Reza et al.

In the semivariogarm analysis, the nugget values

represent the variability of measured heavy metals

level at zero distance, which are positive in this

study for all the heavy metals. This spatial random

variance is caused by the artificial nature of heavy

metal pollution in soil; meaning that anthropogenic

inputs are a significant source of heavy metals in the

study area. The sill, sum of partial sill and nugget,

is the maximum variance between data pairs and

reflects the variations of regionalized variables in the

study area. The ratio of nugget and sill is commonly

used to express the spatial autocorrelation of regional

variables, which also indicates the predominant

factors among all natural and anthropogenic factors

(Robertson et al., 1997). The ratios of nugget and sill

between 0.25 and 0.75 represented moderate spatial

dependence; those below 0.25 represented strong

spatial dependence; and all others represented weak

dependence. Cr and Pb were strongly spatially

dependent suggesting that they are affected by

anthropogenic factors only while Ni was moderately

spatially dependent suggesting that they are affected

by either anthropogenic or natural factors or both.

Table 3. Evaluation performance of ordinary kriged map of

heavy metals through cross-validation

Mean

Heavy

Mean square

Goodness of

absolute error

metals

error (MSE)

prediction (G)

(MAE)

Cr

0.004

160.7

15.7

Cd

0.048

3.8

28.0

Pb

0.107

333.2

36.1

Ni

9.33

661.7

2.3

Spatial distribution and risk assessment of heavy

metals pollution

Using the available measurements for Cr, Cd, Pb

and Ni concentration as well as the aforementioned

structural models, spatial maps of these pollutants

were produced using the ordinary kriging

procedure (Journel and Huijbregts, 1978). The spatial

distribution maps of Cr, Cd, Pb and Ni (Figure 2a−d,

respectively) showed that high concentration of

heavy metals was located in the low lying paddy

Figure 2 Spatial distribution maps of (a) Chromium; (b)

792