1 Introduction
2 Wavelet Analysis
2.1 Discrete Wavelet Transform (DWT)
2.2 Mother Wavelet
3 Artificial Neural Networks
3.1 Method of Network Training
3.2 Selection of Network Architecture
3.3 Method of Combining Wavelet Analysis with ANN
4 Linear Auto-Regressive (AR) Modeling
5 Performance Criteria
6 Study Area and Data Collection
Variable | Data | Minimum | Maximum | Mean | Standard Deviation | Skewness |
---|---|---|---|---|---|---|
Rainfall (mm) | Total | 0.00 | 1401.8 | 235.0 | 284.42 | 1.20 |
Calibration | 0.00 | 1231.3 | 240.1 | 286.61 | 1.19 | |
Validation | 0.00 | 1401.8 | 226.5 | 276.10 | 1.23 | |
Minimum temperature (°C) | Total data | −3.70 | 15.8 | 8.9 | 4.67 | −0.29 |
Calibration | −1.70 | 15.4 | 8.9 | 4.66 | −0.27 | |
Validation | −3.70 | 15.8 | 9.0 | 4.68 | −0.33 | |
Maximum temperature (°C) | Total | 5.50 | 21.5 | 15.6 | 3.95 | −0.65 |
Calibration | 5.50 | 21.5 | 15.3 | 4.04 | −0.57 | |
Validation | 6.10 | 21.4 | 16.2 | 3.74 | −0.75 |
6.1 Development of Wavelet Neural Network Model
Model | Input Variables |
---|---|
I | R(t) = f (R [t-1]) |
II | R(t) = f (R [t-1], R [t-2]) |
III | R(t) = f (R [t-1], R [t-2], TM [t-1]) |
IV | R(t) = f (R [t-1], R [t-2], TM [t-1], TX [t-1]) |
V | R(t) = f (R [t-1], R [t-2], TM [t-1], TM [t-2], TX [t-1]) |
VI | R(t) = f (R [t-1], R [t-2], TM [t-1], TM [t-2], TX [t-1], TX [t-2]) |
7 Results and Discussion
Model | Calibration | Validation | ||||
---|---|---|---|---|---|---|
RMSE | R | COE(%) | RMSE | R | COE(%) | |
WNN | ||||||
I | 102.26 | 0.934 | 87.19 | 117.39 | 0.906 | 81.78 |
II | 52.78 | 0.983 | 96.58 | 63.92 | 0.973 | 94.60 |
III | 40.97 | 0.989 | 97.94 | 81.51 | 0.955 | 91.24 |
IV
|
35.12
|
0.992
|
98.48
|
63.01
|
0.974
|
94.78
|
V | 34.74 | 0.993 | 98.51 | 84.79 | 0.953 | 90.57 |
VI | 35.75 | 0.992 | 98.43 | 82.24 | 0.955 | 91.10 |
ANN | ||||||
I | 205.96 | 0.695 | 48.38 | 203.98 | 0.672 | 45.01 |
II | 176.56 | 0.788 | 62.05 | 171.15 | 0.784 | 61.35 |
III | 145.43 | 0.861 | 74.24 | 178.31 | 0.783 | 58.10 |
IV | 123.23 | 0.902 | 81.49 | 163.79 | 0.807 | 64.73 |
V | 116.75 | 0.913 | 83.36 | 178.08 | 0.786 | 58.42 |
VI | 114.66 | 0.916 | 83.98 | 176.84 | 0.784 | 58.89 |
AR | ||||||
226.00 | 0.659 | 37.70 | 221.82 | 0.642 | 34.91 |