PP of Prochlorococcus, Synechococcus, and picoeukaryotes was estimated from a modification of the carbon-based PP model of Behrenfeld et al. (2005).

where PP is the depth integrated primary production (mg C m^-2 d^-1), C is the carbon biomass of picophytoplankton in the surface layer (mg C m^-3), μ is the growth rate (d^-1), Z_eu is the depth of euphotic zone (m), and h(I₀) describes how changes in surface irradiance influence the depth-dependent profile of carbon fixation.

The C of picophytoplankton was computed as the product of cell abundance and cellular carbon content using published CCF. The minimum, maximum, and average values of CCF of unialgal cultures for Prochlorococcus, Synechococcus, and picoeukaryotes were compiled by Buitenhuis et al. (2012) and shown in Table 1. In this study, the average CCF of 36, 255, and 2590 fg C cell^-1 for Prochlorococcus, Synechococcus, and picoeukaryotes, respectively, were used to calculate the group-specific picophytoplankton biomass.

The temperature-dependent growth rates of Prochlorococcus, Synechococcus, and picoeukaryotes were estimated from published growth–temperature relationships (Johnson et al., 2006; Chen et al., 2014; Pittera et al., 2014). Binominal equation was used to describe the temperature dependence of growth rate of Prochlorococcus, as their relationships were not linear and not suitable for the application of Arrhenius equation. An Arrhenius equation was used to describe the temperature dependence of growth rate of Synechococcus and picoeukaryotes, μ = μ_ce^-E/kT, in which μ is the growth rate varying with temperature, μ_c is a normalization constant, E is the activation energy (eV, 1 eV = 96.49 kJ mol^-1), k is the Boltzmann constant (8.62 × 10^-5 eV K^-1), and T is absolute temperature (K) (Brown et al., 2004).

According to the original model (Behrenfeld et al., 2005), Z_eu was calculated as:

The h(I₀) is computed as:

As Z_eu in the original model was developed for oligotrophic and upwelling waters and may overestimate the Z_eu in the turbid coastal waters (Shang et al., 2011; Tripathy et al., 2012), the MODIS/Aqua Z_eu products based on inherent optical properties (IOP-approach) (Lee et al., 2005, 2007; Shang et al., 2011) was used in the Bohai Sea ¹.

The PPs of Prochlorococcus, Synechococcus, and picoeukaryotes were calculated according to the Eqs 1–3. The PP_Pico is the sum of PPs of Prochlorococcus, Synechococcus, and picoeukaryotes.

To test the reliability and validity of the modified CbPM method, we compared the estimated PP_Pico by CbPM with the actually measured PP_Pico data using the radiolabeled carbon uptake method (i.e., ¹⁴C method). Firstly, for this purpose, a field dataset of PP and abundance of picophytoplankton (Figure 1 and Supplementary Data Sheet 1) was compiled from Atlantic Meridional Transect (Marañón et al., 2003), Southern Ocean (Smetacek et al., 1997), Atlantic Ocean (Li, 1994; Jardillier et al., 2010; Hartmann et al., 2014), South China Sea (Chen et al., 2014; Xie and Huang, unpublished data), and French Polynesian atoll lagoons (Charpy and Blanchot, 1998). In this field datasets, the PP_Pico was measured using the ¹⁴C uptake method, and the abundance of picophytoplankton were measured using flow cytometry.

A case study and test of concept of the modified CbPM was conducted in the Bohai Sea, China to estimate the PP_Pico. The Bohai Sea is a large semi-enclosed shallow sea basin in the western Pacific Ocean (117° 30′–121°E, 37–41°N), with an average depth of 18.7 m (Zhang et al., 2004). It includes three coastal bays (Liaodong, Bohai, and Laizhou Bays) and central Bohai Sea. Summers are wet and warm. Winters are cold and dry, with strong northerly monsoons blowing from late November to March. Spring and autumn are transitional seasons between summer and winter (Tang, 2003). The Bohai Sea in general has been extensively studied since the late 1950s (Zhang et al., 2004). Although the distributions of phytoplankton, Chl a, PP, and nutrients are well defined (Sun et al., 2002; Wei et al., 2004; Zhang et al., 2004), little is known about the PP_Pico in the Bohai Sea.

