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All sourcesNASA NTRSDOE OSTI
NASA NTRS1989

K-distribution and polarimetric terrain radar clutter

A multivariate K-distribution is proposed to model the statistics of fully polarimetric radar data from earth terrain with polarizations HH, HV, VH, and VV. In this approach, correlated polarizations of radar signals, as characterized by a covariance matrix, are treated as the sum of N n-dimensional random vectors; N obeys the negative binomial distribution with a parameter alpha and mean N-bar. Subsequently, an n-dimensional K-distribution, with either zero or nonzero mean, is developed in the limit of infinite N-bar or illuminated area. The probability density function (PDF) of the K-distributed vector normalized by its Euclidean norm is independent of the parameter alpha and is the same as that derived from a zero-mean Gaussian-distributed random vector.

Yueh, S. H.↗
NASA NTRS1997

Microphysical Retrievals Over Stratiform Rain Using Measurements from an Airborne Dual-Wavelength Radar-Radiometer

The need to understand the complementarity of the radar and radiometer is important not only to the Tropical Rain Measuring Mission (TRMM) program but to a growing number of multi-instrumented airborne experiment that combine single or dual-frequency radars with multichannel radiometers. The method of analysis used in this study begins with the derivation of dual-wavelength radar equations for the estimation of a two-parameter drop size distribution (DSD). Defining a "storm model" as the set of parameters that characterize snow density, cloud water, water vapor, and features of the melting layer, then to each storm model there will usually correspond a set of range-profiled drop size distributions that are approximate solutions of the radar equations. To test these solutions, a radiative transfer model is used to compute the brightness temperatures for the radiometric frequencies of interest. A storm model or class of storm models is considered optimum if it provides the best reproduction of the radar and radiometer measurements. Tests of the method are made for stratiform rain using simulated storm models as well as measured airborne data. Preliminary results show that the best correspondence between the measured and estimated radar profiles usually can be obtained by using a moderate snow density (0.1-0.2 g/cu cm), the Maxwell-Garnett mixing formula for partially melted hydrometeors (water matrix with snow inclusions), and low to moderate values of the integrated cloud liquid water (less than 1 kg/sq m). The storm-model parameters that yield the best reproductions of the measured radar reflectivity factors also provide brightness temperatures at 10 GHz that agree well with the measurements. On the other hand, the correspondence between the measured and modeled values usually worsens in going to the higher frequency channels at 19 and 34 GHz. In searching for possible reasons for the discrepancies, It is found that changes in the DSD parameter Mu, the radar constants, or the path-integrated attenuation can affect the high frequency channels significantly. In particular, parameters that cause only modest increases in the median mass diameter of the snow, and which have a minor effect on the radar returns or the low frequency brightness temperature, can produce a strong cooling of the 34 GHz brightness temperature.

Meneghini, Robert↗
NASA NTRS2003

A Three-Parameter Inversion of the Drop Size Distribution Using NASA/TRMM Microwave Link Data

Attenuation measurements at 25 and 38 GHz performed with the NASA/TRMM Microwave Link provide information about the drop size distribution (DSD) along the propagation path. Additional path-average measurements along the Link path, such as a third attenuation measurement or the rain rate from well-calibrated raingauges, can provide further DSD information. This paper explores an inversion procedure for determining simultaneously three parameters of a gamma DSD by using three measurements. Also, some preliminary results obtained using Link data are presented.

Rincon, Rafael F.↗
NASA NTRS1972

Kullback-Leibler information function and the sequential selection of experiments to discriminate among several linear models

The error variance of the process prior multivariate normal distributions of the parameters of the models are assumed to be specified, prior probabilities of the models being correct. A rule for termination of sampling is proposed. Upon termination, the model with the largest posterior probability is chosen as correct. If sampling is not terminated, posterior probabilities of the models and posterior distributions of the parameters are computed. An experiment was chosen to maximize the expected Kullback-Leibler information function. Monte Carlo simulation experiments were performed to investigate large and small sample behavior of the sequential adaptive procedure.

