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All sourcesNASA NTRSDOE OSTI
NASA NTRS1998

Discretization and Preconditioning Algorithms for the Euler and Navier-Stokes Equations on Unstructured Meshes

Several stabilized demoralization procedures for conservation law equations on triangulated domains will be considered. Specifically, numerical schemes based on upwind finite volume, fluctuation splitting, Galerkin least-squares, and space discontinuous Galerkin demoralization will be considered in detail. A standard energy analysis for several of these methods will be given via entropy symmetrization. Next, we will present some relatively new theoretical results concerning congruence relationships for left or right symmetrized equations. These results suggest new variants of existing FV, DG, GLS, and FS methods which are computationally more efficient while retaining the pleasant theoretical properties achieved by entropy symmetrization. In addition, the task of Jacobean linearization of these schemes for use in Newton's method is greatly simplified owing to exploitation of exact symmetries which exist in the system. The FV, FS and DG schemes also permit discrete maximum principle analysis and enforcement which greatly adds to the robustness of the methods. Discrete maximum principle theory will be presented for general finite volume approximations on unstructured meshes. Next, we consider embedding these nonlinear space discretizations into exact and inexact Newton solvers which are preconditioned using a nonoverlapping (Schur complement) domain decomposition technique. Elements of nonoverlapping domain decomposition for elliptic problems will be reviewed followed by the present extension to hyperbolic and elliptic-hyperbolic problems. Other issues of practical relevance such the meshing of geometries, code implementation, turbulence modeling, global convergence, etc, will. be addressed as needed.

Barth, Timothy J.↗
NASA NTRS1997

Discretization and Preconditioning Algorithms for the Euler and Navier-Stokes Equations on Unstructured Meshes

Several stabilized discretization procedures for conservation law equations on triangulated domains will be considered. Specifically, numerical schemes based on upwind finite volume, fluctuation splitting, Galerkin least-squares, and space discontinuous Galerkin discretization will be considered in detail. A standard energy analysis for several of these methods will be given via entropy symmetrization. Next, we will present some relatively new theoretical results concerning congruence relationships for left or right symmetrized equations. These results suggest new variants of existing FV, DG, GLS and FS methods which are computationally more efficient while retaining the pleasant theoretical properties achieved by entropy symmetrization. In addition, the task of Jacobian linearization of these schemes for use in Newton's method is greatly simplified owing to exploitation of exact symmetries which exist in the system. These variants have been implemented in the "ELF" library for which example calculations will be shown. The FV, FS and DG schemes also permit discrete maximum principle analysis and enforcement which greatly adds to the robustness of the methods. Some prevalent limiting strategies will be reviewed. Next, we consider embedding these nonlinear space discretizations into exact and inexact Newton solvers which are preconditioned using a nonoverlapping (Schur complement) domain decomposition technique. Elements of nonoverlapping domain decomposition for elliptic problems will be reviewed followed by the present extension to hyperbolic and elliptic-hyperbolic problems. Other issues of practical relevance such the meshing of geometries, code implementation, turbulence modeling, global convergence, etc. will be addressed as needed.

Barth, Timothy↗
NASA NTRS1992

Some practicable applications of quadtree data structures/representation in astronomy

Development of quadtree as hierarchical data structuring technique for representing spatial data (like points, regions, surfaces, lines, curves, volumes, etc.) has been motivated to a large extent by storage requirements of images, maps, and other multidimensional (spatially structured) data. For many spatial algorithms, time-efficiency of quadtrees in terms of execution may be as important as their space-efficiency concerning storage conditions. Briefly, the quadtree is a class of hierarchical data structures which is based on the recursive partition of a square region into quadrants and sub-quadrants until a predefined limit. Beyond the wide applicability of quadtrees in image processing, spatial information analysis, and building digital databases (processes becoming ordinary for the astronomical community), there may be numerous further applications in astronomy. Some of these practicable applications based on quadtree representation of astronomical data are presented and suggested for further considerations. Examples are shown for use of point as well as region quadtrees. Statistics of different leaf and non-leaf nodes (homogeneous and heterogeneous sub-quadrants respectively) at different levels may provide useful information on spatial structure of astronomical data in question. By altering the principle guiding the decomposition process, different types of spatial data may be focused on. Finally, a sampling method based on quadtree representation of an image is proposed which may prove to be efficient in the elaboration of sampling strategy in a region where observations were carried out previously either with different resolution or/and in different bands.