Four field expeditions were conducted during 2005 (March 26 to April 12, June 10 to July 11, September 9–24, and November 30 to December 8) in the Bohai Sea. During December, samples were collected only from the surface layer of the western areas. During the other sampling periods, when the water depth was less than 10 m, samples were collected only from the surface layer; when the water depth was between 10 and 20 m, samples were collected from the surface, 5 and 10 m layers; and when the water depth was deeper than 20 m, water samples were collected from the surface, 10 and 20 m layers using 10-L Niskin bottles.

Triplicate 2 mL water samples were collected from Niskin bottles mounted on a Rosette sampling assembly and were fixed on-board to a final concentration of 1% glutaraldehyde. After 15–20 min of fixation in dark at room temperature, samples were immersed in liquid nitrogen for 10 min and then stored in -80°C until further analysis. Picophytoplankton were analyzed on an Epics Altra II flow cytometer (Beckman Coulter, United States) with a 306C–5 argon laser (Coherent, United States) according to Jiao et al. (2002).

Environmental variables of Bohai Sea required for estimating PP_Pico were compiled from the monthly average Level-3 4-km MODIS/Aqua data. These include sea surface temperature (°C), the depth of euphotic zone (Z_eu; m), diffuse attention coefficients at 490 nm (k490: m^-1), surface Chl (mg m^-3), and surface photosynthesis active radiation (I₀; moles photons m^-2 h^-1) for the corresponding sampling stations from March to December 2005. Data were downloaded from the NASA Ocean Color website (see text footnote 1). The temperature profile data of Bohai Sea was extracted from the World Ocean Atlas 2013 (Ocean Data View website ²) and the resolution was 0.25° × 0.25° grids.

Analysis of variance (ANOVA) was used to assess differences in picophytoplankton abundances at different depth during each expedition (SPSS 18) and Model 2 regression (Reduced Major Axis) was used to assess the relationships between selected parameters (Ricker, 1973; Blackburn and Gaston, 1998).

The group-specific growth rates of the picophytoplankton community were significantly related to temperature (Figure 2). For Prochlorococcus, the laboratory-determined growth rate of the two most abundant Prochlorococcus ecotypes (eMIT9312 and eMED4) in tropical and temperate waters were compiled from Johnson et al. (2006) and Biller et al. (2015). Temperature was a statistically significant predictor of growth rates for both Prochlorococcus eMIT9312 and eMED4 (r² = 0.78, P < 0.001 and 0.60, P < 0.01, respectively. Figures 2A,B). As the two high light-adapted Prochlorococcus ecotypes are abundant in tropical and temperate waters, the relationships between growth rate and temperature were used to estimate the growth of Prochlorococcus in the CbPM.

For Synechococcus, the average temperature-dependent growth rate of six marine Synechococcus strains (tropical, A15-37 and M16.1; mid-latitude, WH7803 and ROS8604 and high-latitude, MVIR-16-2 and MVIR-18-1; Pittera et al., 2014) was computed for the temperature range of 10–34°C). Temperature was appeared also as a statistically significant predictor (r² = 0.92, P < 0.001; Figure 2C) that closely correlated with the growth rates of Synechococcus.

The dataset used to simulate the relationships between temperature and the growth rates of Prochlorococcus and Synechococcus was from studies that used cultured strains isolated from particular marine sites (Johnson et al., 2006; Pittera et al., 2014; Biller et al., 2015). The data from limited number strains does not represent the full range of growth characteristic of Prochlorococcus and Synechococcus, although these datasets were widely used in other modeling studies (Boyd et al., 2015; Hynes et al., 2015; Stawiarski et al., 2016; Grossowicz et al., 2017). We recognize that the high phenotypic diversity of Prochlorococcus and Synechococcus combined with the limited number of cultured strains for which there are growth rates data represents an inherent limitation of model parameterizations.

