Light absorption by phytoplankton drives marine primary production and determines ocean color. Phytoplankton absorption is a function of the pigment composition, wavelength, intracellular pigment concentration, and the cells' type. This paper presents phytoplankton absorption spectra reconstructed from in situ pigment concentration and a library of pigment-specific absorption coefficients from 32 individual pigment standards, including chlorophylls, caretonoids and phycobilins. The samples dominated by small phytoplankton show no significant difference between calculated absorption and that measured by a spectrophotometer. The component of absorption due to large cells, determined by diagnostic pigments analysis, required correction for the package effect. For the global ocean, the reconstructed phytoplankton absorption was overestimated by 16% at 443 nm and underestimated by 13% over the range between 400 and 700 nm. Following our reconstruction protocol, this approach allows the estimation of phytoplankton absorption spectra from many locations where pigment concentration has been measured, but no directly observed phytoplankton absorption measurements are available.

Key Points

Observation of phytoplankton pigment concentration outnumber the in situ measurements of phytoplankton absorption spectra
This paper has developed a new technique for reconstructing phytoplankton absorption spectra from pigment concentrations alone
Global maps of reconstructed and remotely-sensed absorption at the chlorophyll a maximum shows similar magnitude and spatial distribution

Plain Language Summary

Phytoplankton, the small plant life of aquatic systems, absorb light which, together with available nutrients, determines their biomass and ultimately the productivity of the ocean or water mass. In situ phytoplankton absorption measurements require specialized equipment and expertise and are therefore infrequent, limiting our understating of aquatic photosynthesis. Photosynthetic phytoplankton contain pigments which are easier to measure using standard equipment and analytical methods. As a result, in situ pigment concentrations are 10 times more common than phytoplankton absorption measurements and are obtained in a wide range of global environmental studies. In this study, we show how to reconstruct the phytoplankton light absorption measurement based on the measurements of pigment composition and concentration. The method was applied to a data set of 8,012 pigment samples that were collected from all regions of the world's oceans. We then generated a global map of reconstructed phytoplankton absorption which compares well to maps of phytoplankton absorption derived from satellite imagery. Our paper provides a tool which can be used globally by aquatic scientists to convert measurements of pigment concentration into absorption spectra. As a result, light absorption and the maximum photosynthesis by phytoplankton can be accurately estimated for more oceanic areas of the globe.

1 Introduction

Light absorption by phytoplankton drives primary production and influences the rate of vertical attenuation of light in aquatic environments (Kirk, 1994; Morel, 1988; Smith & Baker, 1981). Phytoplankton absorption is a major factor contributing to the variation in optical properties of oceanic waters. Estimation of the proportion of light absorption due to phytoplankton is an important component of many bio-optical and biogeochemical models (Baird et al., 2016; Prieur & Sathyendranath, 1981; Sathyendranath et al., 1989). Thus, estimates of global primary production rely on accurate estimates of marine phytoplankton absorption.

Phytoplankton absorption (a_ph; m⁻¹) varies due to pigment composition and concentration, the size and shape of the phytoplankton cells (Bricaud et al., 1998; Bricaud & Stramski, 1990; Ciotti et al., 2002; Duysens, 1956; Hoepffner & Sathyendranath, 1991; Sathyendranath et al., 1987), and the arrangement of the photosynthetic apparatus (Johnsen et al., 1994). The most common method to measure the absorption spectra of phytoplankton is the measurement of particle absorption spectra using the quantitative filter technique (QFT) corrected by subtracting detrital absorption. Although this is a standard method, its application has been limited by the experimental setup and expertise required. It also has several limitations such as variations in the geometrical configuration of the experimental set up (IOCCG, 2018; Stramski et al., 2015) and non-uniform retention of particles on the filters. However, the main source of uncertainty in the QFT results from the correction of the amplification of the light pathlength (e.g., Bricaud & Stramski, 1990; IOCCG, 2018; Lefering et al., 2016; Mitchell, 1990; Roesler, 1998; Röttgers & Gehnke, 2012; Stramski et al., 2015; Tassan, 2002; Tassan & Ferrari, 1995).Reflective Tube Absorption Meters (e.g., AC-S) or Integrating Cavity Absorption Meters (e.g., point-source integrating cavity absorption meter or quantitative filter technique-integrating cavity absorption meter; IOCCG, 2018; Kostakis et al., 2021; Röttgers et al., 2005, 2016) provide another means to measure absorption. However, these meters provide the absorption of all particles rather than just phytoplankton.

Alternatively, an indirect method for calculating phytoplankton absorption, the reconstruction technique, uses a linear combination of pigment-specific absorption coefficients of individual pigments and their concentrations. The most common method for measuring concentrations of chlorophylls and caretonoids is High Performance Liquid Chromatography (HPLC), while the concentration of phycobilins is measured spectrophotometrically. HPLC is affected by smaller uncertainties and is more comparable between laboratories (Hooker et al., 2012) than the particulate absorption coefficient measurements using the QFT. The accuracy of the reconstruction technique depends on accurate determination of the concentration of all absorbing pigments and a package effect correction.

