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NASA NTRS1993

A statistical analysis of mesoscale rainfall as a random cascade

The paper considers the random cascade theory for spatial rainfall. Particular attention was given to the following four areas: (1) the relationship of the random cascade theory of rainfall to the simple scaling and the hierarchical cluster-point-process theories, (2) the mathematical foundations for some of the formalisms commonly applied in the develpment of statistical cascade theory, (3) the empirical evidence for a random cascade theory of rainfall, and (4) the way of using data for making estimates of parameters and for making statistical inference within this theoretical framework. An analysis of space-time rainfall data is presented. Cascade simulations are carried out to provide a comparison with methods of analysis that are applied to the rainfall data.

Gupta, Vijay K.↗

NASA NTRS1992

Statistical crystallography of surface micelle spacing

The aggregation of the recently reported surface micelles of block polyelectrolytes is analyzed using techniques of statistical crystallography. A polygonal lattice (Voronoi mosaic) connects center-to-center points, yielding statistical agreement with crystallographic predictions; Aboav-Weaire's law and Lewis's law are verified. This protocol supplements the standard analysis of surface micelles leading to aggregation number determination and, when compared to numerical simulations, allows further insight into the random partitioning of surface films. In particular, agreement with Lewis's law has been linked to the geometric packing requirements of filling two-dimensional space which compete with (or balance) physical forces such as interfacial tension, electrostatic repulsion, and van der Waals attraction.

Noever, David A.↗

NASA NTRS1955

Statistical Measurements of Contact Conditions of 478 Transport-airplane Landings During Routine Daytime Operations

Statistical measurements of contact conditions have been obtained, by means of a special photographic technique, of 478 landings of present-day transport airplanes made during routine daylight operations in clear air at the Washington National Airport. From the measurements, sinking speeds, rolling velocities, bank angles, and horizontal speeds at the instant before contact have been evaluated and a limited statistical analysis of the results has been made and is reported in this report.

Silsby, Norman S↗

NASA NTRS1990

Statistical circuit design for yield improvement in CMOS circuits

This paper addresses the statistical design of CMOS integrated circuits for improved parametric yield. The work uses the Monte Carlo technique of circuit simulation to obtain an unbiased estimation of the yield. A simple graphical analysis tool, the yield factor histogram, is presented. The yield factor histograms are generated by a new computer program called SPICENTER. Using the yield factor histograms, the most sensitive circuit parameters are noted, and their nominal values are changed to improve the yield. Two basic CMOS example circuits, one analog and one digital, are chosen and their designs are 'centered' to illustrate the use of the yield factor histograms for statistical circuit design.

Kamath, H. J.↗

NASA NTRS1988

Mathematical and statistical analysis

The goal of the mathematical and statistical analysis component of RICIS is to research, develop, and evaluate mathematical and statistical techniques for aerospace technology applications. Specific research areas of interest include modeling, simulation, experiment design, reliability assessment, and numerical analysis.

Houston, A. Glen↗

NASA NTRS1992

Advanced statistical methods for improved data analysis of NASA astrophysics missions

The investigators under this grant studied ways to improve the statistical analysis of astronomical data. They looked at existing techniques, the development of new techniques, and the production and distribution of specialized software to the astronomical community. Abstracts of nine papers that were produced are included, as well as brief descriptions of four software packages. The articles that are abstracted discuss analytical and Monte Carlo comparisons of six different linear least squares fits, a (second) paper on linear regression in astronomy, two reviews of public domain software for the astronomer, subsample and half-sample methods for estimating sampling distributions, a nonparametric estimation of survival functions under dependent competing risks, censoring in astronomical data due to nondetections, an astronomy survival analysis computer package called ASURV, and improving the statistical methodology of astronomical data analysis.

