We are most grateful to Dr. Ayotte for having kindly provided the LES results and the sources of some of the codes he used, including the version of the Holtslag and Boville parameterization used in this study. We also want to thank very much Alain Lahellec and Jean-Yves Grandpeix. By their numerous discussions and knowledge of the boundary layer dynamics and mass flux parameterizations of deep convection, they significantly contributed to this work. We also want to thank Denise Cruette for her enlighting descriptions of the thermals reality and Robert Haberle for his help on the revised manuscript. This study was funded by Centre National de la Recherche Scientifique.
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