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NASA NTRS2014

Assessment of Satellite Ocean Colour Radiometry and Derived Geophysical Products

Standardization of methods to assess and assign quality metrics to satellite ocean color radiometry and derived geophysical products has become paramount with the inclusion of the marine reflectance and chlorophyll-a concentration (Chla) as essential climate variables (ECV; [1]) and the recognition that optical remote sensing of the oceans can only contribute to climate research if and when a continuous succession of satellite missions can be shown to collectively provide a consistent, long-term record with known uncertainties. In 20 years, the community has made significant advancements toward that objective, but providing a complete uncertainty budget for all products and for all conditions remains a daunting task. In the retrieval of marine water-leaving radiance from observed top-of-atmosphere radiance, the sources of uncertainties include those associated with propagation of sensor noise and radiometric calibration and characterization errors, as well as a multitude of uncertainties associated with the modeling and removal of effects from the atmosphere and sea surface. This chapter describes some common approaches used to assess quality and consistency of ocean color satellite products and reviews the current status of uncertainty quantification in the field. Its focus is on the primary ocean color product, the spectrum of marine reflectance Rrs, but uncertainties in some derived products such as the Chla or inherent optical properties (IOPs) will also be considered.

Ocean↗

NASA NTRS2018

An Assessment of the Differences Between Spatial Resolution and Grid Size for the SMAP Enhanced Soil Moisture Product over Homogeneous Sites

Satellite-based passive microwave remote sensing typically involves a scanning antenna that makes measurements at irregularly spaced locations. These locations can change on a day to day basis. Soil moisture products derived from satellite-based passive microwave remote sensing are usually resampled to a fixed Earth grid that facilitates their use in applications. In many cases the grid size is finer than the actual spatial resolution of the observation, and often this difference is not well understood by the user. Here, this issue was examined for the Soil Moisture Active Passive (SMAP) enhanced version of the passive-based soil moisture product, which has a grid size of 9-km and a nominal spatial resolution of 33-km. In situ observations from core validation sites were used to compute comparison metrics. For sites that satisfied the established reliability and scaling criteria, the impact of validating the 9-km grid product with in situ data collected over a 9-km versus a 33-km domain was very small for the sites studied (0.039 cu. m/cu. m unbiased root mean square difference for the 9-km case versus 0.037 cu. m/cu. m for the 33-km case). This result does not mean that the resolution of the product is 9-km but that for the conditions studied here the soil moisture estimated from in situ observations over 9-km is a close approximation of the soil moisture estimated from in situ observations over the 33-km resolution. The implication is that using the enhanced SMAP product at its grid resolution of 9-km should not introduce large errors in most applications.

Soil moisture↗

NASA NTRSDate not supplied

Evaluating Retrieval Algorithm Climate Stability: Estimating 3D Optical Thickness Bias Distributions by Cloud Type

Detecting climate trends on large spatiotemporal scales requires accurate, stable measurements and stable retrieval algorithms. We strive to estimate how time-variant retrieval algorithm biases may impact trend detection. Here we focus on the 3D cloud optical thickness (τc) bias, which is among the largest in passive cloud retrieval algorithms. If this bias is time dependent, a possibility with potential decadal changes in cloud morphology, it may obscure genuine trends in τc. Although previous studies have evaluated the cloud- and sun-view geometry-dependent 3D τc bias on small spatial scales, before our current study none have evaluated the stability of this well-known bias on climate-relevant large spatiotemporal scales. These studies must estimate large scale distributions of the 3D τc bias by cloud type and estimate how cloud type amount may change between two climate states. We employ a novel approach to estimate large scale distributions of 3D τc using a proxy of the bias that quantifies the departure of clouds from satisfying the 1D radiative transfer assumption used in passive τc retrievals. This existing globally-distributed proxy is an angular consistency metric that was developed using fused Moderate-Resolution Imaging Spectroradiometer (MODIS) and Multi-angle Imaging Spectroradiometer (MISR) measurements. Calculating the 3D τc bias and the proxy, for known cloud fields enables us to establish statistical relationships between these two quantities, which can be used to calculate large-scale distributions of the 3D τc bias. This approach limits the number of 3D radiative transfer simulations required to only those needed to estimate a statistical relationship between the 3D τc bias for known cloud fields and a proxy of the bias. It is likely that future studies will be needed to evaluate retrieval algorithm bias stability for other geophysical variables as the community develops climate data records from satellite observations and their retrievals. This must be done in addition to monitoring and correcting measurement errors and uncertainties and understanding their impact on retrieved essential climate variables.