The package effect explains the reduced absorption of the same amount of pigment contained within phytoplankton cells comparing to the pigment dissolved in the solvent (Duysens, 1956; Kirk, 1994; Morel & Bricaud, 1981; Stuart et al., 1998). If there is no package effect, the absorption of pigment in the cell is equal to the pigment absorption of the solution. Previous studies (e.g., Kirk, 1994; Morel & Bricaud, 1981) have shown that the effect of packaging increases with the size of the phytoplankton cells. Therefore, the package effect is mostly known for large phytoplankton species, such as diatoms (Bricaud et al., 1995). The package effect can also increase the error estimation of the chl-a concentration from space (Marra et al., 2007; Soja-Woźniak et al., 2020).

The direct measurement of phytoplankton absorption spectra using the QFT technique or other laboratory methods requires a high level of expertise and specialized equipment. As a result, even the largest global databases contain too few estimates to generate a high-resolution global map of phytoplankton absorption. In contrast, pigment concentration sampling is straightforward and commercial HPLC analysis of chlorophylls and carotenoids are readily available and internationally standardized. Furthermore, thousands of pigment analysis measurements have been undertaken for reasons other than aquatic microalgal absorption studies. With the reconstruction technique these pigment measurements can be used to improve our estimates of phytoplankton absorption in freshwater, coastal and open ocean environments. The presented technique provides a tool which can be used globally by aquatic scientists to convert measurements of pigment concentration into absorption spectra. This will increase the sources of phytoplankton absorption spectra which can be used in data modeling or oceanic ecological studies. Moreover, accurate measurements of absorption spectra are required for the development and validation of the algorithms for upcoming hyperspectral ocean color imaging sensors, such as the NASA's Plankton, Aerosol, Cloud, and ocean Ecosystem mission (Kostakis et al., 2021; Werdell et al., 2019).

In this study, we have used the approach of phytoplankton absorption reconstruction and package effect calculation, building on earlier studies (Bidigare et al., 1990; Johnsen et al., 1994; Nelson et al.,1993). Our reconstruction introduces a new calculation of the package effect which allows us to reconstruct the phytoplankton absorption spectra (a_ph(λ)) based on pigment concentration only. Moreover, we classified the phytoplankton based on their size following the definition of phytoplankton size classes presented by Uitz et al. (2006), and applied the package correction just to large cells. With this refined technique we are able for the first time to (a) assess the reconstruction approach against an independent 903-sample global database of joint determinations of pigment concentrations and phytoplankton absorption measured using the QFT, and to (b) provide the global map of reconstructed phytoplankton absorption.

The aims of the present study were as follows: (a) to develop a reconstruction technique to obtain the phytoplankton absorption spectra based on pigment concentration only; (b) to compare the measured and reconstructed phytoplankton absorption spectra with and (c) without a package effect correction; and (d) to apply the reconstruction technique to a global database of 8,012 in situ sampled pigment concentrations to provide a global map of phytoplankton absorption.

2 Materials and Methods

First, we introduce the publicly available data sets used to assess our phytoplankton absorption reconstruction techniques followed by a summary of the technique. This section contains detailed description of the developed reconstruction technique (Section 2.2.), summarized in Figure 2. The Supporting Information S1 contains a MATLAB script (ds04.txt) and required data used (ds01.txt and ds02.txt) in the reconstruction analysis together with User Instructions (Supporting Information S1).

Details are in the caption following the image — **Figure 1**
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Distribution of the datasets used in the study. Black points represent the locations where pigment concentrations were available (8,012 samples); white points show the locations where both pigment concentration and phytoplankton absorption spectra were available (903 samples).

2.1 Data Used in the Study

2.1.1 Absorption Spectra of Individual Pigments

Concentration-specific absorption of 32 individual pigments, including chlorophylls, caretonoids and phycobilins were used in this study. The spectra of chlorophylls and carotenoids were taken from Clementson and Wojtasiewicz (2019a), while spectra of phycobilin were taken from Sobiechowska-Sasim et al. (2014). The spectra were wavelength-adjusted by using the ratio between the refractive index of the solvent and the water as described in Section 2.2.

2.1.2 Absorption Spectra and Pigment Concentrations of Phytoplankton Monoculture

A data set of the phytoplankton absorption spectra and pigment concentrations of 22 phytoplankton species from the Australian National Algae Culture Collection was used in this study (Clementson & Wojtasiewicz, 2019b).

