A total of 2,791 samples collected in the North Atlantic region and analyzed by High Performance Liquid Chromatography (HPLC) were used in this study (Figure 1), spanning 1995–2014. This dataset comprised of samples from: the Atlantic Meridional Transect (AMT) cruises 1-23 (Gibb et al., 2000; Barlow et al., 2002; Aiken et al., 2009; Brewin et al., 2010; Airs and Martinez-Vicente, 2014a,b,c; Brewin et al., 2015); the GeP&CO program (Dandonneau et al., 2004); the North Atlantic bloom experiment (Werdell et al., 2003; Westberry et al., 2010); the eastern Atlantic Ocean (Brotas et al., 2013); the North Atlantic, collected by the Bedford Institute of Oceanography (Sathyendranath et al., 2001; Devred et al., 2006); the Western Channel Observatory in the English Channel (Station L4 and E1; Smyth et al., 2010); a series of UK NERC-funded research cruises (D261, D262, D264, D325, JC011, JC037, and JCR656) in the North Atlantic and North Sea (Tilstone et al., 2015); and from the NASA bio-Optical Marine Algorithm Dataset (NOMAD Version 2.0 ALPHA, Werdell and Bailey, 2005), following the removal of any AMT data so as to avoid duplication. Details of HPLC methods used can be found in the aforementioned references.

Only samples collected within the top 20 m of the water column (or within the 1st optical depth as in the case of the NASA NOMAD dataset) were used [i.e., within the surface mixed-layer depth (rarely < 20 m; de Boyer Montégut et al., 2004)]. To control the quality of the pigment data, we used only HPLC data for which the total chlorophyll concentration was greater than 0.001 mg m⁻³ (Uitz et al., 2006), and the difference between the total chlorophyll concentration and the total accessory pigments was less than 30% of the total pigment concentration (Trees et al., 2000; Aiken et al., 2009; Brewin et al., 2015).

A total of 263 size-fractionated fluorometric chlorophyll (SFF) measurements collected previously in the North Atlantic region were also used in this study (Figure 1), spanning 1996–2015. This comprised of samples from: the Atlantic Meridional Transect cruises 2–23 (see Marañón et al., 2001; Serret et al., 2001; Robinson et al., 2002; Brewin et al., 2014a,b; Tilstone et al., 2017, for details); the Western Channel Observatory in the English Channel (Station L4 and E1; see Barnes et al., 2014, for details); and the NERC shelf seas biogeochemistry programme.

In all cases, ~200–300 ml samples were sequentially filtered through 20, 2, and 0.2 μm polycarbonate filters. Following filtration, pigments were extracted by storing the filters in 90% acetone at −20°C for between 10 and 24 h. Samples were then analyzed using a Turner Design Fluorometer, pre- and post-calibrated using pure chlorophyll-a in 90% acetone as a standard. The total chlorophyll concentration was taken as the sum of the size fractions for each sample. The concentration of chlorophyll passing through the 2 μm filter was designated C_p (picoplankton chlorophyll), chlorophyll retained on the 20 μm filter designated C_m (microplankton chlorophyll) and the chlorophyll retained on the 2 μm filter, having passed through the 20 μm filter, designated C_n (nanoplankton chlorophyll).

As a starting point, we used the three-component model of Brewin et al. (2010) to estimate the chlorophyll concentrations in three phytoplankton size classes [pico- (< 2 μm), nano- (2–20 μm), and micro-phytoplankton (>20 μm)] as a function of total chlorophyll in the study region (Figure 1). This approach has been successfully tuned to the global ocean (Brewin et al., 2015; Ward, 2015) as well as different oceanic regions, including: the Atlantic Ocean (North and South; Brewin et al., 2010, 2014b; Tilstone et al., 2014); the North East Atlantic (Brotas et al., 2013); the Indian Ocean (Brewin et al., 2012b); the Western Iberian coastline (Brito et al., 2015); the Mediterranean Sea (Sammartino et al., 2015); and the South China Sea (Lin et al., 2014). Estimating size-fractionated chlorophyll from satellite data (using satellite total chlorophyll as input to the three-component model) has been tested extensively with in situ data in different oceanic regions (Brewin et al., 2010, 2012b; Lin et al., 2014; Brewin et al., 2015).

The three-component model is based on two exponential functions (Sathyendranath et al., 2001), where the chlorophyll concentration of picoplankton (C_p, cells < 2 μm) and combined pico- and nanoplankton (C_p,n, cells < 20 μm) are obtained from

and

The parameters D_p,n and D_p determine the fraction of total chlorophyll in the two size classes (< 20 μm and < 2 μm, respectively) as total chlorophyll tends to zero, and Cp,nm and Cpm are the asymptotic maximum values for the two size classes (< 20 μm and < 2 μm respectively). The chlorophyll concentration of nano-phytoplankton (C_n) and micro-phytoplankton (C_m) are simply calculated as C_n = C_p,n − C_p and C_m = C − C_p,n.

