An absorption-based approach to improved estimates of phytoplankton biomass and net primary production

Estimates of phytoplankton biomass are essential components of primary production models and are also required for the calculation of other useful model outputs that provide insight into nutrient cycling and carbon transfer through marine food webs. Optical proxies provide observations of phytoplankton carbon at unparalleled spatial and temporal resolution but require scaling factors that have not captured variability driven by changes in community composition or physiology. Here, we describe a new approach that improves model estimates of net primary production by mechanistically scaling optical measurements to phytoplankton carbon in a way that accounts for variation in taxonomy. Abstract The abundance and productivity of phytoplankton constrain energy transfer through marine food webs and the export of organic carbon to the deep ocean. Bio-optical measurements correlate well with phytoplankton carbon (C phyto ), but the effect of taxonomic variability on this relationship is still uncertain. Here, we explore how changes in phytoplankton community composition in ﬂ uence the relationship between the particulate backscatter coef ﬁ cient ( b bp ) and C phyto and present a new approach to estimate phytoplankton biomass more accurately using b bp . We found that using a ﬁ xed scaling factor for the conversion of b bp to C

The abundance and taxonomic composition of marine phytoplankton fundamentally impact the fate of organic carbon fixed through net primary production (NPP).Environmental conditions such as light, nutrient availability, turbulence, and grazing ultimately determine phytoplankton community structure, food web dynamics, and elemental cycling.Cyanobacteria typically dominate (both numerically and as a fraction of biomass) stratified oligotrophic systems that are often associated with rapid carbon cycling driven by the microbial loop (Marañ on et al. 2003;Flombaum et al. 2013).Diatoms are another taxonomic group that are widely distributed in the surface ocean (Kemp and Villareal 2018).When growth conditions in the mixed layer are improving and if nutrient levels are sufficient, the growth rate of diatoms can become temporally decoupled from grazing pressure and a large diatom-dominated bloom can occur (Behrenfeld et al. 2021).These decoupling events sometimes result in high magnitude carbon export events that can include large aggregates of cells, but this is not always the case (Martin et al. 2011;Durkin et al. 2016).As global change alters the physical and chemical nature of the ocean, it will give rise to shifts in the abundance and composition of phytoplankton communities and their role in biogeochemical cycles (Finkel et al. 2010;Henson et al. 2019).
Primary production is the product of phytoplankton growth rate and carbon biomass, but few direct measurements of phytoplankton carbon (C phyto ) exist due to the complex methods required to isolate phytoplankton cells from other components of the particulate organic carbon (POC) pool (Graff et al. 2012).Particulate backscattering (b bp ) correlates well with analytical measurements of C phyto and can also be estimated using satellite remote sensing, thereby allowing the assessment of phytoplankton biomass distribution at a global scale (Behrenfeld et al. 2005;Graff et al. 2015;Martínez-Vicente et al. 2017).After correcting for the background influence of non-algal particles, b bp is converted to C phyto using a scaling factor determined from in situ measurements (Martinez-Vicente et al. 2013;Graff et al. 2015).Multiple scaling factors have been recommended and range in magnitude by twofold (Behrenfeld et al. 2005;Martinez-Vicente et al. 2013;Graff et al. 2015), but the factors impacting the empirical relationship between b bp and C phyto (e.g., phytoplankton taxonomy and size) have not yet been critically evaluated over large spatial scales (Qiu et al. 2021).Here, we employ a new absorption-based method that accounts for taxonomic variability when scaling b bp to C phyto .The new method improves estimates of NPP and can be used to coarsely evaluate phytoplankton community composition across time and space.

Methods
Data from the North Atlantic Aerosol and Marine Ecosystem Study (NAAMES; Chase et al. 2020), the EXport Processes in the Ocean from RemoTe Sensing program (EXPORTS; Siegel et al. 2021), and the 22 nd Atlantic Meridional Transect (AMT22; Graff et al. 2015) were analyzed to investigate how phytoplankton community composition influences the relationship between bio-optical measurements and biomass (Fig. 1).The collective dataset includes near-surface optical properties acquired from semi-continuous inline sampling of the ship's underway water supply, which were used to provide effective proxies for key biological parameters, and discrete samples collected for high-performance liquid chromatography (HPLC) phytoplankton pigments and flow cytometry .Although a brief overview of methods and protocols is provided below, more details on modeled parameters and instrumentation are provided in the supplemental information.

