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A chord length distribution function for simultaneus path lengths in two parallelepipeds is developed, which is applicable to a unidirectional flux. The distribution function measures the probability for an ion trajectory to have a path length exceeding a specified value in one parallelepiped and to simultationsly have a path length exceeding another specified value in another parallelepiped.
Aeolian features on Triton that were imaged during the Voyager Mission have been grouped. The term 'aeolian feature' is broadly defined as features produced by or blown by the wind, including surface and airborne materials. Observations of the latitudinal distributions of the features probably associated with current activity (known plumes, crescent streaks, fixed terminator clouds, and limb haze with overshoot) all occur from latitude -37 deg to latitude -62 deg. Likely indicators of previous activity (dark surface streaks) occur from latitude -5 deg to -70 deg, but are most abundant from -15 deg to -45 deg, generally north of currently active features. Those indicators which give information on wind direction and speed have been measured. Wind direction is a function of altitude. The predominant direction of the surface wind streaks is found to be between 40 deg and 80 deg measured clockwise from north. The average orientation of streaks in the northeast quadrant is 59 deg. Winds at 1- to 3-kilometer altitude are eastward, while those at more than 8 kilometers blow west.
In this paper, we predict the precipitation signatures which are associated with transient magnetopause reconnection, following recent observations of the dependence of dayside ionospheric convection on the orientation of the IMF. We then employ a simple model of the longitudinal motion of flux-transfer-event signatures to show how such events can easily reproduce the local time distribution of cusp occurrence probabilities, as observed by low-altitude satellites. This is true even in the limit where the cusp is a series of discrete events. Furthermore, we investigate the existence of double cusp patches predicted by the simple model and show how these events may be identified in the data.
The present paper describes the application of the computer code IPACS (Integrated Probabilistic Assessment of Composite Structures) to air craft wing type structures. The code performs a complete probabilistic structural analysis for composites taking into account the uncertainties in geometry, boundary conditions, material properties, laminate lay-ups and loads. Results of the analysis are presented in terms of cumulative distribution functions (CDF) and probability density function (PDF) of life of a wing type composite structure under different hygrothermal environments subjected to random pressure. The sensitivity of fatigue life to a number of critical structural/material variables is also computed from the analysis.
The application of the computer code IPACS (Integrated Probabilistic Assessment of Composite Structures) to aircraft wing type structures is described. The code performs a complete probabilistic analysis for composites taking into account the uncertainties in geometry, boundary conditions, material properties, laminate lay-ups, and loads. Results of the analysis are presented in terms of cumulative distribution functions (CDF) and probability density function (PDF) of the fatigue life of a wing type composite structure under different hygrothermal environments subjected to the random pressure. The sensitivity of the fatigue life to a number of critical structural/material variables is also computed from the analysis.
This report investigates two of the most common modes of localized failures, namely, periodic fiber-bridged matrix cracks and transverse matrix cracks. A modification of Daniels' bundle theory is combined with Weibull's weakest link theory to model the statistical distribution of the periodic matrix cracking strength for an individual layer. Results of the model predictions are compared with experimental data from the open literature. Extensions to the model are made to account for possible imperfections within the layer (i.e., nonuniform fiber lengths, irregular crack spacing, and degraded in-situ fiber properties), and the results of these studies are presented. A generalized shear-lag analysis is derived which is capable of modeling the development of transverse matrix cracks in material systems having a general multilayer configuration and under states of full in-plane load. A method for computing the effective elastic properties for the damaged layer at the global level is detailed based upon the solution for the effects of the damage at the local level. This methodology is general in nature and is therefore also applicable to (0(sub m)/90(sub n))(sub s) systems. The characteristic stress-strain response for more general cases is shown to be qualitatively correct (experimental data is not available for a quantitative evaluation), and the damage evolution is recorded in terms of the matrix crack density as a function of the applied strain. Probabilistic effects are introduced to account for the statistical nature of the material strengths, thus allowing cumulative distribution curves for the probability of failure to be generated for each of the example laminates. Additionally, Oh and Finney's classic work on fracture location in brittle materials is extended and combined with the shear-lag analysis. The result is an analytical form for predicting the probability density function for the location of the next transverse crack occurrence within a crack bounded region. The results of this study verified qualitatively the validity of assuming a uniform crack spacing (as was done in the shear-lag model).
