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NASA NTRS2015

Observing System Simulations for Small Satellite Formations Estimating Bidirectional Reflectance

The bidirectional reflectance distribution function (BRDF) gives the reflectance of a target as a function of illumination geometry and viewing geometry, hence carries information about the anisotropy of the surface. BRDF is needed in remote sensing for the correction of view and illumination angle effects (for example in image standardization and mosaicing), for deriving albedo, for land cover classification, for cloud detection, for atmospheric correction, and other applications. However, current spaceborne instruments provide sparse angular sampling of BRDF and airborne instruments are limited in the spatial and temporal coverage. To fill the gaps in angular coverage within spatial, spectral and temporal requirements, we propose a new measurement technique: Use of small satellites in formation flight, each satellite with a VNIR (visible and near infrared) imaging spectrometer, to make multi-spectral, near-simultaneous measurements of every ground spot in the swath at multiple angles. This paper describes an observing system simulation experiment (OSSE) to evaluate the proposed concept and select the optimal formation architecture that minimizes BRDF uncertainties. The variables of the OSSE are identified; number of satellites, measurement spread in the view zenith and relative azimuth with respect to solar plane, solar zenith angle, BRDF models and wavelength of reflection. Analyzing the sensitivity of BRDF estimation errors to the variables allow simplification of the OSSE, to enable its use to rapidly evaluate formation architectures. A 6-satellite formation is shown to produce lower BRDF estimation errors, purely in terms of angular sampling as evaluated by the OSSE, than a single spacecraft with 9 forward-aft sensors. We demonstrate the ability to use OSSEs to design small satellite formations as complements to flagship mission data. The formations can fill angular sampling gaps and enable better BRDF products than currently possible.

small satellite↗

NASA NTRS1989

Determination of the area and mass distribution of orbital debris fragments

A technique is described to estimate the area-to-mass ratio of debris fragments using orbital fragments obtained by radar. The area-to-mass ratio of about 2600 fragments arising from the breakup of 24 artificial satellites was determined; an analysis of the data on about 200 objects with known mass, size, and shape has been made, and a calibration of the observed radar cross-section (RCS) to the effective area of these objects has provided a method to estimate the effective area of debris fragments. From the knowledge of the effective area and the estimated area-to-mass ratio, the mass and area distribution of each of the known breakup has been obtained. As a function of time, the orbital elements can be used to invert any propagation algorithm to yield the area-to-mass ratio of an orbiting object.

Badhwar, Gautam D.↗

NASA NTRS1992

Detecting change as it occurs

Traditionally climate changes have been detected from long series of observations and long after they have happened. Our 'inverse sequential' procedure, for detecting change as soon as it occurs, describes the existing or most recent data by their frequency distribution. Its parameter(s) are estimated both from the existing set of observations and from the same set augmented by 1,2,....j new observations. Individual-value probability products ('likelihoods') are used to form ratios which yield two probabilities for erroneously accepting the existing parameter(s) as valid for the augmented data set, and vice versa. A genuine parameter change is signaled when these probabilities (or a more stable compound probability) show a progressive decrease. New parameter values can then be estimated from the new observations alone using standard statistical techniques. The inverse sequential procedure will be illustrated for global annual mean temperatures (assumed normally distributed), and for annual numbers of North Atlantic hurricanes (assumed to represent Poisson distributions). The procedure was developed, but not yet tested, for linear or exponential trends, and for chi-squared means or degrees of freedom, a special measure of autocorrelation.

