Vertical structure of the upper ocean from profiles fitted to physically consistent functional forms

A method for characterizing the upper ocean structure is developed. Each temperature (density) profile is fitted by an ideal function based on the assumption that the permanent and seasonal thermoclines can be approximated respectively by steady state and transients of turbulent-diffusive processes and that the mixed layer can advance sharply under external forcing. The ideal profile is composed of two pieces joined at the mixed layer depth (MLD). The upper part is a constant; the part below the MLD is a product of an exponential decay and a Gaussian, representing the seasonal thermocline and decaying asymptotically to a straight line that describes the permanent thermocline. The composition of an exponential decay and a Gaussian accurately fits a wide family of solutions of the diffusion equation and includes the case of a shift of the boundary. The ideal fit for each profile relies on six adjustable parameters including the MLD. As the function is non-linear and non-differentiable, a Differential Evolution optimization algorithm is proposed to make the fitting. The solution gives a good estimate of the MLD based on the topology of the profile. It also provides a measure of the gradient and the shape of each profile, which are intuitive parameters for characterizing the upper ocean structure with direct applicability in ecosystem models. The algorithm is applied to a time series of monthly conductivity–temperature–depth (CTD) profiles from a hydrographical station in the southern Bay of Biscay. The construction of a local climatology of the vertical structure evolution (mixed layer development) is presented as a practical application. Other potential uses of the method are also discussed.