2.1.3 Global Data Set of Phytoplankton Absorption Spectra and Pigment Concentrations

We used a data set of 8,012 samples of pigment concentration collected from the global ocean, 903 of which contained additional determinations of a_ph(λ) (Figure 1). Data were downloaded from a global compilation of HPLC phytoplankton pigment concentrations from the PANGAEA database (Kramer & Siegel, 2019) and the NASA SeaBASS database (Werdell & Bailey, 2002), which included data from NOMAD (Werdell & Bailey, 2005), the Integrated Marine Observing System (IMOS; Lynch et al., 2014), the North Atlantic Aerosols and Marine Ecosystems Study series of cruises (SeaBASS, 2014), cruise ANT-XXVIII/3 onboard r/v POLARSTERN (Bracher, 2014) and SO202/2 cruise on R/V Sonne (Taylor & Bracher, 2012) as well as other smaller datasets. The acquired a_ph(λ) was derived by spectroscopy with QFT.

2.1.4 Satellite Data

Global distribution of phytoplankton absorption at 443 nm reconstructed with the presented method was compared with corresponding data of 9 km monthly climatology (MC) Moderate Resolution Imaging Spectroradiometer (MODIS) level-3 data and 4 km daily MODIS level-3 data derived from Generalized Inherent Optical Properties (GIOP) model (Werdell et al., 2013). Data were downloaded through NASA's Ocean Color website.

2.2 Phytoplankton Absorption Reconstructed From Pigment Concentration Including Correction for Pigment Packaging

As a first approximation, phytoplankton absorption spectra a_ph(λ) (m⁻¹) were reconstructed as the sum of the products of the concentration of n individual phytoplankton pigments in the water column and the pigment-specific absorption spectra of the pigment using Equation 1:

(1)

where c_i is the in situ measured concentration of pigment i (mg m⁻³) and

is a pigment-specific absorption coefficient of pigment i at wavelength λ (m² mg⁻¹). The pigment-specific absorption spectra of individual pigments were derived from absorption measurements of pure standards (included in DS1 following Clementson & Wojtasiewicz, 2019a; Sobiechowska-Sasim et al., 2014).

The laboratory determination of pigment-specific absorption coefficients from samples dissolved in solvents introduces a wavelength-shift in the absorption spectra, resulting in the absorption peak being seen at a lower wavelength in ethanol and acetone than in water (Reichardt & Welton, 2011). Ultimately, we seek the pigment-specific absorption spectra of the pigment in water. Therefore, for measurements undertaken in solvent, we wavelength-shifted the spectra from their raw measurement by multiplying the wavelength by the ratio of the refractive index of the solvent to the refractive index of water (1.333 for water; 1.359 for acetone; 1.361 for ethanol at λ = 590 nm). Inspection of the location of multiple spectral peaks (not shown) for a number of pigments demonstrated that this approach works well across the spectra.

Equation 1 calculates phytoplankton absorption assuming pigments are dissolved in the water. The impact of distributing pigments within cells, called the package effect, reduces phytoplankton absorption. The package effect for a given wavelength can also be calculated as a ratio of “packed” and dissolved absorption. The impact of pigment packaging increases with attenuation within a cell and with cell size.

To estimate the package effect at a variety of wavelengths for a sample with a distribution of cell sizes and a range of pigments, we first take advantage of the fact that phytoplankton absorption at 675 nm is due to chl-a. By concentrating on one pigment and one wavelength, we are able to develop a relationship for the phytoplankton absorption (including the package effect) as a function of three size classes quantified by diagnostic pigment analysis (DPA). We followed the equations presented by Uitz et al. (2006) to calculate the fraction (F) of picophytoplankton (<2 μm), nanophytoplankton (2–20 μm) and microphytoplankton (>20 μm) of total chlorophyll. Morel and Bricaud (1981) describe an equation that relates the package effect to a non-dimensional quantity (ρ), which is a product of pigment-specific absorption coefficient and two quantities we do not know for our samples: an internal concentration of pigment (C_i) and a characteristic cell diameter (d) (Equation 5). Our new approach is to estimate a_ph(675), and assuming this is due only to a_chla, to determine the product of the two unknowns (C_i × d). As shown below, with this product we can then calculate the package effect for the whole spectrum and, knowing the sample pigment concentration, the phytoplankton absorption of the sample due to all pigments at all wavelengths.

To calculate the package effect correction in the large phytoplankton cells, we have followed Morel and Bricaud (1981) by assuming that the phytoplankton cells are homogenous spheres. The package effect

can be calculated with the Equation 2:

(2)

where Q_a(λ) is an absorption efficiency defined as Equation 3:

(3)

and ρ′(λ) is a product of the absorption coefficient of cell material (a_cm(λ)) and the cell diameter (d) as shown in Equation 4:

(4)

The chlorophyll-specific reconstructed phytoplankton absorption

is equivalent to

, the concentration-specific absorption coefficient of the cell material. Thus Equation 4 for ρ′(λ) can be written as Equation 5:

(5)

where C_i is intracellular chl-a concentration.

The package effect for a given wavelength can also be calculated as a ratio of measured () and reconstructed () absorption. Assuming that at 675 nm phytoplankton absorption is dominated by chlorophyll a we have calculated first. In order to avoid the necessity of having measured values of and be able to reconstruct the phytoplankton absorption with the package effect correction from measurements of pigment concentrations only, we assume that phytoplankton absorption at 675 nm is dominated by chlorophyll a.

