Abstract

The particulate backscattering coefficient (bbp) provides effective proxies for particulate organic carbon (POC) and phytoplankton carbon (Cphy); however, their bio-optical relationships in the oligotrophic ocean are rarely reported. In this work, based on the in-situ synchronous optical and biogeochemical measurements in the oligotrophic South China Sea (SCS) basin, we refined the regional relationships between POC (and Cphy) and bbp and investigated the impacts of phytoplankton community compositions and size classes on the bbp variability. The observations showed that: 1) POC and Cphy exhibited good linear relationships with bbp; 2) the relationship between Cphy and POC could also be fitted in a linear function with a positive POC intercept, and the POC contributed by phytoplankton-covarying non-algal particles was nearly two-fold of Cphy; and 3) the POC-specific bbp (b*bp) was positively correlated with the fraction of the phytoplankton groups haptophytes (Type 8) and diatoms to total Chla, but negatively correlated with the fraction of pico-phytoplankton to Chla (fpico). These findings suggest that in oligotrophic waters, the variability of b*bp was mainly determined by the variability in the relative contribution of large phytoplankton with complex structures.

© 2021 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

1. Introduction

When light propagates in water it is scattered by water molecules and suspended particles. The optical backscattering coefficient (bb) represents the amount of light scattered in the backward directions. bb is the sum of pure seawater backscattering coefficient (bbw) and particulate backscattering coefficient (bbp). bbw is dependent on temperature, salinity, and pressure [1,2]. bbp is determined by the concentration of particles and their assemblage which vary greatly in different waters [3]. Measurements and understanding of bbp are of great importance to the application of ocean color remote sensing [4]. Moreover, new generations of miniature, low-power sensors for measuring bbp have been developed and deployed on autonomous platforms such as profiling floats, gliders, and moorings, providing bbp at high temporal and spatial resolutions [5].

Particulate organic carbon (POC) in the ocean includes autotrophic and heterotrophic organisms and biogenic detrital particles. The downward transport of POC from surface to deep ocean is one major process of the biological pump, critical for the long-term sequestration of atmospheric CO2 [6]. However, in-situ measurements of POC using either by filtering with small-volume bottles or large-volume pumps are time consuming, thus it is essential to develop new approaches to obtain POC at high resolutions using proxy measurements. To first order, bbp is determined by the total suspended particulate matter (SPM), and in the waters lacking significant inorganic particles, serves as a good proxy for POC [7]. Several studies have developed proxy-relationships between bbp and POC based on in-situ measurements [79].

Phytoplankton are major contributors to POC [10], and their organic carbon concentration (Cphy) is directly related to primary production and global carbon cycle. The most common and practical method for in-situ measuring Cphy relies on cell counts and biovolume-carbon conversions using empirical relationships [11,12]. The cell abundance of small phytoplankton can be counted by a flow cytometer [13,14], and the abundance of large phytoplankton can be enumerated using microscopy [15] or imaging flow cytometry [16]. Another innovative method is sorting phytoplankton cells from other particles using a sorting flow cytometer and measuring the carbon associated with the sorted phytoplankton by elemental analysis [17]. As these approaches are time-consuming and challenging to operate, numerous studies have attempted to use optical measurements to estimate Cphy, finding that bbp has a good linear relationship with Cphy [12,18,19]. However, these previously published relationships vary greatly, which can lead to a significant difference in the POC or Cphy prediction.

Oligotrophic oceans are the largest ecosystems where the surface nutrients are scarce [20]. These regions exhibit low phytoplankton and POC. However, owing to their immense area, the oligotrophic oceans make a significant contribution to the global primary production and carbon cycle [21]. Several studies have investigated the characteristics of bbp [22], the bio-optical relationships between POC and bbp [7], and the contribution of pico-phytoplankton to total POC [23] in the oligotrophic oceans. However, the bio-optical relationship between Cphy and bbp in these regions have received less attention. Moreover, the variability of bbp is greatly impacted by the particle compositions, shapes, structure, and size distribution [24]. The particle assemblages are rather complex even in oligotrophic waters, and fewer studies have investigated their impacts on the bio-optical relationships between POC and bbp [9].

The South China Sea (SCS) is the largest marginal sea in the northwestern Pacific Ocean, extending from equator to 23 °N and from 99 °E to 120 °E. It is a semi-enclosed deep basin with extensive continental shelves on the north and south sides. The surface current circulation is primarily driven by the East Asian Monsoon associated with strong northeasterly wind in the winter and southwesterly wind in summer. The basin-scale circulation isolates the interior water from the coastal turbid water. In addition, due to net surface heat flux and weak wind stirring, the upper ocean exhibits strong stratification in the summer [25], which inhibits the upward transport of the deep nutrient. Therefore, the SCS basin is a typical oligotrophic region in the summer [26].

A summer cruise was carried out in the SCS during 26 August and 23 September, 2011 (Fig. 1). The observations were performed in the oligotrophic basin with sea depths >1000 m. A profiling optical package comprised of a HOBI Labs Hydroscat-6 (HS6) and a Seabird SBE19 conductivity-temperature-depth (CTD) system were used to obtain the vertical distributions of optical backscattering, temperature, and conductivity (salinity). Moreover, discrete water samples for determining phytoplankton cell abundance, pigment concentration, POC concentration, and optical absorption were collected using Niskin bottles triggered at 5 depths (5, 25, 50, 75, 100 m) during CTD/rosette casts.

 figure: Fig. 1.

Fig. 1. Map of the study region. Black solid circles stand for the sampling stations while the magenta plus signs represent the flow cytometer stations, and the two cyan diamonds are the remote-sensing reflectance stations (‘S2086’ and ‘S2097’). The orange contours indicate the 1000 m isobaths.

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In this study, based on these in-situ measurements, we established the empirical relationships between particulate matters (POC and Cphy) and bbp, compared with previously published relationships observed in other regions, and evaluated how particle assemblages (particle compositions, phytoplankton community compositions, and phytoplankton size classes) impact bbp variability. Although our observations are performed in the oligotrophic SCS basin, the established bio-optical relationships could be generalized to other low-latitude oligotrophic regions with similar physical (relatively weak sea-surface mixing and deep nutricline) and biological properties (pico-phytoplankton dominating in the upper-layer ocean).

2. Data and methods

2.1 Measured data

2.1.1 Biogeochemical measurements

The determination of POC was made following a modified approach of JGOFS protocol [27]. The samples were collected by filtering 4.3 L of water onto pre-combusted (450 °C for 5 hours) 25-mm Whatman GF/F filters (0.7 µm pore size) under pressure <100 mm Hg. After filtration, additional 2 mL of 0.01 N HCL was added to remove the inorganic carbon on the filters. Then the filters were dried at 55 °C for 6 hours and stored in tissue capsules until post-cruise analysis. The organic carbon mass of the samples was measured with a Perkin Elmer PE-2400 SERIES II CHNS/O analyzer following the high temperature combustion method [7]. To quantify the uncertainty introduced by the adsorption of dissolved organic carbon (DOC) on the filters, a blank pre-combusted GF/F filter was placed on the filter manifold and wetted in 20 mL of ‘pure’ seawater for 1 hour so that it was saturated similarly to the POC samples. Here the ‘pure’ seawater refers to seawater filtered through a 0.22 µm Millipore cellulose acetate membrane. The rest of the processing of the blank samples followed the same operations as POC samples. The final POC concentration was determined by subtracting the mean carbon mass of the blanks from the carbon mass of the POC sample, and then dividing this value by the filtered water volume. In this cruise, the measured carbon blank was 27.3 ± 5.3 (mean ± standard deviation) µg C, with a range of 18.5–37.1 µg C (n=19), and thus the final POC value has an uncertainty of 1.2 mg m−3 (Supplement 1, Text S1).

Phytoplankton pigment concentrations were determined through high performance liquid chromatography (HPLC) following a modified approach of Furuya et al. [28], which has been described in detail in Wang et al. [29]. Typically, 8 L of water was filtered through 25-mm GF/F filters under pressure <100 mm Hg. Then the filters were wrapped with aluminum foil and stored in liquid nitrogen. After cruise, concentrations of the pigments were measured with Agilent series 1100 HPLC system fitted with a 3.5 µm Eclipse XDB C8 column. Up to 17 pigments were detected [30]. The total chlorophyll-a concentration (Chla) is the sum of monovinyl chlorophyll-a (MVChla) and divinyl chlorophyll-a (DVChla).

The pico-phytoplankton mainly includes Prochlocococcus, Synechococcus and pico-eukaryotic algae [31]. Their cell abundances were enumerated with a Beckman Coulter Epics Altra II flow cytometer based on their side scattering and fluorescence following Jiao et al. [32]. Water samples (2 mL) were fixed with a 0.5% buffered paraformaldehyde at 4 °C for 30 minutes and then stored in −80 °C liquid nitrogen until analysis. BD Trucount beads (1 µm) were used to calibrate the flow rate to achieve an accurate cell enumeration.

2.1.2 Inherent optical properties

The particulate absorption coefficient was determined using quantitative filter technique (QFT) [33]. The samples were collected by filtering 4.3 L of water on 25-mm Whatman GF/F filters under pressure <100 mm Hg. The particulate optical density was measured with Agilent CARY 100 spectrophotometer in spectral range of 350–800 nm and resolution of 1 nm. Then the sample filter was extracted with methanol to remove phytoplankton pigments [34], and the remained non-algal optical density was measured. The optical density was corrected by assuming the particulate absorption in the near-infrared band was negligible and subtracting an average value over 750–800 nm from the measured optical density spectrum. The particulate absorption coefficient (ap) and non-algal absorption coefficient (anap) were estimated from their corresponding optical densities. The pathlength amplification effect was corrected following the approach by Moore et al. [35]. The phytoplankton absorption coefficient (aph) was determined by the difference of ap and anap; the phytoplankton-specific absorption (a*ph) refers to the Chla-normalized aph.

Particulate backscattering coefficients (bbp) at 6 bands (420, 442, 470, 510, 590 and 700 nm) were estimated from measurements with an HS6, which provided the volume scattering function (β(θ)) at a fixed backward direction of θ=140°. The HS6 was calibrated before the cruise following the calibration protocol [36]. After 5 minutes of device adaptation near the surface (∼5 m), the optical package was lowered down to ∼300 m at a descending rate of ∼0.3 m s−1. Only the downcast measurements were used for analysis, because during upcast particles could be significantly disturbed by the package wake. The bbp was calculated as:

$${b_{\textrm{bp}}} = 2\mathrm{\pi } \cdot {\chi _\textrm{p}}({140^\circ } )\cdot {\beta _\textrm{p}}({140^\circ } )= 2\mathrm{\pi } \cdot {\chi _\textrm{p}}({140^\circ } )\cdot [{\beta ({140^\circ } )- {\beta_\textrm{w}}({140^\circ } )} ],$$
where χp(140°) is a conversion factor between bbp and particle volume scattering function (βp(140°)), while βw(140°) is the seawater volume scattering function at 140°. The total backscattering coefficient (bb) is contributed by seawater and particles:
$${b_\textrm{b}} = {b_{\textrm{bw}}} + {b_{\textrm{bp}}}.$$

Due to the path length attenuation, the measured backscattering was underestimated to some extent, and a compensated correction (the so-called ‘sigma correction’) was implemented following the ‘User’s Manual v2.8’. The values of βw(140°) and bbw were estimated with the CTD-measured temperature, salinity, and a depolarization ratio of 0.039 [2]. A spectral constant value of 1.167 ± 0.049 was used for the χp(140°) [37]. The uncertainty of bbp and bb mainly resulted from χp(140°), and was estimated as 4.2% (0.049/1.167). The details of backscattering correction can be found in Supplement 1, Text S2. A closure test proved a good performance of the in-situ optical measurements (Supplement 1, Text S3).

The POC-specific particulate backscattering is denoted as ‘b*bp(λ)’.

2.2 Derived data

2.2.1 Phytoplankton carbon

Pico-phytoplankton carbon biomass (Cpico, in mg m−3) was estimated from the cell abundances measured by flow cytometer and their cellular carbon [12,14]:

$${C_{\textrm{pico}}} = \sum\limits_{i = 1}^3 {{{10}^{ - 6}} \cdot {N_i} \cdot {\varepsilon _i} \cdot \left( {\frac{\pi }{6}D_i^3} \right)} ,$$
where i represents each group of the pico-phytoplankton (Prochlocococcus, Synechococcus, and pico-eukaryotic algae); Ni is cell abundances (in cell mL−1); ɛi is bio-volume conversion factor (in fg µm−3); Di is the cell diameter (in µm), and 10−6 is the unit conversion from fg mL−1 to mg m−3. In this study, the values of cell size and cellular carbon were from the estimates of Liu et al. [38], which measured the pico-phytoplankton carbon biomass in the SCS basin in summer and winter. For Prochlorococcus and Synechococcus, we used ɛi 280 ± 10 fg µm−3 [39], with Di 0.55 ± 0.03 µm and 0.76 ± 0.11 µm above 60 m, respectively, while 0.73 ± 0.12 µm and 1.01 ± 0.16 µm below 60 m [38]. Because the size fractionation method in their study was not suitable for pico-eukaryotes due to the breaking of delicate cells during filtration, a constant cellular carbon of 1500 fg cell−1, determined by Zubkov et al. [14], was used following [38].

