Geology Reference
In-Depth Information
6.4.1 Gamma Test for Data Length Selection and Input
Identi
cation
6.4.1.1 Gamma Test with Daily Data
The Gamma Test analysis can provide vital information which would help in
rainfall runoff modelling. There are 2
n
1 possible combinations of inputs from
which the best one can be determined by the gamma statistic values. Major com-
binations of inputs evaluated in this study are shown in Fig.
6.3
. The least Gamma
value was observed when we used the input data combination equivalent to [4, 4]
combination i.e. four antecedent runoff and four antecedent rainfall information as
inputs. However, the M-test analysis results showed high complexity and low
predictability for [4, 4], because of relatively high values of Gradient (A) and V
ratio
.
The next best value of the Gamma Statistic (
−
), gradient (A) and V-ratio were
observed when we used the three steps antecedent runoff values (Q(t
Г
1),Q(t
2),
−
−
Q(t
1)) and current rainfall information
(P(t)). The quantity of the available input data to predict the desirable output was
analysed, using the M-test. The Gamma statistic (
3)), one step antecedent rainfall (P(t
−
−
) and Standard Error (SE) var-
iation with unique data points obtained from M-Test analysis and is shown in
Fig.
6.4
. The test produced an asymptotic convergence of the Gamma statistic to a
value of 0.0192 at around 1,056 data points (i.e. M = 1,056). The SE corresponding
to M = 1,056 is relatively small as
Г
0.0073 [
19
].
*
The embedding 11101010 model (
(five input and one output set of I/O pairs) was
identi
ed as the best structure for the daily rainfall runoff data from the Brue
catchment because of the following reasons viz. its low noise level (
Г
value), the
Fig. 6.3 The gamma test results on the daily rainfall-runoff data of Brue catchment for different
input combinations. Note Combination 1 denotes [1, 1]*, Combination 2 denotes [2, 2],
Combination 3 denotes [3, 3], Combination 4 denotes [2, 1], Combination 5 denotes [3, 2],
Combination 6 denotes [2, 3] and combination 7 denotes [4, 4] [a, b]
*
where, a denotes the number
of antecedent runoff data sets used for M Test and b denotes the corresponding b
−
1 number of
