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NASA NTRS2012

SBUV version 8.6 Retrieval Algorithm: Error Analysis and Validation Technique

SBUV version 8.6 algorithm was used to reprocess data from the Back Scattered Ultra Violet (BUV), the Solar Back Scattered Ultra Violet (SBUV) and a number of SBUV/2 instruments, which 'span a 41-year period from 1970 to 2011 (except a 5-year gap in the 1970s)[see Bhartia et al, 2012]. In the new version Daumont et al. [1992] ozone cross section were used, and new ozone [McPeters et ai, 2007] and cloud climatologies Doiner and Bhartia, 1995] were implemented. The algorithm uses the Optimum Estimation technique [Rodgers, 2000] to retrieve ozone profiles as ozone layer (partial column, DU) on 21 pressure layers. The corresponding total ozone values are calculated by summing ozone columns at individual layers. The algorithm is optimized to accurately retrieve monthly zonal mean (mzm) profiles rather than an individual profile, since it uses monthly zonal mean ozone climatology as the A Priori. Thus, the SBUV version 8.6 ozone dataset is better suited for long-term trend analysis and monitoring ozone changes rather than for studying short-term ozone variability. Here we discuss some characteristics of the SBUV algorithm and sources of error in the SBUV profile and total ozone retrievals. For the first time the Averaging Kernels, smoothing errors and weighting functions (or Jacobians) are included in the SBUV metadata. The Averaging Kernels (AK) represent the sensitivity of the retrieved profile to the true state and contain valuable information about the retrieval algorithm, such as Vertical Resolution, Degrees of Freedom for Signals (DFS) and Retrieval Efficiency [Rodgers, 2000]. Analysis of AK for mzm ozone profiles shows that the total number of DFS for ozone profiles varies from 4.4 to 5.5 out of 6-9 wavelengths used for retrieval. The number of wavelengths in turn depends on solar zenith angles. Between 25 and 0.5 hPa, where SBUV vertical resolution is the highest, DFS for individual layers are about 0.5.

Kramarova, N. A.↗
NASA NTRS1998

Robust Flutter Margin Analysis that Incorporates Flight Data

An approach for computing worst-case flutter margins has been formulated in a robust stability framework. Uncertainty operators are included with a linear model to describe modeling errors and flight variations. The structured singular value, mu, computes a stability margin that directly accounts for these uncertainties. This approach introduces a new method of computing flutter margins and an associated new parameter for describing these margins. The mu margins are robust margins that indicate worst-case stability estimates with respect to the defined uncertainty. Worst-case flutter margins are computed for the F/A-18 Systems Research Aircraft using uncertainty sets generated by flight data analysis. The robust margins demonstrate flight conditions for flutter may lie closer to the flight envelope than previously estimated by p-k analysis.

Lind, Rick↗
NASA NTRS2002

Role of Satellite Rainfall Information in Improving Understanding of the Dynamical Link Between the Tropics and Extratropics Prospects of Improved Forecasts of Weather and Short-Term Climate Variability on Sub-Seasonal Time Scales

The tropics and extratropics are two dynamically distinct regimes. The coupling between these two regimes often defies simple analytical treatment. Progress in understanding of the dynamical interaction between the tropics and extratropics relies on better observational descriptions to guide theoretical development. However, global analyses currently contain significant errors in primary hydrological variables such as precipitation, evaporation, moisture, and clouds, especially in the tropics. Tropical analyses have been shown to be sensitive to parameterized precipitation processes, which are less than perfect, leading to order-one discrepancies between estimates produced by different data assimilation systems. One strategy for improvement is to assimilate rainfall observations to constrain the analysis and reduce uncertainties in variables physically linked to precipitation. At the Data Assimilation Office at the NASA Goddard Space Flight Center, we have been exploring the use of tropical rain rates derived from the TRMM Microwave Imager (TMI) and the Special Sensor Microwave/ Imager (SSM/I) instruments in global data assimilation. Results show that assimilating these data improves not only rainfall and moisture fields but also related climate parameters such as clouds and radiation, as well as the large-scale circulation and short-range forecasts. These studies suggest that assimilation of microwave rainfall observations from space has the potential to significantly improve the quality of 4-D assimilated datasets for climate investigations (Hou et al. 2001). In the next few years, there will be a gradual increase in microwave rain products available from operational and research satellites, culminating to a target constellation of 9 satellites to provide global rain measurements every 3 hours with the proposed Global Precipitation Measurement (GPM) mission in 2007. Continued improvements in assimilation methodology, rainfall error estimates, and model parameterizations are needed to ensure that we derive maximum benefits from these observations.

