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All sourcesNASA NTRSDOE OSTI
NASA NTRS1992

Uncertainties in obtaining high reliability from stress-strength models

There has been a recent interest in determining high statistical reliability in risk assessment of aircraft components. The potential consequences are identified of incorrectly assuming a particular statistical distribution for stress or strength data used in obtaining the high reliability values. The computation of the reliability is defined as the probability of the strength being greater than the stress over the range of stress values. This method is often referred to as the stress-strength model. A sensitivity analysis was performed involving a comparison of reliability results in order to evaluate the effects of assuming specific statistical distributions. Both known population distributions, and those that differed slightly from the known, were considered. Results showed substantial differences in reliability estimates even for almost nondetectable differences in the assumed distributions. These differences represent a potential problem in using the stress-strength model for high reliability computations, since in practice it is impossible to ever know the exact (population) distribution. An alternative reliability computation procedure is examined involving determination of a lower bound on the reliability values using extreme value distributions. This procedure reduces the possibility of obtaining nonconservative reliability estimates. Results indicated the method can provide conservative bounds when computing high reliability. An alternative reliability computation procedure is examined involving determination of a lower bound on the reliability values using extreme value distributions. This procedure reduces the possibility of obtaining nonconservative reliability estimates. Results indicated the method can provide conservative bounds when computing high reliability.

Neal, Donald M.↗
NASA NTRS1994

Statistic analysis of annual total ozone extremes for the period 1964-1988

Annual extremes of total column amount of ozone (in the period 1964-1988) from a network of 29 Dobson stations have been examined using the extreme value analysis. The extremes have been calculated as the highest deviation of daily mean total ozone from its long-term monthly mean, normalized by the monthly standard deviations. The extremes have been selected from the direct-Sun total ozone observations only. The extremes resulting from abrupt changes in ozone (day to day changes greater than 20 percent) have not been considered. The ordered extremes (maxima in ascending way, minima in descending way) have been fitted to one of three forms of the Fisher-Tippet extreme value distribution by the nonlinear least square method (Levenberg-Marguard method). We have found that the ordered extremes from a majority of Dobson stations lie close to Fisher-Tippet type III. The extreme value analysis of the composite annual extremes (combined from averages of the annual extremes selected at individual stations) has shown that the composite maxima are fitted by the Fisher-Tippet type III and the composite minima by the Fisher-Tippet type I. The difference between the Fisher-Tippet types of the composite extremes seems to be related to the ozone downward trend. Extreme value prognoses for the period 1964-2014 (derived from the data taken at: all analyzed stations, the North American, and the European stations) have revealed that the prognostic extremes are close to the largest annual extremes in the period 1964-1988 and there are only small regional differences in the prognoses.

Krzyscin, Janusz W.↗
NASA NTRS2016

Evaluation of NASA's MERRA Precipitation Product in Reproducing the Observed Trend and Distribution of Extreme Precipitation Events in the United States

This study evaluates the performance of NASA's Modern-Era Retrospective Analysis for Research and Applications (MERRA) precipitation product in reproducing the trend and distribution of extreme precipitation events. Utilizing the extreme value theory, time-invariant and time-variant extreme value distributions are developed to model the trends and changes in the patterns of extreme precipitation events over the contiguous United States during 1979-2010. The Climate Prediction Center (CPC) U.S.Unified gridded observation data are used as the observational dataset. The CPC analysis shows that the eastern and western parts of the United States are experiencing positive and negative trends in annual maxima, respectively. The continental-scale patterns of change found in MERRA seem to reasonably mirror the observed patterns of change found in CPC. This is not previously expected, given the difficulty in constraining precipitation in reanalysis products. MERRA tends to overestimate the frequency at which the 99th percentile of precipitation is exceeded because this threshold tends to be lower in MERRA, making it easier to be exceeded. This feature is dominant during the summer months. MERRA tends to reproduce spatial patterns of the scale and location parameters of the generalized extreme value and generalized Pareto distributions. However, MERRA underestimates these parameters, particularly over the Gulf Coast states, leading to lower magnitudes in extreme precipitation events. Two issues in MERRA are identified: 1) MERRA shows a spurious negative trend in Nebraska and Kansas, which is most likely related to the changes in the satellite observing system over time that has apparently affected the water cycle in the central United States, and 2) the patterns of positive trend over the Gulf Coast states and along the East Coast seem to be correlated with the tropical cyclones in these regions. The analysis of the trends in the seasonal precipitation extremes indicates that the hurricane and winter seasons are contributing the most to these trend patterns in the southeastern United States. In addition, the increasing annual trend simulated by MERRA in the Gulf Coast region is due to an incorrect trend in winter precipitation extremes.

