Evaluation of ANFIS, ANN, and geostatistical models to spatial distribution of groundwater quality (case study: Mashhad plain in Iran)

Groundwater is one of the major sources of exploitation in arid and semiarid regions. Spatial and temporal quality distribution is an important factor in groundwater management. Thus for protecting groundwater quality, data on spatial and temporal distribution are important. Geostatistical models are the most advanced techniques for interpolation and spatial prediction of groundwater parameters. Determining the best and the most suitable model is also very essential which is the main aim in this study. In this research, inverse distance weighted (IDW), kriging, and cokriging methods in geostatistical and artificial neural network (ANN) and adaptive network-based fuzzy inference system (ANFIS) models were used for predicting the spatial distribution of groundwater electrical conductivity (EC) and those were compared together. EC and chloride (Cl−) are two important indicators for water quality assessment. Data were related to 120 wells in Mashhad plain (Iran). Groundwater resources have an important role in this region due to surface water deficit. After normalization of data, to geostatistical models, variograme was drawn; for selecting a suitable model for fitness on experimental variograme, less RSS value was used. Then using cross-validation and root mean square error (RMSE), the best method for interpolation was selected. To compare these three models, we used 25 % of observation data and determined the R2, RMSE, and MAE parameters. Different ANFIS structures were examined. Also in ANFIS method, different types of membership function, such as Gaussian, bell shape, and trapezoid for inputs of model, were used. Results showed that for interpolation of groundwater quality, cokriging method is superior to kriging method in geostatistical model. In cokriging method, Cl parameter was selected as auxiliary variable which had the highest correlation with EC. Results showed that ANN model had the best accuracy (R2 = 0.932, RMSE = 367.9, MAE = 265.78 μmos/cm) than ANFIS and geostatistical models.