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OPEN Interpolation methods for spatial

distribution of groundwater
mapping electrical conductivity
Saeed Salehi1, Reza Barati2, Mozareza Baghani3, Saeed Sakhdari4 & Mohsen Maghrebi5
This study was carried out to develop a conceptual framework for determining the best interpolation
method which mainly is employed to calculate the variability maps of electrical conductivity (EC)
in neighboring regions. The considered case study is parts of the Khorasan Razavi province, Iran
(including five aquifers Kashmar, Fariman, Doruneh, Sarakhs and Joveyn). In the first step, the
empirical variogram (semi-variogram) was computed for the study area. The methods of the variability
of a variable with spatial or temporal distance were considered to measure the semi-variogram
function. In the next step, the best variogram model (e.g. spherical, exponential or Gaussian) was
considered in the Geographic Information System (GIS) environment and f for the Environmental
Sciences (GS+) software. By plotting the semi-variogram in GS+ program based on different method
as Global Polynomial Interpolation (GPI), Inverse distance weighing (IDW), Radial basis function
(RBF), Kriging method, Global Polynomial Interpolation (GPI), Local Polynomial Interpolation (LPI),
the best variogram model fitted to spatial structure of the EC. Finally, by considering the acceptable
range for different parameters which impact on EC and evaluating their impacts by scaling, the best
interpolation method has been selected for that area for employing their neighborhood basin. Result
indicated that the precipitation located within the range of 140 to 180 mm, RBI has the priority. This
process is continued for all 14 parameters and eventually one method gets the most points.

Keywords Groundwater, Spatial variation, Electrical conductivity, Spatial distribution method, Geo-statistics
Framework

Recent anthropogenic activity like industrialization or land use change pattern threat agricultural area via
water detrition. This challenge is much more important in groundwater resources due to its sustainability and
participation in agricultural applications1–6. Groundwater is always considered as the one of accessible and
cheapest sources to provide the requirements of the water, especially in arid and semiarid regions. These facts
show the importance of providing an accurate picture of the status of groundwater resources for future planning.
The proper exploitation can perform an important role in sustainable development of the society. However, over
exploitation of the groundwater can cause irreversible damage to this valuable resource which can impact directly
on the quality and quantity of the water. Overexploitation of the groundwater, pouring the municipal, husbandry
and industrial wastewaters into plains has contaminated these valuable resources7–11. The population growth in
recent decades causes a lot of hostile conditions in arid regions like raising the EC through the agricultural areas.
For the proper management of water resources, it is important to know the spatial variation of qualitative
parameters of the groundwater like EC. In the past for analyzing of variability of groundwater parameters, classic
statistical approaches were applied which were very time consuming and costly. Nowadays, geo-statistics is used
as an efficient technique to study spatial distribution of qualitative parameters12. Also, it is supposed that some
novel and new solutions were introduced based on the numerical models to assess the alluvia aquifer by using
the genetic DRASTIC model13. Geo-statistics is introduced as a process which the value of a quantity in the
considered point is estimated by employing the value of the same quantity in another given point14–18. It should
be noted that, recently, artificial intelligence technologies have been widely used in the area of environmental
pollution controls [e.g.19–22. However, most of these technologies suffer from time-consuming validation, black-
box modeling without considering physical concepts beyond the considered problem, failing to achieve the
desired accuracy, etc., as discussed by23.

1Dept. of Civil Engineering, Lakehead University, Thunder Bay, ON P7B 5E1, Canada. 2Department of Civil
Engineering, Tarbiat Modares University, Tehran, Iran. 3Department of Biosystem, Ferdowsi university , Mashhad,
Iran. 4Department of Civil Engineering, University of Sistan and Baluchestan, Zahedan, Iran. 5Department of Civil
Engineering, University of Gonabad, Gonabad 9691957678, Iran. email: r88barati@gmail.com

