Study of <inline-formula><tex-math id="M2">\begin{document}${\boldsymbol C_{\boldsymbol n}^{\boldsymbol 2}}$\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="6-20221985_M2.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="6-20221985_M2.png"/></alternatives></inline-formula> profile model by atmospheric optical turbulence model

Owing to the existence of atmospheric turbulence, a series of turbulence effects such as phase fluctuation and light intensity scintillation will occur when the electromagnetic waves propagates through the atmosphere, which seriously affects the performance of the electro-optic system, resulting in the difficulty of astronomical observation. The atmospheric refractive index structure constant (\begin{document}$ C_n^2 $\end{document}) profile is an important parameter to evaluate the turbulence effects. This paper summarizes several representative \begin{document}$ C_n^2 $\end{document} profile models and analyzes the data using balloon-borne microthermal probes at five sites i.e. Gaomeigu, Lhasa, Dachaidan, Maoming, and Rongcheng. The atmospheirc optical parameters are calculated, such as coherence length, seeing, isoplanatie angle, coherence time, equivalent height, equivalent wind speed, drop-off rate and integrated contribution from each atmosphere layer. The formulas of five sites are developed by fitting the arithmetic average of measurements. Several troubling basic problems such as suspicion the H-V (5/7) model, the model developed by arithmetic average or geometric average, the problem whether there is a uniform lapse rate in the low stratosphere, are discussed and solved. The modified CLEAR I night model is given.