The particulate optical backscattering coefficient (bbp) is a fundamental optical property that allows monitoring of marine suspended particles both in situ and from space. Backscattering measurements in the open ocean are still scarce, however, especially in oligotrophic regions. Consequently, uncertainties remain in bbp parameterizations as well as in satellite estimates of bbp. In an effort to reduce these uncertainties, we present and analyze a dataset collected in surface waters during the 19th Atlantic Meridional Transect. Results show that the relationship between particulate beam-attenuation coefficient (cp) and chlorophyll-a concentration was consistent with published bio-optical models. In contrast, the particulate backscattering per unit of chlorophyll-a and per unit of cp were higher than in previous studies employing the same sampling methodology. These anomalies could be due to a bias smaller than the current uncertainties in bbp. If that was the case, then the AMT19 dataset would confirm that bbp:cp is remarkably constant over the surface open ocean. A second-order decoupling between bbp and cp was, however, evident in the spectral slopes of these coefficients, as well as during diel cycles. Overall, these results emphasize the current difficulties in obtaining accurate bbp measurements in the oligotrophic ocean and suggest that, to first order, bbp and cp are coupled in the surface open ocean, but they are also affected by other geographical and temporal variations.
© 2012 Optical Society of America
Ocean biogeochemical cycles are tightly linked to the dynamics of suspended particles such as phytoplankton, heterotrophic organisms, detritus, and minerals. Understanding these dynamics is an important objective of oceanographic research and much can be learned by interpreting optical scattering measurements. Optical scattering can be measured remotely either by inversion of satellite ocean color data  or by in situ autonomous platforms, such as floats and gliders [2–5]. Unraveling the links between optical scattering and the concentrations and characteristics of oceanic particles, therefore, has the potential of extending the range over which these particles and their dynamics can be observed.
The following inherent optical properties are typically employed to characterize the scattering of light by marine particles: the particulate backscattering, scattering, and beam-attenuation coefficients (bbp, bp, and cp, respectively). Note that bp and cp are approximately equal in clear waters, due to the low influence of particulate absorption (ap) on cp [7, 8].
Previous studies demonstrated that bbp, bp and cp are to first order correlated to the concentration of chlorophyll-a (Chl), which is often considered an index of phytoplankton abundance [7,9,10]. More recently, however, it has been shown that these relationships are inherently noisy, because the Chl signal is strongly impacted by physiological variability [8, 11–13].
The particulate optical scattering is thought to be generated by particles in the phytoplankton size range (0.5–20 μm, e.g., ref. [14, 15]). The particle size domain responsible for bbp, on the other hand, remains uncertain. Some studies suggest that bbp is governed by submicron detrital particles and minerals [15–18], while others have shown the importance of larger particles (including phytoplankton cells) in generating the observed bbp variability [12, 19, 20].
The particulate backscattering efficiency (bbp:bp) is less dependent on the absolute concentration of particles than either property alone and is largely governed by particle size, composition, and morphology [22, 23]. Highly refractive particles, such as the minerals contained in atmospheric dust or coccolithophorids, are expected to be associated with high bbp:bp [22–24]. On the other hand, bbp:bp for a given particle composition should, to first order, increase when small particles become relatively more abundant than large particles [22,23]. However, the uncertainties on the sources of bp and bbp as well as potential limitations in current optical models of oceanic particles may limit the interpretation of the bbp:bp ratio.
Experimental studies have demonstrated a relatively large range of variation for bbp:bp (i.e., approximately 0.2%–2%, refs. [8, 12, 13, 24–26]), in part due to difficulties in accurately determining bbp in clear oligotrophic waters. Nevertheless, a surprisingly coherent value for bbp:bp of around 1% was recently reported in diverse surface open-ocean waters, using data from a series of cruises where scattering measurements were conducted using a consistent methodology . Although other studies have also measured similar backscattering ratios , this finding suggests that methodology may be an important source of uncertainty in bbp and bp measurements, especially in clear oligotrophic waters.
Both cp and bbp vary spectrally and their spectral dependency is commonly modelled as a power law :6]; ; see also ). This latter equation establishes a link between the spectral properties of cp and the relative distribution of large vs. small particles and it has been verified with in situ measurements from coastal waters . A drawback of using the spectral slope of cp to infer information on the particle size distribution is that the particulate beam-attenuation coefficient cannot be determined from space. Moreover, due to the finite acceptance angle of commercial instruments, cp and bp are never exactly measured .