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Using the interpolation methods is always known as an effective approach to make relation between field
data like groundwater level and the level of the electrical conductivity (EC). Hu et al.24 plotted the map of
the groundwater contaminated by nitrate which was generated by employing the indicator Kriging (IK) and
the ordinary Kriging (OK) methods. Their results indicated that the IK method is useful to evaluate the risk
of the nitrate in groundwater and the OK method could not correctly reflect the concentration of nitrate
through the groundwater. They also found that the regions with waste water irrigation were featured with
high level EC. Measurement of the nitrate concentration suggested that the high level of EC in regions was
associated with high values of nitrate concentration. Finally, they suggested that the assessment of the threat
of the nitrate pollution could be useful to manage the groundwater resource. Finding the consequences of the
human activities on the underground pollution is one of important issues that can be studied by employing the
interpolation techniques. Goovaerts et al.25 compared multi-Gaussian and indicator Kriging for modeling the
spatial probabilistically distribution of arsenic concentrations in groundwater of southeast Michigan. Ta et al.26
by employing the geospatial analysis of spatiotemporal variability of groundwater level analyzed the impacts
of the war on the pollution of the groundwater in real basin. They expounded that the Kriging interpolation
technique can estimate the directions of the groundwater with good agreement compared by the reality. They
presented that the fluctuations of the flow direction can be predicted based on the Kriging method. Adhikary
et al.27used ordinary Kriging and indicator Kriging methods for spatial analysis of bicarbonate, calcium,
chloride, EC, magnesium, nitrate, sodium, and sulphate at Najafgarh, NCT of Delhi. The thematic maps of all
the groundwater quality parameters indicated an increasing trend of pollution from the northern and western
part of the study area towards the southern and eastern part. Kazemi and Hosseini28 estimated the spatial
distribution of the six heavy metals such as Arsenic, Cadmium, Copper, Mercury, Plumbum, and Zinc through
the sediment of the Caspian Sea in Volga delta. The results of the Ordinary Kriging method (OK) showed that
the spatial variability of the pollution of the six heavy metals which were fluctuated between maximum and
minimum values. Seyedmohammadi et al.29 focused on the determination of the most suitable interpolation
method for spatial analysis of groundwater EC in central regions of Guilan province. They used inverse distance
weighting (IDW), global polynomial interpolation (GPI), local polynomial interpolation (LPI), radial basis
function (RBF) and ordinary Kriging (OK) methods for estimation of groundwater EC, and they find that the
best estimator OK method that consists of several performance evaluation criteria. Kumar30 studied spatial
variation of the fluoride and nitrate parameters of groundwater resources. He observed a definite correlation
with the geological formations and water quality parameters, which indicated importance of geo-statistics in
groundwater management. Rawat et al.31 developed a new approach to define a patio-temporal function (NDDI)
for groundwater quality parameters (e.g., PH, EC, milligram/ litter of the TH, Ca, and Mg materials). NDDI
is defined as a compact index which is used for the analysis of water pollution states for spatial distribution
in different time durations. It has the capability of conversion of parameter concentration between − 1 and
+ 1. They depicted the contour plots of the groundwater quality parameters during the different seasons. The
frequency distribution and inter correlation of analysis information of the data bank was coherence. Karami et
al.32 used geostatistical methods for spatial analysis of seven main quality parameters including total dissolved
solids, sodium adsorption ratio, EC, sodium, total hardness, chloride and sulfate. Their results showed that
Kriging method is more accurate than the traditional interpolation methods. Safarbeiranvnd et al.33 evaluated
variations of water quality parameters of the Central Plain Aquifer using Kriging and IDW methods. They find
that the effect of the structural conditions on aquifer properties such as transmissivity and flow direction were
important factors on the spatial variation of water quality parameters. Maroufpoor et al.34 applied geostatistical
methods and hybrid intelligent models to predict the spatial distribution of chlorine (Cl), EC, and sodium
absorption ratio (SAR) parameters of groundwater. Among Kriging, inverse distance weighting (IDW), and
radial basis function (RBF) methods, the Kriging was found more accurate based on the employed comparisons
among the interpolated values and field data with same coordination. Bon et al.35assessed the pollution index of
the shallow quaternary aquifer of the Lake Chad Basin using a geostatistical model of EC. A spatial heterogeneity
of EC was observed where it is possible to distinguish six groups EC. Folorunso36 studied the spatial salinity flow
of surface water into coastal groundwater in Okun-Ajah and its environ. Azlaoui et al.37evaluated the suitability
of groundwater for agriculture and drinking in the Ain Oussera plains. They created a spatial distribution map
for EC using IDW. Bhunia and Shit38 developed a geostatistical-based water quality index to analyze the spatial
variation of contamination zone in Surguja district of Chhattisgarh, India. Their results indicated that north
and north-east of the district have low groundwater quality and the north-west and central part of the district
have very good groundwater quality. Ghachoui et al.39 assessed the groundwater status of the Souk El Arbaa by
collecting 14 samples in 2022 from different locations and analyzing their physicochemical characteristics. They
used IDW tool spatial distribution mapping. Jamal et al.40 evaluated spatial distribution and hydrogeochemical
of tubewell water of six unions of Kaligonj upazila in Satkhira district using IDW.
The background of the present study shows that the use of geo-statistics methods is unavoidable in the
analysis of spatial variation of groundwater quality as the decision making is based upon discrete observation
sampling points. Tam and Wong41 findings illustrated that the geostatistical methods are appropriate for an area
that depends on the type of variable and regional factors and could not be generalized to other regions. To the
best of knowledge of the authors, there is no available practical framework to select appropriate geo-statistics
methods for a given aquifer with specific hydrological and hydrogeological features. These facts motivated the
authors to develop a conceptual framework to select the best interpolation method for spatial distribution of
groundwater EC. The assumptions used in this study are, predicting trend of qualitative variation in an aquifer in
the coming years and taking protective and managerial action before the crisis is possible, appropriate areas for
exploitation of groundwater for drinking and irrigation purposes can be determined, and geo-statistics methods
are accurate enough for analysis of spatial variation of qualitative parameters of groundwater. The following
tasks were accomplished as variation of EC was studied in five aquifers (including Kashmar, Fariman, Doruneh,

