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NASA NTRS1995

Mapping target signatures via partial unmixing of AVIRIS data

A complete spectral unmixing of a complicated AVIRIS scene may not always be possible or even desired. High quality data of spectrally complex areas are very high dimensional and are consequently difficult to fully unravel. Partial unmixing provides a method of solving only that fraction of the data inversion problem that directly relates to the specific goals of the investigation. Many applications of imaging spectrometry can be cast in the form of the following question: 'Are my target signatures present in the scene, and if so, how much of each target material is present in each pixel?' This is a partial unmixing problem. The number of unmixing endmembers is one greater than the number of spectrally defined target materials. The one additional endmember can be thought of as the composite of all the other scene materials, or 'everything else'. Several workers have proposed partial unmixing schemes for imaging spectrometry data, but each has significant limitations for operational application. The low probability detection methods described by Farrand and Harsanyi and the foreground-background method of Smith et al are both examples of such partial unmixing strategies. The new method presented here builds on these innovative analysis concepts, combining their different positive attributes while attempting to circumvent their limitations. This new method partially unmixes AVIRIS data, mapping apparent target abundances, in the presence of an arbitrary and unknown spectrally mixed background. It permits the target materials to be present in abundances that drive significant portions of the scene covariance. Furthermore it does not require a priori knowledge of the background material spectral signatures. The challenge is to find the proper projection of the data that hides the background variance while simultaneously maximizing the variance amongst the targets.

Boardman, Joseph W.↗
NASA NTRS2001

The Computational Complexity, Parallel Scalability, and Performance of Atmospheric Data Assimilation Algorithms

The computational complexity of algorithms for Four Dimensional Data Assimilation (4DDA) at NASA's Data Assimilation Office (DAO) is discussed. In 4DDA, observations are assimilated with the output of a dynamical model to generate best-estimates of the states of the system. It is thus a mapping problem, whereby scattered observations are converted into regular accurate maps of wind, temperature, moisture and other variables. The DAO is developing and using 4DDA algorithms that provide these datasets, or analyses, in support of Earth System Science research. Two large-scale algorithms are discussed. The first approach, the Goddard Earth Observing System Data Assimilation System (GEOS DAS), uses an atmospheric general circulation model (GCM) and an observation-space based analysis system, the Physical-space Statistical Analysis System (PSAS). GEOS DAS is very similar to global meteorological weather forecasting data assimilation systems, but is used at NASA for climate research. Systems of this size typically run at between 1 and 20 gigaflop/s. The second approach, the Kalman filter, uses a more consistent algorithm to determine the forecast error covariance matrix than does GEOS DAS. For atmospheric assimilation, the gridded dynamical fields typically have More than 10(exp 6) variables, therefore the full error covariance matrix may be in excess of a teraword. For the Kalman filter this problem can easily scale to petaflop/s proportions. We discuss the computational complexity of GEOS DAS and our implementation of the Kalman filter. We also discuss and quantify some of the technical issues and limitations in developing efficient, in terms of wall clock time, and scalable parallel implementations of the algorithms.

Lyster, Peter M.↗
NASA NTRS2013

EO-1 Hyperion Reflectance Time Series at Calibration and Validation Sites: Stability and Sensitivity to Seasonal Dynamics

