Abstract

An iterative algorithm is presented in this study for simultaneous determination of both the aerosol optical thickness and the exponent of the Junge power law from the total reflectance data of two satellite-based, near-infrared bands over the ocean. The atmospheric aerosol model is assumed as the Junge power-law size distribution in retrieval of the data. Numerical simulations show that relative errors in retrieval of the aerosol optical thickness and the exponent of the Junge power law are less than 5% when the actual atmospheric aerosol follows the Junge power-law size distribution. For other aerosol size distributions, relative errors of the aerosol optical thickness are less than approximately 10%. The proposed method is applied to a case study of the data of two near-infrared channels of the Sea-Viewing Wide Field-of-View Sensor (SeaWiFS) over the East China Sea area. The results show that reasonable spatial distribution of the exponent of the Junge law and the aerosol optical thickness may be obtained on a pixel-by-pixel basis through use of the proposed retrieval algorithm.

© 2007 Optical Society of America

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References

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  1. C. R. N. Rao, E. P. McClain, and L. L. Stowe, "Remote sensing of aerosols over the oceans using AVHRR data theory, practice, and applications," Int. J. Remote Sens. 10, 743-749 (1989).
    [CrossRef]
  2. 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, 443-452 (1994).
    [CrossRef] [PubMed]
  3. D. A. Siegal, M. Wang, S. Maritorena, and W. Robinson, "Atmospheric correction of satellite ocean color imagery: the black pixel assumption," Appl. Opt. 39, 3582-3591 (2000).
    [CrossRef]
  4. D. Tanre, Y. J. Kaufman, M. Herman, and S. Mattoo, "Remote sensing of aerosol properties over oceans using the MODIS/EOS spectral radiances," J. Geophys. Res. 102, 16971-16988 (1997).
    [CrossRef]
  5. F. S. Zhao and T. Nakajima, "Simultaneous determination of water-leaving reflectance and aerosol optical thickness from coastal zone color scanner measurements," Appl. Opt. 36, 6949-6956 (1997).
    [CrossRef]
  6. F. Zhao, Y. Li, C. Dong, and N. Lu, "An algorithm for determination of aerosol optical thickness from AVHRR imagery over oceans," Meteorol. Atmos. Phys. 80, 73-88 (2002).
    [CrossRef]
  7. S. S. Rao, Optimization Theory and Applications (Wiley Eastern, Ltd., New Delhi, 1978).
  8. R. M. Chomko and 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, 5560-5572 (1998).
    [CrossRef]
  9. P. E. Gill and W. Murray, "Quasi-Newton methods for unconstrained optimization," J. Inst. Math. Appl. 9, 91-108 (1972).
    [CrossRef]
  10. M. Wang and H. R. Gordon, "Retrieval of the columnar aerosol phase function and single-scattering albedo from sky radiance over the ocean: simulations," Appl. Opt. 32, 4598-4609 (1993).
    [CrossRef] [PubMed]
  11. A. Angström, "Techniques of determining the turbidity of the atmosphere," Tellus 13, 214-223 (1961).
    [CrossRef]
  12. K. Bullrich, "Scattered radiation in the atmosphere and the natural aerosol," Adv. Geophys. 10, 99-260 (1964).
    [CrossRef]
  13. P. Y. Deschamps, M. Herman, and D. Tanre, "Modeling of the atmospheric effects and its application to the remote sensing of ocean color," Appl. Opt. 22, 3751-3758 (1983).
    [CrossRef] [PubMed]
  14. E. F. Vermote, D. Tanre, J. L. Deuze, M. Herman, and J. J. Morcrette, The Second Simulation of the Satellite Signal in the Solar Spectrum (6S) User Guide (Laboratoire d'Optique Atmosphérique, France, 1997).
  15. Q. Xu, H. W., and F. Zhao, "Retrieval of reflectance along coastal zone with SeaWiFS," J. Remote Sens.(in Chinese) 6, 352-356 (2002).
  16. E. M. Patterson and D. A. Gillette, "Commonalities in measured size distributions for aerosol having a soil-derived component," J. Geophys. Res. 82, 2074-2082 (1997).
    [CrossRef]
  17. Y. Kim, H. Sievering, and J. F. Boatmann, "Airborne measurement of atmospheric aerosol particles in the lower troposphere over the central United States," J. Geophys. Res. 93, 12631-12644 (1988).
    [CrossRef]
  18. E. F. Vermote, D. Tanre, J. L. Deuze, M. Herman, and J. J. Morcrette, "Second simulation of the satellite signal in the solar spectrum: an overview," IEEE Trans. Geosci. Remote Sens. 35, 675-686 (1997).
    [CrossRef]

2002 (2)

F. Zhao, Y. Li, C. Dong, and N. Lu, "An algorithm for determination of aerosol optical thickness from AVHRR imagery over oceans," Meteorol. Atmos. Phys. 80, 73-88 (2002).
[CrossRef]

Q. Xu, H. W., and F. Zhao, "Retrieval of reflectance along coastal zone with SeaWiFS," J. Remote Sens.(in Chinese) 6, 352-356 (2002).