Yolanda Shea↗

NASA NTRS2013

Dynamics and Control of a Disordered System in Space

In this paper, we present some ideas regarding the modeling, dynamics and control aspects of granular spacecraft. Granular spacecraft are complex multibody systems composed of a spatially disordered distribution of a large number of elements, for instance a cloud of N grains in orbit, with N greater than 10(exp 3). These grains can be large (Cubesat-size) or small (mm-size), and can be active, i.e., a fully equipped vehicle capable sensing their own position and attitude, and enabled with propulsion means, or entirely passive. The ultimate objective would be to study the behavior of the single grains and of large ensembles of grains in orbit and to identify ways to guide and control the shape of a cloud composed of these grains so that it can perform a useful function in space, for instance, as an element of an optical imaging system for astrophysical applications. This concept, in which the aperture does not need to be continuous and monolithic, would increase the aperture size several times compared to large NASA observatories such as ATLAST, allowing for a true Terrestrial Planet Imager that would be able to resolve exo-planet details and do meaningful spectroscopy on distant world. In the paper, we address the modeling and autonomous operation of a distributed assembly (the cloud) of large numbers of highly miniaturized space-borne elements (the grains). A multi-scale, multi-physics model is proposed of the dynamics of the cloud in orbit, as well as a control law for cloud shape maintenance, and preliminary simulation studies yield an estimate of the computational effort, indicating a scale factor of approximately N(exp 1.4) as a function of the number of grains. A granular spacecraft can be defined as a collection of a large number of space-borne elements (in the 1000s) designed and controlled such that a desirable collective behavior emerges, either from the interactions among neighboring grains, and/or between the grains and the environment. In this paper, each grain is considered to be a highly miniaturized spacecraft which has limited size and mass, hence it has limited actuation, limited propulsive capability, limited power, limited sensing, limited communication, limited computational resources, limited range of motion, limited lifetime, and may be expendable. The modeling and dynamics of clouds of vehicles is more challenging than with conventional vehicles because we are faced with a probabilistic vehicle composed of a large number of physically disconnected vehicles. First, different scales of motion occur simultaneously in a cloud: translations and rotations of the cloud as a whole (macro-dynamics), relative rotation and translation of one cloud member with respect to another (meso-dynamics), and individual cloud member dynamics (micro-dynamics). Second, the control design needs to be tolerant of the system complexity, of the system architecture (centralized vs. decentralized large scale system control) as well as robust to un-modeled dynamics and noise sources. Figure 1, top left, shows the kinematic parameters of a 1000 element cloud in orbit. The motion of the system is described with respect to a local vertical-local horizontal (LV-LH) orbiting reference frame (x,y,z)=F(sub ORF) of origin O(sub ORF) which rotates with mean motion omega and orbital semi-major axis R(sub 0). The orbital geometry at the initial time is defined in terms of its six orbital elements, and the orbital dynamics equation for point O(sub ORF) is propagated forward in time under the influence of the gravitational field of the primary and other external perturbations, described below. The origin of this frame coincides with the initial position of the center of mass of the system, and the coordinate axes are z along the local vertical, x toward the flight direction, and y in the orbit normal direction. The assumptions we used to model the dynamics are as follows: 1) The inertial frame is fixed at Earth's center. 