Size Distributions of Arctic Waterbodies Reveal Consistent Relations in Their Statistical Moments in Space and Time

Arctic lowlands are characterized by large numbers of small waterbodies, which are known to affect surface energy budgets and the global carbon cycle. Statistical analysis of their size distributions has been hindered by the shortage of observations at sufficiently high spatial resolutions. This situation has now changed with the high-resolution (<5 m) circum-Arctic Permafrost Region Pond and Lake (PeRL) database recently becoming available. We have used this database to make the first consistent, high-resolution estimation of Arctic waterbody size distributions, with surface areas ranging from 0.0001 km(2) (100 m(2)) to 1 km(2). We found that the size distributions varied greatly across the thirty study regions investigated and that there was no single universal size distribution function (including power-law distribution functions) appropriate across all of the study regions. We did, however, find close relationships between the statistical moments (mean, variance, and skewness) of the waterbody size distributions from different study regions. Specifically, we found that the spatial variance increased linearly with mean waterbody size (R-2 = 0.97, p < 2.2e-16) and that the skewness decreased approximately hyperbolically. We have demonstrated that these relationships (1) hold across the 30 Arctic study regions covering a variety of (bio)climatic and permafrost zones, (2) hold over time in two of these study regions for which multi-decadal satellite imagery is available, and (3) can be reproduced by simulating rising water levels in a high-resolution digital elevation model. The consistent spatial and temporal relationships between the statistical moments of the waterbody size distributions underscore the dominance of topographic controls in lowland permafrost areas. These results provide motivation for further analyses of the factors involved in waterbody development and spatial distribution and for investigations into the possibility of using statistical moments to predict future hydrologic dynamics in the Arctic.