To develop the estimation of the phytoplankton absorption at 675 nm we have used the chlorophyll-specific absorption coefficient at 675 nm of single species from the different size classes from Clementson and Wojtasiewicz (2019b). In their paper it is shown that the magnitude of chlorophyll-specific absorption coefficient decreases with the size of the phytoplankton cell. The most significant differences are noticed at the wavelengths of maximum absorption. Based on those results and phytoplankton size fractions (F_micro, F_nano, F_pico) calculated using the DPA, following Uitz et al. (2006), we developed the approximation Equation 6:

(6)

The package effect at 675 nm was then calculated as shown in Equation 7:

(7)

The estimation

using Equations 2 and 3 allowed us to find ρ′(675) by solving Equation 8:

(8)

Then by using Equation 5 and the calculated ρ^'(675), the wavelength-independent product of C_i × d was estimated with Equation 9:

(9)

Next, using Equations 2-3 and 5, ρ′(λ) and of the whole spectrum was calculated. By using we are able to account for the additional pigments that are important at wavelengths other than 675 nm.

The package effect

correction was then applied to the large-sized cell fraction of the reconstructed phytoplankton absorption with the following Equation 10:

(10)

where F_L is a fraction of large cells and is defined as

(11)

Nanophytoplankton is a group including both quite small phytoplankton cells, between 2 and 5 μm, as well as larger cells, between 5 and 20 μm. In our study we have applied the package effect correction just to the part of nanophytoplankton group containing large cells. We assumed that the distribution of phytoplankton cell size is logarithmic. So, if the population of the microphytoplankton group is bigger than the population of the picophytoplankton then a higher fraction of nanophytoplankton will contain large cells.

The developed reconstruction technique is summarized in the flow chart (Figure 2).

2.3 Assessment of the Reconstructed Spectra

Assessment of the reconstructed phytoplankton absorption was based on 903 locations where we had both reconstructed and measured phytoplankton absorption spectra. We have used the quantitative metrics (Bias, Root Mean Square Error (RMSE), Normalized Mean Bias (NMB), Normalized Root Mean Square Error (NRMSE), Similarity Index (SI) summarized in Table 1. Beside the comparison at the individual wavelengths, we have also compared the phytoplankton absorption spectra integrated over the spectral range (λ_min = 400 and λ_max = 700 nm) of the photosynthetically active radiation (PAR) calculated with Equation 12:

(12)

Table 1. Quantitative Metrices Used in the Assessment of Reconstructed Spectra

Metrices	Mathematical expression	Units
Bias		m⁻¹
Root mean square error		m⁻¹
Normalized mean bias		%
Normalized root mean square error		%
Similarity index		Unitless

Note. N, total number of points, reconstructed absorption spectra (with or without correction due to package effect), measured absorption spectra, the dot (⋅) operator is the scalar dot product of two vectors and |A| is the vector magnitude operator. NMB, Normalized Mean; NRMSE, Normalized Root Mean Square Error; PAR, photosynthetically active radiation; RMCE, Root Mean Square Error; SI, Similarity Index.

Moreover, the degree of similarity between the shape of measured and reconstructed absorption spectra was computed with Similarity Index (SI) (Millie et al., 1997).

3 Results and Discussion

In this section, we present the phytoplankton absorption spectra (a_ph(λ)) reconstructed from pigment concentration and the pigment pigment-specific absorption spectra. First, we will present the reconstructed absorption derived for phytoplankton monocultures grown in the laboratory conditions (Clementson & Wojtasiewicz, 2019b). Then the reconstructed a_ph(λ) using the same method are applied to the field samples. We will show un-corrected and corrected spectra for the effect of pigment packaging which varies with the cell dimension and its internal concentration.

3.1 Reconstructed Phytoplankton Absorption of Monocultures

First, the phytoplankton absorption spectra were reconstructed for the phytoplankton monocultures from the laboratory experiments (Clementson & Wojtasiewicz, 2019b). We have noticed that the reconstructed spectra significantly overestimated the measured for the species with large cells (micro- and nano-phytoplankton; Figures 3c and 3d), while for the small-sized phytoplankton (e.g., Synechococcus sp. and Nannochloropsis oculata) reconstructed was found lower than measured . Synechococcus sp. is classified as a pico-phytoplankton, while Nannochloropsis oculata depending on the classification can be assigned to ultra-phytoplankton with the size between 2 and 5 μm (Ciotti & Bricaud, 2006) or to nano-phytoplankton with the size between 2 and 20 μm (Brewin et al., 2010; Uitz et al., 2006). The reconstructed was found to be lower than measured in four out of 22 cases for small sized phytoplankton. For two large-sized phytoplankton, A. minutum and Woloszynskia sp. Dinophyceae, the blue portion of the reconstructed absorption spectra overestimated the measured spectra, though a package effect correction was not applied as was lower than . Synechococcus sp. is a cyanobacteria species rich in phycocyanin, one of the phycobilin pigments which is not measured with HPLC analysis. The reconstructed absorption spectrum for Synechococcus sp, based on the pigments measured just with HPLC (chlorophylls and carotenoids), was missing the important peak due to phycocyanin at 620 nm (Figure 3a). Unfortunately, during the experiment the samples for spectrophotometric analyses of phycobilin pigments were not taken, so we estimated phycobilin concentration based on pigment ratios reported in another experiment with Synechococcus sp. (Wojtasiewicz & Stoń-Egiert, 2016) as a proportion of chl-a concentration (PC = 2.5⋅chl−a, PE = 0). However, the proportion between phycobilin pigments and chl-a can vary significantly in nature, therefore presented estimation cannot be verified without available phycobilin measurements. Phycobilins are not measured with HPLC and therefore they are not commonly included in pigment analysis. Figure 3a shows that in the case when phycobilins are a significant fraction of the absorption spectra, and phycobilin concentrations are not measured, we underestimate the absorption spectra between 525 and 650 nm.

