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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.

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NASA NTRSDate not supplied

AeroFusion: Data Fusion and Uncertainty Quantification for Entry Vehicles

AeroFusion is a NASA Langley initiative to incorporate advances in data science into the aerodynamic modeling process to improve efficiency. The effort can largely be categorized in three components: reduced-order modeling techniques, surrogate modeling techniques, and uncertainty quantification. By combining various methods from these categories, AeroFusion aims to reduce the development cost of aerodynamic models, both in terms of time and money.

Steven Snyder↗
NASA NTRSDate not supplied

AeroFusion: Data Fusion and Uncertainty Quantification for Entry Vehicles

AeroFusion is a NASA Langley initiative to incorporate advances in data science into the aerodynamic modeling process to improve efficiency. The effort can largely be categorized in three components: reduced-order modeling techniques, surrogate modeling techniques, and uncertainty quantification. By combining various methods from these categories, AeroFusion aims to reduce the development cost of aerodynamic models, both in terms of time and money.

Steven Snyder↗
NASA NTRS2010

Aerosol Mapping From Space: Strengths, Limitations, and Applications

The aerosol data products from the NASA Earth Observing System's MISR and MODIS instruments provide significant advances in regional and global aerosol optical depth (AOD) mapping, aerosol type measurement, and source plume characterization from space. These products have been and are being used for many applications, ranging from regional air quality assessment, to aerosol air mass type identification and evolution, to wildfire smoke injection height and aerosol transport model validation. However, retrieval uncertainties and coverage gaps still limit the quantitative constraints these satellite data place on some important questions, such as global-scale long-term trends and direct aerosol radiative forcing. Major advances in these areas seem to require a different paradigm, involving the integration of satellite with suborbital data and with models. This presentation will briefly summarize where we stand, and what incremental improvements we can expect, with the current MISR and MODIS aerosol products, and will then elaborate on some initial steps aimed at the necessary integration of satellite data with data from other sources and with chemical transport models.

Kahn, Ralph↗
NASA NTRSDate not supplied

Testing of Mars Retropropulsion Concepts in the Langley Unitary Plan Wind Tunnel

Future Mars human lander missions will require using retrorockets beginning at supersonic conditions, something which has never been done before at Mars. Significant aerosciences challenges exist due to interactions between the retrorocket exhaust plumes, the freestream flow, and the vehicle that alter the aerodynamic behavior. Historical retropropulsion ground and flight data do not provide a basis for calibrating the computational uncertainties for aerodynamic interference forces and moments on proposed Mars descent vehicles, either because of insufficient data or dissimilar vehicles geometries and/or conditions. A new retropropulsion wind tunnel test was conducted in the NASA Langley Unitary Plan Wind Tunnel in order to address some of the deficiencies of previous tests and to provide a basis for computational model comparisons on relevant geometries. The test included improvements in model design and measured data. Two sub-scale model geometries derived from full-scale vehicle concepts were tested: a blunt low lift-to-drag vehicle and a more slender geometry. The first model includes variations in nozzle parameters that were estimated to have first-order effects on the measurements: location, pointing direction, size, and exit-to-throat area ratio. Both models were instrumented with discrete steady and unsteady pressure sensors on the aerodynamic and interior flow path surfaces. The heats shields of both models also were covered with pressure sensitive paint that effectively measures a steady pressure distribution in an otherwise unsteady flow field. This pressure distribution was integrated over the surface geometry in order to estimate the steady aerodynamic force and moment coefficient contribution from the painted surfaces; this approach was used as a replacement for using a flow-through balance. This paper will cover the test objectives, model design, test matrix, and available test results for each model configuration at different freestream Mach numbers, model attitude, and non-dimensional thrust magnitude. A subsequent publication will cover uncertainty quantification of the test data and comparisons to computational fluid dynamics model results.

