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

Abstract

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.A number of schemes suitable for implementation in the embedded Lagrangian model are derived. Two dynamically passive schemes are derived that emulate existing parameterisations and two dynamically active schemes are also derived that evolve Lagrangian parcels of water (termed “blobs”) according to a set of physical equations. Some details of the implementation into the Geophysical Fluid Dynamics Modular Ocean Model are also given. Finally, results are presented that show that the dynamically passive schemes are able to emulate their Eulerian counterparts to within roundoff error in idealised test cases.