Table 5 : Particle sizes actual and predicted 
[.No. Soil number 
Location 
Particle size 
d 10 
d 20 
d 30 
d 40 
d 50 
d 60 
d 70 
Cl 
00 
O 
d 90 
Actual 
0.26 
0.42 
0.62 
0.95 
1.45 
2.15 
3.80 
6.00 
9.00 
1 20 
Neral 
Predicted 
0.50 
0.89 
1.30 
1.92 
2.68 
3.59 
4.88 
7.13 
9.28 
Actual 
0.20 
0.40 
0.82 
1.40 
2.30 
4.10 
5.20 
6.00 
7.20 
2 21 
Pondichéry 
Predicted 
0.48 
0.87 
1.28 
1.96 
2.79 
3.94 
5.46 
7.39 
9.93 
Actual 
0.40 
0.90 
1.20 
1.60 
2.20 
3.20 
5.00 
6.40 
9.00 
3 22 
Ozhar 
Predicted 
0.74 
1.43 
2.12 
3.23 
4.48 
5.90 
7.39 
9.40 
10.99 
Actual 
0.54 
0.75 
0.95 
1.20 
1.45 
1.85 
2.36 
3.40 
5.20 
4 23 
Thagaram 
Predicted 
0.47 
0.93 
1.36 
1.90 
2.59 
3.52 
4.37 
5.25 
6.83 
Actual 
0.98 
1.35 
1.80 
2.40 
3.30 
4.60 
5.70 
6.80 
10.50 
5 24 
Rihand Dam 
Predicted 
0.41 
0.73 
1.06 
1.50 
2.09 
2.86 
3.95 
5.85 
8.05 
Actual 
0.24 
0.34 
0.54 
0.80 
1.15 
2.00 
3.80 
5.70 
7.00 
6 25 
Neyvelli 
Predicted 
0.53 
1.08 
1.59 
2.38 
3.31 
4.35 
5.67 
7.88 
9.86 
All diameters are in mm 
THANE 
BOMBAY 
BYAHATTI 
MALAPRABHA 
POWAI 
MADAPAKKAM 
RED HILLS 
JAMSHEDPUR 
PALAYAM KOTTAI 
CAPE COMARINE 
PATTUKOTTAI 
MADRAS 
NHAVA SHEVA 
PONNERY 
NASIK 
VALLNADU 
NHAVA SHEVA 
VASHI BOMBAY 
MALAPRABHA 
NERAL 
PONDICHERY 
OZHAR 
THAGARAM 
RIHAND DAM 
NEYVELI 
Figure l. Soil sample locations. 
4 TEST OF HYPOTHESES AND ANALYSIS OF RESULTS 
The simple linear model for five soils based on the 
regression of diameter of particles on the third Princi 
pal Component has a correlation coefficient of 0.66 
only. The results show that the model can be used 
to explain 44 percent of the vairations in grain sizes 
with the help of the third Principal Components. 
The bi-linear model for five soils having independ 
ent variables as PPC^ and SPC^ has an average corre 
lation coefficient of ^0.94 and There is a considerable 
reduction in the standard error of estimate. Results 
of the model based on non-linear optimization technique 
show that the model has a correlation coefficient 
of 1.0 for all grain sizes from d^ to d^ • However, 
the test of hypothesis for slope 1 coefficient (m = 0) 
cannot be rejected as the sample size is small. 
Results of the regression analysis of the model const 
ructed for 14 soil samples using optimization technique 
show that the magnitude of the standard error of 
estimate is much lower than the standard deviation 
of the dependent variables. This suggests that there 
is a considerable improvement in the use of the regre 
ssion model (Parson 77). Test of hypothesis for the 
slope coefficient ( m= 0 ) shows that the null hypothesis 
is rejected in all cases at a critical probability level 
of less than 1 percent. That means, the confidence 
level for M ± 0 is more than 99 percent. This suggests 
that the model is highly reliable in a statistical sense 
and proves the existence of a definite linear relationship 
between the grain sizes and the transformed reflectance 
values. 
5 CONCLUSIONS 
1. A simple linear model based on optimization tech 
niques has been suggested for predicting the grain 
sizes of soils from their reflectance values in the 
visible and near infra-red regions. This model is statis 
tically highly reliable. 
2 The laboratory studies confirm the usefulness 
of the techniques suggested herein. However, further 
studies are required for adapting this technique for 
Landsat data.