Determining Sampling Numbers For Survey Of Soil Heavy Metals

Determining the optimum sampling numbers of heavy metals in soil is the premise and foundation for research of heavy metals in soil.It is one critical issue to achieve credible results when surveying heavy metals in soil and sustainable land use or remediation decisions.Previous research for determining sampling numbers were more focused on statistics under a normal distribution,but there were few by statistics under a log-normal distribution.Although some scientists proposed the methods under a log-normal distribution to determine optimum sampling numbers in decision-making units with known variations of soil heavy metals,the methods had been limited because the high precision method was too complex.Moreover,the correction equations for the high precision method not only overestimated or underestimated the sampling numbers,but also these equations had not been applied to estimate the sampling numbers for survey of soil heavy metals.Most importantly,whether the methods under a normal or log-normal distribution,prior information about the variation was a prerequisite.In decision-making units with unknown variations of soil heavy metals,the methods under a log-normal distribution to determine sampling number have also been little reported.T herefore,taking soil cadmium(Cd)as an example,the database of Cd from 17 units at different scales was collected by field sampling,and databases of soil cadmium were built by setting different sampling densities or areas in the 17 units.Combined the database of soil cadmium with published literatures,the objective of the present study was to find different methods in the units with unknown or known variations to determine the sampling numbers of soil heavy metals.The main methods and results were as follows:(1)First,in decision-making units with known variations(i.e.geometric standard deviation)of soil Cd,the ordinary least-squares were used to adjust the classical lognormal formula by setting different fitted models.Second,both predicted sum of squares of errors and coefficient of determination(R2)were used to evaluate the different models.Finally,a simple adjustment of the classic log-normal equation by ordinary least-squares(i.e.OSN OLS method)was used to determine sampling numbers in decision-making units with known variations.The method not only was computationally simple and straightforward because of its without relying on consulting the Land's published tables(the method with high precision),but also effectively avoided the risk of overestimation or underestimation of sampling numbers.Moreover,compared with other methods(e.g.classical equation,classical log-normal equation,Hale's method,Armstrong's method,and quadratic term approximate equation),determining sampling numbers by OSN_OLS method were closer to the optimum numbers.Finally,mapping by OSN_OLS not only described overall trends of the spatial variation,but also improved the prediction accuracy for soil heavy metals compared with other methods.(2)In decision-making units with known variations(i.e.coefficient of variation)of soil Cd,the relationships between geometric standard deviation and coefficient of variation characterizing the log-normal distribution were built by statistical methods.Combined the relationships,the OSN OLS method was further deduced.Therefore,an effective method to estimate sampling numbers was proposed in decision-making units with the known coefficient of variation.(3)In decision-making units with unknown variations of soil Cd,the relationships between sampling areas and coefficient of variation were built by boundary line analysis.Combined the relationships with an aforementioned method(i.e.the method to estimate sampling numbers based on known coefficient of variation),a simple equation as a function of sampling areas could be used to determine sampling numbers,with the errors ranging from 13%to 33%at the sampling areas of 0.03-10 km2.Moreover,when the sampling cost was enough and the improved accuracy was requested,the increased sampling numbers were recommended as 1.53 times as the numbers calculated by the simple equation.Therefore,this study systematically established the equations to determine sampling numbers in the units with known or unknown variations of soil heavy metals,which provided the effective and scientifi c guidance for surveying heavy metals in soil and sustainable land use or remediation decisions.