## 1 Introduction  
Knowledge of the flow disturbances in the boundary layer of the atmosphere is very important for the design of wind turbines, the landing and takeoff of airplanes, the design of bridges, etc. The kinetic energy of air mass motion in the ABL \(E_{\Sigma}\) is the sum of two components: the kinetic energy of the ordered motion \(E_{M}\), associated with the mean wind velocity \(\overline{V}\), and the turbulence kinetic energy \(E_{T}\), associated with the wind velocity variance \(\sigma^{2}\). The vector of the wind velocity components \(V(x,t,z)=\left(V_{x},V_{y},V_{z}\right)\) forms the non-stationary random process defined by different \(n\)-dimensional distributions depending on a great number of factors. It is clear that to construct a mathematical model of the wind velocity in the ABL based on these \(n\)-dimensional distributions is extremely difficult if, indeed, it is possible. Usually simpler problems with fixed stable factors (locality, underlying surface, time, altitude) are considered for which particular mathematical models are developed and solutions are obtained. For a fixed altitude, consider the quasi-stationary period \(T\) during which the wind velocity \(V\) with distribution \(F(\zeta,\overset{\rightarrow}{\theta})\) is represented as a superposition of the stationary process \(V_{0}\) characterizing the stationary motion of air masses with the prior distribution \(G(\zeta,\overset{\rightarrow}{\theta})\) and the small outlier fraction \(\varepsilon\) with the velocity \(V_{\text{out}}\) and the distribution \(H(\zeta)\). By the outliers, we mean any wind velocities, including wind gusts, the distribution \(H(\zeta)\) of which deviates from the main wind velocity distribution \(G(\zeta,\overset{\rightarrow}{\theta})\) during the period \(T\)[1; 2; 3]. For this model, the kinetic wind energy \(E\) in the ABL is the sum of two components \(E=E_{0}+E_{\text{out}}\), where \(E_{0}\) is the kinetic energy of the reference stationary process, and \(E_{\text{out}}\) is the kinetic energy of the outliers. The probabilistic problem formulation is defined by the prior information on the basic types of three distributions \(F(\zeta,\overset{\rightarrow}{\theta})\), \(G(\zeta,\overset{\rightarrow}{\theta})\), and \(H(\zeta,\overset{\rightarrow}{\theta})\). The kinetic energy of the motion of air masses includes both the prior distribution \(G(\zeta,\overset{\rightarrow}{\theta})\) that characterizes the stationary motion used to predict the wind energy potential of wind turbines, and the distribution \(H(\zeta,\overset{\rightarrow}{\theta})\) that characterizes the kinetic energy of wind outliers, used to estimate the effect of wind outliers on objects in the ABL, for example, light drones, bridges, and high-rise buildings. The appearance of Doppler acoustic radars (sodars) makes it possible to obtain information on the altitude profiles of wind velocity vector components with high spatial (up to several meters) and temporal resolution [4]. However, usually the outliers are detected and then eliminated from raw wind field data [5; 6]. Thus, in [7], various outlier detection and elimination methods were analyzed, and the conclusion was drawn that in the previous works, outliers were simply removed and considered as missing data. In [8], a visual inspection method was used to eliminate the outliers. In this case, the information on the outliers and their contribution to the kinetic wind energy in the ABL was completely lost. In the present work, we succeeded in analyzing the spatiotemporal dynamics of kinetic wind energy with and without allowance being made for the kinetic energy of outliers. We first represented the distribution \(F(\zeta,\overset{\rightarrow}{\theta})\) as a mixture of distributions \(G(\zeta,\overset{\rightarrow}{\theta})\) and \(H(\zeta)\); we separated the contributions of the mean kinetic energy and the kinetic energy of the outliers, and estimated the latter using robust parametric, semiparametric, and semi-nonparametric algorithms developed by us.