Entrainment Parameterization in Convective Boundary Layers

Margreet C. vanZanten Institute for Marine and Atmospheric Research Utrecht, Utrecht University, Utrecht, the Netherlands

Search for other papers by Margreet C. vanZanten in
Current site
Google Scholar
PubMed
Close
,
Peter G. Duynkerke Institute for Marine and Atmospheric Research Utrecht, Utrecht University, Utrecht, the Netherlands

Search for other papers by Peter G. Duynkerke in
Current site
Google Scholar
PubMed
Close
, and
Joannes W. M. Cuijpers Institute for Marine and Atmospheric Research Utrecht, Utrecht University, Utrecht, the Netherlands

Search for other papers by Joannes W. M. Cuijpers in
Current site
Google Scholar
PubMed
Close
Restricted access

Abstract

Various runs were performed with a large eddy simulation (LES) model to evaluate different types of entrainment parametrizations. For this evaluation, three types of boundary layers were simulated: a clear convective boundary layer (CBL), a boundary layer containing a smoke concentration, and a cloud-topped boundary layer. It is shown that the assumption that the entrainment flux equals the product of the entrainment rate and the jump over a discontinuous inversion is not valid in CBLs simulated by an LES model. A finite inversion thickness (i.e., a first-order jump model) is needed to define an entrainment flux for which this approximation of the flux is valid. This entrainment flux includes not only the buoyancy flux at the inversion, but also the surface heat flux. The parameterization of the buoyancy flux at the inversion is evaluated for different closures, as suggested in the literature (i.e., Eulerian partitioning, process partitioning, and a closure developed by Deardorff), and where needed is extended for use in a first-order jump model. The closure based on process partitioning is found to yield consistent results in all types of convective boundary layers and shows the best agreement with the limit found in LES results if the longwave radiative flux divergence takes place in a much shallower layer than the mixed layer.

Corresponding author address: Margreet C. vanZanten, Institute for Marine and Atmospheric Research Utrecht, Utrecht University, Princetonplein 5, 3584 CC Utrecht, the Netherlands.

Email: M.C.vanZanten@phys.uu.nl

Abstract

Various runs were performed with a large eddy simulation (LES) model to evaluate different types of entrainment parametrizations. For this evaluation, three types of boundary layers were simulated: a clear convective boundary layer (CBL), a boundary layer containing a smoke concentration, and a cloud-topped boundary layer. It is shown that the assumption that the entrainment flux equals the product of the entrainment rate and the jump over a discontinuous inversion is not valid in CBLs simulated by an LES model. A finite inversion thickness (i.e., a first-order jump model) is needed to define an entrainment flux for which this approximation of the flux is valid. This entrainment flux includes not only the buoyancy flux at the inversion, but also the surface heat flux. The parameterization of the buoyancy flux at the inversion is evaluated for different closures, as suggested in the literature (i.e., Eulerian partitioning, process partitioning, and a closure developed by Deardorff), and where needed is extended for use in a first-order jump model. The closure based on process partitioning is found to yield consistent results in all types of convective boundary layers and shows the best agreement with the limit found in LES results if the longwave radiative flux divergence takes place in a much shallower layer than the mixed layer.

Corresponding author address: Margreet C. vanZanten, Institute for Marine and Atmospheric Research Utrecht, Utrecht University, Princetonplein 5, 3584 CC Utrecht, the Netherlands.

Email: M.C.vanZanten@phys.uu.nl

Save
  • Ball, F. K., 1960: Control of inversion height by surface heating. Quart. J. Roy. Meteor. Soc.,86, 483–494.

  • Betts, A. K., 1973: Non-precipitating cumulus convection and its parametrization. Quart. J. Roy. Meteor. Soc.,99, 178–196.

  • ——, 1974: Reply to comment on the paper ‘Non-precipitating cumulus convection and its parametrization’. Quart. J. Roy. Meteor. Soc.,100, 469–471.

  • Bretherton, C. S., and Coauthors, 1998: An intercomparison of radiatively-driven entrainment and turbulence in a smoke cloud, as simulated by different numerical models. Quart. J. Roy. Meteor. Soc., in press.

