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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 NTRS1981

Airplane wing vibrations due to atmospheric turbulence

The magnitude of error introduced due to wing vibration when measuring atmospheric turbulence with a wind probe mounted at the wing tip was studied. It was also determined whether accelerometers mounted on the wing tip are needed to correct this error. A spectrum analysis approach is used to determine the error. Estimates of the B-57 wing characteristics are used to simulate the airplane wing, and von Karman's cross spectrum function is used to simulate atmospheric turbulence. It was found that wing vibration introduces large error in measured spectra of turbulence in the frequency's range close to the natural frequencies of the wing.

Pastel, R. L.↗

NASA NTRS1988

In-flight inertial guidance alignment

This work reports on an extension of a recent work by Goshen-Meskin and Bar-Itzhack (1988). That work dealt with the observability analysis of inertial-navigation systems during in-flight alignment. The work was confined to the analysis of altitude damped systems; hence, the error model considered was a two-channel model. The present work deals with an undamped three-channel error model. An analysis similar to the previous one is carried out. It is shown that it is possible to fully observe, and thus estimate, all the states of the system. This is in contrast to the previous two-channel system, in which it is impossible to fully observe and estimate all the states of the system. The conclusions of the analysis presented in this paper are verified through covariance simulation which yields identical results.

Bar-Itzhack, I. Y.↗

NASA NTRS1982

Errors in fixed and moving frame of references - Applications for conventional and Doppler radar analysis

Techniques for the correction of errors in Doppler radar scans due to advection effects are presented. A moving frame of reference is shown to be useful in least-squares estimates with stationary observations expressed in scalars or Cartesian coordinates. For non-Cartesian coordinates, such as the deduction of radial velocities from triple Doppler radar data, an integral is defined for accounting for advection effects and consequent coordinate transformations. The multiple radars are necessary for unambiguous characterization of the horizontal wind velocity. A scale analysis is employed to estimate errors with and without the error correction procedure. Improvements in correlations between scans are demonstrated when the error correction method is used.

Tzvi, G.-C.↗

DOE OSTI2021

Subtropical Eastern North Pacific SST bias in earth system models

Karthik Balaguru (PNNL), Luke Van Roekel (LLNL), L. Ruby Leung (PNNL) and Milena Veneziani (LLNL) Abstract: This study systematically evaluates the warm SST bias in the Subtropical Eastern North Pacific (SENP), a problem plaguing most CMIP6 models, using the Energy Exascale Earth System Model version 1 (E3SM). Compared to the model at its standard resolution (1o atmosphere, 30-60 km ocean), the SST bias improves in several regions at high resolution (0.25o atmosphere, 18-6 km ocean) except in subtropical eastern boundary regions, such as the SENP. A mixed layer heat budget analysis reveals that errors in the surface radiative fluxes and horizontal heat advection are primarily responsible for the bias. Analysis of HighResMIP models indicates that the lack of improvement in the SENP SST bias with resolution is not native to E3SM alone. A larger CMIP6 inter-model correlation of SST bias with biases in surface winds than radiation highlights the important role of large-scale circulation biases in the SENP SST bias in coupled models.

Balaguru, Karthik↗

NASA NTRS2013

The Role of Model and Initial Condition Error in Numerical Weather Forecasting Investigated with an Observing System Simulation Experiment

A series of experiments that explore the roles of model and initial condition error in numerical weather prediction are performed using an observing system simulation experiment (OSSE) framework developed at the National Aeronautics and Space Administration Global Modeling and Assimilation Office (NASA/GMAO). The use of an OSSE allows the analysis and forecast errors to be explicitly calculated, and different hypothetical observing networks can be tested with ease. In these experiments, both a full global OSSE framework and an 'identical twin' OSSE setup are utilized to compare the behavior of the data assimilation system and evolution of forecast skill with and without model error. The initial condition error is manipulated by varying the distribution and quality of the observing network and the magnitude of observation errors. The results show that model error has a strong impact on both the quality of the analysis field and the evolution of forecast skill, including both systematic and unsystematic model error components. With a realistic observing network, the analysis state retains a significant quantity of error due to systematic model error. If errors of the analysis state are minimized, model error acts to rapidly degrade forecast skill during the first 24-48 hours of forward integration. In the presence of model error, the impact of observation errors on forecast skill is small, but in the absence of model error, observation errors cause a substantial degradation of the skill of medium range forecasts.

