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Resolved Versus Parametrized Boundary-Layer Plumes. Part III: Derivation of a Statistical Scheme for Cumulus Clouds

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Abstract

We present a statistical cloud scheme based on the subgrid-scale distribution of the saturation deficit. When analyzed in large-eddy simulations (LES) of a typical cloudy convective boundary layer, this distribution is shown to be bimodal and reasonably well-fitted by a bi-Gaussian distribution. Thanks to a tracer-based conditional sampling of coherent structures of the convective boundary layer in LES, we demonstrate that one mode corresponds to plumes of buoyant air arising from the surface, and the second to their environment, both within the cloud and sub-cloud layers. According to this analysis, we propose a cloud scheme based on a bi-Gaussian distribution of the saturation deficit, which can be easily coupled with any mass-flux scheme that discriminates buoyant plumes from their environment. For that, the standard deviations of the two Gaussian modes are parametrized starting from the top-hat distribution of the subgrid-scale thermodynamic variables given by the mass-flux scheme. Single-column model simulations of continental and maritime case studies show that this approach allows us to capture the vertical and temporal variations of the cloud cover and liquid water.

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Notes

  1. The computed condensed water \(q_\mathrm{c}\) is not exactly superimposed on the LES results as should be the case, due to numerical instabilities in the computation of \(k\) in the inverse procedure.

References

  • Bechtold P, Cuijpers JWM, Mascart P, Trouilhet P (1995) Modeling of trade wind cumuli with a low-order turbulence model: toward a unified description of Cu and Sc clouds in meteorological models. J Atmos Sci 52:455–463

    Article  Google Scholar 

  • Bogenschutz PA, Krueger SK, Khairoutdinov M (2010) Assumed Probability Density Functions for shallow and deep convection. J Adv Model Earth Syst 42:Art. \(\#\)10, 24 pp

  • Bony S, Emanuel KA (2001) A parametrization of cloudiness associated with cumulus convection; evaluation using Toga Coare data. J Atmos Sci 58:3158–3183

    Article  Google Scholar 

  • Bougeault P (1981) Modeling the trade-wind cumulus boundary layer. Part I: testing the ensemble cloud relations against numerical data. J Atmos Sci 38:2414–2428

    Google Scholar 

  • 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 R Meteorol Soc 128:1075–1093

    Article  Google Scholar 

  • Chaboureau JP, Bechtold P (2002) A simple cloud parametrization derived from cloud resolving model data: Diagnostic and prognostic applications. J Atmos Sci 59:2362–2372

    Article  Google Scholar 

  • 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 R Meteorol Soc 131:2665–2693

    Article  Google Scholar 

  • 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 123:269–294

    Article  Google Scholar 

  • Couvreux F, Hourdin F, Rio C (2010) Resolved versus parametrized boundary layer thermals. Part I: a parametrization oriented conditional sampling in large eddy simulations. Boundary-Layer Meteorol 134:441–458

    Article  Google Scholar 

  • Deardorff JW (1972) Theoretical expression for the countergradient vertical heat flux. J Geophys Res 77:5900–5904

    Article  Google Scholar 

  • Dufresne J-L, Quaas J, Boucher O, Denvil S, Fairhead L (2005) Contrasts in the effects on climate of anthropogenic sulfate aerosols between the 20th and the 21st century. Geophys Res Lett 32:L21703. doi:10.1029/2005GL0236619

    Article  Google Scholar 

  • Emanuel KA (1993) A cumulus representation based on the episodic mixing model: the importance of mixing and microphysics in predicting humidity. The representation of cumulus convection in numerical models of the atmosphere. Meteorological Monograph No. 46. American Meteorological Society, Boston, pp 185–192

  • Fouquart Y, Bonnel B (1980) Computations of solar heating of the Earth’s atmosphere: a new parametrization. Contrib Atmos Phys 53:35–62

    Google Scholar 

  • Golaz J-C, Larson VE, Cotton WR (2002a) A PDF-based model for boundary layer clouds. Part I: method and model description. J Atmos Sci 59:3540–3551

    Google Scholar 

  • Golaz J-C, Larson VE, Cotton WR (2002b) A PDF-based model for boundary layer clouds. Part II: model results. J Atmos Sci 59:3552–3571

    Google Scholar 

  • Heus T, Jonker HJJ (2008) Subsiding shells around shallow cumulus clouds. J Atmos Sci 65:1003–1018