However, the upper detection limit of flow cytometer is usually 3 µm, above which phytoplankton cells are rare in the volume analyzed and thus cannot be accurately numerated. In this study, total phytoplankton carbon biomass (Cphy) was calculated from the estimated Cpico and the fraction of Cpico to Cphy (ffc) empirically. The fraction ffc was estimated following a method of allometric considerations combined with phytoplankton absorption [40]. The details of this method were described in Roy et al. [40,41], and only the principal steps are repeated here. The phytoplankton size distribution is assumed to follow a power law distribution, such that the number of phytoplankton cells per unit water volume with diameter D can be expressed as: $N(\textrm{D} )\textrm{ = k}{\textrm{D}^{\textrm{ - }\mathrm{\xi }}}$, with ξ as the exponent of the phytoplankton size spectrum, and k a constant related to the total phytoplankton abundance. The allometric relationships between cellular carbon (Ccell) and cell volume (Vcell) of phytoplankton is expressed as [42]:

$${C_{\textrm{cell}}} = pV_{\textrm{cell}}^q,$$
where the parameters p and q are constants. It follows that Cphy within diameter range [Dmin, Dmax] can be expressed as:
$$\begin{aligned} {C_{\textrm{phy}}} &= \int_{{D_{\min }}}^{{D_{\max }}} {N(D){C_{\textrm{cell}}}dD} \\ &= \int_{{D_{\min }}}^{{D_{\max }}} {(k{D^{ - \xi }})[{{10}^{ - 9}}p{{({{10}^{18}}\frac{\pi }{6}{D^\textrm{3}})}^q}]dD} \\ &= {10^{ - 9}}kp{({10^{18}}\frac{\pi }{6})^q}(\frac{{D_{\max }^{3q - \xi + 1} - D_{\min }^{3q - \xi + 1}}}{{3q - \xi + 1}}), \end{aligned}$$
where the values 10−9 and 1018 are the conversions of units from pg to mg, and m3 to µm3. With an upper boundary of phytoplankton practically chosen as 200 µm, the ratio ffc can be solved for:
$${f_{\textrm{fc}}} = \frac{{\int_{0.2}^\textrm{3} {N(D){C_{cell}}dD} }}{{\int_{0.2}^{200} {N(D){C_{cell}}dD} }} = \frac{{\textrm{3}_{}^{3q - \xi + 1} - 0.2_{}^{3q - \xi + 1}}}{{200_{}^{3q - \xi + 1} - 0.2_{}^{3q - \xi + 1}}}.$$

Thus Cphy can be computed from Cpico:

$${C_{\textrm{phy}}} = \frac{{{C_{\textrm{pico}}}}}{{{f_{\textrm{fc}}}}} = \frac{{200_{}^{3q - \xi + 1} - 0.2_{}^{3q - \xi + 1}}}{{\textrm{3}_{}^{3q - \xi + 1} - 0.2_{}^{3q - \xi + 1}}}{C_{\textrm{pico}}}.$$

The parameter ξ was estimated from a*ph(676) empirically [41]. The allometric parameter q was set to 0.85 [40]. For the data presented here the estimated ratio ffc was 0.91 ± 0.09, with the range of 0.6–0.97 (n=47). It follows that the pico-phytoplankton contributed the most to the total phytoplankton carbon biomass, consistent with the previous observations in other oligotrophic waters [10,31].

Pearson correlation coefficient (R) was used to evaluate the strength of the linear relationship between two variables. To evaluate the performance of the established bio-optical algorithms, three statistical indicators including coefficient of determination (R2), root mean square error (RMSE), and mean absolute percentage error (MAPE) were used in this study. The latter two are calculated as follows:

$$RMSE = \sqrt {\frac{1}{n}\sum\limits_{j = 1}^n {{{({y_j} - {x_j})}^2}} } ,$$
$$MAPE = \frac{1}{n}\sum\limits_{j = 1}^n {\frac{{|{y_j} - {x_j}|}}{{{x_j}}}} \times 100\%,$$
where xj and yj represent the measured (or independent) and the algorithm-derived (or dependent) variables for the jth sample, and n is the number of samples.

Considering the complexity of the Cphy calculations and the number of parameters it depends on, a Monte Carlo approach was used to estimate its uncertainties. The parameters ɛi and Di were considered normally distributed with means and standard deviations reported in Liu et al. [38]. ξ was estimated from a*ph(676) by using a non-linear optimization algorithm. The error in ξ was within 40% in the global scale, but <20% in the open SCS [41]. Here ξ was assumed to follow normal distributions, and its largest error (3 folds of the variation coefficient) was set as 20%. For each sample, 10000 runs were conducted, then the mean and standard deviation values were calculated. The averaged value of the Cphy based on the Monte Carlo estimation were nearly the same as those directly calculated from Eq.4 (R2=0.996, RMSE=0.48 mg m−3, MAPE=4.9%, n=47). The uncertainties in the estimated Cphy varied 5–62%, with a mean value of 21 ± 13%.

2.2.2 Community compositions and size classes of phytoplankton and spectral slope of particulate backscattering

Phytoplankton community compositions were examined using the chemical taxonomy program (CHEMTAX) based on the measured HPLC pigments [43] after the parameters were adjusted for the SCS [29]. Nine phytoplankton groups including Dinoflagellates (Dino), Diatoms (Diat), Haptophytes (Type 8) (Hapt8), Haptophytes (Type 6) (Hapt6), Chlorophytes (Chlor), Cryptophytes (Crypt), Prochlorococcus (Proc), Synechococcus (Syn), and Prasinophytes (Pras) were determined using thirteen diagnostic pigments [29,30]. These measured pigments and derived community compositions have been well described in an early study of Xiao et al. [30], which showed that, for major phytoplankton groups, their chlorophyll concentrations estimated from CHEMTAX were highly correlated with their cell abundances estimated from flow cytometer in the SCS. The processing details including initial input ratios of the diagnostic pigments to Chla, samples grouping, and output assessments were not repeated here. The fraction to total Chla associated with each phytoplankton group was denoted as ‘f’ with its abbreviation in subscript, e.g. ‘fDiat’ represents the contribution by Diatoms.

Three phytoplankton size classes (PSCs) were proposed practically: pico-phytoplankton (0.2–2 µm), nano-phytoplankton (2–20 µm) and micro-phytoplankton (20–200 µm) [44]. The fraction to total Chla associated with each class (fpico, fnano, and fmicro) was derived through 7 diagnostic pigments following Chase et al. [16]. In their study, the diagnostic pigment analysis was evaluated using a phytoplankton size distribution obtained by combining measurements of imaging and conventional flow cytometry.

The spectral particulate backscattering (bbp(λ)) decreased with wavelength (λ), and could be approximated by a power law: $b_\textrm{bp}\mathrm{(\lambda })\; \sim \; \mathrm{\lambda}^{- \mathrm{\gamma bbp}}$ [45], and the exponent γbbp was determined by regressing log(bbp(λ)) with wavelength.

3. Results and discussion

3.1 Variability of the measurements

The surface Chla was 0.045 ± 0.02 mg m−3 with 90% of the samples <0.1 mg m−3 (n=47, Fig. 2(a)), consistent with previous observations in this region [46]. Also, the surface Cphy was 4.98 ± 0.77 mg m−3 (n=13, Fig. 2(b)), comparable to the observations in other oligotrophic regions, such as North Pacific gyre [19] and Atlantic subtropical gyres [12]. The surface POC concentration was 35.6 ± 6.9 mg m−3 (n=25, Fig. 2(b)), also similar to the observations in other oligotrophic oceans [7,47]. The in-situ measurements confirm that the SCS basin was a typical oligotrophic region. Vertically, both Chla and Cphy exhibited a subsurface maximum layer at 50 m, and this phenomenon is ubiquitous in stratified oligotrophic waters [48]. The POC exhibited a similar vertical distribution with a subsurface maximum at 50 m. In the SCS basin, the fraction of POC contributed by phytoplankton (fCphy) was 0.2 ± 0.1 (n=41) with a subsurface maximum of 0.27 ± 0.05 at 50 m (Fig. 2(b)), suggesting that the POC was mainly dominated by the non-algal particles [10].

 figure: Fig. 2.

Fig. 2. Vertical distributions of (a) chlorophyll-a concentration (Chla) and the associated phytoplankton community compositions, (b) phytoplankton carbon biomass (Cphy), particulate organic carbon (POC), and their ratio (fCphy), (c) fractions of four typical phytoplankton groups to total Chla (fPro, fSyn, fHapt8, and fHapt6), (d) fraction of each phytoplankton size class to total Chla (fpico, fnano, and fmicro), (e) particulate backscattering coefficient (bbp), and (f) the POC-specific bbp at 510 nm (b*bp(510)). In each sub-figure, the dots stand for the samples, and the solid line and horizontal bar represent their mean value and standard deviation

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According to the CHEMTAX analysis, Prochlorococcus, Synechococcus and Haptophytes (Type 8) were the three major phytoplankton groups, which made a total contribution of 0.91 ± 0.06 to Chla (n=231, Fig. 2(a)). Above the subsurface chlorophyll maximum layers (SCMLs), the pico-phytoplankton Prochlorococcus and Synechococcus dominated; below that, the nano-phytoplankton Haptophytes (Type 8) also showed a comparable contribution. The vertical distribution of fPro did not change much with a mean of 0.34 ± 0.17 and relatively larger value of 0.45 ± 0.15 at 25 m; however, the fSyn decreased from 0.58 ± 0.16 at surface to 0.013 ± 0.01 at 100 m, and the fHapt8 showed a reverse trend increasing from 0.07 ± 0.04 to 0.61 ± 0.12 (Fig. 2(c)). In particular, Haptophytes (Type 6) is a unique group contributed mainly by coccolithophores, and contributes to biogenic calcite particles largely [49]. In the SCS basin, however, Haptophytes (Type 6) was quite rare with a mean fraction to total Chla (fHapt6) of 0.04 ± 0.03. Vertically, fHapt6 increased from 0.03 ± 0.02 at surface to 0.06 ± 0.05 at 100 m (Fig. 2(c)).

PSCs fractions revealed that the phytoplankton was mainly dominated by pico-phytoplankton above the SCMLs and contributed largely by nano-phytoplankton below that (Fig. 2(d)). Vertically, the fpico decreased from 0.85 ± 0.08 at surface to 0.22 ± 0.1 at 100 m; while both fnano and fmicro showed a opposite trend. The fnano increased from 0.13 ± 0.06 to 0.66 ± 0.06. In the whole water column, the fmicro was generally small with a largest value of 0.14 ± 0.06 at 100 m. The fractions of the PSCs were compared with those of the three major phytoplankton groups (Fig. 2(c) and (d)). The group Haptophytes (Type 8) are generally found in the nano-size, and the vertical distribution of fHapt8 was basically consistent with that of fnano. Both Prochlorococcus and Synechococcus are the major groups in pico-size. Above the SCMLs, the sum of fPro and fSyn is comparable with fpico; however, below that, the sum fraction is slightly greater than fpico. Considering the uncertainty, the comparison proves that both estimates are consistent.

The particulate backscattering values were very small, e.g., the observed bbp(420) was 0.0017 ± 0.0003 m−1 (n=280, Fig. 2(e)). The ratio bbp(420)/bb(420) was 0.39 ± 0.04 (Supplement 1, Fig. S3), showcasing that seawater contributed more to bb(420) than particles in the SCS basin. Vertically, the distribution of bbp(λ) also exhibited a subsurface maximum at 50 m (Fig. 2(e)). The POC-specific bbp(510), b*bp(510), exhibited a ∼ 3-fold variability with a range of (1.55–5.35)х10−5 m2 mg−1, and a mean value of (2.95 ± 0.81)х10−5 m2 mg−1 (n=213, Fig. 2(f)), suggesting a variable particulate assemblage in the SCS basin. Vertically, b*bp(510) increased from (2.27 ± 0.39)х10−5 m2 mg−1 at surface to (3.69 ± 1.22)х10−5 m2 mg−1 at 100 m.

