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  • Arakawa A. 1966. Computational design for long-term numerical integration of the equations of fluid motion: Two-dimensional incompressible flow. Part I. J. Comput. Phys. 1: 119143.
  • Arakawa A, Konor CS. 1996. Vertical differencing of the primitive equations based on the Charney–Phillips grid in hybrid σ−p vertical coordinates. Mon. Weather Rev. 124: 511528.
  • Bannon PR. 2002. Theoretical foundations for models of moist convection. J. Atmos. Sci. 59: 19671982.
  • Bannon PR. 2003. Hamiltonian description of idealized binary geophysical fluids. J. Atmos. Sci. 60: 28092819.
  • Bonaventura L, Ringler T. 2005. Analysis of discrete shallow-water models on geodesic Delauney grids with C-type staggering. Mon. Weather Rev. 133: 23512373.
  • Catry B, Geleyn J-F, Tudor M, Bénard P, Trojáková A. 2007. Flux-conservative thermodynamic equations in a mass-weighted framework. Tellus 59A: 7179.
  • Davies T, Cullen MJP, Malcolm AJ, Mawson MH, Staniforth A, White AA, Wood N. 2005. A new dynamical core for the Met Office's global and regional modelling of the atmosphere. Q. J. R. Meteorol. Soc. 131: 17591782.
  • Doms G, Herbert F. 1985. Fluid- und Mikrodynamik in numerischen Modellen konvektiver Wolken. Berichte Inst. Meteorologie un Geodynamik: Univ. Frankfurt aM, Germany.
  • Doms G, Schättler U. 2002. ‘A description of the non-hydrostatic regional model LM. Part I: Dynamics and numerics’. Deutscher Wetterdienst: Offenbach. Available online at http://cosmo-model.cscs.ch/public/documentation.htm#p1.
  • Dubinkina S, Frank J. 2007. Statistical mechanics of Arakawa's discretizations. J. Comput. Phys. 227: 12861305.
  • Ertel H. 1942. Ein neuer hydrodynamischer Wirbelsatz. Meteorol. Z. 59: 277281.
  • Gassmann A, Herzog H-J. 2007. A consistent time-split numerical scheme applied to the non-hydrostatic compressible equations. Mon. Weather Rev. 135: 2036.
  • Gyarmati I. 1970. Non-equilibrium thermodynamics. Springer: Berlin.
  • Herbert F. 1975. Irreversible Prozesse in der Atmosphäre, Teil 3. Contrib. Atmos. Phys. 48: 129.
  • Herzog H-J, Gassmann A. 2005. Lorenz- and Charney–Phillips vertical grid experimentation using a compressible non-hydrostatic toy model relevant to the fast-mode part of the ‘Lokal-Modell’. COSMO Tech. Rep. 7, Deutscher Wetterdienst: Offenbach, Germany. Available online at http://cosmo-model.cscs.ch/public/downloads/techReport_07.pdf.gz.
  • Hesselberg Th. 1925. Die Gesetze der ausgeglichenen Bewegung. Beitr. Phys. freien Atmos. 12: 141160.
  • Kurgansky MV. 2006. Helicity production and maintenance in a baroclinic atmosphere. Meteorol. Z. 15: 409416.
  • Lagally M, Franz W. 1964. Vorlesungen über Vektorrechnung Akad. Verlagsgesellschaft. Geest & Portig: Leipzig.
  • Lange H-J. 2002. Die Physik des Wetters und des Klimas. Reimer: Berlin.
  • Morrison PJ. 1998. Hamiltonian description of the ideal fluid. Rev. Modern Phys. 70: 467521.
  • Névir P. 1998. Die Nambu-Felddarstellungen der Hydro-Thermody namik und ihre Bedeutung für die dynamische Meteorologie. Habilitationsschrift at Freie Universität Berlin, 317 pp.
  • Névir P. 2004. Ertel's vorticity theorems, the particle relabelling symmetry and the energy-vorticity theory of fluid mechanics. Meteorol. Z. 13: 114.
  • Névir P, Blender R. 1993. A Nambu representation of incompressible hydrodynamics using helicity and enstrophy. J. Phys. 26A: L1189L1193.
  • Nic̆ković S, Gavrilov MB, Tošić IA. 2002. Geostrophic adjustment on hexagonal grids. Mon. Weather Rev. 130: 668683.
  • Pielke RA. 1984. Mesoscale Meteorological Modeling Academic Press.
  • Rogers RR, Yau MK. 1989. A short course in cloud physics. Pergamon Press.
  • Sadourny R. 1975. The dynamics of finite difference models of the shallow-water equations. J. Atmos. Sci. 32: 680689.
  • Salmon R. 2004. Poisson-bracket approach to the construction of energy- and potential-enstrophy-conserving algorithms for the shallow-water equations. J. Atmos. Sci. 61: 20162036.
  • Salmon R. 2005. A general method for conserving quantities related to potential vorticity in numerical models. Nonlinearity 18: R1R16.
  • Salmon R. 2007. A general method for conserving energy and potential enstrophy in shallow-water models. J. Atmos. Sci. 64: 515531.
  • Salmon R, Talley LD. 1989. Generalizations of Arakawa's Jacobian. J. Comput. Phys. 83: 247259.
  • Satoh M. 2002. Conservative scheme for the compressible non-hydrostatic models with the horizontally explicit and vertically implicit time integration scheme. Mon. Weather Rev. 130: 12271245.
  • Satoh M. 2003. Conservative scheme for a compressible non-hydrostatic model with moist processes. Mon. Weather Rev. 131: 10331050.
  • Schubert WH, Hausman SA, Garcia M, Ooyama KV, Kuo H-C. 2001. Potential vorticity in a moist atmosphere. J. Atmos. Sci. 58: 31483157.
  • Thuburn J. 2008. Some conservation issues for the dynamical cores of NWP and climate models. J. Comput. Phys. 227: 37153730. doi:10.1016/j.jcp.2006.08.016.
  • Torsvik T, Thiem Ø, Berntsen J. 2005. Stability analysis of geostrophic adjustment on hexagonal grids for regions with variable depth. Mon. Weather Rev. 133: 33353344.
  • Tripoli GJ. 1992. A non-hydrostatic mesoscale model designed to simulate scale interaction. Mon. Weather Rev. 120: 13421359.
  • Tripoli GJ, Mayor SD. 2000. ‘Numerical simulation of the neutral boundary layer: A comparison of enstrophy conserving with momentum conserving finite difference schemes’. Pp. 376379 in proceedings of 14th Symposium on boundary layers and turbulence, 7–11 Aug, Aspen, CO. Available online from http://lidar.ssec.wisc.edu/papers/conferences/ekman_blt2000.pdf.
  • Wacker U, Frisius Th, Herbert F. 2006. Evaporation and precipitation surface effects on local mass continuity laws of moist air. J. Atmos. Sci. 63: 26422652.