, T. Hirata, S. J. Lavender, R. M. Barciela, and N. J. Hardman-Mountford, “A
three-component model of phytoplankton size class for the Atlantic Ocean,” Ecol. Modell. 221(11), 1472–1483
(2010).
16. S. Roy, S. Sathyendranath, and T. Platt, “Retrieval of phytoplankton size from bio-optical measurements: theory
and applications,” J. R. Soc. Interface 8(58), 650–660 (2011).
17. A. Bricaud, H. Claustre, J. Ras, and K. Oubelkheir, “Natural variability of phytoplanktonic absorption in oceanic
waters: Influence of the size structure of algal populations,” J. Geophys. Res. 109, C11010 (2004).
18. S. E. Lohrenz, A. D. Weidemann, and M. Tuel, “Phytoplankton spectral absorption as influenced by community
size structure and pigment composition,” J. Plankton Res. 25(1), 35–61 (2003).
19. C. S. Yentsch, “Measurement of visible light absorption by particulate matter in the ocean,” Limnol. Oceanogr.
7(2), 207–217 (1962).
20. O. Schofield, T. Bergmann, M. J. Oliver, A. Irwin, G. Kirkpatrick, W. P. Bissett, M. A. Moline, and C. Orrico,
“Inversion of spectral absorption in the optically complex coastal waters of the Mid-Atlantic Bight,” J. Geophys.
Res. 109, C12S04 (2004).
21. L. N. Duysens, “The flattening of the absorption spectrum of suspensions, as compared to that of solutions,”
Biochim. Biophys. Acta 19(1), 1–12 (1956).
22. H. C. Hulst and H. C. van de Hulst, Light Scattering by Small Particles (Courier Dover, 1957).
23. A. Morel and A. Bricaud, “Theoretical results concerning light absorption in a discrete medium, and application
to specific absorption of phytoplankton,” Deep Sea Res. A, Oceanogr. Res. Pap. 28(11), 1375–1393 (1981).
24. D. Ficek, S. Kaczmarek, J. Stoñ-Egiert, B. Wozniak, R. Majchrowski, and J. Dera, “Spectra of light absorption
by phytoplankton pigments in the Baltic; conclusions to be drawn from a Gaussian analysis of empirical data,”
Oceanologia 46, 533–555 (2004).
25. N. Hoepffner and S. Sathyendranath, “Effect of pigment composition on absorption properties of
phytoplankton,” Mar. Ecol. Prog. Ser. 73, 11–23 (1991).
26. N. Hoepffner and S. Sathyendranath, “Determination of the major groups of phytoplankton pigments from the
absorption spectra of total particulate matter,” J. Geophys. Res. 98(C12), 22789–22803 (1993).
27. E. Marañón, P. Cermeño, J. Rodríguez, M. V. Zubkov, and R. P. Harris, “Scaling of phytoplankton
photosynthesis and cell size in the ocean,” Limnol. Oceanogr. 52(5), 2190–2198 (2007).
28. W. Zhou, G. Wang, Z. Sun, W. Cao, Z. Xu, S. Hu, and J. Zhao, “Variations in the optical scattering properties of
phytoplankton cultures,” Opt. Express 20(10), 11189–11206 (2012).
29. R. R. Bidigare, M. E. Ondrusek, J. H. Morrow, and D. A. Kiefer, “In-vivo absorption properties of algal
pigments,” Proc. SPIE 1302, 290–302 (1990).
30. T. Kostadinov, D. Siegel, and S. Maritorena, “Retrieval of the particle size distribution from satellite ocean color
observations,” J. Geophys. Res. 114(C9), C09015 (2009).
31. T. Kostadinov, D. Siegel, and S. Maritorena, “Global variability of phytoplankton functional types from space:
assessment via the particle size distribution,” Biogeosci. Discuss. 7(3), 4295–4340 (2010).
32. R. D. Vaillancourt, C. W. Brown, R. R. Guillard, and W. M. Balch, “Light backscattering properties of marine
phytoplankton: relationships to cell size, chemical composition and taxonomy,” J. Plankton Res. 26(2), 191–212
(2004).
