Skip to main content

Advertisement

SpringerLink
Log in

A Parameterization of Dry Thermals and Shallow Cumuli for Mesoscale Numerical Weather Prediction

  • Article
  • Published:
Boundary-Layer Meteorology Aims and scope Submit manuscript

Abstract

For numerical weather prediction models and models resolving deep convection, shallow convective ascents are subgrid processes that are not parameterized by classical local turbulent schemes. The mass flux formulation of convective mixing is now largely accepted as an efficient approach for parameterizing the contribution of larger plumes in convective dry and cloudy boundary layers. We propose a new formulation of the EDMF scheme (for Eddy Diffusivity\Mass Flux) based on a single updraft that improves the representation of dry thermals and shallow convective clouds and conserves a correct representation of stratocumulus in mesoscale models. The definition of entrainment and detrainment in the dry part of the updraft is original, and is specified as proportional to the ratio of buoyancy to vertical velocity. In the cloudy part of the updraft, the classical buoyancy sorting approach is chosen. The main closure of the scheme is based on the mass flux near the surface, which is proportional to the sub-cloud layer convective velocity scale w *. The link with the prognostic grid-scale cloud content and cloud cover and the projection on the non- conservative variables is processed by the cloud scheme. The validation of this new formulation using large-eddy simulations focused on showing the robustness of the scheme to represent three different boundary layer regimes. For dry convective cases, this parameterization enables a correct representation of the countergradient zone where the mass flux part represents the top entrainment (IHOP case). It can also handle the diurnal cycle of boundary-layer cumulus clouds (EUROCS\ARM) and conserve a realistic evolution of stratocumulus (EUROCS\FIRE).

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  • Arakawa A (2004) The cumulus parameterization problem: past present and future. J Clim 17: 2493–2525

    Article  Google Scholar 

  • Arakawa A, Schubert WH (1974) Interaction of a cumulus cloud ensemble with the large-scale environment, Part 1. J Atmos Sci 31: 674–700

    Article  Google Scholar 

  • Bechtold P, Cuijpers JWM (1995) Cloud perturbations of temperature and humidity: a LES study. Boundary-Layer Meteorol 76: 377–386

    Article  Google Scholar 

  • Bechtold P, Bazile E, Guichard F, Mascart P, Richard E (2001) A mass-flux convection scheme for regional and global models. Q J Roy Meteorol Soc 127: 869–886

    Article  Google Scholar 

  • Berg LK, Stull RB (2002) Accuracy of point and line measures of boundary layer cloud amount. J Appl Meteorol 41: 640–650

    Article  Google Scholar 

  • Betts AK (1973) Nonprecipitatting cumulus convection and its parameterization. Q J Roy Meteorol Soc 99: 178–196

    Article  Google Scholar 

  • Bougeault P, Lacarrère P (1989) Parameterization of orography-induced turbulence in a mesobeta-scale model. Mon Weather Rev 117: 1872–1890

    Article  Google Scholar 

  • Brown A, Cederwall RT, Chlond A, Duynkerke PG, Golaz JC, Khairoutdinov M, Lewellen D, Lock AP, Macvean MK, Moeng CH, Neggers RAJ, Siebesma P, Stevens B (2002) Large-eddy simulation of the diurnal cycle of shallow cumulus convection over land. Q J Roy Meteorol Soc 128: 1075–1093

    Article  Google Scholar 

  • Browning KA (1993) The GEWEX Cloud System Study (GCSS). Bull Am Meteorol Soc 74: 387–399

    Article  Google Scholar 

  • Buckingham E (1914) On physically similar systems: illustrations of the use of dimensional equations. Phys Rev IV: 345–376

    Article  Google Scholar 

  • Cheinet S (2003) A multiple mass-flux parameterization for the surface-generated convection, Part 1: dry plumes. J Atmos Sci 60: 2313–2327

    Article  Google Scholar 

  • Clarke RH, Dyer AJ, Reid DG, Troup AJ (1971) The Wangara experiment: boundarylayer data. Division Meteorological Physics Paper No. 19: CSIRO, Australia

