“…These five indices were frequently used in related research (Butcher et al, ; Fang & Stefan, ; Kraemer et al, ; Schwefel et al, ; Valerio et al, ). The Schmidt stability, reflecting the difference in potential energy between a stratified lake and the same lake at hypothetically mixed conditions (Boehrer & Schultze, ; Boehrer, Kiwel, Rahn, & Schultze, ; Idso, ; Schmidt, ), was defined as: where g is the gravitational acceleration, A 0 the surface area, ρ z and A z are the water density and area at depth z , z * , and ρ * are the center depth of the volume and its corresponding density. The open water stratification ratio is defined as the fraction of simulation time in which the temperature difference between the top and bottom layer of the water is greater than 1 K (Fang & Stefan, ).…”