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A theoretical model for the range error covariance was derived by assuming that the residual refraction errors are due entirely to errors in the meteorological data which are used to calculate the atmospheric correction. The properties of the covariance function are illustrated by evaluating the theoretical model for the special case of a dense network of weather stations uniformly distributed within a circle.
Two massively parallel data assimilation systems in which the model forecast-error covariances are estimated from the distribution of an ensemble of model integrations are applied to the assimilation of 97-98 TOPEX/POSEIDON altimetry and TOGA/TAO temperature data into a Pacific basin version the NASA Seasonal to Interannual Prediction Project (NSIPP)ls quasi-isopycnal ocean general circulation model. in the first system, ensemble of model runs forced by an ensemble of atmospheric model simulations is used to calculate asymptotic error statistics. The data assimilation then occurs in the reduced phase space spanned by the corresponding leading empirical orthogonal functions. The second system is an ensemble Kalman filter in which new error statistics are computed during each assimilation cycle from the time-dependent ensemble distribution. The data assimilation experiments are conducted on NSIPP's 512-processor CRAY T3E. The two data assimilation systems are validated by withholding part of the data and quantifying the extent to which the withheld information can be inferred from the assimilation of the remaining data. The pros and cons of each system are discussed.
Analysis of 211 very long baseline interferometry observing sessions carried out between November 1979 and August 1984 has yielded estimates of the distances between various radio telescopes located in North America and Europe. The average rate of change of the distances between four radio telescopes in North America (Haystack Observatory, Massachusetts; Westford Radio Telescope, Massachusetts; George R. Agassiz Station, Texas; and Owens Valley Radio Observatory, California) and one in Europe (Onsala Space Observatory, Sweden) obtained from the analysis of these data is 19 + or 10 mm/yr, where the (68 percent confidence interval) standard deviation is for the estimate of the rate of change of the Haystack-Onsala baseline length, the one determined most accurately from these data. This estimate of the standard deviation is dominated by the effects of correlated systematic errors due mostly to errors in the model used for the atmospheric delay which introduces errors in each baseline length estimate of 40 mm standard deviation and 60 days correlation time. (By contrast the statistical standard deviation is only 2 mm/yr). The estimated geologic rates of change of these baseline lengths, averaged over 10 to the 6th years, are 15 to 17 + or - 3 mm/yr for the various North American sites to Ondala.
In a parameter study of satellite orbits, sampling errors of area-time averaged rain rate due to temporal sampling by satellites were estimated. The sampling characteristics were studied by accounting for the varying visiting intervals and varying fractions of averaging area on each visit as a function of the latitude of the grid box for a range of satellite orbital parameters. The sampling errors were estimated by a simple model based on the first-order Markov process of the time series of area averaged rain rates. For a satellite of nominal Tropical Rainfall Measuring Mission (Thiele, 1987) carrying an ideal scanning microwave radiometer for precipitation measurements, it is found that sampling error would be about 8 to 12 pct of estimated monthly mean rates over a grid box of 5 X 5 degrees. It is suggested that an observation system based on a low inclination satellite combined with a sunsynchronous satellite simultaneously might be the best candidate for making precipitation measurements from space.
This paper examines bipolar junction transistor models suitable for calculating the effects of large excursions of some of the variables determining the operation of a transistor. Both the Ebers-Moll and Gummel-Poon models are studied, and the junction and diffusion capacitances are evaluated on the basis of the latter model. The most interesting result of this analysis is that a bipolar junction transistor when struck by a cosmic particle may cause a single event upset in an electronic circuit if the transistor is operated at a low forward base-emitter bias.
Proposal of a new concept of model testing which makes use of imperfect models and is based on the heuristic argument of representing the error states in a multidimensional Euclidean space when the errors in the modeling parameter are sufficiently small. By a separation of these errors into positive and negative groups, and from a consideration of the error paths in the hyperspaces, it is shown that the global effect of these errors may be evaluated with a good degree of approximation. Conditions under which the procedure would yield satisfactory results are discussed. To test the usefulness of the theory a computer experiment was conducted for the prediction of both transient and steady state thermal behavior of a hypothetical spacecraft using perfect, as well as imperfect, models.
Scale error correction technique for structural impact modeling using dissimilar materials, involving permanent deformation of spherical caps impacted into liquids
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.
Integrated and spectral error energetics of the Goddard Laboratory for Atmospheric Sciences (GLAS) general circulation model are compared with observations for periods in January 1975, 1976, and 1977. For two cases the model shows significant skill in predicting integrated energetics quantities out to two weeks, and for all three cases, the integrated monthly mean energetics show qualitative improvements over previous versions of the model in eddy kinetic energy and barotropic conversions. Fundamental difficulties remain with leakage of energy to the stratospheric level. General circulation model spectral energetics predictions are compared with the corresponding observational spectra on a day by day basis. Eddy kinetic energy can be correct while significant errors occur in the kinetic energy of wavenumber three. Single wavenumber dominance in eddy kinetic energy and the correlation of spectral kinetic and potential energy are demonstrated.
