Abstract

For a particle population with known size, composition, structure, and shape distributions, its volume scattering function (VSF) can be estimated from first principles through a governing relationship, the Fredholm linear integral equation of the first kind. Inverting the Fredholm equation to derive the composition and size distribution of particles from measured VSFs remains challenging because 1) the solution depends on the kernel function, and 2) the kernel function needs to be constructed to avoid singularity. In this study, a thorough review of the earlier and current inversion techniques is provided. An inversion method based on nonnegative least squares is presented and evaluated using the VSFs measured by a prototype volume scattering meter at the LEO-15 site off the New Jersey coast. The kernel function was built by a compilation of individual subpopulations, each of which follows a lognormal size distribution and whose characteristic size and refractive index altogether cover the entire ranges of natural variability of potential marine particles of the region. Sensitivity analyses were conducted to ensure the kernel function being constructed is neither singular nor pathological. A total of 126 potential subpopulations were identified, among which 11 are common in more than half of the inversions and only five consistently present (>90% of measurements). These five subpopulations can be interpreted as small colloidal type particles of sizes around 0.02μm, submicrometer detritus-type particles (nr=1.02, rmode=0.2μm), two micrometer-sized subpopulations with one relatively soft (nr=1.04 and rmode=1.6μm) and the other relatively refringent (nr=1.10 and rmode=3.2μm), and bubbles of relatively large sizes (nr=0.75 and rmode=10μm). Reconstructed PSDs feature a bimodal shape, with the smaller peak dominated by the colloidal subpopulations and the larger particles closely approximated by a power-law function. The Junge-type slope averages 4.0±0.2, in close agreement with the well-known mean value of 4.0 over the global ocean. The distribution of the refractive index suggested a dominance of particles of higher water content, also in agreement with earlier results based on the backscattering ratio and attenuation coefficients at the same area. Surprisingly, the colloidal-type subpopulations, which have often been operationally classified as “dissolved” and neglected for their scattering, exhibit significant backscattering with contributions of up to 40% over the entire backward angles.

© 2011 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. S. Twomey, Introduction to the Mathematics of Inversion in Remote Sensing and Indirect Measurements, Developments in Geomathematics (Elsevier, 1977).
  2. M. R. Jones, B. P. Curry, M. Q. Brewster, and K. H. Leong, “Inversion of light-scattering measurements for particle size and optical constants: theoretical study,” Appl. Opt. 33, 4025–4034 (1994).
    [CrossRef]
  3. A. Morel, “The scattering of light by seawater: experimental results and theoretical approach,” in Optics of the Sea, Interface and In-Water Transmission and Imaging (NATO Advisory Group for Aerospace Research and Development, 1973).
  4. M. E. Lee and M. R. Lewis, “A new method for the measurement of the optical volume scattering function in the upper ocean,” J. Atmos. Ocean. Technol. 20, 563–571 (2003).
    [CrossRef]
  5. J. M. Sullivan and M. S. Twardowski, “Angular shape of the oceanic particulate volume scattering function in the backward direction,” Appl. Opt. 48, 6811–6819 (2009).
    [CrossRef]
  6. M. S. Twardowski, C. Moore, J. Sullivan, M. Slivkoff, S. Freeman, and J. R. V. Zaneveld, are preparing a manuscript to be called “Volume scattering functions for selected ocean waters: revisited.”
  7. Y. C. Agrawal and H. C. Pottsmith, “Instruments for particle size and settling velocity observations in sediment transport,” Mar. Geol. 168, 89–114 (2000).
    [CrossRef]
  8. E. Boss, W. S. Pegau, M. Lee, M. Twardowski, E. Shybanov, and G. Korotaev, “Particulate backscattering ratio at LEO 15 and its use to study particle composition and distribution,” J. Geophys. Res. 109, C01014 (2004).
    [CrossRef]
  9. X. Zhang, M. R. Lewis, M. Lee, B. D. Johnson, and G. Korotaev, “Volume scattering function of natural bubble populations,” Limnol. Oceanogr. 47, 1273–1282 (2002).
    [CrossRef]
  10. J.-F. Berthon, E. Shybanov, M. E. G. Lee, and G. Zibordi, “Measurements and modeling of the volume scattering function in the coastal northern Adriatic Sea,” Appl. Opt. 46, 5189–5203(2007).
    [CrossRef]
  11. M. Chami, E. B. Shybanov, T. Y. Churilova, G. A. Khomenko, M. E. G. Lee, O. V. Martynov, G. A. Berseneva, and G. K. Korotaev, “Optical properties of the particles in the Crimea coastal waters (Black Sea),” J. Geophys. Res. 110, C11020 (2005).
    [CrossRef]
  12. M. S. Twardowski, E. Boss, J. B. Macdonald, W. S. Pegau, A. H. Barnard, and J. R. V. Zaneveld, “A model for estimating bulk refractive index from the optical backscattering ratio and the implications for understanding particle composition in case I and case II waters,” J. Geophys. Res. 106, 14129–14142(2001).
    [CrossRef]
  13. G. Kullenberg, “Scattering of light by Sargasso Sea water,” Deep-Sea Res. 15, 423–432 (1968).
  14. G. Kullenberg, “Observed and computed scattering functions,” in Optical Aspects of Oceanography, N.G.Jerlov and E.Steeman-Nielsen, eds. (Academic, 1974), pp. 25–49.
  15. H. R. Gordon and O. B. Brown, “A theoretical model of light scattering by Sargasso Sea particulates,” Limnol. Oceanogr. 17, 826–832 (1972).
    [CrossRef]
  16. O. B. Brown and H. R. Gordon, “Two component Mie scattering models of Sargasso Sea particles,” Appl. Opt. 12, 2461–2465 (1973).
    [CrossRef]
  17. J. R. V. Zaneveld and H. Pak, “Method for the determination of the index of refraction of particles suspended in the ocean,” J. Opt. Soc. Am. 63, 321–324 (1973).
    [CrossRef]
  18. F. T. Manheim, R. H. Meade, and G. C. Bond, “Suspended matter in surface waters of the Atlantic continental margin from Cape Cod to the Florida Keys,” Science 167, 371–376(1970).
    [CrossRef]
  19. G. F. Beardsley, H. J. Pak, and K. L. Carder, “Light scattering and suspended particles in the Eastern Equatorial Pacific ocean,” J. Geophys. Res. 75, 2837–2845 (1970).
    [CrossRef]
  20. D. Stramski and D. A. Kiefer, “Light scattering by microorganisms in the open ocean,” Prog. Oceanogr. 28, 343–383 (1991).
    [CrossRef]
  21. G. Dall’Olmo, T. K. Westberry, M. J. Behrenfeld, E. Boss, and W. H. Slade, “Significant contribution of large particles to optical backscattering in the open ocean,” Biogeosciences 6, 947–967 (2009).
    [CrossRef]
  22. O. B. Brown and H. R. Gordon, “Size-refractive index distribution of clear coastal water particulates from light scattering,” Appl. Opt. 13, 2874–2881 (1974).
    [CrossRef]
  23. M. Jonasz and H. Prandke, “Comparison of measured and computed light scattering in the Baltic,” Tellus 38B, 144–157 (1986).
    [CrossRef]
  24. J. S. Schoonmaker, R. R. Hammond, A. L. Heath, and J. S. Cleveland, “A numerical model for prediction of sublittoral optical visibility,” Proc. SPIE 2258, 685–702 (1994).
    [CrossRef]
  25. T. J. Petzold, “Volume scattering function for selected ocean waters,” SIO Ref. 72-78, Scripps Institute of Oceanography, La Jolla, 1972.
  26. J. R. V. Zaneveld, D. M. Roach, and H. Pak, “The determination of the index of refraction distribution of oceanic particulates,” J. Geophys. Res. 79, 4091–4095 (1974).
    [CrossRef]
  27. R. Fletcher and M. J. D. Powell, “A rapidly convergent descent method for minimization,” Comput. J. 6, 163–168(1963).
  28. O. V. Kopelevich, “Low-parametric model of seawater optical properties,” in Ocean Optics I: Physical Ocean Optics, A.S.Monin, ed. (Nauka, 1983), pp. 208–234.
  29. C. D. Mobley, Light and Water: Radiative Transfer in Natural Waters (Academic, 1994).
  30. K. S. Shifrin, Physical Optics of Ocean Water, AIP Translation Series (American Institute of Physics, 1988).
  31. G. R. Fournier and J. L. Forand, “Analytical phase function for ocean water,” Proc. SPIE 2258, 194–201 (1994).
    [CrossRef]
  32. J. H. Chin, C. M. Sliepcevich, and M. Tribus, “Particle size distributions from angular variation of intensity of forward-scattered light at very small angles,” J. Phys. Chem. 59, 841–844 (1955).
    [CrossRef]
  33. S. D. Coston and N. George, “Particle sizing by inversion of the optical transform pattern,” Appl. Opt. 30, 4785–4794(1991).
    [CrossRef]
  34. J. C. Knight, D. Ball, and G. N. Robertson, “Analytical inversion for laser diffraction spectrometry giving improved resolution and accuracy in size distribution,” Appl. Opt. 30, 4795–4799 (1991).
    [CrossRef]
  35. J. B. Riley and Y. C. Agrawal, “Sampling and inversion of data in diffraction particle sizing,” Appl. Opt. 30, 4800–4817 (1991).
    [CrossRef]
  36. R. A. Reynolds, D. Stramski, V. M. Wright, and S. B. Woźniak, “Measurements and characterization of particle size distributions in coastal waters,” J. Geophys. Res. 115, C08024 (2010).
    [CrossRef]
  37. L. Karp-Boss, L. Azevedo, and E. Boss, “LISST-100 measurements of phytoplankton size distribution: evaluation of the effects of cell shape,” Limnol. Oceanogr. Methods 5, 396–406 (2007).
  38. B. G. Krishnappan, “In situ size distribution of suspended particles in the Fraser River,” J. Hydraul. Eng. 126, 561–569 (2000).
    [CrossRef]
  39. T. Serra, J. Colomer, X. P. Cristina, X. Vila, J. B. Arellano, and X. Casamitjana, “Evaluation of laser in situ scattering instrument for measuring concentration of phytoplankton, purple sulfur bacteria, and suspended inorganic sediments in lakes,” J. Environ. Eng. 127, 1023–1030 (2001).
    [CrossRef]
  40. Y. C. Agrawal and P. Traykovski, “Particles in the bottom boundary layer: concentration and size dynamics through events,” J. Geophys. Res. 106, 9533–9542 (2001).
    [CrossRef]
  41. J. W. Gartner, R. T. Cheng, P.-F. Wang, and K. Richter, “Laboratory and field evaluations of the LISST-100 instrument for suspended particle size determinations,” Mar. Geol. 175, 199–219 (2001).
    [CrossRef]
  42. J. H. Ahn and S. B. Grant, “Size distribution, sources, and seasonality of suspended particles in southern California marine bathing waters,” Environ. Sci. Technol. 41, 695–702 (2007).
    [CrossRef]
  43. R. W. Sheldon, A. Prakash, and W. H. Sutcliffe, “The size distribution of particles in the ocean,” Limnol. Oceanogr. 17, 327–340 (1972).
    [CrossRef]
  44. T. Platt and K. Denman, “Organisation in the pelagic ecosystem,” Helgoland Mar. Res. 30, 575–581 (1977).
  45. T. Fenchel, “Intrinsic rate of natural increase: the relationship with body size,” Oecologia 14, 317–326 (1974).
    [CrossRef]
  46. O. Ulloa, S. Sathyendranath, and T. Platt, “Effect of the particle-size distribution on the backscattering ratio in seawater,” Appl. Opt. 33, 7070–7077 (1994).
    [CrossRef]
  47. J. W. Campbell, “The lognormal distribution as a model for bio-optical variability in the sea,” J. Geophys. Res. 100, 13237–13254 (1995).
    [CrossRef]
  48. A. R. Longhurst, I. Koike, W. K. W. Li, J. Rodriguez, P. Dickie, P. Kepay, F. Partensky, B. Bautista, J. Ruiz, M. Wells, and D. F. Bird, “Sub-micron particles in northwest Atlantic shelf water,” Deep-Sea Res. A 39, 1–7 (1992).
    [CrossRef]
  49. R. D. Vaillancourt and W. M. Balch, “Size distribution of marine submicron particles determined by flow field-flow fractionation,” Limnol. Oceanogr. 45, 485–492 (2000).
    [CrossRef]
  50. M. L. Wells and E. D. Goldberg, “Marine submicron particles,” Mar. Chem. 40, 5–18 (1992).
    [CrossRef]
  51. A. Yamasaki, H. Fukuda, R. Fukuda, T. Miyajima, T. Nagata, H. Ogawa, and I. Koike, “Submicrometer particles in northwest Pacific coastal environments: abundance, size distribution, and biological origins,” Limnol. Oceanogr. 43, 536–542(1998).
    [CrossRef]
  52. C. E. Lambert, C. Jehanno, N. Silverberg, J. C. Brun-Cottan, and R. Chesselet, “Log-normal distribution of suspended particles in the open ocean,” J. Mar. Res. 39, 77–98 (1981).
  53. M. Jonasz, “Nonspherical sediment particles: comparison of size and volume distributions obtained with an optical and a resistive particle counter,” Mar. Geol. 78, 137–142 (1987).
    [CrossRef]
  54. B. Epstein, “The mathematical description of certain breakage mechanisms leading to the logarithmico-normal distribution,” J. Franklin Inst. 244, 471–477 (1947).
    [CrossRef]
  55. F. S. Lai, S. K. Friedlander, J. Pich, and G. M. Hidy, “The self-preserving particle size distribution for Brownian coagulation in the free-molecule regime,” J. Colloid Interface Sci. 39, 395–405 (1972).
    [CrossRef]
  56. J. W. Campbell and C. M. Yentsch, “Variance within homogeneous phytoplankton populations, I: theoretical framework for interpreting histograms,” Cytometry 10, 587–595 (1989).
    [CrossRef]
  57. J. W. Campbell and C. M. Yentsch, “Variance within homogeneous phytoplankton populations, II: Analysis of clonal cultures,” Cytometry 10, 596–604 (1989).
    [CrossRef]
  58. J. W. Campbell, C. M. Yentsch, and T. L. Cucci, “Variance within homogeneous phytoplankton populations, III: analysis of natural populations,” Cytometry 10, 605–611 (1989).
    [CrossRef]
  59. H. C. van de Hulst, Light Scattering by Small Particles(Dover, 1981).
  60. A. Morel and A. Bricaud, “Inherent optical properties of algal cells, including picoplankton. Theoretical and experimental results,” Can. Bull. Fish. Aquat. Sci. 214, 521–559 (1986).
  61. E. Aas, “Refractive index of phytoplankton derived from its metabolite composition,” J. Plankton Res. 18, 2223–2249(1996).
    [CrossRef]
  62. R. E. Green, H. M. Sosik, R. J. Olson, and M. D. DuRand, “Flow cytometric determination of size and complex refractive index for marine particles: comparison with independent and bulk estimates,” Appl. Opt. 42, 526–541 (2003).
    [CrossRef]
  63. W. R. Clavano, E. Boss, and L. Karp-Boss, “Inherent optical properties of non-spherical marine-like particles—from theory to observation,” in Oceanography and Marine Biology: An Annual Review (Taylor & Francis, 2007), Vol.  45, pp. 1–38.
  64. M. Jonasz, “Nonsphericity of suspended marine particles and its influence on light scattering,” Limnol. Oceanogr. 32, 1059–1065 (1987).
    [CrossRef]
  65. J. C. Kitchen and J. R. V. Zaneveld, “A three-layered sphere model of the optical properties of phytoplankton,” Limnol. Oceanogr. 37, 1680–1690 (1992).
    [CrossRef]
  66. X. Zhang, M. R. Lewis, and B. D. Johnson, “Influence of bubbles on scattering of light in the ocean,” Appl. Opt. 37, 6525–6536 (1998).
    [CrossRef]
  67. R. A. Meyer, “Light scattering from biological cells: dependence of backscattering radiation on membrane thickness and refractive index,” Appl. Opt. 18, 585–588 (1979).
    [CrossRef]
  68. C. F. Bohren and D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, 1983).
  69. D. Risovic, “Two-component model of sea particle size distribution,” Deep-Sea Res. I 40, 1459–1473 (1993).
    [CrossRef]
  70. O. Ulloa, S. Sathyendranath, T. Platt, and R. A. Quiñones, “Light scattering by marine heterotrophic bacteria,” J. Geophys. Res. 97, 9619–9629 (1992).
    [CrossRef]
  71. K. L. Carder, G. Beardsley, Jr., and H. Pak, “Particle size distribution in the Eastern Equatorial Pacific,” J. Geophys. Res. 76, 5070–5077 (1971).
    [CrossRef]
  72. M. I. Mishchenko and L. D. Travis, “Light scattering by polydispersions of randomly oriented spheroids with sizes comparable to wavelengths of observation,” Appl. Opt. 33, 7206–7225 (1994).
    [CrossRef]
  73. O. Schofield, T. Bergmann, P. Bissett, J. F. Grassle, D. B. Haidvogel, J. Kohut, M. Moline, and S. M. Glenn, “The Long-term Ecosystem Observatory: an integrated coastal observatory,” IEEE J. Oceanic Eng. 27, 146–154 (2002).
    [CrossRef]
  74. X. Zhang and L. Hu, “Estimating scattering of pure water from density fluctuation of the refractive index,” Opt. Express 17, 1671–1678 (2009).
    [CrossRef]
  75. X. Zhang, L. Hu, and M.-X. He, “Scattering by pure seawater: effect of salinity,” Opt. Express 17, 5698–5710 (2009).
    [CrossRef]
  76. O. Dubovik, “Optimization of numerical inversion in photopolarimetric remote sensing,” in Photopolarimetry in Remote Sensing, G.Videen, Y.Yatskiv, and M.Mishchenko, eds. (Kluwer, 2004), pp. 65–106.
  77. B. P. Curry, “Constrained eigenfunction method for the inversion of remote sensing data: application to particle size determination from light scattering measurements,” Appl. Opt. 28, 1345–1355 (1989).
    [CrossRef]
  78. M. M. Lozano, E. Talu, and M. L. Longo, “Dissolution of microbubbles generated in seawater obtained offshore: behavior and surface tension measurements,” J. Geophys. Res. 112, C12001 (2007).
    [CrossRef]
  79. M. L. Longo, Department of Chemical Engineering and Materials Science, University of California, Davis, Calif., USA (personal communication, 2010).
  80. C. L. Lawson and R. J. Hanson, Solving Least Squares Problems, Automatic Computation (Prentice-Hall, 1974).
  81. L. F. Portugal, J. J. Judice, and L. N. Vicente, “A comparison of block pivoting and interior-point algorithms for linear least squares problems with nonnegative variables,” Math. Comput. 63, 625–643 (1994).
    [CrossRef]
  82. L. Stemmann, D. Eloire, A. Sciandra, G. A. Jackson, L. Guidi, M. Picheral, and G. Gorsky, “Volume distribution for particles between 3.5 to 2000 μm in the upper 200 m region of the South Pacific Gyre,” Biogeosciences 5, 299–310 (2008).
    [CrossRef]
  83. B. D. Johnson, “Bubble populations: background and breaking waves,” in Oceanic Whitecaps and Their Role in Air-Sea Exchange Processes, E.C.Monahan and G.Mac Niocail, eds. (Reidel, 1986), pp. 69–73.
  84. O. Dubovik, A. Smirnov, B. N. Holben, M. D. King, Y. J. Kaufman, T. F. Eck, and I. Slutsker, “Accuracy assessments of aerosol optical properties retrieved from Aerosol Robotic Network (AERONET) Sun and sky radiance measurements,” J. Geophys. Res. 105, 9791–9806(2000).
    [CrossRef]
  85. M. Jonasz and G. R. Fournier, “Approximation of the size distribution of marine particles by a sum of log-normal functions,” Limnol. Oceanogr. 41, 744–754 (1996).
    [CrossRef]
  86. M. L. Wells and E. D. Goldberg, “Occurrence of small colloids in sea water,” Nature 353, 342–344 (1991).
    [CrossRef]
  87. K. E. Wommack and R. R. Colwell, “Virioplankton: viruses in aquatic ecosystems,” Microbiol. Mol. Biol. Rev. 64, 69–114(2000).
    [CrossRef]
  88. A. Morel and Y.-H. Ahn, “Optics of heterotrophic nanoflagellates and ciliates: a tentative assessment of their scattering role in oceanic waters compared to those of bacterial and algal cells,” J. Mar. Res. 49, 177–202 (1991).
    [CrossRef]
  89. D. Stramski, E. Boss, D. Bogucki, and K. J. Voss, “The role of seawater constituents in light backscattering in the ocean,” Prog. Oceanogr. 61, 27–56 (2004).
    [CrossRef]
  90. W. Arnott and P. L. Marston, “Unfolded optical glory of spheroids: backscattering of laser light from freely rising spheroidal air bubbles in water,” Appl. Opt. 30, 3429–3442(1991).
    [CrossRef]
  91. H. M. Nussenzveig, “Does the glory have a simple explanation?,” Opt. Lett. 27, 1379–1381 (2002).
    [CrossRef]
  92. M. I. Mishchenko, L. D. Travis, and A. A. Lacis, Scattering, Absorption, and Emission of Light by Small Particles(Cambridge University, 2002).
  93. C. F. Bohren and S. B. Singham, “Backscattering by nonspherical particles: a review of methods and suggested new approaches,” J. Geophys. Res. 96, 5269–5277 (1991).
    [CrossRef]
  94. M. Twardowski, X. Zhang, S. Freeman, M. Slivkoff, J. Sullivan, H. Czerski, S. Vagle, Y. You, and G. Kattawar, “Inverting the volume scattering function to infer particle composition at the near-surface,” in Proceedings of Ocean Optics XX (2011).
  95. L. Bi, P. Yang, G. W. Kattawar, and R. Kahn, “Modeling optical properties of mineral aerosol particles by using nonsymmetric hexahedra,” Appl. Opt. 49, 334–342 (2010).
    [CrossRef]
  96. H. Czerski, M. Twardowski, S. Vagle, and M. Slivkoff, “Resolving bubble size distributions and dynamics in near-surface waters with optics and acoustics,” in Proceedings of Ocean Optics XX (2011).
  97. M. Jonasz and G. R. Fournier, Light Scattering by Particles in Water: Theoretical and Experimental Foundations(Academic, 2007).
  98. R. D. Vaillancourt, C. W. Brown, R. R. L. Guillard, and W. M. Balch, “Light backscattering properties of marine phytoplankton: relationships to cell size, chemical composition and taxonomy,” J. Plankton Res. 26, 191–212(2004).
    [CrossRef]
  99. H. Volten, J. F. de Haan, J. W. Hovenier, R. Schreurs, W. Vassen, and A. G. Decker, “Laboratory measurements of angular distributions of light scattered by phytoplankton and silt,” Limnol. Oceanogr. 43, 1180–1197 (1998).
    [CrossRef]
  100. 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, 15073–15093(2010).
    [CrossRef]

