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NASA NTRS1994

Search for gamma-ray events in the BATSE data base

We find large location errors and error radii in the locations of channel 1 Cygnus X-1 events. These errors and their associated uncertainties are a result of low signal-to-noise ratios (a few sigma) in the two brightest detectors for each event. The untriggered events suffer from similarly low signal-to-noise ratios, and their location errors are expected to be at least as large as those found for Cygnus X-1 with a given signal-to-noise ratio. The statistical error radii are consistent with those found for Cygnus X-1 and with the published estimates. We therefore expect approximately 20 - 30 deg location errors for the untriggered events. Hence, many of the untriggered events occurring within a few months of the triggered activity from SGR 1900 plus 14 are indeed consistent with the SGR source location, although Cygnus X-1 is also a good candidate.

Lewin, Walter↗

DOE OSTI2022

Impact of point spread function higher moments error on weak gravitational lensing – II. A comprehensive study

ABSTRACT Weak lensing is one of the most powerful probes for dark matter and dark energy science, although it faces increasing challenges in controlling systematic uncertainties as the statistical errors become smaller. The point spread function (PSF) needs to be precisely modeled to avoid systematic error on the weak lensing measurements. The weak lensing biases induced by errors in the PSF model second moments, i.e. its size and shape, are well-studied. However, Zhang et al. showed that errors in the higher moments of the PSF may also be a significant source of systematics for upcoming weak lensing surveys. Therefore, this work comprehensively investigate the modelling quality of PSF moments from the 3rd to 6th order, and propagate the PSFEx higher moments modelling error in the HSC survey data set to the weak lensing shear–shear correlation functions and their cosmological analyses. The overall multiplicative shear bias associated with errors in PSF higher moments can cause an ∼0.1σ shift on the cosmological parameters for LSST Y10, while the associated additive biases can induce 1σ uncertainties in cosmology parameter inference for LSST Y10, if not accounted. We compare the PSFEx model with PSF in Full FOV, and find similar performance in modelling the PSF higher moments. We conclude that PSF higher moment errors of the future PSF models should be reduced from those in current methods, otherwise needed to be explicitly modeled in the weak lensing analysis.

79 ASTRONOMY AND ASTROPHYSICS↗

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↗

DOE OSTI2017

Dark Energy Survey Year 1 results: the impact of galaxy neighbours on weak lensing cosmology with IM3SHAPE

We use a suite of simulated images based on Year 1 of the Dark Energy Survey to explore the impact of galaxy neighbours on shape measurement and shear cosmology. The hoopoe image simulations include realistic blending, galaxy positions, and spatial variations in depth and PSF properties. Using the im3shape maximum-likelihood shape measurement code, we identify four mechanisms by which neighbours can have a non-negligible influence on shear estimation. These effects, if ignored, would contribute a net multiplicative bias of $m \sim 0.03 - 0.09$ in the DES Y1 im3shape catalogue, though the precise impact will be dependent on both the measurement code and the selection cuts applied. This can be reduced to percentage level or less by removing objects with close neighbours, at a cost to the effective number density of galaxies $n_\mathrm{eff}$ of 30%. We use the cosmological inference pipeline of DES Y1 to explore the cosmological implications of neighbour bias and show that omitting blending from the calibration simulation for DES Y1 would bias the inferred clustering amplitude $S_8\equiv \sigma_8 (\Omega _\mathrm{m} /0.3)^{0.5}$ by $2 \sigma$ towards low values. Lastly, we use the hoopoe simulations to test the effect of neighbour-induced spatial correlations in the multiplicative bias. We find the impact on the recovered $S_8$ of ignoring such correlations to be subdominant to statistical error at the current level of precision.