This study evaluated Earth Observing 1 (EO-1) Hyperion reflectance time series at established calibration sites to assess the instrument stability and suitability for monitoring vegetation functional parameters. Our analysis using three pseudo-invariant calibration sites in North America indicated that the reflectance time series are devoid of apparent spectral trends and their stability consistently is within 2.5-5 percent throughout most of the spectral range spanning the 12-plus year data record. Using three vegetated sites instrumented with eddy covariance towers, the Hyperion reflectance time series were evaluated for their ability to determine important variables of ecosystem function. A number of narrowband and derivative vegetation indices (VI) closely described the seasonal profiles in vegetation function and ecosystem carbon exchange (e.g., net and gross ecosystem productivity) in three very different ecosystems, including a hardwood forest and tallgrass prairie in North America, and a Miombo woodland in Africa. Our results demonstrate the potential for scaling the carbon flux tower measurements to local and regional landscape levels. The VIs with stronger relationships to the CO2 parameters were derived using continuous reflectance spectra and included wavelengths associated with chlorophyll content and/or chlorophyll fluorescence. Since these indices cannot be calculated from broadband multispectral instrument data, the opportunity to exploit these spectrometer-based VIs in the future will depend on the launch of satellites such as EnMAP and HyspIRI. This study highlights the practical utility of space-borne spectrometers for characterization of the spectral stability and uniformity of the calibration sites in support of sensor cross-comparisons, and demonstrates the potential of narrowband VIs to track and spatially extend ecosystem functional status as well as carbon processes measured at flux towers.

Calibration↗
NASA NTRS1999

NASA Lewis Launch Collision Probability Model Developed and Analyzed

There are nearly 10,000 tracked objects orbiting the earth. These objects encompass manned objects, active and decommissioned satellites, spent rocket bodies, and debris. They range from a few centimeters across to the size of the MIR space station. Anytime a new satellite is launched, the launch vehicle with its payload attached passes through an area of space in which these objects orbit. Although the population density of these objects is low, there always is a small but finite probability of collision between the launch vehicle and one or more of these space objects. Even though the probability of collision is very low, for some payloads even this small risk is unacceptable. To mitigate the small risk of collision associated with launching at an arbitrary time within the daily launch window, NASA performs a prelaunch mission assurance Collision Avoidance Analysis (or COLA). For the COLA of the Cassini spacecraft, the NASA Lewis Research Center conducted an in-house development and analysis of a model for launch collision probability. The model allows a minimum clearance criteria to be used with the COLA analysis to ensure an acceptably low probability of collision. If, for any given liftoff time, the nominal launch vehicle trajectory would pass a space object with less than the minimum required clearance, launch would not be attempted at that time. The model assumes that the nominal positions of the orbiting objects and of the launch vehicle can be predicted as a function of time, and therefore, that any tracked object that comes within close proximity of the launch vehicle can be identified. For any such pair, these nominal positions can be used to calculate a nominal miss distance. The actual miss distances may differ substantially from the nominal miss distance, due, in part, to the statistical uncertainty of the knowledge of the objects positions. The model further assumes that these position uncertainties can be described with position covariance matrices. With these, and some additional simplifying assumptions, a closed-form solution for the probability of collision is obtained. This solution provides clear insights into how each of the independent parameters affects the probability of collision. It shows that for a given maximum probability of collision and prior knowledge of the objects position uncertainties and sizes, only knowledge of the nominal closest approach distance is required to make the launch/no launch decision. The model was completed and used for the mission assurance COLA analysis for the Cassini spacecraft, which was launched on a Titan IV/Centaur rocket on October 15, 1997. Although the model was specifically developed for the Cassini mission, it is clearly applicable for other launches as well. The effect of COLA closures on the launch window is shown. The bar represents the entire 140-min launch window on October 15, 1997; the blackened areas represent the loss of launch opportunities due to the potential for a collision with an orbiting object.

Bollenbacher, Gary↗
NASA NTRS2022

Observation Impact and Information Retention in the Lower Troposphere of the GMAO GEOS Data Assimilation System

