Abstract

Knowledge on the phenology and distribution of phytoplankton taxonomic groups (PTGs) represent valuable information when studying marine ecosystem, especially in the Arctic Ocean where rapid warming has drastic effects on sea-ice dynamics, which affect the marine food web. Taxonomic groups of phytoplankton can be discriminated based on their pigment signatures, which, in turn, impact their absorption spectra, given that different pigments have different absorption windows in the visible. Using concurrent measurements of phytoplankton diagnostic pigments and absorption spectra (aph) collected in the Bering and Chukchi Seas, a novel and direct approach was designed for simultaneously estimating the biomass concentrations of several PTGs (Ci) as well as their specific absorption coefficient. The chemotaxonomic tool CHEMTAX was applied to twelve diagnostic pigments measured by high-performance liquid chromatography (HPLC). Their results revealed that the phytoplankton community composition was made of nine groups, from which six dominant were identified: diatoms, dinoflagellates, c3-flagellate, haptophytes type 7, two types of prasinophytes. Out of 117 samples, twenty pairs of Ci derived by CHEMTAX and measured aph were randomly selected and used in a linear unmixing model to extract the specific absorption spectral of each group. This step was repeated 1000 times to provide the mean specific absorption of a given phytoplankton group. These specific absorption spectra were used to reconstruct total aph, which was consistent with the measured aph (R2 from 0.8 to 0.95) at all visible wavelengths (400-700 nm). The derived specific absorption spectra were further used with the measured aph(λ) at ten Moderate Resolution Imaging Spectroradiometer (MODIS) wavebands in a linear unmixing model to test the ability to retrieve the concentrations of PTGs from satellite remote sensing. A comparison between estimated and measured Ci showed that the approach used in this study performed best when retrieving five groups (i.e., dinoflagellates, c3-flagellate, haptophytes, two types of prasinophytes) from the nine initially identified using CHEMTAX with a mean absolute percentage error (MAPE) <35%, except for diatoms with a MAPE value of about 45%. Our approach provides a practical basis for estimation of PTGs using aph(λ) derived from satellite observations and field measurements.

© 2018 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

1. Introduction

Phytoplankton is a key part of the plankton community in ocean waters because of their importance for primary production, carbon cycling, and sustaining the aquatic food web [1,2]. In addition to monitoring distribution and variation of phytoplankton biomass as indicated by its main pigment chlorophyll-a concentration (Chla) [3–5], there is a growing interest in deriving phytoplankton taxonomic groups (PTGs) using field and satellite data in the last decades [6–8]. Often, there is a good correspondence between PTGs and phytoplankton size structure or functional types. For example, diatoms are the major utilizer of silicate and contribute approximately 20% of global carbon fixation, most of which belong to microphytoplankton size class (> 20μm); Cyanobacteria are another key group that belong to picophytoplankton class (< 2μm), some species of which are the major nitrogen fixers, e.g., Trichodesmium genus [6,9]. Therefore, knowledge of phytoplankton taxonomic groups could provide valuable information when studying marine ecosystem, and improve the understanding of many marine ecological and biogeochemical processes.

Several methods are used to determinate phytoplankton taxonomic groups in seawater samples, including optical microscopy, flow cytometry, molecular analyses, and pigments analysis measured by high-performance liquid chromatography (HPLC). Each of these methods contains limitation inherent to the approach they are based on. For instance, optical microscopy is time consuming and relies greatly on the experience of taxonomist, but provides information at the species level [10]. Flow cytometry is limited by identifying small phytoplankton in the 0.5 to 20 μm [11]. Currently, molecular analysis is limited to provide quantitative information and relies on established libraries that are still being developed [12]. HPLC pigment analysis is a widely-used approach for qualitative and quantitative assessment of taxonomy using several marker pigments of distinct phytoplankton groups [13]. The main limitation of this approach is the commonality of several pigments between phytoplankton groups [14]. The chemotaxonomic software CHEMTAX was developed to overcome this limitation by considering a series of synthetic data set of pigments that represent distinct phytoplankton groups [15]. All these methods have in common that they require field water samples, therefore making difficult to continuously monitor the spatiotemporal variations of phytoplankton assemblages on large scales. Such a shortcoming may be addressed with satellite remote-sensing observations if suitable algorithms are developed.

Several satellite-based bio-optical models identify phytoplankton taxonomic composition using phytoplankton biological [16] or bio-optical properties [17–19]. Different algal groups have distinct optical traits that better represent their taxonomic class. Typically, total phytoplankton light absorption spectra (aph(λ)) result from the sum of the absorption of individual pigments contained in the cell and therefore highly depends on the pigment composition and concentration related to phytoplankton taxonomy [20,21]. It is admitted that phytoplankton pigment composition remains constant for a given phytoplankton taxa and that their intra-cellular concentrations change with their physiological state, such as photoacclimation [22,23]. As such, different algal groups could be estimated using the spectral characteristics of phytoplankton absorption. Currently, many techniques are available to obtain phytoplankton absorption coefficients, aph. For field data, aph can be generally obtained by spectrophotometric measurements after filtration of water samples through a GF/F filter. Commercially available field instruments (e.g., immersed spectrophotometer) that measure the light absorption coefficient can be used to derive aph by numerical deconvolution [24]. For synoptic scale applications, satellite aph(λ) can be derived from satellite remote sensing reflectance (Rrs(λ)) using inversion algorithms, such as the linear matrix inversion algorithm [25], the quasi-analytical algorithm (QAA [26],), and the GSM semi-analytical bio-optical model [27]. These approaches to derive aph(λ) provide data required for further estimating PTGs from phytoplankton absorption spectra at a large scale.

Several methods have been proposed to retrieve information on phytoplankton community structure and to identify single algae species from phytoplankton absorption spectra [28–30]. For instance, Sathyendranath et al. [29] discriminated diatoms from other phytoplankton in the Northwest Atlantic using regional observations of phytoplankton absorption. A similarity index analysis was used by Craig et al. [30] to compare the fourth derivatives of the derived aph with a reference K. brevis absorption to assess the feasibility of its detection. Fourth-derivative analysis was also used by Xi et al. [22], in conjunction with clustering analysis, to differentiate six taxonomic groups using laboratory measurements of absorption aph(λ) and corresponding simulated Rrs(λ). Their results revealed that the performance of derivative-analysis approach to identify PTGs from measured aph spectra was better than the performance of Rrs-based approach with only a few misclassified cultures. However, this study did not provide quantitative estimates of PTGs. In general, most methods were only proposed to detect particular phytoplankton species, to differentiate a single phytoplankton group in natural waters or to provide dominance of a given taxonomic group.

The use of linear unmixing models (LMM) for the interpretation of the optical properties of ocean waters has received increasing interest over the past decade because their mathematical formulations are well-adapted to simultaneously derive multiple unknowns algebraically [25,31]. Based on the derived specific absorption coefficients of three phytoplankton size classes (i.e., micro, nano, and pico), Devred et al. [31] applied the LMM to estimate three size fractions from the aph(λ) at five SeaWiFS wavebands in the Northwest Atlantic. In a similar way, Moisan et al. [32] used the linear inverse calculation to extract pigment-specific absorption spectra, which were further used in conjunction with aph(λ) in a second linear inverse calculation to estimate pigment concentrations. These studies support the LMM approach as an effective tool for the determination of specific absorption spectra and for estimating the biomass concentrations of phytoplankton taxonomic groups.

In this study, we used CHEMTAX to obtain the biomass concentrations of phytoplankton taxonomic groups (hereafter called Ci) from HPLC pigments collected in the Bering and Chukchi Seas; and then proposed a novel and direct approach (hereafter called the “aph-LMM” approach) that uses measurements of aph(λ) and Ci to retrieve the specific absorption spectra of several taxonomic groups, which in turn were used to directly estimate the taxonomic group biomass. Although this approach was developed using spectrally resolved phytoplankton absorption (1 nm resolution), we demonstrated that it could be applied to multispectral information such as the one recorded by the Moderate Resolution Imaging Spectroradiometer (MODIS).

2. Materials and methods

2.1 Study area and study sites

The field data set used in this study was collected in the Chukchi and Bering Seas. Sampling was conducted during six cruises in September 2009 - 2013 (except 2011), early October 2010, and June to July 2013 [Fig. 1]. The Chukchi Sea is located at the western edge of the Arctic Ocean and is connected to the Bering Sea through the Bering Strait. The Bering Sea is located at the northern edge of the Pacific Ocean. The continental shelf with water depth < 200m spreads north and south of the Bering Strait, and most of the region are shallower than 50m depth. The Chukchi and Bering Seas are mainly influenced by three types of water masses, including the Alaska Coastal Water (ACW), the Anadyr Water (AW), and the Bering Shelf Water (BSW). The BSW flows between the AW and ACW [33,34]. Because of the similar water densities of the BSW and AW, they pass through the Bering Strait and produce a mixed water mass called Bering Shelf-Anadyr Water (BSAW) [34]. The BSAW supplies nutrient-rich waters to the Bering Strait and the southern Chukchi Sea. Surface water samples were collected in the study area using a clean plastic bucket or Niskin bottles attached to the CTD/Carousel sampler. They were analyzed to determine aph(λ) and pigment concentrations.

 figure: Fig. 1

Fig. 1 Locations of the sampling stations in the Chukchi and Bering Seas.

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2.2 Measurements and analysis of pigments and phytoplankton absorption

Samples for measuring aph(λ) were collected onto GF/F glass-fiber filter (25-mm in diameter, Whatman) by filtering between 800 and 4000 mL of sea water. The optical density of the particles was measured using an MPS-2450 or UV-2400 spectrophotometer (Shimadzu) between 350 and 750 nm in 1 nm increments. Sample filters were rinsed and sealed in methanol for 24-48 h to extract phytoplankton pigments, and optical density of non-algal particles was re-measured [35]. Absorption coefficients of suspended particles, ap(λ), and non-algal particles, ad(λ), were calculated using path length correction factor of multiple-scattering given in Cleveland and Weidemann [36]. Then, aph(λ) was obtained by subtracting ad(λ) from ap(λ).

The concentrations of phytoplankton pigments were obtained from the same water samples than aph(λ). For pigment identification and concentration, between 1000 and 2500 mL of water sample was filtered on to GF/G glass fiber filters (25-mm in diameter, Whatman) immediately after collection and stored in liquid nitrogen or super-cold freezer (−80 °C) until analysis in the laboratory. Sample filters were soaked in N’N-dimethylformamide and sonicated for 30s on ice to fully extract phytoplankton pigments [37]. Information on 19 pigments (Table 1), including Chla, was retrieved using a class VS HPLC system (Shimadzu) following the method of Van Heukelem and Thomas [38].

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Table 1. List of phytoplankton pigments and their taxonomic significance and pigments formulae [13,39]. The name of the twelve pigments used in CHEMTAX to distinguish between nine phytoplankton groups are highlighted in bold.

The HPLC field data set in this study was quality controlled to remove measurements with low precision according to the following rules: (1) samples with total chlorophyll-a concentration (hereafter called C; see Table 1 for calculation) <0.001 mg m−3 were rejected [19]; (2) C and accessory pigments (AP) (see Table 1 for calculation) should be tightly correlated, with a slope ranging from 0.7 to 1.4 and R2 >0.9; (3) the difference of C and the sum of AP should be less than 30% of total pigments (TP) (see Table 1 for calculation) [39]; (4) the number of detectable pigments with concentration >10−4 mg m−3 should be more than six [40]. In addition, the absorption data set was also quality controlled by 1) studying the regression of aph(443) on aph(488), and samples that exhibited more than three standard deviation (SD) were rejected; and 2) by applying three successive regressions of aph(443) on C and eliminating outliers (i.e., >2 SD) at each step [41]. After applying the quality control procedures, 149 pigments (out of 167 initial samples) and 129 aph samples (out of 160 initial samples) were deemed used in this study [Fig. 1]. Among them, 117 of the 129 phytoplankton absorption measurements matched one of the 149 pigments.

