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NASA NTRS2000

Volcanic Signatures in Estimates of Stratospheric Aerosol Size, Distribution Width, Surface Area, and Volume Deduced from Global Satellite-Based Observations

Volcanic signatures in the stratospheric aerosol layer are revealed by two independent techniques which retrieve aerosol information from global satellite-based observations of particulate extinction. Both techniques combine the 4-wavelength Stratospheric Aerosol and Gas Experiment (SAGE) II extinction measurements (0.385 <= lambda <= 1.02 microns) with the 7.96 micron and 12.82 micron extinction measurements from the Cryogenic Limb Array Etalon Spectrometer (CLAES) instrument. The algorithms use the SAGE II/CLAES composite extinction spectra in month-latitude-altitude bins to retrieve values and uncertainties of particle effective radius R(sub eff), surface area S, volume V and size distribution width sigma(sub R). The first technique is a multi-wavelength Look-Up-Table (LUT) algorithm which retrieves values and uncertainties of R(sub eff) by comparing ratios of extinctions from SAGE II and CLAES (e.g., E(sub lambda)/E(sub 1.02) to pre-computed extinction ratios which are based on a range of unimodal lognormal size distributions. The pre-computed ratios are presented as a function of R(sub eff) for a given sigma(sub g); thus the comparisons establish the range of R(sub eff) consistent with the measured spectra for that sigma(sub g). The fact that no solutions are found for certain sigma(sub g) values provides information on the acceptable range of sigma(sub g), which is found to evolve in response to volcanic injections and removal periods. Analogous comparisons using absolute extinction spectra and error bars establish the range of S and V. The second technique is a Parameter Search Technique (PST) which estimates R(sub eff) and sigma(sub g) within a month-latitude-altitude bin by minimizing the chi-squared values obtained by comparing the SAGE II/CLAES extinction spectra and error bars with spectra calculated by varying the lognormal fitting parameters: R(sub eff), sigma(sub g), and the total number of particles N(sub 0). For both techniques, possible biases in retrieved-parameters caused by assuming a unimodal functional form are removed using correction factors computed from representative in situ measurements of bimodal size distributions. Some interesting features revealed by the LUT and PST retrievals include: (1) Increases in S and V (but not R(sub eff)) after the Ruiz and Kelut injections, (2) Increases in S, V, R(sub eff) after Pinatubo, (3) Post-Pinatubo increases in S, V, and R(sub eff) that are more rapid in the tropics than elsewhere, (4) Mid-latitude post-Pinatubo increases in R(sub eff) that lag increases in S and V, (5) S and V returning to pre-Pinatubo values sooner than R(sub eff) does, (6) Sharp increases in sigma(sub g), after Pinatubo and slight increases in sigma(sub g) after Ruiz, Etna, Kelut, Spurr and Rabaul, and (7) Gradual declines in the heights at which R(sub eff), S and V peak after Pinatubo.

Bauman, J. J.↗

NASA NTRS2011

Emissions of Black Carbon, Organic, and Inorganic Aerosols From Biomass Burning in North America and Asia in 2008

Reliable assessment of the impact of aerosols emitted from boreal forest fires on the Arctic climate necessitates improved understanding of emissions and the microphysical properties of carbonaceous (black carbon (BC) and organic aerosols (OA)) and inorganic aerosols. The size distributions of BC were measured by an SP2 based on the laser-induced incandescence technique on board the DC-8 aircraft during the NASA ARCTAS campaign. Aircraft sampling was made in fresh plumes strongly impacted by wildfires in North America (Canada and California) in summer 2008 and in those transported from Asia (Siberia in Russia and Kazakhstan) in spring 2008. We extracted biomass burning plumes using particle and tracer (CO, CH3CN, and CH2Cl2) data. OA constituted the dominant fraction of aerosols mass in the submicron range. The large majority of the emitted particles did not contain BC. We related the combustion phase of the fire as represented by the modified combustion efficiency (MCE) to the emission ratios between BC and other species. In particular, we derived the average emission ratios of BC/CO = 2.3 +/- 2.2 and 8.5 +/- 5.4 ng/cu m/ppbv for BB in North America and Asia, respectively. The difference in the BC/CO emission ratios is likely due to the difference in MCE. The count median diameters and geometric standard deviations of the lognormal size distribution of BC in the BB plumes were 136-141 nm and 1.32-1.36, respectively, and depended little on MCE. These BC particles were thickly coated, with shell/core ratios of 1.3-1.6. These parameters can be used directly for improving model estimates of the impact of BB in the Arctic.

