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NASA NTRS2015

Random Predictor Models for Rigorous Uncertainty Quantification: Part 2

This and a companion paper propose techniques for constructing parametric mathematical models describing key features of the distribution of an output variable given input-output data. By contrast to standard models, which yield a single output value at each value of the input, Random Predictors Models (RPMs) yield a random variable at each value of the input. Optimization-based strategies for calculating RPMs having a polynomial dependency on the input and a linear dependency on the parameters are proposed. These formulations yield RPMs having various levels of fidelity in which the mean, the variance, and the range of the model's parameter, thus of the output, are prescribed. As such they encompass all RPMs conforming to these prescriptions. The RPMs are optimal in the sense that they yield the tightest predictions for which all (or, depending on the formulation, most) of the observations are less than a fixed number of standard deviations from the mean prediction. When the data satisfies mild stochastic assumptions, and the optimization problem(s) used to calculate the RPM is convex (or, when its solution coincides with the solution to an auxiliary convex problem), the model's reliability, which is the probability that a future observation would be within the predicted ranges, is bounded rigorously.

Crespo, Luis G.↗
NASA NTRS2015

Thermal Protection System Mass Estimating Relationships For Blunt-Body, Earth Entry Spacecraft

Mass estimating relationships (MERs) are developed to predict the amount of thermal protection system (TPS) necessary for safe Earth entry for blunt-body spacecraft using simple correlations that are non-ITAR and closely match estimates from NASA's highfidelity ablation modeling tool, the Fully Implicit Ablation and Thermal Analysis Program (FIAT). These MERs provide a first order estimate for rapid feasibility studies. There are 840 different trajectories considered in this study, and each TPS MER has a peak heating limit. MERs for the vehicle forebody include the ablators Phenolic Impregnated Carbon Ablator (PICA) and Carbon Phenolic atop Advanced Carbon-Carbon. For the aftbody, the materials are Silicone Impregnated Reusable Ceramic Ablator (SIRCA), Acusil II, SLA- 561V, and LI-900. The MERs are accurate to within 14% (at one standard deviation) of FIAT prediction, and the most any MER can under predict FIAT TPS thickness is 18.7%. This work focuses on the development of these MERs, the resulting equations, model limitations, and model accuracy.

Spacecraft↗
NASA NTRS2015

Random Predictor Models for Rigorous Uncertainty Quantification: Part 1

This and a companion paper propose techniques for constructing parametric mathematical models describing key features of the distribution of an output variable given input-output data. By contrast to standard models, which yield a single output value at each value of the input, Random Predictors Models (RPMs) yield a random variable at each value of the input. Optimization-based strategies for calculating RPMs having a polynomial dependency on the input and a linear dependency on the parameters are proposed. These formulations yield RPMs having various levels of fidelity in which the mean and the variance of the model's parameters, thus of the predicted output, are prescribed. As such they encompass all RPMs conforming to these prescriptions. The RPMs are optimal in the sense that they yield the tightest predictions for which all (or, depending on the formulation, most) of the observations are less than a fixed number of standard deviations from the mean prediction. When the data satisfies mild stochastic assumptions, and the optimization problem(s) used to calculate the RPM is convex (or, when its solution coincides with the solution to an auxiliary convex problem), the model's reliability, which is the probability that a future observation would be within the predicted ranges, can be bounded tightly and rigorously.

Crespo, Luis G.↗
NASA NTRS1986

Seven years of IUE observations of the BL Lacertae object PKS 2155-304

Over 50 IUE spectra of the brightest known BL Lac object at ultraviolet wavelengths, PKS 2155-304, were reanalyzed using Gaussian extraction techniques that maximize the signal-to-noise. The ultraviolet continuum of PKS 2155-304 is well fitted by a power law model Fv varies as V sup-alpha, with an average spectral index for the combined SWP-LWR-P fits of less than alpha greater than 0.89 + or - 0.11 (standard deviation). While the ultraviolet intensity of PKS 2155-304 varies by a factor of 2, the spectral index changes very little and is uncorrelated with intensity. Timescales for ultraviolet variability are as short as 10 days. In one case, a well-matched pair of IUE images was obtained nearly simultaneously with a very soft X-ray measurement; the combined spectra clearly show a steepening between the ultraviolet and soft X-ray bands. The relevance of these findings to jet models and accretion models is discussed.