  • Couvreux F, Guichard F, Redelsperger JL, Kiemle C, Masson V, Lafore JP, Flamant C (2005) Water–vapour variablility within a convective boundary-layer assessed by large-eddy simulations and IHOP2002 observations. Q J Roy Meteorol Soc 131: 2665–2693

    Article  Google Scholar 

  • Cuijpers JWM, Holtslag AM (1998) Impact of skewness and nonlocal effects on scalar and buoyancy fluxes in convective boundary layers. J Atmos Sci 55: 151–162

    Article  Google Scholar 

  • Cuxart J, Bougeault P, Redelsperger JL (2000) A turbulence scheme allowing for mesoscale and large-eddy simulations. Q J Roy Meteorol Soc 126: 1–30

    Article  Google Scholar 

  • De Roode SR, Duynkerke PG, Siebesma P (2000) Analogies between mass-flux and Reynolds-averaged equations. J Atmos Sci 57: 1585–1598

    Article  Google Scholar 

  • De Rooy WC, Siebesma P (2008) A simple parameterization for detrainment in shallow cumulus. Mon Weather Rev 136: 560–576

    Article  Google Scholar 

  • Deardorff JW (1966) The counter-gradient heat flux in the lower atmosphere and in the laboratory. J Atmos Sci 23: 503–506

    Article  Google Scholar 

  • Deardorff JW (1980a) Cloud top entrainment instability. J Atmos Sci 37: 131–147

    Article  Google Scholar 

  • Deardorff JW (1980b) Stratocumulus-capped mixed layers derived from a three-dimensionnal model. Boundary-Layer Meteorol 18: 495–527

    Article  Google Scholar 

  • Duynkerke PG, Hignett P (1995) Simulation of diurnal variation in a stratocumulus-capped marine boundary layer during FIRE. Mon Weather Rev 52: 2763–2777

    Google Scholar 

  • Duynkerke PG, Zhang H, Jonker PJ (1995) Microphysical and turbulent structure of nocturnal stratocumulus as observed during astex. J Atmos Sci 52: 2763–2777

    Article  Google Scholar 

  • Duynkerke PG, De Roode SR, Van Zanten MC, Calvo J, Cuxart J, Cheinet S, Chlond A, Grenier H, Jonker PJ, Kohler M, Lenderink G, Lewellen D, Lappen CL, Lock AP, Moeng CH, Muller F, Olmeda D, Piriou JM, Sanchez E, Sednev I (2004) Observations and numerical simulations of the diurnal cycle of the EUROCS stratocumulus case. Q J Roy Meteorol Soc 130: 3269–3296

    Article  Google Scholar 

  • Grant ALM (2001) Cloud-base fluxes in the cumulus-capped boundary layer. Q J Roy Meteorol Soc 127: 407–421

    Article  Google Scholar 

  • Gregory D, Kershaw R, Inness PM (1997) Parametrization of momentum transport by convection. II: tests in single-column and general circulation models. Q J Roy Meteorol Soc 123: 1153–1183

    Article  Google Scholar 

  • Hignett P (1991) Observations of the diurnal variation in the cloud-capped marine boundary layer. J Atmos Sci 45: 1474–1482

    Article  Google Scholar 

  • Holland JZ, Rasmusson EM (1973) Measurement of atmospheric mass, energy and Momentum budgets over a 500-kilometer square of tropical ocean. Mon Weather Rev 101: 44–55

    Article  Google Scholar 

  • Holtslag AAM, Moeng CH (1991) Eddy diffusivity and countergradient transport in the convective atmospheric boundary layer. J Atmos Sci 48: 1690–1698

    Article  Google Scholar 

  • Hourdin F, Couvreux F, Menut L (2002) Parameterization of the dry convective boundary layer based on a mass flux representation of thermals. J Atmos Sci 59: 1105–1122

    Article  Google Scholar 

  • Kain JS, Fritsch JM (1990) A one-dimensionnal entraining/detraining plume model and its application in convective parameterization. J Atmos Sci 47: 2784–2802

