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

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