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NASA NTRS1986

Radar backscatter measurement accuracies using digital Doppler processors in spaceborne scatterometers

The normalized standard deviation, Kp, of radar backscatter measurements using digital Doppler processors in spaceborne scatterometers is derived. The Kp expression for analog Doppler filter processors, such as that used in the Seasat scatterometer is shown to be a special case of the derived Kp expression. A connection to Welch's (1967) power spectrum estimation rsults is also made. Tradeoff studies in digital filter design such as hardware complexity, computational speed, and system performance can be performed based on this Kp expression. A current application in the design of the NASA scatterometer to be flown in 1990 is discussed. This derivation should be useful for system design and analysis of other radar remote-sensing instruments.

Chi, C.-Y.↗
NASA NTRS1986

The influence of earthquakes on the Chandler wobble during 1977-1983

Variations in the Chandler wobble's excitation function are examined in order to study the effect of 1287 earthquakes on the Chandler wobble. The computation of the moment tensor data using the centroid-moment tensor solution technique is described. An excitation function is calculated from the moment tensor data and compared to an observed excitation function derived from the polar motion observations of Gross and Chao (1985). It is observed, based on the power spectrum of the earthquake excitation function, that the earthquakes' static deformation fields have little influence on the Chandler wobble during 1977-1983.

Gross, R. S.↗
NASA NTRS1986

Observations of vertical velocity power spectra with the SOUSY VHF radar

A data set taken with the SOUSY VHF radar from October 28 to November 13, 1981 was used to calculate the power spectrum of the vertical velocities directly from the vertical beam measurements. The spectral slopes for the frequency spectra have been determined out to periods of several days and have been found to have values near -1 in the troposphere and shallower slopes in the lower stratosphere. The value of -1 is in agreement with the value found by Larsen et al. (1985) and Balsley and Carter (1982) in the range from a few minutes to 1 hr.

Larsen, M. F.↗
NASA NTRS1986

An evaluation of errors observed in the measurement of low wind velocities

Measurements of low wind velocities (the absolute value of V sub H is approx. equal to 6 m/s) with a VHF wind profiler can be difficult if ground clutter or other biases in the system dominate in altering the position of the perceived peak in the calculated power spectrum. A variety of methods for ground clutter suppression are used in profiler systems today (Cornish, 1983). An editing method called zero suppression takes the spectral value of selectable number of points (N) on each side of 0 velocity (one point on either side, in this study) and sets them equal to the mean value of the points exterior to the specified N points on either side of 0. Analysis done with the PSU VHF(1) radar, shows that this zero-suppression method can systematically bias horizontal wings V sub H below 6 m/s. With the zero suppression, an artificial increase in absolute wind velocities occurs when the spectral peaks fall within the plus or minus N points of the FFT (personal communication, Strauch, 1985). It was also established that the method artificially decreases the absolute wind velocities inferred from spectral peaks that are outside but near the suppressed region. Comparisons of wind profiles observed with and without zero suppression are given. The range of the biased velocities extends to about plus or minus 6 m/s. Biases have been deduced to be as much as 2 m/s, but more commonly they are on the order of 1.0 m/s.

Williams, S. R.↗
NASA NTRS1986

Beam steering system

A simple technique for steering the beam of a multimodule phased array MST (mesosphere, stratosphere, troposphere) radar antenna is described. It is desirable to be able to point the antenna in multiple directions, so as to derive all components of the horizontal velocity. This was done on an experimental basis by adding parallel wire line to the feed and achieving a southward tilt of the antenna. It is proved possible to steer the beam through most of the available range without adversely affecting the VSWR seen from the transmitter. Calibrating the antenna direction can be accomplished by observing radio sources, though there are an inadequate number to cover all directions. For various assumed values of the aspect sensitivity in dB/deg, and the calculated antenna pattern, it is possible to calculate the effective pointing angle of the antenna, defined as that angle which would give an identical location for the centroid of the power spectrum if aspect sensitivity were absent. Using averaged apparent steering directions, eastward and northward winds were calculated for special radar runs simultaneous with 14 balloon launches at Peoria and results are presented.

