Abstract

An inversion algorithm is implemented to retrieve the surface chlorophyll a (Chl) concentration using satellite observation data from the MODIS instrument. The algorithm employs a simple and flexible index (LCI) to combine with the Chl without explicit correction for aerosol scattering. To investigate the sensitivity of LCI to Chl and other influence factors, an oceanic radiative transfer model coupled with a comprehensive bio-optical module is developed. It is studied that the LCI is significantly linear to Chl and not sensitive to other influence factors, except in very low oceanic salinity or scattering angle conditions, where over a 12% relative difference of derived Chl exists. Inversion results show the retrieved Chl are highly consistent with the MODIS operational data products in waters near Hokkaido, with the correlation coefficient, root mean square deviation, and average percentage difference of 0.9702, 0.3756 mg m−3, and 13.89%, respectively. Investigation of the validity of this algorithm with a variety of atmospheric conditions indicates that the residual influence of atmosphere on the LCI index, after Rayleigh scattering correction, is generally within ± 0.001, allowing the retrieval error of Chl at less than 25% in most cases. A good comparison between retrieval and in situ measurements is also identified and implies that the retrieval accuracy via the LCI method depends on the linear combination coefficients used and the bio-optical module selected, while effects of polarization can be ignored.

© 2017 Optical Society of America

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2016 (2)

F. Xu, O. Dubovik, P.-W. Zhai, D. J. Diner, O. V. Kalashnikova, F. C. Seidel, P. Litvinov, A. Bovchaliuk, M. J. Garay, G. van Harten, and A. B. Davis, “Joint retrieval of aerosol and water-leaving radiance from multispectral, multiangular and polarimetric measurements over ocean,” Atmos. Meas. Tech. 9(7), 2877–2907 (2016).
[Crossref]

C. Shi, T. Nakajima, and M. Hashimoto, “Simultaneous retrieval of aerosol optical thickness and chlorophyll concentration from multiwavelength measurement over East China Sea,” J. Geophys. Res. 121, 14084–14101 (2016).

2015 (1)

C. Shi, P. Wang, T. Nakajima, Y. Ota, S. Tan, and G. Shi, “Effects of Ocean Particles on the Upwelling Radiance and Polarized Radiance in the Atmosphere–Ocean System,” Adv. Atmos. Sci. 32(9), 1186–1196 (2015).
[Crossref]

2013 (1)

2012 (3)

2011 (3)

O. Dubovik, M. Herman, A. Holdak, T. Lapyonok, D. Tanré, J. Deuzé, F. Ducos, A. Sinyuk, and A. Lopatin, “Statistically optimized inversion algorithm for enhanced retrieval of aerosol properties from spectral multi-angle polarimetric satellite observations,” Atmos. Meas. Tech. 4(5), 975–1018 (2011).
[Crossref]

O. P. Hasekamp, P. Litvinov, and A. Butz, “Aerosol properties over the ocean from PARASOL multiangle photopolarimetric measurements,” J. Geophys. Res. 116(D14), D14204 (2011).
[Crossref]

T. Harmel and M. Chami, “Influence of polarimetric satellite data measured in the visible region on aerosol detection and on the performance of atmospheric correction procedure over open ocean waters,” Opt. Express 19(21), 20960–20983 (2011).
[Crossref] [PubMed]

2010 (3)

Y. Ota, A. Higurashi, T. Nakajima, and T. Yokota, “Matrix formulations of radiative transfer including the polarization effect in a coupled atmosphere–ocean system,” J. Quant. Spectrosc. Radiat. Transf. 111(6), 878–894 (2010).
[Crossref]

A. A. Kokhanovsky, V. P. Budak, C. Cornet, M. Duan, C. Emde, I. L. Katsev, D. A. Klyukov, S. V. Korkin, L. C-Labonnote, B. Mayer, Q. Min, T. Nakajima, Y. Ota, A. S. Prikhach, V. V. Rozanov, T. Yokota, and E. P. Zege, “Benchmark results in vector atmospheric radiative transfer,” J. Quant. Spectrosc. Radiat. Transf. 111(12-13), 1931–1946 (2010).
[Crossref]

P.-W. Zhai, Y. Hu, J. Chowdhary, C. R. Trepte, P. L. Lucker, and D. B. Josset, “A vector radiative transfer model for coupled atmosphere and ocean systems with a rough interface,” J. Quant. Spectrosc. Radiat. Transf. 111(7-8), 1025–1040 (2010).
[Crossref]

2009 (3)

X. Zhang, L. Hu, and M.-X. He, “Scattering by pure seawater: Effect of salinity,” Opt. Express 17(7), 5698–5710 (2009).
[Crossref] [PubMed]

G. Zibordi, F. Mélin, J.-F. Berthon, B. Holben, I. Slutsker, D. Giles, D. D’Alimonte, D. Vandemark, H. Feng, G. Schuster, B. E. Fabbri, S. Kaitala, and J. Seppälä, “AERONET-OC: a network for the validation of ocean color primary products,” J. Atmos. Ocean. Technol. 26(8), 1634–1651 (2009).
[Crossref]

B.-C. Gao, M. J. Montes, C. O. Davis, and A. F. Goetz, “Atmospheric correction algorithms for hyperspectral remote sensing data of land and ocean,” Remote Sens. Environ. 113, S17–S24 (2009).
[Crossref]

2008 (3)

W. Li, K. Stamnes, R. Spurr, and J. Stamnes, “Simultaneous retrieval of aerosol and ocean properties by optimal estimation: SeaWiFS case studies for the Santa Barbara Channel,” Int. J. Remote Sens. 29(19), 5689–5698 (2008).
[Crossref]

M. Sekiguchi and T. Nakajima, “A k-distribution-based radiation code and its computational optimization for an atmospheric general circulation model,” J. Quant. Spectrosc. Radiat. Transf. 109(17-18), 2779–2793 (2008).
[Crossref]

Y. Huot, A. Morel, M. S. Twardowski, D. Stramski, and R. A. Reynolds, “Particle optical backscattering along a chlorophyll gradient in the upper layer of the eastern South Pacific Ocean,” Biogeosciences 5(2), 495–507 (2008).
[Crossref]

2007 (2)

Z. Lee, A. Weidemann, J. Kindle, R. Arnone, K. L. Carder, and C. Davis, “Euphotic zone depth: Its derivation and implication to ocean-color remote sensing,” J. Geophys. Res. 112, C03009 (2007).

