# Observation and Numerical Simulation of a Windshear Case at an Airport in the Qinghai-Tibet Plateau
## 2 Materials and Methods
### The Research Method: Setup of the Numerical Model and Calculation of EDR  
The objective of the numerical simulation is to study the feasibility of reproducing the main features of the wind in this windshear case, namely, the easterly jet, the intrusion of  
Figure 3: A closer look at the time–height cross-section of the wind (**a**) from DWL with the height to be above ground level, and the time series of the wind at the jet core as well as around the jet (**b**). The instances with higher wind speeds are highlighted in arrows in (**b**).  
westerly wind, the EDR distribution with time and height, and the wind speed of the jet core and the pulsation of the wind speeds in the jet. Apart from the changes in the synoptic weather pattern, such features are believed to be closely associated with the complex terrain in the region. In order to capture the terrain features, a numerical weather prediction model, namely, the Regional Atmospheric Modeling System (RAMS) version 6.3 with a high horizontal resolution (40 m), has been adopted for the simulation. The setup of the model is similar to that reported by [PERSON] et al. (2021) [4].  
The terrain considered in the simulation is shown in Figure 4. As in the previous study, five nested domains have been used. The outermost domain uses the reanalysis data from the National Centers for Environmental Prediction. It is nested downward and the innermost domain (G5) is shown in Figure 4c around the airport area. The physical schemes used in the model are the same as those in [PERSON] et al. (2021) [4].  
Figure 4: _Cont._  
For the turbulence parameterization scheme, as the first attempt, the [PERSON] (1963) [16] scheme was used in the first two nested domains, and the [PERSON] (1980) [17] scheme is used in the last three domains. The sensitivity to the choice of turbulence parameterization scheme would be discussed later.  
The wind field data from numerical simulations with a rectangular grid can be utilized to calculate EDR by using the explicit filtering and reconstruction in turbulence parameterization ([PERSON] et al., 2005) [18]. In this method, Subfilter scales can be divided into resolvable subfilter scales (RSFS) and subgrid scales (SGS). We only calculated RSFS part since it accounts for most of the energy. We did zero-order reconstruction in this study so we have \(\widetilde{\mathbf{u}_{i}^{*}}=\widetilde{\widetilde{\mathbf{u}}_{i}}\). Here, the overline represents the filter, the tilde represents discretization, and \(\widetilde{\widetilde{\mathbf{u}}_{i}}\) is the variable from the model.  
The RSFS turbulent kinetic energy (TKE) is calculated by  
\[\text{TKE}=\frac{\mathbf{1}}{2}\left(\widetilde{\mathbf{u}_{i}^{*}\widetilde{\mathbf{u}_{ i}^{*}}}-\widetilde{\widetilde{\mathbf{u}}_{i}^{*}\widetilde{\mathbf{u}_{i}^{*}}}\right)\]  
Assuming the scale of turbulence is included in inertial subrange, the EDR can be expressed as follows:  
\[\mathbf{\varepsilon^{1/3}}=\left(\text{TKE}^{3/2}/\mathbf{L}\right)^{1/3}\]  
Here, we used Butterworth filter horizontally and 1-2-1 filter ([PERSON] et al., 2005) [18] vertically. \(\mathbf{L}=\left(\Lambda\Delta\mathbf{x}\Delta\mathbf{y}\Delta\mathbf{z}\right)^{1/3}\) is the scale of the turbulence, \(\Delta\mathbf{x}\), \(\Delta\mathbf{y}\) and \(\Delta\mathbf{z}\) are grid spacings, and the \(\lambda\) can be derived based on the cutoff wavelength of the filter.  
Basically, the same simulation setup as in [PERSON] et al. (2021) [4] is adopted here. But this is the first time that this simulation setup is applied outside Hong Kong, especially in an area of complex terrain as in the Plateau. Moreover, the new formulation of the calculation of EDR is adopted for this model setup for the first time. These are the novel features of the present paper.