The scattering and backscattering coefficients of 15 phytoplankton species were determined in the laboratory using the acs and BB9 instruments. The spectral variability of scattering properties was investigated and the homogenous sphere model based on Mie theory was also evaluated. The scattering efficiencies at 510 nm varied from 1.42 to 2.26, and the backscattering efficiencies varied from 0.003 to 0.020. The backscattering ratios at 510 nm varied from 0.17% to 0.97%, with a mean value of 0.58%. The scattering properties were influenced by algal cell size and cellular particulate organic carbon content rather than the chlorophyll a concentration. Comparison of the measured results to the values estimated using the homogenous sphere model showed that: (1) The model could well reproduce the spectral scattering coefficient with relative deviations of 5–39%, which indicates that cell shape and internal structure have no significant effects on predicting the scattering spectra; (2) Although the homogenous sphere model generally reflected the spectral trend of backscattering spectra for most species, it severely underestimated the backscattering coefficients by 1.4–48.6 folds at 510 nm. The deviations for Chaetoceros sp. and Microcystis aeruginosa were large and might be due to algal cell chain links and intracellular gas vacuoles, respectively.
© 2012 OSA
Light scattering and backscattering coefficients of diverse phytoplankton are key parameters determining the optical variability of oceanic waters and their reflectance properties. Thus, knowledge of these parameters could be extremely useful in the optical detection of dominant phytoplankton species during blooms [1,2] and in the evaluation of phytoplankton community structure in the ocean [3,4]. To date, however, variations in the scattering properties of diverse phytoplankton species remain poorly understood. This is especially true for backscattering properties, which are difficult to measure at sufficient angular and spectral ranges.
Historically, theoretical calculations have been used to interpret the variability of the scattering and backscattering coefficients of phytoplankton. A homogenous sphere model, which is based on the anomalous diffraction approach of van de Hulst, was developed to predict scattering and backscattering coefficients [5–7]. This model was tested on data measured using a spectrophotometer equipped with an integrating sphere [5,8,9]. It has been used in numerous types of optical oceanography studies, including investigation of the variability of the scattering properties of phytoplankton under varying environmental conditions [10–12] and in assessments of the role of the phytoplankton community in light scattering and backscattering in the ocean [13,14]. However, the hypothesis of a homogenous sphere, which is central to this model, is a potential shortcoming when estimating the scattering properties of phytoplankton. In reality, algal cells might possess a variety of complex internal structures and shapes, many of which would significantly deviate from the homogeneous spherical structure. Theoretical calculations for layered particles [15–17] and non-spherical particles  indicate that both cell shape and intracellular structure have a significant effect on scattering properties. A limited number of measurements also have shown a potential departure from the homogenous sphere simulation for scattering properties , especially for the volume scattering function [20–22].
Recently, commercial instruments (e.g., acs, ac9, BB9 (WET Labs Inc.), or HS6 (HOBI Inc.)) became available for direct estimation of scattering properties. The scattering properties of several algae species have been estimated in the laboratory using commercial ac9 and HS6 meters [23,24]. For example, Vaillancourt et al.  observed that the backscattering spectra of 29 species followed the power law function, and plankton backscattering coefficients at 510 nm were well correlated with particulate organic carbon (POC) content rather than chlorophyll a (Chl a) concentration and cell density. They found that the refractive indices derived from inversion of Mie theory to backscattering were generally higher than published values for phytoplankton, which therefore suggested that the Mie theory for homogenous spherical particles could not adequately reproduce the backscattering of phytoplankton. Whitmire et al. , who estimated the backscattering coefficients of 13 phytoplankton species, observed large intra- and interspecific variability in the backscattering spectra. They established a relationship between cell size and both the backscattering ratio and backscattering cross-section. They also found that their observed backscattering cross-section was up to one order of magnitude higher than that the modeled values from Stramski et al. . Thus, they suggested that Mie theory was likely to underestimate backscattering for non-spherical and inhomogeneous particles. Other work in the field also suggests that backscattering from phytoplankton is underestimated using the Mie theory for homogenous sphere .
