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NASA NTRS1972

Correlation techniques and measurements of wave-height statistics

Statistical measurements of wave height fluctuations have been made in a wind wave tank. The power spectral density function of temporal wave height fluctuations evidenced second-harmonic components and an f to the minus 5th power law decay beyond the second harmonic. The observations of second harmonic effects agreed very well with a theoretical prediction. From the wave statistics, surface drift currents were inferred and compared to experimental measurements with satisfactory agreement. Measurements were made of the two dimensional correlation coefficient at 15 deg increments in angle with respect to the wind vector. An estimate of the two-dimensional spatial power spectral density function was also made.

Guthart, H.↗

NASA NTRS1972

Absence of the plasma sheet at lunar distance during geomagnetically quiet times.

Evaluation of plasma data from the Apollo 14 charge particle lunar environment experiment showing that, contrary to previously published analyses, the plasma sheet does not extend to the lunar orbit with a thickness of 8 earth radii. Two electron spectral types are observed: (1) low-energy photoelectrons with no statistically significant medium and high energy fluxes, and (2) double-peaked medium- and high-energy electrons. The second type is observed either coincident with auroral substorms or at the center of the tail during quiet times. These spectra are one to several orders of magnitude less intense than plasma sheet spectra measured near 20 earth radii.

Burke, W. J.↗

NASA NTRS1976

Investigations of scaling laws for jet impingement

The statistical properties of tangential flows over surfaces were investigated by two techniques. In one, a laser-Doppler velocimeter was used in a smoke-laden jet to measure one-point statistical properties, including mean velocities, turbulent intensities, intermittencies, autocorrelations, and power spectral densities. In the other technique, free stream and surface pressure probes connected to 1/8 inch microphones were used to obtain single point rms and 1/3 octave pressures, as well as two point cross correlations, the latter being converted to auto spectra, amplitude ratios, phase lags, and coherences. The results of these studies support the vortex model of jets, give some insights into the effects of surface impingement, and confirm that jet diameter and velocity are the scaling parameters for circular jets, while Reynolds number is relatively unimportant.

Morton, J. B.↗

NASA NTRS1989

Determination of design and operation parameters for upper atmospheric research instrumentation to yield optimum resolution with deconvolution, appendix 4

The power spectrum for a stationary random process can be defined with the Wiener-Khintchine Theorem, which says that the power spectrum and the auto correlation function are a Fourier transform pair. To implement this theorem for signals that are discrete and of finite length we can use the Blackman-Tukey method. Blackman and Tukey (1958) show that a function w(tau), called a lag window, can be applied to the auto correlation estimates to obtain power spectrum estimates that are statistically stable. The Fourier transform of w(r) is called a spectral window. Typical choices for spectral windows show a distinct trade-off between the main lobe width and side lobe strength. A new idea for designing windows by taking linear combinations of the standard windows to produce hybrid windows was introduced by Smith (1985). We implement Smith's idea to obtain spectral windows with narrow main lobes and smaller (compared with typical windows) near side lobes. One of the main contributions of this thesis is that we show that Smith's problem is equivalent to a Quadratic Programming (QP) problem with linear equality and inequality constraints. A computer program was written to produce hybrid windows by setting up and solving the QP problem. We also developed and solved two variations of the original problem. The two variations involved changing the inequality constraints in both cases from non negativity on the combination coefficients to non negativity on the hybrid lag window itself. For the second variation, the window functions used to construct the hybrid window were changed to a frequency-variable set of truncated cosinusoids. A series of tests was run with the three computer programs to investigate the behavior of the hybrid spectral and lag windows. Emphasis was put on obtaining spectral windows with both relatively narrow main lobes and the lowest possible (for these algorithms) near side lobes. Some success was achieved for this goal. A 10 dB peak side lobe reduction over the rectangular spectral window without significant main lobe broadening was achieved. Also, average side lobe levels of -117 dB were reached at a cost of doubling the main lobe width (at the -3 dB point).

Ioup, George E.↗

NASA NTRS2006

AstroBiology Explorer Mission Concepts (ABE/ASPIRE)