A single set of model parameters was first derived by fitting (Equations 10 and 11) using a standard, nonlinear least-squared fitting procedure (Levenberg-Marquardt, IDL Routine MPFITFUN, Moré, 1978; Markwardt, 2008) with relative weighting (Brewin et al., 2011a). The parameters D_p,n and D_p were constrained to be less than or equal to one, since size-fractionated chlorophyll cannot exceed total chlorophyll. We used the method of bootstrapping (Efron, 1979; Brewin et al., 2015) to compute a parameter distribution, and from the resulting parameter distribution, median values and 95% confidence intervals were computed (see Table 3). The parameters D_p,n and D_p were found to be significantly different from the global parameters derived in Brewin et al. (2015) (see Table 3). The model was found to capture the trends in the fractions (F_p, F_n, F_p,n, and F_m) and absolute concentrations (C_p, C_n, C_p,n, and C_m) of the size classes as a function of total chlorophyll for the North Atlantic parameterization dataset (Figure 4).

Brewin et al. (2015) and Ward (2015) have investigated the influence of light availability and SST respectively on the parameterization of the three-component model. In the North Atlantic, seasonal variations in SST and the average light in the mixed-layer are highly correlated (Figure 1). Therefore, considering: (i) that there is, regionally, a covariation of SST with the average light in the mixed-layer (Figure 1); (ii) that three inputs are required to compute the average light in the mixed-layer (photosynthetically-active radiation, diffuse attenuation and mixed-layer depth), one of which is not amenable from remote-sensing (mixed-layer depth); and (iii) that the maturity (operational use) and accuracy of SST retrievals is very high (Merchant et al., 2014), we chose to investigate the influence of SST on model parameters in the study area, similar to the study of Ward (2015) for a global dataset.

Figure 4 illustrates the general inverse correlation between SST and total chlorophyll (r = −0.67 for SST and log₁₀(C)), highlighting that higher fractions of smaller cells (lower fractions of large cells) are typically associated with higher SST. To investigate if SST has any influence on the parameters of the three-component model, we partitioned the parameterization data into lower temperature waters (< 15°C) and higher temperature waters (≥15°C), and fitted the model separately to the two datasets of a roughly equal number (>1,000, see Table 3). We observed significantly different model parameters for high and low temperature waters (see Table 3 and Figure 4), suggesting a relationship between SST and model parameters. We then sorted the dataset according to SST, and conducted a running fit of the three-component model (Equations 10 and 11) as a function of SST with a bin size of 600 samples [chosen to ensure each fit had reasonable representation of observations over the entire trophic range (low to high chlorophyll)]. We used the method of bootstrapping (100 iterations) and derived median values and 95% confidence intervals on each parameter distribution (Figure 5).

Significant relationships between all model parameters (Cp,nm, Cpm, D_p,n, and D_p) and SST were observed (Figure 5). The relationship between SST and model parameters could be represented using a logistic function, such that Cp,nm and Cpm may be expressed as

and

where G₁ and G₄ control the upper and lower bounds of Cp,nm, G₂ represents the slope of change in Cp,nm with SST, and G₃ is the SST mid-point of the slope between Cp,nm and SST. For Cpm, H_i, where i = 1–4, is analogous to G_i for Cp,nm. The parameter D_p,n and D_p were expressed as

and

where J₁ and J₄ control the upper and lower bounds of D_p,n, J₂ represents the slope of change in D_p,n with SST, and J₃ is the SST mid-point of the slope between D_p,n and SST. For D_p, K_i is analogous to J_i for D_p,n. The parameters for Equations (12)–(15) were fitted using a nonlinear least-squared fitting procedure (Levenberg-Marquardt) with bootstrapping, and parameter values are provided in Table 4. The equations are seen to capture the relationships between parameters and SST accurately (Figure 5 and Table 4).

Figure 6 shows simulations of size-fractionated chlorophyll as a function of total chlorophyll for different SST, when incorporating (Equations 12–15) into the three-component model (Equations 10 and 11). In general, the performance for all size classes improved when using the SST-dependent parameterization, when compared with that using a single set of parameters (Figure 7), with a significant improvement in the correlation coefficient for C_p (Z-test, p < 0.05). Whereas modeled C_p,n, C_n, and C_p reach static asymptotes at high concentrations when using a single set of parameters (see Figure 7, top-row, horizontal purple dashed lines), the SST-dependent parameterization does not, and captures the variability in the size-fractionated chlorophyll at these higher concentrations.

