A Bayesian approach to map oceanic structures, with an application to the Gulf Stream

A Bayesian approach is proposed to map position and evolution of oceanic structures. In the simplest formulation, the prior probability density function (PDF), i.e., the probability that a given point at a given time belongs to the considered structure, is modulated through the Bayes theorem by the likelihood and the marginal PDF. The likelihood represents the PDF of the observed data, conditioned on the fact that the examined point belongs to the structure at the examined time. The marginal PDF represents the probability of observing the field data, independently of the fact that the point belongs or not to the structure. A procedure to model prior PDF, likelihood and marginal PDF from observed data and to obtain the posterior PDF, namely the probability that a point belongs to the structure at a given time, conditioned on observed data, is proposed. The procedure is tested to map the Gulf Stream, based on observations of physical properties at the sea surface: temperature (SST), velocity (SSV) and salinity (SSS). The results of a single-variable model, based on SST only, are compared with those obtained from double-variable (SST and SSV) and multiple-variable (SST, SSV, SSS) models. The results show the relevance of data resolution and the importance of the proper modeling of the marginal PDF.