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NASA NTRS2019

The NASA Orbital Debris Engineering Model 3.1: Development, Verification, and Validation

The NASA Orbital Debris Program Office has developed the Orbital Debris Engineering Model (ORDEM) primarily as a tool for spacecraft designers and other users to understand the long-term risk of collisions with orbital debris. The newest version, ORDEM 3.1, incorporates the latest and highest fidelity datasets available to build and validate representative orbital debris populations encompassing low Earth orbit (LEO) to geosynchronous orbit (GEO) altitudes for the years 2016-2050. ORDEM 3.1 models fluxes for object sizes > 10 μm within or transiting LEO and > 10 cm in GEO. The deterministic portion of the populations in ORDEM 3.1 is based on the U.S. Space Surveillance Network (SSN) catalog, which provides coverage down to approximately 10 cm in LEO and 1 m in GEO. Observational datasets from radar, in situ, and optical sources provide a foundation from which the model populations are statistically extrapolated to smaller sizes and orbit regions that are not well-covered by the SSN catalog, yet may pose the greatest threat to operational spacecraft. Objects in LEO ranging from approximately 5 mm to 10 cm are modeled using observational data from ground-based radar, namely the Haystack Ultrawideband Satellite Imaging Radar (HUSIR – formerly known as Haystack). The LEO population smaller than approximately 3 mm in size is characterized based on a reanalysis of in situ data from impacts to the windows and radiators of the U.S. Space Transportation System orbiter vehicle, i.e., the Space Shuttle. Data from impacts on the Hubble Space Telescope are also used to validate the sub-millimeter model populations in LEO. Debris in GEO with sizes ranging from 10 cm to 1 m is modeled using optical measurement data from the Michigan Orbital DEbris Survey Telescope (MODEST). Specific, major debris-producing events, including the Fengyun-1C, Iridium 33, and Cosmos 2251 debris clouds, and unique populations, such as sodium-potassium droplets, have been re-examined and are modeled and added to the ORDEM environment separately. The debris environment greater than 1 mm is forecast using NASA’s LEO-to- GEO ENvironment Debris model (LEGEND). Future explosions of intact objects and collisions involving objects greater than 10 cm are assessed statistically, and the NASA Standard Satellite Breakup Model is used to generate fragments from these events. Fragments smaller than 10 cm are further differentiated based on material density categories, i.e., high-, medium-, and low-density, to better characterize the potential debris risk posed to spacecraft. The future projection of the sub-millimeter environment is computed using a special small-particle degradation model where small particles are created from intact spacecraft and rocket bodies. This work discusses the development, features, and capabilities of the ORDEM 3.1 model; the ne new data analyses used to build the model populations; and sample verification and validation results.

Matney, M.↗

NASA NTRS1999

Optimal Scales for Comparing Satellite and Rain-Gauge Rainfall Estimates for Verification Purposes

In spite of all their problems, rain gauges measure rainfall in such a direct way when compared with other methods of estimating rainfall that comparing their totals to satellite estimates remains an essential tool in the validation of satellite products. Some disagreement between averages of satellite data and rain-gauge data is expected because of the very different sampling patterns of the two systems--the satellite provides only occasional snapshots of large areas, whereas rain gauges provide continuous measurements over very small areas. The comparison of the two requires that some quantitative measure be supplied for the amount of disagreement that can be tolerated due to the differences in sampling. As part of an effort to determine the sampling error of satellite averages, a space-time model for rainfall statistics was developed and its parameters fit to radar data from a field experiment conducted near the Inter-Tropical Convergence Zone (ITCZ) in the eastern Atlantic (GATE). Although the model was intended to represent the statistics of relatively large scale fluctuations of rain, it is surprisingly consistent with the very different scales on which rain gauges observe. It can therefore be used to study some of the issues involved with comparing rain-gauge averages to satellite averages. Its implications for the best time and space scales for comparing the two will be discussed.

