There is no magic number of increments that will control the GSE for all sampling situations, but 60 increments is suggested as a minimum for soils containing residues of energetics at military installations. However, this is completely dependent on the degree of distributional heterogeneity of the material within the DU. Thus, there will exist materials and/or sample quality criteria where 100 or more increments are required [19, 20]. The number of increments is never based on what is easy to collect but is based on the number required to minimize the GSE where it does not impact the confidence in and the ability to legally and scientifically defend the decision. It may be appropriate to use 50 increments; however, this number must be justified.
Materialization error
Materialization errors (MEs) are caused by a lack of sample correctness that creates a sampling bias. While analytical biases are routinely estimated for analytical measurements, sampling bias is very difficult, if not impossible, to estimate. Sampling bias is inconsistent and therefore conventional bias correction techniques to estimate and correct bias cannot be employed. It is therefore critical that errors of bias are minimized as much as possible so the effect on sampling error is minimized to an insignificant level.
The correct increment shape for surface soils is a cylinder. Incorrect shaped increments will cause a bias in the concentration estimation. The concentration of the analyte in the increment will differ between the examples shown below for analytes that reside primarily on the surface. Only the mass collected in a core configuration will give the true concentration to the desired depth. Increments also need to be approximately the same mass to ensure uniform representation of the areas within the DU from which they are taken. Consistent increment mass is more easily controlled by using a coring device than a scoop or trowel. Scoops should only be used in the rare instance when a coring device will not work. Trowels are strongly discouraged because of their gross inaccuracy. When a scoop is used, great care must be taken to ensure that an approximately cylindrical shape is collected and that the increment masses are consistent. CRREL has developed a tool for the collection of unbiased surface soil (0–5 cm) samples (see the next section on error). This tool allows for the rapid and consistent collection of multiple increments [21].
2.3.4 Data evaluation and inference
Once the samples have been properly subsampled and analyzed, the analytical data needs to be reviewed to ensure that SQC was met. This will include not only the standard analytical quality control (QC) but also the QC associated with estimations of sampling and sample processing errors [22, 23]. A good test of the adequacy of the mass and the number of increments collected is to determine the confidence limits for replicate samples (3–5 reps are needed). If confidence limits are not met, the sampling error must be reduced by increasing mass and/or increments. For example, if the number of increments being collected in a project’s DUs is 50 increments and the confidence limits or relative standard deviation goals are not being met, it is likely that the number of increments is not being properly considered and will need to be increased. For similar sized increments, an increase in the number of increments will result in an increase in mass per sample, further reducing the sampling error.
After the data has passed the data evaluation step, inferences can be made. There may be only one inference or there may be many [16]. Each inference is performed separately. The inference may be as simple as using the single result from the laboratory to estimate the concentration in the DU or it may involve calculations such as the average from multiple test portions.
2.4 Error and error reduction
The previous section discussed sampling theory and the primary sources of error described by that theory. There are two types of errors associated with all sampling: FSE, which is caused by compositional heterogeneity of the contaminant, and GSE, caused by the heterogeneous spatial distribution of the contaminant particles in the area to be characterized (DU) [7]. The DU cannot be sampled by simply going to the field, obtaining a few grams of soil, and analyzing the sample, unless there is no compositional or distributional error associated with the contaminant. FSE and GSE associated with a contaminant in a DU will render a discrete or grab sample meaningless. Inferences associated with any sample are based on distributional and compositional error and, for a grab sample, these inferences are quite limited. Rasemann goes into great detail on developing a range of values quantifying these errors for the sampling and analysis of industrial waste dumps [24]. His conclusion at the time of publication was that the greatest source of error in characterization is sampling error.
2.4.1 Magnitude of error
In the past, the majority of effort to reduce error in sampling has been misdirected. Rasemann has found that the greatest error in environmental characterization occurs not in the analytical lab, where 95% of the effort to reduce error occurs, but in the field while collecting the original sample. Little or no real effort had been expended in the field to reduce sampling error in the past. Much of the reason for this is because little or no quality assurance (QA), such as replicate sampling, had occurred in the field. It is also much easier to go to the field, fill a jar with 250 g of soil, and analyze 5 g taken from the top of the sample while back in the lab. With no QA, the results of the analysis are often presented as the definitive, usually to five or six significant figures. The perception of the immutability of the grab sample began to come into question when sites declared clean (or dirty) turned out, at great expense, to be just the opposite. Rudimentary QA, generally consisting of obtaining co-located ‘replicate’ samples, had contaminant concentrations that were sometimes 3–4 orders of magnitude different from each other. Rasemann estimated that sampling error is around 1000%, sample preparation error is around 300%, and analytical error, where the greatest effort to reduce error occurs, amounts to only about 3% (table 2.1).
Table 2.1. Three common sources of measurement error [24].
| Process | Error (% of true value) |
|---|---|
| Sampling | 1000% |
| Sample preparation | 100%–300% |
| Analytical measurement | 2%–20% |
2.4.2 Controlling for error
Table 2.2 illustrates the effect that controlling for various error sources has on the root mean square (RMS) global estimation error (GEE) of the final estimation of the mean concentration of a contaminant in a DU. Sampling error obviously has the greatest effect on the GEE until the maximum feasible sampling error reduction is achieved, at which point sample preparation error begins to dominate. Error reduction effects are illustrated in figure 2.1. Note that there will always be error associated with every step of the characterization process, and that sampling error is likely to be the largest source, even when