    Article  Google Scholar 

  • Lafore JP, Stein J, Asencio N, Bougeault P, Ducrocq V, Duron J, Fisher C, Hereil P, Mascart P, Masson V, Pinty JP, Redelsperger JL, Richard E, Arellano JV (1998) The meso-NH atmospheric simulation system, Part I: adiabatic formulation and control simulations. Ann Geophys 16: 90–109

    Article  Google Scholar 

  • Lappen CL, Randall DA (2001) Toward a unified parameterization of the boundary layer and moist convection, Part 2: lateral mass exchanges and subplume-scale fluxes. J Atmos Sci 58: 2037–2051

    Article  Google Scholar 

  • Lenderink G, Siebesma P, Cheinet S, Irons S, Jones CG, Marquet P, Muller F, Olmeda D, Calvo J, Sanchez E, Soares PMM (2004) The diurnal cycle of shallow cumulus clouds over land: a single column model intercomparaison study. Q J Roy Meteorol Soc 130: 3339–3364

    Article  Google Scholar 

  • Lewellen D, Lewellen W (1998) Large-eddy boundary layer entrainment. J Atmos Sci 55: 2645–2665

    Article  Google Scholar 

  • Lewellen D, Lewellen W (2002) Entrainment and decoupling relations for cloudy boundary layers. J Atmos Sci 59: 2966–2987

    Article  Google Scholar 

  • Lilly DK (1968) Models of cloud-topped mixed layers under a strong inversion. Q J Roy Meteorol Soc 94: 292–309

    Article  Google Scholar 

  • Neggers RAJ, Siebesma P, Jonker HJJ (2002) A multiparcel model for shallow cumulus convection. J Atmos Sci 59: 1655–1668

    Article  Google Scholar 

  • Neggers RAJ, Siebesma AP, Lenderink G, Holtslag AM (2004) An evaluation of mass flux closures for diurnal cycles of shallow cumulus. Mon Weather Rev 132: 2525–2538

    Article  Google Scholar 

  • Nicholls S (1984) The dynamics of stratocumulus: aircraft observations and comparisons with a mixed layer model. Q J Roy Meteorol Soc 110: 783–820

    Article  Google Scholar 

  • Ooyama K (1971) A theory on parameterization of cumulus convection. J Meteorol Soc Jpn 49: 744–756

    Google Scholar 

  • Randall DA (1980) Conditionnal instability of the first kind upside-down. J Atmos Sci 37: 125–130

    Article  Google Scholar 

  • Rio C, Hourdin F (2008) A thermal plume model for the convective boundary layer. J Atmos Sci 65: 407–425

    Article  Google Scholar 

  • Schumann U (1987) The countergradient heat flux in stratified turbulent flows. Nucl Eng Des 100: 255–262

    Article  Google Scholar 

  • Siebesma P (1998) Shallow cumulus convection. In: Plate EJ et al (eds) Buoyant convection in geophysical flows. Kluwer, Amsterdam, pp 441–486

    Google Scholar 

  • Siebesma P, Cuijpers JWM (1995) Evaluation of parametric assumptions for shallow cumulus convection. J Atmos Sci 53: 650–666

    Article  Google Scholar 

  • Siebesma P, Holtslag AM (1996) Model impacts of entrainment and detrainment rates in shallow cumulus convection. J Atmos Sci 53: 2354–2364

    Article  Google Scholar 

  • Siebesma P, Teixeira J (2000) An advection-diffusion scheme for the convective boundary layer, description and 1D results. In: Proceedings of 14th symposium on boundary layers and turbulence, Aspen, USA, pp 133–136

  • Siebesma P, Bretherton CS, Brown A, Chlond A, Cuxart J, Duynkerke PG, Jiang H, Khairoutdinov M, Lewellen D, Moeng CH, Sanchez E, Stevens B, Stevens DE (2003) A large eddy simulation intercomparison study of shallow cumulus convection. J Atmos Sci 60: 1201–1219

    Article  Google Scholar 

  • Siebesma P, Soares PMM, Teixeira J (2007) A combined eddy-diffusivity mass-flux approach for the convective boundary layer. J Atmos Sci 64: 1230–1248