2010 (3)

2009 (4)

2008 (1)

L. Stemmann, D. Eloire, A. Sciandra, G. A. Jackson, L. Guidi, M. Picheral, and G. Gorsky, “Volume distribution for particles between 3.5 to 2000 μm in the upper 200 m region of the South Pacific Gyre,” Biogeosciences 5, 299–310 (2008).
[CrossRef]

2007 (4)

M. M. Lozano, E. Talu, and M. L. Longo, “Dissolution of microbubbles generated in seawater obtained offshore: behavior and surface tension measurements,” J. Geophys. Res. 112, C12001 (2007).
[CrossRef]

L. Karp-Boss, L. Azevedo, and E. Boss, “LISST-100 measurements of phytoplankton size distribution: evaluation of the effects of cell shape,” Limnol. Oceanogr. Methods 5, 396–406 (2007).

J. H. Ahn and S. B. Grant, “Size distribution, sources, and seasonality of suspended particles in southern California marine bathing waters,” Environ. Sci. Technol. 41, 695–702 (2007).
[CrossRef]

J.-F. Berthon, E. Shybanov, M. E. G. Lee, and G. Zibordi, “Measurements and modeling of the volume scattering function in the coastal northern Adriatic Sea,” Appl. Opt. 46, 5189–5203(2007).
[CrossRef]

2005 (1)

M. Chami, E. B. Shybanov, T. Y. Churilova, G. A. Khomenko, M. E. G. Lee, O. V. Martynov, G. A. Berseneva, and G. K. Korotaev, “Optical properties of the particles in the Crimea coastal waters (Black Sea),” J. Geophys. Res. 110, C11020 (2005).
[CrossRef]

2004 (3)

E. Boss, W. S. Pegau, M. Lee, M. Twardowski, E. Shybanov, and G. Korotaev, “Particulate backscattering ratio at LEO 15 and its use to study particle composition and distribution,” J. Geophys. Res. 109, C01014 (2004).
[CrossRef]

D. Stramski, E. Boss, D. Bogucki, and K. J. Voss, “The role of seawater constituents in light backscattering in the ocean,” Prog. Oceanogr. 61, 27–56 (2004).
[CrossRef]

R. D. Vaillancourt, C. W. Brown, R. R. L. Guillard, and W. M. Balch, “Light backscattering properties of marine phytoplankton: relationships to cell size, chemical composition and taxonomy,” J. Plankton Res. 26, 191–212(2004).
[CrossRef]

2003 (2)

M. E. Lee and M. R. Lewis, “A new method for the measurement of the optical volume scattering function in the upper ocean,” J. Atmos. Ocean. Technol. 20, 563–571 (2003).
[CrossRef]

R. E. Green, H. M. Sosik, R. J. Olson, and M. D. DuRand, “Flow cytometric determination of size and complex refractive index for marine particles: comparison with independent and bulk estimates,” Appl. Opt. 42, 526–541 (2003).
[CrossRef]

2002 (3)

H. M. Nussenzveig, “Does the glory have a simple explanation?,” Opt. Lett. 27, 1379–1381 (2002).
[CrossRef]

O. Schofield, T. Bergmann, P. Bissett, J. F. Grassle, D. B. Haidvogel, J. Kohut, M. Moline, and S. M. Glenn, “The Long-term Ecosystem Observatory: an integrated coastal observatory,” IEEE J. Oceanic Eng. 27, 146–154 (2002).
[CrossRef]

X. Zhang, M. R. Lewis, M. Lee, B. D. Johnson, and G. Korotaev, “Volume scattering function of natural bubble populations,” Limnol. Oceanogr. 47, 1273–1282 (2002).
[CrossRef]

2001 (4)

M. S. Twardowski, E. Boss, J. B. Macdonald, W. S. Pegau, A. H. Barnard, and J. R. V. Zaneveld, “A model for estimating bulk refractive index from the optical backscattering ratio and the implications for understanding particle composition in case I and case II waters,” J. Geophys. Res. 106, 14129–14142(2001).
[CrossRef]

T. Serra, J. Colomer, X. P. Cristina, X. Vila, J. B. Arellano, and X. Casamitjana, “Evaluation of laser in situ scattering instrument for measuring concentration of phytoplankton, purple sulfur bacteria, and suspended inorganic sediments in lakes,” J. Environ. Eng. 127, 1023–1030 (2001).
[CrossRef]

Y. C. Agrawal and P. Traykovski, “Particles in the bottom boundary layer: concentration and size dynamics through events,” J. Geophys. Res. 106, 9533–9542 (2001).
[CrossRef]

J. W. Gartner, R. T. Cheng, P.-F. Wang, and K. Richter, “Laboratory and field evaluations of the LISST-100 instrument for suspended particle size determinations,” Mar. Geol. 175, 199–219 (2001).
[CrossRef]

2000 (5)

B. G. Krishnappan, “In situ size distribution of suspended particles in the Fraser River,” J. Hydraul. Eng. 126, 561–569 (2000).
[CrossRef]

Y. C. Agrawal and H. C. Pottsmith, “Instruments for particle size and settling velocity observations in sediment transport,” Mar. Geol. 168, 89–114 (2000).
[CrossRef]

R. D. Vaillancourt and W. M. Balch, “Size distribution of marine submicron particles determined by flow field-flow fractionation,” Limnol. Oceanogr. 45, 485–492 (2000).
[CrossRef]

O. Dubovik, A. Smirnov, B. N. Holben, M. D. King, Y. J. Kaufman, T. F. Eck, and I. Slutsker, “Accuracy assessments of aerosol optical properties retrieved from Aerosol Robotic Network (AERONET) Sun and sky radiance measurements,” J. Geophys. Res. 105, 9791–9806(2000).
[CrossRef]

K. E. Wommack and R. R. Colwell, “Virioplankton: viruses in aquatic ecosystems,” Microbiol. Mol. Biol. Rev. 64, 69–114(2000).
[CrossRef]

1998 (3)

H. Volten, J. F. de Haan, J. W. Hovenier, R. Schreurs, W. Vassen, and A. G. Decker, “Laboratory measurements of angular distributions of light scattered by phytoplankton and silt,” Limnol. Oceanogr. 43, 1180–1197 (1998).
[CrossRef]

X. Zhang, M. R. Lewis, and B. D. Johnson, “Influence of bubbles on scattering of light in the ocean,” Appl. Opt. 37, 6525–6536 (1998).
[CrossRef]

A. Yamasaki, H. Fukuda, R. Fukuda, T. Miyajima, T. Nagata, H. Ogawa, and I. Koike, “Submicrometer particles in northwest Pacific coastal environments: abundance, size distribution, and biological origins,” Limnol. Oceanogr. 43, 536–542(1998).
[CrossRef]

1996 (2)

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

E. Aas, “Refractive index of phytoplankton derived from its metabolite composition,” J. Plankton Res. 18, 2223–2249(1996).
[CrossRef]

1995 (1)

J. W. Campbell, “The lognormal distribution as a model for bio-optical variability in the sea,” J. Geophys. Res. 100, 13237–13254 (1995).
[CrossRef]

1994 (6)

J. S. Schoonmaker, R. R. Hammond, A. L. Heath, and J. S. Cleveland, “A numerical model for prediction of sublittoral optical visibility,” Proc. SPIE 2258, 685–702 (1994).
[CrossRef]

G. R. Fournier and J. L. Forand, “Analytical phase function for ocean water,” Proc. SPIE 2258, 194–201 (1994).
[CrossRef]

L. F. Portugal, J. J. Judice, and L. N. Vicente, “A comparison of block pivoting and interior-point algorithms for linear least squares problems with nonnegative variables,” Math. Comput. 63, 625–643 (1994).
[CrossRef]

M. R. Jones, B. P. Curry, M. Q. Brewster, and K. H. Leong, “Inversion of light-scattering measurements for particle size and optical constants: theoretical study,” Appl. Opt. 33, 4025–4034 (1994).
[CrossRef]

O. Ulloa, S. Sathyendranath, and T. Platt, “Effect of the particle-size distribution on the backscattering ratio in seawater,” Appl. Opt. 33, 7070–7077 (1994).
[CrossRef]

M. I. Mishchenko and L. D. Travis, “Light scattering by polydispersions of randomly oriented spheroids with sizes comparable to wavelengths of observation,” Appl. Opt. 33, 7206–7225 (1994).
[CrossRef]

1993 (1)

