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All sourcesNASA NTRSDOE OSTI
NASA NTRS1990

Newton/Poisson-Distribution Program

NEWTPOIS, one of two computer programs making calculations involving cumulative Poisson distributions. NEWTPOIS (NPO-17715) and CUMPOIS (NPO-17714) used independently of one another. NEWTPOIS determines Poisson parameter for given cumulative probability, from which one obtains percentiles for gamma distributions with integer shape parameters and percentiles 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. Program written in C.

Bowerman, Paul N.↗
NASA NTRS2020

Characteristics of DSD Bulk Parameters: Implication to Radar Rain Retrieval

With the use of 213,456 one-minute measured data of droplet-size distribution (DSD) of rain collected during several National Aeronautics and Space Administration (NASA)-sponsored field campaigns, the relationships between rainfall rate R, mass-weighted diameter D(m) and normalized intercept parameter N(w) of the gamma DSD are studied. It is found, based on the simulations of the gamma DSD model, that R, D(m) and N(w) are closely interrelated, and that the ratio of R to N(w) is solely a function of D(m), independent of the shape factor μ of the gamma distribution. Furthermore, the model-produced ratio agrees well with those from the DSD data. When a power-law equation is applied to fit the model data, we have: R=aN(w)D(sup b, sub m) , where a=1.588×10(exp −4) , b=4.706 . Analysis of two-parameter relationships such as R–D(m), N(w)–R and N(w)–D(m) reveals that R and D(m) are moderately correlated while N(w) and D(m) are negatively correlated. N(w) and R, however, are uncorrelated. The gamma DSD model also reveals that variation of R–D(m) relation is caused primarily by N(w). For the application of the Ku- and Ka-band dual-frequency radar for the retrieval of the DSD bulk parameters as well as the specific radar attenuations, the study is carried out to relate the dual-frequency radar reflectivity factors to the DSD and attenuation parameters.

Liang Liao↗
NASA NTRS2016

Towards a Global Water Scarcity Risk Assessment Framework: Incorporation of Probability Distributions and Hydro-Climatic Variability

Changing hydro-climatic and socioeconomic conditions increasingly put pressure on fresh water resources and are expected to aggravate water scarcity conditions towards the future. Despite numerous calls for risk-based water scarcity assessments, a global-scale framework that includes UNISDR's definition of risk does not yet exist. This study provides a first step towards such a risk based assessment, applying a Gamma distribution to estimate water scarcity conditions at the global scale under historic and future conditions, using multiple climate change and population growth scenarios. Our study highlights that water scarcity risk, expressed in terms of expected annual exposed population, increases given all future scenarios, up to greater than 56.2% of the global population in 2080. Looking at the drivers of risk, we find that population growth outweigh the impacts of climate change at global and regional scales. Using a risk-based method to assess water scarcity, we show the results to be less sensitive than traditional water scarcity assessments to the use of fixed threshold to represent different levels of water scarcity. This becomes especially important when moving from global to local scales, whereby deviations increase up to 50% of estimated risk levels.

Populations↗
NASA NTRS2015

Resolving Ice Cloud Optical Thickness Biases Between CALIOP and MODIS Using Infrared Retrievals

