Editorial Type:
Article
Article Type:
Research Article

Testing of a Cell-Integrated Semi-Lagrangian Semi-Implicit Nonhydrostatic Atmospheric Solver (CSLAM-NH) with Idealized Orography

May Wong University of British Columbia, Vancouver, British Columbia, Canada

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William C. Skamarock National Center for Atmospheric Research, Boulder, Colorado

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Peter H. Lauritzen National Center for Atmospheric Research, Boulder, Colorado

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Joseph B. Klemp National Center for Atmospheric Research, Boulder, Colorado

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Roland B. Stull University of British Columbia, Vancouver, British Columbia, Canada

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Print Publication:
01 Apr 2015
DOI:
https://doi.org/10.1175/MWR-D-14-00059.1
Page(s):
1382–1398
Restricted access

Abstract

A recently developed cell-integrated semi-Lagrangian (CISL) semi-implicit nonhydrostatic atmospheric solver that uses the conservative semi-Lagrangian multitracer (CSLAM) transport scheme is extended to include orographic influences. With the introduction of a new semi-implicit CISL discretization of the continuity equation, the nonhydrostatic solver, called CSLAM-NH, has been shown to ensure inherently conservative and numerically consistent transport of air mass and other scalar variables, such as moisture and passive tracers. The extended CSLAM-NH presented here includes two main modifications: transformation of the equation set to a terrain-following height coordinate to incorporate orography and an iterative centered-implicit time-stepping scheme to enhance the stability of the scheme associated with gravity wave propagation at large time steps. CSLAM-NH is tested for a suite of idealized 2D flows, including linear mountain waves (dry), a downslope windstorm (dry), and orographic cloud formation.

Current affiliation: Pacific Northwest National Laboratory, Richland, Washington.

The National Center for Atmospheric Research is sponsored by the National Science Foundation.

Corresponding author address: May Wong, Pacific Northwest National Laboratory, Atmospheric Sciences and Global Change Division, 902 Battelle Blvd., P.O. Box 999, MSIN K9-24, Richland, WA 99352. E-mail: may.wong@pnnl.gov

Abstract

A recently developed cell-integrated semi-Lagrangian (CISL) semi-implicit nonhydrostatic atmospheric solver that uses the conservative semi-Lagrangian multitracer (CSLAM) transport scheme is extended to include orographic influences. With the introduction of a new semi-implicit CISL discretization of the continuity equation, the nonhydrostatic solver, called CSLAM-NH, has been shown to ensure inherently conservative and numerically consistent transport of air mass and other scalar variables, such as moisture and passive tracers. The extended CSLAM-NH presented here includes two main modifications: transformation of the equation set to a terrain-following height coordinate to incorporate orography and an iterative centered-implicit time-stepping scheme to enhance the stability of the scheme associated with gravity wave propagation at large time steps. CSLAM-NH is tested for a suite of idealized 2D flows, including linear mountain waves (dry), a downslope windstorm (dry), and orographic cloud formation.

Current affiliation: Pacific Northwest National Laboratory, Richland, Washington.

The National Center for Atmospheric Research is sponsored by the National Science Foundation.

Corresponding author address: May Wong, Pacific Northwest National Laboratory, Atmospheric Sciences and Global Change Division, 902 Battelle Blvd., P.O. Box 999, MSIN K9-24, Richland, WA 99352. E-mail: may.wong@pnnl.gov
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  • Bonaventura, L., 2000: A semi-implicit semi-Lagrangian scheme using the height coordinate for a nonhydrostatic and fully elastic model of atmospheric flows. J. Comput. Phys., 158, 186–213, doi:10.1006/jcph.1999.6414.

    • Search Google Scholar
    • Export Citation

  • Cordero, E., N. Wood, and A. Staniforth, 2005: Impact of semi-Lagrangian trajectories on the discrete normal modes of a non-hydrostatic vertical-column model. Quart. J. Roy. Meteor. Soc., 131, 93–108, doi:10.1256/qj.04/34.

    • Search Google Scholar
    • Export Citation

  • Côté, J., S. Gravel, A. Méthot, A. Patoine, M. Roch, and A. Staniforth, 1998: The operational CMC-MRB global environmental multiscale (GEM) model. Part I: Design considerations and formulation. Mon. Wea. Rev., 126, 1373–1395, doi:10.1175/1520-0493(1998)126<1373:TOCMGE>2.0.CO;2.

    • Search Google Scholar
    • Export Citation

  • Cullen, M. J. P., 2001: Alternative implementations of the semi-Lagrangian semi-implicit schemes in the ECMWF model. Quart. J. Roy. Meteor. Soc., 127, 2787–2802, doi:10.1002/qj.49712757814.

