Chlorophyll-a specific light volume scattering functions (VSFs) by cultured phytoplankton in visible spectrum range is presented. Chlorophyll-a specific VSFs were determined based on the linear least squares method using a measured VSFs with different chlorophyll-a concentrations. We found obvious variability of it in terms of spectral and angular shapes of VSF between cultures. It was also presented that chlorophyll-a specific scattering significantly affected on spectral variation of the remote sensing reflectance, depending on spectral shape of b. This result is useful for developing an advance algorithm of ocean color remote sensing and for deep understanding of light in the sea.
© 2017 Optical Society of America
The light propagation within the ocean and the color of ocean are controlled by the inherent optical properties (IOPs) of scattering and absorption by sea water constituents such as phytoplankton . The variations of ocean color in open sea are mainly governed with chlorophyll-a concentration of phytoplankton (hereafter chl-a). The empirical relationship between IOPs and chl-a concentration, so called chl-a specific IOPs as bio-optical models, has thus been applied to retrieve chl-a concentration from ocean color, e.g. Loisel et al. .
Understanding or predicting the lights field within the ocean requires both the absorption coefficient and the scattering coefficient as a function of scattering angle, i.e. volume scattering function (VSF), by the medium. Over the past decades, there are number of studies that chl-a specific absorption coefficient of phytoplankton is considerably variable, e.g. Bricaud et al. . However, in opposition to the absorption, chl-a specific VSF has still remained as one of the least known IOPs, because of measurement difficulties: the chl-a specific VSF is not presently well documented. As a result, the reflectance models [4, 5] have not been validated yet.
The main aim of this study is thus to investigate and present the chl-a specific VSF, in terms of spectral shape and magnitude, by five species of phytoplankton cultures. We also obtained chl-a specific absorption coefficient as auxiliary data. Furthermore, we show how measured spectral VSF affect the remote sensing reflectance just under sea surface, applying a numerical model based on the successive order of scattering method , in order to demonstrate the usefulness of chl-a specific VSF. The results imply that it is important and useful for developing improved ocean color remote sensing algorithm, for instance, retrieving phytoplankton functional types or applying to phytoplankton rich coastal water.
VSF, β(θ,λ), is defined as the scattered radiant intensity dI(θ,λ) of the wavelength λ from an infinitesimal volume element, dv in a given direction forming the angle θ to the incident beam per unit irradiance E(λ) on the volume and per unit volume  as:8].
2.2 VSFs measurement
VSFs in the visible wavelength were measured using a prototype of an imaging VSFs Meter (iVSFM) developed at the Helmholtz-Zentrum Geesthacht, Germany. Note that the development and the specification of iVSFM are described in detail by Tan et al. . The iVSFM applies the combination of the reflectors. Shortly, the most distinctive feature of the iVSFM is that it is able to simultaneously observe the scattering intensities with wide-angles using an image sensor. In this study, a cooled CCD camera was used as the detector. The iVSFM thus can take a picture of the angular scattered intensities from 8° to 172° at a given wavelength within just a few seconds without changing the sensitivity of the camera. Finally, the iVSFM permits the spectral VSF measurements in practical time; from 400 nm to 700 nm at 20 nm intervals within 30 minutes. The iVSFM has angular resolution of 1° and the maximum error in the VSF measurement of <15% at 90° (Fig. 2(c) in ).
With the help of a specially customized cylindrical glass chamber with a light trap, it drastically reduces the specular reflections of the primary beam at the water-glass and glass-air boundaries. So that, it does not harm the scattering measurement in backward angles. Ca. 200ml of the water sample in the triangular flask at the center of the chamber is surrounded with the purified distilled water (MilliQ water). A magnetic mixer stirs gently the water sample to prevent the sedimentation of the particles. A removable optical short-pass filter attached on the detector blocks the chl-a fluorescence emission into the CCD camera, when water sample is illuminated with λ<480 nm. In this study, we assume that a fluorescence due to the other fluorescent materials are relatively low influence on VSF measurement.
