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Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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NASA NTRS2005

Tools for Basic Statistical Analysis

Statistical Analysis Toolset is a collection of eight Microsoft Excel spreadsheet programs, each of which performs calculations pertaining to an aspect of statistical analysis. These programs present input and output data in user-friendly, menu-driven formats, with automatic execution. The following types of calculations are performed: Descriptive statistics are computed for a set of data x(i) (i = 1, 2, 3 . . . ) entered by the user. Normal Distribution Estimates will calculate the statistical value that corresponds to cumulative probability values, given a sample mean and standard deviation of the normal distribution. Normal Distribution from two Data Points will extend and generate a cumulative normal distribution for the user, given two data points and their associated probability values. Two programs perform two-way analysis of variance (ANOVA) with no replication or generalized ANOVA for two factors with four levels and three repetitions. Linear Regression-ANOVA will curvefit data to the linear equation y=f(x) and will do an ANOVA to check its significance.

Luz, Paul L.↗
NASA NTRS1976

Vector wind and vector wind shear models 0 to 27 km altitude for Cape Kennedy, Florida, and Vandenberg AFB, California

The techniques are presented to derive several statistical wind models. The techniques are from the properties of the multivariate normal probability function. Assuming that the winds can be considered as bivariate normally distributed, then (1) the wind components and conditional wind components are univariate normally distributed, (2) the wind speed is Rayleigh distributed, (3) the conditional distribution of wind speed given a wind direction is Rayleigh distributed, and (4) the frequency of wind direction can be derived. All of these distributions are derived from the 5-sample parameter of wind for the bivariate normal distribution. By further assuming that the winds at two altitudes are quadravariate normally distributed, then the vector wind shear is bivariate normally distributed and the modulus of the vector wind shear is Rayleigh distributed. The conditional probability of wind component shears given a wind component is normally distributed. Examples of these and other properties of the multivariate normal probability distribution function as applied to Cape Kennedy, Florida, and Vandenberg AFB, California, wind data samples are given. A technique to develop a synthetic vector wind profile model of interest to aerospace vehicle applications is presented.

Smith, O. E.↗
NASA NTRS1988

On the long-tail solar wind electron velocity distribution

The role of the log-normal distribution in the description of the high-energy tail of the electron velocity distribution in the solar wind plasma is examined. Specifically, it is shown that the core-halo solar wind distribution function can be understood in terms of a simple phenomenological model of general applicability in which the core has a Maxwellian or normal distribution and the halo a log-normal distribution. In the presence of structures in the interplanetary medium capable of interacting with the electrons, the model predicts a transition at the highest velocities to a secondary halo distribution.

Shlesinger, Michael F.↗
NASA NTRS1956

Comparison of experimental and theoretical normal-force distributions (including Reynolds number effects) on an ogive-cylinder body at Mach number 1.98

Effects of Reynolds number and angle of attack on the pressure distribution and normal-force characteristics of a body of revolution consisting of a fineness ratio 3 ogival nose tangent to a cylindrical afterbody 7 diameters long have been determined. The test Mach number was 1.98 and the angle-of-attack range from 0 degree to 20 degrees. The Reynolds numbers, based on body diameter, were 0.15 x 10(6) and 0.45 x 10(6). The experimental results are compared with theory.

Perkins, Edward W↗
NASA NTRS2006

Effect of EMIC Wave Normal Angle Distribution on Relativistic Electron Scattering

