## Abstract

Turbulence is well represented by atmospheric models at very fine grid sizes, from 10 to 100 m, for which turbulent movements are mainly resolved, and by atmospheric models with grid sizes greater than 2 km, for which those movements are entirely parameterized. But what happens at intermediate scales, Wyngaard’s so-called terra incognita?

Here an original method is presented that provides a new diagnostic by calculating the subgrid and resolved parts of five variables at different scales: turbulent kinetic energy (TKE), heat and moisture fluxes, and potential temperature and mixing ratio variances. They are established at intermediate scales for dry and cumulus-topped convective boundary layers. The similarity theorem allows the determination of the dimensionless variables of the problem. When the subgrid and resolved parts are studied, a new dimensionless variable, the dimensionless mesh size *h* is the boundary layer height and *h _{c}* is the height of the cloud layer. Similarity functions for the subgrid and resolved parts are assumed to be the product of the similarity function of the total (subgrid plus resolved) variables and a “partial” similarity function that depends only on

The evolution of the subgrid and resolved parts in the boundary layer with

This new diagnostic gives a reference for evaluating current and future parameterizations at kilometric scales. As an illustration, the parameterizations of a mesoscale model are eventually evaluated at intermediate scales. In its standard version, the model produces too many resolved movements, as the turbulence scheme does not sufficiently represent the impact of the subgrid thermal. This is not true when a mass-flux scheme is introduced. However in this case, a completely subgrid thermal is modeled leading to an overestimation of the subgrid part.

*Corresponding author address:*Rachel Honnert, CNRM/GAME, 42, avenue Gaspard Coriolis, 31057 Toulouse CEDEX 01, France. E-mail: rachel.honnert@meteo.fr