The reconstructed a_ph(λ) of the phytoplankton species with large cells was improved with the package effect correction, which resulted in a reduction of NMB from 31% to −9% and NRMSE from 43% to 12% in PAR integrated absorption.

3.2 Reconstructed Phytoplankton Absorption From the Field Samples

Next, we applied the same reconstruction approach for the data set of pigment concentrations measured from water samples collected in the global ocean. The package effect function calculated at 675 nm as a ratio between measured and reconstructed absorption showed that 41% of the samples had values lower than 1, meaning the package effect correction was required. Figure 4 shows examples of reconstructed phytoplankton absorption spectra for different phytoplankton size compositions. The “unpacked” and “packed” spectra are shown in the comparison with the measured phytoplankton absorption. Figures 4a and 4b show that when phytoplankton class size (PCS) is dominated by microphytoplankton, the reconstructed absorption coefficient overestimates the measured absorption, especially in the range where most of the pigments have their absorption maximum. The reconstructed absorption coefficient after package correction is closer to the measured spectrum. Figure 4d illustrates the case when PCS is dominated by picophytoplankton and the reconstructed absorption coefficient is very close to the measured absorption and the package effect correction was not applied. Figure 4c illustrates the situation when our approach does not calculate the phytoplankton absorption correctly. The reconstructed spectrum before the package effect correction, especially in the range between 400 and 500 nm, is relatively close to measured spectrum. However, at 675 nm was lower than the measured leading to an improper package effect correction. This example shows the importance of the accurate estimation of a_ph(675) for further calculation of the package effect correction and will be addressed later.

Comparisons of and at 443 and 675 nm (chlorophyll absorption maxima), at 550 nm (phytoplankton absorption minima), and integrated over the PAR spectrum from 903 samples are shown in Figure 5 and Table 2. Overall, we can see that applying the package effect correction significantly improved the results at 443 nm, reducing NRMSE by over 30%. Even though the NMB increases after package effect correction at 675 nm and integrated over the PAR region, NRMSE shows improvement of 6% and 7% respectively. Our results show that with the simple calculation (Equation 1), phytoplankton absorption over the PAR range can be reconstructed with an NMB of −2%. The largest difference between reconstructed and measured values occurs in the region of minimum absorption (around 550 nm), where is systematically lower than the observed values. Median value of similarity between and measured by SI for 903 samples was 0.87 (with 3rd and 97th percentile equal to 0.75 and 0.93 respectively), where 0 indicates no similarity and 1 is perfect overlap of the spectra.

Table 2. Metrices Calculated for the Assessment of Reconstructed Spectra at Three Wavelngths (443, 555, 675 nm) and Within PAR Region

N = 903	Bias (m⁻¹)	RMSE (m⁻¹)	NMB (%)	NRMSE (%)
443 nm	7.70e−03	0.02	37	97
	3.20e−03	0.013	16	64
555 nm	−1.80e−03	0.0029	−59	78
	−1.80e−03	0.0029	−59	79
675 nm	6.30e−05	0.0047	1	45
	−6.70e−04	0.0041	−7	39
PAR	−1.60e−04	0.0036	−2	39
	−1.20e−03	0.003	−13	32

Note. Rows highlighted with gray show the results without the correction due to package effect. NMB, normalized mean; NRMSE, normalized root mean square error; PAR, photosynthetically active radiation; RMCE, root mean square error.

As mentioned before, the most common and reliable method of measuring pigment concentration is HPLC which is missing phycobilins. In our data only 26 of 903 field samples, collected in the east coast of Australia, were analyzed with HPLC and spectrophotometer and provided measured concentration of chlorophylls, carotenoids and phycobilins. These data show that adding phycobilins to the pigment analysis decrease NMB by 3% at 560 nm and by 1% at 620 nm, the wavelengths of absorption maximum of phycoerthirin and phycocyanin, respectively. At 443 nm there was no difference (data not shown).

