As part of this study, more than 12,000 observations of picophytoplankton abundance have been collated from coastal and oceanic regions (Table 1), building upon a dataset compiled by the modeling community through MAREDAT (http://maremip.uea.ac.uk/maredat.html) (Buitenhuis et al., 2012). Additional data come from a long-term observation program, the Atlantic Meridional Transect (AMT); as well as recently available data collected independently during AMT-22 and in the Pacific (Graff et al., 2015) and from other regions in the Atlantic ocean (Taylor et al., 2013). The dataset assembled consists of cell counts (in cells per milliliter), from water samples originating between 0 and 200 m depth, and collected in the period between 1997 and 2014, to match satellite observations available. Flow cytometry analysis of the samples provides cell abundances segregated into different types of phytoplankton. At this stage, the database consisted of 12,431 sample entries. Only the picophytoplankton cells (<2 μm) were available in the MAREDAT dataset, which were separated into Prochlorococcus spp., Synechococcus spp. and picoeukaryotic phytoplankton. For consistency, only information on the same phytoplankton types were extracted from the additional data sources (Zubkov et al., 1998; Tarran et al., 2001, 2006; Taylor et al., 2013; Graff et al., 2015; Tarran, 2015; Tarran and Bruun, 2015) (see Table 1). The carbon concentration (C_phy, in mg C m⁻³) for each phytoplankton group (i) and for each sample (j), C_phy(i, j), was calculated as follows:

where N(i, j) is cell abundance (cell mL⁻¹) for each of the three phytoplankton types (i = Prochlorococcus spp., Synechococcus spp. or picoeukaryotic phytoplankton) at sample j; and ε(i) is cellular carbon per cell (fgC cell⁻¹) for each of the picophytoplankton types. The factor 10⁻⁶ converts mL to m³ and fgC to mgC. We used the mean ε(i) for each phytoplankton type proposed by Buitenhuis et al. (2012): 60 fgC cell⁻¹ for Prochlorococcus spp., 154 fgC cell⁻¹ for Synechococcus spp. and 1319 fgC cell⁻¹ for picoeukaryotic phytoplankton. These values of ε(i) are comparable to values from the Bermuda Atlantic Time-series Study (BATS) (Casey et al., 2013), for Prochlorococcus spp. and Synechococcus spp., whereas picoeukaryotic phytoplankton ε(i) values are lower than in BATS. The total picophytoplankton carbon concentration per sample j, i.e., C_phy(j) is the sum of the contributions from each picophytoplankton type (i.e., C_phy(i, j)), and will be hereafter referred to as C_phy at a given location and depth.

The choice of phytoplankton types included in this computation, as well as the parameters used for the conversion to carbon, matches the modeling community approach as represented in Buitenhuis et al. (2012). The choice of phytoplankton types is such that phytoplankton types with diameter >2 μm are not taken into account. Furthermore, the choice of a mean carbon concentration per cell for each phytoplankton type does not permit accounting for any variations in size or cellular carbon spatially or temporally for each type of phytoplankton. To test our choice of carbon conversion parameters we compared direct measurements of C_phy with estimates computed using the conversion factors above. In samples from the AMT-22 (N = 15) (Graff et al., 2015), the slope of the regression between direct measurements of C_phy and computed C_phy, was 0.8 (r² = 0.6, p < 0.05). According to this result, the estimates of picoplankton C_phy in our dataset are significantly correlated with direct estimates of phytoplankton carbon, and could be an overestimate of direct observations of C_phy, which include nanophytoplankton, although a larger sample is required to support this conclusion.

The in situ database described above was matched with merged ocean-color satellite data from the Ocean Color Climate Change Initiative (OC-CCI) (Sathyendranath et al., 2012). These merged products were used to maximize the possibility of finding matching in situ data as well as to use a set of common inputs to the different algorithms. The OC-CCI version 2 data had a daily sinusoidal projection (binned) and a 4 km spatial resolution. These satellite data were used as inputs for C_phy algorithms: total B from OC4v6, b_bp from the Quasi-Analytical Algorithm (QAA) v5 (a modification to v4 in Lee et al., 2002, 2007, but that does not include Raman scattering, Westberry et al., 2013; Lee and Huot, 2014). Second, the water class membership (Moore et al., 2001, 2009; Jackson et al., 2017).