2000 (1)

1998 (1)

1997 (4)

F. S. Zhao and T. Nakajima, "Simultaneous determination of water-leaving reflectance and aerosol optical thickness from coastal zone color scanner measurements," Appl. Opt. 36, 6949-6956 (1997).
[CrossRef]

E. M. Patterson and D. A. Gillette, "Commonalities in measured size distributions for aerosol having a soil-derived component," J. Geophys. Res. 82, 2074-2082 (1997).
[CrossRef]

E. F. Vermote, D. Tanre, J. L. Deuze, M. Herman, and J. J. Morcrette, "Second simulation of the satellite signal in the solar spectrum: an overview," IEEE Trans. Geosci. Remote Sens. 35, 675-686 (1997).
[CrossRef]

D. Tanre, Y. J. Kaufman, M. Herman, and S. Mattoo, "Remote sensing of aerosol properties over oceans using the MODIS/EOS spectral radiances," J. Geophys. Res. 102, 16971-16988 (1997).
[CrossRef]

1994 (1)

1993 (1)

1989 (1)

C. R. N. Rao, E. P. McClain, and L. L. Stowe, "Remote sensing of aerosols over the oceans using AVHRR data theory, practice, and applications," Int. J. Remote Sens. 10, 743-749 (1989).
[CrossRef]

1988 (1)

Y. Kim, H. Sievering, and J. F. Boatmann, "Airborne measurement of atmospheric aerosol particles in the lower troposphere over the central United States," J. Geophys. Res. 93, 12631-12644 (1988).
[CrossRef]

1983 (1)

1972 (1)

P. E. Gill and W. Murray, "Quasi-Newton methods for unconstrained optimization," J. Inst. Math. Appl. 9, 91-108 (1972).
[CrossRef]

1964 (1)

K. Bullrich, "Scattered radiation in the atmosphere and the natural aerosol," Adv. Geophys. 10, 99-260 (1964).
[CrossRef]

1961 (1)

A. Angström, "Techniques of determining the turbidity of the atmosphere," Tellus 13, 214-223 (1961).
[CrossRef]

Angström, A.

A. Angström, "Techniques of determining the turbidity of the atmosphere," Tellus 13, 214-223 (1961).
[CrossRef]

Boatmann, J. F.

Y. Kim, H. Sievering, and J. F. Boatmann, "Airborne measurement of atmospheric aerosol particles in the lower troposphere over the central United States," J. Geophys. Res. 93, 12631-12644 (1988).
[CrossRef]

Bullrich, K.

K. Bullrich, "Scattered radiation in the atmosphere and the natural aerosol," Adv. Geophys. 10, 99-260 (1964).
[CrossRef]

Chomko, R. M.

Deschamps, P. Y.

Deuze, J. L.

E. F. Vermote, D. Tanre, J. L. Deuze, M. Herman, and J. J. Morcrette, "Second simulation of the satellite signal in the solar spectrum: an overview," IEEE Trans. Geosci. Remote Sens. 35, 675-686 (1997).
[CrossRef]

Dong, C.

F. Zhao, Y. Li, C. Dong, and N. Lu, "An algorithm for determination of aerosol optical thickness from AVHRR imagery over oceans," Meteorol. Atmos. Phys. 80, 73-88 (2002).
[CrossRef]

Gill, P. E.

P. E. Gill and W. Murray, "Quasi-Newton methods for unconstrained optimization," J. Inst. Math. Appl. 9, 91-108 (1972).
[CrossRef]

Gillette, D. A.

E. M. Patterson and D. A. Gillette, "Commonalities in measured size distributions for aerosol having a soil-derived component," J. Geophys. Res. 82, 2074-2082 (1997).
[CrossRef]

Gordon, H. R.

Gordon, R.

Herman, M.