Pasztor, L.↗
NASA NTRS1998

Baseline Observations of Hemispheric Sea Ice with the Nimbus 7 Scanning Multichannel Microwave Radiometer

The Scanning Multichannel Microwave Radiometer (SMMR) on board the NASA Nimbus 7 satellite was designed to obtain data for sea surface temperatures (SSTs), near-surface wind speeds, sea ice coverage and type, rainfall rates over the oceans, cloud water content, snow water equivalent, and soil moisture. In this paper, I shall emphasize the sea ice observations and mention briefly some important SST observations. A prime factor contributing to the importance of SMMR sea ice observations lies in their successful integration into a long-term time series, presently being extended by observations from the series of Special Sensor Microwave/Imager (SSMI) on board the DOD/DMSP F8, Fl1, and F12 satellites. This currently constitutes a 19-year data set. Almost half of this was provided by the SMMR. Unfortunately, the 4-year data set produced earlier by the single-channel Electrically Scanned Microwave Radiometer (ESMR) was not successfully integrated into the SMMR/SSMI data set. This resulted primarily from the lack of an overlap period to provide intersensor adjustment, but also because of the large difference between the algorithms to produce ice concentrations and large temporal gaps in the ESMR data. The lack of overlap between the SeaSat and Nimbus 7 SMMR data sets was an important consideration for also excluding the SeatSat one, but the spatial gaps especially in the Southern Hemisphere daily SeaSat observations was another. The sea ice observations will continue into the future by means of the Advanced Microwave Scanning Radiometer (AMSR) on board the ADEOS II and EOS satellites due to be launched in mid- and late-2000, respectively. Analysis of the sea ice data has been carried out by a number of different techniques. Long-term trends have been examined by means of ordinary least squares and band-limited regression. Oscillations in the data have been examined by band-limited Fourier analysis. Here, I shall present results from a novel combination of Principal Component analysis and the recently-developed Empirical Mode Decomposition (EMD). In this method, the data are first separated into spatial and temporal parts, and then the temporal parts of the first few PCs are broken into intrinsic modes by the EMD method.

Gloersen, Per↗
NASA NTRS2011

Image Segmentation, Registration, Compression, and Matching

A novel computational framework was developed of a 2D affine invariant matching exploiting a parameter space. Named as affine invariant parameter space (AIPS), the technique can be applied to many image-processing and computer-vision problems, including image registration, template matching, and object tracking from image sequence. The AIPS is formed by the parameters in an affine combination of a set of feature points in the image plane. In cases where the entire image can be assumed to have undergone a single affine transformation, the new AIPS match metric and matching framework becomes very effective (compared with the state-of-the-art methods at the time of this reporting). No knowledge about scaling or any other transformation parameters need to be known a priori to apply the AIPS framework. An automated suite of software tools has been created to provide accurate image segmentation (for data cleaning) and high-quality 2D image and 3D surface registration (for fusing multi-resolution terrain, image, and map data). These tools are capable of supporting existing GIS toolkits already in the marketplace, and will also be usable in a stand-alone fashion. The toolkit applies novel algorithmic approaches for image segmentation, feature extraction, and registration of 2D imagery and 3D surface data, which supports first-pass, batched, fully automatic feature extraction (for segmentation), and registration. A hierarchical and adaptive approach is taken for achieving automatic feature extraction, segmentation, and registration. Surface registration is the process of aligning two (or more) data sets to a common coordinate system, during which the transformation between their different coordinate systems is determined. Also developed here are a novel, volumetric surface modeling and compression technique that provide both quality-guaranteed mesh surface approximations and compaction of the model sizes by efficiently coding the geometry and connectivity/topology components of the generated models. The highly efficient triangular mesh compression compacts the connectivity information at the rate of 1.5-4 bits per vertex (on average for triangle meshes), while reducing the 3D geometry by 40-50 percent. Finally, taking into consideration the characteristics of 3D terrain data, and using the innovative, regularized binary decomposition mesh modeling, a multistage, pattern-drive modeling, and compression technique has been developed to provide an effective framework for compressing digital elevation model (DEM) surfaces, high-resolution aerial imagery, and other types of NASA data.