While the prokaryotic fraction of picophytoplankton is dominated by two genera, Prochlorococcus and Synechococcus, the picoeukaryotic fraction is much more diverse and nearly every algal classes contain its representative species (Vaulot et al., 2008; de Vargas et al., 2015; Worden et al., 2015). Hence, the temperature-dependent growth rate of single picoeukaryotic taxa would not have been suitable for estimating growth rate of total picoeukaryotic community. Therefore, the temperature-dependent growth rate of picoeukaryotes was estimated using the field-measured growth rates of picoeukaryotic community reported by Chen et al. (2014). When the total Chl concentration is higher than 0.5 mg m^-3, the growth rates of picoeukaryotes were related with temperature (r² = 0.41, P < 0.001; Figure 2D). However, when the total Chl concentration is less than 0.5 mg m^-3, the growth rates of picoeukaryotes were not significantly related with temperature (P > 0.05). The variability in the relationship between growth rates of picoeukaryotes and temperature is relatively large (Figure 2D), suggests that environmental factors which were not included in our model (e.g., light intensity, nutrients, Chl concentration, etc.) were important for the growth rates of picoeukaryotes (Chen et al., 2014). Based on the analyses presented in Figure 2D, the model may overestimate the growth rate of picoeukaryotes by an average of 58%. Picoeukaryotes represent variable fraction of the total picophytoplankton community (Table 2) and contribution to their photosynthetic carbon production (Figure 3). Hence, the proposed model introduces a level of uncertainty to the estimation of PP_Pico. More field data about the relationship between temperature and the growth rates of picoeukaryotes and the integration of other environmental factors into the estimation of the growth rates of picoeukaryotes would help to improve the accuracy of the model estimates.

To test the influence of CCF on the calculated PP_Pico, the PP_Pico is calculated according to Eq. 4 (PP = C × μ), in which C is the product of the measured cell abundances and CCF values. The CCFs for each functional type of picophytoplankton is selected from the minimum to the maximum at increments of 10% (Buitenhuis et al., 2012). Sensitivity analysis showed that there is some uncertainty in the CCF, with larger variations for picoeukaryotes (∼5-fold) than Prochlorococcus and Synechococcus (two- to threefold), and this can lead to a ∼3-fold variation in computed PP_Pico (Figure 3). It follows that the determination of appropriate CCF is essential for accurate estimation of the picophytoplankton biomass and production. Besides the use a fixed CCF, the CCF could be calculated from cell size or volume (Buitenhuis et al., 2012). However, the cell size of different phytoplanktonic group could not be separated by the traditional flow cytometry method (Jiao et al., 2002; Buitenhuis et al., 2012). In future, the applications of new technologies (e.g., multi-laser flow cytometry method and the combination of fluorescence in situ hybridization and flow cytometry, etc.) into the measurement of calibrated cell size of particular picophytoplankton group could improve the accurate estimation of the picophytoplankton biomass (Thompson and van den Engh, 2016; Riou et al., 2017).

