A.3.1 Methods

Simulations were run to evaluate the effect of spatial autocorrelation on the performance of ISM. Figure A-2shows a map generated from a real data set of more than 200 observations. The sample results were interpolated with inverse distance weighting techniques to yield a 2-D surface of concentrations. Such spatial "smoothing" is likely to underestimate the small-scale heterogeneity (DH) in concentrations that exists at most sites. Therefore, the results with ISM may underestimate the variance. Four ISM sampling protocols were applied to this map, assuming the map represents a single DU:

  • Systematic grid with a random start location—no division of the DU
  • Systematic grid with a random start location—division of DU into quadrants
  • Simple random sample—no division of the DU
  • Simple random sample—division of the DU into quadrants

Figure A-2. Example of a map with high spatial autocorrelation (Moran’s I z-score = 3.8).
Throughout the entire DU (all grid cells combined), the population mean is 8564 and standard deviation is 6507 (CV = 0.7).

For the scenario in which the site is divided into quadrants, each quadrant was sampled with the specified number of replicates; therefore, the simulations with quadrants represent an overall four-fold increase in the sampling effort. Alternative evaluations of the "quadrant" scenario were evaluated with different maps to illustrate the performance metrics for quadrants in which a single ISM sample is collected from each quadrant, yielding a total sample size of r = 4.