Considering diatoms are known to dominate the microphytoplankton community in the North Atlantic during the initiation of the spring bloom when SST is still relatively low and nutrient concentrations high (Ducklow and Harris, 1993; Sieracki et al., 1993; Savidge et al., 1995), and that dinoflagellates typically increase in late summer and early autumn (McQuatters-Gollop et al., 2007; Widdicombe et al., 2010) when SST is generally at its highest in the North Atlantic, we investigated the use of SST to partition microplankton chlorophyll (C_m) into diatoms (C_diat) and dinoflagellates (C_dino). Figure 8A shows a significant relationship between ratio of C_dino to C_m and SST (r = 0.28, p < 0.001), with the ratio increasing with increasing SST. We modeled this relationship by fitting a logistic function to the data (Figure 8A), such that (16)CdinoCm=11+exp[−α(SST−β)], where α = 0.10 (0.08↔0.13) and β = 32.5 (29.7↔36.1). Figures 8B,C show model estimates of C_dino (obtained by multiplying the modeled ratio (Equation 16) by C_m) plotted against measured C_dino, and estimates of C_diat (obtained as C_m(1−(C_dino/C_m))) against measured C_diat. In general, there is good agreement between the estimates and measurements, with higher correlations and lower root mean square errors for C_diat compared with C_dino (Figures 8B,C). Combining estimates of C_m using the three component model (Equations 10–15) with estimates of the ratio of C_dino to C_m (Equation 16), C_dino and C_diat can be estimated as a function of total chlorophyll (C) and SST.

The performance of a model is tightly related to the quality of data used to tune it. We used estimates of phytoplankton group chlorophyll principally from HPLC. Whereas recent refinements in the use of HPLC to infer size-fractionated chlorophyll (Uitz et al., 2006; Brewin et al., 2010; Devred et al., 2011; Brewin et al., 2015) were used, diagnostic pigments determined by HPLC can be found in a variety of phytoplankton taxa and size classes, such that its use as a single in situ method may not always be dependable (Nair et al., 2008). Therefore, we combined data on size-fractionated chlorophyll estimated from HPLC with those from SFF, which encouragingly, were found to be in reasonable agreement with each other for surface waters in the North Atlantic region (Figure 2). Yet, biases between the two techniques have been observed in Atlantic waters (Brewin et al., 2014a). Uncertainties in the SFF technique can arise from filter clogging, inaccurate pore sizes and cell breakage. The partitioning of microplankton chlorophyll into diatoms and dinoflagellates was based on the assumption that fucoxanthin in microphytoplankton can be attributed to diatoms and peridinin to dinoflagellates (Equations 8 and 9). Yet, there can also be fucoxanthin-containing dinoflagellates (e.g., Kryptoperidinium foliaceum) in Atlantic waters (Kempton et al., 2002), though there occurrence is generally not well known. Greater efforts to combine other sources of in situ data (e.g., flow cytometry, video imagery, optical measurements and microscopy) should help improve, and quantify uncertainty in, estimates of phytoplankton group chlorophyll in situ and ultimately, the parameterization of satellite models.

The conceptual framework of the Brewin et al. (2010) model has been supported by data from: phytoplankton spectral absorption measurements (Brewin et al., 2011a); spectral particle backscattering measurements (Brewin et al., 2012a); chlorophyll estimated by size-fractionated filtration (Raimbault et al., 1988; Chisholm, 1992; Riegman et al., 1993; Gin et al., 2000; Marañón et al., 2012; Brewin et al., 2014a; Ward, 2015); flow cytometry and microscopy (Brotas et al., 2013). The model has also been found to reproduce inter-annual variations in size structure consistent with theories on coupling between physical-chemical processes and ecosystem structure (Brewin et al., 2012b), and found to reproduce the typical normalized-biomass size-spectrum of phytoplankton (Brewin et al., 2014b). The model has captured relationships between size structure and total chlorophyll in a variety of contrasting regions (e.g., Lin et al., 2014; Brito et al., 2015; Sammartino et al., 2015).

Yet, as with any abundance-based method, the model does not directly detect the phytoplankton groups: it simply infers the concentrations of chlorophyll in each group based on relationships, developed using data collected in the past, with properties that can by derived accurately from space (e.g., chlorophyll concentration and sea surface temperature). The model is not expected to capture blooms that deviate from the general trends observed in the parameterization dataset (Figures 4,5). For this reason, such techniques may not be appropriate for certain applications. For instance, under a climate-change scenario, there is the possibility that the relationships between properties (e.g., total chlorophyll and group-specific chlorophyll) may change, which may not be detected using an abundance-based approach (Sathyendranath et al., submitted). For such applications, spectral-based methods are likely to be preferable.

