Shoreline development index
The shoreline development index of a lake is the ratio of the length of the lake's shoreline to the circumference of a circle with the same area as the lake. It is given in equation form as formula_1, where formula_2 is shoreline development, formula_3 is the length of the lake's shoreline, and formula_4 is the lake's area. The length and area should be measured in the units (e.g., m and m, or km and km). The shoreline development index is formula_5 for perfectly circular lakes. formula_6 for lakes with complex shapes. Patterns. Shoreline development  correlates strongly with lake area, although this partly reflects the scale dependence of the index (see Limitations) To some extent, the shoreline development index reflects the mode of origin for lakes. For example, volcanic crater lakes often have shoreline development index values near 1, where are fluvial oxbow lakes often have very high shoreline development index values. Application to lakes with islands. The index can also include the length of island shoreline, modifying the formula to formula_7, where formula_8 is the combined length of the lake's islands' shoreline. Limitations. Lake shorelines are fractal. This means that measurements of shore  length are scale-dependent. In other words, lake shorelines are longer when measured on high-resolution maps compared to low-resolution maps. 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. Consequently, shoreline development index values cannot be compared for lakes with shorelines measured from maps with different scales. 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. Shoreline