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NASA NTRS1978

Measurement and analysis of magnetic field variation during a class 2b flare

A digital analysis of high-time-resolution videomagnetograms taken during a class 2b flare that occurred at 60 deg east is reported. The data were obtained at the Big Bear Observatory and calibrated by a Mt. Wilson magnetogram. Changes of weak magnetic fields (less than 100 G) with an amplitude of 30% to 100% have been detected over 55% of the optical flare region, apparently taking place at the initial phase of the flare. Statistical considerations suggest a real flare association with most of these changes. H-alpha observations show that large changes took place over the footpoints of heavily inclined structures like penumbral fibrils, while smaller changes took place over the plage region. An apparent polarity reversal was found at the feet of erupted fibrils. Based on force-free field calculations these changes can be reasonably explained as a transformation of the current-carrying fields to potential fields which produced large changes in the field-line inclination and rotation.

Tanaka, K.↗
NASA NTRS1993

Are the 1986-1988 changes in solar free-oscillation frequency splitting significant?

The solar normal-mode splitting coefficients deduced from Big Bear Solar Observatory (BBSO) data differ between 1986 and 1988; inversions for equatorial rotation are slower at depth and faster near the surface in 1988 than in 1986. The significance of the change has been disputed. The data sets overlap for five splitting coefficients (a(j))super 5 sub j = 1 associated with 710 multiplets. On the assumption that rotation rate varies smoothly with radius, both data sets are satisfied by the same rotation model at all colatitudes except near 30-40 deg and near 70 deg (and at their southern hemisphere reflections 140-150 deg and 110 deg). The evidence for equatorial change is weak. Nonparametric tests show a significant offset in the magnitudes of a(1), a(2), and a(4), and of linear combinations sensitive to rotation at colatitudes of 60-80 deg (and 120 deg). Nonparametric tests show significant radial trends in the changes to a(2), a(4), and (less significantly) a(5). There is strong anticorrelation between a(2) and a(4), a(1) and a(3), and a(3) and a(5), suggesting that the estimates are not independent. Individual coefficients a(j) show more evidence for change than do 'physical' linear combinations, adding weight to this hypothesis. Some of the changes in splitting might be related to solar activity, which changed most near colatitude 70 deg from 1986 to 1988.

Gough, Douglas↗
NASA NTRS1995

Uncertainties for two-dimensional models of solar rotation from helioseismic eigenfrequency splitting

Observed solar p-mode frequency splittings can be used to estimate angular velocity as a function of position in the solar interior. Formal uncertainties of such estimates depend on the method of estimation (e.g., least-squares), the distribution of errors in the observations, and the parameterization imposed on the angular velocity. We obtain lower bounds on the uncertainties that do not depend on the method of estimation; the bounds depend on an assumed parameterization, but the fact that they are lower bounds for the 'true' uncertainty does not. Ninety-five percent confidence intervals for estimates of the angular velocity from 1986 Big Bear Solar Observatory (BBSO) data, based on a 3659 element tensor-product cubic-spline parameterization, are everywhere wider than 120 nHz, and exceed 60,000 nHz near the core. When compared with estimates of the solar rotation, these bounds reveal that useful inferences based on pointwise estimates of the angular velocity using 1986 BBSO splitting data are not feasible over most of the Sun's volume. The discouraging size of the uncertainties is due principally to the fact that helioseismic measurements are insensitive to changes in the angular velocity at individual points, so estimates of point values based on splittings are extremely uncertain. Functionals that measure distributed 'smooth' properties are, in general, better constrained than estimates of the rotation at a point. For example, the uncertainties in estimated differences of average rotation between adjacent blocks of about 0.001 solar volumes across the base of the convective zone are much smaller, and one of several estimated differences we compute appears significant at the 95% level.