Currently, many questions remain about the spectral variability of phytoplankton backscattering and the inappropriateness of theoretical models. For example, it is unclear how phytoplankton characteristics such as size, shape, and internal structure affect their backscattering properties. Some studies have reported that Mie theory for homogenous spheres underestimates the magnitude of spectral backscattering properties of phytoplankton cells [23,24]. However, spectral backscattering measurements of phytoplankton cultures determined using commercial backscattering instruments are rare in the literature. Furthermore, few studies have reported quantitative results of comparisons between the spectral backscattering properties estimated using instruments and those spectra predicted by the homogenous sphere model.
In this study, we estimated the spectral scattering and backscattering coefficients of 15 phytoplankton species from 6 taxa in the laboratory using acs and BB9 meters. We also measured algal cell size, POC content, and Chl a concentration. The objective of this study was to investigate the spectral variability of the scattering properties of algal cultures and to identify the factors that influence these scattering properties. We also quantitatively compared the measurements with the results predicted by the homogenous sphere model in order to rigorously assess the appropriateness of using this model for algal species with diverse cell morphology and intracellular structure.
2.1 Phytoplankton cultures
Cultures representing 15 species from 6 major taxa (Table 1 ) were supplied by the Marine Biology Group of the South China Sea Institute of Oceanography. All cultures were grown in f2-enriched medium that was sterilized and filtered using 0.45 μm filter membranes. The cultures were incubated at 20 ± 1 °C under a 12:12 dark: light cycle. The algal cell density was counted by light microscopy every day to identify the exponential growth stage for all species. These cultures were not axenic. The bacterial contamination accounted for about 2–5% of the algal cell density in most cultures. Many of the bacteria were about 0.2 µm in size.
2.2 Optical measurements
All measurements were completed during the exponential growth stage of the cultures. The spectral absorption and attenuation coefficients were measured using an acs meter (WET Labs Inc.). The volume scattering functions at 117° were measured using a BB9 meter, and measurements were then converted to estimate the backscattering coefficients.
BB9 measurements were performed in a 320320400 mm3 (length, width, and height, respectively) plexiglass box wrapped with an opaque black cloth.
The BB9 meter was suspended above the container so that the divergence lights emitted from the light sources of the BB9 instrument were completely directed into the bottom of the container. We rotated the BB9 in the container and collected measurements in several orientations; none of the data were significantly different among these varying orientations. However, the same instrument orientation was used in each experiment to eliminate any possible deviation. The acs measurements were conducted by circulating the sample medium from the box through tubing to the acs and then back into the box. The measurements were recorded when stable absorption and attenuation readings were obtained. During each experiment, the container was covered with an opaque black cloth in order to prevent extraneous light from entering the container.
We performed serial dilution tests with each culture to check for linearity of response over five or six concentrations. At the beginning of the experiments for each species, the container was filled with 25 L of 0.45 μm-filtered seawater for marine algae or distilled water for freshwater algae. First, the steady clean-water baseline for each instrument was established, which would be expected to represent the possible effects of the container or filtered media. Next, 30–300 mL samples of culture were added into the container, and the measurements were taken after the algal suspension was thoroughly mixed. Sequential additions of culture were conducted in this fashion until the entire culture had been added. We performed linear regression of the backscattering coefficient and cell density for each culture and found good linearity of response over the range of algal densities tested.
The absorption and attenuation measurements obtained using the acs meter were processed using the software provided with the instrument. Temperature and salinity corrections were performed using contemporaneously recorded CT data (JFE ALEC Inc. ACW-CAR) . The scattering corrections were performed using the baseline method. The backscattering measurements obtained using the BB9 (at 412, 440, 488, 510, 532, 595, 660, 676, and 715 nm) were also processed according to the document provided by the manufacturer. The attenuation corrections were made using the contemporaneously recorded beam attenuation and absorption (i.e., acs) data. The value = 1.1 was used to convert the particulate volume scattering function to the particulate backscattering coefficient . To account for the effect of the container and filtered media, the clean-water baselines were subtracted from the absorption, attenuation, and backscattering coefficients for each cultured suspension. We also had to interpolate some values of the acs scattering estimation in order to match wavelengths for the backscattering ratio calculation.