Despite its importance as one of the key radiative properties that determines the impact of upper tropospheric clouds on the radiation balance, ice cloud optical thickness (IOT) has proven to be one of the more challenging properties to retrieve from space-based remote sensing measurements. In particular, optically thin upper tropospheric ice clouds (cirrus) have been especially challenging due to their tenuous nature, extensive spatial scales, and complex particle shapes and light scattering characteristics. The lack of independent validation motivates the investigation presented in this paper, wherein systematic biases between MODIS Collection 5 (C5) and CALIOP Version 3 (V3) unconstrained retrievals of tenuous IOT (< 3) are examined using a month of collocated A-Train observations. An initial comparison revealed a factor of two bias between the MODIS and CALIOP IOT retrievals. This bias is investigated using an infrared (IR) radiative closure approach that compares both products with MODIS IR cirrus retrievals developed for this assessment. The analysis finds that both the MODIS C5 and the unconstrained CALIOP V3 retrievals are biased (high and low, respectively) relative to the IR IOT retrievals. Based on this finding, the MODIS and CALIOP algorithms are investigated with the goal of explaining and minimizing the biases relative to the IR. For MODIS we find that the assumed ice single scattering properties used for the C5 retrievals are not consistent with the mean IR COT distribution. The C5 ice scattering database results in the asymmetry parameter (g) varying as a function of effective radius with mean values that are too large. The MODIS retrievals have been brought into agreement with the IR by adopting a new ice scattering model for Collection 6 (C6) consisting of a modified gamma distribution comprised of a single habit (severely roughened aggregated columns); the C6 ice cloud optical property models have a constant g approx. = 0.75 in the mid-visible spectrum, 5-15% smaller than C5. For CALIOP, the assumed lidar ratio for unconstrained retrievals is fixed at 25 sr for the V3 data products.This value is found to be inconsistent with the constrained (predominantly nighttime) CALIOP retrievals. An experimental data set was produced using a modified lidar ratio of 32 sr for the unconstrained retrievals (an increase of 28%), selected to provide consistency with the constrained V3 results. These modifications greatly improve the agreement with the IR and provide consistency between the MODIS and CALIOP products. Based on these results the recently released MODIS C6 optical products use the single habit distribution given above, while the upcoming CALIOP V4 unconstrained algorithm will use higher lidar ratios for unconstrained retrievals.

Cloud↗
NASA NTRS1987

Simulation of radar reflectivity and surface measurements of rainfall

Raindrop size distributions (RSDs) are often estimated using surface raindrop sampling devices (e.g., disdrometers) or optical array (2D-PMS) probes. A number of authors have used these measured distributions to compute certain higher-order RSD moments that correspond to radar reflectivity, attenuation, optical extinction, etc. Scatter plots of these RSD moments versus disdrometer-measured rainrates are then used to deduce physical relationships between radar reflectivity, attenuation, etc., which are measured by independent instruments (e.g., radar), and rainrate. In this paper RSDs of the gamma form as well as radar reflectivity (via time series simulation) are simulated to study the correlation structure of radar estimates versus rainrate as opposed to RSD moment estimates versus rainrate. The parameters N0, D0 and m of a gamma distribution are varied over the range normally found in rainfall, as well as varying the device sampling volume. The simulations are used to explain some possible features related to discrepancies which can arise when radar rainfall measurements are compared with surface or aircraft-based sampling devices.

Chandrasekar, V.↗
NASA NTRSDate not supplied

Evolution of Drop Size Distributions during Hurricane Harvey and Their Effects on Rain Intensity

Hurricane Harvey hit the Texas Gulf Coast as a major hurricane on August 25, 2017, before exiting the state as a tropical storm on August 29, 2017. Left in its wake was historic flooding over southeast Texas with some locations measuring more than 60 inches of rain. The Houston NEXRAD radar (KHGX) maintained operations for the entirety of the event and is utilized in this study to better understand the evolution of the drop size distribution (DSD) in the lower (liquid) portions of the storm and how changes in the DSD were tied to observed and measured changes in rain intensities. From the KHGX dual-polarimetric radar data several DSD parameters were retrieved, including three different rain rate retrievals, as well as the mass-weighted mean-drop diameter Dm, and the normalized intercept parameter NW of the gamma distribution. Two of the rain retrievals are popular hybrid approaches, where reflectivity, differential and specific differential phase are used. The other is an attenuation-based retrieval. In a previous study, it was found that both hybrid retrievals significantly underestimated the rainfall during the heaviest rain periods, while the attenuation-based retrieval, with proper adjustment, agreed quite well with a large network of gauges from the Harris County Flood Warning System. Using Dm and NW as proxies for drop size and concentration, respectively, we will show that the heaviest rain intensities were associated in areas of the storm where there was a large concentration of large drops present. It is envisaged that results of this study can be used to develop a near-real-time tuning of the attenuation-based retrieval, thus providing timely, and possibly life-saving warnings during inundating rainfall.