Genovese, Christopher R.↗
NASA NTRS2002

Seeing Red and Shooting Blanks: A Study of Red Quasars and Blank Field X-Ray Sources

We have identified a population of 'blank field sources' (or 'blanks') among the ROSAT (Roentgen Satellite) bright unidentified X-ray sources with faint optical counterparts. The extreme X-ray over optical flux ratio of blank field sources is not compatible with the main classes of X-ray emitters except for extreme BL Lacertae objects at fx/fv is equal to or less than 35. From the analysis of ROSAT archival data we found evidence for only three sources, out of 16, needing absorption in excess of the Galactic value and no indication of variability. We also found evidence for an extended nature for only one of the five blanks with a serendipitous HRI (High Resolution Imager) detection; this source (1WGA J1226.9+3332) was confirmed as a z=0.89 cluster of galaxies. Palomar images reveal the presence of a red (O - E is equal to or greater than 2) counterpart in the X-ray error circle for six blanks. The identification process brought to the discovery of another high z cluster of galaxies, one (possibly extreme) BL Lac and two apparently normal type 1 AGNs (Active Galactic Nuclei). These AGNs, together with four more AGN-like objects seem to form a well defined group: they present type 1 X-ray spectra but red Palomar counterparts. We discuss the possible explanations for the discrepancy between the X-ray and optical data, among which: a suppressed big blue bump emission, an extreme dust to gas (approximately 40 - 60 the Galactic ratio) ratio value and a high redshift (z is greater than or equal to 3.5) QSO (Quasi-Stellar Object) nature. These AGN-like blanks seem to be the bright (and easier to study) analogs of the sources which are being found in deep Chandra observations. Five more blanks have a still an unknown nature.

Elvis, Martin↗
NASA NTRS2010

DSD Characteristics of a Mid-Winter Tornadic Storm Using C-Band Polarimetric Radar and Two 2D-Video Disdrometers

Drop size distributions in an evolving tornadic storm are examined using C-band polarimetric radar observations and two 2D-video disdrometers. The E-F2 storm occurred in mid-winter (21 January 2010) in northern Alabama, USA, and caused widespread damage. The evolution of the storm occurred within the C-band radar coverage and moreover, several minutes prior to touch down, the storm passed over a site where several disdrometers including two 2D video disdrometers (2DVD) had been installed. One of the 2DVDs is a low profile unit and the other is a new next generation compact unit currently undergoing performance evaluation. Analyses of the radar data indicate that the main region of precipitation should be treated as a "big-drop" regime case. Even the measured differential reflectivity values (i.e. without attenuation correction) were as high as 6-7 dB within regions of high reflectivity. Standard attenuation-correction methods using differential propagation phase have been "fine tuned" to be applicable to the "big drop" regime. The corrected reflectivity and differential reflectivity data are combined with the co-polar correlation coefficient and specific differential phase to determine the mass-weighted mean diameter, Dm, and the width of the mass spectrum, (sigma)M, as well as the intercept parameter , Nw. Significant areas of high Dm (3-4 mm) were retrieved within the main precipitation areas of the tornadic storm. The "big drop" regime assumption is substantiated by the two sets of 2DVD measurements. The Dm values calculated from 1-minute drop size distributions reached nearly 4 mm, whilst the maximum drop diameters were over 6 mm. The fall velocity measurements from the 2DVD indicate almost all hydrometeors to be fully melted at ground level. Drop shapes for this event are also being investigated from the 2DVD camera data.

Thurai, M.↗
NASA NTRS2016

An Integrated Gate Turnaround Management Concept Leveraging Big Data/Analytics for NAS Performance Improvements

The Integrated Gate Turnaround Management (IGTM) concept was developed to improve the gate turnaround performance at the airport by leveraging relevant historical data to support optimization of airport gate operations, which include: taxi to the gate, gate services, push back, taxi to the runway, and takeoff, based on available resources, constraints, and uncertainties. By analyzing events of gate operations, primary performance dependent attributes of these events were identified for the historical data analysis such that performance models can be developed based on uncertainties to support descriptive, predictive, and prescriptive functions. A system architecture was developed to examine system requirements in support of such a concept. An IGTM prototype was developed to demonstrate the concept using a distributed network and collaborative decision tools for stakeholders to meet on time pushback performance under uncertainties.