The procedure for match-up selection was the same as that used for particulate organic carbon (POC) data (Evers-King et al., 2017). The day of year the in situ sample was collected was matched with the same day of year from the merged satellite products. Then all relevant data were extracted from a 3 × 3 pixel set with the sample location at the center. The number of valid data, within the 3 × 3 grid, and mean and standard deviation of the valid points were recorded for each computed C_phy product. The 3 × 3 grid was used to identify where sufficient satellite data were available. In this dataset only 11 matched points had 3 valid pixels or less. The C_phy algorithms were applied to the central pixel of the satellite matched up data. The match-up process reduced the sample size considerably. Further reduction came from depth-averaging (between 0 and 10 m) the C_phy profiles that matched the satellite data, and ignoring the deeper samples, leaving 647 data points. Finally, to remove outliers, the top and bottom 2 percentile were removed from the dataset, leaving N = 557 for the analysis. The geographical distribution of match-up database for the picophytoplankton carbon concentration, C_phy, is given in Figure 1. The match-up dataset usable for the algorithm comparison was only about 5% of the inital data (Table 1). It is worth emphasizing that the match-up data set has not been used for the calibration or development of most of the algorithms compared (see section 4).

The following section describes the six algorithms compared in this exercise. All the phytoplankton algorithms were implemented using as input data the appropriate OC-CCI product for consistency and to isolate the effects of the different algorithms. Table 2 provides a comparison of the input data and the phytoplankton size range that is included in the outputs of each algorithm. These are important characteristics of the algorithms, required for the interpretation of the results. For phytoplankton carbon, C_phy in mg C m⁻³, six products were derived and they are briefly described in this section. According to their common characteristics, they can be grouped into chlorophyll-based, backscattering-based and allometric algorithms.

Ranking of algorithms according to their performance is a classic exercise for the ocean-color community, that has evolved from comparisons of chlorophyll algorithms (O'Reilly et al., 1998) to more complex and comprehensive approaches recently (Brewin et al., 2015; Kostadinov et al., 2017). Typically, a battery of statistical metrics is used to construct an index of overall performance against a set of matched data with in situ observations (Brewin et al., 2015). In this exercise, however, we do not use a scoring system to rank algorithms, since one of the aims of this work is to provide an overall idea of the current accuracy of the phytoplankton Carbon product from a group of algorithms. The Kolmogorov-Smirnov test for normality of the in situ match-up data showed a significant deviation from normality for log₁₀ transformed and un-transformed data and the residuals (p < 0.001). Therefore, statistical metrics that assume normality would be less reliable. For completeness, the statistical tests were computed for log₁₀ transformed data, using parametric tests; and for un-transformed data, using non parametric, rank-based, statistics. Statistical metrics computed were:

To provide an indication of the stability of the statistics and to compute confidence intervals on them, bootstrapping (Efron, 1979; Efron and Tibshirani, 1993) with random re-sampling and replacement was used to construct 1,000 different datasets from which confidence intervals were computed for some of the statistical metrics above. These metrics were computed for all the algorithms tested against the match-up dataset as a whole and, in adition, they were also computed after segregating the match-up dataset according to the dominant water class at the central match-up pixel. Because of the nature of the ocean color CCI satellite data and the C_phy algorithms, it is expected that algorithm performance will degrade toward more turbid environments (water classes 8 and over). Furthermore, the statistical results per water class provided a measure of dispersion of the phytoplankton Carbon product among algorithms, describing in which optical environments the algorithms show greater agreement. The statistics per water class were used to produce uncertainty maps (RMSD and bias). To generate the uncertainty maps, the optical class memberships at each pixel, and the per-class uncertainty values for each class were used to produce a weighted average uncertainty value for the pixel, with the weighting function being provided by the class membership. This is the method followed by the OC-CCI and described fully in Jackson et al. (2017).