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Sarakhs and Joveyn) of Khorasan Razavi province, Iran, spatial and temporal variation of parameters in these five
regions with seven different geo-statistics methods were analyzed and the best method for interpolation of EC
was selected in each region based hydrologic and meteorological data, examination of trend of variations in each
region based on the physics of the region (hydrology and hydrogeology), developing a conceptual framework
between the best interpolation method and hydrologic and hydrogeological factors in each region. Since we
need a great deal of geographic and qualitative data for finding the best interpolation method, GIS was used
as a powerful tool to create spatial variability maps. The considered interpolation methods are IDW (inverse
distance weighing), RBF (radial basis function), GPI (global polynomial interpolation), LPI (local polynomial
interpolation), Kriging and Cokriging.
Interpolation methods in GIS are divided into two groups of deterministic and geo-statistics. In deterministic
methods, mathematical functions are used, but in geostatistical methods statistical methods are used; however,
in to the considered functions involved the main part of this solution. The interpolation methods are included
IDW (inverse distance weighing), RBF (radial basis function), GPI (global polynomial interpolation), LPI (local
polynomial interpolation) are deterministic and Kriging and Cokriging which are classified as the geo-statistics
methods43–50.
There are many sources of uncertainty in the selection of interpolation methods for different parameters
including groundwater EC, and these probably lead to some issues in spatial distribution assessment. For
example, different interpolation methods for spatial distribution of a specific parameter are suitable in different
regions. In addition, different interpolation methods show better performance in a specific region in different
seasons. These facts motivated the authors to discover other ways to improve spatial distribution mapping,
including linking between interpolation methods selection and hydraulic, hydrologic and meteorological
characteristics of considered regions. To the best of the authors’ knowledge, this is the first study to analyze this
issue, and the first to propose an algorithm for choosing the best interpolation method for spatial distribution of
groundwater mapping electrical conductivity by considering physical criteria instead of only using mathematical
concepts. This research aims to reduce uncertainty associated with spatial interpolation methods. As following,
the general conceptions of the employed interpolation method were discussed. Initially, the empirical variogram
(semi-variogram) was computed for the study area based on the EC values. Due to the best variogram model
(spherical, exponential or Gaussian) by considering the GS+, some different interpolation methods including:
IDW, RBF, OK, SK, UK, GPI and LPI were applied in GIS to find out the best of them based on the “cross
validation” technique. Secondly, by using the selected method, the variability EC maps of the study area were
plotted. Then, hydraulic, hydrologic and meteorological characteristics of considered studied regions were
analyzed and, and by discussing achieved results a conceptual framework to select the best interpolation method
for spatial distribution of groundwater EC will be proposed. Finally, the proposed algorithm can be used to rank
the interpolation methods for other new area (e.g., some region which were located near the studied basin).
Most of the tools used in GIS are recurrent and time consuming. Thus, for easier solution of a problem in
GIS, instead of using conventional methods, the programmability potential of that can be used. One of the
programing languages that is compatible with GIS the most is Python. In this way, instead of producing different
layers and entering data into GIS, the process of problem solving and getting results is programmed and part of
the program is allocated to entering data which is EC. The benefit of this work is that programing the EC of the
groundwater based on the environmental, morphologic and hydraulic parameters can ease the calculation and
estimate of this parameter for different basin.
The present study, the variations of EC were defined as several important field data such as the annual
precipitation, temperature index, evaporation from the evaporation pan, flood and discharge, average height of
the study area, SAR (sodium absorption ratio) and EC of the wells of the study area, percentage of clay, percentage
of the sand and silt, bedrock inclination and the basin slope, hydraulic conductivity, storage coefficient of the
basin and also the types of the land usage. Finally, result of this study indicated that the proposed algorithm and
considering the hydrologic and meteorological data can proposed the suitable method of interpolation to attain
the EC values nearby the studied basin.

