# Retrieval of Phytoplankton Pigments from Underway Spectrophotometry in the Fram Strait

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## Abstract

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## 1. Introduction

## 2. Data and Methods

#### 2.1. Data Collection

#### 2.2. Retrieval of Phytoplankton Pigments

#### 2.2.1. Gaussian Decomposition

#### 2.2.2. Matrix Inversion Technique

#### Singular Value Decomposition—Non-Negative Least Squares (SVD-NNLS)

#### Non-Negative Least Squares—Non-Negative Least Squares (NNLS-NNLS)

#### Sensitivity Analysis

#### 2.2.3. Normalization of ${a}_{ph}\left(\lambda \right)$ by Pigment Package Effect

#### 2.2.4. Statistics

## 3. Results

#### 3.1. Characteristics of the Pigment Retrieval Data Set

#### 3.2. Gaussian Decomposition

#### 3.3. Matrix Inversion Technique

#### 3.3.1. The Number of Pigment Types to Be Estimated

#### 3.3.2. SVD-NNLS

#### 3.3.3. Intercomparison between SVD-NNLS Applications

#### 3.3.4. Feasibility of SVD-NNLS-9 for Multispectral ${a}_{ph}\left(\lambda \right)$

#### 3.4. Gaussian Decomposition versus SVD-NNLS

## 4. Discussion

#### 4.1. Gaussian Decomposition

#### 4.2. Matrix Inversion Technique

#### 4.3. Applications

## 5. Conclusions

## Supplementary Materials

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## Abbreviations

Symbol | Description |

${a}_{gaus}\left(\lambda \right)$ | Gaussian absorption coefficient (Equation (2)) |

${a}_{NAP}\left(\lambda \right)$ | spectral absorption coefficient by non-algal particles |

${a}_{p}\left(\lambda \right)$ | spectral particulate absorption coefficient |

${a}_{ph}\left(\lambda \right)$ | spectral phytoplankton absorption coefficient |

${\widehat{a}}_{ph}\left(\lambda \right)$ | pigment package effect normalized ${a}_{ph}\left(\lambda \right)$ (Equation (7)) |

A${}_{ph}$ | matrix of ${a}_{ph}\left(\lambda \right)$ (Equations (4) and (5)) |

${a}^{*}\left(\lambda \right)$ | real or measured pigment-specific absorption coefficient |

${\tilde{a}}^{*}\left(\lambda \right)$ | SVD or NNLS derived pigment-specific absorption coefficient (Equations (4) and (5)) |

${\tilde{a}}^{*+}\left(\lambda \right)$ | absolute values of ${\tilde{a}}^{*}\left(\lambda \right)$ (Equation (6)) |

$\left|\right|{\tilde{a}}^{*}\left(\lambda \right)\left|\right|$ | norm of ${\tilde{a}}^{*}\left(\lambda \right)$ (Equation (6)) |

$\tilde{\mathrm{A}}$ | matrix of ${\tilde{a}}^{*}\left(\lambda \right)$ (Equations (4) and (5)) |

A | regression coefficient of pigment concentration-${a}_{gaus}\left({\lambda}_{0}\right)$ power relationship (Equation (3)) |

B | regression coefficient (power) of pigment concentration-${a}_{gaus}\left({\lambda}_{0}\right)$ power relationship |

(Equation (3)) | |

c | HPLC derived pigment concentration |

C | matrix of c (Equation (4)) |

C${}^{+}$ | Moore–Penrose pseudoinverse of matrix C |

${c}_{TChl-a}$ | HPLC derived TChl-a concentration |

${\tilde{c}}^{*}$ | estimated pigment concentration |

$\tilde{C}$ | matrix of ${\tilde{c}}^{*}$ (Equation (5)) |

CD | quartile coefficient of dispersion |

m | number of pigment types |

MAE | mean absolute error (Equation (8)) |

MPE | median absolute percentage error (Equation (9)) |

n | number of samples |

${n}_{cond}$ | condition number of matrix C |

${R}^{2}$ | determination coefficient |

S | spectral exponent of ${a}_{NAP}\left(\lambda \right)$ (Equation (1)) |

$SI$ | similarity index between two ${\tilde{a}}^{*+}\left(\lambda \right)$ (Equation (6)) |

Spearman’s $\rho $ | Spearman${}^{\prime}$s rank correlation coefficient |

${Q}_{a}^{*}\left(\lambda \right)$ | pigment package effect index |

${\lambda}_{0}$ | peak wavelength of a Gaussian function |

$\sigma $ | width of a Gaussian function |

${\sigma}_{SD}\left(\lambda \right)$ | standard deviation of the 20-minute averaged matched AC-S ${a}_{p}\left(\lambda \right)$ spectra (Equation (2)) |

${\chi}^{2}$ | cost function of Gaussian decomposition (Equation (2)) |

## Appendix A. Cross-Validation Results of NNLS-NNLS

**(a)**NNLS-NNLS-6 (${a}_{\mathit{ph}}\left(\lambda \right)$ Based) and NNLS-NNLS-9 (${\widehat{a}}_{\mathit{ph}}\left(\lambda \right)$ Based)

Pigments | Perturb 1 ${}^{\mathbf{a}}$ | Perturb 2 ${}^{\mathbf{a}}$ | Perturb 3 ${}^{\mathbf{a}}$ | Perturb 1 ${}^{\mathbf{b}}$ | Perturb 2 ${}^{\mathbf{b}}$ | Perturb 3 ${}^{\mathbf{b}}$ | ||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|

MAE | MPE | MAE | MPE | MAE | MPE | MAE | MPE | MAE | MPE | MAE | MPE | |

TChl-a | 0.22(0.16) | 24.2 | 0.22(0.17) | 21.5 | 0.22(0.16) | 23.6 | 0.05(0.04) | 4.2 | 0.07(0.05) | 6.6 | 0.08(0.05) | 6.6 |

TChl-b | - | - | - | - | - | - | 0.03(0.24) | 64.4 | 0.03(0.24) | 55.2 | 0.03(0.24) | 58.2 |

Chl-c1/2 | - | - | - | - | - | - | 0.11(0.32) | 59.7 | 0.12(0.34) | 66.6 | 0.12(0.33) | 69.6 |

But | - | - | - | - | - | - | 0.03(0.22) | 82.2 | 0.03(0.22) | 76.0 | 0.03(0.23) | 79.6 |

Diadino | 0.14(0.38) | 267.8 | 0.45(0.43) | 2496 | 0.15(0.37) | 210.4 | 0.33(0.60) | 238.2 | 0.21(0.48) | 161.2 | 0.23(0.48) | 222.3 |

Fuco | 0.10(0.27) | 46.5 | 0.10(0.27) | 46.0 | 0.10(0.27) | 46.4 | 0.13(0.22) | 61.8 | 0.11(0.20) | 50.1 | 0.13(0.21) | 60.1 |

Hex | 0.10(0.23) | 57.4 | 0.13(0.24) | 61.0 | 0.14(0.25) | 65.3 | 0.09(0.20) | 45.4 | 0.08(0.21) | 42.1 | 0.09(0.21) | 49.1 |

Peri | 0.04(0.25) | 185.5 | 0.04(0.25) | 164.7 | 0.04(0.24) | 162.2 | 0.02(0.13) | 67.4 | 0.02(0.20) | 104.0 | 0.02(0.19) | 91.9 |

Pheo-a | 0.01(0.02) | 88.5 | 0.02(0.02) | 94.3 | 0.02(0.02) | 97.4 | 0.07(0.05) | 322.9 | 0.05(0.05) | 231.7 | 0.05(0.05) | 234.1 |

Pigments | Perturb 1 ${}^{\mathbf{a}}$ | Perturb 2 ${}^{\mathbf{a}}$ | Perturb 3 ${}^{\mathbf{a}}$ | |||
---|---|---|---|---|---|---|

MAE | MPE | MAE | MPE | MAE | MPE | |

TChl-a | 0.21(0.14) | 22.0 | 0.18(0.12) | 18.4 | 0.21(0.07) | 21.5 |

TChl-b | 0.04(0.31) | 71.9 | 0.04(0.29) | 62.5 | 0.04(0.27) | 64.2 |

Chl-c1/2 | 0.06(0.22) | 34.1 | 0.06(0.21) | 32.4 | 0.06(0.30) | 34.4 |

PPC | 0.18(0.27) | 96.1 | 0.18(0.28) | 85.0 | 0.17(0.22) | 81.5 |

PSC | 0.21(0.20) | 46.0 | 0.20(0.20) | 41.0 | 0.22(0.22) | 45.2 |

Pigments | Perturb 1 ${}^{\mathbf{a}}$ | Perturb 2 ${}^{\mathbf{a}}$ | Perturb 3 ${}^{\mathbf{a}}$ | Perturb 1 ${}^{\mathbf{b}}$ | Perturb 2 ${}^{\mathbf{b}}$ | Perturb 3 ${}^{\mathbf{b}}$ | ||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|