33. A. L. Whitmire, W. S. Pegau, L. Karp-Boss, E. Boss, and T. J. Cowles, “Spectral backscattering properties of
marine phytoplankton cultures,” Opt. Express 18(14), 15073–15093 (2010).
34. W. R. Clavano, E. Boss, and L. Karp-Boss, “Inherent optical properties of non-spherical marine-like particles—
from theory to observation,” Oceanogr. Mar. Biol. Annu. Rev. 45, 1–38 (2007).
1. Introduction
Phytoplankton size is a major biological factor, which governs the functioning of pelagic
food-webs, thereby affecting the rate of carbon flux from the upper ocean to the deep layers
[1, 2]. Many biogeochemical processes are related directly to the phytoplankton size in a
given environment. For example, small cells absorb nutrients with higher efficiency, while
large cells sink faster than small cells [3, 4].
However, direct measurements of phytoplankton size have remained elusive due to a lack
of reliable methods. The current methods used to quantify phytoplankton size rely on
microscopy and flow cytometry. Microscopy is used to enumerate the larger phytoplankton
cells (i.e., diameter >20 μm [5],), whereas flow cytometry is used to count the smaller cells
(often with an upper limit of <20 μm [6],). High-performance liquid chromatography (HPLC)
pigment analyses have also been performed systematically to estimate different size classes
[7, 8], but this method is time-consuming and some pigment groups may not strictly reflect
the true size of cells [9, 10]. In addition, the absorption characteristics of phytoplankton have
been used to infer the fractions of small and large cells in a sample [11–13]. For example,
Ciotti et al. [14] proposed a parameterized model for extracting the dominant cell size in
#207741 - $15.00 USD
(C) 2014 OSA
Received 5 Mar 2014; revised 3 Apr 2014; accepted 4 Apr 2014; published 23 Apr 2014
5 May 2014 | Vol. 22, No. 9 | DOI:10.1364/OE.22.010467 | OPTICS EXPRESS 10468
natural phytoplankton communities based on the spectral shape of the absorption coefficient.
Brewin et al. [15] determined the fractional contributions of three phytoplankton size classes
(micro, nano, and pico) to the overall chlorophyll a concentration using a three-component
model. Unfortunately, these absorption-based methods cannot provide quantitative estimates
of the actual cell sizes. Recently, a method has been proposed by Roy et al. [16] for
determining the size of phytoplankton based on the absorption at 676 nm and the chlorophyll
a concentration. In practice, however, it is often difficult to ensure the matching of these
measurements, which are generally determined with two different instruments, and the
accuracy of this method is affected greatly by the input parameters.
Therefore, it would be beneficial to develop a new approach for quantifying the size of
phytoplankton. We know that changes in phytoplankton size are linked directly to variations
in phytoplankton absorption [17, 18], which can be measured directly using the quantitative
filter pad technique [19] or in situ instruments (e.g. ACS meter) [20]. However, quantitative
evaluations of cell size based on phytoplankton absorption are always challenging. Thus, the
objective of the present study was to develop a new method based on phytoplankton
absorption to facilitate quantitative estimates of the mean cell size of phytoplankton.
