Abstract

We introduced a two-dimensional radiative transfer model for aerosols in the thermal infrared [Appl. Opt. 45, 6860–6875 (2006)]. In that paper we superimposed two orthogonal plane-parallel layers to compute the radiance due to a two-dimensional (2D) rectangular aerosol cloud. In this paper we revisit the model and correct an error in the interaction of the two layers. We derive new expressions relating to the signal content of the radiance from an aerosol cloud based on the concept of five directional thermal contrasts: four for the 2D diffuse radiance and one for direct radiance along the line of sight. The new expressions give additional insight on the radiative transfer processes within the cloud. Simulations for Bacillus subtilis var. niger (BG) bioaerosol and dustlike kaolin aerosol clouds are compared and contrasted for two geometries: an airborne sensor looking down and a ground-based sensor looking up. Simulation results suggest that aerosol cloud detection from an airborne platform may be more challenging than for a ground-based sensor and that the detection of an aerosol cloud in emission mode (negative direct thermal contrast) is not the same as the detection of an aerosol cloud in absorption mode (positive direct thermal contrast).

© 2008 Optical Society of America

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Corrections

Avishai Ben-David, Charles E. Davidson, and Janon F. Embury, "Radiative transfer model for aerosols at infrared wavelengths for passive remote sensing applications: revisited--erratum," Appl. Opt. 48, 903-903 (2009)
https://www.osapublishing.org/ao/abstract.cfm?uri=ao-48-5-903

References

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    [CrossRef]
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2006 (1)

2005 (1)

2003 (2)

1999 (1)

A. Berk, G. P. Anderson, L. S. Bernstein, P. K. Acharya, H. Dothe, M. W. Matthew, S. M. Adler-Golden, J. H. Chetwynd, Jr., S. C. Richtsmeier, B. Pukall, C. L. Allred, L. S. Jeong, and M. L. Hoke, “MODTRAN4 radiative transfer modeling for atmospheric correction” Proc. SPIE 3756, 348-353 (1999).
[CrossRef]

1996 (1)

1980 (2)

A. Ben-Shalom, B. Barzilai, D. Cabib, A. D. Devir, S. G. Lipson, and U. P. Oppenheim, “Sky radiance at wavelengths between 7 and 14 μm: measurement, calculation, and comparison with LOWTRAN-4 predictions,” Appl. Opt. 19, 838-839 (1980).
[CrossRef] [PubMed]

W. E. Meador and W. R. Weaver, “Two-stream approximations to radiative transfer in planetary atmospheres: a unified description of existing methods and new improvement,” J. Atmos. Sci. 37, 630-643 (1980).
[CrossRef]

Acharya, P. K.

A. Berk, G. P. Anderson, L. S. Bernstein, P. K. Acharya, H. Dothe, M. W. Matthew, S. M. Adler-Golden, J. H. Chetwynd, Jr., S. C. Richtsmeier, B. Pukall, C. L. Allred, L. S. Jeong, and M. L. Hoke, “MODTRAN4 radiative transfer modeling for atmospheric correction” Proc. SPIE 3756, 348-353 (1999).
[CrossRef]

Adler-Golden, S. M.

A. Berk, G. P. Anderson, L. S. Bernstein, P. K. Acharya, H. Dothe, M. W. Matthew, S. M. Adler-Golden, J. H. Chetwynd, Jr., S. C. Richtsmeier, B. Pukall, C. L. Allred, L. S. Jeong, and M. L. Hoke, “MODTRAN4 radiative transfer modeling for atmospheric correction” Proc. SPIE 3756, 348-353 (1999).
[CrossRef]

Allred, C. L.

A. Berk, G. P. Anderson, L. S. Bernstein, P. K. Acharya, H. Dothe, M. W. Matthew, S. M. Adler-Golden, J. H. Chetwynd, Jr., S. C. Richtsmeier, B. Pukall, C. L. Allred, L. S. Jeong, and M. L. Hoke, “MODTRAN4 radiative transfer modeling for atmospheric correction” Proc. SPIE 3756, 348-353 (1999).
[CrossRef]

Anderson, G. P.

A. Berk, G. P. Anderson, L. S. Bernstein, P. K. Acharya, H. Dothe, M. W. Matthew, S. M. Adler-Golden, J. H. Chetwynd, Jr., S. C. Richtsmeier, B. Pukall, C. L. Allred, L. S. Jeong, and M. L. Hoke, “MODTRAN4 radiative transfer modeling for atmospheric correction” Proc. SPIE 3756, 348-353 (1999).
[CrossRef]

Barzilai, B.