MERRA↗
NASA NTRS1988

Winds aloft statistical analysis in support of day of launch Shuttle systems evaluation

In connection with the development of the Meteorological Interactive Data Display System (MIDDS) for utilization by the Launch Systems Evaluation Advisory Team (LSEAT), requirements have been established to expand the pre-launch analysis of winds aloft for the Space Shuttle. Statistical analyses developed for the system include: comparison of pre-launch wind component profiles to wind component extremes at each altitude calculated from launch site historical data; conditional probability ellipses for wind vectors at a future time given the wind vector at an initial time; comparison of observed extreme wind shear and associated wind speed with launch site historical data utilizing the bivariate extreme value (Gumbel) distribution; estimation of extremes of wind speed or wind shear at a future time given the extremes of either variable at an initial time, utilizing the conditional extreme value distribution; power spectrum analysis for tracking wind perturbation energy in sequential pre-launch Jimsphere wind profiles.

Adelfang, S. I.↗
NASA NTRS1998

Isosurface Extraction in Time-Varying Fields Using a Temporal Hierarchical Index Tree

Many high-performance isosurface extraction algorithms have been proposed in the past several years as a result of intensive research efforts. When applying these algorithms to large-scale time-varying fields, the storage overhead incurred from storing the search index often becomes overwhelming. this paper proposes an algorithm for locating isosurface cells in time-varying fields. We devise a new data structure, called Temporal Hierarchical Index Tree, which utilizes the temporal coherence that exists in a time-varying field and adoptively coalesces the cells' extreme values over time; the resulting extreme values are then used to create the isosurface cell search index. For a typical time-varying scalar data set, not only does this temporal hierarchical index tree require much less storage space, but also the amount of I/O required to access the indices from the disk at different time steps is substantially reduced. We illustrate the utility and speed of our algorithm with data from several large-scale time-varying CID simulations. Our algorithm can achieve more than 80% of disk-space savings when compared with the existing techniques, while the isosurface extraction time is nearly optimal.

Shen, Han-Wei↗
NASA NTRS1992

On the modeling of scalar diffusion in isotropic turbulence

The objectives of the study were to establish the behavior of conditional scalar dissipation and diffusion at the extreme values of mass fraction and to derive and evaluate closure models for these terms using the scalar probability density function. The conditional scalar dissipation, its derivative with respect to mass fraction, and conditional scalar diffusion are all found to be zero at extreme values of mass fraction. A model for conditional scalar dissipation is derived which exhibits the correct behavior at the extreme values of scalar concentration.

Girimaji, Sharath S.↗
NASA NTRS1975

Estimating maximum instantaneous distortion from inlet total pressure rms and PSD measurements

An inexpensive method is developed to determine the extreme values of instantaneous inlet distortion. This method also provides insight into the basic mechanics of unsteady inlet flow and the associated engine reaction. The analysis is based on fundamental fluid dynamics and statistical methods to provide an understanding of the turbulent inlet flow and quantitatively relate the rms level and power spectral density (PSD) function of the measured time variant total pressure fluctuations to the strength and size of the low pressure regions. The most probable extreme value of the instantaneous distortion is then synthesized from this information in conjunction with the steady state distortion. Results of the analysis show the extreme values to be dependent upon the steady state distortion, the measured turbulence rms level and PSD function, the time on point, and the engine response characteristics. Analytical projections of instantaneous distortion are presented and compared with data obtained by a conventional, highly time correlated, 40 probe instantaneous pressure measurement system.