2) The orbiting Frame ORF follows Keplerian orbit. 3) the cloud system dynamics is referred to ORF. 4) the attitude of each grain uses the principal body frame as body fixed frame. 5) the atmosphere is assumed to be rigidly rotating with the Earth. Regarding the grains forming the cloud: 1) each grain is modeled as a rigid body; 2) a simple attitude estimator provides attitude estimates, 3) a simple guidance logic commands the position and attitude of each grain, 4) a simple local feedback controller based on PD control of local states is used to stabilize the attitude of the vehicle. Regarding the cloud: 1) the cloud as a whole is modeled as an equivalent rigid body in orbit, and 2) an associated graph establishes agent connectivity and enables coupling between modes of motion at the micro and macro scales; 3) a simple guidance and estimation logic is modeled to estimate and command the attitude of this equivalent rigid body; 4) a cloud shape maintenance controller is based on the dynamics of a stable virtual truss in the orbiting frame. Regarding the environmental perturbations acting on the cloud: 1) a non-spherical gravity field including JO (Earth's spherical field) zonal component, J2 (Earth's oblateness) and J3 zonal components is implemented; 2) atmospheric drag is modeled with an exponential model; 3) solar pressure is modeled assuming the Sun is inertially fixed; and 4) the Earth's magnetic field is model using an equivalent dipole model. The equations of motion are written in a referential system with respect to the origin of the orbiting frame and the state is propagated forward in time using an incremental predictor-corrector scheme. A representative cloud with varying number of grains is simulated to identify the limitations in computation time as the number of grains grows. We derive a control law to track a desired surface in the ORF (equivalently to maintain a reference cloud shape) by defining an error from a desired surface shape, and designing a control law that is exponentially stable and reduces the tracking error to zero. Figure 1 (top right) shows a comparison of various requirements for simulation of single spacecraft vs. granular spacecraft, indicating the high degree of complexity that needs to be taken into consideration. The ORF components of control force required by one of the grains is, for this particular case, in the micro-Newton range. However, no attempt has been made yet to reconfigure (or re-orient) the cloud configuration internally, for which forces in the milli-Newton level are expected, depending on the time required to do the reconfiguration. Figure 1, bottom, shows the computation time as a function of the number of grains, indicating an order N(exp 1.43) scaling on a 8 Gb, 1067 MHz RAM MacOSX computer with a 3.06 GHz Intel Core 2 Duo processor. With this metric, the same simulation for a system of N=1000 grains would take 5.4 hours, and 146 hours (i.e., 6 days) for a system with N=10,000 grains. Therefore, efficient ways to simulate this complex system, where not only the time scales of natural system dynamics, but also the sampling times of the Guidance, Navigation, and Control are included, remain to be explored. Additional details on the cloud modeling, dynamics, and control will be described in the paper.