3.2 Relationships between POC and particulate backscattering

In the SCS basin, the relationships between POC and bbp are well fitted by a linear (Type-II) function (Fig. 3 and Table 1). Type-II linear regression is more appropriate than Type-I regression when both measured variables are affected by uncertainties [50]. However, some bio-optical relationships in previous studies were established with the Type-I linear regression. In order to compare the regressed coefficients, we provided the relevant Type-I linear regressions as well (Fig. 3 and Table 1). For our Type-II regressions, both RMSE and MAPE exhibited gradual increases with wavelength, varying from 7.69 mg m−3 (20.6%) at 442 nm to 10.22 mg m−3 (29%) at 700 nm; R2 showed a decrease trend with wavelength, varying from 0.6 at 442 nm to 0.36 at 700 nm. It should be noted that R2 is largely affected by the dynamic range of the data. Due to the relatively narrow dynamic range in bbp(700), the R2 between POC and bbp(700) was somewhat lower than the regression values for other bands, which does not imply that bbp(700) was not a good proxy for POC. The bbp measured at all wavelengths can be used to estimate POC without significant differences. All Type-II regressions exhibited a positive bbp intercept, which was contributed by the background inorganic particles. The empirical regressions based on the observations at different layers also showed some difference (Fig. 3(c) and Table 1). The slope of POC versus bbp(510) fitted using the measurements at surface layer (above the SCMLs) was 61300 ± 6400 mg m−2, much larger than the values (43200 ± 4000 and 43800 ± 3900 mg m−2) observed at and below the SCMLs. The phytoplankton was dominated by pico-size phytoplankton groups at the surface, but was composed also of nano-size groups below the surface (Fig. 2(c) and (d)). The fitted slope was highly related to the phytoplankton community compositions and size classes. The intercepts of the regressions from different layers exhibited no obvious difference, suggesting that the inorganic particles in different layers did not vary greatly. Comparatively, the intercept at the SCMLs ((1.57 ± 1.03)х10−4 m−1) was slightly lower than the values ((2.58 ± 0.96)х10−4 and (2.44 ± 0.75)х10−4 m−1) for the observations above and below the SCMLs. The relatively lower intercept was probably related to the higher fraction of phytoplankton to total POC (Fig. 2(b)). Also due to the narrow data dynamic range, the R2 of the regressions above and below the SCMLs were smaller (0.4 and 0.43) (Table 1).

 figure: Fig. 3.

Fig. 3. Scatter plots between particulate organic carbon (POC) and particulate backscattering coefficient (bbp(λ)), and their associated linear (Type-II) regressions (black solid lines). In the sub-figure (c), the solid red, green, and blue lines show the linear (Type-II) regressions for the samples observed at surface (red dots), at SCMLs (green dots), and below SCMLs (blue dots); the dashed black and red lines show the linear (Type-I) regressions for all and only surface samples; the dashed magenta line represents the linear (Type-I) regression from Stramski et al. [7]. In the sub-figure (d), the black dashed line shows the linear (Type-I) regression for the measurements, and the dashed magenta line represents the linear (Type-I) regression from Cetinić et al. [9].

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Tables Icon

Table 1. The regressed relationships and their error statistics.

Numerous studies have developed the regional relationships between POC and bbp based on in-situ measurements in different regions [79]. However, these empirical relationships demonstrated obvious discrepancy, which can be explained from two aspects [9]. The first one was associated with the different methodologies to measure POC or bbp, and the second one was related to the natural variability of the particle assemblages in waters. In order to remove the influences induced by the methodology, bbp obtained in previous studies were re-calculated according the same χp and βw as our approaches. Figure 3(c) showed the linear (Type-I) regression of Stramski et al. [7], which was derived from the surface measurements in the eastern South Pacific and eastern Atlantic Oceans without upwelling regions. Their bbp(555) were measured through a HS6 but with the parameter χp(140°) of 1.13 [51] and the βw(555, 140°) of 0.00017 m−1 sr−1 [1]. If the χp(140°) of 1.167 [37] and the βw(555, 140°) of 0.00015 m−1 sr−1 [2] were adopted, their original regression would be: $\textrm{POC = 52223}{b_{\textrm{bp}}}({\textrm{555}} )\textrm{ - 2}\textrm{.2}$. Furthermore, if the mean bbp spectral slope (γbbp) of 1.32 observed in the SCS basin was considered, the equation can be re-calculated as:$\textrm{POC = 46708}{b_{\textrm{bp}}}({\textrm{510}} )\textrm{ - 2}\textrm{.2}$. The standard deviation of γbbp was 0.33, thus the uncertainty of the re-calculated slope induced by converting bbp(555) to bbp(510) was about 2.5%. Our slope of the linear (Type-I) regression between POC and bbp(510) (36600 ± 4900 mg m−2) was 22% lower than their re-calculated value, while the intercept (−0.3 ± 4.4 mg m−3) was very close. It should be pointed out that, their relationship was established using only surface samples, whereas ours was made using all the samples within 100 m. As described above, the particulate compositions in different layers varies. In the upper layer the phytoplankton was dominated by pico-phytoplankton, while in the subsurface layer it was also contributed by nano-phytoplankton (Fig. 2(a)). If their equation was applied to our observations above the SCMLs, it would fit well to the in-situ observed POC (R2 = 0.4, RMSE=7.17 mg m−3, MAPE = 17.7%, n = 70). The study regions in Stramski et al. [7] were typical oligotrophic oceans where the surface phytoplankton and POC are very low. Due to the similar physical and biological properties, the relationship between POC and bbp derived from the surface measurements in Stramski et al. [7] is also well suitable for the estimate of surface POC in the SCS basin, but not for depth below the surface.

Figure 3(d) showed the comparison with the linear (Type-I) regression of Cetinić et al. [9], which was established using the measurements during the North Atlantic Bloom of 2008. If the value of χp(140°) was changed from 1.13 to1.167 as used here, their original relationship can be re-calculated as:$\textrm{POC = 34299}{b_{\textrm{bp}}}({\textrm{700}} )\textrm{ - 14}\textrm{.4}$. Our slope of the linear (Type-I) regression between POC and bbp(700) (37400 ± 6700mg m−2) was only 9% higher than theirs, but the intercept (7.8 ± 4.6 mg m−3) was significantly higher than theirs. Their bbp(700) were measured with a WETLabs ECO FLNTU, while ours were made with an HS6. Both instruments share the same measuring concept and scattering angle near 140°, but their weighting functions and calibration procedures are quite different. Sullivan et al. [52] reviewed the sources of such uncertainty in detail, and found that the bbp measured through different commercial instruments showed a very good consistency. Especially, the measurements conducted in clear waters, such as South Pacific [22] and Crater Lake [53], showed that two types of instrument could agree within 3%. Thus, the methodology of bbp measurement is unlikely to be the cause for the difference of these two regressions. For the POC measurement, both procedures generally followed the JGOFS protocol except the blank estimates. Our POC blank (27.3 ± 5.3 µg C) was close to their averaged value (19.1 µg C), thus the methodology of POC measurement is unlikely to be the cause for the difference as well. Therefore, the large difference of the two regressions is likely to be due to natural variability of particles suspended in waters. Their observations were conducted in the North Atlantic spring bloom waters with high productivity. The concentrations of their POC and Chla were four times larger than our measurements. Moreover, the phytoplankton functional groups exhibited significant differences; while micro-phytoplankton dominated their observations, pico-phytoplankton dominated our observations. If their empirical relationship was applied to our observations, the derived values would underestimate our field measurements (R2 = 0.36, RMSE = 25.9 mg m−3, MAPE = 76.1%, n = 212). These results suggest that to reduce biases and uncertainties empirical bio-optical relationships established in a specific region should be applied in similar bio-optical regions.

3.3 Relationships between phytoplankton carbon and particulate backscattering

The relationships between Cphy and bbp were also well fitted with linear functions (Fig. 4 and Table 1). The statistical performance of these linear (Type-II) regressions at different wavelengths showed slight difference (R2 = 0.54, RMSE = 3 mg m−3, MAPE = 34%, n=47). Thus, the bbp measured at any band can be used as a useful proxy for the Cphy.

 figure: Fig. 4.

Fig. 4. Scatter plots between the derived phytoplankton carbon biomass (Cphy) and particulate backscattering coefficient (bbp(λ)), and their associated linear (Type-II) regressions (black lines). In the sub-figure (a), the dashed black line shows the linear (Type-I) regression for the measurements, and the dashed red and green lines show the original linear (Type-I) relationship from Behrenfeld et al. [18] and its recalculated relationship with bbw(442) from Zhang et al. [2]. In the sub-figure (b), the dashed black line shows the linear (Type-I) regression for the measurements, and the dashed red line shows the linear (Type-I) regression from Graff et al. [19], and the solid green line shows the linear (Type-II) regression from Martinez-Vicente et al. [12].

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The particles sampled covered a broad size range from molecular size of the order of 0.1 nm to the large particles of the order of 1 mm [3]. All the particles scatter light though with different scattering efficiency, and thus the measured bbp is comprised of contributions from all particle sizes rather than by a few. Consequently, the bbp exhibited a closer relationship with POC than Cphy (Table 1). The fact that both POC and Cphy were linearly correlated with bbp implies that Cphy should also have a good linear relationship with POC (Fig. 5(a) and Table 1).

 figure: Fig. 5.

Fig. 5. (a) Scatter plots between phytoplankton carbon biomass (Cphy) and particulate organic carbon (POC). The solid black line represents the linear (Type-II) regression. (b) Scatter plots between fCphy and Cphy. The black line represents their exponent regression.

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The organic particles of optical importance in the natural waters are composed of a variety of living organisms (viruses, bacteria, phytoplankton, and zooplankton species) and a wide range of non-algal particles (NAP). The NAP are comprised of two different types of particles [18]: the first including zooplankton and the detritus generated by phytoplankton and zooplankton [3], is directly related to the variability of phytoplankton, which is likely covarying with phytoplankton (i.e. phytoplankton-covarying NAP); while the second including non-covarying virus, bacteria, and detritus, contributes to the background of the total POC (i.e. phytoplankton-non-covarying NAP). Consequently, the linear (Type-II) regression between POC and Cphy had a positive POC intercept. In our observations, the estimated phytoplankton-non-covarying NAP was 16.4 ± 6.9 mg m−3 (Fig. 5(a)). The slope suggests that the phytoplankton contributed to 0.35 ± 0.06 of the total POC pool without phytoplankton-non-covarying NAP. That is, in the oligotrophic SCS basin, the carbon of phytoplankton-covarying NAP was nearly twice Cphy.

Also due to the phytoplankton-non-covarying NAP, the fraction Cphy/POC (fCphy) exhibited a high variability, ranging from 0.03 to 0.41 with a mean value of 0.2 ± 0.1 (n=41). The ratio rarely exceeded 0.4, consisting with the observations in other oligotrophic waters where POC was mainly dominated by NAP [10,19]. The observed ratio fCphy increased with Cphy, which can be fitted by an exponential function (R2=0.7, RMSE=0.056, MAPE=20.5%, n=41, Fig. 5(b)):

$${f_{\textrm{Cphy}}} = 1 - \textrm{exp} ({ - 0.0294{C_{\textrm{phy}}}} ).$$

It suggests that the fraction of the POC contributed by the phytoplankton increases from the low to high productive waters. This result is consistent with the observations the South Pacific [23] and Atlantic Ocean [12].

Figure 4(a) shows the comparison with the previously published linear (Type-I) relationship of Behrenfeld et al. [18], which was obtained on the analysis of the linear Chla versus bbp regression and an assuming constant Chla/Cphy of 0.013, and was expressed as:$\; {\textrm{C}_{\textrm{phy}}}\textrm{ = 13000(}{b_{\textrm{bp}}}\textrm{(440) - 0}\textrm{.00035)}$. Compared with our linear (Type-I) regression between Cphy and bbp(442), both slopes were quite close with a small difference of 8% (Table 1), but our bbp background was 0.00062 m−1, nearly double theirs. This background difference may be caused by the different methods in estimating bbp. In their study, the bbp(440) were derived from the satellite water-leaving radiances using the Garver-Siegel-Maritorena (GSM) semi-analytical algorithm [54]. Their bbw(440) (0.0025 m−1) was from the measurements of Morel [1], which was slightly larger than our bbw(442) (0.0021 m−1) estimated using Zhang et al. [2]. If bbw(442) of 0.0021 m−1 was considered, their relationship can be re-calculated as:$\; {\textrm{C}_{\textrm{phy}}}\textrm{ = 13000(}{b_{\textrm{bp}}}\textrm{(440) - 0}\textrm{.00075)}$, which was closer to our relationship (Fig. 4(a)). It suggests that the relationship of Behrenfeld et al. [18] is also suitable for the SCS basin.