Bell, Thomas L.↗

NASA NTRS2003

Jet Noise Physics and Modeling Using First-principles Simulations

An extensive analysis of our jet DNS database has provided for the first time the complex correlations that are the core of many statistical jet noise models, including MGBK. We have also for the first time explicitly computed the noise from different components of a commonly used noise source as proposed in many modeling approaches. Key findings are: (1) While two-point (space and time) velocity statistics are well-fitted by decaying exponentials, even for our low-Reynolds-number jet, spatially integrated fourth-order space/retarded-time correlations, which constitute the noise "source" in MGBK, are instead well-fitted by Gaussians. The width of these Gaussians depends (by a factor of 2) on which components are considered. This is counter to current modeling practice, (2) A standard decomposition of the Lighthill source is shown by direct evaluation to be somewhat artificial since the noise from these nominally separate components is in fact highly correlated. We anticipate that the same will be the case for the Lilley source, and (3) The far-field sound is computed in a way that explicitly includes all quadrupole cancellations, yet evaluating the Lighthill integral for only a small part of the jet yields a far-field noise far louder than that from the whole jet due to missing nonquadrupole cancellations. Details of this study are discussed in a draft of a paper included as appendix A.

Freund, Jonathan B.↗

NASA NTRS2020

Evaluation of GEOS-Simulated L-Band Microwave Brightness Temperature using Aquarius Observations over Non-Frozen Land across North America

L-band brightness temperature (T(sub b)) is one of the key remotely-sensed variables that provides information regarding surface soil moisture conditions. In order to harness the information in T(sub b) observations, a radiative transfer model (RTM) is investigated for eventual inclusion into a data assimilation framework. In this study, T(sub b) estimates from the RTM implemented in the NASA Goddard Earth Observing System (GEOS) were evaluated against the nearly four-year record of daily T(sub b) observations collected by L-band radiometers onboard the Aquarius satellite. Statistics between the modeled and observed T(sub b) were computed over North America as a function of soil hydraulic properties and vegetation types. Overall, statistics showed good agreement between the modeled and observed T(sub b) with a relatively low, domain-average bias (0.79 K (ascending) and -2.79 K (descending)), root mean squared error (11.0 K (ascending) and 11.7 K (descending)), and unbiased root mean squared error (8.14 K (ascending) and 8.28 K (descending)). In terms of soil hydraulic parameters, large porosity and large wilting point both lead to high uncertainty in modeled T(sub b) due to the large variability in dielectric constant and surface roughness used by the RTM. The performance of the RTM as a function of vegetation type suggests better agreement in regions with broadleaf deciduous and needleleaf forests while grassland regions exhibited the worst accuracy amongst the five different vegetation types.

L-band radiometry↗

NASA NTRS1982

Quantiles, parametric-select density estimation, and bi-information parameter estimators

A quantile-based approach to statistical analysis and probability modeling of data is presented which formulates statistical inference problems as functional inference problems in which the parameters to be estimated are density functions. Density estimators can be non-parametric (computed independently of model identified) or parametric-select (approximated by finite parametric models that can provide standard models whose fit can be tested). Exponential models and autoregressive models are approximating densities which can be justified as maximum entropy for respectively the entropy of a probability density and the entropy of a quantile density. Applications of these ideas are outlined to the problems of modeling: (1) univariate data; (2) bivariate data and tests for independence; and (3) two samples and likelihood ratios. It is proposed that bi-information estimation of a density function can be developed by analogy to the problem of identification of regression models.

Parzen, E.↗

NASA NTRS2010

Model Robust Calibration: Method and Application to Electronically-Scanned Pressure Transducers

This article presents the application of a recently developed statistical regression method to the controlled instrument calibration problem. The statistical method of Model Robust Regression (MRR), developed by Mays, Birch, and Starnes, is shown to improve instrument calibration by reducing the reliance of the calibration on a predetermined parametric (e.g. polynomial, exponential, logarithmic) model. This is accomplished by allowing fits from the predetermined parametric model to be augmented by a certain portion of a fit to the residuals from the initial regression using a nonparametric (locally parametric) regression technique. The method is demonstrated for the absolute scale calibration of silicon-based pressure transducers.

