## 3 Experimental Results and Analysis
### Verification  
Since there is no synchronous-sounding data for comparison, we use the atmospheric turbulence profile model for comparison and verification. The most commonly used model is the Hufnagel-Valley (HV) model, which allows for changes in the upper air speed and near-ground turbulence levels to be applied to atmospheric conditions at different locations. The model is given by [40]  
\[C_{n}^{2}(h)=5.94\times 10^{-53}h^{10}e^{-\frac{h}{100}}\left(\frac{v}{27} \right)^{2}+2.7\times 10^{-16}e^{-\frac{h}{1500}}+Ae^{-\frac{h}{100}} \tag{13}\]  
where \(v\) is the wind speed in the upper air; and \(A\) denotes \(C_{n}^{2}\) in the near-surface boundary layer. The most commonly used value is \(v\) = 21 m/s and \(A\) = 1.7 \(\times\) 10\({}^{-14}\) m\({}^{-2/3}\), so it is also called the HV-21 model. The HV model is modified to conform to the night-time meteorological conditions of the Yinchuan area. In Equation (13), the first term represents the strong turbulent layer conditions that often occur in the tropopause, the second term represents the turbulent layer conditions in the boundary layer, and the third term represents the turbulent layer conditions in the free atmosphere [41]. According to our inquiry of relevant data and the data of the National Meteorological Center, the wind speed during the experiment was about 2 m/s [42]. As for the turbulence in the boundary layer and the free atmosphere, according to the long-term observation results in the laboratory, it is found that the turbulence intensity in the boundary layer in Yinchuan is about 3.02 \(\times\) 10\({}^{-18}\) m\({}^{-2/3}\), and that in the free atmosphere is about 5.01 \(\times\) 10\({}^{-17}\) m\({}^{-2/3}\). Therefore, the \(C_{n}^{2}\) profile model conforming to the Yinchuan area is fitted, and the model formula is shown as follows:  
\[C_{n}^{2}(h)=3.26\times 10^{-55}h^{10}e^{-\frac{h}{1000}}+3.02\times 10^{-18}e^{ -\frac{h}{1500}}+5.01\times 10^{-17}e^{-\frac{h}{100}} \tag{14}\]  
Figure 12: Non-Kolmogorov turbulence intensity profiles with different spectral power laws, \(\alpha\). (**a**) Non-Kolmogorov turbulence intensity profiles with different spectral power laws, \(\alpha\) at 20:42 on 5 September 2022. (**b**) Non-Kolmogorov turbulence intensity profiles with different spectral power laws, \(\alpha\) at 20:33 on 6 September 2022. The laser light source was 532 nm, the emission frequency was 10 Hz, and the diameter of the telescope diaphragm \(d_{0}\) = 0.5 mm. The day of the experiment was clear and windless. Kolmogorov turbulence intensity and Non-Kolmogorov turbulence intensity were detected, respectively, and the Kolmogorov turbulence and the non-Kolmogorov turbulence profiles were compared with the \(C_{n}^{2}\) model of Yinchuan. In order to simplify the comparison process, the spectral power law \(\alpha\) = 3.1 was used uniformly to represent non-Kolmogorov turbulence. Figure 13 shows the comparison results. Regarding the comparison, it can be seen that the overall variation trend of the \(\widetilde{C}_{n}^{2}\) profile detected by Mie-scattering lidar is consistent with the HV-night model in the Yinchuan area, which shows that \(\widetilde{C}_{n}^{2}\) at low altitude decreases with the increase in altitude, while \(\widetilde{C}_{n}^{2}\) at high altitude gradually increases with the increase in altitude and tends to be stable. Both the Kolmogorov turbulence \(C_{n}^{2}\) profile and the non-Kolmogorov turbulence \(\widetilde{C}_{n}^{2}\) profile reach their minimum values at approximately 600 m. When compared with the HV-night model of the Yinchuan area, the \(C_{n}^{2}\) profile and the \(\widetilde{C}_{n}^{2}\) profile are both one order of magnitude smaller in the low-altitude range, and approximately one order of magnitude larger in the high-altitude range. The actual detection results fluctuate near the theoretical value. The average relative error of Kolmogorov turbulence is 47.07%, and that of non-Kolmogorov turbulence is 52.54%. This phenomenon has been analyzed in detail, and there are two reasons for this.