Boundary-Layer Meteorology

, Volume 135, Issue 3, pp 469–483 | Cite as

Resolved Versus Parametrized Boundary-Layer Plumes. Part II: Continuous Formulations of Mixing Rates for Mass-Flux Schemes



The conditional sampling of coherent structures in large-eddy simulations of the convective boundary layer (Couvreux et al. Boundary-layer Meteorol 134:441–458, 2010) is used to propose and evaluate formulations of fractional entrainment and detrainment rates for mass-flux schemes. The proposed formulations are physically-based and continuous from the surface to the top of clouds. Entrainment is related to the updraft vertical velocity divergence, while detrainment depends on the thermal vertical velocity, on buoyancy and on the moisture contrast between the mean plume and its environment. The proposed formulations are first directly evaluated in simulations of shallow clouds. They are then tested in single-column simulations with the thermal plume model, a mass-flux representation of boundary-layer thermals.


Boundary-layer thermals Entrainment and detrainment Large-eddy simulations Mass-flux parametrization 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. Blyth AM, Cooper WA, Jensen JB (1988) A study of the source of entrained air in Montana cumuli. J Atmos Sci 45: 3944–3964CrossRefGoogle Scholar
  2. Bretherton C, Smolarkiewicz P (1989) Gravity waves, compensating subsidence and detrainment around cumulus clouds. J Atmos Sci 46: 740–759CrossRefGoogle Scholar
  3. Bretherton C, McCaa J, Grenier H (2004) A new parameterization for shallow cumulus convection and its application to marine subtropical cloud-topped boundary layers. Part I: description and 1D results. Mon Weather Rev 132: 864–882CrossRefGoogle Scholar
  4. Brown A, Cederwall R, Chlond A, Duynkerke P, Golaz J-C, Khairoutdinov M, Lewellen D, Lock A, Macvean M, Moeng C-H, Neggers R, Siebesma A, Stevens B (2002) Large-eddy simulation of the diurnal cycle of shallow cumulus convection over land. Q J Roy Meteorol Soc 128: 1075–1093CrossRefGoogle Scholar
  5. Chatfield RB, Brost RA (1987) A two-stream model of the vertical transport of trace species in the convective boundary layer. J Geophys Res 92: 13263–13276CrossRefGoogle Scholar
  6. Coindreau O, Hourdin F, Haeffelin M, Mathieu A, Rio C (2007) Assessment of physical parameterizations using a global climate model with stretchable grid and nudging. Mon Weather Rev 135: 1474–1489CrossRefGoogle Scholar
  7. Couvreux F, Guichard F, Redelsperger J-L, Flamant C, Masson V, Kiemle C, Lafore J-P (2005) Water vapour variability within a convective boundary layer assessed by large eddy simulations and IHOP observations. Q J Roy Meteorol Soc 131:2665–2693CrossRefGoogle Scholar
  8. Couvreux F, Guichard F, Masson V, Redelsperger J-L (2007) Negative water vapour skewness and dry tongues in the convective boundary layer: observations and large-eddy simulation budget analysis. Boundary-Layer Meteorol 123: 269–294CrossRefGoogle Scholar
  9. Couvreux F, Hourdin F, Rio C (2010) Resolved versus parameterized boundary layer thermals. Part I: a parameterization oriented conditional sampling in large Eddy simulations. Boundary-Layer Meteorol 134: 441–458CrossRefGoogle Scholar
  10. Rooy WC, Siebesma AP (2008) A simple parameterization for detrainment in shallow cumulus. Mon Weather Rev 136: 560–576CrossRefGoogle Scholar
  11. Deardorff JW (1972) Theoretical expression for the countergradient vertical heat flux. J Geophys Res 77: 5900–5904CrossRefGoogle Scholar
  12. Gregory D (2001) Estimation of entrainment rate in simple models of convective clouds. Q J Roy Meteorol Soc 127: 53–72CrossRefGoogle Scholar
  13. Grossman RL (1984) Bivariate conditional sampling of moisture flux over a tropical ocean. J Atmos Sci 41: 3238–3253CrossRefGoogle Scholar
  14. Heus T, Jonker HJJ (2008) Subsiding shells around cumulus clouds. J Atmos Sci 65: 1003–1018CrossRefGoogle Scholar
  15. Heus T, Dijk G, Jonker HJJ, Akker HEA (2008) Mixing in shallow cumulus clouds studied by lagrangian particle tracking. J Atmos Sci 65: 2581–2597CrossRefGoogle Scholar
  16. Hourdin F, Couvreux F, Menut L (2002) Parameterisation of the dry convective boundary layer based on a mass flux representation of thermals. J Atmos Sci 59: 1105–1123CrossRefGoogle Scholar