Melick, H. C., Jr.↗
NASA NTRS2016

Persistence Mapping Using EUV Solar Imager Data

We describe a simple image processing technique that is useful for the visualization and depiction of gradually evolving or intermittent structures in solar physics extreme-ultraviolet imagery. The technique is an application of image segmentation, which we call "Persistence Mapping," to isolate extreme values in a data set, and is particularly useful for the problem of capturing phenomena that are evolving in both space and time. While integration or "time-lapse" imaging uses the full sample (of size N ), Persistence Mapping rejects (N - 1)/N of the data set and identifies the most relevant 1/N values using the following rule: if a pixel reaches an extreme value, it retains that value until that value is exceeded. The simplest examples isolate minima and maxima, but any quantile or statistic can be used. This paper demonstrates how the technique has been used to extract the dynamics in long-term evolution of comet tails, erupting material, and EUV dimming regions.

Thompson, B. J.↗
NASA NTRS2015

Minimum-Cost Aircraft Descent Trajectories with a Constrained Altitude Profile

An analytical formula for solving the speed profile that accrues minimum cost during an aircraft descent with a constrained altitude profile is derived. The optimal speed profile first reaches a certain speed, called the minimum-cost speed, as quickly as possible using an appropriate extreme value of thrust. The speed profile then stays on the minimum-cost speed as long as possible, before switching to an extreme value of thrust for the rest of the descent. The formula is applied to an actual arrival route and its sensitivity to winds and airlines' business objectives is analyzed.

altitude restrictions↗
NASA NTRS1998

A Compendium of Wind Statistics and Models for the NASA Space Shuttle and Other Aerospace Vehicle Programs

The wind profile with all of its variations with respect to altitude has been, is now, and will continue to be important for aerospace vehicle design and operations. Wind profile databases and models are used for the vehicle ascent flight design for structural wind loading, flight control systems, performance analysis, and launch operations. This report presents the evolution of wind statistics and wind models from the empirical scalar wind profile model established for the Saturn Program through the development of the vector wind profile model used for the Space Shuttle design to the variations of this wind modeling concept for the X-33 program. Because wind is a vector quantity, the vector wind models use the rigorous mathematical probability properties of the multivariate normal probability distribution. When the vehicle ascent steering commands (ascent guidance) are wind biased to the wind profile measured on the day-of-launch, ascent structural wind loads are reduced and launch probability is increased. This wind load alleviation technique is recommended in the initial phase of vehicle development. The vehicle must fly through the largest load allowable versus altitude to achieve its mission. The Gumbel extreme value probability distribution is used to obtain the probability of exceeding (or not exceeding) the load allowable. The time conditional probability function is derived from the Gumbel bivariate extreme value distribution. This time conditional function is used for calculation of wind loads persistence increments using 3.5-hour Jimsphere wind pairs. These increments are used to protect the commit-to-launch decision. Other topics presented include the Shuttle Shuttle load-response to smoothed wind profiles, a new gust model, and advancements in wind profile measuring systems. From the lessons learned and knowledge gained from past vehicle programs, the development of future launch vehicles can be accelerated. However, new vehicle programs by their very nature will require specialized support for new databases and analyses for wind, atmospheric parameters (pressure, temperature, and density versus altitude), and weather. It is for this reason that project managers are encouraged to collaborate with natural environment specialists early in the conceptual design phase. Such action will give the lead time necessary to meet the natural environment design and operational requirements, and thus, reduce development costs.

Smith, O. E.↗
NASA NTRS1975

Seasonal variations of NO and O3 at altitudes of 18.3 and 21.3 km

Nitric oxide and ozone concentrations have been measured in situ from a high-altitude research aircraft. Data which show the variations of NO and O3 with the time of year are presented for altitudes of 18.3 and 21.3 km. The extreme values of the observed NO concentrations at 21.3 km are 1.2 billion per cu cm in summer and 0.2 billion per cu cm in winter. At 18.3 km the extreme values are 1.6 billion per cu cm in summer and 0.1 billion per cu cm in winter. The smoothed NO seasonal data show a variation of about a factor of 2.5 at 21.3 km and a factor of 4 at 18.3 km. The ozone data show the generally expected magnitude and seasonal variation. We have used a photochemical model employing the measured ozone concentrations, the mean solar zenith angle, and seasonal HNO3 data reported by others to predict the seasonal NO variation at 20 km. The result is a summer-to-winter NO ratio of 2.5 which is in fair agreement with the observed ratios.

