Abstract

Multiple scattering is an inevitable effect in spaceborne oceanic lidar because of the large footprint size and the high optical density of seawater. The effective attenuation coefficient klidar in the oceanic lidar equation, which indicates the influence of the multiple scattering effect on the formation of lidar returns, is an important parameter in the retrieval of inherent optical properties (IOPs) of seawater. In this paper, the relationships between klidar of the spaceborne lidar signal and the IOPs of seawater are investigated by solving the radiative transfer equation with an improved semianalytic Monte Carlo model. Apart from the geometric loss factors, klidar is found to decrease exponentially with the increase of depth in homogeneous waters. klidar is given as an exponential function of depth and IOPs of seawater. The mean percentage errors between klidar calculated by the exponential function and the simulated ones in three typical stratified waters are within 0.5%, proving the effectiveness and applicability of this klidar-IOPs function. The results in this paper can help researchers have a better understanding of the multiple scattering effect of spaceborne lidar and improve the retrieval accuracy of the IOPs and the chlorophyll concentration of case 1 water from spaceborne lidar measurements.

© 2018 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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2018 (1)

B. L. Collister, R. C. Zimmerman, C. I. Sukenik, V. J. Hill, and W. M. Balch, “Remote sensing of optical characteristics and particle distributions of the upper ocean using shipboard lidar,” Remote Sens. Environ. 215, 85–96 (2018).
[Crossref]

2017 (3)

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(12), 13577–13587 (2017).
[Crossref] [PubMed]

C. A. Hostetler, M. J. Behrenfeld, Y. Hu, J. W. Hair, and J. A. Schulien, “Spaceborne Lidar in the Study of Marine Systems,” Ann. Rev. Mar. Sci. 10, 121–147 (2017).

L. Dong, L. Qun, B. Jian, and Z. Yupeng, “Data processing algorithms of the space-borne lidar CALIOP: a review,” Infr. Laser Eng. 46(12), 1202001 (2017).
[Crossref]

2016 (2)

M. J. Behrenfeld, Y. Hu, R. T. O’Malley, E. S. Boss, C. A. Hostetler, D. A. Siegel, J. L. Sarmiento, J. Schulien, J. W. Hair, and X. Lu, “Annual boom-bust cycles of polar phytoplankton biomass revealed by space-based lidar,” Nat. Geosci. 10, 118 (2016).

X. Lu, Y. Hu, J. Pelon, C. Trepte, K. Liu, S. Rodier, S. Zeng, P. Lucker, R. Verhappen, J. Wilson, C. Audouy, C. Ferrier, S. Haouchine, B. Hunt, and B. Getzewich, “Retrieval of ocean subsurface particulate backscattering coefficient from space-borne CALIOP lidar measurements,” Opt. Express 24(25), 29001–29008 (2016).
[Crossref] [PubMed]

2015 (2)

X. Lu, Y. Hu, C. Trepte, S. Zeng, and J. H. Churnside, “Ocean subsurface studies with the CALIPSO spaceborne lidar,” J. Geophys. Res. Oceans 119(7), 4305–4317 (2015).
[Crossref]

B. H. Hokr, J. N. Bixler, G. Elpers, B. Zollars, R. J. Thomas, V. V. Yakovlev, and M. O. Scully, “Modeling focusing Gaussian beams in a turbid medium with Monte Carlo simulations,” Opt. Express 23(7), 8699–8705 (2015).
[Crossref] [PubMed]

2014 (1)

J. H. Churnside, “Review of profiling oceanographic lidar,” Opt. Eng. 53(5), 051405 (2014).
[Crossref]

2013 (4)

C. Gabriel, M. A. Khalighi, P. Léon, S. Bourennane, and V. Rigaud, “Monte-Carlo-Based Channel Characterization for Underwater Optical Communication Systems,” J. Opt. Commun. Netw. 5(1), 1–12 (2013).
[Crossref]

J. H. Churnside, B. J. Mccarty, and X. Lu, “Subsurface Ocean Signals from an Orbiting Polarization Lidar,” Remote Sens. 5(7), 3457–3475 (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(16), 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(4), 786–794 (2013).
[Crossref] [PubMed]

2009 (2)