2.3 Ancillary measurements
The cell size distribution and cell density of the cultures were determined using a Multisizer III Coulter Counter (Beckman Inc.), which provided a reliable size range from 2 to 60 µm in equivalent spherical diameter (ESD). The filtered media counts from the cultures had a negligible effect on the algal cell size distribution and density, so the blank value of the filtered media was not removed from the measurements. The average of three measurements was used to characterize the algal cell size distribution and density.
The POC concentration was obtained using a method described in the JGOFS protocol . The algal suspension was filtered through pre-combusted 25 mm Whatman GF/F filters (450 °C for 5 h) under low vacuum. Following filtration, filters wrapped in aluminum-foil paper were dried at 55 °C and stored in liquid nitrogen until carbon analysis. The determination of POC was made following a standard CHN analysis involving high temperature combustion of sample filters. A CEC 440HA Elemental Analyzer was used. Prior to combustion, 0.25 mL of 10% HCl was applied to each filter to remove inorganic carbon, and the acid-treated filters were re-dried at 55 °C. The final POC concentration values were calculated by subtracting the blank values and then dividing by the measured volume of filtered suspension.
High-performance liquid chromatography (HPLC) was used for pigment analysis using the method developed by Vidussi et al. . Water sample were filtered through 25 mm Whatman GF/F filters. Pigment extraction was performed in 3 ml of methanol. Prior to injection, 500 μl of extract were mixed with 250 μl of 1M ammonium acetate. The extract then was injected through a 200 μl loop into the HPLC system, which was equipped with a 3 μm Hypersil® MOS, 10 cm, 4.6 mm (ID) C8 column (Shandon).
2.4 Optical cross-sections and optical mean efficiency factors
The backscattering cross-section by the population of phytoplankton cells, (m2 cell–1), was calculated from the backscattering coefficient (m–1) and the algal cell density (cells ml–1) as follows:5]. Equations similar to Eq. (1) and Eq. (2) link the scattering cross-section and mean efficiency factor of scattering to the scattering coefficient.
2.5 Homogeneous sphere model for estimating the scattering and backscattering coefficients
The homogenous sphere model was built using an integration of published methods, which were introduced in Bricaud and Morel  and refined by Stramski et al.  and Bernard et al. . Figure 1 presents a schematic outline of the computational methods.
In this computation, the algal cells are presented as homogenous spheres and are characterized by the complex refractive index relative to that of the surrounding water. First, the imaginary part of the refractive index is determined using the iterative anomalous diffraction approximation (ADA) procedure of Bricaud and Morel , which uses the measured absorption spectrum and particle size distribution (PSD). Next, the real part of the refractive index is divided into two parts: the central value and the spectral variations. The variationis deduced from according to the Kramers-Kronig relationship. In spectra, there are several cases of wavelength where. In this study, the single wavelength was used where is minimum. This wavelength is denoted as. At this wavelength, the theoretical value of predicted from Mie theory is iteratively forced to equal the theoretical value of, where is the mean efficiency factor for attenuation and represents the value for the non-absorbing equivalent population with = 0. The varying parameter in this procedure is the central value. The derived results of may converge at several different values. To avoid possible multiple solutions, the final choice of would be based on a comparison of the spectral attenuation pattern predicted by Mie theory using the selected with the experimental pattern. Finally, with the best value of , the complex refractive index is built, and the scattering and backscattering spectra can be estimated based on Mie theory for each species using the measured PSD.