Model Error↗

NASA NTRS1982

Tolerance analysis of optical telescopes using coherent addition of wavefront errors

A near diffraction-limited telescope requires that tolerance analysis be done on the basis of system wavefront error. One method of analyzing the wavefront error is to represent the wavefront error function in terms of its Zernike polynomial expansion. A Ramsey-Korsch ray trace package, a computer program that simulates the tracing of rays through an optical telescope system, was expanded to include the Zernike polynomial expansion up through the fifth-order spherical term. An option to determine a 3 dimensional plot of the wavefront error function was also included in the Ramsey-Korsch package. Several assimulation runs were analyzed to determine the particular set of coefficients in the Zernike expansion that are effected by various errors such as tilt, decenter and despace. A 3 dimensional plot of each error up through the fifth-order spherical term was also included in the study. Tolerance analysis data are presented.

Davenport, J. W.↗

NASA NTRS2016

The Viability of Trajectory Analysis for Diagnosing Dynamical and Chemical Influences on Ozone Concentrations in the UTLS

The viability of trajectory analysis for diagnosing the interplay between chemistry and dynamics is investigated by comparing ozone mixing ratios modelled using air-parcel pathways to values observed along flight tracks during ATTREX (Airborne Tropical TRopopause EXperiment). Trajectories are initiated at the locations of ozone observations and tracked backward in time to their sources at termini of backward trajectories. The modelled values of ozone utilize 3-dimensional analysis fields from WACCM (Whole Atmosphere Community Climate Model) (a chemical-climate model with dynamical fields nudged towards MERRA (Modern-Era Retrospective Analysis and Research Applications) reanalysis) and ERA-interim (product of ECMWF - the European Centre for Medium-Range Weather Forecasts) to determine source mixing ratios with chemical production and loss terms derived from the ozone chemistry used in WACCM. A statistical base of modelled ozone is constructed with 6 trajectory platforms (adiabatic, diabatic, and kinematic forced by ERA-interim and MERRA), two chemical models (WACCM chemistry and no chemistry), and 4 trajectory lengths (5, 10, 20, and 30 days). Linear regression is employed to separate systematic errors from random errors and to characterize the impact of source mixing ratios, path length, vertical motion, and chemistry on modelled ozone errors. Errors in the analysis ozone fields are large, if not dominant, contributors to model error. Random errors are particularly large for point-by-point comparisons, however averaging over 800 km (75 minutes) flight segments substantially reduces random error and exposes systematic errors. Of the two analysis ozone data sets, WACCM, which incorporates detailed chemistry, provides the smaller systematic errors while ERA-interim, which has crude chemistry but assimilates observational data, has the smaller random errors. Of the different trajectory platforms, adiabatic calculations produce the smaller random errors (irrespective of the use of chemistry) but both vertical motion and chemistry are required to optimally reduce systematic errors. These results suggest that meaningful analysis of dynamical and chemical interactions that control ozone mixing ratios are viable on spatial scales larger than a few reanalysis grid spaces, that errors in the analyzed ozone data sets are large but not prohibitively so, and that vertical velocities and heating rates from reanalysis data, while problematic, contain useful information [on the ozone concentrations in the UTLS (Upper Troposphere/Lower Stratosphere)].

