REMOTE SENSING OF PHYTOPLANKTON SIZE CLASSES ON THE NORTHEAST U.S. CONTINENTAL SHELF

The size structure of phytoplankton communities influences important ecological and biogeochemical processes, including the transfer of energy through marine food webs. A variety of algorithms have been developed to estimate phytoplankton size classes (PSCs) from satellite ocean color data. However, many of these algorithms were developed for application to the open ocean, and their performance in more productive, optically complex continental shelf systems has not been fully evaluated. In this study, several existing PSC algorithms were applied in the Northeast U.S. continental shelf (NES) and assessed by comparison to in situ PSC estimates derived from a regional HPLC pigment data set. The effect of regional re-parameterization and incorporation of sea surface temperature (SST) into existing abundance-based model frameworks was investigated, and the models were validated using an independent data set of in situ and satellite matchups. Abundance-based model re-parameterization alone did not result in significant improvement in performance in the NES compared with other models, however, the inclusion of SST led to a consistent reduction in model error for all size classes. Of two absorption-based algorithms tested, the best validating approach displayed similar performance metrics to the regional abundance-based model that included SST. The SST-dependent model was applied to monthly imagery composites of the NES region for April and September 2019, and qualitatively compared with imagery from the absorption-based approach. The results indicate the benefit of considering SST in abundance-based models and the applicability of absorption-based approaches in optically dynamic regions.