Powered Descent↗
NASA NTRS2012

Efficient Global Aerodynamic Modeling from Flight Data

A method for identifying global aerodynamic models from flight data in an efficient manner is explained and demonstrated. A novel experiment design technique was used to obtain dynamic flight data over a range of flight conditions with a single flight maneuver. Multivariate polynomials and polynomial splines were used with orthogonalization techniques and statistical modeling metrics to synthesize global nonlinear aerodynamic models directly and completely from flight data alone. Simulation data and flight data from a subscale twin-engine jet transport aircraft were used to demonstrate the techniques. Results showed that global multivariate nonlinear aerodynamic dependencies could be accurately identified using flight data from a single maneuver. Flight-derived global aerodynamic model structures, model parameter estimates, and associated uncertainties were provided for all six nondimensional force and moment coefficients for the test aircraft. These models were combined with a propulsion model identified from engine ground test data to produce a high-fidelity nonlinear flight simulation very efficiently. Prediction testing using a multi-axis maneuver showed that the identified global model accurately predicted aircraft responses.

Morelli, Eugene A.↗
NASA NTRS2011

User Selection Criteria of Airspace Designs in Flexible Airspace Management

A method for identifying global aerodynamic models from flight data in an efficient manner is explained and demonstrated. A novel experiment design technique was used to obtain dynamic flight data over a range of flight conditions with a single flight maneuver. Multivariate polynomials and polynomial splines were used with orthogonalization techniques and statistical modeling metrics to synthesize global nonlinear aerodynamic models directly and completely from flight data alone. Simulation data and flight data from a subscale twin-engine jet transport aircraft were used to demonstrate the techniques. Results showed that global multivariate nonlinear aerodynamic dependencies could be accurately identified using flight data from a single maneuver. Flight-derived global aerodynamic model structures, model parameter estimates, and associated uncertainties were provided for all six nondimensional force and moment coefficients for the test aircraft. These models were combined with a propulsion model identified from engine ground test data to produce a high-fidelity nonlinear flight simulation very efficiently. Prediction testing using a multi-axis maneuver showed that the identified global model accurately predicted aircraft responses.

Lee, Hwasoo E.↗
NASA NTRS2018

Trajectory Reconstruction of Orion Ground Test Article Water Impact Tests

The Orion Crew Module is a component of NASA’s Multi-Purpose Crew Vehicle that will be used for future missions to low Earth orbit and beyond. Ten water impact tests of the Orion Ground Test Article (GTA) were conducted at the Hydro Impact Basin at NASA Langley Research Center in 2016 and were designed to provide data for the validation of the LS-DYNA model used to determine the Crew Module structural loads during ocean splashdown, and the determination of an acceptable Model Uncertainty Factor to apply to simulation results used to drive the design. Post-test data obtained from the onboard sensors were used to reconstruct the GTA trajectories both before and after water impact. Results from one vertical test and two swing tests are presented and compared to videos taken for each test.

Lugo, Rafael A.↗
NASA NTRS2016

Global Carbon Budget 2016

Accurate assessment of anthropogenic carbon dioxide (CO2) emissions and their redistribution among the atmosphere, ocean, and terrestrial biosphere the global carbon budget is important to better understand the global carbon cycle, support the development of climate policies, and project future climate change. Here we describe data sets and methodology to quantify all major components of the global carbon budget, including their uncertainties, based on the combination of a range of data, algorithms, statistics, and model estimates and their interpretation by a broad scientific community. We discuss changes compared to previous estimates and consistency within and among components, alongside methodology and data limitations. CO2 emissions from fossil fuels and industry (EFF) are based on energy statistics and cement production data, respectively, while emissions from land-use change (ELUC), mainly deforestation, are based on combined evidence from land-cover change data, fire activity associated with deforestation, and models. The global atmospheric CO2 concentration is measured directly and its rate of growth (GATM) is computed from the annual changes in concentration. The mean ocean CO2 sink (SOCEAN) is based on observations from the 1990s, while the annual anomalies and trends are estimated with ocean models. The variability in SOCEAN is evaluated with data products based on surveys of ocean CO2 measurements. The global residual terrestrial CO2 sink (SLAND) is estimated by the difference of the other terms of the global carbon budget and compared to results of independent dynamic global vegetation models. We compare the mean land and ocean fluxes and their variability to estimates from three atmospheric inverse methods for three broad latitude bands. All uncertainties are reported as +/- 1(sigma), reflecting the current capacity to characterize the annual estimates of each component of the global carbon budget. For the last decade available (2006-2015), EFF was 9.3+/-0.5 GtC/yr, ELUC 1.0+/-0.5 GtC/yr,GATM 4.5+/-0.1 GtC/yr, SOCEAN 2.6+/-0.5 GtC/yr, and SLAND 3.1+/-0.9 GtC/yr. For year 2015 alone, the growth in EFF was approximately zero and emissions remained at 9.9+/-0.5 GtC/yr, showing a slowdown in growth of these emissions compared to the average growth of 1.8/yr that took place during 2006-2015.Also, for 2015, ELUC was 1.3+/-0.5 GtC/yr, GATM was 6.3+/-0.2 GtC/yr, SOCEAN was 3.0+/-0.5 GtC/yr, and SLAND was 1.9+/-0.9 GtC/yr. GATM was higher in 2015 compared to the past decade (2006-2015), reflecting a smaller SLAND for that year. The global atmospheric CO2 concentration reached 399.4+/-0.1 ppm averaged over 2015. For 2016, preliminary data indicate the continuation of low growth in EFF with +0.2% (range of -1.0 to +1.8% ) based on national emissions projections for China and USA, and projections of gross domestic product corrected for recent changes in the carbon intensity of the economy for the rest of the world. In spite of the low growth of EFF in 2016, the growth rate in atmospheric CO2 concentration is expected to be relatively high because of the persistence of the smaller residual terrestrial sink (SLAND) in response to El Nino conditions of 2015-2016. From this projection of EFF and assumed constant ELUC for 2016, cumulative emissions of CO2 will reach 565+/-55 GtC (2075+/-205 GtCO2) for 1870-2016, about 75% from EFF and 25% from ELUC. This living data update documents changes in the methods and data sets used in this new carbon budget compared with previous publications of this data set.

