Abstract

Small particles (<10μm) are often considered to play the dominant role in controlling scattering and absorption due to their relatively large numbers, which are typically found in the ocean. Here we present an approach for quantifying the size range of particles that contribute significantly to bulk inherent optical properties. We present a numerical assessment of the variability in optically significant particle sizes for simplistic populations that conform to the assumptions of homogeneous, spherical particles, and power-law size distributions. We use numerical predictions from Mie theory to suggest minimum and maximum particle sizes required for accurate predictions and observations of ocean optics for different particle size distributions (PSDs). When considering observed ranges of PSDs, our predictions suggest the need for measurements of optical properties and particles to capture information from particle sizes between diameters of 0.05–2000 μm in order to properly constrain relationships between particles and their associated optical properties. Natural particle populations in the ocean may present more complex PSDs that could be analyzed using the method presented here to establish optically significant size classes.

© 2014 Optical Society of America

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References

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  1. D. Eisma, “Flocculation and de-flocculation of suspended matter in estuaries,” Netherlands J. Sea Res. 20, 183–199 (1986).
  2. T. G. Milligan, “Particle (floc) size measurements with benthos 373 plankton silhouette camera,” J. Sea Res. 1, 93–100 (1996).
  3. R. A. Reynolds, D. Stramski, A. M. Wright, and S. B. Wozniak, “Measurements and characterization of particle size distributions in coastal waters,” J. Geophys. Res. 115, C08024 (2010).
  4. G. W. Graham, E. J. Davies, W. A. M. Nimmo-Smith, D. G. Bowers, and K. M. Braithwaite, “Interpreting LISST-100X measurements of particles with complex shape using digital in-line holography,” J. Geophys. Res. 117, C05034 (2012).
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
  9. D. Stramski and D. A. Kiefer, “Light scattering by microorganisms in the open ocean,” Prog. Oceanogr. 28, 343–383 (1991).
    [CrossRef]
  10. M. Babin, A. Morel, V. Fournier-Sicre, F. Fell, and D. Stramski, “Light scattering properties of marine particles in coastal and open ocean waters as related to the particle mass concentration,” Limnol. Oceanogr. 48, 843–859 (2003).
    [CrossRef]
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    [CrossRef]
  13. C. F. Bohren and D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, 1983).
  14. E. Aas, “Refractive index of phytoplankton derived from its metabolite composition,” J. Plankton Res. 12, 2223–2249 (1996).
  15. H. C. van de Hulst, Light Scattering by Small Particles (Dover, 1955).
  16. A. Khelifa and P. S. Hill, “Models for effective density and settling velocity of flocs,” J. Hydraul. Res. 44, 390–401 (2006).
  17. E. Boss, W. H. Slade, and P. S. Hill, “Effect of particulate aggregation in aquatic environments on the beam attenuation and its utility as a proxy for particulate mass,” Opt. Express 17, 9408–9420 (2009).
  18. G. Dall’Olmo, T. K. Westberry, M. J. Behrenfeld, E. Boss, and W. H. Slade, “Significant contribution of large particle to optical backscattering in the open ocean,” Biogeosciences 6, 947–967 (2009).

2012

G. W. Graham, E. J. Davies, W. A. M. Nimmo-Smith, D. G. Bowers, and K. M. Braithwaite, “Interpreting LISST-100X measurements of particles with complex shape using digital in-line holography,” J. Geophys. Res. 117, C05034 (2012).

2010

R. A. Reynolds, D. Stramski, A. M. Wright, and S. B. Wozniak, “Measurements and characterization of particle size distributions in coastal waters,” J. Geophys. Res. 115, C08024 (2010).

2009

2006

D. McKee and A. Cunningham, “Identification and characterization of two optical water types in the Irish Sea from in-situ inherent optical properties and seawater constituents,” Estuar. Coast. Shelf Sci. 68, 305–316 (2006).
[CrossRef]

A. Khelifa and P. S. Hill, “Models for effective density and settling velocity of flocs,” J. Hydraul. Res. 44, 390–401 (2006).

W. H. Slade and E. Boss, “Calibrated near-forward volume scattering function obtained from the LISST particle sizer,” Opt. Express 14, 8, 3602–3615 (2006).
[CrossRef]

2003

M. Babin, A. Morel, V. Fournier-Sicre, F. Fell, and D. Stramski, “Light scattering properties of marine particles in coastal and open ocean waters as related to the particle mass concentration,” Limnol. Oceanogr. 48, 843–859 (2003).
[CrossRef]

1996

E. Aas, “Refractive index of phytoplankton derived from its metabolite composition,” J. Plankton Res. 12, 2223–2249 (1996).