Inverse distance weighing (IDW)

It is a deterministic method suggested which is based on the assumption that as distance between the position
of the observation and estimate increases, its influence on the interpolated value decreases. Let r = (x, y), be the
position of a given point, the IDW formula would be as following:
F (r)Σn
k=1 w(rk )(f (rk ))(1)

where F (r) is interpolated value at, n is the number of observations, f (rk) is value observed at location rk= (xk,
yk) at station i and w (rk) w (rk) is the weight of that station obtained from the following relation:

dk (r)−p
W (rk ) = (2)
ΣK=1 dk (r)−p
n

√
where dk(r) is Euclidean distance between r and rk obtained from dk (r) = (x − xk )2 + (y − yk )2 , p = sole
model parameter that indicates the rate of lessening of influence of observations with distance. Value of pcan
have an enormous impact on the result of interpolation. More details on weights have been offered by51–53.

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Radial basis function (RBF)

An important group of interpolation methods which fall under the category of RBFs were offered by54,55. As
following:
F (r) = Σn
k=1 λk ϕ(||r − rk ||)(3)

where ∅ is definite positive RBF, r ∥ −rk ∥ is the Euclidean norm and λ k is the set of unknown weights
obtained as following:
F (rk ) = f (rk )(4)

Combining the Eqs. (3) and (4) yields a system of linear equations as following:
ϕA = φ(5)

where ∅ is a n×n matrix called the interpolation matrix and A = λk and ∅ = [fk ] are respectively, n×1 columns
of (unknown) weights and observed vales.
The RBF interpolation (obtained by solution of Eq. (5) for A) is dependent on the basis of function ∅
chosen (choices are usually, inverse multiquadric, multilog, natural cubic spline and thin plate spline) which
are dependent, on the Euclidean distance between points r and rk and the priori specification of R as a shape
parameter. More details can be found in56–58.

Kriging method
The theoretical basis for the method was put forward by the French mathematician Georges Matheron in 1960,
based on the Master’s dissertation of Danie G. Krige, who was a mining engineer in South Africa. Krige was
trying to estimate the most likely distribution of gold based on the samples obtained from boreholes.
Kriging is an interpolation method like IDW, in which the weights, unlike IDW are determined from spatial
and statistical relations obtained from the plot of empirical semi-variogram defined by:

r̂(h) = Σk=1 [f (rk ) − f (rk + h)]2 (6)

n(h)

where n (h) is the number of sample pairs f(rk), f(rk+h), which are separated by distance h.
γ (h)is an empirical function that is fitted to a specific functional form (variogram model) and some of its
most commonly used models are linear variogram59, exponential60, rational quadratic60, wave60, logarithmic61,
pentaspherical62and cubic62.
The assumption of the ordinary Kriging (OK) is that in the local neighborhood of each observation point, the
mean is constant63. Resulting in Eq. 1 with the condition:
Σn
k=1 W (rk ) = 1(7)

To make sure that the estimate is uniformly unbiased when making the variance of estimated error minimum.

Global polynomial interpolation (GPI)

In this method a mathematical function is used for fitting a smooth surface to sample points. The GPI surface
gradually changes from region to region, over the favorite area, so the global trend in the data is captured. In
comparison with IDW, in GPI, calculation of the predictions takes place using the whole dataset instead of using
the measured points within neighborhoods. A single global polynomial doesn’t fit a surface with a varying shape
very well and multiple polynomial planes would do a better job64.

Local polynomial interpolation (LPI)

Unlike GPI, LPI fits the local polynomial and uses the points only within the given neighborhood, rather than
the whole data. Then the neighborhoods overlap and the surface value at the center of neighborhood is set to be
the predicted value. GPI is mostly suitable for determining long-range trends in dataset, while LPI can be used
for generating surfaces that capture the short-range variation64.

