Relationships between optical backscattering, particulate organic carbon, and phytoplankton carbon in the oligotrophic South China Sea basin.

The particulate backscattering coefficient (bbp) provides effective proxies for particulate organic carbon (POC) and phytoplankton carbon (Cphy); however, their bio-optical relationships in the oligotrophic ocean are rarely reported. In this work, based on the in-situ synchronous optical and biogeochemical measurements in the oligotrophic South China Sea (SCS) basin, we refined the regional relationships between POC (and Cphy) and bbp and investigated the impacts of phytoplankton community compositions and size classes on the bbp variability. The observations showed that: 1) POC and Cphy exhibited good linear relationships with bbp; 2) the relationship between Cphy and POC could also be fitted in a linear function with a positive POC intercept, and the POC contributed by phytoplankton-covarying non-algal particles was nearly two-fold of Cphy; and 3) the POC-specific bbp (b*bp) was positively correlated with the fraction of the phytoplankton groups haptophytes (Type 8) and diatoms to total Chla, but negatively correlated with the fraction of pico-phytoplankton to Chla (fpico). These findings suggest that in oligotrophic waters, the variability of b*bp was mainly determined by the variability in the relative contribution of large phytoplankton with complex structures.


Text SUncertainty analysis of POC
The accuracy of POC measurement was based on several potential sources of errors [1,2]. Firstly, the carbon mass on the filters can be underestimated due to insufficient sampling of the rare large particles, incomplete retention of small particles, and breakage of the large particles. However, it is currently not possible for us to evaluate these. To mitigate these potential biases, a relatively large volume (4.3 L) of water was filtrated so as to include a larger number of rare particles, and a small vacuum pressure (<100 mm Hg) was adopted to increase the retention of the small particles and decrease the breakage of the large particles. Secondly, the carbon mass can be overestimated due to the adsorption of dissolved organic carbon (DOC) on the filters. To quantify this positive bias, each day a blank pre-combusted GF/F filter was placed on the filter manifold and wetted in 20 mL of 'pure' seawater for 1 hour so that it was saturated similarly to the POC samples. Here the 'pure' seawater refers to seawater filtered through a 0.22 µm Millipore cellulose acetate membrane. In this cruise, the measured carbon blank was 27.3±5.3 (mean ± standard deviation) µg C, with a range spanning 18.5-37.1 µg C (n=19). This result was comparable to previously published values, e.g., 21±9.4 µg C through double filter blanks approach, 18.9±10.6 µg C through triple-volume intercept blanks approach, and 25.4 µg C for the samples collected at 600 m [3], 48 µg C through volume intercept blanks approach [4]. Thus, carbon blanks represent a small uncertainty of 1.2 (5.3/4.3) mg m -3 of the final POC value.