The AstroBiology Explorer (ABE) and the Astrobiology Space InfraRed Explorer (ASPIRE) Mission Concepts are two missions designed to address the questions (1) Where do we come from? and (2) Are we alone? as outlined in NASA s Origins Program using infrared spectroscopy to explore the identity, abundance, and distribution of molecules of astrobiological importance throughout the Universe. The ABE mission s observational program is focused on six tasks to: (1) Investigate the evolution of ice and organics in dense clouds and star formation regions, and the young stellar/planetary systems that form in them; (2) Measure the evolution of complex organic molecules in stellar outflows; (3) Study the organic composition of a wide variety of solar system objects including asteroids, comets, and the planets and their satellites; (4) Identify organic compounds in the diffuse interstellar medium and determine their distribution , abundance, and change with environment; (5) Detect and identify organic compounds in other galaxies and determine their dependence on galactic type; and (6) Measure deuterium enrichments in interstellar organics and use them as tracers of chemical processes. The ASPIRE mission s observational program expands upon ABE's core mission and adds tasks that (7) Address the role of silicates in interstellar organic chemistry; and (8) Use different resolution spectra to assess the relative roles and abundances of gas- and solid-state materials. ABE (ASPIRE) achieves these goals using a highly sensitive, cryogenically-cooled telescope in an Earth drift-away heliocentric orbit, armed with a suite of infrared spectrometers that cover the 2.5-20(40) micron spectral region at moderate spectral resolution (R>2000). ASPIRE's spectrometer complement also includes a high-resolution (R>25,000) module over the 4-8 micron spectral region. Both missions target lists are chosen to observe a statistically significant sample of a large number of objects of varied types in support of the tasks outline above. The ABE and ASPIRE mission lifetimes are designed to be 14 months and 3 years, respectively, both with significant cryogen and propellant lifetime margins to support an extended observing campaign. The ABE/ASPIRE mission concepts and their supporting Science Teams are led by Principal Investigator Dr. Scott Sandford of NASA s Ames Research Center, with industry partner Ball Aerospace Technologies Ltd., and managed by Jet Propulsion Laboratory. The ABE/ASPIRE Science Operations will be carried out at NASA s Ames Research Center, and the ABE/ASPIRE database will be archived at Caltech/IPAC.

Sandford, Scott↗

NASA NTRS2012

Quality and Consistency of the NASA Ocean Color Data Record

The NASA Ocean Biology Processing Group (OBPG) recently reprocessed the multimission ocean color time-series from SeaWiFS, MODIS-Aqua, and MODIS-Terra using common algorithms and improved instrument calibration knowledge. Here we present an analysis of the quality and consistency of the resulting ocean color retrievals, including spectral water-leaving reflectance, chlorophyll a concentration, and diffuse attenuation. Statistical analysis of satellite retrievals relative to in situ measurements will be presented for each sensor, as well as an assessment of consistency in the global time-series for the overlapping periods of the missions. Results will show that the satellite retrievals are in good agreement with in situ measurements, and that the sensor ocean color data records are highly consistent over the common mission lifespan for the global deep oceans, but with degraded agreement in higher productivity, higher complexity coastal regions.

Franz, Bryan A.↗

NASA NTRS1990

Summary of results and conclusions based on analysis of volume imaging and high spectral resolution lidar data acquired during FIRE phase 1, part 1

The collection of long term global statistics on cloud cover may be most easily accomplished with satellite based observations; however, measurements derived from passive satellite retrieval methods must be calibrated and verified by in situ or ground based remote sensor observations. Verification is not straight forward, however, because the highly variable nature of cloud altitude, morphology, and optical characteristics complicates the scaling of point measurements to satellite footprint sized areas. This is particularly evident for cirrus clouds which may be organized on horizontal scales of 10's of meters to 8 km or more, and have optical depths ranging from less than .003 to greater than 3. Cirrus clouds can strongly influence earths' radiative balance, but, because they are often transmissive, cirrus clouds are difficult to detect and characterize from satellite measurements. Because of its precise ranging capabilities, spatial resolution and sensitivity, lidar observations have played an important role in the detection, depiction, and characterization of cirrus clouds. Some of the characteristics of cirrus clouds are summarized which observed the High Spectral Resolution and Volume Imaging Lidars during the phase 1 IFO and ETO periods.

Grund, Christian J.↗

NASA NTRS1981

The influence of autocorrelation in signature extraction: An example from a geobotanical investigation of Cotter Basin, Montana

The presence of positive serial correlation (autocorrelation) in remotely sensed data results in an underestimate of the variance-covariance matrix when calculated using contiguous pixels. This underestimate produces an inflation in F statistics. For a set of Thematic Mapper Simulator data (TMS), used to test the ability to discriminate a known geobotanical anomaly from its background, the inflation in F statistics related to serial correlation is between 7 and 70 times. This means that significance tests of means of the spectral bands initially appear to suggest that the anomalous site is very different in spectral reflectance and emittance from its background sites. However, this difference often disappears and is always dramatically reduced when compared to frequency distributions of test statistics produced by the comparison of simulated training sets possessing equal means, but which are composed of autocorrelated observations.

