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Results for “total variation regularization”

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NASA NTRS2013

Downscaling Satellite Precipitation with Emphasis on Extremes: A Variational 1-Norm Regularization in the Derivative Domain

The increasing availability of precipitation observations from space, e.g., from the Tropical Rainfall Measuring Mission (TRMM) and the forthcoming Global Precipitation Measuring (GPM) Mission, has fueled renewed interest in developing frameworks for downscaling and multi-sensor data fusion that can handle large data sets in computationally efficient ways while optimally reproducing desired properties of the underlying rainfall fields. Of special interest is the reproduction of extreme precipitation intensities and gradients, as these are directly relevant to hazard prediction. In this paper, we present a new formalism for downscaling satellite precipitation observations, which explicitly allows for the preservation of some key geometrical and statistical properties of spatial precipitation. These include sharp intensity gradients (due to high-intensity regions embedded within lower-intensity areas), coherent spatial structures (due to regions of slowly varying rainfall),and thicker-than-Gaussian tails of precipitation gradients and intensities. Specifically, we pose the downscaling problem as a discrete inverse problem and solve it via a regularized variational approach (variational downscaling) where the regularization term is selected to impose the desired smoothness in the solution while allowing for some steep gradients(called 1-norm or total variation regularization). We demonstrate the duality between this geometrically inspired solution and its Bayesian statistical interpretation, which is equivalent to assuming a Laplace prior distribution for the precipitation intensities in the derivative (wavelet) space. When the observation operator is not known, we discuss the effect of its misspecification and explore a previously proposed dictionary-based sparse inverse downscaling methodology to indirectly learn the observation operator from a database of coincidental high- and low-resolution observations. The proposed method and ideas are illustrated in case studies featuring the downscaling of a hurricane precipitation field.

Hurricanes↗

NASA NTRSDate not supplied

Total Variation Majorization Minimization (TV-MM) Approach to Radiometer Brightness Temperature Gridding and Reconstruction

This paper presents the implementation of an algorithm to enhance the image resolution of the Earth's surface brightness temperature (T B ) data measured by radiometers such as the one onboard of the Soil Moisture Active Passive (SMAP) mission. A key step in radiometer T B processing is the conversion of the swath-based calibrated antenna temperature (T A ) measurements to the Level 3 Earth-centered grid. The simplest algorithm to transform this data from swath to gridded format is called drop-in-the-bucket which simply averages surrounding noisy T A samples to form a T B value at the gridded location. This method reduces noise, however produces low resolution products. To obtain a higher resolution product, SMAP uses other techniques such the Backus-Gilbert (BG) algorithm, which is the conventional method used in microwave radiometry. Although this method performs the required interpolation, it is not effective in denoising and removing blurring effects due to antenna filtering of the radiometer image data. Our motivation for this development is to further improve the resolution through post-processing of the radiometer T B image, a highly cost-effective method of image enhancement. The approach adapted in this work is based on the minimization of the Total Variation (TV) regularized objective function that is used extensively in solving general ill-posed linear inverse problems in image processing. Since the TV-based objective function is convex but not everywhere differentiable, there exists many numerical algorithms that can estimate the solution and the one selected for this work is called Majorization- Minimization (MM). By applying this algorithm, simulation experiments were performed based on synthetic data from the Geophysical model as well as real SMAP data to demonstrate the effectiveness of the technique. Results were then compared against the BG method.

Wing Lee↗

NASA NTRS1993

A long-term study of H(alpha) line variations in FK Comae Berenices

We present observations of H(alpha) V/R ratio variations in FK Comae Berencies obtained during several observing seasons from 1981 to 1992. The raw H(alpha) emission profile is always observed to be double peaked due to the stellar-absorption component. During the most years the V/R ratio varies regularly with the period of the photometric light curve. The V/R periodicity is most obvious when time spans no longer than several stellar rotations are considered. We propose that the bulk of the emission component of the H(alpha) line arises in corotating circumstellar material that may be similar to that of a quiescent solar prominence. The lifetime of these structures appears to be on the order of weeks. A weak contribution from a circumstellar disk is evident and chromospheric emission may also be present. The appearance or disappearance of circumstellar structures over periods longer than a few weeks, or the total absence of such structures, blurs the more regular variations in H(alpha) seen over short time scales. Other more stochastic activity, such as flares, also clearly occurs. Phase shifts of the V/R ratio from year to year rule out the hypothesis that mass tranfer in a close binary system is responsible for the V/R variations.

