In: Wagner W., Székely, B. (eds.): ISPRS TC VII Symposium - 100 Years ISPRS, Vienna, Austria, July 5-7, 2010, IAPRS, Voi. XXXVIII, Part 7B 
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Figure 4. Neural network structure used on ST modeling 
The activation function utilized was the logistic sigmoid and the 
number of training cycles was 600. 
On Figure 5 is presented the modeled ST values (maximum of 
54 °C, minimum of 19.1 °C and average of 39.18 °C) and the 
known ones (maximum of 54 °C, minimum of 25 °C and 
average of 37.39 °C) where is possible to verify a similar 
behavior between the two curves. In terms of discrepancy 
between the modules of ST values the model afforded an 
average value of 2.2 °C with a standard deviation around 1.4 °C. 
If we analyze the obtainment of ST values through processing 
thermal images associated with the Split Window algorithm, 
which its average error is 1.5 °C (Coll and Caselles, 1997), and 
if we compare with the results found on this research, is 
possible to ascertain that the method can be an efficient way to 
obtain the ST. A great advantage of this method is its capability 
to generate ST values based only on climatic and positional 
variables that have easy access. 
ST modeled by ANN X Known ST 
Figure 5. Graph of comparison between ST modeled by ANN 
and Known ST. 
Beyond the regression analysis was implemented a test of 
hypothesis to verify if the proposed model is statistically equal 
to the one taken as real. 
For a significance level of 5%, through the t-student test was 
evaluated the equality from the two averages (Ml e M2).The 
tested hypothesis was HO: Ml = M2 e HI: Ml f M2. In this 
case, if Prob > t was less than 0.05 the hypothesis would be 
rejected and then Ml would be different from M2. Table 1 
shows the results from accomplished statistical test. 
Table 1. Statistic indexes between ST values obtained by ANN 
and taken as real (Ml= real values and M2= simulated values) 
M N Average Standard 
deviation 
Variance 
t 
Degree of 
freedom 
Prob >(i) 
1 60 37.39 8.6S 
2 60 39.18 8.66 
Unequal 
Equal 
1.1276 
1.1276 
118.0 
118.0 
0.261S 
0.2618 
For Ho: variances are equals. F= 1.00 
Prob > F= 0.9898 
Level of significance = 5% 
Ho : Mi = M2 H,:M 1? tM 2 
Analyzing Table 1 and 
comparing 
; the 
values of real and 
modeled temperature with application of t test for independent 
samples was found that the averages are statistically equals. 
Therefore the modeling by ANN was capable to calculate ST 
values that driven to an average value equal to the mean of 
values measured in field with a level of significance of 5%. 
4. CONCLUSIONS 
This research proposed a method to extrapolate ST values for 
the Rio dos Sinos Hydrographic Basin/RS, based on an ANN 
that was trained in a supervised way through a NOAA thermal 
satellite image from 6/12/2003, using on it the split window 
algorithm. The involved variables were positional (UTM 
coordinates and altitude) and climatic information (temperature 
and air relative humidity). The model was tested through an 
experiment realized on 3/18/2008 inside the Vale do Rio dos 
Sinos University campus. Seeing the average error (2.2 °C) and 
the maximum error (5.9 °C), the conclusion that the ANN is 
suitable for simulation will depend on the application of itself. 
If the associated errors for each observation didn’t were relevant 
for practice finalities, then could be concluded that network 
rightly simulates the temperature values. 
New experiments have been realized in direction of better 
evaluations for ANN efficiency on the process to determinate 
ST values based on variables of easy obtainment. 
On regression analysis (Figure 6) was verified a strong 
correlation between modeled and known ST values (R 2 = 0.948) 
given efficiency evidences of ST extrapolation process on 
proposed ANN. 
Figure 6. Linear regression between ST values modeled by 
ANN and Known 
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