Choosing efficient and effective sample spacing (in space or time) for any medium can help to optimize a sampling program. For any site, the applicable environmental media may vary and evaluations may be conducted for multiple environmental media. The purpose for each evaluation may differ by medium as well; see Common Misapplications for information on how these differences can result in misapplication of geospatial methods. Additionally, see the discussion on using geospatial results in selection of sample spacing or sampling plan design.

Geospatial Method:

Variograms (spatial or temporal) can identify distances in space or time where samples would provide independent (noncorrelated) data so that the effort does not yield duplicative information. The range interpreted from the variogram is an indication of the spacing of noncorrelated data. A large fraction of the range is a reasonable basis for sample spacing.

A representative map that effectively portrays the spatial relationships of sampling and measurement results supports optimal site decisions.

Geospatial Methods:

1. Simple geospatial methods such as inverse distance weighting or natural neighbor interpolation
2. More complex geospatial methods such as local spatial regression or splines
3. Advanced methods (kriging)

For treatment design, risk assessment, and other objectives it may be necessary to estimate the average for potentially correlated spatial data. If data are spatially correlated or clustered, geospatial methods may yield more accurate estimates of the average. Another approach to find average concentrations would be to conduct incremental sampling, which provides a physical average (see ITRC ISM-1). For more information, see the discussion of using geospatial results in estimating quantities and average concentrations.

Geospatial Methods:

1. Declustering using Voronoi polygons with values weighted by area of polygons
2. Block kriging to estimate the average concentration in a specific area or block, particularly where data are spatially correlated or clustered.

Inexpensive proxy concentrations are often generated by other means such as real-time field measurements and can be correlated with fewer fixed laboratory data points, can be used together to make better site characterization maps. This method can be used with the Triad approach (ITRC 2003; ITRC 2007; USEPA 2003). For more information, see the discussion of using geospatial results in using proxy information to estimate contaminant concentrations.

Geospatial Methods:

1. Multiple regression
2. Kriging with external trend (drift)
3. Co-kriging

Geospatial analysis can help to optimize the estimate of quantities needing remediation and quantify the uncertainty associated with that estimate. The answer to this question also determines the limits of the media that require treatment. This approach can also be useful for risk assessment and remedial design; see also the discussion of using geospatial results in estimating quantities.

Geospatial Methods:

1. Delaunay triangulation can be used to estimate the areas of exceedance.
2. Indicator kriging provides certainty of exceedances of the standard to assess risk and cost tradeoffs, which is particularly useful for remedial design.
3. Other kriging methods can be used to interpolate between known values to assess limits and uncertainties with kriging variances.
4. Conditional simulation can be conducted to assess the probabilities of volumes or areas exceeding a standard.

Sampling results that are clustered and spatially correlated can skew the background statistics. Geospatial methods address this problem by better representing background concentrations that vary spatially. The products of the analysis can be measurements of spatial correlations of existing data, as well as an estimate of the true background population statistical distribution when working with spatially correlated data. For more information, see the discussion of using geospatial results in background estimation.

Geospatial Methods:

1. Declustering using Voronoi polygons and Delaunay triangulation, with values weighted by area of polygons.
2. Variograms (for assessing if the data are spatially correlated).
3. Kriging, particularly block kriging where background data are spatially correlated or clustered.

Analysis of uncertainty when contouring environmental data may help inform and optimize the decisions about future sampling locations or areas requiring remediation (for example excavation quantity or spatial extent). The analysis provides maps of uncertainty in the estimated or interpolated values. For more information, see the discussion of using geospatial results in quantifying uncertainty.

Geospatial Methods

1. Kriging (various types) with cross-validation, and contouring kriging variance in order to look for areas of high variance as areas of uncertainty
2. Contouring kriging variance, looking for areas of high variance as areas of uncertainty
3. Conditional simulation can be used to assess how the interpolated or predicted values may vary over many realizations. This approach can provide values of probabilities for exceedances.

During regular monitoring or characterization, it is important to delineate localized but very strong contaminant source areas (hot spots). These areas can be identified by sampling on a systematic grid or through use of row- and column-aligned incremental sampling methods (ISM). Traditional statistical analysis can help identify a strategy to find hot spots, but does not take into account any spatial correlation over short distances. Geospatial analysis of data may help identify these hot spots. Examples of geospatial analysis approach include ordnance detection with geophysical data, or characterization of a large area with random storage or disposal of hazardous wastes. Note that geospatial methods require some existing data to guide the collection of additional data. For more information, see the discussion of using geospatial results in Hot Spot Detection/Delineation.

Geospatial Methods:

1. Variograms can help select optimal grid spacing based on the degree of spatial correlation for detecting hotspots of a given size. The variograms can indicate the distances at which the sampling locations can be spaced without too much duplicative information. Hot spots usually have high variability over short distances, so closer spacing is appropriate.