Study areas and data

This study aims to analyze the salinity of groundwater reflected by groundwater EC in five regions of Khorasan
Razavi Province65–67 including Kashmar, Fariman, Doruneh, Sarakhs and Joveyn. Figure 1 shows the locations
of the considered aquifers. Several aquifers with different hydrological and hydrogeological features have been
considered to develop a conceptual framework for selecting the best interpolation method for spatial distribution
of groundwater EC.
The EC data of five aquifers was obtained from the dataset provided by Regional Water Company of Khorasan
Razavi in 2008, 2013 and 2018. EC is an indicator of ability of water to pass electricity through. Distilled or pure
water can’t pass electricity. It is the ions in water that let the electricity pass. So, there is a relation between EC and
concentration of dissolved solids. The EC of pure water in 25 degrees Celsius is 0.056 µmho/cm and in surface
water and groundwater water it may vary from 90 to several thousand µmho/cm.
First of all, the data with wrong x, y coordinates located outside the study areas must be removed. At some
points, there are even more than one sample. And since in ArcGIS, only one value can be assigned to each point,

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Fig. 1. The location of five aquifers of the study areas.

the average of the EC samples has to be calculated. The final data was saved in an Excel sheet with 3 columns,
xutm, yutm, EC as a Unicode Text (.txt) that could be imported into ArcGIS and used for interpolation.
In order to normalizing the data, EC data of each region was separately explored statistically by using SPSS.
For using data in ArcGIS, the data must be normalized and if the data is not normal, it must be normalized
using different methods. Table 1 represents the statistical parameters of data such as, mean, skewness, kurtosis,
maximum and minimum of values, which were calculated using SPSS.

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Year Aquifer Minimum Maximum Mean Stad. dev Skewness Kurtosis

Joveyn 220 12,780 2451 2777.8 1.46 4.90
Sarakhs 1800 8000 399 8615.8 0.620 -0.38
2008 Doruneh 586 10,350 7253.4 1996.7 -0.94 3.89
Fariman 484 4200 1742.8 831.4 519 2.619
Kashmar 363 1959 8080.9 357.1 1.29 3.95
Joveyn 350 14,800 3061.9 3125.6 1.41 0.92
Sarakhs 700 65,000 4017.7 4416.6 11.41 156.4
2013 Doruneh 690 14,180 758.6 2567.9 -0.41 3.93
Fariman 390 8950 1848.1 1088.7 1.85 3.99
Kashmar 395 7710 1113.2 981.5 3.51 14.81
Joveyn 500 7600 1398.3 1014.2 3.50 17.18
Sarakhs 300 13,000 3778.1 2257.1 1.55 3.05
2018 Doruneh 2450 11,100 7855.0 1994.0 -0.62 0.46
Fariman 220 8027 2114.5 1119.2 1.63 5.88
Kashmar 430 22,750 2183.3 3908.4 3.13 9.16

Table 1. Results of statistical analysis summary of EC data for five aquifers.

Fig. 2. Normalizing data: (a) Joveyn 2008, (b) Sarakhs 2008, (c) Doruneh 2008, (d) Fariman 2008, (e)
Kashmar 2008, (f) Joveyn 2013, (g) Sarakhs 2013, (h) Doruneh 2013, (i) Fariman 2013, (j) Kashmar 2013, (k)
Joveyn 2018, (l) Sarakhs 2018, (m) Doruneh 2018, (n) Fariman 2018, (o) Kashmar 2018

Methodology and method

Q-Q plots
In the next step, the Q-Q plots were drawn in ArcGIS. We use these plots to determine if the data is normal.
If the data is distributed about the line y = x, the data (EC) distribution is normal. If the line y = x cannot be
fitted through the data, it must be normalized. Using not normalized date in GIS would lead to great error in
interpolation. In this study, data of three regions of Kashmar, Joveyn and Fariman was normalized, while two
other regions followed normal distribution and left intact.
It must be noted that ArcGIS produces the results based on the real input data and doesn’t involve the
logarithm taking into the results. In fact, the interpolation takes place on the normalized data but the results are
presented in real scale. In Fig. 2, the normalized groundwater EC data for the study area is presented, as it can be
seen, the data has good agreement with normalized data.

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Fig. 3. semi variance and the best fitted model for EC in 2008, 2013 and 2018 for five regions: (a) Joveyn
(spherical), (b) Sarakhs (exponential) (c) Doruneh (linear) (e) Fariman (spherical) (f) Kashmar (spherical).

