scholarly journals Complexity in the scaling of velocity fluctuations in the high-latitude F-region ionosphere

2008 ◽  
Vol 26 (9) ◽  
pp. 2657-2672 ◽  
Author(s):  
M. L. Parkinson
Keyword(s):  
Probability Density ◽  
Spectral Width ◽  
Probability Density Functions ◽  
Closed Field ◽  
Density Functions ◽  
Scaling Exponent ◽  
Scaling Exponents ◽  
Velocity Fluctuations ◽  
F Region ◽  
Field Lines

Abstract. The temporal scaling properties of F-region velocity fluctuations, δvlos, were characterised over 17 octaves of temporal scale from τ=1 s to <1 day using a new data base of 1-s time resolution SuperDARN radar measurements. After quality control, 2.9 (1.9) million fluctuations were recorded during 31.5 (40.4) days of discretionary mode soundings using the Tasmanian (New Zealand) radars. If the fluctuations were statistically self-similar, the probability density functions (PDFs) of δvlos would collapse onto the same PDF using the scaling Ps (δvs, τ)=ταP (δvlos, τ) and δvs=δvlosτ−α where α is the scaling exponent. The variations in scaling exponents α and multi-fractal behaviour were estimated using peak scaling and generalised structure function (GSF) analyses, and a new method based upon minimising the differences between re-scaled probability density functions (PDFs). The efficiency of this method enabled calculation of "α spectra", the temporal spectra of scaling exponents from τ=1 s to ~2048 s. The large number of samples enabled calculation of α spectra for data separated into 2-h bins of MLT as well as two main physical regimes: Population A echoes with Doppler spectral width <75 m s−1 concentrated on closed field lines, and Population B echoes with spectral width >150 m s−1 concentrated on open field lines. For all data there was a scaling break at τ~10 s and the similarity of the fluctuations beneath this scale may be related to the large spatial averaging (~100 km×45 km) employed by SuperDARN radars. For Tasmania Population B, the velocity fluctuations exhibited approximately mono fractal power law scaling between τ~8 s and 2048 s (34 min), and probably up to several hours. The scaling exponents were generally less than that expected for basic MHD turbulence (α=0.25), except close to magnetic dusk where they peaked towards the basic MHD value. For Population A, the scaling exponents were larger than for Population B, having values generally in the range expected for basic MHD and Kolmogorov turbulence (α=0.25–0.33). The α spectra exhibited complicated variations with MLT and τ which must be related to different physical processes exerting more or less influence.

scholarly journals Dynamical critical scaling of electric field fluctuations in the greater cusp and magnetotail implied by HF radar observations of F-region Doppler velocity

2006 ◽  
Vol 24 (2) ◽  
pp. 689-705 ◽  
Author(s):  
M. L. Parkinson
Keyword(s):  
Solar Wind ◽  
Open Field ◽  
Electric Fields ◽  
Spectral Width ◽  
Hf Radar ◽  
Doppler Velocity ◽  
Closed Field ◽  
Scaling Exponent ◽  
Central Plasma ◽  
Field Lines

Abstract. Akasofu's solar wind ε parameter describes the coupling of solar wind energy to the magnetosphere and ionosphere. Analysis of fluctuations in ε using model independent scaling techniques including the peaks of probability density functions (PDFs) and generalised structure function (GSF) analysis show the fluctuations were self-affine (mono-fractal, single exponent scaling) over 9 octaves of time scale from ~46 s to ~9.1 h. However, the peak scaling exponent α0 was a function of the fluctuation bin size, so caution is required when comparing the exponents for different data sets sampled in different ways. The same generic scaling techniques revealed the organisation and functional form of concurrent fluctuations in azimuthal magnetospheric electric fields implied by SuperDARN HF radar measurements of line-of-sight Doppler velocity, vLOS, made in the high-latitude austral ionosphere. The PDFs of vLOS fluctuation were calculated for time scales between 1 min and 256 min, and were sorted into noon sector results obtained with the Halley radar, and midnight sector results obtained with the TIGER radar. The PDFs were further sorted according to the orientation of the interplanetary magnetic field, as well as ionospheric regions of high and low Doppler spectral width. High spectral widths tend to occur at higher latitude, mostly on open field lines but also on closed field lines just equatorward of the open-closed boundary, whereas low spectral widths are concentrated on closed field lines deeper inside the magnetosphere. The vLOS fluctuations were most self-affine (i.e. like the solar wind ε parameter) on the high spectral width field lines in the noon sector ionosphere (i.e. the greater cusp), but suggested multi-fractal behaviour on closed field lines in the midnight sector (i.e. the central plasma sheet). Long tails in the PDFs imply that "microbursts" in ionospheric convection occur far more frequently, especially on open field lines, than can be captured using the effective Nyquist frequency and volume resolution of SuperDARN radars.

scholarly journals Modeling Diameter Distributions with Six Probability Density Functions in Pinus halepensis Mill. Plantations Using Low-Density Airborne Laser Scanning Data in Aragón (Northeast Spain)

2021 ◽  
Vol 13 (12) ◽  
pp. 2307
Author(s):  
J. Javier Gorgoso-Varela ◽  
Rafael Alonso Ponce ◽  
Francisco Rodríguez-Puerta
Keyword(s):  
Probability Density ◽  
Linear Models ◽  
Pinus Halepensis ◽  
Beta Function ◽  
Probability Density Functions ◽  
Lidar Data ◽  
Density Functions ◽  
Minimum Diameter ◽  
Location Parameters ◽  
Diameter Distributions