D. Risovic, “Two-component model of sea particle size distribution,” Deep-Sea Res. I 40, 1459–1473 (1993).
[CrossRef]

1992 (4)

O. Ulloa, S. Sathyendranath, T. Platt, and R. A. Quiñones, “Light scattering by marine heterotrophic bacteria,” J. Geophys. Res. 97, 9619–9629 (1992).
[CrossRef]

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

A. R. Longhurst, I. Koike, W. K. W. Li, J. Rodriguez, P. Dickie, P. Kepay, F. Partensky, B. Bautista, J. Ruiz, M. Wells, and D. F. Bird, “Sub-micron particles in northwest Atlantic shelf water,” Deep-Sea Res. A 39, 1–7 (1992).
[CrossRef]

M. L. Wells and E. D. Goldberg, “Marine submicron particles,” Mar. Chem. 40, 5–18 (1992).
[CrossRef]

1991 (8)

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

M. L. Wells and E. D. Goldberg, “Occurrence of small colloids in sea water,” Nature 353, 342–344 (1991).
[CrossRef]

W. Arnott and P. L. Marston, “Unfolded optical glory of spheroids: backscattering of laser light from freely rising spheroidal air bubbles in water,” Appl. Opt. 30, 3429–3442(1991).
[CrossRef]

S. D. Coston and N. George, “Particle sizing by inversion of the optical transform pattern,” Appl. Opt. 30, 4785–4794(1991).
[CrossRef]

J. C. Knight, D. Ball, and G. N. Robertson, “Analytical inversion for laser diffraction spectrometry giving improved resolution and accuracy in size distribution,” Appl. Opt. 30, 4795–4799 (1991).
[CrossRef]

J. B. Riley and Y. C. Agrawal, “Sampling and inversion of data in diffraction particle sizing,” Appl. Opt. 30, 4800–4817 (1991).
[CrossRef]

A. Morel and Y.-H. Ahn, “Optics of heterotrophic nanoflagellates and ciliates: a tentative assessment of their scattering role in oceanic waters compared to those of bacterial and algal cells,” J. Mar. Res. 49, 177–202 (1991).
[CrossRef]

C. F. Bohren and S. B. Singham, “Backscattering by nonspherical particles: a review of methods and suggested new approaches,” J. Geophys. Res. 96, 5269–5277 (1991).
[CrossRef]

1989 (4)

B. P. Curry, “Constrained eigenfunction method for the inversion of remote sensing data: application to particle size determination from light scattering measurements,” Appl. Opt. 28, 1345–1355 (1989).
[CrossRef]

J. W. Campbell and C. M. Yentsch, “Variance within homogeneous phytoplankton populations, I: theoretical framework for interpreting histograms,” Cytometry 10, 587–595 (1989).
[CrossRef]

J. W. Campbell and C. M. Yentsch, “Variance within homogeneous phytoplankton populations, II: Analysis of clonal cultures,” Cytometry 10, 596–604 (1989).
[CrossRef]

J. W. Campbell, C. M. Yentsch, and T. L. Cucci, “Variance within homogeneous phytoplankton populations, III: analysis of natural populations,” Cytometry 10, 605–611 (1989).
[CrossRef]

1987 (2)

M. Jonasz, “Nonspherical sediment particles: comparison of size and volume distributions obtained with an optical and a resistive particle counter,” Mar. Geol. 78, 137–142 (1987).
[CrossRef]

M. Jonasz, “Nonsphericity of suspended marine particles and its influence on light scattering,” Limnol. Oceanogr. 32, 1059–1065 (1987).
[CrossRef]

1986 (2)

M. Jonasz and H. Prandke, “Comparison of measured and computed light scattering in the Baltic,” Tellus 38B, 144–157 (1986).
[CrossRef]

A. Morel and A. Bricaud, “Inherent optical properties of algal cells, including picoplankton. Theoretical and experimental results,” Can. Bull. Fish. Aquat. Sci. 214, 521–559 (1986).

1981 (1)

C. E. Lambert, C. Jehanno, N. Silverberg, J. C. Brun-Cottan, and R. Chesselet, “Log-normal distribution of suspended particles in the open ocean,” J. Mar. Res. 39, 77–98 (1981).

1979 (1)

1977 (1)

T. Platt and K. Denman, “Organisation in the pelagic ecosystem,” Helgoland Mar. Res. 30, 575–581 (1977).

1974 (3)

T. Fenchel, “Intrinsic rate of natural increase: the relationship with body size,” Oecologia 14, 317–326 (1974).
[CrossRef]

J. R. V. Zaneveld, D. M. Roach, and H. Pak, “The determination of the index of refraction distribution of oceanic particulates,” J. Geophys. Res. 79, 4091–4095 (1974).
[CrossRef]

O. B. Brown and H. R. Gordon, “Size-refractive index distribution of clear coastal water particulates from light scattering,” Appl. Opt. 13, 2874–2881 (1974).
[CrossRef]

1973 (2)

1972 (3)

H. R. Gordon and O. B. Brown, “A theoretical model of light scattering by Sargasso Sea particulates,” Limnol. Oceanogr. 17, 826–832 (1972).
[CrossRef]

R. W. Sheldon, A. Prakash, and W. H. Sutcliffe, “The size distribution of particles in the ocean,” Limnol. Oceanogr. 17, 327–340 (1972).
[CrossRef]

F. S. Lai, S. K. Friedlander, J. Pich, and G. M. Hidy, “The self-preserving particle size distribution for Brownian coagulation in the free-molecule regime,” J. Colloid Interface Sci. 39, 395–405 (1972).
[CrossRef]

1971 (1)

K. L. Carder, G. Beardsley, Jr., and H. Pak, “Particle size distribution in the Eastern Equatorial Pacific,” J. Geophys. Res. 76, 5070–5077 (1971).
[CrossRef]

1970 (2)

F. T. Manheim, R. H. Meade, and G. C. Bond, “Suspended matter in surface waters of the Atlantic continental margin from Cape Cod to the Florida Keys,” Science 167, 371–376(1970).
[CrossRef]

G. F. Beardsley, H. J. Pak, and K. L. Carder, “Light scattering and suspended particles in the Eastern Equatorial Pacific ocean,” J. Geophys. Res. 75, 2837–2845 (1970).
[CrossRef]

1968 (1)

G. Kullenberg, “Scattering of light by Sargasso Sea water,” Deep-Sea Res. 15, 423–432 (1968).

1963 (1)

R. Fletcher and M. J. D. Powell, “A rapidly convergent descent method for minimization,” Comput. J. 6, 163–168(1963).

1955 (1)

J. H. Chin, C. M. Sliepcevich, and M. Tribus, “Particle size distributions from angular variation of intensity of forward-scattered light at very small angles,” J. Phys. Chem. 59, 841–844 (1955).
[CrossRef]

1947 (1)

B. Epstein, “The mathematical description of certain breakage mechanisms leading to the logarithmico-normal distribution,” J. Franklin Inst. 244, 471–477 (1947).
[CrossRef]

Aas, E.

E. Aas, “Refractive index of phytoplankton derived from its metabolite composition,” J. Plankton Res. 18, 2223–2249(1996).
[CrossRef]

Agrawal, Y. C.

Y. C. Agrawal and P. Traykovski, “Particles in the bottom boundary layer: concentration and size dynamics through events,” J. Geophys. Res. 106, 9533–9542 (2001).
[CrossRef]

Y. C. Agrawal and H. C. Pottsmith, “Instruments for particle size and settling velocity observations in sediment transport,” Mar. Geol. 168, 89–114 (2000).
[CrossRef]

J. B. Riley and Y. C. Agrawal, “Sampling and inversion of data in diffraction particle sizing,” Appl. Opt. 30, 4800–4817 (1991).
[CrossRef]

Ahn, J. H.

J. H. Ahn and S. B. Grant, “Size distribution, sources, and seasonality of suspended particles in southern California marine bathing waters,” Environ. Sci. Technol. 41, 695–702 (2007).
[CrossRef]

Ahn, Y.-H.

A. Morel and Y.-H. Ahn, “Optics of heterotrophic nanoflagellates and ciliates: a tentative assessment of their scattering role in oceanic waters compared to those of bacterial and algal cells,” J. Mar. Res. 49, 177–202 (1991).
[CrossRef]

Arellano, J. B.

T. Serra, J. Colomer, X. P. Cristina, X. Vila, J. B. Arellano, and X. Casamitjana, “Evaluation of laser in situ scattering instrument for measuring concentration of phytoplankton, purple sulfur bacteria, and suspended inorganic sediments in lakes,” J. Environ. Eng. 127, 1023–1030 (2001).
[CrossRef]

Arnott, W.

Azevedo, L.

L. Karp-Boss, L. Azevedo, and E. Boss, “LISST-100 measurements of phytoplankton size distribution: evaluation of the effects of cell shape,” Limnol. Oceanogr. Methods 5, 396–406 (2007).

Balch, W. M.

R. D. Vaillancourt, C. W. Brown, R. R. L. Guillard, and W. M. Balch, “Light backscattering properties of marine phytoplankton: relationships to cell size, chemical composition and taxonomy,” J. Plankton Res. 26, 191–212(2004).
[CrossRef]

R. D. Vaillancourt and W. M. Balch, “Size distribution of marine submicron particles determined by flow field-flow fractionation,” Limnol. Oceanogr. 45, 485–492 (2000).
[CrossRef]

Ball, D.

Barnard, A. H.

M. S. Twardowski, E. Boss, J. B. Macdonald, W. S. Pegau, A. H. Barnard, and J. R. V. Zaneveld, “A model for estimating bulk refractive index from the optical backscattering ratio and the implications for understanding particle composition in case I and case II waters,” J. Geophys. Res. 106, 14129–14142(2001).
[CrossRef]

Bautista, B.

A. R. Longhurst, I. Koike, W. K. W. Li, J. Rodriguez, P. Dickie, P. Kepay, F. Partensky, B. Bautista, J. Ruiz, M. Wells, and D. F. Bird, “Sub-micron particles in northwest Atlantic shelf water,” Deep-Sea Res. A 39, 1–7 (1992).
[CrossRef]

Beardsley, G.

K. L. Carder, G. Beardsley, Jr., and H. Pak, “Particle size distribution in the Eastern Equatorial Pacific,” J. Geophys. Res. 76, 5070–5077 (1971).
[CrossRef]

Beardsley, G. F.

G. F. Beardsley, H. J. Pak, and K. L. Carder, “Light scattering and suspended particles in the Eastern Equatorial Pacific ocean,” J. Geophys. Res. 75, 2837–2845 (1970).
[CrossRef]

Behrenfeld, M. J.

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

Bergmann, T.

O. Schofield, T. Bergmann, P. Bissett, J. F. Grassle, D. B. Haidvogel, J. Kohut, M. Moline, and S. M. Glenn, “The Long-term Ecosystem Observatory: an integrated coastal observatory,” IEEE J. Oceanic Eng. 27, 146–154 (2002).
[CrossRef]

Berseneva, G. A.

M. Chami, E. B. Shybanov, T. Y. Churilova, G. A. Khomenko, M. E. G. Lee, O. V. Martynov, G. A. Berseneva, and G. K. Korotaev, “Optical properties of the particles in the Crimea coastal waters (Black Sea),” J. Geophys. Res. 110, C11020 (2005).
[CrossRef]

Berthon, J.-F.

Bi, L.

Bird, D. F.

A. R. Longhurst, I. Koike, W. K. W. Li, J. Rodriguez, P. Dickie, P. Kepay, F. Partensky, B. Bautista, J. Ruiz, M. Wells, and D. F. Bird, “Sub-micron particles in northwest Atlantic shelf water,” Deep-Sea Res. A 39, 1–7 (1992).
[CrossRef]

Bissett, P.

O. Schofield, T. Bergmann, P. Bissett, J. F. Grassle, D. B. Haidvogel, J. Kohut, M. Moline, and S. M. Glenn, “The Long-term Ecosystem Observatory: an integrated coastal observatory,” IEEE J. Oceanic Eng. 27, 146–154 (2002).
[CrossRef]

Bogucki, D.

D. Stramski, E. Boss, D. Bogucki, and K. J. Voss, “The role of seawater constituents in light backscattering in the ocean,” Prog. Oceanogr. 61, 27–56 (2004).
[CrossRef]

Bohren, C. F.

C. F. Bohren and S. B. Singham, “Backscattering by nonspherical particles: a review of methods and suggested new approaches,” J. Geophys. Res. 96, 5269–5277 (1991).
[CrossRef]

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

Bond, G. C.

F. T. Manheim, R. H. Meade, and G. C. Bond, “Suspended matter in surface waters of the Atlantic continental margin from Cape Cod to the Florida Keys,” Science 167, 371–376(1970).
[CrossRef]

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, 15073–15093(2010).
[CrossRef]

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

L. Karp-Boss, L. Azevedo, and E. Boss, “LISST-100 measurements of phytoplankton size distribution: evaluation of the effects of cell shape,” Limnol. Oceanogr. Methods 5, 396–406 (2007).

D. Stramski, E. Boss, D. Bogucki, and K. J. Voss, “The role of seawater constituents in light backscattering in the ocean,” Prog. Oceanogr. 61, 27–56 (2004).
[CrossRef]

E. Boss, W. S. Pegau, M. Lee, M. Twardowski, E. Shybanov, and G. Korotaev, “Particulate backscattering ratio at LEO 15 and its use to study particle composition and distribution,” J. Geophys. Res. 109, C01014 (2004).
[CrossRef]

M. S. Twardowski, E. Boss, J. B. Macdonald, W. S. Pegau, A. H. Barnard, and J. R. V. Zaneveld, “A model for estimating bulk refractive index from the optical backscattering ratio and the implications for understanding particle composition in case I and case II waters,” J. Geophys. Res. 106, 14129–14142(2001).
[CrossRef]

W. R. Clavano, E. Boss, and L. Karp-Boss, “Inherent optical properties of non-spherical marine-like particles—from theory to observation,” in Oceanography and Marine Biology: An Annual Review (Taylor & Francis, 2007), Vol.  45, pp. 1–38.

Brewster, M. Q.

Bricaud, A.

A. Morel and A. Bricaud, “Inherent optical properties of algal cells, including picoplankton. Theoretical and experimental results,” Can. Bull. Fish. Aquat. Sci. 214, 521–559 (1986).

Brown, C. W.

R. D. Vaillancourt, C. W. Brown, R. R. L. Guillard, and W. M. Balch, “Light backscattering properties of marine phytoplankton: relationships to cell size, chemical composition and taxonomy,” J. Plankton Res. 26, 191–212(2004).
[CrossRef]

Brown, O. B.

Brun-Cottan, J. C.

C. E. Lambert, C. Jehanno, N. Silverberg, J. C. Brun-Cottan, and R. Chesselet, “Log-normal distribution of suspended particles in the open ocean,” J. Mar. Res. 39, 77–98 (1981).

Campbell, J. W.

J. W. Campbell, “The lognormal distribution as a model for bio-optical variability in the sea,” J. Geophys. Res. 100, 13237–13254 (1995).
[CrossRef]

J. W. Campbell and C. M. Yentsch, “Variance within homogeneous phytoplankton populations, II: Analysis of clonal cultures,” Cytometry 10, 596–604 (1989).
[CrossRef]

J. W. Campbell and C. M. Yentsch, “Variance within homogeneous phytoplankton populations, I: theoretical framework for interpreting histograms,” Cytometry 10, 587–595 (1989).
[CrossRef]

J. W. Campbell, C. M. Yentsch, and T. L. Cucci, “Variance within homogeneous phytoplankton populations, III: analysis of natural populations,” Cytometry 10, 605–611 (1989).
[CrossRef]

Carder, K. L.