C0 + C C0
Region year RSS R2 C/C0 + C range (sill) (nugget effect)
Joveyn 2008 0.06 1.516 82,600 0.95 0.70 0.78
Sarakhs 2008 0.0036 0.453 0.576 26,470 0.31780 0.13490
Doruneh 2008 6.697e + 11 0.991 1.000 30,450 21,120,000 10,000
Fariman 2008 1.291e + 10 0.97 0.83 13,100 1,207,000 198,000
Kashmar 2008 3.113e-0.4 0.96 0.92 8560 0.18 0.01
Joveyn 2013 0.172 0.90 0.97 84,700 1.41 0.03
Sarakhs 2013 0.01 0.28 0.44 39,100 0.448 0.22
Doruneh 2013 4.22e14 0.598 0.99 81,100 41,300,000 10,000
Fariman 2013 6.63e-3 0.979 0.98 81,100 0.92 0.0180
Kashmar 2013 4.97e-3 0.929 0.997 11,580 0.35 0.001
Joveyn 2018 1.46 0.008 0.01 11266.7 0.52 0.52
Sarakhs 2018 0.07 0.12 0.50 64,500 0.51 0.25
Doruneh 2018 1.072e + 13 0.410 0.675 14,550 4,770,000 154,000
Fariman 2018 0.66 0.93 1 44,500 3.01 0.001
Kashmar 2018 4.66e-3 0.87 0.98 9230 0.21 0.003

Table 2. Specifications of semi-variogram fitted to EC at 2008.

Finding the best variogram model

By plotting the semi-variogram in GS+ program, the best variogram model fitted to spatial structure of the
parameter under analysis (i.e. EC) is determined with least Residual Sum of Squares (RSS) and maximum
coefficient of determination R2.
Figure 3 presents the results of analysis of semi-variogram for normalized data, the values and elements of a
variogram could be obtained for each given region and year. These values are presented in Table 2 for considered
regions.

Validation of interpolation methods

To validate the interpolation methods, the “cross validation” technique was used. In this way, from among the
dataset a sample point is removed, then using all interpolation methods, the value is estimated at that point.
The estimates are compared with the real observed value and the closest value to the sample is assumed to be
the result of the best interpolation method15. In this study, the parameters used for comparing the estimates

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RMSE calculated for each interpolation method

Study area Year SK OK UK IDW GPI LPI RBF
Doruneh 2008 2189.8 2342.2 13676.9 2259 3138 2761.1 7922.6
Sarakhs 2008 4162.5 4197.8 4258.8 4114.6 4171.2 4137.0 4169.4
Joveyn 2008 1275.3 1262.7 1008.0 1103.6 2587.2 1033.6 1059.8
Fariman 2008 280.8 256.2 255.2 257.7 432.1 483.5 259.1
Kashmar 2008 629.9 616.9 625.6 652.4 784.9 631.1 642.4
Doruneh 2013 1686.7 1734.0 1715.2 1771.0 2542.4 2716.6 1560.6
Sarakhs 2013 1103.2 1039.5 1845.7 1130 140 1168.3 1053.8
Joveyn 2013 12211.9 1206.2 1105.1 1162.2 2278.3 1049.2 1156
Fariman 2013 445.2 415.8 1735.4 429 591.8 425.2 425.2
Kashmar 2013 224.4 221.4 225.1 234 313.9 224.2 229.3
Doruneh 2018 2103 2024 1779.1 2209.1 2324.2 2060.1 2042.2
Sarakhs 2018 1216.1 1360.3 1360.2 1410.1 1788.2 1327.3 1399.2
Joveyn 2018 1153.2 1330.1 1331.1 1154.2 1243.2 1168.4 1153.2
Fariman 2018 448 349 331.1 307.2 568.1 292.2 358.2
Kashmar 2018 811.1 742.2 745.1 835.3 1102.2 1101.2 795

Table 3. Results of the best interpolation method for EC for study areas in 2008, 2013 and 2018.

year 2008 2013 2018

Doruneh RBF SK UK
Sarakhs OK IDW LPI
Joveyn LPI UK SK
Fariman OK UK GPI
Kashmar OK OK OK

Table 4. The best interpolation method for five regions in 3 years.

and sample are: the ratio of the nugget effect to range, coefficient of determination of variogram model (r2) and
RMSE (Root Mean Square Error).