    • Search Google Scholar
    • Export Citation

  • Doyle, J. D., and Coauthors, 2000: An intercomparison of model-predicted wave breaking for the 11 January 1972 Boulder windstorm. Mon. Wea. Rev., 128, 901–914, doi:10.1175/1520-0493(2000)128<0901:AIOMPW>2.0.CO;2.

    • Search Google Scholar
    • Export Citation

  • Durran, D. R., 1986: Another look at downslope windstorms. Part I: The development of analogs to supercritical flow in an infinitely deep, continuously stratified fluid. J. Atmos. Sci., 43, 2527–2543, doi:10.1175/1520-0469(1986)043<2527:ALADWP>2.0.CO;2.

    • Search Google Scholar
    • Export Citation

  • Durran, D. R., and J. B. Klemp, 1982: On the effects of moisture on the Brunt–Väisälä frequency. J. Atmos. Sci., 39, 2152–2158, doi:10.1175/1520-0469(1982)039<2152:OTEOMO>2.0.CO;2.

    • Search Google Scholar
    • Export Citation

  • Durran, D. R., and J. B. Klemp, 1983: A compressible model for the simulation of moist mountain waves. Mon. Wea. Rev., 111, 2341–2361, doi:10.1175/1520-0493(1983)111<2341:ACMFTS>2.0.CO;2.

    • Search Google Scholar
    • Export Citation

  • Erath, C., P. H. Lauritzen, J. H. Garcia, and H. M. Tufo, 2012: Integrating a scalable and efficient semi-Lagrangian multi-tracer transport scheme in HOMME. Procedia Comput. Sci., 9, 994–1003, doi:10.1016/j.procs.2012.04.106.

    • Search Google Scholar
    • Export Citation

  • Gal-Chen, T., and R. Somerville, 1975: On the use of a coordinate transformation for the solution of the Navier-Stokes equations. J. Comput. Phys., 17, 209–228, doi:10.1016/0021-9991(75)90037-6.

    • Search Google Scholar
    • Export Citation

  • Jöckel, P., R. von Kuhlmann, M. Lawrence, B. Steil, C. Brenninkmeijer, P. Crutzen, P. Rasch, and B. Eaton, 2001: On a fundamental problem in implementing flux-form advection schemes for tracer transport in 3-dimensional general circulation and chemistry transport models. Quart. J. Roy. Meteor. Soc., 127, 1035–1052, doi:10.1002/qj.49712757318.

    • Search Google Scholar
    • Export Citation

  • Keller, T. L., R. Rotunno, M. Steiner, and R. D. Sharman, 2012: Upstream-propagating wave modes in moist and dry flow over topography. J. Atmos. Sci., 69, 3060–3076, doi:10.1175/JAS-D-12-06.1.

    • Search Google Scholar
    • Export Citation

  • Klemp, J. B., 2011: A terrain-following coordinate with smoothed coordinate surfaces. Mon. Wea. Rev., 139, 2163–2169, doi:10.1175/MWR-D-10-05046.1.

    • Search Google Scholar
    • Export Citation

  • Klemp, J. B., and D. K. Lilly, 1978: Numerical simulation of hydrostatic mountain waves. J. Atmos. Sci., 35, 78–107, doi:10.1175/1520-0469(1978)035<0078:NSOHMW>2.0.CO;2.

    • Search Google Scholar
    • Export Citation

  • Klemp, J. B., W. C. Skamarock, and J. Dudhia, 2007: Conservative split-explicit time integration methods for the compressible nonhydrostatic equations. Mon. Wea. Rev., 135, 2897–2913, doi:10.1175/MWR3440.1.

    • Search Google Scholar
    • Export Citation

  • Klemp, J. B., J. Dudhia, and A. D. Hassiotis, 2008: An upper gravity-wave absorbing layer for NWP applications. Mon. Wea. Rev., 136, 3987–4004, doi:10.1175/2008MWR2596.1.

    • Search Google Scholar
    • Export Citation

  • Lalas, D. P., and F. Einaudi, 1974: On the correct use of the wet adiabatic lapse rate in stability criteria of a saturated atmosphere. J. Appl. Meteor., 13, 318–324, doi:10.1175/1520-0450(1974)013<0318:OTCUOT>2.0.CO;2.

    • Search Google Scholar
    • Export Citation

  • Laprise, J. P. R., and A. Plante, 1995: A class of semi-Lagrangian integrated-mass (SLIM) numerical transport algorithms. Mon. Wea. Rev., 123, 553–565, doi:10.1175/1520-0493(1995)123<0553:ACOSLI>2.0.CO;2.

