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Tundra lakes are key components of the Arctic climate system because theyrepresent a source of methane to the atmosphere. In this paper, we aim toanalyze the geometry of the patterns formed by large ($>0.8$ km$^2$) tundralakes in the Russian High Arctic. We have studied images of tundra lakes inhistorical maps from the State Hydrological Institute, Russia (date 1977; scale$0.21166$ km/pixel) and in Landsat satellite images derived from the GoogleEarth Engine (G.E.E.; date 2016; scale $0.1503$ km/pixel). The G.E.E. is acloud-based platform for planetary-scale geospatial analysis on over fourdecades of Landsat data. We developed an image-processing algorithm to segmentthese maps and images, measure the area and perimeter of each lake, and computethe fractal dimension of the lakes in the images we have studied. Our resultsindicate that as lake size increases, their fractal dimension bifurcates. Forlakes observed in historical maps, this bifurcation occurs among lakes largerthan $100$ km$^2$ (fractal dimension $1.43$ to $1.87$). For lakes observed insatellite images this bifurcation occurs among lakes larger than $\sim$100km$^2$ (fractal dimension $1.31$ to $1.95$). Tundra lakes with a fractaldimension close to $2$ have a tendency to be self-similar with respect to theirarea--perimeter relationships. Area--perimeter measurements indicate that lakeswith a length scale greater than $70$ km$^2$ are power-law distributed.Preliminary analysis of changes in lake size over time in paired lakes (lakesthat were visually matched in both the historical map and the satelliteimagery) indicate that some lakes in our study region have increased in sizeover time, whereas others have decreased in size over time. Lake size changeduring this 39-year time interval can be up to half the size of the lake asrecorded in the historical map.

The Geometry of Large Tundra Lakes Observed in Historical Maps and Satellite Images