Abstract

Synoptic scale knowledge of the size structure of phytoplankton communities can offer insight in to primary ecosystem diversity and biogeochemical variability from operational to the decadal scales. Accordingly, obtaining estimates of size and other phytoplankton functional type descriptors within known confidence limits from remotely sensed data has become a major objective to extend the use of ocean colour data beyond chlorophyll a retrievals. Here, a new forward and inverse modelling structure is proposed to determine information about the cell size of phytoplankton communities using Standard size distributions of two layered spheres to derive a full suite of algal inherent optical properties for a coupled radiative transfer model. This new capability allows explicit quantification of the remote sensing reflectance signal attributable to changes in phytoplankton cell size. Inversion of this model reveals regions within the parameter space where ambiguity may limit potential of inversion algorithms. Validation of the algorithm within the Benguela upwelling system using independent data shows promise for ecosystem applications and further investigation of the interaction between phytoplankton functional types and optical signals. The results here suggest that the utility of assemblage related signals in spectral reflectance is highly sensitive to algal biomass, the presence of other absorbing and scattering constituents and the resultant constituent-specific inherent optical property budget. As such, optimal methods for determining phytoplankton size from (in situ or satellite) ocean colour data will likely rely on appropriately spectrally dense and optimised sensors, well characterised measurement errors including those from atmospheric correction, and an ability to appropriately limit ambiguity within the context of regional inherent optical properties.

© 2014 Optical Society of America

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  1. S. Bernard, R. Kudela, P. J. S. Franks, W. Fennel, A. Kemp, A. Fawcett, and G. C. Pitcher, “The requirements for Forecasting Harmful Algal Blooms in the Benguela,” Large Mar. Ecosyst. 14, 281–302 (2006).
  2. E. Marañón, “Inter-specific scaling of phytoplankton production and cell size in the field,” J. Plankton Res. 30(2), 157–163 (2008).
    [Crossref]
  3. 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, C08005 (2006).
  4. S. Alvain, C. Moulin, and Y. Dandonneau, “Remote sensing of phytoplankton groups in case 1 waters from global SeaWiFS imagery,” Deep Sea Res. I 52, 1989–2004 (2005).
    [Crossref]
  5. A. Ciotti and M. R. Lewis, “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]
  6. T. Konstadinov, D. A. Siegel, and S. Maritorena, “Global variability of phytoplankton functional types from space: assessment via the particle size distribution,” Biogeosciences 7, 3239–3257 (2010).
    [Crossref]
  7. R. J. W. Brewin, N. J. Hardman-Mountford, S. J. Lavender, D. Raitsos, T. Hirata, J. Uitz, E. Devred, A. Bricaud, 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]
  8. J. R. V. Zaneveld, “A theoretical derivation of the dependence of the remotely-sensed reflectance of the ocean on the inherent optical properties,” J. Geophys. Res. 100(C7), 13135–13142 (1995).
    [Crossref]
  9. A. Morel, D. Antoine, and B. Gentili, “Bidirectional reflectance of oceanic waters: accounting for Raman emission and varying particle scattering phase function,” Appl. Opt. 41(30), 6289–6306 (2002).
    [Crossref] [PubMed]
  10. A. Bricaud, M. Babin, A. Morel, and H. Claustre, “Variability in the chlorophyll-specific absorption coefficients of natural phytoplankton: Analysis and parameterization,” J. Geophys. Res. 100(C7), 13321–13332 (1995).
    [Crossref]
  11. A. Bricaud and A. Morel, “Light attenuation and scattering by phytoplanktonic cells: a theoretical modeling,” Appl. Opt. 25(4), 571–580 (1986).
    [Crossref] [PubMed]
  12. A. Quirantes and S. Bernard, “Light scattering by marine algae: two-layer spherical and nonspherical models,” J. Quant. Spectrosc. Radiat. Transfer, 89(1–4), 311–321 (2004).
    [Crossref]
  13. Y.-H. Ahn, A. Bricaud, and A. Morel, “Light backscattering efficiency and related properties of some phyto-plankters,” Deep Sea Res. 39(11–12), 1835–1855 (1992).
    [Crossref]
  14. A. L. Whitmire, W. S. Pegau, L. Karp-Boss, E. Boss, and T. J. Cowles, “Spectral backscattering properties of marine phytoplankton cultures,” Opt. Express 18(14), 15073–15093 (2010).
    [Crossref] [PubMed]
  15. W. Zhou, G. Wang, Z. Sun, W. Cao, Z. Xu, and S. Hu, “Variations in the optical scattering properties of phytoplankton cultures,” Opt. Express 20, 11189–11206 (2012).
    [Crossref] [PubMed]
  16. J. C. Kitchen and J. R. Zaneveld, “A three-layered sphere model of the optical properties of phytoplankton,” Limnol. Oceanogr. 37(8), 1680–1690 (1992).
    [Crossref]
  17. S. Bernard, T. A. Probyn, and A. Quirantes, “Simulating the optical properties of phytoplankton cells using a two-layered spherical geometry,” Biogeosci. Discuss. 6, 1–67 (2009).
    [Crossref]
  18. S. Bernard, F. A. Shillington, and T. A. Probyn, “The use of equivalent size distributions of natural phytoplankton assemblages for optical modeling,” Opt. Express 15(5), 1995–2007 (2007).
    [Crossref] [PubMed]
  19. M. Matthews and S. Bernard, “Using a two-layered sphere model to investigate the impact of gas vacuoles on the inherent optical properties of M. aeruginosa,” Biogeosciences 7, 3239–3257 (2013).
  20. M. Defoin-Platel and M. Chami, “How ambiguous is the inverse problem of ocean color in coastal waters?” J. Geophys. Res. 112, C03004 (2007).
  21. A. Morel and L. Prieur, “Analysis of variations in ocean color,” Limnol. Oceanogr. 22(4), 709–722 (1977).
    [Crossref]
  22. R. G. Barlow, H. Sessions, N. Siliulwane, H. Engel, S. Hooker, J. Aiken, J. Fishwick, V. Vicente, A. Morel, M. Chami, J. Ras, S. Bernard, M. Pfaff, J. W. Brown, and A. Fawcett, “2003: BENCAL Cruise Report, NASA/TM 2003-206892,” Tech. rep. (2003).
  23. C. S. Yentsch, “Measurement of visible light absorption by particulate matter in the ocean,” Limnol. Oceanogr. 7, 207–217 (1962).
    [Crossref]
  24. C. S. Roesler, “Theoretical and experimental approaches to improve the accuracy of particulate absorption coefficients derived from the quantitative filter technique,” Limnol. Oceanogr. 43(7), 1649–1660 (1998).
    [Crossref]
  25. T. R. Parsons, Y. Maita, and C. M. Lalli, A Manual of Chemical and Biological Methods for Seawater Analysis (Pergamon, 1984).
  26. J. E. Hansen and L. D. Travis, “Light scattering in planetary atmospheres,” Space Sci. Rev. 16, 527–610 (1974).
    [Crossref]
  27. C. S. Roesler and M. J. Perry, “In situ phytoplankton absorption, fluorescence emission, and particulate backscattering spectra determined from reflectance,” J. Geophys. Res. 100(C7), 13279–13294 (1995).
    [Crossref]
  28. S. Bernard, T. A. Probyn, and F. A. Shillington, “Towards the validation of SeaWiFS in southern African waters: the effects of gelbstoff,” S. Afr. J. Mar. Sci. 19(1), 15–25 (1998).
    [Crossref]
  29. C. D. Mobley and L. K. Sundman, HydroLight 5.0, Technical Documentation (Sequoia Scientific, Inc., 2008).
  30. H. Dierssen, R. Kudela, and J. Ryan, “Red and black tides: Quantitative analysis of water-leaving radiance and perceived color for phytoplankton, colored dissolved organic matter, and suspended sediments,” Limnol. Oceanogr. 51(6), 2646–2659 (2006).
    [Crossref]
  31. C. D. Mobley, “Fast light calculations for ocean ecosystem and inverse models,” Opt. Express 19(20), 18927–18944 (2011).
    [Crossref] [PubMed]
  32. A. Morel and S. Maritorena, “Bio-optical properties of oceanic waters: A reappraisal,” J. Geophys. Res. 106, 7163–7180 (2001).
    [Crossref]
  33. A. Albert and C. D. Mobley, “An analytical model for subsurface irradiance and remote sensing reflectance in deep and shallow case-2 waters,” Opt. Express 11(22), 2873–2890 (2003).
    [Crossref] [PubMed]
  34. I. Reda and A. Andreas, “Solar position algorithm for solar radiation applications,” Sol. Energy 76(5), 577–589 (2004).
    [Crossref]
  35. P. Werdell and S. Bailey, “An improved bio-optical data set for ocean color algorithm development and satellite data product validation,” Remote Sens. Environ. 98, 122–140 (2005).
    [Crossref]
  36. J. A. Nelder and R. Mead, “A Simplex Method for Function Minimization,” Comput. J. 7(4), 308–313 (1965).
    [Crossref]
  37. J. O’Reilly, S. Maritorena, B. G. Mitchell, D. A. Siegel, K. L. Carder, and S. A. Garver, “Ocean color chlorophyll algorithms for SeaWiFS,” J. Geophys. Res. 103, 24937–24953 (1998).
    [Crossref]
  38. G. Zibordi, F. Mélin, S. Hooker, D. D’Alimonte, and B. Holben, “An autonomous above-water system for the validation of ocean color radiance data,” IEEE Trans. Geosci. Remote Sens. 42(2), 401–415 (2004).
    [Crossref]
  39. M. Matthews, S. Bernard, and L. Robertson, “An algorithm for detecting trophic status (chlorophyll-a), cyanobacterial-dominance, surface scums and floating vegetation in inland and coastal waters,” Remote Sens. Environ. 124, 637–652 (2012).
    [Crossref]
  40. S. Agusti, C. M. Duarte, and J. Kalff, “Algal cell size and the maximum density and biomass of phytoplankton,” Limnol. Oceanogr. 32(4), 983–986 (1987).
    [Crossref]
  41. M. J. Sauer, C. S. Roesler, P. J. Werdell, and A. Barnard, “Under the hood of satellite empirical chlorophyll a algorithms: revealing the dependencies of maximum band ratio algorithms on inherent optical properties,” Opt. Express 20(19), 20920–20933 (2012).
    [Crossref] [PubMed]
  42. E. Rehm and C. D. Mobley, “Estimation of hyperspectral inherent optical properties from in-water radiometry: error analysis and application to in situ data,” Appl. Opt. 52(4), 795–817 (2013).
    [Crossref] [PubMed]
  43. L. Robertson Lain, S. Bernard, and H. Evers-King, “Biophysical modelling of phytoplankton communities from first principles using two-layered spheres: Equivalent Algal Populations (EAP) model,” Opt. Express (to be published).
  44. D. A. Aurin and H. M. Dierssen, “Advantages and limitations of ocean color remote sensing in CDOM-dominated, mineral-rich coastal and estuarine waters,” Remote Sens. Environ. 125, 181–197 (2012).
    [Crossref]