Chlorophyll and POC
Estimates of chlorophyll concentration were derived from the phytoplankton absorption coefficient (a ϕ ) at 676 nm using particulate absorption [a p λ ð Þ] red peak line height as in Boss et al. (2007;Eq. 1).
For each cruise, values of a ϕ 676 ð Þ were then calibrated against chlorophyll a concentrations measured by HPLC to provide a proxy for chlorophyll (Chl ACS ) specific to each region as in Boss et al. (2013).POC was estimated using particulate beam attenuation at 660 nm, c p (660), and scaling coefficients specific to the AMT22 cruise calculated in Fig. 5c of Graff et al. (2015;Eq. 2).The AMT22 values are similar to global and regional coefficients previously calculated for the North Atlantic and South Atlantic (Gardner et al. 2006;Cetini c et al. 2012).

Phytoplankton carbon
Multiple approaches were used to calculate C phyto .The first approach followed the methods of Graff et al. (2015), which calculates phytoplankton biomass using a scaled value of the particulate backscatter coefficient at 470 nm [b bp (470)], here we refer to these values as C b bp : In a second approach, modeled phytoplankton carbon (C mod ) values were calculated using Chl ACS , photosynthetically active radiation (PAR), the light attenuation coefficient (K d ), and the median growth irradiance in the surface mixed layer (I g ) as described in Fox et al. (2020): Hyperspectral measurements of the absorption spectrum were used to develop a simple method for scaling b bp to C phyto that accounts for taxonomic variability.Total non-water particulate absorption, a nw λ ð Þ, measurements across the visible spectrum (400-700 nm) were averaged at 5 nm increments between 400 and 700 nm.A two-wavelength ratio matrix was then created for all available wavelengths before Pearson correlation coefficients and Type II linear regression were used to compare each ratio to model-based scaling factor [SF mod = C mod /b bp ( 470)] values determined a priori using estimates of b bp (470) and C mod (Fig. 2; Supporting Information Fig. S1).Comparative analyses between phytoplankton absorption ratios and SF mod showed the best correlation with the a nw (690 nm)/a nw (580 nm) ratio (r 2 = 0.56, Root Mean Square Error = 3512, scalar units = mg C m À3 ; Fig. 2).This ratio was used to derive a variable scaling factor to estimate phytoplankton biomass (C var , Eq. 5): Here, C var was estimated using b bp after subtracting the "background" value of 0.00027 m À1 before multiplying by the scaling factor of 12,287 that varies with the absorbance ratio.The "background" component was calculated using the slope and x-axis intercept from regression analysis of the bulk community C mod -b bp relationship (Supporting Information Fig. S2) and is consistent with similar estimates made using satellite or in situ data (i.e., 0.00027 m À1 for this study compared to a value of 0.00035 m À1 determined from remotely sensed b bp vs. chl; Behrenfeld et al. 2005) and values of 0.00058 and 0.00067 m À1 derived from flow-cytometric cell volume-based estimates of carbon and b bp (Martinez-Vicente et al. 2013;Qiu et al. 2021).The value of 12,287 was taken from the slope of the regression analysis between C mod and anw 690 ð Þ anw 580 ð Þ (Fig. 2).Finally, phytoplankton carbon measurements derived from flow cytometry (C fcm ) were calculated using group-specific abundance and biovolume data (Graff et al. 2015).Values for the group-specific diameter estimates and biovolume-carbon conversions were taken from previous studies from the AMT program (Heywood et al. 2006;Tarran et al. 2006;Martinez-Vicente et al. 2013).

Phytoplankton taxonomy
A network-based community detection analysis was used to determine the dominant pigment-based phytoplankton groups in the community following Kramer et al. (2020).Five distinguishable groups were determined and combined into three populations roughly based on cell size: (1) cyanobacteria and haptophytes (pico-nano), (2) green algae/mixed (piconano), (3) diatoms and dinoflagellates (nano-micro).