ozone↗

NASA NTRS1993

Experimental analysis of computer system dependability

This paper reviews an area which has evolved over the past 15 years: experimental analysis of computer system dependability. Methodologies and advances are discussed for three basic approaches used in the area: simulated fault injection, physical fault injection, and measurement-based analysis. The three approaches are suited, respectively, to dependability evaluation in the three phases of a system's life: design phase, prototype phase, and operational phase. Before the discussion of these phases, several statistical techniques used in the area are introduced. For each phase, a classification of research methods or study topics is outlined, followed by discussion of these methods or topics as well as representative studies. The statistical techniques introduced include the estimation of parameters and confidence intervals, probability distribution characterization, and several multivariate analysis methods. Importance sampling, a statistical technique used to accelerate Monte Carlo simulation, is also introduced. The discussion of simulated fault injection covers electrical-level, logic-level, and function-level fault injection methods as well as representative simulation environments such as FOCUS and DEPEND. The discussion of physical fault injection covers hardware, software, and radiation fault injection methods as well as several software and hybrid tools including FIAT, FERARI, HYBRID, and FINE. The discussion of measurement-based analysis covers measurement and data processing techniques, basic error characterization, dependency analysis, Markov reward modeling, software-dependability, and fault diagnosis. The discussion involves several important issues studies in the area, including fault models, fast simulation techniques, workload/failure dependency, correlated failures, and software fault tolerance.

Iyer, Ravishankar, K.↗

NASA NTRS1995

Plasma gradient effets on doubel-probe measurements in the magnetosphere

The effects on double-probe electric field measurements induced by electron density and temperature gradients are investigated. We show that on some occasions such gradients may lead to marked spurious electric fields if the probes are assumed to lie at the same probe potential with repect to the plasma. The use of a proper bias current will decrease the magnitude of such an error. When the probes are near the plasma potential, the magnitude of these error signals, delta Epsilon, can vary as delta Epsilon approx. T(sub e)(Delta n(sub e)/n(sub e)) + 0.5 Delta T(sub e), where T(sub e) is the electron temperature, Delta n(sub e)/ n(sub e) the relative electron density variation between the two sensors, and Delta T(sub e) the electron temperature difference between the two sensors. This not only implies that the error signals will increase linearly with the density variations but also that such signatures grow with Delta T(sub e) i.e., such effects are 10 times larger in a 10-eV plasma than in a 1-eV plasma. This type of error is independent of the probe separation distance provided the gradient scale length is much larger than the distance. The largest errors occur when the probes are near to the plasma potential. During the crossing of a small structure (e.g, a double layer) the error signal appears as a bipolar signature. Our analysis shows that errors in double-probe measurements caused by plasma gradients are not significant at large scale (much greater than 1 km) plasma boundaries, and may only be important in cases where small-scale (less than 1 km), internal gradient structures exist. Bias currents tailored for each plasma parameter regime (i.e., variable bias current) would improve the double-probe response to gradient effects considerably.

Laakso, Harri↗

NASA NTRS2018

Adjoint Estimation of Observation Impact Explored with an Observing System Simulation Experiment

In an Observing System Simulation Experiment, the full, true state of the simulated atmosphere is known. This knowledge allows the direct calculation of analysis and forecast errors, and also may be used in conjunction with an adjoint tool to calculate metrics that are unachievable in the real world. For example, the errors that result from the use of the analysis state as verification when running adjoint calculations of observation impact on a forecast can be quantified. The adjoint itself can also be used to operate on the analysis state rather than on the forecast state. Results from these and other adjoint experiments using the NASA/GMAO OSSE framework will be presented.