2.6 Uncertainties in optical parameters
We estimated the standard deviations of the absorption, attenuation, and backscattering coefficients for all cultures and converted the data to the coefficient of variation (CV). We found that for the 15 species cultured, the absorption measurements had an average (across all wavelengths) CV of 0.2–2.7% and the attenuation measurements had an average CV of 0.2–1.4%. By propagation of error, the uncertainty in the scattering coefficient ranged between 0.2% and 1.4%. The backscattering measurement had an average CV of 1–13%. When combined with the uncertainty of 5.1–13.1% in at 120 ° depending on the measurement wavelength , we estimated the average CV of the backscattering coefficient to be 12–24%. We estimated the uncertainty in the backscattering ratio to be 11–23%. We estimated the uncertainty in particle density and equivalent size diameter to be around 2.4% and 1%, respectively. We estimated the maximum CV in the scattering and backscattering cross-section as 5% and 21%. We estimated the maximum CV in the scattering and backscattering efficiency factors as 8.5% and 18.6%. Two kinds of scattering corrections for the acs data were performed for comparison: (1) baseline correction assuming an absorption coefficient m–1, and (2) proportional scattering correction . The results revealed some differences in the magnitude of the retrieved absorption and scattering coefficients between the two correction methods. Such differences varied with the wavelength, and the difference was particularly significant in the green wavebands. For the 15 phytoplankton species tested, the absorption coefficients using different scattering corrections had an average relative deviation of 20%, and accordingly the scattering coefficients had an average relative deviation of 1%. These deviations in absorption coefficients using different scattering corrections would result in an average relative deviation of about 3% and 7% for the estimating scattering and backscattering coefficient using the homogenous sphere model.
3.1 Spectral scattering coefficients
The spectral variations in light scattering for the 15 phytoplankton species tested are shown in Fig. 2 , where is the mean efficiency factor for scattering as defined in Eq. (2). Relevant information about these cultures is presented in Table 1. The values display wide variations from one species to another, ranging between 1.55 and 2.44 at 532 nm. These results are within the range of values (0.28–2.93) reported in the published literature for algal cultures [5,8,9,31,32].
The spectral shape of exhibits large inter- and intraspecific variability, which is mainly attributed to the variations in size () and real refractive index () of algal cells [5,31,33]. Theoretical predictions have shown that the value of is the oscillating function of the parameter for algal cultures polydispersed in size (see Fig. 7 of ). For example, for Thalassirosira pesudonana and Nitzschia closterium with, the values tend to decrease with increasing wavelength, as predicted by theory for lowvalues; for the five species of Chlorophyceae, thevalues increase slightly with wavelength when thevalue is generally between 4 and 8. The depressing effect of absorption on spectralis obvious, such as in the neighborhood of the Chl a absorption band (around 440 nm and 675 nm) and of the chlorophyll b (Chl b) absorption band (around 480 nm), especially for Chlorophyceae [8,31]. Morel and Bricaud  provided a detailed theoretical explanation for these behaviors of in the vicinity of absorption bands.
3.2 Spectral backscattering coefficients and backscattering ratios
Figure 3 shows the variability in mean backscattering efficiency factors for all 15 species tested. The magnitude of varies strongly from one species to another. For instance, varies by a factor of nearly 10 and ranges from 0.003 to 0.020. These variations are consistent with the range reported in Vaillancourt et al.  and Whitmire et al.  measured by HS-6, whereas our measurements are slightly higher than the values (0.000013–0.005 around 550 nm) reported in literature obtained using a spectrometric method [9,30].
The spectral shape of for these cultures shows distinct features within and between groups. For some species, such as T. weissflogii, T. pseudonana, and the five species of Chlorophyceae, shows a peak at ~532 nm. For other species, such as M. aeruginosa, Chaetoceros sp., N. closterium, and P. patelliferum, is essentially spectrally neutral or generally tends to decrease from the blue to the red waveband. The enhanced backscattering peak at 676 nm is obvious for all cultures due to the fluorescence emission superimposed on the backscattering light [9,24,35].
The backscattering ratio for these cultures (Fig. 4 ) ranges from 0.18% to 1.1% at 440 nm, with a medium value of 0.54%. This range was on the low side but basically was within the range (0.35–2.9% at 440 nm) measured using HS-6 . Although there is some spectral variability, the differences in backscattering ratios between wavelengths for most species ranges from 11~25%, which is mostly within our measurement deviation of 11~23% for the backscattering ratio. The spectral variability in backscattering ratios for D. tertiolecta and M. aeruginosa (around 22%) was relatively higher than the measurement deviation of 14% for the backscattering ratio.
