Comparison of Artificial Intelligence and Geostatistics Methods Abilities for Spatial Prediction of Arsenic Anomaly in Chahardoli plain

Introduction
Sometimes the temporal, spatial and economic conditions are in a way that sampling of all water resources in a region is not possible. So it is better to use the estimation methods such as interpolation. The aim of the present study is modeling of the distribution of arsenic in the Chahardoli Plain of Naghadeh by using geostatistics, fuzzy logic, and genetic expression programming (GEP). Until now, different studies has been done in which the geostatistics is used to determine the distribution of heavy metals and trace elements (Corwin and Wagenet, 1996; Juang, et al., 2001; Rodriguez, et al., 2009).
Artificial intelligence, a branch of computer science that is able to predict and simulate using models such as fuzzy logic (FL) and genetic programming (GP) models (Fallah-Mehdipour, et al., 2013). Each of the models has its own advantages and uncertainty that can be used of the individual benefits of each these models (Labani, et al., 2010).
Fuzzy method has to offer an appropriate way to reduce human and Estimation error compared to other theories. In a comparative study on the performance of fuzzy inference techniques it concluded that the fuzzy moderated techniques is successful in moderating uncertainty and data intrinsic errors and also in the interpretation of complex situations (Chang, et al., 2001).
Genetic Programming is a recent development in the methods of evolutionary algorithm that it used to solve problems is detailed and complex. Up to now, several studies using different methods of artificial intelligence and genetic programming has taken that have proven excellence in GP methods (Ustoorikar and Deo, 2008; Alvisi, et al., 2005). Many researchers cited GP to study the process of forecasting and simulation of groundwater levels (Fallah-Mehdipour, et al., 2013), river sediment transport (Aytek and Kisi, 2008), estimation of incomplete data (Ustoorikar and Deo, 2008), determine the unit hydrograph (Rabunal et al., 2007), daily discharge determination (Guven, 2009), flow forecasting (Shoaib et al., 2015), simulate rainfall-runoff (Jayawardena et al., 2005), Short-term and long-term weather forecasts (Kisi et al., 2011) and other studies.
In the Qorveh-Bijar area (small zone of Sanandaj-Sirjan), hydrothermal activity of area young volcanoes and the entry of arsenic-rich escape vapors into the hydrothermal system, as well as volcanic activity which are formed Travertine, are the release agent of arsenic in the of this zone. Since arsenic contamination in this area is type of geogenic source, and considering the difficulty of controlling this type of pollution, therefore, the study area should be studied carefully.
Matherials & Methods
Study area
The study area is located in the Northwest of Iran, Kurdistan province and the southesatern of Qorveh City (Figure 1). Based on Emberger method (1930) and average annual rainfall of 332 mm, the prevailing climate in the study area is arid-cold.
Geology
The study area is located in a small part of Sanandaj-Sirjan zone which have the features of this zone such as magmatic rocks and metamorphic activities is due to tectonic movements on large areas. Lithology of the Rhyolite and Rhyodacite is related to the Jurassic and Cretaceous time that is exposed in the central highlands in the West of Chahardoli (Figure 2). Lithology of Nummolities lime and green tuff which is related to Eocene visible is located in a small area in the eastern mountains of Chahardoli. Volcanic, sandstone, and conglomerate lithologies which is related to Oligomiocene visible in a broad area in the highlands of North-East region. The last magmatic phase related to the early Quaternary, continues as lavas from the East of Vinsar Village to the south of the Daskasan Village.
Hydrogeology
In hydrological point of view, study area is located in a tributary of the river Taluoar. Watershed area of Chahardoli is 958.91 km2 and the plain area is about 386.63 km2. The most important surface water resources in the study area (Chahardoli basin) is Cham Shur River. The general direction of groundwater flow is from the highlands of East and West into the Central Plains and finally is to the northwest of the plain.
Data analyses
To investigate the water quality, 31 water samples including groundwater resources of wells, spring and qanat were collected during October, 2014. These samples were analyzed at the hydrogeological laboratory of geology department in University of Tabriz and water and sewage organization of Kurdistan. The water quality parameters of interest were 〖" Ca" 〗^"2+" , 〖"Mg" 〗^"2+" , 〖"Na" 〗^"+" , "K" ^"+" , 〖"CO" 〗_"3" ^"2_" , 〖"HCO" 〗_"3" ^"-" , 〖"Cl" 〗^"-" , 〖"SO" 〗_"4" ^"2-" , 〖"NO" 〗_"3" ^"_" , "F" ^"-" , As, Fe, Mn,Pb, Cr, Cd, EC and pH were determined by the standard methods. The correlation matrix shows the parameters correlated with arsenic are, respectively, including silica, potassium, and sodium ions (Table 2). High correlation of arsenic with these elements is due to their common origin and role of these elements in increasing concentrations of arsenic in the waters of the region.
Discussion of Results
Geostatistics
Data distribution was evaluated using the Q-Q diagram and using logarithmic transformations, data distribution close to the normal distribution. Changeability of the range and sill were evaluated relative to different angles of plotted semivariograms and data variogram was plotted for anisotropic mode.
Urdinary kriging model was used for prediction of arsenic concentration in the study area. In addition to the main variable of arsenic, silica parameter that has the highest correlation with arsenic was used as a secondary variable for cokriging model. In geostatistics method, J-Bessel cross-variogram models having R2 equal to 0.75 and nugget effect of zero was selected to predict arsenic concentration.
Fuzzy
Artificial intelligence models were used to improve efficiency. In this study, Sugeno Fuzzy Logic (SFL) has been used to predict the total arsenic values. In this model, the reduction method for data classification and determining of the membership were used.
Fuzzy model by determining the optimal radius of 0.6 based on the lowest RMSE were accomplished that the value of R2 for training and testing level are in order 0.91 and 0.78 respectively.
Genetic Programming
Data of parameters include sodium, potassium, silica and arsenic were used as input data and also was selected in such a way the minimum and maximum of data be entered in the testing level.
Production of the initial population of program was done by selecting the number 20 chromosome with a head size of 7, 3 number of gene and 2 constant per gene. The mathematical operator of + was selected for the linking function between subtrees. To compare the results of the program, three sets of the function were used as the main operators. According to Table 2, F3 function includes default operators was selected as the major functions for the program and the best fitted compared to other functions.
GEP model by providing the relationship between input and output and more accurate results in the training and testing steps with R2 0.93 and 0.87 respectively was evaluated as the most appropriate model than other models to estimate the arsenic values in the region.
Conclusions
Geostatistical techniques (kriging and Cokriging) were used to estimate the amount of arsenic in the study area do not have precise results. It can be said about its reason is related to heterogeneity of study area and special condition of data that cause the non-linear and unclear general trend. To improve efficiency, artificial intelligence models such as sugeno fuzzy logic (SFL) model and genetic expression programming (GEP) were used. In this study, the results of GEP and SFL model are acceptable for spatial prediction of arsenic anomaly, but the SFL model improved 18% efficiency of GEP model based on the RMSE value. Ability evaluation of other artificial intelligence model like mamdani fuzzy logic, Larsen fuzzy logic, neuro-fuzzy models for spatial prediction of arsenic anomaly proposed for future research topics.