Ben-David, A.

Ben-Shalom, A.

Berk, A.

A. Berk, G. P. Anderson, L. S. Bernstein, P. K. Acharya, H. Dothe, M. W. Matthew, S. M. Adler-Golden, J. H. Chetwynd, Jr., S. C. Richtsmeier, B. Pukall, C. L. Allred, L. S. Jeong, and M. L. Hoke, “MODTRAN4 radiative transfer modeling for atmospheric correction” Proc. SPIE 3756, 348-353 (1999).
[CrossRef]

Bernstein, L. S.

A. Berk, G. P. Anderson, L. S. Bernstein, P. K. Acharya, H. Dothe, M. W. Matthew, S. M. Adler-Golden, J. H. Chetwynd, Jr., S. C. Richtsmeier, B. Pukall, C. L. Allred, L. S. Jeong, and M. L. Hoke, “MODTRAN4 radiative transfer modeling for atmospheric correction” Proc. SPIE 3756, 348-353 (1999).
[CrossRef]

Bohren, C. F.

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

Cabib, D.

Chetwynd, J. H.

A. Berk, G. P. Anderson, L. S. Bernstein, P. K. Acharya, H. Dothe, M. W. Matthew, S. M. Adler-Golden, J. H. Chetwynd, Jr., S. C. Richtsmeier, B. Pukall, C. L. Allred, L. S. Jeong, and M. L. Hoke, “MODTRAN4 radiative transfer modeling for atmospheric correction” Proc. SPIE 3756, 348-353 (1999).
[CrossRef]

Davidson, C. E.

Devir, A. D.

Dothe, H.

A. Berk, G. P. Anderson, L. S. Bernstein, P. K. Acharya, H. Dothe, M. W. Matthew, S. M. Adler-Golden, J. H. Chetwynd, Jr., S. C. Richtsmeier, B. Pukall, C. L. Allred, L. S. Jeong, and M. L. Hoke, “MODTRAN4 radiative transfer modeling for atmospheric correction” Proc. SPIE 3756, 348-353 (1999).
[CrossRef]

Embury, J.

Flanigan, D. F.

Hoke, M. L.

A. Berk, G. P. Anderson, L. S. Bernstein, P. K. Acharya, H. Dothe, M. W. Matthew, S. M. Adler-Golden, J. H. Chetwynd, Jr., S. C. Richtsmeier, B. Pukall, C. L. Allred, L. S. Jeong, and M. L. Hoke, “MODTRAN4 radiative transfer modeling for atmospheric correction” Proc. SPIE 3756, 348-353 (1999).
[CrossRef]

Huffman, D. R.

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

Jeong, L. S.

A. Berk, G. P. Anderson, L. S. Bernstein, P. K. Acharya, H. Dothe, M. W. Matthew, S. M. Adler-Golden, J. H. Chetwynd, Jr., S. C. Richtsmeier, B. Pukall, C. L. Allred, L. S. Jeong, and M. L. Hoke, “MODTRAN4 radiative transfer modeling for atmospheric correction” Proc. SPIE 3756, 348-353 (1999).
[CrossRef]

Lenoble, J.

J. Lenoble, Radiative Transfer in Scattering and Absorbing Atmospheres: Standard Computational Procedures (Deepak, 1985).

Liou, K. N.

K. N. Liou, An Introduction to Atmospheric Radiation, 2nd ed. (Academic, 2002).

K. N. Liou, Radiation and Cloud Processes in the Atmosphere (Oxford University Press, 1992).

Lipson, S. G.

Matthew, M. W.

A. Berk, G. P. Anderson, L. S. Bernstein, P. K. Acharya, H. Dothe, M. W. Matthew, S. M. Adler-Golden, J. H. Chetwynd, Jr., S. C. Richtsmeier, B. Pukall, C. L. Allred, L. S. Jeong, and M. L. Hoke, “MODTRAN4 radiative transfer modeling for atmospheric correction” Proc. SPIE 3756, 348-353 (1999).
[CrossRef]

Meador, W. E.