INTRODUCTION
Phytoplankton form the base of pelagic food webs and are a key component of biogeochemical cycles that impact global climate (i.e., carbon cycle) (Longhurst et al., 1995;Field et al., 1998;Behrenfeld et al., 2006). Phytoplankton in the ocean are taxonomically diverse, spanning nine orders of magnitude in cell volume and exhibiting an array of unique morphological and physiological characteristics (Finkel et al., 2010;Caron et al., 2012). Phytoplankton community composition and biomass are highly variable in time and space, changing in response to both bottom-up (i.e., nutrient availability, environmental conditions) and top-down (i.e., grazing) controls. Understanding the dynamics of phytoplankton in terms of both abundance and community structure is critical to better understanding their role in marine ecology and biogeochemistry.
A number of methods exist for quantifying PSCs in situ, including microscopy, size-fractionated filtration (SFF), conventional and imaging flow cytometry (Olson and Sosik, 2007), and high-performance liquid chromatography (HPLC) marker pigments, each with advantages and limitations (IOCCG, 2014).
While these methods have proven accurate and useful, they are labor-intensive, time-consuming, and expensive. As a result, the availability of in situ PSC data remains quite sparse in space and time, thus limiting their utility in studying and modeling large scale, dynamic ocean and ecosystem processes. Satellite remote sensing, capable of providing regularly repeated, synoptic coverage of upper ocean optical properties, provides a means to characterize PSCs at spatial and temporal resolutions unattainable with in situ sampling techniques. Given this fact, deriving information on PSCs from satellite ocean color data is an active area of research, and a variety of algorithms have been developed for both global ocean (Brewin et al., 2015;Hirata et al., 2011) and regional application (Brito et al., 2015;Di Cicco et al., 2017;Gittings et al., 2019;Lamont et al., 2018;Sun et al., 2019Sun et al., , 2018. Most current approaches for detecting PSCs from remote sensing can be categorized as either "abundance-based" or "absorption-based" (IOCCG, 2014; Mouw et al., 2017b). These approaches differ in terms of their theoretical frameworks and the remotely sensed parameters utilized as inputs.
Abundance-based methods rely on empirical or semi-empirical relationships based on coincident in situ observations of size fractionated biomass (i.e., from HPLC marker pigments or SFF) and [Chl-a] to estimate PSCs as a function of [Chla]. Given that [Chl-a] is perhaps the most widely used and well-validated satellite ocean color product, abundance-based methods offer a straightforward, "userfriendly" approach for estimating PSCs from remote sensing. Yet, these methods are only an indirect approximation of PSCs, and the empirical relationships they are based on are subject to change over time, requiring ongoing assessment and re-calibration (Mouw et al., 2017b). Recent studies have demonstrated that the incorporation of additional environmental information attainable from remote sensing (i.e. sea surface temperature [SST]) can improve the retrieval accuracy of abundance-based models (Ward, 2015;Brewin et al., 2017;Moore and Brown, 2020).
Absorption-based algorithms distinguish PSCs directly from spectral variations in phytoplankton absorption [aph(l)], the amount of light absorbed by phytoplankton across the visible spectrum, which influences, and can be inversely derived from, the reflectance signal measured by a satellite ocean color sensor [remote sensing reflectance; Rrs(l)] (Ciotti et al., 2002;Ciotti and Bricaud, 2006;Devred et al., 2011Devred et al., , 2006Mouw and Yoder, 2010). Smaller cells absorb visible light more efficiently than larger cells due to the way photosynthetic pigments are packaged within larger cells. This "package effect" results in a flattening of the chlorophyll-normalized absorption spectrum [aph * (l)] with increasing cell size, with the most pronounced change at blue wavelengths (i.e., around 440 nm) (Morel and Bricaud, 1981;Morel, 1987;Bricaud et al., 1988). Ciotti et al. (2002) demonstrated that despite physiological and taxonomic variability, cell size could explain >80% of the variance in the spectral shape of aph * (l) over the wavelength range 400-700 nm. An advantage of absorption-based methods over abundancebased approaches is that they are able to detect changes in PSCs that do not covary with [Chl-a] (i.e., blooms of different sized cells may comprise the same [Chla]). Moreover, as absorption-based methods are based on direct optical responses rather than indirect empirical relationships, they are less likely to require recalibration over time or for different ocean regions. However, the limited spectral resolution of current multi-spectral ocean color sensors can make retrieving accurate aph(l) spectral shape challenging, particularly in optically complex coastal and continental shelf waters with high concentrations of colored dissolved organic matter (CDOM) and non-algal particles (NAP), which overlap with phytoplankton in their contribution to the total light absorption in the blue region of the spectra.
Given the unique strengths and limitations of these different approaches to detecting PSCs from remote sensing, evaluating how they perform in different ocean regions, and whether they may be optimized for regional application, is essential. A number of studies have successfully retrieved PSCs at regional scales (i.e., shelf seas), including the Red Sea , the Mediterranean Sea (Di Cicco et al., 2017), the Bohai and Yellow Seas (Sun et al., 2018(Sun et al., , 2019, the Western Iberian coast (Brito et al., 2015), and the southern coast of Africa (Lamont et al., 2018), through re-parameterization of global abundance-based models with local in situ data sets. These studies demonstrate the potential benefit of PSC model optimization for regional applications, including regional-scale foodweb modeling and ecosystem-based fisheries management.
The northeast U.S. continental shelf (denoted NES throughout the remainder of the text), is a highly productive, temperate marine ecosystem that supports many commercially and recreationally important fisheries (Hare et al., 2016;National Marine Fisheries Service, 2018). The NES region is physically dynamic and optically complex (Pan et al., 2008;Mannino et al., 2014), thus necessitating evaluation and potential optimization of existing global PSC algorithms to ensure their accuracy. Phytoplankton species composition and abundance in the NES varies seasonally, with diatoms dominating in a typical winter-spring bloom, and other taxa, such as dinoflagellates, cryptophytes, and cyanobacteria, becoming more prevalent during the summer (O'Reilly and Zetlin, 1998;Pan et al., 2011;Richaud et al., 2016).
The aim of this study is to evaluate and optimize several existing abundance-based and absorption-based PSC algorithms for application to ocean color imagery in the NES region, with the goal of improving PSC imagery products for long-term time series investigations and integration into regional ecosystem and fisheries modeling efforts. Specifically, the following scientific questions are addressed: • To what extent does regional re-parameterization using a local in situ data set improve the performance of abundance-based PSC algorithms in the NES?
• Does the incorporation of SST into abundance-based models improve accuracy for predicting PSCs in the NES?
• How do abundance-based and absorption-based models compare in their estimation of PSCs in the NES?
• What spatial and temporal patterns of phytoplankton size structure are observed in the NES? Csize chlorophyll-a concentration specific to size class "size" mg m -3 C m size asymptotic maximum chlorophyll-a concentration of size class "size" mg m -3 Dsize fraction of size class "size" as total chlorophyll-a tends to zero unitless