Loisel et al. (2006) inverted space-based ocean color measurements to estimate the spectral slope of bbp . These authors found that γbbp exhibited positive values (relatively more small particles) in oligotrophic waters and negative values (relatively more large particles) in more eutrophic waters. Building on this insight, Kostadinov and collaborators  developed an inversion algorithm to relate γbbp to the slope of the particle size distribution and produced global maps of the abundances of three different size classes of phytoplankton .
Despite these developments, simultaneous measurements of bp and bbp in the open ocean are still limited, especially in oligotrophic regions. Here, we present and analyze a dataset of particulate scattering and backscattering measurements collected during the 19th Atlantic Meridional Transect (AMT19). Our main objectives are to investigate the variability of bbp and cp and to test existing bio-optical relationships. We show that bbp was relatively high in the Atlantic compared to previous data from other oceanic regions. This discrepancy could either be due to a more significant contribution from particles smaller than 0.2 μm or, most likely, to a small bias in our measurements. In the latter case, this analysis confirms that the shape of the volume scattering function of marine particles is remarkably constant.
Data were collected on board the RRS James Cook from October 13th to December 1st 2009 covering a meridional transect approximately from 45°N to 40°S (Fig. 1).
2.1. Flow through optical measurements
Optical measurements were conducted on seawater from the ship’s clean flow-through system pumped from a depth of about 5 m. The methodology described in ref.  was followed, including one-minute data binning and the use of a 0.2μm-cartridge filter (Cole Parmer) through which the water supply was diverted every hour for ten minutes to provide a baseline for particulate absorption and attenuation measurements.
Continuous bbp measurements were made using a WET Labs ECO-BB3 meter (S/N 349, thereafter referred to as BB349) in a flow-through chamber, as described in ref. . The characterization of the instrument included an evaluation of the effective wavelengths as described in ref. . The instrument was calibrated by the manufacturer in July 2009. In addition, we conducted calibrations at the beginning (Oct. 20th, 2009) and end (Nov. 22nd, 2009) of the cruise, following the same protocol adopted for our previous studies [8, 12] and described in the Appendix. Table 1 reports the results of these calibrations and shows that the blue and green channels were relatively stable, while the scaling factor of the red channel (656 nm) varied by 21% from the factory calibration. Because of this drift, data from the red channel were not used in this analysis.
Three dark counts determinations were carried out during the cruise (yeardays 293, 313, and 326) by covering the detectors with black tape and submerging the instrument in water. Results from these independent replicate measurements indicated that the dark counts varied at most by 2 counts in the blue and green channels, but as much as 6 counts in the red channel (Table 2). In addition, the dark counts determined during the cruise differed considerably from those provided by the manufacturer.
Average scaling factors, S, and dark counts, D, measured during the cruise were employed in the processing of the BB349 data. The contribution to bbp by reflections from the internal walls of the flow-through chamber, bb,wall, was determined in the laboratory (following the procedure described in ref. ) after the cruise and found to be (3.70 ± 0.83) × 10−4 m−1 and (3.14 ± 0.52) × 10−4 m−1 for the blue and green channels, respectively. Calculation of the particulate backscattering coefficient was conducted as in ref. , after subtracting the contribution of pure sea water, βsw (differences in temperature and salinity were accounted for using data from the ship’s underway CTD system; [36,37]) and using a χp factor of 1.1 to relate the volume scattering function at 117° to bbp :12]).
To understand how the uncertainty in dark counts affects the resulting bbp values, the entire BB349 dataset was reprocessed using the dark counts supplied by the manufacturer. Resulting bbp values were then compared to those derived using dark counts measured during the cruise. Relative differences ranged from 5% to 25% (not shown), with largest values in the clearest waters. This analysis demonstrates the importance of employing field-based determinations of dark counts for achieving maximally accurate bbp estimates in oligotrophic regions .
The combined uncertainty in bbp due to the uncertainties in all its input parameters (Tables 3, 4) was computed using the standard law of propagation of uncertainty  and assuming uncorrelated uncertainties. The median absolute uncertainties were 3.3 × 10−4 m−1 and 2.5 × 10−4 m−1, for the blue and green channels, respectively. Relative uncertainties in bbp ranged approximately from 20% in eutrophic waters to 40% in oligotrophic waters.
