We present a fractal sub-grid scale model for large eddy simulation (LES) of atmospheric flows. The fractal model is based on the fractality assumption of turbulent velocity field with a dynamical hypothesis based on energy dissipation. The fractal model reconstructs the sub-grid velocity field from the knowledge of its filtered values on LES grid, by means of fractal interpolation, proposed by Scotti and Meneveau (1999). The characteristic of the reconstructed signal depends on the (free) stretching parameters, which is related to the fractal dimension of the signal. In previous studies, the stretching parameters was assumed to be constant in space and time and are obtained from experimental velocity signals of homogeneous and isotropic turbulence.
To improve this method and account for the stretching parameter variability, we calculate the probability distribution function of the stretching parameter from direct numerical simulation (DNS) data of stratocumulus-top boundary layer (STBL) (courtesy of Prof. J.-P. Mellado from the Max Planck Institute of Meteorology) using the geometric method proposed by Mazel and Hayes. We perform 1D a priori test and compare statistics of the constructed velocity increment with DNS velocity increments.