Walker, Eric L.↗

NASA NTRSDate not supplied

Flux Comparison of Master-8 and Ordem 3.1 Modelled Space Debris Population

With ESA’s Meteoroid And Space debris Terrestrial Environment Reference (MASTER-8) model and NASA’s Orbital Debris Engineering Model(ORDEM) 3.1, the two premier orbital debris engineering models have been officially released. The two models come with significant enhancements and now represent state-of-the-art orbital debris modelling for their respective agencies. Both models provide the community with estimates of the space debris environment from low Earth orbit (LEO) up to at least geostationary altitude. The MASTER population is an event-based simulation of all known events that generate debris and objects that are part of the U.S. Space Surveillance Network (SSN) catalog, which provides coverage of objects with diameters down to approximately 10cm in LEO and 1 m in geosynchronous Earth orbit (GEO). Different models are used to simulate the artificial objects and their orbit evolution over time. These models are called “sources” since they assign an origin to each individual object and consist of fragments, solid rocket motor (SRM) remainders, sodium-potassium(NaK) droplets, paintflakes, ejecta, and multi-layer insulation (MLI) fragments. The objects from each source are characterized by having individual release mechanisms, as well as orbital distributions, material composition, size, and mass distributions. Dedicated radar and telescope observation data is used to calibrate the model for objects larger than 1 cm in LEO and larger than 10 cm in GEO. For calibrating the small-sized objects, below 1 cm, impact data from returned surfaces are analyzed. Because the >1cm object population is dominated by fragments, the fragmentation event database was updated to include new events, as well as re-evaluate past events. Special attention was drawn to re-evaluating theFengyun-1C anti-satellite test from 2007 and Cosmos-Iridium collision event from 2009 since these events shape the fragment population because of their severity. After 2009, the two largest fragmentations in terms of number of tracked debris are the Briz-M explosion in 2012 and the NOAA-16explosion in 2015. In total, there are 261 confirmed fragmentations in the database up to November 2016.The baseline population for ORDEM 3.1 is based on the U.S. SSN catalog, and observational datasets from radar, in situ, and optical sources provide a foundation from which the model populations are statistically extrapolated to smaller size regions. These regions are not well-covered by the SSN catalog yet may pose the greatest threat to operational spacecraft. The NASA Standard Satellite Breakup Model is used to generate fragments greater than 1mm from collisions and explosions, and these fragment populations are scaled using ground-based radar data. Specific major debris-producing events, including the Fengyun-1C, Iridium 33, and Cosmos2251 debris clouds, and unique populations, such as NaK droplets, were re-examined, modelled, and added to the ORDEM environment separately. Optical measurement data is used to model the GEO population down to 10 cm. The debris environment is propagated using NASA’s LEO-to-GEO Environment Debris model, and future explosions of intact objects and collisions involving objects greater than 10 cm are assessed statistically. The environment from a few millimetres down to 10 𝜇m is modelled using a special degradation model where small particles are generated from intact spacecraft and rocket bodies, then the populations are scaled to fit in situ cratering data from Space Shuttle returned surfaces. Fragments smaller than 10 cm are differentiated based on material density categories, i.e., high-, medium-, and low-density, to better characterize the potential debris risk posed to upper stages and spacecraft. This paper will discuss the MASTER and ORDEM approaches for modelling populations and compare fluxes for specific orbits, including sun-synchronous, ISS-altitude, geosynchronous transfer, and GEO. In the end, a conclusion is drawn towards the importance of having multiple fundamentally different, yet validated, models to estimate the space debris population.