Compared with the linear (Type-II) relationship between Cphy and bbp(470) of Martinez-Vicente et al. [12] (${\textrm{C}_{\textrm{phy}}}\textrm{ = 27700(}{b_{\textrm{bp}}}\textrm{(470) - 0}\textrm{.00067)}$, Fig. 4(b)), which was regressed using the measurements from the first optical depth, their slope was much larger than ours (16600 ± 1800 mg m−2), but the bbp(470) background was very close to ours (0.00058 m−1). Both studies used the similar methods to estimate Cphy and bbp, thus the difference of the relationships was not due to the measurement methodologies, but due to the natural variability of particles. The nearly same bbp(470) intercept suggests that the Atlantic ocean and the open SCS share a similar stable particulate background. Their larger slope was probably due to the fact that some samples in their study were collected in the high productive waters whereas all samples in our study were collected in the oligotrophic waters. However, our relationship was quite different from the linear (Type-I) regression of Graff et al. [19] (${\textrm{C}_{\textrm{phy}}}\textrm{ = 12128(}{b_{\textrm{bp}}}\textrm{(470) + 0}\textrm{.000049)}$, Fig. 4(b)). Their slope was very close to our Type-I regressed slope (13800 ± 3900 mg m−2), but their regressed bbp(470) background was near 0. Their Cphy was estimated through flow cytometric sorting approach which is the most accurate method to date. It suggests that the phytoplankton-non-covarying NAP was negligible in their study region, and their relationship may be not suitable for the SCS basin.

3.4 Impacts of particle assemblage on particulate backscattering

Besides the concentration of total particles suspended in waters, bbp is also affected by the characteristics of particle assemblage, such as variability in particle composition, shape, refractive index, linked to variability in phytoplankton community compositions [7,9,55]. Since the backscattering signal at 510 nm is less affected by particle absorption or solar-induced chlorophyll-a fluorescence, the impacts of particle assemblage on the bbp is examined using the POC-specific bbp(510), b*bp(510). In the SCS basin, the b*bp(510) exhibited a ∼ 3-fold variability (Fig. 2(f)), suggesting a variable particle assemblage. Figure 6 summarized the linear correlation coefficients (R) between phytoplankton biomass, community compositions, size classes and b*bp(510). A p value larger than 0.05 is considered statistically insignificant. It should be noted that, the R value is also largely impacted by the dynamic range of the data, and a small R only indicates a weak relationship strength in the concurrent measurements and does not signify weak predictive value.

 figure: Fig. 6.

Fig. 6. Summarized correlation coefficients between b*bp(510) and particulate assemblage including phytoplankton biomass (Chla and Cphy), and the fraction of each phytoplankton group to total Chla (fProc, fSyn, fDino, fChlor, fPras, fCrypt, fHapt6, fHapt8, and fDiat), and the fraction of each phytoplankton size class to total Chla (fpico, fnano, and fmicro). The red (blue) bars show the correlations are significant (p<0.05) positive (negative), and the gray bars show the correlations are insignificant (p>0.05). In particular, since fDino are very small with the maximum value <0.05, the statistics is not representative although p is <0.05, and we still regard its correlation insignificance.

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The suspended particles are composed of organic and inorganic parts. Due to the typically higher refractive index of inorganic particles, they can make a considerable contribution to bbp even in clear waters. They have been estimated to contribute ∼20% of bbp in the typical non-bloom waters and >75% in the coccolithophore bloom waters [56,57]. In the SCS basin, the inorganic particles are dominated by the biogenic calcite particles including coccolithophores and associated detached coccoliths, while the atmospheric deposition of mineral dust is very limited [58] and terrestrial particles are not transported to this region due to the basin-scale gyre [26]. Based on the CHEMTAX analysis (Fig. 2(a),(c)), the coccolithophores species, belonging to the phytoplankton group Haptophytes (Type 6), contributed only fHapt6 of 0.04 ± 0.03 to Chla, consistent with previous observations that the particulate inorganic carbon (PIC) was an order of magnitude lower than POC in the SCS basin [59]. For our observations, b*bp(510) exhibited a weak positive correlation with fHapt6 (R=0.26, Fig. 6 and Supplement 1, Fig. S5 (g)). For samples with lower fHapt6 (<0.1), the mean b*bp(510) was (2.92 ± 0.81)х10−5 m2 mg−1 (n=178), 32% lower than (4.41 ± 2.5)х10−5 m2 mg−1 for the samples with higher fHapt6 (n=6). After excluding these 6 samples, the re-calculated linear (Type-II) relationship between POC and bbp(510) showed a small difference from the original one, with a slightly lower slope (50100 ± 2900 mg m−2) and a higher intercept (−11.8 ± 2.7 mg m−3). These results suggest that the linear relationships between POC and bbp were influenced some by the biogenic calcite particles loads. A small amount of biogenic inorganic particles showed an insignificant impact on the established relationships, but in the waters with high inorganic particles or coccolithophore blooms, more careful consideration should be taken into estimating POC or Cphy from bbp.

In our observations, b*bp(510) exhibited an insignificant correlation with phytoplankton magnitude in terms of either pigment concentration (Chla) or carbon biomass (Cphy) (Fig. 6 and Supplement 1, Fig. S6), suggesting that in the oligotrophic oceans b*bp was insensitive to the absolute phytoplankton biomass. Many laboratory measurements demonstrate that the scattering characteristics of phytoplankton vary with species or community structure, due to the large variability in cell size, shape, morphology and internal structure [55,60,61]. However, in natural waters, phytoplankton is a mixture of species, and the present understanding of the impacts of phytoplankton community on bbp(λ) is very limited. In the SCS basin, our observations suggest that the phytoplankton community is mainly dominated by Prochlorococcus, Synechococcus, and Haptophytes (Type 8) (Fig. 2(a) and (c)). b*bp(510) exhibit a negative correlation with fProc and fSyn, and a positive correlation with fHapt8 and fDiat, and an insignificant correlation with other groups in very low concentration (Fig. 6 and Supplement 1, Fig. S5). For the same POC concentration, bbp was smaller for more Prochlorococcus and Synechococcus, and larger for more Haptophytes (Type 8) and Diatoms. The particle sizes of both Prochlorococcus and Synechococcus were generally <1 µm [38] with sphere-like shapes, and cell abundances were much higher than other species. Based on the Mie theory, the sub-micron particles are larger contributors for bbp [6264], and thus a higher fraction of Prochlorococcus and Synechococcus was supposed to result in a higher b*bp. However, our in-situ observations are inconsistent with this theory. Owing to the irregular shape and complex internal structure, Haptophytes (Type 8) and Diatoms cannot be considered as homogenous spheres, and it is expected that their scattering characteristics cannot be well modeled by the homogeneous spherical model based on Mie theory. The phytoplankton species with complex structures are likely to scatter more than the prediction by the homogeneous spherical Mie model. Our observations are consistent with b*bp variation being positively correlated to the fractions of phytoplankton with complex structures [55,60,61,65,66].

The PSCs variability is another factor modulating bbp in a consistent way to the groups discussed above. In the SCS basin, the relationships between b*bp(510) and PSCs can be well fitted with linear (Type-II) functions (Supplement 1, Fig. S7):

$${b^\ast }_{\textrm{bp}}(510) = ( - 2.93 \pm 0.21) \times {10^{ - 5}}{f_{\textrm{pico}}} + (4.42 \pm 0.12) \times {10^{ - 5}},$$
$${b^\ast }_{\textrm{bp}}(510) = (3.73 \pm 0.26) \times {10^{ - 5}}{f_{\textrm{nano}}} + (1.41 \pm 0.12) \times {10^{ - 5}},$$
$${b^\ast }_{\textrm{bp}}(510) = (1.17 \pm 0.09) \times {10^{ - 4}}{f_{\textrm{micro}}} + (1.97 \pm 0.1) \times {10^{ - 5}}.$$

The b*bp(510) exhibited a negative correlation with fpico (R=−0.55), and a positive correlation with fnano and fmicro (R=0.57 and 0.47) (Fig. 6 and Supplement 1, Fig. S7). Moreover, the slope of the regression between b*bp(510) and fmicro was much larger than that with fnano. The larger size phytoplankton is likely to induce a more significant change in bbp than the smaller one. This finding was also contrary to the Mie theory. This result was consistent with the impacts of phytoplankton community compositions that the variability of b*bp being mainly controlled by the larger species which shapes and structures are usually more complex.

4. Conclusions

This study examined the empirical relationships between particulate organic and phytoplankton carbon (POC and Cphy) and particulate optical backscattering (bbp) in the oligotrophic SCS basin, and analyzed the impacts of phytoplankton community compositions and size classes on the bbp variability. We found that POC exhibited good linear relationships with bbp. Compared to previously published relationships, the relationship proposed by Stramski et al. [7] was also well suited for the estimate of the surface POC in the SCS basin. The relationship between Cphy and POC can be fitted in a linear function with a positive POC intercept. NAP was divided into two different sources, phytoplankton-covarying and -non-covarying ones. The intercept of the Cphy versus POC regression equation suggests a phytoplankton-non-covarying background NAP on the order of 16.4 ± 6.9 mg m−3 (Type-II linear regression) in the oligotrophic SCS basin; and the slope suggests that the carbon of phytoplankton-covarying NAP was nearly twice as large as Cphy (consistent with Durand et al. [10]). The fraction of POC contributed by the phytoplankton increased with the phytoplankton carbon biomass. It follows that bbp can be used as a reliable proxy for Cphy in the SCS basin, with a relationship similar to Behrenfeld et al. [18].

The relationships between POC and bbp were influenced by the characteristics of particulate assemblage. A correlation analysis revealed that the ratio of bbp(510) to POC (i.e., b*bp(510)) was positively related to the fraction of Haptophytes (Type 8) and Diatoms to total Chla (fHapt8 and fDiat); while it was negatively correlated to the fractions of Prochlorococcus and Synechococcus (fProc and fSyn) and the fraction of pico-phytoplankton to total Chla (fpico). Although some of the correlation coefficients were low, they were consistent with the notion that in the oligotrophic SCS waters the variability of b*bp is mainly modulated by the fraction of large size particles, especially the large phytoplankton. This result was consistent with laboratory analysis and previous field studies that the phytoplankton with complex structures and morphology contribute significantly to bbp [55,60,61]. In this study, the impacts of phytoplankton size distribution on the b*bp variability were discussed based on the empirical PSCs information, but it should be noted that the derived PSCs did not directly reflect the true phytoplankton size. We recommend for future studies that they measure the full phytoplankton size distribution data alongside taxonomy to better constrain their contribution to b*bp, and that they sample multiple seasons and bio-optical provinces.

Funding

National Key Research and Development Program of China (2016YFA0601201); National Natural Science Foundation of China (41630963, 41576100, 41776003, 41876032, 91858202).

Acknowledgments

We thank captain and crew of R/V Dongfanghong II for their cooperation during the cruise.

Disclosures

The authors declare no conflicts of interest.

Supplemental document

See Supplement 1 for supporting content.

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35. L. R. Moore, R. Goericke, and S. W. Chisholm, “Comparative physiology of Synechococcus and Prochlorococcus: influence of light and temperature on growth, pigments, fluorescence and absorptive properties,” Mar. Ecol.: Prog. Ser. 116(1-3), 259–275 (1995). [CrossRef]  

36. Backscattering sensor calibration manual HydroScat-2, HydroScat-4, HydroScat-6, a-Beta and c-Beta, Revision O, Hydro-Optics, Biology and Instrumentation Laboratories, Inc, Aug. 2010.

37. J. M. Sullivan and M. S. Twardowski, “Angular shape of the oceanic particulate volume scattering function in the backward direction,” Appl. Opt. 48(35), 6811–6819 (2009). [CrossRef]  

38. H. Liu, J. Chang, C. M. Tseng, L. S. Wen, and K. K. Liu, “Seasonal variability of picoplankton in the Northern South China Sea at the SEATS station,” Deep Sea Res., Part II 54(14–15), 1602–1616 (2007). [CrossRef]  

39. M. Heldal, D. J. Scanlan, S. Norland, F. Thingstad, and N. H. Mann, “Elemental composition of single cells of various strains of marine Prochlorococcus and Synechococcus using X-ray microanalysis,” Limnol. Oceanogr. 48(5), 1732–1743 (2003). [CrossRef]  

40. S. Roy, S. Sathyendranath, and T. Platt, “Size-partitioned phytoplankton carbon and carbon-to-chlorophyll ratio from ocean colour by an absorption-based bio-optical algorithm,” Remote Sens. Environ. 194, 177–189 (2017). [CrossRef]  

41. S. Roy, S. Sathyendranath, H. Bouman, and T. Platt, “The global distribution of phytoplankton size spectrum and size classes from their light-absorption spectra derived from satellite data,” Remote Sens. Environ. 139, 185–197 (2013). [CrossRef]  

42. S. Menden-Deuer and E. J. Lessard, “Carbon to volume relationships for dinoflagellates, diatoms, and other protist plankton,” Limnol. Oceanogr. 45(3), 569–579 (2000). [CrossRef]  

43. M. D. Mackey, D. J. Mackey, H. W. Higgins, and S. W. Wright, “CHEMTAX: A program for estimating class abundances from chemical markers: Application to HPLC measurements of phytoplankton,” Mar. Ecol. Prog. Ser. 144(1-3), 265–283 (1996). [CrossRef]  

44. J. M. Sieburth, V. Smetacek, and J. Lenz, “Pelagic ecosystem structure: Heterotrophic compartments of the plankton and their relationship to plankton size fractions,” Limnol. Oceanogr. 23(6), 1256–1263 (1978). [CrossRef]  

45. R. A. Reynolds, D. Stramski, and B. G. Mitchell, “A chlorophyll-dependent semianalytical reflectance model derived from field measurements of absorption and backscattering coefficients within the Southern Ocean,” J. Geophys. Res.: Oceans 106(C4), 7125–7138 (2001). [CrossRef]  

46. X. Ning, F. Chai, H. Xue, Y. Cai, C. Liu, and J. Shi, “Physical-biological oceanographic coupling influencing phytoplankton and primary production in the South China Sea,” J. Geophys. Res.: Oceans 109(C10), C10005 (2004). [CrossRef]  

47. W. D. Gardner, A. Mishonov, and M. J. Richardson, “Global POC concentrations from in-situ and satellite data,” Deep Sea Res., Part II 53(5-7), 718–740 (2006). [CrossRef]  

48. J. J. Cullen, “Subsurface Chlorophyll Maximum Layers: Enduring Enigma or Mystery Solved?” Annu. Rev. Mar. Sci. 7(1), 207–239 (2015). [CrossRef]  

49. S. W. Wright and S. W. Jeffrey, “Pigment Markers for Phytoplankton Production,” in Marine Organic Matter: Biomarkers, Isotopes and DNA, J. K. Volkman, ed. (Springer, 2006), pp. 71–104.

