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NASA NTRS2003

Mathematical Inversion of Lightning Data: Techniques and Applications

A survey of some interesting mathematical inversion studies dealing with radio, optical, and electrostatic measurements of lightning are presented. A discussion of why NASA is interested in lightning, what specific physical properties of lightning are retrieved, and what mathematical techniques are used to perform the retrievals are discussed. In particular, a relatively new multi-station VHF time-of-arrival (TOA) antenna network is now on-line in Northern Alabama and will be discussed. The network, called the Lightning Mapping Array (LMA), employs GPS timing and detects VHF radiation from discrete segments (effectively point emitters) that comprise the channel of lightning strokes within cloud and ground flashes. The LMA supports on-going ground-validation activities of the low Earth orbiting Lightning Imaging Sensor (LIS) satellite developed at NASA Marshall Space Flight Center (MSFC) in Huntsville, Alabama. The LMA also provides detailed studies of the distribution and evolution of thunderstorms and lightning in the Tennessee Valley, and offers interesting comparisons with other meteorological/geophysical datasets. In order to take full advantage of these benefits, it is essential that the LMA channel mapping accuracy (in both space and time) be fully characterized and optimized. A new channel mapping retrieval algorithm is introduced for this purpose. To characterize the spatial distribution of retrieval errors, the algorithm has been applied to analyze literally tens of millions of computer-simulated lightning VHF point sources that have been placed at various ranges, azimuths, and altitudes relative to the LMA network. Statistical results are conveniently summarized in high-resolution, color-coded, error maps.

Koshak, William↗

NASA NTRS2013

Aquarius RFI Detection and Mitigation Algorithm: Assessment and Examples

Aquarius is an L-band radiometer system designed to map sea surface salinity from space. This is a sensitive measurement, and protection from radio frequency interference (RFI) is important for success. An initial look at the performance of the Aquarius RFI detection and mitigation algorithm is reported together with examples of the global distribution of RFI at the L-band. To protect against RFI, Aquarius employs rapid sampling (10 ms) and a "glitch" detection algorithm that looks for outliers among the samples. Samples identified as RFI are removed, and the remainder is averaged to produce an RFI-free signal for the salinity retrieval algorithm. The RFI detection algorithm appears to work well over the ocean with modest rates for false alarms (5%) and missed detection. The global distribution of RFI coincides well with population centers and is consistent with observations reported by the Soil Moisture and Ocean Salinity mission.

remote sensing↗

NASA NTRS1993

Asteroid collisions: Target size effects and resultant velocity distributions

To study the dynamic fragmentation of rock to simulate asteroid collisions, we use a 2-D, continuum damage numerical hydrocode which models two-body impacts. This hydrocode monitors stress wave propagation and interaction within the target body, and includes a physical model for the formation and growth of cracks in rock. With this algorithm we have successfully reproduced fragment size distributions and mean ejecta speeds from laboratory impact experiments using basalt, and weak and strong mortar as target materials. Using the hydrocode, we have determined that the energy needed to fracture a body has a much stronger dependence on target size than predicted from most scaling theories. In addition, velocity distributions obtained indicate that mean ejecta speeds resulting from large-body collisions do not exceed escape velocities.

Ryan, Eileen V.↗

NASA NTRS1999

A Simple Two Aircraft Conflict Resolution Algorithm

Conflict detection and resolution methods are crucial for distributed air-ground traffic management in which the crew in the cockpit, dispatchers in operation control centers and air traffic controllers in the ground-based air traffic management facilities share information and participate in the traffic flow and traffic control imctions.This paper describes a conflict detection and a conflict resolution method. The conflict detection method predicts the minimum separation and the time-to-go to the closest point of approach by assuming that both the aircraft will continue to fly at their current speeds along their current headings. The conflict resolution method described here is motivated by the proportional navigation algorithm. It generates speed and heading commands to rotate the line-of-sight either clockwise or counter-clockwise for conflict resolution. Once the aircraft achieve a positive range-rate and no further conflict is predicted, the algorithm generates heading commands to turn back the aircraft to their nominal trajectories. The speed commands are set to the optimal pre-resolution speeds. Six numerical examples are presented to demonstrate the conflict detection and resolution method.