Software simulations provide NASA engineers the ability to experiment with spacecraft systems in a computer-imitated environment. Engineers currently develop software models that encapsulate spacecraft system behavior. These models can be inaccurate due to invalid assumptions, erroneous operation, or system evolution. Increasing accuracy requires manual calibration and domain-specific knowledge. This thesis presents a method for automatically learning system models without any assumptions regarding system behavior. Data stream mining techniques are applied to learn models for critical portions of the International Space Station (ISS) Electrical Power System (EPS). We also explore a knowledge fusion approach that uses traditional engineered EPS models to supplement the learned models. We observed that these engineered EPS models provide useful background knowledge to reduce predictive error spikes when confronted with making predictions in situations that are quite different from the training scenarios used when learning the model. Evaluations using ISS sensor data and existing EPS models demonstrate the success of the adaptive approach. Our experimental results show that adaptive modeling provides reductions in model error anywhere from 80% to 96% over these existing models. Final discussions include impending use of adaptive modeling technology for ISS mission operations and the need for adaptive modeling in future NASA lunar and Martian exploration.
Due to geometrical imperfections in gears and finite tooth stiffnesses, the motion transmitted from an input gear shaft to an output gear shaft will not have conjugate action. In order to strengthen the understanding of transmission error and to verify mathematical models of gear transmission error, a test stand that will measure the transmission error of a gear pair at operating loads, but at reduced speeds would be desirable. This document describes the design and development of a loaded transmission error tester. For a gear box with a gear ratio of one, few tooth meshing combinations will occur during a single test. In order to observe the effects of different tooth mesh combinations and to increase the ability to load test gear pairs with higher gear ratios, the system was designed around a gear box with a gear ratio of two.
A spring 1997 test section calibration program is scheduled for the NASA Glenn Research Center Icing Research Tunnel following the installation of new water injecting spray bars. A set of new five-hole flow angle pressure probes was fabricated to properly calibrate the test section for total pressure, static pressure, and flow angle. The probes have nine pressure ports: five total pressure ports on a hemispherical head and four static pressure ports located 14.7 diameters downstream of the head. The probes were calibrated in the NASA Glenn 3.5-in.-diameter free-jet calibration facility. After completing calibration data acquisition for two probes, two data prediction models were evaluated. Prediction errors from a linear discrete model proved to be no worse than those from a full third-order multiple regression model. The linear discrete model only required calibration data acquisition according to an abridged test matrix, thus saving considerable time and financial resources over the multiple regression model that required calibration data acquisition according to a more extensive test matrix. Uncertainties in calibration coefficients and predicted values of flow angle, total pressure, static pressure. Mach number. and velocity were examined. These uncertainties consider the instrumentation that will be available in the Icing Research Tunnel for future test section calibration testing.
Ocean assimilation systems synthesize diverse in situ and satellite data streams into four-dimensional state estimates by combining the various observations with the model. Assimilation is particularly important for the ocean where subsurface observations, even today, are sparse and intermittent compared with the scales needed to represent ocean variability and where satellites only sense the surface. Developments in assimilation and in the observing system have advanced our understanding and prediction of ocean variations at mesoscale and climate scales. Use of these systems for assessing the observing system helps identify the strengths of each observation type. Results indicate that the ocean remains under-sampled and that further improvements in the observing system are needed. Prospects for future advances lie in improved models and better estimates of error statistics for both models and observations. Future developments will be increasingly towards consistent analyses across components of the Earth system. However, even today ocean synthesis and assimilation systems are providing products that are useful for many applications and should be considered an integral part of the global ocean observing and information system.
Over the 20th and 21st centuries, both anthropogenic greenhouse gas increases and changes in anthropogenic aerosols have affected rainfall in the Sahel. Using multiple characteristics of Sahel precipitation, we construct a multivariate fingerprint that allows us to distinguish between the model-predicted responses to greenhouse gases and anthropogenic aerosols. Models project the emergence of a detectable signal of aerosol forcing in the middle of the 20th century and a detectable signal of greenhouse gas forcing at the beginning of the 21st. However, the signals of both aerosol and greenhouse gas forcing in observations emerge earlier and are stronger than in the models, far stronger in the case of aerosols. The similarity between the response to aerosol forcing and the leading mode of internal variability makes it difficult to attribute this model-observation discrepancy to errors in the forcing, errors in the forced response, model inability to capture the amplitude of internal variability, or some combination of these. For greenhouse gases, however, the forced response is distinct from internal variability as estimated by models, and the observations are largely commensurate with the model projections.