E. F. Vermote, D. Tanre, J. L. Deuze, M. Herman, and J. J. Morcrette, "Second simulation of the satellite signal in the solar spectrum: an overview," IEEE Trans. Geosci. Remote Sens. 35, 675-686 (1997).
[CrossRef]

D. Tanre, Y. J. Kaufman, M. Herman, and S. Mattoo, "Remote sensing of aerosol properties over oceans using the MODIS/EOS spectral radiances," J. Geophys. Res. 102, 16971-16988 (1997).
[CrossRef]

P. Y. Deschamps, M. Herman, and D. Tanre, "Modeling of the atmospheric effects and its application to the remote sensing of ocean color," Appl. Opt. 22, 3751-3758 (1983).
[CrossRef] [PubMed]

Kaufman, Y. J.

D. Tanre, Y. J. Kaufman, M. Herman, and S. Mattoo, "Remote sensing of aerosol properties over oceans using the MODIS/EOS spectral radiances," J. Geophys. Res. 102, 16971-16988 (1997).
[CrossRef]

Kim, Y.

Y. Kim, H. Sievering, and J. F. Boatmann, "Airborne measurement of atmospheric aerosol particles in the lower troposphere over the central United States," J. Geophys. Res. 93, 12631-12644 (1988).
[CrossRef]

Li, Y.

F. Zhao, Y. Li, C. Dong, and N. Lu, "An algorithm for determination of aerosol optical thickness from AVHRR imagery over oceans," Meteorol. Atmos. Phys. 80, 73-88 (2002).
[CrossRef]

Lu, N.

F. Zhao, Y. Li, C. Dong, and N. Lu, "An algorithm for determination of aerosol optical thickness from AVHRR imagery over oceans," Meteorol. Atmos. Phys. 80, 73-88 (2002).
[CrossRef]

Maritorena, S.

Mattoo, S.

D. Tanre, Y. J. Kaufman, M. Herman, and S. Mattoo, "Remote sensing of aerosol properties over oceans using the MODIS/EOS spectral radiances," J. Geophys. Res. 102, 16971-16988 (1997).
[CrossRef]

McClain, E. P.

C. R. N. Rao, E. P. McClain, and L. L. Stowe, "Remote sensing of aerosols over the oceans using AVHRR data theory, practice, and applications," Int. J. Remote Sens. 10, 743-749 (1989).
[CrossRef]

Morcrette, J. J.

E. F. Vermote, D. Tanre, J. L. Deuze, M. Herman, and J. J. Morcrette, "Second simulation of the satellite signal in the solar spectrum: an overview," IEEE Trans. Geosci. Remote Sens. 35, 675-686 (1997).
[CrossRef]

Murray, W.

P. E. Gill and W. Murray, "Quasi-Newton methods for unconstrained optimization," J. Inst. Math. Appl. 9, 91-108 (1972).
[CrossRef]

Nakajima, T.

Patterson, E. M.

E. M. Patterson and D. A. Gillette, "Commonalities in measured size distributions for aerosol having a soil-derived component," J. Geophys. Res. 82, 2074-2082 (1997).
[CrossRef]

Rao, C. R. N.

C. R. N. Rao, E. P. McClain, and L. L. Stowe, "Remote sensing of aerosols over the oceans using AVHRR data theory, practice, and applications," Int. J. Remote Sens. 10, 743-749 (1989).
[CrossRef]

Robinson, W.

Siegal, D. A.

Sievering, H.

Y. Kim, H. Sievering, and J. F. Boatmann, "Airborne measurement of atmospheric aerosol particles in the lower troposphere over the central United States," J. Geophys. Res. 93, 12631-12644 (1988).
[CrossRef]

Stowe, L. L.

C. R. N. Rao, E. P. McClain, and L. L. Stowe, "Remote sensing of aerosols over the oceans using AVHRR data theory, practice, and applications," Int. J. Remote Sens. 10, 743-749 (1989).
[CrossRef]

Tanre, D.

D. Tanre, Y. J. Kaufman, M. Herman, and S. Mattoo, "Remote sensing of aerosol properties over oceans using the MODIS/EOS spectral radiances," J. Geophys. Res. 102, 16971-16988 (1997).
[CrossRef]

E. F. Vermote, D. Tanre, J. L. Deuze, M. Herman, and J. J. Morcrette, "Second simulation of the satellite signal in the solar spectrum: an overview," IEEE Trans. Geosci. Remote Sens. 35, 675-686 (1997).
[CrossRef]

P. Y. Deschamps, M. Herman, and D. Tanre, "Modeling of the atmospheric effects and its application to the remote sensing of ocean color," Appl. Opt. 22, 3751-3758 (1983).
[CrossRef] [PubMed]

Vermote, E. F.

