Effects of Nonlinearity on Convectively Forced Internal Gravity Waves: Application to a Gravity Wave Drag Parameterization

Hye-Yeong Chun Department of Atmospheric Sciences, Yonsei University, Seoul, South Korea

Search for other papers by Hye-Yeong Chun in
Current site
Google Scholar
PubMed
Close
,
Hyun-Joo Choi Department of Atmospheric Sciences, Yonsei University, Seoul, South Korea

Search for other papers by Hyun-Joo Choi in
Current site
Google Scholar
PubMed
Close
, and
In-Sun Song Department of Atmospheric Sciences, Yonsei University, Seoul, South Korea

Search for other papers by In-Sun Song in
Current site
Google Scholar
PubMed
Close
Restricted access

Abstract

In the present study, the authors propose a way to include a nonlinear forcing effect on the momentum flux spectrum of convectively forced internal gravity waves using a nondimensional numerical model (NDM) in a two-dimensional framework. In NDM, the nonlinear forcing is represented by nonlinear advection terms multiplied by the nonlinearity factor (NF) of the thermally induced internal gravity waves for a given specified diabatic forcing. It was found that the magnitudes of the waves and resultant momentum flux above the specified forcing decrease with increasing NF due to cancellation between the two forcing mechanisms. Using the momentum flux spectrum obtained by the NDM simulations with various NFs, a scale factor for the momentum flux, normalized by the momentum flux induced by diabatic forcing alone, is formulated as a function of NF. Inclusion of the nonlinear forcing effect into current convective gravity wave drag (GWD) parameterizations, which consider diabatic forcing alone by multiplying the cloud-top momentum flux spectrum by the scale factor, is proposed. An updated convective GWD parameterization using the scale factor is implemented into the NCAR Whole Atmosphere Community Climate Model (WACCM). The 10-yr simulation results, compared with those by the original convective GWD parameterization considering diabatic forcing alone, showed that the magnitude of the zonal-mean cloud-top momentum flux is reduced for wide range of phase speed spectrum by about 10%, except in the middle latitude storm-track regions where the cloud-top momentum flux is amplified. The zonal drag forcing is determined largely by the wave propagation condition under the reduced magnitude of the cloud-top momentum flux, and its magnitude decreases in many regions, but there are several areas of increasing drag forcing, especially in the tropical upper mesosphere and lower thermosphere.

* Current affiliation: Global Modeling and Assimilation Office, NASA GSFC, Greenbelt, Maryland

Corresponding author address: Prof. Hye-Yeong Chun, Department of Atmospheric Sciences, Yonsei University, Shinchon-dong, Seodaemun-ku, Seoul 120-749, South Korea. Email: chy@atmos.yonsei.ac.kr

Abstract

In the present study, the authors propose a way to include a nonlinear forcing effect on the momentum flux spectrum of convectively forced internal gravity waves using a nondimensional numerical model (NDM) in a two-dimensional framework. In NDM, the nonlinear forcing is represented by nonlinear advection terms multiplied by the nonlinearity factor (NF) of the thermally induced internal gravity waves for a given specified diabatic forcing. It was found that the magnitudes of the waves and resultant momentum flux above the specified forcing decrease with increasing NF due to cancellation between the two forcing mechanisms. Using the momentum flux spectrum obtained by the NDM simulations with various NFs, a scale factor for the momentum flux, normalized by the momentum flux induced by diabatic forcing alone, is formulated as a function of NF. Inclusion of the nonlinear forcing effect into current convective gravity wave drag (GWD) parameterizations, which consider diabatic forcing alone by multiplying the cloud-top momentum flux spectrum by the scale factor, is proposed. An updated convective GWD parameterization using the scale factor is implemented into the NCAR Whole Atmosphere Community Climate Model (WACCM). The 10-yr simulation results, compared with those by the original convective GWD parameterization considering diabatic forcing alone, showed that the magnitude of the zonal-mean cloud-top momentum flux is reduced for wide range of phase speed spectrum by about 10%, except in the middle latitude storm-track regions where the cloud-top momentum flux is amplified. The zonal drag forcing is determined largely by the wave propagation condition under the reduced magnitude of the cloud-top momentum flux, and its magnitude decreases in many regions, but there are several areas of increasing drag forcing, especially in the tropical upper mesosphere and lower thermosphere.

* Current affiliation: Global Modeling and Assimilation Office, NASA GSFC, Greenbelt, Maryland

Corresponding author address: Prof. Hye-Yeong Chun, Department of Atmospheric Sciences, Yonsei University, Shinchon-dong, Seodaemun-ku, Seoul 120-749, South Korea. Email: chy@atmos.yonsei.ac.kr

Save
  • Alexander, M. J., and J. R. Holton, 1997: A model study of zonal forcing in the equatorial stratosphere by convectively induced gravity waves. J. Atmos. Sci., 54 , 408419.

    • Search Google Scholar
    • Export Citation
  • Asselin, R., 1972: Frequency filter for time integrations. Mon. Wea. Rev., 100 , 487490.

  • Baik, J-J., and H-Y. Chun, 1996: Effects of nonlinearity on the atmospheric flow response to low-level heating in a uniform flow. J. Atmos. Sci., 53 , 18561869.

    • Search Google Scholar
    • Export Citation
  • Beres, J. H., 2004: Gravity wave generation by a three-dimensional thermal forcing. J. Atmos. Sci., 61 , 18051815.

  • Betz, V., and R. Mittra, 1992: Comparison and evaluation of boundary conditions for the absorption of guided waves in an FDTD simulation. IEEE Microwave Guided Wave Lett., 2 , 499501.

    • Search Google Scholar
    • Export Citation
  • Choi, H-J., H-Y. Chun, and I-S. Song, 2007: Characteristics and momentum flux spectrum of convectively forced internal gravity waves in ensemble numerical simulations. J. Atmos. Sci., 64 , 37233734.