2. Methods and data
2.1 Methods
The absorption coefficient of phytoplankton cells distributed as discrete particles is less than
that of the same material dispersed in a solution [21]. According to previous studies [22–26],
a quantity (package effect index, Qa*(λ)) can be used to describe this difference. If the
particles have a refractive index that is close to that of the surrounding medium (sea water)
[23], and assuming that they are homogeneous spheres and optically soft particles, an
approximation allows Qa*(λ) to be calculated by
Qa ( λ ) =
∗
exp  − ρ ′ ( λ ) − 1 
3  2 exp  − ρ ′ ( λ ) 
+2
1 +
,
2 ρ ′ ( λ ) 
ρ ′(λ )
ρ ′2 ( λ )

5
Cj
j =1
Cchla
ρ ′ ( λ ) = acm ( λ ) d = CI d 
a ∗j , s ( λ ) ,
(1)
(2)
and
2
 1λ −λ
n
 
max,ij
a ∗j ,s ( λ ) =  a ∗max,ij exp  − 
(3)
  ⋅
 2  σ ij

i =1



The notations used in this study are given in Table 1. In this calculation, the quantity d is
the equivalent spherical diameter, which can also be regarded as the mean cell diameter of a
phytoplankton sample. The pigment package effect index decreases from 1 (no package
effect) to 0 (maximal package effect), and the specific absorption of each pigment in solution
is determined by summing their elementary Gaussian bands [24]. Thus, the absorption
coefficients of phytoplankton (aph(λ)) can be regarded as the combined absorption spectra of
five major pigments (chla, chlb, chlc, PSC, and PPC), which is simply written as follows [17]:
5
a ph ( λ ) = Qa ( λ )  C j a ∗j , s ( λ ) ⋅
∗
(4)
j =1
#207741 - $15.00 USD
(C) 2014 OSA
Received 5 Mar 2014; revised 3 Apr 2014; accepted 4 Apr 2014; published 23 Apr 2014
5 May 2014 | Vol. 22, No. 9 | DOI:10.1364/OE.22.010467 | OPTICS EXPRESS 10469
Table 1. Notations used in the text
Notation
chla, chlb, chlc,
PSC, PPC
Qa*(λ)
d
acm
CI
Cj
a*j,s(λ)
a*max,ij
a*max
λmax,ij
σij
aph
achla,r (λ)
λmax
σk
N(D)
Nt
σf
BWf
Description
chlorophyll a, chlorophyll b, chlorophyll c, photosynthetic
carotenoids, photoprotective carotenoids
package effect index
mean cell diameter
intracellular absorption coefficient
intracellular chlorophyll a concentration
pigment concentration per sample, j = [chla, chlb, chlc, PSC, PPC]
specific absorption coefficient for the j-th group of unpackaged
pigments (i.e. in the solvent)
specific absorption coefficient for the spectral peak of the Gaussian
band
spectral peak of the Gaussian band for unpackaged chlorophyll a
specific absorption with its center at ~676 nm
center of the spectral band
standard deviation of the band (half width equal to 2.35σ)
total absorption coefficient of phytoplankton
packaged chlorophyll a absorption band (Gaussian band) with its
center at ~676 nm
position of the maximum absorption for achla,r (λ)
standard deviation of the Gaussian band for unpackaged chlorophyll
a specific absorption with its center at ~676 nm
phytoplankton abundance with diameter D
total cell number
standard deviation of the band for achla,r (λ)
band width of achla,r (λ) with its center at ~676 nm
Unit
—
—
m
m−1
mg chla m−3
mg pigment m−3
m2(mg pigment)−1
m2(mg pigment)−1
m2(mg pigment)−1
nm
nm
m−1
m−1
nm
nm
—
—
nm
nm
A flowchart of the method is shown in Fig. 1. We aimed to calculate the value of the
product CId. To minimize the influence of absorption attributable to auxiliary pigments, we
selected a red waveband (650–700 nm) where the absorption is mainly due to chla. We used a
peak-fitting code (Signal Processing Tools, http://terpconnect.umd.edu/~toh/spectrum/) to
determine the packaged chla absorption band with its center at ~676 nm (achla,r (λ), also
regarded as a Gaussian band, see Fig. 1 Step1). The specific absorption levels of the auxiliary
pigments in the red waveband are very small and Cchlb is generally much less than Cchla, which
we discuss below. Thus, Eqs. (2) and (4) can be simplified as follows:
ρ ′ ( λ ) = CI da ∗chla , s ( λ ) ,
(5)
 1  λ − λ 2 
∗
max
achla ,r ( λ ) = Qa ( λ ) Cchla a *max exp  − 
 ⋅
 2  σ k  
(6)
and
where λmax is the position of the maximum absorption for achla,r(λ) and λ varies from 650 to
700 nm. The parameters of the unpackaged Gaussian band (σk = 9.2 nm, a*max = 0.02 (m2(mg
chla)−1)) and the specific absorption coefficient of unpackaged chla (a*chla,s(λ)) were known
quantities and obtained from Hoepffner and Sathyendranath [25], which were the mean
values obtained from cultures of phytoplankton groups. The parameter σk indicates the initial
width of Gaussian band (no package effect). The width of Gaussian band is directly affected
by the package effect, and it increases with an enhanced package effect.