M. Wang and W. Shi, “The NIR-SWIR combined atmospheric correction approach for MODIS ocean color data processing,” Opt. Express 15(24), 15722–15733 (2007).
[Crossref] [PubMed]

2006 (2)

R. Frouin, P.-Y. Deschamps, L. Gross-Colzy, H. Murakami, and T. Y. Nakajima, “Retrieval of chlorophyll-a concentration via linear combination of ADEOS-II Global Imager data,” J. Oceanogr. 62(3), 331–337 (2006).
[Crossref]

J. Chowdhary, B. Cairns, and L. D. Travis, “Contribution of water-leaving radiances to multiangle, multispectral polarimetric observations over the open ocean: bio-optical model results for case 1 waters,” Appl. Opt. 45(22), 5542–5567 (2006).
[Crossref] [PubMed]

2005 (1)

2004 (1)

J. R. Morrison and N. B. Nelson, “Seasonal cycle of phytoplankton UV absorption at the Bermuda Atlantic Time- series Study (BATS) site,” Limnol. Oceanogr. 49(1), 215–224 (2004).
[Crossref]

2003 (1)

2002 (1)

2000 (2)

O. Dubovik and M. D. King, “A flexible inversion algorithm for retrieval of aerosol optical properties from Sun and sky radiance measurements,” J. Geophys. Res. 105(D16), 20673–20696 (2000).
[Crossref]

B.-C. Gao, M. J. Montes, Z. Ahmad, and C. O. Davis, “Atmospheric correction algorithm for hyperspectral remote sensing of ocean color from space,” Appl. Opt. 39(6), 887–896 (2000).
[Crossref] [PubMed]

1999 (2)

K. L. Carder, F. Chen, Z. Lee, S. Hawes, and D. Kamykowski, “Semianalytic Moderate-Resolution Imaging Spectrometer algorithms for chlorophyll a and absorption with bio-optical domains based on nitrate-depletion temperatures,” J. Geophys. Res. 104(C3), 5403–5421 (1999).
[Crossref]

D. Antoine and A. Morel, “A multiple scattering algorithm for atmospheric correction of remotely sensed ocean colour (MERIS instrument): principle and implementation for atmospheres carrying various aerosols including absorbing ones,” Int. J. Remote Sens. 20(9), 1875–1916 (1999).
[Crossref]

1998 (3)

H. Fukushima, A. Higurashi, Y. Mitomi, T. Nakajima, T. Noguchi, T. Tanaka, and M. Toratani, “Correction of atmospheric effect on ADEOS/OCTS ocean color data: Algorithm description and evaluation of its performance,” J. Oceanogr. 54(5), 417–430 (1998).
[Crossref]

R. M. Chomko and H. R. Gordon, “Atmospheric correction of ocean color imagery: use of the Junge power-law aerosol size distribution with variable refractive index to handle aerosol absorption,” Appl. Opt. 37(24), 5560–5572 (1998).
[Crossref] [PubMed]

J. E. O’Reilly, S. Maritorena, B. G. Mitchell, D. A. Siegel, K. L. Carder, S. A. Garver, M. Kahru, and C. McClain, “Ocean color chlorophyll algorithms for SeaWiFS,” J. Geophys. Res. 103(C11), 24937–24953 (1998).
[Crossref]

1997 (6)

F. Zhao and T. Nakajima, “Simultaneous determination of water-leaving reflectance and aerosol optical thickness from Coastal Zone Color Scanner measurements,” Appl. Opt. 36(27), 6949–6956 (1997).
[Crossref] [PubMed]

H. R. Gordon, “Atmospheric correction of ocean color imagery in the Earth Observing System era,” J. Geophys. Res. 102(D14), 17081–17106 (1997).
[Crossref]

M. J. Behrenfeld and P. G. Falkowski, “Photosynthetic rates derived from satellite-based chlorophyll concentration,” Limnol. Oceanogr. 42(1), 1–20 (1997).
[Crossref]

H. R. Gordon, “Atmospheric correction of ocean color imagery in the Earth Observing System era,” J. Geophys. Res. 102, 17081–17106 (1997).

R. M. Pope and E. S. Fry, “Absorption spectrum (380-700 nm) of pure water. II. Integrating cavity measurements,” Appl. Opt. 36(33), 8710–8723 (1997).
[Crossref] [PubMed]

P. D. Huibers, “Models for the wavelength dependence of the index of refraction of water,” Appl. Opt. 36(16), 3785–3787 (1997).
[Crossref] [PubMed]

1996 (1)

1995 (2)

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

X. Quan and E. S. Fry, “Empirical equation for the index of refraction of seawater,” Appl. Opt. 34(18), 3477–3480 (1995).
[Crossref] [PubMed]

1994 (3)

H. R. Gordon and M. Wang, “Retrieval of water-leaving radiance and aerosol optical thickness over the oceans with SeaWiFS: a preliminary algorithm,” Appl. Opt. 33(3), 443–452 (1994).
[Crossref] [PubMed]

R. Doerffer and J. Fischer, “Concentrations of chlorophyll, suspended matter, and gelbstoff in case II waters derived from satellite coastal zone color scanner data with inverse modeling methods,” J. Geophys. Res. 99(C4), 7457–7466 (1994).
[Crossref]

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

1993 (1)

1989 (1)

A. Morel and J. F. Berthon, “Surface pigments, algal biomass profiles, and potential production of the euphotic layer: Relationships reinvestigated in view of remote-sensing applications,” Limnol. Oceanogr. 34(8), 1545–1562 (1989).
[Crossref]

1988 (1)

T. Platt and S. Sathyendranath, “Oceanic primary production: estimation by remote sensing at local and regional scales,” Science 241(4873), 1613–1620 (1988).
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1986 (1)

T. Nakajima and M. Tanaka, “Matrix formulations for the transfer of solar radiation in a plane-parallel scattering atmosphere,” J. Quant. Spectrosc. Radiat. Transf. 35(1), 13–21 (1986).
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1983 (1)

T. Nakajima and M. Tanaka, “Effect of wind-generated waves on the transfer of solar radiation in the atmosphere-ocean system,” J. Quant. Spectrosc. Radiat. Transf. 29(6), 521–537 (1983).
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1981 (3)

A. Bricaud, A. Morel, and L. Prieur, “Absorption by dissolved organic matter of the sea (yellow substance) in the UV and visible domains,” Limnol. Oceanogr. 26(1), 43–53 (1981).
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L. Prieur and S. Sathyendranath, “An optical classification of coastal and oceanic waters based on the specific spectral absorption curves of phytoplankton pigments, dissolved organic matter, and other particulate materials,” Limnol. Oceanogr. 26(4), 671–689 (1981).
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R. C. Smith and K. S. Baker, “Optical properties of the clearest natural waters (200-800 nm),” Appl. Opt. 20(2), 177–184 (1981).
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1973 (1)

1954 (1)

Ahmad, Z.

