Chlorophyll-a concentration was estimated optically and by means of high performance liquid chromatography (HPLC). Surface seawater was collected from the ship's clean seawater supply and filtered through pre-combusted (4 h at 450°C) 25-mm Whatman GF/F filters (1–4 liters, depending on the trophic status of the water masses). Samples were flash-frozen in liquid nitrogen, stored at −80°C and then analyzed using HPLC analysis (Van Heukelem and Thomas, 2001; Mueller et al., 2003). The concentration of total chlorophyll-a was calculated as the sum of the chlorophyll-a, monovinylchl-a, divinyl chlorophyll-a, and chlorophyllide-a (Figure 2).

Optically-derived chlorophyll-a was calculated using the height of the particle absorption peak at 676 nm following Boss et al. (2007), using data from both AC-9 and AC-s measurements during AMT-19 (Dall'Olmo et al., 2012) and using only AC-s data for AMT-22. Optically-derived chlorophyll-a concentration was validated by comparing it to the HPLC-based total chlorophyll-a (see Figure 2). Biases of −10 and +3% (median relative differences) were found for AMT-19 and AMT-22, respectively. These biases were then removed from the optically-derived chlorophyll concentrations for the rest of the analysis. This bias-corrected optically-derived chlorophyll-a is henceforth referred to as chl_op whereas HPLC-based total chlorophyll-a is referred as chl_hplc.

Continuous optical measurements were collected on seawater pumped from a nominal depth of 5 m into the clean underway supply of the RRS James Cook. Bubbles were removed by means of two Vortex debubblers connected in series (model VDB-1G, Stony Brook, NY, USA).

During both cruises particulate beam attenuation coefficients (c_p) were determined by two 25-cm WETLabs C-star transmissometers (526 and 650 nm). Hyperspectral c_p and particulate absorption coefficients (a_p) were also measured between 400 and 750 nm by a 25-cm WETLabs spectral absorption and attenuation meter (AC-s, 5-nm spectral sampling, 15-nm band pass). As explained in Dall'Olmo et al. (2012), during AMT-19 the AC-s instrument failed (~year day 298) and was replaced by a WETLabs AC-9 instrument (nine wavelengths between 412 and 715 nm, 10-nm band pass).

Particulate absorption and beam-attenuation coefficients, a_p and c_p, were determined by subtracting from the bulk signals those measured on 0.2-μm filtered (Cole Parmer nylon cartridge) seawater as previously described (Dall'Olmo et al., 2009, 2012; Slade et al., 2010).

Since the AC-9 has a band pass narrower than the AC-s (10 vs. 15 nm), differences are expected between a_p spectra collected simultaneously by the two instruments (Dall'Olmo et al., 2012). To make the a_p data derived from the AC-s comparable with those derived from the AC-9, we performed an intercalibration by computing the ratio of a_p derived from the AC-s to a_p derived from the AC-9 at the same chl_op concentration (±10%) for different values of chl_op concentrations (n = 25, logarithmically spaced between 0.03–5 mg m⁻³) and for the two wavelengths used in this analysis (i.e., 440 and 676 nm). The rationale for this comparison is that, even if collocated spectra of AC-9 and AC-s were not available, for a given chl_op concentration, we expect that in the open ocean the a_p spectra collected by AC-9 and AC-s should, to first order, be comparable. This similarity is a priori expected to be higher at 676 nm, where chl is the most important contributor to a_p, than at 440 nm, where other optically-active constituents (e.g., detritus, accessory pigments) have higher contributions. We avoided green wavelengths due to the very low values of a_p, which would significantly increase uncertainties. Average (± standard deviation) a_p^ACS:a_p^AC9 ratios of 0.68 (±0.05) and 0.60 (±0.02) were found at 440 and 676 nm for AMT-22, and of 0.75 (±0.08) at 676 nm for AMT-19 irrespective of chl_op. In contrast, during AMT-19 the average a_p^ACS:a_p^AC9 ratios at 440 nm varied between 0.90 and 1.4 with chl_op. To account for this variation, we fitted a second-order polynomial (R² = 0.97) between the values of the ratio and chl_op and used the fitted regression coefficients to calculate a_p^ACS:a_p^AC9 ratios at 440 nm for any chl_op value during AMT-19. We finally corrected the a_p values measured by the AC-s instruments by dividing them by (1) the average ratios found for AMT-19 (at 676 nm) and AMT-22 (at 440 and 676 nm), and (2) the a_p^ACS:a_p^AC9 ratios at 440 nm for a given chl_op for AMT-19. These corrected a_p values were used for the rest of the analysis.

