Abstracts: Invited Talks

s of Invited Talks Knut Klingbeil, Leibnitz Institut for Baltic Sea Research Warnemünde: The problem of numerically-induced mixing In this lecture talk numerical mixing of water masses will be presented as one of the most challenging problems in ocean models. It is caused by the truncation errors of numerical advection schemes and can easily dominate over the physical mixing due to well-calibrated turbulence parameterisations. An analysis method for the local quantification of numerical mixing will be explained. Finally, strategies to reduce numerical mixing by smart vertical meshes will be outlined. Piotr Smolarkiewicz, ECMWF An important characteristic of the atmospheric dynamics is that it constitutes a relatively small perturbation about dominant hydrostatic and geostrophic balances established in effect of the Earth gravity, rotation, stably-stratified thermal structure of its atmosphere and the incoming flux of solar energy. Given this specificity, it is compelling to formulate the governing partial differential equations (PDEs) in terms of perturbation variables, defined with respect to an arbitrary "ambient" state of the atmosphere that already satisfies these dominant balances. The role of ambient states is to enhance the efficacy of numerical solution–e.g. by simplifying the initial and boundary conditions and/or improving the conditioning of elliptic boundary value problems–without linearising the system. This talk presents select perturbation forms of nonhydrostatic PDEs that govern dynamics of allscale global atmospheric flows. There can be many alternative perturbation forms for any given system of the governing PDEs, depending on the assumed ambient state about which perturbations are taken and subjective preferences in the numerical model design. All such forms are mathematically equivalent, yet they have different implications for design of effective numerical integrators of the governing PDEs. Arguments are presented in favour of perturbation forms that enhance the efficiency and accuracy of the numerical solution procedure. The different options are implemented in the global all-scale high-performance Finite-Volume Module of ECMWF’s Integrated Forecasting System [1-3]. The presented implementation assumes a class of ambient states of reduced complexity, to verify the theoretical developments, and it provides an effective tool for further study. Numerical simulations of the planetary baroclinic instability, epitomising global weather, illustrate the accuracy of the perturbation equations.