**4. Discussion**

### *4.1. Potential Temperature Gradient*

Equation (2) indicates that the most critical step in the parameterization scheme of atmospheric turbulence is how to parameterize *<sup>C</sup>*2*T*, and *C*2*n* can be calculated logically. According to the dimensional analysis, Tatarski [31] defined the atmospheric temperature structure constant as follows:

$$C\_T^2 = 1.6\varepsilon\_\theta \varepsilon^{-\frac{1}{3}}\tag{8}$$

where *εθ* denotes the molecular diffusivity caused by temperature difference, and *ε* is the turbulent energy dissipation rate. The energy of atmospheric turbulence mainly originates from the dynamic and thermal effects. The former implies that when there is wind direction and wind speed shear, the turbulent shear stress works on the air micro-clusters, whereas the latter implies that in an unstable atmosphere, the buoyant force works on the air micro-clusters that move vertically to increase the turbulence.

Bougeault and Lacarrere [39] parameterized *C*2*T*as follows:

$$
\mathbb{C}\_T^2 = 0.59 L^{4/3} \left(\frac{\delta \overline{\theta}}{\delta z}\right)^2 \mathcal{Q}\_3 \tag{9}
$$

where *L* denotes the Bougeault–Lacarrere mixing length, ∅3 is the reversed turbulent Prandtl number, and *θ* is the potential temperature. Refer to the detailed derivation process in the literature [40].

$$L = \sqrt{\frac{2c}{\frac{\xi \cdot \xi}{\xi \cdot z}}} \tag{10}$$

where *e* denotes the turbulence energy. Parametric Equations (8)–(10) clearly indicate that, the potential temperature gradient is directly related to the buoyancy frequency, turbulent energy dissipation rate, and temperature structure constant. This is an indispensable and important parameter in the parameterization of atmospheric turbulence [41]. Therefore, under different ASMA intensities, the numerical changes in the potential temperature gradient can also reflect the thermal convection intensity.

### *4.2. Discussion on the Temperature Structure in UTLS*

Radiosonde data were used to compare and analyze the atmospheric temperature structure from 12 to 16 August 2018. The temperatures above ~16 km fluctuated significantly during these days, where was stably controlled by ASMA. As shown in Figure 5b, the cold-point tropopause (CPT), which corresponds to the coldest temperature, was higher in the middle of the ASMA than in other stages, and this timing may have coincided with a decrease in static stability [42] and may be related to strong convective activities [43,44].

**Figure 5.** (**a**) Vertical temperature profiles from 12 to 16 August 2018. (**b**) Cold-point tropopause height (the black line) and temperature (the red line) from 12 to 16 August 2018. The lowest layer of the multi-tropopause serves as the CPT height. (**c**) First-order linear piecewise fitting to log10*C*2*n* within the upper troposphere, tropopause, and lower stratosphere.

Table 3 summarizes the fitting results of log10*C*2*n* using first-order linear fitting within the upper troposphere, tropopause, and lower stratosphere (Figure 5c), and the coefficients represent the increase rate of log10*C*2*n*, reaching respective maximum value at tropopause layer. However, when the ASMA intensity is large, the log10*C*2*n* increase rate in the tropopause is weakened, and the log10*C*2*n* in the lower stratosphere decreases.


**Table 3.** Increase rate of log10 *C*2*n* (m7/3) within upper troposphere, tropopause, and lower stratosphere.

During the experimental period, the potential temperature profiles varied significantly in the UTLS (Figure 6a), particularly in the upper troposphere. The potential temperature lapse rate (unit: K/km) within three heights in the range 10–16 km was fitted using the first-order linear piecewise method (Table 4). The potential temperature lapse rates in the ranges of 10–11 km (Figure 6b) and 11–12.5 km (Figure 6c) corresponded to the minimum and maximum recorded values on 13 and 16 August 2018, respectively. Under the control of the high-intensity ASMA on 14 August 2018, the potential temperature lapse rate was approximately equivalent to the values recorded on 12 and 16 August. In particular, in the 10–11 km range, the potential temperature lapse rate on 14 August was approximately 2.2 times as high as that on 13 August owing to high-pressure activity at 500 hPa. This shift suppressed the vertical flow of the atmosphere and enhanced the static stability of the UTLS.

**Figure 6.** (**a**) Vertical profiles of potential temperature on 12–14 and 16 August 2018. (**b**,**<sup>c</sup>**) show magnified views of the 12.5–16 km and 10–12.5 km ranges, respectively.

**Table 4.** Potential temperature lapse rate (K/km) within the range of 10–16 km.


In general, the potential temperature lapse rates for the four days were at the same amplitude within the range of 12.5–16 km. However, the trend of potential temperature on 16 August 2018 was significantly different from that on the other three days within 12.5–16 km. There was a weak thermal inversion layer in the range of 15–16 km on 16 August 2018. The inversion layer was able to block the upward movement of air [45,46], corresponding to a small *C*2*n* value in the range of 10–15 km.

Piecewise linear fitting was performed on the potential temperature profiles within the tropopause and lower stratosphere regions at intervals of 1000 m. The CPT height of the TP was approximately 100 hPa, and the potential temperature lapse rate within 2 km below the CPT varied significantly among the four profiles. The potential temperature change rate on 14 August during the ASMA was twice as high as that on 12 and 16 August. This indicates that the stronger the ASMA, the greater the potential temperature lapse rate in tropopause. Above the CPT, *C*2*n* cannot escape the fate of being affected by the ASMA, but thermal convection is inhibited in the lower stratosphere. The dynamic and thermal structures of the troposphere and stratosphere are completely different, and this difference is mainly characterized by high stability and weak turbulence in the stratosphere [14,47,48].

The tropopause is the mixed layer between the troposphere and stratosphere and it has dual characteristics of both the troposphere and stratosphere [49–51]. The CPT height corresponds to the minimum saturated water vapor mixing ratio, which is considered to be the upper boundary of the tropical tropopause [52]. Figure 7 shows that the potential temperature lapse rate is completely different between the tropopause and lower stratosphere, mainly showing that the potential temperature lapse rate increases sharply in the

lower stratosphere. The turbulence characteristics of the lower stratosphere are hardly affected by the high-pressure activity over the 500-hPa layer, and the ASMA is the strongest influencing factor. Figure 2c shows that the Lhasa area was affected by the decreased ASMA on 12–14 and 16 August 2018. The potential temperature lapse rate in the tropopause area and above the CPT reached a maximum on 14 August and a minimum on 12 August 2018. The area 2 km lower than the CPT belongs to the tropopause mixed layer, and the potential temperature lapse rate in this area was largest on 14 August; the other three days did not differ extensively. It is inferred from the current data that the presence of the ASMA inhibits the vertical movement of the atmosphere in the lower stratosphere and tropopause. However, this conclusion requires additional data for verification.

**Figure 7.** The piecewise fitting lines of potential temperature in tropopause and lower stratosphere. The potential temperature profiles are linearly fitted with the least-square method at intervals of 1000 m. The numbers indicate the coefficients (unit: K/km) of the piecewise fitting, indicating the potential temperature lapse rates. The pink dotted lines represent the corresponding CPT heights. (**a**) 12 August 2018, (**b**) 13 August 2018, (**c**) 14 August 2018, and (**d**) 16 August 2018.