Big Data and Net-enabled ATM↗
NASA NTRS2004

Statistical Analysis of CMC Constituent and Processing Data

Ceramic Matrix Composites (CMCs) are the next "big thing" in high-temperature structural materials. In the case of jet engines, it is widely believed that the metallic superalloys currently being utilized for hot structures (combustors, shrouds, turbine vanes and blades) are nearing their potential limits of improvement. In order to allow for increased turbine temperatures to increase engine efficiency, material scientists have begun looking toward advanced CMCs and SiC/SiC composites in particular. Ceramic composites provide greater strength-to-weight ratios at higher temperatures than metallic alloys, but at the same time require greater challenges in micro-structural optimization that in turn increases the cost of the material as well as increases the risk of variability in the material s thermo-structural behavior. to model various potential CMC engine materials and examines the current variability in these properties due to variability in component processing conditions and constituent materials; then, to see how processing and constituent variations effect key strength, stiffness, and thermal properties of the finished components. Basically, this means trying to model variations in the component s behavior by knowing what went into creating it. inter-phase and manufactured by chemical vapor infiltration (CVI) and melt infiltration (MI) were considered. Examinations of: (1) the percent constituents by volume, (2) the inter-phase thickness, (3) variations in the total porosity, and (4) variations in the chemical composition of the Sic fiber are carried out and modeled using various codes used here at NASA-Glenn (PCGina, NASALife, CEMCAN, etc...). The effects of these variations and the ranking of their respective influences on the various thermo-mechanical material properties are studied and compared to available test data. The properties of the materials as well as minor changes to geometry are then made to the computer model and the detrimental effects observed using statistical analysis software. The ultimate purpose of this study is to determine what variations in material processing can lead to the most critical changes in the materials property. The work I have taken part in this summer explores, in general, the key properties needed In this study SiC/SiC composites of varying architectures, utilizing a boron-nitride (BN)

Fornuff, Jonathan↗
NASA NTRS2016

Using Docker Containers to Extend Reproducibility Architecture for the NASA Earth Exchange (NEX)

NASA Earth Exchange (NEX) is a data, supercomputing and knowledge collaboratory that houses NASA satellite, climate and ancillary data where a focused community can come together to address large-scale challenges in Earth sciences. As NEX has been growing into a petabyte-size platform for analysis, experiments and data production, it has been increasingly important to enable users to easily retrace their steps, identify what datasets were produced by which process chains, and give them ability to readily reproduce their results. This can be a tedious and difficult task even for a small project, but is almost impossible on large processing pipelines. We have developed an initial reproducibility and knowledge capture solution for the NEX, however, if users want to move the code to another system, whether it is their home institution cluster, laptop or the cloud, they have to find, build and install all the required dependencies that would run their code. This can be a very tedious and tricky process and is a big impediment to moving code to data and reproducibility outside the original system. The NEX team has tried to assist users who wanted to move their code into OpenNEX on Amazon cloud by creating custom virtual machines with all the software and dependencies installed, but this, while solving some of the issues, creates a new bottleneck that requires the NEX team to be involved with any new request, updates to virtual machines and general maintenance support. In this presentation, we will describe a solution that integrates NEX and Docker to bridge the gap in code-to-data migration. The core of the solution is saemi-automatic conversion of science codes, tools and services that are already tracked and described in the NEX provenance system, to Docker - an open-source Linux container software. Docker is available on most computer platforms, easy to install and capable of seamlessly creating and/or executing any application packaged in the appropriate format. We believe this is an important step towards seamless process deployment in heterogeneous environments that will enhance community access to NASA data and tools in a scalable way, promote software reuse, and improve reproducibility of scientific results.

