A fractal-based approach to lake size-distributions

Abstract

The abundance and size distribution of lakes is critical to assessing the role of lakes in regional and global biogeochemical processes. Lakes are fractal but do not always conform to the power law size-distribution typically associated with fractal geographical features. Here, we evaluate the fractal geometry of lakes with the goal of explaining apparently inconsistent observations of power law and non-power law lake size-distributions. The power law size-distribution is a special case for lakes near the mean elevation. Lakes in flat regions are power law distributed, while lakes in mountainous regions deviate from power law distributions. Empirical analyses of lake size data sets from the Adirondack Mountains in New York and the flat island of Gotland in Sweden support this finding. Our approach provides a unifying framework for lake size-distributions, indicates that small lakes cannot dominate total lake surface area, and underscores the importance of regional hypsometry in influencing lake size-distributions. Key Points Lakes are fractals but do not always conform to power law size-distributions Lake size-distributions deviate from a power law in mountainous regions Power law relationships emerge in special cases consistent with fractal theory ©2013. American Geophysical Union. All Rights Reserved.