Radok, Uwe↗

NASA NTRS2012

Validation of Airborne FMCW Radar Measurements of Snow Thickness Over Sea Ice in Antarctica

Antarctic sea ice and its snow cover are integral components of the global climate system, yet many aspects of their vertical dimensions are poorly understood, making their representation in global climate models poor. Remote sensing is the key to monitoring the dynamic nature of sea ice and its snow cover. Reliable and accurate snow thickness data are currently a highly sought after data product. Remotely sensed snow thickness measurements can provide an indication of precipitation levels, predicted to increase with effects of climate change in the polar regions. Airborne techniques provide a means for regional-scale estimation of snow depth and distribution. Accurate regional-scale snow thickness data will also facilitate an increase in the accuracy of sea ice thickness retrieval from satellite altimeter freeboard estimates. The airborne data sets are easier to validate with in situ measurements and are better suited to validating satellite algorithms when compared with in situ techniques. This is primarily due to two factors: better chance of getting coincident in situ and airborne data sets and the tractability of comparison between an in situ data set and the airborne data set averaged over the footprint of the antennas. A 28-GHz frequency modulated continuous wave (FMCW) radar loaned by the Center for Remote Sensing of Ice Sheets to the Australian Antarctic Division is used to measure snow thickness over sea ice in East Antarctica. Provided with the radar design parameters, the expected performance parameters of the radar are summarized. The necessary conditions for unambiguous identification of the airsnow and snowice layers for the radar are presented. Roughnesses of the snow and ice surfaces are found to be dominant determinants in the effectiveness of layer identification for this radar. Finally, this paper presents the first in situ validated snow thickness estimates over sea ice in Antarctica derived from an FMCW radar on a helicopterborne platform.

sea ice↗

NASA NTRS1992

Estimating the probability of failure when testing reveals no failures

Formulas for estimating the probability of failure when testing reveals no errors are introduced. These formulas incorporate random testing results, information about the input distribution, and prior assumptions about the probability of failure of the software. The formulas are not restricted to equally likely input distributions, and the probability of failure estimate can be adjusted when assumptions about the input distribution change. The formulas are based on a discrete sample space statistical model of software and include Bayesian prior assumptions. Reusable software and software in life-critical applications are particularly appropriate candidates for this type of analysis.

Miller, Keith W.↗

NASA NTRS1993

Rain-rate data base development and rain-rate climate analysis

The single-year rain-rate distribution data available within the archives of Consultative Committee for International Radio (CCIR) Study Group 5 were compiled into a data base for use in rain-rate climate modeling and for the preparation of predictions of attenuation statistics. The four year set of tip-time sequences provided by J. Goldhirsh for locations near Wallops Island were processed to compile monthly and annual distributions of rain rate and of event durations for intervals above and below preset thresholds. A four-year data set of tropical rain-rate tip-time sequences were acquired from the NASA TRMM program for 30 gauges near Darwin, Australia. They were also processed for inclusion in the CCIR data base and the expanded data base for monthly observations at the University of Oklahoma. The empirical rain-rate distributions (edfs) accepted for inclusion in the CCIR data base were used to estimate parameters for several rain-rate distribution models: the lognormal model, the Crane two-component model, and the three parameter model proposed by Moupfuma. The intent of this segment of the study is to obtain a limited set of parameters that can be mapped globally for use in rain attenuation predictions. If the form of the distribution can be established, then perhaps available climatological data can be used to estimate the parameters rather than requiring years of rain-rate observations to set the parameters. The two-component model provided the best fit to the Wallops Island data but the Moupfuma model provided the best fit to the Darwin data.

Crane, Robert K.↗

DOE OSTI2022

Resource distribution under spatiotemporal uncertainty of disease spread: Stochastic versus robust approaches

We consider the problem of optimizing locations of distribution centers (DCs) and plans for distributing resources such as test kits and vaccines, under spatiotemporal uncertainties of disease spread and demand for the resources. We aim to balance the operational cost (including costs of deploying facilities, shipping, and storage) and quality of service (reflected by demand coverage), while ensuring equity and fairness of resource distribution across multiple populations. We compare a sample-based stochastic programming (SP) approach with a distributionally robust optimization (DRO) approach using a moment-based ambiguity set. Numerical studies are conducted on instances of distributing COVID-19 vaccines in the United States and test kits, to compare SP and DRO models with a deterministic formulation using estimated demand and with the current resource distribution plans implemented in the US. We demonstrate the results over distinct phases of the pandemic to estimate the cost and speed of resource distribution depending on scale and coverage, and show the “demand-driven” properties of the SP and DRO solutions. Furthermore, our results further indicate that if the worst-case unmet demand is prioritized, then the DRO approach is preferred despite of its higher overall cost. Nevertheless, the SP approach can provide an intermediate plan under budgetary restrictions without significant compromises in demand coverage.

