Nine species were selected for cultivation and determination of pigment composition and absorption coefficient, including representatives of green algae (2), diatoms (5), one cyanobacteria and one prymnesiophyte. The objective was to investigate the association between pigments and optical signals, including species with atypical pigmentation in a given class, as the case of diatoms containing Chl c₃. The cyanobacterium Microcystis aeruginosa (DCG 0795), and the clorophytes Desmodesmus armatus (DCG 1000) and Chlamydomonas sp. were cultured in WC-2NP medium (Guillard and Lorenzen, 1972). The diatoms Amphora sp. (DCG 1065), Chaetoceros costatus (DCG 1031), Nitzschia cf. frustulum (DCG 0494), Pseudo-nitzschia azenyensis and Thalassiosira pseudonana (DCG 0943) were cultured in f/2 medium enriched with silicate (Guillard and Ryther, 1962; Guillard, 1975). The prymnesiophyte Emiliania huxleyi was cultured in f/2 medium. All cultures were subjected to a 12:12 h light:dark cycle, under low irradiance (<20 μE m⁻² s⁻¹) provided by a TL5 fluorescent lamp. Temperatures ranged from 15 to 23°C. With the exception of P. azenyensis, all cultures were provided by the Diatom Culture Group (DCG) at UGent, a member of the Belgian Coordinated Collection of Microorganisms (BCCM). Cultures were clonal and non-axenic, but contained only one pigmented species, and are hereafter referred to as pure cultures.

Data for other microorganism cultures with paired pigment composition and absorption coefficient available in the literature (Astoreca et al., 2009; Organelli et al., 2017; Clementson and Wojtasiewicz, 2019b) were compiled and combined with our measurements to provide a single harmonized dataset. Measurements on the mamiellophycean Micromonas pusilla (prasinophyte clade II) are also included (Organelli, unpublished). This is a group of green algae with an atypical pigmentation, having abundant MgDVP and a proprionate derivative of DVChl c₃, known as Chl c_CS-170 (Zapata et al., 2006). Only the spectrophotometric determination of Chl a is available for this culture, but it is included due to its unique pigment composition and optical signal. Additional culture studies with only spectrophotometric determinations of pigment concentrations (Bricaud et al., 1988; Ahn et al., 1992; Dupouy et al., 2008) were included to increase the diversity of the dataset in terms of species, culturing conditions and pigmentation groups. These were used in evaluations that do not require detailed pigment composition information. In total, the compiled dataset of paired absorption and pigment composition contains 71 measurements of 43 species (52 strains) from 11 classes, covering 18 pigmentation groups cultured over a range of irradiances. Details on processing and harmonization of the different datasets and the list of species and strains are presented in the Section S1 and Table S1 of the Supplementary Data Sheet 1. The pigment composition and absorption coefficients of original data from this study and of the measurements by Organelli et al. (2017) are provided in the Supplementary Table 1.

In April and July 2018, the regular monthly sampling campaigns in the BCZ by the coastal LifeWatch BE program were augmented with optical instrumentation to perform reflectance spectroscopy determinations of the water system and to collect samples for determination of inherent optical properties (IOP). These additional data are paired with a suite of other parameters collected as part of the routine campaigns (Mortelmans et al., 2019), the most relevant of which for this research being a suite of pigment concentrations measured with High Performance Liquid Chromatography (HPLC).

Since April 2019, the monthly LifeWatch BE sampling campaigns in the BCZ also include reflectance spectroscopy determinations of the water system (Dierssen et al., in prep). Spectroscopy and pigment data from April to December 2019 were combined with the 2018 dataset for a better representation of the system. Methods for sampling and processing of each data type used in this study are provided in the following sections. Details of the dates and stations available with paired pigment and spectroscopy data are provided in Table 2. Figure 1 presents the nominal positions of the stations visited by the LifeWatch BE sampling campaigns.

During the 2018 campaigns, reflectance spectroscopy measurements were made with a set of three spectroradiometers (VIS-ARC RAMSES, TriOS) fixed on the bow of the RV Simon Stevin. The ship orientation was kept at an azimuth of 135° relative to the Sun, following the above water protocol for reflectance spectroscopy measurements of the water system (Mobley, 1999; Ruddick et al., 2019a,b). From the measurements of downwelling plane irradiance (E_g), sky (L_sky) and water system (L_ws) radiance, the Lambert-equivalent bi-hemispherical water-leaving reflectance (ρwlL(θ,ϕ), unitless) was estimated according to:

where θ is the nadir view angle (40°), ϕ is the azimuth view angle relative to the Sun (135°), λ is the center wavelength of the spectrometer band and ρ_f is the effective Fresnel reflectance estimated from wind speed and L_sky according to Ruddick et al. (2006). The factor π, with units of sr⁻¹, corresponds to the cosine-weighted solid angle integral of an hemisphere and converts from hemispherical-directional to bi-hemispherical reflectance under the assumption that the bi-directional reflectance distribution function (BRDF) of the water-leaving signal in air is well approximated by the Lambert model. Due to departures of the BRDF from the Lambert model, the angular reference is kept for ρwlL defined in this manner. Further details of processing and quality control are described in Ruddick et al. (2006). The RAMSES instruments have a typical bandwidth of 10 nm (full width at half maximum; FWHM) with spectral sampling every ≈3 nm. Radiance and irradiance measurements were automatically resampled to a regular 2.5 nm interval by the vendor's software before Equation (1) was applied.

The reflectance spectroscopy system incorporated into the LifeWatch BE campaigns since 2019 is a WISP-3 (WaterInsight) integrating three spectroradiometers (JAZ, Ocean Optics Inc.). This handheld system is deployed from the bow of the RV Simon Stevin campaigns, following the same nominal orientations as described above. The details of the operator protocol, processing and quality control will be provided in a separate study (Dierssen et al., in prep). The preliminary version of these data is processed here with ρ_f estimated such that the ρwlL(λ)/ρwlL(780) ratio best fits, in a least-squares sense, the water similarity spectrum (Ruddick et al., 2006) in the range from 710 to 800 nm, excluding the O₂ absorption band A centered at 760 nm (Brown and Plymate, 2000).

The available ρwlL(40∘,135∘) are presented in Figure 2A. Second order derivatives were calculated for the estimated ρwlL using the central finite difference approximation with a band separation of 15 nm for the TriOS data and 18 nm for the WISP-3 data (cf., Torrecilla et al., 2011, Figure 2B). Before the derivative calculation, a rectangular moving window of 7.5 nm was used to smooth the TriOS data and a window of 5 nm was used for the WISP-3 data, with the latter receiving an additional smoothing window of 10 nm after the derivative calculation.