    • Search Google Scholar
    • Export Citation
  • Chun, H-Y., 1997: Weakly nonlinear response of a stably stratified shear flow to thermal forcing. Tellus, 49A , 528534.

  • Chun, H-Y., and J-J. Baik, 1994: Weakly nonlinear response of a stably stratified atmosphere to diabatic forcing in a uniform flow. J. Atmos. Sci., 51 , 31093121.

    • Search Google Scholar
    • Export Citation
  • 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 , 32993310.

    • Search Google Scholar
    • Export Citation
  • Chun, H-Y., I-S. Song, and T. Horinouchi, 2005: Momentum flux spectrum of convectively forced gravity waves: Can diabatic forcing be a proxy for convective forcing? J. Atmos. Sci., 62 , 41134120.

    • Search Google Scholar
    • Export Citation
  • Dhaka, S. K., M. K. Yamamoto, Y. Shibagaki, H. Hashiguchi, M. Yamamoto, and S. Fukao, 2005: Convection-induced gravity waves observed by the Equatorial Atmosphere Radar (0.20°S, 100.32°E) in Indonesia. Geophys. Res. Lett., 32 .L14820, doi:10.1029/2005GL022907.

    • Search Google Scholar
    • Export Citation
  • Klemp, J. B., and D. R. Durran, 1983: An upper boundary condition permitting internal gravity wave radiation in numerical mesoscale models. Mon. Wea. Rev., 111 , 430444.

    • Search Google Scholar
    • Export Citation
  • Lane, T. P., M. J. Reeder, and T. L. Clark, 2001: Numerical modeling of gravity wave generation by deep tropical convection. J. Atmos. Sci., 58 , 12491274.

    • Search Google Scholar
    • Export Citation
  • Lin, Y-L., and R. B. Smith, 1986: Transient dynamics of airflow near a local heat source. J. Atmos. Sci., 43 , 4049.

  • Lin, Y-L., and H-Y. Chun, 1991: Effects of diabatic cooling in a shear flow with a critical level. J. Atmos. Sci., 48 , 24762491.

  • Lindzen, R. S., 1981: Turbulence and stress owing to gravity wave and tidal breakdown. J. Geophys. Res., 86 , 97079714.

  • Matsuno, T., 1982: A quasi one-dimensional model of the middle atmosphere circulation interacting with internal gravity waves. J. Meteor. Soc. Japan, 60 , 215227.

    • Search Google Scholar
    • Export Citation
  • Navon, I. M., and H. A. Riphagen, 1979: An implicit compact fourth-order algorithm for solving the shallow-water equation in conservation-law form. Mon. Wea. Rev., 107 , 11071127.

    • Search Google Scholar
    • Export Citation
  • Orlanski, I., 1976: A simple boundary condition for unbounded hyperbolic flow. J. Comput. Phys., 21 , 251269.

  • Pandya, R. E., and M. J. Alexander, 1999: Linear stratospheric gravity waves above connective thermal forcing. J. Atmos. Sci., 56 , 24342446.

    • Search Google Scholar
    • Export Citation
  • Perkey, D. J., 1976: A description and preliminary results from a fine-mesh model for forecasting quantitative precipitation. Mon. Wea. Rev., 104 , 15131526.

    • Search Google Scholar
    • Export Citation
  • Sassi, F., and R. R. Garcia, 1997: The role of equatorial waves forced by convection in the tropical semiannual oscillation. J. Atmos. Sci., 54 , 19251942.

    • Search Google Scholar
    • Export Citation
  • Sassi, F., R. R. Garcia, B. A. Boville, and H. Liu, 2002: On temperature inversions and the mesospheric surf zone. J. Geophys. Res., 107 .4380, doi:10.1029/2001JD001525.

    • Search Google Scholar
    • Export Citation
  • Smith, R. B., and Y-L. Lin, 1982: The addition of heat to a stratified airstream with application to the dynamics of orographic rain. Quart. J. Roy. Meteor. Soc., 108 , 353378.

    • Search Google Scholar
    • Export Citation
  • Song, I-S., and H-Y. Chun, 2005: Momentum flux spectrum of convectively forced internal gravity waves and its application to gravity wave drag parameterization. Part I: Theory. J. Atmos. Sci., 62 , 107124.

    • Search Google Scholar
    • Export Citation
  • Song, I-S., and H-Y. Chun, 2006: A spectral parameterization of convectively forced internal gravity waves and estimation of gravity-wave momentum forcing to the middle atmosphere. J. Korean Meteor. Soc., 42 , 339359.

    • Search Google Scholar
    • Export Citation
  • Song, I-S., H-Y. Chun, and T. P. Lane, 2003: Generation mechanisms of convectively forced internal gravity waves and their propagation to the stratosphere. J. Atmos. Sci., 60 , 19601980.

    • Search Google Scholar
    • Export Citation
  • Song, I-S., H-Y. Chun, R. R. Garcia, and B. A. Boville, 2007: Momentum flux spectrum of convectively forced internal gravity waves and its application to gravity wave drag parameterization. Part II: Impact in a GCM (WACCM). J. Atmos. Sci., 64 , 22862308.

    • Search Google Scholar
    • Export Citation
  • Trier, S. B., W. C. Sckamarock, M. A. Lemone, D. B. Parsons, and D. P. Jorgensen, 1996: Structure and evolution of the 22 February 1993 TOGA COARE squall line: Numerical simulations. J. Atmos. Sci., 53 , 28612886.

    • Search Google Scholar
    • Export Citation
All Time Past Year Past 30 Days
Abstract Views 0 0 0
Full Text Views 102 33 2
PDF Downloads 59 21 1