Abstract
A 3D dynamic core of the non-hydrostatic model GRAPES (Global/Regional Assimilation and Prediction System) is developed on the Yin-Yang grid to address the polar problem and to enhance the computational efficiency. Three-dimensional Coriolis forcing is introduced to the new core, and full representation of the Coriolis forcing makes it straightforward to share code between the Yin and Yang subdomains. Similar to that in the original GRAPES model, a semi-implicit semi-Lagrangian scheme is adopted for temporal integration and advection with additional arrangement for cross-boundary transport. Under a non-centered second-order temporal and spatial discretization, the dry nonhydrostatic frame is summarized as the solution of an elliptical problem. The resulting Helmholtz equation is solved with the Generalized Conjugate Residual solver in cooperation with the classic Schwarz method. Even though the coefficients of the equation are quite different from those in the original model, the computational procedure of the new core is just the same. The bi-cubic Lagrangian interpolation serves to provide Dirichlet-type boundary conditions with data transfer between the subdomains. The dry core is evaluated with several benchmark test cases, and all the tests display reasonable numerical stability and computing performance. Persistency of the balanced flow and development of both the mountain-induced Rossby wave and Rossby-Haurwitz wave confirms the appropriate installation of the 3D Coriolis terms in the semi-implicit semi-Lagrangian dynamic core on the Yin-Yang grid.
Similar content being viewed by others
References
Arakawa, A., and V. R. Lamb, 1997: Computational design of the basic dynamical processes of the UCLA General Circulation Model. Methods in Computational Physics, Vol. 17, J. Chang, Ed., Academic Press, San Francisco, USA, 173–265.
Baba, Y., K. Takahashi, and T. Sugimura, 2010: Dynamical core of an atmospheric general circulation model on a Yin-Yang grid. Mon. Wea. Rev., 138, 3988–4005.
Charney, J. G., and N. A. Philips, 1953: Numerical integration of the quasi-geostrophic equations for barotropic and simple baroclinic Flow. J. Meteor., 10, 71–99.
Chen, D., and Coauthors, 2008: New generation of multi-scale NWP system (GRAPES): General scientific design. Chinese Sci. Bull., 53(22), 3433–3445.
Jablonowski, C., P. Lauritzen, R. Nair, and M. Taylor, 2008: Idealized test cases for the dynamical cores of atmospheric general circulation models: A proposal for the NCAR ASP 2008 summer colloquium. [Available online at http://esse.engin.umich.edu/admg/publications.php.]
Kageyama, A., and T. Sato, 2004: “Yin-Yang grid”: An overset grid in spherical geometry. Geochem. Geophys. Geosyst., 5, Q09005, doi: 10.1029/2004GC000734.
Li, X. L., D. H. Chen, X. D. Peng, F. Xiao, and X. S. Chen, 2006: Implementation of the semi-Lagrangian advection scheme on a quasi-uniform overset grid on a sphere. Adv. Atmos. Sci., 23(5), 792–801, doi: 10.1007/s00376-006-0792-9.
Li, X. L., D. H. Chen, X. D. Peng, K. Takahashi, and F. Xiao, 2008: A multimoment finite-volume shallow-water model on the Yin-Yang overset spherical grid. Mon. Wea. Rev., 136, 3066–3086.
Liu, Y., and J. W. Cao, 2008: ILU preconditioner for NWP system: GRAPES. Computer Engineering and Design, 29(3), 731–734. (in Chinese)
McDonald, A., and J. R. Bates, 1989: Semi-Lagrangian integration of a grid point shallow water model on the sphere. Mon. Wea. Rev., 117, 130–137.
Peng, X., F. Xiao, and K. Takahashi, 2006: Conservative constraint for a quasi-uniform overset grid on the sphere. Quart. J. Roy. Meteor. Soc., 132, 979–996.
Qian, J., F. Semazzi, and J. S. Scroggs, 1998: A global nonhydrastatic semi-Lagrangian atmospheric model with orography. Mon. Wea. Rev., 126, 747–771.
Qaddouri, A., L. Laayouni, J. Côté, and M. Gander, 2008: Optimized Schwarz methods with an overset grid for shallow-water equations: Preliminary results. Appl. Numer. Math., 58(4), 459–471.
Ritchie, H., and C. Beaudoin, 1994: Approximations and sensitivity experiments with a baroclinic semi-Lagrangian spectral model. Mon. Wea. Rev., 122, 2391–2399.
Sadourny, R. A., 1972: Conservative finite-difference approximations of the primitive equations on quasi-uniform spherical grids. Mon. Wea. Rev., 100, 136–144.
Sadourny, R. A., A. Arakawa, and Y. Mintz, 1968: Integration of the nondivergent barotropic vorticity equation with an icosahedral-hexagonal grid for the sphere. Mon. Wea. Rev., 96, 351–356.
Satoh, M., T. Inoue, and H. Miura, 2010: Evaluations of cloud properties of global and local cloud system resolving models using CALIPSO and CloudSat simulators. J. Geophys. Res., 115, D00H14, doi: 10.1029/2009JD012247.
Skamarock, W., J. Klemp, M. Duda, L. Fowler, and S. H. Park, 2012: A multi-scale nonhydrostatic atmospheric model using centroidal Voronoi tesselations and C-grid staggering. Mon. Wea. Rev., 140, 3090–3105.
Semazzi, F., J. H. Qian, and J. S. Scroggs, 1995: A global nonhydrostatic, semi-Lagrangian, atmospheric model without orography. Mon. Wea. Rev., 123, 2534–2550.
Tomita, H., and M. Satoh, 2004: A new dynamical framework of nonhydrostatic global model using the icosahedral grid. Fluid Dyn. Res., 34, 357–400.
Williamson, D. L., 2007: The evolution of dynamical cores for global atmospheric models. J. Meteor. Soc. Japan, 85B, 241–269.
Williamson, D. L., J. B. Drake, J. J. Hack, R. Jackob, and P. N. Swarztrauber, 1992: A standard test for numerical approximations to the shallow water equations in spherical geometry. Journal of Computational Physics, 102, 211–224.
Xue, J. S., and D. H. Chen, 2008: Design of GRAPES dynamical frame and the experiments. Scientific Design and Application of Numerical Prediction System GRAPES, J. H. Wang, Ed., Science Press, Beijing, 65–136. (in Chinese)
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Li, X., Peng, X. & Li, X. An improved dynamic core for a non-hydrostatic model system on the Yin-Yang grid. Adv. Atmos. Sci. 32, 648–658 (2015). https://doi.org/10.1007/s00376-014-4120-5
Received:
Revised:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00376-014-4120-5