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NASA NTRS2001

Development of an Innovative Algorithm for Aerodynamics-Structure Interaction Using Lattice Boltzmann Method

The lattice Boltzmann equation (LBE) is a kinetic formulation which offers an alternative computational method capable of solving fluid dynamics for various systems. Major advantages of the method are owing to the fact that the solution for the particle distribution functions is explicit, easy to implement, and the algorithm is natural to parallelize. In this final report, we summarize the works accomplished in the past three years. Since most works have been published, the technical details can be found in the literature. Brief summary will be provided in this report. In this project, a second-order accurate treatment of boundary condition in the LBE method is developed for a curved boundary and tested successfully in various 2-D and 3-D configurations. To evaluate the aerodynamic force on a body in the context of LBE method, several force evaluation schemes have been investigated. A simple momentum exchange method is shown to give reliable and accurate values for the force on a body in both 2-D and 3-D cases. Various 3-D LBE models have been assessed in terms of efficiency, accuracy, and robustness. In general, accurate 3-D results can be obtained using LBE methods. The 3-D 19-bit model is found to be the best one among the 15-bit, 19-bit, and 27-bit LBE models. To achieve desired grid resolution and to accommodate the far field boundary conditions in aerodynamics computations, a multi-block LBE method is developed by dividing the flow field into various blocks each having constant lattice spacing. Substantial contribution to the LBE method is also made through the development of a new, generalized lattice Boltzmann equation constructed in the moment space in order to improve the computational stability, detailed theoretical analysis on the stability, dispersion, and dissipation characteristics of the LBE method, and computational studies of high Reynolds number flows with singular gradients. Finally, a finite difference-based lattice Boltzmann method is developed for inviscid compressible flows.

Mei, Ren-Wei↗

NASA NTRS1995

Improved Coupled Z-R and k-R Relations and the Resulting Ambiguities in the Determination of the Vertical Distribution of Rain from the Radar Backscatter and the Integrated Attenuation

Several algorithms to calculate a rain-rate profile from a single-frequency air-or spaceborne radar backscatter profile and a given path-integrated attenuation have been proposed. The accuracy of any such algorithm is limited by the ambiguities between the (multiple) exact solutions, which depend on the variability of the parameters in the Z-R and k-R relations used. In this study, coupled Z-R and k-R relations are derived based on the drop size distribution. It is then shown that, because of the coupling, the relative difference between the multiple mutually ambiguous rain-rate profiles solving the problem must remain acceptably low, provided the available path-integrated attenuation value is known to within 0.5 dB.

Haddad, Z. S.↗

NASA NTRS1992

Integrated-Circuit Pseudorandom-Number Generator

Integrated circuit produces 8-bit pseudorandom numbers from specified probability distribution, at rate of 10 MHz. Use of Boolean logic, circuit implements pseudorandom-number-generating algorithm. Circuit includes eight 12-bit pseudorandom-number generators, outputs are uniformly distributed. 8-bit pseudorandom numbers satisfying specified nonuniform probability distribution are generated by processing uniformly distributed outputs of eight 12-bit pseudorandom-number generators through "pipeline" of D flip-flops, comparators, and memories implementing conditional probabilities on zeros and ones.

Steelman, James E.↗

NASA NTRS1991

Atmospheric constituent density profiles from full disk solar occultation experiments

Mathematical methods are described which permit the derivation of the number of density profiles of atmospheric constituents from solar occultation measurements. The algorithm is first applied to measurements corresponding to an arbitrary solar-intensity distribution to calculate the normalized absorption profile. The application of Fourier transform to the integral equation yields a precise expression for the corresponding number density, and the solution is employed with the data given in the form of Laguerre polynomials. The algorithm is employed to calculate the results for the case of uniform distribution of solar intensity, and the results demonstrate the convergence properties of the method. The algorithm can be used to effectively model representative model-density profiles with constant and altitude-dependent scale heights.

Lumpe, J. D.↗

NASA NTRS2001

A Spectral Algorithm for Solving the Relativistic Vlasov-Maxwell Equations

A spectral method algorithm is developed for the numerical solution of the full six-dimensional Vlasov-Maxwell system of equations. Here, the focus is on the electron distribution function, with positive ions providing a constant background. The algorithm consists of a Jacobi polynomial-spherical harmonic formulation in velocity space and a trigonometric formulation in position space. A transform procedure is used to evaluate nonlinear terms. The algorithm is suitable for performing moderate resolution simulations on currently available supercomputers for both scientific and engineering applications.

