The scaling relationship for the length of tributaries to lakes

Globally, the length of tributaries to lakes varies from 0 to more than 15,000 km, but scaling relationships describing this aspect of lake-river connectivity are lacking. In this study, we describe a simple theoretical scaling relationship for tributary length based on the principle of line intercepts of topographic features, and test this theory using data from Scandinavia. Tributary length increases by 73% for each doubling of lake area. This pattern reflects the relationship between catchment and lake area, and is modified by inlet frequency, junction angle, and lake shape—factors related to specific geologic and hydrologic processes. The theory is precise (r2 = 0.74), with low bias (mean error is 14% of mean tributary length) when the characteristic junction angle (∼76°) is estimated statistically. Our study bridges the gap between geomorphic and large-scale statistical relationships to provide simple rules for understanding complex patterns of lake-river connectivity.