For both cultures and seawater samples, the particle absorption coefficient (a_p, m⁻¹) was measured with the filterpad method, with particles concentrated in a glass fiber filter (GF/F, effective mesh size of 0.7 μm). To improve the homogeneity of particle deposition over the filtration area, two stacked filters were used and samples with high abundance of particles were diluted in the filtration funnel with distilled water. Immediately after filtration, filters were transferred to PetriSlides (Merk & Co., USA), wrapped in aluminum foil and frozen in liquid nitrogen. Filters were then stored at –80°C until analysis.

Before the analysis, the filters were allowed to thaw at room temperature and kept hydrated with distilled water. To avoid dislocating large particles deposited over the filter fibers, hydration was performed by raising the filter and adding a droplet of water to the PetriSlide base and resting the filter over it, with the water spreading by capillarity. The optical density of the filters was determined with a benchtop spectrophotometer (PerkinElmer, Lambda-650S) equipped with a 150 mm integrating sphere. The “inside sphere” variant of the quantitative filterpad method was used (Stramski et al., 2015). Filters were read twice, with a 90° rotation between reads to average small deviations from homogeneous deposition. The pathlength amplification correction was taken from Stramski et al. (2015) as recommended in IOCCG (2018). To calculate the in vivo pigment absorption coefficient (a_ϕ, m⁻¹), particles were depigmented by oxidation with 1 mL of sodium hypochlorite (NaClO) before new determination of absorption (Ferrari and Tassan, 1999), and the depigmented absorption was subtracted from a_p.

Particle and in vivo pigment absorption coefficients of monospecific cultures reported in other studies (Bricaud et al., 1988; Ahn et al., 1992; Dupouy et al., 2008; Astoreca et al., 2009; Organelli et al., 2017; Clementson and Wojtasiewicz, 2019b) were combined with our measurements by interpolating to 1 nm resolution between 380 and 750 nm (Figure 3A). This mixing of a_p and a_ϕ was necessary due to the nature of the data reported by each source but it is not expected to influence the analysis as depigmented particle absorption has negligible contribution to the particle absorption in healthy, exponentially growing cultures (Kiefer et al., 1979). We will refer to this mixed dataset as a_p|ϕ. All data were smoothed with a rectangular moving window of 10 nm before analysis. Second order derivatives were calculated for all absorption spectra using the central finite difference approximation with a band separation of 6 nm (cf., Torrecilla et al., 2011, Figure 3B).

For all field campaigns in the BCZ and for the laboratory cultures presented in this work, the pigment content was determined by HPLC following the method of Van Heukelem and Thomas (2001). Sonication was used to break the cells and the suspension was cleared by filtration through a 0.22 μm syringe filter. The HPLC was equipped with a reverse-phase column (Eclipse XDB C₈) and the detection was performed with spectral absorption (Agilent 1100 series, Diode Array Detector). Pigment standards were acquired form the Danish Hydrographic Institute (DHI). To evaluate bloom phenology in the BCZ, we further gathered data from the regular marine LifeWatch BE monthly sampling campaigns for the period 2008-2020 (Flanders Marine Institute, 2019), described in Mortelmans et al. (2019).

Mass and molar pigment ratios from monospecific cultures obtained by HPLC and published in the literature (Buma et al., 1991; Vaulot et al., 1994; Moisan and Mitchell, 1999; Schlüter et al., 2000; Brotas and Plante-Cuny, 2003; Antajan et al., 2004; Latasa et al., 2004; Zapata et al., 2004, 2011, 2012; Rodríguez et al., 2006; Laza-Martinez et al., 2007; Quijano-Scheggia et al., 2008; Astoreca et al., 2009; Seoane et al., 2009; Liu et al., 2011, 2014; van Leeuwe et al., 2014; Organelli et al., 2017; Clementson and Wojtasiewicz, 2019b; Fagín et al., 2019) were compiled and combined with our measurements to produce a harmonized dataset of pigmentation in cyanobacteria and microalgae. By harmonized we mean that the pigment resolving power of each method was taken in consideration together with the pigment distribution across pigmentation groups (Jeffrey et al., 2011) and that mass and molar ratios were inter-converted as necessary by using the molecular weight of each pigment (Egeland et al., 2011). This pigment ratio database is briefly described here and will be fully described elsewhere (Castagna et al., in prep). When available, updated strain information (e.g., code, scientific name, sampling location) was gathered from the publication or the culture collection that holds the strain. Additional ancillary information includes the medium, temperature, irradiance and the light cycle of each culture. Reported species names are kept together with the current accepted names, following the World Register of Marine Species (WoRMS; WoRMS Editorial Board, 2021). The pigmentation group of each entry was assigned based on the pigmentation patterns in Jeffrey et al. (2011) to the maximum resolution possible depending on reported pigments. In total, the database includes 588 entries pertaining to 216 species (440 strains) from 35 pigmentation groups distributed over 21 cyanobacteria and algal classes. Figure 4 presents selected pigmentation patterns in the dataset. However, we note that several cultures could not be presented in Figures 4A,B due to incomplete pigment information. Diatoms containing Chl c₃ are underrepresented in Figure 4B since the more extensive studies on those diatom groups did not provide quantitative information for photoprotective carotenoids (PPC) ratios (Zapata et al., 2011) or Chl c fractions (Stauber and Jeffrey, 1988).

DNA metabarcoding was performed on samples collected during the campaigns of April and July 2018. The molecular analysis was based on replicate filters collected for HPLC analysis, which were previously described. DNA extraction was performed with the DNeasy Plant Mini Kit (Qiagen), with the polymerase chain reaction (PCR) amplification targeting the variable region 4 (V4) of the nuclear 18S ribosomal RNA gene. The 18S rRNA V4 primers were the TAReuk454FWD1 (5' CCAGCASCYGCGGTAATTCC 3') and the TAReukREV3 (5' ACTTTCGTTCTTGATYRA 3'; Stoeck et al., 2010). Paired-end (2 x 300 base pairs) sequencing was performed with the Illumina MiSeq technology (Illumina, San Diego, US) by Genewiz (Leipzig, Germany). The primers were trimmed from the sequenced reads using the FASTX-Toolkit (Gordon and Hannon, 2010). The resulting base-pair sequences were processed with the DADA2 algorithm (Callahan et al., 2016) to resolve amplicon single variants (ASVs). Probable contaminant sequences were removed using negative controls, following the method of Davis et al. (2018). Taxonomic assignment to the ASVs was based on the Protist Ribosomal Reference database (PR² version 4.12; Guillou et al., 2012). The ASV counts were then aggregated to species level, or genera when species could not be identified. This will result in under-representation of the genetic and specific diversity, but is considered adequate for the goals of this study. The data was filtered to remove non-pigmented organisms, with most heterotrophic organisms filtered at division rank. The exceptions were exclusive heterotrophic dinoflagellates, which were filtered at the lowest rank possible, based on reference sources (Hasle et al., 1997; WoRMS Editorial Board, 2021). The data was further annotated to indicate: (1) the pigmentation group (sensu Jeffrey et al., 2011) of each species based on our pigment ratio database; and (2) the toxicity, based on the IOC-UNESCO HAB reference list (Moestrup et al., 2021). The counts were normalized per sample to retrieve relative counts per species at each station. The aggregated and normalized dataset is provided in the Supplementary Table 2.