MAE | MPE | MAE | MPE | MAE | MPE | MAE | MPE | MAE | MPE | MAE | MPE | |

TChl-a | 0.25(0.15) | 26.6 | 0.24(0.15) | 26.0 | 0.25(0.15) | 26.9 | 0.08(0.05) | 5.54 | 0.10(0.06) | 8.1 | 0.10(0.06) | 8.1 |

Chl-c1/2 | 0.05(0.20) | 35.0 | 0.05(0.20) | 35.1 | 0.06(0.21) | 35.7 | 0.06(0.22) | 38.6 | 0.06(0.23) | 41.5 | 0.06(0.23) | 43.1 |

Diadino | 0.14(0.44) | 189.3 | 0.14(0.43) | 188.8 | 0.14(0.43) | 186.0 | 0.10(0.31) | 118.1 | 0.10(0.31) | 117.3 | 0.10(0.32) | 117.4 |

Hex | 0.17(0.35) | 46.2 | 0.17(0.35) | 47.3 | 0.17(0.35) | 48.7 | 0.23(0.37) | 123.1 | 0.24(0.37) | 114.3 | 0.24(0.37) | 110.8 |

## References

- Field, C.B.; Behrenfeld, M.J.; Randerson, J.T.; Falkowski, P. Primary production of the biosphere: Integrating terrestrial and oceanic components. Science
**1998**, 281, 237–240. [Google Scholar] [CrossRef] [PubMed] - Jeffrey, S.W.; Wright, S.W.; Zapata, M. Microalgal classes and their signature pigments. In Phytoplankton Pigments: Characterization, Chemotaxonomy and Applications in Oceanography; Roy, S., Llewellyn, C.A., Egeland, E.S., Johnsen, G., Eds.; Cambridge University Press: Cambridge, UK, 2011; pp. 3–77. [Google Scholar]
- Zhao, K.; Porra, R.J.; Scheer, H. Phycobiliproteins. In Phytoplankton Pigments: Characterization, Chemotaxonomy and Applications in Oceanography; Roy, S., Llewellyn, C.A., Egeland, E.S., Johnsen, G., Eds.; Cambridge University Press: Cambridge, UK, 2011; pp. 375–411. [Google Scholar]
- Müller, P.; Li, X.P.; Niyogi, K.K. Non-photochemical quenching. A response to excess light energy. Plant Physiol.
**2001**, 125, 1558–1566. [Google Scholar] [CrossRef] [PubMed] - Brunet, C.; Johnsen, G.; Lavaud, J.; Roy, S. Pigments and photoacclimation processes. In Phytoplankton Pigments: Characterization, Chemotaxonomy and Applications in Oceanography; Roy, S., Llewellyn, C.A., Egeland, E.S., Johnsen, G., Eds.; Cambridge University Press: Cambridge, UK, 2011; pp. 445–471. [Google Scholar]
- Uitz, J.; Claustre, H.; Griffiths, F.B.; Ras, J.; Garcia, N.; Sandroni, V. A phytoplankton class-specific primary production model applied to the Kerguelen Islands region (Southern Ocean). Deep Sea Res.
**2009**, 56, 541–560. [Google Scholar] [CrossRef] - Mackey, M.D.; Mackey, D.J.; Higgins, H.W.; Wright, S.W. CHEMTAX-a program for estimating class abundances from chemical markers: Application to HPLC measurements of phytoplankton. Mar. Ecol. Progr.
**1996**, 144, 265–283. [Google Scholar] [CrossRef] - Vidussi, F.; Claustre, H.; Manca, B.B.; Luchetta, A.; Marty, J.C. Phytoplankton pigment distribution in relation to upper thermocline circulation in the eastern Mediterranean Sea during winter. J. Geophys. Res.
**1996**, 106, 19939–19956. [Google Scholar] [CrossRef] - Bracher, A.; Bouman, H.A.; Brewin, R.J.; Bricaud, A.; Brotas, V.; Ciotti, A.M.; Clementson, L.; Devred, E.; Di Cicco, A.; Dutkiewicz, S.; et al. Obtaining phytoplankton diversity from ocean color: A scientific roadmap for future development. Front. Mar. Sci.
**2017**, 4, 55. [Google Scholar] [CrossRef] - Sosik, H.M.; Sathyendranath, S.; Uitz, J.; Bouman, H.; Nair, A. In situ methods of measuring phytoplankton functional types. In Phytoplankton Functional Types from Space. Reports of the International Ocean-Colour Coordinating Group (IOCCG), No. 15; Sathyendranath, S., Ed.; IOCCG: Dartmouth, NS, Canada, 2014; pp. 21–38. [Google Scholar]
- Hoepffner, N.; Sathyendranath, S. Determination of the major groups of phytoplankton pigments from the absorption spectra of total particulate matter. J. Geophys. Res.
**1993**, 98, 22789–22803. [Google Scholar] [CrossRef] - Bidigare, R.R.; Ondrusek, M.E.; Morrow, J.H.; Kiefer, D.A. In-vivo absorption properties of algal pigments. Proc. SPIE
**1990**, 1302, 290–303. [Google Scholar] - Bidigare, R.R.; Morrow, J.H.; Kiefer, D.A. Derivative analysis of spectral absorption by photosynthetic pigments in the western Sargasso Sea. J. Mar. Res.
**1989**, 47, 323–341. [Google Scholar] [CrossRef] - Organelli, E.; Bricaud, A.; Antoine, D.; Uitz, J. Multivariate approach for the retrieval of phytoplankton size structure from measured light absorption spectra in the Mediterranean Sea (BOUSSOLE site). Appl. Opt.
**2013**, 52, 2257–2273. [Google Scholar] [CrossRef] - Sathyendranath, S.; Stuart, V.; Platt, T.; Bouman, H.; Ulloa, O.; Maass, H. Remote sensing of ocean colour: Towards algorithms for retrieval of pigment composition. Indian J. Mar. Sci.
**2005**, 34, 333–340. [Google Scholar] - Pan, X.; Mannino, A.; Russ, M.E.; Hooker, S.B.; Harding, L.W., Jr. Remote sensing of phytoplankton pigment distribution in the United States northeast coast. Remote Sens. Environ.
**2010**, 114, 2403–2416. [Google Scholar] [CrossRef] - Pan, X.; Wong, G.T.; Ho, T.Y.; Shiah, F.K.; Liu, H. Remote sensing of picophytoplankton distribution in the northern South China Sea. Remote Sens. Environ.
**2013**, 128, 162–175. [Google Scholar] [CrossRef] - Bracher, A.; Taylor, M.; Taylor, B.; Dinter, T.; Röttgers, R.; Steinmetz, F. Using empirical orthogonal functions derived from remote sensing reflectance for the prediction of phytoplankton pigments concentrations. Ocean Sci.
**2015**, 11, 139–158. [Google Scholar] [CrossRef] - Bricaud, A.; Mejia, C.; Blondeau-Patissier, D.; Claustre, H.; Crepon, M.; Thiria, S. Retrieval of pigment concentrations and size structure of algal populations from their absorption spectra using multilayered perceptrons. Appl. Opt.
**2007**, 46, 1251–1260. [Google Scholar] [CrossRef] [PubMed] - Chazottes, A.; Crépon, M.; Bricaud, A.; Ras, J.; Thiria, S. Statistical analysis of absorption spectra of phytoplankton and of pigment concentrations observed during three POMME cruises using a neural network clustering method. Appl. Opt.
**2007**, 46, 3790–3799. [Google Scholar] [CrossRef] [PubMed] - Lohrenz, S.E.; Weidemann, A.D.; Tuel, M. Phytoplankton spectral absorption as influenced by community size structure and pigment composition. J. Plankton Res.
**2003**, 25, 35–61. [Google Scholar] [CrossRef] - Chase, A.; Boss, E.; Zaneveld, R.; Bricaud, A.; Claustre, H.; Ras, J.; Dall’Olmo, G.; Westberry, T.K. Decomposition of in situ particulate absorption spectra. Methods Oceanogr.
**2013**, 7, 110–124. [Google Scholar] [CrossRef] - Chase, A.; Boss, E.; Cetinić, I.; Slade, W. Estimation of phytoplankton accessory pigments from hyperspectral reflectance spectra: Toward a global algorithm. J. Geophys. Res.
**2017**, 122, 9725–9743. [Google Scholar] [CrossRef] - Wang, G.; Lee, Z.; Mishra, D.R.; Ma, R. Retrieving absorption coefficients of multiple phytoplankton pigments from hyperspectral remote sensing reflectance measured over cyanobacteria bloom waters. Limnol. Oceanogr.-Methods
**2016**, 14, 432–447. [Google Scholar] [CrossRef] - Wang, G.; Lee, Z.; Mouw, C. Multi-spectral remote sensing of phytoplankton pigment absorption properties in cyanobacteria bloom waters: A regional example in the western basin of Lake Erie. Remote Sens.
**2017**, 9, 1309. [Google Scholar] [CrossRef] - Bidigare, R.R.; Smith, R.C.; Baker, K.S.; Marra, J. Oceanic primary production estimates from measurements of spectral irradiance and pigment concentrations. Glob. Biogeochem. Cycles
**1987**, 1, 171–186. [Google Scholar] [CrossRef] - Moisan, J.R.; Moisan, T.A.; Linkswiler, M.A. An inverse modeling approach to estimating phytoplankton pigment concentrations from phytoplankton absorption spectra. J. Geophys. Res.
**2011**, 116. [Google Scholar] [CrossRef] - Moisan, T.A.; Moisan, J.R.; Linkswiler, M.A.; Steinhardt, R.A. Algorithm development for predicting biodiversity based on phytoplankton absorption. Cont. Shelf Res.
**2013**, 55, 17–28. [Google Scholar] [CrossRef] - Press, W.H.; Teukolsky, S.A.; Vetterling, W.T.; Flannery, B.P. Solution of Linear Algebraic Equations. In Numerical Recipes: The Art of Scientific Computing; Press, W.H., Teukolsky, S.A., Vetterling, W.T., Flannery, B.P., Eds.; Cambridge University Press: Cambridge, UK, 2007; pp. 37–109. [Google Scholar]
- Lawson, C.L.; Hanson, R.J. Linear least squares with linear inequality constraints. In Solving Least Squares Problems; Lawson, C.L., Hanson, R.J., Eds.; Prentice-Hall: Upper Saddle River, NJ, USA, 1974; pp. 158–173. [Google Scholar]
- Levenberg, K. A method for the solution of certain non-linear problems in least squares. Q. Appl. Math.
**1944**, 2, 164–168. [Google Scholar] [CrossRef] - Marquardt, D.W. An algorithm for least-squares estimation of nonlinear parameters. J. Soc. Ind. App. Math.
**1963**, 11, 431–441. [Google Scholar] [CrossRef] - Zhang, H.; Devred, E.; Fujiwara, A.; Qiu, Z.; Liu, X. Estimation of phytoplankton taxonomic groups in the Arctic Ocean using phytoplankton absorption properties: Implication for ocean-color remote sensing. Opt. Express
**2018**, 26, 32280–32301. [Google Scholar] [CrossRef] - Moisan, T.A.; Rufty, K.M.; Moisan, J.R.; Linkswiler, M.A. Satellite observations of phytoplankton functional type spatial distributions, phenology, diversity, and ecotones. Front. Mar. Sci.
**2017**, 4, 189. [Google Scholar] [CrossRef] - Devred, E.; Sathyendranath, S.; Stuart, V.; Platt, T. A three component classification of phytoplankton absorption spectra: Application to ocean-color data. Remote Sens. Environ.
**2011**, 115, 2255–2266. [Google Scholar] [CrossRef] - Zhang, X.; Huot, Y.; Bricaud, A.; Sosik, H.M. Inversion of spectral absorption coefficients to infer phytoplankton size classes, chlorophyll concentration, and detrital matter. Appl. Opt.
**2015**, 54, 5805–5816. [Google Scholar] [CrossRef] - Butler, W.T.; Hopkins, D.W. Higher derivative analysis of complex absorption spectra. Photochem. Photobiol.
**1970**, 12, 439–450. [Google Scholar] [CrossRef] - Soja-Woźniak, M.; Craig, S.E.; Kratzer, S.; Wojtasiewicz, B.; Darecki, M.; Jones, C.T. A novel statistical approach for ocean colour estimation of inherent optical properties and cyanobacteria abundance in optically complex waters. Remote Sens.
**2017**, 9, 343. [Google Scholar] [CrossRef] - Boss, E.; Picheral, M.; Leeuw, T.; Chase, A.; Karsenti, E.; Gorsky, G.; Taylor, L.; Slade, W.; Ras, J.; Claustre, H. The characteristics of particulate absorption, scattering and attenuation coefficients in the surface ocean; Contribution of the Tara Oceans expedition. Methods Oceanogr.
