Geology Reference
In-Depth Information
Fig. 6.5 The gamma test results on the rainfall-runoff data of the Brue catchment for different data
frequencies. Note 15 min modelling input space is [4, 4]
*
[Q(t)
…
Q(t
3) and P(t)
…
P(t
3)] with
−
−
65,524 data points, 30 min modelling input space is [2, 2]* [Q(t), Q(t
1), P(t) and P(t
1)],)]
−
−
with 35,031 data points, 60 min modelling input space is [3, 3]* [Q(t)
…
Q(t
2) and P(t)
…
−
P(t
2)] with 17,515 data points and 60 min modelling input space is [4, 3]* [Q(t)
…
Q(t
3) and
−
−
P(t)
2)] with 8,756 data points. Where [a, b] denotes the number of antecedent runoff data
sets used for the M Test and b denotes the corresponding number of antecedent rainfall data
…
P(t
−
6.4.2 Entropy Theory for Data Length Selection and Input
Identi
cation
The study applied the Entropy theory to see the in
uence and effect of inputs on the
modelling through attributes like transinformation, marginal entropy, joint entropy
and conditional entropy. The analysis was performed on the daily rainfall runoff
data from the Brue catchment. The Table
6.1
shows different scenarios and possible
information derived from each time series of consideration in the rainfall runoff
modelling. The analysis results shows that the transinformation value is high when
we used (t
1)) alone compared to other data
series when considered separately. It indicates that in the rainfall-runoff modelling
studies, the (t
1) step of runoff information (Q(t
−
−
1) data of runoff have a predominant position in model making. The
second highest value of transinformation was for the present value of rainfall
information P(t), followed by (t
−
−
2) step of runoff information (Q(t
−
1)), (t
−
3)
step of runoff information (Q(t
−
3)), and (t
−
4) step of runoff information
(Q (t
−
4). These results match with the
finding of GT analysis for the daily
analysis. GT analysis identi
ed three steps antecedent runoff values (Q(t
1),
−
Q(t
1)) and current rainfall
information (P(t)). The transinformation values were less for (t
−
2),Q(t
3)), one step antecedent rainfall (P(t
−
−
−
2) and (t
−
3) step
of rainfall information.
Entropy Theory was applied to the daily rainfall runoff data to ascertain how
many data points are needed to suf
ciently calibrate the correct model from the
available data. The variation of transinformation with increase in data points used
