# Rose Diagrams

A rose diagram shows the circular distribution of directional data.  The diagram plots lines at each of the 360 degrees of a compass distribution, with the length proportional to the number of values in that direction.  With small data sets, directions can be binned.

 From DEMS From Data Bases Aspect distribution by slope on Geomorpometry analysis of Analyze menu Analyze, Elevation-slope plot, Aspect distribution. Rose diagram on Stats button popup menu from database table display window  Rose diagrams for a Copernicus 1" DEM, both in the native floating point format, and rounded to a 16 bit integer. Rose diagram for the Negative Vegetation >  1m

Numbers at the top of the rose, after the DEM name, show the vector average (Fisher, Lewis, & Embleton, 1987), computed by summing the x (sin) and y (cos) components of the aspect, and then computing the average component by averaging the x and y components, and then expressing the result as a vector.  The average magnitude will be between 0 and 1, with 0 being a completely random, uniform distribution, and 1 being all in a single direction.   The aspects use geographic conventions, with 0 as north and the aspect increasing clockwise; both differ from the math and computer science conventions of programming languages.

For the two Copernicus DEMs, the average directions, both direction and magnitude, are virtually identical.  The slope distributions are also virtually identical, but a slope difference map shows random small differences resulting from rounding the elevations.

The last number is the Queen's aspect ratio, showing how much the number of aspects in the 8 cardinal directions compares with a uniform distribution.  It should be close to 1 for floating point DEMs, and much larger for integer DEMs.

Last revision 12/8/2021