On the Mass-Flux Representation of Vertical Transport in Moist Convection

Ping Zhu Department of Earth and Environment, Florida International University, Miami, Florida

Search for other papers by Ping Zhu in
Current site
Google Scholar
PubMed
Close
Restricted access

Abstract

This study investigates to what extent the convective fluxes formulated within the mass-flux framework can represent the total vertical transport of heat and moisture in the cloud layer and whether the same approach can be extended to represent the vertical momentum transport using large-eddy simulations (LESs) of six well-documented cloud cases, including both deep and shallow convection. Two methods are used to decompose the LES-resolved vertical fluxes: decompositions based on the coherent convective features using the mass-flux top-hat profile and by two-dimensional fast Fourier transform (2D-FFT) in terms of wavenumbers. The analyses show that the convective fluxes computed using the mass-flux formula can account for most of the total fluxes of conservative thermodynamic variables in the cloud layer of both deep and shallow convection for an appropriately defined convective updraft fraction, a result consistent with the mass-flux dynamic view of moist convection and previous studies. However, the mass-flux approach fails to represent the vertical momentum transport in the cloud layer of both deep and shallow convection. The 2D-FFT and other analyses suggest that such a failure results from a number of reasons: 1) the complicated momentum distribution in the cloud layer cannot be well described by the simple top-hat profile; 2) shear-driven small-scale eddies are more efficient momentum carriers than coherent convective plumes; 3) the phase relationship between vertical velocity and horizontal momentum components is substantially different from that between vertical velocity and conservative thermodynamic variables; and 4) the structure of horizontal momentum can change substantially from case to case even in the same climate regime.

Corresponding author address: Ping Zhu, Department of Earth and Environment, Florida International University, 11200 SW 8th Street, AHC-5 360, Miami, FL 33199. E-mail: zhup@fiu.edu

Abstract

This study investigates to what extent the convective fluxes formulated within the mass-flux framework can represent the total vertical transport of heat and moisture in the cloud layer and whether the same approach can be extended to represent the vertical momentum transport using large-eddy simulations (LESs) of six well-documented cloud cases, including both deep and shallow convection. Two methods are used to decompose the LES-resolved vertical fluxes: decompositions based on the coherent convective features using the mass-flux top-hat profile and by two-dimensional fast Fourier transform (2D-FFT) in terms of wavenumbers. The analyses show that the convective fluxes computed using the mass-flux formula can account for most of the total fluxes of conservative thermodynamic variables in the cloud layer of both deep and shallow convection for an appropriately defined convective updraft fraction, a result consistent with the mass-flux dynamic view of moist convection and previous studies. However, the mass-flux approach fails to represent the vertical momentum transport in the cloud layer of both deep and shallow convection. The 2D-FFT and other analyses suggest that such a failure results from a number of reasons: 1) the complicated momentum distribution in the cloud layer cannot be well described by the simple top-hat profile; 2) shear-driven small-scale eddies are more efficient momentum carriers than coherent convective plumes; 3) the phase relationship between vertical velocity and horizontal momentum components is substantially different from that between vertical velocity and conservative thermodynamic variables; and 4) the structure of horizontal momentum can change substantially from case to case even in the same climate regime.

Corresponding author address: Ping Zhu, Department of Earth and Environment, Florida International University, 11200 SW 8th Street, AHC-5 360, Miami, FL 33199. E-mail: zhup@fiu.edu
Save
  • Arakawa, A., and W. H. Schubert, 1974: Interaction of a cumulus cloud ensemble with the large-scale environment, part I. J. Atmos. Sci., 31, 674701, doi:10.1175/1520-0469(1974)031<0674:IOACCE>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • Arakawa, A., and C.-M. Wu, 2013: A unified representation of deep moist convection in numerical modeling of the atmosphere. Part I. J. Atmos. Sci., 70, 19771992, doi:10.1175/JAS-D-12-0330.1.