The relations between pigment concentrations or ratios and optical signals of the published algorithms and exploratory analysis were fitted to a mathematical model using the standard major axis model II regression (Legendre and Legendre, 2012). This approach is appropriate when both variables present random variation. Those fits provide a mathematical description of the available data and are not intended for estimation, i.e., they are not proposed as new calibrations nor are they evaluated against independent datasets. We further propose and evaluate a new algorithm to retrieve TChl c₃:TChl c from the absorption signal, that potentially avoids the confounding influences of pigments not present or widespread in red lineage algae and the effect of variable light conditions. These algorithms are described in the results subsections.

The performance metrics used in this study are: the coefficient of determination (R²), the root mean squared difference (RMSD), the mean absolute percentage difference (MAPD) and the bias, calculated as the mean percentage difference. When calculating performance metrics with environmental samples, the MAPD and bias in linear scale are calculated taking into account the higher uncertainty in the reference data, that is, the denominator is the average between the ‘reference' and the retrieved value (IOCCG, 2019). For absolute concentrations of pigments, performance statistics were calculated in log scale (cf. Seegers et al., 2018). All analysis were performed in R (version 3.6.3, R Core Team, 2020) with aid of packages “lmodel2” (version 1.7-3, Legendre, 2018), “vegan” (version 2.5-6, Oksanen et al., 2019), “limSolve” (version 1.5.1, Soetaert et al., 2009), “mgcv” (version 1.8-31, Wood, 2017), “dada2” (version 1.12.1, Callahan et al., 2016), and “decontam” (version 1.6.0, Davis et al., 2018).

A total of 137 taxa were identified, which is a conservative estimate of species diversity considering the aggregation of ASVs that could not be classified to species rank. The most diverse classes were the diatoms (55 taxa), followed by autotrophic dinoflagellates (33 taxa), cryptophytes (11 taxa) and mamiellophytes (11 taxa). All other observed classes were represented by less than five taxa, including the prymnesiophytes, which were represented by only two taxa. The most common (across samples) and abundant (relative ASV counts) species per group where the mamiellophyceans Micromonas bravo and Ostreococcus tauri, the cryptophyceans Plagioselmis prolonga and Teleaulax acuta, the prymnesiophycean Phaeocystis globosa, the dinoflagellates Gymnodinium sp., Tripos fusus and Heterocapsa pygmaea, and the diatoms Chaetoceros sp., Rhizosolenia imbricata, R. delicatula, Cyclotella sp., Cerataulina bergonii, Pseudo-nitzschia pungens and P. delicatissima.

Several species reported to produce toxins were identified in our samples: the dinoflagellates Alexandrium minutum, A. ostenfeldii, Gonyaulax spinifera, Karlodinium veneficum and Prorocentrum cordatum; the diatoms Pseudo-nitzschia delicatissima and P. pungens; and the raphidophytes Fibrocapsa japonica, and Heterosigma akashiwo. Of those species, only Prorocentrum cordatum, Pseudo-nitzschia delicatissima and P. pungens were relatively abundant.

Among the species presenting Chl c₃ were the dinoflagellate Karlodinium veneficum, the prymnesiophytes Phaeocystis globosa and Haptolina sp., and the diatoms Pseudo-nitzschia delicatissima, P. pungens, and several species of the genus Rhizosolenia. That is, with the exception of Rhizosolenia, the identified organisms containing Chl c₃ are all associated with the formation of HABs, either through toxicity or oxygen depletion following the bloom termination, and were among the most common and abundant species in our samples.

The observed diatoms containing Chl c₃ are also known to have a synchronous bloom with Phaeocystis globosa in the southern North Sea (Peperzak et al., 1998; Antajan, 2004; Muylaert et al., 2006), which is also supported by our metabarcoding dataset (Figure 5A). Figure 5B presents a comparison of the pigment ratio profile of two diatom species in our pigment ratio dataset, showing the similarity in their composition of PPC, Fuco and Fuco derivatives with P. globosa. Pseudo-nitzschia pungens diverges from the others in terms of Chl c composition, by both presenting Chl c₁ and a lower TChl c₃:TChl c ratio. We could not find reports on the pigment ratios of Rhizosolenia imbricata and R. delicatula.

The absorption-based algorithm proposed by Astoreca et al. (2009) was developed as a quantitative relation between Chl c₃ concentration and a line height at 468 nm, calculated over an exponential baseline anchored at 450 nm and 480 nm:

The exponential baseline was proposed to compensate for the curvature added by water, detritus, minerals and chromophoric dissolved organic matter (CDOM) absorption in the blue wavelength range, as the algorithm was designed to be applied directly to total absorption, a_t. In order to evaluate the specificity of the algorithm, here we applied it to a_p|ϕ from cultures (Figure 6A). This should not cause a bias as the algorithm was designed to work with variable detritus and CDOM abundances and an evaluation with our field data showed that the line height from a_t, a_ϕ and a_p follow the 1:1 relation (Figure S1 of the Supplementary Data Sheet 1).

The analysis showed that while organisms containing only MgDVP had negative line heights, all strains of red lineage algae had positive values, regardless of the presence of TChl c₃ (Figure 6A). The line height was also positive for M. pusilla, which can be explained by the typical abundance of MgDVP and Chl c_CS-170 in this species, though detailed pigment concentration was not available for this specific culture. We note that the performance log statistics are strongly influenced by the constant of 0.01 mg m⁻³ added to cultures with no TChl c₃, since all cultures with positive line heights were included in the log evaluation statistics. This is of little consequence as the objective is to show that the line height and algorithm proposed by Astoreca et al. (2009) are not specific to TChl c₃ or to P. globosa. Conversely, when evaluated against the TChl c concentration, the line height shows a linear relation over 4 orders of magnitude, from 0.426 to 731.14 mg m⁻³ (Figure 6B).

The reflectance-based version of the line height proposed by Astoreca et al. (2009) attempts to invert the reflectance to total absorption, estimating the backscattering in the NIR by imposing a constant absorption at 700 nm equal to the water absorption coefficient (aw(700)=0.57m-1; Buiteveld et al., 1994):

Reflectance data was not available for the cultures to evaluate the specificity of Equation (3). However, since it is based on the same short-scale absorption feature as Equation (2), it will also capture the signal of TChl c. The application of the reflectance-based algorithm to the field samples in the BCZ cannot help to elucidate the origin of the signal due to the regional correlation between TChl c₃ and TChl c (Figure S2 of the Supplementary Data Sheet 1). Instead, we applied the line heights to absorption and reflectance measured from field samples to evaluate, if in mixed phytoplankton assemblages and with contribution of detritus and CDOM, a relation with TChl c is still observed (Figures 7A,B). While a relation was observed, the absorption-based relation for the field data (Figure 7A) was not described by the same equation as in Figure 6B and presented larger uncertainty. However, the model coefficients for the absorption-based relation are consistent with those calculated for a_t retrieved from reflectance (Figure 7B). The evaluation of the line heights against TChl c₃ concentration (not shown) resulted in slightly worse log performance statistics, except for the coefficient of determination, which was higher due to the larger data range in log scale (small amounts of TChl c₃ outside spring).