T. G. Milligan, “Particle (floc) size measurements with benthos 373 plankton silhouette camera,” J. Sea Res. 1, 93–100 (1996).

M. Jonasz and G. Fournier, “Approximation of the size distribution of marine particles by a sum of log-normal functions,” Limnol. Oceanogr. 41, 744–754 (1996).
[CrossRef]

1993

D. Risović, “Two component model of the sea particle size distribution,” Deep Sea Res. Part I 40, 1459–1473 (1993).

1991

D. Stramski and D. A. Kiefer, “Light scattering by microorganisms in the open ocean,” Prog. Oceanogr. 28, 343–383 (1991).
[CrossRef]

1986

D. Eisma, “Flocculation and de-flocculation of suspended matter in estuaries,” Netherlands J. Sea Res. 20, 183–199 (1986).

Aas, E.

E. Aas, “Refractive index of phytoplankton derived from its metabolite composition,” J. Plankton Res. 12, 2223–2249 (1996).

Babin, M.

M. Babin, A. Morel, V. Fournier-Sicre, F. Fell, and D. Stramski, “Light scattering properties of marine particles in coastal and open ocean waters as related to the particle mass concentration,” Limnol. Oceanogr. 48, 843–859 (2003).
[CrossRef]

Behrenfeld, M. J.

G. Dall’Olmo, T. K. Westberry, M. J. Behrenfeld, E. Boss, and W. H. Slade, “Significant contribution of large particle to optical backscattering in the open ocean,” Biogeosciences 6, 947–967 (2009).

Bohren, C. F.

C. F. Bohren and D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, 1983).

Boss, E.

Bowers, D. G.

G. W. Graham, E. J. Davies, W. A. M. Nimmo-Smith, D. G. Bowers, and K. M. Braithwaite, “Interpreting LISST-100X measurements of particles with complex shape using digital in-line holography,” J. Geophys. Res. 117, C05034 (2012).

Braithwaite, K. M.

G. W. Graham, E. J. Davies, W. A. M. Nimmo-Smith, D. G. Bowers, and K. M. Braithwaite, “Interpreting LISST-100X measurements of particles with complex shape using digital in-line holography,” J. Geophys. Res. 117, C05034 (2012).

Chang, G.

Cunningham, A.

D. McKee and A. Cunningham, “Identification and characterization of two optical water types in the Irish Sea from in-situ inherent optical properties and seawater constituents,” Estuar. Coast. Shelf Sci. 68, 305–316 (2006).
[CrossRef]

Dall’Olmo, G.

G. Dall’Olmo, T. K. Westberry, M. J. Behrenfeld, E. Boss, and W. H. Slade, “Significant contribution of large particle to optical backscattering in the open ocean,” Biogeosciences 6, 947–967 (2009).

Davies, E. J.

G. W. Graham, E. J. Davies, W. A. M. Nimmo-Smith, D. G. Bowers, and K. M. Braithwaite, “Interpreting LISST-100X measurements of particles with complex shape using digital in-line holography,” J. Geophys. Res. 117, C05034 (2012).

Eisma, D.

D. Eisma, “Flocculation and de-flocculation of suspended matter in estuaries,” Netherlands J. Sea Res. 20, 183–199 (1986).

Fell, F.

M. Babin, A. Morel, V. Fournier-Sicre, F. Fell, and D. Stramski, “Light scattering properties of marine particles in coastal and open ocean waters as related to the particle mass concentration,” Limnol. Oceanogr. 48, 843–859 (2003).
[CrossRef]

Fournier, G.

M. Jonasz and G. Fournier, “Approximation of the size distribution of marine particles by a sum of log-normal functions,” Limnol. Oceanogr. 41, 744–754 (1996).
[CrossRef]

Fournier, G. R.

M. Jonasz and G. R. Fournier, Light Scattering by Particles in Water: Theoretical and Experimental Foundations (Elsevier Academic, 2007).

Fournier-Sicre, V.

M. Babin, A. Morel, V. Fournier-Sicre, F. Fell, and D. Stramski, “Light scattering properties of marine particles in coastal and open ocean waters as related to the particle mass concentration,” Limnol. Oceanogr. 48, 843–859 (2003).
[CrossRef]

Graham, G. W.