Loewenstein, M.↗
NASA NTRS2016

Geoelectric Hazard Maps for the Continental United States

In support of a multiagency project for assessing induction hazards, we present maps of extreme-value geoelectric amplitudes over about half of the continental United States. These maps are constructed using a parameterization of induction: estimates of Earth surface impedance, obtained at discrete geographic sites from magnetotelluric survey data, are convolved with latitude-dependent statistical maps of extreme-value geomagnetic activity, obtained from decades of magnetic observatory data. Geoelectric amplitudes are estimated for geomagnetic waveforms having 240 s sinusoidal period and amplitudes over 10 min that exceed a once-per-century threshold. As a result of the combination of geographic differences in geomagnetic activity and Earth surface impedance, once-per-century geoelectric amplitudes span more than 2 orders of magnitude and are an intricate function of location. For north-south induction, once-per-century geoelectric amplitudes across large parts of the United States have a median value of 0.26 Vkm; for east-west geomagnetic variation the median value is 0.23 Vkm. At some locations,once-per-century geoelectric amplitudes exceed 3 Vkm.

Love, Jeffrey J.↗
NASA NTRS2013

Ensemble Statistical Post-Processing of the National Air Quality Forecast Capability: Enhancing Ozone Forecasts in Baltimore, Maryland

An ensemble statistical post-processor (ESP) is developed for the National Air Quality Forecast Capability (NAQFC) to address the unique challenges of forecasting surface ozone in Baltimore, MD. Air quality and meteorological data were collected from the eight monitors that constitute the Baltimore forecast region. These data were used to build the ESP using a moving-block bootstrap, regression tree models, and extreme-value theory. The ESP was evaluated using a 10-fold cross-validation to avoid evaluation with the same data used in the development process. Results indicate that the ESP is conditionally biased, likely due to slight overfitting while training the regression tree models. When viewed from the perspective of a decision-maker, the ESP provides a wealth of additional information previously not available through the NAQFC alone. The user is provided the freedom to tailor the forecast to the decision at hand by using decision-specific probability thresholds that define a forecast for an ozone exceedance. Taking advantage of the ESP, the user not only receives an increase in value over the NAQFC, but also receives value for An ensemble statistical post-processor (ESP) is developed for the National Air Quality Forecast Capability (NAQFC) to address the unique challenges of forecasting surface ozone in Baltimore, MD. Air quality and meteorological data were collected from the eight monitors that constitute the Baltimore forecast region. These data were used to build the ESP using a moving-block bootstrap, regression tree models, and extreme-value theory. The ESP was evaluated using a 10-fold cross-validation to avoid evaluation with the same data used in the development process. Results indicate that the ESP is conditionally biased, likely due to slight overfitting while training the regression tree models. When viewed from the perspective of a decision-maker, the ESP provides a wealth of additional information previously not available through the NAQFC alone. The user is provided the freedom to tailor the forecast to the decision at hand by using decision-specific probability thresholds that define a forecast for an ozone exceedance. Taking advantage of the ESP, the user not only receives an increase in value over the NAQFC, but also receives value for

ozone↗
NASA NTRS1978

Nimbus 6 satellite vs rawinsonde capabilities

The paper establishes rms errors in Nimbus 6 satellite data from discrepancies between satellite and rawinsonde data, compares rms errors in Nimbus 6 with those in rawinsonde data, and examines the capability of Nimbus 6 satellite data to depict such quantities as horizontal gradients of basic variables and computed variables such as vorticity and lapse rate of temperature. The capability of Nimbus 6 data is illustrated by comparisons of rms errors in computed variables obtained through a propagation-of-error method with average and near-extreme values of the variables obtained from two of NASA's Atmospheric Variability Experiments (AVE II and AVE IV). It is shown that the rms errors in Nimbus 6 basic variables (temperature, mixing ratio, geopotential height, and wind speed) are between 2 and 12 times larger than the corresponding errors in rawinsonde data. For all variables examined, the magnitude of the rms errors are smaller than the near-extreme values of the variables determined from AVE II and AVE IV data.

