A statistical model to forecast the profile of the index structure constant $${C_N^2}$$

A statistical study was performed over 145 profiles of meteorological balloons, equipped with microthermal sensors, from the ground to the midstratosphere. This study put into evidence the lognormal distribution of the fluctuations of the structure constant of temperature, the fluctuations of the buoyancy force and the vertical shear of the horizontal wind speed. We show that these quantities, computed over a large scale (100 m), are correlated up to the midstratosphere. A model is adjusted to estimate the optical turbulence strength from the macroscopic meteorological parameters. The model performances, to estimate and forecast the strength and the altitude of the optical turbulent layers, are quantified and compared with other already defined models. This model was shown to have the best performances and put into evidence a new relation to describe the turbulence on a large scale.