50. M. Bellacicco, V. Vellucci, M. Scardi, M. Barbieux, S. Marullo, and F. D’Ortenzio, “Quantifying the Impact of Linear Regression Model in Deriving Bio-Optical Relationships: The Implications on Ocean Carbon Estimations,” Sensors 19(13), 3032 (2019). [CrossRef]  

51. D. R. Dana and R. A. Maffione, “Determining the Backward Scattering Coefficient with Fixed-Angle Backscattering Sensors–Revisited,” in Ocean Optics XVI Conference (2002).

52. J. Sullivan, M. Twardowski, J. R. V. Zaneveld, and C. Moore, “Measuring optical backscattering in water,” in Light Scattering Reviews 7, A. Kokhanovsky, ed. (Springer, 2013), pp. 189–224.

53. E. S. Boss, R. Collier, G. Larson, K. Fennel, and W. S. Pegau, “Measurements of spectral optical properties and their relation to biogeochemical variables and processes in Crater Lake, Crater Lake National Park, OR,” Hydrobiologia 574(1), 149–159 (2007). [CrossRef]  

54. S. Maritorena, D. A. Siegel, and A. R. Peterson, “Optimization of a semianalytical ocean color model for global-scale applications,” Appl. Opt. 41(15), 2705–2714 (2002). [CrossRef]  

55. E. Organelli, G. Dall’Olmo, R. J. W. Brewin, G. A. Tarran, E. Boss, and A. Bricaud, “The open-ocean missing backscattering is in the structural complexity of particles,” Nat. Commun. 9(1), 5439 (2018). [CrossRef]  

56. W. M. Balch, P. M. Holligan, S. G. Ackleson, and K. J. Voss, “Biological and optical properties of mesoscale coccolithophore blooms in the Gulf of Maine,” Limnol. Oceanogr. 36(4), 629–643 (1991). [CrossRef]  

57. W. M. Balch, B. C. Bowler, D. T. Drapeau, A. J. Poulton, and P. M. Holligan, “Biominerals and the vertical flux of particulate organic carbon from the surface ocean,” Geophys. Res. Lett. 37(22) (2010).

58. I. I. Lin, J. P. Chen, G. T. F. Wong, C. W. Huang, and C. C. Lien, “Aerosol input to the South China Sea: Results from the MODerate resolution Imaging Spectro-radiometer, the quick scatterometer, and the measurements of pollution in the troposphere sensor,” Deep Sea Res., Part II 54(14-15), 1589–1601 (2007). [CrossRef]  

59. Z. Cao, M. Dai, Z. M. Lu, and K. Zhou, “CaCO3 to Organic Carbon Ratio in the South China Sea,” in Advances in Geosciences (2009), pp. 109–125.

60. 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]  

61. C. Poulin, X. D. Zhang, P. Yang, and Y. Huot, “Diel variations of the attenuation, backscattering and absorption coefficients of four phytoplankton species and comparison with spherical, coated spherical and hexahedral particle optical models,” J. Quant. Spectrosc. Radiat. Transf. 217, 288–304 (2018). [CrossRef]  

62. Y.-H. Ahn, A. Bricaud, and A. Morel, “Light backscattering efficiency and related properties of some phytoplankters,” Deep Sea Res., Part I 39(11-12), 1835–1855 (1992). [CrossRef]  

63. D. Stramski and D. A. Kiefer, “Light scattering by microorganisms in the open ocean,” Prog. Oceanogr. 28(4), 343–383 (1991). [CrossRef]  

64. D. Stramski, A. Bricaud, and A. Morel, “Modeling the inherent optical properties of the ocean based on the detailed composition of the planktonic community,” Appl. Opt. 40(18), 2929–2945 (2001). [CrossRef]  

65. A. Bricaud, J. R. V. Zaneveld, and J. C. Kitchen, “Backscattering efficiency of coccolithophorids: use of a three-layered sphere model,” Proc. SPIE 1750, 27–33 (1992). [CrossRef]  

66. G. Dall’Olmo, T. K. Westberry, M. J. Behrenfeld, E. Boss, and W. H. Slade, “Significant contribution of large particles to optical backscattering in the open ocean,” Biogeosciences 6(6), 947–967 (2009). [CrossRef]  

References

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  30. W. Xiao, L. Wang, E. Laws, Y. Xie, J. Chen, X. Liu, B. Chen, and B. Huang, “Realized niches explain spatial gradients in seasonal abundance of phytoplankton groups in the South China Sea,” Prog. Oceanogr. 162, 223–239 (2018).
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  34. M. Kisino, M. Takahashi, N. Okami, and S. Ichimura, “Estimation of the spectral absorption coefficients of phytoplankton in the sea,” Bull. Mar. Sci. 37, 634–642 (1985).
  35. L. R. Moore, R. Goericke, and S. W. Chisholm, “Comparative physiology of Synechococcus and Prochlorococcus: influence of light and temperature on growth, pigments, fluorescence and absorptive properties,” Mar. Ecol.: Prog. Ser. 116(1-3), 259–275 (1995).
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    [Crossref]
  38. H. Liu, J. Chang, C. M. Tseng, L. S. Wen, and K. K. Liu, “Seasonal variability of picoplankton in the Northern South China Sea at the SEATS station,” Deep Sea Res., Part II 54(14–15), 1602–1616 (2007).
    [Crossref]
  39. M. Heldal, D. J. Scanlan, S. Norland, F. Thingstad, and N. H. Mann, “Elemental composition of single cells of various strains of marine Prochlorococcus and Synechococcus using X-ray microanalysis,” Limnol. Oceanogr. 48(5), 1732–1743 (2003).
    [Crossref]
  40. S. Roy, S. Sathyendranath, and T. Platt, “Size-partitioned phytoplankton carbon and carbon-to-chlorophyll ratio from ocean colour by an absorption-based bio-optical algorithm,” Remote Sens. Environ. 194, 177–189 (2017).
    [Crossref]
  41. S. Roy, S. Sathyendranath, H. Bouman, and T. Platt, “The global distribution of phytoplankton size spectrum and size classes from their light-absorption spectra derived from satellite data,” Remote Sens. Environ. 139, 185–197 (2013).
    [Crossref]
  42. S. Menden-Deuer and E. J. Lessard, “Carbon to volume relationships for dinoflagellates, diatoms, and other protist plankton,” Limnol. Oceanogr. 45(3), 569–579 (2000).
    [Crossref]
  43. M. D. Mackey, D. J. Mackey, H. W. Higgins, and S. W. Wright, “CHEMTAX: A program for estimating class abundances from chemical markers: Application to HPLC measurements of phytoplankton,” Mar. Ecol. Prog. Ser. 144(1-3), 265–283 (1996).
    [Crossref]
  44. J. M. Sieburth, V. Smetacek, and J. Lenz, “Pelagic ecosystem structure: Heterotrophic compartments of the plankton and their relationship to plankton size fractions,” Limnol. Oceanogr. 23(6), 1256–1263 (1978).
    [Crossref]
  45. R. A. Reynolds, D. Stramski, and B. G. Mitchell, “A chlorophyll-dependent semianalytical reflectance model derived from field measurements of absorption and backscattering coefficients within the Southern Ocean,” J. Geophys. Res.: Oceans 106(C4), 7125–7138 (2001).
    [Crossref]
  46. X. Ning, F. Chai, H. Xue, Y. Cai, C. Liu, and J. Shi, “Physical-biological oceanographic coupling influencing phytoplankton and primary production in the South China Sea,” J. Geophys. Res.: Oceans 109(C10), C10005 (2004).
    [Crossref]
  47. W. D. Gardner, A. Mishonov, and M. J. Richardson, “Global POC concentrations from in-situ and satellite data,” Deep Sea Res., Part II 53(5-7), 718–740 (2006).
    [Crossref]
  48. J. J. Cullen, “Subsurface Chlorophyll Maximum Layers: Enduring Enigma or Mystery Solved?” Annu. Rev. Mar. Sci. 7(1), 207–239 (2015).
    [Crossref]
  49. S. W. Wright and S. W. Jeffrey, “Pigment Markers for Phytoplankton Production,” in Marine Organic Matter: Biomarkers, Isotopes and DNA, J. K. Volkman, ed. (Springer, 2006), pp. 71–104.
  50. M. Bellacicco, V. Vellucci, M. Scardi, M. Barbieux, S. Marullo, and F. D’Ortenzio, “Quantifying the Impact of Linear Regression Model in Deriving Bio-Optical Relationships: The Implications on Ocean Carbon Estimations,” Sensors 19(13), 3032 (2019).
    [Crossref]
  51. D. R. Dana and R. A. Maffione, “Determining the Backward Scattering Coefficient with Fixed-Angle Backscattering Sensors–Revisited,” in Ocean Optics XVI Conference (2002).
  52. J. Sullivan, M. Twardowski, J. R. V. Zaneveld, and C. Moore, “Measuring optical backscattering in water,” in Light Scattering Reviews 7, A. Kokhanovsky, ed. (Springer, 2013), pp. 189–224.
  53. E. S. Boss, R. Collier, G. Larson, K. Fennel, and W. S. Pegau, “Measurements of spectral optical properties and their relation to biogeochemical variables and processes in Crater Lake, Crater Lake National Park, OR,” Hydrobiologia 574(1), 149–159 (2007).
    [Crossref]
  54. S. Maritorena, D. A. Siegel, and A. R. Peterson, “Optimization of a semianalytical ocean color model for global-scale applications,” Appl. Opt. 41(15), 2705–2714 (2002).
    [Crossref]
  55. E. Organelli, G. Dall’Olmo, R. J. W. Brewin, G. A. Tarran, E. Boss, and A. Bricaud, “The open-ocean missing backscattering is in the structural complexity of particles,” Nat. Commun. 9(1), 5439 (2018).
    [Crossref]
  56. W. M. Balch, P. M. Holligan, S. G. Ackleson, and K. J. Voss, “Biological and optical properties of mesoscale coccolithophore blooms in the Gulf of Maine,” Limnol. Oceanogr. 36(4), 629–643 (1991).
    [Crossref]
  57. W. M. Balch, B. C. Bowler, D. T. Drapeau, A. J. Poulton, and P. M. Holligan, “Biominerals and the vertical flux of particulate organic carbon from the surface ocean,” Geophys. Res. Lett. 37(22) (2010).
  58. I. I. Lin, J. P. Chen, G. T. F. Wong, C. W. Huang, and C. C. Lien, “Aerosol input to the South China Sea: Results from the MODerate resolution Imaging Spectro-radiometer, the quick scatterometer, and the measurements of pollution in the troposphere sensor,” Deep Sea Res., Part II 54(14-15), 1589–1601 (2007).
    [Crossref]
  59. Z. Cao, M. Dai, Z. M. Lu, and K. Zhou, “CaCO3 to Organic Carbon Ratio in the South China Sea,” in Advances in Geosciences (2009), pp. 109–125.
  60. 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]
  61. C. Poulin, X. D. Zhang, P. Yang, and Y. Huot, “Diel variations of the attenuation, backscattering and absorption coefficients of four phytoplankton species and comparison with spherical, coated spherical and hexahedral particle optical models,” J. Quant. Spectrosc. Radiat. Transf. 217, 288–304 (2018).
    [Crossref]
  62. Y.-H. Ahn, A. Bricaud, and A. Morel, “Light backscattering efficiency and related properties of some phytoplankters,” Deep Sea Res., Part I 39(11-12), 1835–1855 (1992).
    [Crossref]
  63. D. Stramski and D. A. Kiefer, “Light scattering by microorganisms in the open ocean,” Prog. Oceanogr. 28(4), 343–383 (1991).
    [Crossref]
  64. D. Stramski, A. Bricaud, and A. Morel, “Modeling the inherent optical properties of the ocean based on the detailed composition of the planktonic community,” Appl. Opt. 40(18), 2929–2945 (2001).
    [Crossref]
  65. A. Bricaud, J. R. V. Zaneveld, and J. C. Kitchen, “Backscattering efficiency of coccolithophorids: use of a three-layered sphere model,” Proc. SPIE 1750, 27–33 (1992).
    [Crossref]
  66. G. Dall’Olmo, T. K. Westberry, M. J. Behrenfeld, E. Boss, and W. H. Slade, “Significant contribution of large particles to optical backscattering in the open ocean,” Biogeosciences 6(6), 947–967 (2009).
    [Crossref]

