Based on post-processing of measurements of vertical profiles of the wind velocity vector with an AV4000 minisodar in the boundary layer of the atmosphere at altitudes of 5–200 m, the thin structure of diurnal variations of a change of wind direction with altitude, that is, of the vertical wind veer, has been analyzed. The vertical wind veer, caused by many factors, including the advection force, the friction force, the Coriolis force, and the pressure gradient, is an important characteristic, because it is required to construct atmospheric models and to estimate the wind energy, pollution transport, and fatigue loading on high-rise buildings, bridges, and wind turbines. In the present work, the diurnal behavior of the angle of tuning of the horizontal wind velocity is analyzed with the vertical resolution Δz = 5 m and 10-minute time averaging.
In the present work, the kinetic energy of wind outliers taken to mean wind velocity values exceeding a preset value and including wind gusts are compared with the mean wind kinetic energy component retrieved from minisodar measurements using the robust parametric algorithm proposed by the authors. Allowance for the contribution of the wind outliers in the parametric estimates of the wind kinetic energy enables its fine structure to be determined and its effect on light flying objects, high-rise buildings, bridges to be estimated and the energy potentials of wind turbines to be evaluated.
The present work deals with the problem of constructing nonparametric mathematical models for interpretation of results of acoustic sounding of the atmosphere in the presence of outliers in experimental data. It is shown that the proposed adaptive nonparametric regression estimates are preferable compared to a number of the known robust parametric and nonparametric estimates. These mathematical models can also be recommended for processing of laser sensing data.
In this work, the influence of the averaging periods in the interval 1–30 min on the values and standard deviations of the wind vector components retrieved by post-processing of a big volume of minisodar data is considered. It is shown that in the 5–200 m altitude range, 10- and 30-min averaged horizontal wind vector components differ insignificantly, which has allowed us to recommend the 10-min averaging period as optimal one. The coefficients of conversion of the wind vector components with 1-, 5-, and 30-min averaging periods to the 10-min averaging periods are presented.
In the report, bootstrap procedures for processing of physics experimental data are proposed to solve semi-nonparametric problems. An algorithm for constructing a robust nonparametric generator of random variables is suggested and subsequently implemented in bootstrap procedures. The semi-nonparametric bootstrap procedures are used to process minisodar measurements of wind velocity components in the atmospheric boundary layer.
A method of determining semiparametric robust maximum likelihood estimates for a family of the Tukey distributions is suggested. The method can be used to obtain robust estimates of data comprising not only major, but also minor outliers. It is shown that these estimates converge to the maximum likelihood estimates of semiparametric problems when the fraction and distribution of outliers are unknown. The estimates have been used to process data of minisodar measurements of vertical profiles of the wind velocity components in the ABL comprising a significant fraction of both major and minor outliers. The high efficiency of the suggested estimates is shown on particular examples.
Statistical analysis of minisodar measurements of vertical profiles of the first four moments of wind velocity components in the 5–200 meter atmospheric layer shows that this problem belongs to a class of robust nonparametric problems of mathematical statistics. In the report, a new consecutive nonparametric pendular truncation algorithm is suggested for processing of minisodar measurements of wind velocity components to detect and to select anomalous observations in a data sample. The first four moments of wind velocity components are given, and their comparison with the moments obtained using standard methods of minisodar data processing is performed.
Statistical analysis of sodar measurements of wind velocity components in the atmospheric boundary layer (ABL) shows that data samples consist of nonuniform observations with unknown distributions. In the report, a modified nonparametric pendular truncation method implemented in a modified pendular truncation algorithm (MPTA) is suggested that allows one not only to detect, but also to select anomalous observations in minisodar data samples. The MPTA is tested on model examples. Based on the MPTA, sodar measurements of three wind velocity components in the ABL are censored, and their correlation coefficients and autocorrelation and structure functions are calculated. The calculated functions are compared with classical sample estimates.