The best interpolation method for EC in 2008, 2013 and 2018

Where the best variogram model was chosen, the EC data was input into ArcMap and interpolation was
done using: simple kriging (SK), ordinary Kriging (OK), universal Kriging (UK), Inverse distance weighing
(IDW), Global polynomial interpolator (GPI), Local polynomial interpolator (LPI) and Radial based function
(RBF). Then using the “cross validation” technique and RMSE (lower RMSE indicates a smaller error) the best
interpolation approach was determined for each region. The results are presented in Table 3.
The best interpolation method for five regions were presented in Table 4 based on the maximum value of
RMSE in Table 3. As it can be seen, for different years, different methods have been chosen and it might be
because of the different number of samples with different locations in the same area. So, if there was the same
number of samples with the same coordinates, sure there was more similarity between the results.

Result and discussion

Suitable interpolation methods
Based on the results of Table 4, the variability maps are produced as following.

Doruneh basin
Figure 4 shows the EC variability maps of Doruneh in 2008, 2013 and 2018. The highest level of EC can be
seen in the west and north east of this city and the lowest level in the south east and the center. Considering the
mountains in the north of this sub basin, it seems that in regions with high altitude the EC reach higher values.
Also, the maximum salinity of the area has decreased over the years, but the expanse of the saline soils has
increased over the time. It can be deduced that the salinity is being transferred from regions with saline soils to
regions with no salinity, which could be affected by the precipitation.

Sarakhs basin
The highest EC level was observed in the north and the lowest in the east and center in 2008 (see Fig. 5a).
Comparisons in 2013 and 2018 (see Fig. 5b and c) illustrated that the salinity decreased in the north and became
more uniform. Since 2013 to 2018, the peak of salinity has been transferred from the northern to the central part,
while the minimum level remains in the west.

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Fig. 4. EC map of Doruneh (µmho/cm) (a) Calculated by RBF (2008), (b) calculated by SK (2013), and (c)
calculated by UK (2018).

The maximum and minimum of EC level in 2013 are related to the northern and central parts. In 2018,
the maximum EC is related to central and the minimum EC to the eastern regions. Considering the maps, it is
concluded that over the time, the EC is increasing in the region.
Since Dousti Dam and a river are located near this area, there is a very high hydraulic gradient in the region
which could have a great impact on the EC of the water. Hydraulic gradient of the river bed, leaches the salts and
the EC is decreased.

Fariman basin
In 2008, the maximum EC is found in the south east of the city and the minimum was located in the North West,
(see Fig. 6). Also, in 2013, the maximum EC was still in the south east and the minim was constantly located in
the North West and center of the city. In 2018, the western, south western and central regions of this city, had the
highest level of EC and in north east the minimum EC has been reported.
In total, it can be deduced that the EC has decreased over the study period in Fariman region. Considering
the dominant slope of the region which is from the North West to the south east, the groundwater washes the
mixed salt into the soil and increases the concentration of them over the time.

Joveyn basin
In 2008, the maximum EC is seen in the west and east of this city and the central, northern and southern regions
enjoyed the minimum EC (Fig. 7). Furthermore, the maximum EC was still related to the east and expanding
to the center in 2013. In 2018, the maximum EC is in the west and the minimum is still in the south, center and
north.
Considering the results of the 10-year study period (2008–2018) shows that, the maximum EC in the region
has decreased, but the value of the minimum EC has been increased significantly. Also, the expanse of the
regions with highest EC has reduced. To explain the happened status for EC, as it can be seen in Fig. 7, Joveyn
is located between two mountain ranges, one in the north and the other in the west. Each one with its specific

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Fig. 5. EC map of Sarakhs (µmho/cm). (a) Calculated by OK in 2008, (b) calculated by IDW in 2013, and (c)
calculated by LPI, in 2018.

water yield can have impact on the EC of the region. The lowland located in the north east, can be a place where
the ions carried by groundwater can accumulate and increase the salinity of the water.

Kashmar Basin
In 2008, the maximum EC was located in the south of this regiom and the north of this area were allocated to the
minimum EC. Also, the maximum and minimum EC were the same as 2008 in2013. As it can be seen in Fig. 8c,
the maximum EC was switched to the south and the minimum was in the north and North West, constantly.
By considering the corresponding sub-plots (see Fig. 8), it can be inferred that the EC was increased over the
time in 2008 to 2018. Furthermore, the reduction of expanse of the areas with lower EC diminished over the time
which can show that the salinity is transferring from other regions to the south of this region.
A closer look at the region shows that in places where there are narrow valleys, the water of the ephemeral
rivers is trapped and the EC values are increased consequently.