The hyperspectral algorithm proposed by Lubac et al. (2008) was developed for application to reflectance data of mixed phytoplankton assemblages and defined as a classification tree for P. globosa dominance. Dominance was defined based on a relative biomass higher than 60 %, measured as carbon (C) mass:mass ratio. The algorithm evaluates the wavelength of the maxima in the second derivative of the reflectance spectra in the range of 460–480 nm and the wavelength of the minima between 480 and 510 nm. If the wavelength of the maxima is higher than 471 nm and the wavelength of the minima is higher than 499 nm, a sample is considered dominated by P. globosa biomass:

In order to evaluate the specificity of the algorithm to P. globosa and the pigment-to-signal association, the algorithm was adapted for application to the a_p|ϕ measured on cultures (Figure 8A). This adaptation shifts the wavelength ranges and thresholds by 7 nm toward the blue and inverts the argmin and argmax as the second derivative of the absorption has the inverted sign to that of reflectance. The shift was justified by Lubac et al. (2008) for the second threshold based on possible differences of carotenoid relative abundance between cultures and natural assemblages. However, we found that a shift in the first threshold was also necessary, since the wavelength of minima of absorption for the P. globosa cultures were at 466 nm and 467 nm, shorter than the threshold originally defined at 471 nm for reflectance.

The evaluation showed that most organisms containing Chl c₃ passed the thresholds to be classified as ‘P. globosa dominance'. Exceptions were the benthic diatom Amphora sp., the prymnesiophyte Prymnesium parvum and two cultures of the prymnesiophyte Emiliania huxleyi. Amphora sp. presents the four main Chl c types, with low Chl c₃:TChl c ratio (0.07) and abundance of caretonoids. Though the pigment ratios associated with the absorption of P. parvum are not available, our larger database of pigment ratios shows that P. parvum also presents the four main Chl c types, together with a relatively higher photoprotective carotenoids (PPC) to TChl c ratio (>0.65, mol:mol) than other Chl c₃ containing species. A higher PPC:TChl c ratio also seems to explain the two cultures of E. huxleyi that did not pass the thresholds to be classified as “P. globosa dominance.” One of those cultures was grown at high irradiance (300 μE m⁻² s⁻¹) and presented a PPC:TChl c ratio of 1.33. The pigment composition of the other culture is not available, and although it was grown at comparable irradiances to other E. huxleyi cultures that were classified as “P. globosa dominance,” its absorption spectrum shows a small peak at 500 nm that is related to PPC. We also note that while the algorithm was designed to be used with mixed phytoplankton assemblages and therefore has a threshold that includes up to 40 % diatom biomass, the cultures of P. globosa were not in the extremes, but between diatoms and other prymnesiophytes (Figure 8A). Additionally, the algorithm captured the diatom Pseudo-nitzschia azenyensis, the dinoflagellate Alexandrium pacificum and the majority of the green lineage algae (the exception was Dunaliella tertiolecta) in the classification of ‘P. globosa dominance'.

Within the red lineage algae, a principal component analysis including the ratios of TChl c, PPC and photosynthetic carotenoids (PSC) to Chl a showed a consistent pattern with the classification by the Lubac et al. (2008) algorithm, indicating that the signal arises from a combination of high TChl c:Chl a and low PPC:Chl a (Figure 8B). A high PSC:Chl a provides only a partial separation on the first principal component from the organisms without Chl c₃, but can contribute to the signal. The PCA was performed with aggregated pigments in order to avoid the dominating influence of specific pigment presences and absences among pigmentation groups. This is justified for the pigments included here since the spectral shape and magnitude of the absorption coefficient is similar within the aggregates (cf. section 2; Bricaud et al., 2004; Egeland et al., 2011; Clementson and Wojtasiewicz, 2019a). Unfortunately, β,β-Car:Chl a could not be included in the PPC:Chl a aggregate and analysis since it was not available for all datasets. The cultures with only spectrophotometric determination of pigments could not be included due to the lack of PPC and PSC data. The results of the PCA analysis are in line with the pigmentation trends for organisms with Chl c₃ displayed in Figure 4B: the TChl c:Chl a tends to be higher and the PPC:TChl c tends to be lower in organisms with higher Chl c₃ fraction.

The classification of Pseudo-nitzschia azenyensis as ‘P. globosa dominance' has ecological relevance, since the bloom of other diatoms of the same genus, Pseudo-nitzschia delicatissima and Pseudo-nitzschia pungens, are synchronous to that of P. globosa in the BCZ (e.g., Antajan et al., 2004; Speeckaert et al., 2018; Nohe et al., 2020, cf. Section 4.1). Considering the similarity of pigmentation patterns between P. globosa, Pseudo-nitzschia delicatissima, and Pseudo-nitzschia pungens and their spatio-temporal association (Figure 5), it is not possible to evaluate from the field data the specific taxonomic association proposed by the algorithm. However, the conditions of mixed phytoplankton assemblages and varying environmental conditions that control the abundance of PPC can help evaluate the patterns found in the analysis with pure cultures. The application of the Lubac et al. (2008) algorithm to the field samples of a_p and ρwlL reinforced the interpretation obtained from the PCA analysis (Figure 9). Samples with low PPC:TChl c were well separated in the wavelength range of 475–510 nm. While in principle it is possible that the Sun seasonal cycle influences the analysis presented in Figure 9A, through PPC and PSC relative abundances in spring and summer, the same pattern was observed in Figure 9B, which includes samples also from fall and winter months (Table 2).

The dataset of pigment ratios showed a general association between TChl c₃:TChl c, TChl c:Chl a and PPC:TChl c. This suggests that specific properties of the different Chl c types could be explored for the retrieval of information associated with groups that share this pigmentation pattern. The previous algorithms have focused on the blue end of the spectrum, but the evaluation of the Astoreca et al. (2009) algorithm suggested that the apparent center wavelength of the blue peak (Soret band) of different Chl c types in vivo cannot be used for differentiation. The negative effect of Chl b on the line height can also hamper its use in systems where green lineage algae are seasonally relevant contributors to the pigment pool. Additionally, the shoulder around 465 nm caused by Chl b, though not equal in shape to that caused by PPC:TChl c, is nevertheless captured in the argmax argmin algorithm of Lubac et al. (2008).