Kondo, Y.↗

DOE OSTI2025

Statistical distributions for transient transport

Here, this paper introduces the use of statistical distributions based on transport differential equations for clear distinction of transport modes within transient kinetic experiments. More specifically, novel techniques are developed for the transient data obtained through the Temporal Analysis of Products (TAP) reactor and are applicable to experiments where pulse response into a gas flow is used. The methodology allows distinguishing between two domains of diffusion transport in heterogeneous catalytic systems, i.e., Knudsen and non-Knudsen diffusion, using statistical fingerprints, and finding the transition domain. Two distribution parameters were obtained that directly result in coefficients that correspond to the concentration and the rate of transport. Using a linear relationship between the rate and concentration coefficients, Knudsen diffusion is revealed when the rate of transport is constant and non-Knudsen diffusion is confirmed when the rate of transport coefficient is a function of the concentration coefficient. As a result, accurate transport information can be extracted from experimental data even in the presence of comprising instrument drift or noise particularly when analyzing higher pressure pulse responses with complex transport. This enables more direct investigation of experiments influenced by gas-phase reactions.

TAP reactor↗

NASA NTRS1994

A 'skewed' lognormal approximation to the probablility distribution function of the large-scale density field

I propose a method to fit the probability distribution function (PDF) of the large-scale density field rho, motivated by a Lagrangian version of the continuity equation. It consists in applying the Edgeworth expansion to the quantity Phi identical with log rho - mean value of log rho. The method is tested on the matter particle distribution in two cold dark matter N-body simulations of different physical sizes to cover a large dynamic range. It is seen to be very efficient, even in the nonlinear regime, and may thus be used as an analytical tool to study the effect on the PDF of the transition between the weakly nonlinear regime and the highly nonlinear regime.

Colombi, S.↗

NASA NTRS1994

Evolution of Pinatubo aerosol near 19 km altitude over western North America

Stratospheric aerosols, collected near 19 km altitude on wire impactors over western North America from August 20, 1991 to May 11, 1993, show strong influence of the June 1991 Mt. Pinatubo eruption. Lognormal size distributions are bimodal; each of the mode radii increases and reaches maximum value at about 15 months after eruption. The second (large particle) mode becomes well developed then, and about 40% of the droplets are larger than 0.4 micron radius. The eruption of Mt. Spurr (Alaska) may also have contributed to this. Sulfate mass loading decays exponentially (e-folding 216 days), similar to El Chichon. Silicates are present in samples only immediately after eruption. Two years after eruption, sulfate mass loading is about 0.4 micrograms/cu m, about an order of magnitude higher than background pre-volcanic values. Aerosol size distributions are still bimodal with a very well-defined large droplet mode.

Goodman, Jindra↗

NASA NTRS1995

Viking Lander image analysis of Martian atmospheric dust

We have reanalyzed three sets of Viking Lander 1 and 2 (VL1 and VL2) images of the Martian atmosphere to better evaluate the radiative properties of the atmospheric dust particles. The properties of interest are the first two moments of the size distribution, the single-scattering albedo, the dust single-scattering phase function, and the imaginary index of refraction. These properties provide a good definition of the influence that the atmospheric dust has on heating of the atmosphere. Our analysis represents a significant improvement over past analyses (Pollack et al. 1977, 1979) by deriving more accurate brightness closer to the sun, by carrying out more precise analyses of the data to acquire the quantities of interest, and by using a better representation of scattering by nonspherical particles. The improvements allow us to better define the diffraction peak and hence the size distribution of the particles. For a lognormal particle size distribution, the first two moments of the size distribution, weighted by the geometric cross section, are found. The geometric cross-section weighted mean radius r(sub eff) is found to be 1.85 +/- 0.3 micrometers at VL2 during northern summer when dust loading was low and 1.52 +/- 0.3 micrometers at VL1 during the first dust storm. In both cases the best cross-section weighted mean variance nu(sub eff) of the size distribution is equal to 0.5 +/- 0.2 micrometers. The changes in size distribution, and thus radiative properties, do not represent a substantial change in solar energy deposition in the atmosphere over the Pollak et al. (1977, 1979) estimates.

