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A global non-hydrostatic dynamical core using the spectral element method on a cubed-sphere grid

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Abstract

A new global model with a non-hydrostatic (NH) dynamical core is developed. It employs the spectral element method (SEM) in the horizontal discretization and the finite difference method (FDM) in the vertical discretization. The solver includes a time-split third-order Runge-Kutta (RK3) time-integration technique. Pursuing the quasi-uniform and pole singularity-free spherical geometry, a cubed-sphere grid is employed. To assess the performance of the developed dynamical solver, the results from a number of idealized benchmark tests for hydrostatic and non-hydrostatic flows are presented and compared. The results indicate that the non-hydrostatic dynamical solver is able to produce solutions with good accuracy and consistency comparable to reference solutions. Further evaluation of the model with a full-physics package demonstrates its capability in reproducing heavy rainfall over the Korean Peninsula, which confirms that coupling of the dynamical solver and full-physics package is robust.

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References

  • Alpert, J. C., M. Kanamitsu, P. M. Caplan, J. G. Sela, G. H. White, and E. Kalnay, 1988: Mountain induced gravity wave drag parameterization in the NMC medium-range forecast model. Preprints. 8th Conf. on Numerical Weather Prediction, Baltimore, MD, Amer. Meteor. Soc., 726–733.

    Google Scholar 

  • Bao. L., R. Klöfkorn, and D. Nair, 2015: Horizontally Explicit and Vertically Implicit (HEVI) Time Discretization Scheme for a Discontinuous Galerkin Nonhydrostatic Model. Mon. Wea. Rev., 143, 972–990.

    Article  Google Scholar 

  • Chen, C., and F. Xiao, 2008: Shallow Wter Model On Cubed-Sphere By Multi-Moment Finite Volume Method. J. Comput. Phys., 227, 5019–5044.

    Article  Google Scholar 

  • Chen, F., and J. Dudhia, 2001: Coupling and advanced land surfacehydrology model with the Penn State-NCAR MM5 modeling system. Part I: model implementation and sensitivity. Mon. Wea. Rev., 129, 569–585.

    Article  Google Scholar 

  • Choi, S.-J., F. X. Giraldo, J. Kim, and S. Shin, 2014: Verification of a nonhydrostatic dynamical core using the horizontal spectral element method and vertical finite difference method: 2-D aspects. Geosci. Model Dev., 7, 2717–2731.

    Article  Google Scholar 

  • Chou, M.-D, and K.-T. Lee, 2005: A parameterization of the effective layer emission for infrared radiation calculations. J. Atmos. Sci., 62, 531–541.

    Article  Google Scholar 

  • Chou, M.-D, K.-T. Lee, S.-C. Tsay, and Q. Fu, 1999: Parameterization for cloud longwave scattering for use in atmospheric models. J. Climate, 12, 159–169.

    Article  Google Scholar 

  • Chun, H.-Y., and J.-J. Baik, 1998: Momentum flux by thermally induced internal gravity waves and its approximation for large-scale models. J. Atmos. Sci., 55, 3299–3310.

    Article  Google Scholar 

  • Dennis, J., A. Fournier, W. F. Spotz, A. St.-Cyr, M. A. Taylor, S. J. Thomas, and H. Tufo, 2005: High resolution mesh convergence properties and parallel efficiency of a spectral element atmospheric dynamical core. Int. J. High Perf. Comput. Appl., 19, 225–235.

    Article  Google Scholar 

  • Dennis, J., J. Edwards, K. J. Evans, O. N. Guba, P. H. Lauritzen, A. A. Mirin, A. St-Cyr, M. A. Taylor, and P. H. Worly, 2011: CAM-SE: a scalable spectral element dynamical core for the community atmosphere model. Int. J. High Perf. Comput. Appl., doi:10.1177/1094342011428142.

    Google Scholar 

  • Fournier, A., M. A. Taylor, and J. J. Tribbia, 2004: The spectral element atmosphere model (SEAM): high-resolution parallel computation and localized resolution of regional dynamics. Mon. Wea. Rev., 132, 726–748.

    Article  Google Scholar 

  • Giraldo, F. X., and T. E. Rosmond, 2004: A Scalable Spectral Element Eulerian Atmospheric Model (SEE-AM) for NWP: Dynamical Core Tests. Mon. Wea. Rev., 132, 133–153.

    Article  Google Scholar 

  • Giraldo, F. X., J. F. Kelly, and E. M. Constantinescu, 2013: Implicit-Explicit Formulations for a 3D Nonhydrostatic Unified Model of the Atmosphere (NUMA). SIAM Sci. Comp., 35, B1162–B1194.

    Article  Google Scholar 

  • Govett, M. W., J. Middlecoff, and T. Henderson, 2010: Running the NIM next-generation weather model on GPUs. 10th IEEE Int. Symp. on Cluster Computing and the Grid, IEEE, 792–796.

