Mathematical models of cumulus convection

Clouds remain to be one of the largest factors contributing to uncertainty in models for National Weather Prediction (NWP). The global circulation models (GCMs) used in NWP operate on scales several orders of magnitude greater than the turbulent processes in clouds and as such, are forced to resort to crude, column based approximations to incorporate cumulus convection. While convection permitting models (CPMs) attempt to resolve convective clouds, the computational demand of implementing such models in NWP is too great. The current Met Office NERC model (MONC) makes use of the Large-Eddie Simulation which relies on turbulence closure assumptions, meaning that clouds are not explicitly resolved.

Being able to more accurately resolve convective clouds in GCMs will provide many benefits in NWP, for example, large regions of organised convection can give rise to tropical storms and other forms of severe weather. In the current climate, it is becoming increasingly clear that our ability to model and predict such scenarios requires improvement, and a more effective model of cumulus convection may contribute greatly to such a goal.

Most existing models of convection adopt a grid based (Eulerian) approach to the problem of modelling cumulus convection. The Moist Parcel-in-cell method (MPIC) however, uses a parcel based method in which conserved quantities are carried by individual parcels of fluid. While parcel based models are not necessarily new, this is the first time one has been used in three dimensional simulations of individual clouds. This model possesses several unique benefits due to the Lagrangian nature of its approach including greatly reduced computational expense and a lack of numerical damping. Comparisons of this model to the current MONC model are the topic of an upcoming paper, although refinements to MPIC are currently underway prior to submission.

The project will be focused on the development, testing and application of the MPIC model to more realistic environmental settings than the current idealised test case. For example, more accurate treatments of environmental wind shear and precipitation as well as generalisation of the boundary conditions (incorporating moisture and buoyancy flux at the boundaries etc) will help to increase the applicability of the model. Other modifications may involve the relaxing of the Boussinesq approximation to allow the model to more reliably model deep convection. As refinements are made, it should become possible to use MPIC to model existing environmental case studies and observations to provide a greater measure of its effectiveness. It is hoped that as the model continues to develop, it will start to show further advantages over the current method used in MONC and, if successful, may see implementation in global scale models for NWP.