David B. Wolff↗
NASA NTRS1983

Information retrieval from wide-band meteorological data - An example

The methods proposed by Smith and Adelfang (1981) and Smith et al. (1982) are used to calculate probabilities over rectangles and sectors of the gust magnitude-gust length plane; probabilities over the same regions are also calculated from the observed distributions and a comparison is also presented to demonstrate the accuracy of the statistical model. These and other statistical results are calculated from samples of Jimsphere wind profiles at Cape Canaveral. The results are presented for a variety of wavelength bands, altitudes, and seasons. It is shown that wind perturbations observed in Jimsphere wind profiles in various wavelength bands can be analyzed by using digital filters. The relationship between gust magnitude and gust length is modeled with the bivariate gamma distribution. It is pointed out that application of the model to calculate probabilities over specific areas of the gust magnitude-gust length plane can be useful in aerospace design.

Adelfang, S. I.↗
NASA NTRS1990

Analysis of stratocumulus cloud fields using LANDSAT imagery: Size distributions and spatial separations

Stratocumulus cloud fields in the FIRE IFO region are analyzed using LANDSAT Thematic Mapper imagery. Structural properties such as cloud cell size distribution, cell horizontal aspect ratio, fractional coverage and fractal dimension are determined. It is found that stratocumulus cloud number densities are represented by a power law. Cell horizontal aspect ratio has a tendency to increase at large cell sizes, and cells are bi-fractal in nature. Using LANDSAT Multispectral Scanner imagery for twelve selected stratocumulus scenes acquired during previous years, similar structural characteristics are obtained. Cloud field spatial organization also is analyzed. Nearest-neighbor spacings are fit with a number of functions, with Weibull and Gamma distributions providing the best fits. Poisson tests show that the spatial separations are not random. Second order statistics are used to examine clustering.

Welch, R. M.↗
NASA NTRS1970

Code CUGEL: A code to unfold Ge(Li) spectrometer polyenergetic gamma photon experimental distributions

A FORTRAN code was developed for the Univac 1108 digital computer to unfold lithium-drifted germanium semiconductor spectrometers, polyenergetic gamma photon experimental distributions. It was designed to analyze the combination continuous and monoenergetic gamma radiation field of radioisotope volumetric sources. The code generates the detector system response matrix function and applies it to monoenergetic spectral components discretely and to the continuum iteratively. It corrects for system drift, source decay, background, and detection efficiency. Results are presented in digital form for differential and integrated photon number and energy distributions, and for exposure dose.

Steyn, J. J.↗
NASA NTRS1977

Spectra and angular distributions of atmospheric gamma rays from 0.3 to 10 MeV at lambda = 40 deg

Measurements of the spectral and angular distributions of atmospheric gamma sq cm rays in the energy range 0.3-10 MeV over Palestine, Texas, at residual depths of 2.5 and 70 g/sq cm are reported. In confirmation of the general features of a model prediction, the measurements show at 2.5 g/sq cm upward moving fluxes greater than the downward moving fluxes, the effect increasing with energy, and approximate isotropy at 70 g/sq cm. Numerous characteristic gamma-ray lines were observed, most prominently at 0.511, 1.6, 2.3, 4.4, and 6.1 MeV. Their intensities were also compared with model predictions. Observations were made with an actively shielded scintillator counter with two detectors, one of aperture 50 deg FWHM and the other of 120 deg FWHM. Above 1 MeV, contributions to the counting rate from photons penetrating the shield annulus and from neutron interactions were large; they were studied by means of a Monte Carlo code and are extensively discussed.