C. R. McClain, “A decade of satellite ocean color observations,” Annu. Rev. Mar. Sci. 1(1), 19–42 (2009).
[Crossref] [PubMed]

D. M. Winker, M. A. Vaughan, A. Omar, Y. Hu, K. A. Powell, Z. Liu, W. H. Hunt, and S. A. Young, “Overview of the CALIPSO Mission and CALIOP Data Processing Algorithms,” J. Atmos. Ocean. Tech. 26(11), 2310–2323 (2009).
[Crossref]

2008 (1)

M. Xia, K. Yang, Y. Zheng, and J. Rao, “Influence of Wavy Sea Surface on Airborne Lidar Underwater Beam Quality with Monte Carlo Method,” Chin. J. Lasers 35(2), 178–182 (2008).
[Crossref]

2006 (1)

J. Uitz, H. Claustre, A. Morel, and S. B. Hooker, “Vertical distribution of phytoplankton communities in open ocean: An assessment based on surface chlorophyll,” Jo. Geophys. Res. Oceans 111, C08005 (2006).

2003 (2)

2002 (2)

2001 (1)

A. Morel and S. Maritorena, “Bio‐optical properties of oceanic waters: A reappraisal,” J. Geophys. Res. Oceans 106(C4), 7163–7180 (2001).
[Crossref]

2000 (1)

1999 (1)

1998 (1)

1995 (1)

L. Wang, S. L. Jacques, and L. Zheng, “MCML—Monte Carlo modeling of light transport in multi-layered tissues,” Comput. Meth. Prog. Bio. 47, 131-146 (1995).

1991 (1)

A. Morel, “Light and marine photosynthesis: a spectral model with geochemical and climatological implications,” Prog. Oceanogr. 26(3), 263–306 (1991).
[Crossref]

1984 (1)

D. Phillips and B. Koerber, “A Theoretical Study of an Airborne Laser Technique for determining Sea Water Turbidity,” Aust. J. Phys. 37(1), 75 (1984).
[Crossref]

1982 (1)

1981 (1)

1975 (1)

G. W. Kattawar, “A three-parameter analytic phase function for multiple scattering calculations,” J. Quant. Spectrosc. Ra. 15(9), 839–849 (1975).
[Crossref]

1941 (1)

L. G. Henyey and J. L. Greenstein, “Diffuse radiation in the Galaxy,” Astrophys. J. 93, 70–83 (1941).

Audouy, C.

Balch, W. M.

B. L. Collister, R. C. Zimmerman, C. I. Sukenik, V. J. Hill, and W. M. Balch, “Remote sensing of optical characteristics and particle distributions of the upper ocean using shipboard lidar,” Remote Sens. Environ. 215, 85–96 (2018).
[Crossref]

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,” Ann. Rev. Mar. Sci. 10, 121–147 (2017).

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(12), 13577–13587 (2017).
[Crossref] [PubMed]

M. J. Behrenfeld, Y. Hu, R. T. O’Malley, E. S. Boss, C. A. Hostetler, D. A. Siegel, J. L. Sarmiento, J. Schulien, J. W. Hair, and X. Lu, “Annual boom-bust cycles of polar phytoplankton biomass revealed by space-based lidar,” Nat. Geosci. 10, 118 (2016).

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(16), 4355–4360 (2013).
[Crossref]

Bixler, J. N.

Boss, E.

Boss, E. S.

M. J. Behrenfeld, Y. Hu, R. T. O’Malley, E. S. Boss, C. A. Hostetler, D. A. Siegel, J. L. Sarmiento, J. Schulien, J. W. Hair, and X. Lu, “Annual boom-bust cycles of polar phytoplankton biomass revealed by space-based lidar,” Nat. Geosci. 10, 118 (2016).

Bourennane, S.

Campbell, J. W.

Churnside, J. H.

X. Lu, Y. Hu, C. Trepte, S. Zeng, and J. H. Churnside, “Ocean subsurface studies with the CALIPSO spaceborne lidar,” J. Geophys. Res. Oceans 119(7), 4305–4317 (2015).
[Crossref]

J. H. Churnside, “Review of profiling oceanographic lidar,” Opt. Eng. 53(5), 051405 (2014).
[Crossref]

J. H. Churnside, B. J. Mccarty, and X. Lu, “Subsurface Ocean Signals from an Orbiting Polarization Lidar,” Remote Sens. 5(7), 3457–3475 (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(4), 786–794 (2013).
[Crossref] [PubMed]

J. H. Churnside, “LIDAR detection of plankton in the ocean,” in IEEE International Geoscience and Remote Sensing Symposium (2007), 3174–3177.
[Crossref]

Claustre, H.

