Research progress of methods for determining sampling numbers of soil heavy metals survey

Abstract: The soil contamination by heavy metals is one of the increasingly serious environmental issues worldwide, and it is believed to pose a high risk to natural environments and human health when their accumulation exceeds certain levels. Optimum sampling numbers in a sampling unit can be an effective tool to achieve credible results when surveying heavy metals in topsoil and undertaking risk assessment for sustainable land uses or remediation decisions. Based on a large amount of literatures and available data in the recent years, the current situations of sampling numbers, methods on determining optimum sampling numbers for survey of soil heavy metals were reviewed in this paper and future research issues in this area were discussed. Also, based on empirical methods (e.g. purposive sampling), statistics (including different methods under the normal distribution and lognormal distribution) and empirical methods combined with statistics (e.g. multi-stage sampling), the merits and demerits of these methods on determining optimum sampling numbers for survey of heavy metals in topsoil were then systematically analyzed and compared. The results showed that there were some challenges or issues. First, the consideration of sampling scales or sampling units was lacked when determining optimum sampling numbers for survey of soil heavy metals. Second, researches for determining optimum sampling numbers were more focused on the empirical methods, but there were few by statistics or empirical methods combined with statistics. When determining optimum sampling numbers by statistics, they were more focused upon the methods under the normal distribution, such as classical statistics, geostatistics and simulated annealing algorithm. However, their usefulness was often limited because there was adequate empirical evidence and a theoretical proof to illustrate that the distribution of soil heavy metal content often approximately followed a lognormal distribution. The application in determining optimum sampling numbers for survey of soil heavy metals under the lognormal distribution, which has little been reported to date. Third, although some scientists proposed the methods to determine optimum sampling numbers under the lognormal distribution, including the Land's accurate method and other correction equations of this accurate method (such as Hale's method, Armstrong's method, classical lognormal equation, quadratic term approximate equation and Chebyshev inequality), the Land's accurate method under the lognormal distribution was too complex because of the need for computing by an iterative algorithm and requiring extensive tables. The different correction equations had been limited because they not only were not enough to cover the different coefficient of variation of soil heavy metals, but also overestimated or underestimated the optimum sampling numbers. Moreover, these mentioned different methods under the lognormal distribution had not been applied to estimate the optimum sampling numbers for survey of soil heavy metals. Therefore, sampling scales or sampling units of soil heavy metals were defined when determining optimum sampling numbers. The researches on determining optimum sampling numbers by statistics and empirical methods combined with statistics were strengthened. The accurate methods on determining optimum sampling numbers under the lognormal distribution were explored. The methods suited for determining optimum sampling numbers for survey of soil heavy metals in a sampling unit were sought. These were important guarantees to achieve scientific risk assessment, effective environmental decision-making and pollution control of soil heavy metals.