Shoreline development index

The index can also include the length of island shoreline, modifying the formula to ${\textstyle D_{L+L_{i}}={\frac {L+L_{i}}{2{\sqrt {\pi A}}}}}$, where ${\displaystyle L_{i}}$ is the combined length of the lake's islands' shoreline.^[8]

Lake shorelines are fractal.^[7] This means that measurements of shore length are longer when measured on high-resolution maps compared to low-resolution maps.^[9][10] Therefore, a lake's shoreline development index will be greater when calculated based on shorelines measured from high-resolution maps compared to low-resolution maps.^[10] Consequently, shoreline development index values cannot be compared for lakes with shorelines measured from maps with different scales.^[9][11][12] Additionally, the shoreline development index cannot be compared for lakes with different surface areas because large lakes automatically have higher values than smaller lakes, even if they have the same planform shape.^[10] Hence the shoreline development index can only be used to compare lakes with the same surface area that are also mapped at the same scale.^[10] Making comparisons like this can create spurious correlations between the shoreline development index and ecological variables.^[13]