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NASA NTRS2023

Quantification of Global Cloud Properties with Use of Spherical Harmonic Functions

Spherical harmonic (SH) expansion is a useful tool to study any variable that has valid values at all latitudes and longitudes. The variable can be quantified as a sum of different spherical harmonic components, which are the spherical harmonic functions multiplied by their expansion coefficients. We find that the SH components of cloud radiative effect (CRE) have correlations with El Niño-Southern Oscillation (ENSO) and the Hadley Circulation (HC). In particular, the expansion degree 2 (l = 2) SH power spectrum component anomaly of CRE is strongly correlated with ENSO. The two dipole patterns appearing in the l = 2 SH component anomaly map can be reasonably explained by a known mechanism of ENSO’s impact on cloud properties. The l = 3 and l = 5 SH power spectrum components are correlated with HC intensity, whereas the l = 6 and l = 8 components are correlated with HC latitudinal widths. In ENSO warm and cold phases, the HC-correlated SH components have opposite anomalies, which suggests the impact of ENSO on HC. This study illustrates that the SH expansion technique provides a different perspective to study the impacts of large-scale atmospheric circulation on global cloud properties and radiative effects.

clouds↗
NASA NTRS1988

Spectrometer technology recommendations

A typical heterodyne remote sensing system contains three major elements: the antenna, the radiometer, and the spectrometer. The radiometer consists of the local oscillator, the mixer, and the intermediate frequency amplifiers. This subsystem performs the function of down converting the high frequency incident thermal emission signal to a lower intermediate frequency. The spectrometer measures the power spectrum of the down-converted signal simultaneously in many contiguous frequency channels. Typical spectrum analysis requirements involve measurement of signal bandwidths of 100 to 1000 MHz with a channel resolution of 0.5 to 10 MHz. Three general approaches are used for spectrometers: (1) filter banks, (2) Acousto-Optic Spectrometers (AOS's), and (3) digital autocorrelators. In contrast to the two frequency domain techniques, an autocorrelator works in the time domain. The autocorrelation function (ACF) of the incoming signal is computed and averaged over the integration time. The averaged ACF is then Fourier transformed to obtain the signal power spectrum. Significant progress was made in the development of sub mm antennas and radiometers. It is now time to begin research in the development of low power spaceborne spectrometers and to reduce their size and weight. The near-term research goal will be to develop a prototype digital autocorrelation spectrometer, using VLSI gate array technology, which will have a small size, low power requirements, and can be used in spacecraft mm and sub mm radiometer systems. The long-range objective of this technology development is to make extremely low power, less than 10 mW/channel, small and stable wideband spectrometers which can be used in future mm and sub mm wavelength space missions such as the Large Deployable Reflector.

Wilson, William J.↗
NASA NTRS2008

Magnetofluid Turbulence in the Solar Wind

The solar wind shows striking characteristics that suggest that it is a turbulent magnetofluid, but the picture is not altogether simple. From the earliest observations, a strong correlation between magnetic fluctuations and plasma velocity fluctuations was noted. The high corrections suggest that the fluctuations are Alfven waves. In addition, the power spectrum of the magnetic fluctuation showed evidence of an inertial range that resembled that seen in fully-developed fluid turbulence. Alfven waves, however, are exact solutions of the equations of incompressible magnetohydrodynamics. Thus, there was a puzzle: how can a magnetofluid consisting of Alfven waves be turbulent? The answer lay in the role of velocity shears in the solar wind that could drive turbulent evolution. Puzzles remain: for example, the power spectrum of the velocity fluctuations is less steep than the slope of the magnetic fluctuations, nor do we understand even now why the solar wind appears to be nearly incompressible with a -5/3 power-spectral index.

Goldstein, Melvyn L.↗
NASA NTRS1996

Accurate Predictions of Mean Geomagnetic Dipole Excursion and Reversal Frequencies, Mean Paleomagnetic Field Intensity, and the Radius of Earth's Core Using McLeod's Rule