**2013**, 7, 52–62. [Google Scholar] [CrossRef] - Brewin, R.J.; Dall’Olmo, G.; Pardo, S.; van Dongen-Vogels, V.; Boss, E.S. Underway spectrophotometry along the Atlantic Meridional Transect reveals high performance in satellite chlorophyll retrievals. Remote Sens. Environ.
**2016**, 183, 82–97. [Google Scholar] [CrossRef] - Dall’Olmo, G.; Boss, E.; Behrenfeld, M.J.; Westberry, T.K. Particulate optical scattering coefficients along an Atlantic Meridional Transect. Opt. Express
**2012**, 20, 21532–21551. [Google Scholar] [CrossRef] [PubMed] - Dall’Olmo, G.; Boss, E.; Behrenfeld, M.J.; Westberry, T.K.; Courties, C.; Prieur, L.; Pujo-Pay, M.; Hardman-Mountford, N.; Moutin, T. Inferring phytoplankton carbon and eco-physiological rates from diel cycles of spectral particulate beam-attenuation coefficient. Biogeosciences
**2011**, 8, 3423–3439. [Google Scholar] [CrossRef] - Dall’Olmo, G.; Brewin, R.J.; Nencioli, F.; Organelli, E.; Lefering, I.; McKee, D.; Röttgers, R.; Mitchell, C.; Boss, E.; Bricuad, A.; et al. Determination of the absorption coefficient of chromophoric dissolved organic matter from underway spectrophotometry. Opt. Express
**2017**, 25, A1079–A1095. [Google Scholar] [CrossRef] [PubMed] - Dall’Olmo, G.; Westberry, T.K.; Behrenfeld, M.J.; Boss, E.; Slade, W.H. Significant contribution of large particles to optical backscattering in the open ocean. Biogeosciences
**2009**, 6, 947. [Google Scholar] [CrossRef] - Liu, Y.; Röttgers, R.; Ramírez-Pérez, M.; Dinter, T.; Steinmetz, F.; Nöthig, E.M.; Hellmann, S.; Wiegmann, S.; Bracher, A. Underway spectrophotometry in the Fram Strait (European Arctic Ocean): A highly resolved chlorophyll a data source for complementing satellite ocean color. Opt. Express
**2018**, 26, A678–A696. [Google Scholar] [CrossRef] [PubMed] - Slade, W.H.; Boss, E.; Dall’Olmo, G.; Langner, M.R.; Loftin, J.; Behrenfeld, M.J.; Roesler, C.; Westberry, T.K. Underway and moored methods for improving accuracy in measurement of spectral particulate absorption and attenuation. J. Atmos. Ocean. Technol.
**2010**, 27, 1733–1746. [Google Scholar] [CrossRef] - Westberry, T.K.; Dall’Olmo, G.; Boss, E.; Behrenfeld, M.J.; Moutin, T. Coherence of particulate beam attenuation and backscattering coefficients in diverse open ocean environments. Opt. Express
**2010**, 18, 15419–15425. [Google Scholar] [CrossRef] [PubMed] - Werdell, P.J.; Proctor, C.W.; Boss, E.; Leeuw, T.; Ouhssain, M. Underway sampling of marine inherent optical properties on the Tara Oceans expedition as a novel resource for ocean color satellite data product validation. Methods Oceanogr.
**2013**, 7, 40–51. [Google Scholar] [CrossRef] - Wadhams, P. Sea ice thickness distribution in Fram Strait. Nature
**1983**, 305, 108. [Google Scholar] [CrossRef] - Beszczynska-Möller, A.; Fahrbach, E.; Schauer, U.; Hansen, E. Variability in Atlantic water temperature and transport at the entrance to the Arctic Ocean, 1997–2010. ICES J. Mar. Sci.
**2012**, 69, 852–863. [Google Scholar] [CrossRef] - Widell, K.; Sterhus, S.; Gammelsrød, T. Sea ice velocity in the Fram Strait monitored by moored instruments. Geophys. Res. Lett.
**2003**, 30. [Google Scholar] [CrossRef] - Smedsrud, L.H.; Sorteberg, A.; Kloster, K. Recent and future changes of the Arctic sea-ice cover. Geophys. Res. Lett.
**2008**, 30. [Google Scholar] [CrossRef] - Smedsrud, L.H.; Sirevaag, A.; Kloster, K.; Sorteberg, A.; Sandven, S. Recent wind driven high sea ice area export in the Fram Strait contributes to Arctic sea ice decline. Cryosphere
**2011**, 5, 821–829. [Google Scholar] [CrossRef] - Halvorsen, M.H.; Smedsrud, L.H.; Zhang, R.; Kloster, K. Fram Strait spring ice export and September Arctic sea ice. Cryosphere Discuss.
**2015**, 9, 4205–4235. [Google Scholar] [CrossRef] - Smedsrud, L.H.; Halvorsen, M.H.; Stroeve, J.C.; Zhang, R.; Kloster, K. Fram Strait sea ice export variability and September Arctic sea ice extent over the last 80 years. Cryosphere
**2017**, 11, 65–79. [Google Scholar] [CrossRef] - Nöthig, E.M.; Bracher, A.; Engel, A.; Metfies, K.; Niehoff, B.; Peeken, I.; Bauerfeind, E.; Cherkasheva, A.; Gäbler-Schwarz, S.; Hardge, K.; et al. Summertime plankton ecology in Fram Strait—A compilation of long-and short-term observations. Polar Res.
**2015**, 34, 23349. [Google Scholar] [CrossRef] - Cherkasheva, A.; Bracher, A.; Melsheimer, C.; Köberle, C.; Gerdes, R.; Nöthig, E.M.; Bauerfeind, E.; Boetius, A. Influence of the physical environment on polar phytoplankton blooms: A case study in the Fram Strait. J. Mar. Syst.
**2014**, 132, 196–207. [Google Scholar] [CrossRef] - Hegseth, E.N.; Sundfjord, A. Intrusion and blooming of Atlantic phytoplankton species in the high Arctic. J. Mar. Syst.
**2008**, 74, 108–119. [Google Scholar] [CrossRef] - Bauerfeind, E.; Nöthig, E.M.; Beszczynska, A.; Fahl, K.; Kaleschke, L.; Kreker, K.; Klages, M.; Soltwedel, T.; Lorenzen, C.; Wegner, J. Particle sedimentation patterns in the eastern Fram Strait during 2000–2005: Results from the Arctic long-term observatory HAUSGARTEN. Deep Sea Res.
**2009**, 56, 1471–1487. [Google Scholar] [CrossRef] - Downing, A.L.; Leibold, M.A. Ecosystem consequences of species richness and composition in pond food webs. Nature
**2002**, 416, 837–841. [Google Scholar] [CrossRef] [PubMed] - Narwani, A.; Mazumder, A. Bottom-up effects of species diversity on the functioning and stability of food webs. J. Anim. Ecol.
**2012**, 81, 701–713. [Google Scholar] [CrossRef] [PubMed] - Jakobsson, M.; Mayer, L.; Coakley, B.; Dowdeswell, J.A.; Forbes, S.; Fridman, B.; Hodnesdal, H.; Noormets, R.; Pedersen, R.; Rebesco, M.; et al. The international bathymetric chart of the Arctic Ocean (IBCAO) version 3.0. Geophys. Res. Lett.
**2012**, 39. [Google Scholar] [CrossRef] - Sullivan, J.M.; Twardowski, M.S.; Zaneveld, J.R.V.; Moore, C.M.; Barnard, A.H.; Donaghay, P.L.; Rhoades, B. Hyperspectral temperature and salt dependencies of absorption by water and heavy water in the 400–750 nm spectral range. Appl. Opt.
**2006**, 45, 5294–5309. [Google Scholar] [CrossRef] [PubMed] - Zaneveld, J.R.V.; Kitchen, J.C.; Moore, C.C. Scattering error correction of reflecting-tube absorption meters. Proc. SPIE
**1994**, 2258, 44–55. [Google Scholar] - Hooker, S.B.; Heukelem, L.V. A symbology and vocabulary for an HPLC lexicon. In Phytoplankton Pigments: Characterization, Chemotaxonomy and Applications in Oceanography; Roy, S., Llewellyn, C.A., Egeland, E.S., Johnsen, G., Eds.; Cambridge University Press: Cambridge, UK, 2011; pp. 243–256. [Google Scholar]
- Yentsch, C.S. Measurement of visible light absorption by particulate matter in the ocean. Limnol. Oceanogr.
**1962**, 7, 207–217. [Google Scholar] [CrossRef] - Trüper, H.G.; Yentsch, C.S. Use of glass fiber filters for the rapid preparation of in vivo absorption spectra of photosynthetic bacteria. J. Bacteriol.
**1967**, 94, 1255–1256. [Google Scholar] - Yentsch, C.S.; Phinney, D.A. A bridge between ocean optics and microbial ecology. Limnol. Oceanogr.
**1989**, 34, 1694–1705. [Google Scholar] [CrossRef] - Simis, S.G.; Tijdens, M.; Hoogveld, H.L.; Gons, H.J. Optical changes associated with cyanobacterial bloom termination by viral lysis. J. Plankton Res.
**2005**, 27, 937–949. [Google Scholar] [CrossRef] - Röttgers, R.; Doxaran, D.; Dupouy, C. Quantitative filter technique measurements of spectral light absorption by aquatic particles using a portable integrating cavity absorption meter (QFT-ICAM). Opt. Express
**2016**, 24, A1–A20. [Google Scholar] [CrossRef] [PubMed] - Bricaud, A.; Morel, A.; Babin, M.; Allali, K.; Claustre, H. Variations of light absorption by suspended particles with chlorophyll a concentration in oceanic (case 1) waters: Analysis and implications for bio-optical models. J. Geophys. Res.
**1998**, 103, 31033–31044. [Google Scholar] [CrossRef] - Babin, M.; Stramski, D.; Ferrari, G.M.; Claustre, H.; Bricaud, A.; Obolensky, G.; Hoepffner, N. Variations in the light absorption coefficients of phytoplankton, nonalgal particles, and dissolved organic matter in coastal waters around Europe. J. Geophys. Res.
**2003**, 108, 3211–3231. [Google Scholar] [CrossRef] - Bricaud, A.; Claustre, H.; Ras, J.; Oubelkheir, K. Natural variability of phytoplanktonic absorption in oceanic waters: Influence of the size structure of algal populations. J. Geophys. Res.
**2004**, 109. [Google Scholar] [CrossRef] - Millie, D.F.; Schofield, O.M.; Kirkpatrick, G.J.; Johnsen, G.; Tester, P.A.; Vinyard, B.T. Detection of harmful algal blooms using photopigments and absorption signatures: A case study of the Florida red tide dinoflagellate, Gymnodinium breve. Limnol. Oceanogr.
**1997**, 42, 1240–1251. [Google Scholar] [CrossRef] - Xi, H.; Hieronymi, M.; Krasemann, H.; Röttgers, R. Phytoplankton group identification using simulated and in situ hyperspectral remote sensing reflectance. Front. Mar. Sci.
**2017**, 4, 272. [Google Scholar] [CrossRef] - Morel, A.; Bricaud, A. Theoretical results concerning light absorption in a discrete medium, and application to specific absorption of phytoplankton. Deep Sea Res.
**1981**, 28, 1375–1393. [Google Scholar] [CrossRef] - Craig, S.E.; Jones, C.T.; Li, W.K.; Lazin, G.; Horne, E.; Caverhill, C.; Cullen, J.J. Deriving optical metrics of coastal phytoplankton biomass from ocean colour. Remote Sens. Environ.
**2012**, 119, 72–83. [Google Scholar] [CrossRef] - Lin, J.; Cao, W.; Zhou, W.; Sun, Z.; Xu, Z.; Wang, G.; Hu, S. Novel method for quantifying the cell size of marine phytoplankton based on optical measurements. Opt. Express
**2014**, 22, 10467–10476. [Google Scholar] [CrossRef] [PubMed] - Lawson, C.L.; Hanson, R.J. Perturbation theorems for singular values. In Solving Least Squares Problems; Lawson, C.L., Hanson, R.J., Eds.; Prentice-Hall: Upper Saddle River, NJ, USA, 1974; pp. 23–27. [Google Scholar]
- Wright, S.W.; Jeffrey, S.W. Pigment markers for phytoplankton production. In Marine Organic Matter: Biomarkers, Isotopes and DNA. The Handbook of Environmental Chemistry, Volume 2N; Volkman, J.K., Ed.; Springer: Berlin/Heidelberg, Germany, 2006; pp. 71–104. [Google Scholar]