Shebalin, John V.↗

NASA NTRS1984

Computing approximate random Delta v magnitude probability densities

This paper describes the development and use of an algorithm to compute approximate statistics of the magnitude of a single random trajectory correction maneuver (TCM) Delta v vector. The TCM Delta v vector is modeled as a three component Cartesian vector each of whose components is a random variable having a normal (Gaussian) distribution with zero mean and possibly unequal standard deviations. The algorithm uses these standard deviations as input to produce approximations to (1) the mean and standard deviation of the magnitude of Delta v, (2) points of the probability density function of the magnitude of Delta v, and (3) points of the cumulative and inverse cumulative distribution functions of Delta v. The approximates are based on Monte Carlo techniques developed in a previous paper by the author and extended here. The algorithm described is expected to be useful in both pre-flight planning and in-flight analysis of maneuver propellant requirements for space missions.

Chadwick, C.↗

NASA NTRS2014

Algorithm Development and Validation of CDOM Properties for Estuarine and Continental Shelf Waters Along the Northeastern U.S. Coast

An extensive set of field measurements have been collected throughout the continental margin of the northeastern U.S. from 2004 to 2011 to develop and validate ocean color satellite algorithms for the retrieval of the absorption coefficient of chromophoric dissolved organic matter (aCDOM) and CDOM spectral slopes for the 275:295 nm and 300:600 nm spectral range (S275:295 and S300:600). Remote sensing reflectance (Rrs) measurements computed from in-water radiometry profiles along with aCDOM() data are applied to develop several types of algorithms for the SeaWiFS and MODIS-Aqua ocean color satellite sensors, which involve least squares linear regression of aCDOM() with (1) Rrs band ratios, (2) quasi-analytical algorithm-based (QAA based) products of total absorption coefficients, (3) multiple Rrs bands within a multiple linear regression (MLR) analysis, and (4) diffuse attenuation coefficient (Kd). The relative error (mean absolute percent difference; MAPD) for the MLR retrievals of aCDOM(275), aCDOM(355), aCDOM(380), aCDOM(412) and aCDOM(443) for our study region range from 20.4-23.9 for MODIS-Aqua and 27.3-30 for SeaWiFS. Because of the narrower range of CDOM spectral slope values, the MAPD for the MLR S275:295 and QAA-based S300:600 algorithms are much lower ranging from 9.9 and 8.3 for SeaWiFS, respectively, and 8.7 and 6.3 for MODIS, respectively. Seasonal and spatial MODIS-Aqua and SeaWiFS distributions of aCDOM, S275:295 and S300:600 processed with these algorithms are consistent with field measurements and the processes that impact CDOM levels along the continental shelf of the northeastern U.S. Several satellite data processing factors correlate with higher uncertainty in satellite retrievals of aCDOM, S275:295 and S300:600 within the coastal ocean, including solar zenith angle, sensor viewing angle, and atmospheric products applied for atmospheric corrections. Algorithms that include ultraviolet Rrs bands provide a better fit to field measurements than algorithms without the ultraviolet Rrs bands. This suggests that satellite sensors with ultraviolet capability could provide better retrievals of CDOM. Because of the strong correlations between CDOM parameters and DOM constituents in the coastal ocean, satellite observations of CDOM parameters can be applied to study the distributions, sources and sinks of DOM, which are relevant for understanding the carbon cycle, modeling the Earth system, and to discern how the Earth is changing.

CDOM Properties↗

NASA NTRS2015

Report on GMI Special Study #15: Radio Frequency Interference

This report contains the results of GMI special study #15. An analysis is conducted to identify sources of radio frequency interference (RFI) to the Global Precipitation Measurement (GPM) Microwave Imager (GMI). The RFI impacts the 10 GHz and 18 GHz channels at both polarities. The sources of RFI are identified for the following conditions: over the water (including major inland water bodies) in the earth view, and over land in the earth view, and in the cold sky view. A best effort is made to identify RFI sources in coastal regions, with noted degradation of flagging performance due to the highly variable earth scene over coastal regions. A database is developed of such sources, including latitude, longitude, country and city of earth emitters, and position in geosynchronous orbit for space emitters. A description of the recommended approach for identifying the sources and locations of RFI in the GMI channels is given in this paper. An algorithm to flag RFI contaminated pixels which can be incorporated into the GMI Level 1Base/1B algorithms is defined, which includes Matlab code to perform the necessary flagging of RFI. A Matlab version of the code is delivered with this distribution.

