A Generalized Depth-Integrated Model of the Oceanic Mixed Layer

A generalized depth-integrated model of the oceanic mixed layer is developed by considering the heat and energy budgets of the upper ocean. Unlike the Kraus–Turner-type bulk models, the assumptions of an a priori well mixed layer and a positive density discontinuity at the base of the layer are not required in the present formulation. Relaxation of these restrictions is achieved by dealing directly with time-integrated equations, thus eliminating inaccuracies introduced by forming a differential equation prior to time discretization. The formulation involves a careful accounting of the effects of stratification below the mixed layer and the change in the density of the mixed layer produced by heat absorption and freshwater exchange. Scale analysis of the equation governing changes in mixed layer depth is used to reveal the conditions under which the present model reduces to a standard Kraus–Turner-type bulk model. Model results are compared with observations at OWS Papa in order to confirm the utility of the formulation in a simple one-dimensional application. Potential use of this model for embedding mixed layer thermodynamics into large-scale circulation models is addressed.