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Groundwater is the most reliable source of supply for potable water and supports a wide array of economic and environmental services. There is a significant concern that groundwater levels are declining due to intense aquifer use. The sustainable management of groundwater resources requires good planning and concerted efforts. To manage groundwater resources, it is necessary to predict the groundwater levels and its fluctuations. The prediction groundwater level can guide water managers and engineers effectively. On the other hand, there are multifarious types of equipment for measuring levels of groundwater. Sophisticated water level loggers or divers can measure the groundwater level automatically. Sounding devices with acoustic and light signals are also used to check groundwater levels. The use of devices for measuring the level of groundwater is time-consuming and costly. To reduce the time and cost of the groundwater level measuring process, many methods of Artificial Intelligence (AI) have been utilized for estimating the groundwater level. Among the AI methods, SVMs has great ability in predicting non-linear hydrological processes. Support vector machines (SVMs) is as an intelligent computational method for predicting hydrological processes. Recently, (SVMs) have been successfully applied in classification problems, regression and predicting; as techniques of machine learning, statistics and mathematical analysis. The SVM is based on the structural risk minimization (SRM), which can escape from various difficulties, such as the necessity of a large number of control parameters and a local minimum in artificial neural networks (ANNs). The weighted least squares support vector machines (WLSSVM) was first introduced by Suykens et al., and has proved to be much more robust in several fields, especially for noise mixed data, than least squares version of SVM (LSSVM). Their powerful scientific research provides motivation for employing WLSSVM method in estimating groundwater level. The accurate value of WLSSVM parameters  effect on the estimation, these optimal parameters can be achieved optimization algorithms. Therefore, weighted least square support vector machine (WLS-SVM) model was coupled with particle swarm optimization (PSO) and gravitational search algorithm (GSA) as metaheuristic algorithms for estimating well water level. In this study, an attempt has been made to use the hybrid model with high accuracy to estimate the groundwater level. In order to estimate the groundwater level, ten wells data in Bagheyn plain of Kerman province is considered during ten-year time series. The estimated value obtained by the WLSSVM-PSO and WLSSVM-GSA models are compared with the observed value, and showed the estimated results have nearly coincidence with observed values. Numerical results show the merits of the suggested technique for groundwater level simulation. In order to verify the hybrid learning machine metaheuristic model, Mean Absolute Error (MAE), Root Mean Squared Error (RMSE), Average Absolute Error (AAE), and Model Efficiency (EF) are computed, and these statistical indicators stand on the good acceptable range, and find WLSSVM-GSA is more accurate than WLSSVM-PSO. The results demonstrate that the new hybrid WLSSVM-GSA model has high efficiency and accuracy with observed values, and the modelling method is an innovative and powerful idea in estimating well water level.

Keywords: Groundwater level –Weighted least square support vector machine – Particle swarm optimization– Gravitational search algorithm-Efficiency

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