Chatterji, Gano B.↗

NASA NTRS2006

Convective Weather Forecast Quality Metrics for Air Traffic Management Decision-Making

Since numerical weather prediction models are unable to accurately forecast the severity and the location of the storm cells several hours into the future when compared with observation data, there has been a growing interest in probabilistic description of convective weather. The classical approach for generating uncertainty bounds consists of integrating the state equations and covariance propagation equations forward in time. This step is readily recognized as the process update step of the Kalman Filter algorithm. The second well known method, known as the Monte Carlo method, consists of generating output samples by driving the forecast algorithm with input samples selected from distributions. The statistical properties of the distributions of the output samples are then used for defining the uncertainty bounds of the output variables. This method is computationally expensive for a complex model compared to the covariance propagation method. The main advantage of the Monte Carlo method is that a complex non-linear model can be easily handled. Recently, a few different methods for probabilistic forecasting have appeared in the literature. A method for computing probability of convection in a region using forecast data is described in Ref. 5. Probability at a grid location is computed as the fraction of grid points, within a box of specified dimensions around the grid location, with forecast convection precipitation exceeding a specified threshold. The main limitation of this method is that the results are dependent on the chosen dimensions of the box. The examples presented Ref. 5 show that this process is equivalent to low-pass filtering of the forecast data with a finite support spatial filter. References 6 and 7 describe the technique for computing percentage coverage within a 92 x 92 square-kilometer box and assigning the value to the center 4 x 4 square-kilometer box. This technique is same as that described in Ref. 5. Characterizing the forecast, following the process described in Refs. 5 through 7, in terms of percentage coverage or confidence level is notionally sound compared to characterizing in terms of probabilities because the probability of the forecast being correct can only be determined using actual observations. References 5 through 7 only use the forecast data and not the observations. The method for computing the probability of detection, false alarm ratio and several forecast quality metrics (Skill Scores) using both the forecast and observation data are given in Ref. 2. This paper extends the statistical verification method in Ref. 2 to determine co-occurrence probabilities. The method consists of computing the probability that a severe weather cell (grid location) is detected in the observation data in the neighborhood of the severe weather cell in the forecast data. Probabilities of occurrence at the grid location and in its neighborhood with higher severity, and with lower severity in the observation data compared to that in the forecast data are examined. The method proposed in Refs. 5 through 7 is used for computing the probability that a certain number of cells in the neighborhood of severe weather cells in the forecast data are seen as severe weather cells in the observation data. Finally, the probability of existence of gaps in the observation data in the neighborhood of severe weather cells in forecast data is computed. Gaps are defined as openings between severe weather cells through which an aircraft can safely fly to its intended destination. The rest of the paper is organized as follows. Section II summarizes the statistical verification method described in Ref. 2. The extension of this method for computing the co-occurrence probabilities in discussed in Section HI. Numerical examples using NCWF forecast data and NCWD observation data are presented in Section III to elucidate the characteristics of the co-occurrence probabilities. This section also discusses the procedure for computing throbabilities that the severity of convection in the observation data will be higher or lower in the neighborhood of grid locations compared to that indicated at the grid locations in the forecast data. The probability of coverage of neighborhood grid cells is also described via examples in this section. Section IV discusses the gap detection algorithm and presents a numerical example to illustrate the method. The locations of the detected gaps in the observation data are used along with the locations of convective weather cells in the forecast data to determine the probability of existence of gaps in the neighborhood of these cells. Finally, the paper is concluded in Section V.

Chatterji, Gano B.↗

NASA NTRS2006

A Simple Two Aircraft Conflict Resolution Algorithm

Conflict detection and resolution methods are crucial for distributed air-ground traffic management in which the crew in, the cockpit, dispatchers in operation control centers sad and traffic controllers in the ground-based air traffic management facilities share information and participate in the traffic flow and traffic control functions. This paper describes a conflict detection, and a conflict resolution method. The conflict detection method predicts the minimum separation and the time-to-go to the closest point of approach by assuming that both the aircraft will continue to fly at their current speeds along their current headings. The conflict resolution method described here is motivated by the proportional navigation algorithm, which is often used for missile guidance during the terminal phase. It generates speed and heading commands to rotate the line-of-sight either clockwise or counter-clockwise for conflict resolution. Once the aircraft achieve a positive range-rate and no further conflict is predicted, the algorithm generates heading commands to turn back the aircraft to their nominal trajectories. The speed commands are set to the optimal pre-resolution speeds. Six numerical examples are presented to demonstrate the conflict detection, and the conflict resolution methods.

Chatterji, Gano B.↗

DOE OSTI2025

MCCCS-MN

The MCCCS‒MN (Monte Carlo for Complex Chemical Systems‒Minnesota) software is developed by the Siepmann research group at the University of Minnesota. MCCCS‒MN allows for the simulation of multi-component molecular systems in the canonical, isobaric-isothermal (including constant stress for solids), grand-canonical, semi-grand, and Gibbs (NVT, NPT, and more than two simulation boxes) ensembles. It uses the configurational-bias Monte Carlo method to efficiently sample phase space for linear, branched and cyclic chain molecules, the adiabatic nuclear and electronic sampling Monte Carlo method to treat many-body polarization effects, and the aggregation-volume-bias Monte Carlo algorithm to efficiently sample the spatial distribution of associating molecules. MCCCS-MN employs a molecular representation of the system where force fields contain bonded and non-bonded terms. Funding for the development of MCCCS-MN through grants from the National Science Foundation (simulation of fluid phase equilibria and chromatography) and the Department of Energy (simulation of adsorption equilibria) is gratefully acknowledged.

