Sampling particulate matter for analysis - Controlling uncertainty and bias using the theory of sampling.

Sampling particulate matter for measuring the content of an analyte is a routine operation in many fields of engineering and science. However, sampling can lead to important bias and variance in concentration estimation because of sampling errors stemming from particulate matter heterogeneity. The goal of this study was to quantify bias, reproducibility and the degree of representativeness of a probabilistic sampling (PS) technique following principles from the Theory of sampling (TOS) and grab sampling (GS). PS was designed to control sampling errors, while GS did not exert any control over them. GS also included a step of sieve screening, which is common during sampling in some fields (e.g. soil sampling). Both techniques were used with two different analytes, namely steel microspheres and copper sulfate, at two different concentrations, in order to assess sampling errors and sampling performance. The sampling method had the most significant effect on sampling bias and relative variance, and therefore, on the degree of sampling representativeness. The most important result is the demonstration that probabilistic sampling improves the degree of representativeness of concentrations measurements by more than two orders of magnitudes by significantly decreasing bias and relative variance. The lot containing the physical analyte lead to larger bias and relative variance compared to the lot containing the chemical analyte. GS resulted in largely biased results and a poor degree of representativeness. The results have also highlighted a significant problem associated with the screening of larger particles as performed in GS. This alteration of the primary sample decreased the variability of the resulting concentration measurements, but it also biased them significantly.

Representativeness of laboratory sampling procedures for the analysis of trace metals in soil.

This study was conducted to assess the representativeness of laboratory sampling protocols for purposes of trace metal analysis in soil. Five laboratory protocols were compared, including conventional grab sampling, to assess the influence of sectorial splitting, sieving, and grinding on measured trace metal concentrations and their variability. It was concluded that grinding was the most important factor in controlling the variability of trace metal concentrations. Grinding increased the reproducibility of sample mass reduction by rotary sectorial splitting by up to two orders of magnitude. Combined with rotary sectorial splitting, grinding increased the reproducibility of trace metal concentrations by almost three orders of magnitude compared to grab sampling. Moreover, results showed that if grinding is used as part of a mass reduction protocol by sectorial splitting, the effect of sieving on reproducibility became insignificant. Gy's sampling theory and practice was also used to analyze the aforementioned sampling protocols. While the theoretical relative variances calculated for each sampling protocol qualitatively agreed with the experimental variances, their quantitative agreement was very poor. It was assumed that the parameters used in the calculation of theoretical sampling variances may not correctly estimate the constitutional heterogeneity of soils or soil-like materials. Finally, the results have highlighted the pitfalls of grab sampling, namely, the fact that it does not exert control over incorrect sampling errors and that it is strongly affected by distribution heterogeneity.

Analysis of procedures for sampling contaminated soil using Gy's Sampling Theory and Practice.

Soil sampling is a critical step in environmental site assessment studies. The representativeness of soil samples has a direct influence on financial, liability, environmental and public health issues associated with the outcome of remediation activities. Representativeness must be quantified for assessing and designing soil sampling procedures. Gy's Sampling Theory and Practice (STP) was used to analyze the reproducibility of two soil sampling procedures, namely a procedure based on grab sampling (GSP) and an alternative procedure (ASP) developed from STP principles. Sampling reproducibility, a component of sampling representativeness, was determined by theoretical calculations and experimental measurement of relative variances in trace metals concentrations at each stage of both sampling procedures. The ASP significantly increased the reproducibility of soil sampling compared to the GSP. Larger relative variances occurred during field sampling for the ASP and during laboratory sampling for the GSP. They were due to subsample mass reduction without control over particle size. Relative theoretical and experimental variances were in agreement. However, large discrepancies were observed for all sampling stages of both procedures between absolute theoretical and experimental relative variances. In the case of Pb, theoretical calculations were closer to experimental measurements when using a calculated value of the liberation factor (l) based on mineralogical data rather than l=1. It was shown that the b-exponent had a large influence on theoretical variances. Increasing the estimate of b from 0.5 to 1 largely improved the agreement between theory and experiment. Finally, 99% of experimental relative variance was explained by sampling errors compared to analytical errors.