Feigelson, Eric D.↗

NASA NTRS1993

Statistical results from the Virginia Tech propagation experiment using the Olympus 12, 20, and 30 GHz satellite beacons

Virginia Tech has performed a comprehensive propagation experiment using the Olympus satellite beacons at 12.5, 19.77, and 29.66 GHz (which we refer to as 12, 20, and 30 GHz). Four receive terminals were designed and constructed, one terminal at each frequency plus a portable one with 20 and 30 GHz receivers for microscale and scintillation studies. Total power radiometers were included in each terminal in order to set the clear air reference level for each beacon and also to predict path attenuation. More details on the equipment and the experiment design are found elsewhere. Statistical results for one year of data collection were analyzed. In addition, the following studies were performed: a microdiversity experiment in which two closely spaced 20 GHz receivers were used; a comparison of total power and Dicke switched radiometer measurements, frequency scaling of scintillations, and adaptive power control algorithm development. Statistical results are reported.

Stutzman, Warren L.↗

NASA NTRS1991

Brightness temperature and attenuation statistics at 20.6 and 31.65 GHz

Attenuation and brightness temperature statistics at 20.6 and 31.65 GHz are analyzed for a year's worth of data. The data were collected in 1988 at Denver and Platteville, Colorado. The locations are separated by 49 km. Single-station statistics are derived for the entire year. Quality control procedures are discussed and examples of their application are given.

Westwater, Edgeworth R.↗

NASA NTRS1993

Mars: Noachian hydrology by its statistics and topology

Discrimination between fluvial features generated by surface drainage and subsurface aquifer discharges will provide clues to the understanding of early Mars' climatic history. Our approach is to define the process of formation of the oldest fluvial valleys by statistical and topological analyses. Formation of fluvial valley systems reached its highest statistical concentration during the Noachian Period. Nevertheless, they are a scarce phenomenom in Martian history, localized on the craterized upland, and subject to latitudinal distribution. They occur sparsely on Noachian geological units with a weak distribution density, and appear in reduced isolated surface (around 5 x 10(exp 3)(sq km)), filled by short streams (100-300 km length). Topological analysis of the internal organization of 71 surveyed Noachian fluvial valley networks also provides information on the mechanisms of formation.

Cabrol, N. A.↗

NASA NTRS1993

Computation of large-scale statistics in decaying isotropic turbulence

We have performed large-eddy simulations of decaying isotropic turbulence to test the prediction of self-similar decay of the energy spectrum and to compute the decay exponents of the kinetic energy. In general, good agreement between the simulation results and the assumption of self-similarity were obtained. However, the statistics of the simulations were insufficient to compute the value of gamma which corrects the decay exponent when the spectrum follows a k(exp 4) wave number behavior near k = 0. To obtain good statistics, it was found necessary to average over a large ensemble of turbulent flows.

Chasnov, Jeffrey R.↗

NASA NTRS1969

Numerical results in the statistical theory of thermal turbulence

Several statistical theories of turbulence are applied to thermal convection problem, and are compared in a series of numerical calculations. Results are presented for both the case of very large and very small Prandtl numbers, and for moderate Rayleigh numbers. The theories compared are the direct-interaction approximation, the self-consistent field approximation, the quasi-linear approximation, the quasi-normal approximation, and a 'Markovianized' quasi-normal approximation. Results for these theories are then compared with some simple exact solutions to the statistical problem. The results indicate that the direct-interaction and the self-consistent field method give satisfactory results at all Rayleigh numbers investigated, whereas the procedures based on the quasi-normal approximation give sensible results only at small Rayleigh numbers.