Labovitz, M. L.↗

NASA NTRS1982

The influence of autocorrelation in signature extraction - An example from a geobotanical investigation of Cotter Basin, MT

Labovitz, M. L.↗

NASA NTRS1998

Implementation and Testing of Turbulence Models for the F18-HARV Simulation

This report presents three methods of implementing the Dryden power spectral density model for atmospheric turbulence. Included are the equations which define the three methods and computer source code written in Advanced Continuous Simulation Language to implement the equations. Time-history plots and sample statistics of simulated turbulence results from executing the code in a test program are also presented. Power spectral densities were computed for sample sequences of turbulence and are plotted for comparison with the Dryden spectra. The three model implementations were installed in a nonlinear six-degree-of-freedom simulation of the High Alpha Research Vehicle airplane. Aircraft simulation responses to turbulence generated with the three implementations are presented as plots.

Yeager, Jessie C.↗

NASA NTRS1994

Radiative interactions in multi-dimensional chemically reacting flows using Monte Carlo simulations

The Monte Carlo method (MCM) is applied to analyze radiative heat transfer in nongray gases. The nongray model employed is based on the statistical narrow band model with an exponential-tailed inverse intensity distribution. The amount and transfer of the emitted radiative energy in a finite volume element within a medium are considered in an exact manner. The spectral correlation between transmittances of two different segments of the same path in a medium makes the statistical relationship different from the conventional relationship, which only provides the non-correlated results for nongray methods is discussed. Validation of the Monte Carlo formulations is conducted by comparing results of this method of other solutions. In order to further establish the validity of the MCM, a relatively simple problem of radiative interactions in laminar parallel plate flows is considered. One-dimensional correlated Monte Carlo formulations are applied to investigate radiative heat transfer. The nongray Monte Carlo solutions are also obtained for the same problem and they also essentially match the available analytical solutions. the exact correlated and non-correlated Monte Carlo formulations are very complicated for multi-dimensional systems. However, by introducing the assumption of an infinitesimal volume element, the approximate correlated and non-correlated formulations are obtained which are much simpler than the exact formulations. Consideration of different problems and comparison of different solutions reveal that the approximate and exact correlated solutions agree very well, and so do the approximate and exact non-correlated solutions. However, the two non-correlated solutions have no physical meaning because they significantly differ from the correlated solutions. An accurate prediction of radiative heat transfer in any nongray and multi-dimensional system is possible by using the approximate correlated formulations. Radiative interactions are investigated in chemically reacting compressible flows of premixed hydrogen and air in an expanding nozzle. The governing equations are based on the fully elliptic Navier-Stokes equations. Chemical reaction mechanisms were described by a finite rate chemistry model. The correlated Monte Carlo method developed earlier was employed to simulate multi-dimensional radiative heat transfer. Results obtained demonstrate that radiative effects on the flowfield are minimal but radiative effects on the wall heat transfer are significant. Extensive parametric studies are conducted to investigate the effects of equivalence ratio, wall temperature, inlet flow temperature, and nozzle size on the radiative and conductive wall fluxes.

Liu, Jiwen↗

NASA NTRS2013

A Stochastic Fractional Dynamics Model of Space-time Variability of Rain

Rainfall varies in space and time in a highly irregular manner and is described naturally in terms of a stochastic process. A characteristic feature of rainfall statistics is that they depend strongly on the space-time scales over which rain data are averaged. A spectral model of precipitation has been developed based on a stochastic differential equation of fractional order for the point rain rate, that allows a concise description of the second moment statistics of rain at any prescribed space-time averaging scale. The model is thus capable of providing a unified description of the statistics of both radar and rain gauge data. The underlying dynamical equation can be expressed in terms of space-time derivatives of fractional orders that are adjusted together with other model parameters to fit the data. The form of the resulting spectrum gives the model adequate flexibility to capture the subtle interplay between the spatial and temporal scales of variability of rain but strongly constrains the predicted statistical behavior as a function of the averaging length and times scales. We test the model with radar and gauge data collected contemporaneously at the NASA TRMM ground validation sites located near Melbourne, Florida and in Kwajalein Atoll, Marshall Islands in the tropical Pacific. We estimate the parameters by tuning them to the second moment statistics of radar data. The model predictions are then found to fit the second moment statistics of the gauge data reasonably well without any further adjustment.