The red peaks of Chl c centered (in acetone) at ≈ 630 nm (I) and ≈ 580 nm (II), however could provide a differentiation between its three optical groups (cf. section 2 and Zapata et al., 2006) while also not presenting an overlap with Chl b. The molar absorption cross-section spectra in 90 % acetone of representatives of those groups are presented in Figure 10A. Evidence suggests that those patterns are retained in vivo. In the work of Hoepffner and Sathyendranath (1991), the cultures of E. huxleyi were outside the relation observed for other cultures between the Gaussian peak magnitude at 583 nm and the Chl c concentration (their Figure 3B). This can be explained by the fact that they used the SCOR (1966) method, which estimates Chl c from the absorption in acetone at 630 nm, effectively capturing only the signal of TChl c₁ and TChl c₂ while the peak at 583 nm also contains the signal of TChl c₃. In our dataset of paired absorption and pigment composition we also observed in vivo the patterns expected from the absorption in solution (Figure 10B). The Chl a peaks II at 623 nm and III at 583 nm influence the ratio of a_p|ϕ(594):a_p|ϕ(633) in Figure 10B causing the ratio to be ≈ 1 for cultures with high TChl c₃ fraction and <1 for the others. This effect and the larger variability of TChl c:Chl a in the organisms without Chl c₃ explain the larger variability of the a_p|ϕ(594):a_p|ϕ(633) ratio for this group.

We therefore propose and evaluate a new algorithm to retrieve TChl c₃:TChl c from optical signals, that potentially avoids the confounding influences of pigments not present or widespread in red lineage algae and the effect of variable light conditions. The algorithm uses the spectral information in the range relevant for accessory pigments by fitting the model:

where α is the offset, β_O(λ) is a smooth function of spectral coefficients, O is a transformed optical variable (e.g., normalized a_ϕ or ρwlL) and ϵ is a random error with a Gaussian distribution centered on 0. The main difference of Equation (5) to a classical multiple regression model is that it takes advantage of the continuous and ordered nature of the predictor variables. Further, the smoothness observed on the spectral data is imposed in the coefficients. That is, the lack of independence between the signal in adjacent spectral bands that hampers classical multiple regression analysis in this setting is used to justify the requirement of smoothness in β. This is a typical functional data analysis model applied in chemometrics, known as scalar-on-function regression (Ramsay and Silverman, 1997; Reiss et al., 2017). Here we used the thin plate regression splines as basis expansion (TPRS; Wood, 2003). The fitting is controlled by regularization, with the penalty on the second derivative of the coefficients selected by generalized cross validation (Hastie et al., 2009; Wood, 2017).

For the absorption-based algorithm, the optical variable was chosen to be the a_ϕ normalized by its magnitude at 675 nm. For the reflectance-based algorithm, the optical variable was chosen to be the integral normalized ρwlL subtracted by the minimum value in the wavelength range of interest. The absorption-based algorithm was calibrated with culture data and the fitted algorithm was validated with field data. The reflectance-based algorithm was calibrated with a random subset corresponding to 66 % of the field data from 2018 to 2019, and validated with the remainder 34 % of samples. The O functions for absorption and reflectance are:

The proposed algorithm described by Equation (5) was calibrated against the a_p|ϕ and the TChl c₃:TChl c ratio measured by HPLC from the pure cultures dataset, including green lineage algae and cyanobacteria (Figure 13A). The offset was set to zero and the smooth function term had an estimated 20.18 degrees of freedom. The oscillations in β_ap|ϕ(λ) were found such that the integral product of β_ap|ϕ(λ) and a_p|ϕ(λ)/a_p|ϕ(675) levels off at 0 for organisms that do not present the pigmentation pattern associated with Chl c₃ presence, while it accumulates a value between 0 and 1 when Chl c₃ is present, estimating the TChl c₃ fraction (Figures 11A,B). The position of the peaks follow the center wavelengths of the apparent absorption peaks that are related to the pigmentation pattern associated with Chl c₃, with the oscillation between 480 and 515 nm capturing the signal of the relative ratios of PPC, PSC, and TChl c, and with the oscillation between 590 and 640 nm capturing the signal of Chl c with relative pattern as expected for Chl c₃ (Figures 10A,B). The coefficients also avoid the signal of Chl b, phycocyanin and phycoerythrin by having negative values around 650 nm, 620 nm and 550 nm, respectively. The positions of peaks and valleys are not located exactly at the apparent peak center wavelengths of the pigments in vivo as a consequence of having higher weights in the spectral regions that help differentiate between pigments and pigmentation patterns.

The details of the a_ϕ spectra are typically a minor component of the ρwlL spectra, especially in turbid or organic rich systems. The ρwlL transformed with Equation (7) shows however some broad wavelength features that are associated with the gradient of Chl c₃ fraction (Figure 12A). The estimated coefficient function βρwlL (Figure 12B) captures mainly the inverse of the pattern shown in Figure 10B, i.e. capturing the relative plateau between 600 and 640 nm due to the high II:I absorption peak ratio of Chl c₃, combined with the absorption of Chl a. The evaluation with the calibration set is presented in Figure 13B. The coefficients for absorption and reflectance data at 1 nm resolution are provided in the Supplementary Table 4.

When the absorption-based model was applied to field data at 1 nm resolution with a_ϕ estimated with chemical oxidation, the RMSD was 0.059 (mol:mol), 10 % of the upper limit of TChl c₃:TChl c typically observed in field samples (Figure 13C). The low MAPD of 27.4 % and bias of 7.3 % suggests that if a_ϕ can be measured directly, TChl c₃:TChl c can be estimated with acceptable uncertainty. Similar results were observed for the reflectance-based model, with its application to the validation set resulting in a RMSD of 0.074 (mol:mol), a MAPD of 29.2 % and a bias of 6.1 % (Figure 13D).