Pollack, James B.↗

NASA NTRS1995

Viking Lander image analysis of Martian atmospheric dust

We have reanalyzed three sets of Viking Lander 1 and 2 (VL1 and VL2) images of the Martian atmosphere to better evaluate the radiative properties of the atmospheric dust particles. The properties of interest are the first two moments of the size distribution, the single-scattering albedo, the dust single-scattering phase function, and the imaginary index of refraction. These properties provide a good definition of the influence that the atmospheric dust has on heating of the atmosphere. Our analysis represents a significant improvement over past analyses (Pollack et al. 1977,1979) by deriving more accurate brightnesses closer to the sun, by carrying out more precise analyses of the data to acquire the quantities of interest, and by using a better representation of scattering by nonspherical particles. The improvements allow us to better define the diffraction peak and hence the size distribution of the particles. For a lognormal particle size distribution, the first two moments of the size distribution, weighted by the geometric cross section, are found. The geometric cross-section weighted mean radius (r(sub eff)) is found to be 1.85 +/- 0.3 microns at VL2 during northern summer when dust loading was low and 1.52 +/- 0.3 microns at VL1 during the first dust storm. In both cases the best cross-section weighted mean variance (nu(eff)) of the size distribution is equal to 0.5 +/- 0.2 microns. The changes in size distribution, and thus radiative properties, do not represent a substantial change in solar energy deposition in the atmosphere over the Pollack et al. (1977,1979) estimates.

Pollack, James B.↗

NASA NTRS1992

Black Carbon (Soot) Aerosol in the Lower Stratosphere and Upper Troposphere

We have used two approaches to measure BCA in the stratosphere. The first method consists of collecting aerosols by impaction on quartz rods, upon which are mounted strips of polystyrene filter material. Each 25 mm by 0.5 mm filter strip is alternately masked and exposed in 5 mm long sections. After sampling, the optical density of the exposed sections is measured and compared with the optical density of the masked (unexposed) sections. The filter strip is a Lambertian collector, the scattering property of which is not affected by the deposition of liquid sulfuric acid droplets which dominate the stratospheric aerosol. Hence, all attenuation greater in the exposed than in the non-exposed sections is due to absorption by BCA or rare opaque materials such as meteoritic iron. In a second approach we expose carbon-coated gold or palladium wires to air outside the aircraft boundary layer [Farlow et al., 1979; Pueschel et al., 1989]. With a field emission scanning electron microscope we are able to characterize BCA particles in addition to the dominant sulfuric acid droplets. Typically, soot is comprised of 20 nm diameter spheres linked together as branching chains or loosely packed aggregates (Figure 1a). The microscope has a lateral image resolution of 1.5 nm and can clearly resolve individual spheres making up BCA aggregates. Their morphology is uniquely different from that of the liquid sulfuric acid-water aerosol (Figure 1b). We approximate the size of each BCA particle by that of a sphere of equivalent volume and fit a lognormal size distribution to both the BCA and H2SO4/H2O aerosols. Both sampler types have been mounted on NASA's ER-2 high-altitude research aircraft (altitude ceiling of 70,000 feet), and on NASA's DC-8 (40,000 feet ceiling) aircraft to sample aerosols from a significant portion of the atmosphere.

Pueschel, R. F.↗

NASA NTRS2002

Complex Refractive Index of Ammonium Nitrate in the 2-20 micron Spectral Range

Using high resolution Fourier Transform Infrared Spectroscopy (FTIR) absorbance/transmittance spectral data for ammonium sulfate (AMS), calcium carbonate (CAC) and ammonium nitrate (AMN), comparisons were made with previously published complex refractive indices data for AMS and CAC to infer experimental parameters to determine the imaginary refractive index for AMN in the infrared wavelength range from 2 to 20 microns. Kramers-Kronig mathematical relations were applied to calculate the real refractive index for the three compositions. Excellent agreement for AMS and CAC with the published values was found, validating the complex refractive indices obtained for AMN. Backscatter calculations using a lognormal size distribution for AMS, AMN, and CAC aerosols were performed to show differences in their backscattered spectra.

