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All sourcesNASA NTRSDOE OSTI
NASA NTRS2013

Ensemble Data Assimilation Without Ensembles: Methodology and Application to Ocean Data Assimilation

Two methods to estimate background error covariances for data assimilation are introduced. While both share properties with the ensemble Kalman filter (EnKF), they differ from it in that they do not require the integration of multiple model trajectories. Instead, all the necessary covariance information is obtained from a single model integration. The first method is referred-to as SAFE (Space Adaptive Forecast error Estimation) because it estimates error covariances from the spatial distribution of model variables within a single state vector. It can thus be thought of as sampling an ensemble in space. The second method, named FAST (Flow Adaptive error Statistics from a Time series), constructs an ensemble sampled from a moving window along a model trajectory. The underlying assumption in these methods is that forecast errors in data assimilation are primarily phase errors in space and/or time.

Data Assimilation↗
NASA NTRS1982

Influence of fabrication tolerances on the surface accuracy of large antenna structures

One of the sources of error in radio frequency antennas is the lack of dimensional precision of the surface. This paper presents an approach for estimating the amount of error caused by random dimensional imperfections of the many structural elements which make up a truss-type antenna. A principle of equivalence between the analyses of statistical errors and of the natural vibration frequencies of the structure is developed. Examples are presented to show the application of this equivalence principle to the determination of average surface errors of several types and proportions of antenna structures.

Hedgepeth, J. M.↗
NASA NTRS2019

Prior biosphere model impact on global terrestrial CO2 fluxes estimated from OCO-2 retrievals

This study assesses the impact of different state of the art global biospheric CO2 flux models, when applied as prior information, on inverse model “top-down” estimates of terrestrial CO2 fluxes obtained when assimilating Orbiting Carbon Observatory 2 (OCO-2) observations. This is done with a series of observing system simulation experiments (OSSEs) using synthetic CO2 column-average dry air mole fraction (XCO2) retrievals sampled at the OCO-2 satellite spatiotemporal frequency. The OSSEs utilized a 4-D variational (4D-Var) assimilation system with the GEOS-Chem global chemical transport model (CTM) to estimate CO2 net ecosystem exchange (NEE) fluxes using synthetic OCO-2 observations. The impact of biosphere models in inverse model estimates of NEE is quantified by conducting OSSEs using the NASA-CASA, CASA-GFED, SiB-4, and LPJ models as prior estimates and using NEE from the multi-model ensemble mean of the Multiscale Synthesis and Terrestrial Model Intercomparison Project as the “truth”. Results show that the assimilation of simulated XCO2 retrievals at OCO-2 observing modes over land results in posterior NEE estimates which generally reproduce “true” NEE globally and over terrestrial TransCom-3 regions that are well-sampled. However, we find larger spread among posterior NEE estimates, when using different prior NEE fluxes, in regions and seasons that have limited OCO-2 observational coverage and a large range in “bottom-up” NEE fluxes. Seasonally averaged posterior NEE estimates had standard deviations (SD) of ∼10 % to ∼50 % of the multi-model-mean NEE for different TransCom-3 land regions with significant NEE fluxes (regions/seasons with a NEE flux ≥0.5 PgC/yr). On a global average, the seasonally averaged residual impact of the prior model NEE assumption on the posterior NEE spread is ∼10 %–20 % of the posterior NEE mean. Additional OCO-2 OSSE simulations demonstrate that posterior NEE estimates are also sensitive to the assumed prior NEE flux uncertainty statistics, with spread in posterior NEE estimates similar to those when using variable prior model NEE fluxes. In fact, the sensitivity of posterior NEE estimates to prior error statistics was larger than prior flux values in some regions/times in the tropics and Southern Hemisphere where sufficient OCO-2 data were available and large differences between the prior and truth were evident. Overall, even with the availability of spatiotemporally dense OCO-2 data, noticeable residual differences (up to ∼20 %–30 % globally and 50 % regionally) in posterior NEE flux estimates remain that were caused by the choice of prior model flux values and the specification of prior flux uncertainties.

