Choosing a Random Point on a Map Sheet

You want to choose a random point on a mapsheet. How do you do it? Maybe you want to choose a random point within a Douglas-fir stand or a random point in a clearcut, and those only occupy part of the map. Maybe you do not know if the random point would be suitable until you inspected it on the map.

What you do not do is just point to a place and pretend that it is random. I know ... you’re in a hurry. It doesn’t matter, do it right anyway.

Suppose your mapsheet is 26x36 inches in size. The areas actually mapped are less than the edges of the mapsheet, and often come in slightly different proportions on each map, depending on the way your mapping system works. Let’s assume the actual mapped area is always smaller than 22x30 inches.

Choose two random numbers, one for the "x" (horizontal) coordinate and "y" (perpendicular" coordinate. The random number is technically a "0-1 uniform random number", and has values between 0 and 1. Computers have standard routines for generating these.

Multiply the x random number by 22, and the y random number by 30. This gives the location on the mapsheet measured from the lower left corner. This process will choose all points in the map with equal probability, therefore it chooses stands with a probability proportional to their area.

What if you are looking for a point in a clearcut? In that case, just keep picking points until one of them fall within a clearcut. This kind of process can be set up on a GIS system ahead of time. You can pick a random point, have the stand description shown to you (along with the location on the map) and you can choose to pick another point if necessary.

To do this by hand, you might consider making up some clear plastic overlays ahead of time. Choose the first random point, and label it "1". Draw a line with an arrowhead from this to the second random point, labeled "2", etc. Do a hundred, for instance. If the lines start to get messy, change colors for part of the sequence. If you have a GIS system, it can do this relatively easily.

Once this kind of overlay is prepared it can be dropped on any map that you have a number of possible random points to check. Choose a random number between 1 and 100, and start with that number, moving along the lines in sequence. If the first one does not fall into the correct kind of stand, check point #2, and so on until your get a "hit".

Make up a set of these overlays for occasional use, so you do not have to bother the GIS group each time. Flipping them top-to-bottom or even upside down is OK, since they are random coordinates.

This bit of extra effort not only makes the method more acceptable if you have to go to court, it reinforces an attitude of careful work that is so important in inventory projects. If random location overlays are easily available, the extra time is minimal.

Originally published October 1998

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