Urry, C. M.↗
DOE OSTI2025

Pantex Plant Ogallala Aquifer and Perched Groundwater Contingency Plan

The Pantex Plant Ogallala Aquifer and Perched Groundwater Contingency Plan has been developed in accordance with the requirements identified in the: • Interagency Agreement for the Pantex Superfund Site, Article 8.5 Work to be Performed, • Compliance Plan Provision of Hazardous Waste Permit No. 50284, and • Record of Decision for Groundwater, Soil, and Associated Media, Pantex Plant. A Long‐Term Monitoring System Design has been designed to monitor conditions in the perched groundwater including changes in the perched aquifer as a result of implementing the response actions. Monitoring is required for verifying the effectiveness of perched groundwater response actions (i.e., conditions in the perched aquifer are being affected as intended) and for confirming that the perched aquifer and Ogallala Aquifer characterization as defined in the Resource Conservation and Recovery Act Facility Investigation Report and the Corrective Measure Studies/Feasibility Study remains accurate. If monitoring results obtained through the monitoring network identify an unexpected condition or deviation, contingent actions will be considered and implemented as necessary to ensure continued protection of the Ogallala Aquifer and human health and the environment. Potential deviations to expected technology performance may be encountered for each of the four primary response actions that compose the selected remedy for perched groundwater; Playa 1 Pump and Treat System, Southeast Area Pump and Treat System, Southeast Area In‐Situ Bioremediation System (comprised of the Southeast In‐Situ Bioremediation System Original System, Southeast Area In‐Situ Bioremediation System Extension System, Offsite In‐Situ Bioremediation System, Perchlorate/Chromium ISB, Northeast ISB and County Road 8 ISB), and Zone 11 In‐Situ Bioremediation System. Monitoring will also be conducted to determine if there are deviations to the expected characterization, e.g., contaminants not expected as a result of the RCRA Facility Investigation characterization. Deviations to expected conditions in the Ogallala Aquifer could also be encountered if the response actions in the perched groundwater are not performing as expected, i.e., preventing contaminants from migrating to the Ogallala Aquifer. Currently, Pantex has begun investigation of detections of high explosives above groundwater protection standards in wells on the Texas Tech University property and a plume that is moving to the northeast from that area. Due to those detections, this Plan recognizes the fact that future detections in the Ogallala will be focused on first‐ time detections of analytes. After a remedy is determined, this Plan will require modification to address-deviations and contingent actions. This Plan was developed to identify the contingent actions necessary to mitigate impacts resulting from deviations to site conditions or response action performance. The Plan defines the environmental problem being addressed by the response actions, clarifies the expected conditions and objectives of the response actions, and identifies the potential deviations to the response actions (due to site conditions or technology performance) that could be encountered. The deviations were evaluated to determine the likelihood of occurrence, potential impact, and time to respond to avoid impact. The Plan also identifies the monitoring outlined in the Long‐Term Monitoring System Design Report (Consolidated Nuclear Security, 2024) and Sampling Analysis Plan (PanTeXas Deterrence, 2024) that will be used to detect the deviations. Lastly, the Plan specifies the contingent actions that could be implemented in response to the deviations. Because each response focuses on a discrete portion of the perched aquifer and contaminant plume, each response action has a different set of expected conditions, and therefore differing impacts from deviations to the site and technology expectations. As a result, the contingent actions are identified for each response action and potential deviation including specific constituents, location, and conditions. If deviations are encountered that impact the ability of the response action to meet performance objectives, the contingent actions will be focused on ensuring the response action can meet the performance objective. Contingent actions may be implemented as interim actions (ISMs/removal actions) in accordance with the Record of Decision, Interagency Agreement, and Hazardous Waste Permit‐50284, if warranted by the specific circumstances. For deviations to site characterization expected conditions, the contingent action will focus on determination of the source of the deviation, determination of the appropriate response, and evaluation of additional work to be completed. However, if the deviation to characterization impacts the performance of the response action, the contingent action will again focus on ensuring performance objectives can be met. Early source term removals and cleanup actions have been implemented to protect the Ogallala Aquifer. Because of these actions and based on modeling results, the expected conditions in the Ogallala Aquifer are that constituents of concern will not be detected above the Groundwater Protection Standards (GWPSs) nor will they reach potential points of exposure above the GWPS. The primary deviation of concern for the Ogallala is if constituents are detected in the Ogallala Aquifer near or above GWPSs. If it occurs, this change in expected conditions would require further evaluation of site and contaminant characteristics to determine an appropriate course of action. The evaluation would include additional monitoring, source identification, implementation of interim protective measures (if necessary), and delineation of extent. These evaluations are necessary to determine an appropriate response action for the Ogallala. The primary goal of the Plan is to provide for the continued protection of the Ogallala Aquifer and the health of its consumers. In recognition, this Plan presents a flexible and rational approach for making future decisions associated with confirming the change in perched and Ogallala aquifer conditions and identifying a response (technical activities, changes to response actions, regulatory oversight, and public involvement).

