In: Wagner W., Székely, B. (eds.): ISPRS TC VII Symposium - 100 Years ISPRS, Vienna, Austria, July 5-7, 2010, IAPRS, Vol. XXXVIII, Part 7B 
from a meteorological station located inside the test area. The 
test was made inside Vale do Rio dos Sinos (UNISINOS) 
campus situated on Sao Leopoldo/RS city. The sample points 
for test were located on places with vegetation, concrete and 
asphalt paving. 
Each collected point had the necessary information to be 
inserted in the trained neural model (UTM coordinates, altitude, 
temperature and averages of air relative humidity). The model 
supplied for each point a ST value that was compared with the 
value obtained in field by laser thermometer. 
The statistical analysis used on research results presentation 
were based on a comparison between ST values modeled 
through ANN and ST values considered true by obtainment by a 
laser thermometer. Were used the statistical t-student test and 
coefficient of determination (R 2 ) analysis with linear regression. 
Being x the size of certain elements attribute from an A 
population (ST modeled by ANN); 
Being y the size of the same elements attribute from a B 
population (ST obtained by laser thermometer); 
Being x and y ordinarily distributed with unknown variances; 
Being the hypothesis: px = py which px = average of x and py 
= average of y. 
For testing the hypothesis of averages equality from the two 
populations was utilized the t test, but for that was necessary to 
initially test if the two populations presented equal variances 
using the F test from Fischer: 
F = SQD * (09) 
SQD y 
2 S Q D z (10) 
* ■(»,-!) 
S> V^) (11) 
F ( 12 > 
calculated 2 
where: SQDx and SQDy correspond, respectively, to the 
sums of square deviations from x and y; 
and correspond, respectively, to sample variances 
from x and y; 
nx and ny correspond, respectively, to the number of 
variables from x and y. 
The tested hypothesis (HO) was that the population variance 
from x is equal to the population variance from y. If Prob > F is 
less than 5% then HO is accepted. If Prob > F is bigger than 5% 
then HO is refused. If the population variances were statistically 
equals, then a common variance is calculated (): 
2 {SQD x +SQD y ) 
Ik - IM«, -i)j 
(13) 
[(*M 
,-1))] 
r 
(14) 
Afterward was tested the HO for population average equality 
using the t random variable, defined by: 
-M y 
y/v-fax-My) 
(15) 
Being: 
v-ta -A y ) =v CO +v W=—+- 
»x "j 
where: V correspond to the average variance. 
2 2 2 
Accepting S=S -S there are: 
(16) 
n. 
f 1 1' 
1 
\ n * n yj 
t = 
Mx-My 
2 
il 
n 
s c • 
— + - 
”y) 
In degrees of freedom (ri) = (Yl x + Yl y — 2) 
In case of different variances there are: 
M x -M v 
t = 
, 2 si 
+ — 
72 n 
(17) 
(18) 
(19) 
(20) 
The degree of freedom is calculated with the following 
equation: 
n = 
n yj 
(¿1 
2 
K n y J 
(21) 
n —1 n-1 
3. RESULTS AND DISCUSSIONS 
The ANN that presented the best performance was composed 
with an input layer (5 variables), an intermediate layer (with 4 
neurons) and an output layer (with one neuron), as show on 
Figure 4. The fact that the selected network, with the best 
performance, has only one intermediate layer, is in accord with 
the results found by Kumar et al. (2002) and Zanetti et al. 
(2008), because these authors have modeled the 
évapotranspiration and concluded that an ANN with only one 
intermediate layer was sufficient to represent a nonlinear 
relation between the climatic elements and the modeled 
variable. 
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4 
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