#207741 - $15.00 USD
(C) 2014 OSA
Received 5 Mar 2014; revised 3 Apr 2014; accepted 4 Apr 2014; published 23 Apr 2014
5 May 2014 | Vol. 22, No. 9 | DOI:10.1364/OE.22.010467 | OPTICS EXPRESS 10470
absorption (m-1)
aph ( λ )
achla,r ( λ )
0.15
Initial Guess (CId)
Eq. (5)
0.1
ρ′ ( λ )
0.05
0
400
450
500
550
600
λ (nm)
Step1
650
Eq. (1)
Qa∗ ( λ )
Step3
 1  λ − λ 2 
max
exp − 
 
Qa ( λmax )
 2  σk  
Qa ( λ )
∗
λmax700
∗
Peak Fitting
achla,r ( λ )
absorption (m-1)
0.08
0.06
achla,r ( λ )
1.5
Step2
Normalized
1
achla,r ( λmax )
1
0.04
0.5
0.5
0.02
0
650
665 λmax 685
λ (nm)
0
650
700
665 λmax 685
λ (nm)
Step5
Cchla
Eq. (10)
Qa* ( λmax )
CI d
700
Iterative Solver
Eq. (5)
Eq. (1)
665 λmax 685
λ (nm)
Step4
Eq. (9)
d
0
650
700
Minimize Differences
ρ′ ( λmax )
Step6
Fig. 1. Method flowchart.
When λ = λmax, Eq. (6) can be written as:
achla ,r ( λmax ) = Qa ( λmax ) Cchla a *max .
∗
(7)
To reduce the number of unknown quantities, we divide both sides of Eq. (6) by the
relationship provided by Eq. (7), such that:
achla , r ( λ )
achla ,r ( λmax )
 1  λ − λ 2 
max
exp  − 
 ⋅
Qa ( λmax )
 2  σ k  
Qa ( λ )
∗
=
∗
(8)
By combining Eqs. (1) and (5), we find there is only one unknown parameter (the product CId
in Q*a(λ)) in Eq. (8), which can be represented under the simple form: A(λ) = Q(λ)E(λ). We
used a nonlinear optimization inversion technique (MATLAB, Optimization Toolbox) to
calculate the value of CId. The first step is to attribute initial guess to the product CId (here we
used 100 (mg m−2)). Initial values of A(λ) are then computed for waveband from 650 to 700
nm, using Eq. (8) (see Fig. 1 Step3), and these values are compared to the measured A(λ) as
follows: differences = [Ameasured(λ)–Acomputed(λ)]/Ameasured(λ). An iterative solver routine is then
set up, to vary CId from the initial guess, to minimize the differences between measured and
computed values in all bands, by setting the sum of the differences to be equal to zero, with a
#207741 - $15.00 USD
(C) 2014 OSA
Received 5 Mar 2014; revised 3 Apr 2014; accepted 4 Apr 2014; published 23 Apr 2014
5 May 2014 | Vol. 22, No. 9 | DOI:10.1364/OE.22.010467 | OPTICS EXPRESS 10471
5% tolerance error, and then we obtain the optimal solution (CId) for the current function (see
Fig. 1 Step4).
The product CId is a function of d [16, 27]. Thus, d can be calculated by:
1
 C d 1− m
d = I  ⋅
 c0 
(9)
where c0 = 3.9 × 106 (mg chla m-2.94) and m = 0.06 (dimensionless) [16]. Finally, using Eq.
(7), we can derive Cchla as follows:
Cchla =
achla ,r ( λmax )
Qa ( λmax ) a *max
∗
⋅
(10)
where Q*a(λmax) is calculated using Eqs. (1) and (5) (see Fig. 1 Step6), and a*max is constant
(0.02 (m2(mg chla)−1)). We provide the program code which is developed in MATLAB (see
www.dropbox.com/sh/w16516ikbmakn73/tWl3kjN7pf).