Alexandrov, M.

Antoine, D.

D. Antoine and A. Morel, “A multiple scattering algorithm for atmospheric correction of remotely sensed ocean colour (MERIS instrument): principle and implementation for atmospheres carrying various aerosols including absorbing ones,” Int. J. Remote Sens. 20(9), 1875–1916 (1999).
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Arnone, R.

Z. Lee, A. Weidemann, J. Kindle, R. Arnone, K. L. Carder, and C. Davis, “Euphotic zone depth: Its derivation and implication to ocean-color remote sensing,” J. Geophys. Res. 112, C03009 (2007).

Babin, M.

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

Baker, K. S.

Barnard, A.

Behrenfeld, M. J.

M. J. Behrenfeld and P. G. Falkowski, “Photosynthetic rates derived from satellite-based chlorophyll concentration,” Limnol. Oceanogr. 42(1), 1–20 (1997).
[Crossref]

Berthon, J. F.

A. Morel and J. F. Berthon, “Surface pigments, algal biomass profiles, and potential production of the euphotic layer: Relationships reinvestigated in view of remote-sensing applications,” Limnol. Oceanogr. 34(8), 1545–1562 (1989).
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Berthon, J.-F.

G. Zibordi, F. Mélin, J.-F. Berthon, B. Holben, I. Slutsker, D. Giles, D. D’Alimonte, D. Vandemark, H. Feng, G. Schuster, B. E. Fabbri, S. Kaitala, and J. Seppälä, “AERONET-OC: a network for the validation of ocean color primary products,” J. Atmos. Ocean. Technol. 26(8), 1634–1651 (2009).
[Crossref]

Boi, P.

Boss, E.

Bovchaliuk, A.

F. Xu, O. Dubovik, P.-W. Zhai, D. J. Diner, O. V. Kalashnikova, F. C. Seidel, P. Litvinov, A. Bovchaliuk, M. J. Garay, G. van Harten, and A. B. Davis, “Joint retrieval of aerosol and water-leaving radiance from multispectral, multiangular and polarimetric measurements over ocean,” Atmos. Meas. Tech. 9(7), 2877–2907 (2016).
[Crossref]

Bricaud, A.

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

A. Bricaud, A. Morel, and L. Prieur, “Absorption by dissolved organic matter of the sea (yellow substance) in the UV and visible domains,” Limnol. Oceanogr. 26(1), 43–53 (1981).
[Crossref]

Budak, V. P.

A. A. Kokhanovsky, V. P. Budak, C. Cornet, M. Duan, C. Emde, I. L. Katsev, D. A. Klyukov, S. V. Korkin, L. C-Labonnote, B. Mayer, Q. Min, T. Nakajima, Y. Ota, A. S. Prikhach, V. V. Rozanov, T. Yokota, and E. P. Zege, “Benchmark results in vector atmospheric radiative transfer,” J. Quant. Spectrosc. Radiat. Transf. 111(12-13), 1931–1946 (2010).
[Crossref]

Butz, A.

O. P. Hasekamp, P. Litvinov, and A. Butz, “Aerosol properties over the ocean from PARASOL multiangle photopolarimetric measurements,” J. Geophys. Res. 116(D14), D14204 (2011).
[Crossref]

Cairns, B.

Carder, K. L.

Z. Lee, A. Weidemann, J. Kindle, R. Arnone, K. L. Carder, and C. Davis, “Euphotic zone depth: Its derivation and implication to ocean-color remote sensing,” J. Geophys. Res. 112, C03009 (2007).

K. L. Carder, F. Chen, Z. Lee, S. Hawes, and D. Kamykowski, “Semianalytic Moderate-Resolution Imaging Spectrometer algorithms for chlorophyll a and absorption with bio-optical domains based on nitrate-depletion temperatures,” J. Geophys. Res. 104(C3), 5403–5421 (1999).
[Crossref]

J. E. O’Reilly, S. Maritorena, B. G. Mitchell, D. A. Siegel, K. L. Carder, S. A. Garver, M. Kahru, and C. McClain, “Ocean color chlorophyll algorithms for SeaWiFS,” J. Geophys. Res. 103(C11), 24937–24953 (1998).
[Crossref]

Chami, M.

Chen, F.

K. L. Carder, F. Chen, Z. Lee, S. Hawes, and D. Kamykowski, “Semianalytic Moderate-Resolution Imaging Spectrometer algorithms for chlorophyll a and absorption with bio-optical domains based on nitrate-depletion temperatures,” J. Geophys. Res. 104(C3), 5403–5421 (1999).
[Crossref]

Chomko, R. M.

Chowdhary, J.

C-Labonnote, L.

A. A. Kokhanovsky, V. P. Budak, C. Cornet, M. Duan, C. Emde, I. L. Katsev, D. A. Klyukov, S. V. Korkin, L. C-Labonnote, B. Mayer, Q. Min, T. Nakajima, Y. Ota, A. S. Prikhach, V. V. Rozanov, T. Yokota, and E. P. Zege, “Benchmark results in vector atmospheric radiative transfer,” J. Quant. Spectrosc. Radiat. Transf. 111(12-13), 1931–1946 (2010).
[Crossref]

Claustre, H.

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

Cornet, C.

A. A. Kokhanovsky, V. P. Budak, C. Cornet, M. Duan, C. Emde, I. L. Katsev, D. A. Klyukov, S. V. Korkin, L. C-Labonnote, B. Mayer, Q. Min, T. Nakajima, Y. Ota, A. S. Prikhach, V. V. Rozanov, T. Yokota, and E. P. Zege, “Benchmark results in vector atmospheric radiative transfer,” J. Quant. Spectrosc. Radiat. Transf. 111(12-13), 1931–1946 (2010).
[Crossref]

Cox, C.

D’Alimonte, D.

G. Zibordi, F. Mélin, J.-F. Berthon, B. Holben, I. Slutsker, D. Giles, D. D’Alimonte, D. Vandemark, H. Feng, G. Schuster, B. E. Fabbri, S. Kaitala, and J. Seppälä, “AERONET-OC: a network for the validation of ocean color primary products,” J. Atmos. Ocean. Technol. 26(8), 1634–1651 (2009).
[Crossref]

Davis, A. B.

F. Xu, O. Dubovik, P.-W. Zhai, D. J. Diner, O. V. Kalashnikova, F. C. Seidel, P. Litvinov, A. Bovchaliuk, M. J. Garay, G. van Harten, and A. B. Davis, “Joint retrieval of aerosol and water-leaving radiance from multispectral, multiangular and polarimetric measurements over ocean,” Atmos. Meas. Tech. 9(7), 2877–2907 (2016).
[Crossref]

Davis, C.