79 ASTRONOMY AND ASTROPHYSICS↗

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↗

DOE OSTI2014

Dark matter and halo bispectrum in redshift space: theory and applications

We present a phenomenological modification of the standard perturbation theory prediction for the bispectrum in redshift space that allows us to extend the model to mildly non-linear scales over a wide range of redshifts, z≤1.5. Our model require 18 free parameters that are fitted to N-body simulations using the shapes k{sub 2}/k{sub 1}=1, 1.5, 2.0, 2.5. We find that we can describe the bispectrum of dark matter particles with ∼5% accuracy for k{sub i}∼<0.10 h/Mpc at z=0, for k{sub i}∼<0.15 h/Mpc at z=0.5, for k{sub i}∼<0.17 h/Mpc at z=1.0 and for k{sub i}∼<0.20 h/Mpc at z=1.5. For very squeezed triangles with k{sub 1}=k{sub 2}∼>0.1 hMpc{sup -1} and k{sub 3}≤0.02 hMpc{sup -1}, however, neither SPT nor the proposed fitting formula are able to describe the measured dark matter bispectrum with this accuracy. We show that the fitting formula is sufficiently general that can be applied to other intermediate shapes such as k{sub 2}/k{sub 1}=1.25, 1.75, and 2.25. We also test that the fitting formula is able to describe with similar accuracy the bispectrum of cosmologies with different Ω{sub m}, in the range 0.2∼< Ω{sub m} ∼< 0.4, and consequently with different values of the logarithmic grow rate f at z=0, 0.4∼< f(z=0) ∼< 0.6. We apply this new formula to recover the bias parameters, f and σ{sub 8}, by combining the redshift space power spectrum monopole and quadrupole with the bispectrum monopole for both dark matter particles and haloes. We find that the combination of these three statistics can break the degeneracy between b{sub 1}, f and σ{sub 8}. For dark matter particles the new model can be used to recover f and σ{sub 8} with ∼1% accuracy. For dark matter haloes we find that f and σ{sub 8} present larger systematic shifts, ∼10%. The systematic offsets arise because of limitations in the modelling of the interplay between bias and redshift space distortions, and represent a limitation as the statistical errors of forthcoming surveys reach this level. Conveniently, we find that these residual systematics are mitigated for combinations of parameters. In particular, the quantity fσ{sub 8} is still recovered with ∼1% accuracy for the particular halo population and cosmology studied. The improvement on the modelling of the bispectrum presented in this paper will be useful for extracting information from current and future galaxy surveys.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2015

Improving the Fidelity of Lattice QCD Calculations

I begin with an overview of the various statistical and systematic uncertainties that enter into lattice calculations in nuclear physics, and the hierarchy of computations needed to investigate them. I emphasize in particular the need to obtain as precise a statistical error as possible on a given ensemble of calculations, and the various variance reduction and algorithmic methods that have been proposed recently with the aim of minimizing the statistical uncertainties. I conclude with a description of the fitting methods used in lattice QCD calculations.

Richards, David↗

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↗

DOE OSTI2017

A Simplified Theory of Pile Noise

Here, a theoretical treatment is given of the statistical fluctuations in neutron population which occur in nuclear reactors. The absolute magnitude and frequency dependence of the spectral density of these fluctuations is obtained. The model used assumes that the fluctuations arise from a "noise-equivalent source" whose strength can be easily calculated from fundamental considerations. Calculations are also presented of the fundamental statistical errors in criticality measurements.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

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 OSTI2016

LAMOST spectrograph response curves: Stability and application to flux calibration

The task of flux calibration for Large sky Area Multi-Object Spectroscopic Telescope (LAMOST) spectra is difficult due to many factors, such as the lack of standard stars, flat-fielding for large field of view, and variation of reddening between different stars, especially at low Galactic latitudes. Poor selection, bad spectral quality, or extinction uncertainty of standard stars not only might induce errors to the calculated spectral response curve (SRC) but also might lead to failures in producing final 1D spectra. In this paper, we inspected spectra with Galactic latitude |b|⩾60{sup ∘} and reliable stellar parameters, determined through the LAMOST Stellar Parameter Pipeline (LASP), to study the stability of the spectrograph. To guarantee that the selected stars had been observed by each fiber, we selected 37,931 high-quality exposures of 29,000 stars from LAMOST DR2, and more than seven exposures for each fiber. We calculated the SRCs for each fiber for each exposure and calculated the statistics of SRCs for spectrographs with both the fiber variations and time variations. The result shows that the average response curve of each spectrograph (henceforth ASPSRC) is relatively stable, with statistical errors ≤10%. From the comparison between each ASPSRC and the SRCs for the same spectrograph obtained by the 2D pipeline, we find that the ASPSRCs are good enough to use for the calibration. The ASPSRCs have been applied to spectra that were abandoned by the LAMOST 2D pipeline due to the lack of standard stars, increasing the number of LAMOST spectra by 52,181 in DR2. Comparing those same targets with the Sloan Digital Sky Survey (SDSS), the relative flux differences between SDSS spectra and LAMOST spectra with the ASPSRC method are less than 10%, which underlines that the ASPSRC method is feasible for LAMOST flux calibration.

