Geology Reference
In-Depth Information
7.5.2 Entropy Theory for Data Analysis in Evaporation
Modeling
The study applied entropy theory to analyze the data used for evaporation mod-
eling. The analysis was performed with the help of modeling attributes such as
transinformation, marginal entropy, joint entropy, and conditional entropy to ana-
lyze the in
final data model. The analysis per-
formed on the daily meteorological and evaporation data from the Chahnimeh
reservoirs region and the outcome of the analysis on individual inputs is shown in
Table
7.6
, which shows different scenarios and achievable information from each
data input considered in this case study.
The analysis shows (scenario 1
uence of each model input on the
4) that the transinformation value is higher for
the daily saturation vapor pressure (Ed) followed by air temperature (T), daily wind
speed (W), and relative humidity (RH). The entropy test identi
-
es relative humidity
as the least signi
cant input among the available four inputs in the study region.
Thus, the relative importance of inputs suggested by entropy theory is
Ed > T>W > RH. The Gamma Test has suggested in the previous section that the
input combinations [W, RH, Ed], [W, T, Ed], and [W, T, RH, Ed] are better when
considering different aspects such as Gamma static, error, and complexity. To check
the credibility of that suggestion, and the best one among these three, we have
performed entropy analysis (scenario 5
7) to see the corresponding transinforma-
tion values for input combination [W, RH, Ed], [W, T, Ed], and [W, T, RH, Ed]. It
is interesting to note that the results obtained by entropy analysis for the combi-
nation [W, T, Ed] has shown better transinformation value than for [W, RH, Ed]
and [W, T, RH, Ed]. The analysis has found that in [W, RH, Ed] and [W, T, RH,
Ed] input combinations, the transinformation values are very close to 1.23, whereas
the [W, T, Ed] combination has a better transinformation value of 1.115. Thus the
-
Table 7.6 Entropy analysis results on the daily evaporation data from the Chahnimeh reservoirs
region
Scenario
Inputs
considered
Mask
Joint
entropy
Marginal
entropy
Trans-
information
Conditional
entropy
1
W
1000
13.8312
9.3649
0.5599
5.0262
2
T
0100
9.1995
5.1028
0.9295
5.0262
3
RH
0010
10.5309
5.823
0.3184
5.0263
4
Ed
0001
6.3738
2.3255
0.9779
5.0262
5
W, T, RH,
Ed
1111
12.263
8.123
1.2352
5.0262
6 W, RH, Ed 1011
11.895 7.2365 1.2281 5.0262
7 W, T, Ed 1101
10.259 7.1521 1.1150 5.0262
Mask indicates different combinations of the input effects (inclusion and exclusion indicated by 1
or 0 in the mask). From left to right: daily wind speed (W), daily air temperature (T), relative
humidity (RH), and daily saturation vapor pressure de
cit (Ed)