Continuous measurements of the particulate backscattering coefficient (b_bp) were carried out by means of a WETLabs ECO-BB3 meter (470, 526, and 660 nm) installed in a flow-through chamber as described in Dall'Olmo et al. (2009 and 2012). More details about the b_bp determination as well as the calibration and characterization of the instrument can be found in Dall'Olmo et al. (2009 and 2012) and Behrenfeld et al. (2013, supplementary materials). During AMT-19 flow-through b_bp(470;526) data were validated against in-situ b_bp values measured with an independent instrument that was deployed on a profiling package (see details in Dall'Olmo et al., 2012). Biases of 16 and 13% and precisions of 6 and 7% were found between the two independent methods for the coincident b_bp(470) and b_bp(526) measurements, respectively and demonstrated that the underway system was clean during AMT-19. Unfortunately, we did not conduct a similar intercalibration during AMT-22.

During AMT-22 both methods for determining the blank carbon mass produced consistent results, with average (±standard deviation) masses for the filter and intercept blanks of 15.5 ± 6.5 μg C (n = 196) and 14.9 ± 8.7 μg C (n = 114), respectively (Figure 3B). However, for AMT-19, filter-blanks [averages of 24.9 ± 17.9 μg C (n = 69)] were ~2.3 times larger than intercept-blanks [averages of 10.9 ± 8.7 μg C (n = 68), Figure 3A], indicating a potentially greater contamination of the filter blanks during AMT-19 relative to AMT-22. Nonetheless, the blank values determined in this study with either method were within (or lower than) the range of those reported in the literature (19–25 μg C; Menzel, 1966; Moran et al., 1999; Cetinić et al., 2012), which supports the rigorousness of our POC protocol (e.g., our coefficient of variation had a mean value of 0.06 and ranged between 0.01 and 0.26). Since the intercept-blank method produced values that were consistent between the two cruises, we used the average intercept-blanks calculated for each cruise separately to derive POC. During AMT-22 4% of the intercept-blanks were negative (Figure 3D) and these values were mostly located in productive areas of the Atlantic (63% of the negative intercepts were found where POC > 60 mg m⁻³). These negative values are discussed in section POC Blanks and Accuracy.

The observed range of POC was consistent between the two cruises (15–230 mg m⁻³) and with previous studies for the Atlantic ocean (Poulton et al., 2006; Balch et al., 2010). POC showed a first-order spatial pattern similar (R² = 0.83) to that of chl_hplc (Figures 4A,B). However, the POC:chl_hplc ratio showed an opposite latitudinal pattern (i.e., maxima in the most oligotrophic regions) and varied by a factor of 12 and 14 for AMT-19 and AMT-22, respectively (Figure 4C).

The POC-c_p relationship has been extensively tested in the literature (e.g., Gardner et al., 2006; Cetinić et al., 2012 and references therein) and it has been shown that its slope can vary by up to 1.8-fold between open-ocean regions (Gardner et al., 2006). The power-law fit computed here was similar in the three spectral regions and the POC-c_p(650) relationship (c_p derived from WETLabs C-star transmissometer) was consistent with previous studies, regardless of whether c_p was derived with the same or different (e.g., Sea Tech) transmissometers (Figures 9A,B). To compute the accuracy with which the POC-c_p(650) relationship can predict surface POC, we used the method described above for the POC-chl_hplc relationship. We found that the POC-c_p(650) relationship developed using AMT-19 data can predict the POC values of AMT-22 with a median error of −2.2%, which was similar or lower than that computed from most published relationships (see Table 2). In addition, our POC-c_p relationships have typical uncertainties comparable to our POC-chl_hplc relationship (Table 2).

On the other hand, the lower predictive accuracy of the POC-c_p(660) relationship proposed by Cetinić et al. (2012) could be due to the specific temporal and environmental conditions of their study (e.g., North Atlantic spring bloom, dominance of diatoms). If this was the case, then this relationship may need to be considered specific for the North Atlantic bloom periods. Cetinić et al. (2012) report that the lowest POC-c_p slopes are found in areas with larger phytoplankton communities (e.g., diatoms with low carbon-cell volume ratio), whereas their largest slopes are found in ocean regions where smaller phytoplankton dominate (e.g., pico-eukaryotes). Similarly, DuRand et al. (2002) indicate that c_p per unit of carbon may increase with phytoplankton cell size. Our data are consistent with these earlier studies in that prediction errors of the POC-c_p(660) relationship derived by Cetinić et al. (2012) tend to decrease in highly-productive areas (POC > 60 mg m⁻³, Figures 9A,B) dominated by larger phytoplankton communities.