2.3 Chemotaxonomic analysis of pigment data

The CHEMTAX method was used to estimate the quantitative biomass of phytoplankton taxa from their pigment signature [15]. CHEMTAX has been widely used in the global ocean to derive information on phytoplankton community structure [42,43]. In this study, the pigment ratio matrix (i.e., ratio of twelve pigments to C) for nine algal classes (Table 2) was initialized using Coupel et al. [14], which was constructed using data from the Beaufort Sea under high light levels (i.e., surface samples). Details of CHEMTAX detected taxa were described in Coupel et al [14]. In brief, the c3-flagellates group included the dinoflagellates type 2 lacking pigment peridinin and a larger diversity of flagellates (e.g., raphidophytes, dictyochophytes, and dictyochophytes). The haptophytes type 7, prasinophytes type 2 and 3 are representative of the prymnesiophyte-type Chrysochromulina spp., Pyramimonas sp., and Micromonas sp., respectively. To test the sensitivity of CHEMTAX, 60 further pigment-ratio matrices were generated by multiplying each cell of the initial ratio matrix by a randomly scaling factor in a range from 0.65 to 1.35 (i.e., step 1). This procedure was carried out using the CHEMTAX software version 1.95 provided by the Australian Antarctic Data Centre. Then, each of the 60 ratio matrices was used as input for a CHEMTAX optimization method that was based on an iteration and steepest descent algorithm to find the minimum residual. After completed 60 runs for each of the 60 matrices, we compiled the best 6 ratio matrices (i.e., 6 lowest root mean square of the residuals) and obtained their average ratio as the second initial ratio matrix to provide a new initial matrix (step 2). Steps 1 and 2 were repeated one more time to obtain the final pigment-ratio matrix (Table 3) as the average ratio metrics from the best 6 runs (i.e., with minimum root mean square of the residua). The final ratio matrix was used in this study to quantitatively estimate the individual concentrations, Ci, of each phytoplankton taxonomic group i.

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Table 2. Initial ratio matrices for CHEMTAX analysis. Pigment abbreviations are shown in Table 1. Here Chryso-Pelago: chrysophytes and pelagophytes; Hapto-7: haptophytes type 7; Prasino-3: prasinophytes type 3; Prasino-2: prasinophytes type 2.

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Table 3. Final ratio matrices for CHEMTAX analysis. Abbreviations in this table are same as Table 2.

For most CHEMTAX analysis, the initial matrix ratios for several PTGs were chosen from available literatures and used as “seed” values. It is unlikely to know exactly the pigment-ratios for natural waters in a given region, due to regional variations, strain differences within a given species and local changes in algal physiology affected by environmental factors (e.g., available light, nutrient level and temperature). In this case, the optimal ratio matrix for our study region was obtained through an optimization method and by repeatedly running CHEMTAX on our local data set. Note that the final ratio matrix is not validated here because of a lack of light microscopy data.

2.4 Model development

Considering that absorption properties of phytoplankton are additive, the total absorption coefficient of phytoplankton aph(λ) can be expressed as the sum of the specific absorption coefficients of each phytoplankton taxonomic group, also referred to as endmembers, weighted by their respective concentrations:

aph=i=1mCiai*(λ)
where ai*(λ) and Ci correspond to the specific absorption (m2 mg−1) and the concentration (mg m−3) of the i-th group, respectively; m is the number of the input phytoplankton taxonomic groups, in this case, m = 9.

With the availability of a large number of related samples of aph(λ) and Ci data, it becomes possible to relate the specific absorption coefficients of PTGs and Ci to the level of phytoplankton absorption measured at a given wavelength as

(Ci=1,j=1Ci=m,j=1Ci=1,j=nCi=m,j=n)(a˜i=1*(λ)a˜i=m*(λ))=(aph,j=1(λ)aph,j=n(λ))
where a˜i*(λ) is the specific absorption of the i-th taxonomic group at wavelength λ; Ci,j is the biomass concentration of the i-th taxonomic group and j-th sample, which can be obtained by CHEMTAX; aph,j (λ) is the in situ measured phytoplankton absorption for the j-th sample at a given wavelength λ; n is the number of samples used to derive a˜i*(λ). Equation (2) represents a system of linear equations, which can be expressed in the matrix form as
CA*=Aph
where A* is the vector of a˜i* that we seek to solve; C and Aph are the vector of Ci,j and aph,j, respectively.

In theory, because we are seeking to retrieve a number (m) of specific absorption spectra, this system of equations [Eq. (3)] needs to be written for equal amount of field samples to retrieve a˜i* spectra. It has been showed that an over-constraint system of equations (more equations than unknowns) can improve the comparison of a model with in situ measured data [31]. Therefore, given our database of 117 samples, we used a bootstrapping method where 20 coincidental measurements of aph and Ci were randomly selected to solve the unknowns a˜i*, and this step was repeated 1000 times. In brief, a least-square minimization method with equality constraint (function lsqlin MATLAB program) was used to compute the unknown paraments a˜i*. The lsqlin function solves:

min(12CA*Aph22)

In order to ensure the positive absorption coefficients within the solution, Eq. (4) was solved under the condition: a˜i* >10−5. The solution of this system of equation provided the mean values a˜i*, which were defined as the specific absorption of each phytoplankton taxonomic group, hereafter called a*i,LMM.

Once the specific absorption spectra of each taxonomic group have been determined, the biomass concentrations of phytoplankton taxonomic groups (Ci) can be inferred from phytoplankton absorption through linear unmixing model, combined with the derived a*i,LMM data. In other words, we are solving Eq. (3), but this time one sample at a time, with the vector C to be solved, as expressed by Eq. (5). Therefore, the inversion algorithm [Eqs. (4) and (5)] was applied to the aph data at ten MODIS wavelengths (i.e., 412, 443, 469, 488, 531, 547, 555, 645, 667, and 678 nm) to retrieve the biomass of PTGs. The systems of these equations can be written as,

(ai=1,LMM*(λ=1)ai=m,LMM*(λ=1)ai=1,LMM*(λ=k)ai=m,LMM*(λ=k))(Ci=1Ci=m)=(aph(λ=1)aph(λ=k))
where Ci denotes the biomass of the i-th taxonomic group to be estimated; k is the input wavebands. When solving Eq. (5), we assume that the biomass concentration of each group cannot be lower than the arbitrary value of 0.001 mg m−3.

2.5 Performance matrix and calculation assessments

Statistical description, and correlation and regression analyses were performed using the MATLAB software (MathWorks Inc., Natick, MA). The statistics included minimum, maximum, mean, and linear regression slope and intercept. Some indicators were used to evaluate the consistency between the estimated and measured values in this study, including determination coefficient (R2), root mean square error (RMSE), and mean absolute percentage error (MAPE). These statistical indicators were computed in log10 space for phytoplankton absorption coefficient and biomass concentration as follows:

RMSE=1ni=1n[(xiexim)/xim]2
MAPE(%)=1ni=1n|(xiexim)/xim|×100%
where n is the number of samples. The variables xie and ximx represent the estimated and measured values for the i-th sample, respectively.

The three above statistical indicators (R2, RMSE, and MAPE) were also used to evaluate the feasibility of the aph-LMM approach to retrieve each taxonomic group biomass using multispectral aph(λ), and also determine the optimum set of wavelengths from the 10 initial MODIS wavebands. To quantitatively compare the approach performance, we simplified and referred to the Ocean Colour Climate Change Initiative (OC-CCI) methodology [44,45]. In this study, a point scoring classification was used to objectively rank the performance of the aph-LMM approach, using R2, RMSE, and MAPE values as evaluation indicators when calculating the score. Here, we briefly described the assignation of the evaluation score as follow: (1) Taking one combination of wavebands, and computing the statistical indicators (i.e., R2, RMSE, and MAPE) of the phytoplankton groups, then, computing the mean values of the three indicators for these groups; (2) for N possible combination of input wavebands, a set of N mean values for three statistical indicators was derived; (3) For each statistical indicator, the best combination case is the one with the best evaluation indicator and is assigned N points, whereas the worst receives 0 points. For example, for N = 10 combination cases, the combination case with the highest mean R2 (lowest mean RMSE or MAPE) receives 10 points, while the lowest mean R2 (highest mean RMSE or MAPE) value receives 0 points; (4) Finally, the sum of three indicator’s points are defined as the final score of this combination case.

3. Results

3.1 Phytoplankton taxonomy by CHEMTAX analysis

The biomass concentrations of nine phytoplankton taxonomic groups were obtained by running CHEMTAX on our data set using the final ratio matrix (see section 2.3), and subsequently converted into the relative contributions of these groups to total chlorophyll-a (i.e., Ci/C; hereafter called CTC). Figure 2(a) shows the distribution of CTC and their average values for the nine PTGs in the Chukchi and Bering Seas. High CTCs for diatoms were mainly distributed in the Bering Strait and southern Chukchi Sea, and low CTCs (<10%) were found in the northern Chukchi Sea. For dinoflagellates, high CTCs were found in the northern Bering Strait. The CTCs of c3-flagellates ranged between 1.0% and 44.48% over our study area with an average value of 16.40%. For hapto-7, high CTCs were observed in the northern Chukchi Sea and also in several samples located in the Bering Strait. The CTCs of prasino-2 and prasino-3 had a similar distribution over the entire study area, with relatively high CTCs (>30%) found in the Chukchi Sea and low values in the Bering Strait and Bering Sea. In contrast, the groups which seem to contribute least to total biomass in most samples analyzed by CHEMTAX were chlorophytes with an average CTC of 0.13%, followed by chryso-pelago and cryptophytes with an average of 4.42% and 5.04%, respectively [Fig. 2(b)]. The results of Fig. 2 indicated that the Chukchi and Bering Seas were dominated by six taxonomic groups with an average CTC above 5%, namely, diatom, dinoflagellate, c3-flagellate, hapto-7, prasino-2, and prasino-3.

 figure: Fig. 2

Fig. 2 Distribution of the relative contributions of nine taxonomic groups to C derived from CHEMTAX (a) and their average contributions (b). These measurements were collected at different times of year over multiple years as described above.

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3.2 Determination of specific absorption spectra of PTGs

Analysis of HPLC-derived pigment using CHEMTAX showed that the Chukchi and Bering Seas were dominated by six taxonomic groups, and that three groups with CTC <5% (cryptophytes, chryso-pelago, and chlorophytes) contributed the least to the total biomass [Fig. 2]. In addition, given their small contribution to the total biomass, we assumed that their contribution to the absorption spectral signal was negligible such that it would be difficult, if not impossible, to inverse the total absorption signal to retrieve their individual contribution. Thus, this study focused on estimating the biomass of the six major taxonomic groups (i.e., Case 3 in Table 4) presented in our data set. Considering that prasino-2 and prasino-3 belong to prasinophtyes, the two groups were integrated into one single group, namely prasino (see Case 2 in Table 4). This was comforted by the fact that prasino-2 and −3 have similar absorption spectral shape with different magnitude [Fig. 3]. We tested further the robustness and accuracy of our approach by decreasing the number of taxonomic groups to retrieve; we integrated the prasino group of Case 2 and hapto-7 into one single group, referred to thereafter as hapto-prasino (i.e., Case 1 in Table 4). This was partially motivated by the facts that both these groups are generally classified as the small-sized phytoplankton [46] and that their absorption spectral shapes are similar, with a “shoulder” around 490 nm and low absorption at 550 nm [Fig. 3]. The diatom and dinoflagellate taxonomic groups were kept given their different biogeochemical roles compared to other taxonomic groups. Therefore, in this study, we tested the possibility to retrieve taxonomic assemblages for four (Case 1), five (Case 2) and six taxonomic groups (Case 3) from phytoplankton absorption spectra, as shown in Table 4.

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Table 4. Three cases for phytoplankton taxonomic group assemblages used in this study. Here prasino represents the combination of prasino-2 and prasino-3; Hapto-Prasino represents the combination of hapto-7 and prasino.

 figure: Fig. 3

Fig. 3 The specific absorption spectra of individual phytoplankton taxonomic groups (top) and spectra that were normalized to the value of absorption coefficient at 443 nm (bottom) for the three cases.

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Three different data sets (i.e., one for each of the three cases investigated: case 1, 2 and 3) were created to carry out the inversion of the LMM [Eqs. (3) and (4)] to obtain the specific absorption spectra of each phytoplankton taxonomic group. The a*i,LMM of all groups varied smoothly across the spectra with two peaks at 443 nm and 667 nm [Fig. 3]. For all three cases, diatoms and dinoflagellates specific absorption spectra exhibited the smallest magnitude but with differences in their respective spectral shape. For the Case 2 and 3, the magnitude of the hapto-7 specific absorption was significantly higher than those of other groups.

We also compared the variation of the specific absorption spectra of given taxonomic group within the three cases to study the robustness of the algorithm as we expected consistency in the retrieval of the specific absorption coefficient of a given phytoplankton group from one case to another. These groups were diatoms, dinoflagellates, c3-flagellates, and hapto-7 [Fig. 4]. Note that the spectra of hapto-7 group were compared for the Case 2 and 3 only, because the Case 1 included the combination of hapto-7 and prasino groups. In general, the spectra of the individual groups had similar shape and similar magnitude for the different cases [Fig. 4]. The hapto-7 group had the same spectra for the Case 2 and 3. The dinoflagellate spectra were very similar for the three cases. For diatoms (c3-flagellates), the spectra were the same for the Case 2 and 3, but the Case 1 exhibited a slightly lower (higher) absorption spectrum. The shape of the retrieved diatom specific absorption spectra in this study was in qualitative agreement with field samples dominated by diatom species (see Fig. 2 in Nair et al. [47]).

 figure: Fig. 4

Fig. 4 A comparison of the specific absorption spectra of four groups (diatoms, dinoflagellates, c3-flagellates, and hapto-7) for the different cases.

