Does lake size matter? Combining morphology and process modeling to examine the contribution of lake classes to population-scale processes

Abstract

With lake abundances in the thousands to millions, creating an intuitive understanding of the global distribution of morphology and processes in lakes is challenging. To improve researchers' understanding of large-scale lake processes, we developed a parsimonious mathematical model based on the Pareto distribution to describe the distribution of lake morphology (area, perimeter, and volume). While debate continues over which mathematical representation best fits any one distribution of lake morphometric characteristics, we recognize the need for a simple, flexible model to advance understanding of how the interaction between morphometry and function dictates scaling across large populations of lakes. These models make clear the relative contribution of individual lakes to the total amount of lake surface area, volume, and perimeter. They also highlight the critical thresholds at which total perimeter, area, and volume would be evenly distributed across lake-size classes having Pareto slopes of 0.63, 1.00, and 1.12, respectively. These morphological models can be used in combination with process models to create overarching “lake population” level models of process. To illustrate this potential, we combined the model of surface area distribution with a model of carbon mass accumulation rate. We found that even if smaller lakes contribute relatively less to total surface area than larger lakes, the increasing carbon accumulation rate with decreasing lake size is strong enough to bias the distribution of carbon mass accumulation toward smaller lakes. This analytical framework provides a relatively simple approach to upscaling morphology and process that can be easily generalized to other ecosystem processes.