There will be occasions when it is necessary to determine with a specified high probability that no hot spots of a specified size and shape exist in the study area. A hot spot is a local contiguous area that has concentrations that exceed a threshold value. Initially, the conceptual site model should be developed and used to hypothesize where hot spots are most likely to be present. If no hot spots are found by sampling at the most likely locations, then VSP can be used to set up a systematic square, rectangular or triangular sampling grid to search for hot spots. Samples or measurements are made at the nodes of the systematic grid. The VSP user specifies the size and shape of the hot spot of concern, the available funds for collecting and measuring samples, the false negative rate, and the desired probability of finding a hot spot of critical size and shape. Only circular hot spots can be specified.
For quantitative samples, the false negative rate is the probability that a sample measurement indicates that contamination is below the acceptable threshold, when, in fact, it is at the threshold. For presence/absence measurements, the false negative rate is the probability the sample does not detect contamination when it is present.
The VSP user can direct VSP to compute one or more of the following outputs:
The number and spacing of samples on the systematic sampling grid that are required to achieve a specified high probability that at least one of the samples will fall on a circular hot spot of the specified size.
The probability that at least one of the samples collected at the nodes of the specified systematic sampling grid will fall on a circular spot of specified size.
The probability that at least one of the samples will fall on a hot spot of the specified size given that the spacing between nodes of the systematic sampling grid is the minimum that can be achieved with project funding.
The smallest size circular hot spot that will be detected with specified high probability by sampling at the nodes of the systematic sampling grid.
The method used in VSP to achieve these sampling objectives is described in Sego and Wilson (2007), which builds upon the approach developed by Singer and Wickman (1969). Gilbert (1987) also discussed hot spot sampling design. Additional information is provided in the summary report of the design that VSP automatically generates.
1. The shape of the hot spot of concern is circular.
2. The level of contamination that defines a hot spot is well defined.
3. The location of the hot spot is unknown, and if a hot spot is present, all locations within the sampling area are equally likely to contain the hot spot.
4. Samples are taken on a square, rectangular or triangular grid pattern.
5. Each sample is collected, handled, measured or inspected using approved methods that yield unbiased and sufficiently precise measurements.
6. A very small proportion of the surface being studied will be sampled (the sample is much smaller than the hot spot of interest).
7. Sample locations are independent of the measurement process.
8. The systematic grid is placed at a randomly determined starting place to cover the surface area of interest.
9. There are no false positives (a clean area is not mistakenly identified as a hot spot).
10. The false negative error rate is known and is the same for all measurements.
Gilbert, R.O. 1987. Statistical Methods for Environmental Pollution Monitoring. Wiley & Sons, Inc., New York, NY.
Sego, L.H. and J.E. Wilson. 2007. Accounting for False Negatives in Hot Spot Detection. PNNL-16812. Pacific Northwest National Laboratory, Richland, WA, August 2007. http://www.pnl.gov/main/publications/external/technical_reports/PNNL-16812.pdf
Singer, D.A. and J.E. Wickman. 1969. Probability Tables for Locating Elliptical Targets with Square, Rectangular, and Hexagonal Point Nets. Pennsylvania State University, University Park, Pennsylvania. Special Publication 1-69.
Grid Spacing / # of Samples / Total Cost button