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All sourcesNASA NTRSDOE OSTI
NASA NTRS1987

Order reduction in linear state estimation under performance constraints

The design and analysis of minimal-order state estimators for possibly time-varying linear systems, under constraints on the maximal allowable mean-square error, are considered. A global lower bound on the optimal error is derived, along with a lower bound on the minimal estimator order, needed for meeting the performance constraint. The ideal reduced-order estimator which satisfies the lower bound is derived, along with conditions for its realizability. When the ideal estimator is not realizable, its structure forms a suboptimal estimator, which maintains, in some sense, a local optimality property and is called the pseudoideal estimator. The mean-square error of the pseudoideal estimator defines upper bounds on the optimal error and on the estimator order needed for meeting the performance constraint. The lower and the upper bounds on the order define a reduced search set for the design problem. When the distance between the ideal and the pseudoideal estimators is sufficiently small in a certain numerical sense, the pseudoideal estimator may be considered optimal for practical purposes.

Baram, Yoram↗
NASA NTRS1998

Carbon-Water-Energy Relations for Selected River Basins

A biophysical process-based model was run using satellite, assimilated and ancillary data for four years (1987-1990) to calculate components of total evaporation (transpiration, interception, soil and snow evaporation), net radiation, absorbed photosynthetically active radiation and net primary productivity over the global land surface. Satellite observations provided fractional vegetation cover, solar and photosynthetically active radiation incident of the surface, surface albedo, fractional cloud cover, air temperature and vapor pressure. The friction velocity and surface air pressure are obtained from a four dimensional data assimilation results, while precipitation is either only surface observations or a blended product of surface and satellite observations. All surface and satellite data are monthly mean values; precipitation has been disaggregated into daily values. All biophysical parameters of the model are prescribed according to published records. From these global land surface calculations results for river basins are derived using digital templates of basin boundaries. Comparisons with field observations (micrometeorologic, catchment water balance, biomass production) and atmospheric water budget analysis for monthly evaporation from six river basins have been done to assess errors in the calculations. Comparisons are also made with previous estimates of zonal variations of evaporation and net primary productivity. Efficiencies of transpiration, total evaporation and radiation use, and evaporative fraction for selected river basins will be presented.

Choudhury, B. J.↗
NASA NTRS2021

Validation of Small Satellite Dynamics Simulation Modules using ASTERIA Flight Data

ASTERIA (Arcsecond Space Telescope Enabling Research in Astrophysics) was a CubeSat space telescope that operated in low-Earth orbit, having been deployed from the International Space Station in 2017. The spacecraft has achieved sub-arcsecond pointing stability and millikelvin thermal stability over 20-minute observations. A key enabling feature of the ASTERIA mission is the low level of pointing error that has been demonstrated under ASTERIA’s fine pointing control mode. Prior to launch, the ASTERIA mission performed analysis and simulations to estimate the in-flight pointing performance. This analysis used reaction wheel models provided by JPL’s Small Satellite Dynamics Testbed (SSDT), which had performed Kistler table testing to characterize the jitter caused by the reaction wheels of the Blue Canyon Technologies XACT attitude control unit within ASTERIA. These models were subsequently incorporated into the SSDT simulation. The main source of jitter, the high-frequency attitude disturbance over the camera exposure time, on ASTERIA is the set of rotating reaction wheels that are used for maintaining fine pointing during observations. The reaction wheels impart disturbance forces and torques continuously that cause unwanted motion during imaging. Increased jitter consequently leads to blurring of the image. Therefore, to benefit all SmallSat missions devoted to photometric or spectroscopic astrophysics applications, an on-orbit flight data acquisition and jitter testing campaign was performed in an attempt to help validate the SSDT’s simulation models. This paper describes the process used to validate several simulation models and attempt to characterize the ASTERIA jitter by analyzing the size of the resulting spot size for the target stars as a function of wheel speed, having commanded four wheel speeds for each of three stars of known brightness. After summarizing the on-orbit observation and jitter level measurement process, this paper compares the results obtained from the flight operational environment to the corresponding set of simulation jitter levels. Though the flight data obtained during this experiment was not sufficient to validate the simulation’s jitter model, other models have been validated with flight data, including the magnetic field, orbit propagation, sun position, and long-duration orbit decay models, which may be used by all other projects that use the SSDT’s simulation to increase system capability knowledge.

