Problems with the shoreline development index - a widely used metric of lake shape

Abstract

The shoreline development index-The ratio of a lake's shore length to the circumference of a circle with the lake's area-Is a core metric of lake morphometry used in Earth and planetary sciences. In this paper, we demonstrate that the shoreline development index is scale-dependent and cannot be used to compare lakes with different areas. We show that large lakes will have higher shoreline development index measurements than smaller lakes of the same characteristic shape, even when mapped at the same scale. Specifically, the shoreline development index increases by about 14% for each doubling of lake area. These results call into question previously reported patterns of lake shape. We provide several suggestions to improve the application of this index, including a bias-corrected formulation for comparing lakes with different surface areas.Plain Language Summary Lakes vary in shape from nearly perfect circles to the almost comically convoluted. These shapes reflect their geologic (or anthropogenic) origins, and influence within-lake ecological and chemical processes. As a consequence, the shapes of lakes are often compared, both among lakes on Earth and between Earth's lakes and those on other planetary bodies, to provide context when measuring and interpreting other characteristics. In this paper, we show that a widely-used metric of lake shape-The shoreline development index-Is biased and produces false patterns when comparing the shape of lakes with different areas, a common analysis and primary purpose of the metric. When applying the shoreline development index, we suggest: (a) Reporting the scale at which lakes are mapped; (b) when possible, only comparing lakes mapped at the same scale; (c) explicitly considering how bias may impact interpretation of patterns of lake shape; and (d) reporting a bias-corrected or alternative metric.