Abstract

Properly interpreting lidar (light detection and ranging) signal for characterizing particle distribution relies on a key parameter, ${\chi _p}(\pi )$, which relates the particulate volume scattering function (VSF) at 180° (${\beta _p}(\pi )$) that a lidar measures to the particulate backscattering coefficient (${b_\textit{bp}}$). However, ${\chi _p}(\pi )$ has been seldom studied due to challenges in accurately measuring ${\beta _p}(\pi )$ and ${b_\textit{bp}}$ concurrently in the field. In this study, ${\chi _p}(\pi )$, as well as its spectral dependence, was re-examined using the VSFs measured in situ at high angular resolution in a wide range of waters. ${\beta _p}(\pi )$, while not measured directly, was inferred using a physically sound, well-validated VSF-inversion method. The effects of particle shape and internal structure on the inversion were tested using three inversion kernels consisting of phase functions computed for particles that are assumed as homogenous sphere, homogenous asymmetric hexahedra, or coated sphere. The reconstructed VSFs using any of the three kernels agreed well with the measured VSFs with a mean percentage difference $ \lt {5}\% $ at scattering angles $ \lt {170}^\circ $. At angles immediately near or equal to 180°, the reconstructed ${\beta _p}(\pi )$ depends strongly on the inversion kernel. ${\chi _p}(\pi )$ derived with the sphere kernels was smaller than those derived with the hexahedra kernel but consistent with ${\chi _p}(\pi )$ estimated directly from high-spectral-resolution lidar and in situ backscattering sensor. The possible explanation was that the sphere kernels are able to capture the backscattering enhancement feature near 180° that has been observed for marine particles. ${\chi _p}(\pi )$ derived using the coated sphere kernel was generally lower than those derived with the homogenous sphere kernel. Our result suggests that ${\chi _p}(\pi )$ is sensitive to the shape and internal structure of particles and significant error could be induced if a fixed value of ${\chi _p}(\pi )$ is to be used to interpret lidar signal collected in different waters. On the other hand, ${\chi _p}(\pi )$ showed little spectral dependence.

© 2020 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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2019 (5)

L. Hu, X. Zhang, and M. J. Perry, “Light scattering by pure seawater: effect of pressure,” Deep Sea Res. I 146, 103–109 (2019).
[Crossref]

P. Chen, D. Pan, Z. Mao, and H. Liu, “A feasible calibration method for type 1 open ocean water LiDAR data based on bio-optical models,” Remote Sens. 11, 172 (2019).
[Crossref]

P. Chen and D. Pan, “Ocean optical profiling in South China Sea using airborne LiDAR,” Remote Sens. 11, 1826 (2019).
[Crossref]

L. Hu, X. Zhang, Y. Xiong, and M.-X. He, “Calibration of the LISST-VSF to derive the volume scattering functions in clear waters,” Opt. Express 27, A1188–A1206 (2019).
[Crossref]

V. Shishko, A. Konoshonkin, N. Kustova, D. Timofeev, and A. Borovoi, “Coherent and incoherent backscattering by a single large particle of irregular shape,” Opt. Express 27, 32984–32993 (2019).
[Crossref]

2018 (4)

C. Poulin, X. Zhang, P. Yang, and Y. Huot, “Diel variations of the attenuation, backscattering and absorption coefficients of four phytoplankton species and comparison with spherical, coated spherical and hexahedral particle optical models,” J. Quantum Spectrosc. Radiat. Transfer 217, 288–304 (2018).
[Crossref]

E. Organelli, G. Dall’Olmo, R. J. W. Brewin, G. A. Tarran, E. Boss, and A. Bricaud, “The open-ocean missing backscattering is in the structural complexity of particles,” Nat. Commun. 9, 5439 (2018).
[Crossref]

S. Stamnes, C. Hostetler, R. Ferrare, S. Burton, X. Liu, J. Hair, Y. Hu, A. Wasilewski, W. Martin, B. van Diedenhoven, J. Chowdhary, I. Cetinić, L. K. Berg, K. Stamnes, and B. Cairns, “Simultaneous polarimeter retrievals of microphysical aerosol and ocean color parameters from the “MAPP” algorithm with comparison to high-spectral-resolution lidar aerosol and ocean products,” Appl. Opt. 57, 2394–2413 (2018).
[Crossref]

C. A. Hostetler, M. J. Behrenfeld, Y. Hu, J. W. Hair, and J. A. Schulien, “Spaceborne lidar in the study of marine systems,” Annu. Rev. Mar. Sci. 10, 121–147 (2018).
[Crossref]

2017 (7)

J. H. Churnside and R. D. Marchbanks, “Inversion of oceanographic profiling lidars by a perturbation to a linear regression,” Appl. Opt. 56, 5228–5233 (2017).
[Crossref]

J. A. Schulien, M. J. Behrenfeld, J. W. Hair, C. A. Hostetler, and M. S. Twardowski, “Vertically-resolved phytoplankton carbon and net primary production from a high spectral resolution lidar,” Opt. Express 25, 13577–13587 (2017).
[Crossref]

