Knowledge of the optical refractive index structure parameter $C_n^2$ is of interest for Free Space Optics (FSO) and ground-based optical astronomy, as it depicts the strength of the expected scintillation on the received optical waves. Focus is given here to models using meteorological quantities coming from radiosonde measurements as inputs to estimate the $C_n^2$ profile in the atmosphere. A model relying on the $C_n^2$ statistical definition is presented and applied to recent high-density radiosonde profiles at Trappes (France) and Hilo, HI (USA). It is also compared to thermosonde measurements coming from the T-REX campaign. This model enables to obtain site-specific average profiles and to identify isolated turbulent layers using only pressure and temperature measurements, paving the way for optical site selection. It offers similar performance when compared to a Tatarskii-based model inspired by the literature.