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All sourcesNASA NTRSDOE OSTI
NASA NTRS1994

TOPEX/POSEIDON tides estimated using a global inverse model

Altimetric data from the TOPEX/POSEIDON mission will be used for studies of global ocean circulation and marine geophysics. However, it is first necessary to remove the ocean tides, which are aliased in the raw data. The tides are constrained by the two distinct types of information: the hydrodynamic equations which the tidal fields of elevations and velocities must satisfy, and direct observational data from tide gauges and satellite altimetry. Here we develop and apply a generalized inverse method, which allows us to combine rationally all of this information into global tidal fields best fitting both the data and the dynamics, in a least squares sense. The resulting inverse solution is a sum of the direct solution to the astronomically forced Laplace tidal equations and a linear combination of the representers for the data functionals. The representer functions (one for each datum) are determined by the dynamical equations, and by our prior estimates of the statistics or errors in these equations. Our major task is a direct numerical calculation of these representers. This task is computationally intensive, but well suited to massively parallel processing. By calculating the representers we reduce the full (infinite dimensional) problem to a relatively low-dimensional problem at the outset, allowing full control over the conditioning and hence the stability of the inverse solution. With the representers calculated we can easily update our model as additional TOPEX/POSEIDON data become available. As an initial illustration we invert harmonic constants from a set of 80 open-ocean tide gauges. We then present a practical scheme for direct inversion of TOPEX/POSEIDON crossover data. We apply this method to 38 cycles of geophysical data records (GDR) data, computing preliminary global estimates of the four principal tidal constituents, M(sub 2), S(sub 2), K(sub 1) and O(sub 1). The inverse solution yields tidal fields which are simultaneously smoother, and in better agreement with altimetric and ground truth data, than previously proposed tidal models. Relative to the 'default' tidal corrections provided with the TOPEX/POSEIDON GDR, the inverse solution reduces crossover difference variances significantly (approximately 20-30%), even though only a small number of free parameters (approximately equal to 1000) are actually fit to the crossover data.

Egbert, Gary D.↗
NASA NTRS2014

Ozone Profiles in the Baltimore-Washington Region (2006-2011): Satellite Comparisons and DISCOVER-AQ Observations

Much progress has been made in creating satellite products for tracking the pollutants ozone and NO2 in the troposphere. Yet, in mid-latitude regions where meteorological interactions with pollutants are complex, accuracy can be difficult to achieve, largely due to persistent layering of some constituents. We characterize the layering of ozone soundings and related species measured from aircraft over two ground sites in suburban Washington, DC (Beltsville, MD, 39.05N; 76.9W) and Baltimore (Edgewood, MD, 39.4N; 76.3W) during the July 2011 DISCOVER-AQ (Deriving Information on Surface Conditions from Column and Vertically Resolved Observations Relevant to Air Quality) experiment. First, we compare column-ozone amounts from the Beltsville and Edgewood sondes with data from overpassing satellites. Second, processes influencing ozone profile structure are analyzed using Laminar Identification and tracers: sonde water vapor, aircraft CO and NOy. Third, Beltsville ozone profiles and meteorological influences in July 2011 are compared to those from the summers of 2006-2010. Sonde-satellite offsets in total ozone during July 2011 at Edgewood and Beltsville, compared to the Ozone Monitoring Instrument (OMI), were 3 percent mean absolute error, not statistically significant. The disagreement between an OMIMicrowave Limb Sounder-based tropospheric ozone column and the sonde averaged 10 percent at both sites, with the sonde usually greater than the satellite. Laminar Identification (LID), that distinguishes ozone segments influenced by convective and advective transport, reveals that on days when both stations launched ozonesondes, vertical mixing was stronger at Edgewood. Approximately half the lower free troposphere sonde profiles have very dry laminae, with coincident aircraft spirals displaying low CO (80-110 ppbv), suggesting stratospheric influence. Ozone budgets at Beltsville in July 2011, determined with LID, as well as standard meteorological indicators, resemble those of 4 of the previous 5 summers. The penetration of stratospheric air throughout the troposphere appears to be typical for summer conditions in the Baltimore-Washington region.

satellite validation↗
NASA NTRS2018

Modeling the Proton Radiation Belt With Van Allen Probes Relativistic Electron-Proton Telescope Data