In this study, we have assessed the effectiveness of the use of existing observing systems in the lower troposphere in the GEOS hybrid–4DEnVar data assimilation system through a set of observing system experiments. The results show that microwave radiances have a large impact in the Southern Hemisphere and Tropical ocean, but the large influence is mostly observed above 925 hPa and dissipates relatively quickly with longer forecast lead times. Conventional data information holds better in the forecast ranging from the surface to 100 hPa, depending on the field evaluated, in the Northern Hemisphere and lowest model levels in the Tropics. Infrared radiances collectively have much less impact in the lower troposphere. Removing surface observations has small but persistent impact on specific humidity in the upper atmosphere, but small or negligible impact on planetary boundary layer (PBL) height and temperature. The model responses to the incremental analysis update (IAU) forcing are also analyzed. In the IAU assimilation window, the physics responds strongly to the IAU forcing in the lower troposphere, and the changes of physics tendency in the lower troposphere and hydrodynamics tendency in the mid- and upper troposphere are viewed as beneficial to the reduction of state error covariance. In the subsequent forecast, the model tendencies continue to deviate further from the original free forecast with forecast lead times around 300–400 hPa, but physics tendency has showed signs of returning to its original free forecast mechanisms at 1-day forecast in the lower troposphere.

GEOS↗
NASA NTRS1972

The formation and analysis of a 5 deg equal area block terrestrial gravity field

A set of 23,355 1 degree x 1 degree mean free air anomalies were used to predict a set of 5 degree equal area anomalies and their standard errors. Using the 1 degree data incorporating geophysically predicted values of ACIC, 1283 5 degree blocks were computed. Excluding the geophysically predicted anomalies 1249 blocks were computed. The 1 degree data were also used to compute covariance functions and the equatorial gravity and flattening implied by this data. The predicted anomalies were supplemented by model anomalies to form a complete 1654 global anomaly field. These data were used in a weighted least squares to determine potential coefficients to degree 15, and in a summation type formulation to determine potential coefficients to degree 25. These potential coefficients sets are compared to recent satellite determinations.

Rapp, R. H.↗
NASA NTRS1980

A harmonic analysis of lunar gravity

An improved model of lunar global gravity has been obtained by fitting a sixteenth-degree harmonic series to a combination of Doppler tracking data from Apollo missions 8, 12, 15, and 16, and Lunar Orbiters 1, 2, 3, 4, and 5, and laser ranging data to the lunar surface. To compensate for the irregular selenographic distribution of these data, the solution algorithm has also incorporated a semi-empirical a priori covariance function. Maps of the free-air gravity disturbance and its formal error are presented, as are free-air anomaly and Bouguer anomaly maps. The lunar gravitational variance spectrum has the form V(G; n) = O(n to the -4th power), as do the corresponding terrestrial and martian spectra. The variance spectra of the Bouguer corrections (topography converted to equivalent gravity) for these bodies have the same basic form as the observed gravity; and, in fact, the spectral ratios are nearly constant throughout the observed spectral range for each body. Despite this spectral compatibility, the correlation between gravity and topography is generally quite poor on a global scale.

Bills, B. G.↗
NASA NTRS1989

Analysis of modified SMI method for adaptive array weight control

An adaptive array is applied to the problem of receiving a desired signal in the presence of weak interference signals which need to be suppressed. A modification, suggested by Gupta, of the sample matrix inversion (SMI) algorithm controls the array weights. In the modified SMI algorithm, interference suppression is increased by subtracting a fraction F of the noise power from the diagonal elements of the estimated covariance matrix. Given the true covariance matrix and the desired signal direction, the modified algorithm is shown to maximize a well-defined, intuitive output power ratio criterion. Expressions are derived for the expected value and variance of the array weights and output powers as a function of the fraction F and the number of snapshots used in the covariance matrix estimate. These expressions are compared with computer simulation and good agreement is found. A trade-off is found to exist between the desired level of interference suppression and the number of snapshots required in order to achieve that level with some certainty. The removal of noise eigenvectors from the covariance matrix inverse is also discussed with respect to this application. Finally, the type and severity of errors which occur in the covariance matrix estimate are characterized through simulation.