97 MATHEMATICS AND COMPUTING↗

NASA NTRS1935

Vortex Noise from Rotating Cylindrical Rods

A series of round rods of the some diameter were rotated individually about the mid-point of each rod. Vortices are shed from the rods when in motion, giving rise to the emission of sound. With the rotating system placed in the open air, the distribution of sound in space, the acoustical power output, and the spectral distribution have been studied. The frequency of emission of vortices from any point on the rod is given by the formula von Karman. From the spectrum estimates are made of the distribution of acoustical power along the rod, the amount of air concerned in sound production, the "equivalent size" of the vortices, and the acoustical energy content for each vortex.

Stowell, E Z↗

NASA NTRS1976

Development of a dosimeter for distributed body organs

Calculational methods for estimation of dose from external proton exposure of aribtrary convex bodies is briefly reviewed and all of the necessary information for the estimation of dose in soft tissue is presented. Special emphasis is on retaining the effects of nuclear reaction especially in relation to the dose equivalent.

Khandelwal, G. S.↗

NASA NTRS1979

CLASSY: An adaptive maximum likelihood clustering algorithm

The CLASSY clustering method alternates maximum likelihood iterative techniques for estimating the parameters of a mixture distribution with an adaptive procedure for splitting, combining, and eliminating the resultant components of the mixture. The adaptive procedure is based on maximizing the fit of a mixture of multivariate normal distributions to the observed data using its first through fourth central moments. It generates estimates of the number of multivariate normal components in the mixture as well as the proportion, mean vector, and covariance matrix for each component. The basic mathematical model for CLASSY and the actual operation of the algorithm as currently implemented are described. Results of applying CLASSY to real and simulated LANDSAT data are presented and compared with those generated by the iterative self-organizing clustering system algorithm on the same data sets.

Lennington, R. K.↗

NASA NTRS1991

Retrieval of monthly rainfall indices from microwave radiometric measurements using probability distribution functions

An algorithm for the estimation of monthly rain totals for 5 deg cells over the ocean from histograms of SSM/I brightness temperatures has been developed. There are three novel features to this algorithm. First, it uses knowledge of the form of the rainfall intensity probability density function to augment the measurements. Second, a linear combination of the 19.35 and 22.235 GHz channels has been employed to reduce the impact of variability of water vapor. Third, an objective technique has been developed to estimate the rain layer thickness from the 19.35- and 22.235-GHz brightness temperature histograms. Comparison with climatologies and the GATE radar observations suggest that the estimates are reasonable in spite of not having a beam-filling correction. By-products of the retrievals indicate that the SSM/I instrument noise level and calibration stability are quite good.

Wilheit, Thomas T.↗

NASA NTRSDate not supplied

Assessment of Crew Time for Maintenance and Repairs Activities for Lunar Surface Missions