Mohan, Swati↗
DOE OSTI2022

Angular systematics-free cosmological analysis of galaxy clustering in configuration space

ABSTRACT Galaxy redshift surveys are subject to incompleteness and inhomogeneous sampling due to the various constraints inherent to spectroscopic observations. This can introduce systematic errors on the summary statistics of interest, which need to be mitigated in cosmological analysis to achieve high accuracy. Standard practices involve applying weighting schemes based on completeness estimates across the survey footprint, possibly supplemented with additional weighting schemes accounting for density-dependent effects. In this work, we concentrate on pure angular systematics and describe an alternative approach consisting in analysing the galaxy two-point correlation function where angular modes are nulled. By construction, this procedure removes all possible known and unknown sources of angular observational systematics, but also part of the cosmological signal. We use a modified Landy–Szalay estimator for the two-point correlation function that relies on an additional random catalogue where angular positions are randomly drawn from the galaxy catalogue, and provide an analytical model to describe this modified statistic. We test the model by performing an analysis of the full anisotropic clustering in mock catalogues of luminous red and emission-line galaxies at 0.43 < z < 1.1. We find that the model fully accounts for the modified correlation function in redshift space, without introducing new nuisance parameters. The derived cosmological parameters from the analysis of baryon acoustic oscillations and redshift-space distortions display slightly larger statistical uncertainties, mostly for the growth rate of structure parameter fσ8 that exhibits a $50{{\ \rm per\ cent}}$ statistical error increase, but free from angular systematic error.

79 ASTRONOMY AND ASTROPHYSICS↗
NASA NTRS2001

Diagnosing Tropical Divergent Circulations From Satellite-Derived Diabatic Forcing and Variational Integral Constraints

Large-scale divergent circulations are part of the atmospheric dynamic response to diabatic heating from condensation, radiative processes, and surface energy fluxes. Vertical motion and the associated divergent wind is thus intimately tied to the hydrologic cycle and the global beat balance. Despite its importance, the divergent circulation is too small in comparison to the rotational flow to measure directly with any accuracy. Vertical motions are recovered diagnostically from reanalyses and, as such, are subject to shortcomings in model physics, numerics, and data availability. While reanalysis estimates of tropical divergent circulations are much improved over those from the Global Weather Experiment, there are still substantial differences between products from operational centers. This is because these circulations are still forced largely by model physics and only secondarily by observations. In order to produce a refined estimate of tropical divergence and its interannual variability we have used a number of remotely-sensed data sets along with variational constraints to improve upon reanalysis estimates. Among these are: precipitation from SSM/I and GPCP, TOVS Path-A vertical cloud distributions; ISCCP radiative cooling rates; TOA radiative fluxes from ERBS, surface radiative fluxes from the SRB project, and surface latent and sensible flux estimates from SSM/I. The TOVS Path-A data constrain the divergent outflow in precipitating regions to have the same vertical structure as observed cloudiness. Using integral constraints for moisture, heat, and mass balance, we retrieve consistent divergent wind flows. We examine the ability of this type analysis to capture regional details of ENSO related perturbations to the divergent wind and associated tropical energy balance. Precipitation from satellite is found to be the major constraint in supplying this horizontal structure. We also consider the ability of this analysis to quantify integrated (land vs. ocean) fluctuations in the global monsoonal flow and energy balance. This depends, of course, on the error characteristics of the data constraints. Some estimate of these properties and their relative importance is provided.

Robertson, Franklin R.↗
NASA NTRS2002

On the Choice of Variable for Atmospheric Moisture Analysis

The implications of using different control variables for the analysis of moisture observations in a global atmospheric data assimilation system are investigated. A moisture analysis based on either mixing ratio or specific humidity is prone to large extrapolation errors, due to the high variability in space and time of these parameters and to the difficulties in modeling their error covariances. Using the logarithm of specific humidity does not alleviate these problems, and has the further disadvantage that very dry background estimates cannot be effectively corrected by observations. Relative humidity is a better choice from a statistical point of view, because this field is spatially and temporally more coherent and error statistics are therefore easier to obtain. If, however, the analysis is designed to preserve relative humidity in the absence of moisture observations, then the analyzed specific humidity field depends entirely on analyzed temperature changes. If the model has a cool bias in the stratosphere this will lead to an unstable accumulation of excess moisture there. A pseudo-relative humidity can be defined by scaling the mixing ratio by the background saturation mixing ratio. A univariate pseudo-relative humidity analysis will preserve the specific humidity field in the absence of moisture observations. A pseudorelative humidity analysis is shown to be equivalent to a mixing ratio analysis with flow-dependent covariances. In the presence of multivariate (temperature-moisture) observations it produces analyzed relative humidity values that are nearly identical to those produced by a relative humidity analysis. Based on a time series analysis of radiosonde observed-minus-background differences it appears to be more justifiable to neglect specific humidity-temperature correlations (in a univariate pseudo-relative humidity analysis) than to neglect relative humidity-temperature correlations (in a univariate relative humidity analysis). A pseudo-relative humidity analysis is easily implemented in an existing moisture analysis system, by simply scaling observed-minus background moisture residuals prior to solving the analysis equation, and rescaling the analyzed increments afterward.

