Vertical Variability of Total and Size-Partitioned Phytoplankton Carbon in the South China Sea

Abstract

The standing stock of phytoplankton carbon is a basic and essential property for understanding oceanic ecosystems, biogeochemical cycles, and regional climates. However, current related algorithms mainly focus on remote-sensed application, which cannot describe the vertical profile of phytoplankton carbon throughout the whole euphotic zone. In this study, we modified a previous absorption-based bio-optical algorithm to acquire vertical variabilities of the total and size-partitioned phytoplankton carbon based on field data from the South China Sea (SCS). The mean absolute errors and the biases between estimated and field picophytoplankton carbon were <2.14 and 0.6–2.0, respectively. The results showed that the vertical profile of total phytoplankton carbon displayed a Gaussian distribution in the stratified SCS basin. The picophytoplankton carbon was always the fundamental component of the total phytoplankton carbon within the whole euphotic zone. The dominant picophytoplankton species changed from Synechococcus-like cyanobacteria at the sea surface to pico-sized haptophytes at the phytoplankton carbon maximum layer. The strong covariation between total phytoplankton carbon and chlorophyll-a concentration suggested that they can be converted into each other through an accurate carbon-to-chlorophyll ratio in the open SCS. These results provide essential information that can be used to decipher the three-dimensional structure of total and size-partitioned phytoplankton carbon in the open SCS.

1. Introduction

Marine phytoplankton is a key component of global carbon cycling, accounting for about half (~50 Gt C) of global annual primary production through oxygenic photosynthesis [1,2]. Knowledge of the standing stock and dynamics of marine phytoplankton is crucial for understanding the global carbon cycle and climate. In recent decades, the most commonly used indicator of phytoplankton biomass has been the total chlorophyll-a concentration (Chla, in mg m⁻³) [3,4]. However, in the “photoacclimation regime” [5], the first order changes in Chla are due to intracellular pigment variation resulting from light and nutrient variations [6], thus Chla cannot provide a full description of the state of the ecosystem under such a regime [7]. Instead of Chla, total phytoplankton carbon biomass (C, in mg m⁻³) is the parameter more directly related to the carbon cycle, biogeochemical cycles, and climate [7,8]. Accurate estimation of C provides a means to observe the standing stocks of phytoplankton and their response to environmental variability [9]. However, direct measurement of C remains challenging due to the inability to isolate C from the other particulate forms of carbon in seawater (e.g., zooplankton, detritus, and bacteria) [9]. Consequently, estimating C from other easier to measure proxies, such as optical parameters, maybe an easier approach.

With the development of observed technology, many bio-optical models have been built to derive Chla as well as chlorophyll-a concentrations in three size classes (e.g., [10,11,12]). In terms of C, several bio-optical models for C estimation have been proposed recently as well [6,7,13,14,15]. C is an important component of particulate organic carbon (POC, in mg m⁻³) in the vast oceans. Sathyendranath et al. [14] developed a simple conceptual model to calculate C from Chla based on the assumption that at any given Chla, the lowest POC observed represents the C associated with that Chla. C can also be computed through Chla or POC by assuming a C-to-Chla ($\chi$) or C-to-POC ratio. Based on the assumption that the particles contributing to particulate backscattering coefficients (b_bp($\lambda$), in m⁻¹) are composed of a stable non-algal “background” component and a second component including phytoplankton and other particles that co-vary with phytoplankton, Behrenfeld et al. [6] subtracted the non-algal particulate backscattering coefficients (b_nap($\lambda$), in m⁻¹) based on the relationship between b_bp($\lambda$) and Chla and then calculated C through the remaining b_bp($\lambda$) based on a simple scaling factor. The simple scaling factor was derived such that the resulting C was ~25 to 40% of POC and the average $\chi$ value was within the range observed in laboratory studies [16]. However, b_nap($\lambda$) varies in different oceanic regions (e.g., [17,18]). Bellacicco et al. [17] reported that using a constant b_nap($\lambda$) to estimate C will lead to a 50% overestimation in satellite-based global C estimates with respect to the results based on varied b_nap($\lambda$) in different regions. Meanwhile, based on Biogeochemical-Argo data, Bellacicco et al. [18] also reported that b_nap($\lambda$) in the surface layer increased from Southern to Northern Hemisphere, and b_nap($\lambda$) was the main contributor to b_bp($\lambda$) in the surface oligotrophic waters while the contribution of b_nap($\lambda$) decreased in the surface layer of most productive areas. Besides, variabilities in particle size distributions also lead to differences in backscattering per unit carbon biomass due to different scattering efficiencies [7,19]. Accordingly, Kostadinov et al. [19] built a b_bp($\lambda$) model to estimate particle size distributions (power-law distribution), and later Kostadinov et al. [7] combined the allometric relationships to compute C and size-partitioned phytoplankton carbon biomass based on the assumption that the value of C-to-POC ratio was 30%. However, the uncertainty in C estimation due to contribution of other types of non-algal particles to b_bp($\lambda$) still exists. To avoid this problem, Roy et al. [15] developed a semi-analytical algorithm (R17) to calculate C and size-partitioned phytoplankton carbon that is based on the specific absorption coefficient of phytoplankton (which is defined as the ratio of the absorption coefficient of phytoplankton to Chla, $a_{\mathrm{ph}}^{*}$($\lambda$), in m² mg⁻¹), which is directly related to phytoplankton. These advances in C estimation algorithms provide effective means to estimate C from in situ to remote platforms.

The South China Sea (SCS) is the largest trophic marginal sea in the northwestern Pacific Ocean, and it plays important roles in regulating the regional carbon cycle and climate due to its vast area and volume [20,21]. Macronutrient concentrations in the central basin of SCS are below the detection limit, which suggest the SCS basin is oligotrophic [20,22,23]. Because it is oligotrophic, the open SCS is dominated by picophytoplankton, namely Prochlorococcus, Synechococcus, and picoeukaryotes [20]. Previous studies of the phytoplankton biomass variation in the SCS have been based mostly on Chla. However, photoacclimation is an important factor controlling variability of the Chla in the open SCS [21], and this process limits our understanding of the real distribution and variation of the phytoplankton pool as well as the biological carbon pump in the SCS. Therefore, in this study we estimated the vertical standing stocks of phytoplankton from the perspective of carbon mass rather than Chla. It provides another perspective for studying the distribution and variation of phytoplankton biomass in the SCS.

