Novel method for quantifying the cell size of marine phytoplankton based on optical measurements

Junfang Lin; Wenxi Cao; Wen Zhou; Zhaohua Sun; Zhantang Xu; Guifen Wang; Shuibo Hu

doi:10.1364/OE.22.010467

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 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, Q_a*(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 Q_a*(λ) to be calculated by

Q_{a}^{^{*}} (λ) = \frac{3}{2 ρ^{'} (λ)} {1 + \frac{2 \exp [- ρ^{'} (λ)]}{ρ^{'} (λ)} + 2 \frac{\exp [- ρ^{'} (λ)] - 1}{{ρ^{'}}^{2} (λ)}},

ρ^{'} (λ) = a_{c m} (λ) d = C_{I} d \sum_{j = 1}^{5} \frac{C_{j}}{C_{c h l a}} a_{j, s}^{*} (λ),

and

a_{j, s}^{*} (λ) = \sum_{i = 1}^{n} a_{\max, i j}^{*} \exp [- \frac{1}{2} {(\frac{λ - λ_{\max, i j}}{σ_{i j}})}^{2}] \cdot

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 (a_ph(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]:

Table 1. Notations used in the text

View Table | View all tables in this article

a_{p h} (λ) = Q_{a}^{^{*}} (λ) \sum_{j = 1}^{5} C_{j} a_{j, s}^{*} (λ) \cdot

A flowchart of the method is shown in Fig. 1.We aimed to calculate the value of the product C_Id. 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 (a_chla,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 C_chlb is generally much less than C_chla, which we discuss below. Thus, Eqs. (2) and (4) can be simplified as follows:

ρ^{'} (λ) = C_{I} d a_{c h l a, s}^{*} (λ),

and

a_{c h l a, r} (λ) = Q_{a}^{^{*}} (λ) C_{c h l a} a_{max}^{*} \exp [- \frac{1}{2} {(\frac{λ - λ_{\max}}{σ_{k}})}^{2}] \cdot

where λ_max is the position of the maximum absorption for a_chla,r(λ) and λ varies from 650 to 700 nm. The parameters of the unpackaged Gaussian band (σ_k = 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 σ_k 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.

Fig. 1 Method flowchart.

Download Full Size | PDF

When λ = λ_max, Eq. (6) can be written as:

a_{c h l a, r} (λ_{\max}) = Q_{a}^{^{*}} (λ_{\max}) C_{c h l a} a_{max}^{*} .

To reduce the number of unknown quantities, we divide both sides of Eq. (6) by the relationship provided by Eq. (7), such that:

\frac{a_{c h l a, r} (λ)}{a_{c h l a, r} (λ_{\max})} = \frac{Q_{a}^{^{*}} (λ)}{Q_{a}^{^{*}} (λ_{\max})} \exp [- \frac{1}{2} {(\frac{λ - λ_{\max}}{σ_{k}})}^{2}] \cdot

By combining Eqs. (1) and (5), we find there is only one unknown parameter (the product C_Id 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 C_Id. The first step is to attribute initial guess to the product C_Id (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 = [A_measured(λ)–A_computed(λ)]/A_measured(λ). An iterative solver routine is then set up, to vary C_Id 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 5% tolerance error, and then we obtain the optimal solution (C_Id) for the current function (see Fig. 1 Step4).

The product C_Id is a function of d [16, 27]. Thus, d can be calculated by:

d = {(\frac{C_{I} d}{c_{0}})}^{\frac{1}{1 - m}} \cdot

where c₀ = 3.9 × 10⁶ (mg chla m^-2.94) and m = 0.06 (dimensionless) [16]. Finally, using Eq. (7), we can derive C_chla as follows:

C_{c h l a} = \frac{a_{c h l a, r} (λ_{\max})}{Q_{a}^{^{*}} (λ_{\max}) a_{max}^{*}} \cdot

where Q*_a(λ_max) 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(D_i)D_i³/N_t]^1/3 (N(D_i) is the phytoplankton abundances at the diameter D_i and N_t 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

View Table | View all tables in this article

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:

RMSE (%) = 100 {[\frac{1}{n} \sum_{i = 1}^{n} {(\frac{x_{i, c o m p u t e d} - x_{i, m e a s u r e d}}{x_{i, m e a s u r e d}})}^{2}]}^{1 / 2}

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 a_chla,r (λ) (σ_f, determined using the peak fitting code) were greater than 9.7 nm (σ_f > 9.7 nm). Thus, we assumed that σ_k 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 σ_k would introduce dispersions into the results, but these parameters (MCD and chla concentration) were still obtained within reasonable ranges. In particular, the variation in σ_k 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 σ_k varied from 8.9 to 9.5 nm, the estimated parameters were within the ranges defined by the red bars.

