Corresponding author: V. Martinez-Vicente, Plymouth Marine Laboratory, Propect Place, The Hoe, PL1 3DH, Plymouth, UK (email@example.com)
 Phytoplankton are an important component of the oceanic carbon cycle. Yet, due to methodological constraints, the carbon biomass of phytoplankton is poorly characterized. To address this limitation, we have explored the bio-optical relationship between in situ measurements of the particle backscattering coefficient at 470 nm, bbp(470), and the phytoplankton carbon concentration for cells with diameter less than 20 µm (Cf). We found a significant relationship between bbp(470) and Cf for Atlantic oceanic waters with chlorophyll-a concentrations less than 0.4 mg m−3 (or bbp(470) < 0.003 m−1). This relationship could be used to estimate Cf from data collected by in situ autonomous platforms and from remote sensing of ocean color.
 Phytoplankton are fundamental drivers of the ocean carbon cycle and they sustain the oceanic ecosystems. Yet, direct measurements of phytoplankton carbon remain scarce due to the lack of reliable methods. The most direct method for quantifying phytoplankton carbon in situ relies on cell counts and bio-volume conversion into carbon biomass using empirical relationships [Strathmann, 1967]. Microscopy is used to enumerate the larger phytoplankton cells (i.e., diameter greater than 20 µm [Holligan et al., 1984]), whereas flow cytometry is used to count smaller cells (i.e., Prochlorochoccus spp., Synecoccocus spp. and eukaryotes) [Zubkov et al., 1998; DuRand et al., 2001; Tarran et al., 2001; Tarran et al., 2006]. Transmission electron microscopy and X-ray microanalysis have also been employed to quantify phytoplankton biomass [Heldal et al., 2003].
 An alternative approach to the collection and analysis of water samples is to use the optical backscattering coefficient of particles (bbp) as a proxy for phytoplankton carbon [Behrenfeld et al., 2005]. Particulate backscattering is an inherent optical property retrievable at a global scale from ocean color remote sensing [Lee et al., 2002] or directly measured from in situ autonomous platforms [Boss et al., 2008]. However, evaluation of this approach has not yet been attempted. The objective of this study is to explore the empirical relationship between bbp and phytoplankton carbon using in situ data.
 Samples were collected during the 19th Atlantic Meridional Transect cruise (hereafter AMT19) from 48oN to 41.5oS (13 October to 1 December 2009, Figure 1A). Profiles of particulate optical backscattering at 470 nm, bbp(470), and flow-cytometric phytoplankton cell abundances were measured along the transect following established protocols (Supplementary material: Methods). Surface underway measurements of bbp(470), total chlorophyll-a (TChl-a), and particulate organic carbon (POC) were also determined (Supplementary material: Methods) [Van Heukelem and Thomas, 2001; Behrenfeld and Boss, 2006; Dall'Olmo et al., 2009; Dall'Olmo et al., 2012].
 The relative differences between bbp(470) measurements from the optical package casts and continuous underway system were quantified by the percent residuals . The bias was −16% (i.e., median of R), and the precision was 7% (i.e., half the central 68th percentile of R, N = 24).
 Data were selected from surface to 1.5Zeu where Zeu is the (1%) euphotic depth [Claustre et al., 2008]. We will also refer to the first optical depth, approximated by Zeu/4.6 following Gordon and McCluney .
 The following phytoplankton groups were counted by flow cytometry in this study: Prochlorococcus spp., Synechococcus spp., picoeukaryotic phytoplankton, cryptophytes, coccolithophores, and other nanophytoplankton. Heterotrophic bacteria were not included. The phytoplankton carbon concentration (in mgC m−3) from flow cytometry (f) for each phytoplankton group (i) and each sample (j), Cf(i,j), was calculated as:
where N(i,j) are phytoplankton abundances (cell m−3); ε(i) is cellular carbon per unit of volume (fgC µm−3) and V(i) is the mean cell volume (µm3). The total phytoplankton carbon concentration per sample j, i.e., Cf(j) was the sum of the contributions from each phytoplankton type. A Monte Carlo method was employed to estimate the uncertainty in Cf (i.e., δCf) as well as its major sources of error (Supplementary material: Methods).
 To describe the relationship between Cf and bbp(470) within 1.5Zeu, we used a Type II linear regression, assigning a value of uncertainty to each point. Model performance was evaluated in terms of the root mean square deviation (RMSD, [Gauch et al., 2003; Pineiro et al., 2008], ), where Cm is the modelled phytoplankton carbon. Bias was described by the median of relative (signed) residuals between Cm and Cf, and precision by half the central 68th percentile of the relative residuals between Cm and Cf.