3.3 Factors that influence the variability in scattering and backscattering
Variations in cell size are naturally expected to have a major effect on the scattering and backscattering properties of algal cultures. In Fig. 5 , the scattering cross-section (510.6) and backscattering cross-section (510) as defined in Eq. (1) are plotted against the ESD (μm) at peak cell density. Nonlinear regression analysis indicates that both (510.6) and (510) are well related to ESD following the power law functions:
Similar power law relationships were reported in Vaillancourt et al.  and Whitmire et al. . For a given cell size, our backscattering cross-section values compared well with those reported by Vaillancourt et al. , whereas our data and Vaillancourt’s data are on average lower than those reported in Whitmire et al. . These differences may be largely due to the different conversion coefficient used to convert the to , which was set at ~1.2 in Whitmire et al.  but at 0.82 in Vaillancourt et al. .
The variation in cellular POC content (Carbon, carbon content per cell, pg cell–1) also has an important effect on the scattering and backscattering cross-section of algal cultures. The trend shown in Fig. 6 indicates that the values ofand increase proportionally as carbon increases following these equations:
Vaillancourt et al.  reported a similar relationship. It may be partly due to a close correlation between cellular POC content and cell size (R2 = 0.92). This relationship provides evidence that in situ POC concentration can be derived from scattering measurements .
A weak relationship exists between scattering and backscattering cross-section and intracellular POC concentration (, carbon content per cell volume, kg m−3), which is interpreted as a proxy of the real refractive index of cells . This probably reflects the intraspecies and interspecies variability in the relationship between and the real refractive index for algal cultures.
No significant relationship is found between Chl a per cell and either scattering or backscattering cross-section. Similar conclusions were reached in previous studies of algal cultures [23, 24]. In this study, the ratio : Chl a ranges from 0.042 to 0.523, and :Chl a ranges from 0.0002 to 0.0036 .
4.1 Variability in the spectral backscattering efficiency
In this study, backscattering measurements were made using a BB9 meter at nine wavelengths, which is three more wavelengths than used in Whitmire et al.  using a HS-6 meter, and twice as many as in Vaillancourt et al.  where only four of the six HS-6 wavelengths were reported. Using this approach, we obtained the backscattering signals at 412 nm and 715 nm. The measurements at 412 nm helped to evaluate the absorption effects on the backscattering spectral pattern, as scattering theory predicts that the chlorophyll absorption at 440 nm has a depressive effect on backscattering signals. From our measurements, we did not observe the significant depressive effect of absorption at 440nm on the backscattering signals. The backscattering efficiencies at 412 for most species are close to the values at 440nm. Several of the backscattering spectra even showed a decreasing trend from 440 nm to 412 nm. It is possible that more usable wavelengths measurements in the backscattering meter would provide sufficient information to examine the detailed backscattering spectral feature within the absorption bands. Our measurements also included the backscattering signals at 715 nm, which increased for most species if the fluorescence contamination signals at 676 nm were excluded. It is not clear why the backscattering efficiency at 715nm increases for most species. However, the estimated backscattering spectra from the homogenous sphere model in Stramski et al.  [as shown in their Fig. 3] showed the increasing backscattering at 715 nm for some species. Our backscattering coefficient estimated by the homogenous sphere model also showed an increase at 715 nm for most species (as shown in our Fig. 8 ).
