328 
0 IO 20 30 40 50 60 
MSS 5 MSS 5 
BAND-TO-BAND DISPERSION 
Figure 4. Structure of MSS data for Grootvlei test 
site 
ponents contain very little information (0.03% and 
0.005% of the variance). Thus, the use of combina 
tions of MSS 5 and MSS 7 as vegetation indices utiliz 
es much of the information content of the data. The 
vegetation ratio (VI) and the normalized vegetation 
index NVI defined as 
MSS 7 MSS 7 - MSS 5 
VI = NVI = 
MSS 5 MSS 7 + MSS 5 
The Gram-Schmidt theorem states: 
If A = {X}, X2 ... x s ) is any linearly indepen 
dent set whatever, there exists an orthonormal set 
X = (yi, y2 ••• y s ) such that 
k 
yk = I a ik x i* (Neiring, 1963) 
i=l 
The coefficients of the matrix T were calculated by 
means of the Gram-Schmidt process (Nering, 1963) 
using the averages of four data clusters representa 
tive of dark and light soil, green vegetation and 
senescent vegetation. 
3.3.4. Extraction of field sample means from satel 
lite data 
The mean value for each field sample of standardized 
MSS 4, 5, 6, 7, VI, NVI, SBI, GVI was extracted for 
each satellite overpass. These mean values together 
with the ground reference data set were stored for 
statistical analysis. 
4 RESULTS 
Two types of data were processed in the present 
study, the ground reference data and the MSS data. 
4.1 The analysis of the ground reference data 
were selected (Jordan, 1969; Pearson, 1972; Colwell, 
1974; Rouse et al., 1973; Maxwell, 1976). These 
mathematical combinations of the bands of MSS data 
partially compensate for the inherent error components 
in the LANDSAT data. The effects of external factors 
such as haze, changing illumination conditions, 
viewing aspect, surface slope and atmospheric effects 
over a LANDSAT scene are thought to be reduced by the 
use of vegetation indices. However, since some of the 
above variables are wavelength-dependent, the effects 
of these external factors cannot be eliminated by 
means of a vegetation index alone. 
Despite the high correlation between the signals, 
differences do exist. The range of MSS 4, which is 
centred on the cellulose reflectance peak around 
0.55 ym, extends significantly into the chlorophyll 
absorption region which dominates the reflectance of 
the canopy in the range of MSS 5. Thus differences 
between signals in MSS 4 and MSS 5 are particularly 
significant for vegetative canopies at the yellowing 
stage. 
In view of the above, a vegetation index using data 
in all four spectral bands was investigated. Kauth 
and Thomas (1976) exploited the structure of LANDSAT 
MSS data and proposed the Tasseled cap transformation 
of the four-dimensional LANDSAT MSS data space into 
four indices which they called Brightness (BR), Green 
ness (GR), Yellowness (Y) and Non-such (NS). The 
Tasseled cap transformation is an orthogonal rotation 
of the original LANDSAT data space into four new axes. 
(i) Along the line of soils; called the 
Brightness axis 
(ii) perpendicular to the Brightness axis and 
passing through the peak of Greenness; 
called the Greenness axis 
(iii) perpendicular to Brightness and Greenness 
axis, called the Yellowness axis 
(iv) orthogonal to (i), (ii) and (iii) above; 
called the Non-such axis. 
Thus 
Brightness (SBI) 
MSS 4 
Greenness (GVI) 
= T 
MSS 5 
Yellowness (YVI) 
MSS 6 
Non-such (NS) 
MSS 7 
Planting dates for six crops within nine test sites 
were extracted (see Table 2). 
Figures 5a, b, c illustrate composite temporal 
plots of the growth stages of maize, sorghum and sun 
flower for the WRS 182-79 scene. The planting date 
varies considerably, with resulting variability in 
growth stage. Growth stage is also affected by local 
climatic conditions and cultural practices. 
4.2 The processing of the MSS data 
4.2.1 Standardization of digital counts of MSS data 
As noted above, it was necessary to compensate for 
station-to-station differences in digital count and 
for satellite-to-satellite calibration. 
4.2.1.1 Compensation station-to-station difference 
Absolute radiances R can be calculated from EROS 
digital values y using a linear relationship: 
- Rn 
) • Y + «ir 
(1) 
Similarly CCRS digital values y' can be converted 
to absolute radiances R by means of 
D I R I 
n r 11 max n min ^ , Dl (0 \ 
. R = l J * y' + R min < 2 > 
V 
where Rmax* Rmin> R'max» Rmin -*- n m W/cm Sr. are given 
in Table 4 (Anon, 1976) and Strome et al., 
1975) and 
V and V' are the ranges of digital values of 
EROS and CCRS respectively. 
From (1) and (2) 
y' = A«y + B 
where A 
V (R max - R min) 
— and B 
V (R'max^'min) 
V(Rmin - R'min) 
(R 1 max-R'min)