X. Zhang, G. R. Fournier, and D. J. Gray, “Interpretation of scattering by oceanic particles around 120 degrees and its implication in ocean color studies,” Opt. Express 25, A191–A199 (2017).
[Crossref]

J. Churnside, R. Marchbanks, C. Lembke, and J. Beckler, “Optical backscattering measured by airborne lidar and underwater glider,” Remote Sens. 9, 379 (2017).
[Crossref]

X. Zhang, R. H. Stavn, A. U. Falster, J. J. Rick, D. Gray, and R. W. Gould, “Size distributions of coastal ocean suspended particulate inorganic matter: amorphous silica and clay minerals and their dynamics,” Estuarine Coast. Shelf Sci. 189, 243–251 (2017).
[Crossref]

G. Xu, B. Sun, S. D. Brooks, P. Yang, G. W. Kattawar, and X. Zhang, “Modeling the inherent optical properties of aquatic particles using an irregular hexahedral ensemble,” J. Quantum Spectrosc. Radiat. Transfer 191, 30–39 (2017).
[Crossref]

B. Sun, P. Yang, G. W. Kattawar, and X. Zhang, “Physical-geometric optics method for large size faceted particles,” Opt. Express 25, 24044–24060 (2017).
[Crossref]

2016 (2)

2015 (5)

2014 (5)

2013 (7)

H. Tan, R. Doerffer, T. Oishi, and A. Tanaka, “A new approach to measure the volume scattering function,” Opt. Express 21, 18697–18711 (2013).
[Crossref]

M. J. Behrenfeld, Y. Hu, C. A. Hostetler, G. Dall’Olmo, S. D. Rodier, J. W. Hair, and C. R. Trepte, “Space-based lidar measurements of global ocean carbon stocks,” Geophys. Res. Lett. 40, 4355–4360 (2013).
[Crossref]

J. H. Lee, J. H. Churnside, R. D. Marchbanks, P. L. Donaghay, and J. M. Sullivan, “Oceanographic lidar profiles compared with estimates from in situ optical measurements,” Appl. Opt. 52, 786–794 (2013).
[Crossref]

J. H. Churnside, “Review of profiling oceanographic lidar,” Opt. Eng. 53, 051405 (2013).
[Crossref]

X. Zhang, Y. Huot, D. J. Gray, A. Weidemann, and W. J. Rhea, “Biogeochemical origins of particles obtained from the inversion of the volume scattering function and spectral absorption in coastal waters,” Biogeosciences 10, 6029–6043 (2013).
[Crossref]

L. Bi, P. Yang, G. W. Kattawar, and M. I. Mishchenko, “Efficient implementation of the invariant imbedding T-matrix method and the separation of variables method applied to large nonspherical inhomogeneous particles,” J. Quantum Spectrosc. Radiat. Transfer 116, 169–183 (2013).
[Crossref]

A. Borovoi, A. Konoshonkin, and N. Kustova, “Backscattering by hexagonal ice crystals of cirrus clouds,” Opt. Lett. 38, 2881–2884 (2013).
[Crossref]

2012 (4)

M. Twardowski, X. Zhang, S. Vagle, J. Sullivan, S. Freeman, H. Czerski, Y. You, L. Bi, and G. Kattawar, “The optical volume scattering function in a surf zone inverted to derive sediment and bubble particle subpopulations,” J. Geophys. Res. Oceans 117, C00H17 (2012).
[Crossref]

X. Zhang, D. J. Gray, Y. Huot, Y. You, and L. Bi, “Comparison of optically derived particle size distributions: scattering over the full angular range versus diffraction at near forward angles,” Appl. Opt. 51, 5085–5099 (2012).
[Crossref]

M. Babin, D. Stramski, R. A. Reynolds, V. M. Wright, and E. Leymarie, “Determination of the volume scattering function of aqueous particle suspensions with a laboratory multi-angle light scattering instrument,” Appl. Opt. 51, 3853–3873 (2012).
[Crossref]

C. Li, W. Cao, J. Yu, T. Ke, G. Lu, Y. Yang, and C. Guo, “An instrument for in situ measuring the volume scattering function of water: design, calibration and primary experiments,” Sensors 12, 4514–4533 (2012).
[Crossref]

2011 (2)

X. Zhang, M. Twardowski, and M. Lewis, “Retrieving composition and sizes of oceanic particle subpopulations from the volume scattering function,” Appl. Opt. 50, 1240–1259 (2011).
[Crossref]

H. Czerski, M. Twardowski, X. Zhang, and S. Vagle, “Resolving size distributions of bubbles with radii less than 30 µm with optical and acoustical methods,” J. Geophys. Res. Oceans 116, C00H11 (2011).
[Crossref]

2010 (2)

2009 (4)

2008 (1)

2007 (1)

2006 (1)

