Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “probability distribution”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 73 records · Page 4
All sourcesNASA NTRSDOE OSTI
NASA NTRS1977

Turbulent plane Couette flow using probability distribution functions

A numerical scheme employing a combination of the discrete ordinate method and finite differences is developed for solving the one-dimensional form of Lundgren's (1967) model equation for turbulent plane Couette flow. The approach used requires no a priori assumption about the form of the turbulent distribution function, and the numerical solution is obtained directly from the governing differential equations. Two different types of boundary conditions (zero-gradient and Chapman-Enskog) for the distribution function are evaluated by comparing the numerical results with experimental data. It is found that: (1) the present approach gives convergent and stable results over a wide range of Reynolds numbers; (2) Lundgren's equation yields results that compare well with experimental data for mean velocity and skin friction in the case of simple Couette flow; (3) the zero-gradient boundary condition leads to a logarithmic flow profile; and (4) the Chapman-Enskog boundary condition provides very good agreement with experimental data when applied within the near-wall region.

Srinivasan, R.↗
NASA NTRS1977

Probable distribution of large impact basins on Venus - Comparison with Mercury and the moon

The reported study is based on the 12.5 cm wavelength data of Rumsey et al. (1974). The considered low resolution (80 km) radar image covers an area equivalent to 19% of the surface of Venus. The study had the objective to map potential large impact structures and relate their size frequency distribution to those of Mercury and the moon. The Venus radar map was analyzed using a color television film density slicer system for enhancement of subtle changes and gross patterns of contrasting radar reflectivity. Analysis by this technique permitted the recognition of 12 possible basins with diameters exceeding 600 km on about 8% of the total surface area of the planet. The preliminary basin size frequency distribution determined for Venus from these low resolution data suggests that the cloud-covered planet could be more cratered per unit area by basins than either the moon or Mercury.

Schaber, G. G.↗
NASA NTRS1982

A bivariate gamma probability distribution with application to gust modeling

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. It 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 to wind gust modeling for the ascent flight of the space shuttle are illustrated.

Smith, O. E.↗
NASA NTRS1983

Some properties of a 5-parameter bivariate probability distribution

A five-parameter bivariate gamma distribution having two shape parameters, two location parameters and a correlation parameter was developed. This more general bivariate gamma distribution reduces to the known four-parameter distribution. The five-parameter distribution gives a better fit to the gust data. The statistical properties of this general bivariate gamma distribution and a hypothesis test were investigated. Although these developments have come too late in the Shuttle program to be used directly as design criteria for ascent wind gust loads, the new wind gust model has helped to explain the wind profile conditions which cause large dynamic loads. Other potential applications of the newly developed five-parameter bivariate gamma distribution are in the areas of reliability theory, signal noise, and vibration mechanics.

Tubbs, J. D.↗
NASA NTRS1989

Probability distribution of wind retrieval error for the NASA scatterometer

The NASA scatterometer (NSCAT) is a spaceborne scatterometer scheduled to be deployed in the mid-1990s. An analysis of the wind retrieval error distribution for wind estimates based on backscatter measurements made by the NSCAT instrument is presented. The results are based on an end-to-end simulation of the scatterometer instrument and data processing. In general, the distribution of the wind speed error, when normalized, is independent of the true wind speed and direction. The wind speed error can be characterized by a normal distribution. The wind direction error is independent of the true wind speed, but depends on the true wind direction. Details for wind vectors with true wind speeds from 3 m/s to 33 m/s and true wind directions from 0 to 360 deg are presented.

Leotta, Daniel F.↗
NASA NTRS1993

Comparison of monthly rain rates derived from GPI and SSM/I using probability distribution functions

Three years of monthly rain rates over 5 deg x 5 deg latitude-longitude boxes have been calculated for oceanic regions 50 deg N-50 deg S from measurements taken by the Special Sensor Microwave/Imager on board the Defense Meteorological Satellite Program satellites using the technique developed by Wilheit et al. (1987, 1991). The annual and seasonal zonal-mean rain rates are larger than Jaeger's (1983) climatological estimates but are smaller than those estimated from the GOES precipitation index (GPI) for the same period. Regional comparison with the GPI showed that these rain rates are smaller in the north Indian Ocean and in the southern extratropics where the GPI is known to overestimate. The differences are also dominated by a jump at 170 deg W in the GPI rain rates across the mid-Pacific Ocean. This jump is attributed to the fusion of different satellite measurements in producing the GPI.