NASA is currently evaluating different methods to predict how much time crewmembers will spend conducting repair and maintenance activities on future space missions. As mission scope and spacecraft architectures change, it will be necessary to understand how crew repair and maintenance timelines are impacted by mission operations and technology changes. Past work has been done using historical ISS data to accurately predict crew habitation and operation timelines, resulting in the development of NASA’s Exploration Crew Time Model (ECTM). However, understanding crew maintenance and repair requirements has posed a unique challenge due to the complexity of available datasets, the probabilistic nature of sub-system failures, and the impacts of reliability growth on failure rates. This paper presents a methodology to collect and condition empirical repair and maintenance time data from available data sets, to extrapolate from that data to estimate projected maintenance and repair times for a lunar Surface Habitat, and to assess how uncertainty in repair time could impact utilization time on the lunar surface. NASA International Space Station (ISS) maintenance and crew time data are logged into two central databases, the Maintenance Data Collection (MDC) and the Operations Planning Timeline Integration System (OPTimIS) respectively. Separately, each of these two datasets capture only portions of the complete set of data required to generate an accurate assessment of crew time spent on maintenance activities at a sub-system level. MDC provides a detailed catalog of failure events and an overview of the failure’s required maintenance and OPTimIS provides a description of crew activities and crew time durations dedicated to maintenance. To create a more useful crew time estimate for maintenance timelines, the authors developed a methodology to capture relevant data from each set and combine and utilize that data by linking crew time requirements to specific components. The authors compare the failure logs in the MDC to crew activity logs pulled from OPTimIS and then process the data to estimate required repair times for each failure event. Data is also classified by the outcome of each repair event, whether the failed component was replaced or whether it was repaired in place. The entire maintenance activity dataset is then categorized based on the class of failed component to allow for a statistically significant sample size for each class and to provide accurate crew time estimates for any components lacking relevant data. This resultant component repair time data can be used in the future to generate Mean Time To Repair (MTTR) estimates and confidence intervals for each class of component based on a probabilistic distribution of documented maintenance events. These improved MTTR values can then be applied to candidate element sub-system architectures, along with component Mean Time Between Failure (MTBF) data to generate distributions for potential required system crew repair time estimates for a given mission. Repair time distributions can then be used to develop more accurate crew schedules and to assess potential available utilization time.

Crew Time↗

DOE OSTI2020

A Drift‐Kinetic Method for Obtaining Gradients in Plasma Properties From Single‐Point Distribution Function Data

Abstract In this paper, we derive a new drift‐kinetic method for estimating gradients in the plasma properties through a velocity space distribution at a single point. The gradients are intrinsically related to agyrotropic features of the distribution function. This method predicts the gradients in the magnetized distribution function and can predict gradients of arbitrary moments of the gyrotropic background distribution function. The method allows for estimates on density and pressure gradients on the scale of a Larmor radius, proving to resolve smaller scales than any method currently available to spacecraft. The model is verified with a set of fully kinetic VPIC particle‐in‐cell simulations.

Wetherton, B. A.↗

DOE OSTI2025

Dynamics modeling of molten salt reactor with reduced and expanded representations of delayed neutron precursors

Molten salt reactors (MSRs) present unique challenges in dynamic behavior due to the mobility of their fuel. In these reactors, delayed neutron precursors (DNPs) drift with the fuel circulation through the primary loop. As a result, a fraction of DNPs decays outside the core, effectively reducing the available delayed neutron population for reactivity control. Consequently, precise modeling of the distribution and behavior of DNPs is critical for accurate reactor dynamics simulations. In this study, the System Dynamics Analysis Tool (SDAT) was used to simulate a thermal-spectrum MSR under steady-state conditions and following transients. The effects of using reduced and expanded representations of DNPs with fewer or more groups than the conventional 6-group model were investigated. Their impact on the simulated distribution of precursors in the primary loop, reactivity loss value, and reactor response to transients was analyzed. Simulation results showed that reduced models lead to the loss of the actual DNPs distribution data, resulting in less accurate estimates of reactivity loss. Reactor power predictions using these reduced models showed significant deviations compared to those using the conventional 6-group model in transient simulations. Expanded models offered a more accurate representation of the distribution of DNPs and reactivity loss estimates. Reactor power predictions using expanded models showed minimal deviation from the conventional 6-group model during the simulated transients.

analysis↗

NASA NTRS1973

System statistical reliability model and analysis

A digital computer code was developed to simulate the time-dependent behavior of the 5-kwe reactor thermoelectric system. The code was used to determine lifetime sensitivity coefficients for a number of system design parameters, such as thermoelectric module efficiency and degradation rate, radiator absorptivity and emissivity, fuel element barrier defect constant, beginning-of-life reactivity, etc. A probability distribution (mean and standard deviation) was estimated for each of these design parameters. Then, error analysis was used to obtain a probability distribution for the system lifetime (mean = 7.7 years, standard deviation = 1.1 years). From this, the probability that the system will achieve the design goal of 5 years lifetime is 0.993. This value represents an estimate of the degradation reliability of the system.

