Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “statistics of extremes”

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 613 records · Page 34
All sourcesNASA NTRSDOE OSTI
NASA NTRS2021

Evaluation of Novel NASA MODIS and VIIRS Aerosol Products and Assessment of Smoke Height Boundary Layer Ratio During Extreme Smoke Events in the Western U.S.

We analyze new aerosol products from NASA satellite retrievals over the western U.S. during August 2013, with special attention to locally generated wildfire smoke and downwind plume structures. Aerosol optical depth (AOD) at 550 nm from MODIS (Terra and Aqua Collections 6 and 6.1) and VIIRS Deep Blue (DB) and MODIS (Terra and Aqua) Multi‐Angle Implementation of Atmospheric Correction (MAIAC) retrievals are evaluated against ground‐based AErosol RObotic NETwork (AERONET) observations. We find a significant improvement in correlation with AERONET and other metrics in the latest DB AOD (MODIS C6.1 r^2=0.75, VIIRS r^2=0.79) compared to MODIS C6 (r2=0.62). In general, MAIAC (r^2=0.84) and DB (MODIS C6.1 and VIIRS) present similar statistical evaluation metrics for the western U.S. and are useful tools to characterize aerosol loading associated with wildfire smoke. We also evaluate three novel NASA MODIS plume injection height (PIH) products, one from MAIAC and two from the Aerosol Single scattering albedo and layer Height Estimation (ASHE) (MODIS and VIIRS) algorithm. Both Terra and Aqua MAIAC PIHs statistically agree with ground‐based and satellite lidar observations near the fire source, as do ASHE, although the latter is sensitive to assumptions about aerosol absorption properties. We introduce a first‐order approximation Smoke Height Boundary Layer Ratio (SHBLR) to qualitatively distinguish between aerosol pollution within the planetary boundary layer and the free troposphere. We summarize the scope, limitations, and suggestions for scientific applications of surface level aerosol concentrations specific to wildfire emissions and smoke plumes using these novel NASA MODIS and VIIRS aerosol products.

Plume injection height↗
NASA NTRS1990

Taguchi Approach to Design Optimization for Quality and Cost: An Overview

Calibrations to existing cost of doing business in space indicate that to establish human presence on the Moon and Mars with the Space Exploration Initiative (SEI) will require resources, felt by many, to be more than the national budget can afford. In order for SEI to succeed, we must actually design and build space systems at lower cost this time, even with tremendous increases in quality and performance requirements, such as extremely high reliability. This implies that both government and industry must change the way they do business. Therefore, new philosophy and technology must be employed to design and produce reliable, high quality space systems at low cost. In recognizing the need to reduce cost and improve quality and productivity, Department of Defense (DoD) and National Aeronautics and Space Administration (NASA) have initiated Total Quality Management (TQM). TQM is a revolutionary management strategy in quality assurance and cost reduction. TQM requires complete management commitment, employee involvement, and use of statistical tools. The quality engineering methods of Dr. Taguchi, employing design of experiments (DOE), is one of the most important statistical tools of TQM for designing high quality systems at reduced cost. Taguchi methods provide an efficient and systematic way to optimize designs for performance, quality, and cost. Taguchi methods have been used successfully in Japan and the United States in designing reliable, high quality products at low cost in such areas as automobiles and consumer electronics. However, these methods are just beginning to see application in the aerospace industry. The purpose of this paper is to present an overview of the Taguchi methods for improving quality and reducing cost, describe the current state of applications and its role in identifying cost sensitive design parameters.

Unal, Resit↗
NASA NTRS2005

Structural Health Monitoring of Composite Plates Under Ambient and Cryogenic Conditions

Methods for structural health monitoring are now being assessed, especially in high-performance, extreme environment, safety-critical applications. One such application is for composite cryogenic fuel tanks. The work presented here attempts to characterize and investigate the feasibility of using imbedded piezoelectric sensors to detect cracks and delaminations under cryogenic and ambient conditions. Different types of excitation and response signals and different sensors are employed in composite plate samples to aid in determining an optimal algorithm, sensor placement strategy, and type of imbedded sensor to use. Variations of frequency and high frequency chirps of the sensors are employed and compared. Statistical and analytic techniques are then used to determine which method is most desirable for a specific type of damage and operating environment. These results are furthermore compared with previous work using externally mounted sensors. More work is needed to accurately account for changes in temperature seen in these environments and be statistically significant. Sensor development and placement strategy are other areas of further work to make structural health monitoring more robust. Results from this and other work might then be incorporated into a larger composite structure to validate and assess its structural health. This could prove to be important in the development and qualification of any 2nd generation reusable launch vehicle using composites as a structural element.