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗
NASA NTRS1993

Investigation of the Vortical Flow Above an F/A-18 Using Doppler Global Velocimetry

The flow above an F/A-18 model, set to 25-degrees angle of attack, was measured using a Doppler global velocimeter, (DGV). The investigation indicated that the complex flow contained many similarities to the vortical flow above a simple delta wing set to a high-angle of attack, including flow standard deviations greater than 30-percent of free- stream. These standard deviation levels were also comparable to results found during a previous investigation of the vortical flow above a YF-17 using fringe-type laser velocimetry. The global measurement capability of the DGV provided the first evidence that the burst vortices above the model were structured. These structures were found to maintain their spatial coherence while the flow varied in an overall sense.

Meyers, James F.↗
DOE OSTI2026

Application and performance of the novel Elcomat 5000 autocollimator in slope-measuring profilometry of beamline optics

Autocollimators are used in profilometers for the precise form measurement of beam-shaping optics for synchrotron light sources and x-ray free-electron lasers. This application requires using an aperture stop, typically 2.5 mm in diameter, which limits the footprint of the autocollimator’s measuring beam on the optics to achieve a sufficiently high lateral resolution. Central to the development of profilometry has been the availability of commercial autocollimators, such as the Elcomat 3000 from Möller–Wedel Optical. Although autocollimators are generally not designed for use with small apertures, this device has proven capable and has become the de facto standard. Now that it has been replaced by the Elcomat 5000, we evaluate the performance of several autocollimators of this type at small apertures, including the characterization of instrument transfer functions with a chirped height profile. We demonstrate that the Elcomat 5000 is capable of repeatable angle measurements with a standard deviation of 0.014 arcsec at an aperture diameter of 1.6 mm, whereas the Elcomat 3000 achieves 0.03 arcsec at 2.5 mm, comparing models with modified reticle designs. Here, we also investigate the influence of optical aberrations of the autocollimator’s objective and their changes with the path length to the surface under test. We characterize the sensitivity of the angle measurement to changes in environmental parameters, in particular, barometric pressure. These efforts are aimed at approaching fundamental limits in the characterization of the shape of optical surfaces with autocollimator-based profilometers so that these are ready for characterizing the next generation of synchrotron and XFEL beamline optics.

angle metrology↗
NASA NTRS1972

Line-blanketed model stellar atmospheres applied to Sirius

The primary goal of this analysis is to determine whether the effects of atomic bound-bound transitions on stellar atmospheric structure can be represented well in models. The investigation is based on an approach which is called the method of artificial absorption edges. The method is described, developed, tested, and applied to the problem of fitting a model stellar atmosphere to Sirius. It is shown that the main features of the entire observed spectrum of Sirius can be reproduced to within the observational uncertainty by a blanketed flux-constant model with T sub eff = 9700 K and Log g = 4.26. The profile of H sub gamma is reproduced completely within the standard deviations of the measurements except near line center, where non-LTE effects are expected to be significant. The equivalent width of H sub gamma, the Paschen slope, the Balmer jump, and the absolute flux at 5550 A all agree with the observed values.