3.3 Global Application of Reconstruction Technique

We have applied our approach to a data set of 8,012 pigment concentrations distributed globally (Figure 6a). Using this freely available database of pigment concentrations our technique provides sufficient global coverage of phytoplankton absorption spectra to identify oceanic regions. As expected, the a_ph(443) is low in the ocean gyres and increases close to the coast. There is also a visible trend of increasing a_ph(443) with latitude.

The spatial distribution of (Figure 6a) compared favorably with a_ph(443) of the corresponding month from a 9 km MC MODIS level-3 data derived from the GIOP model (Werdell et al., 2013) (Figure 6b). As would be expected, MC-MODIS data appears smoother than the reconstructed absorption of water samples, but the spatial patterns match well. Although we are comparing satellite data (4 km for daily data and 9 km for MC) with a discrete water sample, the NMB of −1% and −14% and NRMSE of 71% and 41% respectively for MC-MODIS (not shown) and for daily-MODIS (Figure 6c) shows general agreement from two global distributed estimates obtained through very different means. Based on the 2,803 samples for which we had the observed values of MODIS daily data we can show that our approach works well for a_ph(443) up to ∼0.35 m⁻¹ (Figure 6c). The best fit was found in the Atlantic Ocean, while in the region of the Arctic Ocean our estimate was sometimes lower than the MC. In the reconstructed data, high latitude sites characterized by low reconstructed phytoplankton absorption reflected locations with low measured pigment concentrations that would indicate low phytoplankton absorption.

Considering the spatial distribution of package effect correction (, we note that in the open ocean and at low latitudes the values of were 1 or above 1 and a correction was not applied (Figure 7). In regions more likely to incur light limitation to phytoplankton growth, such as high latitude and nutrient-enriched coastal regions, the value of was lower meaning a larger package effect of the reconstructed absorption spectra was applied. The strongest correction was applied around the absorption maxima, at 443 and 675 nm, while at 555 nm, an absorption minima, a weak correction was required. At 443 nm the range of the package effect correction was between 0.4 and 1, at 675 nm it was between 0.5 and 1 and at 555 nm it was above 0.9 in all locations.

3.4 Relative Sources of Error in the Reconstruction Technique

The error in the reconstructed phytoplankton absorption is influenced by both the number of measured pigments and the availability in the data set of the most absorbing pigments. We have analyzed the changes in NMB and in SI of depending on the number of pigments used in the reconstruction (Figures 8a and 8b). Overall, the NMB improves with increasing number of pigments used for . However, a higher number of pigments used in the calculation does not always provide a more accurate estimation of phytoplankton absorption. This could be that the measured pigments were chosen for taxonomical identification purposes rather than their importance in the photosynthesis process (e.g., marker pigments like myxoxanthophyll or its derivatives). We conclude that to estimate a_ph(PAR) with the bias lower than ± 20% we need to have at least 9 pigments for (Figure 8a).

Analysis of the spectral shape shows that with the concentration of more than five pigments SI is higher than 0.95 and close to 0.99 if the absorption is reconstructed from at least 11 pigments (Figure 8b). However, for the accurate reconstruction of a_ph(PAR), more crucial than the number of pigments is which pigment was available.

Figure 8c illustrates the proportion of each pigment in phytoplankton absorption based on the entire database of 8,012 samples. Obviously, the most important is chl-a accounting for almost 30% of the a_ph(PAR), while the second most important is fucoxanthin which is almost 20% of a_ph(PAR) in the global data set. The first 11 pigments, in the order shown in Figure 8c, yield over 90% of a_ph(PAR), while the first 20 pigments, yield over 99% of a_ph(PAR). The contribution of the last 10 pigments is less than 1% each (Figure 8c). Our study showed (Figure 3a) that including phycobilins in routine measurements of pigment concentration could improve the reconstructed phytoplankton absorption in the spectral range between 525 and 600 nm in the case when phycobilins are a significant fraction of the absorption spectra.

The second issue affecting the error in the reconstructed phytoplankton absorption with the correction due to package effect is using the estimated value of a_ph at 675 nm instead of the measured value. If the estimated value is erroneously low as shown in the Figure 4c, the package correction is implemented even though it should be skipped. In less than 30% of cases the incorrect estimation of a_ph(675) led to overcorrecting the reconstructed absorption spectra. However no spatial pattern for this error was found. The calculation of a_ph(675) (Equation 6) underestimates the measured value by 10%.

Another issue which introduces error in the reconstructed phytoplankton absorption is the estimation of the phytoplankton fraction with large cells. Our estimation is based on DPA commonly used in previous studies (Brewin et al., 2011; Brewin et al., 2010, 2015; Chase et al., 2020; Uitz et al., 2006, 2008). The DPA method is much more challenging in optically complex water and can give poor results (Chen, 2009; Sun et al., 2017; Wang, 2006; Zhou, 2006). Additionally, PCS based on DPA may also be problematic because of changing contributions of diagnostic pigments representing different phytoplankton groups to the total phytoplankton biomass (Brewin et al., 2015; Chase et al., 2020; Sun et al., 2017). In our study, approximation of the fraction of nanophytoplankton containing large cells was based on a general understanding of phytoplankton size distribution and it is not confirmed against field measurements. However, our results of the reconstructed spectra of the mono-species show that the nanophytoplankton class contains species both requiring and not requiring package correction, and therefore some sort of class subdivision is needed.

