Uncertainty also arises from errors in data collection and modeling, with error being defined as the difference between a true value in nature and a measured or predicted value (Krivoruchko 2011). Specific examples of error contributing to uncertainty in the distribution of a parameter of interest include:

• Sampling bias and error can result from the collection of samples that are not representative of the spatial and temporal heterogeneity (the underlying variation) of the media being sampled.
• Locational error can result from imprecise measurement of sample collection locations, which is more or less significant at different study scales.
• Error in laboratory or field-based analytical techniques can result from using instruments with different precision. This type of error includes error caused by variation that is below the detection capability of the sampling program.
• Error can be introduced by interpolation methods themselves, which may be caused by using assumptions that are not supported by the data, or by characteristics of the interpolation algorithm such as the tendency of kriging to smooth out spatial variation. The latter example is a form of conditional bias that overestimates small values and underestimates large values (Goovaerts 1997). Interpolation method performance can be evaluated through cross-validation, which compares interpolated to measured values to quantify prediction accuracy.

More complex and advanced geospatial methods recognize that there is error in spatial predictions, and attempt to quantify the resulting uncertainty. At its most basic level, kriging incorporates uncertainty through use of a nugget representing the white noise variation in the model (sampling error, analytical error, or smaller-scale variation that is below the detection of the current sampling program). Kriging also provides prediction standard error estimates that can be used to build a variance map to evaluate uncertainty. Indicator kriging is another way to evaluate uncertainty by generating maps that depict the probability of exceeding threshold values.

Kriging and certain more complex methods of evaluating uncertainty are inherently limited because they focus on local uncertainty associated with single estimate locations and because of the smoothing tendency of kriging. Conditional simulation attempts to better quantify true uncertainty by reconstructing the spatial heterogeneity, or variation, intrinsic to the environmental system investigated. As a result, simulation better assesses spatial uncertainty as whole, or the joint uncertainty considering multiple locations taken together. This method is especially useful for data sets with extreme values and heterogeneity, which is often the case with contaminant concentration data (Goovaerts 1997); see the example of using conditional simulation to create statistical and probability maps for uncertainty analysis.

Stratified random sampling can be a good alternative to avoid such biases. This approach provides information about different spaced samples, which may improve the knowledge of the experimental variogram. Moreover, this strategy allows some flexibility to resolve the access issues when planning the field investigation. Figure 12 includes examples of systematic sampling and stratified random sampling.

Figure 12. Example of systematic sampling (top) and stratified random sampling (bottom).

If the goal is to identify potential contamination sources, a sampling approach using a cross or a spiral sampling geometry can be implemented. Conducting a sampling strategy by drilling closely spaced boreholes improves the understanding of the contamination and provides better data for fitting the empirical variogram. Figure 13 includes an example of sampling using a cross geometry approach with sampling locations at the grid crossings (sampling points S1, S2, S3, S15, S17, S19 and S20) so that there are more closely spaced sampling locations.

Figure 13. Example of sampling by using a cross geometry approach near a contamination source.

When sampling for vertical delineation, collecting samples from each geological unit is a good approach. It is important to collect samples at different depths in the same geological layer (see Figure 14). This approach provides information about the attenuation of the contamination at depth.

Figure 14. Example of vertical sampling near a contamination source on a site consisting of three different geological units.

Often, the delineation of the contamination is less complete in the vertical direction than in the horizontal direction. Using field-based measurement technologies (for example, mobile lab) during the initial characterization step facilitates the complete delineation of contaminant sources (USEPA 2003; ITRC 2003; and ITRC 2007). These methods can reduce uncertainties.

Additional information can be found in the USEPA (2002a) guidance on choosing a sampling design, and the ITRC (2012a) guidance on incremental sampling methodology.

Which analytical results to include in the geospatial modeling should be considered when planning the evaluation. For example, what samples should be included as representative for a contamination source? Samples with concentrations slightly below a remediation threshold may or may not be considered part of the contamination source based on their physical location adjacent to higher concentration results. Also, decisions about concentration results that are below a laboratory detection limit should be considered. More information about managing nondetect data in statistical analyses is included in GSMC-1, Section 5.7.

These and other sources of uncertainty are difficult to manage. The strategy for managing sources of uncertainty for a specific project should be documented so that the geospatial modeling results are more transparent and the impacts of the uncertainties can be minimized.

USEPA offers additional guidance on this topic (USEPA 2006a; USEPA 2006b; USEPA 2008; USEPA 2011a).