Advanced Mathematical Methods to Study Atmospheric Dynamical Processes and Predictability

The summer school was organized by the Dynamical Processes and Predictability Working Group (PDP WG) of THORPEX1. THORPEX is a 10-year international research and development program to accelerate improvements in the accuracy of one-day to two-week high impact weather forecasts for the benefit of society, the economy and the environment. The PDP WG provides the connection between the operational weather prediction and the academic communities in THORPEX. The summer school was organized for early career scientists working on mathematically challenging problems of weather prediction or mathematical problems which are highly relevant for weather forecasting. The physical model of the atmosphere is a high-Reynolds-number, stratified fluid, which can be treated as an ideal fluid except for a narrow boundary layer at the surface of the Earth. Mathematical models of the atmosphere are typically based on the Eulerian equations of fluid dynamics. Since the independent variables in these differential equations are the spatial location and the time, the equations are partial differential equations. Analytical solutions to these equations exist only for very special initial and boundary conditions [35]; thus, the solution of the equations requires a numerical solution strategy for any realistic initial and boundary conditions. The computer code implementation of a particular numerical solution strategy is called a (numerical) model. In addition to weather prediction, atmospheric models are also employed to simulate and predict changes in the climate, and to monitor and predict changes in the chemical composition of the atmosphere. As the skill of the models is continuously tested by operational forecast applications, numerical weather prediction models provide the consistently most accurate solutions of the atmospheric governing equations for realistic initial conditions. Hence, forecast models provide a unique opportunity to study the behavior of a truly complex physical system.