Jarzembski, Maurice A.↗

NASA NTRS2004

Probability Distribution Estimated From the Minimum, Maximum, and Most Likely Values: Applied to Turbine Inlet Temperature Uncertainty

Modern engineering design practices are tending more toward the treatment of design parameters as random variables as opposed to fixed, or deterministic, values. The probabilistic design approach attempts to account for the uncertainty in design parameters by representing them as a distribution of values rather than as a single value. The motivations for this effort include preventing excessive overdesign as well as assessing and assuring reliability, both of which are important for aerospace applications. However, the determination of the probability distribution is a fundamental problem in reliability analysis. A random variable is often defined by the parameters of the theoretical distribution function that gives the best fit to experimental data. In many cases the distribution must be assumed from very limited information or data. Often the types of information that are available or reasonably estimated are the minimum, maximum, and most likely values of the design parameter. For these situations the beta distribution model is very convenient because the parameters that define the distribution can be easily determined from these three pieces of information. Widely used in the field of operations research, the beta model is very flexible and is also useful for estimating the mean and standard deviation of a random variable given only the aforementioned three values. However, an assumption is required to determine the four parameters of the beta distribution from only these three pieces of information (some of the more common distributions, like the normal, lognormal, gamma, and Weibull distributions, have two or three parameters). The conventional method assumes that the standard deviation is a certain fraction of the range. The beta parameters are then determined by solving a set of equations simultaneously. A new method developed in-house at the NASA Glenn Research Center assumes a value for one of the beta shape parameters based on an analogy with the normal distribution (ref.1). This new approach allows for a very simple and direct algebraic solution without restricting the standard deviation. The beta parameters obtained by the new method are comparable to the conventional method (and identical when the distribution is symmetrical). However, the proposed method generally produces a less peaked distribution with a slightly larger standard deviation (up to 7 percent) than the conventional method in cases where the distribution is asymmetric or skewed. The beta distribution model has now been implemented into the Fast Probability Integration (FPI) module used in the NESSUS computer code for probabilistic analyses of structures (ref. 2).

Holland, Frederic A., Jr.↗

NASA NTRS2018

The Kepler Light Curves of AGN: A Detailed Analysis

We present a comprehensive analysis of 21 light curves of Type 1 active galactic nuclei (AGN) from the Kepler spacecraft. First, we describe the necessity and development of a customized pipeline for treating Kepler data of stochastically variable sources like AGN. We then present the light curves, power spectral density functions (PSDs), and flux histograms. The light curves display an astonishing variety of behaviors, many of which would not be detected in ground-based studies, including switching between distinct flux levels. Six objects exhibit PSD flattening at characteristic timescales that roughly correlate with black hole mass. These timescales are consistent with orbital timescales or free-fall accretion timescales. We check for correlations of variability and high-frequency PSD slope with accretion rate, black hole mass, redshift, and luminosity. We find that bolometric luminosity is anticorrelated with both variability and steepness of the PSD slope. We do not find evidence of the linear rms-flux relationships or lognormal flux distributions found in X-ray AGN light curves, indicating that reprocessing is not a significant contributor to optical variability at the 0.1%-10% level.

power spectral density functions(PSDs)↗

DOE OSTI2024

Evaluating the impact of anatomical and physiological variability on human equivalent doses using PBPK models