Chiu, Long S.↗
NASA NTRS1993

Random errors of oceanic monthly rainfall derived from SSM/I using probability distribution functions

Global averages and random errors associated with the monthly oceanic rain rates derived from the Special Sensor Microwave/Imager (SSM/I) data using the technique developed by Wilheit et al. (1991) are computed. Accounting for the beam-filling bias, a global annual average rain rate of 1.26 m is computed. The error estimation scheme is based on the existence of independent (morning and afternoon) estimates of the monthly mean. Calculations show overall random errors of about 50-60 percent for each 5 deg x 5 deg box. The results are insensitive to different sampling strategy (odd and even days of the month). Comparison of the SSM/I estimates with raingage data collected at the Pacific atoll stations showed a low bias of about 8 percent, a correlation of 0.7, and an rms difference of 55 percent.

Chang, Alfred T. C.↗
NASA NTRS1994

Principal modes of variation of rain-rate probability distributions

Radar or satellite observations of an area generate sequences of rain-rate maps. From a gridded map a histogram of rain rates can be obtained representing the relative areas occupied by rain rates of various strengths. The histograms vary with time as precipitating systems in the area evolve and decay and amounts of convective and stratiform rain in the area change. A method of decomposing the histograms into linear combinations of a few empirical distributions with time-dependent coefficients is developed, using principal component analysis as a starting point. When applied to a tropical Atlantic dataset (GATE), two distributions emerge naturally from the analysis, resembling stratiform and convective rain-rate distributions in that they peak at low and high rain rates, respectively. The two 'modes' have different timescales and only the high-rain-rate mode has a statistically significant diurnal cycle. The ability of just two modes to describe rain variabiltiy over an area can explain why methods of estimating area-averaged rain rate from the area covered by rain rates above a certain threshold are so successful.

Bell, Thomas L.↗
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 NTRS1994

Statistical analysis of mesoscale rainfall: Dependence of a random cascade generator on large-scale forcing

Under the theory of independent and identically distributed random cascades, the probability distribution of the cascade generator determines the spatial and the ensemble properties of spatial rainfall. Three sets of radar-derived rainfall data in space and time are analyzed to estimate the probability distribution of the generator. A detailed comparison between instantaneous scans of spatial rainfall and simulated cascades using the scaling properties of the marginal moments is carried out. This comparison highlights important similarities and differences between the data and the random cascade theory. Differences are quantified and measured for the three datasets. Evidence is presented to show that the scaling properties of the rainfall can be captured to the first order by a random cascade with a single parameter. The dependence of this parameter on forcing by the large-scale meteorological conditions, as measured by the large-scale spatial average rain rate, is investigated for these three datasets. The data show that this dependence can be captured by a one-to-one function. Since the large-scale average rain rate can be diagnosed from the large-scale dynamics, this relationship demonstrates an important linkage between the large-scale atmospheric dynamics and the statistical cascade theory of mesoscale rainfall. Potential application of this research to parameterization of runoff from the land surface and regional flood frequency analysis is briefly discussed, and open problems for further research are presented.

Over, Thomas, M.↗
NASA NTRS1978

Summary report of the Turbulence Committee

The effects of atmospheric turbulence are discussed. Aircraft design and aircraft operations are reviewed. Turbulence in terms of intensity and scale in design considerations was examined. Turbulence models were used in the form of discrete gusts, spectral distributions, and probability distributions. Various aspects of the design and operations problems, simulation and training factors of pilots, and weather services and forecasts are reported.

Elderkin, C. E.↗
NASA NTRS1989

A non-homogeneous Markov model for phased-mission reliability analysis

Three assumptions of Markov modeling for reliability of phased-mission systems that limit flexibility of representation are identified. The proposed generalization has the ability to represent state-dependent behavior, handle phases of random duration using globally time-dependent distributions of phase change time, and model globally time-dependent failure and repair rates. The approach is based on a single nonhomogeneous Markov model in which the concept of state transition is extended to include globally time-dependent phase changes. Phase change times are specified using nonoverlapping distributions with probability distribution functions that are zero outside assigned time intervals; the time intervals are ordered according to the phases. A comparison between a numerical solution of the model and simulation demonstrates that the numerical solution can be several times faster than simulation.

Smotherman, Mark↗