Phytoplankton growth and productivity
Phytoplankton growth rate (μ) was modeled using nearsurface optical measurements of Chl ACS , PAR, mixed layer depth (MLD), and K d (see Supporting Information Methods).NPP was estimated as the product of the resultant growth rates and the three different C phyto estimates (e.g., C mod , C b bp , and C var ) (Eq. 6).
Model-based NPP was compared to discrete measurements determined using 14 C uptake incubations ranging between 10 and 24 h in duration (Tilstone et al. 2009;Fox et al. 2020;Siegel et al. 2021).
The code, data, and metadata of this study are available in the Zenodo data repository (Fox et al. 2022).

Scaling particulate backscatter to phytoplankton carbon
Surface measurements of b bp (470) and C mod correlated well for the bulk plankton community (r 2 = 0.76, RMSE = 10.1 mgC m À3 , n = 124; Supporting Information Fig. S2), but regression analysis showed that the scaling factor used to convert b bp to C mod ranges from 3770 to 27,697 and is influenced by taxonomy (Fig. 3).For phytoplankton populations dominated by green algae, the scalar was 13,832 AE 1142 mg C m À3 (i.e., C mod = b bp Â 13,832), which is similar to previous estimates of 13,000 by Behrenfeld et al. (2005) and 12,128 by Graff et al. (2015).However, the scalars best fitting the diatom/dinoflagellate and cyanobacteria/haptophytes communities were 22,641 AE 1714 and 8372 AE 670, respectively, suggesting that the use of a fixed scaling factor leads to underor overestimates of C phyto .Accounting for taxonomic variability in this relationship will therefore yield a more accurate conversion from b bp .

Latitudinal changes in phytoplankton carbon and contribution to total POC
The accuracy of the C var estimates was assessed using nearsurface bio-optical estimates of phytoplankton measured by flow cytometry (C fcm ) during AMT22.Estimates of C var closely matched estimates of C fcm over a broad latitudinal gradient north of 35 S (r 2 = 0.79, RMSE = 1.70 mgC m À3 ; Supporting Information Fig. S3a) and captured a greater amount of the variability observed in the C fcm data than C b bp estimated using a fixed scaling factor (r 2 = 0.46, RMSE = 1.14 mgC m À3 ; Fig. 4a).
Optically-derived POC was used to evaluate the contribution of phytoplankton carbon to the total POC pool over the AMT22 track.C var : POC estimates generally matched well with C fcm : POC in latitudes north of 35 S (r 2 = 0.69, RMSE = 0.05; Supporting Information Fig. S3b), but the relationship deteriorated in more southerly regions (Fig. 4b; Supporting Information Fig. S3d).In the northerly latitudes, the C var : POC relationship was largely driven by changes in the abundance of Synechococcus spp.and Prochlorococcus spp., which often contributed over 80% of the total C fcm .Values of C var effectively tracked changes in picocyanobacterial biomass, while the fixed scalar approach generally led to estimates higher than those of C fcm in areas dominated by picocyanobacteria and showed little spatial change north of 35 S. As a result, C b bp : POC remained relatively consistent

Fox et al.
Scaling optical measurements to phytoplankton carbon to 35 S. South of this latitude, Synechococcus spp.and Prochlorococcus spp.decreased substantially in their relative contributions to total phytoplankton biomass (Fig. 4).The magnitude and spatial variability observed in the C var to POC relationship closely match trends observed in previous AMT campaigns (Martinez-Vicente et al. 2013;Graff et al. 2015).

Modeled primary production across diverse ecosystems
The above analysis implies that estimates of NPP modeled over a wide range of ecosystem states and conditions are improved by using biomass values calculated using a variable scaling factor (C var ) compared to a fixed scaling factor (C b bp ) (Fig. 5; Table 1).This result is most notable for the NAAMES 3 and AMT22 cruises, which sampled predominantly in oligotrophic waters where the phytoplankton communities were dominated by cyanobacteria.All approaches used to estimate C phyto performed similarly in high biomass/high productivity conditions, but C var showed modest improvements over C b bp at two stations during NAAMES 2 (Fig. 5b,c).The second NAAMES cruise took place during the climax of the spring bloom when the phytoplankton community was dominated by eukaryotic phytoplankton, and small diatoms were prevalent at the two stations where the NPP estimates were most improved (Bolaños et al. 2020).Model estimates were typically higher than 14 C estimates of NPP, which could be due to subsurface light levels being overestimated because of an underestimate in K d (Xing and Boss 2021).

