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NASA NTRS2020

Evaluation of adjoint-based observation impacts as a function of forecast length using an Observing System Simulation Experiment

Adjoints of numerical weather prediction models may be employed for Forecast Sensitivity to Observation (FSO) in order to monitor the contribution of ingested observation data on short-term forecast skill. However, the calculation of short-term forecast error is difficult due to the lack of a truly independent dataset for verification. In an Observing System Simulation Experiment framework, the Nature Run is able to provide a true and complete verification dataset and allows accurate evaluation of short term forecast errors. In this work, an OSSE developed at the National Aeronautics and Space Administration Global Modeling and Assimilation Office is used to explore the impact of observational data on forecasts in the 6 to 48 hour range. An adjoint of the Global Earth Observing System model is employed to compare the observation impacts estimated using both self-analysis verification and the true Nature Run verification. Self-analysis verification is found to inflate the estimated forecast error growth during the early forecast period, resulting in overestimations of observation impacts, particularly in the 6-12 hour forecast range. By 48 hours, the self-analysis verification estimates of forecast error and observation impacts more closely match the true values. The fraction of beneficial observations is also overinflated at short forecast times when self-analysis verification is used. The progression of impacts of an individual observation or data type depends on the character of the growth of the initial condition error that each observation affects.

numerical weather prediction↗

NASA NTRS1992

On the Retrieval and Analysis of Multilevel Clouds

An accurate satellite retrieval of cloud properties depends upon the detection and analysis of multilayered, overlapping cloud systems that surface observations show to be common. Multiple cloud layers are often found, for instance, in frontal situations, where cirrus overlays boundary layer convective cloud or low-to mid-level stratus cloud. Surface observers (Hahan et al., 1982) indicate that over ocean in the Northern Hemisphere between 30 deg. N and 60 deg. N, 51 percent of observations are of multilevel clouds. A satellite analysis by Coakley (1983) over the Pacific Ocean finds that more than 50 percent of 500 (250 sq km) frames exhibit evidence of multilayered cloud systems. The questions addressed in this study are the following: What error is introduced when inferring the cloud pressure from a Field-Of-View (FOV) that contains some arbitrary amount of transparent cloud overlaying a lower-level black cloud, such as stratus, by making the assumption that there is only a single cloud layer in the FOV, and what may be done to improve the cloud retrieval? The CO2 slicing methods (e.g. McCleese and Wilson, 1976; Smith and Platt, 1978; Chahine, 1974) have been shown to provide accurate means of inferring cirrus cloud altitude from passive infrared radiance measurements. The CO2 techniques have been applied to radiometric data from several instruments, notably the High Resolution Infrared Radiometric Sounder (HIRS/2, hereafter referred to as HIRS), the VISSR Atmospheric Sounder (VAS) (e.g., Menzel et al., 1983; Wylie and Menzel, 1989), and most recently to the High Resolution Interferometer Sounder (HIS) (Smith and Frey, 1990). The methods take advantage of the fact that infrared CO2 sounding channels spaced closely in wavenumber each have varying opacity to CO2, thereby causing each channel to be sensitive to a different level in the atmosphere. The techniques have been shown to be effective for single-layered, nonblack, mid- to high-level clouds such as cirrus, but are generally applied operationally to any given cloud occurrence. The CO2 slicing algorithms are most accurate for clouds than occur in a single, well-defined layer, or for multi-layered cloud cases in which the uppermost cloud layer is nearly black. Significant cloud height retrieval errors may ensue if the HIRS Field-Of-View (FOV) is cotaminated with low cloud. McCleese and Wilson (1976) have shown that the retrieved cloud height for the case of multiple cloud layers is a weighted average of the cloud heights actually present. The weight is approximately proportional to the product of the cloud heigt and the effective cloud amount. The effect of their result is that the uppermost cloud layer dominates the cloud pressure retrieval. Beyond stating that the higher cloud dominates the cloud pressure retrieval, there is no quantitative information to provide a way of estimating the errors in cloud pressure retrieval one should expect for certain common multilevel cloud situations or any suggestions on how to reduce the errors. In this paper we estimate the magnitude of the errors and use a simple algorithm to reduce the errors in optically thin cloud height retrival.

Baum, Bryan A.↗

NASA NTRS1972

Error model for the SAO 1969 standard earth.