Bowhill, S. A.↗
NASA NTRS1986

An overview of data acquisition, signal coding and data analysis techniques for MST radars

An overview is given of the data acquisition, signal processing, and data analysis techniques that are currently in use with high power MST/ST (mesosphere stratosphere troposphere/stratosphere troposphere) radars. This review supplements the works of Rastogi (1983) and Farley (1984) presented at previous MAP workshops. A general description is given of data acquisition and signal processing operations and they are characterized on the basis of their disparate time scales. Then signal coding, a brief description of frequently used codes, and their limitations are discussed, and finally, several aspects of statistical data processing such as signal statistics, power spectrum and autocovariance analysis, outlier removal techniques are discussed.

Rastogi, P. K.↗
NASA NTRS1986

Jeans criterion in a turbulent medium

According to the classical Jeans analysis, all the molecular clouds of mass larger than a few 100 M(solar), size larger than about 1pc and kinetic temperature Tk less than 30K are gravitationally unstable. We have shown that in clouds supported by internal supersonic motions, local gravitational instabilities may appear within molecular clouds which are globally stable. The argument is threefold: (1) when the turbulent kinetic energy is included into the internal energy term, the virial equilibrium condition shows that molecular clouds such as those observed, which are gravitationally unstable according to the Jeans criterion, are indeed globally stable if supported by a turbulent velocity field of power spectrum steeper than 3; (2) 2D compressible hydrodynamical simulations show that a supersonic turbulent velocity field generates a turbulent pressure within clouds, the gradients of which stabilize the unstable scales (i.e., the largest scales and the cloud itself) against gravitational collapse; (3) an analysis similar to the Jeans approach but including the turbulent pressure gradient term, gives basically the same results as those given in (1). Clouds of mean density lower than a critical value are found to be stable even though more massive than their Jeans mass. In clouds of mean density larger than that critical value, the gravitational instability appears only over a range of scales smaller than the cloud size, the largest scales being stable. In practice, the observed mean densities are lower than this critical value: the observation of a small number of cores and stars of a few solar masses embedded in clouds of several hundred solar masses can only be understood in terms of small scale density fluctuations of large amplitude generated by the supersonic turbulence which would occasionally overtake the limit of gravitational stability.

Bonazzola, S.↗
NASA NTRS1986

Persistent time intervals between features in solar flare hard X-ray emission

Several solar hard X-ray events (greater than 100 keV) were observed simultaneously with identical instruments on the Venera 11, 12, 13, 14, and Prognoz spacecraft. High time resolution (= 2 ms) data were stored in memory when a trigger occurred. The observations of modulation are presented with a period of 1.6 s for the event on December 3, 1978. Evidence is also presented for fast time fluctuations from an event on November 6, 1979, observed from Venera 12 and another on September 6, 1981, observed from the Solar Maximum Mission. Power spectrum analysis, epoch folding, and Monte Carlo simulation were used to evaluate the statistical significance of persistent time delays between features. The results are discussed in light of the MHD model proposed by Zaitsev and Stepanov.

Desai, Upendra D.↗
NASA NTRS1987

Improvements in the perturbation simulations of the global reference atmospheric model

The Global Reference Atmospheric Model (GRAM) program includes the capability for simulating pseudo-random perturbations in density, temperature, pressure, or wind components along a simulated reentry trajectory or other path through the atmosphere. Some concerns were expressed by GRAM users, however, that the mean-square perturbation gradients may be too large for small values of the vertical separation Delta z. The present GRAM perturbation simulations, based on a one-step autoregressive model, yield a power spectrum versus wavenumber k which is proportional to k sup -2 at high wavenumbers. This feature also produces mean-square perturbation differences which are directly proportional to Delta z, and mean-square perturbation gradients which are inversely proportional to Delta z. Thus, root-mean-square gradients, (Delta f/Delta z) sub rms, increase with decreasing Delta a as Delta z sup -1/2. A simple modification to GRAM is suggested which overcomes this problem, i.e., which produce root-mean-square gradient that remain bound as Delta z approaches zero. Possible applications of more sophisticated simulation approaches, e.g., second order autoregressive models, or fractal model techniques, were also explored briefly but found to yield improvements which appear too small to justify their considerable added complexity for use in the GRAM programs.