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For each of the three cases, the retrieved absorption spectra, a*i,LMM, were combined with Ci derived by CHEMTAX in Eq. (1) to reconstruct the total phytoplankton absorption spectra to provide for a way to quantitatively assess the ability of the linear unmixing model at reconstructing total phytoplankton absorption. The determination coefficient (R2) and the slope of the linear regression of the reconstructed versus measured aph(λ) and their statistical results (RMSE and MAPE) as a function of wavelength are shown in Fig. 5. The three cases showed very similar R2, RMSE, MAPE, and linear regression slope. The determination coefficients for the three cases were high (> 0.8), especially for the spectral region between 400 and 550 nm and between 600 and 695 nm (> 0.87). Meanwhile, a marked decrease in R2 values was found in the range of 550 to 640 nm [Fig. 5(a)], which corresponded to the minimum absorption of phytoplankton. For the three cases, the linear regression slope varied between 0.93 and 1.08 over the entire visible wavelength region (400-700 nm), and the RMSE and MAPE were both below 0.25 and 6.5%, receptively [Figs. 5(c) and 5(d)].

 figure: Fig. 5

Fig. 5 The determination coefficients (R2) (a), linear regression slope (b), RMSE (c), and MAPE (d) from comparison of the reconstructed with measured aph(λ) for the three cases.

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3.3 Inversion of the biomass of phytoplankton taxonomic groups

For each of the three cases, the biomass concentration of each phytoplankton taxonomic group was derived using the aph of each sample and the a*i,LMM at MODIS wavelengths [Eq. (5)]. The estimated Ci values were compared to the corresponding values obtained by CHEMTAX to assess the performance of the aph-LMM approach proposed in this study [Fig. 6 and Table 5]. It should be noted here that the Ci derived from the HPLC pigments by CHEMTAX were defined as the “measured Ci” data. Furthermore, for many samples, the biomass concentrations of some taxonomic groups such as diatoms and dinoflagellates were equal to zero, largely because some accessory pigments such as peridinin and fucoxanthin concentrations were below the detection limit. Therefore, to enable the logarithmic transformation of all data, null values of Ci were set arbitrarily to 10−4 mg m−3. For these low values, the relative error between the estimated and measured data may be very high and meaningless, leading to poor statistical performance (e.g., RMSE and MAPE). Therefore, the statistical indicators for each phytoplankton taxonomic group were computed after excluding the values lower than 0.0001 mg m−3. The excluded samples will be nevertheless presented in the scatterplots, in order to show that, when measured Ci are lower than 0.0001 mg m−3, the estimated Ci are also lower than this threshold.

 figure: Fig. 6

Fig. 6 Comparison of the estimated versus measured Ci for the PTGs in Case 1 (a), Case 2 (b), and Case 3 (c). Blue solid points represent the samples where the total CTC value of the three excluded groups is above 20%. Black dashed lines are the 1:1 lines.

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Tables Icon

Table 5. Statistical results of Fig. 6. P-values from the significance level tests were both less than 0.001.

As shown in Fig. 6(a) and Table 5, for the Case 1, the dinoflagellates and c3-flagellates concentrations were retrieved with the lowest MAPE (24.81% and 25.36%, respectively) and high R2 (0.64 and 0.55, respectively), while the diatom concentrations were retrieved with the largest MAPE of 47.17% and relatively high R2 of 0.56 (Table 5). Despite the low R2 value for the hapto-prasino group caused by the very low concentration in a few samples, the retrievals of hapto-prasino were accurate for most samples with a concentration greater than 0.01 mg m−3 [Fig. 6(a)], thus resulting in the lowest MAPE of 25.74%. For the Case 2 [Fig. 6(b)], the retrieval accuracy of diatoms was slightly improved (R2 of 0.62 and MAPE of 41.05%) and the correlation coefficient for c3-flagellates was also improved (R2 of 0.65 and MAPE of 25.90%) compared with the Case 1. The MAPE values were 29.32%, 19.45%, and 27.79% for dinoflagellate, hapto-7, and prasino, respectively (Table 5). For the dinoflagellates, no clear difference in the performance between the three cases was found [Fig. 6]. For the Case 3, the MAPE values for all taxonomic groups were below 28%, except dinoflagellates (34.92%) and diatoms (48.07%) with R2 > 0.6 [Fig. 6(c)]. It should be kept in mind that this study estimated six groups (in other word, excluded three groups, i.e., cryptophytes, chryso-Pelago, and chlorophytes) from nine groups initially identified using the CHEMTAX analysis. Although the mean contribution of these excluded groups to the mean total biomass was very low, a few samples with relatively high proportion of these discarded taxonomic groups (>20%) might be part of the retrieving “outliers” in one or more groups [Fig. 6, blue points]. Note that for all taxonomic groups, the aph-LMM approach had a limited ability to retrieve the zero concentrations, even if the retrieved values generally remained lower than 0.01 mg m−3. Although the MAPE values appeared high for some groups such as diatoms, they were comparable to Chla uncertainties estimated for the global open oceans [5] and regional waters [48] and therefore judged reasonable. We believe that these results support the aph-LMM approach as a viable way to derive the concentrations of PTGs from absorption spectra.

3.4 Feasibility of the aph-LMM approach for multispectral aph(λ)

To determine the importance of each waveband for the aph-LMM approach, a statistical experiment was conducted for aph(λ) at MODIS wavelengths. Here, this study only analyzed one case, i.e., the Case 1 as we anticipated similar results for the Case 2 and 3. During this experiment, each MODIS waveband was removed one at a time, and the remaining wavebands were used to derive the PGTs concentrations using the aph-LMM approach. The final scores of all possible wavelength combinations for the MODIS sensor were calculated using the methods described in section 2.5. During this iterative procedure, the waveband combination with the highest score was selected for the next step, while the combination with the lowest score was discarded, which determined the waveband with the least influence on the performance of the aph-LMM approach. Wavebands were therefore iteratively discarded from ten to a minimum of five wavebands. This minimum number of five wavelengths was selected given that the system of equations is solved for four unknowns (four phytoplankton groups). Figure 7 summarized the performance of the aph-LMM approach under six waveband combinations for the MODIS sensor. The number of wavelengths can be decreased from ten to five without compromising the information when considering a 4-group assemblage [Fig. 7]. The aph-LMM approach using the five wavebands [Fig. 7, C6] showed a good performance, with R2 values of 0.56, 0.57, 0.52, and 0.48 and the corresponding MAPE values of 44.09%, 25.54%, 27.13%, and 25.27% for diatoms, dinoflagellate, c3-flagellates, and hapto-prasino, respectively. These findings indicated that the reduction in the number of wavebands of aph(λ) from ten to five had negligible influence on the capability of the aph-LMM approach to retrieve four phytoplankton groups (Case 1).

 figure: Fig. 7

Fig. 7 R2 (a), RMSE (b), and MAPE (c) of the aph-LMM approach performed on measured aph(λ) with different combinations of MODIS wavebands. Table of MODIS bands combination (d). ‘-’ means the removed band.

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4. Discussion

4.1 Specific absorption spectra of PTGs

Models that link phytoplankton taxonomic groups or functional types to phytoplankton absorption spectra have the potential for advancing the capabilities of inverse models using hyperspectral remote sensing reflectance observations. The aph-LMM approach, which relies on specific absorption spectra, was proposed for estimating the biomass of PTGs from aph(λ). This approach requires the knowledge of the specific absorption spectra of individual taxonomic groups (i.e., endmembers) that are targeted, which can be challenging to obtain. In the field, measurement of PTG specific absorption would require separation techniques to isolate the target cells from the phytoplankton assemblage. The use of laboratory cultures may provide information on the specific absorption of a given species under controlled conditions, but would be far from a measurement of the specific absorption of its taxonomic group in the natural environment, which can be made of tens of different species with different specific absorption spectra. In addition, specific absorption spectra of a given phytoplankton group are likely to change with environmental conditions (e.g., light and nutrients available) [47,49]. The use of global data sets to infer the specific absorption of a given population will not account for regional differences. Several mathematical and statistical methods, such as the linear unmixing model used in this study, present the advantages of accounting for regional and seasonal variability which is included in the “mean” specific absorption spectra of the taxonomic group [32]. The inversion results [Fig. 3] indicated that it is possible to extract specific absorption “endmembers” of individual taxonomic groups using the LMM approach. Again, the difficulty to obtain laboratory-measured specific absorption spectra of PTGs representative of natural phytoplankton population limits direct validation of the specific absorption spectra (a*i,LMM) retrieved in this study. Alternatively, we used the CHEMTAX classification to retain samples that are dominated by a single taxonomic group, and then calculated the average measured a*ph for these samples (hereafter called a*i,HPLC) as an indicator of the specific absorption coefficient of the dominant taxonomic group. Here the a*i,HPLC spectra were compared with a*i,LMM for validation. This analysis was conducted for the Case 3 considering that the a*i,LMM spectra of a given phytoplankton taxonomic group remains the same for the three different cases [Fig. 4].

For a given taxonomic group, we selected samples where the CTC values were above a given proportion of total biomass, k (in %), to calculate a*i,HPLC. This threshold k was dictated by the fact that only few samples showed dominance by a given taxonomic group and that in some cases the contribution to total biomass barely made 50% of the samples (e.g., 42% for prasynophytes). For our data set, k varied between 42% (prasynophytes) and 79% (diatoms) [Fig. 8(a)]. The spectral shape of the a*i,LMM were similar to those of a*i,HPLC [Fig. 8(b)] but with different magnitude. We also noticed that the higher the concentration of one group in a sample, the better the agreement between a*i,LMM and a*i,HPLC, such as dinoflagellates and hapto-7, except for the diatom group. However, there were evidences of some differences in the magnitude between a*i,LMM and a*i,HPLC that arose from the methodology. In one hand, the linear unmixing method is a purely mathematical approach and, in the other hand, the a*i,HPLC spectra selected for comparison do not represent the specific absorption spectra of a “pure” taxonomic group, since their contribution to C reach 90% at best. The result of Fig. 8 could indirectly prove the reliability of the specific absorption obtained using the LMM. It is noteworthy that the a*i,LMM values of diatoms and dinoflagellates were lower than hapto-7, prasino-2, and prasino-3. This was in agreement with results in the literature and likely to be related to the packing effect for distinct phytoplankton size structure [50]. Diatoms and dinoflagellates are generally classified as large-sized phytoplankton [51,52], while hapto- and prasino- type belong to small-sized phytoplankton. Micro-dominated phytoplankton has low a*ph due to high packaging effect, whereas pico-dominated phytoplankton has high a*ph because of low packaging effect [53]. Thus, the specific absorption coefficients of diatoms and dinoflagellates were lower than those of other groups, in agreement with previous studies [22,47,54]. Additionally, we analyzed the LMM-derived specific absorption spectra of PTGs and the specific absorption spectra of the individual marker pigments in solution, which were obtained from Bricaud et al. [21]. Note that the pigment-specific absorption spectra were available for only 14 pigments. For all phytoplankton taxonomic groups, the peak at 443 nm and 667 nm of the ai* spectra were caused by Chla (see green curves in Fig. 9). As shown in Fig. 9(a), the LMM-derived ai*(λ) of diatoms showed a small variation between 450 and 510 nm (red dashed curve), which was also revealed by the second derivatives (red dotted curve). This was in agreement with the specific absorption spectra of fucoxanthin (maximum of absorption centered around 490), which is the marker pigment for diatoms. The specific absorption spectra of prasino-2 and 3 were sharp [Fig. 9(b)] and showed more variability and a peak around 480 nm. A similar phenomenon was observed for the peaks at 460 nm - 490 nm of pigment-specific absorption spectra of zeaxanthin and chlorophyll-b pigments (see black and yellow curves in Fig. 9(b)). We believe that the shape of the specific absorption of phytoplankton taxonomic group were mainly related to the presence of their corresponding marker pigments, as reported by previous studies [55,56].

 figure: Fig. 8

Fig. 8 The samples and their contributions to C (%) used for computing a*i,HPLC (a). The numbers in bar represent the CTC of a given dominant taxonomic group. Comparison of the obtained a*i,LMM (solid curves) with the a*i,HPLC (dashed curves) (b).

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 figure: Fig. 9

Fig. 9 The derived aph* of diatoms and pigment-specific absorption spectral of fucoxanthin (a); the derived aph* of two prasino types and pigment-specific absorption spectra of zeaxanthin and chlorophyll b (b). These pigment-specific absorption spectra were obtained from Bricaud et al. [21].

