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aij = area (m2) of patch ij. A = total landscape area (m2). |
| Description | MESH equals the sum of patch area squared, summed across all patches of the corresponding patch type, divided by the total landscape area (m2), divided by 10,000 (to convert to hectares). Note, total landscape area (A) includes any internal background present. |
| Units | Hectares |
| Range | ratio of cell size to landscape area ≦ MESH ≦ total landscape area (A) The lower limit of MESH is constrained by the ratio of cell size to landscape area and is achieved when the corresponding patch type consists of a single one pixel patch. MESH is maximum when the landscape consists of a single patch. |
| Comments | Mesh is based on the cumulative patch area distribution and is interpreted as the size of the patches when the corresponding patch type is subdivided into S patches, where S is the value of the splitting index. Note, MESH is redundant with DIVISION above, i.e., they are perfectly, but inversely, correlated, but both metrics are included because of differences in units and interpretation. DIVISION is interpreted as a probability, whereas MESH is given as an area. In addition, note the similarity between MESH and area-weight mean patch size (AREA_AM). Conceptually, these two metrics are closely related, but computationally they are quite different at the class level. Specifically, AREA_AM gives the area-weight mean patch size of patches of the corresponding class, where the proportional area of each patch is based on total class area (i.e., the total area of patches of the corresponding patch type). MESH, on the other hand, also gives the area-weighted mean patch size of patches of the corresponding patch size, but the proportional area of each patch is based on the total landscape area, not the class area. In this way, MESH takes into account the patch size distribution of the corresponding class as well as the total landscape area comprised of that class. Thus, holding the patch size distribution (of the corresponding class) constant, as the landscape extent increases (and the percent of the landscape comprised of this class decreases), MESH for the corresponding class will decrease. Hence, AREA_AM provides an absolute measure of patch structure, whereas MESH provides a relative measure of patch structure. |