Given that bbp was accurately determined only at two wavelengths, γbbp was derived as γbbp = −log[bbp(470)/bbp(526)]/log(470/526). These γbbp values should be treated with caution, as they may be affected by uncertainties due to the limited number of wavelengths employed in the computation.
2.1.2. cp, ap, and bp
Spectrally-resolved particulate beam-attenuation, cp, and absorption, ap, measurements were conducted with WET Labs ACs (hyperspectral between 400 and 750 nm, with a spectral resolution of 5 nm and a band pass of 15 nm) and AC9 (nine wavelengths between 412 and 715 nm, with a band pass of 10 nm) absorption and attenuation meters. The ACs was used from the beginning of the cruise, but after 13 days (i.e., yearday 299) the lamp of the attenuation channel (i.e., C-channel) failed. To ensure continuous measurements of spectral cp after the ACs failure, the AC9 meter was added to the flow-through system, without removing the ACs. cp and ap for the ACs were computed after subtraction of baseline signals derived from the 0.2μm-filtered water following established protocols [12, 40]. ap for the AC9 meter was computed by subtracting the 0.2μm-filtered signal and applying a scattering correction . Particulate scattering coefficients, bp, were derived as the difference between cp and ap. AC9 measurements were linearly interpolated to derive cp and bp at 470 and 526 nm. The spectral slope of cp, γcp, was estimated by fitting Eq. (1) to cp spectra.
Discrete water samples (2–4 liters) were collected from the flow-through system during the cruise, filtered onto Whatman GF/F filters and immediately stored in liquid nitrogen. Phytoplankton pigments were determined in the laboratory after the cruise by high performance liquid chromatography (HPLC) analysis . Total chlorophyll-a concentration (TChl-a) was calculated by summing the contributions of monovinylchl-a, divinyl-chl-a (DivChl-a), and chloro-phyllide a.
The concentration of chlorophyll-a (Chl) was also estimated from the ap line height around 676 nm as: Chl = [ap(676) – 39/65ap(650) – 26/65ap(715)]/0.014, ref. . While the AC9 instrument outputs measurements at 650, 676, and 715 nm, the ACs does not. Therefore, the ACs data were linearly interpolated to estimate ap values at 650, 676, and 714 nm.
As mentioned above, two different instruments (i.e., ACs and AC9) were employed to measure ap and estimate Chl during the cruise. Therefore, an intercalibration was required to make Chl estimated from the ACs ap data comparable to the Chl derived from the AC9 ap data. Simultaneous measurements of ap by the ACs and AC9 instruments were, however, available only after the failure of the ACs C-channel, used for the scattering correction required to derive the ap data. Thus, although simultaneous measurements of ap from the two instruments were available, the ap spectra derived from the ACs instrument could not be scattering corrected and thus were, in principle, not comparable to the AC9 ap spectra. The sensitivity of the ap-based Chl on the scattering correction was therefore investigated by exploiting the ACs ap measurements collected at the beginning of the cruise, when the ACs C-channel was still functioning. The first 13 days of ACs ap data were reprocessed without applying any scattering and residual temperature corrections and Chl was derived from these newly processed ap spectra. The ratio between Chl derived from the ACs with and without the scattering correction was statistically indistinguishable from one (median ± σ68 = 1.03 ± 0.08, where σ68 is half the central 68th percentile range and is equivalent to one standard deviation, if the data are normally distributed). This result indicates that Chl can be computed from the ACs ap spectra, even if a scattering correction is not implemented. We therefore compared the Chl values estimated from the simultaneous AC9 and ACs ap data collected after the failure of the ACs C-lamp, even though no scattering correction could be applied to the ACs ap data. The ratio of these ACs-to-AC9 Chl was found to be 0.69± 0.08 (median ± σ68), indicating that the Chl derived from the ACs was about 30% lower than that derived from the AC9. This difference is likely due to the “band pass” of the AC9 that is narrower (10 nm) than that of the ACs (15 nm). The median ACs-to-AC9 Chl ratio was finally employed to correct the Chl derived from the AC9 data.
Figure 2 compares coincident HPLC-derived TChl-a and optically-determined Chl (derived from both AC9 and ACs instruments) and shows that the optically-determined Chl was underestimated by about 10% (in median) and had a precision (σ68 of relative residuals) of about 10%. The 10% bias was removed from Chl for the rest of the analysis.