K. L. Carder, G. Beardsley, Jr., and H. Pak, “Particle size distribution in the Eastern Equatorial Pacific,” J. Geophys. Res. 76, 5070–5077 (1971).
[CrossRef]

G. F. Beardsley, H. J. Pak, and K. L. Carder, “Light scattering and suspended particles in the Eastern Equatorial Pacific ocean,” J. Geophys. Res. 75, 2837–2845 (1970).
[CrossRef]

Casamitjana, X.

T. Serra, J. Colomer, X. P. Cristina, X. Vila, J. B. Arellano, and X. Casamitjana, “Evaluation of laser in situ scattering instrument for measuring concentration of phytoplankton, purple sulfur bacteria, and suspended inorganic sediments in lakes,” J. Environ. Eng. 127, 1023–1030 (2001).
[CrossRef]

Chami, M.

M. Chami, E. B. Shybanov, T. Y. Churilova, G. A. Khomenko, M. E. G. Lee, O. V. Martynov, G. A. Berseneva, and G. K. Korotaev, “Optical properties of the particles in the Crimea coastal waters (Black Sea),” J. Geophys. Res. 110, C11020 (2005).
[CrossRef]

Cheng, R. T.

J. W. Gartner, R. T. Cheng, P.-F. Wang, and K. Richter, “Laboratory and field evaluations of the LISST-100 instrument for suspended particle size determinations,” Mar. Geol. 175, 199–219 (2001).
[CrossRef]

Chesselet, R.

C. E. Lambert, C. Jehanno, N. Silverberg, J. C. Brun-Cottan, and R. Chesselet, “Log-normal distribution of suspended particles in the open ocean,” J. Mar. Res. 39, 77–98 (1981).

Chin, J. H.

J. H. Chin, C. M. Sliepcevich, and M. Tribus, “Particle size distributions from angular variation of intensity of forward-scattered light at very small angles,” J. Phys. Chem. 59, 841–844 (1955).
[CrossRef]

Churilova, T. Y.

M. Chami, E. B. Shybanov, T. Y. Churilova, G. A. Khomenko, M. E. G. Lee, O. V. Martynov, G. A. Berseneva, and G. K. Korotaev, “Optical properties of the particles in the Crimea coastal waters (Black Sea),” J. Geophys. Res. 110, C11020 (2005).
[CrossRef]

Clavano, W. R.

W. R. Clavano, E. Boss, and L. Karp-Boss, “Inherent optical properties of non-spherical marine-like particles—from theory to observation,” in Oceanography and Marine Biology: An Annual Review (Taylor & Francis, 2007), Vol.  45, pp. 1–38.

Cleveland, J. S.

J. S. Schoonmaker, R. R. Hammond, A. L. Heath, and J. S. Cleveland, “A numerical model for prediction of sublittoral optical visibility,” Proc. SPIE 2258, 685–702 (1994).
[CrossRef]

Colomer, J.

T. Serra, J. Colomer, X. P. Cristina, X. Vila, J. B. Arellano, and X. Casamitjana, “Evaluation of laser in situ scattering instrument for measuring concentration of phytoplankton, purple sulfur bacteria, and suspended inorganic sediments in lakes,” J. Environ. Eng. 127, 1023–1030 (2001).
[CrossRef]

Colwell, R. R.

K. E. Wommack and R. R. Colwell, “Virioplankton: viruses in aquatic ecosystems,” Microbiol. Mol. Biol. Rev. 64, 69–114(2000).
[CrossRef]

Coston, S. D.

Cowles, T. J.

Cristina, X. P.

T. Serra, J. Colomer, X. P. Cristina, X. Vila, J. B. Arellano, and X. Casamitjana, “Evaluation of laser in situ scattering instrument for measuring concentration of phytoplankton, purple sulfur bacteria, and suspended inorganic sediments in lakes,” J. Environ. Eng. 127, 1023–1030 (2001).
[CrossRef]

Cucci, T. L.

J. W. Campbell, C. M. Yentsch, and T. L. Cucci, “Variance within homogeneous phytoplankton populations, III: analysis of natural populations,” Cytometry 10, 605–611 (1989).
[CrossRef]

Curry, B. P.

Czerski, H.

M. Twardowski, X. Zhang, S. Freeman, M. Slivkoff, J. Sullivan, H. Czerski, S. Vagle, Y. You, and G. Kattawar, “Inverting the volume scattering function to infer particle composition at the near-surface,” in Proceedings of Ocean Optics XX (2011).

H. Czerski, M. Twardowski, S. Vagle, and M. Slivkoff, “Resolving bubble size distributions and dynamics in near-surface waters with optics and acoustics,” in Proceedings of Ocean Optics XX (2011).

Dall’Olmo, G.

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

de Haan, J. F.

H. Volten, J. F. de Haan, J. W. Hovenier, R. Schreurs, W. Vassen, and A. G. Decker, “Laboratory measurements of angular distributions of light scattered by phytoplankton and silt,” Limnol. Oceanogr. 43, 1180–1197 (1998).
[CrossRef]

Decker, A. G.

H. Volten, J. F. de Haan, J. W. Hovenier, R. Schreurs, W. Vassen, and A. G. Decker, “Laboratory measurements of angular distributions of light scattered by phytoplankton and silt,” Limnol. Oceanogr. 43, 1180–1197 (1998).
[CrossRef]

Denman, K.

T. Platt and K. Denman, “Organisation in the pelagic ecosystem,” Helgoland Mar. Res. 30, 575–581 (1977).

Dickie, P.

A. R. Longhurst, I. Koike, W. K. W. Li, J. Rodriguez, P. Dickie, P. Kepay, F. Partensky, B. Bautista, J. Ruiz, M. Wells, and D. F. Bird, “Sub-micron particles in northwest Atlantic shelf water,” Deep-Sea Res. A 39, 1–7 (1992).
[CrossRef]

Dubovik, O.

O. Dubovik, A. Smirnov, B. N. Holben, M. D. King, Y. J. Kaufman, T. F. Eck, and I. Slutsker, “Accuracy assessments of aerosol optical properties retrieved from Aerosol Robotic Network (AERONET) Sun and sky radiance measurements,” J. Geophys. Res. 105, 9791–9806(2000).
[CrossRef]

O. Dubovik, “Optimization of numerical inversion in photopolarimetric remote sensing,” in Photopolarimetry in Remote Sensing, G.Videen, Y.Yatskiv, and M.Mishchenko, eds. (Kluwer, 2004), pp. 65–106.

DuRand, M. D.

Eck, T. F.

O. Dubovik, A. Smirnov, B. N. Holben, M. D. King, Y. J. Kaufman, T. F. Eck, and I. Slutsker, “Accuracy assessments of aerosol optical properties retrieved from Aerosol Robotic Network (AERONET) Sun and sky radiance measurements,” J. Geophys. Res. 105, 9791–9806(2000).
[CrossRef]

Eloire, D.

L. Stemmann, D. Eloire, A. Sciandra, G. A. Jackson, L. Guidi, M. Picheral, and G. Gorsky, “Volume distribution for particles between 3.5 to 2000 μm in the upper 200 m region of the South Pacific Gyre,” Biogeosciences 5, 299–310 (2008).
[CrossRef]

Epstein, B.

B. Epstein, “The mathematical description of certain breakage mechanisms leading to the logarithmico-normal distribution,” J. Franklin Inst. 244, 471–477 (1947).
[CrossRef]

Fenchel, T.

T. Fenchel, “Intrinsic rate of natural increase: the relationship with body size,” Oecologia 14, 317–326 (1974).
[CrossRef]

Fletcher, R.

R. Fletcher and M. J. D. Powell, “A rapidly convergent descent method for minimization,” Comput. J. 6, 163–168(1963).

Forand, J. L.

G. R. Fournier and J. L. Forand, “Analytical phase function for ocean water,” Proc. SPIE 2258, 194–201 (1994).
[CrossRef]

Fournier, G. R.

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

G. R. Fournier and J. L. Forand, “Analytical phase function for ocean water,” Proc. SPIE 2258, 194–201 (1994).
[CrossRef]

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

Freeman, S.

M. S. Twardowski, C. Moore, J. Sullivan, M. Slivkoff, S. Freeman, and J. R. V. Zaneveld, are preparing a manuscript to be called “Volume scattering functions for selected ocean waters: revisited.”

M. Twardowski, X. Zhang, S. Freeman, M. Slivkoff, J. Sullivan, H. Czerski, S. Vagle, Y. You, and G. Kattawar, “Inverting the volume scattering function to infer particle composition at the near-surface,” in Proceedings of Ocean Optics XX (2011).

Friedlander, S. K.

F. S. Lai, S. K. Friedlander, J. Pich, and G. M. Hidy, “The self-preserving particle size distribution for Brownian coagulation in the free-molecule regime,” J. Colloid Interface Sci. 39, 395–405 (1972).
[CrossRef]

Fukuda, H.

A. Yamasaki, H. Fukuda, R. Fukuda, T. Miyajima, T. Nagata, H. Ogawa, and I. Koike, “Submicrometer particles in northwest Pacific coastal environments: abundance, size distribution, and biological origins,” Limnol. Oceanogr. 43, 536–542(1998).
[CrossRef]

Fukuda, R.

A. Yamasaki, H. Fukuda, R. Fukuda, T. Miyajima, T. Nagata, H. Ogawa, and I. Koike, “Submicrometer particles in northwest Pacific coastal environments: abundance, size distribution, and biological origins,” Limnol. Oceanogr. 43, 536–542(1998).
[CrossRef]

Gartner, J. W.

J. W. Gartner, R. T. Cheng, P.-F. Wang, and K. Richter, “Laboratory and field evaluations of the LISST-100 instrument for suspended particle size determinations,” Mar. Geol. 175, 199–219 (2001).
[CrossRef]

George, N.

Glenn, S. M.

O. Schofield, T. Bergmann, P. Bissett, J. F. Grassle, D. B. Haidvogel, J. Kohut, M. Moline, and S. M. Glenn, “The Long-term Ecosystem Observatory: an integrated coastal observatory,” IEEE J. Oceanic Eng. 27, 146–154 (2002).
[CrossRef]

Goldberg, E. D.

M. L. Wells and E. D. Goldberg, “Marine submicron particles,” Mar. Chem. 40, 5–18 (1992).
[CrossRef]

M. L. Wells and E. D. Goldberg, “Occurrence of small colloids in sea water,” Nature 353, 342–344 (1991).
[CrossRef]

Gordon, H. R.

Gorsky, G.

L. Stemmann, D. Eloire, A. Sciandra, G. A. Jackson, L. Guidi, M. Picheral, and G. Gorsky, “Volume distribution for particles between 3.5 to 2000 μm in the upper 200 m region of the South Pacific Gyre,” Biogeosciences 5, 299–310 (2008).
[CrossRef]

Grant, S. B.

J. H. Ahn and S. B. Grant, “Size distribution, sources, and seasonality of suspended particles in southern California marine bathing waters,” Environ. Sci. Technol. 41, 695–702 (2007).
[CrossRef]

Grassle, J. F.

O. Schofield, T. Bergmann, P. Bissett, J. F. Grassle, D. B. Haidvogel, J. Kohut, M. Moline, and S. M. Glenn, “The Long-term Ecosystem Observatory: an integrated coastal observatory,” IEEE J. Oceanic Eng. 27, 146–154 (2002).
[CrossRef]

Green, R. E.

Guidi, L.

L. Stemmann, D. Eloire, A. Sciandra, G. A. Jackson, L. Guidi, M. Picheral, and G. Gorsky, “Volume distribution for particles between 3.5 to 2000 μm in the upper 200 m region of the South Pacific Gyre,” Biogeosciences 5, 299–310 (2008).
[CrossRef]

Guillard, R. R. L.

R. D. Vaillancourt, C. W. Brown, R. R. L. Guillard, and W. M. Balch, “Light backscattering properties of marine phytoplankton: relationships to cell size, chemical composition and taxonomy,” J. Plankton Res. 26, 191–212(2004).
[CrossRef]

Haidvogel, D. B.

O. Schofield, T. Bergmann, P. Bissett, J. F. Grassle, D. B. Haidvogel, J. Kohut, M. Moline, and S. M. Glenn, “The Long-term Ecosystem Observatory: an integrated coastal observatory,” IEEE J. Oceanic Eng. 27, 146–154 (2002).
[CrossRef]

Hammond, R. R.

J. S. Schoonmaker, R. R. Hammond, A. L. Heath, and J. S. Cleveland, “A numerical model for prediction of sublittoral optical visibility,” Proc. SPIE 2258, 685–702 (1994).
[CrossRef]

Hanson, R. J.

C. L. Lawson and R. J. Hanson, Solving Least Squares Problems, Automatic Computation (Prentice-Hall, 1974).

He, M.-X.

Heath, A. L.

J. S. Schoonmaker, R. R. Hammond, A. L. Heath, and J. S. Cleveland, “A numerical model for prediction of sublittoral optical visibility,” Proc. SPIE 2258, 685–702 (1994).
[CrossRef]

Hidy, G. M.

F. S. Lai, S. K. Friedlander, J. Pich, and G. M. Hidy, “The self-preserving particle size distribution for Brownian coagulation in the free-molecule regime,” J. Colloid Interface Sci. 39, 395–405 (1972).
[CrossRef]

Holben, B. N.

O. Dubovik, A. Smirnov, B. N. Holben, M. D. King, Y. J. Kaufman, T. F. Eck, and I. Slutsker, “Accuracy assessments of aerosol optical properties retrieved from Aerosol Robotic Network (AERONET) Sun and sky radiance measurements,” J. Geophys. Res. 105, 9791–9806(2000).
[CrossRef]

Hovenier, J. W.

H. Volten, J. F. de Haan, J. W. Hovenier, R. Schreurs, W. Vassen, and A. G. Decker, “Laboratory measurements of angular distributions of light scattered by phytoplankton and silt,” Limnol. Oceanogr. 43, 1180–1197 (1998).
[CrossRef]

Hu, L.

Huffman, D. R.

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

Jackson, G. A.

L. Stemmann, D. Eloire, A. Sciandra, G. A. Jackson, L. Guidi, M. Picheral, and G. Gorsky, “Volume distribution for particles between 3.5 to 2000 μm in the upper 200 m region of the South Pacific Gyre,” Biogeosciences 5, 299–310 (2008).
[CrossRef]

Jehanno, C.

C. E. Lambert, C. Jehanno, N. Silverberg, J. C. Brun-Cottan, and R. Chesselet, “Log-normal distribution of suspended particles in the open ocean,” J. Mar. Res. 39, 77–98 (1981).

Johnson, B. D.

X. Zhang, M. R. Lewis, M. Lee, B. D. Johnson, and G. Korotaev, “Volume scattering function of natural bubble populations,” Limnol. Oceanogr. 47, 1273–1282 (2002).
[CrossRef]

X. Zhang, M. R. Lewis, and B. D. Johnson, “Influence of bubbles on scattering of light in the ocean,” Appl. Opt. 37, 6525–6536 (1998).
[CrossRef]

B. D. Johnson, “Bubble populations: background and breaking waves,” in Oceanic Whitecaps and Their Role in Air-Sea Exchange Processes, E.C.Monahan and G.Mac Niocail, eds. (Reidel, 1986), pp. 69–73.

Jonasz, M.

M. Jonasz and G. R. 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, “Nonspherical sediment particles: comparison of size and volume distributions obtained with an optical and a resistive particle counter,” Mar. Geol. 78, 137–142 (1987).
[CrossRef]

M. Jonasz, “Nonsphericity of suspended marine particles and its influence on light scattering,” Limnol. Oceanogr. 32, 1059–1065 (1987).
[CrossRef]

M. Jonasz and H. Prandke, “Comparison of measured and computed light scattering in the Baltic,” Tellus 38B, 144–157 (1986).
[CrossRef]

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

Jones, M. R.

Judice, J. J.