Fowler, J. W.↗
NASA NTRS1973

The MATHEMATICA economic analysis of the Space Shuttle System

Detailed economic analysis shows the Thrust Assisted Orbiter Space Shuttle System (TAOS) to be the most economic Space Shuttle configuration among the systems studied. The development of a TAOS Shuttle system is economically justified within a level of space activities between 300 and 360 Shuttle flights in the 1979-1990 period, or about 25 to 30 flights per year, well within the U.S. Space Program including NASA and DoD missions. If the NASA and DoD models are taken at face value (624 flights), the benefits of the Shuttle system are estimated to be $13.9 billion with a standard deviation of plus or minus $1.45 billion in 1970 dollars (at a 10% social rate of discount). If the expected program is modified to 514 flights (in the 1979-1990 period), the estimated benefits of the Shuttle system are $10.2 billion, with a standard deviation of $940 million (at a 10% social rate of discount).

Heiss, K. P.↗
NASA NTRS1981

Computational aspects of geometric correction data generation in the LANDSAT-D imagery processing

A method is presented for systematic and geodetic correction data calculation. It is based on presentation of image distortions as a sum of nominal distortions and linear effects caused by variation of the spacecraft position and attitude variables from their nominals. The method may be used for both MSS and TM image data and it is incorporated into the processing by means of mostly offline calculations. Modeling shows that the maximal of the method are of the order of 5m at the worst point in a frame; the standard deviations of the average errors less than .8m.

Levine, I.↗
NASA NTRS1991

Venusian highlands - Geoid to topography ratios and their implications

Geoid-to-topography ratios (GTRs) are estimated for 12 Venusian highland features to allow comparison with convection calculations and with terrestrial data of oceanic hot spots, swells, and plateaus. The geoid is estimated in the wavenumber domain from the isostatic formula, using the topography and the apparent depths isostatic compensation (ADC) for each region. In the space domain, the GTR is equal to the least squares slope of the linear fit of the geoid to the topograpy. The resulting GTR range is 7-31 m/km, which is much higher than terrestrial oceanic values (-1 to 5 m/km). The features fall into two distinct groups, one with a GTR range of 7-13 m/km, and one with a range of 19-25 m/km. A model for thermal thinning of a 100-km-thick lithosphere fits all values in the lower GTR group to within one standard deviation.

Smrekar, Suzanne E.↗
NASA NTRS1993

Deduction of emissions of source gases using an objective inversion algorithm and a chemical transport model

An inversion algorithm, constructed to deduce the emissions of a source gas required to produce a specified surface concentration, is applied to the observed surface concentrations of CFC 11, methylchloroform, and methane, using a two-dimensional chemical transport model. The information utilized for this deduction process is limited to the measured atmospheric concentration of the source gas, including the associated standard deviations of these measurements. In this way the amount of objective information available in these measurements is assessed. The algorithm is shown to be capable of producing a latitudinal emissions distribution as well as the error bounds on the deduced emission distribution. The 'ill posed' nature of this inverse problem is discussed as well as the implications this has on the spatial and temporal resolution at which emissions can be resolved. Finally, a methane emission distribution is deduced which has the expected seasonal variations and consistent with results from other, more subjective, deduction studies.

Brown, Margaret↗
NASA NTRS2008

Utilizing Mars Global Reference Atmospheric Model (Mars-GRAM 2005) to Evaluate Entry Probe Mission Sites

The Mars Global Reference Atmospheric Model (Mars-GRAM 2005) is an engineering-level atmospheric model widely used for diverse mission applications. An overview is presented of Mars-GRAM 2005 and its new features. The "auxiliary profile" option is one new feature of Mars-GRAM 2005. This option uses an input file of temperature and density versus altitude to replace the mean atmospheric values from Mars-GRAM's conventional (General Circulation Model) climatology. Any source of data or alternate model output can be used to generate an auxiliary profile. Auxiliary profiles for this study were produced from mesoscale model output (Southwest Research Institute's Mars Regional Atmospheric Modeling System (MRAMS) model and Oregon State University's Mars mesoscale model (MMM5) model) and a global Thermal Emission Spectrometer (TES) database. The global TES database has been specifically generated for purposes of making Mars-GRAM auxiliary profiles. This data base contains averages and standard deviations of temperature, density, and thermal wind components, averaged over 5-by-5 degree latitude-longitude bins and 15 degree Ls bins, for each of three Mars years of TES nadir data. The Mars Science Laboratory (MSL) sites are used as a sample of how Mars-GRAM' could be a valuable tool for planning of future Mars entry probe missions. Results are presented using auxiliary profiles produced from the mesoscale model output and TES observed data for candidate MSL landing sites. Input parameters rpscale (for density perturbations) and rwscale (for wind perturbations) can be used to "recalibrate" Mars-GRAM perturbation magnitudes to better replicate observed or mesoscale model variability.