J. Uitz, H. Claustre, A. Morel, and S. B. Hooker, “Vertical distribution of phytoplankton communities in open ocean: An assessment based on surface chlorophyll,” Jo. Geophys. Res. Oceans 111, C08005 (2006).

Collister, B. L.

B. L. Collister, R. C. Zimmerman, C. I. Sukenik, V. J. Hill, and W. M. Balch, “Remote sensing of optical characteristics and particle distributions of the upper ocean using shipboard lidar,” Remote Sens. Environ. 215, 85–96 (2018).
[Crossref]

Dall’Olmo, G.

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(16), 4355–4360 (2013).
[Crossref]

Donaghay, P. L.

Dong, L.

L. Dong, L. Qun, B. Jian, and Z. Yupeng, “Data processing algorithms of the space-borne lidar CALIOP: a review,” Infr. Laser Eng. 46(12), 1202001 (2017).
[Crossref]

Elpers, G.

Ferrier, C.

Feygels, V. I.

V. I. Feygels, “Mathematical modeling of input signals for oceanographic lidar systems,” Proc. SPIE 5155, 30–39 (2003).
[Crossref]

Gabriel, C.

Getzewich, B.

Gjerstad, K. I.

Gordon, H. R.

Greenstein, J. L.

L. G. Henyey and J. L. Greenstein, “Diffuse radiation in the Galaxy,” Astrophys. J. 93, 70–83 (1941).

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,” Ann. Rev. Mar. Sci. 10, 121–147 (2017).

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(12), 13577–13587 (2017).
[Crossref] [PubMed]

M. J. Behrenfeld, Y. Hu, R. T. O’Malley, E. S. Boss, C. A. Hostetler, D. A. Siegel, J. L. Sarmiento, J. Schulien, J. W. Hair, and X. Lu, “Annual boom-bust cycles of polar phytoplankton biomass revealed by space-based lidar,” Nat. Geosci. 10, 118 (2016).

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(16), 4355–4360 (2013).
[Crossref]

Haltrin, V. I.

Hamre, B.

Haouchine, S.

Henyey, L. G.

L. G. Henyey and J. L. Greenstein, “Diffuse radiation in the Galaxy,” Astrophys. J. 93, 70–83 (1941).

Hill, V. J.

B. L. Collister, R. C. Zimmerman, C. I. Sukenik, V. J. Hill, and W. M. Balch, “Remote sensing of optical characteristics and particle distributions of the upper ocean using shipboard lidar,” Remote Sens. Environ. 215, 85–96 (2018).
[Crossref]

Hokr, B. H.

Hooker, S. B.

J. Uitz, H. Claustre, A. Morel, and S. B. Hooker, “Vertical distribution of phytoplankton communities in open ocean: An assessment based on surface chlorophyll,” Jo. Geophys. Res. Oceans 111, C08005 (2006).

Hostetler, C. A.

C. A. Hostetler, M. J. Behrenfeld, Y. Hu, J. W. Hair, and J. A. Schulien, “Spaceborne Lidar in the Study of Marine Systems,” Ann. Rev. Mar. Sci. 10, 121–147 (2017).

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(12), 13577–13587 (2017).
[Crossref] [PubMed]

M. J. Behrenfeld, Y. Hu, R. T. O’Malley, E. S. Boss, C. A. Hostetler, D. A. Siegel, J. L. Sarmiento, J. Schulien, J. W. Hair, and X. Lu, “Annual boom-bust cycles of polar phytoplankton biomass revealed by space-based lidar,” Nat. Geosci. 10, 118 (2016).

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(16), 4355–4360 (2013).
[Crossref]

Hu, Y.

C. A. Hostetler, M. J. Behrenfeld, Y. Hu, J. W. Hair, and J. A. Schulien, “Spaceborne Lidar in the Study of Marine Systems,” Ann. Rev. Mar. Sci. 10, 121–147 (2017).