Andre Horstmann↗

NASA NTRS2000

The Turbulent/Non-Turbulent Interface Bounding a Far-Wake

The velocity fields of a turbulent wake behind a flat plate obtained from the direct numerical simulations of Moser et al. are used to study the structure of the flow in the intermittent zone where there are, alternately, regions of fully turbulent flow and non-turbulent velocity fluctuations either side of a thin randomly moving interface. Comparisons are made with a wake that is 'forced' by amplifying initial velocity fluctuations. There is also a random temperature field T in the flow; T varies between constant values of 0.0 and 1.0 on the sides of the wake. The value of the Reynolds number based on the centreplane mean velocity defect and halfwidth b of the wake is Re approx. = 2000. It is found that the thickness of the continuous interface is about equal to 0.07b, whereas the amplitude of fluctuations of the instantaneous interface displacement y(sub I)(t) is an order of magnitude larger, being about 0.5b. This explains why the mean statistics of vorticity in the intermittent zone can be calculated in terms of the probability distribution of y(sub I) and the instantaneous discontinuity in vorticity across the interface. When plotted as functions of y - y(sub I), the conditional mean velocity (U) and temperature (T) profiles show sharp jumps Delta(U) and Delta(T) at the interface adjacent to a thick zone where (U) and (T) vary much more slowly. Statistics for the vorticity and velocity variances, available in such detail only from DNS data, show how streamwise and spanwise components of vorticity are generated by vortex stretching in the bulges of the interface. Flow fields around the interface, analyzed in terms of the local streamline pattern, confirm previous results that the advancement of the vortical interface into the irrotational flow is driven by large-scale eddy motion. It is argued that because this is an inviscid mechanism the entrainment process is not sensitive to the value of Re, and that small-scale nibbling only plays a subsidiary role. While mean Reynolds stresses decrease gradually in the intermittent zone, conditional stresses are found to decrease sharply towards zero at the interface. Using one-point turbulence models applied to either unconditional or conditional statistics for the turbulent region and then averaged, the entrainment rate E(sub b) would, if calculated exactly, be zero. But if computed with standard computational methods, E(sub b) would be non-zero because of numerical diffusion. It is concluded that the current practice in statistical models of approximating entrainment by a diffusion process is computationally arbitrary and physically incorrect. An analysis shows how E(sub b) is related to Delta(U) and the jump in shear stress at the interface, and correspondingly to Delta(T) and the heat flux.

Bisset, David K.↗

NASA NTRS2010

Comparison of Iterative and Non-Iterative Strain-Gage Balance Load Calculation Methods

The accuracy of iterative and non-iterative strain-gage balance load calculation methods was compared using data from the calibration of a force balance. Two iterative and one non-iterative method were investigated. In addition, transformations were applied to balance loads in order to process the calibration data in both direct read and force balance format. NASA's regression model optimization tool BALFIT was used to generate optimized regression models of the calibration data for each of the three load calculation methods. This approach made sure that the selected regression models met strict statistical quality requirements. The comparison of the standard deviation of the load residuals showed that the first iterative method may be applied to data in both the direct read and force balance format. The second iterative method, on the other hand, implicitly assumes that the primary gage sensitivities of all balance gages exist. Therefore, the second iterative method only works if the given balance data is processed in force balance format. The calibration data set was also processed using the non-iterative method. Standard deviations of the load residuals for the three load calculation methods were compared. Overall, the standard deviations show very good agreement. The load prediction accuracies of the three methods appear to be compatible as long as regression models used to analyze the calibration data meet strict statistical quality requirements. Recent improvements of the regression model optimization tool BALFIT are also discussed in the paper.