earth exchange↗
NASA NTRS2014

Using the SPoRT POES/GOES Hybrid Product in OCONUS Forecasting

The SPoRT (Short-term Prediction and Research Transition) Program at the NASA/Marshall Space Flight Center has been providing unique NASA and NOAA data and techniques to partner Weather Forecast Offices (WFOs) for ten years. Data are provided in the Decision Support System used by WFO forecasters: AWIPS. For the last couple of years, SPoRT has been producing the POES/GOES Hybrid. This suite of products combines the strength ofl5- minute animations of GOES imagery - providing temporal continuity, with the higher resolution, relatively random availability, of polar orbiting (POES) imagery data. The product was first introduced with only MODIS data from NASA's Terra and Aqua satellites, but recently the VIIRS instrument onboard the Suomi-NPP satellite was added, providing better high-resolution coverage. These products represent SPoRT's efforts to prepare for higher resolution, higher frequency GOES-R imagery - as well as helping to move VIIRS (JPSS) data into the mainstream of weather forecasting. SPoRT generates 5 products for this dataset: Visible, Longwave Infrared (11 micrometers), Shortwave IR (3.7 micrometers), Water Vapor (6.7 micrometers), and Fog (Difference of 11 micrometer and 3.7 micrometer channels). The Water Vapor hybrid product has a Red-Blue-Green image from MODIS inlaid, since it provides even more qualitative information than water vapor alone. Animated examples of the products will be shown in this presentation. While the resolution at nadir of GOES imagery is nominally Han (4km for IR channels), the inlaid polar orbiter imagery has a resolution of 250m (lkm for IR channels). This has tremendous application in the continental US. However, in high latitudes, since the usefulness of GOES degrades poleward rapidly, the contrast of GOES and POES data is stark. The consistent temporal nature of GOES, even though at a reduced resolution at high latitudes, provides basic situational awareness, but the introduction of polar data is very helpful in seeing the big picture with clarity - even if only briefly. This presentation will offer real situations where these products helped forecasters make better informed decisions quickly. Plans to augment the product further with the addition of data from several A VHRR instruments will be described.

Smith, Matt↗
NASA NTRS1999

Ocean Wave Studies with Applications to Ocean Modeling and Improvement of Satellite Altimeter Measurements

Combining analysis of satellite data (altimeter, scatterometer, high-resolution visible and infrared images, etc.) with mathematical modeling of non-linear wave processes, we investigate various ocean wave fields (on scales from capillary to planetary), their role in ocean dynamics and turbulent transport (of heat and biogeochemical quantities), and their effects on satellite altimeter measuring accuracy. In 1998 my attention was focused on long internal gravity waves (10 to 1000 km), known also as baroclinic inertia-gravity (BIG) waves. We found these waves to be a major factor of altimeter measurements "noise," resulting in a greater uncertainty [up to 10 cm in terms of sea surface height (SSH) amplitude] in the measured SSH signal than that caused by the sea state bias variations (up to 5 cm or so). This effect still remains largely overlooked by the satellite altimeter community. Our studies of BIG waves address not only their influence on altimeter measurements but also their role in global ocean dynamics and in transport and turbulent diffusion of biogeochemical quantities. In particular, in collaboration with Prof Peter Weichman, Caltech, we developed a theory of turbulent diffusion caused by wave motions of most general nature. Applied to the problem of horizontal turbulent diffusion in the ocean, the theory yielded the effective diffusion coefficient as a function of BIG wave parameters obtainable from satellite altimeter data. This effort, begun in 1997, has been successfully completed in 1998. We also developed a theory that relates spatial fluctuations of scalar fields (such as sea surface temperature, chlorophyll concentration, drifting ice concentration, etc.) to statistical characteristics of BIG waves obtainable from altimeter measurements. A manuscript is in the final stages of preparation. In order to verify the theoretical predictions and apply them to observations, we are now analyzing Sea-viewing Wide Field of view Sensor (SeaWiFS) and Field of view Sensor (SeaWiFS) and Advanced Very High-Resolution Radiometer (AVHRR) data on sea surface temperature (SST) and chlorophyll concentration jointly with TOPEX/POSEIDON data on SSH variations.

