A dynamic, embedded Lagrangian model for ocean climate models. Part I: Theory and implementation

A framework for embedding a Lagrangian model within ocean climate models that employ horizontal Eulerian grids is presented. The embedded Lagrangian model can be used to explicitly represent processes that are at the subgrid scale to the Eulerian model. The framework is applied to open ocean deep convection and gravity driven downslope flows, both of which are subgridscale in the present generation of level coordinate ocean climate models. In order to apply the embedded Lagrangian framework to these processes, it is necessary to partition the mass and momentum of the model into an Eulerian system and a Lagrangian system. This partitioning allows the Lagrangian model to transport seawater using a more appropriate set of dynamics