2013 (2)

M. Matthews and S. Bernard, “Using a two-layered sphere model to investigate the impact of gas vacuoles on the inherent optical properties of M. aeruginosa,” Biogeosciences 7, 3239–3257 (2013).

E. Rehm and C. D. Mobley, “Estimation of hyperspectral inherent optical properties from in-water radiometry: error analysis and application to in situ data,” Appl. Opt. 52(4), 795–817 (2013).
[Crossref] [PubMed]

2012 (4)

D. A. Aurin and H. M. Dierssen, “Advantages and limitations of ocean color remote sensing in CDOM-dominated, mineral-rich coastal and estuarine waters,” Remote Sens. Environ. 125, 181–197 (2012).
[Crossref]

M. J. Sauer, C. S. Roesler, P. J. Werdell, and A. Barnard, “Under the hood of satellite empirical chlorophyll a algorithms: revealing the dependencies of maximum band ratio algorithms on inherent optical properties,” Opt. Express 20(19), 20920–20933 (2012).
[Crossref] [PubMed]

M. Matthews, S. Bernard, and L. Robertson, “An algorithm for detecting trophic status (chlorophyll-a), cyanobacterial-dominance, surface scums and floating vegetation in inland and coastal waters,” Remote Sens. Environ. 124, 637–652 (2012).
[Crossref]

W. Zhou, G. Wang, Z. Sun, W. Cao, Z. Xu, and S. Hu, “Variations in the optical scattering properties of phytoplankton cultures,” Opt. Express 20, 11189–11206 (2012).
[Crossref] [PubMed]

2011 (2)

R. J. W. Brewin, N. J. Hardman-Mountford, S. J. Lavender, D. Raitsos, T. Hirata, J. Uitz, E. Devred, A. Bricaud, 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]

C. D. Mobley, “Fast light calculations for ocean ecosystem and inverse models,” Opt. Express 19(20), 18927–18944 (2011).
[Crossref] [PubMed]

2010 (2)

A. L. Whitmire, W. S. Pegau, L. Karp-Boss, E. Boss, and T. J. Cowles, “Spectral backscattering properties of marine phytoplankton cultures,” Opt. Express 18(14), 15073–15093 (2010).
[Crossref] [PubMed]

T. Konstadinov, D. A. Siegel, and S. Maritorena, “Global variability of phytoplankton functional types from space: assessment via the particle size distribution,” Biogeosciences 7, 3239–3257 (2010).
[Crossref]

2009 (1)

S. Bernard, T. A. Probyn, and A. Quirantes, “Simulating the optical properties of phytoplankton cells using a two-layered spherical geometry,” Biogeosci. Discuss. 6, 1–67 (2009).
[Crossref]

2008 (1)

E. Marañón, “Inter-specific scaling of phytoplankton production and cell size in the field,” J. Plankton Res. 30(2), 157–163 (2008).
[Crossref]

2007 (2)

S. Bernard, F. A. Shillington, and T. A. Probyn, “The use of equivalent size distributions of natural phytoplankton assemblages for optical modeling,” Opt. Express 15(5), 1995–2007 (2007).
[Crossref] [PubMed]

M. Defoin-Platel and M. Chami, “How ambiguous is the inverse problem of ocean color in coastal waters?” J. Geophys. Res. 112, C03004 (2007).