W. E. Meador and W. R. Weaver, “Two-stream approximations to radiative transfer in planetary atmospheres: a unified description of existing methods and new improvement,” J. Atmos. Sci. 37, 630-643 (1980).
[CrossRef]

Oppenheim, U. P.

Pukall, B.

A. Berk, G. P. Anderson, L. S. Bernstein, P. K. Acharya, H. Dothe, M. W. Matthew, S. M. Adler-Golden, J. H. Chetwynd, Jr., S. C. Richtsmeier, B. Pukall, C. L. Allred, L. S. Jeong, and M. L. Hoke, “MODTRAN4 radiative transfer modeling for atmospheric correction” Proc. SPIE 3756, 348-353 (1999).
[CrossRef]

Ren, H.

Richtsmeier, S. C.

A. Berk, G. P. Anderson, L. S. Bernstein, P. K. Acharya, H. Dothe, M. W. Matthew, S. M. Adler-Golden, J. H. Chetwynd, Jr., S. C. Richtsmeier, B. Pukall, C. L. Allred, L. S. Jeong, and M. L. Hoke, “MODTRAN4 radiative transfer modeling for atmospheric correction” Proc. SPIE 3756, 348-353 (1999).
[CrossRef]

van de Hulst, H. C.

H. C. van de Hulst, Multiple Light Scattering Tables, Formulas and Application (Academic, 1980).

Weaver, W. R.

W. E. Meador and W. R. Weaver, “Two-stream approximations to radiative transfer in planetary atmospheres: a unified description of existing methods and new improvement,” J. Atmos. Sci. 37, 630-643 (1980).
[CrossRef]

Appl. Opt. (5)

J. Atmos. Sci. (1)

W. E. Meador and W. R. Weaver, “Two-stream approximations to radiative transfer in planetary atmospheres: a unified description of existing methods and new improvement,” J. Atmos. Sci. 37, 630-643 (1980).
[CrossRef]

Opt. Express (1)

Proc. SPIE (1)

A. Berk, G. P. Anderson, L. S. Bernstein, P. K. Acharya, H. Dothe, M. W. Matthew, S. M. Adler-Golden, J. H. Chetwynd, Jr., S. C. Richtsmeier, B. Pukall, C. L. Allred, L. S. Jeong, and M. L. Hoke, “MODTRAN4 radiative transfer modeling for atmospheric correction” Proc. SPIE 3756, 348-353 (1999).
[CrossRef]

Other (5)

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

K. N. Liou, An Introduction to Atmospheric Radiation, 2nd ed. (Academic, 2002).

K. N. Liou, Radiation and Cloud Processes in the Atmosphere (Oxford University Press, 1992).

H. C. van de Hulst, Multiple Light Scattering Tables, Formulas and Application (Academic, 1980).

J. Lenoble, Radiative Transfer in Scattering and Absorbing Atmospheres: Standard Computational Procedures (Deepak, 1985).

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Figures (10)

Fig. 1
Fig. 1

Rectangular cloud illuminated by diffuse radiation fields (boundary conditions) D, U, L, and R. The width of the cloud is Δ x , and the height of the cloud is Δ z . The cloud is shown in relation to two specific sensor geometries: LOS 1 is a ground-based sensor looking up through the cloud (see Section 5), and LOS 2 is an airborne sensor looking down at the cloud (see Section 6). x is the distance between the sensor and the cloud, and z is the height of the cloud above the ground.

Fig. 2
Fig. 2

Simulated radiance inputs (boundary conditions) and direct thermal contrast terms for the simulations in Sections 5, 6. (a) Boundary conditions D ( μ 1 ) , U ( μ 1 ) , L ( μ 1 ) , and R ( μ 1 ) are the diffuse radiance inputs upon the cloud; ϕ = L ( μ L & R ) is the direct radiance for the ground-based simulation (Section 5); ϕ = U ( μ D & U ) is the direct radiance for the airborne simulation (Section 6); the cloud blackbody radiance, B ( T = 288.15 K ) , is also shown. (b) Direct thermal contrast terms: Δ T = L ( μ L & R ) B is for the ground-based simulation (Section 5), and Δ T = U ( μ D & U ) B is for the airborne simulation (Section 6).