    • Search Google Scholar
    • Export Citation

  • Lauritzen, P. H., E. Kaas, and B. Machenhauer, 2006: A mass-conservative semi-implicit semi-Lagrangian limited-area shallow-water model on the sphere. Mon. Wea. Rev., 134, 1205–1221, doi:10.1175/MWR3115.1.

    • Search Google Scholar
    • Export Citation

  • Lauritzen, P. H., R. D. Nair, and P. A. Ullrich, 2010: A conservative semi-Lagrangian multi-tracer transport scheme (CSLAM) on the cubed-sphere grid. J. Comput. Phys., 229, 1401–1424, doi:10.1016/j.jcp.2009.10.036.

    • Search Google Scholar
    • Export Citation

  • Lilly, D. K., 1978: A severe downslope windstorm and aircraft turbulence event induced by a mountain wave. J. Atmos. Sci., 35, 59–77, doi:10.1175/1520-0469(1978)035<0059:ASDWAA>2.0.CO;2.

    • Search Google Scholar
    • Export Citation

  • Machenhauer, B., and M. Olk, 1997: The implementation of the semi-implicit scheme in cell-integrated semi-Lagrangian models. Atmos.–Ocean, 35 (Suppl. 1), 103–126, doi:10.1080/07055900.1997.9687344.

    • Search Google Scholar
    • Export Citation

  • Melvin, T., M. Dubal, N. Wood, A. Staniforth, and M. Zerroukat, 2010: An inherently mass-conserving iterative semi-implicit semi-Lagrangian discretization of the non-hydrostatic vertical-slice equations. Quart. J. Roy. Meteor. Soc., 136, 799–814, doi:10.1002/qj.603.

    • Search Google Scholar
    • Export Citation

  • Miglietta, M., and R. Rotunno, 2005: Simulations of moist nearly neutral flow over a ridge. J. Atmos. Sci., 62, 1410–1427, doi:10.1175/JAS3410.1.

    • Search Google Scholar
    • Export Citation

  • Müller, E. H., and R. Scheichl, 2014: Massively parallel solvers for elliptic partial differential equations in numerical weather and climate prediction. Quart. J. Roy. Meteor. Soc., 140, 2608–2624, doi:10.1002/qj.2327.

    • Search Google Scholar
    • Export Citation

  • Nair, R., and B. Machenhauer, 2002: The mass-conservative cell-integrated semi-Lagrangian advection scheme on the sphere. Mon. Wea. Rev., 130, 649–667, doi:10.1175/1520-0493(2002)130<0649:TMCCIS>2.0.CO;2.

    • Search Google Scholar
    • Export Citation

  • Peltier, W. R., and T. L. Clark, 1979: The evolution and stability of finite-amplitude mountain waves. Part II: Surface wave drag and severe downslope windstorms. J. Atmos. Sci., 36, 1498–1529, doi:10.1175/1520-0469(1979)036<1498:TEASOF>2.0.CO;2.

    • Search Google Scholar
    • Export Citation

  • Peltier, W. R., and T. L. Clark, 1983: Nonlinear mountain waves in two and three spatial dimensions. Quart. J. Roy. Meteor. Soc., 109, 527–548, doi:10.1002/qj.49710946106.

    • Search Google Scholar
    • Export Citation

  • Pinty, J. P., R. Benoit, E. Richard, and R. Laprise, 1995: Simple tests of a semi-implicit semi-Lagrangian model on 2D mountain wave problems. Mon. Wea. Rev., 123, 3042–3058, doi:10.1175/1520-0493(1995)123<3042:STOASI>2.0.CO;2.

    • Search Google Scholar
    • Export Citation

  • Rancic, M., 1992: Semi-Lagrangian piecewise biparabolic scheme for two-dimensional horizontal advection of a passive scalar. Mon. Wea. Rev., 120, 1394–1406, doi:10.1175/1520-0493(1992)120<1394:SLPBSF>2.0.CO;2.

    • Search Google Scholar
    • Export Citation

  • Rivest, C., A. Staniforth, and A. Robert, 1994: Spurious resonant response of semi-Lagrangian discretizations to orographic forcing: Diagnosis and solution. Mon. Wea. Rev., 122, 366–376, doi:10.1175/1520-0493(1994)122<0366:SRROSL>2.0.CO;2.

    • Search Google Scholar
    • Export Citation

  • Robert, A., 1981: A stable numerical integration scheme for the primitive meteorological equations. Atmos.–Ocean, 19, 35–46, doi:10.1080/07055900.1981.9649098.

