The size-distribution of earth’s lakes and ponds: Limits to power-law behavior

Abstract

Global-scale characterizations of Earth’s lakes and ponds assume their surface areas are power-law distributed across the full size range. However, empirical power-laws only hold across finite ranges of scales. In this paper, we synthesize evidence for upper and lower limits to power-law behavior in lake and pond size-distributions. We find support for the power-law assumption in general. We also find strong evidence for a lower limit to this power-law behavior, although the specific value for this limit is highly variable (0.001–1 km2), corresponding to orders of magnitude differences of the total number of lakes and ponds. The exact mechanisms that break the power-law at this limit are unknown. The power-law extends to the size of Earth’s largest lake. There is inconsistent evidence for an upper limit at regional-scales. Explaining variations in these limits stands to improve the accuracy of global lake characterizations and shed light on the specific mechanism responsible for forming and breaking lake power-law distributions.

Size Distributions Reveal Regime Transition of Lake Systems Under Different Dominant Driving Forces

“…The other problem with the lake size distribution is that it remains unknown what kind of driving factors and processes, and how they act and interact to produce the power law distributions observed in lake systems (Cael et al., 2022). The formation of lakes is premised on suitable topographic condition and sufficient water available, reflecting the joint control of endogenic and exogenic forces of the Earth (Wirthmann, 2000).…”