## 3 Robust Parametric Algorithms and Their Application for Estimating Kinetic Wind Energy
The minisodar provided one vertical signal profile in all three channels every 4 s, which was used to calculate the wind vector components \(V_{x}(z,t)\), \(V_{y}(z,t)\), and \(V_{z}(z,t)\), and their variances, \(\sigma_{\tau}^{2}(z,t)\), \(\sigma_{y}^{2}(z,t)\), and \(\sigma_{z}^{2}(z,t)\) from the well-known formulas for the Doppler frequency shifts. To investigate their dynamics, we sampled and processed 150 vertical profiles recorded from the beginning of each hour from 00:00 till 23:00 to obtain 10 min averages and to estimate the total kinetic wind energy \(E(z,t)\) and its components caused by the stationary air movement \(E_{0}(z,t)\) and the wind outliers \(E_{\text{out}}(z,t)\). Continuous minisodar measurements were taken in the vicinity of Santa Clarita, CA, USA (34\({}^{\circ}\)23\({}^{\circ}\)29.9904\({}^{\prime\prime}\) N, 118\({}^{\circ}\)32\({}^{\prime}\)33.3096\({}^{\prime\prime}\) W) over a flat underlying surface without tall vegetation [25] from 10 to 17 September 2003. During the period of the measurements, the weather was dry, warm and sunny. Here, we postprocessed 10-min averaged minisodar measurements that started on 10 September at 12:00 LT, and at every hour from 00:00 till 23:00 on 16 September. The temperature during the period of measurements on 10 September was 23 \({}^{\circ}\)C, and the mean wind speed was 3.57 m/s. The maximum daytime temperature on 16 September was 25.7 \({}^{\circ}\)C, and the minimum temperature at night was 16 \({}^{\circ}\)C. The average wind velocity was 9.1 m/s. From Figure 2, it can be seen that without the contribution of the kinetic outlier energy, the curve is quite smooth, whereas with an allowance made for this contribution, its layered structure can clearly be seen. It should also be noted that the atmospheric layers with strong turbulence were also pointed out by [PERSON] et al. in [26] and [PERSON] et al. in [27], where the maximum changes of the turbulence layer strengths were observed in the lower layer of the atmosphere at altitudes up to 70 m, and the diurnal variations of their altitudes were also indicated. The blue curve in Figure 2 also shows that local outlier layers were clearly manifested in the vertical profile of the total kinetic energy starting from an altitude of 50 m; moreover, the thickness of these layers remained practically unchanged to altitudes of 150 m. Above 150 m, the curves synchronously changed with altitude and had kinetic energy maxima at \(z=175\) m. This suggests that new robust algorithms [14] for the detection and selection of outliers of various origins in the observation samples at different levels of a priori statistical uncertainty are especially important for altitude ranges in which the kinetic outlier energy is significant. For this reason, of considerable interest are the physical reasons for the appearance of these features in the kinetic outlier energy. Figure 2b shows an example of the altitude profiles of the turbulence kinetic energy component \(E_{\rm T}\) without (the orange curve) and with allowance for the contribution of the kinetic outlier energy (the blue curve). The comparison of Figure 2a,b demonstrates that, in this situation, the altitude behavior of the orange and blue curves differs quantitatively only in the layer below 25 m; above this altitude, they qualitatively agree. This suggests that at these altitudes, the predominant contribution to the total kinetic wind energy comes from the turbulence kinetic energy component. In Figure 2a,b, the fairly smooth (orange) curves of the parametric estimates of the vertical profiles of the kinetic energy of stationary air motion, disregarding the contribution of the kinetic outlier energy, can be seen. Taking into account the contribution of the kinetic energy of outliers, the blue curves depict the fine structure of the altitude dependence of the total kinetic energy. This testifies that, in this case, attention should be focused on the kinetic energy of the outliers.