Glazman, Roman E.↗
NASA NTRS1991

The ultraviolet spectrum and continuum energy distribution of the bright quasar H1821 + 643

The first UV observations of the bright QSO H1821 + 643 are reported. With V = 14.2 mag and z = 0.297, H1821 + 643 is the second brightest object in the sky at z above 0.1. The IUE data are combined with new optical spectroscopy, and existing IR and X-ray data, to reveal a strong optical/UV 'big bump', which continues past the Lyman limit in the rest frame of the QSO. A possible turnover at the high-frequency side of the UV continuum constrains fits of a thin accretion disk model to a large black hole mass and high accretion rate, but a small disk size. The shape of the UV continuum was found to be variable, with a hardening of the spectrum when the source was brighter. Because of its location, only 3 deg from the ecliptic pole, H1821 + 643 will be an important object for simultaneous UV and soft X-ray monitoring to test for a common origin of the UV bump and soft X-ray excess.

Kolman, Michiel↗
NASA NTRS1994

Interpretation of the COBE FIRAS CMBR spectrum

The cosmic microwave background radiation (CMBR) spectrum measured by the Far-Infrared Absolute Spectrophotometer (FIRAS) instrument on NASA's Cosmic Background Explorer (COBE) is indistinguishable from a blackbody, implying stringent limits on energy release in the early universe later than the time t = 1 yr after the big bang. We compare the FIRAS data to previous precise measurements of the cosmic microwave background spectrum and find a reasonable agreement. We discuss the implications of the absolute value of y is less than 2.5 x 10(exp -5) and the absolute value of mu is less than 3.3 x 10(exp -4) 95% confidence limits found by Mather et al. (1994) on many processes occurring after t = 1 yr, such as explosive structure formation, reionization, and dissipation of small-scale density perturbations. We place limits on models with dust plus Population III stars, or evolving populations of IR galaxies, by directly comparing the Mather et al. spectrum to the model predictions.

Wright, E. L.↗
NASA NTRS2011

Environmental Signatures for Habitability: What to Measure and How to Rank the Habitability Potential of Mars

The environmental signatures for habitability are not necessarily biosignatures, even though on Earth, they are definitive proof of habitability. It is the constant overprint of the chemical signatures of life that makes it difficult to recognize the chemical and physical properties of a potentially habitable environment as distinct from an inhabited one. Mars Science Laboratory (MSL) will soon embark on a mission to Mars to assess its past or present habitability, so it is useful to examine how we measure habitability on Earth and prepare for how that approach may differ for Mars. This exercise includes: (a) articulation of fundamental assumptions about habitability, (b) an inventory of factors that affect habitability, (c) development of metrics, measurement approach and implementation, and (d) a new classification scheme for planetary habitability that goes beyond the binary "yes" or "no." There may be dozens of factors that affect habitability and they can be weighted as a function of specific environment. However a robotic, in situ investigation even on Earth has constraints that prevent the measurement of every environmental factor, so metrics must be reduced to the most relevant subset, given available time, cost, technical feasibility and scientific importance. Many of the factors could be measured with a combination of orbital data and the MSL payload. We propose that, at a minimum, a designation of high habitability potential requires the following conditions be met: (a) thermally stable with respect to extremes and frequency of fluctuation, (b) has more than one energy source, (c) sufficient chemical diversity to make compounds with covalent and hydrogen bonding, (d) can moderate ionizing radiation enough to allow a stable or evolving pool of organic molecules, (e) must have water or other high quality polar solvent, (f) must be able to renew chemical resources (e.g., plate tectonics, volcanism or something else we haven't envisioned). A measurement approach we have taken to measure habitability on Earth is : 1. Study remote sensing data, maps, etc. 2. Decide how big an area to measure. 3. Determine the spatial sampling rate. 4. Determine the temporal sampling rate. 5. Determine the order of measurements 6. Decide where to begin measurements 7. Select locations at field site and proceed While science drives each of the steps, there are additional constraints, e.g., technical, time, cost, safety (risk). This approach is also executable on Mars. Measurement of past habitability is more challenging both for Earth and Mars where access to the past means subsurface access and confrontation with unknowns about preservation of the martian past. Some environments preserve evidence of past habitability better than others, and this is where selection of the landing site to maximize the preservation potential of habitability indicators will be key. Mars presents an opportunity to discover transitional states between habitable or not, and we offer a ranking scale for planetary habitability with Mars as the second test subject: CLASS ONE Uninhabitable and likely has never been so CLASS TWO Has a high potential but no confirmed observation of life (as defined above) CLASS THREE Inhabited (we find life) 3-A Globally inhabited 3-B Primitive life; early in its evolution, but not yet globally established 3-C Exists only in refugia -- planet heading toward class four CLASS FOUR Post-habitable (there once was life, but now it's gone) MSL provides an opportunity to carefully investigate the habitability of at least one site on Mars and it will reveal much about the possible states of planetary habitability