 Surface TChl-a, POC, and Cf varied across the Atlantic Ocean following similar patterns. Lower TChl-a, POC, and Cf were found in the gyres, while greater values were found in the temperate and equatorial provinces (Figures 1B and 1C). The latitudinal variations of bbp(470) were consistent with previous studies in the Atlantic Ocean [Stramski et al., 2008; Balch et al., 2010] (Figure 1D). Similarly, the spatial variations in TChl-a and POC were consistent with observations from previous AMT cruises [Perez et al., 2006; Poulton et al., 2006a, 2006b; Balch et al., 2010]. Cf was higher than in previous studies in this area at different times of the year, but its latitudinal patterns were qualitatively consistent with studies using the same methodology [Zubkov et al., 2000; Tarran et al., 2006]. Furthermore, our Cf values fell within the range determined by other approaches [Maranon et al., 2000; Perez et al., 2006] and were lower than concurrent measurements of POC (Figure 1C). Pico- and nano-plankton contributed to Cf in different proportions with latitude and depth. Overall, Prochlorococcus spp. and nanoeukaryotes contributed most to Cf (median contribution of 55% and 25%, respectively; Supplementary Table 1). The overall median relative uncertainty of the Cf estimates was 18% and ranged from 12 to 38%.
Table 1. Diameters (D, in µm) and Intra-cellular Carbon Concentrations (ε, in fgC µm−3) Means and Standard Error (SE) Used to Compute Cf
Diameter for oligotrophic and eutrophic areas.
Diameter for temperate areas.
SE obtained from size fractionation experiments on board AMT-13, unpublished data, G.Tarran.
SE obtained from all the data points in Mullin et al. .
 For most phytoplankton groups, the relative uncertainties in Cf were similar across provinces. However, the contributions of the uncertainties in N, ε, and D to the uncertainty in Cf were different and varied with phytoplankton group (Supplementary Table 4). For the nanoeukaryotes, most of the uncertainty was related to the uncertainty in diameter, whereas, for picoeukaryotes, the uncertainty related to the carbon-to-volume conversion factor (ε) was more important. For Prochlorococcus spp. and Synechococcus spp., the uncertainties in diameter and ε had similar weights.
 A significant correlation was found between bbp(470) and Cf (Figures 1D and 2), within 1.5Zeu. Type II regression provided the following relationship for bbp(470) < 0.003 m−1 (or TChl-a ~ <0.4 mg m−3):
where the uncertainties are standard deviations. We limited the use of equation ((2)) to bbp(470) < 0.003 m−1 because the samples beyond that boundary value (N = 8) showed a shift in the relationship (see Discussion). The RMSD for equation ((2)) was 5 mgC m−3, bias was 2%, and precision was 47%.
 We also derived a bbp(470)-Cf relationship applicable to remote sensing algorithms, by using the subset of data from the first optical depth:
 A general linear model test revealed that the regression coefficients of equation ((2)) (slope and intercept) were not significantly different (p > 0.5) from those of equation ((3)). RMSD for equation ((3)) was 4 mgC m−3, bias was −5%, and dispersion was 36.1%.
 The model proposed by Behrenfeld et al.  is also shown in Figure 2. Both the slope and the intercept with the x-axis (“background bbp”) of equation ((3)) were approximately double than those reported in Behrenfeld et al. . When compared to our dataset (N = 229), this model had a RMSD of 5 mgC m−3, +7% bias, and 69% dispersion.
 We chose equation ((3)), derived from near-surface data, to illustrate the latitudinal changes in surface phytoplankton carbon at 1 h resolution (Figure 3A). The corresponding Cm:POC predictions (30 ± 20%, median ± half the central 68th percentile, N = 61) broadly agreed with the in situ Cf:POC estimates (40 ± 10%), and showed large latitudinal variability (Figure 3B). These ranges compared well with other in situ estimates of phytoplankton carbon-to-POC in the Atlantic [DuRand et al., 2001].
4 Discussion and Conclusions
 The main purpose of this study was to search for an empirical relationship between phytoplankton carbon and bbp(470). Although this connection has been previously suggested [Behrenfeld et al., 2005], it has not been tested at the scale of an ocean basin with in situ data. We found a significant linear relationship between bbp(470) and phytoplankton carbon estimated from flow cytometry (Cf).