The sources and geographic distribution of the in situ data, as well as the corresponding median values of the picophytoplankton carbon data are summarized in Table 1. The spatial distribution of the match-ups (Figure 1) shows their limited coverage of the oceans, with most of the data (71%) located in the Northern Hemisphere and from the Atlantic Ocean. The overall median value of C_phy from the match-up database was 11.7 ± 5.3 mg C m⁻³ (median ± IQR/2), with values ranging from 1.7 to 60.2 mg C m⁻³. As a comparison, chlorophyll concentration (B) from the coincident satellite data was 0.12 ± 0.08 mg Chla m⁻³, ranging from 0.01 to 3.53 mg Chla m⁻³. The median values of C_phy from the algorithms applied to the matching data (Table 2) were not significantly different to the C_phy in situ (Mann-Witney test, N = 557, p < 0.05). Relative frequency histograms of these data (Figure 2) however, show some bias. The peaks of the histogram of the chlorophyll-based algorithms (Algorithms A and B) were closest to the in situ; the backscattering-based models (Algorithms C and D) were double the median of in situ and allometric algorithms (Algorithms E and F), were half the in situ median value (Figure 2). The distribution spread of chlorophyll-based algorithms were about the same or wider than the in situ (C.V. between 40 and 56%), with backscattering and allometric algorithms having narrower distributions (C.V. lower than 30%).

Figure 3 shows the results from the algorithm estimates of C_phy against in situ derived estimates of C_phy and the relevant statistical metrics are in Table 3. All the algorithms showed different predictions of C_phy, but as expected, there were commonalities among models that shared the same formulation. For example, both chlorophyll-based algorithms (Figures 3A,B) presented an elongated cloud with a weak but positive (~0.6) and significant correlation with in situ data, and stayed mostly along the 1:1 line, with slopes close to 1; whereas both backscattering-based algorithms (Figures 3C,D), had weaker correlations (~0.4) and, although the slopes where also close to 1, the data cloud does not capture the lower C_phy measurements. Contrary to the other two groups of algorithms, the allometric-based do not share a formulation, hence their results (Figures 3E,F) differ significantly among them.

The statistical metrics (Table 3) provide a range of values among the algorithms tested, showing that there is not a clearly superior performance of a single algorithm on all metrics. The bias (δ) ranged from 3.5 mg C m⁻³ for Algorithm B (Marañón et al., 2014) to 15 mg C m⁻³ for the Algorithm D (Martínez-Vicente et al., 2013) as modified in this work. Chlorophyll and backscattering based algorithms had a positive bias, less than 15 mg C m⁻³, whereas allometric algorithms had a negative bias, less than 7 mg C m⁻³. The un-biased RMSD (Δ), which gives an idea of the dispersion of the predictions, ranged from 8.9 mg C m⁻³ for Algorithm E (Kostadinov et al., 2016) to 29 mg C m⁻³ for Algorithm D, (Martínez-Vicente et al., 2013) as modified in this work. The lowest median absolute percentage difference (MAPD), a measure of accuracy, for the untransformed data was for Algorithm B (Marañón et al., 2014), in agreement with the bias indicator for log and non-log transformed data. The inter-quartile range of the MAPD (IQR), a measure of precision of the algorithm, was lowest for Algorithm E (Kostadinov et al., 2016), and coincided with another indication of dispersion (Δ) in the non-log statistics, but differed for the log-transformed data.

Overall, chlorophyll-based algorithms had higher correlation and indicators of lower bias (i.e., δ, MAPD), whereas allometric algorithms had indicators of lower dispersion (i.e., Δ, IQR of MAPD). Between algorithms, there was a factor 4 of difference between the maximum and minimum predictions from the algorithms for all matchups pooled together as a median (i.e., the median of the fractional difference between the minimum and the maximum predictions by the algorithms in each match-up point).