Discussion and conclusions
The overarching objectives of this study were to assess the impact of community composition on in situ b bp -based estimates of phytoplankton biomass and to develop a new method that improves C phyto estimates by accounting for taxonomic variability in the phytoplankton community.While a relationship between b bp and C phyto is well established (Behrenfeld et al. 2005;Martinez-Vicente et al. 2013;Graff et al. 2015), we found that community composition can significantly impact the magnitude of the scaling factor required in these calculations, which is consistent with previous observations in the oligotrophic South China Sea (Qiu et al. 2021).For populations dominated by cyanobacteria or haptophytes, our estimated scaling factor was 25% to 30% lower than the fixed values currently applied to scale in situ or satellite retrievals of b bp to C phyto .The fixed scalars likely result in systematic overestimations of C phyto when employed in areas dominated by picocyanobacteria, such as the permanently stratified gyres and seasonally oligotrophic regions.Conversely, the scalar best fitting diatom and dinoflagellate populations was almost 100% larger than some fixed scalar estimates (Behrenfeld et al. 2005;Graff et al. 2015).Thus, use of a fixed scalar will typically underestimate C phyto when these phytoplankton groups are dominant, especially during high biomass bloom events.The need for alternative scaling factors could explain previously reported inaccuracies in NPP modeled using b bp , where predicted values in the western North Atlantic were higher than discrete 14 C data in summer months but lower in early spring (Yang et al. 2021).
The spectral backscattering properties of laboratory grown phytoplankton cultures vary between major taxa (Whitmire et al. 2010).The group-specific scaling factors presented in this paper are consistent with both optical theory and carbonto-volume relationships of phytoplankton species.Experimental and modeling studies show that cells <10 um can make a disproportionately large contribution to the total backscattering signal (Dall'Olmo et al. 2009;Organelli et al. 2018), but the volume-to-carbon relationship is generally consistent across a range of taxa and sizes (Menden-Deuer and Lessard 2000).As such, our results show that b bp in some populations of larger phytoplankton (nano and micro size classes) such as diatoms and dinoflagellates may require a larger scaling factor than cyanobacteria and other pico-sized Fig. 5. NPP measured using carbon uptake ( 14 C) incubations compared with modeled estimates made using (a) modeled carbon (r 2 = 0.72, log (y) = 1.06 log(x) À 0.33, RMSE = 0.20), (b) phytoplankton carbon estimated following the methods of Graff et al. (2015) where the scaling factor is fixed (r 2 = 0.57, log(y) = 1.10 log(x) À 0.46, RMSE = 0.25) and, (c) phytoplankton carbon estimated with the variable scaling factor using the absorption method (r 2 = 0.78, log(y) = 1.02 log(x) À 0.08, RMSE = 0.18).Symbol shape indicates the cruise.Solid line in each represents the 1 : 1 line.
phytoplankton.This relationship may not apply universally, however, and further analysis is required to improve the relationship between phytoplankton size and field measurements of b bp (Qiu et al. 2021).
The two particulate absorption wavelengths identified to best estimate C var , 690 and 580 nm, were somewhat surprising, but there are several plausible explanations for their selection as taxonomic indicators.Although neither wavelength is associated with absorption peaks of major diagnostic pigments, the two selected regions of the absorption spectrum could be capturing subtle differences in taxon-specific physiology (Supporting Information Fig. 4).The 690 nm wavelength is notably between the absorbance maxima of the 2 nd and 1 st photosystem (PS) reaction centers, which are centered at 680 and 700 nm, respectively (Falkowski & Raven, 2013).The PSII/PSI ratio varies between species, with diatoms often maintaining a higher ratio than haptophytes and green algae across a range of light intensities (Vandenhecke et al. 2015).Major taxonomic differences in the PSII/PSI ratio could therefore lead to differences in absorption in the region of spectral overlap at 690 nm and permit discrimination