    • Search Google Scholar
    • Export Citation
  • Bradshaw, P., 1967: Inactive motion and pressure fluctuations in turbulent boundary layers. J. Fluid Mech., 30, 241258, doi:10.1017/S0022112067001417.

    • Search Google Scholar
    • Export Citation
  • Bretherton, C. S., S. K. Krueger, M. C. Wyant, P. Bechtold, E. van Meijgaard, B. Stevens, and J. Teixeira, 1999: A GCSS boundary layer model intercomparison study of the first ASTEX Lagrangian experiment. Bound.-Layer Meteor., 93, 341380, doi:10.1023/A:1002005429969.

    • Search Google Scholar
    • Export Citation
  • Bryan, G. H., J. C. Wyngaard, and J. M. Fritsch, 2003: Resolution requirements for the simulation of deep moist convection. Mon. Wea. Rev., 131, 2394–2416, doi:10.1175/1520-0493(2003)131<2394:RRFTSO>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • Busch, N. E., 1973: The surface boundary layer (Part I). Bound.-Layer Meteor., 4, 213240, doi:10.1007/BF02265234.

  • Grabowski, W. W., X. Wu, and M. W. Moncrieff, 1996: Cloud-resolving modeling of tropical cloud system during phase III of GATE. Part I: Two-dimensional experiments. J. Atmos. Sci., 53, 36843709, doi:10.1175/1520-0469(1996)053<3684:CRMOTC>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • Högström, U., and H. Bergström, 1996: Organized turbulence structures in the near-neutral atmospheric surface layer. J. Atmos. Sci., 53, 2452–2464, doi:10.1175/1520-0469(1996)053<2452:OTSITN>2.0.CO;2.

  • Houze, R. A., Jr., 1973: A climatological study of vertical transports by cumulus-scale convection. J. Atmos. Sci., 30, 11121123, doi:10.1175/1520-0469(1973)030<1112:ACSOVT>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • Kaimal, J. C., J. C. Wyngaard, Y. Izumi, and O. R. Coté, 1972: Spectral characteristics of surface-layer turbulence. Quart. J. Roy. Meteor. Soc., 98, 563589, doi:10.1002/qj.49709841707.

    • Search Google Scholar
    • Export Citation
  • Kaimal, J. C., J. C. Wyngaard, D. A. Haugen, O. R. Coté, Y. Izumi, S. J. Caughey, and C. J. Readings, 1976: Turbulence structure in the convective boundary layer. J. Atmos. Sci., 33, 21522169, doi:10.1175/1520-0469(1976)033<2152:TSITCB>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • Kershaw, R., and D. Gregory, 1997: Parameterization of momentum transport by convection. I: Theory and cloud modelling results. Quart. Roy. Meteor. Soc., 123, 11331151, doi:10.1002/qj.49712354102.

    • Search Google Scholar
    • Export Citation
  • Khairoutdinov, M. F., and D. A. Randall, 2003: Cloud resolving modeling of the ARM summer 1997 IOP: Model formulation, results, uncertainties, and sensitivities. J. Atmos. Sci., 60, 607625, doi:10.1175/1520-0469(2003)060<0607:CRMOTA>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • Khairoutdinov, M. F., S. K. Krueger, C.-H. Moeng, P. A. Bogenschutz, and D. A. Randall, 2009: Large-eddy simulation of maritime deep tropical convection. J. Adv. Model. Earth Syst., 1, 15, doi:10.3894/JAMES.2009.1.15.

  • Kolmogorov, A. N., 1941: Energy dissipation in local isotropic turbulence. Dokl. Akad. Nauk SSSR, 32, 1921.