2.2 Data
It was difficult to determine the phytoplankton size distribution in natural waters, so
laboratory-cultured phytoplankton species were used to validate the performance of the
method. Batch cultures of 13 individual phytoplankton species were used in this study (Table
2). The spectral absorption coefficients of these phytoplankton groups were measured using
an ACS meter (WET Labs Inc.). The cell size distributions and cell number densities were
determined using a Multisizer III Coulter counter (Beckman Inc.). The mean cell diameter
(MCD) was calculated as: d = [N(Di)Di3/Nt]1/3 (N(Di) is the phytoplankton abundances at the
diameter Di and Nt is the total cell number). The concentration of chla was determined by
HPLC. The methods used to obtain these data were described by Zhou et al. [28].
Table 2. Data set details
Name
Shape
Prymnesium patelliferum
Platymonas subcordiformis
Pyramimonas sp.
Biddulphiales sp.
Amphidinium sp.
Pheaodactylum tricornutum
Nitzschia closterium
Dunaliella tertiolecta
Phaeocystis sp.
Microcystis aeruginosa
Chaetoceros sp.
MCDM
(μm)
8.0
10.3
10.5
8.3
5.3
4.6
4.9
10.3
4.2
4.9
6.6
chlaM (mg
m−3)
16.9
56.1
34.5
27.8
26.0
4.8
—
71.1
4.0
8.5
7.4
MCDE
(μm)
7.8
10.7
10.5
9.7
5.5
4.1
4.9
10.4
5.4
3.6
4.6
Oval
Oval
Obovate
Short box
Bioconical
Fusiform
Fusiform
Oval
Sphere
Oval
Elliptical
cylinder
13.0
12.3
9.8
Thalassirosira weissflogii
Cylinder
—
Tetraselmis levis
Oval
12.5
10.5
MCD is the mean cell diameter. M denotes measured values, and E denotes estimated values.
chlaE (mg
m−3)
12.4
54.2
32.9
27.7
20.1
7.1
8.1
64.2
12.2
7.5
14.4
15.1
8.0
3. Results
The method was applied to the data set of 13 phytoplankton species. The method performance
was quantified in terms of the relative root mean square error (RMSE), which is expressed in
percentages according to:
1 n  x
− xi ,measured
RMSE ( % ) = 100    i ,computed

xi ,measured
 n i =1 

#207741 - $15.00 USD
(C) 2014 OSA



2 1/2




(11)
Received 5 Mar 2014; revised 3 Apr 2014; accepted 4 Apr 2014; published 23 Apr 2014
5 May 2014 | Vol. 22, No. 9 | DOI:10.1364/OE.22.010467 | OPTICS EXPRESS 10472
where x is the variable and n is the number of data points. Comparisons of the estimated and
measured values of the MCD and chla concentration are shown in Fig. 2 and Table 2. The
estimated and measured MCDs were in relatively good agreement, i.e., determination
coefficient R2 = 0.88 and RMSE = 16.35%. For the chla concentration, the performance was
also satisfactory, i.e., the R2 = 0.96 and RMSE = 73.04%. The chla concentrations of three
phytoplankton groups (Phaeocystis sp., Chaetoceros sp., and Thalassirosira weissflogii) were
overestimated, but the other groups were estimated with relatively good accuracy. For all the
measurements of the phytoplankton absorption spectra, the standard deviations of Gaussian
band achla,r (λ) (σf, determined using the peak fitting code) were greater than 9.7 nm (σf > 9.7
nm). Thus, we assumed that σk varied from 8.9 to 9.5 nm and that the values of the estimated
parameters would fall within specific ranges (Fig. 2, red bars). The uncertainty in σk would
introduce dispersions into the results, but these parameters (MCD and chla concentration)
were still obtained within reasonable ranges. In particular, the variation in σk had almost no
effect on the estimated chla concentration.
Fig. 2. Comparisons of the estimated and measured values of the mean cell diameter (MCD)
and chlorophyll a (chla) concentration. A. MCD, B. Chla concentration. When σk varied from
8.9 to 9.5 nm, the estimated parameters were within the ranges defined by the red bars.