In the case of the reconstruction technique, the greatest source of error is in the assumptions that are used in the calculation of the package effect and the fraction of absorbing pigments considered. At 675 nm, the dominant absorbing pigment is chl-a, which is almost always included in pigment analysis. At 675 nm the package effect is relatively small (Figure 7c), so the errors in the mismatch at 675 nm [Bias + RMSE, (0.67 ± 4.1) × 10⁻³ m⁻¹] represent the limits of comparing the QFT and reconstructions samples. These might include sampling errors, errors in correcting for non-algal particulate matter in the QFT technique etc. The larger errors found at other wavelengths, and for PAR integrated calculations, represent errors due to the assumptions of the reconstruction technique. The NRMSE approximately doubles for 443 nm, suggesting half of the errors in the reconstruction technique at this critical wavelength relate to the number of pigments measured and the calculation of the package effect.

The error introduced due to an incomplete number of measured pigments can be approximately disentangled from errors in the package effect calculation for PAR light through consideration of Figure 8a. Above 10 pigments measured (the vast majority of the available pigment data sets), the error statistics do not change significantly. Thus, with the possible exception of the systematic under-analysis of phycobilins (see further discussion), the bulk of the error in the reconstruction technique for individual samples is the calculation of the package effect, with the greatest impact found at the chl-a absorption maximum of about 30% NRMSE. While the package effect error might be significant for individual samples, the mean error across all samples is small. This is in part because while there are significant errors in the package effect, the magnitude of the package effect is by definition constrained between 0 and 1 and even at 443 nm is rarely below 0.4. Thus, for the purpose of generating a global map of phytoplankton absorption from 8,012 samples, the errors in the reconstruction method are small.

3.5 Accuracy of Measured Absorption With the Quantitative Filter Technique

Currently, the standard method to determine the particulate absorption coefficient is the QFT (Stramski et al., 2015 and references therein), though this method still has several limitations. There are many acceptable variations in the geometrical configuration of the experimental set up (IOCCG, 2018; Stramski et al., 2015), and the measured absorption coefficient magnitude and spectral shape can be affected by non-uniform retention of particles on the filters and by the decomposition of phytoplankton pigments both during filtration and at the time of measurement (Stramski, 1990). However, the main source of uncertainty results from the correction of the amplification of the light pathlength (e.g., Bricaud & Stramski, 1990; Mitchell, 1990; Roesler, 1998; Röttgers & Gehnke, 2012; Stramski et al., 2015). Compared to the particulate absorption coefficient measurements, the determination of pigment composition and concentration using the HPLC method is better standardized due to the availability of laboratory standards and inter-laboratory comparison studies (e.g., Hooker et al., 2012). However, HPLC cannot resolve phycobilins and therefore phytoplankton absorption spectra derived with reconstruction technique based on pigments from HPLC analysis only may be less accurate in the range between 550 and 620 nm. Given all these challenges, comparison of QFT and reconstructed a_ph(λ) should be considered as a comparison of two techniques, both with limitations.

4 Conclusions

This study has developed a new reconstruction technique that allows calculation of phytoplankton absorption spectra from pigment concentrations alone. The provided tool can be used globally by aquatic scientists to convert measurements of pigment concentration into absorption spectra. Due to the requirements of a high-level expertise and specialized equipment needed for direct measurement of phytoplankton absorption spectra there is an order of magnitude less data of phytoplankton absorption comparing to pigment concentration. Even the largest global databases contain too few estimates for a high-resolution global map of phytoplankton absorption. The presented technique gives an additional source of phytoplankton absorption spectra which can be used in data modeling, satellite validation or oceanic ecological studies. We show that when phytoplankton absorption spectra derived from reconstruction technique and measured with QFT are available the results are comparable. Using our technique and freely available database of pigment concentrations provides sufficient global coverage of phytoplankton absorption spectra to identify oceanic trends. Thus, the new reconstruction technique is a straightforward approach for estimating phytoplankton absorption from many locations where pigment concentration has been measured, but no spectrophotometric analysis or satellite observations are available.

Acknowledgments

The authors would like to thank three anonymous reviewers for their careful review of our manuscript and for providing us with comments and suggestions which improved the quality of the manuscript. This work includes large data set from many research programs. The authors thank all researchers, technicians, and crew members involved with data collection, preparation, analysis, and submission. M.S-W. thanks the Commonwealth Scientific and Industrial Research Organisation OCE postdoctoral fellowship scheme and the data providers for the commitment and their expertise.