Z. Lee, A. Weidemann, J. Kindle, R. Arnone, K. L. Carder, and C. Davis, “Euphotic zone depth: Its derivation and implication to ocean-color remote sensing,” J. Geophys. Res. 112, C03009 (2007).

Davis, C. O.

B.-C. Gao, M. J. Montes, C. O. Davis, and A. F. Goetz, “Atmospheric correction algorithms for hyperspectral remote sensing data of land and ocean,” Remote Sens. Environ. 113, S17–S24 (2009).
[Crossref]

B.-C. Gao, M. J. Montes, Z. Ahmad, and C. O. Davis, “Atmospheric correction algorithm for hyperspectral remote sensing of ocean color from space,” Appl. Opt. 39(6), 887–896 (2000).
[Crossref] [PubMed]

Deschamps, P.-Y.

R. Frouin, P.-Y. Deschamps, L. Gross-Colzy, H. Murakami, and T. Y. Nakajima, “Retrieval of chlorophyll-a concentration via linear combination of ADEOS-II Global Imager data,” J. Oceanogr. 62(3), 331–337 (2006).
[Crossref]

Deuzé, J.

O. Dubovik, M. Herman, A. Holdak, T. Lapyonok, D. Tanré, J. Deuzé, F. Ducos, A. Sinyuk, and A. Lopatin, “Statistically optimized inversion algorithm for enhanced retrieval of aerosol properties from spectral multi-angle polarimetric satellite observations,” Atmos. Meas. Tech. 4(5), 975–1018 (2011).
[Crossref]

Diner, D. J.

F. Xu, O. Dubovik, P.-W. Zhai, D. J. Diner, O. V. Kalashnikova, F. C. Seidel, P. Litvinov, A. Bovchaliuk, M. J. Garay, G. van Harten, and A. B. Davis, “Joint retrieval of aerosol and water-leaving radiance from multispectral, multiangular and polarimetric measurements over ocean,” Atmos. Meas. Tech. 9(7), 2877–2907 (2016).
[Crossref]

Doerffer, R.

R. Doerffer and J. Fischer, “Concentrations of chlorophyll, suspended matter, and gelbstoff in case II waters derived from satellite coastal zone color scanner data with inverse modeling methods,” J. Geophys. Res. 99(C4), 7457–7466 (1994).
[Crossref]

Duan, M.

A. A. Kokhanovsky, V. P. Budak, C. Cornet, M. Duan, C. Emde, I. L. Katsev, D. A. Klyukov, S. V. Korkin, L. C-Labonnote, B. Mayer, Q. Min, T. Nakajima, Y. Ota, A. S. Prikhach, V. V. Rozanov, T. Yokota, and E. P. Zege, “Benchmark results in vector atmospheric radiative transfer,” J. Quant. Spectrosc. Radiat. Transf. 111(12-13), 1931–1946 (2010).
[Crossref]

Dubovik, O.

F. Xu, O. Dubovik, P.-W. Zhai, D. J. Diner, O. V. Kalashnikova, F. C. Seidel, P. Litvinov, A. Bovchaliuk, M. J. Garay, G. van Harten, and A. B. Davis, “Joint retrieval of aerosol and water-leaving radiance from multispectral, multiangular and polarimetric measurements over ocean,” Atmos. Meas. Tech. 9(7), 2877–2907 (2016).
[Crossref]

O. Dubovik, M. Herman, A. Holdak, T. Lapyonok, D. Tanré, J. Deuzé, F. Ducos, A. Sinyuk, and A. Lopatin, “Statistically optimized inversion algorithm for enhanced retrieval of aerosol properties from spectral multi-angle polarimetric satellite observations,” Atmos. Meas. Tech. 4(5), 975–1018 (2011).
[Crossref]

O. Dubovik and M. D. King, “A flexible inversion algorithm for retrieval of aerosol optical properties from Sun and sky radiance measurements,” J. Geophys. Res. 105(D16), 20673–20696 (2000).
[Crossref]

Ducos, F.

O. Dubovik, M. Herman, A. Holdak, T. Lapyonok, D. Tanré, J. Deuzé, F. Ducos, A. Sinyuk, and A. Lopatin, “Statistically optimized inversion algorithm for enhanced retrieval of aerosol properties from spectral multi-angle polarimetric satellite observations,” Atmos. Meas. Tech. 4(5), 975–1018 (2011).
[Crossref]

Dupouy, C.

Eide, H.

Emde, C.

A. A. Kokhanovsky, V. P. Budak, C. Cornet, M. Duan, C. Emde, I. L. Katsev, D. A. Klyukov, S. V. Korkin, L. C-Labonnote, B. Mayer, Q. Min, T. Nakajima, Y. Ota, A. S. Prikhach, V. V. Rozanov, T. Yokota, and E. P. Zege, “Benchmark results in vector atmospheric radiative transfer,” J. Quant. Spectrosc. Radiat. Transf. 111(12-13), 1931–1946 (2010).
[Crossref]

Fabbri, B. E.

G. Zibordi, F. Mélin, J.-F. Berthon, B. Holben, I. Slutsker, D. Giles, D. D’Alimonte, D. Vandemark, H. Feng, G. Schuster, B. E. Fabbri, S. Kaitala, and J. Seppälä, “AERONET-OC: a network for the validation of ocean color primary products,” J. Atmos. Ocean. Technol. 26(8), 1634–1651 (2009).
[Crossref]

Falkowski, P. G.

M. J. Behrenfeld and P. G. Falkowski, “Photosynthetic rates derived from satellite-based chlorophyll concentration,” Limnol. Oceanogr. 42(1), 1–20 (1997).
[Crossref]

Feng, H.

G. Zibordi, F. Mélin, J.-F. Berthon, B. Holben, I. Slutsker, D. Giles, D. D’Alimonte, D. Vandemark, H. Feng, G. Schuster, B. E. Fabbri, S. Kaitala, and J. Seppälä, “AERONET-OC: a network for the validation of ocean color primary products,” J. Atmos. Ocean. Technol. 26(8), 1634–1651 (2009).
[Crossref]

Fischer, J.

A. Hollstein and J. Fischer, “Effects of salinity, temperature, and polarization on top of atmosphere and water leaving radiances for case 1 waters,” Appl. Opt. 51(33), 8022–8033 (2012).
[Crossref] [PubMed]

R. Doerffer and J. Fischer, “Concentrations of chlorophyll, suspended matter, and gelbstoff in case II waters derived from satellite coastal zone color scanner data with inverse modeling methods,” J. Geophys. Res. 99(C4), 7457–7466 (1994).
[Crossref]

Forand, J. L.

