Forecasting of groundwater level fluctuations using ensemble hybrid multi-wavelet neural network-based models

Abstract

Accurate prediction of groundwater level (GWL) fluctuations can play an important role in water resources management. The aims of the research are to evaluate the performance of different hybrid wavelet-group method of data handling (WA-GMDH) and wavelet-extreme learning machine (WA-ELM) models and to combine different wavelet based models for forecasting the GWL for one, two and three months step-ahead in the Maragheh–Bonab plain, NW Iran, as a case study. The research used totally 367 monthly GWLs (m) datasets (Sep 1985–Mar 2016) which were split into two subsets; the first 312 datasets (85% of total) were used for model development (training) and the remaining 55 ones (15% of total) for model evaluation (testing). The stepwise selection was used to select appropriate lag times as the inputs of the proposed models. The performance criteria such as coefficient of determination (R2), root mean square error (RMSE) and Nash-Sutcliffe efficiency coefficient (NSC) were used for assessing the efficiency of the models. The results indicated that the ELM models outperformed GMDH models. To construct the hybrid wavelet based models, the inputs and outputs were decomposed into sub-time series employing different maximal overlap discrete wavelet transform (MODWT) functions, namely Daubechies, Symlet, Haar and Dmeyer of different orders at level two. Subsequently, these sub-time series were served in the GMDH and ELM models as an input dataset to forecast the multi-step-ahead GWL. The wavelet based models improved the performances of GMDH and ELM models for multi-step-ahead GWL forecasting. To combine the advantages of different wavelets, a least squares boosting (LSBoost) algorithm was applied. The use of the boosting multi-WA-neural network models provided the best performances for GWL forecasts in comparison with single WA-neural network-based models.