Conflict of Interest

The authors declare no conflicts of interest relevant to this study.

Open Research

Data Availability Statement

Data set on the in vivo absorption characteristics and pigment composition of various phytoplankton species is available at https://doi.org/10.1016/j.dib.2019.104020. Data set on the absorption characteristics of extracted phytoplankton pigments is available at https://doi.org/10.1016/j.dib.2019.103875. Data set of the phytoplankton absorption and pigment concentration were downloaded from the SeaBASS database from the following sources:

The Bermuda Bio-Optics Project (BBOP), https://doi.org/10.5067/SeaBASS/BBOP/DATA001
IMOS Ocean Color 1997–2000 Experiment, cruise FR1097 onboard R/V Franklin
Climate Variability and Predictability (CLIVAR), https://doi.org/10.5067/SeaBASS/CLIVAR/DATA001
IMOS SRFME-Coastal Ecosystems Experiment, cruise MV062003 onboard RV Melville
NASA bio-Optical Marine Algorithm Data set, https://seabass.gsfc.nasa.gov/wiki/NOMAD
African Monsoon Multidisciplinary Analyses (AMMA) program, https://doi.org/10.5067/SeaBASS/AMMA/DATA001
PANGAEA Experiment, cruise/so202-2, https://seabass.gsfc.nasa.gov/cruise/so202-2
Exports Experiment, cruise EXPORTSNP, https://doi.org/10.5067/SeaBASS/EXPORTS/DATA001
NSF-BWZ program https://doi.org/10.5067/SeaBASS/NSF-BWZ/DATA001
ANT Experiment, cruise ANT-XXVIII-3, https://doi.org/10.1594/PANGAEA.819614

Additional pigment concentration data set available on PANGAEA, https://doi.org/10.1594/PANGAEA.905883. MODIS level-3 data were downloaded through NASA's Ocean Color website: https://oceancolor.gsfc.nasa.gov/l3/. The code and input data are freely available and can be downloaded from https://data.csiro.au/collection/csiro:53140.

Supporting Information

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Volume127, Issue8

August 2022

e2022JC018494

Filename	Description
2022JC018494-sup-0001-Supporting Information SI-S01.docx50.8 KB	Supporting Information S1
2022JC018494-sup-0002-Data Set SI-S01.txt79 KB	Data Set S1
2022JC018494-sup-0003-Data Set SI-S02.txt18.1 KB	Data Set S2
2022JC018494-sup-0004-Data Set SI-S03.xlsx187.8 KB	Data Set S3
2022JC018494-sup-0005-Data Set SI-S04.txt6.4 KB	Data Set S4

Estimation of the Global Distribution of Phytoplankton Light Absorption From Pigment Concentrations

Abstract

Key Points

Plain Language Summary

1 Introduction

2 Materials and Methods

2.1 Data Used in the Study

2.1.1 Absorption Spectra of Individual Pigments

2.1.2 Absorption Spectra and Pigment Concentrations of Phytoplankton Monoculture

2.1.3 Global Data Set of Phytoplankton Absorption Spectra and Pigment Concentrations

2.1.4 Satellite Data

2.2 Phytoplankton Absorption Reconstructed From Pigment Concentration Including Correction for Pigment Packaging

2.3 Assessment of the Reconstructed Spectra

3 Results and Discussion

3.1 Reconstructed Phytoplankton Absorption of Monocultures

3.2 Reconstructed Phytoplankton Absorption From the Field Samples

3.3 Global Application of Reconstruction Technique

3.4 Relative Sources of Error in the Reconstruction Technique

3.5 Accuracy of Measured Absorption With the Quantitative Filter Technique

4 Conclusions

Acknowledgments

Conflict of Interest

Open Research

Data Availability Statement

Supporting Information

References

Figures

References

Information

RESOURCES

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Estimation of the Global Distribution of Phytoplankton Light Absorption From Pigment Concentrations

Abstract

Key Points

Plain Language Summary

1 Introduction

2 Materials and Methods

2.1 Data Used in the Study

2.1.1 Absorption Spectra of Individual Pigments

2.1.2 Absorption Spectra and Pigment Concentrations of Phytoplankton Monoculture

2.1.3 Global Data Set of Phytoplankton Absorption Spectra and Pigment Concentrations

2.1.4 Satellite Data

2.2 Phytoplankton Absorption Reconstructed From Pigment Concentration Including Correction for Pigment Packaging

2.3 Assessment of the Reconstructed Spectra

3 Results and Discussion

3.1 Reconstructed Phytoplankton Absorption of Monocultures

3.2 Reconstructed Phytoplankton Absorption From the Field Samples

3.3 Global Application of Reconstruction Technique

3.4 Relative Sources of Error in the Reconstruction Technique

3.5 Accuracy of Measured Absorption With the Quantitative Filter Technique

4 Conclusions

Acknowledgments

Conflict of Interest

Open Research

Data Availability Statement

Supporting Information

References

Figures

References

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Information

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PUBLICATION INFO