The geomagnetic spatial power spectrum R(sub n)(r) is the mean square magnetic induction represented by degree n spherical harmonic coefficients of the internal scalar potential averaged over the geocentric sphere of radius r. McLeod's Rule for the magnetic field generated by Earth's core geodynamo says that the expected core surface power spectrum (R(sub nc)(c)) is inversely proportional to (2n + 1) for 1 less than n less than or equal to N(sub E). McLeod's Rule is verified by locating Earth's core with main field models of Magsat data; the estimated core radius of 3485 kn is close to the seismologic value for c of 3480 km. McLeod's Rule and similar forms are then calibrated with the model values of R(sub n) for 3 less than or = n less than or = 12. Extrapolation to the degree 1 dipole predicts the expectation value of Earth's dipole moment to be about 5.89 x 10(exp 22) Am(exp 2)rms (74.5% of the 1980 value) and the expected geomagnetic intensity to be about 35.6 (mu)T rms at Earth's surface. Archeo- and paleomagnetic field intensity data show these and related predictions to be reasonably accurate. The probability distribution chi(exp 2) with 2n+1 degrees of freedom is assigned to (2n + 1)R(sub nc)/(R(sub nc). Extending this to the dipole implies that an exceptionally weak absolute dipole moment (less than or = 20% of the 1980 value) will exist during 2.5% of geologic time. The mean duration for such major geomagnetic dipole power excursions, one quarter of which feature durable axial dipole reversal, is estimated from the modern dipole power time-scale and the statistical model of excursions. The resulting mean excursion duration of 2767 years forces us to predict an average of 9.04 excursions per million years, 2.26 axial dipole reversals per million years, and a mean reversal duration of 5533 years. Paleomagnetic data show these predictions to be quite accurate. McLeod's Rule led to accurate predictions of Earth's core radius, mean paleomagnetic field intensity, and mean geomagnetic dipole power excursion and axial dipole reversal frequencies. We conclude that McLeod's Rule helps unify geo-paleomagnetism, correctly relates theoretically predictable statistical properties of the core geodynamo to magnetic observation, and provides a priori information required for stochastic inversion of paleo-, archeo-, and/or historical geomagnetic measurements.

Voorhies, Coerte V.↗
NASA NTRS1971

Noise analysis of nucleate boiling

The techniques of noise analysis have been utilized to investigate nucleate pool boiling. A simple experimental setup has been developed for obtaining the power spectrum of a nucleate boiling system. These techniques were first used to study single bubbles, and a method of relating the two-dimensional projected size and the local velocity of the bubbles to the auto-correlation functions is presented. This method is much less time consuming than conventional methods of measurement and has no probes to disturb the system. These techniques can be used to determine the contribution of evaporation to total heat flux in nucleate boiling. Also, these techniques can be used to investigate the effect of various parameters upon the frequency response of nucleate boiling. The predominant frequencies of the power spectrum correspond to the frequencies of bubble generation. The effects of heat input, degree of subcooling, and liquid surface tension upon the power spectra of a boiling system are presented. It was found that the degree of subcooling has a more pronounced effect upon bubble size than does heat flux. Also the effect of lowering surface tension can be sufficient to reduce the effect of the degree of subcooling upon the size of the bubbles.

Mcknight, R. D.↗
NASA NTRS2020

The Atacama Cosmology Telescope: Constraints on Cosmic Birefringence

We present new constraints on anisotropic birefringence of the cosmic microwave background polarization using two seasons of data from the Atacama Cosmology Telescope covering 456 square degrees of sky. The birefringence power spectrum, measured using a curved-sky quadratic estimator, is consistent with zero. Our results provide the tightest current constraint on birefringence over a range of angular scales between 5 arc minutes and 9°. We improve previous upper limits on the amplitude of a scale-invariant birefringence power spectrum by a factor of between 2 and 3. Assuming a nearly massless axion field during inflation, our result is equivalent to a 2σ upper limit on the Chern-Simons coupling constant between axions and photons of g(αγ)< 4.0 × 10(exp -2)/H(I), where H(I) is the inflationary Hubble scale.

Toshiya Namikawa↗
NASA NTRS1976

Real time analysis of voiced sounds

A power spectrum analysis of the harmonic content of a voiced sound signal is conducted in real time by phase-lock-loop tracking of the fundamental frequency, (f sub 0) of the signal and successive harmonics (h sub 1 through h sub n) of the fundamental frequency. The analysis also includes measuring the quadrature power and phase of each frequency tracked, differentiating the power measurements of the harmonics in adjacent pairs, and analyzing successive differentials to determine peak power points in the power spectrum for display or use in analysis of voiced sound, such as for voice recognition.

