The fractal scaling relationship for river inlets to lakes

Scaling relationships provide simple rules for understanding complex hydrographic patterns. Globally, river inlet abundance varies among lakes by about three orders of magnitude, but few scaling relationships describe this aspect of lake-river connectivity. In this study, we describe a simple theoretical scaling relationship between lake surface area and river inlet abundance, and test this theory using data from Scandinavia. On average, the number of inlets increases by 67% for each doubling of lake area. However, lakes of vastly different areas can have the same number of inlets with relatively small variations of drainage density, lake shape, or junction angle - characteristics that can often be linked to specific geological processes. Our approach bridges the gap between the detailed understanding of geomorphic processes and large-scale statistical relationships, and engenders predictions about additional patterns including the relationship between lake area and water residence time.