Text SBackscattering correction
The accurate determination of b b and b bp was influenced by some factors including 1) the path length attenuation between instrument and detection volume, 2) the appropriate values of β w and b bw , and 3) the chosen value of parameter χ p (140°).
Due to the path length attenuation, the measured backscattering was underestimated to some extent, and a compensated correction (sigma correction) was conducted following the 'User's Manual v2.8': β=σ(K bb )β u , (S1) σ K bb =k 1 exp(k exp K bb ), (S2) where β u is the uncorrected volume scattering function, k 1 and k exp are constant parameters, and K bb is the attenuation. K bb was not measured in this cruise, and its value can be estimated empirically: K bb =a p +a g +0.4b p , (S3) where a p is the particulate absorption and was from the measured value (see Methods section). The a g is the colored dissolved organic matter absorption and was estimated from a ph empirically [5]: a g λ =0.2a ph λ exp(-0.014 λ-440 ), (S4) where b p is the particulate scattering and was estimated from the uncalibrated particulate backscattering (b bpu ) is backscattering probability and was set as 0.015. Fig. S1 shows that the calculated σ(K bb ) was very small (<1.015). Thus, in the SCS basin, the path attenuation had an insignificant impact on the β measurement.
Seawater scattering is generally very small and contributes <10% of the total scattering (b) even in the clear waters, but it contributes greatly to the total backscattering (b b ) owing to the nearly isotropic nature of water molecular scattering [6]. In the clearest water, the seawater backscattering (b bw ) can contribute 80% of b b in the blue bands [7]. Therefore, accurately estimating b bw is important for the final determination of b bp and b b . The measured or theoretical estimates of β w and b bw reported in previous studies show some difference [8][9][10]. Here two most widely-used estimates (Morel's and Zhang's approaches) were compared. In Morel's approach, β w and b bw can be estimated as follows: where δ is the depolarization ratio, which value was set to 0.09 suggested by Morel [8]. In Zhang's approach, β w and b bw are estimated with dependencies on the measured temperature, salinity, and a depolarization ratio of 0.039. Fig. S2 shows the comparisons of these two approaches. In our observations, the variations of estimated β w (λ, 140°) from Zhang's approach were quite small (<2%), as the variations of temperature and salinity were also not large. The β w (λ,140°) from Zhang's approach were lower than the values from Morel's approach with the largest difference (15%) at 420 nm. In the SCS basin, the total backscattering was mainly contributed by seawater, and the contributions of β w (λ,140°) to β(λ,140°) were up to 40-72% (Zhang's approach) and 43-82% (Morel's approach). Small difference in β w estimates can cause a large difference in β p estimates. Accordingly, the calculated β p (λ,140°) from Zhang's approach were significantly larger than the values from Morel's approach with the largest difference exceeding 60%. Zhang et al. [10] show that their results agreed with laboratory measurements [11,12] with an average difference of 1%. In this study, we therefore used Zhang's approach to estimate β w and b bw .
Theoretically, the best way to estimate b bp is to integrate β p over all the backward angles (90-180°). However, due to the difficulty in measuring β p in the full backward hemisphere, the b bp is practically estimated from β p measured at a fixed angle (e.g. 140° for HS6). The conversion factor χ p (140°) is not constant in the literature, and different values have been reported in many previous works, e.g. 1.18±0.041 from Boss and Pegau [13], 1.13 from Dana and Maffione [14], 1.21±0.062 from Chami et al. [15], and 1.167±0.049 from Sullivan and Twardowski [16]. These values are consistent to each other with a difference of only 7%. Thus, different χ p (140°) could not induce a large difference in calculating b bp . In this study we used the median of these values, 1.167 from Sullivan and Twardowski [16].

Text SClosure test of the optical measurements
The accuracy of the optical measurements was validated using a closure experiment. At two stations 'S2086' and 'S2097' (Fig. 1 in Introduction section), above-surface remote-sensing reflectance (R rs ) were measured with a Trios RAMSES-ACC/ARC meter following the abovewater method [17]. Below-surface remote-sensing reflectance (r rs ) was computed from the measured R rs [18]: r rs =R rs /(0.52+1.7R rs ).
(S8) Based on analyses and simulations of the radiative transfer equation, r rs can be reconstructed from the IOPs (a and b b ), and with an error within 10% in clear waters [19]: r rs =0.0949u+0.0794u 2 , (S9) u=b b /(a+b b )=(b bw +b bp )/(a w +a p +a g +b bw +b bp ), (S10) where a w is the seawater absorption which was estimated from the measurements of Pope and Fry [20], and a g is the colored dissolved organic matter absorption and was estimated from a ph empirically [5]. For a p we used our own estimates (see Methods section). As shown in Fig. S4, r rs estimated by these two methods were in good agreement, e.g. the differences were 5% and 2% at 470 nm, 24% and 21% at 510 nm, and both 0.5% at 700 nm, respectively. This closure experiment suggests that the in-situ optical measurements are of high quality.   β(λ, 140°), and the black line with bar shows its mean and standard deviation. The dashed blue and red lines show the β w (λ, 140°) estimated from Morel [8] and Zhang et al. [10], and the solid blue and red lines with bars show the associated mean β p (λ, 140°) with standard deviation.   S4. Comparisons of the below-surface remote-sensing reflectance (r rs ) estimated from the measured above-surface remote-sensing reflectance (R rs , lines) and the inherent optical properties (IOPs, circles) at the stations 'S2086' (red) and 'S2097' (blue).