Geology Reference
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Fig. 6.9 Variation of gamma value corresponding to different input combinations for different
data intervals
best combination for different data time intervals (15, 30, 60 and 120 min) as [4, 4],
[3, 3], [4, 4] and [4, 4] while the corresponding
findings by the Gamma Test are
[4, 4], [2, 2], [3, 3] [4, 3]. Although there are differences in the identi
ed combi-
nations, it is interesting to note that both techniques found the smallest number of
input vectors for 30 min data sets. The variation of the Gamma Static value for
different input combinations is shown in Fig.
6.9
. This figure illustrates that 30 min
data is the best for modelling as the Gamma static value is the smallest compare
with other data sets. However, for further modelling, we have used the Gamma Test
results [4, 4], [2, 2], [3, 3] [4, 3] combinations because of the less input vectors
compared with the entropy theory
'
s results.
6.4.3 Data Length Selection and Input Identi
cation
with Traditional Approaches
To check the authenticity of above results obtained from GT and entropy theory, we
performed a cross-correlation analysis (between the target runoff data set Q(t), and
different lag time series of precipitation and runoff data (viz Q(t
1),Q(t
2),
−
−
Q(t
4)) [
11
]. The analysis results
are shown in Fig.
6.10
. In the Figure, the cross-correlations are higher for the runoff
information up to a time lag of 3 days, whereas, for the precipitation, the infor-
mation cross-correlation is much smaller
3),Q(t
4),P(t
1),P(t
2),P(t
3) and P(t
−
−
−
−
−
−
just after a time lag of 1 day. It indicates
that the runoff time series with a higher time lag than 3 days and precipitation time
series after a time lag of 1 day, would not possess any signi
—
cant effect on the target
runoff data, Q(t), as the cross correlation values are close to zero. These cross
correlation results are matched with the results obtained from the Gamma test.
However, it should be pointed out that there are two caveats with this procedure.