An additional way to assess model performance is to study their emergent properties (de Mora et al., 2016). Here we have compared the in situ and the algorithm derived C_phy to the chlorophyll concentration, B (standard OC4v6 OC-CCI-product) for the match-ups (Figure 4 and Table 4), to investigate the behavior of the C_phy:B ratio. Figure 4A displays the positive correlation between the satellite derived B (for the whole of the phytoplankton assemblage) and the in situ derived C_phy for the picophytoplankton fraction only, over more than two orders of magnitude of chlorophyll concentration. Because of the mismatch between the particle assemblage in B and C_phy, the overall values reported for the C_phy:B ratio are smaller than they would be if the ratio had been derived from B for picoplankton only. However, with a median value of 91 mg C mg Chla⁻¹, the in situ C_phy-to-satellite-B-ratio falls within or close to observed values in oligotrophic areas. For instance, Sathyendranath et al. (2009) reported average values of this ratio greater than 100 mg C mg Chla⁻¹ for prymnesiophytes, cyanobacteria and Prochlorococcus sp. Direct observations of pico and nano plankton carbon in the Northern and Southern Atlantic gyres produced carbon-to-chlorophyll ratio estimates, on average, of 106 and 190 mg C mg Chla⁻¹, respectively (Graff et al., 2015). Marañón et al. (2014) also reports values in the range of 80–117 mg C mg Chla⁻¹ for oligotrophic regions. Therefore, the C_phy:B ratio used as reference in this study compares well with existing observations reported in the literature, despite the mismatch between the phytoplankton assemblages considered. These data are repeated as the background of the other panels in Figure 4 for reference along with their corresponding regression line. Algorithms A and B are chlorophyll-based, therefore their predictions fall on the line of the equations used, respectively Equations 2, 3 in Figures 4B,C. Their predictions are close to the in situ data cloud and the resulting median phytoplankton carbon-to-chlorophyll ratio encompass the in situ reference value, Algorithm A providing an upper limit, as expected from the assumptions made in its construction. Backscattering-based algorithms (Algorithms C and D, in Figures 4D,E, respectively) overestimate the C_phy:B reference relationship, specially at the lower concentrations of chlorophyll, and produce median phytoplankton carbon-to-chlorophyll ratio values up to two times greater than the reference. However these algoritms capture some of the variability around the prediction line, which is in the same order of the in situ data. Algorithms using inherent optical properties with allometric conversions (Algorithms E and F, in Figures 4F,G, respectively) underestimate the reference C_phy:B reference relationship, with Algorithm E showing a narrower distribution of data points than Algorithm F.

The in situ C_phy dataset is representative only of a fraction of the particle population (picophytoplankton). However, its geographical distribution, the median C_phy concentrations and carbon-to-chlorophyll ratios derived from this dataset are in agreement with existing observations in oligotrophic oceanic conditions. Taking into account this charcteristic of the dataset, the overall performance of the algorithms was on the low side, with chlorophyll-based algorithms producing slightly lower bias and allometric algorihms slightly lower dispersion. Among algorithms there was a median dispersion of a factor 4 between minimum and maximum predictions. The algorithms were also tested on their ability to produce realistic a C_phy:B ratio, which again highlighted great dispersion in predictions among and within algorithms types. Arguably, part of the dispersion in the statistical results may have arised from the fact that the in situ C_phy dataset is representative only of a fraction of the particle population (i.e., picophytoplankton). Therefore if we limited the study to the optical cases where picophytoplankon is expected to dominate the phytoplankton carbon pool and the chlorophyll content, we would expect an improvement on the results from the algorithms. In the next part of this study we present results obtained from segregating the data into optical water types.