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The a*i,LMM spectra were used with the concentrations of PTGs by CHEMTAX to successfully reconstruct phytoplankton absorption spectra [Fig. 5]. The slight differences between the reconstructed and measured aph(λ) can be related to the lack of a complete set of the specific absorption spectra (only 6 dominant groups vs 9 groups in CHEMTAX). A noticeable decline in performance of all absorption spectra reconstructions was observed in the spectral range between 550 nm and 640 nm. This is likely caused by not including the contribution of phytoplankton group containing the pigment phycobilin to phytoplankton absorption spectra reconstruction. It is also the part of the spectra where phytoplankton absorption is lowest such that the optimization method performs least. The lack of phycobilin-containing phytoplankton in this study results from the HPLC analysis that is not able to detect this pigment. In addition, there was a consistent drop in R2 near 700 nm for the three cases in this study [Fig. 5(a)]. Certainly, the absorption levels were very low in this spectral range (i.e., uncertainties are high) compared to most other parts of the absorption spectra [32].

4.2 Implication and limitation of the aph-LMM approach

Compared with current methods, the aph-LMM approach proposed in this study can retrieve the biomass contributions of many phytoplankton taxonomic groups by first inferring the specific absorption of each phytoplankton taxonomic group. These groups showed either consistently better retrievals for dinoflagellates, c3-flagellates, hapto-7, prasino-2, prasino-3 with low MAPE and good retrievals for diatoms with high R2 [Fig. 6 and Table 5]. However, this approach did not permit a proper retrieval of the zero contribution of a given group, although the retrieved values generally remained low. The high MAPE of diatoms may be related to the coexistence of small-sized and large-sized diatoms in our study area [33]. For example, Fujiwara et al. [33] found small diatoms in the Chukchi and Bering Seas, and reported that the optical properties of small-sized diatoms should be accounted to derive phytoplankton size structure more accurately. Thus, the presence of the small-sized diatoms plays a certain role in determining the specific absorption spectral of the diatoms group using the LMM-method, which may increase uncertainty in estimating the biomass concentration when using the retrieved diatoms specific absorption.

A number of factors can affect the retrieval accuracy of PTGs biomass using the aph-LMM approach. The first one is related to the linear unmixing model that is used to generate specific absorption spectra. The concentrations of several phytoplankton taxonomic groups are correlated (data not shown) which can add complexity to the inversion solution, and is mainly related to the interpretation of the mathematical formulation. In addition, the pigment-ratio matrix as input to the CHEMTAX analysis for a specific study region cannot guaranty to provide the accurate “measured” biomass of phytoplankton taxonomic groups that is used for the aph-LMM model development. Provided that the analytical data is of good quality, the determination of PTGs could be improved. If the region of interest is an extensive oceanic area, it would not be a sensible choice to use a constant pigment-ratio matrix for the CHEMTAX analysis across all possible oceanic regime. This is because pigment ratios vary widely in natural waters within a given phytoplankton group and even within given species due to differences in environmental conditions, with the potential to confound CHEMTAX results [42,43]. In that case, the optimal set of pigment-ratios for one specific subarea is required for accurate estimation of PTGs. Meanwhile, the different assemblages of phytoplankton taxonomic groups may produce the variability of the retrieved specific absorption spectra using the linear unmixing model [Fig. 4]. Also, the combination of aph(λ) at different wavelengths is another factor influencing the performance of the aph-LMM approach. Results of a sensitivity approach to test what wavebands carry significant information in a multispectral context (i.e., use of MODIS wavebands) showed that the performance of the aph-LMM approach [Fig. 7] is sensitive not only to the number of wavebands but also to their location on the visible spectrum. The phytoplankton absorption coefficients are possibly contaminated by yellow substances and mineral particles, especially in the coastal environment, and even in the Chukchi Sea having optically complex water due to the high proportion of yellow substances absorption to total absorption [57,58]. When using aph(λ) to estimate phytoplankton size classes, Devred et al. [31] removed the aph signal at 412 nm to avoid any potential effect of absorption by detritus and yellow substances in this region of the spectrum. Ultimately, a minimum of five wavebands was necessary to achieve an acceptable level of accuracy of four PTGs biomass in our study.

Compared with other methods that estimate the biomass of phytoplankton taxonomic groups ([6] and references therein), the aph-LMM approach presented several advantages. It relies on the physical links between PTGs and their distinct light absorption properties. Thus, this approach could be applied to derive specific absorption using a mathematical inverse solution and thereby estimate biomass of taxonomic groups in new regions at a large scales if concurrent measurements of aph and phytoplankton community (or HPLC pigment data) in some samples are available. It can circumvent the difficulty of measuring individual specific absorption spectra of PTGs in the natural environment. Thus, the aph-LMM approach is straightforward and should have good applicability in broader regions. Meanwhile, many algorithms have been proposed for the quantitative retrieval of phytoplankton pigments from aph(λ) and Rrs(λ) data [32,59], and many algorithms have been designed for the retrieval of aph(λ) from satellite remote sensing data ([60] and references therein). Overall, the current study provides a useful technical basis for remote estimation of phytoplankton taxonomic groups using aph(λ) data derived from satellite ocean color.

5. Conclusion

In this study, we proposed an innovative approach to estimate the biomass of phytoplankton taxonomic groups directly from the spectral absorption coefficients of phytoplankton and chlorophyll-a concentration. A critical step in constructing this approach is to determine the specific absorption spectra of individual phytoplankton taxonomic group. First, we used the CHEMTAX software to obtain the concentrations of nine phytoplankton groups from HPLC pigments collected in the Chukchi and Bering Seas. This chemotaxonomic analysis showed that the phytoplankton community composition in this region was dominated by six groups, namely, diatoms, dinoflagellates, c3-flagellate, hapto-7, prasino-2, and prasino-3. The measured aph(λ) and concentrations of PTGs were used as input to a linear unmixing model to determine the specific absorption spectra of each group, which in turn were used to successfully reconstruct total aph(λ) with high R2 values (0.80-0.95) and a slope of linear regressions of the derived-aph(λ) on measured-aph(λ) close to 1. Finally, the approach was applied to the derived specific absorption spectra to retrieve the concentrations of PTGs from aph(λ). The evaluation of the approach showed good performance for dinoflagellates, c3-flagellate, hapto-7, prasino-2 and prasino-3 with low MAPE (<35%) and diatoms with MAPE value of about 45%; however, the main limitation of the method is that it provides low concentration of certain pigments that are not detected in the natural sample. We believe that this limitation occurs across mathematical methods (principal component analysis, Gaussian decomposition) given the complexity and interplay of pigments in phytoplankton cells. Our approach can be easily implemented in other regions, once concurrent measurements of phytoplankton community and aph(λ) are available. Further work will consist of applying the aph-LMM approach to satellite ocean color data to estimate PTGs from space.

Funding

National Key Research and Development Program of China (2016YFC1400904); the National Natural Science Foundation of China (41506200, 41576172, and 41276186); the Natural Science Foundation of the Jiangsu Higher Education Institutions of China (15KJB170015); the Provincial Natural Science Foundation of Jiangsu in China (BK20150914, BK20151526, and BK20161532); the National Program on Global Change and Air-sea Interaction (GASI-03-03-01-01); the Public Science and Technology Research Funds Projects of Ocean (201005030); the Priority Academic Program Development of Jiangsu Higher Education Institutions (PAPD); the Research and Innovation Project for College Graduates of Jiangsu Province (KYLX16_0952); Fisheries and Oceans Canada program Arctic Science Fund; the China Scholarship Council.

Acknowledgments

We would like to thank Ph.D Pierre Coupel for the valuable comments towards improving this manuscript. The authors are grateful for the helpful comments from the two anonymous reviewers.

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45. L. Zheng, Z. Qiu, Y. Zhou, D. Sun, S. Wang, W. Wu, and W. Perrie, “Comparisons of algorithms to estimate water turbidity in the coastal areas of China,” Int. J. Remote Sens. 37(24), 6165–6186 (2016). [CrossRef]  

46. P. Coupel, H. Y. Jin, M. Joo, R. Horner, H. A. Bouvet, M. A. Sicre, J. C. Gascard, J. F. Chen, V. Garçon, and D. Ruiz-Pino, “Phytoplankton distribution in unusually low sea ice cover over the Pacific Arctic,” Biogeosciences 9(11), 4835–4850 (2012). [CrossRef]  

47. A. Nair, S. Sathyendranath, T. Platt, J. Morales, V. Stuart, M.-H. Forget, E. Devred, and H. Bouman, “Remote sensing of phytoplankton functional types,” Remote Sens. Environ. 112(8), 3366–3375 (2008). [CrossRef]  

48. E. Siswanto, J. Tang, H. Yamaguchi, Y.-H. Ahn, J. Ishizaka, S. Yoo, S.-W. Kim, Y. Kiyomoto, K. Yamada, C. Chiang, and H. Kawamura, “Empirical ocean-color algorithms to retrieve chlorophyll-a, total suspended matter, and colored dissolved organic matter absorption coefficient in the Yellow and East China Seas,” J. Oceanogr. 67(5), 627–650 (2011). [CrossRef]  

49. S. Sathyendranath, L. Lazzara, and L. Prieur, “Variations in the spectral values of specific absorption of phytoplankton,” Limnol. Oceanogr. 32(2), 403–415 (1987). [CrossRef]  

50. R. R. Bidigare, M. E. Ondrusek, J. H. Morrow, and D. A. Kiefer, “In-vivo absorption properties of algal pigments,” in Ocean Optics X, (International Society for Optics and Photonics, 1990), pp. 290–303.

51. F. Vidussi, H. Claustre, B. B. Manca, A. Luchetta, and J. C. Marty, “Phytoplankton pigment distribution in relation to upper thermocline circulation in the eastern Mediterranean Sea during winter,” J. Geophys. Res. Oceans 106(C9), 19939–19956 (2001). [CrossRef]  

52. H. Zhang, S. Wang, Z. Qiu, D. Sun, J. Ishizaka, S. Sun, and Y. He, “Phytoplankton size class in the East China Sea derived from MODIS satellite data,” Biogeosciences 15(13), 4271–4289 (2018). [CrossRef]  

53. A. Bricaud, C. Mejia, D. Blondeau-Patissier, H. Claustre, M. Crepon, and S. Thiria, “Retrieval of pigment concentrations and size structure of algal populations from their absorption spectra using multilayered perceptrons,” Appl. Opt. 46(8), 1251–1260 (2007). [CrossRef]   [PubMed]  

54. A. M. Ciotti, M. R. Lewis, and J. J. Cullen, “Assessment of the relationships between dominant cell size in natural phytoplankton communities and the spectral shape of the absorption coefficient,” Limnol. Oceanogr. 47(2), 404–417 (2002). [CrossRef]  

55. A. Ferreira, D. Stramski, C. A. E. Garcia, V. M. T. Garcia, Á. M. Ciotti, and C. R. B. Mendes, “Variability in light absorption and scattering of phytoplankton in Patagonian waters: Role of community size structure and pigment composition,” J. Geophys. Res. Oceans 118(2), 698–714 (2013). [CrossRef]  

56. R. Barlow, J. Aiken, P. Holligan, D. Cummings, S. Maritorena, and S. Hooker, “Phytoplankton pigment and absorption characteristics along meridional transects in the Atlantic Ocean,” Deep Sea Res. Part I Oceanogr. Res. Pap. 49(4), 637–660 (2002). [CrossRef]  

57. W. S. Pegau, “Inherent optical properties of the central Arctic surface waters,” J. Geophys. Res. Oceans 107(10), 16 (2002).

58. J. Wang, G. F. Cota, and D. A. Ruble, “Absorption and backscattering in the Beaufort and Chukchi Seas,” J. Geophys. Res. Oceans 110, C4 (2005).

59. A. Chase, E. Boss, I. Cetinić, and W. Slade, “Estimation of phytoplankton accessory pigments from hyperspectral reflectance spectra: Toward a global algorithm,” J. Geophys. Res. Oceans 122(12), 97125–9743 (2017). [CrossRef]  

60. IOCCG, “Remote sensing of inherent optical properties: fundamentals, tests of algorithms, and applications,” in Reports of International Ocean-Colour Coordinating Group, L. Zhongping, ed. (IOCCG, 2006), pp. 1–125.