    Article  Google Scholar 

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

    Article  Google Scholar 

  • 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 59:1105–1123

    Article  Google Scholar 

  • 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 27:787–813

    Article  Google Scholar 

  • Hourdin F, Grandpeix J-Y, Rio C, Bony S, Jam A, Cheruy F, Rochetin N, Fairhead L, Idelkadi A, Musat I, Dufresne J-L, Lefebvre M-P, Lahellec A, Roehrig R (2012) LMDZ5B: the atmospheric component of the IPSL climate model with revisited parametrizations for clouds and convection. Clim Dyn. doi:10.1007/s00382-012-1343-y

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

    Article  Google Scholar 

  • Larson VE (2002) Small-scale and mesoscale variability in cloudy boundary layers: joint probability density functions. Am Meteorol Soc 59:3519–3539

    Google Scholar 

  • Lemone MA (1973) Modulation of turbulence energy by longitudinal rolls in an unstable planetary boundary layer. J Atmos Sci 33:1308–1320

    Article  Google Scholar 

  • Lemone MA, Pennell WT (1976) The relationship of trade wind cumulus distribution to subcloud layer fluxes and structure. Mon Weather Rev 104:524–539

    Article  Google Scholar 

  • Lewellen WS, Yoh S (1993) Binormal model of ensemble partial cloudiness. J Atmos Sci 50:1228–1237

    Article  Google Scholar 

  • Morcrette JJ, Smith L, Fouquart Y (1986) Pressure and temperature dependence of the absorption in longwave radiation parametrizations. Control Atmos Phys 59:455–469

    Google Scholar 

  • Neggers RAJ (2009) A dual mass flux framework for boundary layer convection. Part 2: clouds. J Atmos Sci 66:1489–1506

    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, Jonker HJJ, Siebesma AP (2003) Size statistics of cumulus clouds populations in large-eddy simulations. J Atmos Sci 60:1060–1074

    Article  Google Scholar 

  • Neggers RAJ, Stevens B, Neelin JD (2007) Variance scaling in shallow cumulus-topped mixed layers. Q J R Meteorol Soc 133:1629–1641

    Article  Google Scholar 

  • Neggers RAJ, Koehler M, Beljaars AMM (2009) A dual mass flux framework for boundary layer convection. Part 1: transport. J Atmos Sci 66:1465–1487

    Article  Google Scholar 

  • Pergaud J, Masson V, Malardel S, Couvreux F (2009) A parametrization of dry thermals and shallow cumuli for mesoscale numerical weather prediction. Boundary-Layer Meteorol 132:83–106

    Article  Google Scholar 

  • Perraud E, Couvreux F, Malardel S, Lac C, Masson V, Thouron O (2010) Evaluation of statistical distributions for the parametrization of subgrid boundary-layer clouds. Boundary-Layer Meteorol 140:263–294

    Article  Google Scholar 

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

    Article  Google Scholar 

  • Rio C, Hourdin F, Couvreux F, Jam A (2010) Resolved versus parametrized boundary layer thermals. Part II: continuous formulations of mixing rates for mass-flux schemes. Boundary-Layer Meteorol 135:469–483

    Article  Google Scholar 

  • 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. AMS, Boston

  • 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 60:1201–1219

    Article  Google Scholar 

  • Smith RNB (1990) A scheme for predicting layer clouds and their water content in general circulation model. Q J R Meteorol Soc 116:435–460

    Article  Google Scholar 

  • Soares P, Miranda P, Siebesma A, J T (2004) An eddy-diffusivity/mass flux parametrization for dry and shallow cumulus convection. Q J R Meteorol Soc 130:3365–3383

    Article  Google Scholar 

  • Sommeria G, Deardorff JW (1977) Subgrid-scale condensation in models of nonprecipitating clouds. J Atmos Sci 34:344–355

    Article  Google Scholar 

  • Tompkins AM (2002) A prognostic parametrization for the subgrid-scale variability of water vapor and clouds in large-scale models and its use to diagnose cloud cover. J Atmos Sci 59:1917–1942

    Article  Google Scholar 

  • Yamada T (1983) Simulations of nocturnal drainage flows by a \(q^2l\) turbulence closure model. J Atmos Sci 40:91–106

    Article  Google Scholar 

Download references

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Authors and Affiliations

  1. LMD-IPSL, 4 pl Jussieu, 75005 , Paris, France

    A. Jam, F. Hourdin & C. Rio

  2. GAME Meteo-France and CNRS, 42 Coriolis, 31057 , Toulouse, France

    F. Couvreux

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  1. A. Jam
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  2. F. Hourdin
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  3. C. Rio
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  4. F. Couvreux
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Correspondence to A. Jam.

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Jam, A., Hourdin, F., Rio, C. et al. Resolved Versus Parametrized Boundary-Layer Plumes. Part III: Derivation of a Statistical Scheme for Cumulus Clouds. Boundary-Layer Meteorol 147, 421–441 (2013). https://doi.org/10.1007/s10546-012-9789-3

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