simulation↗

NASA NTRS2017

The Challenge Posed by Geomagnetic Activity to Electric Power Reliability: Evidence from England and Wales

This paper addresses whether geomagnetic activity challenged the reliability of the electric power system during part of the declining phase of solar cycle 23. Operations by National Grid in England and Wales are examined over the period of 11 March 2003 through 31 March 2005. This paper examines the relationship between measures of geomagnetic activity and a metric of challenged electric power reliability known as the net imbalance volume (NIV). Measured in megawatt hours, NIV represents the sum of all energy deployments initiated by the system operator to balance the electric power system. The relationship between geomagnetic activity and NIV is assessed using a multivariate econometric model. The model was estimated using half-hour settlement data over the period of 11 March 2003 through 31 December 2004. The results indicate that geomagnetic activity had a demonstrable effect on NIV over the sample period. Based on the parameter estimates, out-of-sample predictions of NIV were generated for each half hour over the period of 1 January to 31 March 2005. Consistent with the existence of a causal relationship between geomagnetic activity and the electricity market imbalance, the root-mean-square error of the out-of-sample predictions of NIV is smaller; that is, the predictions are more accurate, when the statistically significant estimated effects of geomagnetic activity are included as drivers in the predictions.

Forbes, Kevin F.↗

DOE OSTI2021

Modeling Subsurface Explosions Recorded on a Distributed Fiber Optic Sensor

Fiber optic distributed acoustic sensors (DAS) are becoming a widely used tool for seismic sensing. Here we examine recordings of two subsurface chemical explosions, DAG-1 and DAG-3, each of which was about one metric ton (TNT equivalent), that were recorded from a helical fiber installed in two boreholes 80 m away from the source location. Several clear phases including the initial P wave, a weak S wave, and a surface reflected P wave are observed on the helical DAS data. We estimate a velocity model using arrival times measured from the fiber. The DAS waveform data were compared with colocated accelerometers at specific depths in both frequency and time domains. Furthermore, the spectra of the DAS data matched spectra estimated from the accelerometer records. Comparisons of observed waveform shape between the accelerometer records and the fiber measurements (strain-rate) show reasonable agreement except for the data near the event depth. The DAS data and the accelerometer agreed in relative amplitudes but we had difficulties in matching absolute amplitudes, possibly due to errors in metadata. Synthetic strain-rate waveforms were calculated using a 2D wavenumber algorithm and matched the waveform shape and relative amplitudes. In general, DAS is effective at recording strong ground motions at high spatial density. Comparison of the synthetic seismograms with observed data indicate that the waveforms are not consistent with a pure isotropic explosion source and that the observed S waves originate from very near the source region.

58 GEOSCIENCES↗

NASA NTRS2020

A Demonstration that Correcting for Completeness and Reliability Is Critical for Robust Occurrence Rates

A measurement of planetary occurrence rates based on a planet catalog should be robust against details of how initial detections were classified as planets or false positives. This is accomplished by supplying the catalog’s rate of missed planets (completeness) and rate of non-planets incorrectly called planets (reliability). The final Kepler data release (DR25) includes products that can be used with the DR25 planet candidate catalog to correct for completeness and reliability in occurrence rate estimates. This is made possible by the Kepler Robovetter, which algorithmically and uniformly selects planets based on a variety of metrics and thresholds. Completeness, reliability, and occurrence rates potentially depend on these Robovetter thresholds. We study the impact of varying these vetting thresholds using the techniques of Bryson et al. 2019 (arXiv:1906.03575). We explore sets of thresholds that result in more or fewer planets (trading off completeness for reliability), as well as thresholds tuned to pass DR25 false positives identified as possible planets by the Kepler False Positive Working Group. We find that when correcting only for completeness, and not reliability, the resulting occurrence rates have a strong dependence on these threshold sets. For example, the value of SAG13 eta-Earth varies by over a factor of 4 when not corrected for reliability. However, when correcting for both completeness and reliability, occurrence rates using our threshold sets are statistically indistinguishable, with differences being well inside 1-sigma error bars. We present occurrence rates integrated over several period-radius ranges. For example, SAG13 eta-Earth is consistent with 0.127 (+0.094)(-0.054) (from Bryson et al. 2019) for all the Robovetter threshold sets. This result emphasizes the importance of correcting occurrence rates for both completeness and reliability. This suggests that inconsistent completeness and reliability correction may be a significant contributor to the large variation of occurrence rates in recent literature. We plan to make the Robovetter results for our threshold sets available, and encourage the community to use them to examine whether other occurrence rate methods yield similarly robust results.

Bryson, S.↗

DOE OSTI2022

Automated Shift Detection in Sensor-Based PV Power and Irradiance Time Series: Preprint

PV power and irradiance sensor-based measurements are prone to error, resulting in issues such as abrupt time series data shifts. These shifts, which are usually unintentional, may be caused by software or hardware configuration changes on a PV system, and do not reflect an actual change in overall system performance. Locating these shifts and segmenting the associated time series aids in more accurate future PV analysis. In this research, an offline changepoint detection (CPD) algorithm that automatically detects these abrupt data shifts in sensor-based time series is introduced. Data shift periods in 101 daily PV power and irradiance time series were labeled manually by two solar experts. These data streams represent sensor-based measurements, and display a variety of data shift behaviors. A changepoint detection algorithm was tuned using the 101 labeled data streams, with each model configuration's ability to detect labeled changepoints benchmarked using metrics such as F1-score, recall, and Rand Index. Best performing models on seasonality-corrected data streams include the Pruned Exact Linear (PELT) method, the Binary Segmentation method, and the Bottom-Up method, all scoring an average F1-score of 0.76 or greater at detecting labeled changepoints within a 30-day window for the labeled data sets. To promote further research in this space, we are releasing the labeled data shift sets on U.S. Department of Energy's (DOE) DuraMAT Data Hub, and the associated algorithm in the Python PVAnalytics package.

