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Results for “Statistical fluctuations”

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NASA NTRS1987

The effect of the dynamic wet troposphere on radio interferometric measurements

A statistical model of water vapor fluctuations is used to describe the effect of the dynamic wet troposphere on radio interferometric measurements. It is assumed that the spatial structure of refractivity is approximated by Kolmogorov turbulence theory, and that the temporal fluctuations are caused by spatial patterns moved over a site by the wind, and these assumptions are examined for the VLBI delay and delay rate observables. The results suggest that the delay rate measurement error is usually dominated by water vapor fluctuations, and water vapor induced VLBI parameter errors and correlations are determined as a function of the delay observable errors. A method is proposed for including the water vapor fluctuations in the parameter estimation method to obtain improved parameter estimates and parameter covariances.

Treuhaft, R. N.↗

NASA NTRS1989

Gravity wave climatology at midlatitude from Rayleigh lidar data

Atmospheric sounding of the middle atmosphere by Rayleigh scattering has been performed in France for several years, from two stations with different orographic situations: one in the Alps, the Observatoire de Haute Provence, one on the Atlantic coast at Biscarosse. The vertical profiles of density and temperature are obtained with a temporal and spatial resolution of, respectively, 15 mn and 300 m between 30 and 80 km. A statistical study of the atmospheric fluctuations due to gravity waves was performed and the main results are presented: climatology of the gravity wave activity, distribution of energy versus vertical wave number and altitude, and comparison of the observations at the two sites. Conclusions are presented on the saturation of the wave field, the filtering by the mean wind, the transfer of energy and momentum into the atmosphere.

Wilson, R.↗

NASA NTRS1991

Simulation of the inertial-conductive subrange

The inertial-conductive subrange spectrum of a passive temperature field of a fluid of small Prandtl number is determined by large-eddy simulation. Results for simulations of both freely decaying and forced turbulence are presented. In the simulations of freely decaying turbulence, a subgrid model is used to simulate a decaying turbulent velocity field with a k exp -5/3 inertial subrange energy spectrum convecting eight different decaying temperature fields with well-resolved conductive subranges. In the simulations of forced turbulence, a subgrid model is again used to simulate an inertial subrange velocity field; however, the velocity field is now forced at the lowest wave numbers of the simulation, and an external uniform mean temperature gradient is imposed. Statistically stationary velocity and temperature fluctuations are generated. The results of the decaying and forced simulations are in excellent agreement with the Batchelor et al. (1959) k exp -17/3 spectrum in the far inertial-conductive subrange, whereas significant departures from the Batchelor spectrum are observed in the near inertial-conductive subrange.

Chasnov, Jeffrey R.↗

NASA NTRS1999

Optimal Scales for Comparing Satellite and Rain-Gauge Rainfall Estimates for Verification Purposes

In spite of all their problems, rain gauges measure rainfall in such a direct way when compared with other methods of estimating rainfall that comparing their totals to satellite estimates remains an essential tool in the validation of satellite products. Some disagreement between averages of satellite data and rain-gauge data is expected because of the very different sampling patterns of the two systems--the satellite provides only occasional snapshots of large areas, whereas rain gauges provide continuous measurements over very small areas. The comparison of the two requires that some quantitative measure be supplied for the amount of disagreement that can be tolerated due to the differences in sampling. As part of an effort to determine the sampling error of satellite averages, a space-time model for rainfall statistics was developed and its parameters fit to radar data from a field experiment conducted near the Inter-Tropical Convergence Zone (ITCZ) in the eastern Atlantic (GATE). Although the model was intended to represent the statistics of relatively large scale fluctuations of rain, it is surprisingly consistent with the very different scales on which rain gauges observe. It can therefore be used to study some of the issues involved with comparing rain-gauge averages to satellite averages. Its implications for the best time and space scales for comparing the two will be discussed.

Bell, Thomas L.↗

NASA NTRS2002

Optimal Strategies for Validating TRMM Rainfall Estimates with Rain-Gauge Data

In spite of all their problems, rain gauges measure rainfall in such a direct way when compared with other methods of estimating rainfall that comparing their totals to satellite estimates remains an essential tool in the validation of satellite products. Some disagreement between averages of satellite data and rain-gauge data is expected because of the very different sampling patterns of the two systems--the satellite provides only occasional snapshots of large areas, whereas rain gauges provide continuous measurements over very small areas. A quantitative estimate of the expected level of disagreement due to the differences in sampling is needed in order for comparisons of the two kinds of averages to be informative. As part of an earlier effort to determine the sampling error of satellite averages, a space-time model for rainfall statistics was developed. Sets of parameter values for the model have been obtained for which the model statistics are found to agree quite well with those of radar data taken over the Atlantic during GATE and the western Pacific during TOGA COARE. Although the model was intended to represent the statistics of relatively large scale fluctuations of rain, it is surprisingly consistent with the very different scales on which rain gauges observe. Implications for maximizing the benefit in comparisons of rain gauge averages and TRMM estimates are derived using the model predictions.