Siepmann, J.Ilja [University of Minnesota - Twin C↗

DOE OSTI2024

Emulator-Based Bayesian Calibration of the CISNET Colorectal Cancer Models

Purpose To calibrate Cancer Intervention and Surveillance Modeling Network (CISNET)'s SimCRC, MISCAN-Colon, and CRC-SPIN simulation models of the natural history colorectal cancer (CRC) with an emulator-based Bayesian algorithm and internally validate the model-predicted outcomes to calibration targets.Methods We used Latin hypercube sampling to sample up to 50,000 parameter sets for each CISNET-CRC model and generated the corresponding outputs. We trained multilayer perceptron artificial neural networks (ANNs) as emulators using the input and output samples for each CISNET-CRC model. We selected ANN structures with corresponding hyperparameters (i.e., number of hidden layers, nodes, activation functions, epochs, and optimizer) that minimize the predicted mean square error on the validation sample. We implemented the ANN emulators in a probabilistic programming language and calibrated the input parameters with Hamiltonian Monte Carlo-based algorithms to obtain the joint posterior distributions of the CISNET-CRC models' parameters. We internally validated each calibrated emulator by comparing the model-predicted posterior outputs against the calibration targets.Results The optimal ANN for SimCRC had 4 hidden layers and 360 hidden nodes, MISCAN-Colon had 4 hidden layers and 114 hidden nodes, and CRC-SPIN had 1 hidden layer and 140 hidden nodes. The total time for training and calibrating the emulators was 7.3, 4.0, and 0.66 h for SimCRC, MISCAN-Colon, and CRC-SPIN, respectively. The mean of the model-predicted outputs fell within the 95% confidence intervals of the calibration targets in 98 of 110 for SimCRC, 65 of 93 for MISCAN, and 31 of 41 targets for CRC-SPIN.Conclusions Using ANN emulators is a practical solution to reduce the computational burden and complexity for Bayesian calibration of individual-level simulation models used for policy analysis, such as the CISNET CRC models. In this work, we present a step-by-step guide to constructing emulators for calibrating 3 realistic CRC individual-level models using a Bayesian approach.

artificial neural networks↗

NASA NTRS1979

Atmospheric scattering corrections to solar radiometry

Whenever a solar radiometer is used to measure direct solar radiation, some diffuse sky radiation invariably enters the detector's field of view along with the direct beam. Therefore, the atmospheric optical depth obtained by the use of Bouguer's transmission law (also called Beer-Lambert's law), that is valid only for direct radiation, needs to be corrected by taking account of the scattered radiation. This paper discusses the correction factors needed to account for the diffuse (i,e., singly and multiply scattered) radiation and the algorithms developed for retrieving aerosol size distribution from such measurements. For a radiometer with a small field of view (half-cone angle of less than 5 deg) and relatively clear skies (optical depths less than 0.4), it is shown that the total diffuse contribution represents approximately 1% of the total intensity.

Box, M. A.↗

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 NTRS1980

The influence of NO and ClO variations at twilight on the interpretation of solar occultation measurements

Measurement of short-lived photochemically-produced species in the stratosphere by solar occultation is difficult because the rapid variation of such species near the terminator introduces ambiguities in interpreting the measured absorption in terms of meaningful atmospheric abundances. These variations produce tangent path concentrations that are asymmetric relative to the tangent point, as opposed to the symmetrical distribution usually assumed in most inversion algorithms. Neglect of this asymmetry may yield an inverted profile that deviates significantly from the true sunset/sunrise profile. In the present paper, the influence of this effect on solar occultation measurements of ClO and NO is examined. The results show that average inhomogeneity factors, which measure the concentration variation along the tangent path and which can be calculated from a photochemical model, can indicate which species require more careful data analysis.

Boughner, R.↗

NASA NTRS1982

Interaction of a cumulus cloud ensemble with the large-scale environment. IV - The discrete model

The Arakawa-Schubert (1974) parameterization is applied to a prognostic model of large-scale atmospheric circulations and used to analyze data in a general circulation model (GCM). The vertical structure of the large-scale model and the solution for the cloud subensemble thermodynamical properties are examined to choose cloud levels and representative regions. A mass flux distribution equation is adapted to formulate algorithms for calculating the large-scale forcing and the mass flux kernel, using either direct solution or linear programming. Finally, the feedback of the cumulus ensemble on the large-scale environment for a given subensemble mass flux is calculated. All cloud subensemble properties were determined from the conservation of mass, moist static energy, and total water.