H. Loisel, J.-M. Nicolas, A. Sciandra, D. Stramski, and A. Poteau, “Spectral dependency of optical backscattering by marine particles from satellite remote sensing of the global ocean,” J. Geophys. Res. Oceans 111, C09024 (2006).
[Crossref]

2005 (1)

2003 (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]

2002 (1)

2001 (2)

1998 (1)

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

1997 (1)

1996 (2)

R. A. Maffione and D. R. Dana, “In-situ characterization of optical backscattering and attenuation for lidar applications,” Proc. SPIE 2964, 152–162 (1996).
[Crossref]

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

1992 (3)

R. A. Maffione and R. C. Honey, “Instrument for measuring the volume scattering function in the backward direction,” Proc. SPIE 1750, 15–26 (1992).
[Crossref]

A. N. Bogaturov, A. A. D. Canas, J. C. Dainty, A. S. Gurvich, V. A. Myakinin, C. J. Solomon, and N. J. Wooder, “Observation of the enhancement of coherence by backscattering through turbulence,” Opt. Commun. 87, 1–4 (1992).
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M. I. Mishchenko, “Enhanced backscattering of polarized light from discrete random media: calculations in exactly the backscattering direction,” J. Opt. Soc. Am. A 9, 978–982 (1992).
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1991 (2)

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

G. D. Hickman, J. M. Harding, M. Carnes, A. Pressman, G. W. Kattawar, and E. S. Fry, “Aircraft laser sensing of sound velocity in water: Brillouin scattering,” Remote Sens. Environ. 36, 165–178 (1991).
[Crossref]

1989 (1)

M. S. Quinby-Hunt, A. J. Hunt, K. Lofftus, and D. Shapiro, “Polarized-light scattering studies of marine Chlorella,” Limnol. Oceanogr. 34, 1587–1600 (1989).
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1988 (2)

H. R. Gordon, O. B. Brown, R. H. Evans, J. W. Brown, R. C. Smith, K. S. Baker, and D. K. Clark, “A semianalytic radiance model of ocean color,” J. Geophys. Res. 93, 10909–10924 (1988).
[Crossref]

A. Ishimaru and L. Tsang, “Backscattering enhancement of random discrete scatters of moderate sizes,” J. Opt. Soc. Am. A 5, 228–236 (1988).
[Crossref]

1986 (1)

1985 (1)

1984 (2)

1982 (2)

1979 (1)

1977 (3)

P. W. Holland and R. E. Welsch, “Robust regression using iteratively reweighted least-squares,” Comm. Statist. Theory Methods 6, 813–827 (1977).
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A. Morel and L. Prieur, “Analysis of variations in ocean color,” Limnol. Oceanogr. 22, 709–722 (1977).
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V. Khare and H. M. Nussenzveig, “Theory of the glory,” Phys. Rev. Lett. 38, 1279–1282 (1977).
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Aas, E.

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

W. H. Slade, Y. C. Agrawal, and O. A. Mikkelsen, “Comparison of measured and theoretical scattering and polarization properties of narrow size range irregular sediment particles,” in OCEANS, San Diego, California, USA, 2013, pp. 1–6.

Audouy, C.

Babin, M.

Baker, K. S.

H. R. Gordon, O. B. Brown, R. H. Evans, J. W. Brown, R. C. Smith, K. S. Baker, and D. K. Clark, “A semianalytic radiance model of ocean color,” J. Geophys. Res. 93, 10909–10924 (1988).
[Crossref]

Beckler, J.

J. Churnside, R. Marchbanks, C. Lembke, and J. Beckler, “Optical backscattering measured by airborne lidar and underwater glider,” Remote Sens. 9, 379 (2017).
[Crossref]

Behrenfeld, M.

J. Hair, C. Hostetler, Y. Hu, M. Behrenfeld, C. Butler, D. Harper, R. Hare, T. Berkoff, A. Cook, J. Collins, N. Stockley, M. Twardowski, I. Cetinić, R. Ferrare, and T. Mack, “Combined atmospheric and ocean profiling from an airborne high spectral resolution lidar,” in EPJ Web of Conferences (2016), Vol. 119, p. 22001.

Behrenfeld, M. J.

C. A. Hostetler, M. J. Behrenfeld, Y. Hu, J. W. Hair, and J. A. Schulien, “Spaceborne lidar in the study of marine systems,” Annu. Rev. Mar. Sci. 10, 121–147 (2018).
[Crossref]

J. A. Schulien, M. J. Behrenfeld, J. W. Hair, C. A. Hostetler, and M. S. Twardowski, “Vertically-resolved phytoplankton carbon and net primary production from a high spectral resolution lidar,” Opt. Express 25, 13577–13587 (2017).
[Crossref]

M. J. Behrenfeld, Y. Hu, C. A. Hostetler, G. Dall’Olmo, S. D. Rodier, J. W. Hair, and C. R. Trepte, “Space-based lidar measurements of global ocean carbon stocks,” Geophys. Res. Lett. 40, 4355–4360 (2013).
[Crossref]

Berg, L. K.