  • Carson, D. J., 1973: The development of a dry inversion-capped convectively unstable boundary layer. Quart. J. Roy. Meteor. Soc.,99, 450–467.

  • Cuijpers, J. W. M., and P. G. Duynkerke, 1993: Large eddy simulation of trade wind cumulus clouds. J. Atmos. Sci.,50, 3894–3908.

  • ——, and A. A. M. Holtslag, 1998: Impact of skewness and nonlocal effects on scalar and buoyancy fluxes in convective boundary layers. J. Atmos. Sci.,55, 151–162.

  • Deardorff, J. W., 1976: On the entrainment rate of a stratocumulus-topped mixed layer. Quart. J. Roy. Meteor. Soc.,102, 563–582.

  • ——, 1979: Prediction of convective mixed-layer entrainment for realistic capping inversion structure. J. Atmos. Sci.,36, 424–436.

  • Driedonks, A. G. M., and P. G. Duynkerke, 1989: Current problems in the stratocumulus-topped atmospheric boundary layer. Bound.-Layer Meteor.,46, 275–303.

  • Fravalo, D., Y. Fouquart, and R. Rosset, 1981: The sensitivity of a model of low stratiform clouds to radiation. J. Atmos. Sci.,38, 1049–1062.

  • Kraus, H., and E. Schaller, 1978: A note on the closure in Lilly-type inversion models. Tellus,30, 284–288.

  • Lilly, D. K., 1968: Models of cloud-topped mixed layers under a strong inversion. Quart. J. Roy. Meteor. Soc.,94, 292–309.

  • Manins, P. C., and J. S. Turner, 1978: The relation between flux ratio and energy ratio in convectively mixed layers. Quart. J. Roy. Meteor. Soc.,104, 39–44.

  • Moeng, C. H., 1987: Large-eddy simulation of a stratus-topped boundary layer. Part II: Implications for mixed-layer modeling. J. Atmos. Sci.,44, 1605–1614.

  • Nicholls, S., and J. D. Turton, 1986: An observational study of the structure of stratiform cloud sheets: Part II. Entrainment. Quart. J. Roy. Meteor. Soc.,112, 461–480.

  • Randall, D. A., 1980a: Conditional instability of the first kind upside-down. J. Atmos. Sci.,37, 125–130.

  • ——, 1980b: Entrainment into a stratocumulus layer with distributed radiative cooling. J. Atmos. Sci.,37, 148–159.

  • ——, 1984: Buoyant production and consumption of turbulence kinetic energy in cloud-topped mixed layers. J. Atmos. Sci.,41, 402–413.

  • Schubert, W. H., 1976: Experiments with Lilly’s cloud-topped mixed layer model. J. Atmos. Sci.,33, 436–446.

  • Siebesma, A. P., and J. W. M. Cuijpers, 1995: Evaluation of parametric assumptions for shallow cumulus convection. J. Atmos. Sci.,52, 650–666.

  • Sorbjan, Z., 1995: Toward evaluation of heat fluxes in the convective boundary layer. J. Appl. Meteor.,34, 1092–1098.

  • Stage, S. A., and J. A. Businger, 1981a: A model for entrainment into a cloud-topped marine boundary layer. Part I: Model description and application to a cold-air outbreak episode. J. Atmos. Sci.,38, 2213–2229.

  • ——, and ——, 1981b: A model for entrainment into a cloud-topped marine boundary layer. Part II: Discussion of model behavior and comparison with other models. J. Atmos. Sci.,38, 2230–2242.

  • Stull, R. B., 1976: The energetics of entrainment across a density interface. J. Atmos. Sci.,33, 1260–1267.

  • Tennekes, H., 1973: A model for the dynamics of the inversion above a convective layer. J. Atmos. Sci.,30, 558–567.

  • Turner, J. S., 1973: Buoyancy Effects in Fluids. Cambridge University Press, 367 pp.

  • Wilczak, J. M., and J. A. Businger, 1983: Thermally indirect motions in the convective atmospheric boundary layer. J. Atmos. Sci.,40, 343–358.

All Time Past Year Past 30 Days
Abstract Views 0 0 0
Full Text Views 429 63 6
PDF Downloads 228 54 5