Structure preserving numerics for atmospheric dynamics: A physics based approach

• Applicants: Privatdozent Dr. Peter Névir; Professor Dr.-Ing. Sebastian Reich
• Subject Area: Atmospheric Science
• Term: from 2007 to 2011
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 32520616

• Final Report Year: 2010

Final Report Abstract

The application of a new method, the Nambu discretization, made the construction of a conservative scheme on a staggered inhomogeneous grid possible. This means that it has become feasible to have simulations of atmospheric dynamics which comply with important physical conservation laws, such as that for energy and that for the quantities associated with vorticity. A prototype of such a program was coded for the simulation of a shallow fluid on a rapidly rotating sphere. It proved to have the expected properties, amongst others a realistic representation of the energy flow through the scales and also very good stability properties. Encouraged by these results, preparatory work for the nonhydrostatic, three-dimensional case was also done. These results are currently being used by the ICON group for the definition of a next-generation combined weather and climate prediction model. It could also be shown, that the proposed method has a significant effect on the phase space volume behaviour of a system. Together with symmetry traits of the time integration scheme, this determines the spread amongst members in ensemble forecasts. Particle methods, while being more complex to implement, offer the additional benefit of highly accurate advection of materially conserved quantities. This property has been verified for several test problems including a barotropic instability, vertical mixing of warm and cold air in a neutrally stratified atmosphere, and propagation of gravity waves under a non-hydrostatic model. Therefore particle methods offer an interesting option for long time simulation of climate models with high number of chemical tracers.

Publications

• An explicit and conservative remapping strategy for semi-Lagrangian advection. In: Atm. Sci. Lett. 8 (2007), 58–63
  Reich, Sebastian
  
• The remapped particle-mesh semi-Lagrangian advection scheme. In: Quart. J. Roy. Meteor. Soc. 133 (2007), 251–260
  Cotter, Colin ; Frank, Jason ; Reich, Sebastian
  
• A conservative scheme for the shallow-water system on a staggered geodesic grid based on a Nambu representation. In: Quart. J. Roy. Meteor. Soc. 135 (2009), 485–494
  Sommer, Matthias ; Névir, Peter
  
• Energy-Vorticity Theory of Ideal Fluid Mechanics. In: J. Atmos. Sci. 66 (2009), 2073–2084
  Névir, Peter ; Sommer, Matthias
  
• Hamiltonian particle-mesh simulations for a non-hydrostatic vertical slice model. In: Atm. Sci. Lett. 10 (2009), 233–240
  Shin, Seoleun ; Reich, Sebastian
  
• Numerische und geometrische Aspekte der Energie-Wirbel-Theorie, Freie Universität Berlin, Doctoral thesis, 2010. - 138 S.
  Sommer, Matthias