The Viking and Mars Pathfinder landing sites and a wide variety of rocky locations on the Earth show size-frequency distributions that follow an exponential when expressed in cumulative fractional area covered by rocks of a given diameter or larger versus diameter plots. Mars lander rock distributions have been fit by an equation of the form: Fk(D) = k exp [-q(k) D], where Fk(D) is the cumulative fractional area covered by rocks of diameter D or larger, k is the total area covered by all rocks, and an exponential q(k) = 1.79 + 0.152/k, which governs how abruptly the area covered by rocks decreases with increasing diameter. These distributions form a family of noncrossing curves that flatten out at small rock diameter at a total rock abundance of 5-40%. Model rock size-frequency distributions indicate a low probability of impacting hazardous rocks during MER landing. Rocks large enough to analyze and abrade by the rover should be plentiful within an easy Sol's drive.
The Pressure Systems Manager at NASA Ames Research Center (ARC) has embarked on a project to collect data and develop risk assessment models to support risk-informed decision making regarding future inspections of underground pipes at ARC. This paper shows progress in one area of this project - a corrosion risk assessment model for the underground high-pressure air distribution piping system at ARC. It consists of a Corrosion Model of pipe-segments, a Pipe Wrap Protection Model; and a Pipe Stress Model for a pipe segment. A Monte Carlo simulation of the combined models provides a distribution of the failure probabilities. Sensitivity study results show that the model uncertainty, or lack of knowledge, is the dominant contributor to the calculated unreliability of the underground piping system. As a result, the Pressure Systems Manager may consider investing resources specifically focused on reducing these uncertainties. Future work includes completing the data collection effort for the existing ground based pressure systems and applying the risk models to risk-based inspection strategies of the underground pipes at ARC.
The characteristics of convective system populations in West Africa and the western Pacific tropical cyclone basin were analyzed to investigate whether interannual variability in convective activity in tropical continental and oceanic environments is driven by variations in the number of events during the wet season or by favoring large and/or intense convective systems. Convective systems were defined from TRMM data as a cluster of pixels with an 85 GHz polarization-corrected brightness temperature below 255 K and with an area at least 64 km 2. The study database consisted of convective systems in West Africa from May Sep for 1998-2007 and in the western Pacific from May Nov 1998-2007. Annual cumulative frequency distributions for system minimum brightness temperature and system area were constructed for both regions. For both regions, there were no statistically significant differences among the annual curves for system minimum brightness temperature. There were two groups of system area curves, split by the TRMM altitude boost in 2001. Within each set, there was no statistically significant interannual variability. Sub-setting the database revealed some sensitivity in distribution shape to the size of the sampling area, length of sample period, and climate zone. From a regional perspective, the stability of the cumulative frequency distributions implied that the probability that a convective system would attain a particular size or intensity does not change interannually. Variability in the number of convective events appeared to be more important in determining whether a year is wetter or drier than normal.
The characteristics of convective system populations in West Africa and the western Pacific tropical cyclone basin were analyzed to investigate whether interannual variability in convective activity in tropical continental and oceanic environments is driven by variations in the number of events during the wet season or by favoring large and/or intense convective systems. Convective systems were defined from Tropical Rainfall Measuring Mission (TRMM) data as a cluster of pixels with an 85-GHz polarization-corrected brightness temperature below 255 K and with an area of at least 64 square kilometers. The study database consisted of convective systems in West Africa from May to September 1998-2007, and in the western Pacific from May to November 1998-2007. Annual cumulative frequency distributions for system minimum brightness temperature and system area were constructed for both regions. For both regions, there were no statistically significant differences between the annual curves for system minimum brightness temperature. There were two groups of system area curves, split by the TRMM altitude boost in 2001. Within each set, there was no statistically significant interannual variability. Subsetting the database revealed some sensitivity in distribution shape to the size of the sampling area, the length of the sample period, and the climate zone. From a regional perspective, the stability of the cumulative frequency distributions implied that the probability that a convective system would attain a particular size or intensity does not change interannually. Variability in the number of convective events appeared to be more important in determining whether a year is either wetter or drier than normal.