A method is developed for estimating an error model for geopotential coefficients using satellite tracking data. A single station's apparent timing error for each pass is attributed to geopotential errors. The root sum of the residuals for each station also depends on the geopotential errors, and these are used to select an error model. The model chosen is 1/4 of the difference between the SAO M1 and the APL 3.5 geopotential.

Martin, C. F.↗

NASA NTRS2000

Results From F-18B Stability and Control Parameter Estimation Flight Tests at High Dynamic Pressures

A maximum-likelihood output-error parameter estimation technique has been used to obtain stability and control derivatives for the NASA F-18B Systems Research Aircraft. This work has been performed to support flight testing of the active aeroelastic wing (AAW) F-18A project. The goal of this research is to obtain baseline F-18 stability and control derivatives that will form the foundation of the aerodynamic model for the AAW aircraft configuration. Flight data have been obtained at Mach numbers between 0.85 and 1.30 and at dynamic pressures ranging between 600 and 1500 lbf/sq ft. At each test condition, longitudinal and lateral-directional doublets have been performed using an automated onboard excitation system. The doublet maneuver consists of a series of single-surface inputs so that individual control-surface motions cannot be correlated with other control-surface motions. Flight test results have shown that several stability and control derivatives are significantly different than prescribed by the F-18B aerodynamic model. This report defines the parameter estimation technique used, presents stability and control derivative results, compares the results with predictions based on the current F-18B aerodynamic model, and shows improvements to the nonlinear simulation using updated derivatives from this research.

Moes, Timothy R.↗

NASA NTRS1980

Simulation study of a geometric shape factor technique for estimating earth-emitted radiant flux densities from wide-field-of-view radiation measurements

Geometric shape factors were computed and applied to satellite simulated irradiance measurements to estimate Earth emitted flux densities for global and zonal scales and for areas smaller than the detector field of view (FOV). Wide field of view flat plate detectors were emphasized, but spherical detectors were also studied. The radiation field was modeled after data from the Nimbus 2 and 3 satellites. At a satellite altitude of 600 km, zonal estimates were in error 1.0 to 1.2 percent and global estimates were in error less than 0.2 percent. Estimates with unrestricted field of view (UFOV) detectors were about the same for Lambertian and limb darkening radiation models. The opposite was found for restricted field of view detectors. The UFOV detectors are found to be poor estimators of flux density from the total FOV and are shown to be much better as estimators of flux density from a circle centered at the FOV with an area significantly smaller than that for the total FOV.

Weaver, W. L.↗

NASA NTRS1997

Correction of Sampling Errors in Ocean Surface Cross-Sectional Estimates from Nadir-Looking Weather Radar

The return from the ocean surface has a number of uses for airborne meteorological radar. The normalized surface cross section has been used for radar system calibration, estimation of surface winds, and in algorithms for estimating the path-integrated attenuation in rain. However, meteorological radars are normally optimized for observation of distributed targets that fill the resolution volume, and so a point target such as the surface can be poorly sampled, particularly at near-nadir look angles. Sampling the nadir surface return at an insufficient rate results in a negative bias of the estimated cross section. This error is found to be as large as 4 dB using observations from a high-altitude airborne radar. An algorithm for mitigating the error is developed that is based upon the shape of the surface echo and uses the returned signal at the three range gates nearest the peak surface echo.

Caylor, I. Jeff↗

NASA NTRS2003

Error Analyses of the North Alabama Lightning Mapping Array (LMA)

Two approaches are used to characterize how accurately the North Alabama Lightning Mapping Array (LMA) is able to locate lightning VHF sources in space and in time. The first method uses a Monte Carlo computer simulation to estimate source retrieval errors. The simulation applies a VHF source retrieval algorithm that was recently developed at the NASA-MSFC and that is similar, but not identical to, the standard New Mexico Tech retrieval algorithm. The second method uses a purely theoretical technique (i.e., chi-squared Curvature Matrix theory) to estimate retrieval errors. Both methods assume that the LMA system has an overall rms timing error of 50ns, but all other possible errors (e.g., multiple sources per retrieval attempt) are neglected. The detailed spatial distributions of retrieval errors are provided. Given that the two methods are completely independent of one another, it is shown that they provide remarkably similar results, except that the chi-squared theory produces larger altitude error estimates than the (more realistic) Monte Carlo simulation.