L. F. Portugal, J. J. Judice, and L. N. Vicente, “A comparison of block pivoting and interior-point algorithms for linear least squares problems with nonnegative variables,” Math. Comput. 63, 625–643 (1994).
[CrossRef]

Kahn, R.

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, 15073–15093(2010).
[CrossRef]

L. Karp-Boss, L. Azevedo, and E. Boss, “LISST-100 measurements of phytoplankton size distribution: evaluation of the effects of cell shape,” Limnol. Oceanogr. Methods 5, 396–406 (2007).

W. R. Clavano, E. Boss, and L. Karp-Boss, “Inherent optical properties of non-spherical marine-like particles—from theory to observation,” in Oceanography and Marine Biology: An Annual Review (Taylor & Francis, 2007), Vol.  45, pp. 1–38.

Kattawar, G.

M. Twardowski, X. Zhang, S. Freeman, M. Slivkoff, J. Sullivan, H. Czerski, S. Vagle, Y. You, and G. Kattawar, “Inverting the volume scattering function to infer particle composition at the near-surface,” in Proceedings of Ocean Optics XX (2011).

Kattawar, G. W.

Kaufman, Y. J.

O. Dubovik, A. Smirnov, B. N. Holben, M. D. King, Y. J. Kaufman, T. F. Eck, and I. Slutsker, “Accuracy assessments of aerosol optical properties retrieved from Aerosol Robotic Network (AERONET) Sun and sky radiance measurements,” J. Geophys. Res. 105, 9791–9806(2000).
[CrossRef]

Kepay, P.

A. R. Longhurst, I. Koike, W. K. W. Li, J. Rodriguez, P. Dickie, P. Kepay, F. Partensky, B. Bautista, J. Ruiz, M. Wells, and D. F. Bird, “Sub-micron particles in northwest Atlantic shelf water,” Deep-Sea Res. A 39, 1–7 (1992).
[CrossRef]

Khomenko, G. A.

M. Chami, E. B. Shybanov, T. Y. Churilova, G. A. Khomenko, M. E. G. Lee, O. V. Martynov, G. A. Berseneva, and G. K. Korotaev, “Optical properties of the particles in the Crimea coastal waters (Black Sea),” J. Geophys. Res. 110, C11020 (2005).
[CrossRef]

Kiefer, D. A.

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

King, M. D.

O. Dubovik, A. Smirnov, B. N. Holben, M. D. King, Y. J. Kaufman, T. F. Eck, and I. Slutsker, “Accuracy assessments of aerosol optical properties retrieved from Aerosol Robotic Network (AERONET) Sun and sky radiance measurements,” J. Geophys. Res. 105, 9791–9806(2000).
[CrossRef]

Kitchen, J. C.

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

Knight, J. C.

Kohut, J.

O. Schofield, T. Bergmann, P. Bissett, J. F. Grassle, D. B. Haidvogel, J. Kohut, M. Moline, and S. M. Glenn, “The Long-term Ecosystem Observatory: an integrated coastal observatory,” IEEE J. Oceanic Eng. 27, 146–154 (2002).
[CrossRef]

Koike, I.

A. Yamasaki, H. Fukuda, R. Fukuda, T. Miyajima, T. Nagata, H. Ogawa, and I. Koike, “Submicrometer particles in northwest Pacific coastal environments: abundance, size distribution, and biological origins,” Limnol. Oceanogr. 43, 536–542(1998).
[CrossRef]

A. R. Longhurst, I. Koike, W. K. W. Li, J. Rodriguez, P. Dickie, P. Kepay, F. Partensky, B. Bautista, J. Ruiz, M. Wells, and D. F. Bird, “Sub-micron particles in northwest Atlantic shelf water,” Deep-Sea Res. A 39, 1–7 (1992).
[CrossRef]

Kopelevich, O. V.

O. V. Kopelevich, “Low-parametric model of seawater optical properties,” in Ocean Optics I: Physical Ocean Optics, A.S.Monin, ed. (Nauka, 1983), pp. 208–234.

Korotaev, G.

E. Boss, W. S. Pegau, M. Lee, M. Twardowski, E. Shybanov, and G. Korotaev, “Particulate backscattering ratio at LEO 15 and its use to study particle composition and distribution,” J. Geophys. Res. 109, C01014 (2004).
[CrossRef]

X. Zhang, M. R. Lewis, M. Lee, B. D. Johnson, and G. Korotaev, “Volume scattering function of natural bubble populations,” Limnol. Oceanogr. 47, 1273–1282 (2002).
[CrossRef]

Korotaev, G. K.

M. Chami, E. B. Shybanov, T. Y. Churilova, G. A. Khomenko, M. E. G. Lee, O. V. Martynov, G. A. Berseneva, and G. K. Korotaev, “Optical properties of the particles in the Crimea coastal waters (Black Sea),” J. Geophys. Res. 110, C11020 (2005).
[CrossRef]

Krishnappan, B. G.

B. G. Krishnappan, “In situ size distribution of suspended particles in the Fraser River,” J. Hydraul. Eng. 126, 561–569 (2000).
[CrossRef]

Kullenberg, G.

G. Kullenberg, “Scattering of light by Sargasso Sea water,” Deep-Sea Res. 15, 423–432 (1968).

G. Kullenberg, “Observed and computed scattering functions,” in Optical Aspects of Oceanography, N.G.Jerlov and E.Steeman-Nielsen, eds. (Academic, 1974), pp. 25–49.

Lacis, A. A.

M. I. Mishchenko, L. D. Travis, and A. A. Lacis, Scattering, Absorption, and Emission of Light by Small Particles(Cambridge University, 2002).

Lai, F. S.

F. S. Lai, S. K. Friedlander, J. Pich, and G. M. Hidy, “The self-preserving particle size distribution for Brownian coagulation in the free-molecule regime,” J. Colloid Interface Sci. 39, 395–405 (1972).
[CrossRef]

Lambert, C. E.

C. E. Lambert, C. Jehanno, N. Silverberg, J. C. Brun-Cottan, and R. Chesselet, “Log-normal distribution of suspended particles in the open ocean,” J. Mar. Res. 39, 77–98 (1981).

Lawson, C. L.

C. L. Lawson and R. J. Hanson, Solving Least Squares Problems, Automatic Computation (Prentice-Hall, 1974).

Lee, M.

E. Boss, W. S. Pegau, M. Lee, M. Twardowski, E. Shybanov, and G. Korotaev, “Particulate backscattering ratio at LEO 15 and its use to study particle composition and distribution,” J. Geophys. Res. 109, C01014 (2004).
[CrossRef]

X. Zhang, M. R. Lewis, M. Lee, B. D. Johnson, and G. Korotaev, “Volume scattering function of natural bubble populations,” Limnol. Oceanogr. 47, 1273–1282 (2002).
[CrossRef]

Lee, M. E.

M. E. Lee and M. R. Lewis, “A new method for the measurement of the optical volume scattering function in the upper ocean,” J. Atmos. Ocean. Technol. 20, 563–571 (2003).
[CrossRef]

Lee, M. E. G.

J.-F. Berthon, E. Shybanov, M. E. G. Lee, and G. Zibordi, “Measurements and modeling of the volume scattering function in the coastal northern Adriatic Sea,” Appl. Opt. 46, 5189–5203(2007).
[CrossRef]

M. Chami, E. B. Shybanov, T. Y. Churilova, G. A. Khomenko, M. E. G. Lee, O. V. Martynov, G. A. Berseneva, and G. K. Korotaev, “Optical properties of the particles in the Crimea coastal waters (Black Sea),” J. Geophys. Res. 110, C11020 (2005).
[CrossRef]

Leong, K. H.

Lewis, M. R.

M. E. Lee and M. R. Lewis, “A new method for the measurement of the optical volume scattering function in the upper ocean,” J. Atmos. Ocean. Technol. 20, 563–571 (2003).
[CrossRef]

X. Zhang, M. R. Lewis, M. Lee, B. D. Johnson, and G. Korotaev, “Volume scattering function of natural bubble populations,” Limnol. Oceanogr. 47, 1273–1282 (2002).
[CrossRef]

X. Zhang, M. R. Lewis, and B. D. Johnson, “Influence of bubbles on scattering of light in the ocean,” Appl. Opt. 37, 6525–6536 (1998).
[CrossRef]

Li, W. K. W.

A. R. Longhurst, I. Koike, W. K. W. Li, J. Rodriguez, P. Dickie, P. Kepay, F. Partensky, B. Bautista, J. Ruiz, M. Wells, and D. F. Bird, “Sub-micron particles in northwest Atlantic shelf water,” Deep-Sea Res. A 39, 1–7 (1992).
[CrossRef]

Longhurst, A. R.

A. R. Longhurst, I. Koike, W. K. W. Li, J. Rodriguez, P. Dickie, P. Kepay, F. Partensky, B. Bautista, J. Ruiz, M. Wells, and D. F. Bird, “Sub-micron particles in northwest Atlantic shelf water,” Deep-Sea Res. A 39, 1–7 (1992).
[CrossRef]

Longo, M. L.

M. M. Lozano, E. Talu, and M. L. Longo, “Dissolution of microbubbles generated in seawater obtained offshore: behavior and surface tension measurements,” J. Geophys. Res. 112, C12001 (2007).
[CrossRef]

M. L. Longo, Department of Chemical Engineering and Materials Science, University of California, Davis, Calif., USA (personal communication, 2010).

Lozano, M. M.

M. M. Lozano, E. Talu, and M. L. Longo, “Dissolution of microbubbles generated in seawater obtained offshore: behavior and surface tension measurements,” J. Geophys. Res. 112, C12001 (2007).
[CrossRef]

Macdonald, J. B.

M. S. Twardowski, E. Boss, J. B. Macdonald, W. S. Pegau, A. H. Barnard, and J. R. V. Zaneveld, “A model for estimating bulk refractive index from the optical backscattering ratio and the implications for understanding particle composition in case I and case II waters,” J. Geophys. Res. 106, 14129–14142(2001).
[CrossRef]

Manheim, F. T.

F. T. Manheim, R. H. Meade, and G. C. Bond, “Suspended matter in surface waters of the Atlantic continental margin from Cape Cod to the Florida Keys,” Science 167, 371–376(1970).
[CrossRef]

Marston, P. L.

Martynov, O. V.

M. Chami, E. B. Shybanov, T. Y. Churilova, G. A. Khomenko, M. E. G. Lee, O. V. Martynov, G. A. Berseneva, and G. K. Korotaev, “Optical properties of the particles in the Crimea coastal waters (Black Sea),” J. Geophys. Res. 110, C11020 (2005).
[CrossRef]

Meade, R. H.

F. T. Manheim, R. H. Meade, and G. C. Bond, “Suspended matter in surface waters of the Atlantic continental margin from Cape Cod to the Florida Keys,” Science 167, 371–376(1970).
[CrossRef]

Meyer, R. A.

Mishchenko, M. I.

M. I. Mishchenko and L. D. Travis, “Light scattering by polydispersions of randomly oriented spheroids with sizes comparable to wavelengths of observation,” Appl. Opt. 33, 7206–7225 (1994).
[CrossRef]

M. I. Mishchenko, L. D. Travis, and A. A. Lacis, Scattering, Absorption, and Emission of Light by Small Particles(Cambridge University, 2002).

Miyajima, T.

A. Yamasaki, H. Fukuda, R. Fukuda, T. Miyajima, T. Nagata, H. Ogawa, and I. Koike, “Submicrometer particles in northwest Pacific coastal environments: abundance, size distribution, and biological origins,” Limnol. Oceanogr. 43, 536–542(1998).
[CrossRef]

Mobley, C. D.

C. D. Mobley, Light and Water: Radiative Transfer in Natural Waters (Academic, 1994).

Moline, M.

O. Schofield, T. Bergmann, P. Bissett, J. F. Grassle, D. B. Haidvogel, J. Kohut, M. Moline, and S. M. Glenn, “The Long-term Ecosystem Observatory: an integrated coastal observatory,” IEEE J. Oceanic Eng. 27, 146–154 (2002).
[CrossRef]

Moore, C.

M. S. Twardowski, C. Moore, J. Sullivan, M. Slivkoff, S. Freeman, and J. R. V. Zaneveld, are preparing a manuscript to be called “Volume scattering functions for selected ocean waters: revisited.”

Morel, A.

A. Morel and Y.-H. Ahn, “Optics of heterotrophic nanoflagellates and ciliates: a tentative assessment of their scattering role in oceanic waters compared to those of bacterial and algal cells,” J. Mar. Res. 49, 177–202 (1991).
[CrossRef]

A. Morel and A. Bricaud, “Inherent optical properties of algal cells, including picoplankton. Theoretical and experimental results,” Can. Bull. Fish. Aquat. Sci. 214, 521–559 (1986).

A. Morel, “The scattering of light by seawater: experimental results and theoretical approach,” in Optics of the Sea, Interface and In-Water Transmission and Imaging (NATO Advisory Group for Aerospace Research and Development, 1973).

Nagata, T.

A. Yamasaki, H. Fukuda, R. Fukuda, T. Miyajima, T. Nagata, H. Ogawa, and I. Koike, “Submicrometer particles in northwest Pacific coastal environments: abundance, size distribution, and biological origins,” Limnol. Oceanogr. 43, 536–542(1998).
[CrossRef]

Nussenzveig, H. M.

Ogawa, H.

A. Yamasaki, H. Fukuda, R. Fukuda, T. Miyajima, T. Nagata, H. Ogawa, and I. Koike, “Submicrometer particles in northwest Pacific coastal environments: abundance, size distribution, and biological origins,” Limnol. Oceanogr. 43, 536–542(1998).
[CrossRef]

Olson, R. J.

Pak, H.

J. R. V. Zaneveld, D. M. Roach, and H. Pak, “The determination of the index of refraction distribution of oceanic particulates,” J. Geophys. Res. 79, 4091–4095 (1974).
[CrossRef]

J. R. V. Zaneveld and H. Pak, “Method for the determination of the index of refraction of particles suspended in the ocean,” J. Opt. Soc. Am. 63, 321–324 (1973).
[CrossRef]

K. L. Carder, G. Beardsley, Jr., and H. Pak, “Particle size distribution in the Eastern Equatorial Pacific,” J. Geophys. Res. 76, 5070–5077 (1971).
[CrossRef]

Pak, H. J.

G. F. Beardsley, H. J. Pak, and K. L. Carder, “Light scattering and suspended particles in the Eastern Equatorial Pacific ocean,” J. Geophys. Res. 75, 2837–2845 (1970).
[CrossRef]

Partensky, F.

A. R. Longhurst, I. Koike, W. K. W. Li, J. Rodriguez, P. Dickie, P. Kepay, F. Partensky, B. Bautista, J. Ruiz, M. Wells, and D. F. Bird, “Sub-micron particles in northwest Atlantic shelf water,” Deep-Sea Res. A 39, 1–7 (1992).
[CrossRef]

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, 15073–15093(2010).
[CrossRef]

E. Boss, W. S. Pegau, M. Lee, M. Twardowski, E. Shybanov, and G. Korotaev, “Particulate backscattering ratio at LEO 15 and its use to study particle composition and distribution,” J. Geophys. Res. 109, C01014 (2004).
[CrossRef]

M. S. Twardowski, E. Boss, J. B. Macdonald, W. S. Pegau, A. H. Barnard, and J. R. V. Zaneveld, “A model for estimating bulk refractive index from the optical backscattering ratio and the implications for understanding particle composition in case I and case II waters,” J. Geophys. Res. 106, 14129–14142(2001).
[CrossRef]

Petzold, T. J.

T. J. Petzold, “Volume scattering function for selected ocean waters,” SIO Ref. 72-78, Scripps Institute of Oceanography, La Jolla, 1972.

Pich, J.