The correction factors for the angular dependence of the scattering volume were obtained by the fluorescence measurement [9, 11]. The attenuation of the scattered intensity was corrected with the total beam attenuation coefficient: Based on a standard attenuation meter with MilliQ water as a reference, the beam attenuation coefficient from 400 nm to 700 nm (2 nm intervals) was measured . The VSF in the absolute unit was obtained by comparing the output signal of the sample with that of spectro-scopic methanol. The inter-comparison of iVSFM with other VSF meters has been carried out and been analyzed in detail by Harmel et al. .
In this study, we analyzed five monospecific phytoplankton cultures, Prorocentrum minimum (P. minimum), Rhodomonas baltica (R. baltica), Synechococcus spp., Nannnochloropsis spp., and Thalassiosira weissflogii (T. weissflogii), provided as stock cultures by Alfred-Wegener institute for Polar and Marine Research, Germany. All cultures were grown in batch using F/2 medium, maintaining in 12 hours light cycles in their exponential growth conditions. Table 1 shows the characteristics of the cultures used in this study with respect to mean diameter obtained by a flow-cytometer (Cytobuoy, Cytosense), the shape after the encyclopedia of phytoplankton , and the color of phytoplankton remained on glass fiber filters after the filtration. Note that, according to the encyclopedia, Synechococcus spp. had the diameter of around 0.8 to 1.5 μm. Our size distribution by the flow-cytometer had two peaks; sharp peak at 1.0 μm and rather broad peak at around 13.0 μm, which may be the particle aggregation.
Just before the IOPs measurements, we prepared the different concentration of phytoplankton samples: a fresh (exponential growth phase) culture is dispensed into several portions first, and then they are diluted with different volume of filtered sea water. We assume in this study that the optical properties between the diluted samples are almost same condition, since the iVSFM can complete all VSF measurements in practical time (within 30 min.). Note that the diluted samples were divided into two sub-samples; one of 200 ml is used for the VSFs measurement, and the second one of 500 ml is used for absorption measurement and pigment determination by HPLC.
2.4 HPLC measurements
The samples after the absorption measurement (explained later) were filtered through WHATMAN glass fiber filter, GF/2 under pressure of −100 hPa. The filters were stored at −80 °C in a deep freezer until the analysis. Chl-a concentrations (μg/l) were determined by HPLC (Jasco).
2.5 Determination of chlorophyll-a specific VSF and scattering coefficient
In principle, chl-a specific particulate VSF, βp*(θ,λ), can be obtained simply dividing βp(θ,λ) by chl-a concentration. However, for lower chl-a concentration, β(θ,λ) consists of predominant of βsw(θ,λ), so that βp*(θ,λ) may introduce larger error when we subtract βsw(θ,λ) from β(θ,λ). Figure 1 shows an example of the relationship between measured βp(θ,λ) at the angle of 30° and chl-a concentrations. Under the single scattering condition, it is expected that βp(θ,λ) is proportional to the chl-a concentration. As shown in the figure, the relation is almost linear, i.e., multiple scattering processes are negligible in chl-a range of our experiments, in other words, small contribution of the packing effect. The gradient for βp(30,λ) with respect to chl-a concentration, gp(30,λ) with the unit of [m−1 sr−1 (μg/l)−1], were determined using the least square method in a linear manner Fig. 1. θ = 30° as the reference angle was selected in this study since βp(30,λ) has sufficient signal-to-noise ratio. Note that, as shown in the figure, the intersection of the regression lines in y axis in this study are not zero, due to the experimental imperfection. The gradient obtained by the least square method is much more reliable than the conventional way. βp*(θ,λ), in this study, for each phytoplankton species were obtained by the following procedure; all measured VSFs normalized at 30° were averaged through all chl-a concentrations in order to obtain representative shape of VSFs,Eq. (2) yields Chl-a specific VSF, βp*(θ,λ), namely:
2.6 Determination of chlorophyll-a specific absorption coefficient
Absorption measurement in the visible range of spectrum, 400 to 700 nm, was carried out using the PSICAM . Since MilliQ water was used as a reference, we can assume that the total absorption coefficient, a(λ), is sum of the absorption by phytoplankton (suspended particles), ap(λ), and colored dissolved organic matter, acdom(λ). acdom(λ) was measured using the filtered sample used for HPLC measurements. Finally, ap(λ) was obtained by subtracting acdom(λ) from a(λ), and then converted into chl-a specific absorption coefficient, ap*(λ) with the traditional way, i.e. ap*(λ) = ap(λ)/the chl-a concentration.