TRMM↗

NASA NTRS1989

Singular spectrum analysis in nonlinear dynamics, with applications to paleoclimatic time series

Two dimensions of a dynamical system given by experimental time series are distinguished. Statistical dimension gives a theoretical upper bound for the minimal number of degrees of freedom required to describe the attractor up to the accuracy of the data, taking into account sampling and noise problems. The dynamical dimension is the intrinsic dimension of the attractor and does not depend on the quality of the data. Singular Spectrum Analysis (SSA) provides estimates of the statistical dimension. SSA also describes the main physical phenomena reflected by the data. It gives adaptive spectral filters associated with the dominant oscillations of the system and clarifies the noise characteristics of the data. SSA is applied to four paleoclimatic records. The principal climatic oscillations and the regime changes in their amplitude are detected. About 10 degrees of freedom are statistically significant in the data. Large noise and insufficient sample length do not allow reliable estimates of the dynamical dimension.

Vautard, R.↗

NASA NTRS1990

Statistical properties of ideal three-dimensional magnetohydrodynamics

Classical Gibbs ensemble methods are used to study the spectral structure of three-dimensional ideal MHD in periodic geometry. In this paper the equilibrium ensemble incorporates constraints of total energy, magnetic helicity, and cross helicity. Several new results are proven for ensemble averages, including the constraint that magnetic energy equal or exceed kinetic energy, and that cross helicity represents a constant fraction of magnetic energy across the spectral domain, for arbitrary size systems. Two zero-temperature limits are considered in detail, emphasizing the role of complete and partial condensaiton of spectral quantities to the longest wavelength states. The ensemble predictions are compared to direct numerical solution using a low-order truncation Galerkin spectral code. Implications for spectral transfer of nonequilibrium, dissipative turbulent MHD systems are discussed.

Stribling, T.↗

NASA NTRS1976

High resolution measurements of Cyg X-1 from rockets

Cyg X-1 was observed on two occasions (Oct. 4, 1973 and Oct. 3, 1974) by the Goddard X-ray rocket payload. This payload consisted of two gas proportional counters (xenon-methane with 710 sq cm and argon-methane with 610 sq cm using the same 128 channel pulse height analyzer and having 320 micro sec temporal resolution on the 1973 flight and 160 micro sec resolution on the 1974 flight. During both flights, bursts of 1 ms duration were observed with very high statistical certainty. To date all 13 of these bursts were analyzed for spectral and temporal character, and the results of this analysis are presented. The spectra of overall X-ray emission from both flights is also presented. In a source known for its variability, it is remarkable that the spectra taken one year apart are virtually identical.

Rothschild, R. E.↗

NASA NTRS1978

Effects of systemic and non-systemic stresses on the thermal characteristics of corn

Experiments were conducted on corn plants using a calibrated spectroradiometer under field conditions in the indium antimonide channel (InSb, 2.8 to 5.6 mm) and the mercury cadmium telluride channel (HgCdTe, 7 to 14 mm). A ground cover experiment, an experiment on nonsystemic corn plants, and an experiment on systemic-stressed corn plants were included. The average spectral radiance temperature of corn plant populations was found (1) to be statistically significantly different for four healthy corn plant populations, (2) to increase with increased blight severity, and (3) to be statistically significantly different for varying rates of nitrogen applications.

Kumar, R.↗

NASA NTRS1982

Application of a computerized vibroacoustic data bank for random vibration criteria development

A computerized data bank system was developed for utilization of large amounts of vibration and acoustic data to formulate component random vibration design and test criteria. This system consists of a computer, graphics tablets, and a dry silver hard copier which are all desk top type hardware and occupy minimal space. Currently, the data bank contains data from the Saturn 5 and Titan 3 flight and static test programs. The vibration and acoustic data are stored in the form of power spectral density and one third octave band plots over the frequency range from 20 to 2000 Hz. The data were stored by digitizing each spectral plot by tracing with the graphics tablet. The digitized data were statistically analyzed, and the resulting 97.5 percent confidence levels were stored on tape along with the appropriate structural parameters. Standard extrapolation procedures were programmed for prediction of component random vibration test criteria for new launch vehicle and payload configurations. A user's manual is included to guide potential users through the programs.

Ferebee, R. C.↗

NASA NTRS1981

Comparison of wheat classification accuracy using different classifiers of the image-100 system

Classification results using single-cell and multi-cell signature acquisition options, a point-by-point Gaussian maximum-likelihood classifier, and K-means clustering of the Image-100 system are presented. Conclusions reached are that: a better indication of correct classification can be provided by using a test area which contains various cover types of the study area; classification accuracy should be evaluated considering both the percentages of correct classification and error of commission; supervised classification approaches are better than K-means clustering; Gaussian distribution maximum likelihood classifier is better than Single-cell and Multi-cell Signature Acquisition Options of the Image-100 system; and in order to obtain a high classification accuracy in a large and heterogeneous crop area, using Gaussian maximum-likelihood classifier, homogeneous spectral subclasses of the study crop should be created to derive training statistics.

Dejesusparada, N.↗