Study Area
The NES region (35ºN-45.5ºN, 64ºW-77ºW) extends along the east coast of the U.S. from Cape Hatteras, NC to Nova Scotia (Fig. 1 (Schollaert et al., 2004;Saba et al., 2015). The NES has experienced rapid warming (Pershing et al., 2015), which has been connected to changes in phytoplankton bloom dynamics (Hunter-Cevera et al., 2016), and the distributions of fish and other marine species (Kleisner et al., 2017 surveys, which provide a range of hydrographic and biological data for the region (National Marine Fisheries Service, 2020). within the upper 10 m, the data were averaged. To limit the effects of shallow water and near-shore processes, stations with a water column <25 m were removed prior to analysis.  Table 2 for information on data sources. Quality assurance (QA) for the HPLC pigment data was carried out following the procedure of Uitz et al. (2006). First, to account for differences in the detection limits and sensitivities of different HPLC processing methods, pigment concentrations <0.001 mg m -3 were set to zero. Then, utilizing the relationship of

Satellite Data
Daily, Level-3 mapped (4-km resolution, sinusoidally projected) estimates For validation of the satellite input products ([Chl-a], aph(l), and adg(l)) and PSC algorithm estimates, in situ samples were matched in time and space with the satellite data. Following standard methods, match-ups were determined as the median of a 3x3 pixel box centered on the sampling location (nearest latitude and longitude), where only match-ups with at least 5 valid pixels and a median coefficient of variation of <0.15 for Rrs(l) bands between 412 and 555 nm were used to ensure spatial homogeneity (Bailey and Werdell, 2006). Given that OC-CCI is a daily, multi-sensor product, a same-day coincidence window was used rather than the more stringent ±3-hour window recommended for a single mission by Bailey and Werdell (2006). This resulted in 368 [Chl-a], 123 aph(l), and 99 adg(l) match-ups (Table 2).

Partitioning of Data for Model Re-parameterization and Validation
To allow for both the re-parameterization of abundance-based PSC models (see Sections 2.7.1.6 and 2.7.1.7) and independent model validation, the HPLC pigment data were split into two separate data sets. Of the 786 total samples, the 368 samples with a satellite [Chl-a] match-up (~47% of the data) were removed and reserved for independent validation and are referred to as the validation data set. The remainder of the in situ pigment data (N = 418) were used for model reparameterization, and are referred to as the parameterization data set.

Statistical Performance Metrics
Several statistical metrics were used to compare algorithm estimates with the in situ data and evaluate performance. As a measure of accuracy, the mean absolute error (MAE) was used. While many studies commonly use root mean square error (RMSE), MAE has been recommended as a more unambiguous and appropriate metric for model assessment (Willmott and Matsuura, 2005;Seegers et al., 2018). As a measure of systematic bias, the mean bias (d) was used. The MAE and d are calculated according to: and where M, O, and N represent the modeled value (e.g., satellite estimate), the observed value (in situ), and the number of observations, respectively. A positive (negative) d indicates a model's tendency to systematically overestimate (underestimate) the variable of interest. The Pearson correlation coefficient (r) and slope of a Type-II linear regression (S) were also computed for additional comparison between modeled and in situ values (Brewin et al., 2015b;Werdell et al., 2013). Type-II regression (MATLAB function lsqfitgm.m) was applied rather than Type-I regression as it accounts for the inherent measurement uncertainties of in situ field data (Laws and Archie, 1981). While values of r and S that are close to one generally indicate better agreement between model estimates and in situ observations, r and S alone provide no information on the accuracy or bias of a given model, and thus are viewed secondarily to the MAE and d when assessing model performance. Statistical calculations involving total or size-specific [Chl-a], aph(l), or adg(l) were performed in log10 space, while calculations involving size fractions were performed in linear space.