Berkoff, T.

J. Hair, C. Hostetler, Y. Hu, M. Behrenfeld, C. Butler, D. Harper, R. Hare, T. Berkoff, A. Cook, J. Collins, N. Stockley, M. Twardowski, I. Cetinić, R. Ferrare, and T. Mack, “Combined atmospheric and ocean profiling from an airborne high spectral resolution lidar,” in EPJ Web of Conferences (2016), Vol. 119, p. 22001.

Bernard, S.

S. Bernard, T. A. Probyn, and A. Quirantes, “Simulating the optical properties of phytoplankton cells using a two-layered spherical geometry,” Biogeosci. Discuss. 2009, 1497–1563 (2009).
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Berthon, J.-F.

Bi, L.

L. Bi, P. Yang, G. W. Kattawar, and M. I. Mishchenko, “Efficient implementation of the invariant imbedding T-matrix method and the separation of variables method applied to large nonspherical inhomogeneous particles,” J. Quantum Spectrosc. Radiat. Transfer 116, 169–183 (2013).
[Crossref]

X. Zhang, D. J. Gray, Y. Huot, Y. You, and L. Bi, “Comparison of optically derived particle size distributions: scattering over the full angular range versus diffraction at near forward angles,” Appl. Opt. 51, 5085–5099 (2012).
[Crossref]

M. Twardowski, X. Zhang, S. Vagle, J. Sullivan, S. Freeman, H. Czerski, Y. You, L. Bi, and G. Kattawar, “The optical volume scattering function in a surf zone inverted to derive sediment and bubble particle subpopulations,” J. Geophys. Res. Oceans 117, C00H17 (2012).
[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]

Bogaturov, A. N.

A. N. Bogaturov, A. A. D. Canas, J. C. Dainty, A. S. Gurvich, V. A. Myakinin, C. J. Solomon, and N. J. Wooder, “Observation of the enhancement of coherence by backscattering through turbulence,” Opt. Commun. 87, 1–4 (1992).
[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. Atmos. 96, 5269–5277 (1991).
[Crossref]

Borovoi, A.

Boss, E.

Brewin, R. J. W.

E. Organelli, G. Dall’Olmo, R. J. W. Brewin, G. A. Tarran, E. Boss, and A. Bricaud, “The open-ocean missing backscattering is in the structural complexity of particles,” Nat. Commun. 9, 5439 (2018).
[Crossref]

Bricaud, A.

Brooks, S. D.

G. Xu, B. Sun, S. D. Brooks, P. Yang, G. W. Kattawar, and X. Zhang, “Modeling the inherent optical properties of aquatic particles using an irregular hexahedral ensemble,” J. Quantum Spectrosc. Radiat. Transfer 191, 30–39 (2017).
[Crossref]

Brown, J. W.

H. R. Gordon, O. B. Brown, R. H. Evans, J. W. Brown, R. C. Smith, K. S. Baker, and D. K. Clark, “A semianalytic radiance model of ocean color,” J. Geophys. Res. 93, 10909–10924 (1988).
[Crossref]

Brown, O. B.

H. R. Gordon, O. B. Brown, R. H. Evans, J. W. Brown, R. C. Smith, K. S. Baker, and D. K. Clark, “A semianalytic radiance model of ocean color,” J. Geophys. Res. 93, 10909–10924 (1988).
[Crossref]

Burton, S.

Butler, C.

J. Hair, C. Hostetler, Y. Hu, M. Behrenfeld, C. Butler, D. Harper, R. Hare, T. Berkoff, A. Cook, J. Collins, N. Stockley, M. Twardowski, I. Cetinić, R. Ferrare, and T. Mack, “Combined atmospheric and ocean profiling from an airborne high spectral resolution lidar,” in EPJ Web of Conferences (2016), Vol. 119, p. 22001.

Cairns, B.

Canas, A. A. D.

A. N. Bogaturov, A. A. D. Canas, J. C. Dainty, A. S. Gurvich, V. A. Myakinin, C. J. Solomon, and N. J. Wooder, “Observation of the enhancement of coherence by backscattering through turbulence,” Opt. Commun. 87, 1–4 (1992).
[Crossref]

Cao, W.

C. Li, W. Cao, J. Yu, T. Ke, G. Lu, Y. Yang, and C. Guo, “An instrument for in situ measuring the volume scattering function of water: design, calibration and primary experiments,” Sensors 12, 4514–4533 (2012).
[Crossref]

Carnes, M.

G. D. Hickman, J. M. Harding, M. Carnes, A. Pressman, G. W. Kattawar, and E. S. Fry, “Aircraft laser sensing of sound velocity in water: Brillouin scattering,” Remote Sens. Environ. 36, 165–178 (1991).
[Crossref]

Cetinic, I.

