The shoreline development index of a

lake A lake is an area filled with water, localized in a basin, surrounded by land, and distinct from any river or other outlet that serves to feed or drain the lake. Lakes lie on land and are not part of the ocean, although, like the much large ...

is the ratio of the length of the lake's

shoreline A shore or a shoreline is the fringe of land at the edge of a large body of water, such as an ocean, sea, or lake. In physical oceanography, a shore is the wider fringe that is geologically modified by the action of the body of water past a ...

to the circumference of a circle with the same area as the lake. It is given in equation form as

D_L = \frac

, where

D_L

is shoreline development,

L

is the length of the lake's shoreline, and

A

is the lake's area. The length and area should be measured in the units (e.g., m and m², or km and km²). The shoreline development index is

D_L = 1

for perfectly circular lakes.

D_L > 1

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 A volcano is a rupture in the crust of a planetary-mass object, such as Earth, that allows hot lava, volcanic ash, and gases to escape from a magma chamber below the surface. On Earth, volcanoes are most often found where tectonic plates a ...

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

D_ = \frac

, where

L_i

is the combined length of the lake's islands' shoreline.

Limitations

Lake shorelines are fractal. This means that measurements of shore length 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. 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.

References

{{reflist Lakes