2.2. Measurements of bbp from profiling package
An independent WetLabs ECO-BB3 backscattering meter (S/N 499, hereafter BB499) was installed on a profiling package that was deployed daily. The instrument was equipped with spectral channels at 470, 526, and 595 nm.
A calibration based on beads was not completed for this instrument at the beginning of the cruise. However, an intercalibration between flow-through and profiling meters was conducted at the beginning of the cruise (Oct. 16th–18th, 2009). This inter comparison consisted of collecting coincident data with the two meters by temporarily installing the profiling meter in a flow-through chamber similar to that where the flow-through meter was installed. Scaling factors, , for the profiling BB499 meter were derived as , where each variable depends on wavelength, S349 is the scaling factor derived for the flow-through instrument as the average of the two cruise calibrations, and are the coincident raw counts recorded by the two instruments, D349 and D499 are the corresponding dark counts, and the 〈〉 brackets indicate that the median value was taken. In addition, a standard calibration was completed towards the end of the cruise using a dilution series of NIST-traceable 2-μm polystyrene beads, Thermo Scientific). The relative differences between the scaling factors derived from the intercalibration and standard calibration and those provided by the factory are presented in Table 1. Dark counts were also measured during the cruise and showed significant deviations from those provided by the manufacturer (Table 2). However, these D499 value were not determined with the BB499 instrument installed on the profiling package and thus could be biased. Data from the 595-nm channel were excluded from the rest of the analysis because of the unexplained large change (23 counts) in its dark counts. The bbp values and corresponding uncertainties derived from the profiling instrument (BB499) were computed following the same methodology employed for the flow-through instrument (BB349) (for in-water measurements no correction for wall effects was needed).
Median bbp data were extracted from each upcast profile between 4 and 10 meters to match the depth of the ship’s water intake. A comparison of coincident bbp values determined by the two independently-calibrated and deployed instruments indicated biases of −16% and −13% and precisions of 7% and 6% for the 470 and 526 nm channels, respectively (Fig. 3). The above biases may be due to uncertainties in dark counts, that were determined with the instrument connected to an electrical system (i.e., power supply and cables) different from the one used to collect measurements.
Chl, bbp and bp displayed largest values in temperate and tropical regions and minimal values in the subtropical gyres (Fig. 4). Chl varied by over two orders of magnitude, while bbp and bp varied by over one order of magnitude. The broadscale patterns of bbp(526) and Chl were in agreement with previous measurements in the Atlantic ocean [45, 46]. The particulate backscattering vs. Chl relationship obtained during AMT19 was also in general agreement existing bio-optical models, although bbp(526) was underestimated by existing models at low Chl (Fig. 5(a)). On the other hand, bp(526) agreed better with existing bio-optical models (Fig. 5(b), [10, 12]).
The particulate backscattering ratio, bbp:bp, varied latitudinally, with maximum values (∼ 0.02) in oligotrophic regions and minimum values in the eutrophic waters (< 0.01, Fig. 6(a)). An important fraction of this variability (∼ 30%) appeared to be due to variations occurring at the diel scale. The chlorophyll-specific particulate scattering and backscattering coefficients ( and , respectively) varied by over an order of magnitude along the transect with maximum values in the most oligotrophic regions and also showed strong diel cycles (Fig. 6(b)). Finally, the spectral slopes of bbp and cp (γbbp and γcp, respectively) were inversely correlated, with γcp displaying higher values in productive regions and lower values in the most oligotrophic waters (Fig. 6(c)). Strong variations of γcp were observed at the end of the transect in the most productive region sampled. While γcp appeared to be affected by diel cycles, γbbp did not.
Particulate absorption contributed, as expected, only a relatively small fraction of cp (data not shown): the largest values of ap:cp were found at 440 nm (8 – 16%, 95th percentile range), while minimum values were found for wavelengths smaller than 532 nm (2 – 6%). The ratio of particulate backscattering to beam-attenuation at 526 nm, bbp:cp, ranged from less than 0.002 to 0.020, with a median value (± σ68) of 0.0130 ± 0.0032 (Fig. 7, solid line). bbp:cp values measured during AMT19 were skewed towards higher values than those of previously published datasets .