Estimation of PSCs from HPLC Pigments
For algorithm re-parameterization and validation, PSCs were estimated from the HPLC pigment data following the Diagnostic Pigment Analysis (DPA) method (Brewin et al., 2010;Brewin et al., 2015a;Claustre, 2005;Devred et al., 2011;Uitz et al., 2006;Vidussi et al., 2001). This method has been extensively used for the development and validation of satellite PSC algorithms, given the relative abundance of HPLC pigment data compared with SFF and other in situ methods. The DPA approach involves first reconstructing the measured [Chl-a] (denoted here as CHPLC) from the weighted sum of seven diagnostic phytoplankton pigments (denoted CDP) according to:  (Vidussi et al., 2001), or the commonly applied weighting coefficients of Uitz et al. (2006), which were derived from a large global pigment database (Fig.   3, Table 3).
The fractional contributions of micro-, nano-, and picoplankton were estimated from the ratios of the diagnostic pigments attributed to each size class to CDP. Two diagnostic pigments were attributed to microplankton: [Fuco] and [Perid], associated with diatoms and dinoflagellates, respectively. Acknowledging where P3 and P4 are the pigments [Hex-fuco] and [But-fuco], respectively, and q1 and q2 are the coefficients of a 1% multi-linear quantile regression of P1 on P3 and P4. Following the same approach, The coefficients q1 and q2 were re-computed for the NES pigment dataset, obtaining values of q1 = 0.999 and q2 = 0.271, and P1,nano was estimated using Eq. (4). In any instance where the estimated P1,nano was found to be greater than P1, it was set equal to P1. The fraction of microplankton (Fmicro) was then calculated according to: Three diagnostic pigments were used to estimate nanoplankton: [Hex-fuco], [But-fuco], and [Allo], attributed to prymnesiophytes, pelagophytes, and cryptophytes, respectively (Brewin et al., 2015a;Roy, 2011;Uitz et al., 2006). Brewin et al. (2010) proposed an adjustment that attributes a portion of [Hex-fuco] to picoeukaryotes (picoplankton) in ultra-oligotrophic environments ([Chl-a] < 0.08 mg m -3 ). However, considering that only one sample in the data set used in this study met this criterion ([Chl-a] = 0.07 mg m -3 ) and the adjustment was found to make only minor difference (not shown), it was excluded for simplicity.
Incorporating the [Fuco] modification of Devred et al. (2011), the fraction of nanoplankton (Fnano) was calculated as: The final two diagnostic pigments: [TChl-b] and [Zea], were attributed to the picoplankton class, the former associated with prochlorophytes and chlorophytes and the latter with prochlorophytes and cyanobacteria (Chisholm et al., 1988;Uitz et al., 2006;Roy, 2011). The fraction of picoplankton (Fpico) was computed as: was calculated by multiplying Fsize by CHPLC, such that:

PSC Algorithms
A variety of PSC algorithms, including purely abundance-based methods, abundance-based methods that include SST, and absorption-based approaches, were selected for optimization and/or evaluation in this study. The abundancebased models chosen are among the most commonly applied in the literature, and have been successfully re-parameterized for studies in diverse ocean regions, including continental shelf systems (Brito et al., 2015;Sun et al., 2018). The absorption-based models were chosen based on their global performance metrics (Mouw et al., 2017b), and consistency with phytoplankton phenology metrics (Kostadinov et al., 2017). The following sections provide brief overviews of each model, including their principal frameworks, methods used for model development/parameterization, and key differences. For more comprehensive information, the reader is referred to the original publications and the reviews of Mouw et al. (2017b) and IOCCG (2014).

Brewin et al. (2010, 2015a)
The three-component model of Brewin et al. (2010) relates the fractional contribution of combined pico-and nanoplankton (Fpico,nano) and picoplankton (Fpico) to [Chl-a] using two exponential functions (Sathyendranath et al., 2001) according to: and where the model parameters C m pico,nano and C m pico represent asymptotic maximum HPLC measurements (N = 5841) to compute the model parameters. These two models are denoted B10 and B15 throughout the remainder of the text. For simplicity, the notation B10 is also used to refer to the general framework that underlies both of these models (i.e., Eqs. 9 and 10), in addition to the parameterization specific to that study. Further, while Brewin et al. (2015a) also investigated the influence of average irradiance in the mixed layer on model parameters, in this study B15 refers to the model without this modification.
Parameter values obtained from the different studies are provided in Table 2.

Brewin et al. (2017)
Brewin et al. (2017) and where Gi, Hi, Ji, and Ki (where i = 1-4) are empirical parameters controlling the shape of the respective logistic curve and are provided in Table 4 of Brewin et al. (2017). In the remainder of this text, the notation B17 is used to refer to the SST-independent parameterization of the model, which uses a single set of model parameters derived from their full data set (Table 4). The SST-dependent parameterization, which uses Equations 11-14 with the published coefficients, is denoted as B17-SST.