**Figure 1.**Cruise tracks for PS93.2 (July–August 2015), PS99.2 (June–July 2016) and PS107 (July–August 2017). Symbols denote locations where both AC-S and HPLC data were collected. Bathymetric grid data are extracted from the International Bathymetric Chart of the Arctic Ocean Version 3.0 [62]. Lambert azimuthal equal-area projection was used for mapping.

**Figure 2.**Schematic overview of the steps of applying Gaussian decomposition for phytoplankton pigment retrieval.

**Figure 3.**Schematic overview of the steps of applying the matrix inversion technique for phytoplankton pigment retrieval.

**Figure 4.**(

**a**) Variations of the AC-S derived ${a}_{p}\left(440\right)$ as a power function of TChl-a concentration; (

**b**) the Spearman${}^{\prime}$s rank correlation coefficients between the concentrations of phytoplankton pigments in our data set (linear color bar scale).

**Figure 5.**Concentrations of phytoplankton pigments measured by HPLC versus the magnitudes of the corresponding Gaussian functions obtained from the Gaussian decomposition of both ${a}_{ph}\left(\lambda \right)$ (

**a**,

**c**,

**e**,

**g**,

**i**) and ${\widehat{a}}_{ph}\left(\lambda \right)$ (

**b**,

**d**,

**f**,

**h**,

**j**,

**l**). The results of Chase et al. [22] are based on ${a}_{ph}\left(\lambda \right)$.

**Figure 6.**Variations in the minimum values of the condition number (${n}_{cond}$) of matrix C in Equation (4) with different pigment combination (m pigment types to be estimated): (

**a**) pigment data unperturbed; (

**b**) pigment data perturbed.

**Figure 7.**Pigment-specific absorption spectra obtained from SVD-NNLS-9 (

**a**,

**b**), SVD-NNLS-5${}^{\prime}$ (

**c**,

**d**) and Bricaud-SVD-NNLS-4 (

**e**,

**f**) without data perturbations, respectively. Cases with and without package effect normalization were compared.

**Figure 8.**Scatter plots of SVD-NNLS-9 estimated pigment concentrations versus measured pigment concentrations for unperturbed training data set. The symbols of green circles, red crosses and blue stars represent the data from the cruises PS93.2, PS99.2 and PS107, respectively. Dash lines denote the 50% error lines, and solid lines are one-to-one lines.

