## 2 Materials and Methods
### Turbulence Clearance
#### 2.2.1 Background  
Turbulence is classified as light, moderate, severe, and extreme depending on the existing wind intensity and changes in the aircraft's speed, in the normal acceleration variation, or in the load factor. Nevertheless, throughout this study, atmospheric turbulence classified as extreme turbulence is omitted, as aircraft operations over this type of turbulence are not possible for safety reasons and the fact that these turbulences occur in extreme cases, such as severe thunderstorms or cumulonimbus formation. Then, the mountain wave intensity can be related to the wind component perpendicular to the mountain range; for example, if the mountain is oriented from east to west, the normal wind component would be either from north or south. For mountain waves to form, the normal wind speed must be higher than a value between 15 and 25 kt, depending on the type of mountain. Once this value is reached, the intensity of the wave depends on the wind speed at the mountain peak and the pressure difference between the peak \begin{table}
\begin{tabular}{c c c c c c c c c c c c c c c} \hline \hline
**Wind Speed [kt]** & 10 & 15 & 20 & 25 & 30 & 35 & 40 & 45 & 50 & 55 & 60 & 65 & 70 & 75 & 80 \\ \hline
**Altimeter Error [ft]** & 20 & 33 & 53 & 80 & 114 & 154 & 201 & 255 & 315 & 382 & 455 & 535 & 621 & 713 & 812 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Altimeter error according to wind speed. and the leeward valley. Thus, the wave intensity can be classified according to the wind that is perpendicular to the mountain range at an altitude equivalent to 700 hPa pressure, resulting in the following classification [39; 40]:  
* Light mountain waves are considered to occur when the normal wind speed is less than 25 kt. * Moderate mountain waves occur when the normal wind speed varies between 25 and 45 kt. * Severe mountain waves are formed with winds greater than 45 kt. These mountain waves generate vertical upward and downward movements, also known as the vertical velocity of mountain waves. In this way, each type of wave corresponds to a range of vertical velocities [39]:  
* Light-intensity waves have upward/downward movements with vertical velocities from 900 to 2700 ft/min (9-27 kt). * Moderate waves have vertical velocities from 2700 to 5400 ft/min (27-53 kt). * Severe waves range in vertical air currents from 5400 to 10,800 ft/min (53-107 kt). On the other hand, turbulence generated by mountain waves causes variations in the aircraft load factor. Depending on the turbulence intensity, these perceived variations are as follows [39; 40; 41; 42]:  
* For light turbulence, the load factor may fluctuate between 0.05 and 0.2 g.
* In moderate turbulence, the load factor varies from 0.2 to 0.5 g.
* In severe turbulence, the load factor variation ranges from 0.5 to 1.5 g.  
Another concept to emphasize is the effective gust velocity, U\({}_{\text{e}}\), which establishes the buffeting intensity as a function of the overloads acting on the aircraft, depending not only on the magnitude of the gust but also on the aircraft characteristics [39]. Each turbulence intensity (light, moderate, severe) has a range of effective gust velocities associated with it [42]:  
* Light turbulence is considered to occur when the effective gust velocity is between 5 and 19 ft/s (3-12 kt). * Moderate turbulence gives rise to an effective gust velocity between 20 and 35 ft/s (12-21 kt). * Severe turbulence reaches up to 49 ft/s (30 kt). The derived gust velocity, U\({}_{\text{de}}\), is established as the true variation in the aircraft's vertical speed due to the wind gusts produced by the upward and downward movements of the mountain waves. The derived gust velocity is defined assuming sinusoidal variations in the effective gust velocity and is approximately 60% greater than the effective gust velocity [39]. Table 3, whose data have been compiled from the information mentioned throughout this section, shows the characteristic values for each type of mountain wave according to its turbulence intensity [39; 40; 41; 42; 43].