Yadegar, Jacob↗
NASA NTRS2020

Satellite Monitoring of Global Surface Soil Organic Carbon Dynamics Using the SMAP Level 4 Carbon Product

Soil organic carbon (SOC) is an important metric of soil health and the terrestrial carbon balance. Short‐term climate variations affect SOC through changes in temperature and moisture, which control vegetation growth and soil decomposition. We evaluated a satellite data‐driven carbon model, operating under the NASA Soil Moisture Active‐Passive (SMAP) mission, as a means of monitoring global surface SOC dynamics. The SMAP Level 4 Carbon (L4C) product estimates a daily global carbon budget including surface (0‐ to 5‐cm depth) SOC. We found that the L4C mean latitudinal SOC distribution is generally consistent with alternative assessments from static soil inventory records and dynamic global vegetation models (r ≥ 0.89). Within forest systems, based on inventory data, L4C SOC is most similar in magnitude to litterfall but is correlated with coarse woody debris ( urn:x-wiley:jgrg:media:jgrg21790:jgrg21790-math-0001) and total SOC ( urn:x-wiley:jgrg:media:jgrg21790:jgrg21790-math-0002). L4C SOC is sensitive to seasonal and annual climate variability, with mean residence times that range from 1.5 years in the wet tropics to 17 years in the cold tundra. Incorporating soil moisture retrievals from the SMAP L‐band (1.4 GHz) microwave radiometer within the L4C algorithm provides enhanced soil moisture sensitivity under low‐to‐moderate vegetation cover (<5 kg/sq.m vegetation water content). The L‐band soil moisture had the greatest impact on the L4C carbon budget in semiarid regions, which span almost 60% of the globe and account for substantial variability in the terrestrial carbon sink. The L4C operational product enables prognostic investigations into effects of recent climate trends and anomalies (e.g., droughts and pluvials) on shallow soil carbon dynamics.

K. Arthur Endsley↗
NASA NTRS1998

Monitoring of Volcanogenic CO2-Induced Tree Kills with AVIRIS Image Data at Mammoth Mountain, California

Elevated cold CO2 emissions from the flank of Mammoth Mountain volcano on the southwest rim of the Long Valley Caldera, eastern California, have been the cause of over 100 acres of dead trees in that area since 1990. The source of the CO2 gas is thought to be from one or more magmatic intrusion(s) beneath Mammoth Mountain and is probably related to a period of seismic unrest that began in 1989. The gas rises to the surface probably from depths of a few kilometers, along faults and fracture zones. The gas is at ambient temperature and diffuses from the soil rather than discharging from distinct vents. Typically, soil gas concentrations in tree-kill areas range from 10% to over 90% CO2 by volume, as compared to normal background of < 1% in healthy forest. The gas composition is predominantly CO2 mixed with air (sulfur gases are not elevated), and C and He isotopic ratios are consistent with a magmatic origin for the gas. The total CO2 emission has been estimated at 1200 tons/day, comparable to the emissions at Kilauea. Some of the dead trees are as old as 250 years, suggesting that similar anomalous gas discharge has not occurred over the previous few hundred years. The delta C-13/12 ratio in the Mammoth Mountain CO2 emission averages about -4.5 (PDB standard). This is consistent with a mantle source for the carbon. However, the large volume of the emission suggests that not all of the CO2 is necessarily being generated from the 1989 intrusion. The voluminous gas could be leaking from a vapor-rich zone, capped by an impermeable layer, that was supplied CO2 from degassing of many small magma bodies that intruded beneath the mountain over a period of decades or centuries. Earthquakes in 1989 could have fractured the capping layer and provided pathways for the escape Of CO2 to the surface. Alternatively, some of the CO2 could be derived from contact metamorphism of carbonate rocks intruded by magma. Carbonate-bearing Paleozoic roof pendents crop out in close proximity to Mammoth Mountain. It is possible that similar rocks could occur at depth beneath Mammoth Mountain, and could have contributed CO2 from thermal decomposition caused from recent intrusions. We hope to determine the C-13/12 ratio of a suite of samples to demonstrate if the carbonate rocks could be the source of at least part of the 1990-97 CO2 emission. To better understand the behavior of the CO2 gas, we have used hyperspectral imagery data of Mammoth Mountain acquired from the Airborne Visual/Infrared Imaging Spectrometer (AVIRIS) to map out areas of dead trees. The areas of tree kill have increased in size from about 50 acres in 1994 to about 100 acres in 1997. Tree kill is the major surface manifestation of the carbon dioxide flux at Mammoth Mountain, is widely dispersed, and has been cursorily mapped by regular field mapping techniques in the area. Initial investigations using airborne digital imagery from the Thematic Mapper Simulator (NS001) and AVIRIS instruments have shown extremely encouraging results for complete delineation of the vegetation anomalies. The most successful maps (when compared with ground truth) were developed using AVIRIS data with spectral angle mapper and matched filter algorithms with a data set that was reduced to maximum variance via the minimum noise fraction transformation. The result of this work is a series of maps that show the tree kill areas occurring in an halo-pattern surrounding the base of Mammoth Mountain. We are applying these same techniques to earlier AVIRIS images of Mammoth Mountain to examine the progression of the tree kill areas over time. Temporal maps of the tree kill areas may assist in constructing a picture of the structure beneath Mammoth Mountain.