An empirical model of the proton radiation belt is constructed from data taken during 2013-2017 by the Relativistic Electron-Proton Telescopes on the Van Allen Probes satellites. The model intensity is a function of time, kinetic energy in the range 18-600 megaelectronvolts, equatorial pitch angle, and L shell of proton guiding centers. Data are selected, on the basis of energy deposits in each of the nine silicon detectors, to reduce background caused by hard proton energy spectra at low L. Instrument response functions are computed by Monte Carlo integration, using simulated proton paths through a simplified structural model, to account for energy loss in shielding material for protons outside the nominal field of view. Overlap of energy channels, their wide angular response, and changing satellite orientation require the model dependencies on all three independent variables be determined simultaneously. This is done by least squares minimization with a customized steepest descent algorithm. Model uncertainty accounts for statistical data error and systematic error in the simulated instrument response. A proton energy spectrum is also computed from data taken during the 8 January 2014 solar event, to illustrate methods for the simpler case of an isotropic and homogeneous model distribution. Radiation belt and solar proton results are compared to intensities computed with a simplified, on-axis response that can provide a good approximation under limited circumstances.

Selesnick, R. S.↗
NASA NTRS2025

Mind the Gap: Addressing Data Gaps and Assessing Noise Mismodeling in LISA

Due to the sheer complexity of the Laser Interferometer Space Antenna (LISA) space mission, data gaps arising from instrumental irregularities and/or scheduled maintenance are unavoidable. Focusing on merger-dominated massive black hole binary signals, we test the appropriateness of the Whittle-likelihood on gapped data in a variety of cases. From first principles, we derive the likelihood valid for gapped data in both the time and frequency domains. Cheap-to-evaluate proxies to p-p plots are derived based on a Fisher-based formalism, and verified through Bayesian techniques. Our tools allow to predict the altered variance in the parameter estimates that arises from noise mismodeling, as well as the information loss represented by the broadening of the posteriors. The result of noise mismodeling with gaps is sensitive to the characteristics of the noise model, with strong low-frequency (red) noise and strong high-frequency (blue) noise giving statistically significant fluctuations in recovered parameters. We demonstrate that the introduction of a tapering window reduces statistical inconsistency errors, at the cost of less precise parameter estimates. We also show that the assumption of independence between inter-gap segments appears to be a fair approximation even if the data set is inherently coherent. However, if one instead assumes fictitious correlations in the data stream, when the data segments are actually independent, then the resultant parameter recoveries could be inconsistent with the true parameters. The theoretical and numerical practices that are presented in this work could readily be incorporated into global-fit pipelines operating on gapped data.

LISA↗
DOE OSTI2015

Measurement of the branching fractions of radiative leptonic τ decays τ → ℓγν anti-ν (ℓ=e,μ) at BABAR

We perform a measurement of the branching fractions for τ → ℓγν anti ν, (ℓ = e, μ) decays for a minimum photon energy of 10 MeV in the τ rest frame using 430 fb -1 of e + e - collisions collected at the center-of-mass energy of the Υ(4S) resonance with the BABAR detector at the PEP-II storage rings. We find B(τ → μγνν) = (3.69±0.03±0.10)×10 3 and B(τ → eγνν) = (1.847 ± 0.015 ± 0.052) × 10 -2 where the first quoted error is statistical and the second is systematic. These results represent a substantial improvement with respect to existing measurements for both channels.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2017

Precise determination of the CKM matrix element $\left| V_{cb}\right|$ with $\bar B^0 \to D^{*\,+} \, \ell^- \, \bar ν_\ell$ decays with hadronic tagging at Belle

The precise determination of the CKM matrix element $\left| V_{cb}\right|$ is important for carrying out tests of the flavour sector of the Standard Model. In this article we present a preliminary analysis of the $\bar B^0 \to D^{*\,+} \, \ell^- \, \bar \nu_\ell$ decay mode and its charge conjugate, selected in events that contain a fully reconstructed $B$-meson, using 772 million $e^+ \, e^- \to \Upsilon(4S) \to B \bar B$ events recorded by the Belle detector at KEKB. Unfolded differential decay rates of four kinematic variables fully describing the $\bar B^0 \to D^{*\,+} \, \ell^- \, \bar \nu_\ell$ decay in the $B$-meson rest frame are presented. We measure the total branching fraction $\mathcal{B}( \bar B^0 \to D^{*\,+} \, \ell^- \, \bar \nu_\ell ) = \left(4.95 \pm 0.11 \pm 0.22 \right) \times 10^{-2}$, where the errors are statistical and systematic respectively. The value of $\left|V_{cb} \right|$ is determined to be $\left( 37.4 \pm 1.3 \right) \times 10^{-3}$. Both results are in good agreement with current world averages.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2022