    Article  Google Scholar 

  • Simpson J, Wiggert V (1969) Models of precipitating cumulus towers. Mon Weather Rev 97: 471–489

    Article  Google Scholar 

  • Soares PMM, Miranda PMA, Siebesma AP, Teixeira J (2004) An eddy-diffusivity/mass-flux parameterization for dry and shallow cumulus convection. Q J Roy Meteorol Soc 130: 3055–3079

    Article  Google Scholar 

  • Stull RB (1988) An introduction to boundary layer meteorology. Kluwer, Dordrecht, p 666

    Google Scholar 

  • Sullivan PP, Moeng CH, Stevens B, Lenschow DH, Mayor SD (1998) Structure of the entrainment zone capping the convective. J Atmos Sci 55: 3042–3064

    Article  Google Scholar 

  • Taylor GR, Baker MB (1991) Entrainment and detrainment in cumulus clouds. J Atmos Sci 48: 112–121

    Article  Google Scholar 

  • Teixeira J, Stevens B, Bretherton CS, Cederwall R, Doyle JD, Golaz JC, Holtslag AMM, Klein SA, Lundquist JK, Randall DA, Siebesma AP, Soares PMM (2008) Parameterization of the atmospheric boundary layer: a view from just above the inversion. Bull Am Meteorol Soc 89: 453–458

    Article  Google Scholar 

  • Tiedtke M (1989) A comprehensive mass-flux scheme for cumulus parameterization in large-scale models. Mon Weather Rev 177: 1779–1800

    Article  Google Scholar 

  • Tomas S, Masson V (2006) A parametrization of third order moments for dry convective boundary layer. Boundary-Layer Meteorol 120: 437–454

    Article  Google Scholar 

  • Troen IB, Mahrt L (1986) A simple model of the atmospheric boundary layer: sensitivity to surface evaporation. Boundary-Layer Meteorol 37: 129–148

    Article  Google Scholar 

  • Wang S, Stevens B (2000) Top-hat representation of turbulence statistics in cloud-topped boundary layers: a large eddy simulation study. J Atmos Sci 57: 423–441

    Article  Google Scholar 

  • Weckwerth TM, Parsons DB, Koch SE, Moore JA, Lemone MA, Demoz BR, Flamant C, Geerts B, Wang J, Feltz W (2004) An overview of the international H2O project (IHOP_2002) and some preliminary highlights. Bull Am Meteorol Soc 85: 253–277

    Article  Google Scholar 

  • Wood R, Bretherton CS, Hartmann DL (2002) Diurnal cycle of liquid water path over the subtropical and tropical oceans. Geophys Res Lett 29: 7.1–7.4

    Google Scholar 

  • Yanai M, Esbensen S, Chu J (1973) Determination of bulk properties of tropical cloud clusters from large-scale heat and moisture budgets. J Atmos Sci 30: 611–627

    Article  Google Scholar 

  • Young GS (1988) Turbulence structure of the convective boundary layer, Part II: Phoenix 78 Aircraft observations of thermals and their environment. J Atmos Sci 45: 727–735

    Article  Google Scholar 

  • Zhao M, Austin PH (2003) Episodic mixing and buoyancy-sorting representations of shallow convection: a diagnostic study. J Atmos Sci 60: 892–912

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. CNRM - GAME, Groupe de Modélisation à Moyenne Échelle, Météo-France, 42 Avenue Gaspard Coriolis, BP 31077, Toulouse, France

    Julien Pergaud, Valéry Masson, Sylvie Malardel & Fleur Couvreux

Authors
  1. Julien Pergaud
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Valéry Masson
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Sylvie Malardel
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Fleur Couvreux
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Julien Pergaud.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Pergaud, J., Masson, V., Malardel, S. et al. A Parameterization of Dry Thermals and Shallow Cumuli for Mesoscale Numerical Weather Prediction. Boundary-Layer Meteorol 132, 83–106 (2009). https://doi.org/10.1007/s10546-009-9388-0

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10546-009-9388-0

Keywords

Search

Navigation