2006 (3)

H. Dierssen, R. Kudela, and J. Ryan, “Red and black tides: Quantitative analysis of water-leaving radiance and perceived color for phytoplankton, colored dissolved organic matter, and suspended sediments,” Limnol. Oceanogr. 51(6), 2646–2659 (2006).
[Crossref]

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, C08005 (2006).

S. Bernard, R. Kudela, P. J. S. Franks, W. Fennel, A. Kemp, A. Fawcett, and G. C. Pitcher, “The requirements for Forecasting Harmful Algal Blooms in the Benguela,” Large Mar. Ecosyst. 14, 281–302 (2006).

2005 (2)

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

P. Werdell and S. Bailey, “An improved bio-optical data set for ocean color algorithm development and satellite data product validation,” Remote Sens. Environ. 98, 122–140 (2005).
[Crossref]

2004 (3)

I. Reda and A. Andreas, “Solar position algorithm for solar radiation applications,” Sol. Energy 76(5), 577–589 (2004).
[Crossref]

A. Quirantes and S. Bernard, “Light scattering by marine algae: two-layer spherical and nonspherical models,” J. Quant. Spectrosc. Radiat. Transfer, 89(1–4), 311–321 (2004).
[Crossref]

G. Zibordi, F. Mélin, S. Hooker, D. D’Alimonte, and B. Holben, “An autonomous above-water system for the validation of ocean color radiance data,” IEEE Trans. Geosci. Remote Sens. 42(2), 401–415 (2004).
[Crossref]

2003 (1)

A. Albert and C. D. Mobley, “An analytical model for subsurface irradiance and remote sensing reflectance in deep and shallow case-2 waters,” Opt. Express 11(22), 2873–2890 (2003).
[Crossref] [PubMed]

2002 (2)

A. Morel, D. Antoine, and B. Gentili, “Bidirectional reflectance of oceanic waters: accounting for Raman emission and varying particle scattering phase function,” Appl. Opt. 41(30), 6289–6306 (2002).
[Crossref] [PubMed]

A. Ciotti and M. R. Lewis, “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 (1)

A. Morel and S. Maritorena, “Bio-optical properties of oceanic waters: A reappraisal,” J. Geophys. Res. 106, 7163–7180 (2001).
[Crossref]

1998 (3)

S. Bernard, T. A. Probyn, and F. A. Shillington, “Towards the validation of SeaWiFS in southern African waters: the effects of gelbstoff,” S. Afr. J. Mar. Sci. 19(1), 15–25 (1998).
[Crossref]

C. S. Roesler, “Theoretical and experimental approaches to improve the accuracy of particulate absorption coefficients derived from the quantitative filter technique,” Limnol. Oceanogr. 43(7), 1649–1660 (1998).
[Crossref]

J. O’Reilly, S. Maritorena, B. G. Mitchell, D. A. Siegel, K. L. Carder, and S. A. Garver, “Ocean color chlorophyll algorithms for SeaWiFS,” J. Geophys. Res. 103, 24937–24953 (1998).
[Crossref]

1995 (3)

C. S. Roesler and M. J. Perry, “In situ phytoplankton absorption, fluorescence emission, and particulate backscattering spectra determined from reflectance,” J. Geophys. Res. 100(C7), 13279–13294 (1995).
[Crossref]

J. R. V. Zaneveld, “A theoretical derivation of the dependence of the remotely-sensed reflectance of the ocean on the inherent optical properties,” J. Geophys. Res. 100(C7), 13135–13142 (1995).
[Crossref]

A. Bricaud, M. Babin, A. Morel, and H. Claustre, “Variability in the chlorophyll-specific absorption coefficients of natural phytoplankton: Analysis and parameterization,” J. Geophys. Res. 100(C7), 13321–13332 (1995).
[Crossref]

1992 (2)

Y.-H. Ahn, A. Bricaud, and A. Morel, “Light backscattering efficiency and related properties of some phyto-plankters,” Deep Sea Res. 39(11–12), 1835–1855 (1992).
[Crossref]

J. C. Kitchen and J. R. Zaneveld, “A three-layered sphere model of the optical properties of phytoplankton,” Limnol. Oceanogr. 37(8), 1680–1690 (1992).
[Crossref]

1987 (1)

S. Agusti, C. M. Duarte, and J. Kalff, “Algal cell size and the maximum density and biomass of phytoplankton,” Limnol. Oceanogr. 32(4), 983–986 (1987).
[Crossref]

1986 (1)

A. Bricaud and A. Morel, “Light attenuation and scattering by phytoplanktonic cells: a theoretical modeling,” Appl. Opt. 25(4), 571–580 (1986).
[Crossref] [PubMed]

1977 (1)

A. Morel and L. Prieur, “Analysis of variations in ocean color,” Limnol. Oceanogr. 22(4), 709–722 (1977).
[Crossref]

1974 (1)

J. E. Hansen and L. D. Travis, “Light scattering in planetary atmospheres,” Space Sci. Rev. 16, 527–610 (1974).
[Crossref]

1965 (1)

J. A. Nelder and R. Mead, “A Simplex Method for Function Minimization,” Comput. J. 7(4), 308–313 (1965).
[Crossref]

1962 (1)

C. S. Yentsch, “Measurement of visible light absorption by particulate matter in the ocean,” Limnol. Oceanogr. 7, 207–217 (1962).
[Crossref]

Agusti, S.

S. Agusti, C. M. Duarte, and J. Kalff, “Algal cell size and the maximum density and biomass of phytoplankton,” Limnol. Oceanogr. 32(4), 983–986 (1987).
[Crossref]

Ahn, Y.-H.

Y.-H. Ahn, A. Bricaud, and A. Morel, “Light backscattering efficiency and related properties of some phyto-plankters,” Deep Sea Res. 39(11–12), 1835–1855 (1992).
[Crossref]

Aiken, J.

R. G. Barlow, H. Sessions, N. Siliulwane, H. Engel, S. Hooker, J. Aiken, J. Fishwick, V. Vicente, A. Morel, M. Chami, J. Ras, S. Bernard, M. Pfaff, J. W. Brown, and A. Fawcett, “2003: BENCAL Cruise Report, NASA/TM 2003-206892,” Tech. rep. (2003).

Albert, A.

A. Albert and C. D. Mobley, “An analytical model for subsurface irradiance and remote sensing reflectance in deep and shallow case-2 waters,” Opt. Express 11(22), 2873–2890 (2003).
[Crossref] [PubMed]

Alvain, S.

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

Andreas, A.

I. Reda and A. Andreas, “Solar position algorithm for solar radiation applications,” Sol. Energy 76(5), 577–589 (2004).
[Crossref]

Antoine, D.

A. Morel, D. Antoine, and B. Gentili, “Bidirectional reflectance of oceanic waters: accounting for Raman emission and varying particle scattering phase function,” Appl. Opt. 41(30), 6289–6306 (2002).
[Crossref] [PubMed]

Aurin, D. A.

D. A. Aurin and H. M. Dierssen, “Advantages and limitations of ocean color remote sensing in CDOM-dominated, mineral-rich coastal and estuarine waters,” Remote Sens. Environ. 125, 181–197 (2012).
[Crossref]

Babin, M.

A. Bricaud, M. Babin, A. Morel, and H. Claustre, “Variability in the chlorophyll-specific absorption coefficients of natural phytoplankton: Analysis and parameterization,” J. Geophys. Res. 100(C7), 13321–13332 (1995).
[Crossref]

Bailey, S.