The study of Antajan et al. (2004) was the first to demonstrate the high correlation between TChl c₃ and P. globosa in the BCZ, though the authors were careful to note that the pigmentation patterns of other major diatoms with similar bloom phenology, including Pseudo-nitzschia and Rhizosolenia, were not known. The studies of Quijano-Scheggia et al. (2008) and Zapata et al. (2011) on the pigmentation patterns of Pseudo-nitzschia species showed that P. delicatissima and P. pungens not only contain DVChl c₃ but also have a similar pigmentation signature to P. globosa. In particular, P. delicatissima can dominate the diatom biomass in the period of April-May in areas of the southern North Sea (Delegrange et al., 2018; Speeckaert et al., 2018) and its co-occurrence with P. globosa has been suggested to result from an ecological association where one of the species uses the other as substrate for growth. Delegrange et al. (2018) have suggested that P. globosa flagellate cells use the diatom as a substrate to form colonies, but data on the temporal evolution of the fraction of P. globosa colonies containing P. delicatissima cells and their abundance in the colony supports the opposite hypothesis (Sazhin et al., 2007). A similar association was observed between Phaeocystis pouchetti and Pseudo-nitzschia granni (Sazhin et al., 2007). While direct observations of similar association are not available for Phaeocystis antarctica, Kang et al. (2001) found that Phaeocystis antarctica colonies and Pseudo-nitzschia species (P. heimii, P. lineola and P. subcurvata) had correlated spatial distribution in the Weddell Sea, with highest abundances in the marginal ice zone. This association is not restricted to Phaeocystis, as Pseudo-nitzschia species have also been found inhabiting colonies of other diatoms (e.g., Rines et al., 2002). If those species associations are present in other environments, the relations observed in our study are likely to be applicable to other Phaeocystis related studies (e.g., Stuart et al., 2000; Bracher and Tilzer, 2001; Orkney et al., 2020; Li et al., 2021) and should be considered for Pseudo-nitzschia studies. Other diatom taxa containing DVChl c₃ observed to bloom just before and during the P. globosa bloom in the BCZ are Thalassionema nitzschioides and Rhizosolenia (Muylaert et al., 2006). Rhizosolenia imbricata was well correlated with the spatio-temporal distribution of P. globosa in our samples, but quantitative pigment information is not available for this species or other species of the same genus. The presence of Chl c₃ in this species is inferred from the presence of the pigment in another species of the same genus (R. setigera; Stauber and Jeffrey, 1988). However, we note that some species may present Chl c₃ at very low or trace concentrations, and quantitative information on pigment composition is necessary to evaluate the potential impact on the optical signals. The spectral shape of the Chl a specific in vivo pigment absorption coefficient of another species of the same genus (R. formosa; Richardson et al., 1996) is more similar to that of the archetypal diatom containing only Chl c₁ and c₂, suggesting both a lower TChl c₃:TChl c ratio and a higher PPC:TChl c ratio. Species containing Chl c₃ that are not necessarily synchronous with P. globosa in the BCZ are the dinoflagellate Karlodinium veneficum and the mamiellophytes Micromonas pusilla, M. commoda and M. bravo (Lagaisse, 2020).

The co-occurrence of multiple species with similar Chl c pools, some of which with close physical associations, brings into question the attribution of Chl c₃ exclusively to P. globosa in the BCZ (Muylaert et al., 2006; Astoreca et al., 2009). While data on PPC:TChl c (mol:mol) ratios were scarce for those species of diatoms co-occurring with P. globosa in the BCZ, the relative composition of TChl c, PPC and PSC of another Pseudo-nitzschia species was similar. This also raises the question of whether it is possible to perform optical monitoring tied to a well defined taxonomic or functional group as has been previously suggested (Lubac et al., 2008; Astoreca et al., 2009; Kurekin et al., 2014; Orkney et al., 2020). The close association between Phaeocystis colonies and Pseudo-nitzschia cells might partially explain why waters with abundant Phaeocystis colonies were observed by Bracher and Tilzer (2001) to have similar packaging effects than waters dominated by diatoms, creating further challenges for their optical separation. This similar packaging effect, despite the nanoplankton size of Phaeocystis cells, is a core assumption in the multistep algorithm developed by Orkney et al. (2020). The specific pigmentation pattern of the North Sea variety of P. globosa (Zhang et al., 2021), lacking or with small amounts of the 19'-Butanoyloxy (But-Fuco) and 19'-Hexanoyloxy (Hex-Fuco) fucoxanthin derivatives (Buma et al., 1991; Vaulot et al., 1994; Antajan et al., 2004; Astoreca et al., 2009; Seoane et al., 2009), also hampers factorization of Chl a between P. globosa and diatoms containing DVChl c₃ based on pigment ratios (e.g., CHEMTAX; Mackey et al., 1996). This limitation can have important consequences, as pigment-based analysis can represent a substantial source of validation for optical algorithms (Dierssen et al., 2020).

Currently, there is insufficient information to evaluate differences in pigmentation and optical patterns between single cell and colonial stages of P. globosa and to evaluate the group dominance in terms of optical signal. Our molecular data cannot help to resolve the dominance in terms of cell counts (and therefore on count-based biomass and pigments estimation), due to the difficulties of extracting quantitative information from amplicon sequencing (e.g., Zhu et al., 2005; van der Loos and Nijland, 2021). Based on previous research, we estimate that, considering the typical diatom assemblages in the BCZ, the evolution of the fraction of the bulk Chl a that can be attributed to P. globosa lags the evolution of its biomass fraction, being approximately the same only at biomass fractions > 60 % (Section S4 of the Supplementary Data Sheet 1). Additionally, the peak of the relative contribution of P. globosa to the Chl a pool does not necessarily coincide with the peak in Chl a concentration (Figure S3 and Section S4 of the Supplementary Data Sheet 1). Indeed, the biomass specifically associated with P. globosa cells can be smaller than that of diatoms even during the P. globosa bloom period (Lancelot, 1995). Additionally, spring blooms with dominance of P. globosa biomass were observed to result in the lowest Chl a per unit cellular carbon through the growth season (Speeckaert et al., 2018). The most detailed information available in terms of biomass is from Sazhin et al. (2007), who quantified the biomass of P. globosa and of diatoms inhabiting the colonies, showing that by the end of the P. globosa bloom more than half of the colony biomass was due to colonizing diatoms. Considering the available information, the relative contributions to the bulk biomass, pigments and, by consequence, optical signals, cannot be assumed to be dominated by P. globosa for the duration of the bloom.

Regardless of the relative contribution of P. globosa to the Chl c pool, our analysis has shown that the line height proposed by Astoreca et al. (2009) is not specific to Chl c₃, instead capturing the signal of TChl c. In solvent, the different Chl c types present slightly varying center wavelengths of the Soret band and magnitudes of its mass specific absorption coefficients (Figure 10; Zapata et al., 2006; Clementson and Wojtasiewicz, 2019a). It is therefore noteworthy that the line height proposed by Astoreca et al. (2009) and the TChl c concentration are described by a single relation over groups with different Chl c types and relative abundances (Figure 4A). It is possible that in vivo, the Soret band center wavelength and the (unpacked) mass specific absorption coefficient of Chl c types are more similar than in solution, or that the apparent peak center wavelength is more similar due to the influence of the adjacent absorption peaks of other pigments. Additionally, in our pigment ratio dataset, Chl c₂ was abundant and for most cultures it comprised > 40 % of the TChl c, significantly influencing the magnitude of the 468 nm peak in organisms with Chl c₃. This would help explain why the a_p|ϕ(450, 468, 480) line height was not specific to TChl c₃. A relation of the line height with TChl c concentration was previously observed by Peperzak et al. (2015). Their study was based on reflectance measurements of mesocosms of P. globosa, and the authors related the Astoreca et al. (2009) line height directly to TChl c.

