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Title
Technical Commission VII

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International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences, Volume XXXIX-B7, 2012
XXII ISPRS Congress, 25 August — 01 September 2012, Melbourne, Australia
2.2.3 Modelling of Atmospheric Quantities: Now 9, can be
parametrized as a function of the observed atmospheric
reflectance à, the view zenith angle 6,, the sun zenith angle 6;,
the relative azimuth angle ¢ and a set of fixed parameters
al...a4.
Ô, = 0,(0,0, ---a4,0,,0,,P) (5)
Since 6, is a nadir looking quantity there is no explicit azimuth
angle dependence. However, the parametrization has to
compensate the azimuth angle dependence of the observed
atmospheric reflectance à at view zenith angle 0,. The azimuth
angle dependence of à is caused by the path radiance Lo which
is defined as the total radiance at ground reflectance 0. The total
radiance is shown for several ground reflectances in Figure 3
for a visibility of 3 km. For a satellite view the variation of Lo
can be modelled with a cos(2*) dependence since it is caused
mostly by Rayleigh scattering. For an airborne view at 1 km
above ground a modelling with a function cos(1.4*@) is more
adequate, since the predominant Mie scattering has a strong
backscattering characteristic.
Taowns Tup» and s do not have an azimuth angle dependence.










5.60E-04
5.40E-04
y 520E-04 *
“ = L(n=8)
e IS j A =
E 5.00E-04 —%——— paf a
un p=0.
t v pare / - = ‘cos(20) (p=0)
9 480E-04 /
2 A f — -tos(29) (p-0.2)
& 460E-04 SC É en
SA di
4 ADE-04 We
A
4.20E-04 1 |
0 50. 100150
Az imuth Angle [*]
2.90E-04
2.70E-04
= —L (p=0)
N =
> 2.50E-04 — | (20.2
> L (p=04)
2308-04 = = 'cos(1.49) (p=0)
o
S === «pOS(1.49) (p-0.2)
3 9 10E-04 = 1.90E-04
1.70E-04

0 50 100 150
Azimuth Angle [']
Figure 3. Variation of the at-sensor radiance as a function of
the view azimuth angle for visibility 3 km and a sensor
elevation of 100 km (upper image) and 1 km (lower image). A
different ground reflectance p only adds a constant radiance
offset. The variation can be modelled with a cosine function.
The atmospheric reflectance 6, is the scaling factor for the other
atmospheric quantities Ly, Tgown, Typ, and s. They are calculated
as a function of the observed atmospheric reflectance 3, the
view zenith angle 6,, the sun zenith angle 6;, the ground level H,
the flight altitude over ground h and a set of fixed parameters
(b;...b;, c,...cs, d;...d,, e;...eg). The parameters for the quantities
in eqns (5)-(9) can be obtained using a multilinear regression
from a sufficient number of model runs with all combinations of
the input variables.
L, = L,(b--5,,0,,0,,0,0,,h,H) (6)
T mm T. miei c6, OS fi EDS (7)
I, =T,(d\-d;.6,,0,) (8)
$zs(e,--:e,, 6, ,h, H) (9)
2.2.4 Broadband Sensors: The above calculation is strictly
valid only for a single wavelength and the outputs being
spectral densities. The evaluation of eqn (2) gives the
contribution to the reflectance at this wavelength. For a
broadband sensor the contributions of a spectral density x have
to be integrated over the spectral response curve of the sensor
using eqn (10) to give the band-averaged quantity.
[x(A)R()aA
ce 10
de Eire a
This would require to parametrize the quantities in eqns (5)-(9)
for each wavelength separately which is not practical. So the
parametrization is done for the band averaged quantities in eqns
(5)-(9) and the reflectance is then calculated from the band-
averaged quantities. (Richter, 2000) has found that the errors in
the VISNIR range (400-1000 nm) are below 2% and therefore
below the calibration accuracy.
In the special case of a narrowband sensor with spectral
sensitivities away from the gaseous absorption bands (like e.g.
the ADS) the atmospheric quantities Lo, Tgown, Tup, and s change
moderately with wavelength. Then the radiative transfer
calculations can be made by using the effective bandwidth of
the sensor and simply averaging the spectral quantities over the
effective bandwidth without using the spectral response
function as a weight.
2.2.5 Reflectance Calibration for Images: Eqns (2) and (5)-
(9) allow a fast image calibration to ground reflectance without
any iteration. Since multiple scattering is a second order process
p can be assumed constant and an average value of 0.15 for a
midlatitude landscape is used.
2.3 Bidirectional Reflectance
2.3.1 Sampling and Model Inversion: As mentioned in
(Beisl et al, 2004) the bidirectional reflectance process is
influenced mainly by microscopic shadow casting and volume
scattering processes with unknown influencing parameters. So
the correction process also requires a model inversion.
As suggested by the viewing geometry shown in sec. 2.1 the
sampling has to be done in image columns for the line scan