We took backscattering measurements at four wavelengths from 500nm to 660 nm (e.g. 510, 532, 595, 660 nm), while Whitmire et al.  reported the values at three wavelengths (e.g. 532, 555, 620 nm) and Vaillancourt et al.  reported the values at only two wavelengths (510 and 620 nm), These wavelengths were used to examine trends in the backscattering spectra of phytoplankton over a range of wavelengths. We found that the backscattering spectra did not follow a generalized decreasing trend from 412 nm to 660 nm for most species, which is inconsistent with the observation in Vaillancourt et al.  using only two wavelengths. Several of our backscattering spectra showed a peak at ~532 nm and a decrease at the adjacent 595 nm. The backscattering measurements in Whitmire et al.  also observed the increasing signals with a peak around 532 nm or 555 nm relative to the values at adjacent wavelengths for some species. Stramski et al. ,who presented the backscattering results derived from models for 18 species, also showed that backscattering signals might exhibit a peak that ranged between 510 nm and 590 nm for different species [as shown in their Fig. 3]. Such measurements and theoretical results indicated that backscattering spectra might have significant spectral variability across 500~600 nm. Therefore, the backscattering measurements taken at more wavelengths might provide a more realistic description of spectral behaviors. Backscattering values measured at more wavelengths, especially around absorption wavebands, might also help to investigate the relationship between backscattering spectral features and phytoplankton properties.
4.2 Variability in the backscattering efficiency and backscattering ratio between cultures
In this study, backscattering efficiencies for the diatoms were highly variable, ranging from 0.003 to 0.016 (Table 1). Both the backscattering efficiency and backscattering ratio appear to be the linear functions of size for these diatoms (R2 = 0.968 and R2 = 0.954, respectively). The larger diatoms generally seemed to have higher backscattering efficiencies and larger backscattering ratios than the smaller diatoms. For two species with similar cell shape and similar internal structure, larger T. weissflogii had much higherand higher values than those for smaller T. pseudonana. These results disagree with the simplistic scattering model interpretation for homogenous particles, because all else being equal, a larger homogenous particle has a lower backscattering ratio than a smaller homogenous particle. Whitmire et al.  also observed a positive relationship between diatom size and backscattering ratio, which they attributed to the influence of detrital and bacterial contamination, the effect of complex internal structure, or the distorted interpretation of the simplistic model. Non-algal particles, such as detritus and bacteria, were also unavoidable components of our cultures. We speculate that larger cells might have much more subtle refractile granules, such as assimilation product starch granules, oil spots, etc. Since these subtle granules have small size and high refractive index, they could increase the backscattering signals significantly. Thus, if the cell shape and internal structure of two species are similar, a larger cell containing more subtle refractile granules might have a higher backscattering ratio.
Compared to the backscattering efficiencies of diatoms, the members of the Chlorophyceae generally had higher backscattering efficiencies (0.0086 to 0.0148, Table 1). This may be due to the large cell size of these species. For example, D. tertiolecta, T. levis, Pyramimonas sp., and P. subcordiformis all are 10–12 µm in diameter, whereas four species of diatom (except T. weissflogii) are <7 µm in size. In addition to large cell size, the Chlorophyceae in our cultures had relatively high real refractive indices, which may increase their high backscattering efficiencies. The high real refractive index for our chlorophytes might be mainly contributed by a large cup-shaped chromatophore and the pyrenoids in cells. The large cup-shaped chromatophore can occupy relative large cell volume, about one-half of the cells especially in Chlorella sp. .The chromatophore is rich in pigments, such as the β-carotenoid in D.tertiolecta could account for 10% of dry weight . The chromatophore and pyrenoids are primarily composed of high density substances (e.g. proteins, lipids and pigments), which can have a refractive index as high as 1.13–1.19 relative to water . Therefore, we speculate that such substances in our chlorophytes would significantly increase the backscattering properties by increasing the real refractive index of the algal cells.
The backscattering efficiency for chlorophytes did not seem to relate to their size. The differences in concentration of the intracellular dispersed substance among species might be another important factor dominating the variability of backscattering efficiency. The intracellular carbon concentration POCi is an indicator of the characterization of concentration of the dispersed substance. If the algal cells among different species have similar proportions of primary elements (e.g. carbon, hydrogen, oxygen and nitrogen), the POCi can be assumed to be related to the density of algal cells, which would be related to the refractive increment . Among our chlorophytes, the small Chlorella sp. has a twice as high POCi (466 kg m−3) as D. tertiolecta, Pyramimonas sp.and P. subcordiformis(around 200 kg m−3).We speculate that the high POCi of Chlorella sp. is related to the high real refractive index, which would contribute to the backscattering efficiency as much as the other three species. Besides, the large T. levis had a low backscattering efficiency. We lacked the measurements of POCi for T. levis. While the measurements from Liu  showed that the ratio of carbon and nitrogen for T. levis (C:N = 4:1) was significantly lower than the ratio(C:N = 8:1) for D. tertiolecta. Although the C:N of the same species cultured might be variable under different environment , such large difference of C:N between T. levis and D. tertiolecta would indicate the difference in cell compositions between them. This speculation might imply that the differences in cell component between species may be responsible for the magnitude in backscattering efficiency.