Quéré, Corinne Le↗
NASA NTRS2010

A Comprehensive Validation Methodology for Sparse Experimental Data

A comprehensive program of verification and validation has been undertaken to assess the applicability of models to space radiation shielding applications and to track progress as models are developed over time. The models are placed under configuration control, and automated validation tests are used so that comparisons can readily be made as models are improved. Though direct comparisons between theoretical results and experimental data are desired for validation purposes, such comparisons are not always possible due to lack of data. In this work, two uncertainty metrics are introduced that are suitable for validating theoretical models against sparse experimental databases. The nuclear physics models, NUCFRG2 and QMSFRG, are compared to an experimental database consisting of over 3600 experimental cross sections to demonstrate the applicability of the metrics. A cumulative uncertainty metric is applied to the question of overall model accuracy, while a metric based on the median uncertainty is used to analyze the models from the perspective of model development by analyzing subsets of the model parameter space.

Norman, Ryan B.↗
NASA NTRSDate not supplied

Entry, Descent, and Landing Simulation for DAVINCI

The Deep Atmosphere Venus Investigation of Noble gases, Chemistry, and Imaging(DAVINCI) mission is currently scheduled to launch in June 2029 to explore Venus via two flybys and a probe descent scheduled for June 2031. The goals of this mission is to study the origin, evolution, and current state of Venus, especially the deep Venusian atmosphere using an atmospheric probe named Zephyr. The Zephyr will take key measurements in the deep atmosphere of Venus and be the first probe to take high-resolution aerial photographs of a mountainous tesserae surface as it descends over the Alpha Regio highlands region, which has the oldest surfaces of Venus. The Zephyr’s descent trajectory, which determines the flight over the Alpha Regio, is crucial to meet the science objectives of the DAVINCI mission. To ensure the success of the DAVINCI mission, the Entry, Descent, and Landing (EDL) modeling has undergone several developments to track its trajectory, its uncertainties, and calculate metrics on the science data that can be transmitted. This paper will cover these developments and the current status of the EDL modeling.

davinci↗
NASA NTRS2012

View Angle Effects on MODIS Snow Mapping in Forests

Binary snow maps and fractional snow cover data are provided routinely from MODIS (Moderate Resolution Imaging Spectroradiometer). This paper investigates how the wide observation angles of MODIS influence the current snow mapping algorithm in forested areas. Theoretical modeling results indicate that large view zenith angles (VZA) can lead to underestimation of fractional snow cover (FSC) by reducing the amount of the ground surface that is viewable through forest canopies, and by increasing uncertainties during the gridding of MODIS data. At the end of the MODIS scan line, the total modeled error can be as much as 50% for FSC. Empirical analysis of MODIS/Terra snow products in four forest sites shows high fluctuation in FSC estimates on consecutive days. In addition, the normalized difference snow index (NDSI) values, which are the primary input to the MODIS snow mapping algorithms, decrease as VZA increases at the site level. At the pixel level, NDSI values have higher variances, and are correlated with the normalized difference vegetation index (NDVI) in snow covered forests. These findings are consistent with our modeled results, and imply that consideration of view angle effects could improve MODIS snow monitoring in forested areas.

