A new method to consider spatial risk assessment of cross-correlated heavy metals using geo-statistical simulation

The soil samples were collected from 170 sampling stations in an arid area in Shahrood and Damghan, characterized by prevalence of mining activity. The levels of Co, Pb, Ni, Cs, Cu, Mn, Sr, V, Zn, Cr, and Tl were recorded in each sampling location. A new method known as min/max autocorrelation factor (MAF) was applied for the first time in the environmental research works to de-correlate these elements before their geo-statistical simulation. The high cross-correlation among some elements, while poor spatial correlation among the others, could have made spectral decomposition of MAFs unstable, resulting in some negative eigenvalues, so it was decided to reduce the dimensionality of the original variables by Principal Component Analysis (PCA). The resultant 6 heavy metals (Cr, Mn, Cu, V, Ni, and Co) were converted to their respective MAFs followed by their geo-statistical simulation using Sequential Gaussian Simulation (SGS) independently. Examination of the cross-variograms of MAFs indicated that the resultant factors had been rigorously de-correlated, especially at zero lag and around ∆ lag distance. Several validation checks including reproduction of variograms in data and normal score space, close matching between distribution of MAFs versus simulated realizations, and reproduction of descriptive statistics and data histograms all confirmed that the data values had been honored by this applied method. The results obtained indicated that this method could reproduce the data values as well as the spatial continuity of heavy metals (e.g. semi-variograms) successfully. In addition, this technique is simpler and more computationally efficient than its equivalent sequential Gaussian co-simulation as fitting a linear model of co-regionalization (LMC) is not required in the data-driven MAF method.