The only dinoflagellate examined in this study, Amphidinium sp., exhibited a relatively low backscattering efficiency of 0.003 at 510 nm in our cultures. This is inconsistent with the fact that dinoflagellates had the highest backscattering efficiency among the phytoplankton studied both in Vaillancourt et al.  and Whitmire et al. . These authors speculated that the high backscattering efficiency might be due to the relatively high intracellular carbon concentration and the presence of some unique internal structures and very unusual chromosome morphology of dinoflagellates. However, Amphidinium sp. does not have a high carbon contentration, and it is also small in size. Vaillancourt et al.  showed that the backscattering efficiency factor would decrease as cell size and intracellular carbon concentration decrease. Thus, it is possible that the relatively low carbon concentration and small size could explain the low backscattering efficiencies we observed for Amphidinium sp.
The sole cyanophyte examined in this study, M. aeruginosa, exhibited the relatively high backscattering efficiency of 0.020 and backscattering ratio of 0.91% at 510 nm. The gas-filled vesicles in M. aeruginosa may greatly contribute to increased backscattering .
The spectral shape of the sole Raphidophyceae C. marina strongly resembled those for five species of chlorophytes. We hypothesize that the similar spectral pattern might be attributed to their similarity in cell shape and cellular structure. First, both C. marina and the chlorophytes are oval or spherical in shape. In addition to their similarity in cell shapes, all of them have no cell wall or thin cell wall, which might imply that their internal structures play a large role in backscattering. Our chlorophytes have a large cup-shape chloroplast. C. marina has numerous radially arranged chloroplasts . Since such arrangements of chloroplasts in C. marina are compact, we speculate the backscattering characteristics of these chloroplasts might be equivalent to backscattering characteristics of one large chloroplast in our chlorophytes. Moreover, The main pigment components in Raphidophyceae are similar to those in our chlorophytes , which might also contribute to the similar spectral behaviors of backscattering among them.
4.3 Comparisons of measured vs. modeled values of scattering and backscattering
We compared the scattering and backscattering coefficients obtained from our measurements with the values predicted by the homogenous sphere model. The main features of the measured spectra for all species were fairly well reproduced by the model, as shown in Fig. 7 . The depressive effects of the absorption bands of Chl a and Chl b on spectra were also reproduced by the model. Both the magnitude and spectral shape of the modeled were generally comparable with the measurements. The mean relative deviation for all species ranged from 5% to 39%, with a mean value of 17%. The minimum deviation was observed for Chlorella sp., which may be largely due to the similarity between the actual morphology of the cell and the assumption of the sphericity and homogeneity of the model. For species with a relatively large deviation, the spectral slopes of the modeled often were steeper than those of the measured results. The non-spherical shape and/or heterogeneities of cells explain these divergences. Some studies have shown that particles with a layered internal structure [8,16,43] or a randomly oriented non-spherical shape  could result in a smoother slope for the scattering spectra than for those represented as homogenous spheres. In our study, the species tested were mostly ovoid and cylinder, and large heterogeneities were also introduced by the highly refractive cell walls for diatom or the presence of peripheral chloroplasts for other species. It is difficult to know if the cellular morphology or the cellular structure causes the measurements to deviate from theory using the homogenous sphere model. The layered sphere model or an non-spherical model might provide more information about the effect of cellular morphology and complex structure on backscattering properties [16,18,43].
In this study, the modeled backscattering spectra were scaled to coincide with the measured data at 510 nm, as shown in Fig. 8. The ratio of measured to theoretical values at 510 nm is denoted Ratio.