P. Werdell and S. Bailey, “An improved bio-optical data set for ocean color algorithm development and satellite data product validation,” Remote Sens. Environ. 98, 122–140 (2005).
[Crossref]

Barlow, R. G.

R. G. Barlow, H. Sessions, N. Siliulwane, H. Engel, S. Hooker, J. Aiken, J. Fishwick, V. Vicente, A. Morel, M. Chami, J. Ras, S. Bernard, M. Pfaff, J. W. Brown, and A. Fawcett, “2003: BENCAL Cruise Report, NASA/TM 2003-206892,” Tech. rep. (2003).

Barnard, A.

M. J. Sauer, C. S. Roesler, P. J. Werdell, and A. Barnard, “Under the hood of satellite empirical chlorophyll a algorithms: revealing the dependencies of maximum band ratio algorithms on inherent optical properties,” Opt. Express 20(19), 20920–20933 (2012).
[Crossref] [PubMed]

Bernard, S.

M. Matthews and S. Bernard, “Using a two-layered sphere model to investigate the impact of gas vacuoles on the inherent optical properties of M. aeruginosa,” Biogeosciences 7, 3239–3257 (2013).

M. Matthews, S. Bernard, and L. Robertson, “An algorithm for detecting trophic status (chlorophyll-a), cyanobacterial-dominance, surface scums and floating vegetation in inland and coastal waters,” Remote Sens. Environ. 124, 637–652 (2012).
[Crossref]

S. Bernard, T. A. Probyn, and A. Quirantes, “Simulating the optical properties of phytoplankton cells using a two-layered spherical geometry,” Biogeosci. Discuss. 6, 1–67 (2009).
[Crossref]

S. Bernard, F. A. Shillington, and T. A. Probyn, “The use of equivalent size distributions of natural phytoplankton assemblages for optical modeling,” Opt. Express 15(5), 1995–2007 (2007).
[Crossref] [PubMed]

S. Bernard, R. Kudela, P. J. S. Franks, W. Fennel, A. Kemp, A. Fawcett, and G. C. Pitcher, “The requirements for Forecasting Harmful Algal Blooms in the Benguela,” Large Mar. Ecosyst. 14, 281–302 (2006).

A. Quirantes and S. Bernard, “Light scattering by marine algae: two-layer spherical and nonspherical models,” J. Quant. Spectrosc. Radiat. Transfer, 89(1–4), 311–321 (2004).
[Crossref]

S. Bernard, T. A. Probyn, and F. A. Shillington, “Towards the validation of SeaWiFS in southern African waters: the effects of gelbstoff,” S. Afr. J. Mar. Sci. 19(1), 15–25 (1998).
[Crossref]

R. G. Barlow, H. Sessions, N. Siliulwane, H. Engel, S. Hooker, J. Aiken, J. Fishwick, V. Vicente, A. Morel, M. Chami, J. Ras, S. Bernard, M. Pfaff, J. W. Brown, and A. Fawcett, “2003: BENCAL Cruise Report, NASA/TM 2003-206892,” Tech. rep. (2003).

L. Robertson Lain, S. Bernard, and H. Evers-King, “Biophysical modelling of phytoplankton communities from first principles using two-layered spheres: Equivalent Algal Populations (EAP) model,” Opt. Express (to be published).

Boss, E.

A. L. Whitmire, W. S. Pegau, L. Karp-Boss, E. Boss, and T. J. Cowles, “Spectral backscattering properties of marine phytoplankton cultures,” Opt. Express 18(14), 15073–15093 (2010).
[Crossref] [PubMed]

Brewin, R. J. W.

R. J. W. Brewin, N. J. Hardman-Mountford, S. J. Lavender, D. Raitsos, T. Hirata, J. Uitz, E. Devred, A. Bricaud, 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.

R. J. W. Brewin, N. J. Hardman-Mountford, S. J. Lavender, D. Raitsos, T. Hirata, J. Uitz, E. Devred, A. Bricaud, 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, M. Babin, A. Morel, and H. Claustre, “Variability in the chlorophyll-specific absorption coefficients of natural phytoplankton: Analysis and parameterization,” J. Geophys. Res. 100(C7), 13321–13332 (1995).
[Crossref]

Y.-H. Ahn, A. Bricaud, and A. Morel, “Light backscattering efficiency and related properties of some phyto-plankters,” Deep Sea Res. 39(11–12), 1835–1855 (1992).
[Crossref]

A. Bricaud and A. Morel, “Light attenuation and scattering by phytoplanktonic cells: a theoretical modeling,” Appl. Opt. 25(4), 571–580 (1986).
[Crossref] [PubMed]

Brown, J. W.

R. G. Barlow, H. Sessions, N. Siliulwane, H. Engel, S. Hooker, J. Aiken, J. Fishwick, V. Vicente, A. Morel, M. Chami, J. Ras, S. Bernard, M. Pfaff, J. W. Brown, and A. Fawcett, “2003: BENCAL Cruise Report, NASA/TM 2003-206892,” Tech. rep. (2003).

Cao, W.

W. Zhou, G. Wang, Z. Sun, W. Cao, Z. Xu, and S. Hu, “Variations in the optical scattering properties of phytoplankton cultures,” Opt. Express 20, 11189–11206 (2012).
[Crossref] [PubMed]

Carder, K. L.

J. O’Reilly, S. Maritorena, B. G. Mitchell, D. A. Siegel, K. L. Carder, and S. A. Garver, “Ocean color chlorophyll algorithms for SeaWiFS,” J. Geophys. Res. 103, 24937–24953 (1998).
[Crossref]

Chami, M.

M. Defoin-Platel and M. Chami, “How ambiguous is the inverse problem of ocean color in coastal waters?” J. Geophys. Res. 112, C03004 (2007).

R. G. Barlow, H. Sessions, N. Siliulwane, H. Engel, S. Hooker, J. Aiken, J. Fishwick, V. Vicente, A. Morel, M. Chami, J. Ras, S. Bernard, M. Pfaff, J. W. Brown, and A. Fawcett, “2003: BENCAL Cruise Report, NASA/TM 2003-206892,” Tech. rep. (2003).

Ciotti, A.

A. Ciotti and M. R. Lewis, “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]

Claustre, H.

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, C08005 (2006).

A. Bricaud, M. Babin, A. Morel, and H. Claustre, “Variability in the chlorophyll-specific absorption coefficients of natural phytoplankton: Analysis and parameterization,” J. Geophys. Res. 100(C7), 13321–13332 (1995).
[Crossref]

Cowles, T. J.

A. L. Whitmire, W. S. Pegau, L. Karp-Boss, E. Boss, and T. J. Cowles, “Spectral backscattering properties of marine phytoplankton cultures,” Opt. Express 18(14), 15073–15093 (2010).
[Crossref] [PubMed]

D’Alimonte, D.

G. Zibordi, F. Mélin, S. Hooker, D. D’Alimonte, and B. Holben, “An autonomous above-water system for the validation of ocean color radiance data,” IEEE Trans. Geosci. Remote Sens. 42(2), 401–415 (2004).
[Crossref]

Dandonneau, Y.

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

Defoin-Platel, M.