Ling, J. C.↗
NASA NTRS1972

Gamma time-dependency in Blaxter's compartmental model.

A new two-compartment model for the passage of particles through the gastro-intestinal tract of ruminants is proposed. In this model, a gamma distribution of lifetimes is introduced in the first compartment; thereby, passage from that compartment becomes time-dependent. This modification is strongly suggested by the physical alteration which certain substances, e.g. hay particles, undergo in the digestive process. The proposed model is applied to experimental data.

Matis, J. H.↗
NASA NTRS1975

The role of large particles in the formation of the radio echo

The contribution to the total reflectivity of separate parts of a particle spectrum described by a gamma distribution is estimated. It is shown that the largest individual particles, whose percent concentration is 0.1 - 1, originate approximately 60 - 70% of the total reflectivity of the spectrum. Explanations are given of a number of effects which confirm the dominant role of large particles in the formation of the echo.

Salman, Y. M.↗
NASA NTRS1983

Vector wind profile gust model

A five parameter gamma distribution (BGD) having two shape parameters, two location parameters, and a correlation parameter is investigated. This general BGD is expressed as a double series and as a single series of the modified bessel function, and reduces to the known special case for equal shape parameters. Practical functions for computer evaluations for the general BGD and for special cases are presented. Applications are to be bound in reliability theory, signal noise, and meteorology. Applications to wind gust modeling for the ascent flight of the space shuttle are illustrated.

Adelfang, S. I.↗
NASA NTRS1983

Approximation to the Probability Density at the Output of a Photmultiplier Tube

The probability density of the integrated output of a photomultiplier tube (PMT) is approximated by the Gaussian, Rayleigh, and Gamma probability densities. The accuracy of the approximations depends on the signal energy alpha: the Gamma distribution is accurate for all alpha, the Raleigh distribution is accurate for small alpha (approximate or less than 1 photon) and the Gaussian distribution is accurate for large alpha (approximate or greater than 10 photons).

Stokey, R. J.↗
NASA NTRS1983

Analysis of Wind Gust Data

Wind gust data were analyzed by statistical and mathematical procedures, developed for the bivariate gamma distribution. The results of the analysis are summarized.

Tubbs, J. D.↗
NASA NTRS1983

Optimal design and use of retry in fault tolerant real-time computer systems

A new method to determin an optimal retry policy and for use in retry of fault characterization is presented. An optimal retry policy for a given fault characteristic, which determines the maximum allowable retry durations to minimize the total task completion time was derived. The combined fault characterization and retry decision, in which the characteristics of fault are estimated simultaneously with the determination of the optimal retry policy were carried out. Two solution approaches were developed, one based on the point estimation and the other on the Bayes sequential decision. The maximum likelihood estimators are used for the first approach, and the backward induction for testing hypotheses in the second approach. Numerical examples in which all the durations associated with faults have monotone hazard functions, e.g., exponential, Weibull and gamma distributions are presented. These are standard distributions commonly used for modeling analysis and faults.

Lee, Y. H.↗
NASA NTRS1986

Prospecting for planets in circumstellar dust - Sifting the evidence from Beta Pictoris

IRAS and near-IR coronographic data for the A5V star Beta Pic are analyzed for evidence of planetary formation. The light scattered from the central star in the system is integrated along the distance to the star to determine the disk magnitude at various distances from the star. A modified gamma distribution is applied to evaluate the scattering coefficient to test a hypothesis that the inner 30 AU of the disk has been swept out by planets. The scattering from the region around Beta Pic is compared with scattering around other A5V stars. Finally, the IR data at 0.89 micron is compared with scattering at the coronograph wavelengths. No evidence is found to support the hypothesis of clearing in the inner disk, although large particle densities can be found very close to Beta Pic. The study illustrates the effectiveness of using scattered light and IR data to discover and characterize matter distributions circumstellar disks.

Diner, D. J.↗