Download Full Size | PDF

There was a significant linear correlation between the MCD and the bandwidth of a_chla,r(λ) (BW_f, where BW _f = 4.7σ when calculated using the peak-fitting code) (Fig. 3(a)). The species with the lower BW_f values were smaller. The linear regression determined the following relationship for BW_f:

B W_{f} = 0.45 (n m \cdot u m^{- 1}) \cdot d + 45.2 (n m) \begin{matrix}  \end{matrix} (R^{2} = 0.73) \cdot

However, caution is required during the application of this equation because the uncertainty in BW_f may lead to relatively large errors.

Fig. 3 A. Relationship between BW_f 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.

Download Full Size | PDF

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)):

\log_{10} (y) = - 3.1 + 1.12 \log_{10} (x) \begin{matrix}  \end{matrix} (R^{2} = 0.91) \cdot

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.

4. Discussion

The method proposed in this study uses the red waveband to calculate the values of C_Id and C_chla 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 C_chlb relative to C_chla 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 σ_k 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 σ_k (σ_k = 9.27 nm). However, the value of σ_k 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 σ_k. Despite this, the validation conducted in the present study demonstrated that the deviation due to the variation in σ_k (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 C_Id 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).

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).

References and links

1. 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). [CrossRef]

2. 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). [CrossRef]

3. 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). [CrossRef]

4. T. L. Richardson and G. A. Jackson, “Small phytoplankton and carbon export from the surface ocean,” Science 315(5813), 838–840 (2007). [CrossRef] [PubMed]

5. 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).

6. 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). [CrossRef]

7. 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).

8. 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). [CrossRef]

9. 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). [CrossRef]

10. 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). [CrossRef]

11. 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).

12. 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). [CrossRef]

13. 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). [CrossRef] [PubMed]

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). [CrossRef]

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). [CrossRef]

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). [CrossRef] [PubMed]

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). [CrossRef]

19. C. S. Yentsch, “Measurement of visible light absorption by particulate matter in the ocean,” Limnol. Oceanogr. 7(2), 207–217 (1962). [CrossRef]

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). [CrossRef] [PubMed]

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). [CrossRef]

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). [CrossRef]

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). [CrossRef]

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). [CrossRef]

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). [CrossRef] [PubMed]

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). [CrossRef]

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). [CrossRef]

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). [CrossRef]

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). [CrossRef] [PubMed]

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). [CrossRef]

Notation	Description	Unit
chla, chlb, chlc, PSC, PPC	chlorophyll a, chlorophyll b, chlorophyll c, photosynthetic carotenoids, photoprotective carotenoids	—
Q_a(λ)*	package effect index	—
d	mean cell diameter	m
a_cm	intracellular absorption coefficient	m⁻¹
C_I	intracellular chlorophyll a concentration	mg chla m⁻³
C_j	pigment concentration per sample, j = [chla, chlb, chlc, PSC, PPC]	mg pigment m⁻³
a*_j_,s(λ)	specific absorption coefficient for the j-th group of unpackaged pigments (i.e. in the solvent)	m²(mg pigment)⁻¹
a_max,_ij*	specific absorption coefficient for the spectral peak of the Gaussian band	m²(mg pigment)⁻¹
a*_max	spectral peak of the Gaussian band for unpackaged chlorophyll a specific absorption with its center at ~676 nm	m²(mg pigment)⁻¹
λ_max,_ij	center of the spectral band	nm
σ_ij	standard deviation of the band (half width equal to 2.35σ)	nm
a_ph	total absorption coefficient of phytoplankton	m⁻¹
a_chla,r (λ)	packaged chlorophyll a absorption band (Gaussian band) with its center at ~676 nm	m⁻¹
λ_max	position of the maximum absorption for a_chla,r (λ)	nm
σ_k	standard deviation of the Gaussian band for unpackaged chlorophyll a specific absorption with its center at ~676 nm	nm
N(D)	phytoplankton abundance with diameter D	—
N_t	total cell number	—
σ_f	standard deviation of the band for a_chla,r (λ)	nm
BW_f	band width of a_chla,r (λ) with its center at ~676 nm	nm