M. Defoin-Platel and M. Chami, “How ambiguous is the inverse problem of ocean color in coastal waters?” J. Geophys. Res. 112, C03004 (2007).

Devred, E.

R. J. W. Brewin, N. J. Hardman-Mountford, S. J. Lavender, D. Raitsos, T. Hirata, J. Uitz, E. Devred, A. Bricaud, 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]

Dierssen, H.

H. Dierssen, R. Kudela, and J. Ryan, “Red and black tides: Quantitative analysis of water-leaving radiance and perceived color for phytoplankton, colored dissolved organic matter, and suspended sediments,” Limnol. Oceanogr. 51(6), 2646–2659 (2006).
[Crossref]

Dierssen, H. M.

D. A. Aurin and H. M. Dierssen, “Advantages and limitations of ocean color remote sensing in CDOM-dominated, mineral-rich coastal and estuarine waters,” Remote Sens. Environ. 125, 181–197 (2012).
[Crossref]

Duarte, C. M.

S. Agusti, C. M. Duarte, and J. Kalff, “Algal cell size and the maximum density and biomass of phytoplankton,” Limnol. Oceanogr. 32(4), 983–986 (1987).
[Crossref]

Engel, H.

R. G. Barlow, H. Sessions, N. Siliulwane, H. Engel, S. Hooker, J. Aiken, J. Fishwick, V. Vicente, A. Morel, M. Chami, J. Ras, S. Bernard, M. Pfaff, J. W. Brown, and A. Fawcett, “2003: BENCAL Cruise Report, NASA/TM 2003-206892,” Tech. rep. (2003).

Evers-King, H.

L. Robertson Lain, S. Bernard, and H. Evers-King, “Biophysical modelling of phytoplankton communities from first principles using two-layered spheres: Equivalent Algal Populations (EAP) model,” Opt. Express (to be published).

Fawcett, A.

S. Bernard, R. Kudela, P. J. S. Franks, W. Fennel, A. Kemp, A. Fawcett, and G. C. Pitcher, “The requirements for Forecasting Harmful Algal Blooms in the Benguela,” Large Mar. Ecosyst. 14, 281–302 (2006).

R. G. Barlow, H. Sessions, N. Siliulwane, H. Engel, S. Hooker, J. Aiken, J. Fishwick, V. Vicente, A. Morel, M. Chami, J. Ras, S. Bernard, M. Pfaff, J. W. Brown, and A. Fawcett, “2003: BENCAL Cruise Report, NASA/TM 2003-206892,” Tech. rep. (2003).

Fennel, W.

S. Bernard, R. Kudela, P. J. S. Franks, W. Fennel, A. Kemp, A. Fawcett, and G. C. Pitcher, “The requirements for Forecasting Harmful Algal Blooms in the Benguela,” Large Mar. Ecosyst. 14, 281–302 (2006).

Fishwick, J.

R. G. Barlow, H. Sessions, N. Siliulwane, H. Engel, S. Hooker, J. Aiken, J. Fishwick, V. Vicente, A. Morel, M. Chami, J. Ras, S. Bernard, M. Pfaff, J. W. Brown, and A. Fawcett, “2003: BENCAL Cruise Report, NASA/TM 2003-206892,” Tech. rep. (2003).

Franks, P. J. S.

S. Bernard, R. Kudela, P. J. S. Franks, W. Fennel, A. Kemp, A. Fawcett, and G. C. Pitcher, “The requirements for Forecasting Harmful Algal Blooms in the Benguela,” Large Mar. Ecosyst. 14, 281–302 (2006).

Garver, S. A.

J. O’Reilly, S. Maritorena, B. G. Mitchell, D. A. Siegel, K. L. Carder, and S. A. Garver, “Ocean color chlorophyll algorithms for SeaWiFS,” J. Geophys. Res. 103, 24937–24953 (1998).
[Crossref]

Gentili, B.

R. J. W. Brewin, N. J. Hardman-Mountford, S. J. Lavender, D. Raitsos, T. Hirata, J. Uitz, E. Devred, A. Bricaud, 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. Morel, D. Antoine, and B. Gentili, “Bidirectional reflectance of oceanic waters: accounting for Raman emission and varying particle scattering phase function,” Appl. Opt. 41(30), 6289–6306 (2002).
[Crossref] [PubMed]

Hansen, J. E.

J. E. Hansen and L. D. Travis, “Light scattering in planetary atmospheres,” Space Sci. Rev. 16, 527–610 (1974).
[Crossref]

Hardman-Mountford, N. J.

R. J. W. Brewin, N. J. Hardman-Mountford, S. J. Lavender, D. Raitsos, T. Hirata, J. Uitz, E. Devred, A. Bricaud, 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]

Hirata, T.

R. J. W. Brewin, N. J. Hardman-Mountford, S. J. Lavender, D. Raitsos, T. Hirata, J. Uitz, E. Devred, A. Bricaud, 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]

Holben, B.

G. Zibordi, F. Mélin, S. Hooker, D. D’Alimonte, and B. Holben, “An autonomous above-water system for the validation of ocean color radiance data,” IEEE Trans. Geosci. Remote Sens. 42(2), 401–415 (2004).
[Crossref]

Hooker, S.

G. Zibordi, F. Mélin, S. Hooker, D. D’Alimonte, and B. Holben, “An autonomous above-water system for the validation of ocean color radiance data,” IEEE Trans. Geosci. Remote Sens. 42(2), 401–415 (2004).
[Crossref]

R. G. Barlow, H. Sessions, N. Siliulwane, H. Engel, S. Hooker, J. Aiken, J. Fishwick, V. Vicente, A. Morel, M. Chami, J. Ras, S. Bernard, M. Pfaff, J. W. Brown, and A. Fawcett, “2003: BENCAL Cruise Report, NASA/TM 2003-206892,” Tech. rep. (2003).

Hooker, S. B.

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, C08005 (2006).

Hu, S.

W. Zhou, G. Wang, Z. Sun, W. Cao, Z. Xu, and S. Hu, “Variations in the optical scattering properties of phytoplankton cultures,” Opt. Express 20, 11189–11206 (2012).
[Crossref] [PubMed]

Kalff, J.

S. Agusti, C. M. Duarte, and J. Kalff, “Algal cell size and the maximum density and biomass of phytoplankton,” Limnol. Oceanogr. 32(4), 983–986 (1987).
[Crossref]

Karp-Boss, L.

A. L. Whitmire, W. S. Pegau, L. Karp-Boss, E. Boss, and T. J. Cowles, “Spectral backscattering properties of marine phytoplankton cultures,” Opt. Express 18(14), 15073–15093 (2010).
[Crossref] [PubMed]

Kemp, A.

S. Bernard, R. Kudela, P. J. S. Franks, W. Fennel, A. Kemp, A. Fawcett, and G. C. Pitcher, “The requirements for Forecasting Harmful Algal Blooms in the Benguela,” Large Mar. Ecosyst. 14, 281–302 (2006).

Kitchen, J. C.

J. C. Kitchen and J. R. Zaneveld, “A three-layered sphere model of the optical properties of phytoplankton,” Limnol. Oceanogr. 37(8), 1680–1690 (1992).
[Crossref]

Konstadinov, T.