Hong, J. P.↗
NASA NTRS1992

Separability of spatiotemporal spectra of image sequences

The spatiotemporal power spectrum was calculated of 14 image sequences in order to determine the degree to which the spectra are separable in space and time, and to assess the validity of the commonly used exponential correlation model found in the literature. The spectrum was expanded by a Singular Value Decomposition into a sum of separable terms and an index was defined of spatiotemporal separability as the fraction of the signal energy that can be represented by the first (largest) separable term. All spectra were found to be highly separable with an index of separability above 0.98. The power spectra of the sequences were well fit by a separable model. The power spectrum model corresponds to a product of exponential autocorrelation functions separable in space and time.

Eckert, Michael P.↗
NASA NTRS1994

Topological analysis of the CfA redshift survey

We study the topology of large-scale structure in the Center for Astrophysics Redshift Survey, which now includes approximately 12,000 galaxies with limiting magnitude m(sub B) is less than or equal to 15.5. The dense sampling and large volume of this survey allow us to compute the topology on smoothing scales from 6 to 20/h Mpc; we thus examine the topology of structure in both 'nonlinear' and 'linear' regimes. On smoothing scales less than or equal to 10/h Mpc this sample has 3 times the number of resolution elements of samples examined in previous studies. Isodensity surface of the smoothed galaxy density field demonstrate that coherent high-density structures and large voids dominate the galaxy distribution. We compute the genus-threshold density relation for isodensity surfaces of the CfA survey. To quantify phase correlation in these data, we compare the CfA genus with the genus of realizations of Gaussian random fields with the power spectrum measured for the CfA survey. On scales less than or equal to 10/h Mpc the observed genus amplitude is smaller than random phase (96% confidence level). This decrement reflects the degree of phase coherence in the observed galaxy distribution. In other words the genus amplitude on these scales is not good measure of the power spectrum slope. On scales greater than 10/h Mpc, where the galaxy distribution is rougly in the 'linear' regime, the genus ampitude is consistent with the random phase amplitude. The shape of the genus curve reflects the strong coherence in the observed structure; the observed genus curve appears broader than random phase (94% confidence level for smoothing scales less than or equal to 10/h Mpc) because the topolgoy is spongelike over a very large range of density threshold. This departre from random phase consistent with a distribution like a filamentary net of 'walls with holes.' On smoothing scales approaching approximately 20/h Mpc the shape of the CfA genus curve is consistent with random phase. There is very weak evidence for a shift of the genus toward a 'bubble-like' topology. To test cosmological models, we compute the genus for mock CfA surveys drawn from large (L greater than or approximately 400/h Mpc) N-body simulations of three variants of the cold dark matter (CDM) cosmogony. The genus amplitude of the 'standard' CDM model (omega h = 0.5, b = 1.5) differs from the observations (96% confidence level) on smoothing scales is less than or approximately 10/h Mpc. An open CDM model (omega h = 0.2) and a CDM model with nonzero cosmological constant (omega h = 0.24, lambda (sub 0) = 0.6) are consistent with the observed genus amplitude over the full range of smoothing scales. All of these models fail (97% confidence level) to match the broadness of the observed genus curve on smoothing scales is less than or equal to 10/h Mpc.

Vogeley, Michael S.↗
NASA NTRS2016

Far Sidelobe Effects from Panel Gaps of the Atacama Cosmology Telescope

The Atacama Cosmology Telescope is a 6 meter diameter CMB telescope located at 5200 meters in the Chilean desert. ACT has made arc-minute scale maps of the sky at 90 and 150 GHz which have led to precise measurements of the fine angular power spectrum of the CMB fluctuations in temperature and polarization. One of the goals of ACT is to search for the B-mode polarization signal from primordial gravity waves, and thus extending ACT's data analysis to larger angular scales. This goal introduces new challenges in the control of systematic effects, including better understanding of far sidelobe effects that might enter the power spectrum at degree angular scales. Here we study the effects of the gaps between panels of the ACT primary and secondary reflectors in the worst case scenario in which the gaps remain open. We produced numerical simulations of the optics using GRASP up to 8 degrees away from the main beam and simulated timestreams for observations with this beam using real pointing information from ACT data. Maps from these simulated timestreams showed leakage from the sidelobes, indicating that this effect must be taken into consideration at large angular scales.