Sajeev Philip↗
NASA NTRS2021

The role of analysis error in the convergence of reanalysis production streams in MERRA-2

Due to production time constraints, most reanalyses are produced in multiple parallel streams instead of a single continuous one. These streams cover separate segments of the reanalysis time period with short overlaps to allow reconstruction of the official record. A fundamental assumption justifying this approach is that the streams will be assimilating the same observations during the periods where they overlap, and so will eventually converge to a similar atmospheric state, making discontinuities at stream junctions negligible. This assumption is revisited in this work by examining the impact of analysis error on the differences between MERRA-2 overlapping streams in three historical periods. Comparison results are shown in terms of standard deviations of stream differences as well as the spectral decomposition of the variance of their differences. Residual differences were found at the end of each year of overlap, with larger values observed in the earlier segments of the presatellite era. By drawing parallels with analysis error statistics estimated from the GMAO OSSE system, these differences are shown to reflect the varying constraint of data with the varying observing network, and to further carry the imprint of errors that the data assimilation process is not able to mitigate. As such, they are unlikely to be reduced by longer spinup periods. The ability of data assimilation to ensure continuity in the parallel streams is put into question when the observing system coverage is inadequate or simply when the data assimilation system as a whole is suboptimal.

Amal El Akkraoui↗
NASA NTRS1992

Precision X-band radio Doppler and ranging navigation: Mars Observer interplanetary cruise scenario

This article describes an error covariance analysis based on a Mars Observer mission scenario; the study was performed to establish the navigation performance that can potentially be achieved in a demonstration of precision two-way X-band (8.4-GHz) Doppler and ranging with the Mars Observer spacecraft planned for next year, and to evaluate the sensitivity of the predicted performance to variations in ground system error modeling assumptions. Orbit determination error statistics computed for a 182-day Doppler and ranging data arc predicted Mars approach orbit determination accuracies of about 0.45 micro-rad in an angular sense, using a conservative ground system error model as a baseline. When less-conservative error model assumptions were employed, it was found that orbit determination accuracies of 0.19 to 0.30 micro-rad could be obtained; the level of accuracy of the assumed Mars ephemeris is about 0.11 micro-rad. In comparison, Doppler-only performance with the baseline error model was predicted to be about 1.30 to 1.51 micro-rad, although it was found that when improved station location accuracies and Global Positioning System-based tropospheric calibration accuracies were assumed, accuracies of 0.44 to 0.52 micro-rad were predicted. In the Doppler plus ranging cases, the results were relatively insensitive to variations in ranging system and station delay calibration uncertainties of a few meters and tropospheric zenith delay calibration uncertainties of a few centimeters.

Estefan, J. A.↗
DOE OSTI2024

Systematic Uncertainties from Gribov Copies in Lattice Calculation of Parton Distributions in the Coulomb Gauge

Recently, a new method has been proposed to compute parton distributions using boosted correlators fixed in the Coulomb gauge (CG) within the framework of large-momentum effective theory. This approach, which does not involve Wilson lines, could greatly improve the efficiency and precision of lattice quantum chromodynamics calculations. However, concerns remain regarding whether systematic uncertainties from Gribov copies, which correspond to ambiguities in lattice gauge-fixing, are adequately controlled. This work assesses the effects of Gribov copies on Coulomb-gauge-fixed quark correlators. We utilize different strategies for Coulomb-gauge fixing, selecting two different groups of Gribov copies based on lattice gauge configurations. We examine the differences in the resulting spatial quark correlators in both vacuum and pion states. Our findings indicate that the statistical errors of the matrix elements from both Gribov copies, regardless of the correlation range, decrease proportionally to the square root of the number of gauge configurations. The difference between the strategies does not show statistical significance compared to the gauge noise, demonstrating that the effect of the Gribov copies can be neglected in practical lattice calculations of quark parton distributions.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
NASA NTRS1974

Ephemeris data and error analysis in support of a Comet Encke intercept mission

Utilizing an orbit determination based upon 65 observations over the 1961 - 1973 interval, ephemeris data were generated for the 1976-77, 1980-81 and 1983-84 apparitions of short period comet Encke. For the 1980-81 apparition, results from a statistical error analysis are outlined. All ephemeris and error analysis computations include the effects of planetary perturbations as well as the nongravitational accelerations introduced by the outgassing cometary nucleus. In 1980, excellent observing conditions and a close approach of comet Encke to the earth permit relatively small uncertainties in the cometary position errors and provide an excellent opportunity for a close flyby of a physically interesting comet.

Yeomans, D. K.↗
NASA NTRS1994

Observations of geographically correlated orbit errors for TOPEX/Poseidon using the global positioning system

We have compared Global Positioning System (GPS)-based dynamic and reduced-dynamic TOPEX/Poseidon orbits over three 10-day repeat cycles of the ground-track. The results suggest that the prelaunch joint gravity model (JGM-1) introduces geographically correlated errors (GCEs) which have a strong meridional dependence. The global distribution and magnitude of these GCEs are consistent with a prelaunch covariance analysis, with estimated and predicted global rms error statistics of 2.3 and 2.4 cm rms, respectively. Repeating the analysis with the post-launch joint gravity model (JGM-2) suggests that a portion of the meridional dependence observed in JGM-1 still remains, with global rms error of 1.2 cm.

