Detecting Hot Spots

Background

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, and the desired probability of finding a hot spot of critical size and shape. Either circular or elliptical hot spots can be specified.

Objectives of the VSP Hot Spot Design Module

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 or elliptical 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 or elliptical hot 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 or elliptical 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 Gilbert (1987) and was originally developed by Singer and Wickman (1969) and Singer (1972) with refinements by Davidson (1995). Additional information is provided in the summary report of the design that VSP automatically generates.

Assumptions that Underlie the VSP Hot Spot Design Method

1. The shape of the hot spot of concern is circular or elliptical.

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 classification errors (if a hot spot is sampled, it is not mistakenly overlooked or an area is not mistakenly identified as a hot spot).

10. A hot spot is detected if any part of the hot spot lies within a grid cell sample.

References:

Davidson, J.R. 1995. ELIPGRID-PC: Upgraded Version. ORNL/TM-13103. Oak Ridge National Laboratory, Oak Ridge, TN.

Gilbert, R.O. 1987. Statistical Methods for Environmental Pollution Monitoring. Wiley & Sons, Inc., New York, NY.

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.

Singer, D.A. 1972. ELIPGRID: A Fortran IV program for calculating the probability of success in locating elliptical targets with square, rectangular and hexagonal grids. Geocom Programs 4:1-16.