Data Based Solar Radiation Modelling - Hydrological Data Driven Modelling - page 138

signal into two set of series namely detailed coef cients (D) and approximation

(A) sub time series respectively. In this case study, the present value of solar
radiation has been estimated using the three detail resolution levels and third
approximation level of six inputs (i.e. in case of 1st input daily horizontal extra-
terrestrial radiation (ETR) time series, the subseries are 2-day mode (D ETR 1), 4-day
mode (D ETR 2), 8-day mode (D ETR 3) and the third approximation mode A ETR 3.In
case of 2nd input daily mean air temperature (T mean ) time series, the subseries are
2-day mode (D Tmean 1), 4-day mode (D Tmean 2), 8-day mode (D Tmean 3) and the third
approximation mode A Tmean 3. In case of 3rd input daily minimum air temperature
(T min ) time series, the subseries are 2-day mode (D Tmin 1), 4-day mode (D Tmin 2),
8-day mode (D Tmin 3) and the third approximation mode A Tmin 3 . In case of 4th
input daily maximum air temperature (T max ) time series, the subseries are 2-day
mode (D Tmax 1), 4-day mode (D Tmax 2), 8-day mode (D Tmax 3) and the third
approximation mode A Tmax 3. In case of 5th input daily precipitation (P) time series,
the subseries are 2-day mode (D P 1), 4-day mode (D P 2), 8-day mode (D P 3) and the
third approximation mode (P P 3). In case of 6th input daily wind velocity (U) time
series, the subseries are 2-day mode (D U 1), (4-day mode (D U 2), 8-day mode (D U 3)
and the third approximation mode (P U 3)). As we are aware that from the previous
sections, the GT has identi

ed to use all the available six inputs for the modelling
with training data length of 770 data points. Thus DWT is used to decompose the
input data into three wavelet decomposition levels ( 5 − 7 ) and the decomposed
inputs used for modelling. The three detailed coef rst

approximate series of the original data of runoff and rainfall used in this study are
presented in Fig. 5.37 a

cient series and the

f.
The technical details of the W-ANFIS and W-SVM used for the daily solar
radiation modelling are shown in the Chap. 4 . The key point in conjunction models
like W-SVM and W-ANFIS are the wavelet decomposition of input time series and
the utilization of DWs as the inputs. The performance of these hybrid wavelet
models like neuro-wavelet (NW) model, W-ANFIS and W-SVM in terms of sta-
tistical performance indices are summarised in Table 5.2 . Table shows that all
wavelet based hybrid models have a signi

-

cant positive effect on daily solar
radiation prediction. As seen from the table, the NW has the lowest RMSE and the
highest CORR among the other hybrid models. The relative performance of the
hybrid wavelet models was high for NW model followed by W-ANFIS and
W-SVM. While the correlation coef cient obtained by ANFIS model is 0.87, with

wavelet-ANFIS model this value is slightly decreased to 0.85. Similarly, while the
RMSE obtained by ANFIS model is 14.13 W/m 2 (13.03 %), with wavelet-ANFIS
model this value is changed to 14.67 W/m 2 (13.54 %) during training phase. In the
same time the incorporation of wavelet to ANN-LM and SVM produced positive
results, unlike that of ANFIS model. The incorporation of DWs to ANN-LM
improved the CORR value from 0.89 to 0.93 in training phase and the corre-
sponding increase was 0.85 to 0.88 during validation phase. In the case of W-SVM
the CORR values are 0.83 and 0.81 for training and validation phase respectively.
One could see there is considerable increase in performance of SVM when we
incorporated DWT with