2020 (1)

A. P. Chase, S. J. Kramer, N. Haentjens, E. S. Boss, L. Karp-Boss, M. Edmondson, and J. R. Graff, “Evaluation of diagnostic pigments to estimate phytoplankton size classes,” Limnol. Oceanogr.: Methods 18(10), 570–584 (2020).
[Crossref]

2019 (1)

M. Bellacicco, V. Vellucci, M. Scardi, M. Barbieux, S. Marullo, and F. D’Ortenzio, “Quantifying the Impact of Linear Regression Model in Deriving Bio-Optical Relationships: The Implications on Ocean Carbon Estimations,” Sensors 19(13), 3032 (2019).
[Crossref]

2018 (3)

E. Organelli, G. Dall’Olmo, R. J. W. Brewin, G. A. Tarran, E. Boss, and A. Bricaud, “The open-ocean missing backscattering is in the structural complexity of particles,” Nat. Commun. 9(1), 5439 (2018).
[Crossref]

C. Poulin, X. D. Zhang, P. Yang, and Y. Huot, “Diel variations of the attenuation, backscattering and absorption coefficients of four phytoplankton species and comparison with spherical, coated spherical and hexahedral particle optical models,” J. Quant. Spectrosc. Radiat. Transf. 217, 288–304 (2018).
[Crossref]

W. Xiao, L. Wang, E. Laws, Y. Xie, J. Chen, X. Liu, B. Chen, and B. Huang, “Realized niches explain spatial gradients in seasonal abundance of phytoplankton groups in the South China Sea,” Prog. Oceanogr. 162, 223–239 (2018).
[Crossref]

2017 (1)

S. Roy, S. Sathyendranath, and T. Platt, “Size-partitioned phytoplankton carbon and carbon-to-chlorophyll ratio from ocean colour by an absorption-based bio-optical algorithm,” Remote Sens. Environ. 194, 177–189 (2017).
[Crossref]

2015 (3)

L. Wang, B. Q. Huang, X. Liu, and W. P. Xiao, “The modification and optimizing of the CHEMTAX running in the South China Sea,” Acta Oceanol. Sin. 34(2), 124–131 (2015).
[Crossref]

J. R. Graff, T. K. Westberry, A. J. Milligan, M. B. Brown, G. Dall’Olmo, V. van Dongen-Vogels, K. M. Reifel, and J. B. Behrenfeld, “Analytical phytoplankton carbon measurements spanning diverse ecosystems,” Deep Sea Res., Part I 102, 16–25 (2015).
[Crossref]

J. J. Cullen, “Subsurface Chlorophyll Maximum Layers: Enduring Enigma or Mystery Solved?” Annu. Rev. Mar. Sci. 7(1), 207–239 (2015).
[Crossref]

2014 (1)

N. Jiao, T. Luo, R. Zhang, W. Yan, Y. Lin, Z. I. Johnson, J. Tian, D. Yuan, Q. Yang, Q. Zheng, J. Sun, D. Hu, and P. Wang, “Presence of Prochlorococcus in the aphotic waters of the western Pacific Ocean,” Biogeosciences 11(8), 2391–2400 (2014).
[Crossref]

2013 (2)

S. Roy, S. Sathyendranath, H. Bouman, and T. Platt, “The global distribution of phytoplankton size spectrum and size classes from their light-absorption spectra derived from satellite data,” Remote Sens. Environ. 139, 185–197 (2013).
[Crossref]

V. Martinez-Vicente, G. Dall’Olmo, G. Tarran, E. Boss, and S. Sathyendranath, “Optical backscattering is correlated with phytoplankton carbon across the Atlantic Ocean,” Geophys. Res. Lett. 40(6), 1154–1158 (2013).
[Crossref]

2012 (3)

J. R. Graff, A. J. Milligan, and M. J. Behrenfeld, “The measurement of phytoplankton biomass using flow-cytometric sorting and elemental analysis of carbon,” Limnol. Oceanogr.: Methods 10(11), 910–920 (2012).
[Crossref]

I. Cetinić, M. J. Perry, N. T. Briggs, E. Kallin, E. A. D’Asaro, and C. M. Lee, “Particulate organic carbon and inherent optical properties during 2008 North Atlantic Bloom Experiment,” J. Geophys. Res.: Oceans 117(C6), n/a (2012).
[Crossref]

R. Duan, K. Yang, Y. Ma, and T. Hu, “A study of the mixed layer of the South China Sea based on the multiple linear regression,” Acta Oceanol. Sin. 31(6), 19–31 (2012).
[Crossref]

2010 (1)

2009 (3)

2008 (1)

D. Stramski, R. A. Reynolds, M. Babin, S. Kaczmarek, M. R. Lewis, R. Rottgers, A. Sciandra, M. Stramska, M. S. Twardowski, B. A. Franz, and H. Claustre, “Relationships between the surface concentration of particulate organic carbon and optical properties in the eastern South Pacific and eastern Atlantic Oceans,” Biogeosciences 5(1), 171–201 (2008).
[Crossref]

2007 (6)

H. Liu, J. Chang, C. M. Tseng, L. S. Wen, and K. K. Liu, “Seasonal variability of picoplankton in the Northern South China Sea at the SEATS station,” Deep Sea Res., Part II 54(14–15), 1602–1616 (2007).
[Crossref]

G. T. F. Wong, T.-L. Ku, M. Mulholland, C.-M. Tseng, and D.-P. Wang, “The SouthEast Asian Time-series Study (SEATS) and the biogeochemistry of the South China Sea—An overview,” Deep Sea Res., Part II 54(14-15), 1434–1447 (2007).
[Crossref]

M. S. Twardowski, H. Claustre, S. A. Freeman, D. Stramski, and Y. Huot, “Optical backscattering properties of the ‘clearest’ natural waters,” Biogeosciences 4(6), 1041–1058 (2007).
[Crossref]

C. Grob, O. Ulloa, H. Claustre, Y. Huot, G. Alarcon, and D. Marie, “Contribution of picoplankton to the total particulate organic carbon concentration in the eastern South Pacific,” Biogeosciences 4(5), 837–852 (2007).
[Crossref]

I. I. Lin, J. P. Chen, G. T. F. Wong, C. W. Huang, and C. C. Lien, “Aerosol input to the South China Sea: Results from the MODerate resolution Imaging Spectro-radiometer, the quick scatterometer, and the measurements of pollution in the troposphere sensor,” Deep Sea Res., Part II 54(14-15), 1589–1601 (2007).
[Crossref]

E. S. Boss, R. Collier, G. Larson, K. Fennel, and W. S. Pegau, “Measurements of spectral optical properties and their relation to biogeochemical variables and processes in Crater Lake, Crater Lake National Park, OR,” Hydrobiologia 574(1), 149–159 (2007).
[Crossref]

2006 (2)

W. D. Gardner, A. Mishonov, and M. J. Richardson, “Global POC concentrations from in-situ and satellite data,” Deep Sea Res., Part II 53(5-7), 718–740 (2006).
[Crossref]

G. A. Tarran, J. L. Heywood, and M. V. Zubkov, “Latitudinal changes in the standing stocks of nano- and picoeukaryotic phytoplankton in the Atlantic Ocean,” Deep Sea Res., Part II 53(14-16), 1516–1529 (2006).
[Crossref]

2005 (1)

M. J. Behrenfeld, E. Boss, D. A. Siegel, and D. M. Shea, “Carbon-based ocean productivity and phytoplankton physiology from space,” Global Biogeochem. Cycles 19(1), GB1006 (2005).
[Crossref]

2004 (3)

D. Stramski, E. Boss, D. Bogucki, and K. J. Voss, “The role of seawater constituents in light backscattering in the ocean,” Prog. Oceanogr. 61(1), 27–56 (2004).
[Crossref]

E. Boss, D. Stramski, T. Bergmann, W. Pegau, and M. Lewis, “Why should we measure the optical backscattering coefficient?” oceanog 17(2), 44–49 (2004).
[Crossref]

X. Ning, F. Chai, H. Xue, Y. Cai, C. Liu, and J. Shi, “Physical-biological oceanographic coupling influencing phytoplankton and primary production in the South China Sea,” J. Geophys. Res.: Oceans 109(C10), C10005 (2004).
[Crossref]

2003 (2)

K. Furuya, M. Hayashi, Y. Yabushita, and A. Ishikawa, “Phytoplankton dynamics in the East China Sea in spring and summer as revealed by HPLC-derived pigment signatures,” Deep Sea Res., Part II 50(2), 367–387 (2003).
[Crossref]

M. Heldal, D. J. Scanlan, S. Norland, F. Thingstad, and N. H. Mann, “Elemental composition of single cells of various strains of marine Prochlorococcus and Synechococcus using X-ray microanalysis,” Limnol. Oceanogr. 48(5), 1732–1743 (2003).
[Crossref]

2002 (1)

2001 (3)

R. A. Reynolds, D. Stramski, and B. G. Mitchell, “A chlorophyll-dependent semianalytical reflectance model derived from field measurements of absorption and backscattering coefficients within the Southern Ocean,” J. Geophys. Res.: Oceans 106(C4), 7125–7138 (2001).
[Crossref]

D. Stramski, A. Bricaud, and A. Morel, “Modeling the inherent optical properties of the ocean based on the detailed composition of the planktonic community,” Appl. Opt. 40(18), 2929–2945 (2001).
[Crossref]

M. D. DuRand, R. J. Olson, and S. W. Chisholm, “Phytoplankton population dynamics at the Bermuda Atlantic Time-series station in the Sargasso Sea,” Deep Sea Res., Part II 48(8-9), 1983–2003 (2001).
[Crossref]

2000 (2)

E. A. Laws, P. G. Falkowski, W. O. Smith, H. Ducklow, and J. J. McCarthy, “Temperature effects on export production in the open ocean,” Global Biogeochem. Cycles 14(4), 1231–1246 (2000).
[Crossref]

S. Menden-Deuer and E. J. Lessard, “Carbon to volume relationships for dinoflagellates, diatoms, and other protist plankton,” Limnol. Oceanogr. 45(3), 569–579 (2000).
[Crossref]

1999 (1)

D. Stramski, R. A. Reynolds, M. Kahru, and B. G. Mitchell, “Estimation of particulate organic carbon in the ocean from satellite remote sensing,” Science 285(5425), 239–242 (1999).
[Crossref]

1998 (1)

M. V. Zubkov, M. A. Sleigh, G. A. Tarran, P. H. Burkill, and R. J. G. Leakey, “Picoplanktonic community structure on an Atlantic transect from 50°N to 50°S,” Deep Sea Res., Part I 45(8), 1339–1355 (1998).
[Crossref]

1996 (1)

M. D. Mackey, D. J. Mackey, H. W. Higgins, and S. W. Wright, “CHEMTAX: A program for estimating class abundances from chemical markers: Application to HPLC measurements of phytoplankton,” Mar. Ecol. Prog. Ser. 144(1-3), 265–283 (1996).
[Crossref]

1995 (1)

L. R. Moore, R. Goericke, and S. W. Chisholm, “Comparative physiology of Synechococcus and Prochlorococcus: influence of light and temperature on growth, pigments, fluorescence and absorptive properties,” Mar. Ecol.: Prog. Ser. 116(1-3), 259–275 (1995).
[Crossref]

1994 (1)

L. Campbell, H. A. Nolla, and D. Vaulot, “The importance of Prochlorococcus to community structure in the central North Pacific Ocean,” Limnol. Oceanogr. 39(4), 954–961 (1994).
[Crossref]

1992 (2)

A. Bricaud, J. R. V. Zaneveld, and J. C. Kitchen, “Backscattering efficiency of coccolithophorids: use of a three-layered sphere model,” Proc. SPIE 1750, 27–33 (1992).
[Crossref]

Y.-H. Ahn, A. Bricaud, and A. Morel, “Light backscattering efficiency and related properties of some phytoplankters,” Deep Sea Res., Part I 39(11-12), 1835–1855 (1992).
[Crossref]

1991 (2)

D. Stramski and D. A. Kiefer, “Light scattering by microorganisms in the open ocean,” Prog. Oceanogr. 28(4), 343–383 (1991).
[Crossref]

W. M. Balch, P. M. Holligan, S. G. Ackleson, and K. J. Voss, “Biological and optical properties of mesoscale coccolithophore blooms in the Gulf of Maine,” Limnol. Oceanogr. 36(4), 629–643 (1991).
[Crossref]

1990 (1)

B. G. Mitchell, “Algorithms for determining the absorption coefficient of aquatic particulates using the quantitative filter technique (QFT),” Proc. SPIE 1302, 137–148 (1990).
[Crossref]

1989 (1)

A. R. Longhurst and W. G. Harrison, “The biological pump: Profiles of plankton production and consumption in the upper ocean,” Prog. Oceanogr. 22(1), 47–123 (1989).
[Crossref]

1986 (1)

M. R. Lewis, W. G. Harrison, N. S. Oakey, D. Hebert, and T. Platt, “Vertical Nitrate Fluxes in the Oligotrophic Ocean,” Science 234(4778), 870–873 (1986).
[Crossref]

1985 (1)

M. Kisino, M. Takahashi, N. Okami, and S. Ichimura, “Estimation of the spectral absorption coefficients of phytoplankton in the sea,” Bull. Mar. Sci. 37, 634–642 (1985).

