Search NASA⌕ Search

SEARCH · Search NASA

Results for “Probability Distribution Function”

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 379 records · Page 21
All sourcesNASA NTRSDOE OSTI
DOE OSTI2022

On the Statistics of Elsasser Increments in Solar Wind and Magnetohydrodynamic Turbulence

In this Letter we investigate the dependency with scale of the empirical probability distribution functions (PDF) of Elsasser increments using large sets of WIND data (collected between 1995 and 2017) near 1 au. The empirical PDF are compared to the ones obtained from high-resolution numerical simulations of steadily driven, homogeneous reduced MHD turbulence on a 2048 3 rectangular mesh. A large statistical sample of Alfvénic increments is obtained by using conditional analysis based on the solar wind average properties. The PDF tails obtained from observations and numerical simulations are found to have exponential behavior in the inertial range, with an exponential decrement that satisfies power laws of the form α l ∝ l –μ , where l is the scale size, with μ between 0.17 and 0.25 for observations and 0.43 for simulations. PDF tails were extrapolated assuming their exponential behavior extends to arbitrarily large increments in order to determine structure function scaling laws at very high orders. Our results point to potentially universal scaling laws governing the PDF of Elsasser increments and to an alternative approach to investigate high-order statistics in solar wind observations.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2024

Semi-Lagrangian nodal discontinuous Galerkin method for the BGK model

In this work, we propose a semi-Lagrangian (SL) nodal discontinuous Galerkin (DG) solver for the BGK equation. The BGK model was introduced by Bhatnagar, Gross, and Krook [1] as a relaxation model for the fundamental Boltzmann equation [5], which describes the kinetic dynamic of rarefied gases with a probability distribution function. The challenges of designing efficient numerical schemes for the Boltzmann equation mainly come from its high dimensionality and complicated nonlinear collision operator. The BGK model gains interests since it has much lower computational cost, due to the relatively simple structure of the relaxation operator in replacement of the collision operator, while simultaneously preserving several important physical properties, such as macroscopic quantities and dissipation of entropy.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2023

Evaluation of four ground-based retrievals of cloud droplet number concentration in marine stratocumulus with aircraft in situ measurements

Abstract. Cloud droplet number concentration (Nd) is crucial for understanding aerosol–cloud interactions (ACI) and associated radiative effects. We present evaluations of four ground-based Nd retrievals based on comprehensive datasets from the Atmospheric Radiation Measurement (ARM) Aerosol and Cloud Experiments in the Eastern North Atlantic (ACE-ENA) field campaign. The Nd retrieval methods use ARM ENA observatory ground-based remote sensing observations from a micropulse lidar, Raman lidar, cloud radar, and the ARM NDROP (Droplet Number Concentration) value-added product (VAP), all of which also retrieve cloud effective radius (re). The retrievals are compared against aircraft measurements from the fast cloud droplet probe (FCDP) and the cloud and aerosol spectrometer (CAS) obtained from low-level marine boundary layer clouds on 12 flight days during summer and winter seasons. Additionally, the in situ measurements are used to validate the assumptions and characterizations used in the retrieval algorithms. Statistical comparisons of the probability distribution function (PDF) of the Nd and cloud re retrievals with aircraft measurements demonstrate that these retrievals align well with in situ measurements for overcast clouds, but they may substantially differ for broken clouds or clouds with low liquid water path (LWP). The retrievals are applied to 4 years of ground-based remote sensing measurements of overcast marine boundary layer clouds at the ARM ENA observatory to find that Nd (re) values exhibit seasonal variations, with higher (lower) values during the summer season and lower (higher) values during the winter season. The ensemble of various retrievals using different measurements and retrieval algorithms such as those in this paper can help to quantify Nd retrieval uncertainties and identify reliable Nd retrieval scenarios. Of the retrieval methods, we recommend using the micropulse lidar-based method. This method has good agreement with in situ measurements, less sensitivity to issues arising from precipitation and low cloud LWP and/or optical depth, and broad applicability by functioning for both daytime and nighttime conditions.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2018

Estimates of climate system properties incorporating recent climate change

Abstract. Historical time series of surface temperature and ocean heat content changes are commonly used metrics to diagnose climate change and estimate properties of the climate system. We show that recent trends, namely the slowing of surface temperature rise at the beginning of the 21st century and the acceleration of heat stored in the deep ocean, have a substantial impact on these estimates. Using the Massachusetts Institute of Technology Earth System Model (MESM), we vary three model parameters that influence the behavior of the climate system: effective climate sensitivity (ECS), the effective ocean diffusivity of heat anomalies by all mixing processes (Kv), and the net anthropogenic aerosol forcing scaling factor. Each model run is compared to observed changes in decadal mean surface temperature anomalies and the trend in global mean ocean heat content change to derive a joint probability distribution function for the model parameters. Marginal distributions for individual parameters are found by integrating over the other two parameters. To investigate how the inclusion of recent temperature changes affects our estimates, we systematically include additional data by choosing periods that end in 1990, 2000, and 2010. We find that estimates of ECS increase in response to rising global surface temperatures when data beyond 1990 are included, but due to the slowdown of surface temperature rise in the early 21st century, estimates when using data up to 2000 are greater than when data up to 2010 are used. We also show that estimates of Kv increase in response to the acceleration of heat stored in the ocean as data beyond 1990 are included. Further, we highlight how including spatial patterns of surface temperature change modifies the estimates. We show that including latitudinal structure in the climate change signal impacts properties with spatial dependence, namely the aerosol forcing pattern, more than properties defined for the global mean, climate sensitivity, and ocean diffusivity.

