Assessment and estimation the spatial variation of groundwater level by various interpolation methods in Sarab plain

Groundwater (GW) is the most important source of freshwater on our planet. The use of groundwater has increased manifolds in the recent past due to increased water demands owing to the accelerated growth of population and industrialization. Over-exploitation of groundwater resources over the past few decades has caused quantative and qualitative constraints.Today, groundwater resources encounter with numerous problems such as loss, declination of level, chemical wastewater of industries and agriculture inputs, salting and etc. This issue is very significant in arid and semi-arid areas due to low precipitation and limited recharge of aquifers. Considering the issues, it is essential and highly needed for a comprehensive, accurate and reliable estimating of groundwater level in aquifers of arid and semi-arid areas. In this context, various interpolation methods have been initiated in environment of geographic information system (GIS) to determine the spatial variation of groundwater level. Correct selection of one method among several ones is important and basic step related to water resources management. Sarab plain is one of the fertile plains of East Azarbayjan province, NW Iran, where inhabitant’s economy is based on agriculture and ranch. Due to arid and semi-arid climate, life of human associations is greatly depends to water resources supplied in streams and aquifers in this area. Thus, the knowledge of spatial variation of groundwater level based on scientific and accurate estimation is essential in order to optimal exploitation and management of groundwater resources in the study area. This research aimed at optimum estimation of spatial variation of GW over Sarab plain by comparison of various interpolation methods and presentation of zoning map of GW in the area.
Methods and Meterial: Data include the sample data of GW depth collected from 50 wells over Sarab plain were used. We use the data of 2012 year, considering the most newest and reliable data. The process of the research is so that firstly, database of groundwater depth was prepared in GIS environment. Then, spatial statistics of the variable based on various interpolation methods was analyzed. In this regard, the aim is to choose the most suitable method for mapping the groundwater level zoning using cross-validation method and relevant criteria (mean bias error (MBE), root mean square error (RMSE) and square of correlation coefficient (R2) between estimate and observed rates).Used interpolation methods include algebraic and geo-statistical models that follow:- Algebraic Interpolation

In Algebraic methods one or more procedures fitted to set of observed points (z) with definite coordinates. Algebraic interpolation can be exact or approximate, so that if observed values are considered as exact value (having no error or uncertainty) at the sampling sites, using a precise method for interpolation is recommended. But, if we consider some uncertainty for variable, we may select a smoothed method. So, we can use various mathematical functions for fitting the interpolation levels to given points in this group of interpolation methods. Algebraic methods used in this research include Inverse Distance Weighted (IDW) and Radial Basis Functions (RBFs).
- Geo-statistical Interpolation Methods (Kriging) Geostatistics is an effective tool for modeling the spatial structure of various physical parameters. This approach include methods based on statistical properties of the spatial series of given variable such as mean and standard deviation. It analyses the spatial variation of the variable using different semi-variogram models to obtain the best linear unbiased estimators of spatially dependent data.

The results of comparison and validation of the methods are as follow:-Inverse distance weighted (IDW):In this method we used at least 8 to at most 10 neighborhood points for mapping the groundwater level, having lowest error among other points based on cross-validation. RMSE and MBE of this method are 10/78 and 1/26, respectively.
- Radial Basis Functions (RBF):Cross-validation of RBFs showed that the spline with tension model has lowest estimate error among others. RMSE and MBE of the method are 10/62 and 0/27, respectively. Furthermore, resulting map of this method was smoother than IDW map.
- Geo-statistics (Kriging)
Since the used data in this method should have normal distribution, we transformed the data into normal form by log normal method. Results of the comparison of Kriging models based on Cross-Validation showed that the Rational Quadratic model had lowest estimate error in among models of this approach. So, we used this model for zoning of groundwater level. RMSE and MBE of the method are 9/79 and -0/76, respectively.
Totally, the comparison of Algebraic and geo-statistical models indicated that the Kriging method was the most accurate method for estimating the spatial variation of groundwater level in study area (table 1). This fact was attributed to consider the spatial structure of data in one hand, and reduction of variance of them in other hand. Furthermore, zoning maps of groundwater level showed that groundwater level over Sarab plain was high. Spatially, groundwater level was high in southern sections compared to northern sections.

We examine the accuracy and efficiency of interpolation methods including Inverse Distance Weighted (IDW), Radial Basis Functions (RBFs) and Kriging to spatial estimation of groundwater level in Sarab plain, NW Iran. Results indicated that Kriging was the most efficient and accurate model among others for estimation and zoning the groundwater level in the study area, having lowest estimation error (RMSE= 9/79) and highest square of the correlation coefficient between estimate and observed rates (R2= 0/31). This fact can related to considering the spatial distribution and structure of used data by Kriging. In this regard, Kriging minimizes the amount of variance to enhance the prediction power of interpolation model. Also, this method prevents the impact of absolute minimum and maximum rates within data. Resulting zoning map of groundwater level over the plain showed lower groundwater depth in southern areas respect to northern areas. This geographic distGrounwater Level, Interpolation, Algebraic Models, Geo-statistical Models, Sarab plain.
ribution of the variable may be attributed such factors as lithology, drainage system and human activities and exploitations of water resources, need to further study in future. It should be more attention from water resources planners and policy makers to areas with high groundwater level, considering the relationship between GW depth and such hazards as water loss, water pollution and subsidence.