S. Stamnes, C. Hostetler, R. Ferrare, S. Burton, X. Liu, J. Hair, Y. Hu, A. Wasilewski, W. Martin, B. van Diedenhoven, J. Chowdhary, I. Cetinić, L. K. Berg, K. Stamnes, and B. Cairns, “Simultaneous polarimeter retrievals of microphysical aerosol and ocean color parameters from the “MAPP” algorithm with comparison to high-spectral-resolution lidar aerosol and ocean products,” Appl. Opt. 57, 2394–2413 (2018).
[Crossref]

J. Hair, C. Hostetler, Y. Hu, M. Behrenfeld, C. Butler, D. Harper, R. Hare, T. Berkoff, A. Cook, J. Collins, N. Stockley, M. Twardowski, I. Cetinić, R. Ferrare, and T. Mack, “Combined atmospheric and ocean profiling from an airborne high spectral resolution lidar,” in EPJ Web of Conferences (2016), Vol. 119, p. 22001.

Chami, M.

Charlton, F.

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

Chen, P.

P. Chen, D. Pan, Z. Mao, and H. Liu, “A feasible calibration method for type 1 open ocean water LiDAR data based on bio-optical models,” Remote Sens. 11, 172 (2019).
[Crossref]

P. Chen and D. Pan, “Ocean optical profiling in South China Sea using airborne LiDAR,” Remote Sens. 11, 1826 (2019).
[Crossref]

Chowdhary, J.

Churnside, J.

J. Churnside, R. Marchbanks, C. Lembke, and J. Beckler, “Optical backscattering measured by airborne lidar and underwater glider,” Remote Sens. 9, 379 (2017).
[Crossref]

Churnside, J. H.

Clark, D. K.

H. R. Gordon, O. B. Brown, R. H. Evans, J. W. Brown, R. C. Smith, K. S. Baker, and D. K. Clark, “A semianalytic radiance model of ocean color,” J. Geophys. Res. 93, 10909–10924 (1988).
[Crossref]

Collins, J.

J. Hair, C. Hostetler, Y. Hu, M. Behrenfeld, C. Butler, D. Harper, R. Hare, T. Berkoff, A. Cook, J. Collins, N. Stockley, M. Twardowski, I. Cetinić, R. Ferrare, and T. Mack, “Combined atmospheric and ocean profiling from an airborne high spectral resolution lidar,” in EPJ Web of Conferences (2016), Vol. 119, p. 22001.

Cook, A.

J. Hair, C. Hostetler, Y. Hu, M. Behrenfeld, C. Butler, D. Harper, R. Hare, T. Berkoff, A. Cook, J. Collins, N. Stockley, M. Twardowski, I. Cetinić, R. Ferrare, and T. Mack, “Combined atmospheric and ocean profiling from an airborne high spectral resolution lidar,” in EPJ Web of Conferences (2016), Vol. 119, p. 22001.

Cowles, T. J.

Czerski, H.

M. Twardowski, X. Zhang, S. Vagle, J. Sullivan, S. Freeman, H. Czerski, Y. You, L. Bi, and G. Kattawar, “The optical volume scattering function in a surf zone inverted to derive sediment and bubble particle subpopulations,” J. Geophys. Res. Oceans 117, C00H17 (2012).
[Crossref]

H. Czerski, M. Twardowski, X. Zhang, and S. Vagle, “Resolving size distributions of bubbles with radii less than 30 µm with optical and acoustical methods,” J. Geophys. Res. Oceans 116, C00H11 (2011).
[Crossref]

Dainty, J. C.

A. N. Bogaturov, A. A. D. Canas, J. C. Dainty, A. S. Gurvich, V. A. Myakinin, C. J. Solomon, and N. J. Wooder, “Observation of the enhancement of coherence by backscattering through turbulence,” Opt. Commun. 87, 1–4 (1992).
[Crossref]

Dall’Olmo, G.

E. Organelli, G. Dall’Olmo, R. J. W. Brewin, G. A. Tarran, E. Boss, and A. Bricaud, “The open-ocean missing backscattering is in the structural complexity of particles,” Nat. Commun. 9, 5439 (2018).
[Crossref]

M. J. Behrenfeld, Y. Hu, C. A. Hostetler, G. Dall’Olmo, S. D. Rodier, J. W. Hair, and C. R. Trepte, “Space-based lidar measurements of global ocean carbon stocks,” Geophys. Res. Lett. 40, 4355–4360 (2013).
[Crossref]

Dana, D. R.

R. A. Maffione and D. R. Dana, “Instruments and methods for measuring the backward-scattering coefficient of ocean waters,” Appl. Opt. 36, 6057–6067 (1997).
[Crossref]

R. A. Maffione and D. R. Dana, “In-situ characterization of optical backscattering and attenuation for lidar applications,” Proc. SPIE 2964, 152–162 (1996).
[Crossref]

de Haan, J. F.

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

Dekker, A. G.

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

Doerffer, R.

Donaghay, P. L.

Evans, R. H.

