SQG/Baroclinic mode decomposition with idealized stratification

Recently we proposed a method for estimating subsurface (ocean) velocity and density fields from sea surface density and sea surface height. The method employs the surface quasi-geostrophic (SQG) approximation for the density-derived field, then uses the surface height to determine the strength of the gravest baroclinic modes. The solutions were obtained numerically, using realistic stratification.

Here we illustrate the method assuming an idealized (exponential) basic stratification. Then the SQG and baroclinic mode solutions can be obtained analytically, simplifying the application to ocean fields. Solutions which include a surface mixed layer are also derived, and under general conditions these too can be obtained without resorting to numerical solutions.

The construct is then used to examine how the surface mixed layer affects the decomposition onto the SQG and modal solutions. The mixed layer has only a minimal effect on the baroclinic modes but does affect the relative contribution of the SQG solution. The solutions are applied to a model of the North Atlantic and compared to the previously-derived numerical solutions.