Christensen, E. J.↗
NASA NTRS2006

Chandra Observation of NGC 6822

Chandra observed the nearby dwarf galaxy NGC 6822. There are 70 sources in the Chandra field, two of which are fairly extended and likely background clusters of galaxies. A third source was resolved by Chandra and has the same size and position as a known supernova remnant. The suspected variability detected from this source in previous missions is shown to be in error. The majority of the remaining 67 sources are consistent with background sources. Of the 61 sources detected above a completeness limit of 10 events we estimate that 9+/-4+/-8 are associated with the galaxy including both systematic and statistical errors. We compare the X-ray positions of all sources with various catalogs and HST data'and offer tentative identifications for several. Based on the mass and star formation rate of NGC 6822 we only expect about 10 sources mostly high mass systems.

Tennant, Allyn F.↗
NASA NTRS2009

A Method for Retrieving Ground Flash Fraction from Satellite Lightning Imager Data

A general theory for retrieving the fraction of ground flashes in N lightning observed by a satellite-based lightning imager is provided. An "exponential model" is applied as a physically reasonable constraint to describe the measured optical parameter distributions, and population statistics (i.e., mean, variance) are invoked to add additional constraints to the retrieval process. The retrieval itself is expressed in terms of a Bayesian inference, and the Maximum A Posteriori (MAP) solution is obtained. The approach is tested by performing simulated retrievals, and retrieval error statistics are provided. The ability to retrieve ground flash fraction has important benefits to the atmospheric chemistry community. For example, using the method to partition the existing satellite global lightning climatology into separate ground and cloud flash climatologies will improve estimates of lightning nitrogen oxides (NOx) production; this in turn will improve both regional air quality and global chemistry/climate model predictions.

Koshak, William J.↗
NASA NTRSDate not supplied

The Relationship Between Two Methods for Estimating Uncertainties in Data Assimilation

This note examines the relationship between two apparently unrelated methods for estimating error statistics or uncertainties of relevance to data assimilation. The first method is due to (Desroziers et al., 2005, Q. J. R. Meteorol. Soc., 131, 3385–3396; referred to as DBCP hereafter) and relies on residual statistics readily available from data assimilation applications. The second method, the three- cornered hat (3CH) developed by Gray and Allan (1974, IEEE 28th Annual Symp. Freq. Control, 243–246), only recently applied to atmospheric sciences, uses three data sets and can derive estimates of relevant error uncertainties as well. The usefulness of both methods lies in them not requiring knowledge of the true value of the quantities at play. DBCP derives its results by relying explicitly on the constraints as- sociated with the data assimilation minimization problem; 3CH is general and its estimates hold as long as errors in the three data sets of choice are uncorrelated. Establishing the relationship between the methods requires applying the 3CH approach to the same observation, background, and analysis data sets used by DBCP. In this case, the same assumptions of DBCP on residual errors allow for cancellation of error cross–covariance terms in 3CH such that two of its corners derive identical estimates for observation and background error covariances as those of DBCP. The error cross–covariance terms associated with the third corner are shown to add up to twice the analysis error covariance so that the 3CH estimate for the third corner recovers the negative of the analysis error covariance. Illustrations of these findings are provided by deriving uncertainties for radio occultation bending angles.

Ricardo Todling↗
NASA NTRS1993

Sensitivity of trajectory calculations to the temporal frequency of wind data

A mesoscale primitive equation model is used to create a 36-h simulation of the three-dimensional wind field of an intense maritime extratropical cyclone. The control experiment uses the simulated wind field every 15 min in a trajectory model to calculate back trajectories from various horizontal and vertical positions of interest relative to synoptic features of the storm. The latter trajectories are compared to trajectories that were calculated with the simulated wind data degraded in time to 30 min, 1 h, 3 h, 6h, and 12 h. Various error statistics reveal significant deterioration in trajectory accuracy between trajectories calculated with 1- and 3-h data frequencies. Trajectories calculated with 15-min, 30-min, and 1-h data frequencies yielded similar results, while trajectories calculated with data time frequencies 3 h and greater yielded results with unacceptably large errors.

