Third- and fourth-order statistical moments of the turbulent fluctuations of wind velocity and temperature

1999 ◽  
Author(s):  
Alexey L. Afanas'ev ◽  
Viktor A. Banakh ◽  
Andrey P. Rostov
Keyword(s):  
Wind Velocity ◽  
Fourth Order ◽  
Statistical Moments ◽  
Turbulent Fluctuations

scholarly journals 3D Mueller Matrix Reconstruction of the Optical Anisotropy Parameters of Myocardial Histopathology Tissue Samples

2021 ◽  
Vol 9 ◽  
Author(s):  
Benjamin T. Hogan ◽  
Volodimyr A. Ushenko ◽  
Anastasia-Vira Syvokorovskaya ◽  
Alexander V. Dubolazov ◽  
Oleg Ya. Vanchulyak ◽  
...  
Keyword(s):  
Heart Disease ◽  
Fourth Order ◽  
Optical Anisotropy ◽  
Matrix Method ◽  
Mueller Matrix ◽  
Statistical Moments ◽  
Optical Data ◽  
Coronary Insufficiency ◽  
Matrix Reconstruction ◽  
Anisotropy Parameters

Diseases affecting myocardial tissues are currently a leading cause of death in developed nations. Fast and reliable techniques for analysing and understanding how tissues are affected by disease and respond to treatment are fundamental to combating the effects of heart disease. A 3D Mueller matrix method that reconstructs the linear and circular birefringence and dichroism parameters has been developed to image the biological structures in myocardial tissues. The required optical data is gathered using a Stokes polarimeter and then processed mathematically to recover the individual optical anisotropy parameters, expanding on existing 2D Mueller matrix implementations by combining with a digital holography approach. Changes in the different optical anisotropy parameters are rationalised with reference to the general tissue structure, such that the structures can be identified from the anisotropy distributions. The first to fourth order statistical moments characterising the distribution of the parameters of the optical anisotropy of the polycrystalline structure of the partially depolarising layer of tissues in different phase sections of their volumes are investigated and analysed. The third and fourth order statistical moments are found to be the most sensitive to changes in the phase and amplitude anisotropy. The possibility of forensic medical differentiation of death in cases of acute coronary insufficiency (ACI) and coronary heart disease (CHD) is considered as a diagnostic application. The optimal phase plane (θ∗=0.7rad) has been found, in which excellent differentiation accuracy is achieved ACI and CHD -Ac(ΔZ4(θ∗,ΦL,ΔL))=93.05%÷95.8%. A comparative analysis of the accuracy of the Mueller-matrix reconstruction of the parameters of the optical anisotropy of the myocardium in different phase planes (θ=0.9rad and θ=1.2rad), as well as the 2D Mueller-matrix reconstruction method was carried out. This work demonstrates that a 3D Mueller matrix method can be used to effectively analyse the optical anisotropy parameters of myocardial tissues with potential for definitive diagnostics in forensic medicine.

scholarly journals Low-Altitude Atmospheric Turbulence Sounding on the Basis of Unmanned Aerial Vehicle

2020 ◽  
Author(s):  
Alexander Shelekhov ◽  
Aleksey Afanasiev ◽  
Alexey Kobzev ◽  
Evgenia Shelekhova ◽  
Alexey Tel’minov ◽  
...  
Keyword(s):  
Time Series ◽  
Wind Velocity ◽  
Unmanned Aerial Vehicle ◽  
Weather Station ◽  
Velocity Fluctuations ◽  
Turbulent Fluctuations ◽  
Station Data ◽  
Weather Station Data ◽  
Aerial Vehicle ◽  
Turbulent Spectra

Based on the theory of turbulence, equations are derived for estimations of turbulent fluctuations of the longitudinal and transverse components of the wind velocity during ideal hovering of a quadcopter in a turbulent atmosphere. We present the results of experiments which were carried out on the territory of the Geophysical Observatory of Institute of Monitoring of Climatic and Ecological Systems, Siberian Branch, Russian Academy of Sciences, located in Tomsk Akademgorodok on the territory with complex orography, in a parkland zone with buildings of research institutes and motorways. Time series of turbulent fluctuations of the longitudinal and transverse components of wind velocity fluctuations were received with the use of an automated weather station, and time series of estimates of these components, from data of a DJI Phantom 4 Pro quadcopter during hovering. According to the automated weather station data, anisotropy was observed in one experiment during measurements in the atmosphere, but this phenomenon was not observed in the other experiment: the fluctuation spectra of all components of wind speed fluctuations coincide. The spectra of fluctuations of the longitudinal and transverse wind velocity components based on the automated weather station data and UAV telemetry are presented. The fluctuation spectra of these components for the automated weather station data and quadcopter generally coincide. The behavior of the spectra coincides with the spectrum which corresponds to Kolmogorov–Obukhov “–5/3” law within the inertial range. The turbulent spectra of the wind velocity fluctuations obtained with the use of the automatic weather station and with the unmanned aerial vehicle differ in the high-frequency spectral region.