Fig. 3
Fig. 3

Optical parameters and the portion of the signal ( Δ M direct , Δ M diffuse ) in the measurement of a rectangular ( 100 m × 50 m ) BG aerosol cloud (with number density of 12.5 cm 3 ) from a ground-based sensor. (a) Optical properties: optical depth τ, asymmetry parameter g, and single-scattering albedo ϖ for a 100 m thick aerosol layer. (b) Portion of the measurements that contains information on the presence of the cloud. Δ M direct is due to the transmission and scattering of the direct LOS radiance through the cloud, Δ M diffuse is due to scattering of the diffuse radiances, and Δ M total = Δ M direct + Δ M diffuse .

Fig. 4
Fig. 4

Same as Fig. 3 but for a cloud of kaolin aerosols (with number density of 12.5 cm 3 ).

Fig. 5
Fig. 5

Absorption optical depth and portion of the signal due only to thermal processes ( Δ M thermal ) for BG aerosols, ground-based simulation. (a) Absorption optical depth is computed as τ abs * = ( 1 ϖ ) τ * , where τ * is the effective extinction optical depth for the 2D cloud defined in Section 3. (b) Signal portion due to thermal cloud processes only, Δ M thermal = τ abs * Δ T [see Eq. (12)], where Δ T = L ( μ L & R ) B is shown in Fig. 2b.

Fig. 6
Fig. 6

Same as Fig. 5 but for a cloud of kaolin aerosols.

Fig. 7
Fig. 7

Portion of the signal ( Δ M direct , Δ M diffuse ) in the measurement that contain information on the presence of a rectangular ( 100 m × 50 m ) BG aerosol cloud from an airborne sensor. Δ M direct is due to the transmission and scattering of the direct LOS radiance through the cloud, Δ M diffuse is due to scattering of the diffuse radiances, and Δ M total = Δ M direct + Δ M diffuse .

Fig. 8
Fig. 8

Same as Fig. 5 but for a cloud of kaolin aerosols.

Fig. 9
Fig. 9

Absorption optical depth and portion of the signal due only to thermal processes ( Δ M thermal ) for BG aerosols, airborne simulation. (a) Absorption optical depth is computed as τ abs * = ( 1 ϖ ) τ * , where τ * is the effective extinction optical depth for the 2D cloud defined in Section 3. (b) Signal portion due to thermal cloud processes only, Δ M thermal = τ abs * Δ T [see Eq. (12)], where Δ T = U ( μ D & U ) B is shown in Fig. 2a.

Fig. 10
Fig. 10

Same as Fig. 9 but for a cloud of kaolin aerosols.

Equations (17)