Dee, Dick P.↗
NASA NTRS2001

Sensitivity of the Tropical Atmospheric Energy Balance to ENSO-Related SST Changes: Comparison of Climate Model Simulations to Observed Responses

This paper focuses on how fresh water and radiative fluxes over the tropical oceans change during ENSO warm and cold events and how these changes affect the tropical energy balance. At present, ENSO remains the most prominent known mode of natural variability at interannual time scales. While this natural perturbation to climate is quite distinct from possible anthropogenic changes in climate, adjustments in the tropical water and energy budgets during ENSO may give insight into feedback processes involving water vapor and cloud feedbacks. Although great advances have been made in understanding this phenomenon and realizing prediction skill over the past decade, our ability to document the coupled water and energy changes observationally and to represent them in climate models seems far from settled (Soden, 2000 J Climate). In a companion paper we have presented observational analyses, based principally on space-based measurements which document systematic changes in rainfall, evaporation, and surface and top-of-atmosphere (TOA) radiative fluxes. Here we analyze several contemporary climate models run with observed SSTs over recent decades and compare SST-induced changes in radiation, precipitation, evaporation, and energy transport to observational results. Among these are the NASA / NCAR Finite Volume Model, the NCAR Community Climate Model, the NCEP Global Spectral Model, and the NASA NSIPP Model. Key disagreements between model and observational results noted in the recent literature are shown to be due predominantly to observational shortcomings. A reexamination of the Langley 8-Year Surface Radiation Budget data reveals errors in the SST surface longwave emission due to biased SSTs. Subsequent correction allows use of this data set along with ERBE TOA fluxes to infer net atmospheric radiative heating. Further analysis of recent rainfall algorithms provides new estimates for precipitation variability in line with interannual evaporation changes inferred from the da Silva, Young, Levitus COADS analysis. The overall results from our analysis suggest an increase (decrease) of the hydrologic cycle during ENSO warm (cold) events at the rate of about 5 W/sq m per K of SST change. Model results agree reasonably well with this estimate of sensitivity. This rate is slightly less than that which would be expected for constant relative humidity over the tropical oceans. There remain, however, significant quantitative uncertainties in cloud forcing changes in the models as compared to observations. These differences are examined in relationship to model convection and cloud parameterizations Analysis of the possible sampling and measurement errors compared to systematic model errors is also presented.

Robertson, Franklin R.↗
NASA NTRS2018

Comparison of MERRA-2 and ECCO-V4 Ocean Surface Heat Fluxes: Consequences of Different Forcing Feedbacks on Ocean Circulation and Implications for Climate Data Assimilation

Forcing ocean models with reanalysis data is a common practice in ocean modeling. As part of this practice, prescribed atmospheric state variables and interactive ocean SST (Sea Surface Temperature) are used to calculate fluxes between the ocean and the atmosphere. When forcing an ocean model with reanalysis fields, errors in the reanalysis data, errors in the ocean model and errors in the forcing formulation will generate a different solution compared to other ocean reanalysis solutions (which also have their own errors). As a first step towards a consistent coupled ocean-atmosphere reanalysis, we compare surface heat fluxes from a state-of-the-art atmospheric reanalysis, the Modern-Era Retrospective analysis for Research and Applications, Version 2 (MERRA-2), to heat fluxes from a state-of-the-art oceanic reanalysis, the Estimating the Circulation and Climate of the Ocean Version 4, Release 2 (ECCO-v4). Then, we investigate the errors associated with the MITgcm (Massachusetts Institute of Technology general circulation model) ocean model in its ECCO-v4 ocean reanalysis configuration (1992-2011) when it is forced with MERRA- 2 atmospheric reanalysis fields instead of with the ECCO-v4 adjoint optimized ERA-interim state variables. This is done by forcing ECCO-v4 ocean with and without feedbacks from MERRA-2 related to turbulent fluxes of heat and moisture and the outgoing long wave radiation. In addition, we introduce an intermediate forcing method that includes only the feedback from the interactive outgoing long wave radiation. The resulting ocean circulation is compared with ECCO-v4 reanalysis and in-situ observations. We show that, without feedbacks, imbalances in the energy and the hydrological cycles of MERRA-2 (which are directly related to the fact it was created without interactive ocean) result in considerable SST drifts and a large reduction in sea level. The bulk formulae and interactive outgoing long wave radiation, although providing air-sea feedbacks and reducing model-data misfit, strongly relax the ocean to observed SST and may result in unwanted features such as large change in the water budget. These features have implications in a desired forcing recipe to be used. The results strongly and unambiguously argue for next generation data assimilation climate studies to involve fully coupled systems.