**Figure 9.**SVD-NNLS-9 estimated Fuco and Hex concentrations from underway spectrophotometry during the cruise periods of PS93.2 (

**a**), PS99.2 (

**b**) and PS107 (

**c**).

**Table 1.**Abbreviations of phytoplankton pigments and pigment groups analyzed in this study, and the minimum, maximum, mean and standard deviation of the pigment concentrations (mg m${}^{-3}$).

Pigment/Pigment Group | Abbreviation | Minimum | Maximum | Mean | Standard Deviation |
---|---|---|---|---|---|

alloxanthin | Allo | 0.00 | 0.16 | 0.01 | 0.01 |

chlorophyll-c1/2 | Chl-c1/2 | 0.00 | 0.94 | 0.15 | 0.15 |

chlorophyll-c3 | Chl-c3 | 0.00 | 0.83 | 0.08 | 0.11 |

$\alpha $-carotene | $\alpha $-Caro | 0.00 | 0.04 | 0.00 | 0.01 |

$\beta $-carotene | $\beta $-Caro | 0.00 | 0.07 | 0.02 | 0.01 |

diadinoxanthin | Diadino | 0.00 | 0.49 | 0.10 | 0.08 |

diatoxanthin | Diato | 0.00 | 0.05 | 0.01 | 0.01 |

fucoxanthin | Fuco | 0.01 | 1.28 | 0.22 | 0.21 |

${19}^{\prime}$-hexanoyloxyfucoxanthin | Hex | 0.00 | 1.63 | 0.23 | 0.24 |

${19}^{\prime}$-butanoyloxyfucoxanthin | But | 0.00 | 0.51 | 0.04 | 0.05 |

neoxanthin | Neo | 0.00 | 0.02 | 0.00 | 0.00 |

lutein | Lut | 0.00 | 0.01 | 0.00 | 0.00 |

peridinin | Peri | 0.00 | 0.45 | 0.03 | 0.06 |

prasinoxanthin | Prasino | 0.00 | 0.05 | 0.00 | 0.01 |

pheophytin-a | Pheo-a | 0.00 | 1.31 | 0.02 | 0.10 |

pheophorbide-a | Phide-a | 0.00 | 0.17 | 0.01 | 0.02 |

violaxanthin | Viola | 0.00 | 0.03 | 0.01 | 0.01 |

zeaxanthin | Zea | 0.00 | 0.08 | 0.01 | 0.01 |

total chlorophyll-a | TChl-a | 0.06 | 3.87 | 0.86 | 0.66 |

total chlorophyll-b | TChl-b | 0.00 | 0.22 | 0.06 | 0.03 |

total chlorophyll-c | TChl-c | 0.00 | 1.62 | 0.23 | 0.24 |

photosynthetic carotenoids | PSC | 0.02 | 3.56 | 0.52 | 0.49 |

photoprotective carotenoids | PPC | 0.01 | 0.64 | 0.17 | 0.11 |

${\mathit{\lambda}}_{0}\phantom{\rule{4pt}{0ex}}\left[\mathbf{nm}\right]$ | $\mathit{\sigma}\phantom{\rule{4pt}{0ex}}\left[\mathbf{nm}\right]$ | Pigment | A | B | ${\mathit{R}}^{2}$ | MAE ${}^{\mathbf{b}}$ | MPE ${}^{\mathbf{b}}$ | N | MAE ${}^{\mathbf{c}}$ | MPE ${}^{\mathbf{c}}$ |
---|---|---|---|---|---|---|---|---|---|---|

406 | 16 | TChl-a | 17.60 ± 4.03 | 0.90 ± 0.08 | 0.75 | 0.28(0.18) | 26.2 | 274 | - | - |

434 | 12 | TChl-a | 41.61 ± 6.71 | 1.12 ± 0.05 | 0.87 | 0.21(0.13) | 20.7 | 297 | 0.22(0.13) | 20.8 |

453 | 12 | TChl-b & c ${}^{\mathrm{a}}$ | 1.18 ± 0.20 | 1.23 ± 0.05 | 0.92 | 0.00(0.14) | 21.1 | 297 | - | - |

470 | 13 | TChl-b | 0.38 ± 0.11 | 0.50 ± 0.08 | 0.52 | 0.02(0.17) | 29.5 | 296 | - | - |

492 | 16 | PPC | 1.23 ± 0.38 | 0.54 ± 0.09 | 0.50 | 0.06(0.18) | 30.6 | 298 | 0.06(0.18) | 31.5 |

523 | 14 | PSC | 25.25 ± 7.58 | 0.92 ± 0.08 | 0.76 | 0.20(0.21) | 33.4 | 298 | 0.20(0.21) | 34.0 |

550 | 14 | phycoerythrin | - | - | - | - | - | - | - | - |

584 | 16 | Chl-c1/2 | 12.18 ± 5.18 | 0.85 ± 0.09 | 0.68 | 0.07(0.26) | 44.9 | 297 | - | - |

617 | 13 | TChl-a | 21.00 ± 7.85 | 0.57 ± 0.07 | 0.66 | 0.33(0.20) | 36.8 | 295 | - | - |

638 | 11 | Chl-c1/2 | 49.89 ± 16.13 | 1.03 ± 0.06 | 0.81 | 0.05(0.20) | 33.4 | 297 | 0.06(0.20) | 33.5 |

660 | 11 | TChl-b | 0.66 ± 0.21 | 0.44 ± 0.06 | 0.57 | 0.02(0.16) | 29.1 | 293 | 0.02(0.16) | 29.3 |

675 | 10 | TChl-a | 19.70 ± 3.92 | 0.76 ± 0.05 | 0.82 | 0.24(0.14) | 24.9 | 298 | 0.25(0.14) | 25.3 |

${\mathit{\lambda}}_{0}\phantom{\rule{4pt}{0ex}}\left[\mathbf{nm}\right]$ | Pigment | A | B | ${\mathit{R}}^{2}$ | MAE ${}^{\mathbf{b}}$ | MPE ${}^{\mathbf{b}}$ | N | MAE ${}^{\mathbf{c}}$ | MPE ${}^{\mathbf{c}}$ |

406 | TChl-a | 12.50 ± 1.37 | 0.96 ± 0.048 | 0.88 | 0.22(0.15) | 19.5 | 274 | - | - |

434 | TChl-a | 19.23 ± 1.22 | 1.07 ± 0.026 | 0.96 | 0.13(0.08) | 11.9 | 297 | 0.13(0.08) | 12.2 |

453 | TChl-b & c ${}^{\mathrm{a}}$ | 0.39 ± 0.05 | 1.10 ± 0.05 | 0.92 | 0.00(0.15) | 25.8 | 297 | - | - |

470 | TChl-b | 0.30 ± 0.06 | 0.51 ± 0.07 | 0.60 | 0.02(0.15) | 26.3 | 296 | - | - |

492 | PPC | 1.89 ± 0.32 | 0.77 ± 0.06 | 0.77 | 0.05(0.14) | 21.4 | 298 | 0.05(0.14) | 21.8 |

523 | PSC | 44.04 ± 5.31 | 1.19 ± 0.04 | 0.92 | 0.11(0.14) | 20.4 | 298 | 0.11(0.14) | 20.5 |

550 | phycoerythrin | - | - | - | - | - | - | - | - |

584 | Chl-c1/2 | 16.73 ± 4.31 | 1.00 ± 0.06 | 0.82 | 0.06(0.22) | 36.2 | 297 | - | - |

617 | TChl-a | 64.19 ± 13.15 | 0.83 ± 0.04 | 0.84 | 0.22(0.15) | 24.1 | 295 | - | - |

638 | Chl-c1/2 | 34.11 ± 7.20 | 1.06 ± 0.05 | 0.91 | 0.04(0.17) | 27.2 | 297 | 0.04(0.18) | 27.2 |

660 | TChl-b | 0.47 ± 0.12 | 0.41 ± 0.05 | 0.62 | 0.02(0.15) | 27.9 | 293 | 0.02(0.15) | 27.4 |

675 | TChl-a | 33.57 ± 0.72 | 1.00 ± 0.01 | 1.00 | 0.05(0.03) | 3.6 | 298 | 0.05(0.03) | 3.6 |

Method | Pigments | ${\mathit{a}}_{\mathit{ph}}\left(\mathit{\lambda}\right)$ Based | ${\widehat{\mathit{a}}}_{\mathit{ph}}\left(\mathit{\lambda}\right)$ Based | ||||
---|---|---|---|---|---|---|---|

${\mathit{n}}_{\mathit{cond}}$ | Maximum $\mathit{SI}$ | m | ${\mathit{n}}_{\mathit{cond}}$ | Maximum $\mathit{SI}$ | m | ||