Buitenhuis et al. (2012) compiled the CCF from both unialgal cultures and in situ samples. The in situ CCF was calculated from the cell sizes estimated from flow cytometry and carbon:volume relationships (Campbell et al., 1994; Garrison et al., 2000; Worden et al., 2004; Bec et al., 2008). Due to the large variability of ratio of cell carbon:volume of picoplankton, the use of cell volume does not provide a clear advantage over CCF to estimate carbon biomass. Buitenhuis et al. (2012) compared the influence of the CCF directly measured and in situ estimated (the average values were 60, 154, and 1319 fg C cell^-1 for Prochlorococcus, Synechococcus, and picoeukaryotes, respectively) on the estimation of carbon biomass using they compiled global picophytoplankton abundance dataset. Their analyses showed that the average carbon biomass using the in situ CCFs is 72% of that estimated using from that directly measured. Using the dataset in this study (Supplementary Data Sheet 1), we compared the influence of the direct and in situ CCFs on the estimation of carbon biomass and PP_Pico. The estimated carbon biomass using the direct and in situ CCFs was 10.0 ± 10.8 and 10.0 ± 7.7 mg C m^-3 (n = 171), respectively, and the estimated PP_Pico was 7.3 ± 11.6 and 5.2 ± 6.9 mg C m^-3 d^-1, respectively. Although the differences in cell carbon content in laboratory grown and in situ populations could introduce uncertainties in the estimation of carbon biomass and PP_Pico, other well-accepted models and modeling studies used these CCFs to represent in situ processes (Buitenhuis et al., 2012). In future, the routine measurement of calibrated cell size of particular picophytoplankton group as the additional measurement was strongly recommended and could improve the accurate estimation of the picophytoplankton biomass and production (Thompson and van den Engh, 2016; Riou et al., 2017).

Model-estimated and measured PP_Pico were compared using the CbPM model based on the datasets of picophytoplankton abundance and their concomitantly measured PP using the ¹⁴C-uptake method. The data sets represent a wide geographic area and ocean domains and include the Atlantic Meridional Transect (Marañón et al., 2003), Southern Ocean (Smetacek et al., 1997), Atlantic Ocean (Li, 1994; Jardillier et al., 2010; Hartmann et al., 2014), South China Sea (Chen et al., 2014; Y. Xie and B. Huang, unpublished data), and French Polynesian atoll lagoons (Charpy and Blanchot, 1998) (Figure 1 and Supplementary Data Sheet 1).

The computed PP_Pico (sum of PPs of Prochlorococcus, Synechococcus, and picoeukaryotes), ranged from 0.04 to 104.8 mg C m^-3 d^-1, and the estimated and measured PP_Pico were significantly related (r² = 0.53 and 0.46 for normal and log₁₀-transformed data, respectively, P < 0.001, n = 171; Figure 4). This suggested the practical applicability of CbPM to estimate the PP_Pico. A Model 2 regression was used to assess the relationship between directly measured PP_Pico (using size fractionated ¹⁴C uptake) and model predicted PP_Pico. The slope of the relationship was greater than 1 (i.e., slope = 1.73, CI = 1.49–1.99), suggesting that our model overestimated PP_Pico by an average of 73% comparing to the measured PP_Pico. This overestimation depends on the relative composition of the picophytoplankton as well as the model’s representation of their growth characteristics. The use of variable CCFs and the larger data sets representing diverse community and growth conditions will improve the future model performance.

PP of total phytoplankton community is well characterized in the global ocean (Behrenfeld and Falkowski, 1997; Field et al., 1998; Tilstone et al., 2015). However, the contribution of picophytoplankton to total PP is still poorly understood. This is because that the ratio of in situ PP_Pico to total PP using the ¹⁴C-uptake method is extensively time-consuming and labor-intensive (Uitz et al., 2010; Landry et al., 2011; Laws, 2013). Although pigment-based modeling of PP has been applied to estimate the size-dependent PP (Uitz et al., 2008, 2010, 2012), due to the plasticity of Chl:C in response to the variability of environmental parameters, C rather than Chl is considered more suitable to estimate the PP (Westberry et al., 2008). Moreover, since the picoeukaryotes among picophytoplankton could not be separated from nano- and micro-phytoplanktonic eukaryotes through pigment analysis, the unique contribution of picoeukaryotes to total PP of phytoplankton is hard to be characterized, despite that the contribution of picoeukaryotes could be comparable to picocyanobacteria in some marine environments (Worden et al., 2004, 2015; Jardillier et al., 2010; Uitz et al., 2010). The modified CbPM in this study provides a carbon-based protocol which also takes into consideration the contribution of picoeukaryotes for PP_Pico estimation. As compared to the ¹⁴C-uptake method, due to the simplicity and convenience, CbPM can likely become a promising substitute method for large-scale survey for PP_Pico estimation in future.