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

Fournier, G. R.

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

Franz, B.

C. Hu, Z. Lee, and B. Franz, “Chlorophyll aalgorithms for oligotrophic oceans: A novel approach based on three-band reflectance difference,” J. Geophys. Res. 117(C1), C01011 (2012).
[Crossref]

Frouin, R.

R. Frouin, P.-Y. Deschamps, L. Gross-Colzy, H. Murakami, and T. Y. Nakajima, “Retrieval of chlorophyll-a concentration via linear combination of ADEOS-II Global Imager data,” J. Oceanogr. 62(3), 331–337 (2006).
[Crossref]

Fry, E. S.

Fukushima, H.

H. Fukushima, A. Higurashi, Y. Mitomi, T. Nakajima, T. Noguchi, T. Tanaka, and M. Toratani, “Correction of atmospheric effect on ADEOS/OCTS ocean color data: Algorithm description and evaluation of its performance,” J. Oceanogr. 54(5), 417–430 (1998).
[Crossref]

Gao, B.-C.

B.-C. Gao, M. J. Montes, C. O. Davis, and A. F. Goetz, “Atmospheric correction algorithms for hyperspectral remote sensing data of land and ocean,” Remote Sens. Environ. 113, S17–S24 (2009).
[Crossref]

B.-C. Gao, M. J. Montes, Z. Ahmad, and C. O. Davis, “Atmospheric correction algorithm for hyperspectral remote sensing of ocean color from space,” Appl. Opt. 39(6), 887–896 (2000).
[Crossref] [PubMed]

Garay, M. J.

F. Xu, O. Dubovik, P.-W. Zhai, D. J. Diner, O. V. Kalashnikova, F. C. Seidel, P. Litvinov, A. Bovchaliuk, M. J. Garay, G. van Harten, and A. B. Davis, “Joint retrieval of aerosol and water-leaving radiance from multispectral, multiangular and polarimetric measurements over ocean,” Atmos. Meas. Tech. 9(7), 2877–2907 (2016).
[Crossref]

Garver, S. A.

J. E. O’Reilly, S. Maritorena, B. G. Mitchell, D. A. Siegel, K. L. Carder, S. A. Garver, M. Kahru, and C. McClain, “Ocean color chlorophyll algorithms for SeaWiFS,” J. Geophys. Res. 103(C11), 24937–24953 (1998).
[Crossref]

Gentili, B.

Giles, D.

G. Zibordi, F. Mélin, J.-F. Berthon, B. Holben, I. Slutsker, D. Giles, D. D’Alimonte, D. Vandemark, H. Feng, G. Schuster, B. E. Fabbri, S. Kaitala, and J. Seppälä, “AERONET-OC: a network for the validation of ocean color primary products,” J. Atmos. Ocean. Technol. 26(8), 1634–1651 (2009).
[Crossref]

Goetz, A. F.

B.-C. Gao, M. J. Montes, C. O. Davis, and A. F. Goetz, “Atmospheric correction algorithms for hyperspectral remote sensing data of land and ocean,” Remote Sens. Environ. 113, S17–S24 (2009).
[Crossref]

Gordon, H. R.

Gross-Colzy, L.

R. Frouin, P.-Y. Deschamps, L. Gross-Colzy, H. Murakami, and T. Y. Nakajima, “Retrieval of chlorophyll-a concentration via linear combination of ADEOS-II Global Imager data,” J. Oceanogr. 62(3), 331–337 (2006).
[Crossref]

Hale, G. M.

Harmel, T.

Hasekamp, O. P.

O. P. Hasekamp, P. Litvinov, and A. Butz, “Aerosol properties over the ocean from PARASOL multiangle photopolarimetric measurements,” J. Geophys. Res. 116(D14), D14204 (2011).
[Crossref]

Hashimoto, M.

C. Shi, T. Nakajima, and M. Hashimoto, “Simultaneous retrieval of aerosol optical thickness and chlorophyll concentration from multiwavelength measurement over East China Sea,” J. Geophys. Res. 121, 14084–14101 (2016).

Hawes, S.

K. L. Carder, F. Chen, Z. Lee, S. Hawes, and D. Kamykowski, “Semianalytic Moderate-Resolution Imaging Spectrometer algorithms for chlorophyll a and absorption with bio-optical domains based on nitrate-depletion temperatures,” J. Geophys. Res. 104(C3), 5403–5421 (1999).
[Crossref]

He, M.-X.

Herman, J. R.

Herman, M.

O. Dubovik, M. Herman, A. Holdak, T. Lapyonok, D. Tanré, J. Deuzé, F. Ducos, A. Sinyuk, and A. Lopatin, “Statistically optimized inversion algorithm for enhanced retrieval of aerosol properties from spectral multi-angle polarimetric satellite observations,” Atmos. Meas. Tech. 4(5), 975–1018 (2011).
[Crossref]

Higurashi, A.

Y. Ota, A. Higurashi, T. Nakajima, and T. Yokota, “Matrix formulations of radiative transfer including the polarization effect in a coupled atmosphere–ocean system,” J. Quant. Spectrosc. Radiat. Transf. 111(6), 878–894 (2010).
[Crossref]

H. Fukushima, A. Higurashi, Y. Mitomi, T. Nakajima, T. Noguchi, T. Tanaka, and M. Toratani, “Correction of atmospheric effect on ADEOS/OCTS ocean color data: Algorithm description and evaluation of its performance,” J. Oceanogr. 54(5), 417–430 (1998).
[Crossref]

Holben, B.

G. Zibordi, F. Mélin, J.-F. Berthon, B. Holben, I. Slutsker, D. Giles, D. D’Alimonte, D. Vandemark, H. Feng, G. Schuster, B. E. Fabbri, S. Kaitala, and J. Seppälä, “AERONET-OC: a network for the validation of ocean color primary products,” J. Atmos. Ocean. Technol. 26(8), 1634–1651 (2009).
[Crossref]

T. Nakajima, G. Tonna, R. Rao, P. Boi, Y. Kaufman, and B. Holben, “Use of sky brightness measurements from ground for remote sensing of particulate polydispersions,” Appl. Opt. 35(15), 2672–2686 (1996).
[Crossref] [PubMed]

Holdak, A.

O. Dubovik, M. Herman, A. Holdak, T. Lapyonok, D. Tanré, J. Deuzé, F. Ducos, A. Sinyuk, and A. Lopatin, “Statistically optimized inversion algorithm for enhanced retrieval of aerosol properties from spectral multi-angle polarimetric satellite observations,” Atmos. Meas. Tech. 4(5), 975–1018 (2011).
[Crossref]

Hollstein, A.

Hu, C.