SVD-NNLS | Fram-20 | 54.9 | 0.86 | 9 | 54.9 | 0.85 | 9 |

NNLS-NNLS | Fram-20 | 30.7 | 0.79 | 6 | 54.9 | 0.86 | 9 |

SVD-NNLS-5${}^{\prime}$ | Gauss-5 | 47.8 | 0.81 | 5 | 47.8 | 0.84 | 5 |

NNLS-NNLS-5${}^{\prime}$ | Gauss-5 | 47.8 | 0.79 | 5 | 47.8 | - | 5 |

Bricaud-SVD-NNLS | Bricaud-12 | 45.1 | 0.72 | 4 | 45.1 | 0.76 | 4 |

Bricaud-NNLS-NNLS | Bricaud-12 | 45.1 | 0.83 | 4 | 45.1 | 0.76 | 4 |

Method | Pigments | ${\mathit{a}}_{\mathit{ph}}\left(\mathit{\lambda}\right)$ Based | ${\widehat{\mathit{a}}}_{\mathit{ph}}\left(\mathit{\lambda}\right)$ Based | ||||
---|---|---|---|---|---|---|---|

${\mathit{n}}_{\mathit{cond}}$ | Maximum $\mathit{SI}$ | m | ${\mathit{n}}_{\mathit{cond}}$ | Maximum $\mathit{SI}$ | m | ||

SVD-NNLS | Fram-20 | 59.0 | 0.86 | 9 | 59.0 | 0.81 | 9 |

NNLS-NNLS | Fram-20 | 30.7 | 0.75 | 6 | 59.0 | 0.85 | 9 |

SVD-NNLS-5${}^{\prime}$ | Gauss-5 | 47.8 | 0.74 | 5 | 47.8 | 0.82 | 5 |

NNLS-NNLS-5${}^{\prime}$ | Gauss-5 | 47.8 | 0.78 | 5 | 47.8 | - | 5 |

Bricaud-SVD-NNLS | Bricaud-12 | 45.8 | 0.72 | 4 | 45.8 | 0.76 | 4 |

Bricaud-NNLS-NNLS | Bricaud-12 | 45.8 | 0.83 | 4 | 45.8 | 0.76 | 4 |

Method | Pigments | ${\mathit{a}}_{\mathit{ph}}\left(\mathit{\lambda}\right)$ Based | ${\widehat{\mathit{a}}}_{\mathit{ph}}\left(\mathit{\lambda}\right)$ Based | ||||
---|---|---|---|---|---|---|---|

${\mathit{n}}_{\mathit{cond}}$ | Maximum $\mathit{SI}$ | m | ${\mathit{n}}_{\mathit{cond}}$ | Maximum $\mathit{SI}$ | m | ||

SVD-NNLS | Fram-20 | 54.9 | 0.84 | 9 | 54.9 | 0.81 | 9 |

NNLS-NNLS | Fram-20 | 30.7 | 0.81 | 6 | 54.9 | 0.86 | 9 |

SVD-NNLS-5${}^{\prime}$ | Gauss-5 | 47.8 | 0.79 | 5 | 47.8 | 0.82 | 5 |

NNLS-NNLS-5${}^{\prime}$ | Gauss-5 | 47.8 | 0.80 | 5 | 47.8 | - | 5 |

Bricaud-SVD-NNLS | Bricaud-12 | 45.1 | 0.72 | 4 | 45.1 | 0.76 | 4 |

Bricaud-NNLS-NNLS | Bricaud-12 | 45.1 | 0.83 | 4 | 45.1 | 0.76 | 4 |

Pigments | ${\mathit{a}}_{\mathit{ph}}\left(\mathit{\lambda}\right)$ Based | ${\widehat{\mathit{a}}}_{\mathit{ph}}\left(\mathit{\lambda}\right)$ Based | ||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|

Slope | Intercept | ${\mathit{R}}^{2}$ | MAE | MPE | N | Slope | Intercept | ${\mathit{R}}^{2}$ | MAE | MPE | N | |

TChl-a | 0.97 $\pm \phantom{\rule{4pt}{0ex}}0.04$ | 0.00 $\pm \phantom{\rule{4pt}{0ex}}0.01$ | 0.92 | 0.15(0.10) | 12.8 | 295 | 1.00 $\pm \phantom{\rule{4pt}{0ex}}0.00$ | −0.00 $\pm \phantom{\rule{4pt}{0ex}}0.00$ | 1.00 | 0.01(0.01) | 0.74 | 298 |

TChl-b | 0.31 $\pm \phantom{\rule{4pt}{0ex}}0.15$ | −0.81 $\pm \phantom{\rule{4pt}{0ex}}0.20$ | 0.31 | 0.04(0.32) | 58.3 | 268 | 0.41 $\pm \phantom{\rule{4pt}{0ex}}0.15$ | −0.70 $\pm \phantom{\rule{4pt}{0ex}}0.20$ | 0.25 | 0.04(0.30) | 52.6 | 269 |

Chl-c1/2 | 0.65 $\pm \phantom{\rule{4pt}{0ex}}0.06$ | −0.21 $\pm \phantom{\rule{4pt}{0ex}}0.06$ | 0.72 | 0.06(0.25) | 42.6 | 286 | 0.60 $\pm \phantom{\rule{4pt}{0ex}}0.06$ | −0.27 $\pm \phantom{\rule{4pt}{0ex}}0.07$ | 0.63 | 0.06(0.26) | 37.1 | 275 |

But | 0.43 $\pm \phantom{\rule{4pt}{0ex}}0.10$ | −0.53 $\pm \phantom{\rule{4pt}{0ex}}0.17$ | 0.38 | 0.04(0.43) | 100.0 | 209 | 0.54 $\pm \phantom{\rule{4pt}{0ex}}0.08$ | −0.45 $\pm \phantom{\rule{4pt}{0ex}}0.14$ | 0.62 | 0.03(0.35) | 62.6 | 206 |

Diadino | 0.39 $\pm \phantom{\rule{4pt}{0ex}}0.07$ | −0.45 $\pm \phantom{\rule{4pt}{0ex}}0.08$ | 0.40 | 0.06(0.30) | 57.8 | 283 | 0.38 $\pm \phantom{\rule{4pt}{0ex}}0.08$ | −0.52 $\pm \phantom{\rule{4pt}{0ex}}0.09$ | 0.46 | 0.06(0.30) | 49.2 | 284 |

Fuco | 0.84 $\pm \phantom{\rule{4pt}{0ex}}0.06$ | −0.03 $\pm \phantom{\rule{4pt}{0ex}}0.06$ | 0.82 | 0.08(0.23) | 33.7 | 276 | 0.85 $\pm \phantom{\rule{4pt}{0ex}}0.06$ | −0.07 $\pm \phantom{\rule{4pt}{0ex}}0.06$ | 0.79 | 0.07(0.22) | 31.6 | 286 |

Hex | 0.62 $\pm \phantom{\rule{4pt}{0ex}}0.05$ | −0.16 $\pm \phantom{\rule{4pt}{0ex}}0.05$ | 0.69 | 0.09(0.24) | 37.3 | 266 | 0.72 $\pm \phantom{\rule{4pt}{0ex}}0.04$ | −0.13 $\pm \phantom{\rule{4pt}{0ex}}0.04$ | 0.83 | 0.07(0.20) | 32.0 | 270 |

Peri | 0.74 $\pm \phantom{\rule{4pt}{0ex}}0.15$ | −0.30 $\pm \phantom{\rule{4pt}{0ex}}0.23$ | 0.54 | 0.04(0.36) | 57.5 | 134 | 0.67 $\pm \phantom{\rule{4pt}{0ex}}0.17$ | −0.37 $\pm \phantom{\rule{4pt}{0ex}}0.26$ | 0.43 | 0.05(0.40) | 66.6 | 128 |

Pheo-a | 0.06 $\pm \phantom{\rule{4pt}{0ex}}0.87$ | −0.31 $\pm \phantom{\rule{4pt}{0ex}}0.65$ | -0.16 | 0.59(0.53) | 166.0 | 22 | −0.04 $\pm \phantom{\rule{4pt}{0ex}}1.02$ | −0.39 $\pm \phantom{\rule{4pt}{0ex}}0.77$ | −0.34 | 0.64(0.58) | 132.0 | 22 |

Pigments | ${\mathit{a}}_{\mathit{ph}}\left(\mathit{\lambda}\right)$ Based | ${\widehat{\mathit{a}}}_{\mathit{ph}}\left(\mathit{\lambda}\right)$ Based | ||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|

Slope | Intercept | ${\mathit{R}}^{2}$ | MAE | MPE | N | Slope | Intercept | ${\mathit{R}}^{2}$ | MAE | MPE | N | |

TChl-a | 1.04 $\pm \phantom{\rule{4pt}{0ex}}0.04$ | −0.00 $\pm \phantom{\rule{4pt}{0ex}}0.02$ | 0.91 | 0.16(0.12) | 16.2 | 295 | 1.00 $\pm \phantom{\rule{4pt}{0ex}}0.00$ | −0.00 $\pm \phantom{\rule{4pt}{0ex}}0.00$ | 1.00 | 0.02(0.01) | 1.8 | 298 |