Conrad, Pamela G.↗
NASA NTRS2011

A Study on the Potential Applications of Satellite Data in Air Quality Monitoring and Forecasting

In this study we explore the potential applications of MODIS (Moderate Resolution Imaging Spectroradiometer) -like satellite sensors in air quality research for some Asian regions. The MODIS aerosol optical thickness (AOT), NCEP global reanalysis meteorological data, and daily surface PM(sub 10) concentrations over China and Thailand from 2001 to 2009 were analyzed using simple and multiple regression models. The AOT-PM(sub 10) correlation demonstrates substantial seasonal and regional difference, likely reflecting variations in aerosol composition and atmospheric conditions, Meteorological factors, particularly relative humidity, were found to influence the AOT-PM(sub 10) relationship. Their inclusion in regression models leads to more accurate assessment of PM(sub 10) from space borne observations. We further introduced a simple method for employing the satellite data to empirically forecast surface particulate pollution, In general, AOT from the previous day (day 0) is used as a predicator variable, along with the forecasted meteorology for the following day (day 1), to predict the PM(sub 10) level for day 1. The contribution of regional transport is represented by backward trajectories combined with AOT. This method was evaluated through PM(sub 10) hindcasts for 2008-2009, using ohservations from 2005 to 2007 as a training data set to obtain model coefficients. For five big Chinese cities, over 50% of the hindcasts have percentage error less than or equal to 30%. Similar performance was achieved for cities in northern Thailand. The MODIS AOT data are responsible for at least part of the demonstrated forecasting skill. This method can be easily adapted for other regions, but is probably most useful for those having sparse ground monitoring networks or no access to sophisticated deterministic models. We also highlight several existing issues, including some inherent to a regression-based approach as exemplified by a case study for Beijing, Further studies will be necessa1Y before satellite data can see more extensive applications in the operational air quality monitoring and forecasting.

Li, Can↗
NASA NTRS2003

Deploying Object Oriented Data Technology to the Planetary Data System

How do you provide more than 350 scientists and researchers access to data from every instrument in Odyssey when the data is curated across half a dozen institutions and in different formats and is too big to mail on a CD-ROM anymore? The Planetary Data System (PDS) faced this exact question. The solution was to use a metadata-based middleware framework developed by the Object Oriented Data Technology task at NASA s Jet Propulsion Laboratory. Using OODT, PDS provided - for the first time ever - data from all mission instruments through a single system immediately upon data delivery.