References

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    [Crossref]
  50. R. R. Bidigare, M. E. Ondrusek, J. H. Morrow, and D. A. Kiefer, “In-vivo absorption properties of algal pigments,” in Ocean Optics X, (International Society for Optics and Photonics, 1990), pp. 290–303.
  51. F. Vidussi, H. Claustre, B. B. Manca, A. Luchetta, and J. C. Marty, “Phytoplankton pigment distribution in relation to upper thermocline circulation in the eastern Mediterranean Sea during winter,” J. Geophys. Res. Oceans 106(C9), 19939–19956 (2001).
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  52. H. Zhang, S. Wang, Z. Qiu, D. Sun, J. Ishizaka, S. Sun, and Y. He, “Phytoplankton size class in the East China Sea derived from MODIS satellite data,” Biogeosciences 15(13), 4271–4289 (2018).
    [Crossref]
  53. A. Bricaud, C. Mejia, D. Blondeau-Patissier, H. Claustre, M. Crepon, and S. Thiria, “Retrieval of pigment concentrations and size structure of algal populations from their absorption spectra using multilayered perceptrons,” Appl. Opt. 46(8), 1251–1260 (2007).
    [Crossref] [PubMed]
  54. A. M. Ciotti, M. R. Lewis, and J. J. Cullen, “Assessment of the relationships between dominant cell size in natural phytoplankton communities and the spectral shape of the absorption coefficient,” Limnol. Oceanogr. 47(2), 404–417 (2002).
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    [Crossref]
  56. R. Barlow, J. Aiken, P. Holligan, D. Cummings, S. Maritorena, and S. Hooker, “Phytoplankton pigment and absorption characteristics along meridional transects in the Atlantic Ocean,” Deep Sea Res. Part I Oceanogr. Res. Pap. 49(4), 637–660 (2002).
    [Crossref]
  57. W. S. Pegau, “Inherent optical properties of the central Arctic surface waters,” J. Geophys. Res. Oceans 107(10), 16 (2002).
  58. J. Wang, G. F. Cota, and D. A. Ruble, “Absorption and backscattering in the Beaufort and Chukchi Seas,” J. Geophys. Res. Oceans 110, C4 (2005).
  59. A. Chase, E. Boss, I. Cetinić, and W. Slade, “Estimation of phytoplankton accessory pigments from hyperspectral reflectance spectra: Toward a global algorithm,” J. Geophys. Res. Oceans 122(12), 97125–9743 (2017).
    [Crossref]
  60. IOCCG, “Remote sensing of inherent optical properties: fundamentals, tests of algorithms, and applications,” in Reports of International Ocean-Colour Coordinating Group, L. Zhongping, ed. (IOCCG, 2006), pp. 1–125.

2018 (1)

H. Zhang, S. Wang, Z. Qiu, D. Sun, J. Ishizaka, S. Sun, and Y. He, “Phytoplankton size class in the East China Sea derived from MODIS satellite data,” Biogeosciences 15(13), 4271–4289 (2018).
[Crossref]

2017 (5)

A. Chase, E. Boss, I. Cetinić, and W. Slade, “Estimation of phytoplankton accessory pigments from hyperspectral reflectance spectra: Toward a global algorithm,” J. Geophys. Res. Oceans 122(12), 97125–9743 (2017).
[Crossref]

H. Zhang, Z. Qiu, D. Sun, S. Wang, and Y. He, “Seasonal and interannual variability of satellite-derived chlorophyll-a (2000–2012) in the Bohai Sea, China,” Remote Sens. 9(6), 582 (2017).
[Crossref]

T. S. Kostadinov, A. Cabré, H. Vedantham, I. Marinov, A. Bracher, R. J. Brewin, A. Bricaud, T. Hirata, T. Hirawake, N. J. Hardman-Mountford, C. Mouw, S. Roy, and J. Uitz, “Inter-comparison of phytoplankton functional type phenology metrics derived from ocean color algorithms and earth system models,” Remote Sens. Environ. 190, 162–177 (2017).
[Crossref]

C. B. Mouw, N. J. Hardman-Mountford, S. Alvain, A. Bracher, R. J. Brewin, A. Bricaud, A. M. Ciotti, E. Devred, A. Fujiwara, T. Hirata, T. Hirawake, T. S. Kostadinov, S. Roy, and J. Uitz, “A consumer’s guide to satellite remote sensing of multiple phytoplankton groups in the global ocean,” Front. Mar. Sci. 4, 41 (2017).
[Crossref]

A. Bracher, H. A. Bouman, R. J. Brewin, A. Bricaud, V. Brotas, A. M. Ciotti, L. Clementson, E. Devred, A. Di Cicco, S. Dutkiewicz, N. J. Hardman-Mountford, A. E. Hickman, M. Hieronymi, T. Hirata, S. N. Losa, C. B. Mouw, E. Organelli, D. E. Raitsos, J. Uitz, M. Vogt, and A. Wolanin, “Obtaining phytoplankton diversity from ocean color: a scientific roadmap for future development,” Front. Mar. Sci. 4, 55 (2017).
[Crossref]

2016 (2)

C. M. Swan, M. Vogt, N. Gruber, and C. Laufkoetter, “A global seasonal surface ocean climatology of phytoplankton types based on CHEMTAX analysis of HPLC pigments,” Deep Sea Res. Part I Oceanogr. Res. Pap. 109, 137–156 (2016).
[Crossref]

L. Zheng, Z. Qiu, Y. Zhou, D. Sun, S. Wang, W. Wu, and W. Perrie, “Comparisons of algorithms to estimate water turbidity in the coastal areas of China,” Int. J. Remote Sens. 37(24), 6165–6186 (2016).
[Crossref]

2015 (3)

D. Müller, H. Krasemann, R. J. Brewin, C. Brockmann, P.-Y. Deschamps, R. Doerffer, N. Fomferra, B. A. Franz, M. G. Grant, S. B. Groom, F. Mélin, T. Platt, P. Regner, S. Sathyendranath, F. Steinmetz, and J. Swinton, “The Ocean Colour Climate Change Initiative: I. A methodology for assessing atmospheric correction processors based on in-situ measurements,” Remote Sens. Environ. 162, 242–256 (2015).
[Crossref]

H. Xi, M. Hieronymi, R. Röttgers, H. Krasemann, and Z. Qiu, “Hyperspectral differentiation of phytoplankton taxonomic groups: A comparison between using remote sensing reflectance and absorption spectra,” Remote Sens. 7(11), 14781–14805 (2015).
[Crossref]

P. Coupel, A. Matsuoka, D. Ruiz-Pino, M. Gosselin, D. Marie, J. É. Tremblay, and M. Babin, “Pigment signatures of phytoplankton communities in the Beaufort Sea,” Biogeosciences 12(4), 991–1006 (2015).
[Crossref]

2013 (2)

G. Zheng and D. Stramski, “A model based on stacked constraints approach for partitioning the light absorption coefficient of seawater into phytoplankton and nonphytoplankton components,” J. Geophys. Res. Oceans 118(4), 2155–2174 (2013).
[Crossref]

A. Ferreira, D. Stramski, C. A. E. Garcia, V. M. T. Garcia, Á. M. Ciotti, and C. R. B. Mendes, “Variability in light absorption and scattering of phytoplankton in Patagonian waters: Role of community size structure and pigment composition,” J. Geophys. Res. Oceans 118(2), 698–714 (2013).
[Crossref]

2012 (1)

P. Coupel, H. Y. Jin, M. Joo, R. Horner, H. A. Bouvet, M. A. Sicre, J. C. Gascard, J. F. Chen, V. Garçon, and D. Ruiz-Pino, “Phytoplankton distribution in unusually low sea ice cover over the Pacific Arctic,” Biogeosciences 9(11), 4835–4850 (2012).
[Crossref]

2011 (5)

E. Siswanto, J. Tang, H. Yamaguchi, Y.-H. Ahn, J. Ishizaka, S. Yoo, S.-W. Kim, Y. Kiyomoto, K. Yamada, C. Chiang, and H. Kawamura, “Empirical ocean-color algorithms to retrieve chlorophyll-a, total suspended matter, and colored dissolved organic matter absorption coefficient in the Yellow and East China Seas,” J. Oceanogr. 67(5), 627–650 (2011).
[Crossref]

E. Devred, S. Sathyendranath, V. Stuart, and T. Platt, “A three component classification of phytoplankton absorption spectra: Application to ocean-color data,” Remote Sens. Environ. 115(9), 2255–2266 (2011).
[Crossref]

J. R. Moisan, T. A. H. Moisan, and M. A. Linkswiler, “An inverse modeling approach to estimating phytoplankton pigment concentrations from phytoplankton absorption spectra,” J. Geophys. Res. 116(C9), C09018 (2011).
[Crossref]

A. Fujiwara, T. Hirawake, K. Suzuki, and S. I. Saitoh, “Remote sensing of size structure of phytoplankton communities using optical properties of the Chukchi and Bering Sea shelf region,” Biogeosciences 8(12), 3567–3580 (2011).
[Crossref]

R. J. Brewin, N. J. Hardman-Mountford, S. J. Lavender, D. E. Raitsos, T. Hirata, J. Uitz, E. Devred, A. Bricaud, A. Ciotti, and B. Gentili, “An intercomparison of bio-optical techniques for detecting dominant phytoplankton size class from satellite remote sensing,” Remote Sens. Environ. 115(2), 325–339 (2011).
[Crossref]

2010 (1)

D. G. Boyce, M. R. Lewis, and B. Worm, “Global phytoplankton decline over the past century,” Nature 466(7306), 591–596 (2010).
[Crossref] [PubMed]

2009 (1)

J. Aiken, Y. Pradhan, R. Barlow, S. Lavender, A. Poulton, P. Holligan, and N. Hardman-Mountford, “Phytoplankton pigments and functional types in the Atlantic Ocean: A decadal assessment, 1995–2005,” Deep Sea Res. Part II Top. Stud. Oceanogr. 56(15), 899–917 (2009).
[Crossref]

2008 (3)

T. Hirata, J. Aiken, N. Hardman-Mountford, T. Smyth, and R. Barlow, “An absorption model to determine phytoplankton size classes from satellite ocean colour,” Remote Sens. Environ. 112(6), 3153–3159 (2008).
[Crossref]

A. Nair, S. Sathyendranath, T. Platt, J. Morales, V. Stuart, M.-H. Forget, E. Devred, and H. Bouman, “Remote sensing of phytoplankton functional types,” Remote Sens. Environ. 112(8), 3366–3375 (2008).
[Crossref]

D. E. Raitsos, S. J. Lavender, C. D. Maravelias, J. Haralabous, A. J. Richardson, and P. C. Reid, “Identifying four phytoplankton functional types from space: An ecological approach,” Limnol. Oceanogr. 53(2), 605–613 (2008).
[Crossref]

2007 (2)

2006 (2)

J. Uitz, H. Claustre, A. Morel, and S. B. Hooker, “Vertical distribution of phytoplankton communities in open ocean: an assessment based on surface chlorophyll,” J. Geophys. Res. 111(C8), C08005 (2006).
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S. E. Craig, S. E. Lohrenz, Z. Lee, K. L. Mahoney, G. J. Kirkpatrick, O. M. Schofield, and R. G. Steward, “Use of hyperspectral remote sensing reflectance for detection and assessment of the harmful alga, Karenia brevis,” Appl. Opt. 45(21), 5414–5425 (2006).
[Crossref] [PubMed]

2005 (4)

K. Suzuki, A. Hinuma, H. Saito, H. Kiyosawa, H. Liu, T. Saino, and A. Tsuda, “Responses of phytoplankton and heterotrophic bacteria in the northwest subarctic Pacific to in situ iron fertilization as estimated by HPLC pigment analysis and flow cytometry,” Prog. Oceanogr. 64(2–4), 167–187 (2005).
[Crossref]

S. Alvain, C. Moulin, Y. Dandonneau, and F. M. Bréon, “Remote sensing of phytoplankton groups in case 1 waters from global SeaWiFS imagery,” Deep Sea Res. Part I Oceanogr. Res. Pap. 52(11), 1989–2004 (2005).
[Crossref]

C. L. Quere, S. P. Harrison, I. Colin Prentice, E. T. Buitenhuis, O. Aumont, L. Bopp, H. Claustre, L. Cotrim Da Cunha, R. Geider, X. Giraud, C. Klaas, K. E. Kohfeld, L. Legendre, M. Manizza, T. Platt, R. B. Rivkin, S. Sathyendranath, J. Uitz, A. J. Watson, and D. Wolf-Gladrow, “Ecosystem dynamics based on plankton functional types for global ocean biogeochemistry models,” Glob. Change Biol. 11(11), 2016–2040 (2005).
[Crossref]

J. Wang, G. F. Cota, and D. A. Ruble, “Absorption and backscattering in the Beaufort and Chukchi Seas,” J. Geophys. Res. Oceans 110, C4 (2005).