C. Hu, Z. Lee, and B. Franz, “Chlorophyll aalgorithms for oligotrophic oceans: A novel approach based on three-band reflectance difference,” J. Geophys. Res. 117(C1), C01011 (2012).
[Crossref]

Hu, L.

Hu, Y.

P.-W. Zhai, Y. Hu, J. Chowdhary, C. R. Trepte, P. L. Lucker, and D. B. Josset, “A vector radiative transfer model for coupled atmosphere and ocean systems with a rough interface,” J. Quant. Spectrosc. Radiat. Transf. 111(7-8), 1025–1040 (2010).
[Crossref]

Huibers, P. D.

Huot, Y.

Y. Huot, A. Morel, M. S. Twardowski, D. Stramski, and R. A. Reynolds, “Particle optical backscattering along a chlorophyll gradient in the upper layer of the eastern South Pacific Ocean,” Biogeosciences 5(2), 495–507 (2008).
[Crossref]

Jin, Z.

Josset, D. B.

P.-W. Zhai, Y. Hu, J. Chowdhary, C. R. Trepte, P. L. Lucker, and D. B. Josset, “A vector radiative transfer model for coupled atmosphere and ocean systems with a rough interface,” J. Quant. Spectrosc. Radiat. Transf. 111(7-8), 1025–1040 (2010).
[Crossref]

Kahru, M.

A. P. Vasilkov, J. R. Herman, Z. Ahmad, M. Kahru, and B. G. Mitchell, “Assessment of the ultraviolet radiation field in ocean waters from space-based measurements and full radiative-transfer calculations,” Appl. Opt. 44(14), 2863–2869 (2005).
[Crossref] [PubMed]

J. E. O’Reilly, S. Maritorena, B. G. Mitchell, D. A. Siegel, K. L. Carder, S. A. Garver, M. Kahru, and C. McClain, “Ocean color chlorophyll algorithms for SeaWiFS,” J. Geophys. Res. 103(C11), 24937–24953 (1998).
[Crossref]

Kaitala, S.

G. Zibordi, F. Mélin, J.-F. Berthon, B. Holben, I. Slutsker, D. Giles, D. D’Alimonte, D. Vandemark, H. Feng, G. Schuster, B. E. Fabbri, S. Kaitala, and J. Seppälä, “AERONET-OC: a network for the validation of ocean color primary products,” J. Atmos. Ocean. Technol. 26(8), 1634–1651 (2009).
[Crossref]

Kalashnikova, O. V.

F. Xu, O. Dubovik, P.-W. Zhai, D. J. Diner, O. V. Kalashnikova, F. C. Seidel, P. Litvinov, A. Bovchaliuk, M. J. Garay, G. van Harten, and A. B. Davis, “Joint retrieval of aerosol and water-leaving radiance from multispectral, multiangular and polarimetric measurements over ocean,” Atmos. Meas. Tech. 9(7), 2877–2907 (2016).
[Crossref]

Kamykowski, D.

K. L. Carder, F. Chen, Z. Lee, S. Hawes, and D. Kamykowski, “Semianalytic Moderate-Resolution Imaging Spectrometer algorithms for chlorophyll a and absorption with bio-optical domains based on nitrate-depletion temperatures,” J. Geophys. Res. 104(C3), 5403–5421 (1999).
[Crossref]

Katsev, I. L.

A. A. Kokhanovsky, V. P. Budak, C. Cornet, M. Duan, C. Emde, I. L. Katsev, D. A. Klyukov, S. V. Korkin, L. C-Labonnote, B. Mayer, Q. Min, T. Nakajima, Y. Ota, A. S. Prikhach, V. V. Rozanov, T. Yokota, and E. P. Zege, “Benchmark results in vector atmospheric radiative transfer,” J. Quant. Spectrosc. Radiat. Transf. 111(12-13), 1931–1946 (2010).
[Crossref]

Kattawar, G. W.

Kaufman, Y.

Kindle, J.

Z. Lee, A. Weidemann, J. Kindle, R. Arnone, K. L. Carder, and C. Davis, “Euphotic zone depth: Its derivation and implication to ocean-color remote sensing,” J. Geophys. Res. 112, C03009 (2007).

King, M. D.

O. Dubovik and M. D. King, “A flexible inversion algorithm for retrieval of aerosol optical properties from Sun and sky radiance measurements,” J. Geophys. Res. 105(D16), 20673–20696 (2000).
[Crossref]

Klyukov, D. A.

A. A. Kokhanovsky, V. P. Budak, C. Cornet, M. Duan, C. Emde, I. L. Katsev, D. A. Klyukov, S. V. Korkin, L. C-Labonnote, B. Mayer, Q. Min, T. Nakajima, Y. Ota, A. S. Prikhach, V. V. Rozanov, T. Yokota, and E. P. Zege, “Benchmark results in vector atmospheric radiative transfer,” J. Quant. Spectrosc. Radiat. Transf. 111(12-13), 1931–1946 (2010).
[Crossref]

Knobelspiesse, K.

Kokhanovsky, A. A.

A. A. Kokhanovsky, V. P. Budak, C. Cornet, M. Duan, C. Emde, I. L. Katsev, D. A. Klyukov, S. V. Korkin, L. C-Labonnote, B. Mayer, Q. Min, T. Nakajima, Y. Ota, A. S. Prikhach, V. V. Rozanov, T. Yokota, and E. P. Zege, “Benchmark results in vector atmospheric radiative transfer,” J. Quant. Spectrosc. Radiat. Transf. 111(12-13), 1931–1946 (2010).
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Korkin, S. V.

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C. Shi, P. Wang, T. Nakajima, Y. Ota, S. Tan, and G. Shi, “Effects of Ocean Particles on the Upwelling Radiance and Polarized Radiance in the Atmosphere–Ocean System,” Adv. Atmos. Sci. 32(9), 1186–1196 (2015).
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T. Platt and S. Sathyendranath, “Oceanic primary production: estimation by remote sensing at local and regional scales,” Science 241(4873), 1613–1620 (1988).
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F. Xu, O. Dubovik, P.-W. Zhai, D. J. Diner, O. V. Kalashnikova, F. C. Seidel, P. Litvinov, A. Bovchaliuk, M. J. Garay, G. van Harten, and A. B. Davis, “Joint retrieval of aerosol and water-leaving radiance from multispectral, multiangular and polarimetric measurements over ocean,” Atmos. Meas. Tech. 9(7), 2877–2907 (2016).
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M. Sekiguchi and T. Nakajima, “A k-distribution-based radiation code and its computational optimization for an atmospheric general circulation model,” J. Quant. Spectrosc. Radiat. Transf. 109(17-18), 2779–2793 (2008).
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G. Zibordi, F. Mélin, J.-F. Berthon, B. Holben, I. Slutsker, D. Giles, D. D’Alimonte, D. Vandemark, H. Feng, G. Schuster, B. E. Fabbri, S. Kaitala, and J. Seppälä, “AERONET-OC: a network for the validation of ocean color primary products,” J. Atmos. Ocean. Technol. 26(8), 1634–1651 (2009).
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Shi, C.