Engberg, Robert C.↗
NASA NTRS2019

The Salience of Nonlinearities in the Boreal Winter Response to ENSO: Arctic Stratosphere and Europe

The salience of nonlinearities in the Arctic stratospheric response to El Niño - Southern Oscillation (ENSO) is evaluated in a 41 member ensemble of the period 1980 to 2009 in the NASA Goddard Earth Observing System Chemistry-Climate Model. Central Pacific El Niño (CP EN) events preferentially increase zonal wavenumber 2, while Eastern Pacific El Niño (EP EN) events preferentially increase zonal wavenumber 1, though these nonlinearities become statistically robust only after more than 45 events are considered. This leads to a difference in the morphology of SSW events preferentially forced by each ENSO flavor. While the zonal-mean Arctic stratospheric response is little different between EP and CP EN once one accounts for the relative weakness of CP events, the tropospheric subpolar negative North Atlantic Oscillation response is stronger for CP events. Other nonlinearities are even less salient: there is no indication of any nonlinearities in the wave driving between moderate EP EN and extreme EP EN, nor between EN and La Niña (LN). However in approximately 15% of the integrations within our ensemble, there is no difference in SSW frequency between EN and LN, suggesting that a similar SSW frequency for both EN and LN, as has occurred over the past 60 years, can occur by chance. The intra-ensemble variability in LN SSW frequency can be related back to intra-ensemble variability in the tropospheric response to LN.

Arctic↗
NASA NTRS2022

Regression Bias in using Solar Wind Measurements

Simultaneous solar wind measurements from the solar wind monitors, WIND and ACE, differ due to the spatial and temporal structure of the solar wind. Correlation studies that use these measurements as input may infer an incorrect correlation due to uncertainties arising from this spatial and temporal structure, especially at extreme and rare solar wind values. In particular, regression analysis will lead to a regression function whose slope is biased towards the mean value of the measurement parameter. This article demonstrates this regression bias by comparing simultaneous ACE and WIND solar wind measurements. A non-linear regression analysis between them leads to a perception of underestimation of extreme values of one measurement on average over the other. Using numerical experiments, we show that popular regression analysis techniques such as linear least-squares, orthogonal least-squares, and non-linear regression are not immune to this bias. Hence while using solar wind parameters as an independent variable in a correlation or regression analysis, random uncertainty in the independent variable can create unintended biases in the response of the dependent variable. More generally, the regression to the mean effect can impact both event-based, statistical studies of magnetospheric response to solar wind forcing.

magnetosphere↗
DOE OSTI2021

The size of the Proton: Recent Results from the PRad Experiment

Two new extremely high precision measurements of the proton rms charge radius performed in 2010-2013 with muonic hydrogen atom demonstrated up to six standard deviations smaller values than the accepted average from all previous experiments performed with different methods (scattering and atomic spectroscopy) on ordinary hydrogen. This discrepancy triggered the well-known ?proton radius puzzle? in hadronic physics. To address this puzzle, the PRad collaboration in spring of 2016 performed a novel magnetic-spectrometer-free ep-scattering experiment in Hall B at Jefferson Lab accumulating high statistics and a rich experimental data set. The specifics of the PRad experiment and the final physics results, including the extracted proton radius, as well as, the current status of the puzzle will be presented and discussed in this talk.

Gasparian, Ashot↗
DOE OSTI2020

Analysis of Electric and Magnetic Lightning-Generated Wave Amplitudes Measured by the Van Allen Probes

Herein we provide a statistical analysis of both electric and magnetic field wave amplitudes of very low frequency lightning-generated waves (LGWs) based on the equivalent of 11.5 years of observations made by the Van Allen Probes encompassing ~24.6 × 10 6 survey mode measurements. We complement this analysis with data from the ground-based World Wide Lightning Location Network to explore differences between satellite and ground-based measurements. LGW mean amplitudes are found to be low compared with other whistler mode waves (1 ± 1.6 pT and 19 ± 59 μV/m). Extreme events (1/5,000) can reach 100 pT and contributes strongly to the mean power below $L$ = 2. We find excellent correlations between World Wide Lightning Location Network-based power and wave amplitudes in space at various longitudes. We reveal strong dayside ionospheric damping of the LGW electric field. LGW amplitudes drop for $L$ < 2, contrary to the Earth's intense equatorial lightning activity. We conclude that it is difficult for equatorial LGW to propagate and remain at $L$ < 2.