The Atacama Cosmology Telescope↗
NASA NTRS2007

Bayesian Analysis of the Cosmic Microwave Background

There is a wealth of cosmological information encoded in the spatial power spectrum of temperature anisotropies of the cosmic microwave background! Experiments designed to map the microwave sky are returning a flood of data (time streams of instrument response as a beam is swept over the sky) at several different frequencies (from 30 to 900 GHz), all with different resolutions and noise properties. The resulting analysis challenge is to estimate, and quantify our uncertainty in, the spatial power spectrum of the cosmic microwave background given the complexities of "missing data", foreground emission, and complicated instrumental noise. Bayesian formulation of this problem allows consistent treatment of many complexities including complicated instrumental noise and foregrounds, and can be numerically implemented with Gibbs sampling. Gibbs sampling has now been validated as an efficient, statistically exact, and practically useful method for low-resolution (as demonstrated on WMAP 1 and 3 year temperature and polarization data). Continuing development for Planck - the goal is to exploit the unique capabilities of Gibbs sampling to directly propagate uncertainties in both foreground and instrument models to total uncertainty in cosmological parameters.

methods - statistical↗
NASA NTRS1977

Theoretical jet exhaust noise model for the duct burning turbofan

A model was developed to predict the acoustic power spectrum for a Duct Burning Turbofan (DBTF) whose cycle results in a high velocity, high temperature fan stream and a lower velocity, lower temperature primary stream. Model tests have demonstrated that a DBTF may produce substantially less noise than a conventional turbojet with the same thrust and weight flow. Predictions from the model agreed well with measured data from the model tests. The characteristics of the DBTF acoustic power spectrum were shown to be related to the rapid mixing of the fan and primary streams. The effects of fan to primary velocity ratio, temperature ratio, area ratio, and the effect of nozzle geometry on DBTF jet noise were determined.

Larson, R. S.↗
NASA NTRS1989

Speckle interferometry of asteroids

Steward Observatory's two-dimensional power spectrum signature analysis of speckle interferometry observations is summarized. Results for six asteroids are presented. The poles and triaxial ellipsoid dimensions of 4 Vesta, 433 Eros, 511 Davida, and 532 Herculina have been previously reported. New results for 2 Pallas and 29 Amphitrite are given, as well as further results for Vesta. Image reconstruction is ultimately required to minimize biasing effects of asteroid surface features on the simpler power spectrum analysis. Preliminary imaging results have been achieved for Vesta and Eros, and images for these two are displayed. Speckle interferometry and radiometry diameters are compared, and diameters from the two occultations of Pallas are addressed.

Drummond, Jack D.↗
NASA NTRS2010

Turbulence and Global Properties of the Solar Wind

The solar wind shows striking characteristics that suggest that it is a turbulent magnetofluid, but the picture is not altogether simple. From the earliest observations, a strong correlation between magnetic fluctuations and plasma velocity fluctuations was noted. The high corrections suggest that the fluctuations are Alfven waves. In addition, the power spectrum of the magnetic fluctuation showed evidence of an inertial range that resembled that seen in fully-developed fluid turbulence. Alfven waves, however, are exact solutions of the equations of incompressible magnetohydrodynamics. Thus, there was a puzzle: how can a magnetofluid consisting of Alfven waves be turbulent? The answer lay in the role of velocity shears in the solar wind that could drive turbulent evolution. Puzzles remain: for example, the power spectrum of the velocity fluctuations is less steep than the slope of the magnetic fluctuations. The plasma in the magnetic tail of Earth's magnetosphere also shows aspects of turbulence, as does the plasma in the dayside magnetosphere near the poles the dayside cusps. Recently, new analyses of high time resolution magnetic field data from Cluster have offered a glimpse of how turbulence is dissipated, thus heating the ambient plasma.

Goldstein, Melvyn L.↗
NASA NTRS2007

Turbulence and Global Properties of the Solar Wind

The solar wind shows striking characteristics that suggest that it is a turbulent magnetofluid, but the picture is not altogether simple. From the earliest observations, a strong correlation between magnetic fluctuations and plasma velocity fluctuations as noted. The high corrections suggest that the fluctuations are Alven waves. In addition, the power spectrum of the magnetic fluctuation showed evidence of an inertial range that resembled that seen in fully-developed fluid turbulence. Alfven waves, however, are exact solutions of the equations of an incompressible magnetohydrodynamics. Thus, there was a puzzle: how can a magnetofluid consisting of Alfven waves be turbulent? The answer lay in the role of velocity shears in the solar wind that could drive turbulent evolution. Puzzles remain: for example, the power spectrum of the velocity fluctuations is less steep than the slope of the magnetic fluctuations. The plasma in the magnetic tail of Earth's magnetosphere also shows aspects of turbulence, as does the plasma in the dayside magnetosphere near the poles--the so-called dayside cusps.