Devred et al. (2011)
The model of Devred et al. (2011) (denoted D11) is based on the same exponential functions as the B10 model (Eqs. 9 and 10). The primary difference is that the model parameters C m pico,nano and C m pico were not derived from HPLC pigment-based size classes, but rather by successive application of the twopopulation absorption model of Devred et al. (2006) to aph(l) and [Chl-a] data from the Northwest Atlantic and NASA's NOMAD data set. While the model was originally applied as a spectral-based approach, in this study it is implemented as an abundance-based method, using the parameters provided in Table 2 and where ai and bi (where i = 1-5 and i = 1-3, respectively) are empirical coefficients specific to each size class and X is log10-transformed [Chl-a]. Fnano is then calculated by difference . The H11 model was developed using PSCs derived from a global HPLC data set (N = 2776) following a unique version of DPA that attributes [TChl-b] to nanoplankton rather than picoplankton, as in Brewin et al. (2010Brewin et al. ( , 2015aBrewin et al. ( , 2017 and the present study (see Section 2.6).

Moore and Brown (2020)
The model of Moore and Brown (2020)  The SST-independent model (denoted MB20) was applied using Eq. (16) with the coefficients provided in Table 4 of Moore and Brown (2020). The SSTdependent model (denoted MB20-SST) was applied using the set of parameters from their LUT indexed by SST (obtained from Timothy Moore via personal communication).

Re-parameterized B10 and H11 Models
New model parameters for the B10 and H11 models were computed using the pigment-based estimates of Fsize from the NES parameterization data set (N = 418), (Table 4). To re-parameterize the B10 model, Eqs. (9) and (10) were fit to Fpico,nano, Fpico, and CHPLC using a nonlinear least squares curve fitting procedure (MATLAB function lsqcurvefit.m, Levenberg-Marquardt algorithm) with bootstrapping Brewin et al., 2015a;Efron, 1979). This involved  Table 2) c Refers to coefficients derived using the DPA method [see Table 4 of Moore and Brown (2020)] randomly sub-sampling the data with replacement 1000 times, and re-fitting the model for each sub-sample, resulting in a parameter distribution from which the median value was taken as the new model parameter. Using the same procedure to re-parameterize the H11 model, both Eq. (15) and Eq. (16) were fit to Fpico and CHPLC, and better results were found (not shown) when using the simpler logistic equation (Eq. 16), consistent with the findings of Moore and Brown (2020). Therefore, Eq. (16) was fit to both Fmicro and Fpico and CHPLC to derive new model parameters. These regionally re-parameterized abundance-based models are denoted B-NES and H-NES, respectively.

Regional SST-modified B10 Model
Following a similar methodology to recent studies Moore and Brown, 2020;Sun et al., 2019), the influence of SST on the parameters of the B10 model was investigated. This was done by sorting the pigment-based estimates of Fpico and Fpico,nano from the parameterization data set (N = 418) by increasing SST and conducting a running fit of the model from low to high SST, using a bin size of 125 samples. Starting at the lowest temperature, the bin was moved at one-sample intervals, and at each interval Eqs. (9) and (10) were fit to the data within the bin using a nonlinear least squares curve-fitting method with bootstrapping (as described in Section 2.7.1.6). From each fit, the median values of the model parameters C m size and Dsize from the bootstrap distribution along with the average SST of the binned data were incorporated into a LUT, and subsequently smoothed using a 5-point running average (Fig. 4). A LUT approach was chosen (Moore and Brown, 2020) rather than fitting logistic functions to represent the SST-parameter relationships  in order to capture variability in the relationships that may be ecological meaningful and would

Ciotti et al. (2002)
The model of Ciotti et al. (2002) (denoted C02) estimates the fractional contribution of picoplankton (Fpico), by weighting aph * (l) between two basis spectra representing "pure" micro-and picoplankton. The basis spectra were determined by lab measurements of aph(l) of 16 natural phytoplankton communities of varying dominant cell sizes, and are provided in Ciotti et al. (2002), with an updated picoplankton spectra provided by Ciotti and Bricaud (2006). The model can be expressed as: where ā * pico(l) and ā * micro(l) represent the basis spectra of pico-and microplankton, respectively. Fpico was estimated from Eq. (13)

Mouw and Yoder (2010)
The algorithm of Mouw and Yoder (2010)   To illustrate the application of the models to ocean color imagery and preliminarily explore spatial-seasonal variations of PSCs in the NES region, the best validating abundance-based and absorption-based models were applied to monthly imagery composites for April 2019 and September 2019, and qualitatively compared. A more comprehensive long-term analysis of the spatial-temporal variability of PSCs in the NES region will be presented in a separate publication.