  • LeMone, M. A., and E. J. Zipser, 1980: Cumulonimbus vertical velocity events in GATE. Part I: Diameter, intensity and mass flux. J. Atmos. Sci., 37, 24442457, doi:10.1175/1520-0469(1980)037<2444:CVVEIG>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • Liu, Y.-C., J. Fan, G. J. Zhang, K.-M. Xu, and S. J. Ghan, 2015: Improving representation of convective transport for scale-aware parameterization: 2. Analysis of cloud-resolving model simulations. J. Geophys. Res. Atmos., 120, 3510–3532, doi:10.1002/2014JD022145.

    • Search Google Scholar
    • Export Citation
  • Mahrt, L., and W. Gibson, 1992: Flux decomposition into coherent structures. Bound.-Layer Meteor., 60, 143168, doi:10.1007/BF00122065.

    • Search Google Scholar
    • Export Citation
  • Mason, B. J., 1975: The GARP Atlantic tropical experiment. Nature, 255, 1720, doi:10.1038/255017a0.

  • Mechem, D. B., and A. J. Oberthaler, 2013: Numerical simulation of tropical cumulus congestus during TOGA COARE. J. Adv. Model. Earth Syst., 5, 623637, doi:10.1002/jame.20043.

    • Search Google Scholar
    • Export Citation
  • Redelsperger, J.-L., and Coauthors, 2000: A GCSS model intercomparison for a tropical squall line observed during TOGA-COARE. I: Cloud-resolving models. Quart. J. Roy. Meteor. Soc., 126, 823864, doi:10.1002/qj.49712656404.

    • Search Google Scholar
    • Export Citation
  • Riehl, H., and D. Soltwisch, 1974: On the depth of the friction layer and the vertical transfer of momentum in the trades. Beitr. Phys. Atmos., 47, 5666.

    • Search Google Scholar
    • Export Citation
  • Schneider, E. K., 1975: The Hadley circulation of the Earth’s atmosphere. Ph.D. thesis, Harvard University, 285 pp.

  • Schneider, E. K., and R. S. Lindzen, 1976: A discussion of the parameterization of momentum exchange by cumulus convection. J. Geophys. Res., 81, 31583160, doi:10.1029/JC081i018p03158.

    • Search Google Scholar
    • Export Citation
  • Shaw, W. J., and J. A. Businger, 1985: Intermittency and the organization of turbulence in the near-neutral marine atmospheric boundary layer. J. Atmos. Sci., 42, 25632584, doi:10.1175/1520-0469(1985)042<2563:IATOOT>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • Siebesma, A. P., and J. W. M. Cuijpers, 1995: Evaluation of parametric assumptions for shallow cumulus convection. J. Atmos. Sci., 52, 650666, doi:10.1175/1520-0469(1995)052<0650:EOPAFS>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • Song, X., X. Wu, G. J. Zhang, and R. Arritt, 2008: Dynamical effects of convective momentum transports on global climate simulations. J. Climate, 21, 180194, doi:10.1175/2007JCLI1848.1.

    • Search Google Scholar
    • Export Citation
  • Stevens, and Coauthors, 2005: Evaluation of large-eddy simulations via observations of nocturnal marine stratocumulus. Mon. Wea. Rev., 133, 14431462, doi:10.1175/MWR2930.1.

    • Search Google Scholar
    • Export Citation
  • Stone, P. H., W. J. Quirk, and R. C. J. Somerville, 1974: The effect of small-scale vertical mixing of horizontal momentum in a general circulation model. Mon. Wea. Rev., 102, 765771, doi:10.1175/1520-0493(1974)102<0765:TEOSSV>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • Townsend, A. A., 1961: Equilibrium layers and wall turbulence. J. Fluid Mech., 11, 97120, doi:10.1017/S0022112061000883.

  • Tung, W.-W., and M. Yanai, 2002a: Convective momentum transport observed during the TOGA COARE IOP. Part I: General features. J. Atmos. Sci., 59, 18571871, doi:10.1175/1520-0469(2002)059<1857:CMTODT>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • Tung, W.-W., and M. Yanai, 2002b: Convective momentum transport observed during the TOGA COARE IOP. Part II: Case studies. J. Atmos. Sci., 59, 25352549, doi:10.1175/1520-0469(2002)059<2535:CMTODT>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • VanZanten, M. C., and Coauthors, 2011: Controls on precipitation and cloudiness in simulations of trade-wind cumulus as observed during RICO. J. Adv. Model. Earth Syst., 3, M06001, doi:10.1029/2011MS000056.