radio frequency interference↗

NASA NTRS1986

Color constancy - A method for recovering surface spectral reflectance

An algorithm has been developed for estimating the surface reflectance functions of objects in a scene with incomplete knowledge of the spectral power distribution of the ambient light. An image processing system employing this algorithm can assign colors that are constant despite changes in the lighting of the scene; this capability is essential to correct color rendering in photography, TV, and in the construction of artificial visual systems for robotics. Attention is given to the way in which constraints on lights and surfaces in the environment make color-constancy possible for a visual system, and the algorithm's implications for human color vision are discussed.

Maloney, L. T.↗

NASA NTRS2011

Drop Size Distribution Measurements Supporting the NASA Global Precipitation Measurement Mission: Infrastructure and Preliminary Results

Global Precipitation Measurement Mission (GPM) retrieval algorithm validation requires datasets that characterize the 4-D structure, variability, and correlation properties of hydrometeor particle size distributions (PSD) and accumulations over satellite fields of view (5 -- 50 km). Key to this process is the combined use of disdrometer and polarimetric radar platforms. Here the disdrometer measurements serve as a reference for up-scaling dual-polarimetric radar observations of the PSD to the much larger volumetric sampling domain of the radar. The PSD observations thus derived provide a much larger data set for assessing DSD variability, and satellite-based precipitation retrieval algorithm assumptions, in all three spatial dimensions for a range of storm types and seasons. As one component of this effort, the GPM Ground Validation program recently acquired five 3rd generation 2D Video disdrometers as part of its Disdrometer and Radar Observations of Precipitation Facility (DROP), currently hosted in northern Alabama by the NASA Marshall Space Flight Center and the University of Alabama in Huntsville. These next-generation 2DVDs were operated and evaluated in different phases of data collection under the scanning domain of the UAH ARMOR C-band dual-polarimetric radar. During this period approximately 7500 minutes of PSD data were collected and processed to create gamma size distribution parameters using a truncated method of moments approach. After creating the gamma parameter datasets the DSDs were then used as input to T-matrix code for computation of polarimetric radar moments at C-band. The combined dataset was then analyzed with two basic objectives in mind: 1) the investigation of seasonal variability in the rain PSD parameters as observed by the 2DVDs; 2) the use of combined polarimetric moments and observed gamma distribution parameters in a functional form to retrieve PSD parameters in 4-D using the ARMOR radar for precipitation occurring in different seasons and for different rain system types. Preliminary results suggest that seasonal variations in the DSD parameters do occur, but are most pronounced when comparing tropical PSDs to either winter or summer convective precipitation. For example the previously documented shift to relatively smaller drop diameters in higher number concentrations for equivalent rain rate bins was observed in tropical storm rainbands occurring over Huntsville. On a more inter seasonal basis empirical fits between parameters such as D0 and ZDR do not appear to exhibit robust seasonal biases- i.e., one fit seems to work for all seasons within acceptable standard error (O[10%]) for estimates of D0. In polarimetric retrievals of the vertical variability in PSD (rain layer) for a tropical rainband we find that the Do varies with height when partitioned by specified precipitation categories (e.g., convective or stratiform, heavy and light stratiform etc.) but this variation is of order 10-20% and is smaller than the difference in D0 observed between the basic delineation of convective and stratiform precipitation types. Currently we are expanding our analysis of the vertical structure of the PSD to include several seasonally and/or dynamically-different storm system types (e.g., winter convection and stratiform events; summer mid-latitude convective etc.) sampled by ARMOR. The study will present the results of our combined analyses.