The diameter distributions of trees in 50 temporary sample plots (TSPs) established in Pinus halepensis Mill. stands were recovered from LiDAR metrics by using six probability density functions (PDFs): the Weibull (2P and 3P), Johnson’s SB, beta, generalized beta and gamma-2P functions. The parameters were recovered from the first and the second moments of the distributions (mean and variance, respectively) by using parameter recovery models (PRM). Linear models were used to predict both moments from LiDAR data. In recovering the functions, the location parameters of the distributions were predetermined as the minimum diameter inventoried, and scale parameters were established as the maximum diameters predicted from LiDAR metrics. The Kolmogorov–Smirnov (KS) statistic (Dn), number of acceptances by the KS test, the Cramér von Misses (W2) statistic, bias and mean square error (MSE) were used to evaluate the goodness of fits. The fits for the six recovered functions were compared with the fits to all measured data from 58 TSPs (LiDAR metrics could only be extracted from 50 of the plots). In the fitting phase, the location parameters were fixed at a suitable value determined according to the forestry literature (0.75·dmin). The linear models used to recover the two moments of the distributions and the maximum diameters determined from LiDAR data were accurate, with R2 values of 0.750, 0.724 and 0.873 for dg, dmed and dmax. Reasonable results were obtained with all six recovered functions. The goodness-of-fit statistics indicated that the beta function was the most accurate, followed by the generalized beta function. The Weibull-3P function provided the poorest fits and the Weibull-2P and Johnson’s SB also yielded poor fits to the data.

scholarly journals A synergy of the velocity gradients technique and the probability density functions for identifying gravitational collapse in self-absorbing media

2021 ◽  
Vol 502 (2) ◽  
pp. 1768-1784
Author(s):  
Yue Hu ◽  
A Lazarian
Keyword(s):  
Magnetic Fields ◽  
Probability Density ◽  
Column Density ◽  
Mass Density ◽  
Probability Density Functions ◽  
Emission Lines ◽  
Density Functions ◽  
Star Forming ◽  
Velocity Gradients ◽  
Self Gravity

ABSTRACT The velocity gradients technique (VGT) and the probability density functions (PDFs) of mass density are tools to study turbulence, magnetic fields, and self-gravity in molecular clouds. However, self-absorption can significantly make the observed intensity different from the column density structures. In this work, we study the effects of self-absorption on the VGT and the intensity PDFs utilizing three synthetic emission lines of CO isotopologues 12CO (1–0), 13CO (1–0), and C18O (1–0). We confirm that the performance of VGT is insensitive to the radiative transfer effect. We numerically show the possibility of constructing 3D magnetic fields tomography through VGT. We find that the intensity PDFs change their shape from the pure lognormal to a distribution that exhibits a power-law tail depending on the optical depth for supersonic turbulence. We conclude the change of CO isotopologues’ intensity PDFs can be independent of self-gravity, which makes the intensity PDFs less reliable in identifying gravitational collapsing regions. We compute the intensity PDFs for a star-forming region NGC 1333 and find the change of intensity PDFs in observation agrees with our numerical results. The synergy of VGT and the column density PDFs confirms that the self-gravitating gas occupies a large volume in NGC 1333.

scholarly journals Interactive design of probability density functions for shape grammars

2015 ◽  
Vol 34 (6) ◽  
pp. 1-13 ◽  
Author(s):  
Minh Dang ◽  
Stefan Lienhard ◽  
Duygu Ceylan ◽  
Boris Neubert ◽  
Peter Wonka ◽  
...  
Keyword(s):  
Probability Density ◽  
Probability Density Functions ◽  
Interactive Design ◽  
Density Functions ◽  
Shape Grammars

scholarly journals The Impact of Probability Density Functions Assessment on Model Performance for Slope Stability Analysis

Geosciences ◽  
2021 ◽  
Vol 11 (8) ◽  
pp. 322
Author(s):  
Evelina Volpe ◽  
Luca Ciabatta ◽  
Diana Salciarini ◽  
Stefania Camici ◽  
Elisabetta Cattoni ◽  
...  
Keyword(s):  
Probability Density ◽  
Central Italy ◽  
Model Performance ◽  
Probability Density Functions ◽  
Slope Instability ◽  
Complex Nature ◽  
Density Functions ◽  
Umbria Region ◽  
Input Variables ◽  
The Impact

The development of forecasting models for the evaluation of potential slope instability after rainfall events represents an important issue for the scientific community. This topic has received considerable impetus due to the climate change effect on territories, as several studies demonstrate that an increase in global warming can significantly influence the landslide activity and stability conditions of natural and artificial slopes. A consolidated approach in evaluating rainfall-induced landslide hazard is based on the integration of rainfall forecasts and physically based (PB) predictive models through deterministic laws. However, considering the complex nature of the processes and the high variability of the random quantities involved, probabilistic approaches are recommended in order to obtain reliable predictions. A crucial aspect of the stochastic approach is represented by the definition of appropriate probability density functions (pdfs) to model the uncertainty of the input variables as this may have an important effect on the evaluation of the probability of failure (PoF). The role of the pdf definition on reliability analysis is discussed through a comparison of PoF maps generated using Monte Carlo (MC) simulations performed over a study area located in the Umbria region of central Italy. The study revealed that the use of uniform pdfs for the random input variables, often considered when a detailed geotechnical characterization for the soil is not available, could be inappropriate.

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