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In order to correct for the most significant aircraft motion
effect, the roll was estimated using the navigation data to
calculate lateral pixel shifts for each line. These shifts were
then applied to the entire image cube on a line by line basis.
In the next processing stage, surface reflectances were
computed from calibrated at-sensor radiance data,
compensating for atmospheric absorption and scattering
effects. The procedure is based on a look-up table (LUT)
approach with tunable breakpoints as described in Staenz and
Williams (1997), to reduce significantly the number of
radiative transfer (RT) code runs. MODTRAN3 was used in
forward mode to generate the radiance LUTs, one of each for
a 5% and 60% reflectance. These LUTs were produced for
five pixel locations equally spaced across the swath, including
nadir and swath edges, for a range of water vapour contents,
and for single values of aerosol optical depth (horizontal
visibility) and terrain elevation. The specification of these
parameters and others required for input into the
MODTRANS3 RT code are listed in Table 1. For the retrieval
of the surface reflectance from the Altona cube, the LUT
radiances were adjusted for the ground target's (pixel)
position in the swath and the water vapour content using an n-
dimensional bilinear interpolation (Press et al., 1992). For
this purpose, the water vapour content was estimated on a per
pixel-basis from the image cube with an iterative curve fitting
technique (Staenz et al., 1997). For the Birtle data cube, the
LUTs were only interpolated for the pixel position since a
single water vapour amount was used for the entire cube. The
surface reflectance p was then calculated for each pixel as
follows:
L-L
a
" AsBsS(L-L)' (n
where L is the at-sensor radiance provided by the image cube,
L, is the radiance backscattered by the atmosphere, S is the
spherical albedo of the atmosphere, and A and B are
coefficients that depend on geometric and atmospheric
conditions. The unknowns A, B, S, and L, were calculated
from the equations
Pi
L tL 554 514,2 2
Er iro els Q)
and
P,
L.- tL dol 3
pas ES a (3)
where Lei is the at-sensor radiance reflected by the target and
Lpi is the at-sensor radiance scattered into the path by the
surrounding targets, respectively. These equations can be
solved on a per pixel basis for each set of (p; , Lois and Li)
obtained from the LUTs by interpolation for the different
geometric and atmospheric conditions. With i- 1 and 2 (P ; 7
3%, p, = 60%), this yields a system of four equations with
four unknowns.
In a last step, band-to-band errors due to atmospheric
modelling and calibration effects in the retrieved surface
reflectance spectra were removed using a Gaussian smoothing
International Archives of Photogrammetry and Remote Sensing. Vol. XXXII, Part 7, Budapest, 1998
with a 80 nm window between 820 nm and 1000 nm. A
resulting reflectance spectrum of canola is shown in
comparison with non-smoothed data in Figure 2.
Table 1
Input Parameters for MODTRAN3 Code Runs
Test Site Altona Birtle
Atmospheric model Mid-latitude Mid-latitude
summer summer
Aerosol model Continental Continental
Date of overflight July 25, 1996 | July 25, 1996
Solar zenith angle 31.39 49.7?
Solar azimuth angle 155.9? 109.5?
Sensor zenith angle Variable Variable
Sensor azimuth angle Variable Variable
Terrain elevation above 0.250 km. 0.540 km
sea level
Sensor altitude above 2.745 km 3.035 km
sea level
Water vapour content Variable 2.75 g/cm’
Ozone column as per model as per model
CO» mixing ratio as per model as per model
Horizontal visibility 40 km 30 km
4.0 LAI COMPUTATION
The LAI can be expressed as follows (Chen et al., 1991):
LAI,
LAI= ——, (4)
Q
where LAI, is the effective LAI and Q is the clumping index.
Q varies between 0 and 1 for clumped canopies, but can be
larger than 1 for regularly distributed foliage. For most row
crops such as beans, Q is less than 1. For crops with more
random plant distribution such as canola, Q approximates 1.
Since Q is generally unknown, only LAI, can be calculated
according to the following formula (Ross, 1981):
LAL 7 352 (-mp),, (5)
where P is the probability of a view line or a beam of radiation
at an incident angle a passing through a horizontally uniform
plant canopy with random leaf angular and spatial distribution
and G is the mean projection coefficient of unit foliage area
on a plane perpendicular to a.
In order to estimate LAI, from hyperspectral data, G can be
set to 0.5 for plants with leaf angle randomly distributed such
as for agricultural crops (Norman, 1979). The incident angle
a corresponds to the sensor viewing zenith angle. In our case,
a was set to 0° (nadir looking), which was appropriate for the
viewing angles under consideration (<15°). P represents the
gap fraction, which was determined by spectral unmixing as
follows:
P=1-f, (6)
where f_ is the fraction of the crop endmember. LAI, can
then be expressed from hyperspectral data according to
equations (5) and (6) by
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