3. Results and application
3.1 Variability of chl-a specific VSF
It is now recognized that the magnitude of ap*(λ) has variation of 1 order of magnitude, e.g. Fig. 7(a) in , and ap*(λ) we measured are also within this range, figure not shown. This ap*(λ) variability is mainly attributed to package effect  and pigment composition of phytoplankton cells . gp(30,λ) and βp*(θ,520) on the logarithmic scale for each species are shown in Figs. 2 and 3, respectively. A remarkable feature of gp(30,λ) and βp*(θ,520) for cultures used in this study has the large dynamic range of variation, which is much more than ap*(λ), e.g. ranging from 10−2 up to 100 [m−1 sr−1 (μg/l)−1] in gp(30,λ). The highest magnitude ofgp(30,λ) and βp*(θ,520) are observed for Nannochloropsis spp., whereas the lower magnitudes are for P. minimum and T. weissflogii.
It should be mentioned that we could not see the relationship between gp(30,λ) and our ap*(λ), at least in this study. Furthermore, the large variations of gp(30,λ) and βp*(θ,520) seem, at least in this study, to have no relationship with mean shape, size and the color of phytoplankton (Table 1). As for the spectral shape of gp(30,λ), for all five cultures, gp(30,λ) tend to slowly increase towards ca. 520 nm from 400 nm. They are more likely to gradually decrease with increasing wavelength. Tan et al.  and Zhou et al.  showed that the absorption spectrum influences the spectral property of scattering via the anomalous dispersion of the refractive index . Especially, Tan et al.  revealed that the influence of the anomalous dispersion on the shape of VSFs is pronounced in backscattering rather than forward scattering (Fig. 7 in ). Near the strong absorption band of chl-a, a decline in gp(30,λ) was observed, e.g. gp(30,λ) of P. minimum at 460 nm and at 670 nm. This result indicates that understanding the relationship of the spectral properties between absorption and scattering is important implication to further development of ocean color remote sensing algorithm. Regarding the angular shape of βp*(θ,520), the larger difference was not observed in the forward scattering angles, but in the backward angles, in particular 90° to 150° (Fig. 3(b)). For some phytoplankton, a sharp increment of βp*(θ, 520) after 150° was observed, e.g. R. baltica and Nannochloropsis spp.. Harmel et al.  showed that the significant optical properties in VSFs by phytoplankton cultures were observed for the scattering angles greater than 150°. Our result is consistent well with their result. As a consequence, βp*(θ, λ) is surely dependent upon phytoplankton species in a complex manner.
3.2 Application of chl-a specific IOPs
It is known that IOPs of seawater in terms of its magnitude and spectral shape over the entire spectrum govern the remote sensing reflectance, Rrs(λ), i.e. ocean color. In order to see how determined chl-a specific IOPs affect on the ocean color, Rrs(λ) just below the sea surface was calculated using the successive order of scattering method, so called TRAD, which has been extensively compared with Hydrolight as well as observed radiance distributions . The calculations of Rrs(λ) were carried out under the following assumptions; 1) mono-phytoplankton seawater, 2) homogeneous IOPs through the depth and the horizontal plane, 3) No contribution due to the sea bottom reflection, i.e., deep sea, 4) flat sea surface, and 5) 0° ofthe solar zenith angle. Although these condition are not realistic, it suits for understanding how βp*(θ,λ) influences on Rrs(λ) as a first step.
