Quantifying the Size Distribution of Rivers Across Spatial Scales

Abstract

The surfaces of rivers are hotspots for biogeochemical exchange and emit significant amounts of greenhouse gases globally. Estimates of river surface area are critical to determining fluvial greenhouse gas evasion yet are currently poorly constrained. The relative abundance of narrow rivers to wide rivers is commonly assumed to be fractal, or scale invariant. This assumption aids in statistical estimates of river surface area but has not been tested across spatial scales. We measured river size in four nested basins within the Mississippi River Basin using a combination of remote sensing and field surveying to determine the statistical size distribution of rivers from continental to headwater scales. We found that the relative abundance of narrow rivers to wide rivers consistently fits a log-normal probability density function, supporting the assumption of fractal river size. Using the fractal size distribution of rivers, we estimated a total river surface area of 17,828 ± 5,126 km2 (0.54 ± 0.16 % of land surface area) in the Mississippi River Basin which is comparable to previous studies. Our multi-scale approach revealed the fractal nature of river size and allowed for a more accurate accounting of river surface area with implications for the role of rivers in biogeochemical cycling.