The flux level of outer-zone relativistic electrons (above 1 MeV) is extremely variable during geomagnetic storms, and controlled by a competition between acceleration and loss. Precipitation of these electrons due to resonant pitch-angle scattering by electromagnetic ion cyclotron (EMIC) waves is considered one of the major loss mechanisms. This mechanism was suggested in early theoretical studies more than three decades ago. However, direct experimental evidence of the wave role in relativistic electrons precipitation is difficult to obtain because of lack of concurrent measurements of precipitating electrons at low altitudes and the waves in a magnetically conjugate equatorial region. Recently, the data from balloon-borne X-ray instruments provided indirect but strong evidence on an efficiency of the EMIC wave induced loss for the outer-zone relativistic electrons. These observations stimulated theoretical studies that, particularly, demonstrated that EMIC wave induced pitch-angle diffusion of MeV electrons can operate in the strong diffusion limit and this mechanism can compete with relativistic electron depletion caused by the Dst effect during the initial and main phases of storm. Although an effectiveness of relativistic electron scattering by EMIC waves depends strongly on the wave spectral properties, the most favorable assumptions regarding wave characteristics has been made in all previous theoretical studies. Particularly, only quasi field-aligned EMIC waves have been considered as a driver for relativistic electron loss. At the same time, there is growing experimental and theoretical evidence that these waves can be highly oblique; EMIC wave energy can occupy not only the region of generation, i.e. the region of small wave normal angles, but also the entire wave normal angle region, and even only the region near 90 degrees. The latter can dramatically change he effectiveness of relativistic electron scattering by EMIC waves. In the present study, we calculate the pitch-angle diffusion coefficients using the typical wave normal distributions obtained from our self-consistent ring current-EMIC wave model, and try to quantify the effect of EMIC wave normal angle characteristics on relativistic electron scattering.

Gamayunov, K. V.↗
NASA NTRS1972

Jimsphere wind and turbulence exceedance statistic

Exceedance statistics of winds and gusts observed over Cape Kennedy with Jimsphere balloon sensors are described. Gust profiles containing positive and negative departures, from smoothed profiles, in the wavelength ranges 100-2500, 100-1900, 100-860, and 100-460 meters were computed from 1578 profiles with four 41 weight digital high pass filters. Extreme values of the square root of gust speed are normally distributed. Monthly and annual exceedance probability distributions of normalized rms gust speeds in three altitude bands (2-7, 6-11, and 9-14 km) are log-normal. The rms gust speeds are largest in the 100-2500 wavelength band between 9 and 14 km in late winter and early spring. A study of monthly and annual exceedance probabilities and the number of occurrences per kilometer of level crossings with positive slope indicates significant variability with season, altitude, and filter configuration. A decile sampling scheme is tested and an optimum approach is suggested for drawing a relatively small random sample that represents the characteristic extreme wind speeds and shears of a large parent population of Jimsphere wind profiles.

Adelfang, S. I.↗
NASA NTRS1971

Electron pitch-angle diffusion driven by oblique whistler-mode turbulence.

A general description of cyclotron harmonic resonant pitch-angle scattering is presented. Quasi-linear diffusion coefficients are prescribed in terms of the wave normal distribution of plasma wave energy. Numerical computations are performed for the specific case of relativistic electrons interacting with a band of low frequency whistler-mode turbulence. A parametric treatment of the wave energy distribution permits normalized diffusion coefficients to be presented graphically solely as a function of the electron pitch-angle. The diffusion coefficients generally decrease with increasing cyclotron harmonic number. Higher harmonic diffusion is insignificant at very small electron pitch-angles, but becomes increasingly important as the pitch-angle increases. One thus expected the rate of pitch-angle scattering to decrease with increasing electron energy, since the resonant value of the latter varies proportionately with harmonic number. This indicates that, in mirror-type magnet field geometrics, such as the earth's radiation belts, the diffusion losses of high energy electrons are likely to be appreciably slower than those at low energy.

Lyons, L. R.↗
NASA NTRS2007

Effect of EMIC Wave Normal Angle Distribution on Relativistic Electron Scattering in Outer RB

We present the equatorial and bounce average pitch angle diffusion coefficients for scattering of relativistic electrons by the H+ mode of EMIC waves. Both the model (prescribed) and self consistent distributions over the wave normal angle are considered. The main results of our calculation can be summarized as follows: First, in comparison with field aligned waves, the intermediate and highly oblique waves reduce the pitch angle range subject to diffusion, and strongly suppress the scattering rate for low energy electrons (E less than 2 MeV). Second, for electron energies greater than 5 MeV, the |n| = 1 resonances operate only in a narrow region at large pitch-angles, and despite their greatest contribution in case of field aligned waves, cannot cause electron diffusion into the loss cone. For those energies, oblique waves at |n| greater than 1 resonances are more effective, extending the range of pitch angle diffusion down to the loss cone boundary, and increasing diffusion at small pitch angles by orders of magnitude.