C. Shi, T. Nakajima, and M. Hashimoto, “Simultaneous retrieval of aerosol optical thickness and chlorophyll concentration from multiwavelength measurement over East China Sea,” J. Geophys. Res. 121, 14084–14101 (2016).

C. Shi, P. Wang, T. Nakajima, Y. Ota, S. Tan, and G. Shi, “Effects of Ocean Particles on the Upwelling Radiance and Polarized Radiance in the Atmosphere–Ocean System,” Adv. Atmos. Sci. 32(9), 1186–1196 (2015).
[Crossref]

Shi, G.

C. Shi, P. Wang, T. Nakajima, Y. Ota, S. Tan, and G. Shi, “Effects of Ocean Particles on the Upwelling Radiance and Polarized Radiance in the Atmosphere–Ocean System,” Adv. Atmos. Sci. 32(9), 1186–1196 (2015).
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Siegel, D. A.

J. E. O’Reilly, S. Maritorena, B. G. Mitchell, D. A. Siegel, K. L. Carder, S. A. Garver, M. Kahru, and C. McClain, “Ocean color chlorophyll algorithms for SeaWiFS,” J. Geophys. Res. 103(C11), 24937–24953 (1998).
[Crossref]

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O. Dubovik, M. Herman, A. Holdak, T. Lapyonok, D. Tanré, J. Deuzé, F. Ducos, A. Sinyuk, and A. Lopatin, “Statistically optimized inversion algorithm for enhanced retrieval of aerosol properties from spectral multi-angle polarimetric satellite observations,” Atmos. Meas. Tech. 4(5), 975–1018 (2011).
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G. Zibordi, F. Mélin, J.-F. Berthon, B. Holben, I. Slutsker, D. Giles, D. D’Alimonte, D. Vandemark, H. Feng, G. Schuster, B. E. Fabbri, S. Kaitala, and J. Seppälä, “AERONET-OC: a network for the validation of ocean color primary products,” J. Atmos. Ocean. Technol. 26(8), 1634–1651 (2009).
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Spurr, R.

W. Li, K. Stamnes, R. Spurr, and J. Stamnes, “Simultaneous retrieval of aerosol and ocean properties by optimal estimation: SeaWiFS case studies for the Santa Barbara Channel,” Int. J. Remote Sens. 29(19), 5689–5698 (2008).
[Crossref]

Stamnes, J.

W. Li, K. Stamnes, R. Spurr, and J. Stamnes, “Simultaneous retrieval of aerosol and ocean properties by optimal estimation: SeaWiFS case studies for the Santa Barbara Channel,” Int. J. Remote Sens. 29(19), 5689–5698 (2008).
[Crossref]

Stamnes, J. J.

Stamnes, K.

Stavn, R. H.

Stramski, D.

Y. Huot, A. Morel, M. S. Twardowski, D. Stramski, and R. A. Reynolds, “Particle optical backscattering along a chlorophyll gradient in the upper layer of the eastern South Pacific Ocean,” Biogeosciences 5(2), 495–507 (2008).
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Sundman, L. K.

Tan, S.

C. Shi, P. Wang, T. Nakajima, Y. Ota, S. Tan, and G. Shi, “Effects of Ocean Particles on the Upwelling Radiance and Polarized Radiance in the Atmosphere–Ocean System,” Adv. Atmos. Sci. 32(9), 1186–1196 (2015).
[Crossref]

Tanaka, M.

T. Nakajima and M. Tanaka, “Matrix formulations for the transfer of solar radiation in a plane-parallel scattering atmosphere,” J. Quant. Spectrosc. Radiat. Transf. 35(1), 13–21 (1986).
[Crossref]

T. Nakajima and M. Tanaka, “Effect of wind-generated waves on the transfer of solar radiation in the atmosphere-ocean system,” J. Quant. Spectrosc. Radiat. Transf. 29(6), 521–537 (1983).
[Crossref]

Tanaka, T.

H. Fukushima, A. Higurashi, Y. Mitomi, T. Nakajima, T. Noguchi, T. Tanaka, and M. Toratani, “Correction of atmospheric effect on ADEOS/OCTS ocean color data: Algorithm description and evaluation of its performance,” J. Oceanogr. 54(5), 417–430 (1998).
[Crossref]

Tanré, D.

O. Dubovik, M. Herman, A. Holdak, T. Lapyonok, D. Tanré, J. Deuzé, F. Ducos, A. Sinyuk, and A. Lopatin, “Statistically optimized inversion algorithm for enhanced retrieval of aerosol properties from spectral multi-angle polarimetric satellite observations,” Atmos. Meas. Tech. 4(5), 975–1018 (2011).
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Tonna, G.

Toratani, M.

H. Fukushima, A. Higurashi, Y. Mitomi, T. Nakajima, T. Noguchi, T. Tanaka, and M. Toratani, “Correction of atmospheric effect on ADEOS/OCTS ocean color data: Algorithm description and evaluation of its performance,” J. Oceanogr. 54(5), 417–430 (1998).
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Travis, L. D.

Trepte, C. R.

P.-W. Zhai, Y. Hu, J. Chowdhary, C. R. Trepte, P. L. Lucker, and D. B. Josset, “A vector radiative transfer model for coupled atmosphere and ocean systems with a rough interface,” J. Quant. Spectrosc. Radiat. Transf. 111(7-8), 1025–1040 (2010).
[Crossref]

Tsigaridis, K.

Twardowski, M. S.

Y. Huot, A. Morel, M. S. Twardowski, D. Stramski, and R. A. Reynolds, “Particle optical backscattering along a chlorophyll gradient in the upper layer of the eastern South Pacific Ocean,” Biogeosciences 5(2), 495–507 (2008).
[Crossref]

van Diedenhoven, B.

van Harten, G.

F. Xu, O. Dubovik, P.-W. Zhai, D. J. Diner, O. V. Kalashnikova, F. C. Seidel, P. Litvinov, A. Bovchaliuk, M. J. Garay, G. van Harten, and A. B. Davis, “Joint retrieval of aerosol and water-leaving radiance from multispectral, multiangular and polarimetric measurements over ocean,” Atmos. Meas. Tech. 9(7), 2877–2907 (2016).
[Crossref]

Vandemark, D.