To avoid using preset values of C:POC and effects of the non-algal particles, we chose the absorption-based carbon algorithm to estimate the phytoplankton carbon concentration in the SCS. First, we modified the algorithm described by Roy et al. [15] using the in situ absorption coefficient of phytoplankton [a_ph($\lambda$), in m⁻¹] and Chla dataset, and then we applied it to the non-watery beam absorption [a_pg($\lambda$), in m⁻¹] that was measured by an absorption-and-attenuation-meter (AC-S, WET Lab Inc., Philomath, OR, USA). The algorithm-derived picophytoplankton carbon values were validated by in situ measurements of picophytoplankton carbon. We then analyzed the characteristics of the vertical profiles of total and size-partitioned phytoplankton carbon in the open SCS basin. To ease the conversion between C and Chla, we analyzed the regional relationships between C and Chla as well.

Table 1. The main abbreviations used in this study.

Abbreviations	Definition	Unit
aph($\mathsf{\lambda }$)	The absorption coefficient of phytoplankton	m−1
$a_{\mathrm{ph}}^{*}$($\lambda$)	The ratio of the absorption coefficient of phytoplankton to chlorophyll-a concentration (the specific-absorption coefficient of phytoplankton)	m2 mg−1
apg($\lambda$)	The non-watery beam absorption	m−1
aLH(676)	The absorption line height at 676 nm	m−1
$a_{\mathrm{LH}}^{*}$(676)	The specific-absorption coefficient of phytoplankton at 676 nm derived from apg($\mathsf{\lambda }$)	m2 mg−1
am	The maximum $a_{\mathrm{ph}}^{*}$(676) or $a_{\mathrm{LH}}^{*}$(676) determined from in situ measurements	m2 mg−1
$a_{Chla}^{*}$(676)	The observed specific absorption coefficient of chlorophyll-a at 676 nm derived from $a_{\mathrm{ph}}^{*}$(676) or $a_{\mathrm{LH}}^{*}$(676)	m2 mg−1
$a_{Chla}^{*}\left(676,D\right)$	The theoretical specific absorption coefficient of chlorophyll-a at 676 nm	m2 mg−1
Chla	Total chlorophyll-a concentration	mg m−3
ChlaLH	The value of Chla derived from apg($\mathsf{\lambda }$) based on the absorption line height method	mg m−3
$\xi$	The exponent of the phytoplankton size spectra	Dimensionless
C	Total phytoplankton carbon biomass	mg m−3
Cp	The picophytoplankton carbon biomass	mg m−3
Cn	The nanophytoplankton carbon biomass	mg m−3
Cm	The microphytoplankton carbon biomass	mg m−3
Fp	The fractions of carbon biomass associated with picophytoplankton	Dimensionless
Fn	The fractions of carbon biomass associated with nanophytoplankton	Dimensionless
Fm	The fractions of carbon biomass associated with microphytoplankton	Dimensionless
${\chi }_{\mathrm{p}}$	The ratio of Cp to the chlorophyll-a concentration associated with picophytoplankton	Dimensionless
${\chi }_{\mathrm{n}}$	The ratio of Cn to the chlorophyll-a concentration associated with nanophytoplankton	Dimensionless
${\chi }_{\mathrm{m}}$	The ratio of Cm to the chlorophyll-a concentration associated with microphytoplankton	Dimensionless
$\chi$	The ratio of C to Chla (C:Chla)	Dimensionless
POC	Particulate organic carbon concentration	mg m−3
MLD	The mixed layer depth	m
Zeu	The depth of the euphotic zone	m
ZT22	The depth of 22 $℃$	m
CML	The C maximum layer	none

shows the main abbreviations used in this study. This study provides important information for studying phytoplankton dynamics and the regional carbon cycle and climate in the SCS.

2. Materials and Methods

2.1. Study Area and Field Sampling

The SCS extends from 3$°$ S to 23$°$ N and from 99$°$ E to 121$°$ E, and it includes two wide shallow shelves in the northern and southern parts and a large deep basin in between [24]. The upper ocean layer of the SCS is mainly affected by eastern Asian monsoons [25], periodic typhoons, Kuroshio intrusions, and fresh water inflow [26]. The circulation of the SCS is cyclonic in winter but anticyclonic in summer [24]. The open SCS is generally stratified, warm, and oligotrophic, with low phytoplankton biomass [20,21]. The vertical Chla is generally characterized by a pronounced deep maximum at 60–100 m in the open SCS [21,27,28,29].

Three cruises were carried out in the SCS to collect bio-optical parameters: 27 June to 17 July 2015 (cruise 2015), 3–23 September 2016 (cruise 2016), and 1–22 October 2017 (cruise 2017). The bio-optical parameters (absorption coefficient of phytoplankton [a_ph($\lambda$), in m⁻¹], Chla, picophytoplankton carbon biomass, and POC) were obtained at four depths (0 or 5, 25, 50, and 75 m). POC data were only collected during cruises 2015 and 2017. Additionally, an AC-S instrument was used to measure the vertical profiles of a_pg($\lambda$) during cruises 2015 and 2016. A simultaneously seabird conductivity-temperature-depth (CTD) was used to obtain the profiles of temperature and salinity. The AC-S and CTD were assembled in a cage to measure the optical and hydrographic parameters from surface to about 120 m. Figure 1 shows the locations of the sampling stations.

2.2. Field in Situ Data

2.2.1. Measurement of a_ph($\lambda$) and Calculation of $a_{\mathrm{ph}}^{*}$($676$)

To obtain a_ph($\lambda$) from 350 to 750 nm, 0.5–3.0 L of seawater, depending on the station, were filtered through a 25 mm glass fiber filter (Whatman, GF/F, Maidstone, UK) under low vacuum conditions. Because our laboratory bought a new spectrophotometer in 2016, the measurements of a_ph($\lambda$) for cruise 2015 were made using a Shimadzu UV-2550 spectrophotometer (Kyoto, Japan), and those for cruises 2016 and 2017 were made using a PerkinElmer Lambda 650S spectrophotometer (Waltham, MA, USA) based on the quantitative filtered technique (QFT). The reference blank was a clear filter that was presoaked in pure water. First, the absorption coefficient of total particles [a_p($\lambda$), in m⁻¹] was measured. Then the absorption coefficient of non-algal particles [a_nap($\lambda$), in m⁻¹] was measured after soaking the filters in methanol for 90–180 min to remove phytoplankton pigments. All measurements were corrected for the background signals by subtracting the absorption values at 750 nm over the whole wavelength [30]. Corrections for pathlength amplification were made according to Stramski et al. [31]. Finally, a_ph($\lambda$) was calculated as the difference between a_p($\lambda$) and a_nap($\lambda$). The values of $a_{\mathrm{ph}}^{*}$($676$) were calculated by dividing a_ph($676$) by the corresponding field in situ Chla.