Doty, Kevin G.↗
NASA NTRS2018

Realistic Covariance Generation for the GPM Spacecraft

A covariance realism process for NASA's Global Precipitation Measurement (GPM) spacecraft is detailed. The GPM spacecraft is in a low earth orbit, and performs collision avoidance maneuvers few times a year. Currently GPM is below the International Space Station (ISS). So, in addition to cataloged debris objects, GPM must contend with smallsat/cubesat objects that are deployed from the ISS. Both operational scenarios require complete knowledge of the expected GPM prediction errors as a function of time. In this study, we present a method for generating realistic predicted covariance that uses linear propagation of the covariance with the addition of process noise. Further analyses are presented for the process noise ''tuning'' that generates an inflation factor based on the observed error statistics of the predictive satellite trajectories when compared to the definitive ones. Different tuning strategies are considered and compared via a Goodness-of-Fit testing for the Gaussian properties of the scaled covariance. SpaceNav's realistic covariance generation approach takes into account the contribution of predicted maneuver errors in the increased propagation uncertainty. Corresponding maneuver uncertainty is injected into the state uncertainty, and is used within the collision avoidance process to determine the collision risk for close approach events that follow a maneuver. This is a critical step in the maneuver planning process that provides the satellite operator with an accurate quantification of the collision probability for planned maneuvers. Using this information, an informed decision can be made to proceed with a maneuver if the collision risk is acceptable. This approach is validated by Monte-Carlo simulations and results are presented.

spacecraft uncertainty propagation↗
DOE OSTI2025

Using the optimal combined index weight ratio to improve the probability of anomaly detection in big area additive manufacturing

Big Area Additive Manufacturing (BAAM) of composites requires significant time, energy, and material, so it is critical to reduce production inefficiencies to make functional parts without multiple iterations. Statistical process control coupled with Principal Component Analysis (PCA) is a powerful technique that provides a quick, computationally inexpensive, and intuitive way for operators to detect defects that form in a manufacturing process without massive datasets. Recently, a combined index that is a weighted sum of the Hotelling's T 2 and squared residual error statistics has been proposed that can be monitored in one chart, improving interpretation accuracy and simplicity. However, the literature does not offer a formal method to optimise the weights. Here, we introduce two new approaches to the traditional weight selection approach using simulated and BAAM image data. Approach 1 uses a theoretically motivated optimum inspired by probabilistic principal component analysis. Approach 2 systematically varies the ratio of the weights to find the optimum. We show that approach 1 delivers optimal anomaly detection performance in select cases while approach 2 fares better in practice. Surprisingly, we also show that choosing a more complex PCA model has a minimal negative impact on anomaly detection performance compared to a more simplistic model.

3-dimensional printing↗
NASA NTRS1981

Alterations of the climate of a primitive equation model produced by filtering approximations and subsequent tuning and stochastic forcing

A comparison is made of the simulated climates of nonlinear models based on the primitive equations (PE), balance equations (BE), and quasi-geostrophic (QG) equations. The models and numerical procedures are identical in all possible respects. The models are highly truncated spectral forms of Lorenz's (1960) energy preserving two-layer model. Two means of making use of the information contained in the (presumed known) short-term prediction error statistics are investigated. An unrealistically high level of thermal forcing is used so that the model climates are sufficiently different to allow any improvements due to the empirical methods to be observed. The general tuning problem is outlined and the QG model is tuned, using data obtained from a PE model run, to minimize the mean squared short term prediction error.