The input parameters for TRAD in this study are β(θ,λ), total scattering coefficient, b, and total absorption coefficient, a, calculated from:20] and absorption coefficient by water , respectively (Fig. 4). C is the concentration of chl-a with the unit of μg/l. Figure 5 shows the calculated Rrs(λ) for the chl-a concentrations, C, as 0.1, 1.0 and 30.0 μg/l by R. baltica and Synechococcus spp.. Spectral shape of Rrs(λ) varies over the entire spectrum as chl-a concentration, but varying rate depends upon λ and cultures, i.e. small <460 nm and large >550 nm. The other strong chl-a absorption band at 670 nm induces a dump of Rrs(λ) (Rrs(λ) for the case of C = 30.0 μg/l in Fig. 5). As a result, these features reflect the color of water from the bluish to the specific color of phytoplankton (Table 1 the color remain on the filter): Rrs(λ) for both cultures at the lower chl-a concentration has a higher Rrs(λ) at blue part of spectrum, but it is shifted towards the red spectral range with increasing chl-a concentration. Finally, R. baltica at the highest chl-a concentration has a broad peak reflectance at >560 nm, which might produce the dark reddish color. Synechococcus spp. has the light greenish color due to an enhanced peak of Rrs(λ) at 550 nm.
Finally, it is useful to compare Rrs(λ) calculated by measured b(λ) with that by modeled one often adopted to ocean color remote sensing. The b(λ) model is expressed as a power function as:22]. Further, absolute magnitude of β(θ,λ) is determined so as to be equal to Eq. (8) when β(θ,λ) is integrated over 4π steradian in the case of Rrs(λ) computation assuming the conventional b(λ) model. Figure 6 shows the spectral Rrs(λ) for R. baltica andSynechococcus spp. in the case of C = 1.0 μg/l and 30.0 μg/l, together with calculated Rrs(λ) using bp*(λ) model. Note that measured ap*(λ) were used through all calculations. As shown in Fig. 6, there is a major difference between calculated Rrs(λ) using measured bp*(λ) and that using b(λ) model. In addition, the larger differences were appeared at a shorter or longer wavelength depending on phytoplankton cultures; e.g. at 440 nm for R. baltica and at 660 nm for Synechococcus spp.. In short, these gaps may introduce large estimation error when we retrieve IOPs from Rrs(λ) if we adopt simple spectral model of b(λ) or VSF in ocean color retrieving algorithm. In particular, this result is important when we apply ocean color remote sensing to coastal waters.
The spectral chl-a specific VSFs, βp*(θ,λ), based upon the least square method, by phytoplankton cultures are presented. βp*(θ,λ) in this study are largely variable, 2 orders of magnitude, depending upon not only phytoplankton species but also in the wavelength in a complex manner. Although detritus or bacteria were not well controlled in this study, they do not significantly contribute the angular shape of VSFs including the backscattering since the experiments were carried out during their exponential growth phase. However, taking these uncertainties into account, it is still open question and should be deeply studies in future why βp*(θ,λ) has such larger variation, much more than ap*(λ). At least in this study, this result implies that it is difficult to devise a systematic model describing βp*(θ,λ) that is adaptable to phytoplankton.
With the Rrs(λ) calculation, we demonstrated how the spectral shape of chl-a specific scattering affects on Rrs(λ), applying measured bp*(λ) as well as modeled b(λ). The significant difference appeared in shorter and longer wavelength depending on phytoplankton culture. Some further investigation of βp*(θ,λ) and ap*(λ) for different phytoplankton are required. Understanding of the variability in βp*(θ,λ) will give us a chance to develop an improved chl-a retrieval algorithms from remotely sensed ocean color data. The radiative transfer computations using chl-a specific IOPs is also useful for understanding the light propagation in the ocean (results to be published soon). Further, we believe that the establishment of chl-a specific IOPs database will be effective measure for application to the phytoplankton functional types (PFTs) algorithms.
German Academic Exchange Service (Deutsche Akademische Austauschdienst Dienst) (A0604137); Japan Society for the Promotion of Science (JSPS) (15K05290).
The authors would like to thank Kerstin Heymann (HZG) for performing the HPLC measurement. We are also grateful to AWI for providing the cultures. Finally, we dedicate this article to the late Dr. Motoaki Kishino.
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