Electric wave power↗
DOE OSTI2025

Hestia-SWIFL: hourly anthropogenic fossil fuel CO2 and heat on the 2km WRF grid, version 1.1

The Hestia-SWIFL version 1.1 anthropogenic heat (AH) and fossil fuel CO2 (FFCO2) emissions data product represent emissions due to the combustion of fossil fuel and cement production within the state of Arizona from 2019 to 2022. This product was developed as part of the Southwest Urban Corridor Integrated Field Laboratory (SW-IFL) project, which aims to provide new knowledge and tools that address extreme heat, air quality, climate change and related urban environmental issues by integrating high-resolution observations, modeling, and civic engagement. The emissions are generated using a bottom-up/engineering approach and are tied to results generated by the Vulcan Project version 4, an effort to quantify space/time-resolved FFCO2 & AH emissions for the entire United States landscape. A large number of data sources are combined to best estimate the emissions at fine scales such as air quality emissions data, traffic flow data, building information, sociodemographic information, and fuel statistics. The AH product provides emissions for two emissions sources (transportation and point source emissions) in units of Watts per hour per square meter (W/m2) per year (annual files) or per hour (hourly files). The FFCO2 product provides emissions from nine individual emission sectors as well as the total, and in units of tons of carbon (tC) per grid cell per year or per hour. The output made available here places the native spatial resolution of the Hestia FFCO2 & AH emissions data product (points, lines, and polygons) into a regularized 2km x 2km grid at hourly and annual temporal resolutions, and stored in netCDF files. The exact spatial extent is defined by the ASU Weather Research Forecast (WRF) simulation grid. All data are processed using R/Python pm high-performance computing system. 2-27-2026 updates: Bugs in airport hourly profile (both AH and FFCO2) and building spatial patterns (FFCO2 only) were fixed. Hourly emissions are reprocessed for all years to reflect those changes.

54 ENVIRONMENTAL SCIENCES↗
NASA NTRS1986

Molecular clouds and supernova remnants in the outer galaxy

The study of extragalactic supernova (SNs) suggests that Type II SNs, not Type I, tend to occur near extreme optical Population I objects, but the detection of these objects in the Galaxy is limited by heavy local obscuration. A CO survey has been conducted toward every confirmed outer Galaxy SNR from l = 70 to 210 deg, for a total of 26, and it is found that roughly half of them, within uncertainties of distance estimates, revealed spatial coincidences with large molecular cloud complexes. Most of the cloud complexes in these coincidences probably are the birthplaces of the progenitors of the corresponding Type II SNRs, because it is statistically improbable that the coincidences result from change superposition.

Huang, Y.-L.↗
NASA NTRS1997

Global Analysis of Empirical Relationships Between Annual Climate and Seasonality of NDVI

This paper describes the use of satellite data to calibrate a new climate-vegetation greenness relationship for global change studies. We examined statistical relationships between annual climate indexes (temperature, precipitation, and surface radiation) and seasonal attributes If the AVHRR Normalized Difference Vegetation Index (NDVI) time series for the mid-1980's in order to refine our understanding of intra-annual patterns and global abiotic controls on natural vegetation dynamics. Multiple linear regression results using global 1o gridded data sets suggest that three climate indexes: degree days (growing/chilling), annual precipitation total, and an annual moisture index together can account to 70-80 percent of the geographic variation in the NDVI seasonal extremes (maximum and minimum values) for the calibration year 1984. Inclusion of the same annual climate index values from the previous year explains no substantial additional portion of the global scale variation in NDVI seasonal extremes. The monthly timing of NDVI extremes is closely associated with seasonal patterns in maximum and minimum temperature and rainfall, with lag times of 1 to 2 months. We separated well-drained areas from lo grid cells mapped as greater than 25 percent inundated coverage for estimation of both the magnitude and timing of seasonal NDVI maximum values. Predicted monthly NDVI, derived from our climate-based regression equations and Fourier smoothing algorithms, shows good agreement with observed NDVI for several different years at a series of ecosystem test locations from around the globe. Regions in which NDVI seasonal extremes are not accurately predicted are mainly high latitude zones, mixed and disturbed vegetation types, and other remote locations where climate station data are sparse.