E. F. Vermote, D. Tanre, J. L. Deuze, M. Herman, and J. J. Morcrette, "Second simulation of the satellite signal in the solar spectrum: an overview," IEEE Trans. Geosci. Remote Sens. 35, 675-686 (1997).
[CrossRef]

Wang, M.

Xu, Q.

Q. Xu, H. W., and F. Zhao, "Retrieval of reflectance along coastal zone with SeaWiFS," J. Remote Sens.(in Chinese) 6, 352-356 (2002).

Zhao, F.

F. Zhao, Y. Li, C. Dong, and N. Lu, "An algorithm for determination of aerosol optical thickness from AVHRR imagery over oceans," Meteorol. Atmos. Phys. 80, 73-88 (2002).
[CrossRef]

Zhao, F. S.

Adv. Geophys. (1)

K. Bullrich, "Scattered radiation in the atmosphere and the natural aerosol," Adv. Geophys. 10, 99-260 (1964).
[CrossRef]

Appl. Opt. (6)

IEEE Trans. Geosci. Remote Sens. (1)

E. F. Vermote, D. Tanre, J. L. Deuze, M. Herman, and J. J. Morcrette, "Second simulation of the satellite signal in the solar spectrum: an overview," IEEE Trans. Geosci. Remote Sens. 35, 675-686 (1997).
[CrossRef]

Int. J. Remote Sens. (1)

C. R. N. Rao, E. P. McClain, and L. L. Stowe, "Remote sensing of aerosols over the oceans using AVHRR data theory, practice, and applications," Int. J. Remote Sens. 10, 743-749 (1989).
[CrossRef]

J. Geophys. Res. (3)

D. Tanre, Y. J. Kaufman, M. Herman, and S. Mattoo, "Remote sensing of aerosol properties over oceans using the MODIS/EOS spectral radiances," J. Geophys. Res. 102, 16971-16988 (1997).
[CrossRef]

E. M. Patterson and D. A. Gillette, "Commonalities in measured size distributions for aerosol having a soil-derived component," J. Geophys. Res. 82, 2074-2082 (1997).
[CrossRef]

Y. Kim, H. Sievering, and J. F. Boatmann, "Airborne measurement of atmospheric aerosol particles in the lower troposphere over the central United States," J. Geophys. Res. 93, 12631-12644 (1988).
[CrossRef]

J. Inst. Math. Appl. (1)

P. E. Gill and W. Murray, "Quasi-Newton methods for unconstrained optimization," J. Inst. Math. Appl. 9, 91-108 (1972).
[CrossRef]

J. Remote Sens. (1)

Q. Xu, H. W., and F. Zhao, "Retrieval of reflectance along coastal zone with SeaWiFS," J. Remote Sens.(in Chinese) 6, 352-356 (2002).

Meteorol. Atmos. Phys. (1)

F. Zhao, Y. Li, C. Dong, and N. Lu, "An algorithm for determination of aerosol optical thickness from AVHRR imagery over oceans," Meteorol. Atmos. Phys. 80, 73-88 (2002).
[CrossRef]

Tellus (1)

A. Angström, "Techniques of determining the turbidity of the atmosphere," Tellus 13, 214-223 (1961).
[CrossRef]

Other (2)

S. S. Rao, Optimization Theory and Applications (Wiley Eastern, Ltd., New Delhi, 1978).

E. F. Vermote, D. Tanre, J. L. Deuze, M. Herman, and J. J. Morcrette, The Second Simulation of the Satellite Signal in the Solar Spectrum (6S) User Guide (Laboratoire d'Optique Atmosphérique, France, 1997).

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Figures (2)

Fig. 1.
Fig. 1.

Spatial distribution of ν retrieved from local SeaWiFS data on January 1, 2001.

Fig. 2.
Fig. 2.

Spatial distribution of τa (550) retrieved from local SeaWiFS data on January 1, 2001.

Tables (9)

Tables Icon

Table 1. Relative errors (%) of the size distribution parameters ν.

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Table 2. Relative errors (%) of the aerosol optical thickness τa (550).

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Table 3. Relative errors (%) of ν in the iterative algorithm.

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Table 4. Relative errors (%) of τa (550) in the iterative algorithm.

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Table 5. Microphysical characteristics of the four components for the standard 6S aerosol type.

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Table 6. Volume percentages of the four basic components for the standard 6S aerosol model.

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Table 7. Values of ν and τa (550) and their errors retrieved by the iterative algorithm with the aerosol type of the lognormal distribution (maritime).

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Table 8. Values of ν and τa (550) and their errors retrieved by the iterative algorithm with the aerosol type of the lognormal distribution (continental).