M. J. Behrenfeld, Y. Hu, R. T. O’Malley, E. S. Boss, C. A. Hostetler, D. A. Siegel, J. L. Sarmiento, J. Schulien, J. W. Hair, and X. Lu, “Annual boom-bust cycles of polar phytoplankton biomass revealed by space-based lidar,” Nat. Geosci. 10, 118 (2016).

X. Lu, Y. Hu, J. Pelon, C. Trepte, K. Liu, S. Rodier, S. Zeng, P. Lucker, R. Verhappen, J. Wilson, C. Audouy, C. Ferrier, S. Haouchine, B. Hunt, and B. Getzewich, “Retrieval of ocean subsurface particulate backscattering coefficient from space-borne CALIOP lidar measurements,” Opt. Express 24(25), 29001–29008 (2016).
[Crossref] [PubMed]

X. Lu, Y. Hu, C. Trepte, S. Zeng, and J. H. Churnside, “Ocean subsurface studies with the CALIPSO spaceborne lidar,” J. Geophys. Res. Oceans 119(7), 4305–4317 (2015).
[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(16), 4355–4360 (2013).
[Crossref]

D. M. Winker, M. A. Vaughan, A. Omar, Y. Hu, K. A. Powell, Z. Liu, W. H. Hunt, and S. A. Young, “Overview of the CALIPSO Mission and CALIOP Data Processing Algorithms,” J. Atmos. Ocean. Tech. 26(11), 2310–2323 (2009).
[Crossref]

Hunt, B.

Hunt, W. H.

D. M. Winker, M. A. Vaughan, A. Omar, Y. Hu, K. A. Powell, Z. Liu, W. H. Hunt, and S. A. Young, “Overview of the CALIPSO Mission and CALIOP Data Processing Algorithms,” J. Atmos. Ocean. Tech. 26(11), 2310–2323 (2009).
[Crossref]

Jacques, S. L.

L. Wang, S. L. Jacques, and L. Zheng, “MCML—Monte Carlo modeling of light transport in multi-layered tissues,” Comput. Meth. Prog. Bio. 47, 131-146 (1995).

Jian, B.

L. Dong, L. Qun, B. Jian, and Z. Yupeng, “Data processing algorithms of the space-borne lidar CALIOP: a review,” Infr. Laser Eng. 46(12), 1202001 (2017).
[Crossref]

Kattawar, G. W.

G. W. Kattawar, “A three-parameter analytic phase function for multiple scattering calculations,” J. Quant. Spectrosc. Ra. 15(9), 839–849 (1975).
[Crossref]

Khalighi, M. A.

Koerber, B.

D. Phillips and B. Koerber, “A Theoretical Study of an Airborne Laser Technique for determining Sea Water Turbidity,” Aust. J. Phys. 37(1), 75 (1984).
[Crossref]

Krekov, G. M.

Krekova, M. M.

Lee, J. H.

Léon, P.

Liu, K.

Liu, Z.

D. M. Winker, M. A. Vaughan, A. Omar, Y. Hu, K. A. Powell, Z. Liu, W. H. Hunt, and S. A. Young, “Overview of the CALIPSO Mission and CALIOP Data Processing Algorithms,” J. Atmos. Ocean. Tech. 26(11), 2310–2323 (2009).
[Crossref]

Z. Liu, P. Voelger, and N. Sugimoto, “Simulations of the observation of clouds and aerosols with the Experimental Lidar in Space Equipment system,” Appl. Opt. 39(18), 3120–3137 (2000).
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X. Lu, Y. Hu, C. Trepte, S. Zeng, and J. H. Churnside, “Ocean subsurface studies with the CALIPSO spaceborne lidar,” J. Geophys. Res. Oceans 119(7), 4305–4317 (2015).
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J. H. Churnside, B. J. Mccarty, and X. Lu, “Subsurface Ocean Signals from an Orbiting Polarization Lidar,” Remote Sens. 5(7), 3457–3475 (2013).
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Omar, A.