changepoint detection↗

NASA NTRS2023

Atmospheric Correction Inter-comparison eXercise, ACIX-II Land: An Assessment of Amospheric Correction Processors for Landsat 8 and Sentinel-2 Over Land

The correction of the atmospheric effects on optical satellite images is essential for quantitative and multi-temporal remote sensing applications. In order to study the performance of the state-of-the-art methods in an integrated way, a voluntary and open-access benchmark Atmospheric Correction Inter-comparison eXercise (ACIX) was initiated in 2016 in the frame of Committee on Earth Observation Satellites (CEOS) Working Group on Calibration & Validation (WGCV). The first exercise was extended in a second edition wherein twelve atmospheric correction (AC) processors, a substantially larger testing dataset and additional validation metrics were involved. The sites for the inter-comparison analysis were defined by investigating the full catalogue of the Aerosol Robotic Network (AERONET) sites for coincident measurements with satellites' overpass. Although there were more than one hundred sites for Copernicus Sentinel-2 and Landsat 8 acquisitions, the analysis presented in this paper concerns only the common matchups amongst all processors, reducing the number to 79 and 62 sites respectively. Aerosol Optical Depth (AOD) and Water Vapour (WV) retrievals were consequently validated based on the available AERONET observations. The processors mostly succeeded in retrieving AOD for relatively light to medium aerosol loading (AOD < 0.2) with uncertainties <0.08, while the overall uncertainty values were typically 0.23 ± 0.15. Better performances were observed for WV retrievals with >90% of the results falling within the suggested empirical specifications and with the Root Mean Square Error (RMSE) being mostly <0.25 g/cm2. Regarding Surface Reflectance (SR) validation two main approaches were followed. For the first one, a simulated SR reference dataset was computed over all of the test sites by using the 6SV (Second Simulation of the Satellite Signal in the Solar Spectrum vector code) full radiative transfer modelling (RTM) and AERONET measurements for the required aerosol variables and water vapour content. The performance assessment demonstrated that the retrievals were not biased for most of the bands. The uncertainties ranged from approximately 0.003 to 0.01 (excluding B01) for the best performing processors in both sensors' analyses. For the second one, measurements from the radiometric calibration network RadCalNet over La Crau (France) and Gobabeb (Namibia) were involved in the validation. The performance of the processors was in general consistent across all bands for both sensors and with low standard deviations (<0.04) between on-site and estimated surface reflectance. Overall, our study provides a good insight of AC algorithms' performance to developers and users, pointing out similarities and differences for AOD, WV and SR retrievals. Such validation though still lacks of ground-based measurements of known uncertainty to better assess and characterize the uncertainties in SR retrievals.