The backscattering signal measured on 0.2μm filtered samples after subtraction of the pure seawater signal (i.e., bb02) varied latitudinally with larger values in the most productive regions of the transect (Fig. 8). 95% confidence intervals suggest that bb02 was not significantly higher than zero along most of the transect (Fig. 8). This finding is in agreement with a previous study that reported negligible bb02 values in the surface equatorial Pacific , although the average bb02 values measured during AMT19 appeared larger than previously observed. bb02 contributed a relatively important fraction of bbp: 0.19 ± 0.06 and 0.11 ± 0.04 at 470 and 526 nm, respectively (Fig. 8). bb02 was positively, but weakly related to Chl and bulk values of cp, bbp and ap (not shown).
4.1. bbp:Chl, bp:Chl
In this study, a dataset of surface optical scattering measurements collected along the 19th Atlantic Meridional Transect is presented. As previously observed, bbp and bp were, to first order, related to Chl [8, 10, 12, 13], although considerable variability exists in these relationships. At least three reasons may explain this relatively large variability. First, changes in the ratio of backscattering to Chl may register changes in the phytoplankton carbon-to-Chl ratio associated with changes in phytoplankton acclimation to the diverse temperature, nutrient, light environments, and species compositions encountered during the transect [8, 11, 21, 47–49]. Second, since the AMT samples a wide range of ecological provinces, the large variability observed in bbp:Chl may have also been driven by changes in the efficiency with which phytoplankton backscatter light due to variations in cell size, composition, and morphology. Third, bbp:Chl may depend on both phytoplankton (driving changes in Chl) and other particles (mostly driving changes in bbp) and the coupling between these drivers may vary with the trophic status of the ocean [13, 48, 50]. Most likely, a combination of these factors explains the observed variability in the and ratios.
The bbp:cp ratio over most of the transect was higher than in previous cruises that employed the same flow-through methodology [8,12]. This observation, if verified, is at odds with the findings of refs.  and  that there is a consistent relationship between bbp and cp in the surface open ocean. These authors argued that, since the particulate beam-attenuation coefficient is likely controlled by variations in phytoplankton carbon biomass, then a consistent bbp:cp ratio would imply that one could estimate cp, and thus phytoplankton carbon, from remotely sensed bbp [8, 12, 21]. Results from the analysis of the AMT19 dataset suggest that such endeavour might be more complex than previously thought and could require regional parametrizations. Alternatively, the deviation of the measured bbp:cp ratio from published values could be also due to a small bias in bbp (∼ 1 × 10−4 m−1 at 526 nm; see sections 4.3 and 4.4). Importantly, this bias is smaller than the median uncertainty of our bbp measurements (∼ 2.5 × 10−4 m−1 at 526 nm, Table 4).
Previous studies reported bbp:bp measurements from two independent datasets of optical scattering collected in the ultra-oligotrophic South Pacific sub-tropical gyre [25,26,45]. Despite the general agreement demonstrated between the bbp values measured in these two datasets , the near-surface bbp:bp values reported showed considerable variability ranging from less that 0.004 at 650 nm (Fig. 5 in ref. ) to more than 0.015 at 555 nm (Fig. 11 in ). These large discrepancies are unexpected given the relatively neutral spectral shape of bbp:bp (refs. [22, 24, 25]). However, although in the more productive waters the bbp:bp ratio at 555 nm was relatively stable and similar to the average value reported in ref. , higher values of bbp:bp were observed in the most oligotrophic waters sampled (Chl < 0.075 – 0.100 mg m−3 see Figs. 2 and 11 in [26, 45]). The bbp:bp values recorded during AMT19 were also maximal in the most oligotrophic waters (Figs. 4 and 6). This similarity suggests that the increase of bbp:bp in oligotrophic waters could be a general bio-optical feature [9, 28] or could be related to a decrease in the achievable bbp accuracy in very clear waters.
The backscattering measured on sample water that passed through the 0.2-μm filter was found to be higher than zero, although not significantly at the 95% confidence level, and contributed about 10% of the bbp signal at 526 nm (Fig. 8). Previously, bb02(526) was found to be indistinguishable from zero (at the 95% confidence level) in the Equatorial Pacific  and in the Mediterranean Sea (Dall’Olmo G., unpublished data), or significantly higher than zero, but negligible with respect to the bulk bbp, in the North Atlantic and North Pacific (Westberry T.K., unpublished data).
