Table 1 Landform characteristics and their descriptions.

Aggregation

Patch Cohesion Index (COHESION)

\({COHESION}=[1-\frac{\mathop{\sum }\limits_{i=1}^{m}\mathop{\sum }\limits_{j=1}^{n}{p}_{{ij}}^{\ast }}{\mathop{\sum }\limits_{i=1}^{m}{\sum }_{j=1}^{n}{p}_{{ij}}^{\ast }\sqrt{{a}_{{ij}}^{\ast }}}]\ast {\left[1,-,\frac{1}{\sqrt{Z}}\right]}^{-1}\ast 100\)

This descriptor measures the physical connectedness of the corresponding patch type. The index value monotonically increases with an increase in category composition. If the landscape is composed of a single nonbackground unit, this index is 0. Higher values indicate higher patch cohesion within the patch type.

\({p}_{{ij}}^{\ast }\) is the perimeter of patch ij in terms of number of cell surfaces; \({a}_{{ij}}^{\ast }\) is the area of patch ij in terms of number of cells; Z is the total number of cells in the landscape.

Landscape Division Index (DIVISION)

\({DIVISION}=[1-\mathop{\sum }\limits_{i=1}^{m}\mathop{\sum }\limits_{j=1}^{a}{\left(\frac{{a}_{{ij}}}{A}\right)}^{2}]\)

This descriptor reveals the probability that two randomly selected pixels in are not located within the same patch of the corresponding patch type.

a_ij is the area of patch ij (m²); A is the total landscape area (m²).

Landscape Shape Index (LSI)

\({\rm{LSI}}=\frac{0.25\ast E}{\sqrt{{\rm{A}}}}\)

It provides a standardized measure of total edge adjusted for the size of the landscape. LSI increases without limit as landscape shapes become more irregular or as the length of the edge within the landscape increases.

E is the total length (m) of the edge in the landscape; A is the total landscape area (m²).

Splitting Index (SPLIT)

\({SPLIT}=\frac{{A}^{2}}{\mathop{\sum }\limits_{i=1}^{m}\mathop{\sum }\limits_{j=1}^{n}{a}_{{ij}}^{2}}\)

This index is calculated based on the cumulative patch area distribution and can be interpreted as the effective number of patches.

a_ij is the area of patch ij (m²); A is the total landscape area (m²).

Diversity

Shannon’s Diversity Index (SHDI)

\({SHDI}=-\mathop{\sum }\limits_{i=1}^{m}({P}_{i}\ast \mathrm{ln}{P}_{i})\)

This index is one of the commonly used indices in landscape ecology research. When the landscape contains only one type (i.e., no diversity), SHDI = 0. As the number of patch types increases, SHDI also increases.

P_i represents the proportion of the landscape occupied by patch type (class) i.

Shannon’s Evenness Index (SHEI)

\(SHEI=-\frac{-\mathop{\sum }\limits_{i=1}^{m}({P}_{i}\ast {\rm{l}}{\rm{n}}{P}_{i}))}{{\rm{l}}{\rm{n}}(m)}\)

This index represents the evenness of the distribution among patch types. SHEI = 0 indicates that the landscape consists of only one patch type, with no diversity, while SHEI = 1 indicates that all patch types are evenly distributed, representing maximum diversity.

P_i represents the proportion of the landscape occupied by patch type (class) i; m is the number of patch types (classes) present in the landscape, excluding the landscape border if present.