Scoggins, J. R.↗
NASA NTRS2017

The Relationships Between the Trends of Mean and Extreme Precipitation

This study provides a better understanding of the relationships between the trends of mean and extreme precipitation in two observed precipitation data sets: the Climate Prediction Center Unified daily precipitation data set and the Global Precipitation Climatology Program (GPCP) pentad data set. The study employs three kinds of definitions of extreme precipitation: (1) percentile, (2) standard deviation and (3) generalize extreme value (GEV) distribution analysis for extreme events based on local statistics. Relationship between trends in the mean and extreme precipitation is identified with a novel metric, i.e. area aggregated matching ratio (AAMR) computed on regional and global scales. Generally, more (less) extreme events are likely to occur in regions with a positive (negative) mean trend. The match between the mean and extreme trends deteriorates for increasingly heavy precipitation events. The AAMR is higher in regions with negative mean trends than in regions with positive mean trends, suggesting a higher likelihood of severe dry events, compared with heavy rain events in a warming climate. AAMR is found to be higher in tropics and oceans than in the extratropics and land regions, reflecting a higher degree of randomness and more important dynamical rather than thermodynamical contributions of extreme events in the latter regions.

global warming↗
NASA NTRS2013

Detection of Extremes with AIRS and CrIS

Climate change is expected to be detected first as changes in extreme values rather than in mean values. The availability of data of from two instruments in the same orbit, AIRS data for the past eleven years and AIRS and CrIS data from the past year, provides an opportunity to evaluate this using examples of climate relevance: Desertification, seen as changes in hot extremes, severe storm, seen as a change in extremely cold clouds and the warming of the polar zone. We use AIRS to establish trends for the 1%tile, the mean and 99%tile brightness temperatures measured with the 900 cm(exp -1) channel from AIRS for the past 11 years. This channel is in the clearest part of the 11 micron atmospheric window. Substantial trends are seen for land and ocean, which in the case of the 1%tile (cold) extremes are related to the current shift of deep convection from ocean to land. Changes are also seen in the 99%tile for day tropical land, but their interpretation is at present unclear. We also see dramatic changes for the mean and 99%tile of the North Polar area. The trends are an order of magnitude larger than the instrument trend of about 3 mK/year. We use the statistical distribution from the past year derived from AIRS to evaluate the accuracy of continuing the trends established with AIRS with CrIS data. We minimize the concern about differences in the spectral response functions by limiting the analysis to the channel at 900 cm(exp -1).While the two instruments agree within 100 mK for the global day/night land/ocean mean values, there are significant differences when evaluating the1% and 99%tiles. We see a consistent warm bias in the CrIS data relative to AIRS for the 1%tile (extremely cold, cloudy) data in the tropical zone, particularly for tropical land, but the bias is not day/night land/ocean consistent. At this point the difference appears to be due to differences in the radiometric response of AIRS and CrIS to differences in the day/night land/ocean cloud types. Unless the effect can be mitigated by a future reprocessing the CrIS data, it will significantly complicate the concatenation of the AIRS and CrIS data records for the continuation of trends in extreme values.

sampling bias↗
NASA NTRS1979

Extreme Mean and Its Applications

Extreme value statistics obtained from normally distributed data are considered. An extreme mean is defined as the mean of p-th probability truncated normal distribution. An unbiased estimate of this extreme mean and its large sample distribution are derived. The distribution of this estimate even for very large samples is found to be nonnormal. Further, as the sample size increases, the variance of the unbiased estimate converges to the Cramer-Rao lower bound. The computer program used to obtain the density and distribution functions of the standardized unbiased estimate, and the confidence intervals of the extreme mean for any data are included for ready application. An example is included to demonstrate the usefulness of extreme mean application.

Swaroop, R.↗