    Google Scholar 

  • Hall, D. M., P. A. Ullrich, L. A. Reed, C. Jablonowski, R. D. Nair, H. M. Tufo, 2016: Dynamical Core Model Intercomparison Project (DCMIP) Tracer Transoprt Test Results for CAM-SE. Quart. J. Roy. Meteor. Soc., 142, 1672–1687.

    Article  Google Scholar 

  • Held, I. M., and M. J. Suarez, 1994: A proposal for the intercomparison of the dynamical cores of atmospheric general circulation models. Bull. Amer. Meteor. Soc., 75, 1825–1830.

    Article  Google Scholar 

  • Hong, S.-Y., 2010: A new stable boundary-layer mixing scheme and its impact on the simulated East Asian summer monsoon. Quart. J. Roy. Meteor. Soc., 136, 1481–1496.

    Article  Google Scholar 

  • Hong, S.-Y., H.-M. H. Juang, and Q. Zhao, 1998: Implementation of prognostic cloud scheme for a regional spectral model. Mon. Wea. Rev., 126, 2621–2639.

    Article  Google Scholar 

  • Hong, S.-Y., Y. Noh, and J. Dudhia, 2006: A new vertical diffusion package with an explicit treatment of entrainment processes. Mon. Wea. Rev., 134, 2318–2341.

    Article  Google Scholar 

  • Hong, S.-Y., H. Park, H.-B. Cheong, J.-E. E. Kim, and co-authors, 2013: The global/regional integrated model system (GRIMs). Asia-Pac. J. Atmos. Sci., 49, 219–243.

    Article  Google Scholar 

  • Hundsdorfer, W., B. Koren, M. van Loon, and K. G. Verwer, 1995: A positive finite-difference advection scheme. J. Comput. Phys., 117, 35–46.

    Article  Google Scholar 

  • Jablonowski, C., and D. L. Williamson, 2006: A baroclinic instabilitiy test case for atmospheric model dynamical cores. Quart. J. Roy. Meteor. Soc., 132, 2943–2975.

    Article  Google Scholar 

  • Kelly, J. F., and F. X. Giraldo, 2012: Continuous and discontinuous Galerkin methods for a scalable three-dimensional nonhydrostatic atmospheric model: Limited-area mode. J. Comput. Phys., 231, 7988–8008.

    Article  Google Scholar 

  • Kent, J, P. A. Ullrich, and C. Jablonowski, 2014: Dynamical core model intercomparison project: Tracer transport test cases. Quart. J. Roy. Meteor. Soc., 140, 1279–1293.

    Article  Google Scholar 

  • Klemp, J. B., W. C. Skamarock, and J. Dudhia, 2007: Conservative splitexplicit time integration methods for the compressible nonhydrostatic equations. Mon. Wea. Rev., 135, 2897–2913.

    Article  Google Scholar 

  • Lauritzen, P. H., C. Jablonowski, M. A. Taylor, and R. D. Nair, 2010: Rotated versions of the Jablonowski steady-state and baroclinic wave test cases: A dynamical core intercomparison. J. Adv. Model. Earth Syst., 2, doi:10.3894/JAMES.2010.2.15.

    Google Scholar 

  • Nair, R. D., S. J. Thomas, and R. D. Loft, 2005a: A discontinuous Galerkin transport scheme on the cubed sphere. Mon. Wea. Rev., 133, 814–828.

    Article  Google Scholar 

  • Nair, R. D., S. J. Thomas, and R. D. Loft, 2005b: A discontinuous Galerkin global shallow water model. Mon. Wea. Rev., 133, 876–888.

    Article  Google Scholar 

  • Nair, R. D., H.-W. Choi, and H. M. Tufo, 2009: Computational aspect of a scalable high-order discontinuous Galerkin atmospheric dynamical core. Comput. Fluids, 38, 309–319.

    Article  Google Scholar 

  • Park, H., and S.-Y. Hong, 2007: An evaluation of a mass-flux cumulus parameterization scheme in the KMA global forecast system. J. Meteor. Soc. Japan, 85, 151–169.

    Article  Google Scholar 

  • Park, S.-H., W. C. Skamarock, J. B. Klemp, L. D. Fowler, and M. G. Duda, 2013: Evaluation of global atmospheric solvers using extensions of the Jablonowski and Williamson baroclinic wave test case. Mon. Wea. Rev., 141, 3116–3129.

    Article  Google Scholar 

  • Ran i, M., J. Purser, and F. Mesinger, 1996: A global shallow water model using an expanded spherical cube: gnomonic versus conformal coordinates. J. Roy. Meteor. Soc., 122, 959–982.

    Article  Google Scholar 

  • Sadourny, R., 1972: Conservative finite-difference approximations of the primitive equations on quasi-uniform spherical grids. Mon. Wea. Rev., 100, 136–144.

    Article  Google Scholar 

  • Satoh, M., T. Matsuno, H. Tomita, H. Miura, T. Nasuno, and S. Iga, 2008: Nonhydrostatic icosahedral atmospheric model (NICAM) for global cloud resolving simulations. J. Comput. Phys., 227, 3486–3514.