D. M. Winker, M. A. Vaughan, A. Omar, Y. Hu, K. A. Powell, Z. Liu, W. H. Hunt, and S. A. Young, “Overview of the CALIPSO Mission and CALIOP Data Processing Algorithms,” J. Atmos. Ocean. Tech. 26(11), 2310–2323 (2009).
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M. Xia, K. Yang, Y. Zheng, and J. Rao, “Influence of Wavy Sea Surface on Airborne Lidar Underwater Beam Quality with Monte Carlo Method,” Chin. J. Lasers 35(2), 178–182 (2008).
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M. J. Behrenfeld, Y. Hu, R. T. O’Malley, E. S. Boss, C. A. Hostetler, D. A. Siegel, J. L. Sarmiento, J. Schulien, J. W. Hair, and X. Lu, “Annual boom-bust cycles of polar phytoplankton biomass revealed by space-based lidar,” Nat. Geosci. 10, 118 (2016).

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M. J. Behrenfeld, Y. Hu, R. T. O’Malley, E. S. Boss, C. A. Hostetler, D. A. Siegel, J. L. Sarmiento, J. Schulien, J. W. Hair, and X. Lu, “Annual boom-bust cycles of polar phytoplankton biomass revealed by space-based lidar,” Nat. Geosci. 10, 118 (2016).

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D. M. Winker, M. A. Vaughan, A. Omar, Y. Hu, K. A. Powell, Z. Liu, W. H. Hunt, and S. A. Young, “Overview of the CALIPSO Mission and CALIOP Data Processing Algorithms,” J. Atmos. Ocean. Tech. 26(11), 2310–2323 (2009).
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Yan, B.

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D. M. Winker, M. A. Vaughan, A. Omar, Y. Hu, K. A. Powell, Z. Liu, W. H. Hunt, and S. A. Young, “Overview of the CALIPSO Mission and CALIOP Data Processing Algorithms,” J. Atmos. Ocean. Tech. 26(11), 2310–2323 (2009).
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M. Xia, K. Yang, Y. Zheng, and J. Rao, “Influence of Wavy Sea Surface on Airborne Lidar Underwater Beam Quality with Monte Carlo Method,” Chin. J. Lasers 35(2), 178–182 (2008).
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B. L. Collister, R. C. Zimmerman, C. I. Sukenik, V. J. Hill, and W. M. Balch, “Remote sensing of optical characteristics and particle distributions of the upper ocean using shipboard lidar,” Remote Sens. Environ. 215, 85–96 (2018).
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Chin. J. Lasers (1)

M. Xia, K. Yang, Y. Zheng, and J. Rao, “Influence of Wavy Sea Surface on Airborne Lidar Underwater Beam Quality with Monte Carlo Method,” Chin. J. Lasers 35(2), 178–182 (2008).
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Comput. Meth. Prog. Bio. (1)

L. Wang, S. L. Jacques, and L. Zheng, “MCML—Monte Carlo modeling of light transport in multi-layered tissues,” Comput. Meth. Prog. Bio. 47, 131-146 (1995).

Geophys. Res. Lett. (1)

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(16), 4355–4360 (2013).
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Infr. Laser Eng. (1)

L. Dong, L. Qun, B. Jian, and Z. Yupeng, “Data processing algorithms of the space-borne lidar CALIOP: a review,” Infr. Laser Eng. 46(12), 1202001 (2017).
[Crossref]

J. Atmos. Ocean. Tech. (1)

D. M. Winker, M. A. Vaughan, A. Omar, Y. Hu, K. A. Powell, Z. Liu, W. H. Hunt, and S. A. Young, “Overview of the CALIPSO Mission and CALIOP Data Processing Algorithms,” J. Atmos. Ocean. Tech. 26(11), 2310–2323 (2009).
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Figures (8)