It is important to recognize that bb02 may not accurately represent the backscattering of colloids smaller than 0.2 μm. This is because it may be affected by biases due to the use of filters to partition the particle size distribution, including particle breakage and retention of particles smaller than the nominal pore size (see discussion in ref. ). However, the same methodology was employed in the current and previous studies. Thus, similar biases should apply, which supports the comparison of bb02 values between cruises. Excessive clogging of filters or particle accumulation on the optical surface of the flow-through instrument were limited during AMT19, as shown by the negligible changes in bb02 after filters were replaced and after the flow-through system was cleaned, respectively (Fig. 8). Therefore, the unusually high bb02 values measured during AMT19 could either represent the contribution of particles smaller than 0.2 μm to the bulk bbp coefficient, or reflect the magnitude of the small bias that seems to affect our bbp measurements.
To quantify the importance of bb02 on the observed bbp:cp ratio, we subtracted bb02 from bbp and recomputed the backscattering efficiency: (bbp−bb02)/cp. We found that (bbp−bb02)/cp was in good agreement with previous estimates of bbp:cp obtained using the same methodology (dashed line in Fig. 7(b)) and thus that most of the anomaly observed during AMT19 in the bbp:cp ratio was removed by subtracting bb02 from bbp. One advantage of subtracting bb02 from bbp is that any bias caused by uncertainties in dark counts and/or in bb,wall should cancel out. Thus, the improved agreement between (bbp−bb02)/cp and published values of bbp:cp supports the hypothesis that a bias of the same magnitude as the estimated uncertainties in bb may affect our measurements.
Ancillary measurements would otherwise be needed to explain the real origin of bb02 and why it was higher during AMT19 than in other previous cruises in oligotrophic waters. Unfortunately these ancillary data (e.g., colloidal size distributions) were not collected. Some potential explanations are therefore discussed below.
If bb02 was indeed related to the presence of very small particles (i.e., colloids), it would seem reasonable to find a correlation between bb02 and the concentration of dissolved organic carbon (DOC). No measurements of DOC were available during AMT19, but some insights can be gained by comparing the spatial distributions of bb02 and existing DOC measurements. In general, DOC is relatively high in the tropical and subtropical surface ocean, where a stable mixed layer allows refractory DOC to accumulate . On the other hand, DOC is lower at higher latitudes where the water column is less stable and DOC-depleted deep waters are mixed to the surface . The observed bb02 values have a spatial distribution opposite to that expected for DOC, with higher values in the regions where the mixed layer was less stable (Fig. 8(a)). DOC, therefore, is unlikely to be the dominant control of bb02, possibly because colloids are thought to contribute only 10% of DOC [52, 53].
Another potential explanation for the relatively high values of bb02 could be the presence of fine Saharan dust particles in the water. Dust deposition, however, is estimated to be one order of magnitude more intense in the northern than in the southern Atlantic (e.g., ref. ). If atmospheric dust was responsible for the relatively elevated bb02 values, one would expect bb02 to be higher in the north than in the south Atlantic. Figure 8, however, does not show important differences in bb02 values between the northern and southern parts of the transect, suggesting that atmospheric dust is unlikely to be the cause of the elevated bb02.
In conclusion, the bb02 measurements were anomalously higher than in previous cruises in meso- and oligotrophic regions, accounted for about 10% of the bbp signal at 526 nm, and could explain the observed anomalies in the bbp:cp ratio. However, based on the available data, no clear biogeochemical explanation can be provided for this anomaly. It therefore seems most plausible that the bb02 values could be due to a bias of about 1 × 10−4 m−1 in our bbp(526) determinations. Importantly, such bias is well within the uncertainties of bbp(526). If such a bias was indeed the cause of the observed anomalies in bbp:cp and bb02, then we could conclude that the AMT19 dataset confirmed the previous finding that bbp:cp is remarkably constant in the surface open ocean.