Atmospheric correction↗

DOE OSTI2022

Automated Shift Detection in Sensor-Based PV Power and Irradiance Time Series

changepoint detection↗

NASA NTRS2017

Mind the Gap: Exploring the Underground of the NASA Space Cancer Risk Model

The REID quantifies the lifetime risk of death from radiation-induced cancer in an exposed astronaut. The NASA Space Cancer Risk (NSCR) 2012 mode incorporates elements from physics, biology, epidemiology, and statistics to generate the REID distribution. The current model quantifies the space radiation environment, radiation quality, and dose-rate effects to estimate a NASA-weighted dose. This weighted dose is mapped to the excess risk of radiation-induced cancer mortality from acute exposures to gamma rays and then transferred to an astronaut population. Finally, the REID is determined by integrating this risk over the individual's lifetime. The calculated upper 95% confidence limit of the REID is used to restrict an astronaut's permissible mission duration (PMD) for a proposed mission. As a statistical quantity characterized by broad, subjective uncertainties, REID estimates for space missions result in wide distributions. Currently, the upper 95% confidence level is over 350% larger than the mean REID value, which can severely limit an astronaut's PMD. The model incorporates inputs from multiple scientific disciplines in the risk estimation process. Physics and particle transport models calculate how radiation moves through space, penetrates spacecraft, and makes its way to the human beings onboard. Epidemiological studies of exposures from atomic bombings, medical treatments, and power plants are used to quantify health risks from acute and chronic low linear energy transfer (LET) ionizing radiation. Biological studies in cellular and animal models using radiation at various LETs and energies inform quality metrics for ions present in space radiation. Statistical methodologies unite these elements, controlling for mathematical and scientific uncertainty and variability. Despite current progress, these research platforms contain knowledge gaps contributing to the large uncertainties still present in the model. The NASA Space Radiation Program Element (SRPE) defines the knowledge gaps that impact our understanding of the cancer risks. These gaps are outlined in NASA's Human Research Roadmap [4], which identifies the research questions and actions recommended for reducing the uncertainty in the current NSCR model and for formulation of future models. The greatest contributors to uncertainty in the current model include radiation quality, dose rate effects, and the transfer of exposure-based risk from other populations to an astronaut population. Future formulations of the risk model may benefit from including other potential sources of uncertainty such as space dosimetry, errors in human epidemiology data, and the impact of microgravity and other spaceflight stressors. Here, we discuss the current capabilities of the NSCR-2012 model and several immediate research needs, highlighting areas expected to have an operational impact on the current model schema. The following subway-style route map outlines the NSCR-2012 model (Green Line), emphasizing the research gaps in the Human Research Roadmap for risk of radiation-induced carcinogenesis (Stops on Dashed Lines). The map diagrams how these research gaps feed specific portions of the model.

Chappell, L. J.↗

NASA NTRS2019

Application of Machine Learning Techniques to Delay Tolerant Network Routing

This dissertation discusses several machine learning techniques to improve routing in delay tolerant networks (DTNs). These are networks in which there may be long one-way trip times, asymmetric links, high error rates, and deterministic as well as non-deterministic loss of contact between network nodes, such as interplanetary satellite networks, mobile ad hoc networks and wireless sensor networks. This work uses historical network statistics to train a multi-label classifier to predict reliable paths through the network. In addition, a clustering technique is used to predict future mobile node locations. Both of these techniques are used to reduce the consumption of resources such as network bandwidth, memory and data storage that is required by replication routing methods often used in opportunistic DTN environments. Thesis contributions include: an emulation tool chain developed to create a DTN test bed for machine learning, the network and software architecture for a machine learning based routing method, the development and implementation of classification and clustering techniques and performance evaluation in terms of machine learning and routing metrics.

Dudukovich, Rachel M.↗

DOE OSTI2023

Differentiable Earth mover’s distance for data compression at the high-luminosity LHC

Abstract The Earth mover’s distance (EMD) is a useful metric for image recognition and classification, but its usual implementations are not differentiable or too slow to be used as a loss function for training other algorithms via gradient descent. In this paper, we train a convolutional neural network (CNN) to learn a differentiable, fast approximation of the EMD and demonstrate that it can be used as a substitute for computing-intensive EMD implementations. We apply this differentiable approximation in the training of an autoencoder-inspired neural network (encoder NN) for data compression at the high-luminosity LHC at CERN The goal of this encoder NN is to compress the data while preserving the information related to the distribution of energy deposits in particle detectors. We demonstrate that the performance of our encoder NN trained using the differentiable EMD CNN surpasses that of training with loss functions based on mean squared error.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗

NASA NTRS2017

Similarity Assessment of Land Surface Model Outputs in the North American Land Data Assimilation System

