## Wind Gust Definition  
The wind gust speed, \(U_{max}\), is defined as a short-duration maximum of the horizontal wind speed during a longer sampling period (\(T\)). Mathematically, it is expressed as the maximum of the moving averages with a moving average window length equal to the gust duration (\(t_{g}\)). Traditionally in meteorological applications, the gusts are measured and the wind forecasts issued using a gust duration \(t_{g}=3\) s and a sample length \(T=10\) min [29]. However, sometimes, other durations are used, as well; for example, until the early 2000s wind gusts at the Automated Surface Observing System (ASOS) network of the U.S. National Weather Service (NWS) were based on hourly (\(T=1\) h) records with \(t_{g}=5\) s [41; 42; 43]. Originally, the definition of a wind gust had been based on the response characteristics of old anemometers, whose response times were about 2-5 s [44]. The ratio of the wind gust speed \(U_{max}\) to the mean horizontal wind speed \(U\) is called the gust factor:  
\[G=\frac{U_{max}}{U}. \tag{1}\]  
Thus, \(G\) is proportional to the inverse of the mean wind speed. In practice, the measured \(G\) values show a large variability at low mean wind speeds, but at strong wind speeds (neutral conditions), \(G\) typically reaches a constant value characteristic of the measurement site. The mean \(G\) depends on various environmental factors, such as the measurement height, surface roughness, atmospheric static stability (more in Section 7) and on the temporal scales used in the gust definition, the gust duration \(t_{g}\) and the sample period \(T\)[38; 45; 46]. Another measure of gustiness is the peak factor:  
\[g_{x}=\frac{U_{max}-U}{\sigma_{u}}, \tag{2}\]  
which is the deviation of the wind gust speed from the mean normalized by the standard deviation of the horizontal wind speed (\(\sigma_{u}\)). Because of the normalization, the peak factor can be considered to be invariant of environmental conditions contrary to the gust factor (Equation (1)), but instead, it is, above all, a function of the gust time scales, \(t_{g}\) and \(T\). Moreover, the peak factor can be derived from theoretical considerations, as shown below in this section. The peak factor is a useful tool in scaling wind speed maxima from a low-response system to provide wind gust measurements comparable with weather station measurements [39]. Peak factors can also be used for comparison of spatial and temporal scales [38]. The peak factor can be estimated from theoretical considerations. It is based on a statistical approach to estimate the maximum value in the time series when the mean statistical properties (\(U\), \(\sigma_{u}\), power spectrum) of the wind speed are known. This statistical theory of maxima was first proposed by [PERSON] (1944, 1945) and is therefore called the Rice theory [47; 48]. Since then, the theory has been applied in various studies with small modifications. [PERSON] (1964) applied the Rice theory to wind speed measurements ([PERSON] et al., 1991). [PERSON] (1979) tested the method against wind tunnel measurements and evaluated the effect of filtering on the gust factor to estimate loads on structures ([PERSON] et al., 1991), [PERSON] (1987) used the method to derive a parameterization for NWP models ([PERSON], 1964). His approach is still used in the operational Integrated Forecasting System (IFS) of the European Centre for Medium-Range Weather Forecasts (ECMWF) with a small modification to account for convective gusts ([PERSON] et al., 1991). [PERSON] et al. (1991) compared the method to the Gumbel theory of extremes and suggested that these theories are equivalent ([PERSON] et al., 1991), although this is not exactly true. [PERSON] and [PERSON] (2008) took one step further and combined the Rice theory to include Turbulence Kinetic Energy (TKE) from a weather model when it is available ([PERSON] et al., 1991). In ([PERSON] et al., 1991), the theory was validated against observations from a 100 m-high meteorological mast. [PERSON] et al.