# Influence of Atmospheric Flow Structure on Optical Turbulence Characteristics
## 2 Used Methods
Based on meteorological data and topography within the BAO region, we used parameterization schemes for the configuration of the WRF model, as shown in Table 1.  
We should note that the WRF model separately parameterizes the processes in the atmospheric boundary layer and the so-called surface layer. The surface layer exhibits the most dramatic temporal and height variations in mean meteorological characteristics and turbulent parameters, including \(\mathbb{C}_{n}^{2}\)[28; 29]. The choice of the Yonsei University parameterization scheme for the BAO and SSO region was confirmed by recent studies on atmospheric processes [30]. Within the middle- and high-latitude regions of China, as well as the Baikal region, various parameterization schemes were investigated, including the Medium-Range Forecast scheme (MRF), the Mellor-Yamada Nakanishi and Niino Level 2.5 scheme (MYN), the Bougeault and Lacarrere scheme (BLS), the Yonsei University scheme (YSU), the Asymmetric Convective Model Version 2 scheme (ACM), the Grenier-Bretherton-McCaa scheme (GBM) and the University of Washington moist turbulence scheme (UWS). [PERSON] et al. estimated the performances of these parameterization schemes and the recovery accuracy of wind speeds at heights of 10 and 100 m, the surface air temperature at 2 m and surface atmospheric pressure. The largest correlation coefficients and smallest root mean square deviations between the measured and simulated wind speeds (as well as air temperatures) corresponded with the MRF and YSU schemes. In our study, we performed about 240 h of simulations above the BAO and SSO. Due to the need for diagnostics and forecasting of atmospheric characteristics that determine the quality of solar images, we selected only daytime hours. In the WRF model, we applied a combination of the YSU and revised MM5 parametrization schemes. Vertical diffusion of parameter \(C\) is described by the equation:  
\[\frac{\partial C}{\partial t}=\frac{\partial}{\partial z}\left(K\left(\frac{ \partial C}{\partial z}-\gamma\right)-\overline{w^{\prime}c^{\prime}}\left( \frac{z}{h_{ABL}}\right)^{3}\right), \tag{1}\]  
where \(K\) is the turbulent diffusion coefficient, \(z\) is the height, \(h_{ABL}\) is the height of the atmospheric boundary layer (ABL) and \(t\) is time. The YSU scheme determines the ABL height to be where the bulk Richardson number exceeds a threshold value of 0. The first term on the right-hand side of Equation (1) describes vertical nonlocal air mixing by convective eddies. \(\gamma\) is a counter-gradient transport term that incorporates the contribution of convective eddies to the total flux. \(\overline{w^{\prime}c^{\prime}}\) is the vertical turbulent flux at the inversion layer. The turbulent diffusion coefficient is calculated from:  
\[K=kw_{s}z\left(1-\frac{z}{h_{ABL}}\right)^{p}, \tag{2}\]  
\[w_{s}=u_{s}/\phi_{m}, \tag{3}\] \begin{table}
\begin{tabular}{c c} \hline \hline
**Physical Schemes of Parametrization** & **Description** \\ \hline Yonsei University scheme & Atmospheric boundary layer \\ MMS-similarity scheme & Surface layer \\ Kain–Fritsch scheme & Cloudiness \\ Simple scheme based on Dudhia & Short-wave radiation \\ Rapid Radiative Transfer Model scheme & Long-wave radiation \\ Thompson scheme & Microphysical processes in clouds \\ RUC scheme & Land surface model \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Parameterization schemes in the WRF model. where \(p=2\), \(k\) is the von Karman constant, \(w_{s}\) is the mixed-layer velocity scale, \(u_{s}\) is the friction velocity and \(\phi_{m}\) is the non-dimensional function described by [PERSON] et al. [31]. This model uses a parabolic \(K\)-profile in an unstable mixed layer with the addition of an explicit term to treat the entrainment layer at the top of the ABL.