An optical water class, in this context, is defined by a mean remote sensing reflectance spectrum representative of particular optical characteristics, i.e., an end-member spectrum. Each extracted satellite pixel coinciding with a match-up in situ data has contributions from the different end-members in different proportions. The water class contributing with the largest proportion to the pixel water class membership is classed as belonging to that water class (Jackson et al., 2017). The geographic locations of the match-up points per water class and the number of observations per class are shown in Figure 5. There was a good correspondence between the geographic location of the optical water types (note that the classes are numbered such that i = 1 is the most oceanic type and i = 14 the most coastal type) in Figure 5A and the C_phy concentrations (Figure 1), such that the higher-numbered optical classes tend to be representative of higher concentrations of phytoplankton carbon. The majority of the data (63%), though can be classed as representative of an oligotrophic environment (i 1 to 6, B < 0.15 mg Chla m⁻³). A boxplot summary of the descriptive statistics per optical water class per algorithm is provided (Figure 6). Table 5 summarizes the median C_phy values highlighting a steady increase from oceanic to coastal waters, except for i = 13, which only has N = 5 observations, and is hereafter discarded from the analysis. The magnitude and the increase of the picophytoplankton carbon is in agreement with oceanic and coastal data (Tarran et al., 2006). For instance, using the current carbon conversion parameters on existing abundance data (Tarran and Bruun, 2015), C_phy median in the coastal area of the Western English Channel is 12.1 ± 6.1 mg C m⁻³ (N = 68).

Algorithm performance per water class was quantified by the signed bias (δ) and the center-pattern RMSD (Δ) (see Table 5 and Figure 7). These statistical indicators of performance improved by limiting the analysis to oligotrophic waters (i 1 to 6) as expected: bias, δ, was similar or lower than those obtained when considering all data, for all the algorithms (section 3.1, Table 3). Center-pattern RMSD, Δ an indicator of precision, was, on average, half that when considering all data, indicating decreased noise in the retrieval for all algorithms (for non-log results, section 3.1). Chlorophyll-based algorithms had, on average, similar δ and Δ to the allometric-based algorithms, with back-scattering based algorithms producing higher bias and higher Δ values.

Mesotrophic waters (0.15 < B < 0.7 mg Chla m⁻³, or optical water classes 7–10) comprise 32% of data. With respect to the results obtained for all data available (section 3.1), the chlorophyll based algorithms had an increased δ, whereas Δ was similar. Backscattering-based algorithms had higher uncertainties than chlorophyll-based algorithms in the more turbid waters (high optical class numbers) in the untransformed data (Figure 7D). Bias increased for all of the algorithms for these water classes except for Algorithm E, which remained negative and relatively constant at −60%. However, the results for mesotrophic and more turbid waters, should be taken with caution as the use of in situ C_phy data comprising only picophytoplankton is more problematic in these waters.

The in situ median C_phy:B ratio by optical water class were also compared to the median C_phy:B ratio from the algorithms (Figure 8). The in situ data (solid gray line and error bars) is repeated as a reference throughout Figure 8, showing that for i from 1 to 6 (oligotrophic waters), the range of variation is narrow (106 to 165 mg C mg Chla⁻¹, median 133 mg C mg Chla⁻¹) and error bars are overlapping among the optical water classes 1 to 6. For mesotrophic waters (i from 7 to 10), there was a decreasing tendency of the in situ C_phy:B ratio.

The analysis of the algorithm predictions of the C_phy:B ratio focusses on the optical water classes 1 to 6, where C_phy and B are expected to describe the same phytoplankton assemblage. Essentially, the behavior observed for the C_phy is also repeated here. Algorithm A was an upper limit to the C_phy, it is also an upper limit to C_phy:B ratio, which decreases with increasing optical water class number (Figure 8A). Algorithm B shows relatively little variation of the median C_phy:B ratio for the optical water classes of interest and beyond (i > 6). Backscattering-based algorithms, Algorithm C (Behrenfeld et al., 2005) and Algorithm D (Martínez-Vicente et al., 2013), showed also decreasing median C_phy:B ratio with increasing water class number, with large overestimations with respect to the in situ C_phy:B ratio at the clearest waters. The allometric-based algorithms, Algorithm E (Kostadinov et al., 2016) and Algorithm F (Roy et al., 2017), were generally predicting lower than observed C_phy, and also predicted lower median C_phy:B ratios. However, both algorithms had a decreasing tendency for the median values with increasing turbidity (or water class number, in this study), with Algorithm E being closest to observations for i from 1 to 3.