Justh, Hilary L.↗
NASA NTRSDate not supplied

Effects of Natural Variability on the Use of Standard Deviation to Represent Measurement Uncertainties in Atmospheric Composition Studies

Measurement uncertainty is defined as a “non-negative parameter characterizing the dispersion of the quantity values being attributed to a measurand”. It is most common that the uncertainties of GAW hourly measurements, such as greenhouse gas measurements, are reported as standard deviations derived from individual sampling at a higher time resolution (e.g., 1 min). In contrast, the uncertainties of GAW measurements of reactive gases and aerosol properties are reported in percentiles covering the same probability. A quick look at hourly CO 2 data from Cape Grim, Australia yielded some interesting findings: the hourly standard deviation is, on average, more than a factor of 10 higher for the measurements under non-background conditions (over 50% observations), while the difference in average CO 2 amount fraction was less than 2 ppm. The dramatic contrast cannot be explained by the difference in measurement uncertainties, but can largely be attributed the natural variability, or episodic ambient CO 2 variation reflecting changes in meteorological conditions or emissions. These initial findings motivated a more in-depth analysis of the ground-based measurements of trace gases and aerosol properties. This analysis will be using continuous 1 min ground site observations to construct time averaged statistical indicators to evaluate whether the standard deviation is adequate to represent the dispersion, especially under marked influence by natural variability. The suitability of this representation can be determined by examining the difference between the standard deviation and percentiles encompassing the same probability. We will examine time intervals of 1 hour, 3 hours, and 24 hours, with the latter time intervals chosen to match those commonly used in model assessments. We will also investigate how natural variability can alter the probability distribution of the measurands and how adequate the quadrature propagation of uncertainties is under these conditions. The results will include several trace gases (e.g., CO 2 , CO, O 3 , and NO 2 ) with a range of measurement techniques (e.g., PANDORA, in situ), atmospheric lifetimes, and aerosol properties (e.g. scattering coefficient). The findings from this analysis should provide some useful feedback on the best practices for uncertainty reporting.

Measurement Uncertainty↗
NASA NTRS2019

Retrieval of Snow Freeboard of Antarctic Sea Ice Using Waveform Fitting of CryoSat-2 Returns

In this paper we develop a CryoSat-2 algorithm to retrieve the surface elevation of the air–snow interface over Antarctic sea ice. This algorithm utilizes a two-layer physical model that accounts for scattering from a snow layer atop sea ice as well as scattering from below the snow surface. The model produces waveforms that are fit to CryoSat-2 level 1B data through a bounded trust region least-squares fitting process. These fit waveforms are then used to track the air–snow interface and retrieve the surface elevation at each point along the CryoSat-2 ground track, from which the snow freeboard is computed. To validate this algorithm, we compare retrieved surface elevation measurements and snow surface radar return power levels with those from Operation IceBridge, which flew along a contemporaneous CryoSat-2 orbit in October 2011 and November 2012. Average elevation differences (standard deviations) along the flight lines (IceBridge Airborne Topographic Mapper, ATM – CryoSat-2) are found to be 0.016 cm (29.24 cm) in 2011 and 2.58 cm (26.65 cm) in 2012. The spatial distribution of monthly average pan-Antarctic snow freeboard found using this method is similar to what was observed from NASA's Ice, Cloud, and land Elevation Satellite (ICESat), where the difference (standard deviation) between October 2011–2017 CryoSat-2 mean snow freeboard and spring 2003–2007 mean freeboard from ICESat is 1.92 cm (9.23 cm). While our results suggest that this physical model and waveform fitting method can be used to retrieve snow freeboard from CryoSat-2, allowing for the potential to join laser and radar altimetry data records in the Antarctic, larger (∼30 cm) regional differences from ICESat and along-track differences from ATM do exist, suggesting the need for future improvements to the method. Snow–ice interface elevation retrieval is also explored as a potential to obtain snow depth measurements. However, it is found that this retrieval method often tracks a strong scattering layer within the snow layer instead of the actual snow–ice interface, leading to an overestimation of ice freeboard and an underestimation of snow depth in much of the Southern Ocean but with promising results in areas such as the East Antarctic sector.