Bell, Thomas L.↗

NASA NTRS1973

A variation of the Davis-Smith method for in-flight determination of spacecraft magnetic fields.

A variation of a procedure developed by Davis and Smith (1968) is presented for the in-flight determination of spacecraft magnetic fields. Both methods take statistical advantage of the observation that fluctuations in the interplanetary magnetic field over short periods of time are primarily changes in direction rather than in magnitude. During typical solar wind conditions between 0.8 and 1.0 AU, a statistical analysis of 2-3 days of continuous interplanetary field measurements yields an estimate of a constant spacecraft field with an uncertainty of plus or minus 0.25 gamma in the direction radial to the sun and plus or minus 15 gammas in the directions transverse to the radial. The method is also of use in estimating variable spacecraft fields with gradients of the order of 0.1 gamma/day and less and in other special circumstances.

Belcher, J. W.↗

NASA NTRS1991

Early results from the MIT millimeter and sub-millimeter balloon-borne anisotropy measurement

The MIT balloon-borne bolometric search for Cosmic Microwave Background Radiation (CMBR) anisotropies places the most stringent constraints to date on fluctuations in the CMBR. Four maps of half of the Northern Hemisphere at 1.8, 1.1, 0.63 and 0.44 mm wavelength, have a beam size of 3.8 deg with a 1 sigma sensitivity of less than 0.1 mK (thermodynamic) per FOV in each of the first two channels. Analysis of the sky map at 1.8 mm wavelength using a likelihood ratio test for galactic latitudes of 15 deg and greater yields a 95 percent confidence level (CL) upper limit on fluctuations of the CMBR at DeltaT/T less than or equal to 1.6 x 10 exp -5 with a statistical power of 92 percent for Gaussian fluctuations at a correlation angle of 13 deg. Between 3 deg and 22 deg, the upper limit for fluctuations is DeltaT/T less than or equal to 4.0 x 10 exp -5 (95 percent CL).

Meyer, Stephan S.↗

NASA NTRS2018

Magnetospheric Multiscale Observations of Turbulent Magnetic and Electron Velocity Fluctuations in Earth's Magnetosheath Downstream of a Quasi-Parallel Bow Shock

We present statistical single-spacecraft observations of magnetic and electron velocity fluctuations in Earth's magnetosheath, likely in the vicinity of the magnetopause, downstream of a bow shock immersed in quasi-parallel interplanetary magnetic field conditions, a situation conducive to plasma turbulence in the downstream flow. These fluctuations exhibit scale-dependent behavior, wherein histograms of their Partial Variance of Increments (PVIB or PVIV(sub e)) demonstrate highly non-Gaussian forms at small scales and are reasonably well-described by kappa distributions, albeit with fitted values of the kappa parameter only slightly larger than 1.5, exemplifying their power law nature at large values of PVI. At larger scales, the PVI histograms lose their non-Gaussian nature and are well described by both Gaussian and kappa distributions with large values of the kappa parameter. The PVI histograms furthermore exhibit kurtosis that increases with decreasing scale, a characteristic that is much more prominent in the magnetic fluctuations than in the electron velocity fluctuations. This feature that is not yet explained. In both cases, the results are characteristic of turbulent intermittency.

Pollock, C. J.↗

NASA NTRS2000

'Atomistic' Simulation of Decanano Devices

When the devices are scaled to decanano dimensions the discreteness of charge and matter introduces significant 'intrinsic' parameter fluctuations. Atomic level 3D process and device modelling on statistical scale is required to understand the effects, the scale of the fluctuations and to design fluctuation resistant devices.

Asenov, Asen↗

NASA NTRS1978

Laser amplification of incoherent radiation

The amplification of noise in a laser amplifier is treated theoretically. The model for the active medium and its description using density-matrix techniques, are taken from the theory of laser operation. The spectral behavior of the radiation in the nonlinear regime is studied and the formalism is written from the onset in the frequency domain. The statistics of the light are gradually modified by the nonlinear amplification process, and expressions are derived for the rate of change of fluctuations in intensity as a measure of statistical changes. In addition, the range of validity of Litvak's Gaussian-statistics approximation is discussed. In the homogeneous-broadening case, the evolution of initially broadband Gaussian radiation toward quasimonochromatic oscillations with laserlike statistics is explored in several numerical examples. The connections of this study with the time-domain work on self-pulsing in a ring-laser configuration, are established. Finally, spectral-narrowing and -rebroadening effects in Doppler-broadened media are discussed both analytically and with numerical examples. These examples show the distinct contribution of pulsations in the population ('Raman-type terms'), and saturation phenomena.