Relationship between meteorological parameters and EC

After finding the best interpolation method for the study areas, finding the best interpolation method for a new
neighboring region is considered which can assess to predict the best interpolation by using its meteorological
parameters. An algorithm has been designed to generalize the best interpolation method of the study area to other
regions in Fig. 9. For solving this flowchart an Excel sheet has been designed. The details of the analyses of the
meteorology, morphology, hydrology and hydraulic data of the study areas are presented as the supplementary
sections.
In flowchart shown in Figs. 9 and 14 parameters which are effective on EC in any region were considered as
the input data. Classification of the parameters for giving points is depicted in Fig. 10. First of all, in Khorasan
Razavi, the best interpolation method was determined for several sub basins using the “cross validation”
technique in GIS. In the next step, the best interpolation method was generalized to the neighboring sub basins
using the proposed algorithm. The algorithm is based on classification of all 14 parameters and putting the
interpolation methods into any of them. For example, if the precipitation of the new sub basin is 130 mm, the
priority is given to the method which located in the range of 100 to 140 mm (see Fig. 10). For a new sub-basin,
the values of 14 parameters are studied to see which class they fall in and based on that, the new sub basin gains

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Fig. 6. EC map of Fariman (µmho/cm) (a) Calculated by OK in 2008, (b) calculated by IDW in 2013, and (c)
calculated by LPI, in 2018.

some points for each interpolation method. The interpolating method that has got the most points is set to be
the best interpolation method for the new sub basin. If the precipitation in a basin is 150 mm, it is located within
the range of 140 to 180 mm as it can be seen in this class, RBI has the priority. This process is continued for all
14 parameters and eventually one method gets the most points. An Excel sheet has been designed that shows the
procedure. Also, it should be mentioned that the used hydraulic and methodology parameters were presented
into the supplementary section.
In the following sections the hydrology, meteorology and hydraulic data of the study area are presented.
These parameters are classified and the new region falls into one of these classes and if it gains the necessary
points, the interpolation method of that region is assigned to that.

Conclusion
By plotting the semi-variogram in GS + program based on different method as Global Polynomial Interpolation
(GPI), Inverse distance weighing (IDW), Radial basis function (RBF), Kriging method, Global Polynomial
Interpolation (GPI), Local Polynomial Interpolation (LPI), the best variogram model fitted to spatial structure
of electrical conductivity. Finally, by considering the acceptable range for different parameters which impact
on EC and evaluating their impacts by scaling, the best interpolation method has been selected for that area
for employing their neighborhood basin. Result indicated that the precipitation located within the range of 140
to 180 mm, RBI has the priority. This process is continued for all 14 parameters and eventually one method
gets the most points. Finally, by using the provided algorithm, the best interpolation methods were proposed
based on the input parameters. It worth to be mentioned that using the interpolation methods based on the
environmental parameters can provide a numerical process to predict the EC.
In future studies, the spatial distribution of groundwater EC can be studied by the use of equations governing
the flow of water and solutes in the soil and the results compare with the present approach. Also, an optimization
model can be added in the presented methodology. Moreover, other interpolation methods can be used to
increase the applicability of the present methodology.

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Fig. 7. EC map of Joveyn (µmho/cm) (a) Calculated by OK in 2008, (b) calculated by IDW in 2013, (c)
calculated by LPI in 2018.

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Fig. 8. EC map of Kashmar (µmho/cm) (a) Calculated by OK in 2008, (b) calculated by IDW in 2013, (c)
calculated by LPI in 2018.

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Fig. 9. Proposed algorithm for giving points and choosing the best interpolation method.

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Fig. 10. Classification of parameters for the algorithm.

Data availability
If necessary, the data base could be made available upon request to the authors.

Received: 26 May 2024; Accepted: 29 November 2024

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Author contributions
S.S.: methodology, formal analysis, software, visualization, and writing-original draft. R.B.: conceptualization,
supervision, formal analysis, and Writing-review and editing. M.B.: visualization, and writing-review and edit-
ing. S.S.: writing-review and editing and formal analysis. M.M.: writing-review and editing and formal analysis.

Funding
There is no funding source.

Declarations

Competing interests
The authors declare no competing interests.

Ethics approval
There are no relevant waivers or approvals.

Consent to participate
Authors consent to their participation in the entire review process.

Additional information
Supplementary Information The online version contains supplementary material available at ​h​t​t​p​s​:​/​/​d​oi​ ​.​o​r​g​/​1​
0​.​10​ ​3​8​/​s​4​1​5​9​8-​ ​0​2​4​-​8​1​8​9​3​-​y​​​​.​ ​​
Correspondence and requests for materials should be addressed to R.B.
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