TChl-b | 0.54 $\pm \phantom{\rule{4pt}{0ex}}0.21$ | −0.54 $\pm \phantom{\rule{4pt}{0ex}}0.29$ | 0.12 | 0.05(0.38) | 72.6 | 250 | 0.55 $\pm \phantom{\rule{4pt}{0ex}}0.19$ | −0.54 $\pm \phantom{\rule{4pt}{0ex}}0.26$ | 0.18 | 0.05(0.34) | 62.0 | 247 |

Chl-c1/2 | 0.55 $\pm \phantom{\rule{4pt}{0ex}}0.06$ | −0.25 $\pm \phantom{\rule{4pt}{0ex}}0.07$ | 0.67 | 0.09(0.33) | 62.4 | 268 | 0.52 $\pm \phantom{\rule{4pt}{0ex}}0.06$ | −0.31 $\pm \phantom{\rule{4pt}{0ex}}0.07$ | 0.61 | 0.08(0.30) | 59.1 | 269 |

PPC | 0.50 $\pm \phantom{\rule{4pt}{0ex}}0.10$ | −0.26 $\pm \phantom{\rule{4pt}{0ex}}0.09$ | 0.50 | 0.10(0.27) | 55.2 | 278 | 0.51 $\pm \phantom{\rule{4pt}{0ex}}0.08$ | −0.25 $\pm \phantom{\rule{4pt}{0ex}}0.08$ | 0.58 | 0.10(0.27) | 55.9 | 288 |

PSC | 0.66 $\pm \phantom{\rule{4pt}{0ex}}0.05$ | −0.02 $\pm \phantom{\rule{4pt}{0ex}}0.03$ | 0.75 | 0.20(0.22) | 37.8 | 288 | 0.70 $\pm \phantom{\rule{4pt}{0ex}}0.04$ | −0.02 $\pm \phantom{\rule{4pt}{0ex}}0.02$ | 0.83 | 0.15(0.19) | 32.1 | 292 |

Pigments | ${\mathit{a}}_{\mathit{ph}}\left(\mathit{\lambda}\right)$ Based | ${\widehat{\mathit{a}}}_{\mathit{ph}}\left(\mathit{\lambda}\right)$ Based | ||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|

Slope | Intercept | ${\mathit{R}}^{2}$ | MAE | MPE | N | Slope | Intercept | ${\mathit{R}}^{2}$ | MAE | MPE | N | |

TChl-a | 0.85 $\pm \phantom{\rule{4pt}{0ex}}0.06$ | 0.01 $\pm \phantom{\rule{4pt}{0ex}}0.02$ | 0.75 | 0.26(0.15) | 25.5 | 298 | 0.98 $\pm \phantom{\rule{4pt}{0ex}}0.01$ | 0.01 $\pm \phantom{\rule{4pt}{0ex}}0.00$ | 0.98 | 0.08(0.05) | 5.3 | 298 |

Chl-c1/2 | 0.69 $\pm \phantom{\rule{4pt}{0ex}}0.04$ | −0.20 $\pm \phantom{\rule{4pt}{0ex}}0.05$ | 0.80 | 0.05(0.19) | 31.2 | 294 | 0.69 $\pm \phantom{\rule{4pt}{0ex}}0.06$ | −0.24 $\pm \phantom{\rule{4pt}{0ex}}0.07$ | 0.65 | 0.06(0.22) | 36.3 | 278 |

Diadino | 0.60 $\pm \phantom{\rule{4pt}{0ex}}0.08$ | −0.22 $\pm \phantom{\rule{4pt}{0ex}}0.10$ | 0.71 | 0.08(0.33) | 75.6 | 245 | 0.68 $\pm \phantom{\rule{4pt}{0ex}}0.16$ | −0.04 $\pm \phantom{\rule{4pt}{0ex}}0.18$ | 0.37 | 0.14(0.44) | 111.8 | 206 |

Hex | 0.10 $\pm \phantom{\rule{4pt}{0ex}}0.12$ | −0.66 $\pm \phantom{\rule{4pt}{0ex}}0.12$ | −0.01 | 0.32(0.60) | 83.2 | 227 | 0.15 $\pm \phantom{\rule{4pt}{0ex}}0.13$ | −0.41 $\pm \phantom{\rule{4pt}{0ex}}0.14$ | 0.10 | 0.40(0.62) | 126.2 | 175 |

Pigments | Perturb 1 ${}^{\mathbf{a}}$ | Perturb 2 ${}^{\mathbf{a}}$ | Perturb 3 ${}^{\mathbf{a}}$ | Perturb 1 ${}^{\mathbf{b}}$ | Perturb 2 ${}^{\mathbf{b}}$ | Perturb 3 ${}^{\mathbf{b}}$ | ||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|

MAE | MPE | MAE | MPE | MAE | MPE | MAE | MPE | MAE | MPE | MAE | MPE | |

TChl-a | 0.22(0.15) | 22.3 | 0.17(0.12) | 16.5 | 0.21(0.15) | 21.0 | 0.01(0.01) | 1.1 | 0.05(0.03) | 4.3 | 0.05(0.03) | 4.3 |

TChl-b | 0.04(0.29) | 60.2 | 0.03(0.27) | 53.7 | 0.03(0.27) | 53.6 | 0.04(0.28) | 61.4 | 0.03(0.27) | 52.9 | 0.04(0.27) | 56.3 |

Chl-c1/2 | 0.07(0.26) | 45.3 | 0.07(0.25) | 41.1 | 0.08(0.26) | 44.1 | 0.09(0.30) | 52.9 | 0.08(0.27) | 44.6 | 0.09(0.29) | 50.4 |

But | 0.03(0.32) | 104.8 | 0.03(0.31) | 80.7 | 0.03(0.31) | 81.8 | 0.02(0.25) | 68.7 | 0.02(0.26) | 67.2 | 0.03(0.27) | 69.8 |

Diadino | 0.07(0.32) | 64.4 | 0.08(0.31) | 61.9 | 0.08(0.31) | 65.2 | 0.07(0.32) | 66.0 | 0.07(0.31) | 59.7 | 0.08(0.32) | 64.7 |

Fuco | 0.09(0.22) | 44.5 | 0.09(0.21) | 36.9 | 0.09(0.22) | 38.4 | 0.12(0.27) | 53.1 | 0.10(0.23) | 40.0 | 0.11(0.25) | 44.5 |

Hex | 0.09(0.24) | 43.1 | 0.10(0.26) | 42.6 | 0.11(0.26) | 44.9 | 0.09(0.23) | 42.4 | 0.08(0.22) | 36.2 | 0.10(0.24) | 42.1 |

Peri | 0.02(0.17) | 66.8 | 0.03(0.23) | 90.4 | 0.03(0.23) | 90.4 | 0.02(0.17) | 68.3 | 0.02(0.21) | 74.8 | 0.03(0.21) | 76.3 |

Pheo-a | 0.04(0.04) | 123.7 | 0.02(0.03) | 88.7 | 0.02(0.03) | 90.0 | 0.04(0.04) | 107.0 | 0.02(0.03) | 95.2 | 0.02(0.03) | 91.7 |

Pigments | Perturb 1 ${}^{\mathbf{a}}$ | Perturb 2 ${}^{\mathbf{a}}$ | Perturb 3 ${}^{\mathbf{a}}$ | Perturb 1 ${}^{\mathbf{b}}$ | Perturb 2 ${}^{\mathbf{b}}$ | Perturb 3 ${}^{\mathbf{b}}$ | ||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|

MAE | MPE | MAE | MPE | MAE | MPE | MAE | MPE | MAE | MPE | MAE | MPE | |

TChl-a | 0.22(0.17) | 23.3 | 0.18( 0.13) | 17.3 | 0.22(0.16) | 21.7 | 0.02(0.02) | 2.2 | 0.05(0.03) | 4.7 | 0.05(0.04) | 4.9 |

TChl-b | 0.04(0.32) | 73.1 | 0.04(0.30) | 58.5 | 0.04(0.30) | 59.5 | 0.04(0.29) | 66.2 | 0.04(0.28) | 58.3 | 0.04(0.29) | 61.2 |

Chl-c1/2 | 0.09(0.30) | 68.5 | 0.07(0.26) | 49.2 | 0.08(0.27) | 50.4 | 0.09(0.31) | 67.1 | 0.07(0.26) | 47.9 | 0.09(0.29) | 54.3 |

PPC | 0.11(0.28) | 62.1 | 0.09(0.24) | 47.9 | 0.10(0.25) | 51.1 | 0.11(0.28) | 66.2 | 0.09(0.25) | 53.2 | 0.10(0.26) | 57.6 |

PSC | 0.21(0.23) | 42.8 | 0.20(0.22) | 35.0 | 0.21(0.23) | 38.0 | 0.20(0.24) | 42.8 | 0.16(0.19) | 28.7 | 0.20(0.23) | 37.9 |