H. R. Gordon, O. B. Brown, R. H. Evans, J. W. Brown, R. C. Smith, K. S. Baker, and D. K. Clark, “A semianalytic radiance model of ocean color,” J. Geophys. Res. 93, 10909–10924 (1988).
[Crossref]

Falster, A. U.

X. Zhang, R. H. Stavn, A. U. Falster, J. J. Rick, D. Gray, and R. W. Gould, “Size distributions of coastal ocean suspended particulate inorganic matter: amorphous silica and clay minerals and their dynamics,” Estuarine Coast. Shelf Sci. 189, 243–251 (2017).
[Crossref]

X. Zhang, R. H. Stavn, A. U. Falster, D. Gray, and R. W. Gould, “New insight into particulate mineral and organic matter in coastal ocean waters through optical inversion,” Estuarine Coast. Shelf Sci. 149, 1–12 (2014).
[Crossref]

Ferrare, R.

S. Stamnes, C. Hostetler, R. Ferrare, S. Burton, X. Liu, J. Hair, Y. Hu, A. Wasilewski, W. Martin, B. van Diedenhoven, J. Chowdhary, I. Cetinić, L. K. Berg, K. Stamnes, and B. Cairns, “Simultaneous polarimeter retrievals of microphysical aerosol and ocean color parameters from the “MAPP” algorithm with comparison to high-spectral-resolution lidar aerosol and ocean products,” Appl. Opt. 57, 2394–2413 (2018).
[Crossref]

J. Hair, C. Hostetler, Y. Hu, M. Behrenfeld, C. Butler, D. Harper, R. Hare, T. Berkoff, A. Cook, J. Collins, N. Stockley, M. Twardowski, I. Cetinić, R. Ferrare, and T. Mack, “Combined atmospheric and ocean profiling from an airborne high spectral resolution lidar,” in EPJ Web of Conferences (2016), Vol. 119, p. 22001.

Ferrier, C.

Fournier, G. R.

Freeman, S.

M. Twardowski, X. Zhang, S. Vagle, J. Sullivan, S. Freeman, H. Czerski, Y. You, L. Bi, and G. Kattawar, “The optical volume scattering function in a surf zone inverted to derive sediment and bubble particle subpopulations,” J. Geophys. Res. Oceans 117, C00H17 (2012).
[Crossref]

Fry, E. S.

G. D. Hickman, J. M. Harding, M. Carnes, A. Pressman, G. W. Kattawar, and E. S. Fry, “Aircraft laser sensing of sound velocity in water: Brillouin scattering,” Remote Sens. Environ. 36, 165–178 (1991).
[Crossref]

Getzewich, B.

Gordon, H. R.

H. R. Gordon, O. B. Brown, R. H. Evans, J. W. Brown, R. C. Smith, K. S. Baker, and D. K. Clark, “A semianalytic radiance model of ocean color,” J. Geophys. Res. 93, 10909–10924 (1988).
[Crossref]

H. R. Gordon, “Interpretation of airborne oceanic lidar: effects of multiple scattering,” Appl. Opt. 21, 2996–3001 (1982).
[Crossref]

Gould, R. W.

X. Zhang, R. H. Stavn, A. U. Falster, J. J. Rick, D. Gray, and R. W. Gould, “Size distributions of coastal ocean suspended particulate inorganic matter: amorphous silica and clay minerals and their dynamics,” Estuarine Coast. Shelf Sci. 189, 243–251 (2017).
[Crossref]

X. Zhang, R. H. Stavn, A. U. Falster, D. Gray, and R. W. Gould, “New insight into particulate mineral and organic matter in coastal ocean waters through optical inversion,” Estuarine Coast. Shelf Sci. 149, 1–12 (2014).
[Crossref]

Gray, D.

X. Zhang, R. H. Stavn, A. U. Falster, J. J. Rick, D. Gray, and R. W. Gould, “Size distributions of coastal ocean suspended particulate inorganic matter: amorphous silica and clay minerals and their dynamics,” Estuarine Coast. Shelf Sci. 189, 243–251 (2017).
[Crossref]

X. Zhang, R. H. Stavn, A. U. Falster, D. Gray, and R. W. Gould, “New insight into particulate mineral and organic matter in coastal ocean waters through optical inversion,” Estuarine Coast. Shelf Sci. 149, 1–12 (2014).
[Crossref]

Gray, D. J.

X. Zhang, G. R. Fournier, and D. J. Gray, “Interpretation of scattering by oceanic particles around 120 degrees and its implication in ocean color studies,” Opt. Express 25, A191–A199 (2017).
[Crossref]

X. Zhang and D. J. Gray, “Backscattering by very small particles in coastal waters,” J. Geophys. Res. Oceans 120, 6914–6926 (2015).
[Crossref]

X. Zhang, Y. Huot, D. J. Gray, A. Weidemann, and W. J. Rhea, “Biogeochemical origins of particles obtained from the inversion of the volume scattering function and spectral absorption in coastal waters,” Biogeosciences 10, 6029–6043 (2013).
[Crossref]

X. Zhang, D. J. Gray, Y. Huot, Y. You, and L. Bi, “Comparison of optically derived particle size distributions: scattering over the full angular range versus diffraction at near forward angles,” Appl. Opt. 51, 5085–5099 (2012).
[Crossref]

Guo, C.