4.4. Uncertainties in bbp and bb02
Particulate backscattering estimates in oligotrophic regions are extremely sensitive to measurement uncertainties . In this study, the main source of bbp error was the uncertainty in the scaling factors (S) (Table 4). These uncertainties in S, in turn, depend on the uncertainties in multiple variables including the spectral and angular weighting functions of the instrument, as well as the complex refractive index and size of the beads used in the dilution series . The relatively strong dependency between the uncertainties in S and bbp, as well as the sensitivity analysis to the dark counts described in the method section highlight the need for a detailed understanding, characterization, and validation of the the instrument(s) employed for the measurements and the importance of identifying, quantifying and minimizing all sources of uncertainty affecting bbp . In particular, future studies should strive to validate particulate backscattering estimates by comparing measurements collected using instruments that employ different calibration procedures [35, 43, 61]. It is noteworthy that a recent publication by WET Labs scientists  has re-evaluated the angular weighting function, W, of WET Labs ECO-BB meters and suggests that W is centered at 124 degrees (instead of 117 degrees) and it is significantly wider than what was previously reported . Nevertheless, to be consistent with our previous studies and until independent verification of this new specification is provided, in this study we have chosen to maintain the “standard” W function .
Overall our results and the above considerations emphasize the difficulties in obtaining accurate particulate backscattering measurements in the open ocean with the current instrumentation. This limitation is likely biasing the development and validation of open-ocean remote-sensing algorithms and it is hampering progress in the understanding of the sources of bbp and in the application of bbp measurements to the study of ocean biology and biogeochemistry.
4.5. Spectral slopes of cp and bbp
Important qualitative differences in the spectral slopes of bbp and cp were observed in this study (Figs. 6, 9). Under the hypotheses described in the introduction, the spectral slope of cp should, theoretically, be linearly related to the slope of particle size distribution (PSD). Thus, γcp should increase as small particles become relatively more abundant than large ones [6, 29, 30]. Similarly, spectral bbp has also been used to estimate the parameters of the particle size distribution .
During AMT19, bbp spectra followed expected patterns [32, 33]: γbbp increased from the most eutrophic regions, where large cells are abundant, to the most oligotrophic regions that are dominated by small cells (Fig. 6). In contrast, γcp was maximal in eutrophic regions and minimal in oligotrophic waters (Fig. 6). To account for this anomalous behavior in γcp, one or more of the above hypotheses must be invalid. Indeed, deviations from the power law approximation of the PSD are common in the open ocean, both in oligotrophic  and productive regions and have been shown to cause significant perturbations to γcp in coastal waters . In addition, the acceptance angles of the AC9 and ACs transmissometers (0.93°) are known to reduce the instrument sensitivity to particles larger than about 10–20 μm .
During diel cycles, on the other hand, γcp followed expected dynamics, increasing during the day and decreasing at night (Figs. 6 and 9). These patterns have been previously observed [40,57,58] and are thought to be caused by the increase in size of synchronous cell populations during the day and their decrease at night following cell division [58, 59].
4.6. Diel variability
Although spatial and temporal variability are superimposed in this dataset, diel cycles appeared to considerably affect the measured optical properties. As in previous studies [12, 40, 57, 58], these diel variations became most evident when the dependence on particle concentration was minimised by plotting ratios of optical properties (Fig. 6). bbp:cp, bp*, bbp*, γcp, and on closer inspection cp, all showed diel variations, while bbp and γbbp did not. Chl also showed clear diel cycles, at least during some parts of the transect, decreasing during the day and increasing at night (Fig. 9). These diel cycles of Chl are confirmed by discrete HPLC measurements (Fig. 9). Diel cycles in optical properties are believed to be related to the dynamics of synchronized populations of phytoplankton cells (and associated living and non-living particles) [59,60]. Our dataset further demonstrates that this phenomenon is widespread in the surface Atlantic ocean.
An extensive data set of flow-through optical scattering properties collected in the surface Atlantic ocean was analyzed. The the main results are:
- The bbp:cp and bbp:Chl ratios were higher than those predicted by existing bio-optical relationships and measured using the same methodology in other oceanic regions.
- bbp from water filtered through 0.2 μm filters was higher than previous studies and contributed about 10% of the bulk bbp(526).
- The most parsimonious explanation for these anomalously high values of bbp and bb02 is that a bias of the same order of magnitude of the measurement uncertainties (1×10−4 m−1 at 526 nm) affected our bbp and bb02 measurements.
- If such bias indeed affected our bbp measurements, then bbp:cp and bbp:Chl ratios measured during AMT19 would be consistent with other global data sets and confirm the constancy of the bbp:cp ratio in surface open-ocean waters.
- These results emphasize the difficulties in obtaining accurate bbp measurements in the oligotrophic open ocean.