Name	Shape	MCD_M (μm)	MCD_E (μm)	chla_M (mg m⁻³)	chla_E (mg m⁻³)
Prymnesium patelliferum	Oval	8.0	7.8	16.9	12.4
Platymonas subcordiformis	Oval	10.3	10.7	56.1	54.2
Pyramimonas sp.	Obovate	10.5	10.5	34.5	32.9
Biddulphiales sp.	Short box	8.3	9.7	27.8	27.7
Amphidinium sp.	Bioconical	5.3	5.5	26.0	20.1
Pheaodactylum tricornutum	Fusiform	4.6	4.1	4.8	7.1
Nitzschia closterium	Fusiform	4.9	4.9	—	8.1
Dunaliella tertiolecta	Oval	10.3	10.4	71.1	64.2
Phaeocystis sp.	Sphere	4.2	5.4	4.0	12.2
Microcystis aeruginosa	Oval	4.9	3.6	8.5	7.5
Chaetoceros sp.	Elliptical cylinder	6.6	4.6	7.4	14.4
Thalassirosira weissflogii	Cylinder	13.0	12.3	9.8	15.1
Tetraselmis levis	Oval	12.5	10.5	—	8.0

Notation	Description	Unit
chla, chlb, chlc, PSC, PPC	chlorophyll a, chlorophyll b, chlorophyll c, photosynthetic carotenoids, photoprotective carotenoids	—
Q_a(λ)*	package effect index	—
d	mean cell diameter	m
a_cm	intracellular absorption coefficient	m⁻¹
C_I	intracellular chlorophyll a concentration	mg chla m⁻³
C_j	pigment concentration per sample, j = [chla, chlb, chlc, PSC, PPC]	mg pigment m⁻³
a*_j_,s(λ)	specific absorption coefficient for the j-th group of unpackaged pigments (i.e. in the solvent)	m²(mg pigment)⁻¹
a_max,_ij*	specific absorption coefficient for the spectral peak of the Gaussian band	m²(mg pigment)⁻¹
a*_max	spectral peak of the Gaussian band for unpackaged chlorophyll a specific absorption with its center at ~676 nm	m²(mg pigment)⁻¹
λ_max,_ij	center of the spectral band	nm
σ_ij	standard deviation of the band (half width equal to 2.35σ)	nm
a_ph	total absorption coefficient of phytoplankton	m⁻¹
a_chla,r (λ)	packaged chlorophyll a absorption band (Gaussian band) with its center at ~676 nm	m⁻¹
λ_max	position of the maximum absorption for a_chla,r (λ)	nm
σ_k	standard deviation of the Gaussian band for unpackaged chlorophyll a specific absorption with its center at ~676 nm	nm
N(D)	phytoplankton abundance with diameter D	—
N_t	total cell number	—
σ_f	standard deviation of the band for a_chla,r (λ)	nm
BW_f	band width of a_chla,r (λ) with its center at ~676 nm	nm

Name	Shape	MCD_M (μm)	MCD_E (μm)	chla_M (mg m⁻³)	chla_E (mg m⁻³)
Prymnesium patelliferum	Oval	8.0	7.8	16.9	12.4
Platymonas subcordiformis	Oval	10.3	10.7	56.1	54.2
Pyramimonas sp.	Obovate	10.5	10.5	34.5	32.9
Biddulphiales sp.	Short box	8.3	9.7	27.8	27.7
Amphidinium sp.	Bioconical	5.3	5.5	26.0	20.1
Pheaodactylum tricornutum	Fusiform	4.6	4.1	4.8	7.1
Nitzschia closterium	Fusiform	4.9	4.9	—	8.1
Dunaliella tertiolecta	Oval	10.3	10.4	71.1	64.2
Phaeocystis sp.	Sphere	4.2	5.4	4.0	12.2
Microcystis aeruginosa	Oval	4.9	3.6	8.5	7.5
Chaetoceros sp.	Elliptical cylinder	6.6	4.6	7.4	14.4
Thalassirosira weissflogii	Cylinder	13.0	12.3	9.8	15.1
Tetraselmis levis	Oval	12.5	10.5	—	8.0

Novel method for quantifying the cell size of marine phytoplankton based on optical measurements

Abstract

1. Introduction

2. Methods and data

2.1 Methods

2.2 Data

3. Results

4. Discussion

5. Conclusion

Acknowledgments

References and links

Cited By

Figures (3)

Tables (2)

Equations (13)

Optics Express