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{ I ( 0 , μ , τ 1 < 0.1 ) = t 0 U ( μ ) + r D ( μ 1 ) + t U ( μ 1 ) + ξ B I ( τ 1 , μ , τ 1 < 0.1 ) = t 0 D ( μ ) + t D ( μ 1 ) + r U ( μ 1 ) + ξ B where t 0 = 1 τ 1 μ ; t = ϖ ( 1 + g ) / 2 μ τ 1 ; r = ϖ ( 1 g ) / 2 μ τ 1 ; ξ = 1 ϖ μ τ 1 = 1 r t t 0 } .
I ( 0 , μ ; τ 1 < 0.1 ) = B + r [ D ( μ 1 ) B ] + t [ U ( μ 1 ) B ] + t 0 [ U ( μ ) B ] , I ( τ 1 , μ ; τ 1 < 0.1 ) = B + r [ U ( μ 1 ) B ] + t [ D ( μ 1 ) B ] + t 0 [ D ( μ ) B ] .
Δ T = D ( μ 1 ) B , Δ T = U ( μ 1 ) B , Δ T = L ( μ 1 ) B , Δ T = R ( μ 1 ) B , Δ T = ϕ B ,
{ I D & U = t 0 D ( μ D & U ) + t D ( μ 1 ) + r U ( μ 1 ) + ξ B = B + r Δ T + t Δ T + t 0 Δ T where t 0 = 1 τ Δ z μ D & U ; t = ϖ ( 1 + g ) / 2 μ D & U τ Δ z ; r = ϖ ( 1 g ) / 2 μ D & U τ Δ z ; ξ = 1 ϖ μ D & U τ Δ z = 1 r t t 0 μ D & U = | cos ( θ LOS ) | } ,
{ I L & R = t 0 L ( μ L & R ) + t L ( μ 1 ) + r R ( μ 1 ) + ξ B = B + r Δ T + t Δ T + t 0 Δ T where t 0 = 1 τ Δ x μ L & R ; t = ϖ ( 1 + g ) / 2 μ L & R τ Δ x ; r = ϖ ( 1 g ) / 2 μ L & R τ Δ x ; ξ = 1 ϖ μ L & R τ Δ x = 1 r t t 0 μ L & R = | cos ( π 2 θ LOS ) | } ,
I cloud = η D & U I D & U + η L & R I L & R ,
M ( θ LOS , no cloud ) = M atm + t atm ϕ , M ( θ LOS ) = M atm + t atm I cloud ,
M ( θ LOS ; ϖ = 0 ) = M ( θ LOS , no cloud ) t atm ( η L & R τ Δ x μ L & R + η D & U τ Δ z μ D & U ) Δ T , M ( θ LOS ; 0 ϖ 1 ) = M ( θ LOS ; ϖ = 0 ) + t atm [ η L & R τ Δ x μ L & R ϖ ( 1 + g 2 Δ T + 1 g 2 Δ T ) + η D & U τ Δ z μ D & U ϖ ( 1 + g 2 Δ T + 1 g 2 Δ T ) ] ,
1 + g 2 Δ T + 1 g 2 Δ T
1 + g 2 Δ T + 1 g 2 Δ T
M ( θ LOS ; 0 ϖ 1 ) = M ( θ LOS ; ϖ = 0 ) + t atm [ η L & R τ Δ x μ L & R ϖ 2 ( Δ T + Δ T + g Δ T ) + η D & U τ Δ z μ D & U ϖ 2 ( Δ T + Δ T + g Δ T ) ] ,
M ( θ LOS ; ϖ = 1 ) = M atm + t atm ( 1 τ * ) ϕ + t atm { η L & R τ Δ x μ L & R [ L ( μ 1 ) + R ( μ 1 ) 2 + g Δ T 2 ] + η D & U τ Δ z μ D & U [ D ( μ 1 ) + U ( μ 1 ) 2 + g Δ T 2 ] } ,
Δ M direct = ( η L & R τ Δ x μ L & R + η D & U τ Δ z μ D & U ) Δ T , Δ M diffuse = η L & R τ Δ x μ L & R ϖ ( 1 + g 2 Δ T + 1 g 2 Δ T ) + η D & U τ Δ z μ D & U ϖ ( 1 + g 2 Δ T + 1 g 2 Δ T ) .
Δ M thermal = ( 1 ϖ ) ( η L & R τ Δ x μ L & R + η D & U τ Δ z μ D & U ) Δ T , Δ M scatter = η L & R τ Δ x μ L & R ϖ 2 ( Δ T Δ T + Δ T Δ T + g Δ T ) + η D & U τ Δ z μ D & U ϖ 2 ( Δ T Δ T + Δ T Δ T + g Δ T ) .
{ I D & U = t 0 U ( μ D & U ) + t U ( μ 1 ) + r D ( μ 1 ) + ξ B = B + r Δ T + t Δ T + t 0 Δ T where t 0 = 1 τ Δ z μ D & U ; t = ϖ ( 1 + g ) / 2 μ D & U τ Δ z ; r = ϖ ( 1 g ) / 2 μ D & U τ Δ z ; ξ = 1 ϖ μ D & U τ Δ z = 1 r t t 0 μ D & U = | cos θ LOS | ; Δ T = U ( μ D & U ) B } ,
{ Δ M direct = ( η L & R τ Δ x μ L & R + η D & U τ Δ z μ D & U ) Δ T Δ M thermal = ( 1 ϖ ) ( η L & R τ Δ x μ L & R + η D & U τ Δ z μ D & U ) Δ T Δ M diffuse = η L & R τ Δ x μ L & R ϖ ( 1 + g 2 Δ T + 1 g 2 Δ T ) + η D & U τ Δ z μ D & U ϖ ( 1 + g 2 Δ T + 1 g 2 Δ T ) Δ M scatter = η L & R τ Δ x μ L & R ϖ 2 ( Δ T Δ T + Δ T Δ T + g Δ T ) + η D & U τ Δ z μ D & U ϖ 2 ( Δ T Δ T + Δ T Δ T + g Δ T ) where μ L & R = | cos ( π 2 θ LOS ) | ; μ D & U = | cos θ LOS | ; Δ T = Δ T Δ T ; Δ T = Δ T Δ T } .
t atm = M ( θ LOS , no cloud ) M atm ϕ ,

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