Koshak, W. J.↗

NASA NTRS2003

Error Analyses of the North Alabama Lightning Mapping Array (LMA)

Koshak, W. J.↗

NASA NTRS1989

EAC: A program for the error analysis of STAGS results for plates

A computer code is now available for estimating the error in results from the STAGS finite element code for a shell unit consisting of a rectangular orthotropic plate. This memorandum contains basic information about the computer code EAC (Error Analysis and Correction) and describes the connection between the input data for the STAGS shell units and the input data necessary to run the error analysis code. The STAGS code returns a set of nodal displacements and a discrete set of stress resultants; the EAC code returns a continuous solution for displacements and stress resultants. The continuous solution is defined by a set of generalized coordinates computed in EAC. The theory and the assumptions that determine the continuous solution are also outlined in this memorandum. An example of application of the code is presented and instructions on its usage on the Cyber and the VAX machines have been provided.

Sistla, Rajaram↗

NASA NTRS1972

Decision-directed adaptive recursive estimators - Divergence prevention.

A method is proposed for dealing with the divergence phenomenon problem encountered in applications of minimum-variance recursive estimators when the error covariance calculated by the estimator becomes inconsistent with the actual error covariance. The proposed method differs from previous ones in that the state model and statistics are accepted as given. The form of the optimal estimator is used, but a constant check is made on the consistency of the calculated and actual error covariances. The method is independent of the source of error, whether it be inaccuracies in the system model, incorrect values of the a priori and random process statistics, approximations required in the case of nonlinear systems, or computational roundoff. Several simulated examples, in which inconsistencies in the calculated and actual error covariances exist, show a significant improvement in the performance of the estimator when the given procedure is applied.

Nahi, N. E.↗

NASA NTRS2010

Lightning Reporting at 45th Weather Squadron: Recent Improvements

The 45th Weather Squadron (45 WS) provides daily lightning reports to space launch customers at CCAFS/KSC. These reports are provided to assess the need to inspect the electronics of satellite payloads, space launch vehicles, and ground support equipment for induced current damage from nearby lightning strokes. The 45 WS has made several improvements to the lightning reports during 2008-2009. The 4DLSS, implemented in April 2008, provides all lightning strokes as opposed to just one stroke per flash as done by the previous system. The 45 WS discovered that the peak current was being truncated to the nearest kilo amp in the database used to generate the daily lightning reports, which led to an up to 4% underestimate in the peak current for average lightning. This error was corrected and led to elimination of this underestimate. The 45 WS and their mission partners developed lightning location error ellipses for 99% and 95% location accuracies tailored to each individual stroke and began providing them in the spring of 2009. The new procedure provides the distance from the point of interest to the best location of the stroke (the center of the error ellipse) and the distance to the closest edge of the ellipse. This information is now included in the lightning reports, along with the peak current of the stroke. The initial method of calculating the error ellipses could only be used during normal duty hours, i.e. not during nights, weekends, or holidays. This method was improved later to provide lightning reports in near real-time, 24/7. The calculation of the distance to the closest point on the ellipse was also significantly improved later. Other improvements were also implemented. A new method to calculate the probability of any nearby lightning stroke. being within any radius of any point of interest was developed and is being implemented. This may supersede the use of location error ellipses. The 45 WS is pursuing adding data from nine NLDN sensors into 4DLSS in real-time. This will overcome the problem of 4DLSS missing some of the strong local strokes. This will also improve the location accuracy, reduce the size and eccentricity of the location error ellipses, and reduce the probability of nearby strokes being inside the areas of interest when few of the 4DLSS sensors are used in the stroke solution. This will not reduce 4DLSS performance when most of the 4DLSS sensors are used in the stroke solution. Finally, several possible future improvements were discussed, especially for improving the peak current estimate and the error estimate for peak current, and upgrading the 4DLSS. Some possible approaches for both of these goals were discussed.

