VARIANCE OF ANGLES

[Giovanna Ranci]

I need a FORMULA to calculate VARIANCE when arguments are ANGLES (in degree).
For example, I need to calculate variance of aspect map in 3x3 neighborhood.
Aspect is expressed in degrees. It's clear that a cell with value 5 and a cell with value 355 are almost the same aspect so variance formula has to consider it.
I got already a formula with sin and cosine but there should be some mistakes in it
(I calculate variance using command r.mapcalc and r.neighbors but results are strange...definetely unreal. I'm sure error is in the formula not in my procedure in Grassland).
If somebody knows the rigth formula, I will be glad to receive it.
Thanks,

Giovanna Ranci Ortigosa
e-mail: ranci at quercia.elet.polimi.it