T. Konstadinov, D. A. Siegel, and S. Maritorena, “Global variability of phytoplankton functional types from space: assessment via the particle size distribution,” Biogeosciences 7, 3239–3257 (2010).
[Crossref]

Kudela, R.

S. Bernard, R. Kudela, P. J. S. Franks, W. Fennel, A. Kemp, A. Fawcett, and G. C. Pitcher, “The requirements for Forecasting Harmful Algal Blooms in the Benguela,” Large Mar. Ecosyst. 14, 281–302 (2006).

H. Dierssen, R. Kudela, and J. Ryan, “Red and black tides: Quantitative analysis of water-leaving radiance and perceived color for phytoplankton, colored dissolved organic matter, and suspended sediments,” Limnol. Oceanogr. 51(6), 2646–2659 (2006).
[Crossref]

Lalli, C. M.

T. R. Parsons, Y. Maita, and C. M. Lalli, A Manual of Chemical and Biological Methods for Seawater Analysis (Pergamon, 1984).

Lavender, S. J.

R. J. W. Brewin, N. J. Hardman-Mountford, S. J. Lavender, D. Raitsos, T. Hirata, J. Uitz, E. Devred, A. Bricaud, 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]

Lewis, M. R.

A. Ciotti and M. R. Lewis, “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]

Maita, Y.

T. R. Parsons, Y. Maita, and C. M. Lalli, A Manual of Chemical and Biological Methods for Seawater Analysis (Pergamon, 1984).

Marañón, E.

E. Marañón, “Inter-specific scaling of phytoplankton production and cell size in the field,” J. Plankton Res. 30(2), 157–163 (2008).
[Crossref]

Maritorena, S.

T. Konstadinov, D. A. Siegel, and S. Maritorena, “Global variability of phytoplankton functional types from space: assessment via the particle size distribution,” Biogeosciences 7, 3239–3257 (2010).
[Crossref]

A. Morel and S. Maritorena, “Bio-optical properties of oceanic waters: A reappraisal,” J. Geophys. Res. 106, 7163–7180 (2001).
[Crossref]

J. O’Reilly, S. Maritorena, B. G. Mitchell, D. A. Siegel, K. L. Carder, and S. A. Garver, “Ocean color chlorophyll algorithms for SeaWiFS,” J. Geophys. Res. 103, 24937–24953 (1998).
[Crossref]

Matthews, M.

M. Matthews and S. Bernard, “Using a two-layered sphere model to investigate the impact of gas vacuoles on the inherent optical properties of M. aeruginosa,” Biogeosciences 7, 3239–3257 (2013).

M. Matthews, S. Bernard, and L. Robertson, “An algorithm for detecting trophic status (chlorophyll-a), cyanobacterial-dominance, surface scums and floating vegetation in inland and coastal waters,” Remote Sens. Environ. 124, 637–652 (2012).
[Crossref]

Mead, R.

J. A. Nelder and R. Mead, “A Simplex Method for Function Minimization,” Comput. J. 7(4), 308–313 (1965).
[Crossref]

Mélin, F.

G. Zibordi, F. Mélin, S. Hooker, D. D’Alimonte, and B. Holben, “An autonomous above-water system for the validation of ocean color radiance data,” IEEE Trans. Geosci. Remote Sens. 42(2), 401–415 (2004).
[Crossref]

Mitchell, B. G.

J. O’Reilly, S. Maritorena, B. G. Mitchell, D. A. Siegel, K. L. Carder, and S. A. Garver, “Ocean color chlorophyll algorithms for SeaWiFS,” J. Geophys. Res. 103, 24937–24953 (1998).
[Crossref]

Mobley, C. D.

E. Rehm and C. D. Mobley, “Estimation of hyperspectral inherent optical properties from in-water radiometry: error analysis and application to in situ data,” Appl. Opt. 52(4), 795–817 (2013).
[Crossref] [PubMed]

C. D. Mobley, “Fast light calculations for ocean ecosystem and inverse models,” Opt. Express 19(20), 18927–18944 (2011).
[Crossref] [PubMed]

A. Albert and C. D. Mobley, “An analytical model for subsurface irradiance and remote sensing reflectance in deep and shallow case-2 waters,” Opt. Express 11(22), 2873–2890 (2003).
[Crossref] [PubMed]

C. D. Mobley and L. K. Sundman, HydroLight 5.0, Technical Documentation (Sequoia Scientific, Inc., 2008).

Morel, A.

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, C08005 (2006).

A. Morel, D. Antoine, and B. Gentili, “Bidirectional reflectance of oceanic waters: accounting for Raman emission and varying particle scattering phase function,” Appl. Opt. 41(30), 6289–6306 (2002).
[Crossref] [PubMed]

A. Morel and S. Maritorena, “Bio-optical properties of oceanic waters: A reappraisal,” J. Geophys. Res. 106, 7163–7180 (2001).
[Crossref]

A. Bricaud, M. Babin, A. Morel, and H. Claustre, “Variability in the chlorophyll-specific absorption coefficients of natural phytoplankton: Analysis and parameterization,” J. Geophys. Res. 100(C7), 13321–13332 (1995).
[Crossref]

Y.-H. Ahn, A. Bricaud, and A. Morel, “Light backscattering efficiency and related properties of some phyto-plankters,” Deep Sea Res. 39(11–12), 1835–1855 (1992).
[Crossref]

A. Bricaud and A. Morel, “Light attenuation and scattering by phytoplanktonic cells: a theoretical modeling,” Appl. Opt. 25(4), 571–580 (1986).
[Crossref] [PubMed]

A. Morel and L. Prieur, “Analysis of variations in ocean color,” Limnol. Oceanogr. 22(4), 709–722 (1977).
[Crossref]

R. G. Barlow, H. Sessions, N. Siliulwane, H. Engel, S. Hooker, J. Aiken, J. Fishwick, V. Vicente, A. Morel, M. Chami, J. Ras, S. Bernard, M. Pfaff, J. W. Brown, and A. Fawcett, “2003: BENCAL Cruise Report, NASA/TM 2003-206892,” Tech. rep. (2003).

Moulin, C.

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

Nelder, J. A.

J. A. Nelder and R. Mead, “A Simplex Method for Function Minimization,” Comput. J. 7(4), 308–313 (1965).
[Crossref]

O’Reilly, J.

J. O’Reilly, S. Maritorena, B. G. Mitchell, D. A. Siegel, K. L. Carder, and S. A. Garver, “Ocean color chlorophyll algorithms for SeaWiFS,” J. Geophys. Res. 103, 24937–24953 (1998).
[Crossref]

Parsons, T. R.

T. R. Parsons, Y. Maita, and C. M. Lalli, A Manual of Chemical and Biological Methods for Seawater Analysis (Pergamon, 1984).

Pegau, W. S.

A. L. Whitmire, W. S. Pegau, L. Karp-Boss, E. Boss, and T. J. Cowles, “Spectral backscattering properties of marine phytoplankton cultures,” Opt. Express 18(14), 15073–15093 (2010).
[Crossref] [PubMed]

Perry, M. J.

C. S. Roesler and M. J. Perry, “In situ phytoplankton absorption, fluorescence emission, and particulate backscattering spectra determined from reflectance,” J. Geophys. Res. 100(C7), 13279–13294 (1995).
[Crossref]

Pfaff, M.