1984 (1)

P. M. Holligan, R. P. Harris, R. C. Newell, D. S. Harbour, R. N. Head, E. A. S. Linley, 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(2-3), 111–127 (1984).
[Crossref]

1978 (1)

J. M. Sieburth, V. Smetacek, and J. Lenz, “Pelagic ecosystem structure: Heterotrophic compartments of the plankton and their relationship to plankton size fractions,” Limnol. Oceanogr. 23(6), 1256–1263 (1978).
[Crossref]

1977 (1)

A. Morel and L. Prieur, “Analysis of Variation in Ocean Color,” Limnol. Oceanogr. 22(4), 709–722 (1977).
[Crossref]

1967 (1)

R. R. Strathmann, “Estimating the Organic Carbon Content of Phytoplankton from Cell Volume or Plasma Volume,” Limnol. Oceanogr. 12(3), 411–418 (1967).
[Crossref]

Ackleson, S. G.

W. M. Balch, P. M. Holligan, S. G. Ackleson, and K. J. Voss, “Biological and optical properties of mesoscale coccolithophore blooms in the Gulf of Maine,” Limnol. Oceanogr. 36(4), 629–643 (1991).
[Crossref]

Ahn, Y.-H.

Y.-H. Ahn, A. Bricaud, and A. Morel, “Light backscattering efficiency and related properties of some phytoplankters,” Deep Sea Res., Part I 39(11-12), 1835–1855 (1992).
[Crossref]

Alarcon, G.

C. Grob, O. Ulloa, H. Claustre, Y. Huot, G. Alarcon, and D. Marie, “Contribution of picoplankton to the total particulate organic carbon concentration in the eastern South Pacific,” Biogeosciences 4(5), 837–852 (2007).
[Crossref]

Babin, M.

D. Stramski, R. A. Reynolds, M. Babin, S. Kaczmarek, M. R. Lewis, R. Rottgers, A. Sciandra, M. Stramska, M. S. Twardowski, B. A. Franz, and H. Claustre, “Relationships between the surface concentration of particulate organic carbon and optical properties in the eastern South Pacific and eastern Atlantic Oceans,” Biogeosciences 5(1), 171–201 (2008).
[Crossref]

Balch, W. M.

W. M. Balch, P. M. Holligan, S. G. Ackleson, and K. J. Voss, “Biological and optical properties of mesoscale coccolithophore blooms in the Gulf of Maine,” Limnol. Oceanogr. 36(4), 629–643 (1991).
[Crossref]

W. M. Balch, B. C. Bowler, D. T. Drapeau, A. J. Poulton, and P. M. Holligan, “Biominerals and the vertical flux of particulate organic carbon from the surface ocean,” Geophys. Res. Lett. 37(22) (2010).

Barbieux, M.

M. Bellacicco, V. Vellucci, M. Scardi, M. Barbieux, S. Marullo, and F. D’Ortenzio, “Quantifying the Impact of Linear Regression Model in Deriving Bio-Optical Relationships: The Implications on Ocean Carbon Estimations,” Sensors 19(13), 3032 (2019).
[Crossref]

Behrenfeld, J. B.

J. R. Graff, T. K. Westberry, A. J. Milligan, M. B. Brown, G. Dall’Olmo, V. van Dongen-Vogels, K. M. Reifel, and J. B. Behrenfeld, “Analytical phytoplankton carbon measurements spanning diverse ecosystems,” Deep Sea Res., Part I 102, 16–25 (2015).
[Crossref]

Behrenfeld, M. J.

J. R. Graff, A. J. Milligan, and M. J. Behrenfeld, “The measurement of phytoplankton biomass using flow-cytometric sorting and elemental analysis of carbon,” Limnol. Oceanogr.: Methods 10(11), 910–920 (2012).
[Crossref]

G. Dall’Olmo, T. K. Westberry, M. J. Behrenfeld, E. Boss, and W. H. Slade, “Significant contribution of large particles to optical backscattering in the open ocean,” Biogeosciences 6(6), 947–967 (2009).
[Crossref]

M. J. Behrenfeld, E. Boss, D. A. Siegel, and D. M. Shea, “Carbon-based ocean productivity and phytoplankton physiology from space,” Global Biogeochem. Cycles 19(1), GB1006 (2005).
[Crossref]

Bellacicco, M.

M. Bellacicco, V. Vellucci, M. Scardi, M. Barbieux, S. Marullo, and F. D’Ortenzio, “Quantifying the Impact of Linear Regression Model in Deriving Bio-Optical Relationships: The Implications on Ocean Carbon Estimations,” Sensors 19(13), 3032 (2019).
[Crossref]

Bergmann, T.

E. Boss, D. Stramski, T. Bergmann, W. Pegau, and M. Lewis, “Why should we measure the optical backscattering coefficient?” oceanog 17(2), 44–49 (2004).
[Crossref]

Bogucki, D.

D. Stramski, E. Boss, D. Bogucki, and K. J. Voss, “The role of seawater constituents in light backscattering in the ocean,” Prog. Oceanogr. 61(1), 27–56 (2004).
[Crossref]

Boss, E.

E. Organelli, G. Dall’Olmo, R. J. W. Brewin, G. A. Tarran, E. Boss, and A. Bricaud, “The open-ocean missing backscattering is in the structural complexity of particles,” Nat. Commun. 9(1), 5439 (2018).
[Crossref]

V. Martinez-Vicente, G. Dall’Olmo, G. Tarran, E. Boss, and S. Sathyendranath, “Optical backscattering is correlated with phytoplankton carbon across the Atlantic Ocean,” Geophys. Res. Lett. 40(6), 1154–1158 (2013).
[Crossref]

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]

G. Dall’Olmo, T. K. Westberry, M. J. Behrenfeld, E. Boss, and W. H. Slade, “Significant contribution of large particles to optical backscattering in the open ocean,” Biogeosciences 6(6), 947–967 (2009).
[Crossref]

M. J. Behrenfeld, E. Boss, D. A. Siegel, and D. M. Shea, “Carbon-based ocean productivity and phytoplankton physiology from space,” Global Biogeochem. Cycles 19(1), GB1006 (2005).
[Crossref]

D. Stramski, E. Boss, D. Bogucki, and K. J. Voss, “The role of seawater constituents in light backscattering in the ocean,” Prog. Oceanogr. 61(1), 27–56 (2004).
[Crossref]

E. Boss, D. Stramski, T. Bergmann, W. Pegau, and M. Lewis, “Why should we measure the optical backscattering coefficient?” oceanog 17(2), 44–49 (2004).
[Crossref]

Boss, E. S.

A. P. Chase, S. J. Kramer, N. Haentjens, E. S. Boss, L. Karp-Boss, M. Edmondson, and J. R. Graff, “Evaluation of diagnostic pigments to estimate phytoplankton size classes,” Limnol. Oceanogr.: Methods 18(10), 570–584 (2020).
[Crossref]

E. S. Boss, R. Collier, G. Larson, K. Fennel, and W. S. Pegau, “Measurements of spectral optical properties and their relation to biogeochemical variables and processes in Crater Lake, Crater Lake National Park, OR,” Hydrobiologia 574(1), 149–159 (2007).
[Crossref]

Bouman, H.

S. Roy, S. Sathyendranath, H. Bouman, and T. Platt, “The global distribution of phytoplankton size spectrum and size classes from their light-absorption spectra derived from satellite data,” Remote Sens. Environ. 139, 185–197 (2013).
[Crossref]

Bowler, B. C.

W. M. Balch, B. C. Bowler, D. T. Drapeau, A. J. Poulton, and P. M. Holligan, “Biominerals and the vertical flux of particulate organic carbon from the surface ocean,” Geophys. Res. Lett. 37(22) (2010).

Brewin, R. J. W.

E. Organelli, G. Dall’Olmo, R. J. W. Brewin, G. A. Tarran, E. Boss, and A. Bricaud, “The open-ocean missing backscattering is in the structural complexity of particles,” Nat. Commun. 9(1), 5439 (2018).
[Crossref]

Bricaud, A.

E. Organelli, G. Dall’Olmo, R. J. W. Brewin, G. A. Tarran, E. Boss, and A. Bricaud, “The open-ocean missing backscattering is in the structural complexity of particles,” Nat. Commun. 9(1), 5439 (2018).
[Crossref]

D. Stramski, A. Bricaud, and A. Morel, “Modeling the inherent optical properties of the ocean based on the detailed composition of the planktonic community,” Appl. Opt. 40(18), 2929–2945 (2001).
[Crossref]

Y.-H. Ahn, A. Bricaud, and A. Morel, “Light backscattering efficiency and related properties of some phytoplankters,” Deep Sea Res., Part I 39(11-12), 1835–1855 (1992).
[Crossref]

A. Bricaud, J. R. V. Zaneveld, and J. C. Kitchen, “Backscattering efficiency of coccolithophorids: use of a three-layered sphere model,” Proc. SPIE 1750, 27–33 (1992).
[Crossref]

Briggs, N. T.

I. Cetinić, M. J. Perry, N. T. Briggs, E. Kallin, E. A. D’Asaro, and C. M. Lee, “Particulate organic carbon and inherent optical properties during 2008 North Atlantic Bloom Experiment,” J. Geophys. Res.: Oceans 117(C6), n/a (2012).
[Crossref]

Brown, M. B.

J. R. Graff, T. K. Westberry, A. J. Milligan, M. B. Brown, G. Dall’Olmo, V. van Dongen-Vogels, K. M. Reifel, and J. B. Behrenfeld, “Analytical phytoplankton carbon measurements spanning diverse ecosystems,” Deep Sea Res., Part I 102, 16–25 (2015).
[Crossref]

Burkill, P. H.

M. V. Zubkov, M. A. Sleigh, G. A. Tarran, P. H. Burkill, and R. J. G. Leakey, “Picoplanktonic community structure on an Atlantic transect from 50°N to 50°S,” Deep Sea Res., Part I 45(8), 1339–1355 (1998).
[Crossref]

Cai, Y.

X. Ning, F. Chai, H. Xue, Y. Cai, C. Liu, and J. Shi, “Physical-biological oceanographic coupling influencing phytoplankton and primary production in the South China Sea,” J. Geophys. Res.: Oceans 109(C10), C10005 (2004).
[Crossref]

Campbell, L.

L. Campbell, H. A. Nolla, and D. Vaulot, “The importance of Prochlorococcus to community structure in the central North Pacific Ocean,” Limnol. Oceanogr. 39(4), 954–961 (1994).
[Crossref]

Cao, Z.

Z. Cao, M. Dai, Z. M. Lu, and K. Zhou, “CaCO3 to Organic Carbon Ratio in the South China Sea,” in Advances in Geosciences (2009), pp. 109–125.

Cetinic, I.

I. Cetinić, M. J. Perry, N. T. Briggs, E. Kallin, E. A. D’Asaro, and C. M. Lee, “Particulate organic carbon and inherent optical properties during 2008 North Atlantic Bloom Experiment,” J. Geophys. Res.: Oceans 117(C6), n/a (2012).
[Crossref]

Chai, F.

X. Ning, F. Chai, H. Xue, Y. Cai, C. Liu, and J. Shi, “Physical-biological oceanographic coupling influencing phytoplankton and primary production in the South China Sea,” J. Geophys. Res.: Oceans 109(C10), C10005 (2004).
[Crossref]

Chang, J.

H. Liu, J. Chang, C. M. Tseng, L. S. Wen, and K. K. Liu, “Seasonal variability of picoplankton in the Northern South China Sea at the SEATS station,” Deep Sea Res., Part II 54(14–15), 1602–1616 (2007).
[Crossref]

Chase, A. P.