Satellite Validation of [Chl-a], aph(l) and adg(l)
As the performance of PSC algorithms is largely dependent on the quality of the satellite products used as inputs, the satellite retrievals of [Chl-a], aph(l) and adg(l) in the NES study region were first validated. Of the two [Chl-a] algorithms assessed, the standard OC-CCI algorithm (Fig. 6a) Brewin et al. (2015b) (Model E in their study). Considering the reasonable performance of the standard OC-CCI aph(l) and adg(443) products (443 nm is the only wavelength required for adg(l) as input into the MY10 algorithm), no regional optimization of these products was attempted in this study. Figure 7 shows the in situ pigment-based estimates of Fsize and Csize from the parameterization data set (N = 418) with the SST-independent abundance-based models overlain. Fsize and Csize exhibited trends with CHPLC that are consistent with established relationships of phytoplankton size structure and total biomass (Uitz et al., 2006;Brewin et al., 2010;Hirata et al., 2011). The abundance-based models all followed to first order these general trends, with some variations that can be attributed to differences in the model frameworks, data sets, and approaches used for model development/parameterization. For example, the B10 model parameters C m pico,nano and C m pico impose asymptotic maximums to Cpico,nano and Cpico respectively, while the purely empirical H11 model does not impose any strict maximums. This can be seen when comparing Cpico predicted by the H-NES model, which increases continuously with CHPLC, with that of the B-NES model, which levels off at the imposed maximum concentration (C m pico = 0.2 mg m -3 ) (Fig. 7h). The H11-modeled Fpico is based on a different empirical function (Eq. 15) than the one used in this study (see Section 2.7.1.5), and goes to zero at CHPLC > 4 mg m -3 (Fig. 7d), accounting for the breakdown in this model at higher CHPLC for Cpico, Cnano, and

Comparison of SST-independent Abundance-based Models
Cpico,nano (Fig. 7f-h). Compared with the other models examined, the B-NES model   predicted a slightly higher Fmicro and lower Fpico,nano and Fpico at low CHPLC ( Fig.   7a,b,d). Further, the B-NES-modeled Fnano leveled off at low CHPLC rather than decreasing as with the other models (Fig. 7c). Despite the variability between the different models, the range of variability in the pigment-based estimates of Fsize and Csize was generally greater across the entire trophic domain. Statistical comparison between the in situ and modeled Fsize and Csize for both the parameterization and validation data sets yielded very similar metrics between the models (Table 5). Overall, minimal improvement in performance was observed for the regionally re-parameterized models (B-NES and H-NES) compared with the other models examined, although there was a reduction in error and bias for the nanoplankton size class compared with the original global models (B10 and H11).
This could in part be due to differences in the DPA methods used in the development of these models relative to the version used for model parameterization and validation in this study (see Section 2.7.1.4).  Table 6. For both the parameterization and validation data sets, the B-NES-SST model performed with lower error and significantly higher correlation coefficients than the other two SST-dependent models across all size classes. There was also a consistent improvement in performance (i.e., reduction in error, increase in correlation coefficient) for the B-NES-SST model relative to the SST-independent B-NES model for both data sets.

Regional SST-Dependent Model (B-NES-SST)
Considering the statistical results from the validation set, the inclusion of SST led to a reduction in MAE of 10-12% for Fsize and 4-10% for Csize, with the largest reductions for Fnano and Cpico,nano, respectively. Likewise, the inclusion of SST increased the correlation coefficient (r) for Fsize and Csize, with the largest increases for Fnano and Cpico, respectively. Interestingly, the B17-SST model exhibited slightly worse performance relative to the SST-independent B17 model for estimating Fmicro, Fpico,nano, and Cpico,nano, with essentially no change for Cmicro. The MB20-SST model displayed general improvement over the MB20 model.