Two versions of the re-tuned Brewin et al. (2010) model were carried forward in this study: one using a fixed set of parameters (Table 3); and the other where the parameters were tied with SST (Table 4). The Brewin et al. (2010) model with a fixed parameter set has an advantage that only four parameters are required to compute the size fractions (Table 3), compared with 16 that are used in the SST-dependent model (Table 4). A larger dataset is required to tune the SST-dependent model for regional applications, when compared with the model with a fixed parameter set. Furthermore, when considering all samples together, only a slight improvement in model performance (Ψ and δ) was achieved when using the SST-dependent model (Figures 7, 9). Yet, the SST-dependent model captured variations in model parameters, such as the asymptotic maximum values for small cells (Cp,nm and Cpm), that are known to vary with changes in bottom-up (e.g., nutrients and light) and top-down (grazing) processes (Riegman et al., 1993; Brewin et al., 2014b). The fixed parameter model simply failed to capture these variations, resulting in unrealistic static asymptotes (Figures 7, 9 top-row, horizontal purple dashed lines).

Variations in the relationships of size structure with total chlorophyll and with SST were generally consistent with those proposed by Ward (2015), with the fractions of larger cells (e.g., microplankton) generally increasing with decreasing SST, for concentrations of total chlorophyll less than 1 mg m⁻³, and the fractions of small cells (picoplankton) increasing (Figure 6). Yet, in the Ward (2015) study these variations were typically observed at lower temperature (< 5°C) than those shown in this study (< 17°C). Results are also relatively consistent for small cells (picoplankton) with those proposed by Brewin et al. (2015), when using average light in the mixed-layer, rather than SST, to vary model parameters, though differ for microplankton (see Figures 4, 5 of Brewin et al., 2015). Differences between studies are possibly due to the regional-tuning of the model when compared with the global studies of Ward (2015) and Brewin et al. (2015). There are also differences in the two approaches: whereas Ward (2015) introduces an additional term to the three-component model to account for temperature dependence, here we have let the model parameters change in response to SST variation.

Motivated by the need to provide satellite products of phytoplankton groups that match those as defined in ecosystem models, particularly ERSEM (Table 2), we proposed a partitioning of microplankton chlorophyll (C_m) into diatoms (C_diat) and dinoflagellates (C_dino), by modeling the ratio of C_dino to C_m as a function of SST (Figure 8A). This differs to that proposed by Hirata et al. (2011) which is based solely on total chlorophyll. We observed a significant relationship between C_dino/C_m and SST that was consistent with known seasonal variations of the two phytoplankton groups in the region (McQuatters-Gollop et al., 2007; Widdicombe et al., 2010). Yet, there still are significant variations surrounding this relationship (Figure 8A), and C_dino was found to have the highest errors in the satellite model (Figures 11, 12). The approach may fail to capture blooms of microplankton chlorophyll (C_m) entirely dominated by dinoflagellates (Figure 8A), that can occur in the region (Widdicombe et al., 2010). Future improvements in C_dino satellite estimates may be possible by incorporating spectral information (Shang et al., 2014) or other environmental data (Raitsos et al., 2008). Such improvements may significantly aid ecosystem models considering the difficulties in modeling this group due to their motility and complex trophic behavior (Ciavatta et al., 2011).

In-line with methods used in the OC-CCI project (Jackson and Sathyendranath, 2015), our satellite estimates of the chlorophyll concentration of each phytoplankton group come with per-pixel uncertainty (Figure 12), an essential requirement for use in many applications, such as ecosystem model validation, data assimilation and quantifying evidence of trends in a time-series. Yet, estimates of uncertainty we provide are based on the assumption that the in situ data is the truth. As discussed in the previous section, in situ measurements of phytoplankton group chlorophyll also have their uncertainties, which are difficult to quantify (Brewin et al., 2014a). In addition, the estimates of uncertainty are based on comparisons of co-incident discrete in situ point measurements, representing volumes of sea water of the order of 5 litres or less, with 4 km satellite pixels representing a signal from ~16 × 10¹⁰ litres of water, assuming a 10 m optical depth. Additional uncertainties can occur because of vast differences in the temporal scales associated with the two types of measurements. In the future, such uncertainties may be reduced with the aid of new in situ methods capable of continuously measuring the optical and biogeochemical properties of the water (Dall'Olmo et al., 2012; Boss et al., 2013; Chase et al., 2013; Werdell et al., 2013b; Brewin et al., 2016).

By computing uncertainty statistics for each OWT, we can overcome issues with the distribution of data used in the validation. For instance, in our validation dataset, the majority of samples came from three OWTs (10, 11, and 12, see Figure 11), yet in the satellite image (Figure 12B), the majority of the region is dominated by OWTs less than 10. If one were to consider a single value of any statistical metric (as provided in Figures 9, 10) as representative of the uncertainty in the entire satellite data, it would not be well representative of the majority of the region. Yet, as the number of samples in each OWT vary, so does our confidence in the error statistics for each OWT. Some OWTs (e.g., 1, 2, and 14) have very few observations (Table 5), and consequently we have low confidence in the uncertainty estimates for these OWTs.