There was a significant linear correlation between the MCD and the bandwidth of achla,r(λ)
(BWf, where BW f = 4.7σ when calculated using the peak-fitting code) (Fig. 3(A)). The species
with the lower BWf values were smaller. The linear regression determined the following
relationship for BWf:
BW f = 0.45( nm ⋅ um −1 ) ⋅ d + 45.2( nm ) ( R 2 = 0.73) ⋅
(12)
However, caution is required during the application of this equation because the uncertainty
in BWf may lead to relatively large errors.
#207741 - $15.00 USD
(C) 2014 OSA
Received 5 Mar 2014; revised 3 Apr 2014; accepted 4 Apr 2014; published 23 Apr 2014
5 May 2014 | Vol. 22, No. 9 | DOI:10.1364/OE.22.010467 | OPTICS EXPRESS 10473
We also tested the relationship between the mean cell volume and cell-specific chla
concentration, which were linked by a significant linear relationship after logarithmic
transformation (Fig. 3(B)):
log10 ( y ) = −3.1 + 1.12 log10 ( x )
(R
2
= 0.91) ⋅
(13)
where y is the cell-specific chla concentration and x is the mean cell volume. The model
proposed by Maranón et al. [27] is also shown in Fig. 3(B). Both the slope and the intercept
with x-axis are slightly different, probably because of photo-adaptation.
Fig. 3. A. Relationship between BWf and measured the mean cell diameter (MCD). B.
Relationship between the mean cell volume and cell-specific chlorophyll a (chla)
concentration, where the relationship proposed by Maranón et al. [27] is also shown.
4. Discussion
The method proposed in this study uses the red waveband to calculate the values of CId and
Cchla because the effect of absorption attributable to auxiliary pigments is very small in this
waveband. The values of a*chlc,s(λ), a*PSC,s(λ), and a*PPC,s(λ) in the red waveband can be
neglected, but a*chlb,s(λ) may still be taken into account. However, the average ratio of
a*chlb,s(676) relative to a*chla,s(676) was less than 15% [25, 26, 29]. Moreover, using the HPLC
data set in the NASA bio-Optical Marine Algorithm Data set (NOMAD), we also found that
the mean ratio of Cchlb relative to Cchla was ~8.3%. Thus, the uncertainty related to the
simplification of the Eq. (2) had almost no effect on the ultimate estimation.
The uncertainty in the parameter σk accounted for a relatively large part of the uncertainty
in the estimated cell size. Using the peak-fitting code (see Material and Methods), we fitted
the specific absorption spectra of chla measured in solvent by Bidigare et al. [29] to obtain the
Gaussian band in the red waveband, and we then obtained an approximate value of σk (σk =
#207741 - $15.00 USD
(C) 2014 OSA
Received 5 Mar 2014; revised 3 Apr 2014; accepted 4 Apr 2014; published 23 Apr 2014
5 May 2014 | Vol. 22, No. 9 | DOI:10.1364/OE.22.010467 | OPTICS EXPRESS 10474
9.27 nm). However, the value of σk should not be a constant in natural waters, so a future
research should aim to reduce the uncertainty when estimating the cell size by adjusting the
parameter σk. Despite this, the validation conducted in the present study demonstrated that the
deviation due to the variation in σk (which ranged from 8.9 to 9.5 nm) was still reasonable and
acceptable. For the parameter a*max, it had a negligible effect on the cell size estimation (Eq.
(8)), but the accuracy of the estimated chla concentration was affected greatly by this
parameter. For example, if 0.03 m2(mg chla)−1 is used as the value of a*max, the chla
concentrations would be underestimated by 66.7% according to Eq. (10).
Some errors in the estimated diameter were related to uncertainties when assigning the
parameters c0 and m. A sensitivity analysis was performed in a previous study by Roy et al.
[16], which suggested that a small uncertainty in these parameters need not lead to magnified
errors during size estimation. However, the relationship between CId and d is likely to change
with the light environment, so future research is required to achieve improvements in this
area.