Finn, Frank C.↗

NASA NTRS2000

A Method for Assessing the Quality of Model-Based Estimates of Ground Temperature and Atmospheric Moisture Using Satellite Data

A method is developed for validating model-based estimates of atmospheric moisture and ground temperature using satellite data. The approach relates errors in estimates of clear-sky longwave fluxes at the top of the Earth-atmosphere system to errors in geophysical parameters. The fluxes include clear-sky outgoing longwave radiation (CLR) and radiative flux in the window region between 8 and 12 microns (RadWn). The approach capitalizes on the availability of satellite estimates of CLR and RadWn and other auxiliary satellite data, and multiple global four-dimensional data assimilation (4-DDA) products. The basic methodology employs off-line forward radiative transfer calculations to generate synthetic clear-sky longwave fluxes from two different 4-DDA data sets. Simple linear regression is used to relate the clear-sky longwave flux discrepancies to discrepancies in ground temperature ((delta)T(sub g)) and broad-layer integrated atmospheric precipitable water ((delta)pw). The slopes of the regression lines define sensitivity parameters which can be exploited to help interpret mismatches between satellite observations and model-based estimates of clear-sky longwave fluxes. For illustration we analyze the discrepancies in the clear-sky longwave fluxes between an early implementation of the Goddard Earth Observing System Data Assimilation System (GEOS2) and a recent operational version of the European Centre for Medium-Range Weather Forecasts data assimilation system. The analysis of the synthetic clear-sky flux data shows that simple linear regression employing (delta)T(sub g)) and broad layer (delta)pw provides a good approximation to the full radiative transfer calculations, typically explaining more thin 90% of the 6 hourly variance in the flux differences. These simple regression relations can be inverted to "retrieve" the errors in the geophysical parameters, Uncertainties (normalized by standard deviation) in the monthly mean retrieved parameters range from 7% for (delta)T(sub g) to approx. 20% for the lower tropospheric moisture between 500 hPa and surface. The regression relationships developed from the synthetic flux data, together with CLR and RadWn observed with the Clouds and Earth Radiant Energy System instrument, ire used to assess the quality of the GEOS2 T(sub g) and pw. Results showed that the GEOS2 T(sub g) is too cold over land, and pw in upper layers is too high over the tropical oceans and too low in the lower atmosphere.

Wu, Man Li C.↗

NASA NTRS1978

Adaptive finite element analysis based on p-convergence

The results of numerical experiments are presented in which a posteriori estimators of error in strain energy were examined on the basis of a typical problem in linear elastic fracture mechanics. Two estimators were found to give close upper and lower bounds for the strain energy error. The potential significance of this is that the same estimators may provide a suitable basis for adaptive redistribution of the degrees of freedom in finite element models.

Szabo, B. A.↗

NASA NTRS1997

Accurate Magnetometer/Gyroscope Attitudes Using a Filter with Correlated Sensor Noise

Magnetometers and gyroscopes have been shown to provide very accurate attitudes for a variety of spacecraft. These results have been obtained, however, using a batch-least-squares algorithm and long periods of data. For use in onboard applications, attitudes are best determined using sequential estimators such as the Kalman filter. When a filter is used to determine attitudes using magnetometer and gyroscope data for input, the resulting accuracy is limited by both the sensor accuracies and errors inherent in the Earth magnetic field model. The Kalman filter accounts for the random component by modeling the magnetometer and gyroscope errors as white noise processes. However, even when these tuning parameters are physically realistic, the rate biases (included in the state vector) have been found to show systematic oscillations. These are attributed to the field model errors. If the gyroscope noise is sufficiently small, the tuned filter 'memory' will be long compared to the orbital period. In this case, the variations in the rate bias induced by field model errors are substantially reduced. Mistuning the filter to have a short memory time leads to strongly oscillating rate biases and increased attitude errors. To reduce the effect of the magnetic field model errors, these errors are estimated within the filter and used to correct the reference model. An exponentially-correlated noise model is used to represent the filter estimate of the systematic error. Results from several test cases using in-flight data from the Compton Gamma Ray Observatory are presented. These tests emphasize magnetometer errors, but the method is generally applicable to any sensor subject to a combination of random and systematic noise.