Libardoni, Alex G.↗
DOE OSTI2023

Evaluation of Four Ground-based Retrievals of Cloud Droplet Number Concentration in Marine Stratocumulus with Aircraft In Situ Measurements

Cloud droplet number concentration (N d ) is crucial for understanding aerosol-cloud interactions (ACI) and associated radiative effects. We present evaluations of four ground-based N d retrievals based on comprehensive datasets from the Atmospheric Radiation Measurements (ARM) Aerosol and Cloud Experiments in the Eastern North Atlantic (ACE-ENA) field campaign. The N d retrieval methods use ARM ENA observatory ground-based remote sensing observations from a Micropulse lidar, Raman lidar, cloud radar, and the ARM NDROP Value-added Product (VAP), all of which also retrieve cloud effective radius (r e ). The retrievals are compared against aircraft measurements from the Fast-Cloud Droplet Probe (FCDP) and the Cloud and Aerosol Spectrometer (CAS) obtained from low-level marine boundary layer clouds on 12 flight days during summer and winter seasons. Additionally, the in situ measurements are used to validate the assumptions and characterizations used in the retrieval algorithms. Statistical comparisons of the probability distribution function (PDF) of the N d and cloud r e retrievals with aircraft measurements demonstrate that these retrievals align well with in situ measurements for overcast clouds, but they may substantially differ for broken clouds or clouds with low liquid water path (LWP). The retrievals are applied to four years of ground-based remote sensing measurements of overcast marine boundary layer clouds at the ARM ENA observatory to find that N d (r e ) values exhibit seasonal variations, with higher (lower) values during the summer season and lower (higher) values during the winter season. The ensemble of various retrievals using different measurements and retrieval algorithms such as those in this paper can help to quantify N d retrieval uncertainties and identify reliable N d retrieval scenarios. Of the retrieval methods, we recommend using the using the Micropulse lidar-based method given its good agreement with in situ measurements, it has less sensitivity to issues arising from precipitation and low cloud LWP/optical depth, and it has broad applicability by functioning for both day and nighttime conditions.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2021

Effects of coupling a stochastic convective parameterization with the Zhang–McFarlane scheme on precipitation simulation in the DOE E3SMv1.0 atmosphere model

Abstract. A stochastic deep convection parameterization is implemented into the US Department of Energy (DOE) Energy Exascale Earth System Model (E3SM) Atmosphere Model version 1.0 (EAMv1). This study evaluates its performance in simulating precipitation. Compared to the default model, the probability distribution function (PDF) of rainfall intensity in the new simulation is greatly improved. The well-known problem of “too much light rain and too little heavy rain” is alleviated, especially over the tropics. As a result, the contribution from different rain rates to the total precipitation amount is shifted toward heavier rain. The less frequent occurrence of convection contributes to suppressed light rain, while more intense large-scale and convective precipitation contributes to enhanced heavy total rain. The synoptic and intraseasonal variabilities of precipitation are enhanced as well to be closer to observations. The sensitivity of the rainfall intensity PDF to the model vertical resolution is examined. The relationship between precipitation and dilute convective available potential energy in the stochastic simulation agrees better with that in the Atmospheric Radiation Measurement (ARM) observations compared with the standard model simulation. The annual mean precipitation is largely unchanged with the use of the stochastic scheme except over the tropical western Pacific, where a moderate increase in precipitation represents a slight improvement. The responses of precipitation and its extremes to climate warming are similar with or without the stochastic deep convection scheme.

54 ENVIRONMENTAL SCIENCES↗
NASA NTRS1972

System efficiency of a microwave power tube with a multistage depressed collector

The efficiencies of a microwave power tube with a multistage depressed collector and of the power supply driving the tube are computed. An analytical expression for the collector efficiency, which includes the effect of secondary emission and the radial component of velocity, is derived for a hypothetical current probability distribution function. In addition, collector efficiency is calculated with the aid of a digital computer for a specific current distribution. The efficiency of the power supply required to operate the tube in a space environment is estimated by using a simple parallel inverter system.

