Geoscientific Model Development Discussions www.geosci-model-dev-discuss.net 1991-9611 1991-962X 2 1 2009 10.5194/gmdd-2-581-2009 http://www.geosci-model-dev-discuss.net/2/581/2009/ http://www.geosci-model-dev-discuss.net/2/581/2009/gmdd-2-581-2009.html http://www.geosci-model-dev-discuss.net/2/581/2009/gmdd-2-581-2009.pdf 581 638 2009-06-16 Icosahedral Shallow Water Model (ICOSWM): results of shallow water test cases and sensitivity to model parameters P. Rípodas maria-pilar.ripodas@dwd.de A. Gassmann J. Förstner D. Majewski M. Giorgetta P. Korn L. Kornblueh H. Wan G. Zängl L. Bonaventura T. Heinze Deutscher Wetterdienst, Offenbach, Germany Max Planck Institute for Meteorology, Hamburg, Germany now at: Politecnico di Milano, Milan, Italy now at: Freelance Scientist The Icosahedral Shallow Water Model (ICOSWM) has been a first step in the development of the ICON (acronym for ICOsahedral Nonhydrostatic) models. ICON is a joint project of the Max Planck Institute for Meteorology in Hamburg (MPI-M) and Deutscher Wetterdienst (DWD) for the development of new unified general circulation models for climate modeling and numerical weather forecasting on global or regional domains. A short description of ICOSWM is given. Standard test cases are used to test the performance of ICOSWM. The National Center for Atmospheric Research (NCAR) Spectral Transform Shallow Water Model (STSWM) has been used as reference for test cases without an analytical solution. The sensitivity of the model results to different model parameters is studied. The kinetic energy spectra are calculated and compared to the STSWM spectra. A comparison to the shallow water version of the current operational model GME at DWD is presented. In the framework of the ICON project an hydrostatic dynamical core has been developed, and a local grid refinement option and a non-hydrostatic dynamical core are under development. The results presented in this paper use the ICOSWM version at the end of 2008 and are a benchmark for the new options implemented in the development of these models. Arakawa, A. and Lamb, V.: A potential enstrophy and energy conserving scheme for the shallow water equations, Mon. Weather Rev., 109, 18–136, 1981. Asselin, R.: Frequency filter for time integrations, Mon. Weather Rev., 100, 487–490, 1972. Baumgardner, J. and Frederickson, P.: Icosahedral discretization of the two-sphere, SIAM Journal of Scientific Computing, 22, 1107–1115, 1985. Bonaventura, L.: Development of the ICON dynamical core: modelling strategies and preliminary results, in: Proceedings of the ECMWF/SPARC Workshop on Modelling and Assimilation for the Stratosphere and Tropopause, 197–213, ECMWF, 2003. Bonaventura, L.: The ICON project: Development of a unified model using triangular geodesic grid, in: Proceedings of the ECMWF Annual Seminar on Development in Numerical Methods for Atmosphere and Ocean Modeling, 75–86, ECMWF, 2004. Bonaventura, L. and Ringler, T.: Analysis of discrete shallow water models on geodesic Delaunay grids with C-type staggering, Mon. Weather Rev., 133, 2351–2373, 2005. Bonaventura, L., Kornblueh, L., Heinze, T., and R\'\ipodas, P.: A semi-implicit method conserving mass and potential vorticity for the shallow water equations on the sphere, Int. J. Numer. Meth. Fl., 47, 863–869, 2005. Cullen, M.: Integration of the primitive barotropic equations on a sphere using the finite element method, Q. J. Roy. Meteorol. Soc., 100, 555–562, 1974. Gassmann, A. and Heinze, T.: Icosahedral grid optimization strategies for triangular C grids, in: Proceedings of Solution of Partial Differential Equations on