Satellite Validation of Csize
Using the satellite data as input, estimates of Csize from the reparameterized abundance-based models (B-NES-SST, B-NES, and H-NES) and absorption-based algorithms (C02 and MY10) were compared with the in situ pigment-based Csize from the independent validation data set (N = 368). The B-NES-SST, B-NES, and H-NES models displayed fairly similar statistical performance ( Fig. 9), although the SST-dependent model performed considerably better across all statistical metrics for Cmicro (Fig. 9a). The B-NES-SST model generally performed better than the SST-independent B-NES model, and was less constrained by static maximums for Cpico,nano, Cnano, and Cpico ( Fig. 9 f-h, dashed green lines), particularly for Cpico, for which a substantial increase in the correlation coefficient was observed, consistent with previous studies Sun et al., 2019). Like the OC-CCI [Chl-a] input product, the satellite-estimated Csize from these models tended to be underestimated at higher concentrations and overestimated at low concentrations, especially for Cnano and Cpico below 0.1 mg m -3 and 0.05 mg m -3 , respectively.
The C02 and MY10 algorithms performed comparably to the reparameterized abundance-based models (Fig. 10). The MY10 algorithm estimated

H-NES
the abundance-based methods, with the exception of Cmicro,nano estimated by C02 model (Fig. 10a).

Examples of Satellite Imagery
Considering the overall improved performance of the B-NES-SST algorithm compared with the other abundance-based models, and the statistically similar validation metrics of the MY10 absorption-based approach, monthly composite imagery from these algorithms was generated for April 2019 and September 2019 for visualization and spatial-temporal comparison. These months were chosen as they were relatively cloud free and displayed contrasting SST and [Chl-a], thus providing some insight into the seasonal variability of phytoplankton size structure in the NES. Figure 11 shows the monthly imagery of OC-CCI [Chl-a] (Fig. 11a) and MUR SST (Fig. 11b)

