Evaluating sample sizes and design for monitoring and characterizing the spatial variations of potentially toxic...

Cost-effective, representative and spatial coverage sampling designs are required to monitor the effects of potentially toxic elements (PTEs) in the soil. This study aims to evaluate the minimum sample sizes and placement of soil sampling designs to monitor and characterize the spatial variation of the PTEs (Cu, Zn, Cd, Cr, Pb, and Ni) in the soils. However, there is no standardized approach for evaluating the optimum soil sample size and monitoring location because of the spatial heterogeneity of PTEs in the soil. As a result, three broad techniques were applied. The first step was to use Global Moran's I and q-statistic values to describe the variability of soil PTEs and select appropriate evaluation methods. Second, using simple random sampling (SRS), ordinary kriging (OK), and Mean of Surface with Non-homogeneity (MSN), we estimated and evaluated soil PTEs in the current soil sampling schemes. Finally, MSN and spatial simulated annealing (SSA) optimization techniques were used to assess the required sample sizes and placements in the existing designs. Method performance was evaluated using a standard error (SE) and a relative standard error of the mean (RSE). Except for Zn and Cd, all PTEs tested showed heterogeneous distributions over the area. The MSN lowered the predicted SE by 79-86 % compared with SRS. The OK approach also outperformed the SRS method regarding mean estimated values of soil PTEs by 42-57 %. After SSA refined the initial design, the predicted SE by MSN of Cr and Zn was lowered by 13 % and 39 %, respectively. The MSN was effective with small sample sizes, reducing sample sizes and surveying costs by 39 % after SSA optimized the existing sample numbers. Thus, integrating various sampling strategies may be efficient for building optimal sample designs to monitor PTEs in the soil.