Multimodel ensembles are often used to produce ensemble mean estimates that tend to have increased simulation skill over any individual model output. If multimodel outputs are too similar, an individual LSM would add little additional information to the multimodel ensemble, whereas if the models are too dissimilar, it may be indicative of systematic errors in their formulations or configurations. The article presents a formal similarity assessment of the North American Land Data Assimilation System (NLDAS) multimodel ensemble outputs to assess their utility to the ensemble, using a confirmatory factor analysis. Outputs from four NLDAS Phase 2 models currently running in operations at NOAA/NCEP and four new/ upgraded models that are under consideration for the next phase of NLDAS are employed in this study. The results show that the runoff estimates from the LSMs were most dissimilar whereas the models showed greater similarity for root zone soil moisture, snow water equivalent, and terrestrial water storage. Generally, the NLDAS operational models showed weaker association with the common factor of the ensemble and the newer versions of the LSMs showed stronger association with the common factor, with the model similarity increasing at longer time scales. Trade-offs between the similarity metrics and accuracy measures indicated that the NLDAS operational models demonstrate a larger span in the similarity-accuracy space compared to the new LSMs. The results of the article indicate that simultaneous consideration of model similarity and accuracy at the relevant time scales is necessary in the development of multimodel ensemble.

land surface models↗

NASA NTRS2011

Finding Every Root of a Broad Class of Real, Continuous Functions in a Given Interval

One of the most pervasive needs within the Deep Space Network (DSN) Metric Prediction Generator (MPG) view period event generation is that of finding solutions to given occurrence conditions. While the general form of an equation expresses equivalence between its left-hand and right-hand expressions, the traditional treatment of the subject subtracts the two sides, leaving an expression of the form Integral of(x) = 0. Values of the independent variable x satisfying this condition are roots, or solutions. Generally speaking, there may be no solutions, a unique solution, multiple solutions, or a continuum of solutions to a given equation. In particular, all view period events are modeled as zero crossings of various metrics; for example, the time at which the elevation of a spacecraft reaches its maximum value, as viewed from a Deep Space Station (DSS), is found by locating that point at which the derivative of the elevation function becomes zero. Moreover, each event type may have several occurrences within a given time interval of interest. For example, a spacecraft in a low Moon orbit will experience several possible occultations per day, each of which must be located in time. The MPG is charged with finding all specified event occurrences that take place within a given time interval (or pass ), without any special clues from operators as to when they may occur, for the entire spectrum of missions undertaken by the DSN. For each event type, the event metric function is a known form that can be computed for any instant within the interval. A method has been created for a mathematical root finder to be capable of finding all roots of an arbitrary continuous function, within a given interval, to be subject to very lenient, parameterized assumptions. One assumption is that adjacent roots are separated at least by a given amount, xGuard. Any point whose function value is less than ef in magnitude is considered to be a root, and the function values at distances xGuard away from a root are larger than ef, unless there is another root located in this vicinity. A root is considered found if, during iteration, two root candidates differ by less than a pre-specified ex, and the optimum cubic polynomial matching the function at the end and at two interval points (that is within a relative error fraction L at its midpoint) is reliable in indicating whether the function has extrema within the interval. The robustness of this method depends solely on choosing these four parameters that control the search. The roots of discontinuous functions were also found, but at degraded performance.

Tausworthe, Robert C.↗

NASA NTRS2012

Reynolds-Averaged Turbulence Model Assessment for a Highly Back-Pressured Isolator Flowfield