G. W. Graham, E. J. Davies, W. A. M. Nimmo-Smith, D. G. Bowers, and K. M. Braithwaite, “Interpreting LISST-100X measurements of particles with complex shape using digital in-line holography,” J. Geophys. Res. 117, C05034 (2012).

Hill, P. S.

Huffman, D. R.

C. F. Bohren and D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, 1983).

Jonasz, M.

M. Jonasz and G. Fournier, “Approximation of the size distribution of marine particles by a sum of log-normal functions,” Limnol. Oceanogr. 41, 744–754 (1996).
[CrossRef]

M. Jonasz and G. R. Fournier, Light Scattering by Particles in Water: Theoretical and Experimental Foundations (Elsevier Academic, 2007).

Khelifa, A.

A. Khelifa and P. S. Hill, “Models for effective density and settling velocity of flocs,” J. Hydraul. Res. 44, 390–401 (2006).

Kiefer, D. A.

D. Stramski and D. A. Kiefer, “Light scattering by microorganisms in the open ocean,” Prog. Oceanogr. 28, 343–383 (1991).
[CrossRef]

McKee, D.

D. McKee and A. Cunningham, “Identification and characterization of two optical water types in the Irish Sea from in-situ inherent optical properties and seawater constituents,” Estuar. Coast. Shelf Sci. 68, 305–316 (2006).
[CrossRef]

Milligan, T. G.

T. G. Milligan, “Particle (floc) size measurements with benthos 373 plankton silhouette camera,” J. Sea Res. 1, 93–100 (1996).

Morel, A.

M. Babin, A. Morel, V. Fournier-Sicre, F. Fell, and D. Stramski, “Light scattering properties of marine particles in coastal and open ocean waters as related to the particle mass concentration,” Limnol. Oceanogr. 48, 843–859 (2003).
[CrossRef]

Nimmo-Smith, W. A. M.

G. W. Graham, E. J. Davies, W. A. M. Nimmo-Smith, D. G. Bowers, and K. M. Braithwaite, “Interpreting LISST-100X measurements of particles with complex shape using digital in-line holography,” J. Geophys. Res. 117, C05034 (2012).

Reynolds, R. A.

R. A. Reynolds, D. Stramski, A. M. Wright, and S. B. Wozniak, “Measurements and characterization of particle size distributions in coastal waters,” J. Geophys. Res. 115, C08024 (2010).

Risovic, D.

D. Risović, “Two component model of the sea particle size distribution,” Deep Sea Res. Part I 40, 1459–1473 (1993).

Slade, W. H.

Stramski, D.

R. A. Reynolds, D. Stramski, A. M. Wright, and S. B. Wozniak, “Measurements and characterization of particle size distributions in coastal waters,” J. Geophys. Res. 115, C08024 (2010).

M. Babin, A. Morel, V. Fournier-Sicre, F. Fell, and D. Stramski, “Light scattering properties of marine particles in coastal and open ocean waters as related to the particle mass concentration,” Limnol. Oceanogr. 48, 843–859 (2003).
[CrossRef]

D. Stramski and D. A. Kiefer, “Light scattering by microorganisms in the open ocean,” Prog. Oceanogr. 28, 343–383 (1991).
[CrossRef]

van de Hulst, H. C.

H. C. van de Hulst, Light Scattering by Small Particles (Dover, 1955).

Westberry, T. K.

G. Dall’Olmo, T. K. Westberry, M. J. Behrenfeld, E. Boss, and W. H. Slade, “Significant contribution of large particle to optical backscattering in the open ocean,” Biogeosciences 6, 947–967 (2009).

Whitmire, A. L.

Wozniak, S. B.

R. A. Reynolds, D. Stramski, A. M. Wright, and S. B. Wozniak, “Measurements and characterization of particle size distributions in coastal waters,” J. Geophys. Res. 115, C08024 (2010).

Wright, A. M.

R. A. Reynolds, D. Stramski, A. M. Wright, and S. B. Wozniak, “Measurements and characterization of particle size distributions in coastal waters,” J. Geophys. Res. 115, C08024 (2010).

Biogeosciences

G. Dall’Olmo, T. K. Westberry, M. J. Behrenfeld, E. Boss, and W. H. Slade, “Significant contribution of large particle to optical backscattering in the open ocean,” Biogeosciences 6, 947–967 (2009).

Deep Sea Res. Part I

D. Risović, “Two component model of the sea particle size distribution,” Deep Sea Res. Part I 40, 1459–1473 (1993).

Estuar. Coast. Shelf Sci.

