f surface 
h yellow 
wn to black 
yellow-brown 
brown-black 
m to brown 
iwn to black 
in to brown 
I black-brown 
) yellow-brown 
iwn to black 
i yellow-brown 
I brown-black 
>wn to black 
) yellow-brown 
\NALYSIS 
md to analyse 
rmatted 
O I960 
X 1981 
figure 3. Solar elevation of LANDSAT MSS WRS 182-79 
as a function of data. 
registered visually to the field boundaries image. An 
accuracy of ±1 pixel can be expected by this method. 
3.3 Standardization of satellite data 
The extraction of meaningful quantitative crop charac 
teristics from MSS data collected by LANDSAT sensors 
requires the application of correction and standardi 
zation procedures. These procedures fall into three 
categories, namely 
• calibration to standard conditions 
• corrections for external effects 
• reduction of the data by transformation. 
Table 3. Coefficients for satellite-to-satellite 
calibration (Rice et al., 1983) 
A 
B 
LANDSAT 2 
1.0 
0 
before 
1.0 
0 
16 July 1975 
1.0 
0 
1.0 
0 
LANDSAT 2 
1.275 
-1.445 
after 
1.141 
-2.712 
16 July 1975 
1.098 
-2.950 
0.470 
0.446 
LANDSAT 3 
1.1371 
0 
any 
1.1725 
0 
date 
1.2470 
0 
1.1260 
0 
3.3.2 Normalization of the data to a fixed sun angle 
The LANDSAT sensors have the capability of collecting 
imagery over broad areas with short acquisition data 
times. Consequently, to a good approximation, the 
data for each overpass on flat terrain are obtained 
under a constant, normal sensor viewing angle and 
constant solar illumination angle. This solar illu 
mination angle has a seasonal variation which may be 
normalized to a first approximation by considering 
the following condition: If the surface behaves 
according to Lambert's Laws of Illumination (Colwell, 
1984), then the radiance in the simplified special 
case as defined above is given by 
d 
fined 
from satellite 
ach test site 
see Table 2). 
is of display- 
wth stages for 
'9 in 1981 (in 
3 
329 
329-3 
39 days 
test site at 
jred in raster 
onitored field 
lata sets were 
3.3.1 Recalibration of the data to a standard LANDSAT 
count 
Due to differences in the radiometric processing 
carried out on MSS products produced by the EROS Data 
Center and SRSC a conversion was required. 
In order to calibrate SRSC data to EROS digital 
count, the relationship between the digital values of 
each pixel and the scene radiance observed by the 
satellite was determined for both receiving stations 
and compared (see Table 4). The linear transformation 
y' = A»y + B 
was derived and used to calibrate SRSC data to the 
EROS LANDSAT 2 count, where 
y is the vector representing the MSS data in 
SRSC defined digital count 
y' is the vector representing MSS data recali 
brated to EROS defined digital count, 
and 
A and B are given in Table 5. 
Furthermore, satellite-to-satellite calibration is 
required for the effective utilization of data from 
two satellites. It is conventional to use EROS LAND 
SAT 2 before 16 July 1975 as the standard reference 
and recalibrate other data to this standard. Data 
were recalibrated to the standard reference (EROS 
LANDSAT 2 before 16 July 1975) by means of a further 
linear transformation defined by 
y" = C*y' + D 
where y' is defined above 
y" is the vector representing MSS data recali 
brated to LANDSAT 2 MSS data before 16 July 
1975 defined in terms of EROS digital count. 
The coefficients of the linear transformation C and 
D as prepared by Parris and Rice (Rice et al., 1983) 
were used (see Table 3). 
L(\,0) = Lcos9 
for a wavelength X and effective solar incidence 
angle 9. 
Each band of the MSS may be normalized by 
cosa 
y II I — ______ y" 
COS0 
where y"* and y" are the vectors representing the 
MSS data before and after normalization 
0 is the solar zenith angle at the time of 
data acquisition and 
a is a constant angle (39 ° being accepted by 
US investigators as the standard). 
The solar elevation angles were extracted from the 
ancillary data on each of the LANDSAT data sets. The 
temporal variations of the solar elevation angle for 
the WRS 182-79 for the 1980-81 season are displayed 
in Fig. 3. The elevation angle varies between 54 ° 
in midsummer to 24 ° in midwinter. 
3.3.3 Reduction of the data by transformation 
A preliminary examination of the structure of MSS 
data by means of scatter plots discloses that there 
is a high degree of correlation between data recorded 
in the visible channels, MSS 4 and MSS 5, and between 
the data recorded in the two infrared bands MSS 6 and 
MSS 7. Figure 4 illustrates these correlations and 
the inherent redundancies in the MSS data. It also 
suggests that the dimensionality of the MSS data can 
be reduced. Principal component analysis (PCA) is 
the standard statistical technique used to determine 
the dimensionality of the point distribution in a 
multi-dimensional space. A PCA on the MSS data for a 
typical test site reveals that the first component 
(PCI) accounts for the majority of the scene variance 
(98.7%), and the second component (PC2) accounts for 
1.27% of the total variance. The remaining two com-