It is a common experience that rainfall is intermittent in space and time. This is reflected by the fact that the statistics of area- and/or time-averaged rain rate is described by a mixed distribution with a nonzero probability of having a sharp value zero. In this paper we have explored the dependence of the probability of zero rain on the averaging space and time scales in large multiyear data sets based on radar and rain gauge observations. A stretched exponential fannula fits the observed scale dependence of the zero-rain probability. The proposed formula makes it apparent that the space-time support of the rain field is not quite a set of measure zero as is sometimes supposed. We also give an ex.planation of the observed behavior in tenus of a simple probabilistic model based on the premise that rainfall process has an intrinsic memory.
This work presents a novel formulation of the ice nucleation spectrum, i.e. the function relating the ice crystal concentration to cloud formation conditions and aerosol properties. The new formulation is physically-based and explicitly accounts for the dependency of the ice crystal concentration on temperature, supersaturation, cooling rate, and particle size, surface area and composition. This is achieved by introducing the concepts of ice nucleation coefficient (the number of ice germs present in a particle) and nucleation probability dispersion function (the distribution of ice nucleation coefficients within the aerosol population). The new formulation is used to generate ice nucleation parameterizations for the homogeneous freezing of cloud droplets and the heterogeneous deposition ice nucleation on dust and soot ice nuclei. For homogeneous freezing, it was found that by increasing the dispersion in the droplet volume distribution the fraction of supercooled droplets in the population increases. For heterogeneous ice nucleation the new formulation consistently describes singular and stochastic behavior within a single framework. Using a fundamentally stochastic approach, both cooling rate independence and constancy of the ice nucleation fraction over time, features typically associated with singular behavior, were reproduced. Analysis of the temporal dependency of the ice nucleation spectrum suggested that experimental methods that measure the ice nucleation fraction over few seconds would tend to underestimate the ice nuclei concentration. It is shown that inferring the aerosol heterogeneous ice nucleation properties from measurements of the onset supersaturation and temperature may carry significant error as the variability in ice nucleation properties within the aerosol population is not accounted for. This work provides a simple and rigorous ice nucleation framework where theoretical predictions, laboratory measurements and field campaign data can be reconciled, and that is suitable for application in atmospheric modeling studies.
Pluto's bulk composition and the composition of the surface layers hold clues to the origin and evolution of a number of other Solar System bodies of comparable size in the region beyond Neptune. The July 14, 2015 flyby of the Pluto system with the New Horizons spacecraft afforded the opportunity to corroborate and greatly improve discoveries about the planet and its satellites derived Earth-based studies. It also revealed extraordinary details of the surface and atmosphere of Pluto, as well as the geology and composition of Charon and two smaller satellites. With a mean density of 1.86 g/sq cm, the bulk composition of Pluto is about two-thirds anhydrous solar composition rocky material and one-third volatiles (primarily H2O in liquid and solid states) by mass, the surface is a veneer of ices dominated by N2, with smaller amounts of CH4 and CO, as well as limited exposures of H2O ice (considered to be "bedrock"). N2, CH4, and CO occur as solid solutions at temperature-dependent mutual concentrations, each component being soluble in the others. Frozen C2H6 as a minor component has also been identified. Sublimation and recondensation of N2, CH4, and CO over seasonal (248 y) and Milankovich-type megaseasons (approx. 3 My) result in the redistribution of these ices over time and with latitude control. Solid N2 is found in glaciers originating in higher elevations and flowing at the present time into a basin structure larger than the State of Texas, forming a convecting lens of N2 that overturns on a timescale of order 10 My. The varied colors of Pluto's landscape arise from the energetic processing of the surface ices in processes that break the simple molecules and reassemble complex organic structures consisting of groups of aromatic rings connected by aliphatic chains. When synthesized in the laboratory by UV or electron irradiation of a Pluto mix of ice, this material, called tholin, has colors closely similar to Pluto. The Pluto ice tholin analog contains carboxylic acids, urea, ketones, aldehydes, amines, and some nitriles. The largest satellite, Charon has density 1.70 g/sq cm and it is about 3/5 anhydrous solar composition rock, with the remainder in H2O ice. The surface H2O ice is infused in some way with NH3, probably as a hydrate, distributed nonuniformly, but to some degree related to geological structures. Pluto's atmosphere is N2, CH4, with CO, C2-hydrocarbons, HCN, and other molecules in trace but detectable amounts. The atmosphere supports a complex haze structure with about 20 discrete layers, and suspected clouds. The haze is presumed to be made of aggregates of complex hydrocarbons (tholins) produced by photolysis of the atmospheric gases, and with similar composition to the ice tholins made on the planet's surface. Urea and a suite of carboxylic acids are of interest for prebiotic and biological chemistries.