2.2.2. Measurement of a_pg($\mathsf{\lambda }$)

The vertical profiles of a_pg($\lambda$) were measured using a 25 cm pathlength AC-S with 82 wavebands from 401.6 to 744.1 nm. Pure water was used to calibrate the drift of the AC-S instrument and as the reference blank before cruises. To avoid the influence of bubble, the AC-S was lowered below the water’s surface for ~5 min to warm up, and after the warm up period, the AC-S was steadily lowered through the water column to collect data. Before data correction, the software “WET Labs Archive File Processing” (WAP) was used to merge the AC-S and CTD data. The corrections for temperature and salinity effects were made using contemporaneously recorded CTD data [32]. All measurements were corrected for scattering by setting the absorption values as zero around the infrared wavelengths [33].

2.2.3. Pigment Concentration Measurement and Determination of Dominant Phytoplankton Species

The values of Chla were measured in two ways: fluorescence method and high-performance liquid chromatography (HPLC). For the fluorescence method, 0.5–1.0 L of seawater were filtered through a 25 mm Whatman GF/F filter with 0.7 $\mathsf{\mu }$m pore size to obtain Chla. In the laboratory, filters were soaked in acetone in the dark for 24 h to extract the chlorophyll a. Then, Chla was measured using a Turner Design 10 fluorometer (Sunnyvale, CA, USA) [34]. For HPLC, 2.5–10 L of seawater were filtered through 25 mm or 47 mm Whatman GF/F filters with 0.7 $\mathsf{\mu }$m pore size and stored in liquid nitrogen until analysis in the laboratory. For surface samples (0 or 5 m), 8–10 L of seawater were filtered on the 47 mm Whatman GF/F filters. As for the samples at 25, 50 and 75 m, 2.5–5 L of seawater were filtered on the 25 mm Whatman GF/F filters. The collection of HPLC samples was generally according to the Joint Global Ocean Flux Study (JGOFS) protocols [35]. See Vidussi et al. [36] for analysis details. The HPLC data were also used to calculate the size-partitioned Chla according to the method in Brewin et al. [10].

Determination of dominant phytoplankton species was made according to the criteria in Table 4 from Alvain et al. [37] and this method was based on the relative concentrations of main biomarkers of the Prochlorococcus, Synechococcus-like cyanobacteria, haptophytes, dinoflagellates and diatoms of the water samples to determine the dominate phytoplankton species.

2.2.4. Picophytoplankton Carbon Biomass and POC Measurements

To measure picophytoplankton carbon biomass, seawater samples were filtered through a 20 μm sieve and preserved with formaldehyde (2% final concentration) for picophytoplankton cell (Prochlorococcus, Synechococcus and autotrophic picoeukaryotes) counting. The samples were freeze-trapped in liquid nitrogen after 15 min of standing in the dark. Measurements of picophytoplankton cell abundances were made using a BD FACSCanto II flow cytometer (Franklin Lakes, NJ, USA). Before measurement, velocity correction was carried out according to Marie et al. [38]. According to the scatterplots of different fluorescence or side scattering, cell abundances of the three picophytoplankton categories were determined. Carbon contents of the three picophytoplankton categories were estimated from cell abundances by assuming conversion factors of 17.6 fg C cell⁻¹ for Prochlorococcus, 74.55 fg C cell⁻¹ for Synechococcus, and 779.9 fg C cell⁻¹ for picoeukaryotes respectively [summer-winter averaged values in Chen et al. [20]]. The sum of the carbon contents of the three picophytoplankton types is defined as the field picophytoplankton carbon biomass.

For POC measurement, 0.5–4.0 L seawater was filtered onto a pre-combusted (450 °C for 5 h) 25 mm Whatman GF/F fiberglass filter and then stored in a −20 °C fridge. The method of POC measurements was generally consistent with the Joint Global Ocean Flux Study (JGOFS) protocols [35,39]. In the laboratory, the POC samples were dried at 60 °C for 8 h and then acidified by hydrochloric acid fumigation to remove the inorganic carbon. Finally, the filters were dried again and the POC concentrations were measured using a Vario UNICUBE elemental analyzer (Elementar Analysensysteme GmbH, Langenselbold, Germany).

2.3. Derived Data

2.3.1. Physical and Biogeochemical Layer Depths (Layers) of the Water Column

The mixed layer depth (MLD, in m) was estimated based on a threshold potential density difference (0.03 kg m⁻³) from a near-surface value (at 10 m) [21]. The depth of the euphotic zone (Z_eu, in m) was estimated based on average Chla within 10 m (Chla_surf, in mg m⁻³) as Z_eu = 35 Chla_surf ^−0.35 (from Cao et al. (2002) [40]. The depth of 22 °C isotherm (Z_T22, in m) was used as the proxy for the nutricline [24]. The C maximum layer (CML) was defined as the layer where a pronounced C maximum appeared in the vertical profile.

2.3.2. Definition of Trophic Categories

The trophic category (for stratified waters) of each station was defined by the value of Chla at 0 or 5 m according to the threshold in Table 3 from Uitz et al. [41]. The trophic level increased sequentially from S1 (the most oligotrophic) to S9 (the most nutritious) in the stratified waters.

2.3.3. Algorithm Performance Metrics

The mean absolute error (MAE), the root mean square (RMSE), and bias between algorithm estimations and field observations were calculated to evaluate the performance of the algorithm [42]:

$$MAE = 10^(\frac{{{\displaystyle \sum }}_{i=1}^n\left|\log \left(C_{\mathrm{derived}}\right)-\log \left(C_{\mathrm{field}}\right)\right|}{n}),$$

(1)

$$RMSE = \sqrt{\frac{1}{n}\sum {\left[C_{\mathrm{derived}}-C_{\mathrm{field}}\right]}^2},$$

(2)

$$Bias = 10^(\frac{{{\displaystyle \sum }}_{i=1}^n\mathit{log}\left(C_{derived}\right)-\mathit{log}\left(C_{field}\right)}{n}),$$

(3)

where n, C_derived, and C_field represent the number of samples, the estimated products, and field measurements, respectively.

2.4. Phytoplankton Carbon Estimation

Figure 2 shows the flow chart of the phytoplankton carbon estimation. The a_ph($\lambda$) was first used to validate the phytoplankton carbon model, and then we applied the model to the a_pg($\lambda$) data to obtain high-resolution vertical distribution profiles of total and size-partitioned phytoplankton carbon in the SCS.

