Standard deviation fractal dimension index (Shape metric)
Usage
lsm_l_frac_sd(landscape, directions = 8)
Value
tibble
Arguments
landscape
A categorical raster object: SpatRaster; Raster* Layer, Stack, Brick; stars or a list of SpatRasters.
directions
The number of directions in which patches should be
connected: 4 (rook's case) or 8 (queen's case).
Details
$$FRAC_{SD} = sd(FRAC[patch_{ij}])$$
where \(FRAC[patch_{ij}]\) equals the fractal dimension index of each patch.
FRAC_SD is a 'Shape metric'. The metric summarises the landscape
as the standard deviation of the fractal dimension index of all patches
in the landscape. The fractal dimension index is based on the patch perimeter and
the patch area and describes the patch complexity.
Units
None
Range
FRAC_SD>= 0
Behaviour
Equals FRAC_SD = 0 if the fractal dimension index is identical
for all patches. Increases, without limit, as the variation of the fractal dimension
indices increases.
References
McGarigal K., SA Cushman, and E Ene. 2023. FRAGSTATS v4: Spatial Pattern Analysis
Program for Categorical Maps. Computer software program produced by the authors;
available at the following web site: https://www.fragstats.org
Mandelbrot, B. B. 1977. Fractals: Form, Chance, and Dimension.
San Francisco. W. H. Freeman and Company.