Dilsavor, R. L.↗
NASA NTRS1996

Uncertainty Modeling for Structural Control Analysis and Synthesis

The development of an accurate model of uncertainties for the control of structures that undergo a change in operational environment, based solely on modeling and experimentation in the original environment is studied. The application used throughout this work is the development of an on-orbit uncertainty model based on ground modeling and experimentation. A ground based uncertainty model consisting of mean errors and bounds on critical structural parameters is developed. The uncertainty model is created using multiple data sets to observe all relevant uncertainties in the system. The Discrete Extended Kalman Filter is used as an identification/parameter estimation method for each data set, in addition to providing a covariance matrix which aids in the development of the uncertainty model. Once ground based modal uncertainties have been developed, they are localized to specific degrees of freedom in the form of mass and stiffness uncertainties. Two techniques are presented: a matrix method which develops the mass and stiffness uncertainties in a mathematical manner; and a sensitivity method which assumes a form for the mass and stiffness uncertainties in macroelements and scaling factors. This form allows the derivation of mass and stiffness uncertainties in a more physical manner. The mass and stiffness uncertainties of the ground based system are then mapped onto the on-orbit system, and projected to create an analogous on-orbit uncertainty model in the form of mean errors and bounds on critical parameters. The Middeck Active Control Experiment is introduced as experimental verification for the localization and projection methods developed. In addition, closed loop results from on-orbit operations of the experiment verify the use of the uncertainty model for control analysis and synthesis in space.

Campbell, Mark E.↗
NASA NTRS1977

Updated dispersion analysis for the first Orbital Flight Test (OFT-1) mission

A dispersion analysis considering 3-sigma uncertainties (or perturbations) in platform, vehicle, and environmental parameters was performed for the first orbital flight test (OFT-1) mission. The dispersion analysis is based on the nominal trajectory for the OFT-1 reference flight profile and was performed to determine state vector and performance dispersions (or variations) which result from the indicated 3 sigma uncertainties. The dispersions are determined at major mission events and fixed times from liftoff (time slices). Principal error contributors to the covariance matrix are listed. The dispersion data indicates that the largest position error occurs in the down range component. At main engine cutoff and circularization, the vehicle performance uncertainties are the major contributors to down range error.

Snow, L. S.↗
NASA NTRS2013

Space Weather Impacts to Conjunction Assessment: A NASA Robotic Orbital Safety Perspective

National Aeronautics and Space Administration (NASA) recognizes the risk of on-orbit collisions from other satellites and debris objects and has instituted a process to identify and react to close approaches. The charter of the NASA Robotic Conjunction Assessment Risk Analysis (CARA) task is to protect NASA robotic (unmanned) assets from threats posed by other space objects. Monitoring for potential collisions requires formulating close-approach predictions a week or more in the future to determine analyze, and respond to orbital conjunction events of interest. These predictions require propagation of the latest state vector and covariance assuming a predicted atmospheric density and ballistic coefficient. Any differences between the predicted drag used for propagation and the actual drag experienced by the space objects can potentially affect the conjunction event. Therefore, the space environment itself, in particular how space weather impacts atmospheric drag, is an essential element to understand in order effectively to assess the risk of conjunction events. The focus of this research is to develop a better understanding of the impact of space weather on conjunction assessment activities: both accurately determining the current risk and assessing how that risk may change under dynamic space weather conditions. We are engaged in a data-- ]mining exercise to corroborate whether or not observed changes in a conjunction event's dynamics appear consistent with space weather changes and are interested in developing a framework to respond appropriately to uncertainty in predicted space weather. In particular, we use historical conjunction event data products to search for dynamical effects on satellite orbits from changing atmospheric drag. Increased drag is expected to lower the satellite specific energy and will result in the satellite's being 'later' than expected, which can affect satellite conjunctions in a number of ways depending on the two satellites' orbits and the geometry of the conjunction. These satellite time offsets can form the basis of a new technique under development to determine whether space weather perturbations, such as coronal mass ejections, are likely to increase, decrease, or have a neutral effect on the collision risk due to a particular close approach.