2.4.1. Phytoplankton Carbon Estimation Algorithm

The phytoplankton carbon estimation algorithm, R17, uses the a_ph(676) and Chla as inputs and combines the allometric relationship between phytoplankton cell size and carbon content to calculate total and size-partitioned phytoplankton carbon. A main assumption of R17 is that the phytoplankton size spectrum follows a power-law distribution. In preparation for estimation of C, the exponent of the phytoplankton size spectra ($\xi$) is first computed from $a_{\mathrm{ph}}^{*}$(676) using the method described in Roy et al. [12]. The $\xi$ can be computed following Equation (4) in MATLAB using a single-variable bound non-linear-function minimization method based on golden section search and parabolic interpolation [12]:

$$a_{Chla}^{*}\left(676\right) = \frac{4-\xi -m}{D_{max}^{4-\xi -m}-D_{min}^{4-\xi -m}}{\int }_{D_{min}}^{D_{max}}\left[D^{3-\xi -m}\times a_{Chla}^{*}\left(676,D\right)\right]dD,$$

(4)

where $a_{Chla}^{*}$(676) on the left-hand side is the observed specific absorption coefficient of cholorophyll-a at 676 nm [43]; $a_{Chla}^{*}$(676, D) on the right-hand side is the theoretical value of specific absorption coefficient of chlorophyll-a at 676 nm, which is expressed as a function of the equivalent spherical diameter D of phytoplankton [43]; m is the exponent of the relationship between intracellular Chla (Chla_cell, mg m⁻³) and D (Chla_cell = c₀D^−m), here set as m = 0.06 (dimensionless) and c₀ = 3.9 $\times$ 10⁶ (mg Chla m^−2.94) [43]; minimum diameter D_min = 0.2 µm; and maximum diameter D_max = 50 µm [15].

The allometric relationship between the cellular content of phytoplankton carbon (C_cell) and cell volume (V_cell) for phytoplankton communities was then used to calculate C [44]:

$$C_{\mathrm{cell}} = a{V}_{\mathrm{cell}}^b,$$

(5)

where V_cell is the volume of a phytoplankton cell expressed in µm³, C_cell is expressed in pg C cell⁻¹, and a = 0.54 and b = 0.85 are constants [15]. C within a diameter range [D_min, D_max] can then be expressed as:

$$C = \chi Chla = \frac{{10}^{-9}a{\left(\frac{{10}^{18}\pi }{6}\right)}^b}{\left(\frac{\pi }{6}\right)c_0}\left(\frac{D_{max}^{3b-\xi +1}-D_{min}^{3b-\xi +1}}{D_{max}^{4-\xi -m}-D_{min}^{4-\xi -m}}\right)\left(\frac{4-\xi -m}{3b-\xi +1}\right)Chla.$$

(6)

It should be noted that 10⁻⁹ and 10¹⁸ are the conversions of units from pg to mg and from m³ to µm³, respectively. The diameter ranges of pico-, nano-, and micro-sizes were set at 0.2–2.0, 2–20, and 20–50 µm, respectively [15]. The carbon biomass of pico- (C_p, in mg m⁻³), nano- (C_n, in mg m⁻³), and microphytoplankton (C_m, in mg m⁻³) was calculated through the product of ${\chi }_i$ and Chla_i, where i represents pico-, nano-, or microphytoplankton. ${\chi }_i$ is expressed as a function of $\xi$, m, and the upper and lower bounds of diameter of the three size classes. The Chla_i was estimated using the Chla and chlorophyll-a fractions of the three size classes (see Roy et al. [12] for details). Finally, the fractions of carbon associated with pico- (F_p), nano- (F_n), and microphytoplankton (F_m) were calculated through C_i and C.

2.4.2. Modification of the Algorithm

The $a_{\mathrm{ph}}^{*}$(676) is not necessarily equal to $a_{Chla}^{*}$(676), especially in low-Chla conditions [43]. Therefore, $a_{\mathrm{ph}}^{*}$(676) values were converted to the corresponding $a_{Chla}^{*}$(676) values using an ad-hoc non-linear function [43]:

$$a_{Chla}^{*}(676) = \frac{a_{\mathrm{ph}}^{*}\left(676\right)}{1+\sigma a_{\mathrm{ph}}^{*}\left(676\right)},$$

(7)

where $\sigma$ = $\frac{1}{a_{ci}^{*}}-\frac{1}{a^m}$, and $a_{ci}^{*}$ = 0.028 m² (mg Chla) ⁻¹ was the maximum numerical value of $a_{Chla}^{*}$(676) reported for laboratory cultures, and a^m was the maximum $a_{\mathrm{ph}}^{*}$(676) determined from in situ measurements. To estimate $\xi$ over a realistic range of measured $a_{\mathrm{ph}}^{*}$(676), a^m was set to 0.0226 m² mg⁻¹ for the $a_{\mathrm{ph}}^{*}$(676) dataset; for the a_pg(λ) dataset, a^m was set to 0.0128 m² mg⁻¹. In addition, the upper bounds for $a_{\mathrm{ph}}^{*}$(676) were the a^m values in different datasets, respectively, and the lower bound for $a_{\mathrm{ph}}^{*}$(676) was set to 0.007 m² mg⁻¹.

2.4.3. Application of the Algorithm to a_pg($\mathsf{\lambda }$)

It is not enough to apply R17 to remote sensing data (which only observes the surface distribution) and QFT-$a_{\mathrm{ph}}^{*}$(676) data (which only observes the variations at several discrete depths) to obtain a three-dimensional distribution of C, C_p, C_n, and C_m. Thus, we tried to apply the R17 algorithm to a_pg($\lambda$) data to obtain the high-spatial-resolution vertical profiles of total and size-partitioned phytoplankton carbon. To do this, the values of Chla were first derived using the absorption line height method (Chla_LH, in mg m⁻³) [45]. The absorption line height at 676 nm [a_LH(676), in m⁻¹] was calculated from a_pg($\lambda$) as follows:

a_LH(676) = a_pg(676) − [0.52 × [a_pg(700) − a_pg(650)] + a_pg(650)].

(8)

The Chla_LH was then calculated using a_LH(676) based on a regional empirical power-law relationship between field Chla and a_LH(676) in the SCS:

Chla_LH = 65.57 × a_LH(676)^0.96.

(9)

The correlation coefficient (R), RMSE, bias, and MAE between field Chla and Chla_LH were 0.88, 0.11 mg m⁻³, 1.03, and 1.45, respectively (Figure 3). The specific-absorption coefficient of phytoplankton from a_pg($\lambda$) ($a_{\mathrm{LH}}^{*}$, in m² mg⁻¹) was defined as: $a_{\mathrm{LH}}^{*}$(676) = a_LH(676)/Chla_LH. Finally, the Chla_LH and $a_{\mathrm{LH}}^{*}$(676) were used to estimate the total and size-partitioned phytoplankton carbon.

3. Results

3.1. Algorithm Validation

To evaluate the applicability of R17, validation of R17 was carried out using field data (both QFT-$a_{ph}^{*}\left(676\right)$ and AC-S-a_pg(676) data) from the SCS. Because field C, C_n, and C_m are difficult to obtain, validations were limited to C_p. The field observed C_p for algorithm validation was the product of flow-cytometry-measured picophytoplankton cell abundance and the corresponding carbon conversion coefficient. The field observed C_p was independent of the algorithm-derived C_p. The details of the field observed C_p measurement were in Section 2.2.4.