The POC-c_p relationship has the advantage that c_p(660) has been measured during the last decade from oceanographic rosettes. However, c_p cannot be derived directly from satellite data and optical transmissometers are not routinely deployed on autonomous platforms. Thus, there is still a need to evaluate other optical proxies of POC.

As with all inherent optical properties, particulate backscattering covaries to first order with the concentration of suspended matter, but it is also sensitive to changes in particle composition and size, which vary spatially and temporally as a result of external events (e.g., atmospheric deposition) as well as physical (e.g., aggregation-disaggregation) and biogeochemical processes (e.g., mineralization-dissolution) (Stramski et al., 2004a). In addition, it is challenging to measure b_bp in the open ocean with high accuracy because of limitations of current sensors (Twardowski et al., 2007; Dall'Olmo et al., 2012). This optical property, however, has the advantages of being retrievable from ocean-color remote sensing and being measured in situ by autonomous platforms. Thus, b_bp has been used as a proxy of POC in open-ocean waters where optical properties are dominated by biogenic organic matter (Morel and Prieur, 1977; Smith and Baker, 1978; Stramski et al., 2008).

We computed power-law fits between POC and b_bp for two spectral regions (470 and 526 nm, Tables 1, 3, Figures 8, 9). We found that the slopes of the relationships were almost equivalent between the cruises (Tables 1, 3), and we thus concluded that the underway system was also clean during AMT-22 (see also the section Particulate Backscattering). However, the POC-b_bp(470) relationship derived during AMT-19 predicted POC with the largest median error (25%, Table 3). Dall'Olmo et al. (2012) reported that during AMT-19 relatively large b_bp signals were measured on 0.2-μm filtered seawater, likely due to a small, but unidentified bias in their b_bp measurements. We therefore subtracted the 0.2μm filtered signal (b_b02) from b_bp to re-evaluate our POC relationships (Figure 12). Resultant median errors for the POC-b_bp(470) and POC-b_bp(526) relationships decreased by 7- and 2-fold, respectively (Table 3, Figure 12). These results indicate that even small biases in b_bp measurements can significantly affect the accuracy of the POC-b_bp relationship.

Additional factors that can affect the accuracy of POC-b_bp relationships between independent studies are: (1) uncertainties of POC estimates, (2) uncertainties in b_bp measurements, and (3) variability in the particles assemblages between regions (Gardner et al., 2006; Stramski et al., 2008; Cetinić et al., 2012). Published POC-b_bp relationships predict biased estimates (by ~±60%) of surface POC measured during AMT-22 (Table 3, Figure 9). The POC-b_bp(555) relationship proposed by Stramski et al. (2008) is based on data collected in waters similar to those found during AMT (e.g., similarly to our dataset, POC, POC:chl and b_bp/b_p ratios measured by Stramski et al. (2008), range between 12 and 270 mg m⁻³, 100–1,000, and 0.007–0.018, respectively). This relationship, however, was developed using b_bp data measured by Hydroscat-6 and a-βeta sensors (calibrated by the plaque method) installed on a CTD-rosette, whereas we used an ECO-BB sensor (calibrated by the micro-sphere method) installed in a flow-through chamber connected to the ship's underway system (see detail description in Dall'Olmo et al., 2009, 2012). The prediction error of the Stramski et al. (2008) POC-b_bp(555) relationship (median error of −27%) was slightly higher than that found in this study (Table 3). However, their prediction error was within the range (in absolute value) of the uncertainties in b_bp measurements (20–40%, Dall'Olmo et al., 2012). We therefore suggest that the difference between the POC-b_bp relationships derived from Stramski et al. (2008) and in this study could be due to the different methods applied to measure b_bp(526), as well as uncertainties in b_bp measurements. This hypothesis is supported by the agreement found between the POC-c_p relationships of Stramski et al. (2008) and in this study in the red spectral region (Table 2, Figure 9).