KEYWORDS: Statistical analysis, Data processing, Data modeling, Wind measurement, Atmospheric optics, Acoustics, Signal processing, Monte Carlo methods, Statistical modeling, Doppler effect
A method of robust nonparametric estimations of wind velocity functionals and their confidence intervals is suggested in the report that allows the estimations to be adapted depending on the initial functional distribution and outliers. It is shown that standard methods of data processing lead to considerable shift of location and low efficiency of the estimations in comparison with the nonparametric estimations of the weighed maximum likelihood method.
Since the late 70s, Doppler sodars have been widely used to study the statistical characteristics of wind velocity field in the atmospheric boundary layer and to analyze their dynamics. However, the distribution functions of the wind velocity components are asymmetric with the presence of outliers, which significantly reduces the efficiency of application of the classical parametric methods of statistics. In the report, an algorithm is suggested for nonparametric robust estimations of the first four moments of wind velocity components and their confidence intervals from minisodar measurements in the atmospheric boundary layer.
The application of robust methods of statistics to processing of data of minisodar measurements of vertical profiles of three wind velocity components at altitudes 5–200 m is considered in the report. The statistical characteristics of three wind velocity components obtained using nonparametric methods based on the weighted maximum likelihood method and classical methods are analyzed. Results of minisodar data processing showed that the standard methods of processing lead to considerable bias and low efficiency of estimations in comparison with the nonparametric WMLM estimations.
In the report the spatiotemporal dynamics of three components of wind velocity vector retrieved from Doppler minisodar measurements in the atmospheric boundary layer is analyzed. Robust nonparametric methods of data processing based on the weighed maximum likelihood method (WMLM) are used for analysis. It is demonstrated that the efficiency (mean square error, MSE) of the adaptive estimates of the parameters of wind velocity components measured by the sodar based on the WMLM is much higher that the efficiency of the classical parametric estimates based on the LSM.
In this report the identification problem of laser and acoustic sounding of the atmosphere is considered in the presence of outliers in experimental data. The efficiency of estimates of the regression by the weighed method of maximum likelihood is investigated. Expressions for the efficiency of estimates are derived. It is demonstrated that the estimates of the regression by the weighed maximum likelihood method are more efficient in comparison with a number of well-known robust estimates for the examined outlier distributions, both symmetric and asymmetric.
The problem of testing the hypothesis H0: θ = θ0 against the alternative hypothesis H1:θl=θ0+▵(√N)-1 is examined for the Shurygin noise model, where θ =T(Fθ) is an unknown parameter. In the present report, a class of
criteria robust in the sense of the significance value and power density function is considered for parametric and
nonparametric problem formulation on statistics of the form SN=√N((θN-θ)/(√V(θN))), where V(θN) is the θN variance and
θN =T(FN) is the robust parametric or nonparametric estimate of the parameter θ =T(Fθ) obtained by the weighted
maximum likelihood method.
In the present study, a class of algorithms of robust regression estimates is synthesized by the weighted maximum
likelihood method based on a priori information.
In the present study, a class of nonparametric robust estimates of the shift and scale parameters (μ, S) of the form (please see manuscript for formula) is synthesized by the weighted maximum likelihood method based on parametric density estimates, where (see manuscript for formula) are the Walsh half-sums, K(u) is the kernel function, and W(u) is the weighting function: (see formula in manuscript.) The radicalness parameter I determines the weighting functions W(zij) executing the process of soft truncation of the estimates depending on a priori information on outliers: the estimates converge to maximum likelihood estimates (MLE) at l = 1 and to radical estimates at l = 0.5. The adaptive estimates converge to radical ones. They belong to the class of nonparametric estimates of implicit parameters, and their
study is performed based on the generalized M-estimates.
An analysis of the radicalness criteria and robust estimation algorithms allows us to conclude that all these estimates can
be derived based on the weighted maximum likelihood method (WMLM) with the estimation function of the form (see manuscript for formula). In the present study, robust estimates of shifts and scales are synthesized in the class of Student's global supermodels and approximately normal distributions depending on the radicalness parameter l. Algorithms of adaptive robust estimates are suggested. They allow estimates to be adapted to distribution types and local deviations.
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