Prive, Nikki↗

DOE OSTI2025

Quantification of regional net CO 2 flux errors in the Orbiting Carbon Observatory-2 (OCO-2) v10 model intercomparison project (MIP) ensemble using airborne measurements

Inverse model intercomparison projects (MIPs) provide a chance to assess the uncertainties in inversion estimates arising from various sources. However, accurately quantifying ensemble CO 2 flux errors remains challenging and often relies on the ensemble spread. This study proposes a method for quantifying the errors in regional net surface–atmosphere CO 2 flux estimates from models taken from the Orbiting Carbon Observatory-2 (OCO-2) v10 MIP by using independent airborne CO 2 measurements for the period 2015–2017. We first calculate the root mean square error (RMSE) between the ensemble mean of posterior CO 2 concentrations and airborne observations and then isolate the CO 2 concentration errors caused solely by the ensemble mean of posterior net fluxes by subtracting the observation, representation, and transport errors from seven regions. Our analysis reveals that the flux errors projected onto CO 2 space account for 55 %–85 % of the regional average RMSE over the 3 years, ranging from 0.88 to 1.91 ppm. In five regions, the error estimates based on observations exceed those computed from the ensemble spread of posterior fluxes by a factor of 1.33–1.93, implying an underestimation of the actual flux errors, while their magnitudes are comparable in two regions. The adjoint sensitivity analysis identifies that the underestimation of flux errors is prominent where the magnitudes of fossil fuel emissions exceed those of terrestrial-biosphere fluxes by a factor of 3–31 over the 3 years. This suggests the presence of systematic biases in the inversion estimates associated with errors in the prescribed fossil fuel emissions common to all models. Our study emphasizes the value of airborne measurements for quantifying regional errors in ensemble net CO 2 flux estimates.

54 ENVIRONMENTAL SCIENCES↗

DOE OSTI2019

Impact of non-Maxwellian electron velocity distribution functions on inferred plasma parameters in collective Thomson scattering

Optical collective Thomson scattering provides precise density and temperature measurements in numerous plasma-physics experiments. The accuracy of such measurements depends on the core assumption that the underlying electron distribution functions in under-dense laser-produced plasmas are Maxwellian. A statistically based, quantitative analysis of the errors in the measured electron density and temperature is presented when synthetic data calculated using a non-Maxwellian electron distribution function is fit assuming a Maxwellian electron distribution. Such analysis can lead to errors of up to 50% in temperature and 30% in density, in the specific case of super-Gaussian distributions characteristic of inverse bremsstrahlung heating. Furthermore including the proper family of non-Maxwellian electron distribution functions, as a fitting parameter, in Thomson-scattering analysis removes the model-dependent errors in the inferred parameters at a minimal cost to the statistical uncertainty.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2022

QGLab v0.0.1

A software program for experimenting with holographic teleportation protocol on quantum computers. The code implements the protocol that was proposed in https://arxiv.org/abs/1911.06314. The code is an end-to-end software solution that facilitates conducting the holographic teleportation experiments on state-of-the-art and emergent generations of QPUs supported by the Qiskit and tket SDKs. The code bundles all stages of an experiment as a single configurable workflow allowing faster development and experimentation cycles. Features: 1. Easy switching between Qiskit and tket quantum compilers. 2. Semi-automatic facilities for finding optimal compilation solutions beyond what Qiskit and tket provide by default. 3. Experiment resolution scaling (based on automatic jobs' batching). 4. Automatic experiment scaling over qubits. 5. Automatic readout error mitigation. 6. Automatic reproducibility analysis. 7. Standalone error-mitigation tools (randomized compiling, mitigation with estimation circuits, zero-noise extrapolation)

Shapoval, Illya↗

DOE OSTI2021

System Calibration Including Time Delay Estimation for GNSS/INS-Assisted Pushbroom Scanners Onboard UAV Platforms

Unmanned aerial vehicles (UAVs ) equipped with imaging sensors and integrated global navigation satellite system/inertial navigation system (GNSS/INS ) units are used for numerous applications. Deriving reliable 3D coordinates from such UAVs is contingent on accurate geometric calibration, which encompasses the estimation of mounting parameters and synchronization errors. Through a rigorous impact analysis of such systematic errors, this article proposes a direct approach for spatial and temporal calibration (estimating system parameters through a bundle adjustment procedure) of a GNSS/INS -assisted pushbroom scanner onboard a UAV platform. The calibration results show that the horizontal and vertical accuracies are within the ground sampling distance of the sensor. Unlike for frame camera systems, this article also shows that the indirect approach is not a feasible solution for pushbroom scanners due to their limited ability for decoupling system parameters. This finding provides further support that the direct approach is recommended for spatial and temporal calibration of UAV pushbroom scanner systems.