Menegozzi, L. N.↗

NASA NTRS2016

Pressure Fluctuations Induced by a Hypersonic Turbulent Boundary Layer

Direct numerical simulations (DNS) are used to examine the pressure fluctuations generated by a spatially-developed Mach 5.86 turbulent boundary layer. The unsteady pressure field is analyzed at multiple wall-normal locations, including those at the wall, within the boundary layer (including inner layer, the log layer, and the outer layer), and in the free stream. The statistical and structural variations of pressure fluctuations as a function of wall-normal distance are highlighted. Computational predictions for mean velocity pro les and surface pressure spectrum are in good agreement with experimental measurements, providing a first ever comparison of this type at hypersonic Mach numbers. The simulation shows that the dominant frequency of boundary-layer-induced pressure fluctuations shifts to lower frequencies as the location of interest moves away from the wall. The pressure wave propagates with a speed nearly equal to the local mean velocity within the boundary layer (except in the immediate vicinity of the wall) while the propagation speed deviates from the Taylor's hypothesis in the free stream. Compared with the surface pressure fluctuations, which are primarily vortical, the acoustic pressure fluctuations in the free stream exhibit a significantly lower dominant frequency, a greater spatial extent, and a smaller bulk propagation speed. The freestream pressure structures are found to have similar Lagrangian time and spatial scales as the acoustic sources near the wall. As the Mach number increases, the freestream acoustic fluctuations exhibit increased radiation intensity, enhanced energy content at high frequencies, shallower orientation of wave fronts with respect to the flow direction, and larger propagation velocity.

Lian Duan↗

NASA NTRS1986

Numerical study of sink-flow boundary layers

Direct numerical simulations of sink-flow boundary layers, with acceleration parameters K between 1.5 x 10 to the -6th and 3.0 x 10 to the -6th, are presented. The three-dimensional, time-dependent Navier-Stokes equations are solved numerically, using a spectral method, with about one million degrees of freedom. The flow is assumed to be statistically steady, and self-similar. A multiple-scale approximation and periodic conditions are applied to the fluctuations. The turbulence is studied using instantaneous and statistical results. Good agreement with the experiments of Jones and Launder (1972) is observed. The two effects of the favorable pressure gradient are to extend the logarithmic layer, and to alter the energy balance of the turbulence near the edge of the boundary layer. At low Reynolds number the logarithmic layer is shortened and slightly displaced, but wall-layer streaks are present even at the lowest values of R(theta) for which turbulence can be sustained. Large quiescent patches appear in the flow. Relaminarization occurs at K = 3.0 x 10 to the -6th, corresponding to a Reynolds number R(theta) of about 330.

Spalart, Philippe R.↗

NASA NTRS1986

Numerical simulation of boundary layers. Part 3: Turbulence and relaminarization in sink flows

Direct numerical simulations of sink-flow boundary layers, with acceleration parameters K between 1.5 and 3.0 x 10 to the -6 power, are presented. The three-dimensional, time-dependent Navier-Stokes equations are solved numerically using a spectral method, with about 10 to the -6 degrees of freedom. The flow is assumed to be statistically steady, and self-similar. A multiple-scale approximation and periodic conditions are applied to the fluctuations. The turbulence is studied using instantaneous and statistical results. Good agreement with the experiments of Jones and Launder is observed. Two effects of the favorable pressure gradient are to extend the logarithmic layer, and to alter the energy balance of the turbulence near the edge of the boundary layer. At very low Reynolds number the logarithmic layer is shortened and slightly displaced, but wall-layer streaks are present even at the lowest values of the Reynolds number for which turbulence can be sustained. Large quiescent patches appear in the flow. Relaminarization occurs at K = 3.0 x 10 to the -6 power, corresponding to a Reynolds number, based on momentum thickness, of about 330.

Spalart, Philippe R.↗

NASA NTRS1959

Effect of Contraction on Turbulence and Temperature Fluctuations Generated by a Warm Grid

Hot-wire anemometer measurements were made of several statistical properties of approximately homogeneous and isotropic fields of turbulence and temperature fluctuations generated by a warm grid in a uniform airstream sent through a 4-to-1 contraction. These measurements were made both in the contraction and in the axisymmetric domain farther downstream. In addition to confirming the well-known turbulence anisotropy induced by strain, the data show effects on the skewnesses of both longitudinal velocity fluctuation (which has zero skewness in isotropic turbulence) and its derivative. The concomitant anisotropy in the temperature field accelerates the decay of temperature fluctuations.