3.1.1. Validation of Estimations from $a_{ph}^{*}$(676)

Figure 4a shows validation results for estimations from $a_{ph}^{*}$(676). The value of R between field C_p and estimated C_p based on R17 was 0.58 (p < 0.001), and the values of MAE and bias between field C_p and the $a_{ph}^{*}$(676)-derived estimations were 2.14 and 0.62. The scatter points were distributed near the 1:1 line (black line in Figure 4a). Uncertainties in the carbon conversion factors would lead to 2- to 3-fold overestimation of field C_p [46]. The median value of the estimated C_p was lower than that of the default field estimations but higher than those of a 2- or 3-fold overestimations of the field observations (Figure 4b). In addition, the field ${\chi }_p$ was calculated as the ratio of field C_p and picophytoplankton chlorophyll-a concentration derived from HPLC measured pigments [10]. In Figure 5, the median value of algorithm-estimated $\chi$_p (82.26) was between the median value of field $\chi$_p (120.44) and the median value of 2-fold-error field $\chi$_p (60.22). These results suggested that the $a_{ph}^{*}$(676)-derived C_p compared well with the corresponding field C_p.

3.1.2. Validation of Estimations from $a_{\mathrm{LH}}^{*}$(676)

Figure 6 shows the validation results for $a_{\mathrm{LH}}^{*}$(676) estimations. The MAE and bias between $a_{\mathrm{LH}}^{*}$(676)-estimated and field C_p were 1.9 and 1.39, respectively. The scatter points fell around the 1:1 line. The median value of the estimated C_p was similar to but slightly higher than that of the default field estimates (Figure 6b), which may result from the uncertainty of a^m and Chla_LH (see Section 4.1 for detailed discussion). The median value of the derived ${\chi }_p$ was 91.17, which was lower than the median value of field $\chi$_p (120.44) but higher than the median value of 2-fold-error field $\chi$_p (60.22) shown in Figure 5. Figure 7 shows the performances of R17 when using different input data. The values of R, RMSE, and MAE between $a_{\mathrm{LH}}^{*}$(676)-derived and field C_p were similar to those between $a_{ph}^{*}$(676)-derived and field C_p. This result suggested that the performance of R17 applied to the $a_{\mathrm{LH}}^{*}$(676) was similar to that of R17 applied to the $a_{ph}^{*}\left(676\right)$. Accordingly, the $a_{\mathrm{LH}}^{*}$(676) can be used to estimate the phytoplankton carbon in the SCS.

3.2. Vertical Variation of Phytoplankton Carbon and Related Bio-Parameters

3.2.1. Statistical Results from $a_{ph}^{*}$(676)

We analyzed the variations of total and size-partitioned phytoplankton carbon and related bio-parameters based on the results derived from $a_{ph}^{*}$(676) data within the euphotic layer covering the coastal region to the deep basin in the SCS. As shown in

Table 2. Variations of C, size-partitioned phytoplankton carbon, POC, C:POC, $\chi$, and the ratios of size-partitioned phytoplankton carbon to size-partitioned phytoplankton carbon based on the $a_{ph}^{*}$(676) dataset in the SCS.

Parameters	Units	Mean	Max	Min	SD	Num
C	mg m−3	16.53	62.02	2.38	12.57	215
Cp	mg m−3	11.91	47.21	0.62	10.47	215
Cn	mg m−3	3.69	25.70	0.21	3.46	215
Cm	mg m−3	0.93	13.45	0.0056	1.36	215
$\chi$	None	53.77	91.44	25.85	17.55	215
${\chi }_p$	None	83.09	96.36	72.15	5.96	215
${\chi }_n$	None	33.85	39.26	29.39	2.43	215
${\chi }_m$	None	17.44	17.91	17.04	0.21	215
POC	mg m−3	60.84	185.48	27.23	32.59	83
C:POC	%	41.27	95.32	5.54	25.80	83

Notes: Mean, Max, Min, SD, and Num represent the average value, maximum, minimum, standard deviation, and number of samples, respectively.

, the C varied from 2.38 to 62.02 mg m⁻³, with an average value of 16.53 mg m⁻³. The ranges of C_p, C_n, and C_m were 0.62–47.21, 0.21–25.70, and 0.0056–13.45 mg m⁻³, respectively. The average values of C_p, C_n, and C_m were 11.91, 3.69, and 0.93 mg m⁻³. Figure 8 shows the boxplot of F_p, F_n, and F_m. The median of F_p (0.67) was higher than the median of F_n (0.27), and the median of F_m (0.06) was lowest. Moreover, 87.44% of F_p were higher than the corresponding F_n and F_m. These results suggested that the picophytoplankton was the major contributor to C in the SCS, which is consistent with previous studies reporting that the open SCS is oligotrophic and that the picophytoplankton constitutes an essential component of the phytoplankton community [20,29,47]. The values of $\chi$ varied from 25.85 to 91.44, with an average value of 53.77. The value ranges of ${\chi }_p$, ${\chi }_n$, and ${\chi }_m$ were 72.15–96.36, 29.39–39.26, and 17.04–17.91, respectively. The value of C:POC is an important input in other phytoplankton carbon estimation models, and it is usually set to 30% [6,7]. However, the value of C:POC is not a constant, and it varies from 14% to 85% in different oceanic regions [13,48,49,50,51]. In our study, the C:POC value in the SCS ranged from 5.54% to 95.32%, and the average value was 41.27 ± 25.8% (Table 2). This variability of C:POC is consistent with the results reported in previous studies across a variety of oceanic regions [13,48,49,50,51].

3.2.2. Vertical Profiles in the SCS Basin

To understand the basic vertical profile of total and size-partitioned phytoplankton carbon as well as χ in the open SCS, we plotted the results from the stations > 1000 m with strong stratification in the oligotrophic SCS basin. Figure 9 shows the values of C, size-partitioned phytoplankton carbon, and χ at four depths (0 or 5, 25, 50, and 75 m) derived from $a_{ph}^{*}$(676). Figure 10 shows the continuous high spatial resolution vertical profiles of these parameters derived from $a_{\mathrm{LH}}^{*}$(676).