the sphere, 24–27 September 2007, Exeter, 2007. Gill, A.: Atmosphere-Ocean Dynamics, Academic Press, 1982. Giraldo, F X.: Lagrange-Galerkin methods on spherical geodesic grids: The shallow water equations, J. Comp. Phys., 160, 336–368, 2000. Heikes, R. and Randall, D.: Numerical integration of the shallow-water equations on a twisted icosahedral grid. Part I: Basic design and results of tests, Mon. Weather Rev., 123, 1862–1880, 1995a. Heikes, R. and Randall, D.: Numerical integration of the shallow-water equations on a twisted icosahedral grid. Part II: A detailed description of the grid and an analysis of numerical accuracy, Mon. Weather Rev., 123, 1881–1887, 1995b. Heinze, T. and Hense, A.: The Shallow Water Equations on the Sphere and their Lagrange-Galerkin solution, Meteorol. Atmos. Phys., 81, 129–137, 2002. Hoskins, B.: Stability of the Rossby – Haurwitz wave, Q. J. Roy. Meteorol. Soc., 99, 723–745, 1973. Jakob-Chien, R., Hack, J., and Williamson, D.: Spectral transform solutions to the shallow water test set, J. Comput. Phys., 119, 164–187, 1995. Lin, S. and Rood, R.: An explicit flux-form semi-Lagrangian shallow water model on the sphere, Q. J. Roy. Meteorol. Soc., 123, 2477–2498, 1997. Majewski, D., Liermann, D., Prohl, P., Ritter, B., Buchhold, M., Hanisch, T., Paul, G., Wergen, W., and Baumgardner, J.: The operational global icosahedral-hexagonal gridpoint model GME: description and high resolution tests, Mon. Weather Rev., 130, 319–338, 2002. Narcowich, F. and Ward, J.: Generalized Hermite interpolation via matrix-valued conditionally positive definite functions, Math. Comput., 63, 661–687, 1994. Quarteroni, A. and Valli, A.: Numerical approximation of partial differential equations, chap. 9: The Stokes problem, Springer Verlag, 1994. Quiang, D., Gunzburger, M., and Lili, J.: Voronoi-based finite volume methods, optimal Voronoi meshes and PDEs on the sphere, Comput. Method. Appl. M., 192, 3933–3957, 2003. Raviart, P. and Thomas, J.: A mixed finite element method for 2nd order elliptic problems., in: Mathematical aspects of finite element methods, 292–315, Springer Verlag, 1977. Ringler, T. and Randall, D.: A potential enstrophy and energy conserving numerical scheme for solution of the shallow-water equations a geodesic grid, Mon. Weather Rev., 130, 1397–1410, 2002. Ringler, T., Heikes, R., and Randall, D.: Modeling the atmospheric general circulation using a spherical geodesic grid: A new class of dynamical cores, Mon. Weather Rev., 128, 2471–2490, 2000. Ruppert, T.: Diploma-thesis. Vector Field Reconstruction by Radial Basis Functions, Tech. Rep. 1089046, TU Darmstadt, 2007. Sadourny, R.: The dynamics of finite difference models of the shallow water equations, J. Atmos. Sci., 32, 680–689, 1975. Skamarock, W C.: Evaluating Mesoscale NWP Models Using Kinetic Energy Spectra, Mon. Weather Rev., 132, 3019–3032, 2004. Smith, R. and Dritschel, D.: Revisiting the Rossby-Haurwitz wave test case with contour advection, J. Comp. Phys., 217, 473–484, 2006. Thuburn, J. and Li, Y.: Numerical simulation of Rossby-Haurwitz waves, Tellus A, 52, 181–189, 2000. Wan, H.: Developing and testing a hydrostatic atmospheric dynamical core on triangular grids, Reports on Earth System Science No 65, Max Planck Institute for Meteorology, Hamburg, Germany, online available at: http://www.mpimet.mpg.de/en/wissenschaft/publikationen/erdsystemforschung.html#c2612, 2009. Williamson, D., Drake, J., Hack, J., Jakob, R., and Swarztrauber, R.: A standard test set for numerical approximations to the shallow water equations in spherical geometry, J. Comp. Phys., 102, 221–224, 1992.