Among the red lineage algae, a strong correlation was observed in our dataset between the TChl c:Chl a, PPC:Chl a and Chl c₃:TChl c ratios (Figure 4B). The exception was the archetypal dinoflagellate with pigmentation pattern DINO 1 (sensu Jeffrey et al., 2011), which presents a wide range of TChl c:Chl a while lacking Chl c₃ (however, presenting high PPC:TChl c). That is, in general, with the notable exception of DINO 1 as a group, organisms with Chl c₃ and higher Chl c₃ fraction tend to have higher TChl c and lower PPC per unit Chl a, defining a pigmentation pattern. To our knowledge, this pigmentation pattern has not been previously described and offers an alternative explanation to observations of the impact of Chl c₃ on the Chl c absorption magnitude at ≈ 461 nm in natural assemblages (Stuart et al., 1998). A general trend of increasing TChl c:Chl a with decreasing PPC:Chl a has also been observed for a globally distributed set of natural samples (Bricaud et al., 2004). In that study, the pattern was related to the increase of Chl a concentration, but was not discussed and not enough chemical (e.g., Chl c₃ concentration) or taxonomic information was made available to discard the possibility that the trend was related to light conditions, as PSC:Chl a ratio was also increasing with the Chl a concentration. A similar relation was also observed in the longer set of pigment data for the BCZ from 2008 to the present (Figure S2 of the Supplementary Data Sheet 1). The described pattern in pure cultures is also inline with observations of a similar pigment signature between dictyochophyceans, dinoflagellates and prymnesiophyceans having Chl c₃ (Johnsen et al., 2011b).

The pigmentation trend may help to explain the linear relations of the line height against the Chl c₃ concentration observed by Astoreca et al. (2009), but likely the combination of the absolute nature of the line height and the phenology of the phytoplankton in the BCZ were more determinant. In the BCZ, the highest Chl a, TChl c and TChl c₃ concentrations are observed during the spring bloom of P. globosa, reaching ≈300 % higher than the concentrations observed in the May-February period (Figure S2 of the Supplementary Data Sheet 1). This surge in TChl c caused by intense blooms of P. globosa accompanied by blooms of DVChl c₃ containing diatoms, both naturally presenting higher TChl c:Chl a, would result in a good correlation by a magnitude effect between the absolute line height and the TChl c₃ concentration gradient observed in situ. The pigment-to-signal association proposed here could not be detected in the Astoreca et al. (2009) study, as Chl c₁ and c₂ were not quantified in their field samples. This analysis highlights the challenge of algorithm calibration based on a restricted set of field data in terms of spatial, temporal or ecological coverage. In such cases, local correlations may confuse the association between optical signals and the system's properties of interest.

Considering the overlap in center wavelength of the Soret bands of Chl b and Chl c types in vivo (e.g., Hoepffner and Sathyendranath, 1991; Bricaud et al., 2004), the near zero line height for green lineage algae without significant amounts of Chl c while positive for red lineage algae and M. pusilla can be unexpected. A potential explanation lies in the height and width of those bands, with the Soret band of Chl b having a molar absorption cross-section two times lower than Chl c and a half width at half maximum of 45 nm, two times larger than that of Chl c (Hoepffner and Sathyendranath, 1991). In combination with the trifurcated peaks of carotenoids that present local minima around the Soret band of Chls b and c (e.g., carotenes, Lut, Viola, Neo), the shorter and broader Soret band of Chl b results in a flatter absorption curve in the range 450 nm to 480 nm. In M. pusilla, the contribution of the narrower Soret absorption bands of MgDVP and Chl c_CS-170 protrudes from the flatter and broader peak caused by Chl b and carotenoids. The presence of a peak around 465 nm, superimposed on the shoulder typical of green lineage algae, has also been observed in other prasinophytes with similar pigmentation pattern (e.g., Figure 13.3B in Johnsen et al., 2011a). The presence of abundant Chl c in M. pusilla with a clear signal in the absorption spectra of this species is relevant considering it can be the dominant species of picoplanktonic eukaryotes (Not et al., 2004).

Our analysis has also shown that while the hyperspectral algorithm proposed by Lubac et al. (2008) mainly captures the signal of low PPC:TChl c, this pigmentation pattern is not exclusive to P. globosa even in the BCZ and presents a general trend associated with the presence of Chl c₃. The similarity of the optical signal of species containing Chl c₃ was also noted by Johnsen et al. (1994), with all species containing Chl c₃ forming a cluster in their linear discriminant analysis, regardless of taxonomic affiliation. This clustering was observed even when only three wavelengths were used (481, 535, and 649 nm). Conversely, prymnesiophytes without Chl c₃ (e.g., Isochrysis and Pavlova) typically present an apparent carotenoid peak at 500 nm similar to diatoms without Chl c₃ (Mao et al., 2010; Clementson and Wojtasiewicz, 2019b). However, the dependency of the Lubac et al. (2008) algorithm on PPC may make its association to a specific taxonomic or functional group sensitive to environmental conditions. In our dataset, the prymnesiophyte E. huxleyi cultured at high irradiances had higher amounts of PPC, which affected its spectral absorption resulting in its classification outside the region of ‘P. globosa dominance', where other cultures of E. huxleyi were classified. It is possible, however, that specifically for Phaeocystis species this might be a minor issue, as available experiments show resilience in the PPC:TChl c ratio across broad ranges of irradiance (e.g., Moisan and Mitchell, 1999; Rodríguez et al., 2006; Astoreca et al., 2009; Liu et al., 2011). Peperzak et al. (2015) showed that nitrogen limitation will result in the increase of carotenoids (mainly Fuco) to total Chl (a+c), which would likely reinforce the derivative signal as Fuco absorbs in the green wavelength range (cf. Figures 8A,B). The algorithm also classifies most green lineage algae tested as ‘P. globosa dominance'. Though green lineage algae are not in general an important component of the phytoplankton assemblage of the southern North Sea (Muylaert et al., 2006), the application of this algorithm to other environments must be made with caution.

Considering the general pigmentation patterns associated with the presence of Chl c₃, the dependence of the Lubac et al. (2008) algorithm on PPC and its misclassification of green lineage algae, we explored an algorithm that also includes information of the Chl c absorption peaks in the red end of the spectrum to retrieve the TChl c₃:TChl c ratio. It is in the ratios of peaks I and II that the different Chl c optical groups mostly diverge and this information will reduce the dependence on the optical signal of the PPC:TChl c. In general, models covering a wide range of wavelengths shift the focus from trying to capture the signal of a single pigment, which might not be possible to differentiate from optics alone, to capture the signal of a pigmentation pattern (Kirkpatrick et al., 2000). We have therefore opted for an approach of functional data analysis commonly used in chemometrics. This frame work encompasses principal components regression (PCR; Kendall, 1957; Massy, 1965) and partial least squares regression (PLSR), which have found successful applications in hydrology optics (e.g., Moberg et al., 2002; Organelli et al., 2013; Xi et al., 2020). However, instead of projecting the data onto an empirical orthogonal basis derived from the data itself, we used TPRS as a basis. This avoids the selection of principal components to be discarded for regularization of the fit (e.g., Massy, 1965; Jolliffe, 1982; Hastie et al., 2009) and the selection of the number and position of knots of the B-splines and similar basis (Wood, 2003). Composition ratios are commonly fitted using a logit link function between the model and the response to ensure that the predicted values fall in the range [0, 1]. This is relevant when modeling multi-part compositions (cf. Aitchison, 1986), but it is not a requirement (e.g., regression of an indicator matrix, Hastie et al., 2009) and the predictions of the model with an identity link can be truncated at 0 and 1. We have chosen to do so due to the superior performance with the absorption and reflectance calibration sets for a fit without a logit transformation.

