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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