Kelly, S.↗
NASA NTRS2020

Near 40 Years MERRA-2 Data at NASA GES DISC -Opportunity and Challenge to Support Extremes Study

To the end of 2019, 40 years NASA climate reanalysis data sets from the Modern Era Retrospective-analysis for Research and Applications, Version 2 (MERRA-2) will be available at NASA Goddard Earth Sciences Data and Information Services Center (GES DISC). MERRA-2 consists atmosphere, land, and ocean data, which may be used for the studies ranging from the short scale weather events to the large scale decadal vulnerabilities. The hourly products, such as precipitation, soil moisture, temperature, and aerosols etc., have been used widely to study extreme events.In supporting users from broad communities, GES DISC have developed various data access services, including subsetter for downloading only data of interest with preferred format; OPeNDAP - for machine-to-machine data access; and Giovanni- for online visualization and analysis, etc. A big challenge for extreme study is to downloading and processing long-term hourly or daily data. The data downloading performance is not very satisfied by many users with current services and the native archived data structure. Late June 2019, many people in Europe had experienced extreme heat waves. The temperatures in several countries exceeded 40°C (104°F). For example, MERRA-2 shows that the near surface daily maximum temperature of June 28 2019 over Marseille, a city in southern France, reached 41.1 °C (106°F), which is the record breaking temperature in the last 40 years. GES DISC is working together with domain science experts to improve the performance of long time series access, making analysis ready data sets in supporting application researches, such as extreme study. In this presentation, using Europe heat wave as an example, we will show prototype of the in developing service for finding extremes from near 40 years MERRA-2 data at a given location. MERRA-2 data can be accessed from NASA GES DISC(https://disc.gsfc.nasa.gov/ ) by search keyword "MERRA-2".

Shen, Suhung↗
NASA NTRS2000

Multiresolution With Super-Compact Wavelets

The solution data computed from large scale simulations are sometimes too big for main memory, for local disks, and possibly even for a remote storage disk, creating tremendous processing time as well as technical difficulties in analyzing the data. The excessive storage demands a corresponding huge penalty in I/O time, rendering time and transmission time between different computer systems. In this paper, a multiresolution scheme is proposed to compress field simulation or experimental data without much loss of important information in the representation. Originally, the wavelet based multiresolution scheme was introduced in image processing, for the purposes of data compression and feature extraction. Unlike photographic image data which has rather simple settings, computational field simulation data needs more careful treatment in applying the multiresolution technique. While the image data sits on a regular spaced grid, the simulation data usually resides on a structured curvilinear grid or unstructured grid. In addition to the irregularity in grid spacing, the other difficulty is that the solutions consist of vectors instead of scalar values. The data characteristics demand more restrictive conditions. In general, the photographic images have very little inherent smoothness with discontinuities almost everywhere. On the other hand, the numerical solutions have smoothness almost everywhere and discontinuities in local areas (shock, vortices, and shear layers). The wavelet bases should be amenable to the solution of the problem at hand and applicable to constraints such as numerical accuracy and boundary conditions. In choosing a suitable wavelet basis for simulation data among a variety of wavelet families, the supercompact wavelets designed by Beam and Warming provide one of the most effective multiresolution schemes. Supercompact multi-wavelets retain the compactness of Haar wavelets, are piecewise polynomial and orthogonal, and can have arbitrary order of approximation. The advantages of the multiresolution algorithm are that no special treatment is required at the boundaries of the interval, and that the application to functions which are only piecewise continuous (internal boundaries) can be efficiently implemented. In this presentation, Beam's supercompact wavelets are generalized to higher dimensions using multidimensional scaling and wavelet functions rather than alternating the directions as in the 1D version. As a demonstration of actual 3D data compression, supercompact wavelet transforms are applied to a 3D data set for wing tip vortex flow solutions (2.5 million grid points). It is shown that high data compression ratio can be achieved (around 50:1 ratio) in both vector and scalar data set.

Lee, Dohyung↗