Sidik, S. M.↗
NASA NTRS1991

Airborne lidar measurements of ozone during the 1989 airborne Arctic stratospheric expedition

The NASA/NOAA Airborne Arctic Stratospheric Expedition (AASE) was conducted during the winter to study the conditions leading to possible ozone (O3) destruction in the wintertime Arctic stratosphere. As part of this experiment, the NASA-Langley airborne differential absorption lidar (DIAL) system was configured for operation on the NASA-Ames DS-8 aircraft to make measurements of O3 profiles from about 1 km above the aircraft to altitudes of 22 to 26 km. The airborne DIAL system remotely sensed O3 above the DC-8 by transmitting two laser beams at 10 Hz using wavelengths of 301.5 and 311 nm. Large scale distributions of O3 were obtained on 15 long range flights into the polar vortex during the AASE. Selected data samples are presented of O3 observed during these flights, general trends observed in O3 distributions, and correlations between these measurements and meteorological and chemical parameters. The O3 distribution observed on the first flight of the DC-8 into the polar vortex on Jan. 6 reflected the result of diabatic cooling of the air inside the vortex during the winter compared to the warmer air outside the vortex. On a potential temperature surface, the O3 mixing ratio generally increases when going from outside to inside the vortex.

Browell, Edward V.↗
NASA NTRS2011

Reliability-Based Design Optimization of a Composite Airframe Component

A stochastic optimization methodology (SDO) has been developed to design airframe structural components made of metallic and composite materials. The design method accommodates uncertainties in load, strength, and material properties that are defined by distribution functions with mean values and standard deviations. A response parameter, like a failure mode, has become a function of reliability. The primitive variables like thermomechanical loads, material properties, and failure theories, as well as variables like depth of beam or thickness of a membrane, are considered random parameters with specified distribution functions defined by mean values and standard deviations.

Pai, Shantaram S.↗
NASA NTRS1973

Some observed seasonal changes in extratropical general circulation: A study in terms of vorticity

Extratropical eddy distributions in four months typical of the four seasons are treated in terms of temporal mean and temporal r.m.s. values of the geostrophic relative vorticity. The geographical distributions of these parameters at the 300 mb level show that the arithmetic mean fields are highly biased representatives of the extratropical eddy distributions. The zonal arithmetic means of these parameters are also presented. These show that the zonal-and-time mean relative vorticity is but a small fraction of the zonal mean of the temporal r.m.s. relative vorticity, K. The reasons for considering the r.m.s. values as the temporal normal values of vorticity in the extratropics are given in considerable detail. The parameter K is shown to be of considerable importance in locating the extratropical frontal jet streams (EFJ) in time-and-zonal average distributions. The study leads to an understanding of the seasonal migrations of the EFJ which have not been explored until now.

Srivatsangam, S.↗
NASA NTRS1973

A summary of selected early results from the ERTS-1 menhaden experiment

The author has identified the following significant results. Imagery from ERTS-1 satellite was used in conjunction with aerial photographically-sensed menhaden distribution information, sea truth oceanographic measurements, and commercial fishing information from a 8685 square kilometer study area in the north-central portion of the Gulf of Mexico to demonstrate relationships between selected oceanographic parameters and menhaden distribution, ERTS-1 imagery and menhaden distribution, and ERTS-1 imagery and oceanographic parameters. ERTS-1, MSS band 5 imagery density levels correlated with photographically detected menhaden distribution patterns and could be explained based on sea truth Secchi disc transparency and water depth measurements. These two parameters, together with surface salinity, Forel-Ule color, and chlorophyll-a also were found to correlate significantly with menhaden distribution. Eight empirical models were developed which provided menhaden distribution predictions for the study area on combinations of Secchi disc transparency, water depth, surface salinity, and Forel-Ule color measurements.

Stevenson, W. H.↗
NASA NTRS1988

Measurements of induced voltages and currents in a distribution power line and associated atmospheric parameters

The frequency and intensity of thunderstorms around the Kennedy Space Center (KSC) has affected scheduled launch, landing, and other ground operations for many years. In order to protect against and provide safe working facilities, KSC has performed and hosted several studies on lightning phenomena. For the reasons mentioned above, KSC has established the Atmospheric Science Field Laboratory (ASFL). At these facilities KSC launches wire-towing rockets into thunderstorms to trigger natural lightning to the launch site. A program named Rocket Triggered Lightning Program (RTLP) is being conducted at the ASFL. This report calls for two of the experiments conducted in the summer 1988 Rocket Triggered Lightning Program. One experiment suspended an electric field mill over the launching areas from a balloon about 500 meters high to measure the space charges over the launching area. The other was to connect a waveform recorder to a nearby distribution power line to record currents and voltages wave forms induced by natural and triggered lightning.