of communities dominated by diatoms from other groups.At 580 nm, the major pigments contributing to light absorption are phycocyanin and phycoerythrin, which are diagnostic marker pigments for red cyanobacteria, and Chl c, which is a dominant pigment in red algae (including diatoms, dinoflagellates, haptophytes, and others) (Chase et al. 2013;Luimstra et al. 2018).Small changes in absorption at 580 nm could therefore reflect shifts in phytoplankton community composition and the a nw (690)/a nw (580) ratio may amplify small differences in both signals.A simpler explanation may be that 690 nm serves as a near-baseline for variation driven by the accessory pigments represented by 580 nm, but this idea does not explain why the ratios a nw (695)/a nw (580) and a nw (700)/a nw (580) yielded poorer correlations with C mod /b bp (470) compared to a nw (690)/a nw (580).
Accounting for phytoplankton group variability in the b bp to C phyto relationship is one step toward more reliable estimates of phytoplankton biomass but other considerations remain, such as the effects of particle composition and the non-algal contribution to scattering (Cetini c et al. 2012).The background component of the optical backscatter signal is variable and may be a notable contributor to total b bp in oligotrophic waters (Bellacicco et al. 2018;Bellacicco et al. 2019).Correcting for this background component is particularly important in low biomass/low b bp waters where non-algal particles impact the b bp signal (Stramski et al. 2004;Organelli et al. 2018).The breakdown in relationships between C var and C fcm (and C var : POC; Fig. 4) south of 35 S could be caused by an increased prevalence of pico-and nano-eukaryotes in the flow cytometry biomass estimation which relies on an empirical carbon-to-volume relationship.This result brings in a degree of uncertainty which is compounded by the difficulty in estimating size and volume for these pico-and nano-sized cells (Martinez-Vicente et al. 2013).
Further exploration into the influence of taxonomy on the scalar required for b bp -derived biomass will help constrain uncertainty in measurements of phytoplankton carbon and provide more accurate model estimates of NPP.Improved estimates of biomass and NPP are also important for other rate measurements, such as net community production or carbon export, that provide key metrics of marine ecosystem health and function.The method put forward here is simple but shows that absorption-based approaches warrant further exploration to obtain taxon-specific estimates of phytoplankton carbon.Currently, most platforms that measure optical oceanographic parameters at high spatial or temporal resolution (e.g., autonomous floats, gliders or satellites) do not possess the hyperspectral capabilities required for our method.Future satellite missions (e.g., NASA's Plankton, Aerosol, Cloud, ocean Ecosystem) offer the required spectral resolution however, and optical technology is progressing at such a rate that we could soon see spectral absorption sensors incorporated into global arrays of ocean profilers.Until then, easily obtainable estimates of SF mod can be used to evaluate phytoplankton group composition throughout the annual cycle using data from autonomous underwater vehicles and satellite ocean color.

Fig. 1 .
Fig. 1.Cruise tracks for the NAAMES field campaigns, the EXPORTS program in the North Pacific, and AMT22.

Fig. 4 .
Fig. 4. Latitudinal trends in surface (a) phytoplankton carbon estimated using b bp (470) scaled using a variable (C var , orange line) and fixed (C bbp , blue line) scaling factor, flow cytometry (C fcm , gray circles) and a model (C mod , black crosses), and (b) phytoplankton carbon-to-POC ratios calculated using C var (orange line) and C b bp (blue line) during AMT22.Black circles are the total carbon of Synechococcus spp.and Prochlorococcus spp.when they contribute over 80% of the total biomass estimated by flow cytometry.

Table 1 .
Population specific daily estimates of modeled and measured depth-integrated NPP (ʃNPP).Values are group means and standard deviation apart from ΔʃNPP (C b bp -C var ) which is medium and range values.Units are mg C m À2 d À1 .Population ʃNPP(C mod ) ʃNPP (C b bp ) ʃNPP (C var ) ʃNPP ( 14 C) ΔʃNPP (C b bp -C var )