Hausback, Brian P.↗
NASA NTRS1996

Structure Identification Within a Transitioning Swept-Wing Boundary Layer

Extensive measurements are made in a transitioning swept-wing boundary layer using hot-film, hot-wire and cross-wire anemometry. The crossflow-dominated flow contains stationary vortices that breakdown near mid-chord. The most amplified vortex wavelength is forced by the use of artificial roughness elements near the leading edge. Two-component velocity and spanwise surface shear-stress correlation measurements are made at two constant chord locations, before and after transition. Streamwise surface shear stresses are also measured through the entire transition region. Correlation techniques are used to identify stationary structures in the laminar regime and coherent structures in the turbulent regime. Basic techniques include observation of the spatial correlations and the spatially distributed auto-spectra. The primary and secondary instability mechanisms are identified in the spectra in all measured fields. The primary mechanism is seen to grow, cause transition and produce large-scale turbulence. The secondary mechanism grows through the entire transition region and produces the small-scale turbulence. Advanced techniques use Linear Stochastic Estimation (LSE) and Proper Orthogonal Decomposition (POD) to identify the spatio-temporal evolutions of structures in the boundary layer. LSE is used to estimate the instantaneous velocity fields using temporal data from just two spatial locations and the spatial correlations. Reference locations are selected using maximum RMS values to provide the best available estimates. POD is used to objectively determine modes characteristic of the measured flow based on energy. The stationary vortices are identified in the first laminar modes of each velocity component and shear component. Experimental evidence suggests that neighboring vortices interact and produce large coherent structures with spanwise periodicity at double the stationary vortex wavelength. An objective transition region detection method is developed using streamwise spatial POD solutions which isolate the growth of the primary and secondary instability mechanisms in the first and second modes, respectively. Temporal evolutions of dominant POD modes in all measured fields are calculated. These scalar POD coefficients contain the integrated characteristics of the entire field, greatly reducing the amount of data to characterize the instantaneous field. These modes may then be used to train future flow control algorithms based on neural networks.

Chapman, Keith↗
NASA NTRS2018

Polarization Decomposition and Temperature Bias Resolution for SMAP Passive Soil Moisture Retrieval Using Time Series Brightness Temperature Observations

In passive microwave remote sensing of soil moisture, the tau-omega (τ-ω) model has often been used to provide soil moisture estimates at a spatial scale representative of the satellite footprint dimensions. For modeling simplicity, model parameters such as the single scattering albedo (ω) and vegetation opacity (τ) that go into the geophysical inversion process are often assumed to be independent of polarizations. Although this absence of polarization dependence can often be justified in special cases as in low-frequency remote sensing or under dense vegetation conditions, it is not a robust assumption in general. Additional model parameterization errors arising from this assumption are possible, leading to degradation in soil moisture estimation accuracy. In this paper, we propose a time series approach to try to resolve the polarization dependence of several τ-ω model parameters as well as the temperature bias arising from the ancillary temperature data. The Version 4 of the Soil Moisture Active Passive (SMAP) Level 1B brightness temperature time series observations were used to illustrate the mechanics of this approach, with an emphasis on a comparison between resulting satellite soil moisture retrievals and in situ data collected at several core validation sites. It was found that this time series approach resulted in significant reduction of the dry bias exhibited in the current SMAP passive soil moisture data products, while retaining the same performance in other metrics of the current baseline passive soil moisture retrieval algorithm.

time series↗
NASA NTRS2007

Persistent Nature of Secondary Diurnal Modes of Precipitation over Oceanic and Continental Regimes