scholarly journals Characterization of Boundary Layer Turbulent Processes by the Raman Lidar BASIL in the frame of HD(CP)<sup>2</sup>) Observational Prototype Experiment

2016 ◽  
Author(s):  
Paolo Di Girolamo ◽  
Marco Cacciani ◽  
Donato Summa ◽  
Andrea Scoccione ◽  
Benedetto De Rosa ◽  
...  
Keyword(s):  
Boundary Layer ◽  
Water Vapour ◽  
Temporal Resolution ◽  
Fourth Order ◽  
Temperature Fluctuations ◽  
Temperature Measurements ◽  
Order Moment ◽  
Mixing Ratio ◽  
Raman Lidar ◽  
Turbulent Fluctuations

Abstract. Measurements carried out by the University of BASILicata Raman lidar system (BASIL) are reported to demonstrate the capability of this instrument to characterize turbulent processes within the convective boundary layer (CBL). In order to resolve the vertical profiles of turbulent variables, high resolution water vapour and temperature measurements, with a temporal resolution of 10 s and a vertical resolution of 90 m and 30 m, respectively, are considered. Measurements of higher-order moments of the turbulent fluctuations of water vapour mixing ratio and temperature are obtained based on the application of auto-covariance analyses to the water vapour mixing ratio and temperature time series. The algorithms are applied to a case study (11:30–13:30 UTC, 20 April 2013) from the High Definition Clouds and Precipitation for Climate Prediction (HD(CP)2) Observational Prototype Experiment (HOPE), held in Western Germany in the spring 2013. A new correction scheme for the elastic-signal leakage in the low-quantum number rotational Raman signal is applied. The noise errors are small enough to derive up to fourth-order moments for both water vapour mixing ratio and temperature fluctuations. To the best of our knowledge, BASIL is the first Raman lidar with a demonstrated capability to simultaneously retrieve daytime profiles of water vapour turbulent fluctuations up to the fourth order throughout the atmospheric CBL, this capability being combined with the one to also measure daytime profiles of temperature fluctuations up to the fourth order. For the considered case study, which represents a well-mixed and quasi-stationary CBL, the mean boundary layer height is found to be 1290 ± 77 m a.g.l. Values of the integral scale for water vapour and temperature fluctuations at the top of the CBL are in the range of 70–125 s and 75–225 s, respectively; these values are much larger than the temporal resolution of the measurements (10 s), which testifies that the temporal resolution considered for the measurements is sufficiently high to resolve turbulence processes down to the inertial sub-range and consequently resolve the major part of the turbulent fluctuations. Peak values of all moments are found in the interfacial layer in the proximity of the top of the CBL. Specifically, water vapour and temperature second-order moment (variance) has a maximum value of 0.29 g2 kg−2 and 0.26 K2, respectively, water vapour and temperature third-order moment has a peak value of 0.156 g3 kg−3 and −0.067 K3, respectively, while water vapour and temperature fourth-order moment has a maximum value of 0.28 g4 kg−4 and 0.24 K4, respectively. Water vapour and temperature kurtosis have values of ~ 3 in the entrainment zone, which indicate normally distributed humidity and temperature fluctuations. Reported values of the higher-order moments result to be in good agreement with previous measurements at different locations, thus providing confidence on the possibility to use them for turbulence parameterization in weather and climate models. In the determination of the temperature profiles, particular care was dedicated to minimize potential effects associated with elastic signal leakage in the rotational Raman signals. For this purpose, a specific algorithm was defined and tested to identify and remove signal leakages and to assess the residual systematic uncertainty affecting temperature measurements after correction. The application of this approach confirms that for the present Raman lidar system the leakage factor keeps constant with time, and consequently an appropriate assessment of its constant value allows for a complete removal of the leaking elastic signal from the rotational Raman lidar signals at any time (with a residual error on temperature measurements after correction not exceeding 0.16 K).