Justus, C. G.↗
NASA NTRS1986

Observations of low-degree p-mode oscillations in 1984

Analysis of Stanford differential velocity observations has been extended through the 1984 observing season. Excellent quality observations were obtained in 1984 on 38 days in a 49 day interval from June 20th through August 7th. The power spectrum of this data has been examined and improved frequency determinations have been made for p-modes of degree 2 through 5 and order 5 through 34. Of special interest are the modes of the lower orders, n ranging from 5 to 10, which have not been identified previously.

Henning, Harald M.↗
NASA NTRS1986

The topology of the large-scale structure of the universe

It has been suggested recently that the topology of a distribution of galaxies can be characterized by the mean Gaussian curvature per unit volume of surfaces of constant density. An expression is derived which relates the mean curvature of isodensity surfaces to the power spectrum of density fluctuations in the linear regime of Gaussian fluctuations with random phases. The result may be compared to real galaxy catalogs if the galaxy density is smoothed over scales larger than a correlation length. The implications of the result for understanding the large-scale structure of the universe are discussed.

Hamilton, A. J. S.↗
NASA NTRS1987

Pioneer 10 observations of the Beta Cephei stars Gamma Pegasi and Delta Ceti

The results of analyzing broad-band Pioneer 10 photometric observations of the low-amplitude pulsating Beta Cephei stars Gamma Pegasi and Delta Ceti are reported. Periods and light curve amplitudes of 3.649 + or - 0.020 hr, 0.05 + or - 0.02 mag for Gamma Peg and 3.869 + or - 0.020 hr, 0.13 + or - 0.02 mag for Delta Ceti are obtained; a power spectrum analysis of the data reveals no other periods. No evidence is found for a phase shift between the light curve maxima in the UV and visible regions. The observed amplitudes combined with published visual and near-UV data suggest a flux and temperature variability of about 200 solar luminosities and 250 K for Gamma Peg and about 600 solar luminosities and 450 K for Delta Cet. These results are compared with others obtained with satellite and ground-based instrumentation.

Peters, Geraldine J.↗
NASA NTRS1987

Use of a minimum rate of change formalism to quantify variability of extragalactic X-ray sources

A method to obtain rigorous, quantitative constraints on the rate of variability is suggested. The method is motivated by the case when the existence of time variability is unequivocal, but the statistical uncertainties are too large to apply more direct methods such as power spectrum analysis. Conceptually the data are fitted to a function of time and a set of free parameters. The method of Lagrange multipliers is used to solve for that parameter set which minimizes the value of the derivative at time t(m). The result can be related physically to the minimum efficiency with which rest mass must be converted to radiation energy. Slightly different formulations of the general principal are used to estimate maximum source size scales associated with the variability.

Schwartz, Daniel A.↗
NASA NTRS1987

Spectral analysis of sinus arrhythmia - A measure of mental effort

The validity of the spectral analysis of sinus arrhythmia as a measure of mental effort was investigated using a computer simulation of a hovercraft piloted along a river as the experimental task. Strong correlation was observed between the subjective effort-ratings and the heart-rate variability (HRV) power spectrum between 0.06 and 0.14 Hz. Significant correlations were observed not only between subjects but, more importantly, within subjects as well, indicating that the spectral analysis of HRV is an accurate measure of the amount of effort being invested by a subject. Results also indicate that the intensity of effort invested by subjects cannot be inferred from the objective ratings of task difficulty or from performance.