Khazanov, G. V.↗
NASA NTRS2014

Smooth Pursuit of Flicker-Defined Motion

We examined the pursuit response to stimuli defined by space-variant flicker of a dense random dot carrier pattern. On each frame, every element of the pattern could change polarity, with a probability given by a two-dimensional Gaussian distribution. A normal distribution produces a circular region of twinkle, while inverting the distribution results in a spot of static texture in a twinkling surround. In this latter case, the carrier texture could be stationary, or could move with the twinkle modulator, thereby producing first-order motion in the region of the spot. While the twinkle-defined spot produces a strong sensation of motion, the complementary stimulus defined by the absence of twinkle does not, when viewed peripherally, it appears to move in steps even when the generating distribution moves smoothly. We examined pursuit responses to these stimuli using two techniques: 1) the eye movement correlogram, obtained by cross-correlating eye velocity with the velocity of a randomly-moving stimulus; and 2) delayed visual feedback, where transient stabilization of a target can produce spontaneous oscillations of the eye, with a period empirically observed to vary linearly with the applied delay. Both techniques provide an estimate of the internal processing time, which can be as short as 100 milliseconds for a first-order target. Assessed by the correlogram method, the response to flicker-defined motion is delayed by more than 100 milliseconds, and significantly weaker (especially in the vertical dimension). When initially presented in the delayed feedback condition, purely saccadic oscillation is observed. One subject eventually developed smooth oscillations (albeit with significant saccadic intrusions), showing a period-versus-delay slope similar to that observed for first-order targets. This result is somewhat surprising, given that we interpret the slope of the period-versus-delay-function as reflecting the balance between position- and velocity-sensitive inputs to pursuit.

eye movements↗
NASA NTRS2014

Smooth Pursuit of Flicker-Defined Motion

We examined the pursuit response to stimuli defined by space-variant flicker of a dense random dot carrier pattern. On each frame, every element of the pattern could change polarity, with a probability given by a two-dimensional Gaussian distribution. A normal distribution produces a circular region of twinkle, while inverting the distribution results in a spot of static texture in a twinkling surround. In this latter case, the carrier texture could be stationary, or could move with the twinkle modulator,thereby producing first-order motion in the region of the spot. While the twinkle-defined spot produces a strong sensation of motion, the complementary stimulus defined by the absence of twinkle does not;when viewed peripherally, it appears to move in steps even when the generating distribution moves smoothly. We examined pursuit responses to these stimuli using two techniques: 1) the eye movement correlogram, obtained by cross-correlating eye velocity with the velocity of a randomly-moving stimulus; and 2) delayed visual feedback, where transient stabilization of a target can produce spontaneous oscillations of the eye, with a period empirically observed to vary linearly with the applied delay. Both techniques provide an estimate of the internal processing time, which can be as short as100 milliseconds for a first-order target. Assessed by the correlogram method, the response to flicker defined motion is delayed by more than 100 milliseconds, and significantly weaker (especially in the vertical dimension). When initially presented in the delayed feedback condition, purely saccadic oscillation is observed. One subject eventually developed smooth oscillations (albeit with significant saccadic intrusions), showing a period-versus-delay slope similar to that observed for first-order targets. This result is somewhat surprising, given that we interpret the slope of the period-versus-delayfunction as reflecting the balance between position- and velocity-sensitive inputs to pursuit.

smooth pursuit↗
NASA NTRS1986

Field size distributions for selected agricultural crops in the United States and Canada

Digitized agricultural field boundary taken in the United States and Canada during the LACIE and AgRISTARS programs, in 1977 through 1980, were used to construct histograms showing the distributions of field area, width, and length for crops for which there were data for 700 or more fields per state. The observed distributions of area and width for fields of 10 crops grown in 13 states of the United States and Canada were compared with best-fit inverse Gaussian distributions and with log-normal distributions. For 28 distributions of area and 16 distributions of width there was found to be a probability of greater than .01 of their being inverse Gaussian. There were 10 distributions of area for which there was probability of greater than .005 of their being log-normal. Distributions of area and width stratified by state and crop type appear to be unique. The inverse Gaussian, which represents a wide range of statistical distributions from skewed to almost symmetrical, can provide a useful model for distributions of field area.