Vertical Profiles at Four Discrete Depths

According to the trophic categories, 92% of stations shown in Figure 9 were in the most oligotrophic environment (trophic categories were within S2–S4). The subsurface C maximums usually appeared at 50 or 75 m and were accompanied by the subsurface Chla maximums. The vertical profiles of C_p were similar to those of C at all stations. The values of C_p were the highest among C_p, C_n, and C_m at the depths of the subsurface C maximum. While 67% of vertical profiles of C_n were similar to those of C, 80% of vertical profiles of C_m were different from those of C, whereby the C_m maximums did not appear at the depths of the subsurface C maximum. Additionally, 88% of vertical profiles of F_p were similar to those of C. At the depth of the subsurface C maximum, the maximum values of F_p (generally > 0.5) were also observed at all stations. Most of vertical distributions of F_n and F_m showed the opposite trend as those of F_p, and the vertical maximum of F_p always coincided with the minimums of F_n and F_m and the highest $\chi$ value. This result indicated that at the depths of subsurface C maximum, the picophytoplankton was increasing, either in terms of total carbon biomass or fraction, which is consistent with the results reported in Uitz et al. [41] for S2–S4 waters and the results reported in Sauzède et al. [11] at the Bermuda Atlantic Times Series Study site from June to October. In most areas of the SCS basin, strong density stratification results in oligotrophic waters [52], thus the pico- and nanophytoplankton are dominant at the CML, and the contribution of C_m is low [41].

High Spatial Resolution Vertical Profile

Figure 10 shows seven higher spatial resolution vertical profiles of the phytoplankton carbon and bio-parameters, which were obtained from the $a_{\mathrm{LH}}^{*}$(676) in the SCS basin. The stations with strong stratification, where water depths were >1000 m and measuring depths were >100 m, were chosen as the display stations. These vertical profiles derived from $a_{\mathrm{LH}}^{*}$(676) show more detail about the variabilities of phytoplankton carbon and related bio-parameters within the whole euphotic zone. The $a_{\mathrm{LH}}^{*}$(676)-derived vertical profiles of C, size-partitioned phytoplankton carbon, and related bio-parameters were similar to those derived from the $a_{ph}^{*}$(676) data. The CML was a universal feature at the seven stations, and the depths of the CML were all above the Z_eu and Z_T22. The subsurface C maximum (>20 mg m⁻³) appeared at 50–100 m with the subsurface Chla maximum layer and highest $\chi$ values. The values of C_p and C_n increased while the values of C_m decreased slightly at the CML. Figure 10g–i show that the F_p increased while F_n and F_m decreased at the CML. These results suggested that the contribution of picophytoplankton still increased while the contributions of nano- and microphytoplankton decreased at the CML.

4. Discussion

4.1. Sources of Uncertainty in the Algorithm

Two main sources of uncertainties in R17 are those associated with estimated values of $\xi$ and those in the allometric parameterization [13]. Deriving a new allometric relationship for phytoplankton in the SCS was out of the scope of our study, thus, we mainly focused on the uncertainties associated with $\xi$. The value of $\xi$ was estimated based on the observed $a_{\mathrm{ph}}^{*}$(676) or $a_{\mathrm{LH}}^{*}$(676) [12]. If the value of $a_{ci}^{*}$ is reliable, the uncertainty of the $\xi$-estimated method in [12] is mainly due to the error in the value of a^m based on the field data. The value of a^m directly impacts the estimated values of $\xi$ from $a_{\mathrm{ph}}^{*}$(676) or $a_{\mathrm{LH}}^{*}$(676). To evaluate the overall uncertainties in the estimations of C and size-partitioned phytoplankton carbon, we added 0 to 30% uncertainties in the a^m into the algorithm. Regardless of whether $a_{\mathrm{ph}}^{*}$(676) or $a_{\mathrm{LH}}^{*}$(676) was used, the overestimation of a^m resulted in underestimation of C and C_p and overestimation of C_n and C_m (Figure 11). For the C derived from $a_{\mathrm{ph}}^{*}$(676), when $a_{\mathrm{ph}}^{*}$(676) was >0.025 m² mg⁻¹, a small underestimation (~5%) was observed, even when >20% uncertainty of a^m was added into the algorithm. However, significant underestimation (~30%) was observed when $a_{\mathrm{ph}}^{*}$(676) was in the range of 0.020–0.025 m² mg⁻¹ and >20% uncertainty of a^m was added into the algorithm. For other cases, the uncertainty of algorithm-derived C showed an increasing trend with increasing uncertainty in a^m, but underestimation was generally <25%. For the C_p derived from the $a_{\mathrm{ph}}^{*}$(676), when $a_{\mathrm{ph}}^{*}$(676) was >0.025 m² mg⁻¹, a small underestimation (~5%) was observed even when >20% uncertainty of a^m was added into the algorithm. The underestimation increased up to 20–50% when $a_{\mathrm{ph}}^{*}$(676) was <0.025 m² mg⁻¹ and >10% uncertainty of a^m was added into the algorithm. As for C_n and C_m, when $a_{\mathrm{ph}}^{*}$(676) was in the range of 0.020–0.025 m² mg⁻¹, a significant overestimation (>100% for C_n and >1000% for C_m) was observed even when only 5% uncertainty of a^m was added into the algorithm. For other cases, smaller overestimation (~10% for C_n and ~30% for C_m) was observed. For $a_{\mathrm{LH}}^{*}$(676), the uncertainty of algorithm-derived C and C_p showed an increasing trend with increasing uncertainty in a^m when $a_{\mathrm{LH}}^{*}$(676) ranged from 0.011 to 0.013 m² mg⁻¹. Approximately 20% underestimation of C and 35% underestimation of C_p occurred when 10% uncertainty of a^m was added into the algorithm. For C_n and C_m, when $a_{\mathrm{LH}}^{*}$(676) was >0.012 m² mg⁻¹, significant overestimations (>60% for C_n and >110% for C_m) were observed when >5% uncertainty of a^m was added into the algorithm.

On the whole, the effect of the uncertainty of a^m was relatively weak for underestimation of C [<35% for $a_{\mathrm{ph}}^{*}$(676) data and <45% for $a_{\mathrm{LH}}^{*}$(676)] and C_p [<40% for $a_{\mathrm{ph}}^{*}$(676) data and <60% for $a_{\mathrm{LH}}^{*}$(676)]. However, the effect of the uncertainty of a^m was significant for overestimation of C_n and C_m when $a_{\mathrm{ph}}^{*}$(676) ranged from 0.02 to 0.025 m² mg⁻¹ or $a_{\mathrm{LH}}^{*}$(676) was >0.012 m² mg⁻¹. Overall, the impact of uncertainty of a^m on the $a_{\mathrm{LH}}^{*}$(676) data was greater than that on the $a_{\mathrm{ph}}^{*}$(676) data. In this study, 80% of $a_{\mathrm{ph}}^{*}$(676) values were in the range of 0.012–0.021 m² mg⁻¹, and 80% of $a_{\mathrm{LH}}^{*}$(676) values were within 0.0116–0.0125 m² mg⁻¹, and different a^m values were chosen according to 95% quantile values for $a_{\mathrm{ph}}^{*}$(676) and $a_{\mathrm{LH}}^{*}$(676) data, respectively.