MODIS↗
NASA NTRS2007

Uncertainty Analysis of Historical Hurricane Data

An analysis of variance (ANOVA) study was conducted for historical hurricane data dating back to 1851 that was obtained from the U. S. Department of Commerce National Oceanic and Atmospheric Administration (NOAA). The data set was chosen because it is a large, publicly available collection of information, exhibiting great variability which has made the forecasting of future states, from current and previous states, difficult. The availability of substantial, high-fidelity validation data, however, made for an excellent uncertainty assessment study. Several factors (independent variables) were identified from the data set, which could potentially influence the track and intensity of the storms. The values of these factors, along with the values of responses of interest (dependent variables) were extracted from the data base, and provided to a commercial software package for processing via the ANOVA technique. The primary goal of the study was to document the ANOVA modeling uncertainty and predictive errors in making predictions about hurricane location and intensity 24 to 120 hours beyond known conditions, as reported by the data set. A secondary goal was to expose the ANOVA technique to a broader community within NASA. The independent factors considered to have an influence on the hurricane track included the current and starting longitudes and latitudes (measured in degrees), and current and starting maximum sustained wind speeds (measured in knots), and the storm starting date, its current duration from its first appearance, and the current year fraction of each reading, all measured in years. The year fraction and starting date were included in order to attempt to account for long duration cyclic behaviors, such as seasonal weather patterns, and years in which the sea or atmosphere were unusually warm or cold. The effect of short duration weather patterns and ocean conditions could not be examined with the current data set. The responses analyzed were the storm latitude, longitude and intensity, as recorded in the data set, 24 or 120 hours beyond the current state. Several ANOVA modeling schemes were examined. Two forms of validation were used: 1) comparison with official hurricane prediction performance metrics and 2) cases studies conducted on hurricanes from the 2005 season, which were not included within the model construction and ANOVA assessment. In general, the ANOVA technique did not perform as well as the established official prediction performance metrics published by NOAA; still, the technique did remarkably well in this demonstration with a difficult data set and could probably be made to perform better with more knowledge of hurricane development and dynamics applied to the problem. The technique provides a repeatable prediction process that eliminates the need for judgment in the forecast.

Green, Lawrence L.↗
NASA NTRSDate not supplied

Characterizing Spatiotemporal Uncertainty in Interpolated Meteorological Data

Interpolated meteorological data invariably contain errors. These errors have structure in time and space, particularly autocorrelation, which can cause the effects of errors to compound when model outputs are aggregated temporally or spatially. One way to account for this uncertainty is with a probabilistic model from which samples can be drawn that are coherent with respect to underlying spatial and temporal covariance structure. This work describes a probabilistic method for spatial interpolation of point-wise meteorological time series. Observational data from weather stations are generally sparse in space and dense in time (but sometimes missing). The method works by projecting time series onto orthogonal basis vectors and spatially interpolating each resulting component independently. Under suitable assumptions, and data transformations to better satisfy those assumptions, Gaussian process regression provides a complete description of the joint predictive distribution over a Gaussian random field. Spatiotemporally coherent realizations are generated as the sum of conditional (spatial) simulations of each orthogonal (temporal) component. Data-derived and generic orthogonal bases are considered. In addition to spatial interpolation, imputation of missing observational data is examined. The method is applied using near-surface air temperature over the Western United States and validated by comparing theoretical versus actual coverage of predictive distributions and analyzing the degree to which spatial and temporal covariance structure is reproduced. Computational considerations, relating to conditional simulation of random fields, are also addressed.