MERRA-2↗
NASA NTRS2000

A Posteriori Error Estimation for Finite Volume and Finite Element Approximations Using Broken Space Approximation

We consider a posteriori error estimates for finite volume and finite element methods on arbitrary meshes subject to prescribed error functionals. Error estimates of this type are useful in a number of computational settings: (1) quantitative prediction of the numerical solution error, (2) adaptive meshing, and (3) load balancing of work on parallel computing architectures. Our analysis recasts the class of Godunov finite volumes schemes as a particular form of discontinuous Galerkin method utilizing broken space approximation obtained via reconstruction of cell-averaged data. In this general framework, weighted residual error bounds are readily obtained using duality arguments and Galerkin orthogonality. Additional consideration is given to issues such as nonlinearity, efficiency, and the relationship to other existing methods. Numerical examples are given throughout the talk to demonstrate the sharpness of the estimates and efficiency of the techniques. Additional information is contained in the original.

Barth, Timothy J.↗
DOE OSTI2024

Analyzing Prospects for Quantum Advantage in Topological Data Analysis

Lloyd [Nat. Commun. , 10138 (2016)] were first to demonstrate the promise of quantum algorithms for computing Betti numbers, a way to characterize topological features of data sets. Here, we propose, analyze, and optimize an improved quantum algorithm for topological data analysis (TDA) with reduced scaling, including a method for preparing Dicke states based on inequality testing, a more efficient amplitude estimation algorithm using Kaiser windows, and an optimal implementation of eigenvalue projectors based on Chebyshev polynomials. We compile our approach to a fault-tolerant gate set and estimate constant factors in the Toffoli complexity. Our analysis reveals that superquadratic quantum speedups are only possible for this problem when targeting a multiplicative error approximation and the Betti number grows asymptotically. Further, we propose a dequantization of the quantum TDA algorithm that shows that having exponentially large dimension and Betti number are necessary, but insufficient conditions, for superpolynomial advantage. We then introduce and analyze specific problem examples which have parameters in the regime where superpolynomial advantages may be achieved, and argue that quantum circuits with tens of billions of Toffoli gates can solve seemingly classically intractable instances. Published by the American Physical Society 2024

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2021

Extreme metrics from large ensembles: investigating the effects of ensemble size on their estimates

Abstract. We consider the problem of estimating the ensemble sizes required to characterize the forced component and the internal variability of a number of extreme metrics. While we exploit existing large ensembles, our perspective is that of a modeling center wanting to estimate a priori such sizes on the basis of an existing small ensemble (we assume the availability of only five members here). We therefore ask if such a small-size ensemble is sufficient to estimate accurately the population variance (i.e., the ensemble internal variability) and then apply a well-established formula that quantifies the expected error in the estimation of the population mean (i.e., the forced component) as a function of the sample size n, here taken to mean the ensemble size. We find that indeed we can anticipate errors in the estimation of the forced component for temperature and precipitation extremes as a function of n by plugging into the formula an estimate of the population variance derived on the basis of five members. For a range of spatial and temporal scales, forcing levels (we use simulations under Representative Concentration Pathway 8.5) and two models considered here as our proof of concept, it appears that an ensemble size of 20 or 25 members can provide estimates of the forced component for the extreme metrics considered that remain within small absolute and percentage errors. Additional members beyond 20 or 25 add only marginal precision to the estimate, and this remains true when statistical inference through extreme value analysis is used. We then ask about the ensemble size required to estimate the ensemble variance (a measure of internal variability) along the length of the simulation and – importantly – about the ensemble size required to detect significant changes in such variance along the simulation with increased external forcings. Using the F test, we find that estimates on the basis of only 5 or 10 ensemble members accurately represent the full ensemble variance even when the analysis is conducted at the grid-point scale. The detection of changes in the variance when comparing different times along the simulation, especially for the precipitation-based metrics, requires larger sizes but not larger than 15 or 20 members. While we recognize that there will always exist applications and metric definitions requiring larger statistical power and therefore ensemble sizes, our results suggest that for a wide range of analysis targets and scales an effective estimate of both forced component and internal variability can be achieved with sizes below 30 members. This invites consideration of the possibility of exploring additional sources of uncertainty, such as physics parameter settings, when designing ensemble simulations.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2024

Multi-Tiered Estimation for Correlation Spectroscopy in 3D (MTECS3D) v0.1

This innovative software estimates rotational diffusion coefficients of particles from X-ray photon correlation spectroscopy (XPCS) data of monodispersed particle systems. It is the first method capable of extracting rotational diffusion information from three-dimensional particle systems using XPCS. Using the angular-temporal cross-correlation of the XPCS images, this software is able to estimate the rotational diffusion coefficients with only a few percent relative errors while requiring minimal prior knowledge of particle structures. This software enhances XPCS analysis capabilities, allowing researchers to study translational and rotational Brownian dynamics of particles in suspension across various temporal and spatial scales.

