Spherical Variance or Standard Deviation of Surface

Derives the spherical standard deviation of a raster surface

spherical.sd(r, d, variance = FALSE, ...)

Arguments

r	Raster class object
d	Size of focal window or a matrix to use in focal function
variance	(FALSE\|TRUE) Output spherical variance rather than standard deviation
...	Additional arguments passed to calc (can write raster to disk here)

Value

rasterLayer class object of the spherical standard deviation

Details

Surface variability using spherical variance/standard deviation. The variation can be assessed using the spherical standard deviation of the normal direction within a local neighborhood. This is found by expressing the normal directions on the surfaces cells in terms of their displacements in a Cartesian (x,y,z) coordinate system. Averaging the x-coordinates, y-coordinates, and z-coordinates separately gives a vector (xb, yb, zb) pointing in the direction of the average normal. This vector will be shorter when there is more variation of the normals and it will be longest--equal to unity--when there is no variation. Its squared length is (by the Pythagorean theorem) given by: R^2 = xb^2 + yb^2 + zb^2 where; x = cos(aspect) * sin(slope) and xb = nXn focal mean of x y = sin(aspect) * sin(slope) and yb = nXn focal mean of y z = cos(slope) and zb = nXn focal mean of z

The slope and aspect values are expected to be in radians. The value of (1 - R^2), which will lie between 0 and 1, is the spherical variance. and it's square root can be considered the spherical standard deviation.

Author

Jeffrey S. Evans <jeffrey_evans<at>tnc.org>

Examples

# \donttest{
 library(raster)
 data(elev)
 
 ssd <- spherical.sd(elev, d=5)
 
 slope <- terrain(elev, opt='slope')
 aspect <- terrain(elev, opt='aspect')
 hill <- hillShade(slope, aspect, 40, 270)
 plot(hill, col=grey(0:100/100), legend=FALSE, 
      main='terrain spherical standard deviation')
   plot(ssd, col=rainbow(25, alpha=0.35), add=TRUE)
# }