Toward Accurate Modeling of Galaxy Clustering on Small Scales: Constraining the Galaxy-halo Connection with Optimal Statistics

Applying halo models to analyze the small-scale clustering of galaxies is a proven method for characterizing the connection between galaxies and their host halos. Such works are often plagued by systematic errors or limited to clustering statistics that can be predicted analytically. In this work, we employ a numerical mock-based modeling procedure to examine the clustering of Sloan Digital Sky Survey DR7 galaxies. We apply a standard halo occupation distribution (HOD) model to dark matter only simulations with a ΛCDM cosmology. To constrain the theoreStical models, we utilize a combination of galaxy number density and selected scales of the projected correlation function, redshift-space correlation function, group multiplicity function, average group velocity dispersion, mark correlation function, and counts-in-cells statistics. We design an algorithm to choose an optimal combination of measurements that yields tight and accurate constraints on our model parameters. Compared to previous work using fewer clustering statistics, we find a significant improvement in the constraints on all parameters of our halo model for two different luminosity-threshold galaxy samples. Most interestingly, we obtain unprecedented high-precision constraints on the scatter in the relationship between galaxy luminosity and halo mass. However, our best-fit model results in significant tension (>4σ) for both samples, indicating the need to add second-order features to the standard HOD model. To guarantee the robustness of these results, we perform an extensive analysis of the systematic and statistical errors in our modeling procedure, including a first of its kind study of the sensitivity of our constraints to changes in the halo mass function due to baryonic physics.

79 ASTRONOMY AND ASTROPHYSICS↗
NASA NTRS1980

Magnetic field directional discontinuities. I - Minimum variance errors

The paper deals with a statistical analysis of the errors associated with a minimum variance analysis of directional discontinuities by use of an idealized model of these discontinuities and various simulations, and also by an examination of actual Mariner 10 interplanetary magnetic field data. An empirical expression is derived for the magnitude of the error in an estimated discontinuity normal component, relative to the total field across the directional discontinuity. The analysis was performed primarily to aid in differentiating between interplanetary tangential and rotational discontinuities observed by Mariner 10.

Lepping, R. P.↗
DOE OSTI2016

Prediction on Underestimation of Statistical Uncertainty in Monte Carlo Eigenvalue Calculation for Two-dimensional Heterogeneous Color Set Geometry

In a Monte Carlo calculation, statistical uncertainty is inevitably included in the result. The statistical uncertainty is commonly estimated by the central limit theorem without considering correlation among generations. The statistical uncertainty is usually expected to decrease at the inverse square root of the number of neutron histories. However, in a Monte Carlo eigenvalue calculation in a large geometry whose dominance ratio is close to unity, the central limit theorem would not be valid and thus the statistical uncertainty of fission source distribution can be significantly underestimated when inter-cycle correlation is not appropriately taken into account. The true statistical uncertainty can be calculated by statistical processing of the results obtained by multiple Monte Carlo runs using different initial random seeds, but this approach has a drawback of large calculation cost. Therefore, prediction of true statistical uncertainty by alternate approach is desirable. One of the solutions for this issue is an evaluation method of statistical uncertainty based on the eigenfunction expansion and the Autoregressive model (AR model). In this method, the true statistical uncertainty is theoretically derived by applying the AR model to behavior of expansion coefficients of eigenfunction in fission source distribution during cycles. Underestimation ratio of statistical uncertainty of fission source distribution can be predicted by this method. Note that the underestimation ratio of statistical uncertainty is defined by the ratio of estimated error by a Monte Carlo calculation to the true statistical error. In the previous study, the proposed method was verified in a simple condition such as one energy group, one dimensional homogeneous slab geometry. Contributions of this summary are as follows. Firstly, expression of the noise term that is appeared in the AR model is theoretically derived. Secondly, prediction on underestimation ratio of statistical uncertainty is carried out in a more general case, i.e., flux of each fuel cell in 2 x 2 heterogeneous assembly geometry taken from the C5G7 benchmark problem. Through the present study, applicability of the theoretical prediction for underestimation of statistical uncertainty in practical problems will be verified. (authors)

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗
DOE OSTI2016

Constraining the mass–richness relationship of redMaPPer clusters with angular clustering