 Particulate backscattering in the water column is generated by both phytoplankton and non-algal particles (i.e., bacteria, detritus, and minerals). The observed relationship between Cf and bbp(470) therefore implies that either phytoplankton is the dominant source of bbp or that most non-algal particles covary with phytoplankton in our surface dataset. Furthermore, the intercept of equations ((2)) and ((3)) suggests the existence of another source of backscattering, which is relatively constant and independent of phytoplankton. This source may have either a natural origin (i.e., non-algal particles [Behrenfeld et al., 2005]) or could result from systematic uncertainties in Cf and/or bbp [Dall'Olmo et al., 2012].
 The uncertainty in Cf was dominated by the contributions of its most important components: nanoeukaryotes and Prochlorococcus spp. The uncertainty in the cell size, and to a lesser extent, uncertainties in the C-to-volume ratio accounted for the larger part of the uncertainty in Cf. Our choice of parameters has been dictated by the desire of using the most up-to-date results for picoplankton [e.g., Heldal et al., 2003], while being consistent with previous AMT work. Nonetheless, we acknowledge that the characterization of these parameters (ε and D) is subject to research [Montagnes et al., 1994; Menden-Deuer and Lessard, 2000]. An alternative way to reduce the uncertainty in Cf could be by calibrating the flow cytometry measurements to estimate directly Cf, as in DuRand et al. .
 Our data showed that the bbp:Cf ratio was lower in eutrophic (i.e., bbp(470) > 0.003 m−1) than in oligotrophic regions (Figure 2B). Concurrently, the fractional Cf contribution of pico- and nano-eukaryotes increased, and that of Prochlorococcus spp. decreased from the regions with bbp(470) < 0.0015 m−1 to bbp(470) > 0.003 m−1 (Supplementary Figure 1). Inclusion of Cf due to microphytoplankton (missed by flow cytometry) is expected to further decrease the bbp:Cf ratio. Although only eight points are present for bbp > 0.003 m−1, our observations are qualitatively consistent with optical theory that predicts a decrease in the bbp:volume ratio with an increase in particle size (where volume is a proxy to Cf [Boss et al., 2004]). However, opposite predictions are obtained by using experimentally determined backscattering efficiencies [Martinez-Vicente et al., 2012]. Clearly, a single linear function may be insufficient to describe the relationship between bbp and Cf over the entire oceanic range, and more work is needed to characterize bbp and Cf in eutrophic waters dominated by large cells.
 We have also found that the parameters of our equation ((3)) are approximately double than those reported by Behrenfeld et al. . It is unlikely that the change in wavelength between studies (470 vs 440 nm) could account for such discrepancy: by assuming a backscattering spectral slope of −1 [Morel and Maritorena, 2001], we expect parameter differences of ~6%. A more plausible explanation could be that the variation in model coefficients is due to uncertainties in satellite and in situ estimates of bbp and/or differences in the spatio-temporal scales of the two studies. An extension of this work would be to compare backscattering-based models with Chl-a-based models of Cm [Sathyendranath et al., 2009].
 Finally, we found that a smaller fraction of the POC was accounted for by phytoplankton in oligotrophic than in productive regions (Figure 3B). This result is consistent with the study of Grob et al.  in the South Pacific, and we hypothesize that it is related to a change from a microbially dominated community (oligotrophic) to one dominated by primary producers (eutrophic).
 The ability to derive Cf from bbp(470), for bbp(470) values below 0.003 m−1, means that estimates of pico- and nano-phytoplankton carbon biomass could be obtained from ocean-color satellites and in situ autonomous platforms. Although the range of validity of the proposed bio-optical model encompasses most of the open ocean, the regional and temporal variations of the coefficients need to be verified.
 The authors thank the captain, officers, and crew aboard RRS James Cook for their help during the AMT cruise. C. Gallienne is thanked for his help in deploying the optical package. This study was supported by the UK NERC through the UK marine research institutes' strategic research program Oceans 2025 awarded to PML and NOC, Southampton. This is contribution number 216 of the AMT programme. V.M.V. acknowledges the support of Royal Society ITG102226. Collection of optical measurements was funded by NASA grant NNX09AK30G to G.D.O. G.D.O. acknowledges support from UK NCEO and Marie Curie FP7-PIRG08-GA-2010-276812. Part of Figure 1 was made using ODV [Schlitzer, 2010]. Comments from T. Platt are gratefully acknowledged. We acknowledge H. Sosik and an unknown reviewer for their comments.