scholarly journals Characterisation of boundary layer turbulent processes by the Raman lidar BASIL in the frame of HD(CP)<sup>2</sup> Observational Prototype Experiment

2017 ◽  
Vol 17 (1) ◽  
pp. 745-767 ◽  
Author(s):  
Paolo Di Girolamo ◽  
Marco Cacciani ◽  
Donato Summa ◽  
Andrea Scoccione ◽  
Benedetto De Rosa ◽  
...  
Keyword(s):  
Boundary Layer ◽  
Water Vapour ◽  
Temporal Resolution ◽  
Fourth Order ◽  
Temperature Fluctuations ◽  
Temperature Measurements ◽  
Mixing Ratio ◽  
Raman Lidar ◽  
Turbulent Fluctuations ◽  
Signal Crosstalk

Abstract. Measurements carried out by the University of Basilicata Raman lidar system (BASIL) are reported to demonstrate the capability of this instrument to characterise turbulent processes within the convective boundary layer (CBL). In order to resolve the vertical profiles of turbulent variables, high-resolution water vapour and temperature measurements, with a temporal resolution of 10 s and vertical resolutions of 90 and 30 m, respectively, are considered. Measurements of higher-order moments of the turbulent fluctuations of water vapour mixing ratio and temperature are obtained based on the application of autocovariance analyses to the water vapour mixing ratio and temperature time series. The algorithms are applied to a case study (11:30–13:30 UTC, 20 April 2013) from the High Definition Clouds and Precipitation for Climate Prediction (HD(CP)2) Observational Prototype Experiment (HOPE), held in western Germany in the spring 2013. A new correction scheme for the removal of the elastic signal crosstalk into the low quantum number rotational Raman signal is applied. The noise errors are small enough to derive up to fourth-order moments for both water vapour mixing ratio and temperature fluctuations.To the best of our knowledge, BASIL is the first Raman lidar with a demonstrated capability to simultaneously retrieve daytime profiles of water vapour turbulent fluctuations up to the fourth order throughout the atmospheric CBL. This is combined with the capability of measuring daytime profiles of temperature fluctuations up to the fourth order. These measurements, in combination with measurements from other lidar and in situ systems, are important for verifying and possibly improving turbulence and convection parameterisation in weather and climate models at different scales down to the grey zone (grid increment  ∼  1 km; Wulfmeyer et al., 2016).For the considered case study, which represents a well-mixed and quasi-stationary CBL, the mean boundary layer height is found to be 1290 ± 75 m above ground level (a.g.l.). Values of the integral scale for water vapour and temperature fluctuations at the top of the CBL are in the range of 70–125 and 75–225 s, respectively; these values are much larger than the temporal resolution of the measurements (10 s), which testifies that the temporal resolution considered for the measurements is sufficiently high to resolve turbulent processes down to the inertial subrange and, consequently, to resolve the major part of the turbulent fluctuations. Peak values of all moments are found in the interfacial layer in the proximity of the top of the CBL. Specifically, water vapour and temperature second-order moments (variance) have maximum values of 0.29 g2 kg−2 and 0.26 K2; water vapour and temperature third-order moments have peak values of 0.156 g3 kg−3 and −0.067 K3, while water vapour and temperature fourth-order moments have maximum values of 0.28 g4 kg−4 and 0.24 K4. Water vapour and temperature kurtosis have values of  ∼  3 in the upper portion of the CBL, which indicate normally distributed humidity and temperature fluctuations. Reported values of the higher-order moments are in good agreement with previous measurements at different locations, thus providing confidence in the possibility of using these measurements for turbulence parameterisation in weather and climate models.In the determination of the temperature profiles, particular care was dedicated to minimise potential effects associated with elastic signal crosstalk on the rotational Raman signals. For this purpose, a specific algorithm was defined and tested to identify and remove the elastic signal crosstalk and to assess the residual systematic uncertainty affecting temperature measurements after correction. The application of this approach confirms that, for the present Raman lidar system, the crosstalk factor remains constant with time; consequently an appropriate assessment of its constant value allows for a complete removal of the leaking elastic signal from the rotational Raman lidar signals at any time (with a residual error on temperature measurements after correction not exceeding 0.18 K).

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