  17. Hourdin F, Musat I, Bony S, Braconnot P, Codron F, Dufresne J-L, Fairhead L, Filiberti M-A, Friedlingstein P, Grandpeix J-Y, Krinner G, LeVan P, Li Z-X, Lott F (2006) The LMDZ4 general circulation model: climate performance and sensitivity to parametrized physics with emphasis on tropical convection. Clim Dyn 27: 787–813CrossRefGoogle Scholar
  18. LeMone MA, Pennell WT (1976) The relationship of trade wind cumulus distribution to subcloud layer fluxes and structure. Mon Weather Rev 104: 524–539CrossRefGoogle Scholar
  19. Moeng C, Wyngaard JC (1988) Spectral analysis of large-eddy simulations of the convective bounadary layer. J Atmos Sci 45(23): 3573–3587CrossRefGoogle Scholar
  20. Neggers RAJ, Siebesma P, Jonker HJJ (2002) A multiparcel model for shallow cumulus convection. J Atmos Sci 59:1655–1668CrossRefGoogle Scholar
  21. Neggers RAJ, Jonker HJJ, Siebesma AP (2003) Size statistics of cumulus clouds populations in large-eddy simulations. J Atmos Sci 60: 1060–1074CrossRefGoogle Scholar
  22. Nordeng TE (1994) Extended versions of the convective parametrization scheme at ECMWF and their impact on the mean and transient activity of the model in the Tropics. Technical memo. 206, ECMWFGoogle Scholar
  23. Paluch IR (1979) The entrainment mechanism in Colorado cumuli. J Atmos Sci 36: 2467–2478CrossRefGoogle Scholar
  24. Pergaud J, Masson V, Malardel S, Couvreux F (2009) A parameterization of dry thermals and shallow cumuli for mesoscale numerical weather prediction. Boundary-Layer Meteorol 132, 83–106CrossRefGoogle Scholar
  25. Rio C, Hourdin F (2008) A thermal plume model for the convective boundary layer: representation of cumulus clouds. J Atmos Sci 65: 407–425CrossRefGoogle Scholar
  26. Siebesma AP (1998) Shallow cumulus convection. In: Plate EJ, Fedorovich EE, Viegas DX, Wyngaard JC (eds) Buoyant convection in geophysical flow. Kluwer, Dordrecht, pp 441–486Google Scholar
  27. Siebesma A, Cuijpers J (1995) Evaluation of parametric assumptions for shallow cumulus convection. J Atmos Sci 52: 650–666CrossRefGoogle Scholar
  28. Siebesma AP, Jonker HJJ (2000) Anomalous scaling of cumulus cloud boundaries. Phys Rev Lett 85: 214–217CrossRefGoogle Scholar
  29. Siebesma A, Teixera J (2000) An advection–diffusion scheme for the convective boundary layer, description and 1D results. In: Proceedings of 14th AMS symposium on boundary layers and turbulence, AMSGoogle Scholar
  30. Siebesma AP, Bretherton CS, Brown A, Chlond A, Cuxart J, Duynkerke PG, Jiang H, Khairoutdinov M, Lewellen D, Moeng C-H, Sanchez E, Stevens B, Stevens DE (2003) A large eddy simulation intercomparison study of shallow cumulus convection. J Atmos Sci 60: 1201–1219CrossRefGoogle Scholar
  31. Simpson J, Wiggert V (1969) Models of precipitating cumulus towers. Mon Weather Rev 97: 471–489CrossRefGoogle Scholar
  32. Soares P, Miranda P, Siebesma A, Teixeira J (2004) An eddy-diffusivity/mass flux parameterization for dry and shallow cumulus convection. Q J Roy Meteorol Soc 130:3365–3383CrossRefGoogle Scholar
  33. Stith JL (1992) Observations of cloud-top entrainment in cumuli. J Atmos Sci 49: 1334–1347CrossRefGoogle Scholar
  34. Stull RB (1984) Transilient turbulence theory. Part I: the concept of eddy-mixing across finite distances. J Atmos Sci 41: 3351–3367CrossRefGoogle Scholar
  35. Tiedtke M (1989) A comprehensive mass flux scheme for cumulus parameterization in large-scale models. Mon Weather Rev 117: 1179–1800CrossRefGoogle Scholar
  36. Salzen K, McFarlane NA (2002) Parameterization of the bulk effects of lateral and cloud-top entrainment in transient shallow cumulus clouds. J Atmos Sci 59: 1405–1430CrossRefGoogle Scholar
  37. Williams AG, Hacker JM (1992) The composite shape and structure of coherent eddies in the convective boundary layer. Boundary-Layer Meteorol 61: 213–245CrossRefGoogle Scholar
  38. Yamada T (1983) Simulations of nocturnal drainage flows by a q 2 l turbulence closure model. J Atmos Sci 40: 91–106CrossRefGoogle Scholar
  39. 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: 727–735CrossRefGoogle Scholar
  40. Zhao M, Austin P (2005) Life cycle of numerically simulated shallow cumulus clouds. Part I: mixing dynamics. J Atmos Sci 62: 1291–1310CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media B.V. 2010

Authors and Affiliations

  1. 1.GAME Meteo-France and CNRSToulouseFrance
  2. 2.LMD-IPSL, pl JussieuParisFrance

Personalised recommendations