Long-Term Groundwater-Level Forecasting in Shallow and Deep Wells Using Wavelet Neural Networks Trained by an Improved Harmony Search Algorithm

Abstract

This study proposes a model using wavelet neural networks (WNNs) trained by a novel improved harmony search (IHS) algorithm to forecast daily groundwater level (GWL) in a shallow well and a deep well in Florida and Arkansas, respectively, for 1 year. Statistical characteristics of the GWL time series and the autocorrelation functions were determined first. Measured GWL series were then decomposed into several subseries using wavelet transform, and imposed as input patterns to the proposed model to forecast GWL in both wells. Efficiency of the IHS algorithm was affirmed by comparing its results with those of differential evolution (DE), harmony search (HS), and particle swarm optimization (PSO) training algorithms. Similarly, the efficiency of WNN was verified by comparing its results with those of the radial basis function (RBF) and multilayer perceptron (MLP) networks, all trained by the IHS algorithm. Predictive capability of the models was determined by Nash-Sutcliffe efficiency (NSE), Pearson correlation coefficients (PCC), normalized root-mean-squared error (nRMSE), and normalized mean absolute error (nMAE) indices. Results reflect that the wells have different statistical characteristics in their GWL series. The shallow well, in contrast to the deep one, has both homoscedasticity and stationarity properties in its observed noisy GWL fluctuations. The proposed model performed much better in both wells, with lower errors and higher PCC and NSE values compared to models with alternative training algorithms or network structures. All forecasts were more accurate for the deep well, as opposed to the shallow one, probably because of the highly noisy GWL fluctuations in the latter.