A theory for the relationship between lake surface area and maximum depth

Maximum depth is crucial for many lake processes and biota, but attempts to explain its variation have achieved little predictive power. In this paper, we describe the probability distribution of maximum depths based on recent developments in theory fractal Brownian motions. The theoretical right-tailed adequately captures variations a dataset 8164 lakes (maximum 0.1–135 m) from northeastern United States. increases with surface area, substantial random variation—the 95% prediction interval spans more than an order magnitude any specific area. Our results observed variability depths, capture link between topographic characteristics bathymetry, provide means upscale depth-dependent processes, which illustrate by upscaling diffusive flux methane northern atmosphere.