C. Li, W. Cao, J. Yu, T. Ke, G. Lu, Y. Yang, and C. Guo, “An instrument for in situ measuring the volume scattering function of water: design, calibration and primary experiments,” Sensors 12, 4514–4533 (2012).
[Crossref]

Gurvich, A. S.

A. N. Bogaturov, A. A. D. Canas, J. C. Dainty, A. S. Gurvich, V. A. Myakinin, C. J. Solomon, and N. J. Wooder, “Observation of the enhancement of coherence by backscattering through turbulence,” Opt. Commun. 87, 1–4 (1992).
[Crossref]

Hair, J.

S. Stamnes, C. Hostetler, R. Ferrare, S. Burton, X. Liu, J. Hair, Y. Hu, A. Wasilewski, W. Martin, B. van Diedenhoven, J. Chowdhary, I. Cetinić, L. K. Berg, K. Stamnes, and B. Cairns, “Simultaneous polarimeter retrievals of microphysical aerosol and ocean color parameters from the “MAPP” algorithm with comparison to high-spectral-resolution lidar aerosol and ocean products,” Appl. Opt. 57, 2394–2413 (2018).
[Crossref]

J. Hair, C. Hostetler, Y. Hu, M. Behrenfeld, C. Butler, D. Harper, R. Hare, T. Berkoff, A. Cook, J. Collins, N. Stockley, M. Twardowski, I. Cetinić, R. Ferrare, and T. Mack, “Combined atmospheric and ocean profiling from an airborne high spectral resolution lidar,” in EPJ Web of Conferences (2016), Vol. 119, p. 22001.

Hair, J. W.

C. A. Hostetler, M. J. Behrenfeld, Y. Hu, J. W. Hair, and J. A. Schulien, “Spaceborne lidar in the study of marine systems,” Annu. Rev. Mar. Sci. 10, 121–147 (2018).
[Crossref]

J. A. Schulien, M. J. Behrenfeld, J. W. Hair, C. A. Hostetler, and M. S. Twardowski, “Vertically-resolved phytoplankton carbon and net primary production from a high spectral resolution lidar,” Opt. Express 25, 13577–13587 (2017).
[Crossref]

M. J. Behrenfeld, Y. Hu, C. A. Hostetler, G. Dall’Olmo, S. D. Rodier, J. W. Hair, and C. R. Trepte, “Space-based lidar measurements of global ocean carbon stocks,” Geophys. Res. Lett. 40, 4355–4360 (2013).
[Crossref]

Haouchine, S.

Harding, J. M.

G. D. Hickman, J. M. Harding, M. Carnes, A. Pressman, G. W. Kattawar, and E. S. Fry, “Aircraft laser sensing of sound velocity in water: Brillouin scattering,” Remote Sens. Environ. 36, 165–178 (1991).
[Crossref]

Hare, R.

J. Hair, C. Hostetler, Y. Hu, M. Behrenfeld, C. Butler, D. Harper, R. Hare, T. Berkoff, A. Cook, J. Collins, N. Stockley, M. Twardowski, I. Cetinić, R. Ferrare, and T. Mack, “Combined atmospheric and ocean profiling from an airborne high spectral resolution lidar,” in EPJ Web of Conferences (2016), Vol. 119, p. 22001.

Harmel, T.

Harper, D.

J. Hair, C. Hostetler, Y. Hu, M. Behrenfeld, C. Butler, D. Harper, R. Hare, T. Berkoff, A. Cook, J. Collins, N. Stockley, M. Twardowski, I. Cetinić, R. Ferrare, and T. Mack, “Combined atmospheric and ocean profiling from an airborne high spectral resolution lidar,” in EPJ Web of Conferences (2016), Vol. 119, p. 22001.

He, M.-X.

Hickman, G. D.

G. D. Hickman, J. M. Harding, M. Carnes, A. Pressman, G. W. Kattawar, and E. S. Fry, “Aircraft laser sensing of sound velocity in water: Brillouin scattering,” Remote Sens. Environ. 36, 165–178 (1991).
[Crossref]

Hieronymi, M.

Holland, P. W.

P. W. Holland and R. E. Welsch, “Robust regression using iteratively reweighted least-squares,” Comm. Statist. Theory Methods 6, 813–827 (1977).
[Crossref]

Honey, R. C.

R. A. Maffione and R. C. Honey, “Instrument for measuring the volume scattering function in the backward direction,” Proc. SPIE 1750, 15–26 (1992).
[Crossref]

Hoogenboom, H. J.