Dayton, J. A., Jr.↗
NASA NTRS1973

Space shuttle solid rocket booster recovery system definition. Volume 2: SRB water impact Monte Carlo computer program, user's manual

The HD 220 program was created as part of the space shuttle solid rocket booster recovery system definition. The model was generated to investigate the damage to SRB components under water impact loads. The random nature of environmental parameters, such as ocean waves and wind conditions, necessitates estimation of the relative frequency of occurrence for these parameters. The nondeterministic nature of component strengths also lends itself to probabilistic simulation. The Monte Carlo technique allows the simultaneous perturbation of multiple independent parameters and provides outputs describing the probability distribution functions of the dependent parameters. This allows the user to determine the required statistics for each output parameter.

Source record↗
NASA NTRS1974

Statistical time-dependent model for the interstellar gas

We present models for temperature and ionization structure of low, uniform-density (approximately 0.3 per cu cm) interstellar gas in a galactic disk which is exposed to soft X rays from supernova outbursts occurring randomly in space and time. The structure was calculated by computing the time record of temperature and ionization at a given point by Monte Carlo simulation. The calculation yields probability distribution functions for ionized fraction, temperature, and their various observable moments. These time-dependent models predict a bimodal temperature distribution of the gas that agrees with various observations. Cold regions in the low-density gas may have the appearance of clouds in 21-cm absorption. The time-dependent model, in contrast to the steady-state model, predicts large fluctuations in ionization rate and the existence of cold (approximately 30 K), ionized (ionized fraction equal to about 0.1) regions.

Gerola, H.↗
NASA NTRS1975

Theory of fluctuations of extended air showers

The Monte Carlo method was used to calculate the probability distribution functions of shower characteristics for primary protons at sea level. The calculation was based on the following model of the elementary event: the interaction paths are 90 g/sq cm for nucleons and 120 g/sq cm for pions. The nonelasticity coefficient for nucleons is uniformly distributed between 0.1 and 0.9, and for pions it is equal to 1. Isobaric pions are taken into account. The spectra of secondary particles were determined using Cocconi's approximation formula. The calculation for the nuclei was carried out on the assumption of a breakup of the nucleus into component nucleons. The mean number of particles and the variances of the distributions for electrons when the number of muons was fixed, and for muons when the number of electrons was fixed, were calculated.

Dedenko, L. G.↗
NASA NTRS1975

Distribution and moments of radial error

An investigation of the moments and probability distribution of the resultant of two normally distributed random variables is presented. This is the so-called generalized Rayleigh distribution which has many applications in the study of wind shear, random noise, and radar. The most general formula was derived, and two special cases were considered for which tables of the moments and probability distribution functions are included as an appendix. One of the special cases was generalized to n-dimensions.

White, R. G.↗
NASA NTRS1978

Feature discrimination/identification based upon SAR return variations

A study of the statistics of The look-to-look variation statistics in the returns recorded in-flight by a digital, realtime SAR system are analyzed. The determination that the variations in the look-to-look returns from different classes do carry information content unique to the classes was illustrated by a model based on four variants derived from four look in-flight SAR data under study. The model was limited to four classes of returns: mowed grass on a athletic field, rough unmowed grass and weeds on a large vacant field, young fruit trees in a large orchard, and metal mobile homes and storage buildings in a large mobile home park. The data population in excess of 1000 returns represented over 250 individual pixels from the four classes. The multivariant discriminant model operated on the set of returns for each pixel and assigned that pixel to one of the four classes, based on the target variants and the probability distribution function of the four variants for each class.

Rasco, W. A., Sr.↗
NASA NTRS1981

A comprehensive model to determine the effects of temperature and species fluctuations on reactions in turbulent reacting flows

The joint probability distribution function (pdf), which is a modification of the bivariate Gaussian pdf, is discussed and results are presented for a global reaction model using the joint pdf. An alternative joint pdf is discussed. A criterion which permits the selection of temperature pdf's in different regions of turbulent, reacting flow fields is developed. Two principal approaches to the determination of reaction rates in computer programs containing detailed chemical kinetics are outlined. These models represent a practical solution to the modeling of species reaction rates in turbulent, reacting flows.

Antaki, P. J.↗
NASA NTRS1982

Closed-form solutions of performability

It is noted that if computing system performance is degradable then system evaluation must deal simultaneously with aspects of both performance and reliability. One approach is the evaluation of a system's performability which, relative to a specified performance variable Y, generally requires solution of the probability distribution function of Y. The feasibility of closed-form solutions of performability when Y is continuous are examined. In particular, the modeling of a degradable buffer/multiprocessor system is considered whose performance Y is the (normalized) average throughput rate realized during a bounded interval of time. Employing an approximate decomposition of the model, it is shown that a closed-form solution can indeed be obtained.

Meyer, J. F.↗
NASA NTRS1984

A performability solution method for degradable nonrepairable systems

The present performability model-solving algorithm identifies performance with 'reward', representing the state behavior of a system S by a finite-state stochastic process and determining reward by means of reward rates that are associated with the states of the base model. A general method is obtained for determining the probability distribution function of the performance (reward) variable, and therefore the performability, of the corresponding system. This is done for bounded utilization periods, and the result is an integral expression which is either analytically or numerically solvable.

Furchtgott, D. G.↗