The method proposed in the present is based on the anomalous diffraction approximation
of the Mie theory, which provides a solution to the bulk inherent optical properties of a
known particle suspension. We assumed that the phytoplankton cells were homogeneous
spheres and optically soft particles, but these assumptions rarely hold in natural
phytoplankton species. The phytoplankton species used in the present study were
characterized by their different cell shapes. For example, the cells of Prymnesium
patelliferum are oval in shape, whereas Biddulphiales sp. has a relatively short box shape.
These differences would also introduce some errors into the estimated results. Nevertheless,
some studies have shown that these assumptions are acceptable [30–34]. In our study, a
Coulter counter was used to determine the cell size distribution based on the equivalent
spherical diameter and our proposed method produced similar estimation. This consistency
probably reduced the dispersion between the estimated and measured mean cell size in the
validation. In addition, it indicated that the cell shape of phytoplankton species should not be
a major source of uncertainty when estimating the mean cell size.
In this study, all of the cultures were grown in enriched medium, which was filtered
through 0.45-μm filter membranes. The algal cell density was counted during the exponential
growth stage for all species, so the degraded detritus attributable to dead algae was not
significant. Light microscopy was also used to confirm the negligible effect of detritus. Thus,
the effect of detritus on the phytoplankton absorption and cell size density measurements was
shown to be negligible. In addition, bacteria only accounted for ~2–5% of the algal cell
density in most cultures and the majority of the bacteria measured ~0.2 μm in size [28].
Therefore, bacteria also had a negligible effect on the algal cell size density.
A peak-fitting code was used to obtain the Gaussian band of the absorption spectra. The
code decomposed a complex and overlapping peak signal into its component parts, regardless
of noise effects. This peak-fitting method may be applied directly to non-water total
absorption spectra when they are measured using an ACS meter, because the absorption
contributions of detritus and colored dissolved organic matter to the red waveband are always
small, and they can also be regarded as noise.
In the present study, the method was validated using individual samples of each
phytoplankton group, which were cultured separately, rather than a mixture of cultured
phytoplankton groups. Thus, it is still not clear whether this method could be applied to
mixed populations of phytoplankton, which are always found in natural waters. However, the
validation showed that the proposed method performed with good accuracy, regardless of the
cell shape and phytoplankton species, so this method could probably also be applied to
natural waters. In addition, compared with existing methods (e.g., Flow Cytometer and
Microscopy), this method is more efficient regardless of size distribution and it can be applied
directly using current optical instruments (e.g., ACS meter and hyper-spectral sensors).
#207741 - $15.00 USD
(C) 2014 OSA
Received 5 Mar 2014; revised 3 Apr 2014; accepted 4 Apr 2014; published 23 Apr 2014
5 May 2014 | Vol. 22, No. 9 | DOI:10.1364/OE.22.010467 | OPTICS EXPRESS 10475
5. Conclusion
In this study, we developed a new method for quantifying the size of phytoplankton cells.
Although some uncertainties may affect the estimation accuracy, the analysis indicated that
the estimated errors attributable to these uncertainties are acceptable. This method facilitates
the determination of the cell size and chla concentration in phytoplankton, and it has great
potential for application to current in situ optical instruments.
Acknowledgments
We thank the Marine Biology Group of the South China Sea institute of Oceanography
(SCSIO) for providing the algal species and algae cultivation. We appreciate the thoughtful
comments from all reviewers, which helped to greatly improve an earlier version of this
manuscript. This study was supported by the National Natural Science Foundation of China
(Grant Nos. 41376042, 41076014, U0933005, and 41176035), the Natural Science for Youth
Foundation (Grant No. 41206029), the Open Project Program of the State Key Laboratory of
Tropical Oceanography (No. LT0ZZ1201), and the Strategic Priority Research Program of
the Chinese Academy of Sciences (Grant No. XDA11040302).
#207741 - $15.00 USD
(C) 2014 OSA
Received 5 Mar 2014; revised 3 Apr 2014; accepted 4 Apr 2014; published 23 Apr 2014
5 May 2014 | Vol. 22, No. 9 | DOI:10.1364/OE.22.010467 | OPTICS EXPRESS 10476