Finally, Figure 9 shows an example of the C_phy product from algorithms A to D using the OC-CCI monthly product from May 2005. All algorithms reproduce the broad patterns that would be associated with C_phy i.e., increased values in high-chlorophyll areas (upwelling sites and coastal regions) and lower concentrations in the gyres, however the salient point of this Figure is the large differences in predictions among the algorithms, as expected from the statistical results.

This study has compiled a large in situ database of picophytoplankton carbon, building on a combination of a substantial pre-existing effort by the modeling community (the MAREDAT data) and long time series observation programmes in the open ocean (Atlantic Meridional Transect, AMT). The ambition is to see this dataset growing with time, as new data are incorporated.

There are a number of advantages and limitations for this dataset with respect to its use for algorithm testing and validation. An advantage is that only a small fraction of the data have been used for the development of any of the algorithms tested here. Algorithms A, B, C, and E are completely independent of the match-up dataset. Algorithm D as implemented by Martínez-Vicente et al. (2013), was developed using a small subset of the new database, N < 70, but the subset included nanoplankton. Algorithm F used MAREDAT for testing algorithm performance, but not for its development. So the data for the validation presented here are mostly independent of the data used in the construction of algorithms. The geographic distribution of the match-up database, though largely limited to the Atlantic, with some additional points from the Pacific, does cover a variety of oceanic regions. It is a purpose-built database for satellite validation studies, and therefore, only an average of the matching data in the top 10 m have been selected for convenience.

However, the dataset also has limitations. One of them is that it is only composed of picophytoplankton: though they are important contributors to the open-ocean phytoplankton biomass, picophytoplankton form a decreasing proportion of the phytoplankton biomass in more productive waters, where larger cells tend to become more important (Marañón et al., 2012; Marañón, 2015). One interesting avenue would be to expand the database with other phytoplankton groups (Buitenhuis et al., 2013; Sal et al., 2013). Nanoplankton can also be counted using flow cytometry, and microphytoplankton groups counted using microscope or automated image processing (Sosik and Olson, 2007; Álvarez et al., 2012), but the relationship between carbon and abundance becomes more variable for larger and more irregularly-shaped phytoplankton (Moberg and Sosik, 2012; Saccà, 2016).

Because the data are confined to the surface layers, they may also be adversely affected by underestimation of Prochlorococcus sp. abundance by flow cytometry because of extremely low fluorescence per cell (Partensky et al., 1996; Heywood et al., 2006). Furthermore, by limiting our dataset to the top 10 m, we have precluded the possibility of testing any potential impact that the vertical structure in the first optical depth might have on algorithm performance. Examples exist in the literature where the depth variations in particulate organic carbon been taken into account (Duforêt-Gaurier et al., 2010), and this may be an avenue worth exploring also for phytoplankton carbon algorithms.

Finally, the conversion of abundance to carbon using estimates from the laboratory could cause errors in the computed C_phy in the field, if the laboratory estimates do not hold under natural environmental conditions. These factors can vary with physiological state and with depth (Casey et al., 2013) and have been discussed previously (Buitenhuis et al., 2012; Martínez-Vicente et al., 2013). It is important to highlight that in this study we have used indirect estimates of phytoplankton carbon (through cell counts and cell size) only because of the lack of direct measurements. However, methods for direct quantification of C_phy have recently become available (Graff et al., 2012; Casey et al., 2013) and the expectation is that there will be more direct C_phy data available in the future.

Limiting the study to the optical water classes where the composition of the phytoplankton assemblage is expected to be dominated by picoplankton (i 1 to 6, B up to 0.15 mg Chl m⁻³) median values of C_phy and C_phy:B ratio matching the literature (Marañón et al., 2001; Marañón, 2015), were obtained, and the algorithms results showed more stability and less dispersion. However, some algorithms displayed significant differences which are discussed hereafter.

The algorithms presented here were broadly classified into three classes: chlorophyll-based, back-scattering based and allometric. In the results presented here, it is evident that algorithms based on similar approaches perform alike. So it is worth examining each of these approaches in some detail, to explain the differences observed in the results for oligotrophic waters.