When the R17 algorithm was transplanted into the a_pg($\lambda$) data, Chla_LH, which was determined using the absorption line height method [45], also introduced uncertainties into the algorithm. Compared to the in situ Chla, the averaged relative error of Chla_LH could reach 20%. We evaluated the uncertainties in the estimations of C and size-partitioned phytoplankton carbon when 0–20% uncertainties were added into Chla_LH (Figure 12). The uncertainty of algorithm-derived C and size-partitioned phytoplankton carbon showed an increasing trend with increasing uncertainty in Chla_LH. A small uncertainty of C (around −20% to 10%) was observed when $a_{\mathrm{LH}}^{*}$(676) was >0.0135 m² mg⁻¹ and even when 20% uncertainty was added into Chla_LH. For other cases, the uncertainty of C slightly increased but was <35% underestimation even if 20% uncertainty was added into the Chla_LH. Similarly, a small uncertainty of C_p (around −25% to 10%) was observed when $a_{\mathrm{LH}}^{*}$(676) was >0.013 m² mg⁻¹ and 10% uncertainty was added into Chla_LH. The uncertainty of C_p (around −40% to −55%) increased when $a_{\mathrm{LH}}^{*}$(676) was <0.0125 m² mg⁻¹ and >10% uncertainty was added into the Chla_LH. As for C_n and C_m, a small overestimation (<10%) was observed when $a_{\mathrm{LH}}^{*}$(676) was >0.013 m² mg⁻¹ and 5% uncertainty was added into Chla_LH. When >10% uncertainty was added into Chla_LH, significant overestimation of C_n and C_m (>200% for C_n and >1000% for C_m) was observed when $a_{\mathrm{LH}}^{*}$(676) ranged from 0.012 to 0.014 m² mg⁻¹.

Overall, the effect of Chla_LH uncertainty on C and C_p estimations (−35% to 10% for C and −55% to 10% for C_p when uncertainty of Chla_LH was <20%) was smaller than that on C_n and C_m estimations, which could reach >100% for C_n and >1000% for C_m when uncertainty of Chla_LH was >10%.

4.2. Relationship between C and Chla

The values of C and Chla are both used as proxies for the standing stock of phytoplankton biomass, and whether C or Chla is the appropriate proxy is controversial. The arguments for Chla are as follows: (i) chlorophyll-a is the transducer in the energy-ecosystem, and (ii) measurement of Chla is the simplest of all biological parameters [8]. For C, the argument is that C is a more direct parameter in the study of the carbon cycle and other climate-relevant variables in the ocean [8]. However, C and Chla can convert into each other through $\chi$, and it is no longer necessary to make a choice between C and Chla [8]. Considering that the demand is for C in biogeochemical research but that Chla is the most commonly measured biological parameter, whether in situ or in remote sensing platform, we analyzed the relationship between C and Chla to facilitate the conversion between the two parameters. Because the value of $\chi$ varies among different algae species, we also analyzed the variability in relationships between C and Chla among different dominant phytoplankton species to provide more precise conversion parameters. As shown in Figure 13a, we detected significant covariation between C and Chla, which was consistent with the results reported in previous studies [8,53,54]. In previous studies, the form of C = iChla^j, where i and j are fitted parameters, was used to describe the relationship between C and Chla. The results from Buck et al. [54], Sathyendranath et al. [14], Marañón et al. [53], and Loisel et al. [55] are plotted in Figure 13a. The empirical relationships from Buck et al. [54] (C = 83Chla^0.69) and Sathyendranath et al. [14] (C = 64Chla^0.63) overestimated C when Chla was <0.3 mg m⁻³. The empirical relationships from Marañón et al. [53] (C = 62Chla^0.89) and Loisel et al. [55] (C = 73Chla^0.91) performed better for our data, although they also overestimated C when Chla was <0.2 mg m⁻³. The empirical relationship between C and Chla in our study was C = 46Chla^0.8 (

Table 3. Empirical power-law relationships between C and Chla in samples containing different dominant phytoplankton species in previous studies and this study.

Empirical Relationship	Reference/Dominated Phytoplankton Species	Num	R	RMSE	Bias	MAE
C = $83Chl{a}^{0.69}$	Buck et al. (1996) [54]	215	0.90	19.96	2.53	2.53
C = $64Chl{a}^{0.63}$	Sathyendranath et al. (2009) [14]	215	0.90	13.29	2.13	2.13
C = $62Chl{a}^{0.89}$	Marañón et al. (2014) [53]	215	0.88	8.19	1.42	1.51
C = $73Chl{a}^{0.91}$	Loisel et al. (2018) [55]	215	0.88	11.50	1.63	1.66
C = $46Chl{a}^{0.80}$	This study/All data	215	0.89	5.85	1.20	1.40
C = $78Chl{a}^{1.28}$	This study/Prochlorococcus	65	0.91	1.60	1.02	1.19
C = $64Chl{a}^{1.08}$	This study/Synechococcus-like cyanobacteria	29	0.82	4.25	1.08	1.36
C = $53Chl{a}^{0.74}$	This study/Haptophytes	60	0.82	6.21	1.06	1.24
C = $49Chl{a}^{0.84}$	This study/Diatoms	7	0.84	9.97	1.09	1.29

). The value of j could be used to describe how $\chi$ varied with Chla. The $\chi$ became constant when j = 1, which suggested that values of $\chi$ decreased as Chla increased when j was < 1, whereas the values of $\chi$ increased as Chla increased when j was > 1. All values of j in the five relationships were < 1. The value of j in our relationship was lower than those reported by Marañón et al. [53] and Loisel et al. [55] but higher than those reported by Buck et al. [54] and Sathyendranath et al. [14]. These results suggested that the values of $\chi$ decreased as Chla increased and that the variability in $\chi$ with Chla in our study was more significant than that found by Marañón et al. [53] and Loisel et al. [55] but more modest than that reported by Buck et al. [54] and Sathyendranath et al. [14].