2004 (4)

W. W. Gregg and N. W. Casey, “Global and regional evaluation of the SeaWiFS chlorophyll data set,” Remote Sens. Environ. 93(4), 463–479 (2004).
[Crossref]

P. G. Falkowski, M. E. Katz, A. H. Knoll, A. Quigg, J. A. Raven, O. Schofield, and F. J. Taylor, “The evolution of modern eukaryotic phytoplankton,” Science 305(5682), 354–360 (2004).
[Crossref] [PubMed]

A. Bricaud, H. Claustre, J. Ras, and K. Oubelkheir, “Natural variability of phytoplanktonic absorption in oceanic waters: Influence of the size structure of algal populations,” J. Geophys. Res. Oceans 109(11), 45–50 (2004).

S. Sathyendranath, L. Watts, E. Devred, T. Platt, C. Caverhill, and H. Maass, “Discrimination of diatoms from other phytoplankton using ocean-colour data,” Mar. Ecol. Prog. Ser. 272, 59–68 (2004).
[Crossref]

2003 (1)

G. Zeidner, C. M. Preston, E. F. Delong, R. Massana, A. F. Post, D. J. Scanlan, and O. Béjà, “Molecular diversity among marine picophytoplankton as revealed by psbA analyses,” Environ. Microbiol. 5(3), 212–216 (2003).
[Crossref] [PubMed]

2002 (6)

C. L. Sabine, R. M. Key, R. A. Feely, and D. Greeley, “Inorganic carbon in the Indian Ocean: distribution and dissolution processes,” Global Biogeochem. Cycles 16(4), 1–18 (2002).

Z. Lee, K. L. Carder, and R. A. Arnone, “Deriving inherent optical properties from water color: a multiband quasi-analytical algorithm for optically deep waters,” Appl. Opt. 41(27), 5755–5772 (2002).
[Crossref] [PubMed]

S. Maritorena, D. A. Siegel, and A. R. Peterson, “Optimization of a semianalytical ocean color model for global-scale applications,” Appl. Opt. 41(15), 2705–2714 (2002).
[Crossref] [PubMed]

R. Barlow, J. Aiken, P. Holligan, D. Cummings, S. Maritorena, and S. Hooker, “Phytoplankton pigment and absorption characteristics along meridional transects in the Atlantic Ocean,” Deep Sea Res. Part I Oceanogr. Res. Pap. 49(4), 637–660 (2002).
[Crossref]

W. S. Pegau, “Inherent optical properties of the central Arctic surface waters,” J. Geophys. Res. Oceans 107(10), 16 (2002).

A. M. Ciotti, M. R. Lewis, and J. J. Cullen, “Assessment of the relationships between dominant cell size in natural phytoplankton communities and the spectral shape of the absorption coefficient,” Limnol. Oceanogr. 47(2), 404–417 (2002).
[Crossref]

2001 (3)

F. Vidussi, H. Claustre, B. B. Manca, A. Luchetta, and J. C. Marty, “Phytoplankton pigment distribution in relation to upper thermocline circulation in the eastern Mediterranean Sea during winter,” J. Geophys. Res. Oceans 106(C9), 19939–19956 (2001).
[Crossref]

L. Van Heukelem and C. S. Thomas, “Computer-assisted high-performance liquid chromatography method development with applications to the isolation and analysis of phytoplankton pigments,” J. Chromatogr. A 910(1), 31–49 (2001).
[Crossref] [PubMed]

W. K. Li and P. M. Dickie, “Monitoring phytoplankton, bacterioplankton, and virioplankton in a coastal inlet (Bedford Basin) by flow cytometry,” Cytometry 44(3), 236–246 (2001).
[Crossref] [PubMed]

2000 (1)

C. C. Trees, D. K. Clark, R. R. Bidigare, M. E. Ondrusek, and J. L. Mueller, “Accessory pigments versus chlorophylla concentrations within the euphotic zone: a ubiquitous relationship,” Limnol. Oceanogr. 45(5), 1130–1143 (2000).
[Crossref]

1996 (2)

M. Mackey, D. Mackey, H. Higgins, and S. Wright, “CHEMTAX-a program for estimating class abundances from chemical markers: application to HPLC measurements of phytoplankton,” Mar. Ecol. Prog. Ser. 144, 265–283 (1996).
[Crossref]

F. E. Hoge and P. E. Lyon, “Satellite retrieval of inherent optical properties by linear matrix inversion of oceanic radiance models: an analysis of model and radiance measurement errors,” J. Geophys. Res. Oceans 101(C7), 16631–16648 (1996).
[Crossref]

1993 (2)

J. Cleveland and A. D. Weidemann, “Quantifying absorption by aquatic particles: A multiple scattering correction for glass fiber filters,” Limnol. Oceanogr. 38(6), 1321–1327 (1993).
[Crossref]

N. Hoepffner and S. Sathyendranath, “Determination of the major groups of phytoplankton pigments from the absorption spectra of total particulate matter,” J. Geophys. Res. Oceans 98(C12), 22789–22803 (1993).
[Crossref]

1991 (1)

N. Hoepffner and S. Sathyendranath, “Effect of pigment composition on absorption properties of phytoplankton,” Mar. Ecol. Prog. Ser. 73(1), 11–23 (1991).
[Crossref]

1988 (1)

J. M. Grebmeier, C. P. McRoy, and H. M. Feder, “Pelagic-benthic coupling on the shelf of the northern Bering and Chukchi Seas. I. Food supply source and benthic biomass,” Mar. Ecol. Prog. Ser. 48(1), 57–67 (1988).
[Crossref]

1987 (1)

S. Sathyendranath, L. Lazzara, and L. Prieur, “Variations in the spectral values of specific absorption of phytoplankton,” Limnol. Oceanogr. 32(2), 403–415 (1987).
[Crossref]

1985 (1)

M. Kishino, M. Takahashi, N. Okami, and S. Ichimura, “Estimation of the spectral absorption coefficients of phytoplankton in the sea,” Bull. Mar. Sci. 37(2), 634–642 (1985).

Ahn, Y.-H.

E. Siswanto, J. Tang, H. Yamaguchi, Y.-H. Ahn, J. Ishizaka, S. Yoo, S.-W. Kim, Y. Kiyomoto, K. Yamada, C. Chiang, and H. Kawamura, “Empirical ocean-color algorithms to retrieve chlorophyll-a, total suspended matter, and colored dissolved organic matter absorption coefficient in the Yellow and East China Seas,” J. Oceanogr. 67(5), 627–650 (2011).
[Crossref]

Aiken, J.

J. Aiken, Y. Pradhan, R. Barlow, S. Lavender, A. Poulton, P. Holligan, and N. Hardman-Mountford, “Phytoplankton pigments and functional types in the Atlantic Ocean: A decadal assessment, 1995–2005,” Deep Sea Res. Part II Top. Stud. Oceanogr. 56(15), 899–917 (2009).
[Crossref]

T. Hirata, J. Aiken, N. Hardman-Mountford, T. Smyth, and R. Barlow, “An absorption model to determine phytoplankton size classes from satellite ocean colour,” Remote Sens. Environ. 112(6), 3153–3159 (2008).
[Crossref]

R. Barlow, J. Aiken, P. Holligan, D. Cummings, S. Maritorena, and S. Hooker, “Phytoplankton pigment and absorption characteristics along meridional transects in the Atlantic Ocean,” Deep Sea Res. Part I Oceanogr. Res. Pap. 49(4), 637–660 (2002).
[Crossref]

Alvain, S.

C. B. Mouw, N. J. Hardman-Mountford, S. Alvain, A. Bracher, R. J. Brewin, A. Bricaud, A. M. Ciotti, E. Devred, A. Fujiwara, T. Hirata, T. Hirawake, T. S. Kostadinov, S. Roy, and J. Uitz, “A consumer’s guide to satellite remote sensing of multiple phytoplankton groups in the global ocean,” Front. Mar. Sci. 4, 41 (2017).
[Crossref]

S. Alvain, C. Moulin, Y. Dandonneau, and F. M. Bréon, “Remote sensing of phytoplankton groups in case 1 waters from global SeaWiFS imagery,” Deep Sea Res. Part I Oceanogr. Res. Pap. 52(11), 1989–2004 (2005).
[Crossref]

Arnone, R. A.

Aumont, O.

C. L. Quere, S. P. Harrison, I. Colin Prentice, E. T. Buitenhuis, O. Aumont, L. Bopp, H. Claustre, L. Cotrim Da Cunha, R. Geider, X. Giraud, C. Klaas, K. E. Kohfeld, L. Legendre, M. Manizza, T. Platt, R. B. Rivkin, S. Sathyendranath, J. Uitz, A. J. Watson, and D. Wolf-Gladrow, “Ecosystem dynamics based on plankton functional types for global ocean biogeochemistry models,” Glob. Change Biol. 11(11), 2016–2040 (2005).
[Crossref]

Babin, M.

P. Coupel, A. Matsuoka, D. Ruiz-Pino, M. Gosselin, D. Marie, J. É. Tremblay, and M. Babin, “Pigment signatures of phytoplankton communities in the Beaufort Sea,” Biogeosciences 12(4), 991–1006 (2015).
[Crossref]

Barlow, R.

J. Aiken, Y. Pradhan, R. Barlow, S. Lavender, A. Poulton, P. Holligan, and N. Hardman-Mountford, “Phytoplankton pigments and functional types in the Atlantic Ocean: A decadal assessment, 1995–2005,” Deep Sea Res. Part II Top. Stud. Oceanogr. 56(15), 899–917 (2009).
[Crossref]

T. Hirata, J. Aiken, N. Hardman-Mountford, T. Smyth, and R. Barlow, “An absorption model to determine phytoplankton size classes from satellite ocean colour,” Remote Sens. Environ. 112(6), 3153–3159 (2008).
[Crossref]

R. Barlow, J. Aiken, P. Holligan, D. Cummings, S. Maritorena, and S. Hooker, “Phytoplankton pigment and absorption characteristics along meridional transects in the Atlantic Ocean,” Deep Sea Res. Part I Oceanogr. Res. Pap. 49(4), 637–660 (2002).
[Crossref]

Béjà, O.

G. Zeidner, C. M. Preston, E. F. Delong, R. Massana, A. F. Post, D. J. Scanlan, and O. Béjà, “Molecular diversity among marine picophytoplankton as revealed by psbA analyses,” Environ. Microbiol. 5(3), 212–216 (2003).
[Crossref] [PubMed]

Bidigare, R. R.

C. C. Trees, D. K. Clark, R. R. Bidigare, M. E. Ondrusek, and J. L. Mueller, “Accessory pigments versus chlorophylla concentrations within the euphotic zone: a ubiquitous relationship,” Limnol. Oceanogr. 45(5), 1130–1143 (2000).
[Crossref]

Blondeau-Patissier, D.

Bopp, L.

C. L. Quere, S. P. Harrison, I. Colin Prentice, E. T. Buitenhuis, O. Aumont, L. Bopp, H. Claustre, L. Cotrim Da Cunha, R. Geider, X. Giraud, C. Klaas, K. E. Kohfeld, L. Legendre, M. Manizza, T. Platt, R. B. Rivkin, S. Sathyendranath, J. Uitz, A. J. Watson, and D. Wolf-Gladrow, “Ecosystem dynamics based on plankton functional types for global ocean biogeochemistry models,” Glob. Change Biol. 11(11), 2016–2040 (2005).
[Crossref]

Boss, E.

A. Chase, E. Boss, I. Cetinić, and W. Slade, “Estimation of phytoplankton accessory pigments from hyperspectral reflectance spectra: Toward a global algorithm,” J. Geophys. Res. Oceans 122(12), 97125–9743 (2017).
[Crossref]

Bouman, H.

A. Nair, S. Sathyendranath, T. Platt, J. Morales, V. Stuart, M.-H. Forget, E. Devred, and H. Bouman, “Remote sensing of phytoplankton functional types,” Remote Sens. Environ. 112(8), 3366–3375 (2008).
[Crossref]

Bouman, H. A.

A. Bracher, H. A. Bouman, R. J. Brewin, A. Bricaud, V. Brotas, A. M. Ciotti, L. Clementson, E. Devred, A. Di Cicco, S. Dutkiewicz, N. J. Hardman-Mountford, A. E. Hickman, M. Hieronymi, T. Hirata, S. N. Losa, C. B. Mouw, E. Organelli, D. E. Raitsos, J. Uitz, M. Vogt, and A. Wolanin, “Obtaining phytoplankton diversity from ocean color: a scientific roadmap for future development,” Front. Mar. Sci. 4, 55 (2017).
[Crossref]

Bouvet, H. A.