The Cetinić et al. (2012) POC-b_bp(700) relationship underestimated by 60% the POC measured during AMT-22 and we hypothesize this is due to the different protocols used for measuring b_bp and/or different wavelengths (for example, see Table 3), as explained above. However, the difference between the structural compositions of the particles between studies seems to be a significant factor determining the accuracy of their POC-b_bp relationships. For example, large phytoplankton assemblages predominated (diatoms with low carbon:volume-cell ratio) in Cetinić et al. (2012), whereas small and large phytoplankton assemblages were included in our case. Interestingly, and similar to what was found for the POC-c_p(660) relationship, the relative errors in POC prediction derived from their POC-b_bp(700) relationship fell to the lowest values in productive areas (Figure 9).

It is also reasonable to suggest that uncertainties in the Cetinić et al. (2012) POC measurements (POC <60 mg m⁻³) could be another factor that contributed to the difference between their predicted POC and those measured for AMT-22 in oligotrophic regions (Figure 9). For example, to increase the POC signal-to-blank ratios and decrease potential uncertainties in places with low POC concentration (POC <60 mg m⁻³, see sections Particulate Organic Carbon and Figure 3C), we calculated POC by using samples with the largest volume of seawater filtered (the volumes of the samples were ≥2 l for 80% (n = 296) of our POC measurements in these areas). As a result, low standard deviations were found for oligotrophic POC concentration (POC concentration in oligotrophic regions (mean ± standard deviation) = (27.2 ± 1.42) mg m⁻³; n = 148). In contrast, Cetinić et al. (2012) calculated POC by using smaller volumes (1.1 l) than those used here for a similar range of POC (<60 mg m⁻³). This in turns could decrease their POC signal-to-blank ratios and increase the errors in their POC measurements (Moran et al., 1999).

During both cruises, we sampled trophic states (oligotrophic and eutrophic) characterized by different POC concentration and structural composition of the particle assemblages. For example, the greatest POC concentration and the lowest POC:chl_hplc ratios were found in the productive areas (Figure 4). In these areas, large phytoplankton cells are also typically observed. Therefore, the influence of POC concentration and particle assemblages in the accuracy of POC-b_bp relationships was assessed by excluding POC and b_bp data from productive areas (POC >60 mg m⁻³, which is equivalent to ~b_bp > 1.5 × 10⁻³ m⁻¹) and by re-evaluating the relationships. The prediction error of the POC-b_bp relationships did not decrease significantly (only by 4%, Table 3), because approximately 80% of our data are located in oligotrophic regions. However, with the revised relationships the POC was underestimated by 55% (±14) in productive areas (Figure 12). Similarly, Stramski et al. (2008) found that their POC-b_bp(500) slope decreased by 1.3-fold when they excluded POC-b_bp data from productive upwelling regions. These results corroborate the suggestion that, to derive robust global POC-b_bp relationships, it is important to include POC-b_bp data from different trophic states (e.g., Gardner et al., 2006).

The variability in the particulate absorption coefficient is driven by the variability in particulate organic and inorganic components (phytoplankton biomass, biogenic detritus, bacteria, atmospheric dust), (Bricaud et al., 1998; Stramski et al., 2004b). Because POC potentially comprises all the organic components mentioned above and because the concentration of inorganic material is generally low in the surface open-ocean, we expect to find correlations between POC and a_p. As an example, a relatively strong relationship exists between POC and remote-sensing reflectance ratios and the latter quantity is mainly dependent on a_p in the surface open-ocean (Allison et al., 2010a). Indeed, in our study, the relationships based on a_p predicted POC with a median error of −6.4 and −12.6% in the blue and red spectral regions, respectively (Table 2). The POC-a_p relationships, however, also depends on the variability in POC:chl ratios, because a_p is mostly driven by phytoplankton pigments in the surface open ocean (Bricaud et al., 1998; Allison et al., 2010a), (section Relationship between POC and chl). Therefore, the arguments that explain why we can predict POC from a_p in this study, and why we cannot warrant application of this model to other seasons or other ocean regions, are the same as described above for the POC chl relationship (section Relationship between POC and chl). Nevertheless, the median prediction error of a_p(440) is similar to those computed for c_p and b_bp (Tables 2, 3), and a_p(440) can be retrieved from remote sensing (e.g., Mitchell et al., 2014). We therefore suggest that, similarly to chl, a_p could be used as a global POC proxy, only when the factors affecting the variability in the POC:chl ratio are accounted for in the bio-optical model (e.g., Behrenfeld et al., 2015; Arteaga et al., 2016).