Ghrist, Richard↗
NASA NTRS2022

Evaluating Approaches Relating Ecosystem Productivity with Desis Spectral Information

Data from the DLR Earth Sensing Imaging Spectrometer (DESIS), mounted on the International Space Station (ISS), were used to develop and test algorithms for remotely retrieving ecosystem productivity. Twenty DESIS images were used from three widely separated forested study sites representing deciduous and conifer forests. Gross primary production (GPP) values from eddy covariance flux towers at the sites were matched with DESIS spectral reflectances collected on the same days. Multiple algorithms were successful relating spectral reflectance with GPP, including: spectral vegetation indices (SVI) sensitive to chlorophyll content, SVI used in a photosynthetic light-use efficiency model framework, spectral shape characteristics through spectral derivatives and absorption feature analysis, and statistical models leading to multiband hyperspectral indices from partial least squares regression. Successful algorithms were able to achieve R2 better than 0.7 using a diverse set of observations combining data from different sites from multiple years and at multiple times during the year. The demonstrated robustness of the algorithms provides some confidence in using DESIS imagery to map spatial patterns of GPP.

K F Huemmrich↗
NASA NTRS1989

Remote sensing and numerical modeling of suspended sediment in Laguna de Terminos, Campeche, Mexico

It is necessary to understand the complex physical processes at work in coastal lagoons in order to manage them effectively. Improved methods of data collection and analysis must be found to provide synoptic, timely hydrodynamic information because of the sheer size of some lagoons and the difficulty of acquiring in situ data (particularly in the tropics). This paper summarizes research to model salinity and suspended sediment distributions in Laguna de Terminos, Mexico, using (1) a coupled hydrodynamic and dispersion model and (2) analysis of two Landsat Thematic Mapper images collected on November 25, 1984 and April 24, 1987. Atmospherically corrected chromaticity data derived from Thermatic Mapper data were significantly correlated with modeled total suspended sediment concentrations for the two dates. Comparison between numerically modeled and remotely sensed suspended sediment maps at 1.5 x 1.5 km resolution yielded a covariation map useful for identifying areas of discrepancy between the remotely sensed data and model output.

Jensen, John R.↗
NASA NTRS1991

Analysis of altimetry over the Aral Sea

Satellite based altimetric data taken by GEOS-3, SEASAT, and GEOSAT over the Aral Sea are analyzed and a least squares collocation technique is used to predict the geoid undulations on a 0.25 by 0.25 degree grid and to transform these geoid undulations to free air gravity anomalies. Rapp's 180 by 180 geopotential model is taken as the empirical model. The collocation procedure is performed with a set of local residual empirical covariance functions. For comparison, Rapp's global covariance functions and Jordan's self-consistent theoretical covariance functions based on Jordan's formulation and on locally derived parameters are also used to grid geoid undulations and to predict gravity anomalies. The sensitivity of the collocation results to the choice of covariance functions is discussed.

Au, Andrew Y.↗
NASA NTRS2004

Recent Climate Variability in Antarctica from Satellite-derived Temperature Data

Recent Antarctic climate variability on month-to-month to interannual time scales is assessed through joint analysis of surface temperatures from satellite thermal infrared observations (T(sub IR)) and passive microwave brightness temperatures (T(sub B)). Although Tw data are limited to clear-sky conditions and T(sub B) data are a product of the temperature and emissivity of the upper approx. 1m of snow, the two data sets share significant covariance. This covariance is largely explained by three empirical modes, which illustrate the spatial and temporal variability of Antarctic surface temperatures. T(sub B) variations are damped compared to TIR variations, as determined by the period of the temperature forcing and the microwave emission depth; however, microwave emissivity does not vary significantly in time. Comparison of the temperature modes with Southern Hemisphere (SH) 500-hPa geopotential height anomalies demonstrates that Antarctic temperature anomalies are predominantly controlled by the principal patterns of SH atmospheric circulation. The leading surface temperature mode strongly correlates with the Southern Annular Mode (SAM) in geopotential height. The second temperature mode reflects the combined influences of the zonal wavenumber-3 and Pacific South American (PSA) patterns in 500-hPa height on month-to-month timescales. ENSO variability projects onto this mode on interannual timescales, but is not by itself a good predictor of Antarctic temperature anomalies. The third temperature mode explains winter warming trends, which may be caused by blocking events, over a large region of the East Antarctic plateau. These results help to place recent climate changes in the context of Antarctica's background climate variability and will aid in the interpretation of ice core paleoclimate records.