79 ASTRONOMY AND ASTROPHYSICS↗

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↗

DOE OSTI2020

Monte Carlo control loops for cosmic shear cosmology with DES Year 1 data

Weak lensing by large-scale structure is a powerful probe of cosmology and of the dark universe. This cosmic shear technique relies on the accurate measurement of the shapes and redshifts of background galaxies and requires precise control of systematic errors. Monte Carlo control loops (MCCL) is a forward modeling method designed to tackle this problem. It relies on the ultra fast image generator (UFig) to produce simulated images tuned to match the target data statistically, followed by calibrations and tolerance loops. Here, we present the first end-to-end application of this method, on the Dark Energy Survey (DES) Year 1 wide field imaging data. We simultaneously measure the shear power spectrum $C_ℓ$ and the redshift distribution $n(z)$ of the background galaxy sample. The method includes maps of the systematic sources, point spread function (PSF), an approximate Bayesian computation (ABC) inference of the simulation model parameters, a shear calibration scheme, and a fast method to estimate the covariance matrix. We find a close statistical agreement between the simulations and the DES Y1 data using an array of diagnostics. In a nontomographic setting, we derive a set of $C_ℓ$ and $n(z)$ curves that encode the cosmic shear measurement, as well as the systematic uncertainty. Following a blinding scheme, we measure the combination of $Ω_m$, $σ_8$, and intrinsic alignment amplitude $A_{IA}$, defined as $S_8D_{IA}=σ_8(Ω_m/0.3)^{0.5}D_{IA}$, where $D_{IA}=1-0.11(A_{IA}-1)$. We find $S_8D_{IA}=0.8954_{-0.039}^{+0.054}$, where systematics are at the level of roughly 60% of the statistical errors. We discuss these results in the context of earlier cosmic shear analyses of the DES Y1 data. Our findings indicate that this method and its fast runtime offer good prospects for cosmic shear measurements with future wide-field surveys.

79 ASTRONOMY AND ASTROPHYSICS↗

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.↗

DOE OSTI2016

Compensation for nonlinear effects in an optical orthogonal frequency-division multiplexed signal using adaptive modulation

We study the influence of nonlinear effects on symbol error statistics when a 16-QAM orthogonal frequency-division multiplexed signal is transmitted in a 1000 km length of fibre. A technique of adaptive modulation is proposed for generating signals that are resistant to nonlinear distortions. A considerable improvement of the transmission quality is shown to take effect in using an adaptive modulation scheme. (paper)

42 ENGINEERING↗

DOE OSTI2023

Extrapolation of the Rainflow-Counted Load Ranges for Fatigue Assessment of the Wind Turbine's Blades

Wind turbine design standards recommend the use of statistical modeling coupled with extrapolation of the short-term load data to long-term periods for fatigue reliability assessment. However, statistical error and computational expense can limit the accuracy of such approaches. In the case of wind turbine blades, the errors are more significant because of the high material fatigue exponent that makes the damage estimations more sensitive to variations. In addition, due to different excitation sources, the flapwise load range histogram is not unimodal, and thus its statistical modeling is complex. In the present work, we provide three methods for statistical modeling of the flapwise bending moment ranges including a novel approach based on frequency-based separation of the modes. The first two methods are simplified approaches for modeling the most crucial load ranges using unimodal distributions and the third method involves multimodal distribution fitting. The research is based on 3600 10-minute aeroelastic simulations of DTU 10MW case study wind turbine from which a benchmark damage equivalent load (DEL) is calculated. The DEL calculated by each of the three proposed methods is compared to this reference. The results show that the conventional approach based on using 6 seeds as well as using mixture models fitted on the limited data lead to under-conservative results with errors up to 23%. On the other hand, the simplified unimodal approaches provided in this work can provide conservative estimations of the fatigue damage with mean values 5% and 12% higher than the benchmark. However, the variability of the DEL estimates is higher when using unimodal extrapolation of the load ranges, and the data can be conservative by 17.5%. The proposed unimodal fits suggested for modeling and extrapolation of the blade's load ranges provide less errors relatively and most importantly conservative DEL estimations while maintaining computational efficiency.

blade fatigue↗

DOE OSTI2020

Improved Fast Randomized Iteration Approach to Full Configuration Interaction

In this work, we present three modifications to our recently introduced fast randomized iteration method for full configuration interaction (FCI-FRI) and investigate their effects on the method’s performance for Ne, H 2 O, and N 2 . The initiator approximation, originally developed for full configuration interaction quantum Monte Carlo, significantly reduces statistical error in FCI-FRI when few samples are used in compression operations, enabling its application to larger chemical systems. The semistochastic extension, which involves exactly preserving a fixed subset of elements in each compression, improves statistical efficiency in some cases but reduces it in others. We also developed a new approach to sampling excitations that yields consistent improvements in statistical efficiency and reductions in computational cost. We discuss possible strategies based on our findings for improving the performance of stochastic quantum chemistry methods more generally.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