295
different optimization methods for the same data set: no real trend can be observed for the accuracy; on the
other hand, there are great disparities in the computation time. MQ is on average the fastest method, at least 3
times faster than QN, twice faster than SP, while GQ takes far more computation time. These results are
consistent with simulations of Renders et al. (1992) mainly performed on "clean" synthetic data.
In conclusion, the choice of an optimization method may depend on the priority given to the solution
(accuracy or computation time). Concerning the accuracy, QN and GQ are the most outstanding when the
number of data is much greater than the number of parameters, SP when only few measurements are available.
Concerning the computation time, MQ emerges as the winner of this comparison for almost all the cases.
22. Airborne Data
In order to test the applicability of such optimization methods on real remote sensing data, measurements
acquired in Flevoland (The Netherlands) during the 1991 Mac Europe Campaign have been investigated.
Several CAESAR images were recorded on three dates during the growing season (July 4 th , 23 rd , and August
29 th 1991) for several crops but. due to the perfect atmospheric conditions observed on July 4 th , only data
acquired at that time have been analysed. We selected fives differents crops (peas, sugar beet, wheat, onions,
and potato) for which radiometric and ground measurements were available (Bilker et al„ 1992a, 1992b). To
create angular variability on the reflectance, two images of the same target were obtained in down-looking
mode (0o=O) and in forward-looking mode (0o=52°). In fact, this latter angle is a nominal value only valid for
the near infrared band; the viewing angles in the green and red are respectively 45° and 59° but, due to the low
reflectance levels in these two bands and to the non-significant variation of the reflectance induced by a 7°
variation of 0o outside the hot spot region, we used the nominal value. At flight time, the solar zenith angle 0s
was 36.1° and the relative azimuth angle qpo (angle between solar plane and forward-looking plane) estimated
at 7.4°. The calibration of CAESAR was performed by using reference targets in the field (Bilker et al„ 1992b).
Since plots were not too distant, we assigned to them the same soil spectral reflectance (Figure 1) measured in
the field during the experiment. Although soil roughness may induce great variations of reflectance from one
measurement configuration to another, we assumed that soil reflectance was lambertian.
As for the theoretical study, inversions were performed on each surface using QN, MQ, SP, and QG.
Let us introduce the root mean square error of the fit (RMSE) defined as (A 2 /n)^ where n is the number of data
points (n=6): RMSE gives an information on how well the calculated canopy reflectances (using the model and
the estimated parameters values) compare with the corresponding measured values. The fitted parameters, the
computation time (Cntr), and RMSE's are presented in Table 3.
surface
method
N
Cab
LAI
01
Si
Cntr
RMSE
peas
QN
1.00
51.7
1.03
43.5
0.05
135
0.0081
LAI-1
MQ
1.41
36.4
0.80
39.3
0.05
177
0.0184
SP
1.00
51.7
1.03
43.6
0.05
350
0.0081
GQ
1.00
51.7
1.03
43.5
0.05
948
0.0081
sugar
QN
1.00
59.5
2.84
42.8
0.05
174
0.0116
beet
MQ
2.50
35.1
1.59
20.7
0.05
243
0.0253
LAI-2
SP
1.02
59.1
2.81
42.5
0.05
489
0.0116
GQ
1.00
59.5
2.84
42.9
0.05
951
0.0116
wheat
QN
2.50
79.2
4.93
61.3
0.05
446
0.0069
LAI-2-5
MQ
2.50
74.3
6.06
62.6
0.05
116
0.0114
SP
2.48
79.5
4.80
61.0
0.05
260
0.0070
GQ
2.50
79.2
4.93
61.3
0.05
1041
0.0069
onions
QN
1.00
58.8
2.64
45.7
0.05
156
0.0126
LAI?
MQ
1.90
38.8
2.16
46.9
0.05
122
0.0188
SP
1.00
58.8
2.64
45.7
0.05
441
0.0126
GQ
1.00
58.8
2.64
45.7
0.05
938
0.0126
potato
QN
1.77
73.5
10.0
39.6
0.07
302
0.0129
LAI>5
MQ
1.86
62.8
9.94
30.9
0.05
97
0.0148
SP
1.60
74.6
8.45
41.7
0.09
452
0.0130
GQ
1.77
73.5
10.0
39.6
0.07
1108
0.0126
Table 3. Inversion of the PROSFECT+SAIL model on CAESAR data.