Petersen, Walter A.↗

NASA NTRS2006

LDCM Grid Prototype (LGP)

The LGP successfully demonstrated that grid technology could be used to create a collaboration among research scientists, their science development machines, and distributed data to create a science production system in a nationally distributed environment. Grid technology provides a low cost and effective method of enabling production of science products by the science community. To demonstrate this, the LGP partnered with NASA GSFC scientists and used their existing science algorithms to generate virtual Landsat-like data products using distributed data resources. LGP created 48 output composite scenes with 4 input scenes each for a total of 192 scienes processed in parallel. The demonstration took 12 hours, which beat the requirement by almost 50 percent, well within the LDCM requirement to process 250 scenes per day. The LGP project also showed the successful use of workflow tools to automate the processing. Investing in this technology has led to funding for a ROSES ACCESS proposal. The proposal intends to enable an expert science user to produce products from a number of similar distributed instrument data sets using the Land Cover Change Community-based Processing and Analysis System (LC-ComPS) Toolbox. The LC-ComPS Toolbox is a collection of science algorithms that enable the generation of data with ground resolution on the order of Landsat-class instruments.

Weinstein, Beth↗

NASA NTRS2015

Resolving Ice Cloud Optical Thickness Biases Between CALIOP and MODIS Using Infrared Retrievals

Despite its importance as one of the key radiative properties that determines the impact of upper tropospheric clouds on the radiation balance, ice cloud optical thickness (IOT) has proven to be one of the more challenging properties to retrieve from space-based remote sensing measurements. In particular, optically thin upper tropospheric ice clouds (cirrus) have been especially challenging due to their tenuous nature, extensive spatial scales, and complex particle shapes and light scattering characteristics. The lack of independent validation motivates the investigation presented in this paper, wherein systematic biases between MODIS Collection 5 (C5) and CALIOP Version 3 (V3) unconstrained retrievals of tenuous IOT (< 3) are examined using a month of collocated A-Train observations. An initial comparison revealed a factor of two bias between the MODIS and CALIOP IOT retrievals. This bias is investigated using an infrared (IR) radiative closure approach that compares both products with MODIS IR cirrus retrievals developed for this assessment. The analysis finds that both the MODIS C5 and the unconstrained CALIOP V3 retrievals are biased (high and low, respectively) relative to the IR IOT retrievals. Based on this finding, the MODIS and CALIOP algorithms are investigated with the goal of explaining and minimizing the biases relative to the IR. For MODIS we find that the assumed ice single scattering properties used for the C5 retrievals are not consistent with the mean IR COT distribution. The C5 ice scattering database results in the asymmetry parameter (g) varying as a function of effective radius with mean values that are too large. The MODIS retrievals have been brought into agreement with the IR by adopting a new ice scattering model for Collection 6 (C6) consisting of a modified gamma distribution comprised of a single habit (severely roughened aggregated columns); the C6 ice cloud optical property models have a constant g approx. = 0.75 in the mid-visible spectrum, 5-15% smaller than C5. For CALIOP, the assumed lidar ratio for unconstrained retrievals is fixed at 25 sr for the V3 data products.This value is found to be inconsistent with the constrained (predominantly nighttime) CALIOP retrievals. An experimental data set was produced using a modified lidar ratio of 32 sr for the unconstrained retrievals (an increase of 28%), selected to provide consistency with the constrained V3 results. These modifications greatly improve the agreement with the IR and provide consistency between the MODIS and CALIOP products. Based on these results the recently released MODIS C6 optical products use the single habit distribution given above, while the upcoming CALIOP V4 unconstrained algorithm will use higher lidar ratios for unconstrained retrievals.

Cloud↗

NASA NTRS1991

Transform methods for precision continuum and control models of flexible space structures

An open loop optimal control algorithm is developed for general flexible structures, based on Laplace transform methods. A distributed parameter model of the structure is first presented, followed by a derivation of the optimal control algorithm. The control inputs are expressed in terms of their Fourier series expansions, so that a numerical solution can be easily obtained. The algorithm deals directly with the transcendental transfer functions from control inputs to outputs of interest, and structural deformation penalties, as well as penalties on control effort, are included in the formulation. The algorithm is applied to several structures of increasing complexity to show its generality.