D. McKee and A. Cunningham, “Identification and characterization of two optical water types in the Irish Sea from in-situ inherent optical properties and seawater constituents,” Estuar. Coast. Shelf Sci. 68, 305–316 (2006).
[CrossRef]

J. Geophys. Res.

R. A. Reynolds, D. Stramski, A. M. Wright, and S. B. Wozniak, “Measurements and characterization of particle size distributions in coastal waters,” J. Geophys. Res. 115, C08024 (2010).

G. W. Graham, E. J. Davies, W. A. M. Nimmo-Smith, D. G. Bowers, and K. M. Braithwaite, “Interpreting LISST-100X measurements of particles with complex shape using digital in-line holography,” J. Geophys. Res. 117, C05034 (2012).

J. Hydraul. Res.

A. Khelifa and P. S. Hill, “Models for effective density and settling velocity of flocs,” J. Hydraul. Res. 44, 390–401 (2006).

J. Plankton Res.

E. Aas, “Refractive index of phytoplankton derived from its metabolite composition,” J. Plankton Res. 12, 2223–2249 (1996).

J. Sea Res.

T. G. Milligan, “Particle (floc) size measurements with benthos 373 plankton silhouette camera,” J. Sea Res. 1, 93–100 (1996).

Limnol. Oceanogr.

M. Jonasz and G. Fournier, “Approximation of the size distribution of marine particles by a sum of log-normal functions,” Limnol. Oceanogr. 41, 744–754 (1996).
[CrossRef]

M. Babin, A. Morel, V. Fournier-Sicre, F. Fell, and D. Stramski, “Light scattering properties of marine particles in coastal and open ocean waters as related to the particle mass concentration,” Limnol. Oceanogr. 48, 843–859 (2003).
[CrossRef]

Netherlands J. Sea Res.

D. Eisma, “Flocculation and de-flocculation of suspended matter in estuaries,” Netherlands J. Sea Res. 20, 183–199 (1986).

Opt. Express

Prog. Oceanogr.

D. Stramski and D. A. Kiefer, “Light scattering by microorganisms in the open ocean,” Prog. Oceanogr. 28, 343–383 (1991).
[CrossRef]

Other

H. C. van de Hulst, Light Scattering by Small Particles (Dover, 1955).

C. F. Bohren and D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, 1983).

M. Jonasz and G. R. Fournier, Light Scattering by Particles in Water: Theoretical and Experimental Foundations (Elsevier Academic, 2007).

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Figures (5)

Fig. 1.
Fig. 1.

VSFs, normalized to β(0) at 100 μm for single-sized particles for a mineral refractive index (a) and (b) of 1.55+0i, and a plankton refractive index (c) and (d) of 1.45+0.001i. The wavelength of incident light is 532 nm and refractive index of water is 1.33. Note the use of linear x axis for (a) and (c) and logx axis for (b) and (d) to expand the detail of the scattering function for large and small angles.

Fig. 2.
Fig. 2.

Scattering and backscattering coefficients for single-sized particles for mineral (mp=1.55+0i) and plankton (mp=1.45+0.001i) refractive indices (a), and the associated backscattering ratios (b). The wavelength of incident light is 532 nm, and the refractive index of water is 1.33.

Fig. 3.
Fig. 3.

VSFs for PSDs with Dmax values of 0.1, 1, and 100 μm, and a fixed Dmin of 0.001 μm for mineral (a) and plankton (b) particles with refractive indices of 1.55+0i and 1.45+0.001i, respectively.

Fig. 4.
Fig. 4.

Cumulative scattering (a) and backscattering (b) for mineral (mp=1.55+0i) and plankton (mp=1.45+0.001i). Line colors are indicative of refractive index, and the line style indicates the power-law exponent (J). The gray shaded region indicates the areas within the middle 95% (i.e., from 2.5% to 97.5%) change in scattering and backscattering coefficients.

Fig. 5.
Fig. 5.

Estimations of Dmin and Dmax required to account for up to 95% of total scattering (a) and backscattering (b) for mineral (mp=1.55+0i), nonabsorbing plankton (mp=1.45+0i), and absorbing plankton (mp=1.45+0.001i) refractive indices. Line colors are indicative of refractive index; line style indicates the minimum and maximum significant diameters, respectively.

Equations (5)

Equations on this page are rendered with MathJax. Learn more.

β=0N(D)β˜CscadD,
b=2π0πβsin(θ)dθ,
bb=2ππ2πβsin(θ)dθ.
N(D)=KDJ,
β=DminDmaxN(D)β˜CscadD0N(D)β˜CscadD.

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