Boundary-Layer Meteorology

, Volume 120, Issue 3, pp 437–454 | Cite as

A Parameterization of Third-order Moments for the Dry Convective Boundary Layer

  • Séverine TomasEmail author
  • Valéry Masson
Original Article


We describe one-dimensional (1D) simulations of the countergradient zone of mean potential temperature \(\overline{\theta}\) observed in the convective boundary layer (CBL). The method takes into account the third-order moments (TOMs) in a turbulent scheme of relatively low order, using the turbulent kinetic energy equation but without prognostic equations for other second-order moments. The countergradient term is formally linked to the third-order moments \(\overline{w^{\prime 2}\theta'}\) and \(\overline{w'\theta^{\prime 2}}\), and a simple parameterization of these TOMs is proposed. It is validated for several cases of a dry CBL, using large-eddy simulations that have been realized from the MESO-NH model. The analysis of the simulations shows that TOMs are responsible for the inversion of the sign of \(\partial \overline{\theta}\,/\,\partial z\) in the higher part of the CBL, and budget analysis shows that the main terms responsible for turbulent fluxes and variances are now well reproduced.


Convective boundary layer Countergradient term Heat flux Parameterization Third-order moments Turbulence 


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Copyright information

© Springer Science+Business Media, Inc. 2006

Authors and Affiliations

  1. 1.CNRM/GMME/TURBAUMETEO FranceCedex 01France

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