Abstract Addressing human anatomical and physiological variability is a crucial component of human health risk assessment of chemicals. Experts have recommended probabilistic chemical risk assessment paradigms in which distributional adjustment factors are used to account for various sources of uncertainty and variability, including variability in the pharmacokinetic behavior of a given substance in different humans. In practice, convenient assumptions about the distribution forms of adjustment factors and human equivalent doses (HEDs) are often used. Parameters such as tissue volumes and blood flows are likewise often assumed to be lognormally or normally distributed without evaluating empirical data for consistency with these forms. In this work, we performed dosimetric extrapolations using physiologically based pharmacokinetic (PBPK) models for dichloromethane (DCM) and chloroform that incorporate uncertainty and variability to determine if the HEDs associated with such extrapolations are approximately lognormal and how they depend on the underlying distribution shapes chosen to represent model parameters. We accounted for uncertainty and variability in PBPK model parameters by randomly drawing their values from a variety of distribution types. We then performed reverse dosimetry to calculate HEDs based on animal points of departure for each set of sampled parameters. Corresponding samples of HEDs were tested to determine the impact of input parameter distributions on their central tendencies, extreme percentiles, and degree of conformance to lognormality. This work demonstrates that the measurable attributes of human variability should be considered more carefully and that generalized assumptions about parameter distribution shapes may lead to inaccurate estimates of extreme percentiles of HEDs.

Toxicology↗

NASA NTRS1995

Earth-space links and fade-duration statistics

In recent years, fade-duration statistics have been the subject of several experimental investigations. A good knowledge of the fade-duration distribution is important for the assessment of a satellite communication system's channel dynamics: What is a typical link outage duration? How often do link outages exceeding a given duration occur? Unfortunately there is yet no model that can universally answer the above questions. The available field measurements mainly come from temperate climatic zones and only from a few sites. Furthermore, the available statistics are also limited in the choice of frequency and path elevation angle. Yet, much can be learned from the available information. For example, we now know that the fade-duration distribution is approximately lognormal. Under certain conditions, we can even determine the median and other percentiles of the distribution. This paper reviews the available data obtained by several experimenters in different parts of the world. Areas of emphasis are mobile and fixed satellite links. Fades in mobile links are due to roadside-tree shadowing, whereas fades in fixed links are due to rain attenuation.

Davarian, Faramaz↗

NASA NTRS1996

Earth-Space Links and Fade-Duration Statistics

Davarian, Faramaz↗

NASA NTRS2011

Magnetic Field Strength Fluctuations in the Heliosheath: Voyager 1 Observations during 2009

We analyze the "microscale fluctuations" of the magnetic field strength Beta on a scale of several hours observed by Voyager I (VI) in the heliosheath during 2009. The microscale fluctuations of Beta range from coherent to stochastic structures. The amplitude of microscale fluctuations of Beta during 1 day is measured by the standard deviation (SD) of 48 s averages of B. The distribution of the daily values of SD is lognormal. SD(t) from day of year (DOY) I to 331, 2009, is very intermittent. SD(t) has a 1/f or "pink noise" spectrum on scales from I to 100 days, and it has a broad multi fractal spectrum f(alpha) with 0.57 much < alpha much < 1.39. The time series of increments SD(t + r) - SD(t) has a pink noise spectrum with alpha' = 0.88 +/- 0.14 on scales from 1 to 100 days. The increments have a Tsallis (q-Gaussian) distribution on scales from 1 to 165 days, with an average q = 1.75 +/- 0.12. The skewness S and kurtosis K have Gaussian and lognormal distributions, respectively. The largest spikes in K(t) and Set) are often associated with a change in Beta across a data gap and with identifiable physical structures. The "turbulence" observed by VI during 2009 was weakly compressible on average but still very intermittent, highly variable, and highly compressible at times. The turbulence observed just behind the termination shock by Voyager 2 was twice as strong. These observations place strong constraints on any model of "turbulence" in the heliosheath.

Burlaga, L. F.↗

NASA NTRS2012

Magnetic Field Strength Fluctuations in the Heliosheath: Voyager 1 Observations During 2009

We analyze the microscale fluctuations of the magnetic field strength B on a scale of several hours observed by Voyager1 (V1) in the heliosheath during 2009. The microscale fluctuations of B range from coherent to stochastic structures. The amplitude of microscale fluctuations of B during 1 day is measured by the standard deviation (SD) of 48 s averages of B. The distribution of the daily values of SD is lognormal. SD(t) from day of year (DOY) 1 to 331, 2009, is very intermittent. SD(t) has a 1/f or "pink noise" spectrum on scales from 1 to 100 days, and it has a broad multifractal spectrum f(alpha) with 0.57 less than or equal to alpha less than or equal to 1.39. The time series of increments SD(t + tau) -- SD(t) has a pink noise spectrum with alpha(1) = 0.88 plus or minus 0.14 on scales from 1 to 100 days. The increments have a Tsallis (q-Gaussian) distribution on scales from 1 to 165 days, with an average q = 1.75 plus or minus 0.12. The skewness S and kurtosis K have Gaussian and lognormal distributions, respectively. The largest spikes in K(t) and S(t) are often associated with a change in B across a data gap and with identifiable physical structures. The "turbulence" observed by V1 during 2009 was weakly compressible on average but still very intermittent, highly variable, and highly compressible at times. The turbulence observed just behind the termination shock by Voyager 2 was twice as strong. These observations place strong constraints on any model of turbulence in the heliosheath.