Potter, C. S.↗
NASA NTRS1997

Global Analysis of Empirical Relationships Between Annual Climate and Seasonality of NDVI

This study describes the use of satellite data to calibrate a new climate-vegetation greenness function for global change studies. We examined statistical relationships between annual climate indexes (temperature, precipitation, and surface radiation) and seasonal attributes of the AVHRR Normalized Difference Vegetation Index (NDVI) time series for the mid-1980s in order to refine our empirical understanding of intraannual patterns and global abiotic controls on natural vegetation dynamics. Multiple linear regression results using global l(sup o) gridded data sets suggest that three climate indexes: growing degree days, annual precipitation total, and an annual moisture index together can account to 70-80 percent of the variation in the NDVI seasonal extremes (maximum and minimum values) for the calibration year 1984. Inclusion of the same climate index values from the previous year explained no significant additional portion of the global scale variation in NDVI seasonal extremes. The monthly timing of NDVI extremes was closely associated with seasonal patterns in maximum and minimum temperature and rainfall, with lag times of 1 to 2 months. We separated well-drained areas from l(sup o) grid cells mapped as greater than 25 percent inundated coverage for estimation of both the magnitude and timing of seasonal NDVI maximum values. Predicted monthly NDVI, derived from our climate-based regression equations and Fourier smoothing algorithms, shows good agreement with observed NDVI at a series of ecosystem test locations from around the globe. Regions in which NDVI seasonal extremes were not accurately predicted are mainly high latitude ecosystems and other remote locations where climate station data are sparse.

Potter, C. S.↗
NASA NTRS2015

Evaluation of the 7-km GEOS-5 Nature Run

This report documents an evaluation by the Global Modeling and Assimilation Office (GMAO) of a two-year 7-km-resolution non-hydrostatic global mesoscale simulation produced with the Goddard Earth Observing System (GEOS-5) atmospheric general circulation model. The simulation was produced as a Nature Run for conducting observing system simulation experiments (OSSEs). Generation of the GEOS-5 Nature Run (G5NR) was motivated in part by the desire of the OSSE community for an improved high-resolution sequel to an existing Nature Run produced by the European Centre for Medium-Range Weather Forecasts (ECMWF), which has served the community for several years. The intended use of the G5NR in this context is for generating simulated observations to test proposed observing system designs regarding new instruments and their deployments. Because NASA's interest in OSSEs extends beyond traditional weather forecasting applications, the G5NR includes, in addition to standard meteorological components, a suite of aerosol types and several trace gas concentrations, with emissions downscaled to 10 km using ancillary information such as power plant location, population density and night-light information. The evaluation exercise described here involved more than twenty-five GMAO scientists investigating various aspects of the G5NR performance, including time mean temperature and wind fields, energy spectra, precipitation and the hydrological cycle, the representation of waves, tropical cyclones and midlatitude storms, land and ocean surface characteristics, the representation and forcing effects of clouds and radiation, dynamics of the stratosphere and mesosphere, and the representation of aerosols and trace gases. Comparisons are made with observational data sets when possible, as well as with reanalyses and other long model simulations. The evaluation is broad in scope, as it is meant to assess the overall realism of basic aspects of the G5NR deemed relevant to the conduct of OSSEs. However, because of the relatively short record and other practical considerations, these comparisons cannot provide a definitive, statistically sound assessment of all model deficiencies, or guarantee the G5NR's suitability for all OSSE applications. Differences between the observed and simulated behavior also must be judged in the context of basic internal atmospheric variability which can introduce variations that are not necessarily controlled by the prescribed sea surface temperatures used in generating the G5NR. The results show that the G5NR performs well as measured by the majority of metrics applied in this evaluation. Particular benefits derived from the 7-km resolution of G5NR include realistic representations of extreme weather events in both the tropics and extratropics including tropical cyclones, Nor'easters and mesoscale convective complexes; improved representation of the diurnal cycle of precipitation over land; well-resolved surface-atmosphere interactions such as katabatic wind flows over Antarctica and Greenland; and resolution of orographically generated gravity waves that propagate into the upper atmosphere and influence the large scale circulation. Obvious deficiencies in the G5NR include a "splitting" of the inter-tropical convergence zone, which leads to a weaker-than-observed Hadley circulation and related deficiencies in the depiction of stationary wave patterns. Also, while the G5NR captures global cloud features and radiative effects well in general, close comparison with observations reveals higher-than-observed cloud brightness, likely due to an overabundance of cloud condensate; less distinct cloud minima in subtropical subsidence zones, consistent with a weak Hadley circualtion; and too few near-coastal marine stratocumulus clouds.