In principle, it is possible to avoid the variable TChl c:Chl a signal to extract the TChl c II:I ratio by performing a decomposition of the absorption spectra into symmetric band models (e.g., Gaussian, Cauchy-Lorentz or Voigt; Hoepffner and Sathyendranath, 1991; Chase et al., 2013; Liu et al., 2019) and compensating for the Chl a signal at 583 nm. This approach may not be possible in environments where phycocyanin is abundant, due to its absorption at ≈ 619 nm (Simis and Kauko, 2012). If the decomposition successfully captures peaks I and II of Chl c, the ratio II:I will be proportional to the TChl c₃:TChl c. We have indeed evaluated this method with measured a_ϕ and though we achieved some success (not shown), the uncertainty of estimation of peak magnitudes propagates to large uncertainty in the II:I ratio and consequently a poor performance of the algorithm retrieval (MAPD ≈ 100 %).

The absorption-based algorithm we calibrated is specified in terms of a_ϕ, requiring it to be chemically or mathematically decomposed from a_p. The additional uncertainty of the mathematical decomposition can represent a major limitation for application to automatic in situ monitoring, especially in turbid waters, but site specific tuning can result in acceptable uncertainty for application to a submersible spectrophotometer (e.g., AC-S, SeaBird Scientific; Figure S4 and Section S5 of the Supplementary Data Sheet 1). We could not calibrate the absorption-based version of the algorithm in terms of a_p or a_t as the calibration was based on IOPs measured in pure cultures, where the depigmented particle absorption is not expected to be representative of the natural environment and CDOM absorption was not measured.

The same functional model could be applied directly to reflectance, despite the strong influence of detritus, minerals and CDOM on the reflectance of this turbid coastal system. The main adaptation necessary was to find the proper wavelength range and transformation to minimize the influence of non-phytoplankton signal. Avoiding the red edge reflectance peak and the reflectance saturation in the blue end (Luo et al., 2018) is important to avoid a spurious correlation with bloom magnitude. The reflectance-based version of the Chl c₃ fraction algorithm was calibrated to data measured by systems with high spectral sampling frequency (<3 nm) but relatively broad bandwidths (≈ 10 nm). Those are typical specifications of hyperspectral radiometers used in situ. Current and future spaceborne hyperspectral sensors have a lower spectral sampling frequency while maintaining comparable bandwidths (cf. Dierssen et al., 2021). The fit was performed on data after spline interpolation to 1 nm. In principle, such interpolation could also be applied to remote sensors, considering that the coefficient function captures only major variations in the spectra, ignoring the high frequency features. The evaluation of this application is beyond the scope of this study and should be performed before application to air- or spaceborne sensors. Additionally, in contrast with the absorption-based version that was calibrated against a diverse set of organisms with different optical signatures, the reflectance-based version had to be calibrated with in situ measurements. This requires careful evaluation before application of the reflectance-based algorithm to other aquatic systems.

Learning from the evaluation of the previous studies and considering the pigmentation trends related to Chl c₃, we have avoided association of the TChl c₃ fraction with a specific taxonomic or functional group. This separation between the signal and the interpretation is advantageous for the clarity of communication within the field of hydrology optics and in its interface with other research areas and potential users that might apply spectroscopic methods for monitoring. The interpretation of the signal is dependent on the phytoplankton assemblage of the system and its environmental conditions. In this regard, spectroscopic methods are no different than chemotaxonomic methods, as pigmentation patterns are not unique and most pigments do not present a unique optical signal. When conditions allow, however, it is possible to narrow the interpretation of the signal to an ecologically relevant group. In the case of the southern North Sea, the TChl c₃:TChl c ratio may be associated with HABs. P. globosa is a nuisance species with adverse effects on the marine system (Lancelot, 1995; Peperzak and Poelman, 2008). P. delicatissima and P. pungens populations in the southern North Sea have been associated with the presence of the neurotoxin domoic acid (Delegrange et al., 2018, and references therein). The ecological relation between those species and their potential detrimental effects for the ecosystem and society provide ecological value for monitoring the aggregate, though it may not be possible to evaluate with those tools how the individual species respond to changes in environmental conditions. Long-term trend analysis on diatom assemblages in the southern North Sea have indicated that Pseudo-nitzschia species have become more abundant in the last 50 years (Lefebvre and Dezécache, 2020; Nohe et al., 2020) while P. globosa has shown a more complex pattern, with decreasing presence in regions where it was previously abundant, while increasing in others (Lefebvre and Dezécache, 2020). We note however that the extent to which Rhizosolenia species contribute to the Chl c₃ is as yet unknown.

The application of the reflectance-based algorithm to the water-leaving signal assumes that the phytoplankton assemblage is composed by well mixed populations of the different component species and well mixed in the water column, which is observed in the southern bight of the North Sea (van Beusekom and Diel-Christiansen, 1993). In this case, the bulk water-leaving optical signal is representative of the phytoplankton assemblage composition and the algorithms presented here may be applied directly. However, if the assemblage composition varies with depth, the signal will be mostly representative of the assemblage composition closer to the surface. Additionally, the non-uniform vertical distribution of the well mixed assemblage in the water column will cause changes to the reflectance spectral shape (e.g., Xue et al., 2017), which might impact algorithm performance.

In addition to the hyperspectral algorithms evaluated here, Lubac et al. (2008) also proposed a band ratio of the reflectance at 490 nm to that of 510 nm that could be applied to the MERIS sensor and its successor, the Ocean and Land Color Instrument (OLCI/Sentinel-3), but have not demonstrated its application from those sensors. Though the authors concluded that the ratio was not sensitive to the magnitude of the bloom, using simulations for sensitivity analysis, the particle scattering was independent of particle load and its dependence on Chl a independent of the species modeled. Due to the non-linear effect of backscattering magnitude on reflectance and described seasonal dependence of IOPs in the BCZ (Astoreca et al., 2012), it is likely that the ratio is sensitive to biomass magnitude. Kurekin et al. (2014) also proposed a multispectral algorithm for P. globosa detection, based on Linear Discriminant Analysis (LDA) for the MERIS and the MODIS sensors. Since the algorithm was directly calibrated from remote sensing images, and includes the absolute magnitudes of the normalized water-leaving radiance at 665 nm and inverted absorption, it likely suffers from the same magnitude effect correlation.