Simulation of time-series groundwater parameters using a hybrid metaheuristic neuro-fuzzy model

The estimation of qualitative and quantitative groundwater parameters is an essential task. In this regard, artificial intelligence (AI) techniques are extensively utilized as accurate, trustworthy, and cost-effective tools. In the present paper, two hybrid neuro-fuzzy models are implemented for the prediction of groundwater level (GWL) fluctuations, as well as variations of Cl − and HCO3 − in the Karnachi well, Kermanshah, Iran in monthly intervals within a 13-year period from 2005 to 2018. In order to develop AI models, the adaptive neuro-fuzzy inference system (ANFIS), firefly algorithm (FA), and wavelet transform (WT) are used. In other words, two hybrid models including ANFIS-FA (adaptive neuro-fuzzy inference system-firefly algorithm) and WANFIS-FA (wavelet-adaptive neuro-fuzzy inference system-firefly algorithm) are utilized for the estimation of the quantitative and qualitative parameters. Firstly, influencing lags of the time-series of the qualitative and quantitative parameters are identified using the autocorrelation function. Then, four and eight separate models are developed for the approximation of GWLs and qualitative parameters (i.e. Cl − and HCO3 −), respectively. It is worth to mention that about 75% of observed values are assigned to train the hybrid AI models, while the rest (i.e. 25%) to test them. Sensitivity analysis results reveal that the WANFIS-FA models display more acceptable performance than the ANFIS-FA ones. Also, the estimations of MAE, NSC, and SI for the simulation of HCO3 − by the superior model of the WANFIS-FA are obtained to be 0.040, 0.988, and 0.022, respectively. In addition, the lags (t-1), (t-2), (t-3), and (t-4) are ascertained as the most effective time-series lags for the estimation of Cl − .