The Scaling Relationship for the Length of Tributaries to Lakes

• Published in: Geophysical research letters 2022-04, Vol.49 (7), p.n/a
• Main Authors: Seekell, D., Cael, B., Byström, P.
• Format: Article
• Language: English
• Subjects: Catchment area; Catchment areas; Catchments; Connectivity; Geological processes; Geology; Geomorphology; hydrography; Hydrologic processes; Hydrology; Inland waters; Inlets; Inlets (waterways); junction angle; lake-river connectivity; Lakes; limnology; Physiographic features; Regional climates; Rivers; Scaling; Statistics; Tributaries
• ISSN: 0094-8276; 1944-8007; 1944-8007
• DOI: 10.1029/2022GL098183

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. Plain Language Summary Patterns of connectivity between lakes and rivers are poorly described because lakes and rivers are typically studied separately. In this study, we develop and test simple rules that describe lake‐river connectivity. Specifically, we focus on predicting the length of river tributaries, which varies among lakes from 0 to more than 15,000 km. The most important factors controlling tributary length in our analysis were catchment area, lake area, inlet abundance, and river‐lake junction angle. These factors reflect regional climate and bed rock characteristics, lake origin, and catchment geomorphology. Our results connect large‐scale statistical patterns with geologic processes, demonstrating how simple rules like those developed in our study can enrich understanding of inland waters. Key Points The length of tributaries to lakes varies between 0 and 15,000+ kilometers Scaling relationships provide simple rules for understanding patterns and variation of river‐lake connectivity The factors affecting tributary length are: Catchment area, lake area, inlet abundance, and junction angle