Post-Survey Probability of Sampling within a Hot Spot

Background

When field crews implement a VSP sampling plan, they may find that obstacles and other factors make it undesirable, difficult or impossible to follow the sampling plan exactly as it was originally designed. VSP can be used to approximate the probability that a hot spot of specified size and shape would have been traversed and sampled.

To begin the process, the user should set up the map and import the survey location data into the VSP project.

Probability of Sampling in a Hot Spot

The probability of sampling within an elliptical or circular hot spot is approximated by using a Monte-Carlo simulation.

The simulation uses these parameters:

\(n\): Number of trials

\(r\): Radius of hot spot (semi-major axis for ellipses)

\(s\): Shape of hot spot (height to width ratio)

\(\theta\): Orientation of hot spot with respect to the x-axis (random or a set angle)

When the Hot Spot Traversal Simulate button is pushed, VSP places \(n\) trial hot spots and counts the number that contain at least one sample location. The probability of detection is computed as the number of hits divided by the number of trial hot spots. This probability is displayed as a percentage.

If the Place samples on map to show simulation check-box is selected, VSP places a marker (square grid cell of a user-specified size) on the map where any trial hot spot was not traversed.

References:

Gilbert, R.O., B.A. Pulsipher, D.K. Carlson, R.F. O, J.E. Wilson, D.J. Bates and G.A. Sandness. 2001. Designing UXO Sensor Surveys for Decision Making, Pacific Northwest National Laboratory, Richland, WA.

Gilbert, R.O., J.E. Wilson, R.F. O, D.K. Carlson, B.A. Pulsipher and D.J. Bates. 2003. Version 2.0 Visual Sample Plan (VSP): UXO Module Code Verification, Pacific Northwest National Laboratory, Richland, WA.

The dialog contains the following controls:

Detection Simulation Page

Place markers on map to show simulation

Marker size

Number of trials

Hot Spot Traversal Simulate Button

Hot Spot Page

Area of Hot Spot

Area Units

Length of Semi-Major Axis

Length Units

Length of Semi-Minor Axis

Shape

Orientation Parameters

Degrees Radio Button

Degrees Spinner

Random Radio Button