R. G. Barlow, H. Sessions, N. Siliulwane, H. Engel, S. Hooker, J. Aiken, J. Fishwick, V. Vicente, A. Morel, M. Chami, J. Ras, S. Bernard, M. Pfaff, J. W. Brown, and A. Fawcett, “2003: BENCAL Cruise Report, NASA/TM 2003-206892,” Tech. rep. (2003).

Pitcher, G. C.

S. Bernard, R. Kudela, P. J. S. Franks, W. Fennel, A. Kemp, A. Fawcett, and G. C. Pitcher, “The requirements for Forecasting Harmful Algal Blooms in the Benguela,” Large Mar. Ecosyst. 14, 281–302 (2006).

Prieur, L.

A. Morel and L. Prieur, “Analysis of variations in ocean color,” Limnol. Oceanogr. 22(4), 709–722 (1977).
[Crossref]

Probyn, T. A.

S. Bernard, T. A. Probyn, and A. Quirantes, “Simulating the optical properties of phytoplankton cells using a two-layered spherical geometry,” Biogeosci. Discuss. 6, 1–67 (2009).
[Crossref]

S. Bernard, F. A. Shillington, and T. A. Probyn, “The use of equivalent size distributions of natural phytoplankton assemblages for optical modeling,” Opt. Express 15(5), 1995–2007 (2007).
[Crossref] [PubMed]

S. Bernard, T. A. Probyn, and F. A. Shillington, “Towards the validation of SeaWiFS in southern African waters: the effects of gelbstoff,” S. Afr. J. Mar. Sci. 19(1), 15–25 (1998).
[Crossref]

Quirantes, A.

S. Bernard, T. A. Probyn, and A. Quirantes, “Simulating the optical properties of phytoplankton cells using a two-layered spherical geometry,” Biogeosci. Discuss. 6, 1–67 (2009).
[Crossref]

A. Quirantes and S. Bernard, “Light scattering by marine algae: two-layer spherical and nonspherical models,” J. Quant. Spectrosc. Radiat. Transfer, 89(1–4), 311–321 (2004).
[Crossref]

Raitsos, D.

R. J. W. Brewin, N. J. Hardman-Mountford, S. J. Lavender, D. Raitsos, T. Hirata, J. Uitz, E. Devred, A. Bricaud, 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]

Ras, J.

R. G. Barlow, H. Sessions, N. Siliulwane, H. Engel, S. Hooker, J. Aiken, J. Fishwick, V. Vicente, A. Morel, M. Chami, J. Ras, S. Bernard, M. Pfaff, J. W. Brown, and A. Fawcett, “2003: BENCAL Cruise Report, NASA/TM 2003-206892,” Tech. rep. (2003).

Reda, I.

I. Reda and A. Andreas, “Solar position algorithm for solar radiation applications,” Sol. Energy 76(5), 577–589 (2004).
[Crossref]

Rehm, E.

E. Rehm and C. D. Mobley, “Estimation of hyperspectral inherent optical properties from in-water radiometry: error analysis and application to in situ data,” Appl. Opt. 52(4), 795–817 (2013).
[Crossref] [PubMed]

Robertson, L.

M. Matthews, S. Bernard, and L. Robertson, “An algorithm for detecting trophic status (chlorophyll-a), cyanobacterial-dominance, surface scums and floating vegetation in inland and coastal waters,” Remote Sens. Environ. 124, 637–652 (2012).
[Crossref]

Robertson Lain, L.

L. Robertson Lain, S. Bernard, and H. Evers-King, “Biophysical modelling of phytoplankton communities from first principles using two-layered spheres: Equivalent Algal Populations (EAP) model,” Opt. Express (to be published).

Roesler, C. S.

M. J. Sauer, C. S. Roesler, P. J. Werdell, and A. Barnard, “Under the hood of satellite empirical chlorophyll a algorithms: revealing the dependencies of maximum band ratio algorithms on inherent optical properties,” Opt. Express 20(19), 20920–20933 (2012).
[Crossref] [PubMed]

C. S. Roesler, “Theoretical and experimental approaches to improve the accuracy of particulate absorption coefficients derived from the quantitative filter technique,” Limnol. Oceanogr. 43(7), 1649–1660 (1998).
[Crossref]

C. S. Roesler and M. J. Perry, “In situ phytoplankton absorption, fluorescence emission, and particulate backscattering spectra determined from reflectance,” J. Geophys. Res. 100(C7), 13279–13294 (1995).
[Crossref]

Ryan, J.

H. Dierssen, R. Kudela, and J. Ryan, “Red and black tides: Quantitative analysis of water-leaving radiance and perceived color for phytoplankton, colored dissolved organic matter, and suspended sediments,” Limnol. Oceanogr. 51(6), 2646–2659 (2006).
[Crossref]

Sauer, M. J.

M. J. Sauer, C. S. Roesler, P. J. Werdell, and A. Barnard, “Under the hood of satellite empirical chlorophyll a algorithms: revealing the dependencies of maximum band ratio algorithms on inherent optical properties,” Opt. Express 20(19), 20920–20933 (2012).
[Crossref] [PubMed]

Sessions, H.

R. G. Barlow, H. Sessions, N. Siliulwane, H. Engel, S. Hooker, J. Aiken, J. Fishwick, V. Vicente, A. Morel, M. Chami, J. Ras, S. Bernard, M. Pfaff, J. W. Brown, and A. Fawcett, “2003: BENCAL Cruise Report, NASA/TM 2003-206892,” Tech. rep. (2003).

Shillington, F. A.

S. Bernard, F. A. Shillington, and T. A. Probyn, “The use of equivalent size distributions of natural phytoplankton assemblages for optical modeling,” Opt. Express 15(5), 1995–2007 (2007).
[Crossref] [PubMed]

S. Bernard, T. A. Probyn, and F. A. Shillington, “Towards the validation of SeaWiFS in southern African waters: the effects of gelbstoff,” S. Afr. J. Mar. Sci. 19(1), 15–25 (1998).
[Crossref]

Siegel, D. A.

T. Konstadinov, D. A. Siegel, and S. Maritorena, “Global variability of phytoplankton functional types from space: assessment via the particle size distribution,” Biogeosciences 7, 3239–3257 (2010).
[Crossref]

J. O’Reilly, S. Maritorena, B. G. Mitchell, D. A. Siegel, K. L. Carder, and S. A. Garver, “Ocean color chlorophyll algorithms for SeaWiFS,” J. Geophys. Res. 103, 24937–24953 (1998).
[Crossref]

Siliulwane, N.

R. G. Barlow, H. Sessions, N. Siliulwane, H. Engel, S. Hooker, J. Aiken, J. Fishwick, V. Vicente, A. Morel, M. Chami, J. Ras, S. Bernard, M. Pfaff, J. W. Brown, and A. Fawcett, “2003: BENCAL Cruise Report, NASA/TM 2003-206892,” Tech. rep. (2003).

Sun, Z.

W. Zhou, G. Wang, Z. Sun, W. Cao, Z. Xu, and S. Hu, “Variations in the optical scattering properties of phytoplankton cultures,” Opt. Express 20, 11189–11206 (2012).
[Crossref] [PubMed]

Sundman, L. K.

C. D. Mobley and L. K. Sundman, HydroLight 5.0, Technical Documentation (Sequoia Scientific, Inc., 2008).

Travis, L. D.