Brulaga, L. F.↗

NASA NTRS2018

Improvement of Stratospheric Aerosol Extinction Retrieval from OMPS/LP Using a New Aerosol Model

The Ozone Mapping and Profiler Suite Limb Profiler (OMPS/LP) has been flying on the Suomi National Polar-orbiting Partnership (S-NPP) satellite since October 2011. It is designed to produce ozone and aerosol vertical profiles at 2-kilometer vertical resolution over the entire sunlit globe. Aerosol extinction profiles are computed with Mie theory using radiances measured at 675 nanometers. The operational Version 1.0 (V1.0) aerosol extinction retrieval algorithm assumes a bimodal lognormal aerosol size distribution (ASD) whose parameters were derived by combining an in situ measurement of aerosol microphysics with the Stratospheric Aerosol and Gas Experiment (SAGE II) aerosol extinction climatology. Internal analysis indicates that this bimodal lognormal ASD does not sufficiently explain the spectral dependence of LP-measured radiances. In this paper we describe the derivation of an improved aerosol size distribution, designated Version 1.5 (V1.5), for the LP retrieval algorithm. The new ASD uses a gamma function distribution that is derived from Community Aerosol and Radiation Model for Atmospheres (CARMA)-calculated results. A cumulative distribution fit derived from the gamma function ASD gives better agreement with CARMA results at small particle radii than bimodal or unimodal functions. The new ASD also explains the spectral dependence of LP-measured radiances better than the V1.0 ASD. We find that the impact of our choice of ASD on the retrieved extinctions varies strongly with the underlying reflectivity of the scene. Initial comparisons with collocated extinction profiles retrieved at 676 nanometers from the SAGE III instrument on the International Space Station (ISS) show a significant improvement in agreement for the LP V1.5 retrievals. Zonal mean extinction profiles agree to within 10 percent between 19 and 29 kilometers, and regression fits of collocated samples show improved correlation and reduced scatter compared to the V1.0 product. This improved agreement will motivate development of more sophisticated ASDs from CARMA results that incorporate latitude, altitude and seasonal variations in aerosol properties.

Ozone Mapping Profiler Suite Limb Profiler (OMPS/L↗

NASA NTRS1993

Rain-rate data base development and rain-rate climate analysis

The single-year rain-rate distribution data available within the archives of Consultative Committee for International Radio (CCIR) Study Group 5 were compiled into a data base for use in rain-rate climate modeling and for the preparation of predictions of attenuation statistics. The four year set of tip-time sequences provided by J. Goldhirsh for locations near Wallops Island were processed to compile monthly and annual distributions of rain rate and of event durations for intervals above and below preset thresholds. A four-year data set of tropical rain-rate tip-time sequences were acquired from the NASA TRMM program for 30 gauges near Darwin, Australia. They were also processed for inclusion in the CCIR data base and the expanded data base for monthly observations at the University of Oklahoma. The empirical rain-rate distributions (edfs) accepted for inclusion in the CCIR data base were used to estimate parameters for several rain-rate distribution models: the lognormal model, the Crane two-component model, and the three parameter model proposed by Moupfuma. The intent of this segment of the study is to obtain a limited set of parameters that can be mapped globally for use in rain attenuation predictions. If the form of the distribution can be established, then perhaps available climatological data can be used to estimate the parameters rather than requiring years of rain-rate observations to set the parameters. The two-component model provided the best fit to the Wallops Island data but the Moupfuma model provided the best fit to the Darwin data.

Crane, Robert K.↗