Mills, Robert R., Jr.↗

NASA NTRS1975

The effects of random path fluctuations on the accuracy of laser ranging systems

The precision of satellite ranging systems, limited in part by atmospheric refraction and scattering, is examined. The effects of atmospheric turbulence on the accuracy of single color and multicolor ranging systems is discussed. The statistical characteristics of the random path length fluctuations induced by turbulence are examined. Correlation and structure functions are derived using several proposed models for the variations of the optical path length. For single color systems it is shown that the random path length fluctuations can limit the accuracy of a range measurement to a few centimeters. Two color systems can partially correct for the random path fluctuations so that in most cases their accuracy is limited to a few millimeters. However, at low elevation angles and over long horizontal paths two color systems can also have errors approaching a few centimeters.

Gardner, C. S.↗

NASA NTRS1978

Climate diagnostics

Diagnoses of climate fluctuations is examined emphasizing the assemblage of a host of observations, to develop a clearer physical picture of the nature and causal interrelationships of the climate events. Development of better statistical methods for making predictions of climate fluctuations and improving numerical climate prediction models is considered along with obtaining data for areas for which meager records exist such as the tropics and the southern hemisphere. The major circulation systems in the tropics, energy transports by the oceans and atmosphere, and the reflected or absorbed solar radiation values from the earth's surface are among the phenomena to be studied.

Source record↗

NASA NTRS1981

Interplanetary Alfvenic fluctuations - A stochastic model

The concept of minimum variance is investigated for nonplanar interplanetary Alfvenic fluctuations in which the field direction varies randomly. The theory of the random wandering of a vector of constant length is developed as a representation of the magnetic field, and it is found that the minimum variance tends to coincide with the mean field directions over the correlation time of the fluctuations. The Fokker-Planck limit of the theory is then developed and used to analyze the statistic distribution of field directions with and without a reflecting barrier. Results suggest that the tendency of the Alfvenic fluctuations to have a direction of minimum variance statistically aligned with the mean magnetic field may be purely a consequence of the randomness of the fluctuation and not imply that the fluctuations are necessarily plane waves. Extensive statistical studies of the observed directional variations of the interplanetary magnetic field are necessary to test this hypothesis.

Barnes, A.↗

NASA NTRS2011

Calibrated Noise Measurements with Induced Receiver Gain Fluctuations

The lack of well-developed techniques for modeling changing statistical moments in our observations has stymied the application of stochastic process theory in science and engineering. These limitations were encountered when modeling the performance of radiometer calibration architectures and algorithms in the presence of non stationary receiver fluctuations. Analyses of measured signals have traditionally been limited to a single measurement series. Whereas in a radiometer that samples a set of noise references, the data collection can be treated as an ensemble set of measurements of the receiver state. Noise Assisted Data Analysis is a growing field of study with significant potential for aiding the understanding and modeling of non stationary processes. Typically, NADA entails adding noise to a signal to produce an ensemble set on which statistical analysis is performed. Alternatively as in radiometric measurements, mixing a signal with calibrated noise provides, through the calibration process, the means to detect deviations from the stationary assumption and thereby a measurement tool to characterize the signal's non stationary properties. Data sets comprised of calibrated noise measurements have been limited to those collected with naturally occurring fluctuations in the radiometer receiver. To examine the application of NADA using calibrated noise, a Receiver Gain Modulation Circuit (RGMC) was designed and built to modulate the gain of a radiometer receiver using an external signal. In 2010, an RGMC was installed and operated at the National Institute of Standards and Techniques (NIST) using their Noise Figure Radiometer (NFRad) and national standard noise references. The data collected is the first known set of calibrated noise measurements from a receiver with an externally modulated gain. As an initial step, sinusoidal and step-function signals were used to modulate the receiver gain, to evaluate the circuit characteristics and to study the performance of a variety of calibration algorithms. The receiver noise temperature and time-bandwidth product of the NFRad are calculated from the data. Statistical analysis using temporal-dependent calibration algorithms reveals that the natural occurring fluctuations in the receiver are stationary over long intervals (100s of seconds); however the receiver exhibits local non stationarity over the interval over which one set of reference measurements are collected. A variety of calibration algorithms have been applied to the data to assess algorithms' performance with the gain fluctuation signals. This presentation will describe the RGMC, experiment design and a comparative analysis of calibration algorithms.

Racette, Paul↗