Editorial Type:
Article
Article Type:
Research Article

Implementation of the CIP as the Advection Solver in the MM5

Xindong Peng Earth Simulator Center, Yokohama, Japan

Search for other papers by Xindong Peng in
Current site
Google Scholar
PubMed Close
,
Feng Xiao Tokyo Institute of Technology, Tokyo, Japan

Search for other papers by Feng Xiao in
Current site
Google Scholar
PubMed Close
,
Takashi Yabe Tokyo Institute of Technology, Tokyo, Japan

Search for other papers by Takashi Yabe in
Current site
Google Scholar
PubMed Close
, and
Keiji Tani Earth Simulator Center, Yokohama, Japan

Search for other papers by Keiji Tani in
Current site
Google Scholar
PubMed Close
Print Publication:
01 Jul 2003
DOI:
https://doi.org/10.1175/1520-0493(2003)131<1256:IOTCAT>2.0.CO;2
Page(s):
1256–1271
Restricted access

Abstract

A semi-Lagrangian-type advection scheme, cubic-interpolated pseudoparticle (CIP) method is implemented to the fifth-generation Pennsylvania State University–NCAR Mesoscale Model (MM5, version 3.4). A dimensional splitting CIP algorithm, with spatial third-order and temporal second-order accuracy, is derived to compute the advection in the MM5. The modified model is evaluated with ideal tests and real case studies in comparing with the leapfrog scheme, which was originally employed in the MM5. The CIP method appears remarkably superior to the leapfrog scheme in respect to both dissipative and dispersive errors, especially when discontinuities or large gradients exist in the advected quantity. Two real cases of severe mesoscale phenomena were simulated by using both the CIP scheme and the leapfrog scheme. In the advection dominant regions, the CIP shows remarkable advantages in capturing the detail structures of the predicted field. As computations with high resolution become more and more popular in experimental and/or operational modeling, implementing more accurate advection in numerical models, as is done in the present study, will be increasingly demanded.

Corresponding author address: Dr. Xindong Peng, Earth Simulator Center, 3173-25 Showamachi, Kanazawa-ku, Yokohama, Kanagawa 236-0001, Japan. Email: peng@es.jamstec.go.jp

Abstract

A semi-Lagrangian-type advection scheme, cubic-interpolated pseudoparticle (CIP) method is implemented to the fifth-generation Pennsylvania State University–NCAR Mesoscale Model (MM5, version 3.4). A dimensional splitting CIP algorithm, with spatial third-order and temporal second-order accuracy, is derived to compute the advection in the MM5. The modified model is evaluated with ideal tests and real case studies in comparing with the leapfrog scheme, which was originally employed in the MM5. The CIP method appears remarkably superior to the leapfrog scheme in respect to both dissipative and dispersive errors, especially when discontinuities or large gradients exist in the advected quantity. Two real cases of severe mesoscale phenomena were simulated by using both the CIP scheme and the leapfrog scheme. In the advection dominant regions, the CIP shows remarkable advantages in capturing the detail structures of the predicted field. As computations with high resolution become more and more popular in experimental and/or operational modeling, implementing more accurate advection in numerical models, as is done in the present study, will be increasingly demanded.

Corresponding author address: Dr. Xindong Peng, Earth Simulator Center, 3173-25 Showamachi, Kanazawa-ku, Yokohama, Kanagawa 236-0001, Japan. Email: peng@es.jamstec.go.jp

Save
Cover Monthly Weather Review
Monthly Weather Review

  • Anthes, R. A., 1977: A cumulus parameterization scheme utilizing a one-dimensional cloud model. Mon. Wea. Rev., 105 , 270–286.

  • Bartello, P., and S. J. Thomas, 1996: The cost effectiveness of semi-Lagrangian advection. Mon. Wea. Rev., 124 , 2883–2897.

  • Carpenter, R. L., K. K. Droegemeier, P. R. Woodward, and C. E. Hane, 1990: Application of the piecewise parabolic method (PPM) to meteorological modeling. Mon. Wea. Rev., 118 , 586–612.

    • Search Google Scholar
    • Export Citation

  • Colella, P., and P. R. Woodward, 1984: The piecewise parabolic method (PPM) for gas-dynamical simulations. J. Comput. Phys., 54 , 174–201.

    • Search Google Scholar
    • Export Citation

  • Dudhia, J., 1993: A nonhydrostatic version of the Penn State/NCAR mesoscale model: Validation tests and simulation of an Atlantic cyclone and cold front. Mon. Wea. Rev., 121 , 1493–1513.

    • Search Google Scholar
    • Export Citation

  • Grell, G. A., 1993: Prognostic evaluation of assumptions used by cumulus parameterizations. Mon. Wea. Rev., 121 , 764–787.

  • Harten, A., 1983: High resolution schemes for hyperbolic conservation laws. J. Comput. Phys., 49 , 357–393.

  • Hong, S-Y., and H-L. Pan, 1996: Nonlocal boundary layer vertical diffusion in a medium-range forecast model. Mon. Wea. Rev., 124 , 2322–2339.

    • Search Google Scholar
    • Export Citation

  • Hsie, E-Y., R. A. Anthes, and D. Keyser, 1984: Numerical simulation of frontogenesis in a moist atmosphere. J. Atmos. Sci., 41 , 2581–2593.

    • Search Google Scholar
    • Export Citation

  • Staniforth, A., and J. Côté, 1991: Semi-Lagrangian integration scheme for atmospheric model—A review. Mon. Wea. Rev., 119 , 2206–2223.

    • Search Google Scholar
    • Export Citation

  • Tanaka, R., T. Nakamura, T. Yabe, and H. Wu, 1999: A class of constructing formulation of the CIP method. Comput. Fluid Dyn. J., 8 , 1–5.

    • Search Google Scholar
    • Export Citation

  • van Leer, B., 1977: Toward the ultimate conservative difference scheme. IV. A new approach to numerical convection. J. Comput. Phys., 23 , 276–299.

    • Search Google Scholar
    • Export Citation

  • van Leer, B., 1979: Toward the ultimate conservative difference scheme. V. A second-order sequel to Godunov's method. J. Comput. Phys., 32 , 101–136.

    • Search Google Scholar
    • Export Citation

  • Xiao, F., T. Yabe, and T. Ito, 1996: Constructing oscillation preventing scheme for advection equation by rational function. Comput. Phys. Commun., 93 , 1–12.

    • Search Google Scholar
    • Export Citation

  • Yabe, T., and T. Aoki, 1991: A universal solver for hyperbolic-equations by cubic-polynomial interpolation. I. One-dimensional solver. Comput. Phys. Commun., 66 , 219–232.

    • Search Google Scholar
    • Export Citation

  • Yabe, T., T. Ishikawa, P. Y. Wang, T. Aoki, Y. Kodota, and F. Ikeda, 1991: A universal solver for hyperbolic-equations by cubic-polynomial interpolation. II. Two- and three-dimensional solvers. Comput. Phys. Commun., 66 , 233–242.

    • Search Google Scholar
    • Export Citation

  • Yabe, T., R. Tanaka, T. Nakamura, and F. Xiao, 2001: An exactly conservative semi-Lagrangian scheme (CIP-CSL) in one dimension. Mon. Wea. Rev., 129 , 332–344.

    • Search Google Scholar
    • Export Citation
All Time Past Year Past 30 Days
Abstract Views 0 0 0
Full Text Views 293 138 2
PDF Downloads 67 22 1