The PP_Pico model was applied in the Bohai Sea, China, using the in situ picophytoplankton abundance and remotely sensed environmental variables. A total of 131 picophytoplankton abundance samples were collected during four seasonal 2005 cruises. Synechococcus and picoeukaryotes were identified and enumerated using flow cytometry (Jiao et al., 2002). Prochlorococcus was not detected in all samples. Previous studies showed that although Prochlorococcus was detected in the offshore waters of East China Sea and South China Sea, they were not detected in the Yellow Sea and Bohai Sea (Jiao and Yang, 2002; Jiao et al., 2002, 2005; Bai et al., 2012; Guo et al., 2014).

The abundance and distributions of Synechococcus and picoeukaryotes were shown in Table 2 and Figure 5. During March 2005, the abundances and distributions of Synechococcus and picoeukaryotes were similar and higher in the southern region than northern regions (Figures 5A,B). During June, the abundances of Synechococcus were higher in Laizhou Bay and Liaodong Bay mouth (Figure 5C). Picoeukaryotes abundance was higher in the Liaodong and Laizhou Bays (Figure 5D). During September, Synechococcus and picoeukaryotic abundance were generally higher along the eastern and north regions of the Bohai Sea (Figures 5E,F). During December, Synechococcus and picoeukaryotic abundance were generally higher in the offshore areas of the western areas of the Bohai Sea (Figure 5G). No significant depth-dependent variation in the abundance of picophytoplankton was observed during any of the cruises (ANOVA, P > 0.05; Supplementary Figures S1A–C).

Table 2 and Supplementary Figures S2, S3 present the environmental variables in the Bohai Sea. The temperature increased from March to September (Supplementary Figure S2 and Table 2) and was isothermal during the March, September, and December (Supplementary Figure S3). Chl concentration was relatively stable and higher than 4.2 mg m^-3 during the four cruises. I₀ and Z_eu increased from December to June. k490 was relatively stable during the four cruises (Table 2). The equations for Z_eu in the original CbPM model were derived from the oligotrophic and upwelling waters. The application of the equations for Z_eu might overestimate the Z_eu in turbid coastal water which is a seasonal condition in the Bohai Sea, and thus overestimate the calculated PP_Pico using modified CbPM model (Behrenfeld et al., 2005; Shang et al., 2011; Tripathy et al., 2012). Shang et al. (2011) showed that the MODIS/Aqua Z_eu products based on IOP-approach (Lee et al., 2005, 2007) were well related with the field-measured Z_eu in the China Sea (including the coastal and shelf waters). Hence, the MODIS/Aqua Z_eu products was used in the Bohai Sea.

The estimated PPs of Synechococcus, picoeukaryotes and picophytoplankton were shown in the Table 2 and Figure 6. The PP_Pico ranged from 0.1 to 11.9, 29.9 to 432.8, 5.5 to 214.9, and 2.4 to 65.8 mg C m^-2 d^-1 during March, June, September, and December, respectively in Bohai Sea. The PP_Syn, PP_Euk, and PP_Pico were higher in June and September than that in March and December (Figure 6). Though the abundance of picoeukaryotes was lower than Synechococcus (Figure 5), since picoeukaryotes have higher CCF and growth rate as compared with Synechococcus (Buitenhuis et al., 2012; Chen et al., 2014), the PP_Euk was comparable with the PP_Syn (Figure 6), which is in accordance with the results in the Atlantic Ocean (Worden et al., 2004; Jardillier et al., 2010). In future, the simultaneously measurement of the abundance, PP and growth rates of the picophytoplankton during the field campaigns could give more information and opportunity for the improvement of the PP_Pico model.