## 5 Airborne Measurements  
### Research Aircraft  
Research aircraft, such as the one in Figure 7, have been used for turbulence measurements already for decades, but only recently have wind gusts been assessed based on this type of measurement [38]. [PERSON] et al. (2016) investigated the possibilities of estimating wind gusts from turbulence measurements taken on board a research aircraft under the assumption that the gusts can be produced by many different factors, for instance turbulent fluctuations or intermittency. Research aircraft measure over a fairly long distance during a short time interval. Therefore, the definition of a gust can no longer be based on temporal, but instead on spatial averaging. To derive the length scales \(x_{g}\) and \(X\) corresponding to the time scales \(t_{g}\) and \(T\) (Section 2), four different methods were tested. One of the methods was based on [PERSON]'s hypothesis of frozen turbulence [90], which assumes that a stationary wind field is advected past a fixed point by the mean wind speed \(U\). Then, the relationship between the distance and the time becomes \(x=Ut\). Another method used by [38] to convert between the scales is based on the assumption that the sampling frequencies represent the same scales of motion. If the sampling frequency of the five-hole probe on board the research aircraft was \(f_{o,a}\) and the sampling frequency at a fixed point \(f_{o,p}\), then with a ground speed \(V_{a}\) of the aircraft, the length scale becomes \(x=\frac{f_{o,p}}{f_{o,a}}V_{c}t\). The third method used by [38] to derive the length scales was just to assume that the ratio of \(t_{g}\) and \(T\) is equal to the ratio of \(x_{g}\) and \(X\). [PERSON] et al. (2016) [38] further developed a new method to convert between temporal and spatial scales. It is based on the comparison of median peak factors from a research aircraft and from a meteorological mast. Although the datasets used by [38] were from different locations (research aircraft measurements from the marine Arctic and the meteorological mast measurements from over flat grassland terrain in Denmark) and periods (spring 1998 and full year 2010, respectively), it was possible to apply the method, because it is assumed that statistically, the behavior of the time series in an  
Figure 7: Polar 5 research aircraft of Alfred Wegener Institute, Germany. ensemble of samples does not depend on location or on the period, if the conditions are homogeneous and stationary (Section 2). To compare the statistical behavior of peak factors from both data sources, median peak factors were computed with different combinations of \([x_{g},X]\) and \([t_{g},T]\) from the research aircraft data and from the meteorological mast measurements, denoted here as \(g_{x}(x_{g},X)\) and \(g_{x}(t_{g},T)\), respectively. A fixed range of temporal averages was set for \(t_{g}\) from 1-10 s and for \(T\) from 5-30 min. Corresponding ranges of the length scales \(x_{g}\) and \(X\) that minimize the difference between \(g_{x}(x_{g},X)\) and \(g_{x}(t_{g},T)\) in the least squared sense were then determined. One of the resulting fitted field pairs is shown in Figure 8. From this, it is possible to find the length scale counterparts for any pair of gust time scales. For example, in Figure 8, the time scales \(t_{g}=3\) s and \(T=10\) min correspond to length scales \(x_{g}=15.6\) m and \(X=4.7\) km. Sensitivity tests showed that by choosing data from different heights of the meteorological mast, the gust length \(x_{g}\) increases with increasing mast height, whereas the sample length \(X\) decreases with height. The first result was an expected one, since the integral length scale of the horizontal wind speed typically increases with height [91]. However, in eddy covariance calculations, a longer sample length \(X\) is usually required at higher measurement heights in order to cover all the scales of turbulent motion contributing to the flux. Because of this discrepancy, [PERSON] et al.