hijr = distance (m) between cell ijr [located within patch ij] and the centroid of patch ij (the average location), based on cell center-to-cell center distance.
z = number of cells in patch ij.
Description GYRATE equals the mean distance (m) between each cell in the patch and the patch centroid.
Units Meters
Range GYRATE ≥ 0, without limit.
GYRATE = 0 when the patch consists of a single cell and increases without limit as the patch increases in extent. GYRATE achieves its maximum value when the patch comprises the entire landscape.
Comments Radius of gyration is a measure of patch extent (i.e., how far-reaching it is); thus, it is effected by both patch size and patch compaction. Note that the choice of the 4-neighbor or 8-neighbor rule for delineating patches will have an impact on this metric.