Hu, Zixi↗
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 NTRS1990

Computation of the factorized error covariance of the difference between correlated estimators

A state estimation problem where some of the measurements may be common to two or more data sets is considered. Two approaches for computing the error covariance of the difference between filtered estimates (for each data set) are discussed. The first algorithm is based on postprocessing of the Kalman gain profiles of two correlated estimators. It uses UD factors of the covariance of the relative error. The second algorithm uses a square root information filter applied to relative error analysis. In the absence of process noise, the square root information filter is computationally more efficient and more flexible than the Kalman gain (covariance update) method. Both the algorithms (covariance and information matrix based) are applied to a Venus orbiter simulation, and their performances are compared.

Wolff, Peter J.↗
NASA NTRS2000

Optimal Reflectance, Transmittance, and Absorptance Wavebands and Band Ratios for the Estimation of Leaf Chlorophyll Concentration

The present study utilized regression analysis to identify: wavebands and band ratios within the 400-850 nm range that could be used to estimate total chlorophyll concentration with minimal error; and simple regression models that were most effective in estimating chlorophyll concentrations were measured for two broadleaved species, a broadleaved vine, a needle-leaved conifer, and a representative of the grass family.Overall, reflectance, transmittance, and absorptance corresponded most precisely with chlorophyll concentration at wavelengths near 700 nm, although regressions were strong as well in the 550-625 nm range.

Carter, Gregory A.↗
NASA NTRS2006

SSC Geopositional Assessment of the Advanced Wide Field Sensor

The geopositional accuracy of the standard geocorrected product from the Advanced Wide Field Sensor (AWiFS) was evaluated using digital orthophoto quarter quadrangles and other reference sources of similar accuracy. Images were analyzed from summer 2004 through spring 2005. Forty to fifty check points were collected manually per scene and analyzed to determine overall circular error, estimates of horizontal bias, and other systematic errors. Measured errors were somewhat higher than the specifications for the data, but they were consistent with the analysis of the distributing vendor.

Ross, Kenton↗
NASA NTRS2011

System Identification Applied to Dynamic CFD Simulation and Wind Tunnel Data

Demanding aerodynamic modeling requirements for military and civilian aircraft have provided impetus for researchers to improve computational and experimental techniques. Model validation is a key component for these research endeavors so this study is an initial effort to extend conventional time history comparisons by comparing model parameter estimates and their standard errors using system identification methods. An aerodynamic model of an aircraft performing one-degree-of-freedom roll oscillatory motion about its body axes is developed. The model includes linear aerodynamics and deficiency function parameters characterizing an unsteady effect. For estimation of unknown parameters two techniques, harmonic analysis and two-step linear regression, were applied to roll-oscillatory wind tunnel data and to computational fluid dynamics (CFD) simulated data. The model used for this study is a highly swept wing unmanned aerial combat vehicle. Differences in response prediction, parameters estimates, and standard errors are compared and discussed

Murphy, Patrick C.↗
NASA NTRS2012

View Angle Effects on MODIS Snow Mapping in Forests

Binary snow maps and fractional snow cover data are provided routinely from MODIS (Moderate Resolution Imaging Spectroradiometer). This paper investigates how the wide observation angles of MODIS influence the current snow mapping algorithm in forested areas. Theoretical modeling results indicate that large view zenith angles (VZA) can lead to underestimation of fractional snow cover (FSC) by reducing the amount of the ground surface that is viewable through forest canopies, and by increasing uncertainties during the gridding of MODIS data. At the end of the MODIS scan line, the total modeled error can be as much as 50% for FSC. Empirical analysis of MODIS/Terra snow products in four forest sites shows high fluctuation in FSC estimates on consecutive days. In addition, the normalized difference snow index (NDSI) values, which are the primary input to the MODIS snow mapping algorithms, decrease as VZA increases at the site level. At the pixel level, NDSI values have higher variances, and are correlated with the normalized difference vegetation index (NDVI) in snow covered forests. These findings are consistent with our modeled results, and imply that consideration of view angle effects could improve MODIS snow monitoring in forested areas.

MODIS↗