Hou, Arthur Y.↗
NASA NTRS1985

Mathematical analysis study for radar data processing and enhancement. Part 1: Radar data analysis

A study is performed under NASA contract to evaluate data from an AN/FPS-16 radar installed for support of flight programs at Dryden Flight Research Facility of NASA Ames Research Center. The purpose of this study is to provide information necessary for improving post-flight data reduction and knowledge of accuracy of derived radar quantities. Tracking data from six flights are analyzed. Noise and bias errors in raw tracking data are determined for each of the flights. A discussion of an altiude bias error during all of the tracking missions is included. This bias error is defined by utilizing pressure altitude measurements made during survey flights. Four separate filtering methods, representative of the most widely used optimal estimation techniques for enhancement of radar tracking data, are analyzed for suitability in processing both real-time and post-mission data. Additional information regarding the radar and its measurements, including typical noise and bias errors in the range and angle measurements, is also presented. This is in two parts. This is part 1, an analysis of radar data.

James, R.↗
NASA NTRS1972

Application of Avco data analysis and prediction techniques (ADAPT) to prediction of sunspot activity

The results are presented of the application of Avco Data Analysis and Prediction Techniques (ADAPT) to derivation of new algorithms for the prediction of future sunspot activity. The ADAPT derived algorithms show a factor of 2 to 3 reduction in the expected 2-sigma errors in the estimates of the 81-day running average of the Zurich sunspot numbers. The report presents: (1) the best estimates for sunspot cycles 20 and 21, (2) a comparison of the ADAPT performance with conventional techniques, and (3) specific approaches to further reduction in the errors of estimated sunspot activity and to recovery of earlier sunspot historical data. The ADAPT programs are used both to derive regression algorithm for prediction of the entire 11-year sunspot cycle from the preceding two cycles and to derive extrapolation algorithms for extrapolating a given sunspot cycle based on any available portion of the cycle.

Hunter, H. E.↗
NASA NTRS1984

On the X-ray spectrum of the volume emissivity arising from Abell clusters

HEAO 1 A-2 X-ray spectra (2-15 keV) for an optically selected sample of Abell clusters of galaxies with z less than 0.1 have been analyzed to determine the energy dependence of the cosmological X-ray volume emissivity arising from such clusters. This spectrum is well fitted by an isothermal-bremsstrahlung model with kT = 7.4 + or - 1.5 KeV. This result is a test of the isothermal-volume-emissivity spectrum to be inferred from the conjecture that all contributing clusters may be characterized by kT = 7 keV, as assumed by McKee et al. (1980) in estimating the underlying luminosity function for the same sample. Although satisfied at the statistical level indicated, the analysis of a low-luminosity subsample suggests that this assumption of identical isothermal spectra would lead to a systematic error for a more statistically precise determination of the luminosity function's form.

Stottlemyer, A. R.↗
NASA NTRS1985

Fine guidance sensor design optimization for Space Infrared Telescope Facility (SIRTF)

The present paper is concerned with the general issues of design optimization of a staring mosaic sensor for guide-star tracking, taking into account the choice of the proper interpolation algorithm. It was found that the final choice of algorithm depends on the severity of the positional accuracy requirement and the expected variation in the blur spot shape. The considered track algorithms estimate the position either of the peak or of the centroid of the image of a point source. Attention is given to aspects of problem definition, the total effect of error sources on algorithm accuracy, a parametric analysis of performance behavior, Monte Carlo results, and the design of the SIRTF Fine Guidance Sensor (FGS). The algorithm error, the signal-to-noise error, and the nonuniformity error are examined.