Goldstein, Melvyn L.↗
NASA NTRS2015

Phase-Based Adaptive Estimation of Magnitude-Squared Coherence Between Turbofan Internal Sensors and Far-Field Microphone Signals

A cross-power spectrum phase based adaptive technique is discussed which iteratively determines the time delay between two digitized signals that are coherent. The adaptive delay algorithm belongs to a class of algorithms that identifies a minimum of a pattern matching function. The algorithm uses a gradient technique to find the value of the adaptive delay that minimizes a cost function based in part on the slope of a linear function that fits the measured cross power spectrum phase and in part on the standard error of the curve fit. This procedure is applied to data from a Honeywell TECH977 static-engine test. Data was obtained using a combustor probe, two turbine exit probes, and far-field microphones. Signals from this instrumentation are used estimate the post-combustion residence time in the combustor. Comparison with previous studies of the post-combustion residence time validates this approach. In addition, the procedure removes the bias due to misalignment of signals in the calculation of coherence which is a first step in applying array processing methods to the magnitude squared coherence data. The procedure also provides an estimate of the cross-spectrum phase-offset.

Combustion↗
NASA NTRS1995

Testing higher-order Lagrangian perturbation theory against numerical simulations. 2: Hierarchical models

We present results showing an improvement of the accuracy of perturbation theory as applied to cosmological structure formation for a useful range of scales. The Lagrangian theory of gravitational instability of Friedmann-Lemaitre cosmogonies is compared with numerical simulations. We study the dynamics of hierarchical models as a second step. In the first step we analyzed the performance of the Lagrangian schemes for pancake models, the difference being that in the latter models the initial power spectrum is truncated. This work probed the quasi-linear and weakly non-linear regimes. We here explore whether the results found for pancake models carry over to hierarchical models which are evolved deeply into the non-linear regime. We smooth the initial data by using a variety of filter types and filter scales in order to determine the optimal performance of the analytical models, as has been done for the 'Zel'dovich-approximation' - hereafter TZA - in previous work. We find that for spectra with negative power-index the second-order scheme performs considerably better than TZA in terms of statistics which probe the dynamics, and slightly better in terms of low-order statistics like the power-spectrum. However, in contrast to the results found for pancake models, where the higher-order schemes get worse than TZA at late non-linear stages and on small scales, we here find that the second-order model is as robust as TZA, retaining the improvement at later stages and on smaller scales. In view of these results we expect that the second-order truncated Lagrangian model is especially useful for the modelling of standard dark matter models such as Hot-, Cold-, and Mixed-Dark-Matter.

Melott, A. L.↗
NASA NTRS2006

The 2004 Hyperflare from SGR 1806-20: Further Evidence for Global Torsional Vibrations

We report an analysis of the archival Rossi X-ray Timing Explorer (RXTE) data from the December 2004 hyperflare from SGR 1806-20. In addition to the approx. equal to 90 Hz QPO first discovered by Israel et al., we report the detection of higher frequency oscillations at approx. equal to 150, 625, and 1,835 Hz. In addition to these frequencies there are indications of oscillations at approx. equal to 720, and 2,384 Hz, but with lower significances. The 150 Hz QPO has a width (FWHM) of about 17 Hz, an average amplitude (rms) of 6.5%, and is detected in average power spectra centered on the rotational phase of the strongest peak in the pulse profile. This is approximately half a rotational cycle from the phase at which the 90 Hz QPO is strongly detected. The 625 Hz oscillation was first detected in an average power spectrum from nine successive cycles beginning approximately 180 s after the initial hard spike. It has a width (FWHM) of approx. equal to 2 Hz and an average amplitude (rms) during this interval of 9%. We find a strong detection of the 625 Hz oscillation in a pair of successive rotation cycles beginning about 230 s after the start of the flare. In these cycles we also detect the 1,835 Hz QPO with the 625 Hz oscillation. The rotational phase in which the 625 Hz &PO is detected is similar to that for the 90 Hz QPO, indeed, this feature is seen in the same average power spectrum. During the time the 625 Hz QPO is detected we also confirm the simultaneous presence of 30 and 92 Hz QPOs, first reported by Israel et al. The centroid frequency of the 625 Hz QPO detected with RXTE is within 1 Hz of the M 626 Hz oscillation recently found in RHESSI data from this hyperflare by Watts & Strohmayer, however, the two detections were made in different phase and energy intervals. Nevertheless, we argue that the two results likely represent detections of the same oscillation frequency intrinsic to the source, but we comment on some of the difficulties in making direct comparisons between the RXTE and RHESSI measurements

Strohmayer, Tod E.↗