Conor T Doherty↗
NASA NTRSDate not supplied

Data Fusion With Uncertainty Quantification for Sub-City-Scale Air Quality Assessment and Forecasting

Many information sources can support air quality assessment and forecasting, including atmospheric chemistry model outputs, satellite retrievals of column chemical and aerosol constituents, and surface-based air quality monitoring data from both regulatory and low-cost instruments. Systematic integration of these data sources provides a major opportunity to improve understanding and management of air quality, but also presents technical barriers, especially in resource- and data-constrained settings in the Global South. This presentation describes a data fusion system, currently under development using the Google Earth Engine platform, which aims to integrate the information sources listed above to support comprehensive sub-city-scale assessment and management of air quality. Furthermore, the data fusion framework includes provisions for the quantification of uncertainties in the resulting fused estimates based on the variability of and among the input data sources. These capabilities will allow air quality managers to better understand their local air quality situation, including relative confidence in the fused estimates for different constituents, locations, and times, leading to better informed air quality management decisions. This presentation covers the underlying methodology of the data fusion and uncertainty quantification approaches, provides an update on the status of its implementation, and presents early qualitative and quantitative results.

Carl Malings↗
NASA NTRSDate not supplied

Towards an Optimal Estimation Retrieval of Cirrus Cloud Optical and Microphysical Properties Using Hyperspectral Shortwave Instruments and A Fast Radiative Transfer Algorithm

Cirrus cloud retrieval products (here, cloud optical depth, effective particle size, and cloud top height) are important inputs into numerical weather and climate models. Uncertainties in such retrieval products, as a matter of course, propagate downstream, impacting model calculations. Improvements in high-quality global cirrus cloud optical and microphysical data products from satellite observations are needed to understand and reduce retrieval uncertainties. Hyperspectral shortwave instruments produce high-resolution and information-dense spectra, thus offering the opportunity to reduce uncertainties in retrieval products. We are in the process of developing a retrieval that uses the very fast Principal Component Radiative Transfer Model in the solar spectral region (PCRTM-Solar) in the forward model calculations. This retrieval will use measured reflectances from the NASA Earth Surface Mineral Dust Source Investigation (EMIT) and the forthcoming Climate Absolute Radiance and Refractivity Observatory Pathfinder (CLARREO-Pathfinder) instruments. In this manuscript we present progress towards a reference retrieval employing a widely used, verified, accurate, yet computationally slower radiative transfer modeling technique. The reference retrieval, while too slow for using the complete hyperspectral measurement, will allow us to study the behavior of retrieval products and help us verify results from our in-development fast retrieval. Both retrievals will use the optimal estimation retrieval framework. In this manuscript we present results from an uncertainty analysis considering three uncertainty sources for a cirrus cloud retrieval in the form of error covariance matrices: reflectance uncertainty due to water vapor, the reflectance uncertainty due to ice crystal scattering assumptions, and the instrument measurement uncertainty. Results show that the uncertainty due to habit selection is the largest, while that due to water vapor is at most 0.6% relative to channel reflectance. As a first step, the retrieval is being designed for single layer ice clouds over open ocean water.

Cirrus cloud↗
NASA NTRS2024

Evaluation of Vertical Patterns in Chlorophyll-A Derived From A Data Assimilating Model of Satellite-Based Ocean Color

Satellite-based sensors of ocean color have become the primary tool to infer changes in surface chlorophyll, while BGC-Argo floats are now filling the information gap at depth. Here we use BGC-Argo data to assess depth-resolved information on chlorophyll-a derived from an ocean biogeochemical model constrained by the assimilation of surface ocean color remote sensing. The data-assimilating model replicates well the general seasonality and meridional gradients in surface and depth-resolved chlorophyll-a inferred from the float array in the Southern Ocean. On average, the model tends to overestimate float-based chlorophyll, particularly at times and locations of high productivity such as the beginning of the spring bloom, subtropical deep chlorophyll maxima, and non-iron limited regions of the Southern Ocean. The highest model RMSE in the upper 50 m with respect to the float array is of 0.6 mg Chl m −3 , which should allow the detection of seasonal changes in float-based biomass (varying between 0.01 and >1 mg Chl m −3 ) but might hinder the identification of subtle changes in chlorophyll at narrow local scales. Both model and float profiling data show good agreement with in situ data from station ALOHA, with model estimates showing a slight accuracy edge in inferring depth-resolved observations. Uncertainties in float bio-optical estimates impede their use as a reliable benchmark for validation, but the general qualitative agreement between model and float data provides confidence in the ability of model to replicate biogeochemical features below the surface, where data is not directly constrained by the assimilation of satellite ocean color.

