# A new Green function approach to the 3D from 2D problem

**Event: **2014 Ocean Surface Topography Science Team Meeting

**Session: **Science Results from Satellite Altimetry: Regional and basin-scale processes and sea level rise

**Presentation type: **Type Poster

A question of fundamental importance in operational oceanography is to evaluate the relative information content of satellite observations of ocean surface properties (mainly sea surface height, sea surface temperature, sea surface colour) versus interior observations (e.g., ARGO floats), in order to determine how best to combine the two kinds of information for constructing optimal estimates of the full three-dimensional structure of the ocean circulation. From a practical viewpoint, the problem has been traditionally approached in the context of data assimilation using empirical regressions between surface and interior properties. Each data assimilation technique, however, use different ways to encode the surface and interior informations to produce optimal state estimates, which makes it hard to understand which approach is best, or how to improve each method. From a theoretical viewpoint, the problem has been primarily approached in the context of quasi-geostrophic (QG) theory as one primarily concerned with the understanding of the interactions between surface QG modes with interior modes. This description, however, only arises due to the specificity of potential vorticity (PV) thinking in a dynamical system of equations filtering all but balanced motions, but has no real counterpart in the primitive equations, complicating the dialogue between QG theorists and operational oceanographers. The purpose of this talk will provide a new formulation of the problem that will hopefully makes it easier to understand how ideas from QG and SQG theory can naturally be implemented and tested directly for the primitive equations.