Schneider, David P.↗
NASA NTRS2015

Peak Pc Prediction in Conjunction Analysis: Conjunction Assessment Risk Analysis

Satellite conjunction risk typically evaluated through the probability of collision (Pc). Considers both conjunction geometry and uncertainties in both state estimates. Conjunction events initially discovered through Joint Space Operations Center (JSpOC) screenings, usually seven days before Time of Closest Approach (TCA). However, JSpOC continues to track objects and issue conjunction updates. Changes in state estimate and reduced propagation time cause Pc to change as event develops. These changes a combination of potentially predictable development and unpredictable changes in state estimate covariance. Operationally useful datum: the peak Pc. If it can reasonably be inferred that the peak Pc value has passed, then risk assessment can be conducted against this peak value. If this value is below remediation level, then event intensity can be relaxed. Can the peak Pc location be reasonably predicted?

Operations↗
NASA NTRS2004

Three dimensional empirical mode decomposition analysis apparatus, method and article manufacture

An apparatus and method of analysis for three-dimensional (3D) physical phenomena. The physical phenomena may include any varying 3D phenomena such as time varying polar ice flows. A repesentation of the 3D phenomena is passed through a Hilbert transform to convert the data into complex form. A spatial variable is separated from the complex representation by producing a time based covariance matrix. The temporal parts of the principal components are produced by applying Singular Value Decomposition (SVD). Based on the rapidity with which the eigenvalues decay, the first 3-10 complex principal components (CPC) are selected for Empirical Mode Decomposition into intrinsic modes. The intrinsic modes produced are filtered in order to reconstruct the spatial part of the CPC. Finally, a filtered time series may be reconstructed from the first 3-10 filtered complex principal components.

Gloersen, Per↗
NASA NTRS2019

Decomposing Shortwave Top-of-Atmosphere and Surface Radiative Flux Variations in Terms of Surface and Atmospheric Contributions

Adiagnostic tool for determining surface and atmospheric contributions to interannual variations in top-of-atmosphere (TOA) reflected shortwave (SW) and net downward SW surface radiative fluxes is introduced. The method requires only upward and downward radiative fluxes at the TOA and surface as input and therefore can readily be applied to both satellite-derived and model-generated adiative fluxes. Observations from the Clouds and the Earth’s Radiant Energy System (CERES) Energy Balanced and Filled (EBAF) Edition 4.0 product show that 81% of the monthly variability in global mean reflected SW TOA flux anomalies is associated with atmospheric variations (mainly clouds),6%is from surface variations, and 13% is from atmosphere–surface covariability. Over the Arctic Ocean, most of the variability in both reflected SW TOA flux and net downward SW surface flux anomalies is explained by variations in sea ice and cloud fraction alone (r2 5 0.94). Compared to CERES, variability in two reanalyses—the ECMWF interim reanalysis (ERA-Interim) and NASA’s Modern-Era Retrospective Analysis for Research and Applications, version 2 (MERRA-2)—show large differences in the regional distribution of variance for both the atmospheric and surface contributions to anomalies in net downward SW surface flux. For MERRA-2 the atmospheric contribution is 17% too large compared to CERES while ERA-Interim underestimates the variance by 15%. The difference is mainly due to how cloud variations are represented in the reanalyses. The overall surface contribution in both ERA-Interim and MERRA-2 is smaller than CERES EBAF by 15% for ERA-Interim and 58% for MERRA-2, highlighting limitations of the reanalyses in representing surface albedo variations and their influence on SW radiative fluxes.

Norman G. Loeb↗