Grossman, S. B.↗
NASA NTRS1994

Cross-correlation of point series using a new method

Traditional methods of cross-correlation of two time series do not apply to point time series. Here, a new method, devised specifically for point series, utilizes a correlation measure that is based in the rms difference (or, alternatively, the median absolute difference) between nearest neightbors in overlapped segments of the two series. Error estimates for the observed locations of the points, as well as a systematic shift of one series with respect to the other to accommodate a constant, but unknown, lead or lag, are easily incorporated into the analysis using Monte Carlo techniques. A methodological restriction adopted here is that one series be treated as a template series against which the other, called the target series, is cross-correlated. To estimate a significance level for the correlation measure, the adopted alternative (null) hypothesis is that the target series arises from a homogeneous Poisson process. The new method is applied to cross-correlating the times of the greatest geomagnetic storms with the times of maximum in the undecennial solar activity cycle.

Strothers, Richard B.↗
NASA NTRS2013

Assimilation of Quality Controlled AIRS Temperature Profiles using the NCEP GFS

We have previously conducted a number of data assimilation experiments using AIRS Version-5 quality controlled temperature profiles as a step toward finding an optimum balance of spatial coverage and sounding accuracy with regard to improving forecast skill. The data assimilation and forecast system we used was the Goddard Earth Observing System Model , Version-5 (GEOS-5) Data Assimilation System (DAS), which represents a combination of the NASA GEOS-5 forecast model with the National Centers for Environmental Prediction (NCEP) operational Grid Point Statistical Interpolation (GSI) global analysis scheme. All analyses and forecasts were run at a 0.5deg x 0.625deg spatial resolution. Data assimilation experiments were conducted in four different seasons, each in a different year. Three different sets of data assimilation experiments were run during each time period: Control; AIRS T(p); and AIRS Radiance. In the "Control" analysis, all the data used operationally by NCEP was assimilated, but no AIRS data was assimilated. Radiances from the Aqua AMSU-A instrument were also assimilated operationally by NCEP and are included in the "Control". The AIRS Radiance assimilation adds AIRS observed radiance observations for a select set of channels to the data set being assimilated, as done operationally by NCEP. In the AIRS T(p) assimilation, all information used in the Control was assimilated as well as Quality Controlled AIRS Version-5 temperature profiles, i.e., AIRS T(p) information was substituted for AIRS radiance information. The AIRS Version-5 temperature profiles were presented to the GSI analysis as rawinsonde profiles, assimilated down to a case-by-case appropriate pressure level p(sub best) determined using the Quality Control procedure. Version-5 also determines case-by-case, level-by-level error estimates of the temperature profiles, which were used as the uncertainty of each temperature measurement. These experiments using GEOS-5 have shown that forecasts resulting from analyses using the AIRS T(p) assimilation system were superior to those from the Radiance assimilation system, both with regard to global 7 day forecast skill and also the ability to predict storm tracks and intensity.

Susskind, Joel↗
NASA NTRS2019

Camera modeling, centroiding performance, and geometric camera calibration on ASTERIA

The Arcsecond Space Telescope Enabling Research in Astrophysics (ASTERIA) is a 10-kg, 6U CubeSat in low-Earth orbit that was able to achieve subarcsecond pointing stability and repeatability. To date, this is the best pointing on a spacecraft of its size. This paper will analyze various aspects of the performance of its key piece of hardware—the payload. First,a model of the optics and imager, which is used to simulate stellar images, will be presented. The imager parameters used in this model were derived from simple ground measurements. Next, a centroiding algorithm is provided and used on the simulated images to predict centroiding performance. These results will be shown to match on-orbit telemetry of centroiding performance, validating the modeling approach. This paper will then describe an approach for and results of a geometric camera calibration algorithm to estimate the focal length,distortion,and alignment parameters. The modeling, analyses, and results presented in this paper provide key information that can be used in a time domain pointing simulation or a frequency-domain pointing error analysis.

