Lake bottom dynamics and morphometry: The dynamic ratio

Abstract

This paper is a second report on the linkage between lake bottom dynamics and lake morphometry. The areal distribution of erosion and transportation (aE+T) or accumulation (aA = 100 − aE+T) processes at lake bottoms is suggested to be governed by (1) an energy factor E = ( √a/Dmax), where a is the lake area in square kilometers and Dmax is the maximum depth in meters, (2) a slope factor S = 41 exp(0.061 D¯/√a), where D¯ is the mean depth in meters, and (3) a form factor, Vd−l = Dmax/3D¯. This relationship may be given as aE+T = 100 − aA = 25 (√a/D¯) 41 exp 0.061 D¯/√/a) where aE+T is the percentage area of lake bed subject to processes of erosion and transportation. The ratio √a/D¯ is called the dynamic ratio (DR). This formula is physically more sound than an earlier model and more accurate when applied on the available empirical data from nine Swedish lakes. It also reveals new aspects of the relationship between bottom dynamics and lake morphometry. The formula may be useful since it provides a means by which to estimate the percentage of a given lake area that is dominated by erosion and transportation processes (aE+T) or accumulation processes (aA) from only two morphometric standard parameters: lake area a and mean depth D¯.