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Standard deviation perimeter-area ratio (Shape metric)

Usage

lsm_c_para_sd(landscape, directions = 8)

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).

Value

tibble

Details

$$PARA_{SD} = sd(PARA[patch_{ij}]$$ where \(PARA[patch_{ij}]\) is the perimeter area ratio of each patch.

PARA_SD is a 'Shape metric'. It summarises each class as the standard deviation of each patch belonging to class i. The perimeter-area ratio describes the patch complexity in a straightforward way. However, because it is not standarised to a certain shape (e.g. a square), it is not scale independent, meaning that increasing the patch size while not changing the patch form will change the ratio.

Units

None

Range

PARA_SD >= 0

Behaviour

Equals PARA_SD = 0 if the perimeter-area ratio is identical for all patches. Increases, without limit, as the variation of the perimeter-area ratio 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

Examples

landscape <- terra::rast(landscapemetrics::landscape)
lsm_c_para_sd(landscape)
#> # A tibble: 3 × 6
#>   layer level class    id metric  value
#>   <int> <chr> <int> <int> <chr>   <dbl>
#> 1     1 class     1    NA para_sd 1.34 
#> 2     1 class     2    NA para_sd 1.36 
#> 3     1 class     3    NA para_sd 0.521