The potential of using cluster clustering for calibrating the mass–richness relation of galaxy clusters has been recognized theoretically for over a decade. In this paper, we demonstrate the feasibility of this technique to achieve high-precision mass calibration using redMaPPer clusters in the Sloan Digital Sky Survey North Galactic Cap. By including cross-correlations between several richness bins in our analysis, we significantly improve the statistical precision of our mass constraints. The amplitude of the mass–richness relation is constrained to 7 per cent statistical precision by our analysis. However, the error budget is systematics dominated, reaching a 19 per cent total error that is dominated by theoretical uncertainty in the bias–mass relation for dark matter haloes. We confirm the result from Miyatake et al. that the clustering amplitude of redMaPPer clusters depends on galaxy concentration as defined therein, and we provide additional evidence that this dependence cannot be sourced by mass dependences: some other effect must account for the observed variation in clustering amplitude with galaxy concentration. Assuming that the observed dependence of redMaPPer clustering on galaxy concentration is a form of assembly bias, we find that such effects introduce a systematic error on the amplitude of the mass–richness relation that is comparable to the error bar from statistical noise. Finally, the results presented here demonstrate the power of cluster clustering for mass calibration and cosmology provided the current theoretical systematics can be ameliorated.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2026

Robust Design Under Uncertainty in Quantum Error Mitigation

Error mitigation techniques are crucial to achieving near-term quantum advantage. Classical postprocessing of quantum computation outcomes is a popular approach for error mitigation, which includes methods, such as zero noise extrapolation, virtual distillation, and learning-based error mitigation. However, these techniques have limitations due to the propagation of uncertainty resulting from the finite shot number of a quantum measurement. In this work, we introduce general and unbiased methods for quantifying the uncertainty and error of error-mitigated observables based on the strategic sampling of error mitigation outcomes. We then extend our approach to demonstrate the optimization of performance and robustness of error mitigation under uncertainty. To illustrate our methods, we apply them to zero noise extrapolation and Clifford date regression in the ground state of the XY model simulated using depolarizing and International Business Machines Corporation (IBM) Toronto noise models, respectively. In particular, we optimize the choice of noise levels and the allocation of shots for zero noise extrapolation and the distribution of the training circuits for Clifford data regression. While our methods are readily applicable to any postprocessing-based error mitigation approach, in practice they must not be prohibitively expensive—even though they perform optimizations of the error mitigation hyperparameters requiring sampling of a statistical distribution of error mitigation outcomes. By leveraging surrogate-based optimization, we show that our methods can efficiently perform optimal design for a zero noise extrapolation implementation. We then further demonstrate the transferability of learned zero noise extrapolation hyperparameters to other similar circuits.

97 MATHEMATICS AND COMPUTING↗
NASA NTRS1972

Error analysis of bent ray radio occultation measurments

There are two types of experimental measurement errors of the Doppler data associated with the radio occultation, random and systematic. Random errors are due to thermal noise in the transmission channel, and the phase lock loop, and quantization error in the digital circuitry. These are called noise type errors. The systematic errors are due to geometric uncertainty and equipment phase instability. Considered is the amount of uncertainty, due to random measurement errors, in the refractivity profiles reconstructed by this type of indirect sensing experiment. A class of refractivity profiles is defined which approximately fit the set of measured data. Bounds are placed on the extent of this class of solution profiles. To accomplish this, the sensivity of the reconstructed refractivity profiles to errors in the measured quantity and the statistics of the errors in the measurement are examined.

Saintgermain, R. L.↗
NASA NTRS1992

Analyst variability in labeling of unsupervised classifications

Analyst variability in the labeling of unsupervised classifications is tested for Landsat 5 Thematic Mapper image products covering two test sites in southern California. The accuracy of results are tested using samples from a photo interpreted base map of the area. The significance of differences between analysts is indicated by comparing Kappa statistics derived from error matrices. Analyst variability is found to be statistically significant in most cases. Certain analysts provided consistently better results for a given study area or degree of training. This work demonstrates the potential influence of analyst bias on what would otherwise seem to be a fairly objective method and suggests that controls for this subjectivity should be factored into experimental designs.

Mcgwire, Kenneth C.↗
NASA NTRS1982

Optimal GSTDN/TDRSS bit error rate evaluation using limited sample sizes

Statistical studies of telemetry errors were made on data from the Solar Mesosphere Explorer (SME). Examination of frame sync words, as received at the ground station, indicated a wide spread of Bit Error Rates (BER) among stations. A study of the distribution of errors per station pass, however, showed that there was a tendency for the station software to add an even number of spurious errors to the count. A count of wild points in science data, rejecting drop-outs and other system errors, yielded an average random BER of 3.1 x 10 to the -6 with 99% confidence limits of 2.6 and 3.8 x 10 to the -6. The system errors are typically 5 to 100 times more frequent than the truly random errors.

Coffey, R. E.↗