    • Search Google Scholar
    • Export Citation
  • Wang, S., and B. Stevens, 2000: Top-hat representation of turbulence statistics in cloud-topped boundary layers: A large-eddy simulation study. J. Atmos. Sci., 57, 423441, doi:10.1175/1520-0469(2000)057<0423:THROTS>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • Webster, P. J., and R. Lukas, 1992: TOGA COARE: The Coupled Ocean–Atmosphere Response Experiment. Bull. Amer. Meteor. Soc., 73, 13771416, doi:10.1175/1520-0477(1992)073<1377:TCTCOR>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • Wu, C.-M., and A. Arakawa, 2014: A unified representation of deep moist convection in numerical modeling of the atmosphere. Part II. J. Atmos. Sci., 71, 20892103, doi:10.1175/JAS-D-13-0382.1.

    • Search Google Scholar
    • Export Citation
  • Wu, X., and M. Yanai, 1994: Effects of vertical wind shear on the cumulus transport of momentum: Observations and parameterization. J. Atmos. Sci., 51, 16401660, doi:10.1175/1520-0469(1994)051<1640:EOVWSO>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • Wu, X., W. W. Grabowski, and W. M. Moncrieff, 1998: Long-term behavior of cloud systems in TOGA COARE and their interactions with radiative and surface processes. Part I: Two-dimensional modeling study. J. Atmos. Sci., 55, 26932714, doi:10.1175/1520-0469(1998)055<2693:LTBOCS>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • Wu, X., L. Deng, X. Song, and G.-J. Zhang, 2007: Coupling of convective momentum transport with convective heating in global climate simulations. J. Atmos. Sci., 64, 13341349, doi:10.1175/JAS3894.1.

    • Search Google Scholar
    • Export Citation
  • Xu, K.-M., and D. A. Randall, 1996: Explicit simulation of cumulus ensembles with the GATE phase III data: Comparison with observations. J. Atmos. Sci., 53, 37103736, doi:10.1175/1520-0469(1996)053<3710:ESOCEW>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • Zhang, G. J., and H.-R. Cho, 1991a: Parameterization of the vertical transport of momentum by cumulus clouds. Part I: Theory. J. Atmos. Sci., 48, 14831492, doi:10.1175/1520-0469(1991)048<1483:POTVTO>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • Zhang, G. J., and H.-R. Cho, 1991b: Parameterization of the vertical transport of momentum by cumulus clouds. Part II: Application. J. Atmos. Sci., 48, 24482457, doi:10.1175/1520-0469(1991)048<2448:POTVTO>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • Zhang, G. J., and X. Wu, 2003: Convective momentum transport and perturbation pressure field from a cloud-resolving model simulation. J. Atmos. Sci., 60, 11201139, doi:10.1175/1520-0469(2003)060<1120:CMTAPP>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • Zhu, P., and Coauthors, 2005: Intercomparison and interpretation of single-column model simulations of a nocturnal stratocumulus-topped marine boundary layer. Mon. Wea. Rev., 133, 27412758, doi:10.1175/MWR2997.1.

    • Search Google Scholar
    • Export Citation
  • Zhu, P., J. A. Zhang, and F. J. Masters, 2010: Wavelet analyses of turbulence in the hurricane surface layer during landfalls. J. Atmos. Sci., 67, 37933805, doi:10.1175/2010JAS3437.1.

    • Search Google Scholar
    • Export Citation
All Time Past Year Past 30 Days
Abstract Views 0 0 0
Full Text Views 573 190 18
PDF Downloads 257 81 12