G. Zibordi, F. Mélin, J.-F. Berthon, B. Holben, I. Slutsker, D. Giles, D. D’Alimonte, D. Vandemark, H. Feng, G. Schuster, B. E. Fabbri, S. Kaitala, and J. Seppälä, “AERONET-OC: a network for the validation of ocean color primary products,” J. Atmos. Ocean. Technol. 26(8), 1634–1651 (2009).
[Crossref]

Vasilkov, A. P.

Wang, M.

Wang, P.

C. Shi, P. Wang, T. Nakajima, Y. Ota, S. Tan, and G. Shi, “Effects of Ocean Particles on the Upwelling Radiance and Polarized Radiance in the Atmosphere–Ocean System,” Adv. Atmos. Sci. 32(9), 1186–1196 (2015).
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Weidemann, A.

Z. Lee, A. Weidemann, J. Kindle, R. Arnone, K. L. Carder, and C. Davis, “Euphotic zone depth: Its derivation and implication to ocean-color remote sensing,” J. Geophys. Res. 112, C03009 (2007).

Xu, F.

F. Xu, O. Dubovik, P.-W. Zhai, D. J. Diner, O. V. Kalashnikova, F. C. Seidel, P. Litvinov, A. Bovchaliuk, M. J. Garay, G. van Harten, and A. B. Davis, “Joint retrieval of aerosol and water-leaving radiance from multispectral, multiangular and polarimetric measurements over ocean,” Atmos. Meas. Tech. 9(7), 2877–2907 (2016).
[Crossref]

Yan, B.

Yokota, T.

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Figures (8)

Fig. 1
Fig. 1 Variation of nadir reflectance in different salinity (symbolized by “S”) and temperature (symbolized by “T”) in chlorophyll a concentrations (symbolized by “C”) of 0.5 and 3.5 mg m−3. Solar zenith angle was set to 45°.
Fig. 2
Fig. 2 Sensitivity of LCI index to chlorophyll a concentration (Chl) simulated by the oceanic radiative transfer model for different wind speed, oceanic salinity and scattering angle (symbolized by “W”, “PSU” and “SCAG”, respectively)
Fig. 3
Fig. 3 Comparison between Chl from (a) MODIS standard products and those derived from (b) LCI method on 18th September, 2007 in waters near Hokkaido
Fig. 4
Fig. 4 Scatter plot comparisons of Chl between LCI predictions and MODIS standard products (from Fig. 3)
Fig. 5
Fig. 5 Distributions of retrieved relative error from LCI method in each Chl value
Fig. 6
Fig. 6 Spatial distributions of aerosols scattering contribution to the LCI index (a) and aerosol optical thickness (AOT) at 869 nm (b).
Fig. 7
Fig. 7 Comparison of LCI estimated Chl (mg m−3) from (a: current model; b: Pstar model; c: C2 coefficients and current model) with those of in situ products and sensitivity of LCI index to Chl for different models and linear combination coefficients (d)
Fig. 8
Fig. 8 Inter-comparison between the predictions in this study (shown as continuous line) with standard values [57] (shown as dot) for several problems (a: P1; b: P2; c: P3; d: P4; e: P5)

Equations (20)

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R * (λ)= R m (λ)+ R a (λ)+ R ma (λ)+ t m (λ) t a (λ) R w (λ)/(1s(λ) R w (λ)).
R c (λ)=[ R * (λ) R m (λ)]/ t m (λ) =[ R a (λ)+ R ma (λ)]/ t m (λ)+ t a (λ) R w (λ). = R (λ)+ t a (λ) R w (λ)
LCI= i [ a i R c ( λ i )]= i [ a i R ( λ i )]+ i [ a i t a ( λ i ) R w ( λ i )] i { a i j [ b j λ i n j ] }+ i [ a i t a ( λ i ) R w ( λ i )] . = j { b j i [ a i λ i n j ]}+ i [ a i t a ( λ i ) R w ( λ i )]
a w (T,S,λ)= a w ( T 0 , S 0 ,λ)+(T T 0 ) ψ T (λ)+(S S 0 ) ψ S (λ).
b w (T,S,λ)= 8π 3 β w ( 90 ,T,S,λ) 2+ δ w 1+ δ w .
a ph (λ)=A(λ) [Chl] 1B(λ) .
b ph (λ)=0.347 [Chl] 0.766 [λ/660] v([Chl]) v([Chl])=0.5( log 10 ([Chl])0.3)when0.02<[Chl]<2mg m 3 v([Chl])=0when[Chl]>2mg m 3 . B bp =0.002+0.01(0.50.25 log 10 ([Chl]))
P(Θ)= 1 4π (1δ) 2 δ v {v(1δ)(1 δ v )+[δ(1 δ v )v(1δ) sin 2 (Θ/2)]} + 1 δ 180 v 16π( δ 180 1) δ 180 v (3 cos 2 (Θ)1) .
v= 3μ 2 ,δ= 4 3(n1) sin 2 (Θ/2).
B bpFF =1 1 δ 90 v+1 0.5(1 δ 90 v ) (1 δ 90 ) δ 90 v .
n=1.01+0.1542(μ3).
a y (λ)=0.2 a ph (440)exp(0.014(λ440)).
Z pd Z e /4.6; Z e =34.0 [Chl] 0.39 .
[Chl] layer (z)= [Chl] tot Z e { C b + C max exp[ (ξ ξ max ) 2 Δ ξ 2 ]} [Chl] tot =38.0 [Chl] 0.425 when[Chl]<1.0mg m 3 . [Chl] tot =40.2 [Chl] 0.507 when[Chl]>1.0mg m 3
a(λ)= a w (λ)+ a ph (λ)+ a y (λ) b(λ)= b w (λ)+ b ph (λ) b b (λ)=0.5 b w (λ)+ B bp b ph (λ) ω(λ)=a(λ)/[a(λ)+b(λ)] . P(Θ)=[ b w (λ) P w (Θ)+ b ph (λ) P ph (Θ)]/b(λ) τ(Z,λ)= 0 Z [a(λ)+b(λ)] dz
L w (μ,ϕ)= m=0 M1 L w m (μ) cosmϕ π(1+ δ 0m ) .
L w m (μ)= i=1 N s L u m ( τ 0 ; μ i ) T m (μ, μ i ) .
T m (μ, μ i )= 1 μ i μ i 1/2 μ i +1/2 μ d μ 0 2π T(μ, μ ;ϕ) cosmϕdϕ.
Chl=exp[(LCI0.0018)/0.004].
a ph (z)=0.04 [Chl(z)] 0.602 ; b ph (z)=0.33 [Chl(z)] 0.620 .

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