# Automated Aviation Wind Nowcasting: Exploring Feature-Based Machine Learning Methods
## 3 Materials and Methods
### Methods
#### 3.2.2 Data Processing and Feature Creation  
After adjusting the time step, a mathematical approach encompassing standard statistical and entropy methods was employed for feature engineering, enabling the extraction of information, modification of existing features, and generation of new ones from the wind data to identify patterns and randomness for the subsequent stages of the study. Features represent the quantifiable attributes or characteristics of the observed phenomena, serving as the variables that support the model's decision-making or predictive capabilities. The process of feature engineering, which involves the generation of new features or modification of existing ones, encompasses a broad spectrum of transformations that can be applied to numerical data, such as mathematical approaches [28,29]. Consequently, 14 distinct features were derived, per sensor, totaling 56 features at a time resolution of two minutes. Statistical Methods  
The \(\overset{\rightarrow}{u}\) and \(\overset{\rightarrow}{v}\) wind components represent the west-to-east and south-to-north flows, respectively, and can be written as  
\[\overset{\rightarrow}{u}=\frac{\sum_{i=1}^{n}\left[-S_{i}\times\sin\left(D_{ i}\times\left(\frac{\pi}{180}\right)\right)\right]}{n} \tag{1}\]  
\[\overset{\rightarrow}{v}=\frac{\sum_{i=1}^{n}\left[-S_{i}\times\cos\left(D_{ i}\times\left(\frac{\pi}{180}\right)\right)\right]}{n} \tag{2}\]  
where \(D\) is the wind direction in degrees, \(S\) is the wind speed in m/s, and \(n\) is the number of samples in the 2 min timestep [30, 31, 32]. Mean wind speed (\(S\)) and direction (\(D\)):  
\[S=\frac{\sum_{i=1}^{n}(S_{i})}{n} \tag{3}\]  
\[D=\left(\arctan\left(\frac{\overset{\rightarrow}{u}}{\overset{\rightarrow}{ v}}\right)+\pi\right)\times\frac{180}{\pi} \tag{4}\]  
where \(\overset{\rightarrow}{u}\)_and_\(\overset{\rightarrow}{v}\) are the mean 2 min wind components in m/s [30, 31, 32]. The wind speed maximum value, corresponding to the wind gust [27] (\(maxS\)) and standard deviation (\(stdS\)), can be calculated with  
\[maxS=\max_{i=1}^{n}(S_{i}) \tag{5}\]  
\[stdS=\sqrt{\frac{\sum_{i=1}^{n}\left(S_{i}-S\right)^{2}}{n-1}} \tag{6}\]  
while the median (\(mdnS\)), if \(n\) is odd, is given by  
\[smdnS=S_{o\left(\frac{n+1}{2}\right)} \tag{7}\]  
and if \(n\) is even, it is defined as  
\[smdnS=\frac{\left(S_{o\left(\frac{n}{2}\right)}+S_{o\left(\frac{n}{2}+1\right) }\right)}{2} \tag{8}\]  
where \(S_{o}\) represents the wind speed values, in the interval, sorted from the lowest to the highest value [30, 31, 32]. Skewness (_skwS_) and kurtosis (_krtS_) provide insights into the shape and distribution, in addition to the symmetry and tail behavior of the wind data. \[sskwS=\frac{1}{n}{\sum_{i=1}^{n}}{\left(\frac{S_{i}-S}{\sqrt{\frac{\sum_{i=1}^{n} \left(S_{i}-S\right)^{2}}{n-1}}}\right)^{3}} \tag{9}\]  
\[krtS=\frac{1}{n}{\sum_{i=1}^{n}}{\left(\frac{S_{i}-S}{\sqrt{\frac{\sum_{i=1}^{ n}\left(S_{i}-S\right)^{2}}{n-1}}}\right)^{4}} \tag{10}\]  
Entropy Methods  
Shannon entropy (_SlmE_) measures the uncertainty or randomness of the data and can be calculated with  
\[\overset{\rightarrow}{v}=\frac{\sum_{i=1}^{n}\left[-S_{i}\times\cos\left(D_{ i}\times\left(\frac{\pi}{180}\right)\right)\right]}{n} \tag{2}\]0  
where P is the probability of occurrence, and S is the data values [33; 34; 35]. Sample entropy (_SplE_) is used to extract information about the complexity of the time-series data by quantifying the regularity and unpredictability of its fluctuations is given as  
\[\overset{\rightarrow}{v}=\frac{\sum_{i=1}^{n}\left[-S_{i}\times\cos\left(D_{ i}\times\left(\frac{\pi}{180}\right)\right)\right]}{n} \tag{2}\]1  
where \(m\) is the embedding dimension, A is the number of template vectors of length \(m+1\) that are similar, and B is the number of template vectors of length \(m\) that are similar [33; 35; 36].