J. E. Hansen and L. D. Travis, “Light scattering in planetary atmospheres,” Space Sci. Rev. 16, 527–610 (1974).
[Crossref]

Uitz, J.

R. J. W. Brewin, N. J. Hardman-Mountford, S. J. Lavender, D. Raitsos, T. Hirata, J. Uitz, E. Devred, A. Bricaud, 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]

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, C08005 (2006).

Vicente, V.

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Wang, G.

W. Zhou, G. Wang, Z. Sun, W. Cao, Z. Xu, and S. Hu, “Variations in the optical scattering properties of phytoplankton cultures,” Opt. Express 20, 11189–11206 (2012).
[Crossref] [PubMed]

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P. Werdell and S. Bailey, “An improved bio-optical data set for ocean color algorithm development and satellite data product validation,” Remote Sens. Environ. 98, 122–140 (2005).
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M. J. Sauer, C. S. Roesler, P. J. Werdell, and A. Barnard, “Under the hood of satellite empirical chlorophyll a algorithms: revealing the dependencies of maximum band ratio algorithms on inherent optical properties,” Opt. Express 20(19), 20920–20933 (2012).
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Whitmire, A. L.

A. L. Whitmire, W. S. Pegau, L. Karp-Boss, E. Boss, and T. J. Cowles, “Spectral backscattering properties of marine phytoplankton cultures,” Opt. Express 18(14), 15073–15093 (2010).
[Crossref] [PubMed]

Xu, Z.

W. Zhou, G. Wang, Z. Sun, W. Cao, Z. Xu, and S. Hu, “Variations in the optical scattering properties of phytoplankton cultures,” Opt. Express 20, 11189–11206 (2012).
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W. Zhou, G. Wang, Z. Sun, W. Cao, Z. Xu, and S. Hu, “Variations in the optical scattering properties of phytoplankton cultures,” Opt. Express 20, 11189–11206 (2012).
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S. Bernard, T. A. Probyn, and A. Quirantes, “Simulating the optical properties of phytoplankton cells using a two-layered spherical geometry,” Biogeosci. Discuss. 6, 1–67 (2009).
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M. Matthews and S. Bernard, “Using a two-layered sphere model to investigate the impact of gas vacuoles on the inherent optical properties of M. aeruginosa,” Biogeosciences 7, 3239–3257 (2013).

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A. Bricaud, M. Babin, A. Morel, and H. Claustre, “Variability in the chlorophyll-specific absorption coefficients of natural phytoplankton: Analysis and parameterization,” J. Geophys. Res. 100(C7), 13321–13332 (1995).
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[Crossref] [PubMed]

W. Zhou, G. Wang, Z. Sun, W. Cao, Z. Xu, and S. Hu, “Variations in the optical scattering properties of phytoplankton cultures,” Opt. Express 20, 11189–11206 (2012).
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P. Werdell and S. Bailey, “An improved bio-optical data set for ocean color algorithm development and satellite data product validation,” Remote Sens. Environ. 98, 122–140 (2005).
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R. G. Barlow, H. Sessions, N. Siliulwane, H. Engel, S. Hooker, J. Aiken, J. Fishwick, V. Vicente, A. Morel, M. Chami, J. Ras, S. Bernard, M. Pfaff, J. W. Brown, and A. Fawcett, “2003: BENCAL Cruise Report, NASA/TM 2003-206892,” Tech. rep. (2003).

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Figures (8)

Fig. 1
Fig. 1 Ranges of modelled Rrs with variations in size (effective diameter) and biomass ([Chl a]), under low bbs and low agd conditions for a) REFA and b) ES methods. Dots indicate Rrs associated with smallest cells. c) Shows example ranges of spectral Rrs at selected [Chl a] across the modelled size range using ES.

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Fig. 2
Fig. 2 Ranges of modelled Rrs to variations in Deff and [Chl a], under high bbs and high agd conditions. Note the differences in scale, where (b - ES) shows much higher Rrs values than (a - REFA). Dots indicate Rrs associated with smallest cells. c) Shows example ranges of spectral Rrs at selected [Chl a] across the modelled size range using ES.

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Fig. 3
Fig. 3 Root mean squared errors (RMSE) for Deff retrievals at different [Chl a] under various parameter combinations for a) the REFA and b) ES methods.

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Fig. 4
Fig. 4 Errors in Deff and [Chl a] estimation when inverting simulated data from the forward EAP model for low agd and low bbs conditions for a) REFA and b) ES methods.

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Fig. 5
Fig. 5 a) Size dependent ranges of OC4 maximum band reflectance ratios, versus [Chl a] from the forward model using EcoLight-S to simulate the range of water types covered by the NOMAD data set. In all cases larger cells are associated with the higher Rrs ratio. b) Example ranges of spectra from samples with similar (within 10%) Rrs ratios to highlight the significant ambiguity within a reasonable error that could be associated with Rrs measurements.

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Fig. 6
Fig. 6 Correlation between H-TSRB derived (range given by blue fill) and modelled Lu(−0.66 m), with grey shading denoting standard error and root mean squared errors (RMSE) represented by the dot colour (n=75) for a) REFA and b) ES methods.

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Fig. 7
Fig. 7 Correlation between spectrophotometer derived (range given by blue fill) and modelled aϕ. Gray shading denotes standard error and root mean squared errors (RMSE) represented by the dot colour (n=49) for a) REFA and b) ES methods.

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Fig. 8
Fig. 8 Correlations between measured and algorithm predicted a) [Chl a] (n= 73) and b) Deff (n=44). Shaded areas show 95% confidence intervals based on linear regression for each data set. Red and blue dots represent values derived from the REFA and ES approaches respectively. r2 values for [Chl a] estimation were 0.86 (REFA) and 0.80 (ES), and 0.45 (REFA) and 0.25 (ES) for Deff estimates, with p<0.001 in all cases. Estimates of absolute percentage error (|ψ|) and bias (ψ) are given as per the method used in [38].

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Tables (1)

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Table 1 Summary of parameter ranges used in forward model data simulation

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Equations (10)

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R r s = L u ( 0 + , λ ) E d ( 0 + , λ ) = f Q b b ( λ ) a ( λ ) + b b ( λ )
D eff = ∫ 1 100 π 6 d 3 F ( d ) d ( d ) ∫ 1 100 π 4 d 2 F ( d ) d ( d )
a g d ( λ ) ( m − 1 ) = a g d ( 400 ) exp [ − S ( λ − 400 ) ]
a ϕ ( λ ) = [ Chl a ] . a ϕ * ( λ , F * ( d ) ) ;
b b ϕ ( λ ) = [ Chl a ] . b b ϕ * ( λ , F * ( d ) ) ;
F ( d ) = A S F d 2 [ ( 1 − 3 V eff ) / V eff ] exp [ d 2 / ( D eff 2 V eff ) ]
V ¯ = π 6 ∫ F ( d ) d 3 d ( d )
F * ( d ) = F ( d ) V c i
K u = ( a + b b ) [ 1 + ( b b a + b b ) ] 3.452 ( 1 − 0.2786 cos θ s )
L u ( z , λ ) = f Q η 2 τ b b ( λ ) a ( λ ) + b b ( λ ) E d ( λ ) exp ( − K u ( λ ) z )

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