F. S. Lai, S. K. Friedlander, J. Pich, and G. M. Hidy, “The self-preserving particle size distribution for Brownian coagulation in the free-molecule regime,” J. Colloid Interface Sci. 39, 395–405 (1972).
[CrossRef]

Picheral, M.

L. Stemmann, D. Eloire, A. Sciandra, G. A. Jackson, L. Guidi, M. Picheral, and G. Gorsky, “Volume distribution for particles between 3.5 to 2000 μm in the upper 200 m region of the South Pacific Gyre,” Biogeosciences 5, 299–310 (2008).
[CrossRef]

Platt, T.

O. Ulloa, S. Sathyendranath, and T. Platt, “Effect of the particle-size distribution on the backscattering ratio in seawater,” Appl. Opt. 33, 7070–7077 (1994).
[CrossRef]

O. Ulloa, S. Sathyendranath, T. Platt, and R. A. Quiñones, “Light scattering by marine heterotrophic bacteria,” J. Geophys. Res. 97, 9619–9629 (1992).
[CrossRef]

T. Platt and K. Denman, “Organisation in the pelagic ecosystem,” Helgoland Mar. Res. 30, 575–581 (1977).

Portugal, L. F.

L. F. Portugal, J. J. Judice, and L. N. Vicente, “A comparison of block pivoting and interior-point algorithms for linear least squares problems with nonnegative variables,” Math. Comput. 63, 625–643 (1994).
[CrossRef]

Pottsmith, H. C.

Y. C. Agrawal and H. C. Pottsmith, “Instruments for particle size and settling velocity observations in sediment transport,” Mar. Geol. 168, 89–114 (2000).
[CrossRef]

Powell, M. J. D.

R. Fletcher and M. J. D. Powell, “A rapidly convergent descent method for minimization,” Comput. J. 6, 163–168(1963).

Prakash, A.

R. W. Sheldon, A. Prakash, and W. H. Sutcliffe, “The size distribution of particles in the ocean,” Limnol. Oceanogr. 17, 327–340 (1972).
[CrossRef]

Prandke, H.

M. Jonasz and H. Prandke, “Comparison of measured and computed light scattering in the Baltic,” Tellus 38B, 144–157 (1986).
[CrossRef]

Quiñones, R. A.

O. Ulloa, S. Sathyendranath, T. Platt, and R. A. Quiñones, “Light scattering by marine heterotrophic bacteria,” J. Geophys. Res. 97, 9619–9629 (1992).
[CrossRef]

Reynolds, R. A.

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

Richter, K.

J. W. Gartner, R. T. Cheng, P.-F. Wang, and K. Richter, “Laboratory and field evaluations of the LISST-100 instrument for suspended particle size determinations,” Mar. Geol. 175, 199–219 (2001).
[CrossRef]

Riley, J. B.

Risovic, D.

D. Risovic, “Two-component model of sea particle size distribution,” Deep-Sea Res. I 40, 1459–1473 (1993).
[CrossRef]

Roach, D. M.

J. R. V. Zaneveld, D. M. Roach, and H. Pak, “The determination of the index of refraction distribution of oceanic particulates,” J. Geophys. Res. 79, 4091–4095 (1974).
[CrossRef]

Robertson, G. N.

Rodriguez, J.

A. R. Longhurst, I. Koike, W. K. W. Li, J. Rodriguez, P. Dickie, P. Kepay, F. Partensky, B. Bautista, J. Ruiz, M. Wells, and D. F. Bird, “Sub-micron particles in northwest Atlantic shelf water,” Deep-Sea Res. A 39, 1–7 (1992).
[CrossRef]

Ruiz, J.

A. R. Longhurst, I. Koike, W. K. W. Li, J. Rodriguez, P. Dickie, P. Kepay, F. Partensky, B. Bautista, J. Ruiz, M. Wells, and D. F. Bird, “Sub-micron particles in northwest Atlantic shelf water,” Deep-Sea Res. A 39, 1–7 (1992).
[CrossRef]

Sathyendranath, S.

O. Ulloa, S. Sathyendranath, and T. Platt, “Effect of the particle-size distribution on the backscattering ratio in seawater,” Appl. Opt. 33, 7070–7077 (1994).
[CrossRef]

O. Ulloa, S. Sathyendranath, T. Platt, and R. A. Quiñones, “Light scattering by marine heterotrophic bacteria,” J. Geophys. Res. 97, 9619–9629 (1992).
[CrossRef]

Schofield, O.

O. Schofield, T. Bergmann, P. Bissett, J. F. Grassle, D. B. Haidvogel, J. Kohut, M. Moline, and S. M. Glenn, “The Long-term Ecosystem Observatory: an integrated coastal observatory,” IEEE J. Oceanic Eng. 27, 146–154 (2002).
[CrossRef]

Schoonmaker, J. S.

J. S. Schoonmaker, R. R. Hammond, A. L. Heath, and J. S. Cleveland, “A numerical model for prediction of sublittoral optical visibility,” Proc. SPIE 2258, 685–702 (1994).
[CrossRef]

Schreurs, R.

H. Volten, J. F. de Haan, J. W. Hovenier, R. Schreurs, W. Vassen, and A. G. Decker, “Laboratory measurements of angular distributions of light scattered by phytoplankton and silt,” Limnol. Oceanogr. 43, 1180–1197 (1998).
[CrossRef]

Sciandra, A.

L. Stemmann, D. Eloire, A. Sciandra, G. A. Jackson, L. Guidi, M. Picheral, and G. Gorsky, “Volume distribution for particles between 3.5 to 2000 μm in the upper 200 m region of the South Pacific Gyre,” Biogeosciences 5, 299–310 (2008).
[CrossRef]

Serra, T.

T. Serra, J. Colomer, X. P. Cristina, X. Vila, J. B. Arellano, and X. Casamitjana, “Evaluation of laser in situ scattering instrument for measuring concentration of phytoplankton, purple sulfur bacteria, and suspended inorganic sediments in lakes,” J. Environ. Eng. 127, 1023–1030 (2001).
[CrossRef]

Sheldon, R. W.

R. W. Sheldon, A. Prakash, and W. H. Sutcliffe, “The size distribution of particles in the ocean,” Limnol. Oceanogr. 17, 327–340 (1972).
[CrossRef]

Shifrin, K. S.

K. S. Shifrin, Physical Optics of Ocean Water, AIP Translation Series (American Institute of Physics, 1988).

Shybanov, E.

J.-F. Berthon, E. Shybanov, M. E. G. Lee, and G. Zibordi, “Measurements and modeling of the volume scattering function in the coastal northern Adriatic Sea,” Appl. Opt. 46, 5189–5203(2007).
[CrossRef]

E. Boss, W. S. Pegau, M. Lee, M. Twardowski, E. Shybanov, and G. Korotaev, “Particulate backscattering ratio at LEO 15 and its use to study particle composition and distribution,” J. Geophys. Res. 109, C01014 (2004).
[CrossRef]

Shybanov, E. B.

M. Chami, E. B. Shybanov, T. Y. Churilova, G. A. Khomenko, M. E. G. Lee, O. V. Martynov, G. A. Berseneva, and G. K. Korotaev, “Optical properties of the particles in the Crimea coastal waters (Black Sea),” J. Geophys. Res. 110, C11020 (2005).
[CrossRef]

Silverberg, N.

C. E. Lambert, C. Jehanno, N. Silverberg, J. C. Brun-Cottan, and R. Chesselet, “Log-normal distribution of suspended particles in the open ocean,” J. Mar. Res. 39, 77–98 (1981).

Singham, S. B.

C. F. Bohren and S. B. Singham, “Backscattering by nonspherical particles: a review of methods and suggested new approaches,” J. Geophys. Res. 96, 5269–5277 (1991).
[CrossRef]

Slade, W. H.

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

Sliepcevich, C. M.

J. H. Chin, C. M. Sliepcevich, and M. Tribus, “Particle size distributions from angular variation of intensity of forward-scattered light at very small angles,” J. Phys. Chem. 59, 841–844 (1955).
[CrossRef]

Slivkoff, M.

H. Czerski, M. Twardowski, S. Vagle, and M. Slivkoff, “Resolving bubble size distributions and dynamics in near-surface waters with optics and acoustics,” in Proceedings of Ocean Optics XX (2011).

M. S. Twardowski, C. Moore, J. Sullivan, M. Slivkoff, S. Freeman, and J. R. V. Zaneveld, are preparing a manuscript to be called “Volume scattering functions for selected ocean waters: revisited.”

M. Twardowski, X. Zhang, S. Freeman, M. Slivkoff, J. Sullivan, H. Czerski, S. Vagle, Y. You, and G. Kattawar, “Inverting the volume scattering function to infer particle composition at the near-surface,” in Proceedings of Ocean Optics XX (2011).

Slutsker, I.

O. Dubovik, A. Smirnov, B. N. Holben, M. D. King, Y. J. Kaufman, T. F. Eck, and I. Slutsker, “Accuracy assessments of aerosol optical properties retrieved from Aerosol Robotic Network (AERONET) Sun and sky radiance measurements,” J. Geophys. Res. 105, 9791–9806(2000).
[CrossRef]

Smirnov, A.

O. Dubovik, A. Smirnov, B. N. Holben, M. D. King, Y. J. Kaufman, T. F. Eck, and I. Slutsker, “Accuracy assessments of aerosol optical properties retrieved from Aerosol Robotic Network (AERONET) Sun and sky radiance measurements,” J. Geophys. Res. 105, 9791–9806(2000).
[CrossRef]

Sosik, H. M.

Stemmann, L.

L. Stemmann, D. Eloire, A. Sciandra, G. A. Jackson, L. Guidi, M. Picheral, and G. Gorsky, “Volume distribution for particles between 3.5 to 2000 μm in the upper 200 m region of the South Pacific Gyre,” Biogeosciences 5, 299–310 (2008).
[CrossRef]

Stramski, D.

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

D. Stramski, E. Boss, D. Bogucki, and K. J. Voss, “The role of seawater constituents in light backscattering in the ocean,” Prog. Oceanogr. 61, 27–56 (2004).
[CrossRef]

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

Sullivan, J.

M. S. Twardowski, C. Moore, J. Sullivan, M. Slivkoff, S. Freeman, and J. R. V. Zaneveld, are preparing a manuscript to be called “Volume scattering functions for selected ocean waters: revisited.”

M. Twardowski, X. Zhang, S. Freeman, M. Slivkoff, J. Sullivan, H. Czerski, S. Vagle, Y. You, and G. Kattawar, “Inverting the volume scattering function to infer particle composition at the near-surface,” in Proceedings of Ocean Optics XX (2011).

Sullivan, J. M.

Sutcliffe, W. H.

R. W. Sheldon, A. Prakash, and W. H. Sutcliffe, “The size distribution of particles in the ocean,” Limnol. Oceanogr. 17, 327–340 (1972).
[CrossRef]

Talu, E.

M. M. Lozano, E. Talu, and M. L. Longo, “Dissolution of microbubbles generated in seawater obtained offshore: behavior and surface tension measurements,” J. Geophys. Res. 112, C12001 (2007).
[CrossRef]

Travis, L. D.

M. I. Mishchenko and L. D. Travis, “Light scattering by polydispersions of randomly oriented spheroids with sizes comparable to wavelengths of observation,” Appl. Opt. 33, 7206–7225 (1994).
[CrossRef]

M. I. Mishchenko, L. D. Travis, and A. A. Lacis, Scattering, Absorption, and Emission of Light by Small Particles(Cambridge University, 2002).

Traykovski, P.

Y. C. Agrawal and P. Traykovski, “Particles in the bottom boundary layer: concentration and size dynamics through events,” J. Geophys. Res. 106, 9533–9542 (2001).
[CrossRef]

Tribus, M.

J. H. Chin, C. M. Sliepcevich, and M. Tribus, “Particle size distributions from angular variation of intensity of forward-scattered light at very small angles,” J. Phys. Chem. 59, 841–844 (1955).
[CrossRef]

Twardowski, M.

E. Boss, W. S. Pegau, M. Lee, M. Twardowski, E. Shybanov, and G. Korotaev, “Particulate backscattering ratio at LEO 15 and its use to study particle composition and distribution,” J. Geophys. Res. 109, C01014 (2004).
[CrossRef]

M. Twardowski, X. Zhang, S. Freeman, M. Slivkoff, J. Sullivan, H. Czerski, S. Vagle, Y. You, and G. Kattawar, “Inverting the volume scattering function to infer particle composition at the near-surface,” in Proceedings of Ocean Optics XX (2011).

H. Czerski, M. Twardowski, S. Vagle, and M. Slivkoff, “Resolving bubble size distributions and dynamics in near-surface waters with optics and acoustics,” in Proceedings of Ocean Optics XX (2011).

Twardowski, M. S.

J. M. Sullivan and M. S. Twardowski, “Angular shape of the oceanic particulate volume scattering function in the backward direction,” Appl. Opt. 48, 6811–6819 (2009).
[CrossRef]

M. S. Twardowski, E. Boss, J. B. Macdonald, W. S. Pegau, A. H. Barnard, and J. R. V. Zaneveld, “A model for estimating bulk refractive index from the optical backscattering ratio and the implications for understanding particle composition in case I and case II waters,” J. Geophys. Res. 106, 14129–14142(2001).
[CrossRef]

M. S. Twardowski, C. Moore, J. Sullivan, M. Slivkoff, S. Freeman, and J. R. V. Zaneveld, are preparing a manuscript to be called “Volume scattering functions for selected ocean waters: revisited.”

Twomey, S.

S. Twomey, Introduction to the Mathematics of Inversion in Remote Sensing and Indirect Measurements, Developments in Geomathematics (Elsevier, 1977).

Ulloa, O.

O. Ulloa, S. Sathyendranath, and T. Platt, “Effect of the particle-size distribution on the backscattering ratio in seawater,” Appl. Opt. 33, 7070–7077 (1994).
[CrossRef]

O. Ulloa, S. Sathyendranath, T. Platt, and R. A. Quiñones, “Light scattering by marine heterotrophic bacteria,” J. Geophys. Res. 97, 9619–9629 (1992).
[CrossRef]

Vagle, S.

M. Twardowski, X. Zhang, S. Freeman, M. Slivkoff, J. Sullivan, H. Czerski, S. Vagle, Y. You, and G. Kattawar, “Inverting the volume scattering function to infer particle composition at the near-surface,” in Proceedings of Ocean Optics XX (2011).

H. Czerski, M. Twardowski, S. Vagle, and M. Slivkoff, “Resolving bubble size distributions and dynamics in near-surface waters with optics and acoustics,” in Proceedings of Ocean Optics XX (2011).

Vaillancourt, R. D.

R. D. Vaillancourt, C. W. Brown, R. R. L. Guillard, and W. M. Balch, “Light backscattering properties of marine phytoplankton: relationships to cell size, chemical composition and taxonomy,” J. Plankton Res. 26, 191–212(2004).
[CrossRef]

R. D. Vaillancourt and W. M. Balch, “Size distribution of marine submicron particles determined by flow field-flow fractionation,” Limnol. Oceanogr. 45, 485–492 (2000).
[CrossRef]

van de Hulst, H. C.

H. C. van de Hulst, Light Scattering by Small Particles(Dover, 1981).

Vassen, W.

H. Volten, J. F. de Haan, J. W. Hovenier, R. Schreurs, W. Vassen, and A. G. Decker, “Laboratory measurements of angular distributions of light scattered by phytoplankton and silt,” Limnol. Oceanogr. 43, 1180–1197 (1998).
[CrossRef]

Vicente, L. N.

L. F. Portugal, J. J. Judice, and L. N. Vicente, “A comparison of block pivoting and interior-point algorithms for linear least squares problems with nonnegative variables,” Math. Comput. 63, 625–643 (1994).
[CrossRef]

Vila, X.

