Lake Number, a quantitative indicator of mixing used to estimate changes in dissolved oxygen

Lake Number, L_N, values are shown to be quantitative indicators of deep mixing in lakes and reservoirs that can be used to estimate changes in deep water dissolved oxygen (DO) concentrations. L_N is a dimensionless parameter defined as the ratio of the moments about the center of volume of the water body, of the stabilizing force of gravity associated with density stratification to the destabilizing forces supplied by wind, cooling, inflow, outflow, and other artificial mixing devices. To demonstrate the universality of this parameter, L_N values are used to describe the extent of deep mixing and are compared with changes in DO concentrations in three reservoirs in Australia and four lakes in the U.S.A., which vary in productivity and mixing regimes. A simple model is developed which relates changes in L_N values, i.e., the extent of mixing, to changes in near bottom DO concentrations. After calibrating the model for a specific system, it is possible to use real-time L_N values, calculated using water temperature profiles and surface wind velocities, to estimate changes in DO concentrations (assuming unchanged trophic conditions).