Herring, J. R.↗

NASA NTRS1994

Conditional statistics in a turbulent premixed flame derived from direct numerical simulation

The objective of this paper is to briefly introduce conditional moment closure (CMC) methods for premixed systems and to derive the transport equation for the conditional species mass fraction conditioned on the progress variable based on the enthalpy. Our statistical analysis will be based on the 3-D DNS database of Trouve and Poinsot available at the Center for Turbulence Research. The initial conditions and characteristics (turbulence, thermo-diffusive properties) as well as the numerical method utilized in the DNS of Trouve and Poinsot are presented, and some details concerning our statistical analysis are also given. From the analysis of DNS results, the effects of the position in the flame brush, of the Damkoehler and Lewis numbers on the conditional mean scalar dissipation, and conditional mean velocity are presented and discussed. Information concerning unconditional turbulent fluxes are also presented. The anomaly found in previous studies of counter-gradient diffusion for the turbulent flux of the progress variable is investigated.

Mantel, Thierry↗

NASA NTRS1993

Statistics of multi-look AIRSAR imagery: A comparison of theory with measurements

The intensity and amplitude statistics of SAR images, such as L-Band HH for SEASAT and SIR-B, and C-Band VV for ERS-1 have been extensively investigated for various terrain, ground cover and ocean surfaces. Less well-known are the statistics between multiple channels of polarimetric of interferometric SAR's, especially for the multi-look processed data. In this paper, we investigate the probability density functions (PDF's) of phase differences, the magnitude of complex products and the amplitude ratios, between polarization channels (i.e. HH, HV, and VV) using 1-look and 4-look AIRSAR polarimetric data. Measured histograms are compared with theoretical PDF's which were recently derived based on a complex Gaussian model.

Lee, J. S.↗

NASA NTRS1993

Multivariate statistical analysis software technologies for astrophysical research involving large data bases

The existing and forthcoming data bases from NASA missions contain an abundance of information whose complexity cannot be efficiently tapped with simple statistical techniques. Powerful multivariate statistical methods already exist which can be used to harness much of the richness of these data. Automatic classification techniques have been developed to solve the problem of identifying known types of objects in multiparameter data sets, in addition to leading to the discovery of new physical phenomena and classes of objects. We propose an exploratory study and integration of promising techniques in the development of a general and modular classification/analysis system for very large data bases, which would enhance and optimize data management and the use of human research resource.

Djorgovski, George↗

NASA NTRS1994

A statistical equilibrium analysis of interstellar CO toward zeta Ophiuchi as recorded by the Goddard High Resolution Spectrograph

High-resolution and high signal-to-noise ratio echelle observations made by the Goddard High Resolution Spectrograph (GHRS), aboard the Hubble Space Telescope, of molecular (12)C(16)O and (13)C(16)O in the absorbing gas toward zeta Oph are reported. A statistical equilibrium model, incorporating a different way of dealing with the radiation field in the interstellar clouds, is presented. Based upon previous observations, two velocity components of the gas at V(sub LSR) = - 0.79 and 0.39 km/s, corresponding to solar velocity = -14.6 and -13.4 km/s, together with three different sets of velocity dispersions are adopted in our models. The ratios of the computed emergent intensities (I(sub em)) resulting from the emission lines in the lowest transitions (J = 1 goes to 0, 2 goes to 1, 3 goes to 2) of ground state of CO are presented. The ratios for the two velocity components, (I(sub em)(1 goes to 0)(sub 1))/(I(sub em)(1 goes to 0)(sub 2)), and (I(sub em)(2 goes to 1)(sub 1))/I(sub em)(1 goes to 0)(sub 1)) are comparable to the observed corrected antenna temperature ratios. From the solutions to the statistical equilibrium equations including the six lowest rotational transitions of CO and from multiple Voigt profile fits, the observed (12)CO and (13)CO UV abroption features are successfully reproduced. Profile fitting and double cloud curve-of-growth analysis using the GHRS and Copernicus data indicate that the abundance of CO is (1.8 +/- 0.2) x 10(exp 15)/sq cm. The most recently measured wavelength of the (6 goes to 0) (13)CO band by Haridass & Huber (R(0) = 1370.616 A) shows that the tentative (13)CO features in the GHRS data are unquestionably identified. If there is no blending from any other unknown interstellar species, the isotope ratio of (12)CO/(13)CO is approximately 82 +/- 25. This result is close to the terrestrial value of 90 and implies that the CO is not substantially fractionated, and (12)C(16)O experiences little preferential self-shielding through the selective isotopic photodissociation process. This conclusion differs strongly with that of Sheffer et al. Other implications of the results are discussed.