T. Serra, J. Colomer, X. P. Cristina, X. Vila, J. B. Arellano, and X. Casamitjana, “Evaluation of laser in situ scattering instrument for measuring concentration of phytoplankton, purple sulfur bacteria, and suspended inorganic sediments in lakes,” J. Environ. Eng. 127, 1023–1030 (2001).
[CrossRef]

Volten, H.

H. Volten, J. F. de Haan, J. W. Hovenier, R. Schreurs, W. Vassen, and A. G. Decker, “Laboratory measurements of angular distributions of light scattered by phytoplankton and silt,” Limnol. Oceanogr. 43, 1180–1197 (1998).
[CrossRef]

Voss, K. J.

D. Stramski, E. Boss, D. Bogucki, and K. J. Voss, “The role of seawater constituents in light backscattering in the ocean,” Prog. Oceanogr. 61, 27–56 (2004).
[CrossRef]

Wang, P.-F.

J. W. Gartner, R. T. Cheng, P.-F. Wang, and K. Richter, “Laboratory and field evaluations of the LISST-100 instrument for suspended particle size determinations,” Mar. Geol. 175, 199–219 (2001).
[CrossRef]

Wells, M.

A. R. Longhurst, I. Koike, W. K. W. Li, J. Rodriguez, P. Dickie, P. Kepay, F. Partensky, B. Bautista, J. Ruiz, M. Wells, and D. F. Bird, “Sub-micron particles in northwest Atlantic shelf water,” Deep-Sea Res. A 39, 1–7 (1992).
[CrossRef]

Wells, M. L.

M. L. Wells and E. D. Goldberg, “Marine submicron particles,” Mar. Chem. 40, 5–18 (1992).
[CrossRef]

M. L. Wells and E. D. Goldberg, “Occurrence of small colloids in sea water,” Nature 353, 342–344 (1991).
[CrossRef]

Westberry, T. K.

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

Whitmire, A. L.

Wommack, K. E.

K. E. Wommack and R. R. Colwell, “Virioplankton: viruses in aquatic ecosystems,” Microbiol. Mol. Biol. Rev. 64, 69–114(2000).
[CrossRef]

Wozniak, S. B.

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

Wright, V. M.

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

Yamasaki, A.

A. Yamasaki, H. Fukuda, R. Fukuda, T. Miyajima, T. Nagata, H. Ogawa, and I. Koike, “Submicrometer particles in northwest Pacific coastal environments: abundance, size distribution, and biological origins,” Limnol. Oceanogr. 43, 536–542(1998).
[CrossRef]

Yang, P.

Yentsch, C. M.

J. W. Campbell and C. M. Yentsch, “Variance within homogeneous phytoplankton populations, II: Analysis of clonal cultures,” Cytometry 10, 596–604 (1989).
[CrossRef]

J. W. Campbell, C. M. Yentsch, and T. L. Cucci, “Variance within homogeneous phytoplankton populations, III: analysis of natural populations,” Cytometry 10, 605–611 (1989).
[CrossRef]

J. W. Campbell and C. M. Yentsch, “Variance within homogeneous phytoplankton populations, I: theoretical framework for interpreting histograms,” Cytometry 10, 587–595 (1989).
[CrossRef]

You, Y.

M. Twardowski, X. Zhang, S. Freeman, M. Slivkoff, J. Sullivan, H. Czerski, S. Vagle, Y. You, and G. Kattawar, “Inverting the volume scattering function to infer particle composition at the near-surface,” in Proceedings of Ocean Optics XX (2011).

Zaneveld, J. R. V.

M. S. Twardowski, E. Boss, J. B. Macdonald, W. S. Pegau, A. H. Barnard, and J. R. V. Zaneveld, “A model for estimating bulk refractive index from the optical backscattering ratio and the implications for understanding particle composition in case I and case II waters,” J. Geophys. Res. 106, 14129–14142(2001).
[CrossRef]

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

J. R. V. Zaneveld, D. M. Roach, and H. Pak, “The determination of the index of refraction distribution of oceanic particulates,” J. Geophys. Res. 79, 4091–4095 (1974).
[CrossRef]

J. R. V. Zaneveld and H. Pak, “Method for the determination of the index of refraction of particles suspended in the ocean,” J. Opt. Soc. Am. 63, 321–324 (1973).
[CrossRef]

M. S. Twardowski, C. Moore, J. Sullivan, M. Slivkoff, S. Freeman, and J. R. V. Zaneveld, are preparing a manuscript to be called “Volume scattering functions for selected ocean waters: revisited.”

Zhang, X.

X. Zhang and L. Hu, “Estimating scattering of pure water from density fluctuation of the refractive index,” Opt. Express 17, 1671–1678 (2009).
[CrossRef]

X. Zhang, L. Hu, and M.-X. He, “Scattering by pure seawater: effect of salinity,” Opt. Express 17, 5698–5710 (2009).
[CrossRef]

X. Zhang, M. R. Lewis, M. Lee, B. D. Johnson, and G. Korotaev, “Volume scattering function of natural bubble populations,” Limnol. Oceanogr. 47, 1273–1282 (2002).
[CrossRef]

X. Zhang, M. R. Lewis, and B. D. Johnson, “Influence of bubbles on scattering of light in the ocean,” Appl. Opt. 37, 6525–6536 (1998).
[CrossRef]

M. Twardowski, X. Zhang, S. Freeman, M. Slivkoff, J. Sullivan, H. Czerski, S. Vagle, Y. You, and G. Kattawar, “Inverting the volume scattering function to infer particle composition at the near-surface,” in Proceedings of Ocean Optics XX (2011).

Zibordi, G.

Appl. Opt. (16)

O. B. Brown and H. R. Gordon, “Two component Mie scattering models of Sargasso Sea particles,” Appl. Opt. 12, 2461–2465 (1973).
[CrossRef]

O. B. Brown and H. R. Gordon, “Size-refractive index distribution of clear coastal water particulates from light scattering,” Appl. Opt. 13, 2874–2881 (1974).
[CrossRef]

B. P. Curry, “Constrained eigenfunction method for the inversion of remote sensing data: application to particle size determination from light scattering measurements,” Appl. Opt. 28, 1345–1355 (1989).
[CrossRef]

W. Arnott and P. L. Marston, “Unfolded optical glory of spheroids: backscattering of laser light from freely rising spheroidal air bubbles in water,” Appl. Opt. 30, 3429–3442(1991).
[CrossRef]

S. D. Coston and N. George, “Particle sizing by inversion of the optical transform pattern,” Appl. Opt. 30, 4785–4794(1991).
[CrossRef]

J. C. Knight, D. Ball, and G. N. Robertson, “Analytical inversion for laser diffraction spectrometry giving improved resolution and accuracy in size distribution,” Appl. Opt. 30, 4795–4799 (1991).
[CrossRef]

J. B. Riley and Y. C. Agrawal, “Sampling and inversion of data in diffraction particle sizing,” Appl. Opt. 30, 4800–4817 (1991).
[CrossRef]

M. R. Jones, B. P. Curry, M. Q. Brewster, and K. H. Leong, “Inversion of light-scattering measurements for particle size and optical constants: theoretical study,” Appl. Opt. 33, 4025–4034 (1994).
[CrossRef]

O. Ulloa, S. Sathyendranath, and T. Platt, “Effect of the particle-size distribution on the backscattering ratio in seawater,” Appl. Opt. 33, 7070–7077 (1994).
[CrossRef]

M. I. Mishchenko and L. D. Travis, “Light scattering by polydispersions of randomly oriented spheroids with sizes comparable to wavelengths of observation,” Appl. Opt. 33, 7206–7225 (1994).
[CrossRef]

X. Zhang, M. R. Lewis, and B. D. Johnson, “Influence of bubbles on scattering of light in the ocean,” Appl. Opt. 37, 6525–6536 (1998).
[CrossRef]

R. E. Green, H. M. Sosik, R. J. Olson, and M. D. DuRand, “Flow cytometric determination of size and complex refractive index for marine particles: comparison with independent and bulk estimates,” Appl. Opt. 42, 526–541 (2003).
[CrossRef]

J.-F. Berthon, E. Shybanov, M. E. G. Lee, and G. Zibordi, “Measurements and modeling of the volume scattering function in the coastal northern Adriatic Sea,” Appl. Opt. 46, 5189–5203(2007).
[CrossRef]

R. A. Meyer, “Light scattering from biological cells: dependence of backscattering radiation on membrane thickness and refractive index,” Appl. Opt. 18, 585–588 (1979).
[CrossRef]

J. M. Sullivan and M. S. Twardowski, “Angular shape of the oceanic particulate volume scattering function in the backward direction,” Appl. Opt. 48, 6811–6819 (2009).
[CrossRef]

L. Bi, P. Yang, G. W. Kattawar, and R. Kahn, “Modeling optical properties of mineral aerosol particles by using nonsymmetric hexahedra,” Appl. Opt. 49, 334–342 (2010).
[CrossRef]

Biogeosciences (2)

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

L. Stemmann, D. Eloire, A. Sciandra, G. A. Jackson, L. Guidi, M. Picheral, and G. Gorsky, “Volume distribution for particles between 3.5 to 2000 μm in the upper 200 m region of the South Pacific Gyre,” Biogeosciences 5, 299–310 (2008).
[CrossRef]

Can. Bull. Fish. Aquat. Sci. (1)

A. Morel and A. Bricaud, “Inherent optical properties of algal cells, including picoplankton. Theoretical and experimental results,” Can. Bull. Fish. Aquat. Sci. 214, 521–559 (1986).

Comput. J. (1)

R. Fletcher and M. J. D. Powell, “A rapidly convergent descent method for minimization,” Comput. J. 6, 163–168(1963).

Cytometry (3)

J. W. Campbell and C. M. Yentsch, “Variance within homogeneous phytoplankton populations, I: theoretical framework for interpreting histograms,” Cytometry 10, 587–595 (1989).
[CrossRef]

J. W. Campbell and C. M. Yentsch, “Variance within homogeneous phytoplankton populations, II: Analysis of clonal cultures,” Cytometry 10, 596–604 (1989).
[CrossRef]

J. W. Campbell, C. M. Yentsch, and T. L. Cucci, “Variance within homogeneous phytoplankton populations, III: analysis of natural populations,” Cytometry 10, 605–611 (1989).
[CrossRef]

Deep-Sea Res. (1)

G. Kullenberg, “Scattering of light by Sargasso Sea water,” Deep-Sea Res. 15, 423–432 (1968).

Deep-Sea Res. A (1)

A. R. Longhurst, I. Koike, W. K. W. Li, J. Rodriguez, P. Dickie, P. Kepay, F. Partensky, B. Bautista, J. Ruiz, M. Wells, and D. F. Bird, “Sub-micron particles in northwest Atlantic shelf water,” Deep-Sea Res. A 39, 1–7 (1992).
[CrossRef]

Deep-Sea Res. I (1)

D. Risovic, “Two-component model of sea particle size distribution,” Deep-Sea Res. I 40, 1459–1473 (1993).
[CrossRef]

Environ. Sci. Technol. (1)

J. H. Ahn and S. B. Grant, “Size distribution, sources, and seasonality of suspended particles in southern California marine bathing waters,” Environ. Sci. Technol. 41, 695–702 (2007).
[CrossRef]

Helgoland Mar. Res. (1)

T. Platt and K. Denman, “Organisation in the pelagic ecosystem,” Helgoland Mar. Res. 30, 575–581 (1977).

IEEE J. Oceanic Eng. (1)

O. Schofield, T. Bergmann, P. Bissett, J. F. Grassle, D. B. Haidvogel, J. Kohut, M. Moline, and S. M. Glenn, “The Long-term Ecosystem Observatory: an integrated coastal observatory,” IEEE J. Oceanic Eng. 27, 146–154 (2002).
[CrossRef]

J. Atmos. Ocean. Technol. (1)

M. E. Lee and M. R. Lewis, “A new method for the measurement of the optical volume scattering function in the upper ocean,” J. Atmos. Ocean. Technol. 20, 563–571 (2003).
[CrossRef]

J. Colloid Interface Sci. (1)

F. S. Lai, S. K. Friedlander, J. Pich, and G. M. Hidy, “The self-preserving particle size distribution for Brownian coagulation in the free-molecule regime,” J. Colloid Interface Sci. 39, 395–405 (1972).
[CrossRef]

J. Environ. Eng. (1)

T. Serra, J. Colomer, X. P. Cristina, X. Vila, J. B. Arellano, and X. Casamitjana, “Evaluation of laser in situ scattering instrument for measuring concentration of phytoplankton, purple sulfur bacteria, and suspended inorganic sediments in lakes,” J. Environ. Eng. 127, 1023–1030 (2001).
[CrossRef]

J. Franklin Inst. (1)

B. Epstein, “The mathematical description of certain breakage mechanisms leading to the logarithmico-normal distribution,” J. Franklin Inst. 244, 471–477 (1947).
[CrossRef]

J. Geophys. Res. (13)

J. W. Campbell, “The lognormal distribution as a model for bio-optical variability in the sea,” J. Geophys. Res. 100, 13237–13254 (1995).
[CrossRef]

O. Ulloa, S. Sathyendranath, T. Platt, and R. A. Quiñones, “Light scattering by marine heterotrophic bacteria,” J. Geophys. Res. 97, 9619–9629 (1992).
[CrossRef]

K. L. Carder, G. Beardsley, Jr., and H. Pak, “Particle size distribution in the Eastern Equatorial Pacific,” J. Geophys. Res. 76, 5070–5077 (1971).
[CrossRef]

M. M. Lozano, E. Talu, and M. L. Longo, “Dissolution of microbubbles generated in seawater obtained offshore: behavior and surface tension measurements,” J. Geophys. Res. 112, C12001 (2007).
[CrossRef]

O. Dubovik, A. Smirnov, B. N. Holben, M. D. King, Y. J. Kaufman, T. F. Eck, and I. Slutsker, “Accuracy assessments of aerosol optical properties retrieved from Aerosol Robotic Network (AERONET) Sun and sky radiance measurements,” J. Geophys. Res. 105, 9791–9806(2000).
[CrossRef]

Y. C. Agrawal and P. Traykovski, “Particles in the bottom boundary layer: concentration and size dynamics through events,” J. Geophys. Res. 106, 9533–9542 (2001).
[CrossRef]

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

J. R. V. Zaneveld, D. M. Roach, and H. Pak, “The determination of the index of refraction distribution of oceanic particulates,” J. Geophys. Res. 79, 4091–4095 (1974).
[CrossRef]

E. Boss, W. S. Pegau, M. Lee, M. Twardowski, E. Shybanov, and G. Korotaev, “Particulate backscattering ratio at LEO 15 and its use to study particle composition and distribution,” J. Geophys. Res. 109, C01014 (2004).
[CrossRef]

M. Chami, E. B. Shybanov, T. Y. Churilova, G. A. Khomenko, M. E. G. Lee, O. V. Martynov, G. A. Berseneva, and G. K. Korotaev, “Optical properties of the particles in the Crimea coastal waters (Black Sea),” J. Geophys. Res. 110, C11020 (2005).
[CrossRef]

M. S. Twardowski, E. Boss, J. B. Macdonald, W. S. Pegau, A. H. Barnard, and J. R. V. Zaneveld, “A model for estimating bulk refractive index from the optical backscattering ratio and the implications for understanding particle composition in case I and case II waters,” J. Geophys. Res. 106, 14129–14142(2001).
[CrossRef]

G. F. Beardsley, H. J. Pak, and K. L. Carder, “Light scattering and suspended particles in the Eastern Equatorial Pacific ocean,” J. Geophys. Res. 75, 2837–2845 (1970).
[CrossRef]

C. F. Bohren and S. B. Singham, “Backscattering by nonspherical particles: a review of methods and suggested new approaches,” J. Geophys. Res. 96, 5269–5277 (1991).
[CrossRef]

J. Hydraul. Eng. (1)

B. G. Krishnappan, “In situ size distribution of suspended particles in the Fraser River,” J. Hydraul. Eng. 126, 561–569 (2000).
[CrossRef]

J. Mar. Res. (2)

C. E. Lambert, C. Jehanno, N. Silverberg, J. C. Brun-Cottan, and R. Chesselet, “Log-normal distribution of suspended particles in the open ocean,” J. Mar. Res. 39, 77–98 (1981).