Vicente, Kim J.↗
NASA NTRS1987

A quantitative approach to the topology of large-scale structure

A quantitative measure of the topology of large-scale structure: the genus of density contours in a smoothed density distribution, is described and applied. For random phase (Gaussian) density fields, the mean genus per unit volume exhibits a universal dependence on threshold density, with a normalizing factor that can be calculated from the power spectrum. If large-scale structure formed from the gravitational instability of small-amplitude density fluctuations, the topology observed today on suitable scales should follow the topology in the initial conditions. The technique is illustrated by applying it to simulations of galaxy clustering in a flat universe dominated by cold dark matter. The technique is also applied to a volume-limited sample of the CfA redshift survey and to a model in which galaxies reside on the surfaces of polyhedral 'bubbles'. The topology of the evolved mass distribution and 'biased' galaxy distribution in the cold dark matter models closely matches the topology of the density fluctuations in the initial conditions. The topology of the observational sample is consistent with the random phase, cold dark matter model.

Gott, J. Richard, III↗
NASA NTRS1987

Short solar events with evidence of repetitive structures

Several short (less than 40 s) solar hard X-ray events (greater than 100 keV) have been observed simultaneously with identical instruments on the Venera 11, 12, 13, and 14 and Prognoz 7 (Franco-Soviet Signe experiments) spacecraft. High time resolution (equal to or greater than 2 ms) data were stored in memory when a trigger occurred. The observations reported here were made by Prognoz 7 and V12 which were closer to the sun at the time and provided good statistics. Observations of modulation with a period of 1.6 s for the event on 1978 December 3 are presented. Also presented is evidence for fast time fluctuations from an event on 1979 November 6, observed with Venera 12, and another on 1981 September 6, observed with the Solar Maximum Hard X-Ray Burst Spectrometer. Power spectrum analysis, epoch folding, and Monte Carlo simulation to evaluate the statistical significance of persistent time delays between features. The results are discussed in light of the MHD model proposed by Zaitsev and Stepanov (1982) and Zaitsev, Stepanov, and Chernov (1984).

Desai, Upendra D.↗
NASA NTRS1987

Turbulent MHD transport coefficients - An attempt at self-consistency

In this paper, some multiple scale perturbation calculations of turbulent MHD transport coefficients begun in earlier papers are first completed. These generalize 'alpha effect' calculations by treating the velocity field and magnetic field on the same footing. Then the problem of rendering such calculations self-consistent is addressed, generalizing an eddy-viscosity hypothesis similar to that of Heisenberg for the Navier-Stokes case. The method also borrows from Kraichnan's direct interaction approximation. The output is a set of integral equations relating the spectra and the turbulent transport coefficients. Previous 'alpha effect' and 'beta effect' coefficients emerge as limiting cases. A treatment of the inertial range can also be given, consistent with a -5/3 energy spectrum power law. In the Navier-Stokes limit, a value of 1.72 is extracted for the Kolmogorov constant. Further applications to MHD are possible.

Chen, H.↗
NASA NTRS1986

Statistics of the geomagnetic secular variation for the past 5Ma

A new statistical model is proposed for the geomagnetic secular variation over the past 5Ma. Unlike previous models, the model makes use of statistical characteristics of the present day geomagnetic field. The spatial power spectrum of the non-dipole field is consistent with a white source near the core-mantle boundary with Gaussian distribution. After a suitable scaling, the spherical harmonic coefficients may be regarded as statistical samples from a single giant Gaussian process; this is the model of the non-dipole field. The model can be combined with an arbitrary statistical description of the dipole and probability density functions and cumulative distribution functions can be computed for declination and inclination that would be observed at any site on Earth's surface. Global paleomagnetic data spanning the past 5Ma are used to constrain the statistics of the dipole part of the field. A simple model is found to be consistent with the available data. An advantage of specifying the model in terms of the spherical harmonic coefficients is that it is a complete statistical description of the geomagnetic field, enabling us to test specific properties for a general description. Both intensity and directional data distributions may be tested to see if they satisfy the expected model distributions.

Constable, C. G.↗