Retrieval of atmospheric optical parameters from airborne flux
measurements: application to the atmospheric correction of
imagery

N. T. O’Neill, A. Royer, Q. F. Xu, and P. M. Teillet

Author Affiliations

N. T. O’Neill, A. Royer, Q. F. Xu, and P. M. Teillet

^{}N. T. O’Neill, A. Royer, and Q. F. Xu are with the Centre
d’Applications et de Recherches en Télédétection,
Université de Sherbrooke, Sherbrooke, Québec J1K 2R1, Canada.

^{}P.
M. Teillet is with the Canada Centre for Remote Sensing, Ottawa, Ontario,
Canada.

N. T. O’Neill, A. Royer, Q. F. Xu, and P. M. Teillet, "Retrieval of atmospheric optical parameters from airborne flux
measurements: application to the atmospheric correction of
imagery," Appl. Opt. 36, 662-674 (1997)

Methodologies that employ auxilliary flux data collected by upward- and
downward-looking optical sensors to improve atmospheric corrections of
airborne multispectral images are presented and evaluated. Such flux data
often are collected in current airborne sensors to produce bidirectional
reflectance factor (BRF) images and estimates of
hemispherical–hemispherical reflectance. The fact that these images must
then be corrected for atmospheric interference raises the question as to
whether the auxilliary flux information can be employed to estimate some of
the input parameters required by atmospheric correction models. Radiative
transfer simulations are employed to demonstrate that the utilization of the
downwelling and upwelling fluxes as a means of inferring intrinsic atmospheric
optical information can be used to better characterize the local atmosphere
and accordingly to improve the atmospheric corrections applied to the apparent
BRF images.

S. Stamnes, C. Hostetler, R. Ferrare, S. Burton, X. Liu, J. Hair, Y. Hu, A. Wasilewski, W. Martin, B. van Diedenhoven, J. Chowdhary, I. Cetinić, L. K. Berg, K. Stamnes, and B. Cairns Appl. Opt. 57(10) 2394-2413 (2018)

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The ten measurement altitudes were fixed
in terms of an equal aerosol optical depth separation
(Δτ_{
a
} =
τ_{
a
}/8) except for the
3-km altitude that was always present, independent of the
Δτ_{
a
}
criterion.
Haze L phase function defined in Garcia
and Siewert.14

Table 2

Inversion Errors for the Atmosphere of Table 1 that
are Due to an Irradiance rms Noise Error of 1% and an Optical
Depth rms Noise Error of 0.01

〈Δτ_{
g〉}

0.06

0.12

0.16

0.32

Number of altitudes

9

5

4

3

〈δg^{2}〉^{1/2}

0.14

0.072

0.054

0.027

〈δω_{0}^{2}〉^{1/2}

0.12

0.059

0.044

0.022

Table 3

Illustrative Values of the Regression
dτ_{g} =
k_{1} (d H_{+}/H_{-}) + k_{2} for (i) Fixed Scale Height (S_{
a
}) and Variable Total Optical
Depth (Γ) and (ii) Fixed Total Optical Depth and Variable Scale
Heighta

Each regression was computed for the nine
points corresponding to the nine altitudes of Table 1 (i.e., 0–3
km). The atmospheric optical state parameters are also those of Table
1 except for the phase function that was
Henyey–Greenstein rather than haze L.
The slope k_{1} is equivalent to k_{1} ≅ H_{-}/[(∂ H_{+}/∂τ
_{
g
}) _{
h
,
S
a
,
ρ
}] and
H_{-}/[(∂
H_{+}/∂τ
_{g})_{h,Γ,ρ
}
] for (i) and (ii), respectively [i.e., the factor preceding
d H_{+}/H
_{-} in Eq.
(A9)]. k_{2} amounts to an indication of the departure from
constancy of the above partial derivative expressions with
altitude. r is the
correlation coefficient from the multialtitude (multi τ
_{g}) regression.

Table 4

Illustrative Values of the Regression
(∂ P/∂ρ)
_{
h, Γ
},
_{
S
}_{
a
} ≈ (1/dρ)d P
= (kτ
_{
g
} + 1)
a

Each regression was computed for the nine
points corresponding to the nine altitudes of Table
1 (i.e., 0 to 3 km) and for a change dν from
ν = 0.3 to 0.4. The atmospheric optical state parameters are also
those of Table 1 except for the phase function
that was Henyey–Greenstein rather than haze L and the Rayleigh optical
depth that was taken as 0.02 (813.9 nm) to yield a total optical depth of
0.02 + 0.33 = 0.35 (the second column of each set
shows the effect of a decrease in aerosol optical depth from 0.33 to 0.22 or
total optical depth from 0.35 to 0.24). r is the
correlation coefficient from the multialtitude (multi
τ_{g}) regression.

Tables (4)

Table 1

Nominal Atmospheric Optical Conditions for the
Test Simulationa

The ten measurement altitudes were fixed
in terms of an equal aerosol optical depth separation
(Δτ_{
a
} =
τ_{
a
}/8) except for the
3-km altitude that was always present, independent of the
Δτ_{
a
}
criterion.
Haze L phase function defined in Garcia
and Siewert.14

Table 2

Inversion Errors for the Atmosphere of Table 1 that
are Due to an Irradiance rms Noise Error of 1% and an Optical
Depth rms Noise Error of 0.01

〈Δτ_{
g〉}

0.06

0.12

0.16

0.32

Number of altitudes

9

5

4

3

〈δg^{2}〉^{1/2}

0.14

0.072

0.054

0.027

〈δω_{0}^{2}〉^{1/2}

0.12

0.059

0.044

0.022

Table 3

Illustrative Values of the Regression
dτ_{g} =
k_{1} (d H_{+}/H_{-}) + k_{2} for (i) Fixed Scale Height (S_{
a
}) and Variable Total Optical
Depth (Γ) and (ii) Fixed Total Optical Depth and Variable Scale
Heighta

Each regression was computed for the nine
points corresponding to the nine altitudes of Table 1 (i.e., 0–3
km). The atmospheric optical state parameters are also those of Table
1 except for the phase function that was
Henyey–Greenstein rather than haze L.
The slope k_{1} is equivalent to k_{1} ≅ H_{-}/[(∂ H_{+}/∂τ
_{
g
}) _{
h
,
S
a
,
ρ
}] and
H_{-}/[(∂
H_{+}/∂τ
_{g})_{h,Γ,ρ
}
] for (i) and (ii), respectively [i.e., the factor preceding
d H_{+}/H
_{-} in Eq.
(A9)]. k_{2} amounts to an indication of the departure from
constancy of the above partial derivative expressions with
altitude. r is the
correlation coefficient from the multialtitude (multi τ
_{g}) regression.

Table 4

Illustrative Values of the Regression
(∂ P/∂ρ)
_{
h, Γ
},
_{
S
}_{
a
} ≈ (1/dρ)d P
= (kτ
_{
g
} + 1)
a

Each regression was computed for the nine
points corresponding to the nine altitudes of Table
1 (i.e., 0 to 3 km) and for a change dν from
ν = 0.3 to 0.4. The atmospheric optical state parameters are also
those of Table 1 except for the phase function
that was Henyey–Greenstein rather than haze L and the Rayleigh optical
depth that was taken as 0.02 (813.9 nm) to yield a total optical depth of
0.02 + 0.33 = 0.35 (the second column of each set
shows the effect of a decrease in aerosol optical depth from 0.33 to 0.22 or
total optical depth from 0.35 to 0.24). r is the
correlation coefficient from the multialtitude (multi
τ_{g}) regression.