H. Volten, J. F. de Haan, J. W. Hovenier, R. Schreurs, W. Vassen, A. G. Dekker, H. J. Hoogenboom, F. Charlton, and R. Wouts, “Laboratory measurements of angular distributions of light scattered by phytoplankton and silt,” Limnol. Oceanogr. 43, 1180–1197 (1998).
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Figures (8)

Fig. 1.
Fig. 1. Experiment stations during (a) CHB09 (black dots) and SABOR14 (blue dots); (b) MOB09 (black dots) and GOM06 (blue dots); (c) MTB10; (d) LP17 and LP18 (black dots) and EXPORTS18 (blue dots).
Fig. 2.
Fig. 2. Phase functions built for three inversion kernels for the MVSM data using (a) homogenous sphere (HS) and coated sphere (CS) particle models, and (b) homogenous hexahedra (HH) particle model. For better visualization, the $y$ and $x$ axes are in log-log scale at angles $ \lt {15}^\circ $ and in log-linear scale at angles $ \ge {15}^\circ $ .
Fig. 3.
Fig. 3. (a) Particulate VSF ( ${\beta _p}$ ) measured by the MVSM (gray line) at 532 nm at one coastal station during MTB10 [red star in Fig. 1(c)]. The black, blue, and red dotted lines are reconstructed ${\beta _p}$ with homogenous sphere (HS), coated sphere (CS), and homogenous hexahedra (HH) kernels, respectively. The inserted plot highlights the comparison at backward scattering angles. The gray transparent vertical bars highlight the angular range in which the scattering measurements were unreliable and not used in the inversion. (b) The same with (a) but for one LISST-VSF measurement collected at an open water station during LP18 [red star in Fig. 1(d)].
Fig. 4.
Fig. 4. (a) Mean percentage difference (MPD) between measured- and reconstructed-VSFs at all stations for the MVSM (top) and the LISST-VSF data (bottom) using homogenous sphere (HS), coated sphere (CS), and homogenous hexahedra (HH) inversion kernels. The gray transparent vertical bars highlight the angular range in which the scattering measurements were unreliable and not used in the inversion and comparison. (b) Comparison of particulate backscattering coefficient ( ${b_\textit{bp}}$ ) calculated using reconstructed VSFs among the three inversion kernels: ${b_{bp,HS}}$ vs. ${b_{bp,CS}}$ (blue dots) and ${b_{bp,HS}}$ vs. ${b_{bp,HH}}$ (red dots). Note that the blue and red points overlap each other. The number of measurements (N) and MPD are also shown.
Fig. 5.
Fig. 5. Scatter plots between particulate VSF at 180° ( ${\beta _p}(\pi )$ ) and particulate backscattering coefficient ( ${b_\textit{bp}}$ ) estimated from the VSFs measured in (a) CHB09, (b) MOB09, (c) MTB10, (d) SABOR14, (e) GOM16, (f) LP17, (g) LP18, and (h) EXPORTS18. Lines of black, blue, and red colors are robust linear regression lines forcing through the origin for the data derived using homogenous sphere, coated sphere, and homogenous hexahedra inversion kernels, respectively.
Fig. 6.
Fig. 6. Histograms of ${\chi _p}(\pi )$ estimated with homogenous sphere (HS, black color), coated sphere (CS, blue color), and homogenous hexahedra (HH, red color) inversion kernels for all measurements. For comparison, the linearly extrapolated ${\chi _p}(\pi )$ from Sullivan and Twardowski [32] (ST09) and lidar estimated ${\chi _p}(\pi )$ from Hair et al. [22] (H16) are also shown.
Fig. 7.
Fig. 7. Spectral variation of ${\chi _p}(\pi )$ ( ${\rm mean}\;{\pm }$ ${\rm one}\;{\rm standard}\;{\rm deviation}$ ) derived with homogenous sphere (HS), coated sphere (CS), and homogenous hexahedra (HH) inversion kernels using the VSFs measured in CHB09 (black lines), MOB09 (red lines), and MTB10 (blue lines). For better visualization, the wavelength values for CHB09 and MTB10 data were shifted by 1 nm toward shorter and longer wavelength, respectively.
Fig. 8.
Fig. 8. Median values of ${\chi _p}(\pi )$ derived from the measured VSFs using coated sphere kernels with various thicknesses ( ${{D}_c}$ ) and relative refractive indices ( ${{n}_c}$ ) of the cell membrane.

Tables (1)

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Table 1. Summary of Field VSF Measurements Used in This Study and Ranges (Median Values) of the Particulate Backscattering Coefficient ( b b p ) and χ p ( π ) Derived Using the Inverse-Forward Modeling Method with Three Inversion Kernels: Homogenous Sphere (HS), Coated Sphere (CS), and Homogenous Hexahedra (HH)

Equations (4)

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β ( θ ) = lim Δ v 0 I ( θ ) E Δ v .
χ p ( θ ) = b b p / 2 π β p ( θ ) ,
b b p = 2 π π / 2 π β p ( θ ) sin θ d θ .
β p ( θ ) = i = 1 M b p , i β ~ p , i ( θ ) ,

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