Lord, S. J.↗

NASA NTRS1986

CSTAR star catalogue development

The Continuous Stellar Tracking Attitude Reference (CSTAR) system is an in-house project for the Space Station to provide high accuracy, drift free attitude and angular rate information for the GN&C system. Constraints exist on the star catalogue incorporated in the system. These constraints include the following: mass memory allocated for catalogue storage, star tracker imaging sensitivity, the minimum resolvable separation angle between stars, the width of the field of view of the star tracker, and the desired number of stars to be tracked in a field of view. The Smithsonian Astrophysical Observatory (SAO) catalogue is the basis reference for this study. As it stands, the SAO does not meet the requirements of any of the above constraints. Star selection algorithms have been devised for catalogue optimization. Star distribution statistics have been obtained to aid in the development of these rules. VAX based software has been developed to implement the star selection algorithms. The software is modular and provides a design tool to tailor the catalogue to available star tracker technology. The SAO catalogue has been optimized for the requirements of the present CSTAR system.

Uhde-Lacovara, J. A.↗

NASA NTRS1986

Statistical methods for astronomical data with upper limits. II - Correlation and regression

Statistical methods for calculating correlations and regressions in bivariate censored data where the dependent variable can have upper or lower limits are presented. Cox's regression and the generalization of Kendall's rank correlation coefficient provide significant levels of correlations, and the EM algorithm, under the assumption of normally distributed errors, and its nonparametric analog using the Kaplan-Meier estimator, give estimates for the slope of a regression line. Monte Carlo simulations demonstrate that survival analysis is reliable in determining correlations between luminosities at different bands. Survival analysis is applied to CO emission in infrared galaxies, X-ray emission in radio galaxies, H-alpha emission in cooling cluster cores, and radio emission in Seyfert galaxies.

Isobe, T.↗

NASA NTRS1987

SOR and MGR(nu) experiments on the Crystal multicomputer

This report describes distributed implementations of the red/black SOR algorithm and of the MGR(nu) multigrid algorithm on the Crystal multicomputer. Rates of convergence and observed efficiencies for both algorithms are compared.

Kamowitz, David↗

NASA NTRS1990

What FM can offer DFCS design

The results of aircrafts and spacecrafts flight tests are reported. It is shown that the problems of Digital Flight Control Systems (DFCS) are the problems of systems whose complexity has exceeded the reach of the intellectual tools employed. It is also shown that intuition, experience, and techniques derived from mechanical and analog systems are insufficient for complex, integrated, digital systems. Formal Methods (FM) of computer science can offer DFCS systematic techniques for the construction of trustworthy software, including: techniques for the precise specification of requirements and the development of designs; systematic approaches to the design and structuring of distributed and concurrent systems; fault tolerance algorithms; and systematic methods of testing and analytic methods of verification.

Rushby, John↗

NASA NTRS1989

Probability of failure and risk assessment of propulsion structural components

The probabilistic structural analysis method (PSAM) was developed to analyze the effects of fluctuating loads, variable material properties, and uncertain analytical models especially for high performance structures such as the Space Shuttle Main Engine turbopump blades. Risk is calculated after expensive service experience. However, probabilistic structural analysis provides a rational alternative method to quantify uncertainties in the structural performance and durability. NESSUS (Numerical Evaluation of Stochastic Structures Under Stress) was developed as a probabilistic structural analysis computer code which integrates finite element methods and reliability algorithms, capable to predicting the probability distributions of structural response variables such as stress, displacement, natural frequencies, and buckling loads. This computer code is detailed.

Shiao, Michael C.↗

NASA NTRS1992

An efficient HZETRN (a galactic cosmic ray transport code)

An accurate and efficient engineering code for analyzing the shielding requirements against the high-energy galactic heavy ions is needed. The HZETRN is a deterministic code developed at Langley Research Center that is constantly under improvement both in physics and numerical computation and is targeted for such use. One problem area connected with the space-marching technique used in this code is the propagation of the local truncation error. By improving the numerical algorithms for interpolation, integration, and grid distribution formula, the efficiency of the code is increased by a factor of eight as the number of energy grid points is reduced. The numerical accuracy of better than 2 percent for a shield thickness of 150 g/cm(exp 2) is found when a 45 point energy grid is used. The propagating step size, which is related to the perturbation theory, is also reevaluated.

Shinn, Judy L.↗