Tables Icon

Table 9. Values of ν and τa (550) and their errors retrieved by the iterative algorithm with the aerosol type of the

Equations (20)

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

ρ p ( θ 0 , ϕ 0 , θ , ϕ ) = ρ m ( θ 0 , ϕ 0 , θ , ϕ ) + ω a τ a ( λ ) P a ( θ 0 , ϕ 0 , θ , ϕ ) 4 cos θ 0 cos θ ,
τ a ( λ ) = βλ α ,
ln ρ p 1 ( θ 0 , ϕ 0 , θ , ϕ ) ρ m 1 ( θ 0 , ϕ 0 , θ , ϕ ) ρ p 2 ( θ 0 , ϕ 0 , θ , ϕ ) ρ m 2 ( θ 0 , ϕ 0 , θ , ϕ ) = ln ω a 1 P a 1 ( θ 0 , ϕ 0 , θ , ϕ ) ω a 2 P a 2 ( θ 0 , ϕ 0 , θ , ϕ ) α In λ 1 λ 2 ,
σ e = β′ λ α ,
ω a 1 ω a 2 = σ s 1 σ s 2 ( λ 1 λ 2 ) α ,
P a ( φ ) = 4 πβ s ( φ ) σ s ,
P a 1 ( φ ) P a 2 ( φ ) = σ s 2 β s 1 ( φ ) σ s 1 β s 2 ( φ ) .
β s ( φ ) = 0.4343 C ( λ 2 π ) α 1 2 η ( φ ) ,
η ( φ ) = x 1 x 2 ( i 1 + i 2 ) x ( ν + 1 ) dx ,
ω a 1 P a 1 ( φ ) ω a 2 P a 2 ( φ ) = η 1 ( φ ) η 2 ( φ ) 1 .
α = ln ρ p 1 ( θ 0 , ϕ 0 , θ , ϕ ) ρ m 1 ( θ 0 , ϕ 0 , θ , ϕ ) ρ p 2 ( θ 0 , ϕ 0 , θ , ϕ ) ρ m 2 ( θ 0 , ϕ 0 , θ , ϕ ) ln λ 1 λ 2 .
ν = α + 2 .
{ ω a τ a ( λ ) P a ( θ 0 , ϕ 0 , θ , ϕ ) 4 cos θ 0 cos θ τ a ( λ ) . τ a ( λ ) λ α
[ ρ p 1 ( θ 0 , ϕ 0 , θ , ϕ ) ρ m 1 ( θ 0 , ϕ 0 , θ , ϕ ) ] [ ρ p 2 c ( θ 0 , ϕ 0 , θ , ϕ ) ρ m 2 ( θ 0 , ϕ 0 , θ , ϕ ) ] [ ρ p 2 ( θ 0 , ϕ 0 , θ , ϕ ) ρ m 2 ( θ 0 , ϕ 0 , θ , ϕ ) ] [ ρ p 1 c ( θ 0 , ϕ 0 , θ , ϕ ) ρ m 1 ( θ 0 , ϕ 0 , θ , ϕ ) ] ,
= ω a 1 τ a 1 ( λ 1 ) P a 1 ( θ 0 , ϕ 0 , θ , ϕ ) ω a 2 c τ a 2 c ( λ 2 ) P a 2 c ( θ 0 , ϕ 0 , θ , ϕ ) ω a 2 τ a 2 ( λ 2 ) P a 2 ( θ 0 , ϕ 0 , θ , ϕ ) ω a 1 c τ a 1 c ( λ 1 ) P a 1 c ( θ 0 , ϕ 0 , θ , ϕ )
α = ln Y ( ln λ 2 ln λ 1 ) + α n ,
τ a ( 550 ) = ρ p ( θ 0 , ϕ 0 , θ , ϕ ) ρ m ( θ 0 , ϕ 0 , θ , ϕ ) ρ p c ( θ 0 , ϕ 0 , θ , ϕ ) ρ m ( θ 0 , ϕ 0 , θ , ϕ ) τ a n ( 550 )
( ρ p ( θ 0 , ϕ 0 , θ , ϕ ) ρ p c ( θ 0 , ϕ 0 , θ , ϕ ) ) ρ p ( θ 0 , ϕ 0 , θ , ϕ ) < ε
i = 1 2 ( ρ pi ( θ 0 , ϕ 0 , θ , ϕ ) ρ pi c ( θ 0 , ϕ 0 , θ , ϕ ) ) ρ pi ( θ 0 , ϕ 0 , θ , ϕ ) < δ
dN i ( r ) dr = N i 2 π r log σ i ln 10 exp [ 1 2 ( log r log r mod N , i log σ i ) 2 ] ,

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