Santiago-Perez, Julio↗
NASA NTRS2001

Comparison of z-known GRBs with the Main Groups of Bright BATSE Events

The small reference sample of six BATSE gamma-ray bursts with known redshifts from optical afterglows is compared with a comparison group of the 218 brightest BATSE bursts. These two groups are shown to be consistent both with respect to the distributions of the spectral peak parameter in the observer's frame and also with respect to the distributions of the frame-independent cosmological invariant parameter (CIP). Using the known values of the redshifts z for the reference sample, the rest-frame distribution of spectral parameters is built. The de-redshifted distribution of the spectral parameters of the reference sample is compared with distribution of these parameters for the comparison group after de-redshifting by the factor 1/(1+z), with z a free parameter. Requiring consistency between these two distributions produces a collective estimation of the best fitting redshifts z for the comparison group, z=1.8--3.6. These values can be considered as the average cosmological redshift of the sources of the brightest BATSE bursts. The most probable value of the peak energy of the spectrum in the rest frame is 920 keV, close to the rest mass of an electron-positron pair.

Mitrofanov, Igor G.↗
NASA NTRS1994

Effect of magnetospheric convection on thermal plasma in the inner magnetosphere

The effects of E x B convection on the distribution of plasma parameters in the inner magnetosphere have been examined. Analytical solutions describing density distributions along convective trajectories in the equatorial plane have been found. These solutions suggest the following dependence of plasma concentration n on the magnetic field B along convective trajectories: n proportional to B(exp alpha), where the parameter alpha varies between alpha is less than or = between 4/3 and 2. The alpha = 2 case corresponds to disregarding transport parallel to B. The lower bound alpha = 4/3 describes the situation when parallel transport dominates over convective motions perpendicular to B. A solution has also been obtained describing the effect of convection on diffusive equilibrium profiles in the dayside plasmasphere. In addition, ion temperature variations due to adiabatic effects associated with plasma convection have been analyzed in detail. Convective drifts lead to ion temperature anisotropies with the value and sign of the anisotropy contingent on density and temperature variations, local time, and the location of the convective trajectory with respect to the location of the plasmapause. We have also found that convective motions lead to a substantial exchange of energy between the ionosphere and the plasmasphere through electron heat fluxes.

Khazanov, G. V.↗
NASA NTRS1976

The numerical evaluation of maximum-likelihood estimates of the parameters for a mixture of normal distributions from partially identified samples

Likelihood equations determined by the two types of samples which are necessary conditions for a maximum-likelihood estimate are considered. These equations, suggest certain successive-approximations iterative procedures for obtaining maximum-likelihood estimates. These are generalized steepest ascent (deflected gradient) procedures. It is shown that, with probability 1 as N sub 0 approaches infinity (regardless of the relative sizes of N sub 0 and N sub 1, i=1,...,m), these procedures converge locally to the strongly consistent maximum-likelihood estimates whenever the step size is between 0 and 2. Furthermore, the value of the step size which yields optimal local convergence rates is bounded from below by a number which always lies between 1 and 2.

Walker, H. F.↗
NASA NTRS1976

The numerical evaluation of maximum-likelihood estimates of the parameters for a mixture of normal distributions from partially identified samples

Likelihood equations determined by the two types of samples which are necessary conditions for a maximum-likelihood estimate were considered. These equations suggest certain successive approximations iterative procedures for obtaining maximum likelihood estimates. The procedures, which are generalized steepest ascent (deflected gradient) procedures, contain those of Hosmer as a special case.

Walker, H. F.↗
NASA NTRS1990

Cumulative Poisson Distribution Program

Overflow and underflow in sums prevented. Cumulative Poisson Distribution Program, CUMPOIS, one of two computer programs that make calculations involving cumulative Poisson distributions. Both programs, CUMPOIS (NPO-17714) and NEWTPOIS (NPO-17715), used independently of one another. CUMPOIS determines cumulative Poisson distribution, used to evaluate cumulative distribution function (cdf) for gamma distributions with integer shape parameters and cdf for X (sup2) distributions with even degrees of freedom. Used by statisticians and others concerned with probabilities of independent events occurring over specific units of time, area, or volume. Written in C.