A. Morel and Y.-H. Ahn, “Optics of heterotrophic nanoflagellates and ciliates: a tentative assessment of their scattering role in oceanic waters compared to those of bacterial and algal cells,” J. Mar. Res. 49, 177–202 (1991).
[CrossRef]

J. Opt. Soc. Am. (1)

J. Phys. Chem. (1)

J. H. Chin, C. M. Sliepcevich, and M. Tribus, “Particle size distributions from angular variation of intensity of forward-scattered light at very small angles,” J. Phys. Chem. 59, 841–844 (1955).
[CrossRef]

J. Plankton Res. (2)

E. Aas, “Refractive index of phytoplankton derived from its metabolite composition,” J. Plankton Res. 18, 2223–2249(1996).
[CrossRef]

R. D. Vaillancourt, C. W. Brown, R. R. L. Guillard, and W. M. Balch, “Light backscattering properties of marine phytoplankton: relationships to cell size, chemical composition and taxonomy,” J. Plankton Res. 26, 191–212(2004).
[CrossRef]

Limnol. Oceanogr. (9)

H. Volten, J. F. de Haan, J. W. Hovenier, R. Schreurs, W. Vassen, and A. G. Decker, “Laboratory measurements of angular distributions of light scattered by phytoplankton and silt,” Limnol. Oceanogr. 43, 1180–1197 (1998).
[CrossRef]

A. Yamasaki, H. Fukuda, R. Fukuda, T. Miyajima, T. Nagata, H. Ogawa, and I. Koike, “Submicrometer particles in northwest Pacific coastal environments: abundance, size distribution, and biological origins,” Limnol. Oceanogr. 43, 536–542(1998).
[CrossRef]

R. D. Vaillancourt and W. M. Balch, “Size distribution of marine submicron particles determined by flow field-flow fractionation,” Limnol. Oceanogr. 45, 485–492 (2000).
[CrossRef]

M. Jonasz and G. R. 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, “Nonsphericity of suspended marine particles and its influence on light scattering,” Limnol. Oceanogr. 32, 1059–1065 (1987).
[CrossRef]

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

R. W. Sheldon, A. Prakash, and W. H. Sutcliffe, “The size distribution of particles in the ocean,” Limnol. Oceanogr. 17, 327–340 (1972).
[CrossRef]

H. R. Gordon and O. B. Brown, “A theoretical model of light scattering by Sargasso Sea particulates,” Limnol. Oceanogr. 17, 826–832 (1972).
[CrossRef]

X. Zhang, M. R. Lewis, M. Lee, B. D. Johnson, and G. Korotaev, “Volume scattering function of natural bubble populations,” Limnol. Oceanogr. 47, 1273–1282 (2002).
[CrossRef]

Limnol. Oceanogr. Methods (1)

L. Karp-Boss, L. Azevedo, and E. Boss, “LISST-100 measurements of phytoplankton size distribution: evaluation of the effects of cell shape,” Limnol. Oceanogr. Methods 5, 396–406 (2007).

Mar. Chem. (1)

M. L. Wells and E. D. Goldberg, “Marine submicron particles,” Mar. Chem. 40, 5–18 (1992).
[CrossRef]

Mar. Geol. (3)

M. Jonasz, “Nonspherical sediment particles: comparison of size and volume distributions obtained with an optical and a resistive particle counter,” Mar. Geol. 78, 137–142 (1987).
[CrossRef]

J. W. Gartner, R. T. Cheng, P.-F. Wang, and K. Richter, “Laboratory and field evaluations of the LISST-100 instrument for suspended particle size determinations,” Mar. Geol. 175, 199–219 (2001).
[CrossRef]

Y. C. Agrawal and H. C. Pottsmith, “Instruments for particle size and settling velocity observations in sediment transport,” Mar. Geol. 168, 89–114 (2000).
[CrossRef]

Math. Comput. (1)

L. F. Portugal, J. J. Judice, and L. N. Vicente, “A comparison of block pivoting and interior-point algorithms for linear least squares problems with nonnegative variables,” Math. Comput. 63, 625–643 (1994).
[CrossRef]

Microbiol. Mol. Biol. Rev. (1)

K. E. Wommack and R. R. Colwell, “Virioplankton: viruses in aquatic ecosystems,” Microbiol. Mol. Biol. Rev. 64, 69–114(2000).
[CrossRef]

Nature (1)

M. L. Wells and E. D. Goldberg, “Occurrence of small colloids in sea water,” Nature 353, 342–344 (1991).
[CrossRef]

Oecologia (1)

T. Fenchel, “Intrinsic rate of natural increase: the relationship with body size,” Oecologia 14, 317–326 (1974).
[CrossRef]

Opt. Express (3)

Opt. Lett. (1)

Proc. SPIE (2)

J. S. Schoonmaker, R. R. Hammond, A. L. Heath, and J. S. Cleveland, “A numerical model for prediction of sublittoral optical visibility,” Proc. SPIE 2258, 685–702 (1994).
[CrossRef]

G. R. Fournier and J. L. Forand, “Analytical phase function for ocean water,” Proc. SPIE 2258, 194–201 (1994).
[CrossRef]

Prog. Oceanogr. (2)

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

D. Stramski, E. Boss, D. Bogucki, and K. J. Voss, “The role of seawater constituents in light backscattering in the ocean,” Prog. Oceanogr. 61, 27–56 (2004).
[CrossRef]

Science (1)

F. T. Manheim, R. H. Meade, and G. C. Bond, “Suspended matter in surface waters of the Atlantic continental margin from Cape Cod to the Florida Keys,” Science 167, 371–376(1970).
[CrossRef]

Tellus (1)

M. Jonasz and H. Prandke, “Comparison of measured and computed light scattering in the Baltic,” Tellus 38B, 144–157 (1986).
[CrossRef]

Other (19)

G. Kullenberg, “Observed and computed scattering functions,” in Optical Aspects of Oceanography, N.G.Jerlov and E.Steeman-Nielsen, eds. (Academic, 1974), pp. 25–49.

M. S. Twardowski, C. Moore, J. Sullivan, M. Slivkoff, S. Freeman, and J. R. V. Zaneveld, are preparing a manuscript to be called “Volume scattering functions for selected ocean waters: revisited.”

S. Twomey, Introduction to the Mathematics of Inversion in Remote Sensing and Indirect Measurements, Developments in Geomathematics (Elsevier, 1977).

A. Morel, “The scattering of light by seawater: experimental results and theoretical approach,” in Optics of the Sea, Interface and In-Water Transmission and Imaging (NATO Advisory Group for Aerospace Research and Development, 1973).

T. J. Petzold, “Volume scattering function for selected ocean waters,” SIO Ref. 72-78, Scripps Institute of Oceanography, La Jolla, 1972.

O. V. Kopelevich, “Low-parametric model of seawater optical properties,” in Ocean Optics I: Physical Ocean Optics, A.S.Monin, ed. (Nauka, 1983), pp. 208–234.

C. D. Mobley, Light and Water: Radiative Transfer in Natural Waters (Academic, 1994).

K. S. Shifrin, Physical Optics of Ocean Water, AIP Translation Series (American Institute of Physics, 1988).

O. Dubovik, “Optimization of numerical inversion in photopolarimetric remote sensing,” in Photopolarimetry in Remote Sensing, G.Videen, Y.Yatskiv, and M.Mishchenko, eds. (Kluwer, 2004), pp. 65–106.

M. I. Mishchenko, L. D. Travis, and A. A. Lacis, Scattering, Absorption, and Emission of Light by Small Particles(Cambridge University, 2002).

B. D. Johnson, “Bubble populations: background and breaking waves,” in Oceanic Whitecaps and Their Role in Air-Sea Exchange Processes, E.C.Monahan and G.Mac Niocail, eds. (Reidel, 1986), pp. 69–73.

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

M. L. Longo, Department of Chemical Engineering and Materials Science, University of California, Davis, Calif., USA (personal communication, 2010).

C. L. Lawson and R. J. Hanson, Solving Least Squares Problems, Automatic Computation (Prentice-Hall, 1974).

W. R. Clavano, E. Boss, and L. Karp-Boss, “Inherent optical properties of non-spherical marine-like particles—from theory to observation,” in Oceanography and Marine Biology: An Annual Review (Taylor & Francis, 2007), Vol.  45, pp. 1–38.

H. C. van de Hulst, Light Scattering by Small Particles(Dover, 1981).

M. Twardowski, X. Zhang, S. Freeman, M. Slivkoff, J. Sullivan, H. Czerski, S. Vagle, Y. You, and G. Kattawar, “Inverting the volume scattering function to infer particle composition at the near-surface,” in Proceedings of Ocean Optics XX (2011).

H. Czerski, M. Twardowski, S. Vagle, and M. Slivkoff, “Resolving bubble size distributions and dynamics in near-surface waters with optics and acoustics,” in Proceedings of Ocean Optics XX (2011).

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

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (12)

Fig. 1
Fig. 1

Kullenberg’s Sargasso Sea particulate (SSP) VSFs at 632.8 nm (SSP 632.8 nm ) by the laser instrument and at 460 nm (SSP 460 nm ) and 655 nm (SSP 655 nm ) by the β-meter and the derived VSFs by Gordon and Brown (GB1972) [15], Brown and Gordon (BG1973) [16], Zaneveld et al. (Z1974) [26], and Kullenberg (K1974) [14].

Fig. 2
Fig. 2

Backscattering ratios (dark curves) calculated for single particles with different refractive indices (varying n r with n i = 0.001 ) as function of radius (right y axis) are overlaid against the size distributions (gray curves) of two particle subpopulations: a population dominated by small particles with r mode = 0.1 μm and σ = 0.3 , and a population dominated by large particles with r mode = 10 μm and σ = 1.0 .

Fig. 3
Fig. 3

Phase functions for particles of lognormal distributions and of various refractive indexes. In (a), legend entries indicate the values of r mode and σ. Different curves within each group are for different n = 1.01 to 1.20 + 0.001 i ; in (b), legend entries indicate the values of n r . Different curves within each group are for different size distributions with r mode > 10 μm and σ > 1.0 .

Fig. 4
Fig. 4

Sensitivity of phase functions ( R VSF ) with respect to (a)  r mode , (b) σ, (c)  n r , and (d)  n i . In (a), the change in r mode between two values is evaluated as a ratio ( R r mode ), and the curves from bottom to top correspond to R r mode = 1.5 , 2.0, 3.0, 4.0, and 5.0, respectively; in (b), the change in σ is evaluated as a difference ( Δ σ ), and the curves from bottom to top correspond to Δ σ = 0.05 , 0.1, 0.2, 0.3, 0.4, and 0.5, respectively; in (c), the change in n r is evaluated as a difference ( Δ n r ), and the curves from bottom to top correspond to Δ n r = 0.01 , 0.02, 003, and 0.04, respectively; in (d), the change in n i is evaluated against n i = 0.001 . Note the ordinate scale in (d) is different from (a)–(c).

Fig. 5
Fig. 5

(a) Typical phytoplankton PSD is represented by three different functions: Weibull, Lognormal, and Gamma; all have the same peak size and similar measures of spread. (b) Corresponding phase functions (left y axis) and R VSF (right y axis).

Fig. 6
Fig. 6

(a) Measured VSFs at LEO-15 in 2001. (b) Square root of the eigenvalues for the VSFs as a functions of number of angles at which the VSFs are measured. (c) Candidate phase functions calculated based on the parameters defined in Table 3. The curves corresponding to VSPs, particles of intermediate sizes (IP), and LPs are shown with different gray scales. (d) Histogram of backscattering ratios ( b b ratio) for the candidate phase functions.

Fig. 7
Fig. 7

(a) The measured VSF was partitioned through inversion into VSFs due to individual subpopulations; (b) the corresponding size distribution of each subpopulation. The legend shows the values of n, r mode , σ, and b for each subpopulation. The two numbers in (a) indicate the total scattering coefficients estimated from the measured VSF and the cumulative VSFs from the subpopulations, respectively. The two numbers in (b) indicate the Junge slope fitted over the total PSD and the total concentration, respectively, for particles of radii between 0.2 and 200 μm .

Fig. 8
Fig. 8

Same as Fig. 7 except that the subpopulations are grouped together by the refractive index. The legend in (a) shows the values of n and b. Note, for VSPs, the shape of phase functions does not depend on the particular values of index.

Fig. 9
Fig. 9

Same as Fig. 7 except that the subpopulations are grouped together by dominant sizes ( r mode ). The legend in (a) shows the values of r mode and b.

Fig. 10
Fig. 10

(a) Copy of Fig. 4-a from Boss et al. [8] showing the distribution of Junge slope ( ξ ) and the refractive index for particles over the same area but derived using backscattering ratio and attenuation coefficient measured in 2000 [8, 12]; (b) histogram of Junge slopes estimated from the total PSDs of subpopulations of sizes between 0.2 and 200 μm ; (c) histogram of subpopulations with the same refractive index; (c) histogram of subpopulations of similar dominant size ( r mode ).

Fig. 11
Fig. 11

Average fractional contributions of the persistent subpopulations to the (a) observed VSFs and the (b) total PSDs. The legend lists values for n, r mode , and σ for each persistent subpopulation. The same gray scale is used in both (a) and (b).

Fig. 12
Fig. 12

PSDs derived from the VSF measurements at the LEO-15 site (gray) and the mean distribution (black).

Tables (4)

Tables Icon

Table 1 VSF Measurements and Derived Particle-Index–Size Distributions

Tables Icon

Table 2 Measured or Estimated Values of r mode and σ for Particles Following Lognormal Size Distribution

Tables Icon

Table 3 Values of Parameters Defining the Size–Index Spectra for the Subpopulations Used in Inversion

Tables Icon

Table 4 Persistent Subpopulations

Equations (13)

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

β ( θ ) = i = 1 M b i ( n ( r ) , F ( r ) , G ( r ) , S ( r ) ) β ˜ i ( n ( r ) , F ( r ) , G ( r ) , S ( r ) , θ ) .
β ( θ ) = r min r max b ( n ( r ) , F ( r ) , G ( r ) , S ( r ) ) β ˜ ( n ( r ) , F ( r ) , G ( r ) , S ( r ) , θ ) d r ,
C sca = 4 π C ang ( Ω ) d Ω = 2 π 0 π C ang ( θ ) sin θ d θ ,
C bsc = 2 π π / 2 π C ang ( θ ) sin θ d θ ,
b ˜ b = C bsc C sca ,
β ˜ ( θ , n , G , S , F ) = β ( θ , n , G , S , F ) b ( θ , n , G , S , F ) ,
β ( θ , n , G , S , F ) = r min r max C ang ( θ , r , n , S ) F ( r ) d r ,
b ( n , G , S , F ) = r min r max C sca ( r , n , S ) F ( r ) d r .
β ( θ ) = d I ( θ ) E d V ,
F ( r ) = N 0 1 s r max 1 s r min 1 s r s ,
F ( r ) = N 0 exp ( σ 2 2 ) 2 π σ 2 r mode exp ( ( ln ( r ) ln ( r mode ) ) 2 2 σ 2 ) ,
R VSF ( θ , x ) = max ( β ˜ ( θ , x , Y ) ) min ( β ˜ ( θ , x , Y ) ) ,
Λ min < N add 1 / 2 | ε | ,

Metrics