PiscesLogoSmallerStill Circular environmental variables

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Two common examples of circular data are direction (aspect) and day of the year.

Aspect (or compass direction of a slope) can be transformed by trigonometric functions (Roberts 1986). The simplest way to do this is to create two variables, "northerliness" and "easterliness" as follows:

easterliness = cos(aspect)

easterliness = sin(aspect)

Northerliness will take values close to 1 if the aspect is generally northward, close to -1 if the aspect is southward, and close to 0 if the aspect is either east or west. Easterliness behaves similarly, except that values close to 1 represent east-facing slopes.


Another approach is to use dummy variables e.g. N, NE, E, SE, S, SW, W, NW. This approach has the additional advantage of allowing flat surfaces (i.e. no aspect) to have a category.


The day of the year is circular because early January will have low values, and late December will have high values, yet the climates at the two times will be similar. As with compass direction one approach is to construct dummy variables Winter, Spring, Summer and Autumn. If sampling occurred over a limited number of months the Julian date can be used as a variable.


For more advanced work with circular or repeating variables Pisces produce a dedicated package 'Axis', more details of which are available here.