**2. Methods**

### *2.1. Sounding Data*

From 3 to 18 August 2018, a thermal turbulent sounding experiment was conducted at the Lhasa Meteorological Bureau (91◦06E, 29◦36N) ("pentagram" in Figure 1) by the Hefei Institutes of Physical Science, Chinese Academy of Sciences. This experiment collected very precious high vertical resolution thermal turbulence sounding data, which provided a reliable basis for the study of the fine atmospheric structure in UTLS and the verification of model simulation over the TP [30]. The sounding balloons were equipped with conventional meteorological sensors to measure the atmospheric temperature (*T*), humidity, pressure (*P*), and wind speed, along with two-channels turbulent meteorological radiosondes developed by the Anhui Institute of Optics and Fine Mechanics.

**Figure 1.** The elevation height of TP (color shaded) and the geographical location of Lhasa (pentagram). This figure was plotted using the Lambert conformal conic projection.

Each thermal turbulence radiosonde comprises two platinum wire probes (15 μm in diameter) separated by a distance of *r* (=1 m). The platinum wire probes have linear resistance–temperature coefficients. The thermal turbulence radiosondes measure the temperature difference between the distance r and voltage change between the two microthermal probes [28–30]. Then, the temperature structure constant (*C*2*T*) in the inertial subrange can be calculated using the following equation [31]:

$$\left\langle \left[ T \left( \stackrel{\rightarrow}{\mathbf{x}} \right) - T \left( \stackrel{\rightarrow}{\mathbf{x}} + \stackrel{\rightarrow}{r} \right) \right]^2 \right\rangle = \mathcal{C}\_T^2 r^{\frac{2}{3}} \left( l\_0 \ll r \ll L\_0 \right) \tag{1}$$

where *<sup>T</sup>*<sup>→</sup>*x* and *<sup>T</sup>*<sup>→</sup>*x* + →*r* denote the temperatures at two points, ··· represents the ensemble average, and *l*0 and *L*0 represent the inner and outer scales of the turbulence, respectively (units of m).

*<sup>C</sup>*2*n*, the degree of refractive index fluctuation due to variations in atmospheric temperature and density [18,32], can be calculated by inputting temperature (*T*) and pressure (*P*) profiles, according to the relationship between *C*2*n* and *C*2*T* (Equation (2)):

$$\mathbf{C}\_n^2 = \left(79 \times 10^{-6} \frac{P}{T^2}\right)^2 \mathbf{C}\_T^2 \tag{2}$$

The range of the response frequency of the thermal turbulent radiosonde is 0.1–30 Hz, and the minimum measurable standard deviation of the temperature fluctuation does not exceed 0.002 ◦C. In addition, the vertical resolution of the radiosondes was 30 m.

Five thermal turbulence radiosondes were launched during the experiments at about 19:30 local time (LT). The detailed experimental records are summarized in Table 1. Owing to weather and transmission interference problems, four valid data sets were obtained over 20 km above sea level (ASL, the height below refers specifically to ASL except for special explanations) in height.


**Table 1.** Detailed records of radiosonde experiments over the Lhasa.

### *2.2. C*2*n Integrated Parameters*

*C*2*n* integrated parameters (the Fried parameter *r*0, seeing *ε*, isoplanatic angle *θ*0) are of importance evaluation criteria for the astronomical site testing and the design of adaptive optics systems, defining as:

$$r\_0 = \left[0.423 \left(\frac{2\pi}{\lambda}\right)^2 \sec\beta \int\_0^\infty \mathbb{C}\_n^2(h) dh\right]^{-\frac{3}{5}}\tag{3}$$

$$
\varepsilon = 5.25 \lambda^{-\frac{1}{5}} \left[ \int\_0^\infty C\_n^2(h) dh \right]^{-\frac{3}{5}} = 0.98 \frac{\lambda}{r\_0} \tag{4}
$$

$$\theta\_0 = 0.057 \lambda^{\frac{6}{5}} \left[ \int\_0^\infty \mathcal{C}\_n^2(h) h^{\frac{5}{3}} dh \right]^{-\frac{3}{5}} \tag{5}$$

where, *λ* (=550 nm for this study) is a given wavelength for visible light, *β* is the zenith angle.