The homogeneous sphere model severely underestimated the backscattering coefficient by 1.4–48.6 folds at 510 nm. The quantitative results provide further evidence for the inadequacy of the homogenous spherical model for estimating the backscattering of algal cultures [23,44]. Calavano
et al.  reported that backscattering for spheroid particles tends to be several-fold higher than that for spherical particles. In our study, the Ratio seemed to be strongly dependent on cell shape. A relatively small deviation (Ratio = 2) was observed for spherical species, such as Chlorella sp., whereas the Ratio ranged from 2 to 16 for ovoid or ellipsoidal species. Moreover, the Ratio reached 33 for Chaetoceros sp. because of the chain link nature of the cells. Cell heterogeneities also had an influence on the. Some researchers have shown that backscattering predicted by a multi-layered sphere can be higher than that by a homogenous sphere [16,43,44]. In particular, the magnitude of backscattering was most sensitive to the thickness of cell walls . In this study, M. aeruginosa had pronounced gas-filled vacuoles, which would significantly affect the magnitude and spectral pattern of backscattering, and the would reach 48.6. The diatoms had refringent cell walls, and most of the other species had peripheral chloroplasts; these heterogeneities might have contributed to the increased backscattering compared to the predictions made by the homogeneous sphere model.
The spectral scattering and backscattering properties of 15 phytoplankton species were estimated using the acs and BB9 instruments in the laboratory. We also collected samples to measure Chl a concentration, POC content, cell concentration, and the particle size distribution. The objective of the study was to examine the influence of cell size, organic carbon content, shape, and internal structure on variations in scattering properties. In addition, we quantitatively compared the measurements with the scattering and backscattering coefficients predicted by the homogenous sphere model for 15 phytoplankton species.
We observed the variability in the scattering and backscattering spectra of the 15 species studied. The backscattering efficiency at 412 was not always higher than those at 440nm. Several of the backscattering spectra had a peak at ~532 nm, and the backscattering efficiency at 715 nm increased for some species. These observations indicated that there might be significant spectral variability in the backscattering spectra. The backscattering measurements taken at more wavelengths might provide a more realistic description of spectral behavior.
We reconfirmed the strong relationships between backscattering cross-sections and both cell size (ESD) and carbon content. We also found positive correlations between cell size and both backscattering efficiency and backscattering ratio, and these relationships were similar to those reported in Whitmire et al. .
A comparison of our measurements with values modeled using the homogenous sphere model showed that the Mie theory for homogenous spheres could provide a good description of scattering coefficients, both in magnitude and in spectral shape, for the 15 species tested. This indicates that cell shape and internal structure might have no significant effect on predicting the scattering properties using Mie theory. However, the comparison for the backscattering spectra showed that the Mie theory for homogenous spheres is not a good method for modeling backscattering of algal species. The model underestimated the backscattering coefficients by 1.4–48.6 folds. External cell shape, such as the chain link structure, and complex internal structures, such as refractive cell walls, peripheral chloroplasts, gas vacuoles, might significantly affect the model’s prediction of backscattering behavior. Our results suggest that further studies and a better understanding of spectral backscattering properties of non-spherical and non-homogenous algal species are needed. Research using a layered sphere model or an ellipsoidal model might improve our understanding of how morphology or internal structure influences the backscattering properties of algal species.
We thank the Marine Biology Group of the South China Sea institute of Oceanography (SCSIO) for providing the algal species and Wei Xiao for algae cultivation. We thank the team headed by Prof. Xiaoling Chen of the State Key Laboratory of Information Engineering in Surveying, Mapping and Remote Sensing at Wuhan University for providing the acs and BB9 instruments and Liqiong Chen for her help with taking the measurements. We are indebted to all of our associates in the ocean optics group at the SCSIO for their help. We appreciate the thoughtful comments from all reviewers, which helped to greatly improve an earlier version of this manuscript. This study was funded by the National Natural Science Foundation of China (Grant Nos. 40906022, 41076014, U0933005, 40906021) and the Knowledge Innovation Program of the Chinese Academy of Sciences (Grant No. SQ201003).
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