P. Coupel, H. Y. Jin, M. Joo, R. Horner, H. A. Bouvet, M. A. Sicre, J. C. Gascard, J. F. Chen, V. Garçon, and D. Ruiz-Pino, “Phytoplankton distribution in unusually low sea ice cover over the Pacific Arctic,” Biogeosciences 9(11), 4835–4850 (2012).
[Crossref]

Boyce, D. G.

D. G. Boyce, M. R. Lewis, and B. Worm, “Global phytoplankton decline over the past century,” Nature 466(7306), 591–596 (2010).
[Crossref] [PubMed]

Bracher, A.

C. B. Mouw, N. J. Hardman-Mountford, S. Alvain, A. Bracher, R. J. Brewin, A. Bricaud, A. M. Ciotti, E. Devred, A. Fujiwara, T. Hirata, T. Hirawake, T. S. Kostadinov, S. Roy, and J. Uitz, “A consumer’s guide to satellite remote sensing of multiple phytoplankton groups in the global ocean,” Front. Mar. Sci. 4, 41 (2017).
[Crossref]

T. S. Kostadinov, A. Cabré, H. Vedantham, I. Marinov, A. Bracher, R. J. Brewin, A. Bricaud, T. Hirata, T. Hirawake, N. J. Hardman-Mountford, C. Mouw, S. Roy, and J. Uitz, “Inter-comparison of phytoplankton functional type phenology metrics derived from ocean color algorithms and earth system models,” Remote Sens. Environ. 190, 162–177 (2017).
[Crossref]

A. Bracher, H. A. Bouman, R. J. Brewin, A. Bricaud, V. Brotas, A. M. Ciotti, L. Clementson, E. Devred, A. Di Cicco, S. Dutkiewicz, N. J. Hardman-Mountford, A. E. Hickman, M. Hieronymi, T. Hirata, S. N. Losa, C. B. Mouw, E. Organelli, D. E. Raitsos, J. Uitz, M. Vogt, and A. Wolanin, “Obtaining phytoplankton diversity from ocean color: a scientific roadmap for future development,” Front. Mar. Sci. 4, 55 (2017).
[Crossref]

Bréon, F. M.

S. Alvain, C. Moulin, Y. Dandonneau, and F. M. Bréon, “Remote sensing of phytoplankton groups in case 1 waters from global SeaWiFS imagery,” Deep Sea Res. Part I Oceanogr. Res. Pap. 52(11), 1989–2004 (2005).
[Crossref]

Brewin, R. J.

A. Bracher, H. A. Bouman, R. J. Brewin, A. Bricaud, V. Brotas, A. M. Ciotti, L. Clementson, E. Devred, A. Di Cicco, S. Dutkiewicz, N. J. Hardman-Mountford, A. E. Hickman, M. Hieronymi, T. Hirata, S. N. Losa, C. B. Mouw, E. Organelli, D. E. Raitsos, J. Uitz, M. Vogt, and A. Wolanin, “Obtaining phytoplankton diversity from ocean color: a scientific roadmap for future development,” Front. Mar. Sci. 4, 55 (2017).
[Crossref]

T. S. Kostadinov, A. Cabré, H. Vedantham, I. Marinov, A. Bracher, R. J. Brewin, A. Bricaud, T. Hirata, T. Hirawake, N. J. Hardman-Mountford, C. Mouw, S. Roy, and J. Uitz, “Inter-comparison of phytoplankton functional type phenology metrics derived from ocean color algorithms and earth system models,” Remote Sens. Environ. 190, 162–177 (2017).
[Crossref]

C. B. Mouw, N. J. Hardman-Mountford, S. Alvain, A. Bracher, R. J. Brewin, A. Bricaud, A. M. Ciotti, E. Devred, A. Fujiwara, T. Hirata, T. Hirawake, T. S. Kostadinov, S. Roy, and J. Uitz, “A consumer’s guide to satellite remote sensing of multiple phytoplankton groups in the global ocean,” Front. Mar. Sci. 4, 41 (2017).
[Crossref]

D. Müller, H. Krasemann, R. J. Brewin, C. Brockmann, P.-Y. Deschamps, R. Doerffer, N. Fomferra, B. A. Franz, M. G. Grant, S. B. Groom, F. Mélin, T. Platt, P. Regner, S. Sathyendranath, F. Steinmetz, and J. Swinton, “The Ocean Colour Climate Change Initiative: I. A methodology for assessing atmospheric correction processors based on in-situ measurements,” Remote Sens. Environ. 162, 242–256 (2015).
[Crossref]

R. J. Brewin, N. J. Hardman-Mountford, S. J. Lavender, D. E. Raitsos, T. Hirata, J. Uitz, E. Devred, A. Bricaud, A. Ciotti, and B. Gentili, “An intercomparison of bio-optical techniques for detecting dominant phytoplankton size class from satellite remote sensing,” Remote Sens. Environ. 115(2), 325–339 (2011).
[Crossref]

Bricaud, A.

A. Bracher, H. A. Bouman, R. J. Brewin, A. Bricaud, V. Brotas, A. M. Ciotti, L. Clementson, E. Devred, A. Di Cicco, S. Dutkiewicz, N. J. Hardman-Mountford, A. E. Hickman, M. Hieronymi, T. Hirata, S. N. Losa, C. B. Mouw, E. Organelli, D. E. Raitsos, J. Uitz, M. Vogt, and A. Wolanin, “Obtaining phytoplankton diversity from ocean color: a scientific roadmap for future development,” Front. Mar. Sci. 4, 55 (2017).
[Crossref]

C. B. Mouw, N. J. Hardman-Mountford, S. Alvain, A. Bracher, R. J. Brewin, A. Bricaud, A. M. Ciotti, E. Devred, A. Fujiwara, T. Hirata, T. Hirawake, T. S. Kostadinov, S. Roy, and J. Uitz, “A consumer’s guide to satellite remote sensing of multiple phytoplankton groups in the global ocean,” Front. Mar. Sci. 4, 41 (2017).
[Crossref]

T. S. Kostadinov, A. Cabré, H. Vedantham, I. Marinov, A. Bracher, R. J. Brewin, A. Bricaud, T. Hirata, T. Hirawake, N. J. Hardman-Mountford, C. Mouw, S. Roy, and J. Uitz, “Inter-comparison of phytoplankton functional type phenology metrics derived from ocean color algorithms and earth system models,” Remote Sens. Environ. 190, 162–177 (2017).
[Crossref]

R. J. Brewin, N. J. Hardman-Mountford, S. J. Lavender, D. E. Raitsos, T. Hirata, J. Uitz, E. Devred, A. Bricaud, A. Ciotti, and B. Gentili, “An intercomparison of bio-optical techniques for detecting dominant phytoplankton size class from satellite remote sensing,” Remote Sens. Environ. 115(2), 325–339 (2011).
[Crossref]

A. Bricaud, C. Mejia, D. Blondeau-Patissier, H. Claustre, M. Crepon, and S. Thiria, “Retrieval of pigment concentrations and size structure of algal populations from their absorption spectra using multilayered perceptrons,” Appl. Opt. 46(8), 1251–1260 (2007).
[Crossref] [PubMed]

A. Bricaud, H. Claustre, J. Ras, and K. Oubelkheir, “Natural variability of phytoplanktonic absorption in oceanic waters: Influence of the size structure of algal populations,” J. Geophys. Res. Oceans 109(11), 45–50 (2004).

Brockmann, C.

D. Müller, H. Krasemann, R. J. Brewin, C. Brockmann, P.-Y. Deschamps, R. Doerffer, N. Fomferra, B. A. Franz, M. G. Grant, S. B. Groom, F. Mélin, T. Platt, P. Regner, S. Sathyendranath, F. Steinmetz, and J. Swinton, “The Ocean Colour Climate Change Initiative: I. A methodology for assessing atmospheric correction processors based on in-situ measurements,” Remote Sens. Environ. 162, 242–256 (2015).
[Crossref]

Brotas, V.

A. Bracher, H. A. Bouman, R. J. Brewin, A. Bricaud, V. Brotas, A. M. Ciotti, L. Clementson, E. Devred, A. Di Cicco, S. Dutkiewicz, N. J. Hardman-Mountford, A. E. Hickman, M. Hieronymi, T. Hirata, S. N. Losa, C. B. Mouw, E. Organelli, D. E. Raitsos, J. Uitz, M. Vogt, and A. Wolanin, “Obtaining phytoplankton diversity from ocean color: a scientific roadmap for future development,” Front. Mar. Sci. 4, 55 (2017).
[Crossref]

Buitenhuis, E. T.

C. L. Quere, S. P. Harrison, I. Colin Prentice, E. T. Buitenhuis, O. Aumont, L. Bopp, H. Claustre, L. Cotrim Da Cunha, R. Geider, X. Giraud, C. Klaas, K. E. Kohfeld, L. Legendre, M. Manizza, T. Platt, R. B. Rivkin, S. Sathyendranath, J. Uitz, A. J. Watson, and D. Wolf-Gladrow, “Ecosystem dynamics based on plankton functional types for global ocean biogeochemistry models,” Glob. Change Biol. 11(11), 2016–2040 (2005).
[Crossref]

Cabré, A.

T. S. Kostadinov, A. Cabré, H. Vedantham, I. Marinov, A. Bracher, R. J. Brewin, A. Bricaud, T. Hirata, T. Hirawake, N. J. Hardman-Mountford, C. Mouw, S. Roy, and J. Uitz, “Inter-comparison of phytoplankton functional type phenology metrics derived from ocean color algorithms and earth system models,” Remote Sens. Environ. 190, 162–177 (2017).
[Crossref]

Carder, K. L.

Casey, N. W.

W. W. Gregg and N. W. Casey, “Global and regional evaluation of the SeaWiFS chlorophyll data set,” Remote Sens. Environ. 93(4), 463–479 (2004).
[Crossref]

Caverhill, C.

S. Sathyendranath, L. Watts, E. Devred, T. Platt, C. Caverhill, and H. Maass, “Discrimination of diatoms from other phytoplankton using ocean-colour data,” Mar. Ecol. Prog. Ser. 272, 59–68 (2004).
[Crossref]

Cetinic, I.

A. Chase, E. Boss, I. Cetinić, and W. Slade, “Estimation of phytoplankton accessory pigments from hyperspectral reflectance spectra: Toward a global algorithm,” J. Geophys. Res. Oceans 122(12), 97125–9743 (2017).
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H. Zhang, S. Wang, Z. Qiu, D. Sun, J. Ishizaka, S. Sun, and Y. He, “Phytoplankton size class in the East China Sea derived from MODIS satellite data,” Biogeosciences 15(13), 4271–4289 (2018).
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H. Zhang, S. Wang, Z. Qiu, D. Sun, J. Ishizaka, S. Sun, and Y. He, “Phytoplankton size class in the East China Sea derived from MODIS satellite data,” Biogeosciences 15(13), 4271–4289 (2018).
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A. Fujiwara, T. Hirawake, K. Suzuki, and S. I. Saitoh, “Remote sensing of size structure of phytoplankton communities using optical properties of the Chukchi and Bering Sea shelf region,” Biogeosciences 8(12), 3567–3580 (2011).
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Tang, J.

E. Siswanto, J. Tang, H. Yamaguchi, Y.-H. Ahn, J. Ishizaka, S. Yoo, S.-W. Kim, Y. Kiyomoto, K. Yamada, C. Chiang, and H. Kawamura, “Empirical ocean-color algorithms to retrieve chlorophyll-a, total suspended matter, and colored dissolved organic matter absorption coefficient in the Yellow and East China Seas,” J. Oceanogr. 67(5), 627–650 (2011).
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P. G. Falkowski, M. E. Katz, A. H. Knoll, A. Quigg, J. A. Raven, O. Schofield, and F. J. Taylor, “The evolution of modern eukaryotic phytoplankton,” Science 305(5682), 354–360 (2004).
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P. Coupel, A. Matsuoka, D. Ruiz-Pino, M. Gosselin, D. Marie, J. É. Tremblay, and M. Babin, “Pigment signatures of phytoplankton communities in the Beaufort Sea,” Biogeosciences 12(4), 991–1006 (2015).
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Tsuda, A.

K. Suzuki, A. Hinuma, H. Saito, H. Kiyosawa, H. Liu, T. Saino, and A. Tsuda, “Responses of phytoplankton and heterotrophic bacteria in the northwest subarctic Pacific to in situ iron fertilization as estimated by HPLC pigment analysis and flow cytometry,” Prog. Oceanogr. 64(2–4), 167–187 (2005).
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Uitz, J.

