A dynamic, embedded Lagrangian model for ocean climate models

Abstract

A framework is developed for embedding a Lagrangian sub-model into an ocean climate model that has a fixed horizontal Eulerian grid. The embedded Lagrangian model can be used to explicitly represent processes that are at the subgrid scale to the Eulerian. The Lagrangian framework has a number of potential applications. The embedded Lagrangian framework is applied to two different applications in level coordinate ocean climate models, namely open ocean deep convection and gravity driven downslope flows. Both of these processes are subgrid scale in the present generation of global scale level coordinate ocean models. To embed the Lagrangian model in order to represent open ocean deep convection and gravity driven downslope flows, it is necessary to develop a strategy to partition the mass and momentum of the model into an Eulerian component and a Lagrangian component. The Lagrangian parcels, called “blobs,” can be moved around in three dimensions using a more appropriate set of dynamics and may also interact with the Eulerian model. The technique is not a parameterisation, but rather a framework in which a multitude of parameterisations may be implemented. It is thus possible to develop parameterisations which are analogous to many existing and schemes. Initially, several existing parameterisa- tions are emulated. Then, two schemes are developed, one which models open ocean deep convection, and the other (based on a streamtube model) models gravity driven downslope flows. The framework is also tested in several well known idealised test cases. In the test case for deep convection, a 100m resolution non-hydrostatic model of a deep convective patch is used and it is shown that the use of the Lagrangian blobs improved the fidelity of the simulation of a 2km resolution hydrostatic simulation when compared to the use of convective adjustment. Two test cases are used to examine the performance of the scheme for gravity driven downslope flows. The Lagrangain scheme significantly improves the representation of the physics of a plume on a uniform slope and the resultant large scale circulation.