The two chlorophyll-based algorithms were designed to consider all the phytoplankton groups: Algorithm A (Sathyendranath et al., 2009) provides an upper limit to the phytoplankton contribution to the total particulate carbon pool and Algorithm B (Marañón et al., 2014) is based on phytoplankton carbon computed from flow-cytometric data supplemented with microscopic counts for larger phytoplankton. Yet, when compared with only one fraction of the total phytoplankton pool (the picophytoplankton in this study), the results are similar, with Algorithm A slightly overestimating and Algorithm B slightly underestimating in situ C_phy. Algorithm A was designed as the upper limit to the phytoplankton carbon, hence this result is as expected. Algorithm B was computed using a similar conversion method between cell count and carbon concentration to the one used in this study, but with different conversion coefficients. We speculate that a possible reason for the difference observed between the predicted C_phy by Algorithm B and the in situ C_phy could be found in the differences in conversion between cell counts and carbon. Production of datasets with consistent conversion factors would help eliminate this source of discrepancy.

Differences in results are greater with the backscattering-based algorithm, which produced overestimation of C_phy and greater dispersion statistics than the other algorithms. Because it has been verified in situ that b_bp increases with pico and nano plankton carbon (Martínez-Vicente et al., 2013; Graff et al., 2015), the degradation of results may be linked to the backscattering input from the algorithm. Algorithm C equation was derived using the GSM algorithm for obtaining a relationship between the backscattering coefficient and the B. It has been found in situ, that at low B there may be an overestimation of the b_bp by using this satellite-derived relationship (Huot et al., 2008; Antoine et al., 2011; Brewin et al., 2012), yet in situ data also have shown overestimation of backscattering by the QAA algorithm (Behrenfeld et al., 2013). It has been found recently, that Raman scattering plays a role in the discrepancy of the retrievals of the backscattering coefficient in very clear waters from satellite (Westberry et al., 2013), causing an overestimation in backscattering. This effect of Raman scattering has been only identified recently (Lee and Huot, 2014), and was not incorporated in the QAA version used for the production of the OC-CCI version 2 data used for this study, but can be analytically corrected (McKinna et al., 2016), and future versions of the OC-CCI dataset will address this issue.

While validation of the OC-CCI chlorophyll product has been performed intensively in Atlantic oligotrophic waters and showed low error statistics (Brewin et al., 2016), investigations to improve the validation of b_bp and to understand better the relationships of b_bp with particles in oligotrophic areas are still required (Brewin et al., 2015). At a fundamental level, backscattering is dependent on the refractive index of the cells, their abundance and size, whose interplay is not yet fully understood. But in addition to phytoplankton, other particles (e.g., detritus) are known to contribute to the backscattering signal, and their variability relative to phytoplankton could potentially contribute to the discrepancies observed in this study.

Algorithm E used in its original formulation an inversion model to retrieve the backscattering spectral slope (Loisel et al., 2006) that is different from the one used in this comparison as input (i.e., QAAv5). The QAA used here invoked a band ratio to solve for the backscattering spectral slope, and this may account for at least part of the observed tighter coupling between B and Algorithm E. Algorithm E provides consistently low Δ values across the water classes, although it underestimates the in situ data systematically. This may be pointing to a need to re-adjust the size scaling parameter (like N_o), the empirical correction for which is now based on a rather limited in situ validation data set (Kostadinov et al., 2016). Ultimately, a better optical closure is needed between modeled and observed backscattering spectra, and a better understanding of the underlying particle assemblages, their refractive indices, and their relative contributions to the backscattering coeffient. It remains to be validated if at more productive waters, the prediction of low C_phy (from Algorithm E picophytoplankton fraction) remains valid, whereas the current in situ dataset showed an increase (Table 5).

Algorithm F was similar to algorithm E in all water classes except for water classes 8 to 11, where the uncertainty is almost double compared with the rest of the algorithms, pointing perhaps to a vulnerability to uncertainties in the a_ph(676) retrieval in these waters. More accurate estimates of phytoplankton carbon by Algorithm F would possibly require improving the retrievals of the input a_ph(676) values, especially in high-chlorophyll waters.

The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest. The reviewer SA and handling Editor declared their shared affiliation.