GEOS-5↗
NASA NTRS2016

Climatology of the Aerosol Optical Depth by Components from the Multi-Angle Imaging Spectroradiometer (MISR) and Chemistry Transport Models

The Multi-angle Imaging Spectroradiometer (MISR) Joint Aerosol (JOINT_AS) Level 3 product has provided a global, descriptive summary of MISR Level 2 aerosol optical depth (AOD) and aerosol type information for each month over 16+ years since March 2000. Using Version 1 of JOINT_AS, which is based on the operational (Version 22) MISR Level 2 aerosol product, this study analyzes, for the first time, characteristics of observed and simulated distributions of AOD for three broad classes of aerosols: spherical nonabsorbing, spherical absorbing, and nonspherical - near or downwind of their major source regions. The statistical moments (means, standard deviations, and skew-nesses) and distributions of AOD by components derived from the JOINT_AS are compared with results from two chemistry transport models (CTMs), the Goddard Chemistry Aerosol Radiation and Transport (GOCART) and SPectral RadIatioN-TrAnSport (SPRINTARS). Overall, the AOD distributions retrieved from MISR and modeled by GOCART and SPRINTARS agree with each other in a qualitative sense. Marginal distributions of AOD for each aerosol type in both MISR and models show considerable high positive skewness, which indicates the importance of including extreme AOD events when comparing satellite retrievals with models. The MISR JOINT_AS product will greatly facilitate comparisons between satellite observations and model simulations of aerosols by type.

SPRINTARS↗
NASA NTRS2021

Reviews and syntheses: Arctic fire regimes and emissions in the 21st century

In recent years, the pan-Arctic region has experienced increasingly extreme fire seasons. Fires in the northern high latitudes are driven by current and future climate change, lightning, fuel conditions, and human activity. In this context, conceptualizing and parameterizing current and future Arctic fire regimes will be important for fire and land management as well as understanding current and predicting future fire emissions. The objectives of this review were driven by policy questions identified by the Arctic Monitoring and Assessment Programme (AMAP) Working Group and posed to its Expert Group on Short-Lived Climate Forcers. This review synthesizes current understanding of the changing Arctic and boreal fire regimes, particularly as fire activity and its response to future climate change in the pan-Arctic have consequences for Arctic Council states aiming to mitigate and adapt to climate change in the north. The conclusions from our synthesis are the following. (1) Current and future Arctic fires, and the adjacent boreal region, are driven by natural (i.e. lightning) and human-caused ignition sources, including fires caused by timber and energy extraction, prescribed burning for landscape management, and tourism activities. Little is published in the scientific literature about cultural burning by Indigenous populations across the pan-Arctic, and questions remain on the source of ignitions above 70_ N in Arctic Russia. (2) Climate change is expected to make Arctic fires more likely by increasing the likelihood of extreme fire weather, increased lightning activity, and drier vegetative and ground fuel conditions. (3) To some extent, shifting agricultural land use and forest transitions from forest–steppe to steppe, tundra to taiga, and coniferous to deciduous in a warmer climate may increase and decrease open biomass burning, depending on land use in addition to climate-driven biome shifts. However, at the country and landscape scales, these relationships are not well established. (4) Current black carbon and PM2:5 emissions from wildfires above 50 and 65_ N are larger than emissions from heanthropogenic sectors of residential combustion, transportation, and flaring. Wildfire emissions have increased from 2010 to 2020, particularly above 60_ N, with 56% of black carbon emissions above 65_ N in 2020 attributed to open biomass burning – indicating how extreme the 2020 wildfire season was and how severe future Arctic wildfire seasons can potentially be. (5) What works in the boreal zones to prevent and fight wildfires may not work in the Arctic. Fire management will need to adapt to a changing climate, economic development, the Indigenous and local communities, and fragile northern ecosystems, including permafrost and peatlands. (6) Factors contributing to the uncertainty of predicting and quantifying future Arctic fire regimes include underestimation of Arctic fires by satellite systems, lack of agreement between Earth observations and official statistics, and still needed refinements of location, conditions, and previous fire return intervals on peat and permafrost landscapes. This review highlights that much research is needed in order to understand the local and regional impacts of the changing Arctic fire regime on emissions and the global climate, ecosystems, and pan-Arctic communities.

