Determining optimum sampling numbers for survey of soil heavy metals in decision-making units: taking cadmium as an example

Optimum sampling number (OSN) is one critical issue to achieve credible results when surveying heavy metals in soil and undertaking risk assessment for sustainable land use or remediation decisions. Although traditional methods, such as classical statistics, geostatistics, and simulated annealing algorithm, have been used to determine OSN for surveying soil heavy metals, their usefulness is limited because the distribution of soil heavy metal concentration approximately follows a log-normal distribution. Furthermore, existing correction equations for the log-normal distribution may overestimate or underestimate the OSN, and they have not been applied to estimate the OSN of soil heavy metals. The objective of the present study was to find a simple model under the log-normal distribution that determined the OSN for surveying of soil heavy metals in decision-making units. To test the effectiveness and accuracy of this model, soil heavy metals in 17 contaminated areas generating 200 multiscale units were analyzed. Determining equations for OSN, including classical statistics and approximate correction equations, were compared. Results showed that the equation for determining OSN by ordinary least squares (OSN_OLS) was computationally simple and straightforward because of an adjustment of the classic log-normal equation without relying on consulting the adjusted Student t-tables for a noncentralized data distribution. Compared with other OSN determining equations, sampling numbers by OSN_OLS were closer to optimum numbers and effectively avoided the risk of overestimation or underestimation. Descriptive statistics indicated that the estimated pollution results by OSN_OLS in representative units were very similar to original sampling with more sampling information. Furthermore, compared with other OSN-determining equations, the mapping based on OSN_OLS not only described the trends of spatial variation but also improved mapping accuracy. We conclude that OSN_OLS is an effective, straightforward, and exact model to estimate the OSN for surveying of soil heavy metals in decision-making units.