Fig. 1
Fig. 1 The schematic diagram of spaceborne lidar system.
Fig. 2
Fig. 2 Influence of FOV of the lidar receiving system and orbit altitude on klidar. (a) klidar of different optical depths under different FOV with the orbit altitude of 400 km, (b) klidar for different orbit altitudes with the FOV of 0.4 mrad. Here, τ O is the optical depth with = 0.233m-1.
Fig. 3
Fig. 3 (a) Depth profiles of the normalized lidar return signals Pnorm(z) and (b) the corresponding effective attenuation coefficients klidar(z) for [Chl] between 0 to 2 mg/m3.
Fig. 4
Fig. 4 (a) The normalized lidar return signal power with different order of scattering Pnorm(z) and (b) the percentage of each order of scattering (n is the order of scattering) for [Chl] = 0.35 mg/m3. The number represents the order of scattering and ‘total’ depicts the full multiple scattering signal.
Fig. 5
Fig. 5 The influence of IOPs on klidar for (a) b=0.2m-1 and w0=0.3(0.1)0.6, (b) a=0.2m-1 and w0=0.3(0.1)0.6, and (c) [Chl] = 0.35 mg/m3 and g1 = 0.9509(0.01)0.9809.
Fig. 6
Fig. 6 Relationships between the parameters (a) m, (b) n, and (c) p and IOPs.
Fig. 7
Fig. 7 The inherent optical properties (IOPs) and chlorophyll a concentration (Chla) for (a) S1 water, (b) S5 water and (c) S9 water.
Fig. 8
Fig. 8 The inherent optical properties (IOPs) and attenuation coefficients for (a) S1 water, (b) S5 water and (c) S9 water, respectively. klidar represents the effective attenuation coefficient of simulating return signals, and klidar-c is the attenuation coefficient calculated using the klidar-IOPs model shown in Eqs. (19) and (20).

Tables (3)

Tables Icon

Table 1 The values of input parameters of the calculations

Tables Icon

Table 2 Fitting results of klidar for 16 types of case 1 waters.

Tables Icon

Table 3 Values of the parameters to be used in Eq. (21) for S1, S5 and S9, respectively [36].

Equations (22)

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

P ( z ) = P 0 M v τ 2 n T a t m 2 T s u r f 2 A ( n H + z ) 2 β π ( z ) exp ( 2 0 z k l i d a r ( z ) d z ) ,
P n o r m ( z ) = P ( z ) ( n H + z ) 2 P 0 M ( v τ 2 n ) T a t m 2 T s u r f 2 A β π ( z ) = exp ( 2 0 z k l i d a r ( z ) d z ) .
k l i d a r ( z ) = 1 2 d d z ln ( P ( z ) n o r m ) .
c ( λ ) = a ( λ ) + b ( λ ) .
a ( λ ) = [ a w ( λ ) + 0.06 a c ( λ ) [ Chl ] 0.65 ] [ 1 + 0.2 exp ( 0.014 ( λ 440 ) ) ] ,
b ( λ ) = b w ( λ ) + 550 λ × 0.3 × [ Chl ] 0.62 ,
b w ( λ ) = 16.06 × ( 550 / λ ) 4.324 × 1.21 × 10 4 .
K d = a w + b w / 2 + 0.04826 [ Chl ] 0.67224 .
I ( x , y ) = 1 2 π σ s 2 exp ( x 2 + y 2 2 σ s 2 ) ,
r = σ s 2 ln ( R 1 )
φ = 2 π R 2 ,
{ x = r cos φ y = r sin φ z = 0 .
{ u x = x / ( x 2 + y 2 + H 2 ) u y = y / ( x 2 + y 2 + H 2 ) u z = H / ( x 2 + y 2 + H 2 ) .
β ˜ = η β ˜ w + ( 1 η ) β ˜ p .
β ˜ w ( cos θ ) = 0.06225 ( 1 + 0.835 cos 2 θ ) ,
β ˜ p ( cos θ ) = β ˜ H G ( g , cos θ ) = 1 4 π 1 g 2 ( 1 + g 2 2 g cos θ ) 3 / 2 ,
β ˜ p ( cos θ ) = β ˜ T T H G ( cos θ , α , g 1 , g 2 ) = α β ˜ H G ( cos θ , g 1 ) + ( 1 α ) β ˜ H G ( cos θ , g 2 ) ,
E = β ( θ ) 4 π A ( n H + z ) 2 exp ( j = 1 i c ( j ) d ( j ) ) T a t m T s u r f ,
k l i d a r ( z ) = m × exp ( n × z ) + p .
m = 4 .8907 b b 0.00 04 n = 4.2506 b b 0.00 55 . p = a + 0. 3582 b b 0.00 4 2
C ( ζ ) = C b s ζ + C max exp { [ ( ζ ζ max ) / Δ ζ ] 2 } ,
δ = i = 1 i = n | k ( z i ) k l i d a r ( z i ) | / k l i d a r ( z i ) n × 100 %

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