Ulbrich, N.↗

NASA NTRS2014

Combined Uncertainty and A-Posteriori Error Bound Estimates for General CFD Calculations: Theory and Software Implementation

This workshop presentation discusses the design and implementation of numerical methods for the quantification of statistical uncertainty, including a-posteriori error bounds, for output quantities computed using CFD methods. Hydrodynamic realizations often contain numerical error arising from finite-dimensional approximation (e.g. numerical methods using grids, basis functions, particles) and statistical uncertainty arising from incomplete information and/or statistical characterization of model parameters and random fields. The first task at hand is to derive formal error bounds for statistics given realizations containing finite-dimensional numerical error [1]. The error in computed output statistics contains contributions from both realization error and the error resulting from the calculation of statistics integrals using a numerical method. A second task is to devise computable a-posteriori error bounds by numerically approximating all terms arising in the error bound estimates. For the same reason that CFD calculations including error bounds but omitting uncertainty modeling are only of limited value, CFD calculations including uncertainty modeling but omitting error bounds are only of limited value. To gain maximum value from CFD calculations, a general software package for uncertainty quantification with quantified error bounds has been developed at NASA. The package provides implementations for a suite of numerical methods used in uncertainty quantification: Dense tensorization basis methods [3] and a subscale recovery variant [1] for non-smooth data, Sparse tensorization methods[2] utilizing node-nested hierarchies, Sampling methods[4] for high-dimensional random variable spaces.

CFD↗

NASA NTRS2022

NASA Engineering and Safety Center Technical Bulletin No. 22-04: Uncertainty Quantification of Reduced Order Structural Dynamic Models

Uncertainty quantification (UQ) provides statistical bounds on prediction accuracy based on finite element model (FEM) uncertainty. An alternate method for UQ, called the Hybrid Parametric Variation (HPV) combines a parametric variation of the Hurty/Craig-Bampton (HCB) fixed-interface (FI) modal frequencies with a nonparametric variation (NPV) method. This provides a UQ method that can be traced to test data, which can be updated as additional data and improved correlated models become available.

Uncertainty Quantification↗

NASA NTRS2003

Software Reliability 2002

In FY01 we learned that hardware reliability models need substantial changes to account for differences in software, thus making software reliability measurements more effective, accurate, and easier to apply. These reliability models are generally based on familiar distributions or parametric methods. An obvious question is 'What new statistical and probability models can be developed using non-parametric and distribution-free methods instead of the traditional parametric method?" Two approaches to software reliability engineering appear somewhat promising. The first study, begin in FY01, is based in hardware reliability, a very well established science that has many aspects that can be applied to software. This research effort has investigated mathematical aspects of hardware reliability and has identified those applicable to software. Currently the research effort is applying and testing these approaches to software reliability measurement, These parametric models require much project data that may be difficult to apply and interpret. Projects at GSFC are often complex in both technology and schedules. Assessing and estimating reliability of the final system is extremely difficult when various subsystems are tested and completed long before others. Parametric and distribution free techniques may offer a new and accurate way of modeling failure time and other project data to provide earlier and more accurate estimates of system reliability.

Wallace, Dolores R.↗

NASA NTRS1995

On-line estimation of error covariance parameters for atmospheric data assimilation

A simple scheme is presented for on-line estimation of covariance parameters in statistical data assimilation systems. The scheme is based on a maximum-likelihood approach in which estimates are produced on the basis of a single batch of simultaneous observations. Simple-sample covariance estimation is reasonable as long as the number of available observations exceeds the number of tunable parameters by two or three orders of magnitude. Not much is known at present about model error associated with actual forecast systems. Our scheme can be used to estimate some important statistical model error parameters such as regionally averaged variances or characteristic correlation length scales. The advantage of the single-sample approach is that it does not rely on any assumptions about the temporal behavior of the covariance parameters: time-dependent parameter estimates can be continuously adjusted on the basis of current observations. This is of practical importance since it is likely to be the case that both model error and observation error strongly depend on the actual state of the atmosphere. The single-sample estimation scheme can be incorporated into any four-dimensional statistical data assimilation system that involves explicit calculation of forecast error covariances, including optimal interpolation (OI) and the simplified Kalman filter (SKF). The computational cost of the scheme is high but not prohibitive; on-line estimation of one or two covariance parameters in each analysis box of an operational bozed-OI system is currently feasible. A number of numerical experiments performed with an adaptive SKF and an adaptive version of OI, using a linear two-dimensional shallow-water model and artificially generated model error are described. The performance of the nonadaptive versions of these methods turns out to depend rather strongly on correct specification of model error parameters. These parameters are estimated under a variety of conditions, including uniformly distributed model error and time-dependent model error statistics.