Sedlak, J.↗

NASA NTRS2015

An Empirical State Error Covariance Matrix Orbit Determination Example

State estimation techniques serve effectively to provide mean state estimates. However, the state error covariance matrices provided as part of these techniques suffer from some degree of lack of confidence in their ability to adequately describe the uncertainty in the estimated states. A specific problem with the traditional form of state error covariance matrices is that they represent only a mapping of the assumed observation error characteristics into the state space. Any errors that arise from other sources (environment modeling, precision, etc.) are not directly represented in a traditional, theoretical state error covariance matrix. First, consider that an actual observation contains only measurement error and that an estimated observation contains all other errors, known and unknown. Then it follows that a measurement residual (the difference between expected and observed measurements) contains all errors for that measurement. Therefore, a direct and appropriate inclusion of the actual measurement residuals in the state error covariance matrix of the estimate will result in an empirical state error covariance matrix. This empirical state error covariance matrix will fully include all of the errors in the state estimate. The empirical error covariance matrix is determined from a literal reinterpretation of the equations involved in the weighted least squares estimation algorithm. It is a formally correct, empirical state error covariance matrix obtained through use of the average form of the weighted measurement residual variance performance index rather than the usual total weighted residual form. Based on its formulation, this matrix will contain the total uncertainty in the state estimate, regardless as to the source of the uncertainty and whether the source is anticipated or not. It is expected that the empirical error covariance matrix will give a better, statistical representation of the state error in poorly modeled systems or when sensor performance is suspect. In its most straight forward form, the technique only requires supplemental calculations to be added to existing batch estimation algorithms. In the current problem being studied a truth model making use of gravity with spherical, J2 and J4 terms plus a standard exponential type atmosphere with simple diurnal and random walk components is used. The ability of the empirical state error covariance matrix to account for errors is investigated under four scenarios during orbit estimation. These scenarios are: exact modeling under known measurement errors, exact modeling under corrupted measurement errors, inexact modeling under known measurement errors, and inexact modeling under corrupted measurement errors. For this problem a simple analog of a distributed space surveillance network is used. The sensors in this network make only range measurements and with simple normally distributed measurement errors. The sensors are assumed to have full horizon to horizon viewing at any azimuth. For definiteness, an orbit at the approximate altitude and inclination of the International Space Station is used for the study. The comparison analyses of the data involve only total vectors. No investigation of specific orbital elements is undertaken. The total vector analyses will look at the chisquare values of the error in the difference between the estimated state and the true modeled state using both the empirical and theoretical error covariance matrices for each of scenario.

Frisbee, Joseph H., Jr.↗

NASA NTRS1978

Optimal estimation for discrete time jump processes

Optimum estimates of nonobservable random variables or random processes which influence the rate functions of a discrete time jump process (DTJP) are derived. The approach used is based on the a posteriori probability of a nonobservable event expressed in terms of the a priori probability of that event and of the sample function probability of the DTJP. Thus a general representation is obtained for optimum estimates, and recursive equations are derived for minimum mean-squared error (MMSE) estimates. In general, MMSE estimates are nonlinear functions of the observations. The problem is considered of estimating the rate of a DTJP when the rate is a random variable with a beta probability density function and the jump amplitudes are binomially distributed. It is shown that the MMSE estimates are linear. The class of beta density functions is rather rich and explains why there are insignificant differences between optimum unconstrained and linear MMSE estimates in a variety of problems.

Vaca, M. V.↗

NASA NTRS1981

Improving streamflow estimates through the use of LANDSAT

Estimates of low flow and flood frequency in several southwestern Wisconsin basins were improved by determining land cover from LANDSAT imagery. With the use of estimates of land cover in multiple-regression techniques, the standard error of estimate (SE) for the least annual 7-day low flow for 2- and 10-year recurrence intervals of ungaged sites were lowered by 9% each. The SE of flood frequency in the 'Driftless Area' of Wisconsin for 10-, 50-, and 100-year recurrence intervals were lowered by 14%. Four of nine basin characteristics determined from satellite imagery were significant variables in the multiple-regression techniques, whereas only 1 of the 12 characteristics determined from topographic maps was significant. The percentages of land cover categories in each basin were determined by merging basin boundaries, digitized from quadrangles, with a classified LANDSAT scene. Both the basin boundary X-Y polygon coordinates and the satellite coordinates were converted to latitude-longitude for merging compatibility.

Allord, G. J.↗

NASA NTRS1993

Effects of vertical distribution of water vapor and temperature on total column water vapor retrieval error

Results are presented of a test of the physically based total column water vapor retrieval algorithm of Wentz (1992) for sensitivity to realistic vertical distributions of temperature and water vapor. The ECMWF monthly averaged temperature and humidity fields are used to simulate the spatial pattern of systematic retrieval error of total column water vapor due to this sensitivity. The estimated systematic error is within 0.1 g/sq cm over about 70 percent of the global ocean area; systematic errors greater than 0.3 g/sq cm are expected to exist only over a few well-defined regions, about 3 percent of the global oceans, assuming that the global mean value is unbiased.

Sun, Jielun↗