- The spectral slopes of cp and bbp were found to be inversely correlated during the cruise, with γbbp following expected patterns.
- Diel cycles in all optical properties (except bbp and γbbp) and bulk Chl were evident along the entire meridional transect, especially when ratios of properties were computed.
6. Appendix: Calibration of WET Labs ECO-BB3 meters
- The BB3 meter, C-star transmissometer (660 nm) and flow-through chamber were thoroughly cleaned with Milli-Q water and a mild detergent and then thoroughly rinsed with Milli-Q water.
- The BB3 was installed in the flow-through chamber and connected in series to the C-star transmissometer and to a 2L flask that was used as a reservoir.
- A filter holder containing a 0.2-μm cartridge filter (Cole Parmer) was also installed in series in the above system.
- The system was then filled with Milli-Q water. To minimize impurities in the system, the water was continuously recirculated through the 0.2-μm cartridge filter for about 1hr by means of an in-line pump.
- The filter and filter holder were removed from the system.
- With the pump switched off, data were recorded from both the BB3 meter and C-star transmissometer for about 1–2 minutes.
- 1 or 2 drops of 2-μm NIST-traceable polystyrene beads (that had been sonicated for about 5 minutes; Thermo Scientific) were then added inside the reservoir and the pump was switched on to thoroughly mix the beads in the system, as verified by monitoring the data in real time. Note that WET Labs now recommends to use NIST-traceable 0.1-μm beads for channels at blue and green wavelengths , but this information was not available when the instruments used in this study were deployed. The use of 2-μm instead of 0.1-μm beads is expected to cause an underestimation of the scaling factors of about 5–10% (J. Sullivan, personal communication).
- With the pump switched off, data were recorded from both the BB3 meter and C-star transmissometer for about 1–2 minutes.
- The above two steps were repeated until the BB3 meter counts reached a value of 1000 (which was well above the counts encountered during AMT19).
- Median values from the scattering data were linearly regressed vs. the median values of the BB3 counts at each dilution step to determine the slope of the relationship.
- θ is the centroid angle of the BB3 (i.e., 117°). Note that a recent publication  suggests that the centroid angle of ECO-BB3 meters is now believed to be 124°. However, to be consistent with our previous studies [8, 12], we decided to adopt the 117° value until the new 124° value will be independently verified.
- λ is the wavelength (weighted by the spectral response of each instrument).
- [β (θ, λ)/bAC9(λ)] is a theoretical coefficient that relates the volume scattering function at the centroid angle and wavelength of the BB3 instrument to the scattering coefficient measured by a WET Labs AC9 meter at the same wavelength. This coefficient is computed through Mie simulations and depends on the characteristics of the beads (i.e., refractive index and size distribution) used, the spectral response and acceptance angle of the AC9, as well as on the the spectral responses and angular weighting function, W, of the BB3 meter (see definition of W and Eq. (9) in ref. ). Comparisons with the coefficients computed by WET Labs showed absolute differences of 4%, 9% and 1% in the 470, 526, and 656 nm channels, respectively. The larger difference in the green channel could be related to the shift from the nominal green wavelength that we observed . Note also that WET Labs did not routinely employ NIST-traceable beads and that the difference in scaling factors estimated based on dilution series using NIST-traceable and non-NIST-traceable beads (of the same nominal size) can be up to 8% (J. Sullivan, personal communication).
- is a theoretical coefficient used to convert C-star scattering measurements into equivalent AC9 scattering measurements. and are the efficiency factors for scattering. We derived these coefficients by means of Mie simulations that accounted for the characteristics of the beads employed and the spectral responses and acceptance angles of the two instruments.
- [bCstar(650)/C(λ)] is the experimental slope computed by linearly regressing median C-star measurements, bCstar(650), versus the median counts recorded by the BB3 instrument at each wavelength, C(λ), and at each bead dilution step.
The authors would like to thank the captain and crew members of the RSS James Cook. C. Gallienne is thanked for his help in deploying the profiling package. J. Sullivan at WET Labs and an anonymous reviewer are thanked for their comments on an earlier draft of this manuscript. G.D.O. was funded by NASA grant NNX09AK30G and by the UK National Centre for Earth Observations. This study was supported by the UK Natural Environment Research Council National Capability funding to Plymouth Marine Laboratory and the National Oceanography Centre, Southampton. This is contribution number 218 of the AMT programme.
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