DISCUSSION AND CONCLUSIONS
The focus of this study was the regional refinement and evaluation of PSC algorithms in the NES. Like many similar studies, in situ estimates of PSCs derived from HPLC pigment data using the DPA method were used for model reparameterization and statistical comparisons (Uitz et al., 2006;Brewin et al., 2011Brewin et al., , 2015aHirata et al., 2011;Sun et al., 2018). While this approach is a popular choice given the relative abundance of HPLC samples compared with other methods for quantifying PSCs in situ, it has important limitations. First, DPA is not a direct measure of cell size, but rather an approximation of size structure based on assumptions about the taxonomic groups attributed to different pigments, and the size classes represented by those taxa. In reality, pigments are not perfectly diagnostic, and are known to be shared across multiple taxa in varying concentrations dependent on physiological state (Uitz et al., 2008). Further, taxonomic groups may span multiple size classes in ways that are not fully represented by the DPA equations (Leblanc et al., 2018;Nunes et al., 2019).
Although proposed modifications to account for some of these biases were incorporated in this study (Devred et al., 2011), the efficacy of this specific approach for characterizing PSCs in the NES region is uncertain and warrants further investigation. Recently, Chase et al., (2020) evaluated the DPA method by comparing pigment-based PSC estimates to coincident measurements of cell size by imaging-in-flow and conventional flow cytometry in the North Atlantic and found that DPA overestimated micro-and picoplankton and underestimated nanoplankton relative to cytometry. They recommended a revised set of DPA equations to better account for the presence of dinoflagellates and diatoms in the nanoplankton, and the presence of [TChl-b] in both pico-and nanoplankton. To reduce uncertainty on this front, continued efforts to inter-compare multiple in situ PSC methods across different oceanic environments will be extremely valuable.
Abundance-based PSC algorithms are attractive for their ease of implementation, using satellite [Chl-a] as the sole input parameter, and have been shown to perform well globally (Brewin et al., , 2015a and in a variety of oceanic regions (Brito et al., 2015;Di Cicco et al., 2017;Sun et al., 2018;Gittings et al., 2019). Here, the impact of model re-parameterization was tested using a region-specific HPLC pigment data set, as well as the incorporation of remotely sensed SST on the performance of abundance-based PSC models in the NES.
The results indicated that regional re-parameterization alone offered minimal statistical improvement relative to other abundance-based models evaluated, which included both globally and regionally parameterized models. Of the eight different models tested, all performed with similar errors and correlation coefficients, particularly for the micro-and combined pico-and nanoplankton classes, when applied to the in situ [Chl-a] and compared with the pigment-based size class estimates from the independent in situ validation data set. There was slightly more variation in the statistical metrics for nano-and picoplankton, but in no instance were the re-parameterized models exclusively the best performing, except for perhaps the H-NES model for estimating picoplankton, which showed slightly better performance than the other models when applied to both the in situ and satellite data.
While re-parameterization alone provided little benefit in terms of improving abundance-based model performance in the NES, the incorporation of remotely sensed SST into the re-parameterization of the B10 model did serve to improve PSC prediction accuracy. When applied to the in situ validation data set, the shown by previous studies (Ward, 2015;Brewin et al., 2017;Sun et al., 2019;Moore and Brown, 2020) that the addition of SST into abundance-based model frameworks can improve PSC prediction accuracy. The relationships between [Chl-a], SST, and phytoplankton size structure observed in this study were also in general agreement with the findings of these studies, with lower SST associated with an increase in the fraction of microplankton and a decrease in the fraction of smaller cells (i.e. pico-and nanoplankton) at similar [Chl-a]. This relationship is not surprising, given long-established connections between temperature, watercolumn stability, nutrient availability, and phytoplankton community size structure in the marine environment (Margalef, 1978;Bouman et al., 2003). While SST is used as the additional predictor variable in these models, the associated changes in size structure are not necessarily in direct response to changes in SST but rather the result of a combination of co-varying environmental conditions, including light availability, stratification, and nutrient availability.
Absorption-based algorithms are advantageous over abundance-based methods in that they are rooted in a direct spectral response to phytoplankton cell size, as opposed to relying on indirect statistical connections between [Chl-a] and phytoplankton size structure. This means that they can distinguish changes in PSCs that occur outside of the general biomass-size co-variation relationship and are less prone to change over time or geographically. When directly applied to the satellite data, the two absorption-based algorithms examined in this study, C02 and MY10, performed with comparable accuracy to the regionalized abundancebased models. The MY10 algorithm in particular showed statistically similar performance to the SST-dependent model, without including any additional environmental information. Considering that pigment-based size class estimates from DPA were used for validation, the similarity in performance for the absorptionbased algorithms is encouraging, given they were not developed or parameterized based on the same approach, as was the case with the abundance-based models.
This suggests some degree of consistency between estimates of size classes derived from spectral phytoplankton absorption and those determined from HPLC pigment analysis in the NES, as has been previously reported in other regions (Devred et al., 2011).
The PSC algorithms and products evaluated in this study may be useful for validation of or assimilation into regional ecosystem or biogeochemical models (IOCCG, 2020). However, given the uncertainties associated with the pigmentbased size class estimates used for algorithm assessment, as well as the different inputs and outputs between methods, it is difficult to make a definitive determination of which approach is the best choice for such applications. The most suitable method may be dependent on the specifics of the intended application or the questions to be addressed. For instance, biogeochemical models that produce chlorophyll-based phytoplankton size estimates may prefer to compare to abundance-based algorithm outputs, while models that include optics may prefer to compare to output from absorption-based methods -each enabling a more direct comparison dependent on the underlying algorithm/model frameworks and outputs being compared.
In the near future, satellite ocean color remote sensing is moving toward more advanced radiometric instruments with hyperspectral capability and enhanced spatial and temporal resolution (Cetinić et al., 2018). The increased spectral information afforded by these upcoming sensors is anticipated to greatly improve our ability to accurately separate the absorption attributed to different optically significant in-water constituents (i.e., CDOM, NAP, phytoplankton) and retrieve information on phytoplankton community composition and size structure.
This improved capability will be particularly relevant to optically complex waters, including coastal and continental shelf regions like the NES ecosystem. Thus, existing absorption-based PSC models may potentially become more robust, and newer methods that exploit the full range of available spectral information will continue to be developed. Further, to the extent that satellite [Chl-a] estimates improve as a result of the increase in spectral resolution, abundance-based approaches may continue to be an effective option for estimating PSCs, especially when combined with SST or other ecologically relevant environmental parameters.
While not considered in this work, the integration of high-resolution spectral information with environmental data readily attainable from remote sensing should be considered in future PSC algorithm development efforts.