Fons, Steven W.↗
NASA NTRS1979

Analysis of daily latitude variations

The daily latitude measurements of the International Polar Motion Service are analyzed. The annual oscillation in the data was modeled by separate oscillations in each observatory's latitude data. The separate oscillations varied in amplitude from 0.05 sec to 0.15 sec with standard deviations of about 0.007 sec. Within the resolution of the latitude residuals (150 cm), there is no indication of the sharp changes which might be associated with earthquake effects. Then, applying Schuster's test to a periodogram of the residuals indicates that there are probably several processes occurring at amplitudes between 0.007 sec and 0.03 sec whose solution awaits a more precise measurement technique.

Graber, M. A.↗
NASA NTRS1993

Characteristics of vertical and lateral tunnel turbulence measured in air in the Langley Transonic Dynamics Tunnel

Preliminary measurements of the vertical and lateral velocity components of tunnel turbulence were obtained in the Langley Transonic Dynamics Tunnel test section using a constant-temperature anemometer equipped with a hot-film X-probe. For these tests air was the test medium. Test conditions included tunnel velocities ranging from 100 to 500 fps at atmospheric pressure. Standard deviations of turbulence velocities were determined and power spectra were computed. Unconstrained optimization was employed to determine parameter values of a general spectral model of a form similar to that used to describe atmospheric turbulence. These parameters, and others (notably break frequency and integral scale length), were determined at each test condition and compared with those of Dryden and Von Karman atmospheric turbulence spectra. When the data were discovered to be aliased, the spectral model was modified to account for and 'eliminate' the aliasing.

Sleeper, Robert K.↗
NASA NTRS2008

Evaluating Mars Science Laboratory Landing Sites with the Mars Global Reference Atmospheric Model (Mars-GRAM 2005)

The Mars Global Reference Atmospheric Model (Mars-GRAM) is an engineering-level atmospheric model widely used for diverse mission applications. Mars-GRAM s perturbation modeling capability is commonly used, in a Monte-Carlo mode, to perform high fidelity engineering end-to-end simulations for entry, descent, and landing (EDL) [1]. From the surface to 80 km altitude, Mars-GRAM is based on the NASA Ames Mars General Circulation Model (MGCM). Mars-GRAM and MGCM use surface topography from Mars Global Surveyor Mars Orbiter Laser Altimeter (MOLA), with altitudes referenced to the MOLA areoid, or constant potential surface. Traditional Mars-GRAM options for representing the mean atmosphere along entry corridors include: (1) Thermal Emission Spectrometer (TES) mapping years 1 and 2, with Mars-GRAM data coming from NASA Ames Mars General Circulation Model (MGCM) results driven by observed TES dust optical depth or (2) TES mapping year 0, with user-controlled dust optical depth and Mars-GRAM data interpolated from MGCM model results driven by selected values of globally-uniform dust optical depth. Mars-GRAM 2005 has been validated [2] against Radio Science data, and both nadir and limb data from TES [3]. There are several new features included in Mars-GRAM 2005. The first is the option to use input data sets from MGCM model runs that were designed to closely simulate conditions observed during the first two years of TES observations at Mars. The TES Year 1 option includes values from April 1999 through January 2001. The TES Year 2 option includes values from February 2001 through December 2002. The second new feature is the option to read and use any auxiliary profile of temperature and density versus altitude. In exercising the auxiliary profile Mars-GRAM option, values from the auxiliary profile replace data from the original MGCM databases. Some examples of auxiliary profiles include data from TES nadir or limb observations and Mars mesoscale model output at a particular location and time. The final new feature is the addition of two Mars-GRAM parameters that allow standard deviations of Mars-GRAM perturbations to be adjusted. The parameter rpscale can be used to scale density perturbations up or down while rwscale can be used to scale wind perturbations.

Justh, H. L.↗