Hoffman, R. N.↗
NASA NTRS2013

Tuning and Robustness Analysis for the Orion Absolute Navigation System

The Orion Multi-Purpose Crew Vehicle (MPCV) is currently under development as NASA's next-generation spacecraft for exploration missions beyond Low Earth Orbit. The MPCV is set to perform an orbital test flight, termed Exploration Flight Test 1 (EFT-1), some time in late 2014. The navigation system for the Orion spacecraft is being designed in a Multi-Organizational Design Environment (MODE) team including contractor and NASA personnel. The system uses an Extended Kalman Filter to process measurements and determine the state. The design of the navigation system has undergone several iterations and modifications since its inception, and continues as a work-in-progress. This paper seeks to show the efforts made to-date in tuning the filter for the EFT-1 mission and instilling appropriate robustness into the system to meet the requirements of manned space ight. Filter performance is affected by many factors: data rates, sensor measurement errors, tuning, and others. This paper focuses mainly on the error characterization and tuning portion. Traditional efforts at tuning a navigation filter have centered around the observation/measurement noise and Gaussian process noise of the Extended Kalman Filter. While the Orion MODE team must certainly address those factors, the team is also looking at residual edit thresholds and measurement underweighting as tuning tools. Tuning analysis is presented with open loop Monte-Carlo simulation results showing statistical errors bounded by the 3-sigma filter uncertainty covariance. The Orion filter design uses 24 Exponentially Correlated Random Variable (ECRV) parameters to estimate the accel/gyro misalignment and nonorthogonality. By design, the time constant and noise terms of these ECRV parameters were set to manufacturer specifications and not used as tuning parameters. They are included in the filter as a more analytically correct method of modeling uncertainties than ad-hoc tuning of the process noise. Tuning is explored for the powered-flight ascent phase, where measurements are scarce and unmodelled vehicle accelerations dominate. On orbit, there are important trade-off cases between process and measurement noise. On entry, there are considerations about trading performance accuracy for robustness. Process Noise is divided into powered flight and coasting ight and can be adjusted for each phase and mode of the Orion EFT-1 mission. Measurement noise is used for the integrated velocity measurements during pad alignment. It is also used for Global Positioning System (GPS) pseudorange and delta- range measurements during the rest of the flight. The robustness effort has been focused on maintaining filter convergence and performance in the presence of unmodeled error sources. These include unmodeled forces on the vehicle and uncorrected errors on the sensor measurements. Orion uses a single-frequency, non-keyed GPS receiver, so the effects due to signal distortion in Earth's ionosphere and troposphere are present in the raw measurements. Results are presented showing the efforts to compensate for these errors as well as characterize the residual effect for measurement noise tuning. Another robustness tool in use is tuning the residual edit thresholds. The trade-off between noise tuning and edit thresholds is explored in the context of robustness to errors in dynamics models and sensor measurements. Measurement underweighting is also presented as a method of additional robustness when processing highly accurate measurements in the presence of large filter uncertainties.

Holt, Greg N.↗
NASA NTRS1988

Color and population gradients in the core of the postcollapse globular cluster M30

A new technique has been developed for seeking color gradients in multicolor CCD images of a globular cluster. Application of this technique to M30 confirms the radial color gradient reported by others. The B - V and V - R colors show linear gradients, when plotted against log r, that are many times their statistical errors. In the radial range 3-100 arcsec, the B - V and V - R colors increase outwards by about (0.18 + or - 0.015) mag/dex and (0.09 + or - 0.01) mag/dex, respectively. Color-magnitude arrays of the central region show that the Balmer-line strength that accompanies the central blueness is due to an increased proportion of blue-horizontal-branch starlight in the center. This excess does not appear to be statistically significant in terms of star numbers, even though the color gradient is so highly significant.

Piotto, Giampaolo↗
NASA NTRS2014

Carbon Monitoring System Flux Estimation and Attribution: Impact of ACOS-GOSAT X(CO2) Sampling on the Inference of Terrestrial Biospheric Sources and Sinks

Using an Observing System Simulation Experiment (OSSE), we investigate the impact of JAXA Greenhouse gases Observing SATellite 'IBUKI' (GOSAT) sampling on the estimation of terrestrial biospheric flux with the NASA Carbon Monitoring System Flux (CMS-Flux) estimation and attribution strategy. The simulated observations in the OSSE use the actual column carbon dioxide (X(CO2)) b2.9 retrieval sensitivity and quality control for the year 2010 processed through the Atmospheric CO2 Observations from Space algorithm. CMS-Flux is a variational inversion system that uses the GEOS-Chem forward and adjoint model forced by a suite of observationally constrained fluxes from ocean, land and anthropogenic models. We investigate the impact of GOSAT sampling on flux estimation in two aspects: 1) random error uncertainty reduction and 2) the global and regional bias in posterior flux resulted from the spatiotemporally biased GOSAT sampling. Based on Monte Carlo calculations, we find that global average flux uncertainty reduction ranges from 25% in September to 60% in July. When aggregated to the 11 land regions designated by the phase 3 of the Atmospheric Tracer Transport Model Intercomparison Project, the annual mean uncertainty reduction ranges from 10% over North American boreal to 38% over South American temperate, which is driven by observational coverage and the magnitude of prior flux uncertainty. The uncertainty reduction over the South American tropical region is 30%, even with sparse observation coverage. We show that this reduction results from the large prior flux uncertainty and the impact of non-local observations. Given the assumed prior error statistics, the degree of freedom for signal is approx.1132 for 1-yr of the 74 055 GOSAT X(CO2) observations, which indicates that GOSAT provides approx.1132 independent pieces of information about surface fluxes. We quantify the impact of GOSAT's spatiotemporally sampling on the posterior flux, and find that a 0.7 gigatons of carbon bias in the global annual posterior flux resulted from the seasonally and diurnally biased sampling when using a diagonal prior flux error covariance.

biased sampling↗