A. P. Chase, S. J. Kramer, N. Haentjens, E. S. Boss, L. Karp-Boss, M. Edmondson, and J. R. Graff, “Evaluation of diagnostic pigments to estimate phytoplankton size classes,” Limnol. Oceanogr.: Methods 18(10), 570–584 (2020).
[Crossref]

Chen, B.

W. Xiao, L. Wang, E. Laws, Y. Xie, J. Chen, X. Liu, B. Chen, and B. Huang, “Realized niches explain spatial gradients in seasonal abundance of phytoplankton groups in the South China Sea,” Prog. Oceanogr. 162, 223–239 (2018).
[Crossref]

Chen, J.

W. Xiao, L. Wang, E. Laws, Y. Xie, J. Chen, X. Liu, B. Chen, and B. Huang, “Realized niches explain spatial gradients in seasonal abundance of phytoplankton groups in the South China Sea,” Prog. Oceanogr. 162, 223–239 (2018).
[Crossref]

Chen, J. P.

I. I. Lin, J. P. Chen, G. T. F. Wong, C. W. Huang, and C. C. Lien, “Aerosol input to the South China Sea: Results from the MODerate resolution Imaging Spectro-radiometer, the quick scatterometer, and the measurements of pollution in the troposphere sensor,” Deep Sea Res., Part II 54(14-15), 1589–1601 (2007).
[Crossref]

Chisholm, S. W.

M. D. DuRand, R. J. Olson, and S. W. Chisholm, “Phytoplankton population dynamics at the Bermuda Atlantic Time-series station in the Sargasso Sea,” Deep Sea Res., Part II 48(8-9), 1983–2003 (2001).
[Crossref]

L. R. Moore, R. Goericke, and S. W. Chisholm, “Comparative physiology of Synechococcus and Prochlorococcus: influence of light and temperature on growth, pigments, fluorescence and absorptive properties,” Mar. Ecol.: Prog. Ser. 116(1-3), 259–275 (1995).
[Crossref]

Claustre, H.

D. Stramski, R. A. Reynolds, M. Babin, S. Kaczmarek, M. R. Lewis, R. Rottgers, A. Sciandra, M. Stramska, M. S. Twardowski, B. A. Franz, and H. Claustre, “Relationships between the surface concentration of particulate organic carbon and optical properties in the eastern South Pacific and eastern Atlantic Oceans,” Biogeosciences 5(1), 171–201 (2008).
[Crossref]

C. Grob, O. Ulloa, H. Claustre, Y. Huot, G. Alarcon, and D. Marie, “Contribution of picoplankton to the total particulate organic carbon concentration in the eastern South Pacific,” Biogeosciences 4(5), 837–852 (2007).
[Crossref]

M. S. Twardowski, H. Claustre, S. A. Freeman, D. Stramski, and Y. Huot, “Optical backscattering properties of the ‘clearest’ natural waters,” Biogeosciences 4(6), 1041–1058 (2007).
[Crossref]

Close, A.

A. Knap, A. Michaels, A. Close, H. Ducklow, and A. Dickson, “Protocols for the Joint Global Ocean Flux Study (JGOFS) Core Measurements,” in JGOFS Report Nr. 19 (Reprint of the IOC Manuals and Guides No. 29, UNESCO, 1994) (1996), pp. 170.

Collier, R.

E. S. Boss, R. Collier, G. Larson, K. Fennel, and W. S. Pegau, “Measurements of spectral optical properties and their relation to biogeochemical variables and processes in Crater Lake, Crater Lake National Park, OR,” Hydrobiologia 574(1), 149–159 (2007).
[Crossref]

Cowles, T. J.

Cullen, J. J.

J. J. Cullen, “Subsurface Chlorophyll Maximum Layers: Enduring Enigma or Mystery Solved?” Annu. Rev. Mar. Sci. 7(1), 207–239 (2015).
[Crossref]

D’Asaro, E. A.

I. Cetinić, M. J. Perry, N. T. Briggs, E. Kallin, E. A. D’Asaro, and C. M. Lee, “Particulate organic carbon and inherent optical properties during 2008 North Atlantic Bloom Experiment,” J. Geophys. Res.: Oceans 117(C6), n/a (2012).
[Crossref]

D’Ortenzio, F.

M. Bellacicco, V. Vellucci, M. Scardi, M. Barbieux, S. Marullo, and F. D’Ortenzio, “Quantifying the Impact of Linear Regression Model in Deriving Bio-Optical Relationships: The Implications on Ocean Carbon Estimations,” Sensors 19(13), 3032 (2019).
[Crossref]

Dai, M.

Z. Cao, M. Dai, Z. M. Lu, and K. Zhou, “CaCO3 to Organic Carbon Ratio in the South China Sea,” in Advances in Geosciences (2009), pp. 109–125.

Dall’Olmo, G.

E. Organelli, G. Dall’Olmo, R. J. W. Brewin, G. A. Tarran, E. Boss, and A. Bricaud, “The open-ocean missing backscattering is in the structural complexity of particles,” Nat. Commun. 9(1), 5439 (2018).
[Crossref]

J. R. Graff, T. K. Westberry, A. J. Milligan, M. B. Brown, G. Dall’Olmo, V. van Dongen-Vogels, K. M. Reifel, and J. B. Behrenfeld, “Analytical phytoplankton carbon measurements spanning diverse ecosystems,” Deep Sea Res., Part I 102, 16–25 (2015).
[Crossref]

V. Martinez-Vicente, G. Dall’Olmo, G. Tarran, E. Boss, and S. Sathyendranath, “Optical backscattering is correlated with phytoplankton carbon across the Atlantic Ocean,” Geophys. Res. Lett. 40(6), 1154–1158 (2013).
[Crossref]

G. Dall’Olmo, T. K. Westberry, M. J. Behrenfeld, E. Boss, and W. H. Slade, “Significant contribution of large particles to optical backscattering in the open ocean,” Biogeosciences 6(6), 947–967 (2009).
[Crossref]

Dana, D. R.

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Supplementary Material (1)

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Figures (6)

Fig. 1.
Fig. 1. Map of the study region. Black solid circles stand for the sampling stations while the magenta plus signs represent the flow cytometer stations, and the two cyan diamonds are the remote-sensing reflectance stations (‘S2086’ and ‘S2097’). The orange contours indicate the 1000 m isobaths.
Fig. 2.
Fig. 2. Vertical distributions of (a) chlorophyll-a concentration (Chla) and the associated phytoplankton community compositions, (b) phytoplankton carbon biomass (Cphy), particulate organic carbon (POC), and their ratio (fCphy), (c) fractions of four typical phytoplankton groups to total Chla (fPro, fSyn, fHapt8, and fHapt6), (d) fraction of each phytoplankton size class to total Chla (fpico, fnano, and fmicro), (e) particulate backscattering coefficient (bbp), and (f) the POC-specific bbp at 510 nm (b*bp(510)). In each sub-figure, the dots stand for the samples, and the solid line and horizontal bar represent their mean value and standard deviation
Fig. 3.
Fig. 3. Scatter plots between particulate organic carbon (POC) and particulate backscattering coefficient (bbp(λ)), and their associated linear (Type-II) regressions (black solid lines). In the sub-figure (c), the solid red, green, and blue lines show the linear (Type-II) regressions for the samples observed at surface (red dots), at SCMLs (green dots), and below SCMLs (blue dots); the dashed black and red lines show the linear (Type-I) regressions for all and only surface samples; the dashed magenta line represents the linear (Type-I) regression from Stramski et al. [7]. In the sub-figure (d), the black dashed line shows the linear (Type-I) regression for the measurements, and the dashed magenta line represents the linear (Type-I) regression from Cetinić et al. [9].
Fig. 4.
Fig. 4. Scatter plots between the derived phytoplankton carbon biomass (Cphy) and particulate backscattering coefficient (bbp(λ)), and their associated linear (Type-II) regressions (black lines). In the sub-figure (a), the dashed black line shows the linear (Type-I) regression for the measurements, and the dashed red and green lines show the original linear (Type-I) relationship from Behrenfeld et al. [18] and its recalculated relationship with bbw(442) from Zhang et al. [2]. In the sub-figure (b), the dashed black line shows the linear (Type-I) regression for the measurements, and the dashed red line shows the linear (Type-I) regression from Graff et al. [19], and the solid green line shows the linear (Type-II) regression from Martinez-Vicente et al. [12].
Fig. 5.
Fig. 5. (a) Scatter plots between phytoplankton carbon biomass (Cphy) and particulate organic carbon (POC). The solid black line represents the linear (Type-II) regression. (b) Scatter plots between fCphy and Cphy. The black line represents their exponent regression.
Fig. 6.
Fig. 6. Summarized correlation coefficients between b*bp(510) and particulate assemblage including phytoplankton biomass (Chla and Cphy), and the fraction of each phytoplankton group to total Chla (fProc, fSyn, fDino, fChlor, fPras, fCrypt, fHapt6, fHapt8, and fDiat), and the fraction of each phytoplankton size class to total Chla (fpico, fnano, and fmicro). The red (blue) bars show the correlations are significant (p<0.05) positive (negative), and the gray bars show the correlations are insignificant (p>0.05). In particular, since fDino are very small with the maximum value <0.05, the statistics is not representative although p is <0.05, and we still regard its correlation insignificance.

Tables (1)

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Table 1. The regressed relationships and their error statistics.

Equations (13)

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$${b_{\textrm{bp}}} = 2\mathrm{\pi } \cdot {\chi _\textrm{p}}({140^\circ } )\cdot {\beta _\textrm{p}}({140^\circ } )= 2\mathrm{\pi } \cdot {\chi _\textrm{p}}({140^\circ } )\cdot [{\beta ({140^\circ } )- {\beta_\textrm{w}}({140^\circ } )} ],$$
$${b_\textrm{b}} = {b_{\textrm{bw}}} + {b_{\textrm{bp}}}.$$
$${C_{\textrm{pico}}} = \sum\limits_{i = 1}^3 {{{10}^{ - 6}} \cdot {N_i} \cdot {\varepsilon _i} \cdot \left( {\frac{\pi }{6}D_i^3} \right)} ,$$
$${C_{\textrm{cell}}} = pV_{\textrm{cell}}^q,$$
$$\begin{aligned} {C_{\textrm{phy}}} &= \int_{{D_{\min }}}^{{D_{\max }}} {N(D){C_{\textrm{cell}}}dD} \\ &= \int_{{D_{\min }}}^{{D_{\max }}} {(k{D^{ - \xi }})[{{10}^{ - 9}}p{{({{10}^{18}}\frac{\pi }{6}{D^\textrm{3}})}^q}]dD} \\ &= {10^{ - 9}}kp{({10^{18}}\frac{\pi }{6})^q}(\frac{{D_{\max }^{3q - \xi + 1} - D_{\min }^{3q - \xi + 1}}}{{3q - \xi + 1}}), \end{aligned}$$
$${f_{\textrm{fc}}} = \frac{{\int_{0.2}^\textrm{3} {N(D){C_{cell}}dD} }}{{\int_{0.2}^{200} {N(D){C_{cell}}dD} }} = \frac{{\textrm{3}_{}^{3q - \xi + 1} - 0.2_{}^{3q - \xi + 1}}}{{200_{}^{3q - \xi + 1} - 0.2_{}^{3q - \xi + 1}}}.$$
$${C_{\textrm{phy}}} = \frac{{{C_{\textrm{pico}}}}}{{{f_{\textrm{fc}}}}} = \frac{{200_{}^{3q - \xi + 1} - 0.2_{}^{3q - \xi + 1}}}{{\textrm{3}_{}^{3q - \xi + 1} - 0.2_{}^{3q - \xi + 1}}}{C_{\textrm{pico}}}.$$
$$RMSE = \sqrt {\frac{1}{n}\sum\limits_{j = 1}^n {{{({y_j} - {x_j})}^2}} } ,$$
$$MAPE = \frac{1}{n}\sum\limits_{j = 1}^n {\frac{{|{y_j} - {x_j}|}}{{{x_j}}}} \times 100\%,$$
$${f_{\textrm{Cphy}}} = 1 - \textrm{exp} ({ - 0.0294{C_{\textrm{phy}}}} ).$$
$${b^\ast }_{\textrm{bp}}(510) = ( - 2.93 \pm 0.21) \times {10^{ - 5}}{f_{\textrm{pico}}} + (4.42 \pm 0.12) \times {10^{ - 5}},$$
$${b^\ast }_{\textrm{bp}}(510) = (3.73 \pm 0.26) \times {10^{ - 5}}{f_{\textrm{nano}}} + (1.41 \pm 0.12) \times {10^{ - 5}},$$
$${b^\ast }_{\textrm{bp}}(510) = (1.17 \pm 0.09) \times {10^{ - 4}}{f_{\textrm{micro}}} + (1.97 \pm 0.1) \times {10^{ - 5}}.$$