# Influence of Atmospheric Flow Structure on Optical Turbulence Characteristics
## 2 Used Methods
### Method to Estimate the Strength of Small-Scale (Optical) Turbulence  
To calculate the main characteristic of image quality, namely the Fried parameter, we used the classical method based on relation between differential image motion and the Fried parameter [32]. The formula to calculate the Fried parameter \(r_{0}\) can be written as follows:  
\[\sigma_{\alpha}^{2}=K\lambda^{2}r_{0}^{-5/3}D^{-1/3}, \tag{4}\]  
where \(\lambda\) is the light wavelength and \(D\) is the telescope diameter. In Formula (4), the parameter \(r_{0}\) is considered to be a function of the light wavelength and the structure constant of air refractive index fluctuations (\(C_{n}^{2}\)). The coefficient \(K\) used in Formula (4) depends on the ratio of the distance between the centers of the subapertures \(S_{d}\) and the subaperture diameter \(d_{s}\), as well as the direction of image motion and type of wavefront slope. In the present study, we used the formulas for longitudinal and transverse coefficients:  
\[K_{l}=0.34\left(1-0.57\left(\frac{S_{d}}{d_{s}}\right)^{-1/3}-0.04\left(\frac {S_{d}}{d_{s}}\right)^{-7/3}\right), \tag{5}\]  
\[K_{t}=0.34\left(1-0.855\left(\frac{S_{d}}{d_{s}}\right)^{-1/3}+0.03\left(\frac {S_{d}}{d_{s}}\right)^{-7/3}\right). \tag{6}\]  
The measurements of differential sunspot image motion were performed using the Shack-Hartmann wavefront sensor (SHWS). SHWS is the main component of the adaptive optics system of the large solar vacuum telescope [33]. Integral Strength of Optical Turbulence and Spatial Distributions of Surface Wind Speeds over the BAO  
Using the observations of sunspot subimages to calculate the Fried parameter, we estimated the daytime changes of \(r_{0}\). Figure 3 demonstrates daytime changes in the Fried parameter at the BAO site for 8 August 2022. The analysis of daytime changes in the Fried parameter shows that sunspot image quality increases from noon to evening. This scenario does not reflect the usual changes in image quality during the day. In order to improve knowledge about the formation of optical turbulence above the BAO and the influence of atmospheric meso-scale and large-scale movements on it, we calculated the spatial distributions of wind speeds at a height of 200 m above the  
Figure 3: Daytime changes in the Fried parameter at the BAO site for 8 August 2022.  
observatory. We should emphasize that the horizontal resolution of the obtained spatial distributions was 500 m, and the temporal resolution was 3 min. Figure 4a-c shows the spatial distributions of the wind speeds at a height of 200 m above the BAO within the third domain, under conditions of strong optical turbulence. Figure 5a,b shows the wind speed distributions under conditions of moderate intensity of optical turbulence. Analyzing Figures 4 and 5, we note that an increase in the Fried parameter is accompanied by changes in airflow structure in the lower layers of the atmosphere, which makes the greatest contribution to the quality of solar images. The lowest values of the Fried parameter correspond to strong airflows over Lake Baikal. An observed increase of the Fried parameter by 1 cm during the day can be associated with a general decrease in surface wind speeds over Lake Baikal. In the daytime, a meso-scale vortex structure with anticyclonic circulation of air flows forms over the BAO. The velocity of these flows in the vortex structure is low. According to our measurements, the velocity varied from 0.5 to 3 m/s. In order to identify features of the spatial structure of airflows, we also presented the spatial distributions of wind speeds within the third domain, both in the morning and at night (Figure 6a,b). Figure 4: Spatial distributions of wind speeds in the third domain with a horizontal resolution of 500 m under conditions of strong optical turbulence. The streamlines are shown by arrows. The red marker corresponds to the BAO location. The yellow dotted line is the coastline of Lake Baikal. Figure 5: Spatial distributions of wind speeds under conditions of moderate intensity of optical turbulence.