## 1 Introduction  
In the design phase of instrument flight procedures, among other aspects, the minimum flight altitude of each segment should be stated. For this purpose, the designer applies a minimum obstacle clearance (MOC) over the obstacles. When mountainous areas are foreseen in the procedure planning and design, the ICAO establishes the addition of a clearance to compensate for the effects of strong winds. Nevertheless, the ICAO does not determine the precise value to be added, specifying only that it may be up to 100 per cent of the MOC. Since this value is not clearly defined, designers usually apply this maximum of 100% directly, which in many cases can lead to operational constraints. These operational constraints are due to the fact that, by applying a higher MOC, an aircraft will fly at higher altitudes, leading to pronounced descents in the approach and steep ascents in take-off, or resulting in longer distances to comply with the slopes, which translates in any case into a lower flight efficiency. This lower efficiency involves a higher fuel consumption, with its economic and environmental consequences, as well as airspace limitations that may lead to the inability to implement the procedure or make it unnecessarily complex. Furthermore, the ICAO specifies that only the necessary airspace should be used, so any other use of airspace exceeding the need would be inadequate. In addition, raising flight altitudes unnecessarily could also result in unstable approaches, which increases the runway excursion probability during landing, which is an unacceptable consequence. Hence, the need to establish a way to calculate the additional margin for mountainous terrain has prompted the analysis presented in this paper, in order to avoid applying an excessive clearance while maintaining safety. Currently, the early detection of turbulence remains a challenge of which numerous studies have been carried out. Some research tries to identify turbulence areas from the eddy dissipation rate (EDR) or other turbulence indicators, as well as using detection and simulation programmes [1; 2; 3; 4; 5; 6]. Additionally, much research has been based on the observation of these turbulences and on detecting the conditions under which they occur [7; 8; 9; 10; 11]. Turbulences caused by strong winds are very common on mountainous terrain due to the formation of mountain waves that are generated when the wind speed reaches a certain value above 15-20 kt and, at the same time, has a normal direction to the orographic system. Under these conditions, vertical upward and downward waves are generated by pressure differences between hills and valleys, with the winds on the leeward side being particularly severe. These effects have been studied since the beginning of aviation because of the large number of accidents and incidents that have occurred throughout history as a result of the loss of aircraft control [12; 13; 14]. Due to the importance of mountain waves in flights over these areas, there are many articles about mountain wave formation and the types of waves that exist, as well as their characteristics, parameters, and consequences [15; 16; 17; 18]. When an aircraft is flying towards its destination airport, at some point, it will begin to descend and, in many cases, may fly over mountainous areas at minimum flight altitudes, since the objective is to descend to land. Thus, a flight procedure designer faces the challenge of keeping an adequate clearance over obstacles while ensuring that this margin is not excessive, with the consideration that the aircraft should descend with appropriate gradients and flight regimes to maintain safety. Therefore, a methodology for calculating this additional clearance over mountainous terrains must be provided. When the aircraft is over a mountainous terrain, it usually encounters winds with a certain intensity, which can produce two effects on the aircraft: erroneous information from the barometric altimeter and, on the other hand, a loss of altitude due to the effect of turbulence.