Bowerman, Paul N.↗
NASA NTRS1992

High-energy gamma-ray emission from pion decay in a solar flare magnetic loop

The production of high-energy gamma rays resulting from pion decay in a solar flare magnetic loop is investigated. Magnetic mirroring, MHD pitch-angle scattering, and all of the relevant loss processes and photon production mechanisms are taken into account. The transport of both the primary ions and the secondary positrons resulting from the decay of the positive pions, as well as the transport of the produced gamma-ray emission are considered. The distributions of the gamma rays as a function of atmospheric depth, time, emission angle, and photon energy are calculated and the dependence of these distributions on the model parameters are studied. The obtained angular distributions are not sufficiently anisotropic to account for the observed limb brightening of the greater than 10 MeV flare emission, indicating that the bulk of this emission is bremsstrahlung from primary electrons.

Mandzhavidze, Natalie↗
NASA NTRS2020

The AERONET Version 3 Aerosol Retrieval Algorithm, Associated Uncertainties and Comparisons to Version 2

The Aerosol Robotic Network (AERONET) Version 3 (V3) aerosol retrieval algorithm is described, which is based on the Version 2 (V2) algorithm with numerous updates. Comparisons of V3 aerosol retrievals to those of V2 are presented, along with a new approach to estimate uncertainties in many of the retrieved aerosol parameters. Changes in the V3 aerosol retrieval algorithm include (1) a new polarized radiative transfer code (RTC), which replaced the scalar RTC of V2, (2) detailed characterization of gas absorption by adding NO2 and H2O to specify total gas absorption in the atmospheric column, specification of vertical profiles of all the atmospheric species, (3) new bidirectional reflectance distribution function (BRDF) parameters for land sites adopted from the MODIS BRDF/Albedo product, (4) a new version of the extraterrestrial solar flux spectrum, and (5) a new temperature correction procedure of both direct Sun and sky radiance measurements. The potential effect of each change in V3 on single scattering albedo (SSA) retrievals was analyzed. The operational almucantar retrievals of V2 versus V3 were compared for four AERONET sites: GSFC, Mezaira, Mongu, and Kanpur. Analysis showed very good agreement in retrieved parameters of the size distributions. Comparisons of SSA retrievals for dust aerosols (Mezaira) showed a good agreement in 440 nm SSA, while for longer wavelengths V3 SSAs are systematically higher than those of V2, with the largest mean difference at 675 nm due to cumulative effects of both extraterrestrial solar flux and BRDF changes. For non-dust aerosols, the largest SSA deviation is at 675 nm due to differences in extraterrestrial solar flux spectrums used in each version. Further, the SSA 675 nm mean differences are very different for weakly (GSFC) and strongly (Mongu) absorbing aerosols, which is explained by the lower sensitivity to a bias in aerosol scattering optical depth by less absorbing aerosols. A new hybrid (HYB) sky radiance measurement scan is introduced and discussed. The HYB combines features of scans in two different planes to maximize the range of scattering angles and achieve scan symmetry, thereby allowing for cloud screening and spatial averaging, which is an advantage over the principal plane scan that lacks robust symmetry. We show that due to an extended range of scattering angles, HYB SSA retrievals for dust aerosols exhibit smaller variability with solar zenith angles (SZAs) than those of almucantar (ALM), which allows extension of HYB SSA retrievals to SZAs less than 50∘ to as small as 25∘. The comparison of SSA retrievals from closely time-matched HYB and ALM scans in the 50 to 75∘ SZA range showed good agreement with the differences below ∼0.005. We also present an approach to estimate retrieval uncertainties which utilizes the variability in retrieved parameters generated by perturbing both measurements and auxiliary input parameters as a proxy for retrieval uncertainty. The perturbations in measurements and auxiliary inputs are assumed as estimated biases in aerosol optical depth (AOD), radiometric calibration of sky radiances combined with solar spectral irradiance, and surface reflectance. For each set of Level 2 Sun/sky radiometer observations, 27 inputs corresponding to 27 combinations of biases were produced and separately inverted to generate the following statistics of the inversion results: average, standard deviation, minimum and maximum values. From these statistics, standard deviation (labeled U27) is used as a proxy for estimated uncertainty, and a lookup table (LUT) approach was implemented to reduce the computational time. The U27 climatological LUT was generated from the entire AERONET almucantar (1993–2018) and hybrid (2014–2018) scan databases by binning U27s in AOD (440 nm), Angström exponent (AE, 440–870 nm), and SSA (440, 675, 870, 1020 nm). Using this LUT approach, the uncertainty estimates U27 for each individual V3 Level 2 retrieval can be obtained by interpolation using the corresponding measured and inverted combination of AOD, AE, and SSA.

Aliaksandr Siniuk↗