Effective Mesh Size (Aggregation metric)
lsm_l_mesh(landscape, directions = 8)tibble
A categorical raster object: SpatRaster; Raster* Layer, Stack, Brick; stars or a list of SpatRasters.
The number of directions in which patches should be connected: 4 (rook's case) or 8 (queen's case).
$$MESH = \frac{\sum \limits_{i = 1}^{m} \sum \limits_{j = 1}^{n} a_{ij} ^ 2}{A} * \frac{1} {10000}$$ where \(a_{ij}\) is the patch area in square meters and \(A\) is the total landscape area in square meters.
The effective mesh size is an 'Aggregation metric'. Because each patch is squared
before the sum is calculated and the sum is standardized by the
total landscape area, MESH is a relative measure of patch structure. MESH is
perfectly, negatively correlated to lsm_l_division.
Because the metric is based on distances or areas please make sure your data
is valid using check_landscape.
Hectares
cell size / total area <= MESH <= total area
Equals cellsize/total area if class covers only one cell and equals total area if only one patch is present.
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
Jaeger, J. A. 2000. Landscape division, splitting index, and effective mesh size: new measures of landscape fragmentation. Landscape ecology, 15(2), 115-130.
lsm_p_area,
lsm_l_ta,
lsm_c_mesh
landscape <- terra::rast(landscapemetrics::landscape)
lsm_l_mesh(landscape)
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