Quantifying uncertainty in Pareto estimates of global lake area

Size is a critical factor determining the rate and occurrence of specific lake processes such as carbon sequestration and greenhouse gas emissions and emerging evidence suggests that small lakes in particular have particularly large CO2 flux rates. Because we do not have a complete census of all lakes, upscaling estimates of such processes to small lakes at broad spatial scales requires the use of lake size-abundance distributions rather than empirical measurements of area. Existing lake census efforts are incomplete such that as lakes become smaller, they are more likely to be omitted either because they are too small to be resolved from remote sensing products or because of limited ground surveying effort (i.e., censoring of small lakes relative to large lakes). The present study explores one potential shortcoming of prior approaches estimating global lake area using lake size-abundance distributions. Namely, that these prior approaches rely on frequentist curve fitting techniques combined with an ad-hoc cutoff determination strategy (visual inspection to determine a likely censoring point). This yields an over-exact lake area estimate that is typically reported with no uncertainty bounds. I show how these shortcomings can be addressed with a Bayesian model that produces larger estimates of lake area uncertainty relative to the typical approach. When used as part of a sensitivity analysis, such an approach has the potential to enable more robust intercomparisons among studies of aquatic processes upscaling.

Automated summary

Size is a critical factor in determining lake processes such as carbon sequestration and greenhouse gas emissions, with small lakes having particularly high CO2 flux rates. However, incomplete lake census efforts make it challenging to estimate these processes for small lakes at broad spatial scales. Existing approaches rely on curve fitting techniques and visual inspections, leading to over-exact lake area estimates reported without uncertainty bounds. A Bayesian model is proposed to address these shortcomings and provide larger estimates of lake area uncertainty, enabling more robust comparisons among studies.