The use of computational fluid dynamics in scramjet engine component development is widespread in the existing literature. Unfortunately, the quantification of model-form uncertainties is rarely addressed with anything other than sensitivity studies, requiring that the computational results be intimately tied to and calibrated against existing test data. This practice must be replaced with a formal uncertainty quantification process for computational fluid dynamics to play an expanded role in the system design, development, and flight certification process. Due to ground test facility limitations, this expanded role is believed to be a requirement by some in the test and evaluation community if scramjet engines are to be given serious consideration as a viable propulsion device. An effort has been initiated at the NASA Langley Research Center to validate several turbulence closure models used for Reynolds-averaged simulations of scramjet isolator flows. The turbulence models considered were the Menter BSL, Menter SST, Wilcox 1998, Wilcox 2006, and the Gatski-Speziale explicit algebraic Reynolds stress models. The simulations were carried out using the VULCAN computational fluid dynamics package developed at the NASA Langley Research Center. A procedure to quantify the numerical errors was developed to account for discretization errors in the validation process. This procedure utilized the grid convergence index defined by Roache as a bounding estimate for the numerical error. The validation data was collected from a mechanically back-pressured constant area (1 2 inch) isolator model with an isolator entrance Mach number of 2.5. As expected, the model-form uncertainty was substantial for the shock-dominated, massively separated flowfield within the isolator as evidenced by a 6 duct height variation in shock train length depending on the turbulence model employed. Generally speaking, the turbulence models that did not include an explicit stress limiter more closely matched the measured surface pressures. This observation is somewhat surprising, given that stress-limiting models have generally been developed to better predict shock-separated flows. All of the models considered also failed to properly predict the shape and extent of the separated flow region caused by the shock boundary layer interactions. However, the best performing models were able to predict the isolator shock train length (an important metric for isolator operability margin) to within 1 isolator duct height.

Baurle, Robert A.↗

NASA NTRS2012

Development of an OSSE Framework for a Global Atmospheric Data Assimilation System

Observing system simulation experiments (OSSEs) are powerful tools for estimating the usefulness of various configurations of envisioned observing systems and data assimilation techniques. Their utility stems from their being conducted in an entirely simulated context, utilizing simulated observations having simulated errors and drawn from a simulation of the earth's environment. Observations are generated by applying physically based algorithms to the simulated state, such as performed during data assimilation or using other appropriate algorithms. Adding realistic instrument plus representativeness errors, including their biases and correlations, can be critical for obtaining realistic assessments of the impact of a proposed observing system or analysis technique. If estimates of the expected accuracy of proposed observations are realistic, then the OSSE can be also used to learn how best to utilize the new information, accelerating its transition to operations once the real data are available. As with any inferences from simulations, however, it is first imperative that some baseline OSSEs are performed and well validated against corresponding results obtained with a real observing system. This talk provides an overview of, and highlights critical issues related to, the development of an OSSE framework for the tropospheric weather prediction component of the NASA GEOS-5 global atmospheric data assimilation system. The framework includes all existing observations having significant impact on short-term forecast skill. Its validity has been carefully assessed using a range of metrics that can be evaluated in both the OSSE and real contexts, including adjoint-based estimates of observation impact. A preliminary application to the Aeolus Doppler wind lidar mission, scheduled for launch by the European Space Agency in 2014, has also been investigated.

Gelaro, Ronald↗

NASA NTRS2013

A Signal Detection Theory Approach to Evaluating Oculometer Data Quality

Currently, data quality is described in terms of spatial and temporal accuracy and precision [Holmqvist et al. in press]. While this approach provides precise errors in pixels, or visual angle, often experiments are more concerned with whether subjects'points of gaze can be said to be reliable with respect to experimentally-relevant areas of interest. This paper proposes a method to characterize oculometer data quality using Signal Detection Theory (SDT) [Marcum 1947]. SDT classification results in four cases: Hit (correct report of a signal), Miss (failure to report a ), False Alarm (a signal falsely reported), Correct Reject (absence of a signal correctly reported). A technique is proposed where subjects' are directed to look at points in and outside of an AOI, and the resulting Points of Gaze (POG) are classified as Hits (points known to be internal to an AOI are classified as such), Misses (AOI points are not indicated as such), False Alarms (points external to AOIs are indicated as in the AOI), or Correct Rejects (points external to the AOI are indicated as such). SDT metrics describe performance in terms of discriminability, sensitivity, and specificity. This paper presentation will provide the procedure for conducting this assessment and an example of data collected for AOIs in a simulated flightdeck environment.

Latorella, Kara↗