Does the Pareto distribution adequately describe the size-distribution of lakes?

Seekell, David A., and Michael L. Pace

Limnol. Oceanogr., 56(1), 2011, 350-356 | DOI: 10.4319/lo.2011.56.1.0350

ABSTRACT: When it comes to evaluating lakes at regional and global scales, a key need is accurate estimates of the abundance and size-distribution of lakes, which are usually described with the Pareto distribution. We demonstrate the considerable uncertainty that truncation in the lower tail of the Pareto distribution introduces into lake abundance estimates and the selection of the lake size-distribution. Truncation in the lower tail eliminates lakes below a certain size and is generally performed because small lakes are not accurately represented on maps. When simulated data are truncated to mimic available lake size data, non-Pareto distributions are visually and statistically indistinguishable from the Pareto distribution. The Pareto distribution may be one of many possible forms that mimic the global lake size-distribution in the upper tail, but the fit of the Pareto to the lower tail is uncertain, largely because the abundance of small lakes is uncertain. Some other potential size-distributions, such as the lognormal distribution, predict abundances of small lakes to be orders of magnitude lower than do the Pareto distribution predictions. Highly resolved regional lake size data for the Adirondack Mountains of New York and the Northern Highland Lake District of Wisconsin do not conform to the Pareto distribution. Lake sizes on Mars also do not conform to the Pareto. Uncertainty in the lake size-distribution seriously limits understanding of the significance of lakes as repositories of organic carbon as well as the calculation of global greenhouse gas emissions from these systems.

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