Smith, Matthew W.↗
NASA NTRS1998

Stratospheric Assimilation of Chemical Tracer Observations Using a Kalman Filter: Chi-Square Validated Results and Analysis of Variance and Correlation Dynamics - Pt. 2

A Kalman filter system designed for the assimilation of limb-sounding observations of stratospheric chemical tracers, which has four tunable covariance parameters, was developed in Part I (Menard et al. 1998) The assimilation results of CH4 observations from the Cryogenic Limb Array Etalon Sounder instrument (CLAES) and the Halogen Observation Experiment instrument (HALOE) on board of the Upper Atmosphere Research Satellite are described in this paper. A robust (chi)(sup 2) criterion, which provides a statistical validation of the forecast and observational error covariances, was used to estimate the tunable variance parameters of the system. In particular, an estimate of the model error variance was obtained. The effect of model error on the forecast error variance became critical after only three days of assimilation of CLAES observations, although it took 14 days of forecast to double the initial error variance. We further found that the model error due to numerical discretization as arising in the standard Kalman filter algorithm, is comparable in size to the physical model error due to wind and transport modeling errors together. Separate assimilations of CLAES and HALOE observations were compared to validate the state estimate away from the observed locations. A wave-breaking event that took place several thousands of kilometers away from the HALOE observation locations was well captured by the Kalman filter due to highly anisotropic forecast error correlations. The forecast error correlation in the assimilation of the CLAES observations was found to have a structure similar to that in pure forecast mode except for smaller length scales. Finally, we have conducted an analysis of the variance and correlation dynamics to determine their relative importance in chemical tracer assimilation problems. Results show that the optimality of a tracer assimilation system depends, for the most part, on having flow-dependent error correlation rather than on evolving the error variance.

Menard, Richard↗
NASA NTRS2009

Magnetospheric Multiscale (MMS) Mission Commissioning Phase Orbit Determination Error Analysis

The Magnetospheric MultiScale (MMS) mission commissioning phase starts in a 185 km altitude x 12 Earth radii (RE) injection orbit and lasts until the Phase 1 mission orbits and orientation to the Earth-Sun li ne are achieved. During a limited time period in the early part of co mmissioning, five maneuvers are performed to raise the perigee radius to 1.2 R E, with a maneuver every other apogee. The current baseline is for the Goddard Space Flight Center Flight Dynamics Facility to p rovide MMS orbit determination support during the early commissioning phase using all available two-way range and Doppler tracking from bo th the Deep Space Network and Space Network. This paper summarizes th e results from a linear covariance analysis to determine the type and amount of tracking data required to accurately estimate the spacecraf t state, plan each perigee raising maneuver, and support thruster cal ibration during this phase. The primary focus of this study is the na vigation accuracy required to plan the first and the final perigee ra ising maneuvers. Absolute and relative position and velocity error hi stories are generated for all cases and summarized in terms of the ma ximum root-sum-square consider and measurement noise error contributi ons over the definitive and predictive arcs and at discrete times inc luding the maneuver planning and execution times. Details of the meth odology, orbital characteristics, maneuver timeline, error models, and error sensitivities are provided.

Chung, Lauren R.↗
NASA NTRS2011

Estimating Contrail Climate Effects from Satellite Data

An automated contrail detection algorithm (CDA) is developed to exploit six of the infrared channels on the 1-km MODerate-resolution Imaging Spectroradiometer (MODIS) on the Terra and Aqua satellites. The CDA is refined and balanced using visual error analysis. It is applied to MODIS data taken by Terra and Aqua over the United States during 2006 and 2008. The results are consistent with flight track data, but differ markedly from earlier analyses. Contrail coverage is a factor of 4 less than other retrievals and the retrieved contrail optical depths and radiative forcing are smaller by approx.30%. The discrepancies appear to be due to the inability to detect wider, older contrails that comprise a significant amount of the contrail coverage. An example of applying the algorithm to MODIS data over the entire Northern Hemisphere is also presented. Overestimates of contrail coverage are apparent in some tropical regions. Methods for improving the algorithm are discussed and are to be implemented before analyzing large amounts of Northern Hemisphere data. The results should be valuable for guiding and validating climate models seeking to account for aviation effects on climate.