Lupi, Victor D.↗

NASA NTRS2003

Combined Radiometer-Radar Microphysical Profile Estimations with Emphasis on High Frequency Brightness Temperature Observations

Information about the vertical microphysical cloud structure is useful in many modeling and predictive practices. Radiometers and radars are used to observe hydrometeor properties. This paper describes an iterative retrieval algorithm that combines the use of airborne active and wideband (10 to 340 GHz) passive observations to estimate the vertical content and particle size distributions of liquid and frozen hydrometeors. The physically-based retrieval algorithm relies on the high frequencies (greater than 89 GHz) to provide details on the frozen hydrometeors. Neglecting the high frequencies yielded acceptable estimates of the liquid profiles, but the ice profiles were poorly retrieved. Airborne radar and radiometer observations from the third Convection and Moisture EXperiment (CAMEX-3) were used in the retrieval algorithm as constraints. Nadir profiles were estimated for a minute each of flight time (approximately 12.5 km along track) from an anvil, convection, and quasi- stratiform rain. The complex structure of the frozen hydrometeors required the most iterations for convergence for the anvil cloud type. The wideband observations were found to more than double the estimated frozen hydrometeor content as compared to retrievals using only 90-GHz and below. The convective and quasi-stratiform quickly reached convergence (minimized difference between observations and calculations using the estimated profiles). A qualitative validation using coincident in situ CAMEX-3 observations shows that the retrieved particle size distributions are well corroborated with independent measurements.

Gail Skofronick-Jackson↗

NASA NTRS1993

Automatic detection of mass-resolved ion conics

A processing algorithm to automatically detect a specific type of ion distribution (called the ion conic distribution) in data obtained from a space-based mass spectrometer has been devised. Automation of this task is necessary due to the sparseness of conic events within the very large databases typical of space plasma instruments. This paper reports on the algorithm used to perform this automated analysis, along with a description of the methods used to verify the algorithm and a summary of initial results on the characterization of the near-earth space plasma.

Doherty, Mark F.↗

NASA NTRS1985

An algorithm for computing the number of distinct spectral vectors in thematic mapper data

A computationally efficient method was developed to compute the number of distinct spectral vectors and their frequency of occurrence in Landsat-4 Thematic Mapper (TM) data. The algorithm first partitions the image into spectrally disjoint subsets and then computes the frequency distribution of distinct spectral vectors within each subset from a multidimensional histogram. The overall frequency distribution is tabulated by accumulating the results from each subset. The number of distinct spectral vectors could be used as a measure of potential storage compaction of alternate data representations for data compression, or as a measure of information content in the comparison of spectral band combinations and/or spatial resolutions for an image. Results from processing three 512 x 512 pixel Landsat-4 TM images and one Landsat-4 Multispectral Scanner (MSS) image are presented as examples. An algorithm for computing the frequency distribution of distinct spectral vectors in MSS data is given in the Appendix.

Wharton, S. W.↗

NASA NTRS2021

Salvaging Data Records with Missing Data: Data Imputation using the Multivariate t Distribution

When doing multivariate data analysis, one commonobstacle is the presence of incomplete observations, i.e., observationsfor which one or more key fields are blank. Missing datais often countered by deleting entire observations that containmissing data. The negative effects of deleting entire observationsare multiple: deleting observations reduces sample size andcan also result in biased inferences even if data is missing atrandom. In addition, knowledge contained within incompleteobservations is knowledge lost when they are deleted– and theeffort spent collecting that knowledge is effort wasted. Data imputationmethods, or methods of statistically “filling-in” missingdata, can help combat small sample sizes by using the existinginformation in partially complete observations with the end goalof producing less biased and higher confidence inferences. Whena sample from a multivariate normal population is only partiallycomplete, and the missing data meets appropriate assumptions(missing at random), robust data imputation of the missing datacan be implemented with monotone data augmentation (MDA)using the multivariate t distribution.Missing data imputation is applied to data from the NASA InstrumentCost Model (NICM) using the MDA algorithm underthe assumption of having a multivariate t distribution with fixeddegrees of freedom. A sensitivity analysis to the degrees offreedom parameter is presented to demonstrate robustness ofthe multivariate t distribution when dealing with small samplesas compared to the multivariate normal distribution.

DiNicola, Michael↗

NASA NTRS2018

Probabilistic Guidance of a Swarm Deployed from the Back Shell of the Mars Spacecraft

This paper presents a probabilistic guidance algorithm for a swarm of assets deployed from the back shell of the Mars spacecraft. Such a swarm could provide valuable science data, with large spatiotemporal variation, from the Martian surface. Our probabilistic swarm guidance algorithm maximizes the coverage area of the swarm while uniformly distributing the assets on the Martian surface and guaranteeing strong connectivity of the swarm’s communication network topology. Numerical simulations demonstrate the eﬀectiveness and versatility of our probabilistic swarm guidance algorithm.

Hadaegh, Fred↗