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Fig. 6.31 The observed versus the W-ANFIS model predicted daily runoff at the Brue catchment
during training phase
Table 6.5 . The RMSE values in the validation phase obtained by theW-ANFIS model
was 0.702 m 3 is (28.6 %), which is higher than that of the NW model and W-SVM
model. The performance ef
ciency of the W-ANFIS model in the rainfall-runoff
modelling is 3.75 % lower than that of N-SVM model for validation and corre-
sponding value for training data is 1.12 % lower. Compare with the NNARX model,
the ef
ciency values of the W-ANFIS model are 5.57 % and 11.85 % higher for
training and validation data respectively. MAPE values for W-ANFIS were found to
be 0.120 m 3 /s and 0.123 m 3 /s during the training phase and validation phase
respectively. The corresponding MAPE values for NNARX is found to be higher for
both the validation and training phases; whereas for the NWmodel, the MAPE values
was observed to be lower than that of the W-ANFIS model. In terms of MBE and S d ,
the performance of the NW model outperforms all other tested models including
W-ANFIS and W-SVM in the both training and validation phase.
6.6 Conclusions
This case study on rainfall-runoff modelling made an attempt to solve some mod-
elling related issues prevailing in effective runoff prediction from the antecedent
information. The modelling issues in input selection and training data length were
tackled effectively in this study using a novel technique called the Gamma Test (GT).
It demonstrated its successful performance with several data based transfer function
and arti
cial intelligent models. The GT analysis identi
ed the input combination of
three steps antecedent runoff values (Q(t
1),Q(t
2),Q(t
3)), one step antecedent
rainfall (P(t
1)) and current rainfall information (P(t)) (which is equivalent to a
input combination of the ARX(3,2) model) as the best input combination. GT based
M-Test analysis on this selected input combination identi
ed the training data length
 
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