Minnis, Patrick↗
NASA NTRS1996

Common View Time Transfer Using Worldwide GPS and DMA Monitor Stations

Analysis of the on-orbit Navstar clocks and the Global Positioning System (GPS) monitor station reference clocks is performed by the Naval Research Laboratory using both broadcast and postprocessed precise ephemerides. The precise ephemerides are produced by the Defense Mapping Agency (DMA) for each of the GPS space vehicles from pseudo-range measurements collected at five GPS and at five DMA monitor stations spaced around the world. Recently, DMA established an additional site co-located with the US Naval Observatory precise time site. The time reference for the new DMA site is the DoD Master Clock. Now, for the first time, it is possible to transfer time every 15 minutes via common view from the DoD Master Clock to the 11 GPS and DMA monitor stations. The estimated precision of a single common-view time transfer measurement taken over a 15-minute interval was between 1.4 and 2.7 nanoseconds. Using the measurements from all Navstar space vehicles in common view during the 15-minute interval, typically 3-7 space vehicles, improved the estimate of the precision to between 0.65 and 1.13 nanoseconds. The mean phase error obtained from closure of the time transfer around the world using the 11 monitor stations and the 25 space vehicle clocks over a period of 4 months had a magnitude of 31 picoseconds. Analysis of the low noise time transfer from the DoD Master Clock to each of the monitor stations yields not only the bias in the time of the reference clock, but also focuses attention on structure in the behaviour of the reference clock not previously seen. Furthermore, the time transfer provides a a uniformly sampled database of 15-minute measurements that make possible, for the first time, the direct and exhaustive computation of the frequency stability of the monitor station reference clocks. To lend perspective to the analysis, a summary is given of the discontinuities in phase and frequency that occurred in the reference clock at the Master Control Station during the period covered by the analysis.

Reid, Wilson G.↗
NASA NTRS1973

Long and short arc altitude determination for GEOS-C

The accuracy with which the GEOS-C altitude may be estimated over long (7 day) and short (40 minute) orbital arcs is investigated. Over the long are excellent agreement was attained between a simulation of the orbit determination process and a covariance analysis. Both approaches yielded RMS altitude errors of about 1.5 meters over the Caribbean calibration area and approximately 7.5 meters overall. The geopotential was identified as the largest error source. For the short arc, the covariance analysis revealed that the propagated altitude error is linearly dependent upon station survey component errors which are also the largest source of altitude errors. An Appendix contains the mathematics of covariance analysis as applied to orbit determination.

Koch, D.↗
NASA NTRS1975

Stochastic process approximation for recursive estimation with guaranteed bound on the error covariance

An approach, is proposed for the design of approximate, fixed order, discrete time realizations of stochastic processes from the output covariance over a finite time interval, was proposed. No restrictive assumptions are imposed on the process; it can be nonstationary and lead to a high dimension realization. Classes of fixed order models are defined, having the joint covariance matrix of the combined vector of the outputs in the interval of definition greater or equal than the process covariance; (the difference matrix is nonnegative definite). The design is achieved by minimizing, in one of those classes, a measure of the approximation between the model and the process evaluated by the trace of the difference of the respective covariance matrices. Models belonging to these classes have the notable property that, under the same measurement system and estimator structure, the output estimation error covariance matrix computed on the model is an upper bound of the corresponding covariance on the real process. An application of the approach is illustrated by the modeling of random meteorological wind profiles from the statistical analysis of historical data.

Menga, G.↗
NASA NTRS1983

Application of in-flight thrust determination uncertainty

A numerical example is given of a previously proposed methodology for the evaluation of in-flight thrust measurement uncertainty, using data extracted from a performance report comparing two different missile prototypes under a variety of flight conditions. Attention is given to the data for the AGM-68B Air Launched Cruise Missile, which is powered by the F107 dual-spool, mixed flow turbofan engine. Assessments are made of the definition of the measurement process, instrumentation error estimation, the propagation of errors to thrust calculation, mathematical model errors, the in-flight thrust error component, and correction to standard conditions. It is concluded that in-flight thrust measurement uncertainty limits can be evaluated from measurement system error analysis results and test data for the missile evaluation process presently described.

Adams, G. R.↗
NASA NTRS1985

Statistical magnetic anomalies from satellite measurements for geologic analysis

The errors of numerically averaging satellite magnetic anomaly data for geologic analysis are investigated using orbital anomaly simulations of crustal magnetic sources by Gauss-Legendre quadrature integration. These simulations suggest that numerical averaging errors constitute small and relatively minor contributions to the total error-budget of higher orbital estimates (approx. 400 km), whereas for lower orbital estimates the error of averaging may increase substantially. Least-squares collocation is also investigated as an alternative to numerical averaging and found to produce substantially more accurate anomaly estimates as the elevation of prediction is decreased towards the crustal sources.

Goyal, H. K.↗