The WANN algorithm is summarized as follows:

Step 1: Multilevel wavelet analysis using DWT decomposes a signal into details (D

_{1}, D_{2}… D_{N}) and approximation (A_{N}), where N is the decomposition level. Water table time series data were decomposed into details D_{1}and D_{2}and an approximation A_{1}in this study. Decomposition levels have been selected with respect to the number of data used for each piezometer (the data of water table used for each piezometer) and they are shown in Table 1. For decomposition level, DL = log(No. Data) formula was used, following the suggestion of Wang & Ding (2003), Partal & Kisi (2007) and Nourani*et al.*(2009).Step 2: ANN is trained and tested using the details and approximation as input and the model performance is evaluated.

Table 1

Piezometer . | 3 . | 4 . | 5 . | 6 . | 7 . | 8 . | 10 . | 11 . | 12 . | 14 . | 19 . | 21 . | 23 . |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|

No. data^{a} | 236 | 249 | 141 | 141 | 200 | 196 | 238 | 236 | 281 | 141 | 217 | 141 | 141 |

Wavelet type | db4 | db4 | db4 | db4 | db4 | db4 | db4 | db4 | db4 | db4 | db4 | db4 | db4 |

Level | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 |

Hidden layer | 8 | 8 | 6 | 6 | 8 | 8 | 8 | 8 | 8 | 6 | 8 | 6 | 6 |

Piezometer . | 3 . | 4 . | 5 . | 6 . | 7 . | 8 . | 10 . | 11 . | 12 . | 14 . | 19 . | 21 . | 23 . |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|

No. data^{a} | 236 | 249 | 141 | 141 | 200 | 196 | 238 | 236 | 281 | 141 | 217 | 141 | 141 |

Wavelet type | db4 | db4 | db4 | db4 | db4 | db4 | db4 | db4 | db4 | db4 | db4 | db4 | db4 |

Level | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 |

Hidden layer | 8 | 8 | 6 | 6 | 8 | 8 | 8 | 8 | 8 | 6 | 8 | 6 | 6 |

^{a}The number of data for each piezometer (number of months).

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