Influence of Lake Surface Area and Depth Upon Thermal Stratification and the Depth of the Summer Thermocline

Abstract

Among the important physical characteristics of a lake are whether it stratifies seasonally, and if so, the depth to which wind-mixing is limited by the stratification. It is generally known that sufficiently shallow lakes tend to remain isothermal throughout the year and that the depth of the thermocline in stratified lakes correlates positively with the surface area of the lake. Observations from lakes in several different regions of the temperate zone of the northern hemisphere show that whether a lake stratifies depends on both the maximum depth and the surface area of the lake, whereas the depth of the thermocline depends primarily on the surface area. A modification of previously published scaling arguments provides a plausible theoretical basis for some of this behavior. These arguments account for additional shear-induced mixing associated with the fundamental internal seiche in small lakes and with near-inertial motion in big lakes. For lakes of cross-basin diameter less than 5,000 m (surface area less than 25 km 2), an estimate of the depth of the thermocline, h, at the time of maximum heat content is given by: h ≅ 2.0 ( τ g Δ ρ ) 1 / 2 L 1 / 2 where τ is the wind stress associated with late summer storms, Δp is the density contrast between epilimnion and hypolimnion typical for lakes in that region near the time of maximum heat content, g is the gravitational acceleration, and L is the square root of the surface area of the lake. A consistent set of units must be employed.