    • Search Google Scholar
    • Export Citation

  • Robert, A., T. Yee, and H. Ritchie, 1985: A semi-Lagrangian and semi-implicit numerical-integration scheme for multilevel atmospheric models. Mon. Wea. Rev., 113, 388–394, doi:10.1175/1520-0493(1985)113<0388:ASLASI>2.0.CO;2.

    • Search Google Scholar
    • Export Citation

  • Schär, C., D. Leuenberger, O. Fuhrer, D. Lüthi, and C. Girard, 2002: A new terrain-following vertical coordinate formulation for atmospheric prediction models. Mon. Wea. Rev., 130, 2459–2480, doi:10.1175/1520-0493(2002)130<2459:ANTFVC>2.0.CO;2.

    • Search Google Scholar
    • Export Citation

  • Skamarock, W. C., and J. B. Klemp, 1994: Efficiency and accuracy of the Klemp–Wilhelmson time-splitting technique. Mon. Wea. Rev., 122, 2623–2630, doi:10.1175/1520-0493(1994)122<2623:EAAOTK>2.0.CO;2.

    • Search Google Scholar
    • Export Citation

  • Skamarock, W. C., P. K. Smolarkiewicz, and J. B. Klemp, 1997: Preconditioned conjugate-residual solvers for Helmholtz equations in nonhydrostatic models. Mon. Wea. Rev., 125, 587–599, doi:10.1175/1520-0493(1997)125<0587:PCRSFH>2.0.CO;2.

    • Search Google Scholar
    • Export Citation

  • Smith, R. B., 1979: The influence of mountains on the atmosphere. Advances in Geophysics, Vol. 21, Academic Press, 87–230, doi:10.1016/S0065-2687(08)60262-9.

    • Search Google Scholar
    • Export Citation

  • Smith, R. B., 1980: Linear theory of stratified hydrostatic flow past an isolated mountain. Tellus, 32A, 348–364, doi:10.1111/j.2153-3490.1980.tb00962.x.

    • Search Google Scholar
    • Export Citation

  • Smolarkiewicz, P., and J. Pudykiewicz, 1992: A class of semi-Langragian approximations for fluids. J. Atmos. Sci., 49, 2082–2096, doi:10.1175/1520-0469(1992)049<2082:ACOSLA>2.0.CO;2.

    • Search Google Scholar
    • Export Citation

  • Ullrich, P. A., P. H. Lauritzen, and C. Jablonowski, 2013: Some considerations for high-order ‘incremental remap’-based transport schemes: Edges, reconstructions, and area integration. Int. J. Numer. Methods Fluids, 71, 1131–1151, doi:10.1002/fld.3703.

    • Search Google Scholar
    • Export Citation

  • Wong, M., W. C. Skamarock, P. H. Lauritzen, and R. B. Stull, 2013: A cell-integrated semi-Lagrangian semi-implicit shallow-water model (CSLAM-SW) with conservative and consistent transport. Mon. Wea. Rev., 141, 2545–2560, doi:10.1175/MWR-D-12-00275.1.

    • Search Google Scholar
    • Export Citation

  • Wong, M., W. C. Skamarock, P. H. Lauritzen, J. B. Klemp, and R. B. Stull, 2014: A compressible nonhydrostatic cell-integrated semi-Lagrangian semi-implicit solver (CSLAM-NH) with consistent and conservative transport. Mon. Wea. Rev., 142, 1669–1687, doi:10.1175/MWR-D-13-00210.1.

    • Search Google Scholar
    • Export Citation

  • Xue, M., K. K. Droegemeier, and V. Wong, 2000: The Advanced Regional Prediction System (ARPS)—A multi-scale nonhydrostatic atmospheric simulation and prediction model. Part I: Model dynamics and verification. Meteor. Atmos. Phys., 75, 161–193, doi:10.1007/s007030070003.

    • Search Google Scholar
    • Export Citation

  • Zerroukat, M., N. Wood, and A. Staniforth, 2002: SLICE: A semi-Lagrangian inherently conserving and efficient scheme for transport problems. Quart. J. Roy. Meteor. Soc., 128, 2801–2820, doi:10.1256/qj.02.69.

    • Search Google Scholar
    • Export Citation

  • Zhang, K., H. Wan, B. Wang, and M. Zhang, 2008: Consistency problem with tracer advection in the atmospheric model GAMIL. Adv. Atmos. Sci., 25, 306–318, doi:10.1007/s00376-008-0306-z.

    • Search Google Scholar
    • Export Citation
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