The NASA CERES SYN1deg product provides the scientific community regional hourly TOA and surface broadband fluxes and clouds. For consistent geostationary (GEO) derived fluxes and clouds the GEO imagers are radiometrically scaled to the Aqua-MODIS calibration reference. The CERES project utilizes GEO and MODIS or VIIRS analogous channel coincident, collocated, and co-angled radiance pairs as the primary method to inter-calibrate the GEO imagers. Tropical deep convective clouds (DCC) are bright, near Lambertian, top of atmosphere pseudo invariant Earth targets that do not rely on coincident ray-matched radiance pairs to radiometrically scale sensors to a common calibration reference. The DCC invariant target (DCC-IT) methodology collectively analyzes all tropical DCC identified pixel radiances by way of probability density function (PDF) distributions. Perfectly inter-calibrated sensor pairs should reveal nearly identical PDF distributions given the same DCC identification criterion. The PDF median, mean, mode, and inflection point statistics were tested as a function of DCC identification criterion using SNPP-VIIRS and Himawari-8 AHI 0.65μm channel radiances during January 2019. It was found that the PDF inflection point provided inter-calibration factors within 0.25% that were nearly independent of DCC identification criterion. The PDF median provided inter-calibration factors within 0.25% for the coldest BT and most stringent homogeneity factors. The PDF mean and mode statistics were inadequate under any DCC conditions. It is critical for the DCC pixel radiances to be anisotropically corrected. The DCC-IT methodology will also be tested for other visible and SWIR bands.
Digitized agricultural field boundary taken in the United States and Canada during the LACIE and AgRISTARS programs, in 1977 through 1980, were used to construct histograms showing the distributions of field area, width, and length for crops for which there were data for 700 or more fields per state. The observed distributions of area and width for fields of 10 crops grown in 13 states of the United States and Canada were compared with best-fit inverse Gaussian distributions and with log-normal distributions. For 28 distributions of area and 16 distributions of width there was found to be a probability of greater than .01 of their being inverse Gaussian. There were 10 distributions of area for which there was probability of greater than .005 of their being log-normal. Distributions of area and width stratified by state and crop type appear to be unique. The inverse Gaussian, which represents a wide range of statistical distributions from skewed to almost symmetrical, can provide a useful model for distributions of field area.
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.
The homogeneity of the burst source population in space with the log N(greater than P sub c)-log P sub c and log (dN/dP sub c)-log P sub c relations is studied on the basis of a sample of 225 observed gamma-ray bursts between September 1978 and July 1988 from the Pioneer Venus Orbiter. The relations N(greater than P sub c) is approximately equal to P sub c exp -1.5 and dN/dP sub c is approximately equal to P sub c exp -2.5 are expected if the gamma bursters are uniformly distributed in space. The Kolmogorov-Smirnov statistic gives a probability of 0.93 that the observed integral distribution N(greater than P sub c) is drawn from the expected uniform distribution P sub c exp -1.5. A least-squares 1 standard deviation fit to the observed differential distribution yields dN/dP sub c of about P sub c -2.42 +/- 0.07. Both are consistent with a uniform distribution in space of the parent population of burst sources.
Upper atmospheric turbulence velocity probability density investigated in 90 to 110 km region