This investigation seeks a better understanding of the assorted mechanisms controlling the global distribution of precipitation diurnal variability based on the use of Tropical Rainfall Measuring Mission (TRMM) microwave radiometer and radar data. The horizontal distributions of precipitation's diurnal cycle are derived from eight years of TRMM Microwave Imager (TMI) and Precipitation Radar (PR) measurements involving three TRMM standard rain rate retrieval algorithms -- the resultant distributions analyzed at various spatiotemporal scales. The results reveal the prominent and expected late-evening to early-morning (LE-EM) precipitation maxima over oceans and the counterpart prominent and expected mid- to late-afternoon (MLA) maxima over continents. Moreover, and not generally recognized, the results reveal a widespread distribution of secondary maxima occurring over both oceans and continents -- maxima which generally mirror their counterpart regime's behavior. That is, many ocean regions exhibit clearcut secondary MLA precipitation maxima while many continental regions exhibit just as evident secondary LE-EM maxima. This investigation is the first comprehensive study of these globally prevalent secondary maxima and their widespread nature, a type of study only made possible when the analysis procedure is applied to a high-quality global-scale precipitation dataset. The characteristics of the secondary maxima are mapped and described on global grids using an innovative clock-face format, while a current study to be published at a later date provides physically-based explanations of the seasonal-regional distributions of the secondary maxima. In addition to an "explicit" maxima identification scheme, a "Fourier decomposition" maxima identification scheme is used to examine the amplitude and phase properties of the primary and secondary maxima -- as well as tertiary and quaternary maxima. Accordingly, the advantages, ambiguities, and pitfalls resulting from use of Fourier harmonic analysis are explained.

Yang, S.↗
NASA NTRS1994

VLSI neuroprocessors

Electronic and optoelectronic hardware implementations of highly parallel computing architectures address several ill-defined and/or computation-intensive problems not easily solved by conventional computing techniques. The concurrent processing architectures developed are derived from a variety of advanced computing paradigms including neural network models, fuzzy logic, and cellular automata. Hardware implementation technologies range from state-of-the-art digital/analog custom-VLSI to advanced optoelectronic devices such as computer-generated holograms and e-beam fabricated Dammann gratings. JPL's concurrent processing devices group has developed a broad technology base in hardware implementable parallel algorithms, low-power and high-speed VLSI designs and building block VLSI chips, leading to application-specific high-performance embeddable processors. Application areas include high throughput map-data classification using feedforward neural networks, terrain based tactical movement planner using cellular automata, resource optimization (weapon-target assignment) using a multidimensional feedback network with lateral inhibition, and classification of rocks using an inner-product scheme on thematic mapper data. In addition to addressing specific functional needs of DOD and NASA, the JPL-developed concurrent processing device technology is also being customized for a variety of commercial applications (in collaboration with industrial partners), and is being transferred to U.S. industries. This viewgraph p resentation focuses on two application-specific processors which solve the computation intensive tasks of resource allocation (weapon-target assignment) and terrain based tactical movement planning using two extremely different topologies. Resource allocation is implemented as an asynchronous analog competitive assignment architecture inspired by the Hopfield network. Hardware realization leads to a two to four order of magnitude speed-up over conventional techniques and enables multiple assignments, (many to many), not achievable with standard statistical approaches. Tactical movement planning (finding the best path from A to B) is accomplished with a digital two-dimensional concurrent processor array. By exploiting the natural parallel decomposition of the problem in silicon, a four order of magnitude speed-up over optimized software approaches has been demonstrated.

Kemeny, Sabrina E.↗
NASA NTRS1996

From Competence to Efficiency: A Tale of GA Progress

Genetic algorithms (GAs) - search procedures based on the mechanics of natural selection and genetics - have grown in popularity for the solution of difficult optimization problems. Concomitant with this growth has been a rising cacaphony of complaint asserting that too much time must be spent by the GA practitioner diddling with codes, operators, and GA parameters; and even then these GA cassandras continue, and the user is still unsure that the effort will meet with success. At the same time, there has been a rising interest in GA theory by a growing community - a theorocracy - of mathematicians and theoretical computer scientists, and these individuals have turned their efforts increasingly toward elegant abstract theorems and proofs that seem to the practitioner to offer little in the way of answers for GA design or practice. What both groups seem to have missed is the largely unheralded 1993 assembly of integrated, applicable theory and its experimental confirmation. This theory has done two key things. First, it has predicted that simple GAs are severely limited in the difficulty of problems they can solve, and these limitations have been confirmed experimentally. Second, it has shown the path to circumventing these limitations in nontraditional GA designs such as the fast messy GA. This talk surveys the history, methodology, and accomplishment of the 1993 applicable theory revolution. After arguing that these accomplishments open the door to universal GA competence, the paper shifts the discussion to the possibility of universal GA efficiency in the utilization of time and real estate through effective parallelization, temporal decomposition, hybridization, and relaxed function evaluation. The presentation concludes by suggesting that these research directions are quickly taking us to a golden age of adaptation.

Goldberg, David E.↗