47 OTHER INSTRUMENTATION↗

NASA NTRS1983

Thermal analysis considerations for large space structures

A number of issues and needs relative to thermal analysis of large space structures and space stations are discussed. Some indications of trends in the Langley thermal-structural analysis research program consistent with the issues and needs are also presented. The main heat transfer mechanism in space is radiation; consequently, there is a need for a strong thrust on improved radiation analysis capability. Also the important interactions among temperatures, deformations, and controls need to be accounted for. Finite element analysis capability seems to be lagging behind lumped-parameter capability or heat pipe analysis. The Langley plan will include improving radiation analysis capability, evaluating the errors involved in certain approximate analysis and modeling techniques for large space trusses, and continuing the development of integrated thermal-structural finite elements with an emphasis on radiation heat transfer. Work will be initiated to develop finite element analysis techniques for heat pipes. Finally, optimization research activities will be oriented toward methods to design flexible orbiting structures to account for thermal and thermal deformation requirements.

Adelman, H. M.↗

NASA NTRS1990

Failure analysis and modeling of a multicomputer system

This thesis describes the results of an extensive measurement-based analysis of real error data collected from a 7-machine DEC VaxCluster multicomputer system. In addition to evaluating basic system error and failure characteristics, we develop reward models to analyze the impact of failures and errors on the system. The results show that, although 98 percent of errors in the shared resources recover, they result in 48 percent of all system failures. The analysis of rewards shows that the expected reward rate for the VaxCluster decreases to 0.5 in 100 days for a 3 out of 7 model, which is well over a 100 times that for a 7-out-of-7 model. A comparison of the reward rates for a range of k-out-of-n models indicates that the maximum increase in reward rate (0.25) occurs in going from the 6-out-of-7 model to the 5-out-of-7 model. The analysis also shows that software errors have the lowest reward (0.2 vs. 0.91 for network errors). The large loss in reward rate for software errors is due to the fact that a large proportion (94 percent) of software errors lead to failure. In comparison, the high reward rate for network errors is due to fast recovery from a majority of these errors (median recovery duration is 0 seconds).

Subramani, Sujatha Srinivasan↗

DOE OSTI2026

Unsupervised anomaly detection in MeV ultrafast electron diffraction

MeV ultrafast electron diffraction (MUED) is a pump-probe technique used to study the dynamic structural evolution of materials. An ultrashort laser pulse triggers structural changes, which are then probed by an ultrashort relativistic electron beam. To overcome low signal-to-noise ratios, diffraction patterns are averaged over thousands of shots. However, shot-to-shot instabilities in the electron beam can distort individual patterns, introducing uncertainty. Improving MUED accuracy requires detecting and removing these anomalous patterns from large datasets. In this work, we developed a fully unsupervised methodology for the detection of anomalous diffraction patterns. Using a convolutional autoencoder, we calculate the reconstruction mean squared error of the diffraction patterns. Based on the statistical analysis of this error, we provide the user an estimation of the probability that the pattern is normal, which also allows a posterior visual inspection of the images that are difficult to classify. This method has been trained with only 100 diffraction patterns and tested on 1521 patterns, resulting in a false positive rate between 0.2% and 0.4%, with a training time of 10 s per image and a test time of about 1 s per image. Here, the proposed methodology can also be applied to other diffraction techniques in which large datasets are collected that include faulty images due to instrumental instabilities.

43 PARTICLE ACCELERATORS↗