In reality, changes in nutrients, irradiance, temperature, cell size (phytoplankton species) and Chla are all intimately related to each other in the marine environment, thus, it would be difficult to rule out the possible effects of these factors on $\chi$ [8]. As shown in Figure 13a, the dominant phytoplankton species varied from Prochlorococcus at the lowest Chla (~0.1 mg m⁻³) to diatoms at the highest Chla (~1 mg m⁻³). Xing et al. (2019) [21] reported that variability of phytoplankton community dominated the values of Chla:b_bp at subsurface chlorophyll maximum layer in the SCS based on Bio-Argo data. Accordingly, in the SCS basin, change in dominant phytoplankton species may be one of the main factors resulting in variability in $\chi$. To study the influence of variability in $\chi$ among different dominant algae species on Chla-to-C relationships, different empirical relationships between C and Chla were established among different dominant phytoplankton species based on our dataset (Table 3). Since dominant phytoplankton species will vary in the different specific range of Chla, the values of i in the relationships can be used to describe the rough $\chi$ values of different phytoplankton species. The values of i in Prochlorococcus (i = 78), Synechococcus-like cyanobacteria (i = 64), haptophytes (i = 53), and diatoms (i = 49) decreased sequentially, which suggested that the values of $\chi$ gradually decreased from Prochlorococcus to diatom dominant waters. The relative error between different relationship-estimated and $a_{ph}^{*}\left(676\right)$-estimated C was calculated as 100%$\frac{C_{\mathrm{relationship}}-C}{C}$, where C_relationship was calculated using the empirical relationships in Table 3 for waters dominated by different phytoplankton species, and C was estimated based on $a_{ph}^{*}\left(676\right)$. As shown in Figure 13b, the median relative error of the Prochlorococcus relationship (~4%) was around 0 when the dominant phytoplankton species was Prochlorococcus, whereas it increased to ~47% in diatom dominant waters. The median relative error of the Synechococcus-like cyanobacteria relationship was ~11% in Synechococcus-like cyanobacteria dominant waters, but the median relative errors of the Synechococcus-like cyanobacteria relationship had a greater deviation from 0% in Prochlorococcus (~24%), haptophyte (~–11%), and diatom (30%) dominant waters. For the haptophyte and diatom relationships, the largest median relative errors (both > 50%) were observed in Prochlorococcus dominant waters, and the median relative errors decreased as the cell size of the dominant algae increased. The smallest median relative errors of haptophytes (~4%) and diatoms (~9%) were observed in the haptophyte and diatom dominant waters, respectively. For the total relationship, the trend of median relative errors was similar to that of the diatoms relationship. The median relative errors of the total relationship decreased as the cell size of dominant algae increased. The largest median relative error of the total relationship was ~57% in the Prochlorococcus dominant waters, and in diatom dominant waters, the median relative error was ~3%. These results suggested that variability in values of $\chi$ due to changes in phytoplankton species can introduce apparent uncertainty to C converted from Chla when using a constant value of $\chi$. Therefore, it is better to identify the dominant phytoplankton species to derive an accurate $\chi$ before converting Chla to C through $\chi$.

4.3. General Vertical Profile of Phytoplankton Carbon in the SCS Basin

Figure 14a shows the general vertical distribution of C, size-partitioned phytoplankton carbon, and $\chi$ for oligotrophic stratified waters in the open SCS that is based on the profile shape shown in Figure 9 and Figure 10. It should be noted that C_n and C_m are sensitive to the choice of a^m, thus, interpretation of their profile shape should be made with caution. Overall, in the open SCS, the vertical profile of C displayed a Gaussian distribution with a peak near the bottom of the euphotic zone and the top of the nutricline, which was similar to that of the vertical Chla distribution [11,56]. C and Chla exhibited significant covariation (Figure 10 and Figure 13a), and it indicated that photoacclimation has little impact on the formation of the subsurface Chla maximum layer, which was consistent with results of Xing et al. [21].

The open SCS is an oligotrophic environment that is characterized by a “microbial loop” or “microbial food web” due to strong stratification [57]. Most (92%) of our survey stations were in the most oligotrophic condition. As shown in Figure 14a, the picophytoplankton dominated the phytoplankton biomass in the euphotic zone, and vertical distribution of C_p was similar to that of C (displayed a Gaussian distribution). This phenomenon was also reported by Uitz et al. [41], who found that the picophytoplankton biomass displayed a distinct deep maximum that was slightly sharper than that for nanophytoplankton biomass in S1–S4 trophic conditions. Meanwhile, the results in Sauzède et al. [11] at the Bermuda Atlantic Times Series Study site also showed that the picophytoplankton dominated the whole euphotic zone from June to October, and the deep maximum of picophytoplankton biomass was also sharper than that of nanophytoplankton biomass. We used HPLC data to analyze the dominant phytoplankton species and found that the phytoplankton community varied from Synechococcus-like cyanobacteria dominating at the sea surface to haptophytes dominating at the CML (Figure 14b). However, haptophytes are always classified as nanophytoplankton in many oceanic regions, ranging from tropical to polar systems [58,59], which was contrary to our result that the picophytoplankton was dominant at the CML. Moon-van der Staay et al. [59] reported that prymnesiophytes (class Prymnesiophyceae, division Haptophyta) was dominant among picoeukaryotes in the Pacific Ocean based on molecular biological techniques. Similarly, Ho et al. [60] suggested that haptophytes were the major picoeukaryotic phytoplankton in the northern SCS based on the relationship between concentrations of 19′hexanoyloxy-fucoxanthin and cell abundances of picoeukaryotes. Figure 14c shows a strong covariation between 19′hexanoyloxy-fucoxanthin concentrations and cell abundances of picoeukaryotes based on our data. A reasonable explanation for this contradictory result (haptophytes dominated the CML but picophytoplankton also dominated the CML) is that haptophytes in the open SCS were mostly pico-size. Therefore, the increase of haptophytes was the main factor involved in the formation of the CML. Thus, it was not surprising that the values of F_p and $\mathsf{\chi }$ increased at the CML (Figure 9 and Figure 10) in the open stratified SCS.

5. Conclusions

We transplanted the remote sensing absorption-based phytoplankton carbon algorithm (R17) from Roy et al. [15] into field $a_{ph}^{*}$(676) and $a_{\mathrm{LH}}^{*}$(676) to obtain vertical profiles of C and size-partitioned phytoplankton carbon in the SCS. The accuracy of a^m was an important factor affecting the accuracy of C and size-partitioned phytoplankton carbon estimations. Different values of a^m were chosen according to the 95% quantile values in the $a_{ph}^{*}$(676) and $a_{\mathrm{LH}}^{*}$(676) datasets, respectively. For $a_{ph}^{*}$(676), the values of R, MAE, and bias between estimated and field C_p were 0.58, 2.14, and 0.62, respectively, and for a_pg(676) the values were 0.53, 1.9, and 1.39, respectively. The algorithm performed well for field data from the SCS. The vertical profiles of C and size-partitioned phytoplankton carbon in the SCS were then derived from field $a_{ph}^{*}$(676) and $a_{\mathrm{LH}}^{*}$(676). The vertical profiles of C and C_p displayed Gaussian distributions, and the CML appeared at the bottom of the euphotic zone and the top of the nutricline in the stratified open SCS basin. Picophytoplankton was the dominant phytoplankton carbon contributor within the whole euphotic zone. The dominant picophytoplankton species varied from Synechococcus-like cyanobacteria at surface to pico-sized haptophytes at the CML. We detected strong covariation between C and Chla, and they can be converted to each other through an accurate value of $\chi$. These results show the vertical profiles of phytoplankton biomass from the perspective of carbon mass and provide basic information for understanding primary production, the carbon cycle, and climate change in the SCS.