Dee, Dick P.↗

NASA NTRS1975

Subgrid or Reynolds stress-modeling for three-dimensional turbulence computations

A review is given of recent advances in two distinct computational methods for evaluating turbulence fields, namely, statistical Reynolds stress modeling and turbulence simulation, where large eddies are followed in time. It is shown that evaluation of the mean Reynolds stresses, rather than use of a scalar eddy viscosity, permits an explanation of streamline curvature effects found in several experiments. Turbulence simulation, with a new volume averaging technique and third-order accurate finite-difference computing is shown to predict the decay of isotropic turbulence in incompressible flow with rather modest computer storage requirements, even at Reynolds numbers of aerodynamic interest.

Rubesin, M. W.↗

NASA NTRS1993

Process and representation in graphical displays

Our initial model of graphic comprehension has focused on statistical graphs. Like other models of human-computer interaction, models of graphical comprehension can be used by human-computer interface designers and developers to create interfaces that present information in an efficient and usable manner. Our investigation of graph comprehension addresses two primary questions: how do people represent the information contained in a data graph?; and how do they process information from the graph? The topics of focus for graphic representation concern the features into which people decompose a graph and the representations of the graph in memory. The issue of processing can be further analyzed as two questions: what overall processing strategies do people use?; and what are the specific processing skills required?

Gillan, Douglas J.↗

NASA NTRS1994

Abundance gradients in cooling flow clusters: Ginga Large Area Counters and Einstein Solid State Spectrometer spectra of A496, A1795, A2142, and A2199

We analyze the Ginga Large Area Counters (LAC) and Einstein Solid State Spectrometer (SSS) spectra of four cooling flow clusters, A496, A1795, A2142, and A2199, each of which shows firm evidence of a relatively cool component. The inclusion of such cool spectral components in joint fits of SSS and LAC data leads to somewhat higher global temperatures than are derived from the high-energy LAC data alone. We find little evidence of cool emission outside the SSS field of view. Metal abundances appear to be centrally enhanced in all four clusters, with varying degrees of model dependence and statistical significance: the evidence is statistically strongest for A496 and A2142, somewhat weaker for A2199 and weakest for A1795. We also explore the model dependence in the amount of cold, X-ray-absorbing matter discovered in these clusters by White et al.

White, Raymond E., III↗

NASA NTRS2014

Development and Implementation of Dynamic Scripts to Execute Cycled GSI/WRF Forecasts

The Weather Research and Forecasting (WRF) numerical weather prediction (NWP) model and Gridpoint Statistical Interpolation (GSI) data assimilation (DA) are the operational systems that make up the North American Mesoscale (NAM) model and the NAM Data Assimilation System (NDAS) analysis used by National Weather Service forecasters. The Developmental Testbed Center (DTC) manages and distributes the code for the WRF and GSI, but it is up to individual researchers to link the systems together and write scripts to run the systems, which can take considerable time for those not familiar with the code. The objective of this project is to develop and disseminate a set of dynamic scripts that mimic the unique cycling configuration of the operational NAM to enable researchers to develop new modeling and data assimilation techniques that can be easily transferred to operations. The current version of the SPoRT GSI/WRF Scripts (v3.0.1) is compatible with WRF v3.3 and GSI v3.0.

Zavodsky, Bradley↗

NASA NTRS2014

Development and Implementation of Dynamic Scripts to Execute Cycled GSI/WRF Forecasts

Zavodsky, Bradley↗