Numerical modelling of geophysical fluids on geodesic grids

Abstract

Global numerical models for weather and climate simulations historically employ latitude-longitude grids on the sphere. However, the pole singularities and the related anisotropies tend to cause a loss of computational efficiency in modern massively parallel computers. Several research groups have been investigating alternatives, considering more isotropic spherical grids. One of the most promising approaches seems to be the geodesic grids, formed by polygonal geodesic cells.An important step in the development of weather or climate models is the study of simplified models, including shallow water models, which describe most of the horizontal dynamical processes of the atmosphere. Although many shallow water models on icosahedral grids have already been developed, there are still open questions related to the discretizations and many issues to be addressed. An efficient approach is to use finite volume methods with good mimetic properties, such as the ones proposed in \cite{Thuburn2009} and \cite{Ringler2010}. This methodology is very low accurate, essentially due its strong geometry dependency, which is irregular in geodesic grids. Nevertheless, it is currently being used with success, for example, on the MPAS model \cite{Skamarock2012}. Based on previous works (\cite{Peixoto2013, Peixoto2014}), where we analysed some relations between cell geometries and finite volume discretizations, we believe that the approach of \cite{Thuburn2009} may be improved.Also, the use of semi-Lagrangian semi-implicit schemes, for example, has still been little explored within geodesic grids. This methodology has been applied in grid-point and spectral models with great success. From our previous work (\cite{Peixoto2013b}), in which we developed a semi-Lagrangian transport model on geodesic icosahedral grids, we believe that this approach will be successful for other models as well.We intend to work on these two front-lines for one year together with Prof. John Thuburn and the GungHo project group, who are currently developing the Highly Optimized Globally Uniform Next Generation Model in UK. The project will be developed within the University of Exeter's dependencies with collaborations with the Met Office and other universities involved with the GungHo project. (AU)