## 3 Calculated and Measured Seeing: WRF Model and Solar Image Motion Observations

Table 2: Main parameters of Shack–Hartmann wavefront sensor. Figure 8: Adaptive optics system at the Large Solar Vacuum Telescope. The subaperture size is 10.0 cm. The focal spot pattern detected via the Shack-Hartmann sensor is shown in Figure 9.  
The system frame rate is 100 Hz. In measurements, we used light wavelength 535 nm. The seeing values from measurements were estimated using formulas (6)-(9) [29; 32]:  
\[seeing=\frac{0.98\lambda}{r_{0}}, \tag{8}\]  
\[\sigma_{\alpha}^{2}=K_{i}\lambda^{2}r_{0}^{-5/3}D^{-1/3}, \tag{9}\]  
where \(\lambda\) is the light wavelength and \(D\) is the telescope diameter. In formula (9), the Fried parameter \(r_{0}\) is the quantity that characterizes the spatial scale of atmospheric turbulence, on which the dispersion of the phase fluctuations of a light wave is equal to 1 rad\({}^{2}\). The Fried parameter \(r_{0}\) in formula (9) is a quantity estimated from the differential motion of solar images. The coefficient \(K_{i}\) used in formula (9) 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:  
\[K_{l}=0.34\left(1-0.57\left(\frac{S_{d}}{d_{s}}\right)^{-1/3}-0.04\left(\frac {S_{d}}{d_{s}}\right)^{-7/3}\right), \tag{10}\]  
\[K_{t}=0.34\left(1-0.855\left(\frac{S_{d}}{d_{s}}\right)^{-1/3}+0.03\left(\frac {S_{d}}{d_{s}}\right)^{-7/3}\right). \tag{11}\]  
Figure 10 shows time changes in seeing measured with the help of a Shack-Hartmann sensor of the Large Solar Vacuum Telescope (8 August 2022). Figure 9: The focal solar spot pattern detected via the Shack–Hartmann sensor. Analysis of Figure 10 shows that, on average, the quality of the astronomical image improved in the evening: seeing values changed from 2.8\({}^{\prime\prime}\) to 2.2\({}^{\prime\prime}\). This behaviour, when seeing values decrease in the evening, is a classic scenario for the Baikal Astrophysical Observatory. Modified Model for Estimation of \(C_{n}^{2}\) Parameter at the Site of the Baikal Astrophysical Observatory  
The structure of atmospheric turbulence changes significantly not only in time, but also depends on the site coordinates. In general, the turbulence is largely determined by the regional features of the interaction of airflows with the underlying surface as well as local factors of generation and dissipation of turbulence energy, as well as the transformation between the kinetic and potential energies of turbulence [33; 34]. Following the classic Dewan model, the seeing values derived from WRF simulations are underestimated. For more accurate estimates, we analyzed the data of mast measurements of average and turbulent characteristics in the atmospheric surface layer at the BAO site. The measurements were taken using a meteorological ultrasonic complex. The measurements are based on the change in the time delay of ultrasonic waves in the air with different temperatures [35]. The complex is mounted on the Large Solar Vacuum Telescope near the primary mirror of the telescope at height 35 m above the ground, as shown in Figure 11. This complex is supplemented with the same sonic measurements of turbulent characteristics near the ground (at a height of 5 m). Thus, the anemometers make it possible to measure both turbulent characteristics, including fluctuations in the air refractive index at the height of the primary mirror and vertical gradients of meteorological characteristics in the atmospheric layer 5-35 m.  
Figure 10: Seeing variations at the BAO site (8 August 2022). The blue line corresponds to changes in averaged seeing values. The fill shows the standard deviations of seeing. The atmospheric surface layer is a \"laboratory\" in which the relationships between the mean parameters and microturbulent characteristics of the atmosphere may be determined or clarified.