Pigments | Perturb 1 ${}^{\mathbf{a}}$ | Perturb 2 ${}^{\mathbf{a}}$ | Perturb 3 ${}^{\mathbf{a}}$ | Perturb 1 ${}^{\mathbf{b}}$ | Perturb 2 ${}^{\mathbf{b}}$ | Perturb 3 ${}^{\mathbf{b}}$ | ||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|

MAE | MPE | MAE | MPE | MAE | MPE | MAE | MPE | MAE | MPE | MAE | MPE | |

TChl-a | 0.26(0.16) | 26.3 | 0.26(0.15) | 25.3 | 0.27(0.16) | 26.6 | 0.08(0.05) | 5.7 | 0.10(0.06) | 8.3 | 0.10(0.06) | 8.4 |

Chl-c1/2 | 0.05(0.19) | 33.2 | 0.05(0.20) | 32.6 | 0.05(0.20) | 33.5 | 0.06(0.22) | 39.0 | 0.06(0.23) | 41.6 | 0.06(0.23) | 43.1 |

Diadino | 0.06(0.28) | 77.2 | 0.07(0.28) | 78.2 | 0.07(0.28) | 80.1 | 0.10(0.31) | 118.1 | 0.10(0.31) | 117.6 | 0.10(0.32) | 118.3 |

Hex | 0.24(0.46) | 83.6 | 0.24(0.44) | 82.1 | 0.24(0.45) | 82.7 | 0.23(0.37) | 123.2 | 0.24(0.37) | 112.2 | 0.24(0.38) | 109.8 |

^{a}${a}_{\mathit{ph}}\left(\lambda \right)$ based;

^{b}${\widehat{a}}_{\mathit{ph}}\left(\lambda \right)$ based.

**Table 6.**Statistics of phytoplankton pigment retrieval using SVD-NNLS-9 with ${a}_{ph}\left(\lambda \right)$ at ten MODIS bands based on leave-one-out cross-validation. MAE is in mg m${}^{-3}$ (values outside the parentheses were calculated with linear-scale values, while inside the parentheses with log10-scale values) and MPE in %. “Perturb 1, 2 and 3” represent the input data with perturbations of pigment concentrations solely, ${a}_{ph}\left(\lambda \right)$ solely and both, respectively.

Pigments | Perturb 1 ${}^{\mathbf{a}}$ | Perturb 2 ${}^{\mathbf{a}}$ | Perturb 3 ${}^{\mathbf{a}}$ | Perturb 1 ${}^{\mathbf{b}}$ | Perturb 2 ${}^{\mathbf{b}}$ | Perturb 3 ${}^{\mathbf{b}}$ | ||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|

MAE | MPE | MAE | MPE | MAE | MPE | MAE | MPE | MAE | MPE | MAE | MPE | |

TChl-a | 0.25(0.18) | 28.8 | 0.21(0.14) | 19.8 | 0.28(0.18) | 29.9 | 0.01(0.01) | 0.3 | 0.03(0.02) | 2.0 | 0.03(0.02) | 1.9 |

TChl-b | 0.04(0.28) | 60.7 | 0.04(0.24) | 68.2 | 0.03(0.23) | 67.0 | 0.06(0.31) | 74.7 | 0.04(0.24) | 67.2 | 0.04(0.25) | 73.3 |

Chl-c1/2 | 0.13(0.37) | 85.3 | 0.16(0.38) | 78.3 | 0.15(0.37) | 80.9 | 0.18(0.43) | 95.0 | 0.14(0.37) | 72.2 | 0.18(0.40) | 87.6 |

But | 0.06(0.39) | 185.5 | 0.08(0.41) | 265.0 | 0.08(0.40) | 266.3 | 0.03(0.30) | 87.1 | 0.05(0.33) | 162.1 | 0.05(0.34) | 165.8 |

Diadino | 0.15(0.49) | 151.7 | 0.24(0.48) | 188.5 | 0.23(0.45) | 196.0 | 0.18(0.49) | 168.5 | 0.20(0.45) | 165.4 | 0.23(0.47) | 193.4 |

Fuco | 0.24(0.38) | 114.7 | 0.23(0.34) | 76.9 | 0.21(0.32) | 76.0 | 0.35(0.47) | 148.4 | 0.23(0.36) | 78.8 | 0.31(0.39) | 97.1 |

Hex | 0.15(0.33) | 64.7 | 0.18(0.34) | 70.4 | 0.19(0.34) | 73.4 | 0.18(0.34) | 73.3 | 0.13(0.28) | 58.4 | 0.18(0.31) | 73.2 |

Peri | 0.02(0.14) | 89.7 | 0.04(0.26) | 196.6 | 0.05(0.26) | 211.8 | 0.02(0.12) | 82.2 | 0.03(0.21) | 141.0 | 0.04(0.22) | 148.6 |

Pheo-a | 0.07(0.05) | 312.4 | 0.05(0.04) | 296.1 | 0.06(0.04) | 281.0 | 0.08(0.05) | 341.4 | 0.05(0.04) | 309.0 | 0.05(0.04) | 285.9 |

**Table 7.**The range of values, median and quartile coefficient of dispersion (CD) for the Gaussian decomposition derived pigment-specific absorption coefficient at the corresponding wavelength ${a}_{i}^{*}\left({\lambda}_{0}\right)$ (in m${}^{2}$ mg${}^{-1}$).

${\mathit{\lambda}}_{0}$ (nm) | Pigment | Decomposition of ${\mathit{a}}_{\mathit{ph}}\left(\mathit{\lambda}\right)$ | Decomposition of ${\widehat{\mathit{a}}}_{\mathit{ph}}\left(\mathit{\lambda}\right)$ | Chase et al. (2013) [22] | ||||||
---|---|---|---|---|---|---|---|---|---|---|

Range | Median | CD [%] | Range | Median | CD [%] | Range | Median | CD [%] | ||

434 | TChl-a | 0.006-0.153 | 0.036 | 21.2 | 0.020-0.179 | 0.064 | 12.9 | 0.015-0.165 | 0.065 | 35.5 |

675 | TChl-a | 0.007-0.060 | 0.017 | 28.8 | 0.024-0.046 | 0.030 | 5.9 | 0.007-0.065 | 0.019 | 22.6 |

660 | TChl-b | 0.003-0.346 | 0.060 | 38.7 | 0.006-0.540 | 0.100 | 44.5 | 0-0.408 | 0.072 | 43.0 |

638 | Chl-c1/2 | 0.004-0.163 | 0.024 | 40.0 | 0.010-0.333 | 0.039 | 31.6 | 0.010-0.247 | 0.051 | 41.2 |

492 | PPC | 0.059-0.827 | 0.142 | 31.9 | 0.077-1.012 | 0.253 | 21.5 | 0.049-0.797 | 0.097 | 40.7 |

523 | PSC | 0.011-0.192 | 0.029 | 41.5 | 0.024-0.483 | 0.048 | 28.3 | 0.010-0.243 | 0.035 | 47.2 |

**Table 8.**Statistics of phytoplankton pigments retrieval using Gaussian decomposition with package effect normalization based on leave-one-out cross-validation. Package effect normalization was performed with ${c}_{TChl-a}$ in Equation (7) calculated using cruise-specific ${a}_{ph}\left(675\right)$ (AC-S)-TChl-a (HPLC) relationships (see Section 3.1). MAE values outside the parentheses were calculated with linear-scale values, while inside the parentheses with log10-scale values.

${\mathit{\lambda}}_{0}$ [$\mathbf{nm}$] | Pigment | MAE [mg m${}^{-3}$] | MPE [%] |
---|---|---|---|

434 | TChl-a | 0.19(0.13) | 19.2 |

675 | TChl-a | 0.14(0.09) | 12.4 |

660 | TChl-b | 0.02(0.16) | 28.0 |

638 | Chl-c1/2 | 0.06(0.18) | 30.7 |

492 | PPC | 0.05(0.15) | 24.5 |

523 | PSC | 0.16(0.16) | 25.6 |

© 2019 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Liu, Y.; Boss, E.; Chase, A.; Xi, H.; Zhang, X.; Röttgers, R.; Pan, Y.; Bracher, A. Retrieval of Phytoplankton Pigments from Underway Spectrophotometry in the Fram Strait. *Remote Sens.* **2019**, *11*, 318.
https://doi.org/10.3390/rs11030318

**AMA Style**

Liu Y, Boss E, Chase A, Xi H, Zhang X, Röttgers R, Pan Y, Bracher A. Retrieval of Phytoplankton Pigments from Underway Spectrophotometry in the Fram Strait. *Remote Sensing*. 2019; 11(3):318.
https://doi.org/10.3390/rs11030318

**Chicago/Turabian Style**

Liu, Yangyang, Emmanuel Boss, Alison Chase, Hongyan Xi, Xiaodong Zhang, Rüdiger Röttgers, Yanqun Pan, and Astrid Bracher. 2019. "Retrieval of Phytoplankton Pigments from Underway Spectrophotometry in the Fram Strait" *Remote Sensing* 11, no. 3: 318.
https://doi.org/10.3390/rs11030318