Lekach, V. S.↗

NASA NTRS2018

A Singular Value Decomposition Framework for Retrievals with Vertical Distribution Information from Greenhouse Gas Column Absorption Spectroscopy Measurements

We review the singular value decomposition (SVD) framework and use it for quantifying and discerning vertical information in greenhouse gas retrievals from column integrated absorption measurements. While the commonly used traditional Bayesian optimal estimation (OE) assumes a prior distribution in order to regularize the inversion problem, the SVD approach identifies principal components that can be retrieved from the measurement without explicitly specifying a prior mean and prior covariance matrix. We review the SVD method, explicitly recognize the use of an uninformative prior and show it to incur no bias from the choice of the prior. We also make the connection between the SVD method and the pseudo-inverse, which makes it more intuitive and easy to understand. We illustrate the use of the SVD method on an integrated path differential absorption CO2 lidar measurement model and verify our derivations and bias-free properties versus optimal estimation using numerical simulations. In contrast, traditional OE retrievals exhibit bias when the prior mean used in the retrieval differs from the true mean. Hence, the SVD method is particularly useful for situations in which knowledge of the prior mean and prior covariance of the true state (e.g., greenhouse gas profiles) is inadequate.

Ramanathan, Anand K.↗

NASA NTRS2012

Active Region Moss: Doppler Shifts from Hinode/EIS Observations

Studying the Doppler shifts and the temperature dependence of Doppler shifts in moss regions can help us understand the heating processes in the core of the active regions. In this paper we have used an active region observation recorded by the Extreme-ultraviolet Imaging Spectrometer (EIS) onboard Hinode on 12-Dec- 2007 to measure the Doppler shifts in the moss regions. We have distinguished the moss regions from the rest of the active region by defining a low density cut-off as derived by Tripathi et al. (2010). We have carried out a very careful analysis of the EIS wavelength calibration based on the method described in Young, O Dwyer and Mason (2012). For spectral lines having maximum sensitivity between log T = 5.85 and log T = 6.25 K, we find that the velocity distribution peaks at around 0 km/s with an estimated error of 4 km/s. The width of the distribution decreases with temperature. The mean of the distribution shows a blue shift which increases with increasing temperature and the distribution also shows asymmetries towards blue-shift. Comparing these results with observables predicted from different coronal heating models, we find that these results are consistent with both steady and impulsive heating scenarios. Further observational constraints are needed to distinguish between these two heating scenarios.

Tripathi, Durgesh↗

NASA NTRS2025

Efficient GPU-Accelerated MultiSource Global Fit Pipeline for LISA Data Analysis

The large-scale analysis task of deciphering gravitational-wave signals in the LISA data stream will be difficult, requiring a large amount of computational resources and extensive development of computational methods. Its high dimensionality, multiple model types, and complicated noise profile require a global fit to all parameters and input models simultaneously. In this work, we detail our global fit algorithm, called “Erebor,” designed to accomplish this challenging task. It is capable of analyzing current state-of-the-art datasets and then growing into the future as more pieces of the pipeline are completed and added. We describe our pipeline strategy, the algorithmic setup, and the results from our analysis of the LDC2A Sangria dataset, which contains massive black hole binaries, compact galactic binaries, and a parametrized noise spectrum whose parameters are unknown to the user. The Erebor algorithm includes three unique and very useful contributions: GPU acceleration for enhanced computational efficiency; ensemble Markov Chain Monte Carlo (MCMC) sampling with multiple MCMC walkers per temperature for better mixing and parallelized sample creation; and special online updates to reversible-jump (or transdimensional) sampling distributions to ensure sampler mixing and accurate initial estimates for detectable sources in the data.We recover posterior distributions for all 15 (6) of the injected massive black hole binaries (MBHB) in the LDC2A training (hidden) dataset. We catalog ∼12000 galactic binaries (∼8000 as high confidence detections) for both the training and hidden datasets. All of the sources and their posterior distributions are provided in publicly available catalogs.

LISA↗