Lyu, Cheng-Hsuan↗

NASA NTRS1994

Solar granulation and statistical crystallography: A modeling approach using size-shape relations

The irregular polygonal pattern of solar granulation is analyzed for size-shape relations using statistical crystallography. In contrast to previous work which has assumed perfectly hexagonal patterns for granulation, more realistic accounting of cell (granule) shapes reveals a broader basis for quantitative analysis. Several features emerge as noteworthy: (1) a linear correlation between number of cell-sides and neighboring shapes (called Aboav-Weaire's law); (2) a linear correlation between both average cell area and perimeter and the number of cell-sides (called Lewis's law and a perimeter law, respectively) and (3) a linear correlation between cell area and squared perimeter (called convolution index). This statistical picture of granulation is consistent with a finding of no correlation in cell shapes beyond nearest neighbors. A comparative calculation between existing model predictions taken from luminosity data and the present analysis shows substantial agreements for cell-size distributions. A model for understanding grain lifetimes is proposed which links convective times to cell shape using crystallographic results.

Noever, D. A.↗

NASA NTRS1994

Statistics and topology of the COBE differential microwave radiometer first-year sky maps

We use statistical and topological quantities to test the Cosmic Background Explorer (COBE) Differential Microwave Radiometer (DMR) first-year sky maps against the hypothesis that the observed temperature fluctuations reflect Gaussian initial density perturbations with random phases. Recent papers discuss specific quantities as discriminators between Gaussian and non-Gaussian behavior, but the treatment of instrumental noise on the data is largely ignored. The presence of noise in the data biases many statistical quantities in a manner dependent on both the noise properties and the unknown cosmic microwave background temperature field. Appropriate weighting schemes can minimize this effect, but it cannot be completely eliminated. Analytic expressions are presented for these biases, and Monte Carlo simulations are used to assess the best strategy for determining cosmologically interesting information from noisy data. The genus is a robust discriminator that can be used to estimate the power-law quadrupole-normalized amplitude, Q(sub rms-PS), independently of the two-point correlation function. The genus of the DMR data is consistent with Gaussian initial fluctuations with Q(sub rms-PS) = (15.7 +/- 2.2) - (6.6 +/- 0.3)(n - 1) micro-K, where n is the power-law index. Fitting the rms temperature variations at various smoothing angles gives Q(sub rms-PS) = 13.2 +/- 2.5 micro-K and n = 1.7(sup (+0.3) sub (-0.6)). While consistent with Gaussian fluctuations, the first year data are only sufficient to rule out strongly non-Gaussian distributions of fluctuations.

Smoot, G. F.↗

NASA NTRS1995

Gaussian statistics of the cosmic microwave background: Correlation of temperature extrema in the COBE DMR two-year sky maps

We use the two-point correlation function of the extrema points (peaks and valleys) in the Cosmic Background Explorer (COBE) Differential Microwave Radiometers (DMR) 2 year sky maps as a test for non-Gaussian temperature distribution in the cosmic microwave background anisotropy. A maximum-likelihood analysis compares the DMR data to n = 1 toy models whose random-phase spherical harmonic components a(sub lm) are drawn from either Gaussian, chi-square, or log-normal parent populations. The likelihood of the 53 GHz (A+B)/2 data is greatest for the exact Gaussian model. There is less than 10% chance that the non-Gaussian models tested describe the DMR data, limited primarily by type II errors in the statistical inference. The extrema correlation function is a stronger test for this class of non-Gaussian models than topological statistics such as the genus.

Kogut, A.↗