Ferguson, M. C.↗
NASA NTRS2020

Studies in Astronomical Time Series Analysis: VII. An Enquiry Concerning Non-Linearity, the RMS-Mean Flux Relation, and log-Normal Flux Distributions

A broad and widely used class of stationary, linear, additive time series models can have statistical properties which many authors have asserted imply that the underlying process must be non-linear, non-stationary, multiplicative, or inconsistent with shot noise. This result is demonstrated with exact and numerical evaluation of the model flux distribution function and dependence of flux standard deviation on mean flux (here and in the literature called the rms-flux relation). These models can: (1) exhibit normal, log-normal or other flux distributions; (2) show linear or slightly non-linear rms-mean flux dependencies; as well as (3) match arbitrary second order statistics of the time series data. Accordingly the above assertions cannot be made on the basis of statistical time series analysis alone. Also idscussed are ambiguities in the meaning of terms relevant to this study – linear, stationary and multiplicative – and functions that can transform observed fluxes to a normal distribution as well or better than the logarithm.

Jeffrey D Scargle↗
NASA NTRS2007

Effect of EMIC Wave Normal Angle Distribution on Relativistic Electron Scattering Based on the Newly Developed Self-consistent RC/EMIC Waves Model by Khazanov et al. [2006]

It is well known that the effects of EMIC waves on RC ion and RB electron dynamics strongly depend on such particle/wave characteristics as the phase-space distribution function, frequency, wave-normal angle, wave energy, and the form of wave spectral energy density. Therefore, realistic characteristics of EMIC waves should be properly determined by modeling the RC-EMIC waves evolution self-consistently. Such a selfconsistent model progressively has been developing by Khaznnov et al. [2002-2006]. It solves a system of two coupled kinetic equations: one equation describes the RC ion dynamics and another equation describes the energy density evolution of EMIC waves. Using this model, we present the effectiveness of relativistic electron scattering and compare our results with previous work in this area of research.

Khazanov, G. V.↗
NASA NTRS2005

Statistical Considerations of Data Processing in Giovanni Online Tool

The GES DISC Interactive Online Visualization and Analysis Infrastructure (Giovanni) is a web-based interface for the rapid visualization and analysis of gridded data from a number of remote sensing instruments. The GES DISC currently employs several Giovanni instances to analyze various products, such as Ocean-Giovanni for ocean products from SeaWiFS and MODIS-Aqua; TOMS & OM1 Giovanni for atmospheric chemical trace gases from TOMS and OMI, and MOVAS for aerosols from MODIS, etc. (http://giovanni.gsfc.nasa.gov) Foremost among the Giovanni statistical functions is data averaging. Two aspects of this function are addressed here. The first deals with the accuracy of averaging gridded mapped products vs. averaging from the ungridded Level 2 data. Some mapped products contain mean values only; others contain additional statistics, such as number of pixels (NP) for each grid, standard deviation, etc. Since NP varies spatially and temporally, averaging with or without weighting by NP will be different. In this paper, we address differences of various weighting algorithms for some datasets utilized in Giovanni. The second aspect is related to different averaging methods affecting data quality and interpretation for data with non-normal distribution. The present study demonstrates results of different spatial averaging methods using gridded SeaWiFS Level 3 mapped monthly chlorophyll a data. Spatial averages were calculated using three different methods: arithmetic mean (AVG), geometric mean (GEO), and maximum likelihood estimator (MLE). Biogeochemical data, such as chlorophyll a, are usually considered to have a log-normal distribution. The study determined that differences between methods tend to increase with increasing size of a selected coastal area, with no significant differences in most open oceans. The GEO method consistently produces values lower than AVG and MLE. The AVG method produces values larger than MLE in some cases, but smaller in other cases. Further studies indicated that significant differences between AVG and MLE methods occurred in coastal areas where data have large spatial variations and a log-bimodal distribution instead of log-normal distribution.

Suhung, Shen↗
NASA NTRS1973

Statistics for ionospherically diffracted VHF/UHF signals.

In this paper, a general characterization of the statistics for an ionospherically diffracted, monochromatic plane wave is presented. The main results are restricted to weak scatter, although two possible extensions that accommodate large phase perturbations and multiple scatter are discussed. A detailed discussion of the first-order statistics of amplitude is given. The general Gaussian distribution is discussed together with its Nakagami-distribution approximation and the log-normal distribution. By using a segment of ATS-3 satellite data recorded at Lima, Peru, we show equally good fits to Gaussian and log-normal distributions at least for the limited dynamic range available. The Nakagami distribution provides only a poor approximation.

Rino, C. L.↗