    Article  Google Scholar 

  • Skamarock, W. C., 2004: Evaluating Mesoscale NWP Models Using Kinetic Energy Spectra. Mon. Wea. Rev., 132, 3019–3032.

    Article  Google Scholar 

  • Skamarock, W. C., and J. B. Klemp, 1992: The Stability of Time-Split Numerical Methods for the Hydrostatic and the Nonhydrostatic Elastic Equations. Mon. Wea. Rev., 120, 2109–2127.

    Article  Google Scholar 

  • Skamarock, W. C., and J. B. Klemp, 2008: A time-split nonhydrostatic atmospheric model for weather research and forecasting applications. J. Comput. Phys., 227, 3465–3485.

    Article  Google Scholar 

  • Skamarock, W. C., J. B. Klemp, J. Dudhia, D. O. Gill, D. M. Barker, M. G. Duda, X. Y. Huang, W. Wang, and J. G. Powers, 2008: A desciption of the advanced research WRF version 3. NCAR Tech. Note TN-475+STR.

    Google Scholar 

  • Skamarock, W. C., J. B. Klemp, M. G. Duda, L. D. Fowler, S.-H. Park, and T. D. Ringler, 2012: A multi-scale nonhydrostatic atmospheric model using centroidal Voronoi tesselations and C-grid staggering. Mon. Wea. Rev., 240, 3090–3105.

    Article  Google Scholar 

  • Taylor, M. A., J. Tribbia, and M. Iskandarani, 1997: The spectral element method for the shallow water equations on the sphere. J. Comput. Phys., 130, 92–108.

    Article  Google Scholar 

  • Taylor, M. A., A. St. Cyr, and A. Fournier, 2009: A non-oscillatory advection operator of the compatible spectral element method. Comutational Science-ICCS 2009, Part II, G. Allen et al., Eds., Springer Berlin Heidelberg, 273–282.

    Chapter  Google Scholar 

  • Taylor, M. A., J. Edwards, S. Thomas, and R. D. Nair, 2007: A mass and energy conserving spectral element atmospheric dynamical core on the cubedsphere grid. J. Phys. Conf. Ser., 78, 012074, doi:10.1088/1742-6596/78/1/012074.

    Article  Google Scholar 

  • Thomas, S. J., and R. D. Loft, 2002: Semi-implicit spectral element atmospheric model. J. Sci. Comput., 17, 339–350.

    Article  Google Scholar 

  • Tumolo, G., and L. Bonaventura, 2015: A semi-implicit, semi-Lagrangian discontinuous Galerkin framework for adaptive numerical weather prediction. Quart. J. Roy. Meteor. Soc., 141, 2582–2601.

    Article  Google Scholar 

  • Ullrich, P. A., and C. Jablonowski, 2012: MCore: a non-hydrostatic atmospheric dynamical core utilizing high-order finite-volume methods. J. Comput. Phys., 231, 5078–5108.

    Article  Google Scholar 

  • Ullrich, P. A., C. Jablonowski, and B. L. van Leer, 2010: High-order finite-volume models for the shallow-water equations on the sphere. J. Comput. Phys., 229, 6104–6134.

    Article  Google Scholar 

  • Ullrich, P. A., C. Jablonowski, J. Kent, P. H. Lauritzen, R. D. Nair, and M. A. Taylor, 2012: Dynamical Core Model Intercomparison Project (DCMIP) Test Case Document. [Available online at https://www.earthsystemcog.org/site_media/docs/DCMIP-TestCaseDocument_v1.7.pdf].

    Google Scholar 

  • Wan, H., M. A. Giorgetta, and L. Bonaventura, 2008: Ensemble Held-Suarez test with a spectral transform model: Variability, Sensitivity, and Convergence. Mon. Wea. Rev., 136, 1075–1092.

    Article  Google Scholar 

  • Wedi, N. P., and P. K. Smolarkiewicz, 2009: A framework for testing global non-hydrostatic models. Quart. J. Roy. Meteor. Soc., 135, 469–484.

    Article  Google Scholar 

  • Wedi, N. P., K. Yessad, and A. Untch, 2009: The nonhydrostatic global IFS/ARPEGE: model formulation and testing. Technical Memorandum, No. 594, European Centre for Medium-Range Weather Forecasts, 36 pp.

    Google Scholar 

  • Wood, N., and Coauthors, 2014: An inherently mass-conserving semiimplicit semi-Lagrangian discretization of the deep-atmosphere global non-hydrostatic equations. Quart. J. Roy. Meteor. Soc., 140, 1505–1520.

    Article  Google Scholar 

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Choi, SJ., Hong, SY. A global non-hydrostatic dynamical core using the spectral element method on a cubed-sphere grid. Asia-Pacific J Atmos Sci 52, 291–307 (2016). https://doi.org/10.1007/s13143-016-0005-0

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