Cases of absorbing aerosols above clouds (AACs), such as smoke or mineral dust, are omitted from most routinely processed space-based aerosol optical depth (AOD) data products, including those from the Moderate Resolution Imaging Spectroradiometer (MODIS). This study presents a sensitivity analysis and preliminary algorithm to retrieve above-cloud AOD and liquid cloud optical depth (COD) for AAC cases from MODIS or similar sensors, for incorporation into a future version of the "Deep Blue" AOD data product. Detailed retrieval simulations suggest that these sensors should be able to determine AAC AOD with a typical level of uncertainty approximately 25-50 percent (with lower uncertainties for more strongly absorbing aerosol types) and COD with an uncertainty approximately10-20 percent, if an appropriate aerosol optical model is known beforehand. Errors are larger, particularly if the aerosols are only weakly absorbing, if the aerosol optical properties are not known, and the appropriate model to use must also be retrieved. Actual retrieval errors are also compared to uncertainty envelopes obtained through the optimal estimation (OE) technique; OE-based uncertainties are found to be generally reasonable for COD but larger than actual retrieval errors for AOD, due in part to difficulties in quantifying the degree of spectral correlation of forward model error. The algorithm is also applied to two MODIS scenes (one smoke and one dust) for which near-coincident NASA Ames Airborne Tracking Sun photometer (AATS) data were available to use as a ground truth AOD data source, and found to be in good agreement, demonstrating the validity of the technique with real observations.
Although solar activity prediction uncertainty normally dominates decay prediction error budget for near-Earth spacecraft, the effect of drag force modeling errors for given levels of solar activity needs to be considered. Two atmospheric density models, the modified Harris-Priester model and the Jacchia-Roberts model, to reproduce the decay histories of the Solar Mesosphere Explorer (SME) and Solar Maximum Mission (SMM) spacecraft in the 490- to 540-kilometer altitude range were analyzed. Historical solar activity data were used in the input to the density computations. For each spacecraft and atmospheric model, a drag scaling adjustment factor was determined for a high-solar-activity year, such that the observed annual decay in the mean semimajor axis was reproduced by an averaged variation-of-parameters (VOP) orbit propagation. The SME (SMM) calibration was performed using calendar year 1983 (1982). The resulting calibration factors differ by 20 to 40 percent from the predictions of the prelaunch ballistic coefficients. The orbit propagations for each spacecraft were extended to the middle of 1988 using the calibrated drag models. For the Jaccia-Roberts density model, the observed decay in the mean semimajor axis of SME (SMM) over the 4.5-year (5.5-year) predictive period was reproduced to within 1.5 (4.4) percent. The corresponding figure for the Harris-Priester model was 8.6 (20.6) percent. Detailed results and conclusions regarding the importance of accurate drag force modeling for lifetime predictions are presented.
A set of observing system simulation experiments (OSSEs) was performed to investigate the utility of a constellation of passive infrared spectrometers, strategically designed with the aim of deriving the three-dimensional retrievals of the horizontal wind via atmospheric motion vectors (AMVs) from instruments with the spectral resolution of an infrared sounder. The instrument and constellation designs were performed in the context of the Midwave Infrared Sounding of Temperature and humidity in a Constellation for Winds (MISTiC Winds). The Global Modeling and Assimilation Office OSSE system, which includes a full suite of operational meteorological observations, served as the control. To illustrate the potential impact of this observing strategy, two experiments were performed by adding the new simulated observations to the control. First, perfect (error free) simulated AMVs and radiances were assimilated. Second, the data were made imperfect by adding realistic modeled errors to the AMVs and radiances that were assimilated. The experimentation showed beneficial impacts on both the mass and wind fields, as based on analysis verification, forecast verification, and the assessment of the observations using the forecast sensitivity to observation impact (FSOI) metric. In all variables and metrics, the impacts of the imperfect observations were smaller than those of the perfect observations, although much of the positive benefit was retained. The FSOI metric illustrated two key points. First, the largest impacts were seen in the middle troposphere AMVs, which is a targeted capability of the constellation strategy. Second, the addition of modeled errors showed that the assimilation system was unable to fully exploit the 4.3-μm carbon dioxide absorption radiances.
The objective of this paper is to design a discrete-time controller which forces y(t) = F(q(t),q'(t)) to follow a desired trajectory, when non-linearities may be uncertain. A self-tuning adaptive control algorithm is then developed that addresses three types of errors: (1) error due to model linearization; (2) errors due to controlling a time-varying plant; and (3) errors due to discretization.