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Fig. 7.24 Variation of transinformation with increase in unique data points for the evaporation
data corresponding to three GT suggested input sets
entropy analysis helped to identify the best model [W, T, Ed] out of the three
suggested by the GT in evaporation modelling precisely. We have performed an
analysis to identify the variation of transinformation with increase data points to
assess the training data length required for the modeling. For this purpose, we have
used three GT suggested inputs to see their transinformation variation with the
increase in unique data points. The analysis result are shown in Fig. 7.24 .
Figure 7.24 shows that the transinformation values increase with increase of data
points throughout the data length. The entropy-based analysis failed to identify an
optimum training data length within the available 4,019 data points in this case
study. However, one could see in Fig. 7.24 that, after data points 3,465, the increase
in entropy information is at a decreasing rate. The Gamma Test suggested that the
optimum training data length was 2,327 for the [W, T, Ed] input combination. Even
though both suggestions are a bit close, we cannot
rm the success of
entropy theory in this case, as the information values are increasing, even after the
3465 (at a decreasing rate). The variation of other attributes such as marginal
entropy, conditional entropy, and joint entropy with the increase in unique data
points is shown in Fig. 7.25 . The
firmly con
figure shows that the higher value information is
associated with joint entropy followed by marginal and conditional entropy values.
These three curves in Fig. 7.25 show the same trend throughout the unique data
points used for evaporation modeling.
Entropy theory failed to identify the training data length in this case study,
whereas the entropy analysis results were perfectly matching with the
finding of GT
in previous two case studies in Chap. 6 . This highlights the need for further
exploration of this approach, using evaporation/evapotranspiration data from other
catchments and other data frequency.
 
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