Arctic↗
DOE OSTI2021

Ab initio prediction of an order-disorder transition in Mg 2 Ge O 4 : Implication for the nature of super-Earth's mantles

Here we present an ab initio prediction of an order-disorder transition (ODT) from a I¯42d-type to Th 3 P 4 -type phase in the cation sublattices of Mg 2 GeO 4 , a post-post-perovskite phase. This uncommon type of prediction is achieved by carrying out a high-throughput sampling of atomic configurations in a 56-atom supercell followed by a Boltzmann ensemble statistics calculation. Mg 2 GeO 4 is a low-pressure analog of I¯42d-type Mg 2 SiO 4 , a predicted major planet-forming phase of super-Earths' mantles. Therefore, a similar ODT is anticipated in I¯42d-type Mg 2 SiO 4 as well, which should impact the internal structure and dynamics of these planets. Furthermore, the prediction of this Th 3 P 4 -type phase in Mg 2 GeO 4 further enhances the relationship between the crystal structures of Earth/planet-forming silicates and oxides at extreme pressures and those of rare-earth sesquisulfides at low pressures.

36 MATERIALS SCIENCE↗
NASA NTRS1996

Is the Non-Dipole Magnetic Field Random?

Statistical modelling of the Earth's magnetic field B has a long history. In particular, the spherical harmonic coefficients of scalar fields derived from B can be treated as Gaussian random variables. In this paper, we give examples of highly organized fields whose spherical harmonic coefficients pass tests for independent Gaussian random variables. The fact that coefficients at some depth may be usefully summarized as independent samples from a normal distribution need not imply that there really is some physical, random process at that depth. In fact, the field can be extremely structured and still be regarded for some purposes as random. In this paper, we examined the radial magnetic field B(sub r) produced by the core, but the results apply to any scalar field on the core-mantle boundary (CMB) which determines B outside the CMB.

Walker, Andrew D.↗
NASA NTRS2004

Methods and Piezoelectric Imbedded Sensors for Damage Detection in Composite Plates Under Ambient and Cryogenic Conditions

New methods for structural health monitoring are being assessed, especially in high-performance, extreme environment, safety-critical applications. One such application is for composite cryogenic fuel tanks. The work presented here attempts to characterize and investigate the feasibility of using imbedded piezoelectric sensors to detect cracks and delaminations under cryogenic and ambient conditions. A variety of damage detection methods and different Sensors are employed in the different composite plate samples to aid in determining an optimal algorithm, sensor placement strategy, and type of imbedded sensor to use. Variations of frequency, impedance measurements, and pulse echoing techniques of the sensors are employed and compared. Statistical and analytic techniques are then used to determine which method is most desirable for a specific type of damage. These results are furthermore compared with previous work using externally mounted sensors. Results and optimized methods from this work can then be incorporated into a larger composite structure to validate and assess its structural health. This could prove to be important in the development and qualification of any 2" generation reusable launch vehicle using composites as a structural element.

Engberg, Robert↗
NASA NTRS1980

Solar particle fluxes and the ancient sun

The implications of the statistical data on solar flare particle fluxes, for the present and the ancient sun, considering modern data from the past two solar cycles, C-14 data from the past 7000 years, and Al-26 and Mn-53 data in lunar samples for the last 10-million years are reviewed. All of these records suggest that there is a maximum proton fluence (greater than 10 MeV) from a solar flare on the order of 10 to the 10th p/sq cm, above which the size-frequency distribution steepens sharply. From this it is extremely unlikely that energetic particles from solar flares could have contributed to extinction catastrophes in the fossil record.

Lingenfelter, R. E.↗