A. Bracher, H. A. Bouman, R. J. Brewin, A. Bricaud, V. Brotas, A. M. Ciotti, L. Clementson, E. Devred, A. Di Cicco, S. Dutkiewicz, N. J. Hardman-Mountford, A. E. Hickman, M. Hieronymi, T. Hirata, S. N. Losa, C. B. Mouw, E. Organelli, D. E. Raitsos, J. Uitz, M. Vogt, and A. Wolanin, “Obtaining phytoplankton diversity from ocean color: a scientific roadmap for future development,” Front. Mar. Sci. 4, 55 (2017).
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C. B. Mouw, N. J. Hardman-Mountford, S. Alvain, A. Bracher, R. J. Brewin, A. Bricaud, A. M. Ciotti, E. Devred, A. Fujiwara, T. Hirata, T. Hirawake, T. S. Kostadinov, S. Roy, and J. Uitz, “A consumer’s guide to satellite remote sensing of multiple phytoplankton groups in the global ocean,” Front. Mar. Sci. 4, 41 (2017).
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T. S. Kostadinov, A. Cabré, H. Vedantham, I. Marinov, A. Bracher, R. J. Brewin, A. Bricaud, T. Hirata, T. Hirawake, N. J. Hardman-Mountford, C. Mouw, S. Roy, and J. Uitz, “Inter-comparison of phytoplankton functional type phenology metrics derived from ocean color algorithms and earth system models,” Remote Sens. Environ. 190, 162–177 (2017).
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R. J. Brewin, N. J. Hardman-Mountford, S. J. Lavender, D. E. Raitsos, T. Hirata, J. Uitz, E. Devred, A. Bricaud, A. Ciotti, and B. Gentili, “An intercomparison of bio-optical techniques for detecting dominant phytoplankton size class from satellite remote sensing,” Remote Sens. Environ. 115(2), 325–339 (2011).
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J. Uitz, H. Claustre, A. Morel, and S. B. Hooker, “Vertical distribution of phytoplankton communities in open ocean: an assessment based on surface chlorophyll,” J. Geophys. Res. 111(C8), C08005 (2006).
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C. L. Quere, S. P. Harrison, I. Colin Prentice, E. T. Buitenhuis, O. Aumont, L. Bopp, H. Claustre, L. Cotrim Da Cunha, R. Geider, X. Giraud, C. Klaas, K. E. Kohfeld, L. Legendre, M. Manizza, T. Platt, R. B. Rivkin, S. Sathyendranath, J. Uitz, A. J. Watson, and D. Wolf-Gladrow, “Ecosystem dynamics based on plankton functional types for global ocean biogeochemistry models,” Glob. Change Biol. 11(11), 2016–2040 (2005).
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Van Heukelem, L.

L. Van Heukelem and C. S. Thomas, “Computer-assisted high-performance liquid chromatography method development with applications to the isolation and analysis of phytoplankton pigments,” J. Chromatogr. A 910(1), 31–49 (2001).
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F. Vidussi, H. Claustre, B. B. Manca, A. Luchetta, and J. C. Marty, “Phytoplankton pigment distribution in relation to upper thermocline circulation in the eastern Mediterranean Sea during winter,” J. Geophys. Res. Oceans 106(C9), 19939–19956 (2001).
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H. Zhang, S. Wang, Z. Qiu, D. Sun, J. Ishizaka, S. Sun, and Y. He, “Phytoplankton size class in the East China Sea derived from MODIS satellite data,” Biogeosciences 15(13), 4271–4289 (2018).
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H. Zhang, Z. Qiu, D. Sun, S. Wang, and Y. He, “Seasonal and interannual variability of satellite-derived chlorophyll-a (2000–2012) in the Bohai Sea, China,” Remote Sens. 9(6), 582 (2017).
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S. Sathyendranath, L. Watts, E. Devred, T. Platt, C. Caverhill, and H. Maass, “Discrimination of diatoms from other phytoplankton using ocean-colour data,” Mar. Ecol. Prog. Ser. 272, 59–68 (2004).
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J. Cleveland and A. D. Weidemann, “Quantifying absorption by aquatic particles: A multiple scattering correction for glass fiber filters,” Limnol. Oceanogr. 38(6), 1321–1327 (1993).
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A. Bracher, H. A. Bouman, R. J. Brewin, A. Bricaud, V. Brotas, A. M. Ciotti, L. Clementson, E. Devred, A. Di Cicco, S. Dutkiewicz, N. J. Hardman-Mountford, A. E. Hickman, M. Hieronymi, T. Hirata, S. N. Losa, C. B. Mouw, E. Organelli, D. E. Raitsos, J. Uitz, M. Vogt, and A. Wolanin, “Obtaining phytoplankton diversity from ocean color: a scientific roadmap for future development,” Front. Mar. Sci. 4, 55 (2017).
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C. L. Quere, S. P. Harrison, I. Colin Prentice, E. T. Buitenhuis, O. Aumont, L. Bopp, H. Claustre, L. Cotrim Da Cunha, R. Geider, X. Giraud, C. Klaas, K. E. Kohfeld, L. Legendre, M. Manizza, T. Platt, R. B. Rivkin, S. Sathyendranath, J. Uitz, A. J. Watson, and D. Wolf-Gladrow, “Ecosystem dynamics based on plankton functional types for global ocean biogeochemistry models,” Glob. Change Biol. 11(11), 2016–2040 (2005).
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M. Mackey, D. Mackey, H. Higgins, and S. Wright, “CHEMTAX-a program for estimating class abundances from chemical markers: application to HPLC measurements of phytoplankton,” Mar. Ecol. Prog. Ser. 144, 265–283 (1996).
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G. Zheng and D. Stramski, “A model based on stacked constraints approach for partitioning the light absorption coefficient of seawater into phytoplankton and nonphytoplankton components,” J. Geophys. Res. Oceans 118(4), 2155–2174 (2013).
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L. Zheng, Z. Qiu, Y. Zhou, D. Sun, S. Wang, W. Wu, and W. Perrie, “Comparisons of algorithms to estimate water turbidity in the coastal areas of China,” Int. J. Remote Sens. 37(24), 6165–6186 (2016).
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L. Zheng, Z. Qiu, Y. Zhou, D. Sun, S. Wang, W. Wu, and W. Perrie, “Comparisons of algorithms to estimate water turbidity in the coastal areas of China,” Int. J. Remote Sens. 37(24), 6165–6186 (2016).
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Appl. Opt. (4)

Biogeosciences (4)

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G. Zeidner, C. M. Preston, E. F. Delong, R. Massana, A. F. Post, D. J. Scanlan, and O. Béjà, “Molecular diversity among marine picophytoplankton as revealed by psbA analyses,” Environ. Microbiol. 5(3), 212–216 (2003).
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C. L. Quere, S. P. Harrison, I. Colin Prentice, E. T. Buitenhuis, O. Aumont, L. Bopp, H. Claustre, L. Cotrim Da Cunha, R. Geider, X. Giraud, C. Klaas, K. E. Kohfeld, L. Legendre, M. Manizza, T. Platt, R. B. Rivkin, S. Sathyendranath, J. Uitz, A. J. Watson, and D. Wolf-Gladrow, “Ecosystem dynamics based on plankton functional types for global ocean biogeochemistry models,” Glob. Change Biol. 11(11), 2016–2040 (2005).
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L. Zheng, Z. Qiu, Y. Zhou, D. Sun, S. Wang, W. Wu, and W. Perrie, “Comparisons of algorithms to estimate water turbidity in the coastal areas of China,” Int. J. Remote Sens. 37(24), 6165–6186 (2016).
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E. Siswanto, J. Tang, H. Yamaguchi, Y.-H. Ahn, J. Ishizaka, S. Yoo, S.-W. Kim, Y. Kiyomoto, K. Yamada, C. Chiang, and H. Kawamura, “Empirical ocean-color algorithms to retrieve chlorophyll-a, total suspended matter, and colored dissolved organic matter absorption coefficient in the Yellow and East China Seas,” J. Oceanogr. 67(5), 627–650 (2011).
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Prog. Oceanogr. (1)

K. Suzuki, A. Hinuma, H. Saito, H. Kiyosawa, H. Liu, T. Saino, and A. Tsuda, “Responses of phytoplankton and heterotrophic bacteria in the northwest subarctic Pacific to in situ iron fertilization as estimated by HPLC pigment analysis and flow cytometry,” Prog. Oceanogr. 64(2–4), 167–187 (2005).
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H. Zhang, Z. Qiu, D. Sun, S. Wang, and Y. He, “Seasonal and interannual variability of satellite-derived chlorophyll-a (2000–2012) in the Bohai Sea, China,” Remote Sens. 9(6), 582 (2017).
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H. Xi, M. Hieronymi, R. Röttgers, H. Krasemann, and Z. Qiu, “Hyperspectral differentiation of phytoplankton taxonomic groups: A comparison between using remote sensing reflectance and absorption spectra,” Remote Sens. 7(11), 14781–14805 (2015).
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A. Nair, S. Sathyendranath, T. Platt, J. Morales, V. Stuart, M.-H. Forget, E. Devred, and H. Bouman, “Remote sensing of phytoplankton functional types,” Remote Sens. Environ. 112(8), 3366–3375 (2008).
[Crossref]

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[Crossref] [PubMed]

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Figures (9)

Fig. 1
Fig. 1 Locations of the sampling stations in the Chukchi and Bering Seas.
Fig. 2
Fig. 2 Distribution of the relative contributions of nine taxonomic groups to C derived from CHEMTAX (a) and their average contributions (b). These measurements were collected at different times of year over multiple years as described above.
Fig. 3
Fig. 3 The specific absorption spectra of individual phytoplankton taxonomic groups (top) and spectra that were normalized to the value of absorption coefficient at 443 nm (bottom) for the three cases.
Fig. 4
Fig. 4 A comparison of the specific absorption spectra of four groups (diatoms, dinoflagellates, c3-flagellates, and hapto-7) for the different cases.
Fig. 5
Fig. 5 The determination coefficients (R2) (a), linear regression slope (b), RMSE (c), and MAPE (d) from comparison of the reconstructed with measured aph(λ) for the three cases.
Fig. 6
Fig. 6 Comparison of the estimated versus measured Ci for the PTGs in Case 1 (a), Case 2 (b), and Case 3 (c). Blue solid points represent the samples where the total CTC value of the three excluded groups is above 20%. Black dashed lines are the 1:1 lines.
Fig. 7
Fig. 7 R2 (a), RMSE (b), and MAPE (c) of the aph-LMM approach performed on measured aph(λ) with different combinations of MODIS wavebands. Table of MODIS bands combination (d). ‘-’ means the removed band.
Fig. 8
Fig. 8 The samples and their contributions to C (%) used for computing a*i,HPLC (a). The numbers in bar represent the CTC of a given dominant taxonomic group. Comparison of the obtained a*i,LMM (solid curves) with the a*i,HPLC (dashed curves) (b).
Fig. 9
Fig. 9 The derived aph* of diatoms and pigment-specific absorption spectral of fucoxanthin (a); the derived aph* of two prasino types and pigment-specific absorption spectra of zeaxanthin and chlorophyll b (b). These pigment-specific absorption spectra were obtained from Bricaud et al. [21].

Tables (5)

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Table 1 List of phytoplankton pigments and their taxonomic significance and pigments formulae [13,39]. The name of the twelve pigments used in CHEMTAX to distinguish between nine phytoplankton groups are highlighted in bold.

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Table 2 Initial ratio matrices for CHEMTAX analysis. Pigment abbreviations are shown in Table 1. Here Chryso-Pelago: chrysophytes and pelagophytes; Hapto-7: haptophytes type 7; Prasino-3: prasinophytes type 3; Prasino-2: prasinophytes type 2.

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Table 3 Final ratio matrices for CHEMTAX analysis. Abbreviations in this table are same as Table 2.

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Table 4 Three cases for phytoplankton taxonomic group assemblages used in this study. Here prasino represents the combination of prasino-2 and prasino-3; Hapto-Prasino represents the combination of hapto-7 and prasino.

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Table 5 Statistical results of Fig. 6. P-values from the significance level tests were both less than 0.001.

Equations (7)

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a p h = i = 1 m C i a i * ( λ )
( C i = 1 , j = 1 C i = m , j = 1 C i = 1 , j = n C i = m , j = n ) ( a ˜ i = 1 * ( λ ) a ˜ i = m * ( λ ) ) = ( a p h , j = 1 ( λ ) a p h , j = n ( λ ) )
C A * = A p h
min ( 1 2 C A * A p h 2 2 )
( a i = 1 , L M M * ( λ = 1 ) a i = m , L M M * ( λ = 1 ) a i = 1 , L M M * ( λ = k ) a i = m , L M M * ( λ = k ) ) ( C i = 1 C i = m ) = ( a p h ( λ = 1 ) a p h ( λ = k ) )
R M S E = 1 n i = 1 n [ ( x i e x i m ) / x i m ] 2
M A P E ( % ) = 1 n i = 1 n | ( x i e x i m ) / x i m | × 100 %

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