Lionel A Quintero↗
NASA NTRS1999

Comparison of CFD Predictions of the TCA Baseline

The computational fluid dynamics (CFD) comparisons being presented are compared to each other and to wind tunnel (WT) data on the baseline TCA. Some of the CFD computations were done prior to the tests and others later. Only force data (CL vs CD) from CFD will be presented as part of this report. The WT data presented comes from the testing of the baseline TCA in the Langley Unitary Plan Wind Tunnel (UPWT), Test Section #2. There are 2 sets of wind tunnel data being presented: one from test 1671 of model 2a (flapped wing) and the other from test 1679 of model 2b (solid wing). Most of the plots show only one run from each of the WT tests per configuration. But many repeat runs were taken during the tests. The WT repeat runs showed an uncertainty in the drag of +/- 0.5 count. There were times when the uncertainty in drag was better, +/- 0.25 count. Test 1671 data was of forces and pressures measured from model 2a. The wing had cutouts for installing various leading and trailing edge flaps at lower Mach numbers. The internal duct of the nacelles are not designed and fabricated as defined in the outer mold lines (OML) iges file. The internal duct was fabricated such that a linear transition occurs from the inlet to exhaust. Whereas, the iges definition has a constant area internal duct that quickly transitions from the inlet to exhaust cross sectional shape. The nacelle internal duct was fabricated, the way described, to save time and money. The variation in the cross sectional area is less than 1% from the iges definition. The nacelles were also installed with and without fairings. Fairings are defined as the build up of the nacelles on the upper wing surface so that the nacelles poke through the upper surface as defined in the OML iges file. Test 1679 data was of forces measured from model 2a and 2b. The wing for model 2b was a solid wing. The nacelles were built the same way as for model 2a, except for the nacelle base pressure installation. The nacelles were only tested with the fairings for model 2a and 2b during test 1679.

Cappuccio, Gelsomina↗
NASA NTRS2022

Quantifying Errors in 3D CME Parameters Derived from Synthetic Data Using White-Light Reconstruction Techniques

Current efforts in space weather forecasting of CMEs have been focused on predicting their arrival time and magnetic structure. To make these predictions, methods have been developed to derive the true CME speed, size, position, and mass, among others. Difficulties in determining the input parameters for CME forecasting models arise from the lack of direct measurements of the coronal magnetic fields and uncertainties in estimating the CME 3D geometric and kinematic parameters after eruption. White-light coronagraph images are usually employed by a variety of CME reconstruction techniques that assume more or less complex geometries. This is the first study from our International Space Science Institute (ISSI) team “Understanding Our Capabilities in Observing and Modeling Coronal Mass Ejections”, in which we explore how subjectivity affects the 3D CME parameters that are obtained from the Graduated Cylindrical Shell (GCS) reconstruction technique, which is widely used in CME research. To be able to quantify such uncertainties, the “true” values that are being fitted should be known, which are impossible to derive from observational data. We have designed two different synthetic scenarios where the “true” geometric parameters are known in order to quantify such uncertainties for the first time. We explore this by using two sets of synthetic data: 1) Using the ray-tracing option from the GCS model software itself, and 2) Using 3D magnetohydrodynamic (MHD) simulation data from the Magnetohydrodynamic Algorithm outside a Sphere code. Our experiment includes different viewing configurations using single and multiple viewpoints. CME reconstructions using a single viewpoint had the largest errors and error ranges overall for both synthetic GCS and simulated MHD white-light data. As the number of viewpoints increased from one to two, the errors decreased by approximately 4° in latitude, 22° in longitude, 14° in tilt, and 10° in half-angle. Our results quantitatively show the critical need for at least two viewpoints to be able to reduce the uncertainty in deriving CME parameters. We did not find a significant decrease in errors when going from two to three viewpoints for our specific hypothetical three spacecraft scenario using synthetic GCS white-light data. As we expected, considering all configurations and numbers of viewpoints, the mean absolute errors in the measured CME parameters are generally significantly higher in the case of the simulated MHD white-light data compared to those from the synthetic white-light images generated by the GCS model. We found the following CME parameter error bars as a starting point for quantifying the minimum error in CME parameters from white-light reconstructions: Δθ (latitude)=6° +2° -3° , Δϕ (longitude)=11° +18° -6° , Δγ (tilt)=25° +8° -7° , Δx (half-angle)=10° +12° -6° , Δh (height)=0.6 +1.2 -0.4 R ⨀ , and Δκ (ratio)=0.1 +0.03 -0.02 .

Coronal mass ejections↗