Welty, Alan D.↗

NASA NTRS1994

Ozone and nitrogen dioxide above the northern Tien Shan

The results of systematic perennial measurements of the total ozone (since 1979) and nitrogen dioxide column (since 1983) in the atmosphere in the European-Asian continent center above the mountainmass of the Tien Shan are given. This region is distinguished by a great number of sunny days during a year. The observation station is at the Northern shore of Issyk Kul Lake (42.56 N 77.04 E 1650 m above the sea level). The measurement results are presented as the monthly averaged atmospheric total ozone and NO2 stratospheric column abundances (morning and evening). The peculiarities of seasonal variations of ozone and nitrogen dioxide atmospheric contents, their regular variances with a quasi-biennial cycles and trends have been noticed. Irregular variances of ozone and nitrogen dioxide atmospheric contents, i.e. their positive and negative anomalies in the monthly averaged contents relative to the perennial averaged monthly means, have been analyzed. The synchronous and opposite in phase anomalies in variations of ozone and nitrogen dioxide atmospheric contents were explained by the transport and zonal circulation in the stratosphere (Kamenogradsky et al., 1990).

Arefev, Vladimir N.↗

NASA NTRS1974

Changes in atmospheric composition inferred from ionospheric production rates

Changes in the total electron content of the ionosphere near sunrise are used to determine the integrated production rate in the ionosphere (Q) from 1965 to 1971 at latitudes of 34S, 20N, and 34N. The observed regular semiannual variation in Q through a range of 1:3:1 is interpreted as an increase in the ratio O/N2 (relative densities) near the equinoxes. It follows that there is a worldwide semiannual variation in atmospheric composition, with the above ratio maximum just after the equinoxes. There is a large seasonal variation in the Northern hemisphere with a maximum in mid-summer. This effect is absent in the Southern hemisphere. At all times except solar maximum in the Northern hemisphere there is a global asymmetry. The ratio O/N2 is about three times as large in the Northern hemisphere. The overall mechanism appears to be N2 absorption.

Titheridge, J. E.↗

NASA NTRS1985

Monthly mean distribution of ozone and temperature

Global monthly mean charts for both hemispheres are given for four mid-season months, and for the pressure levels 30, 10, 1, and 0.1 mbar for temperature and 0.4 mbar for ozone. Charts of total ozone are provided separately. This set of charts shows clearly the very close coupling between the temperature and ozone distributions and demonstrates the influence of the large-scale planetary waves which give rise to very large longitudinal variations. The regular and interannual variability of temperature and ozone are discussed.

Labitzke, K.↗

NASA NTRS1992

A time-accurate high-resolution TVD scheme for solving the Navier-Stokes equations

A total variation diminishing (TVD) scheme has been developed and incorporated into an existing time-accurate high-resolution Navier-Stokes code. The accuracy and the robustness of the resulting solution procedure have been assessed by performing many calculations in four different areas: shock tube flows, regular shock reflection, supersonic boundary layer, and shock boundary layer interactions. These numerical results compare well with corresponding exact solutions or experimental data.

Kim, Hyun Dae↗

NASA NTRS1993

A time-accurate high-resolution TVD scheme for solving the Navier-Stokes equations

Kim, Hyun D.↗

NASA NTRS1993

The Galileo solar redshift experiment

From the October 1989 launch to the first December 1990 earth gravity assist, we regularly obtained frequency measurements of the spacecraft clock - an ultrastable crystal oscillator (USO) supplied by Frequency Electronics, Inc. The solar gravitational redshift in frequency was readily detectable, and because of the unique variations in heliocentric distance we could separate the general relativistic effects from the USO's intrinsic frequency variations. We have verified the total frequency shift predicted by general relativity to 0.5 percent accuracy, and the solar gravitational redshift to 1 percent accuracy.

Krisher, Timothy P.↗

NASA NTRS1982

Solar irradiance variations and solar activity

A mean value for the 1 AU total solar irradiance of 1368.2 W/sq m and a downward trend of 0.05% per year were derived from measurements by the Active Cavity Radiometer Irradiance Monitor (ACRIM) experiment on the Solar Maximum Mission during 1980. Distinct temporary solar irradiance decreases associated with solar activity maxima were observed with a series of nine dips from April to October recurring at fairly regular intervals averaging 24 days. The decreases correlate inversely with sunspot area, 2800-MHz flux, and Zurich sunspot number. Dominant periods common to the irradiance and sunspot area power spectra link the irradiance decreases to sunspot flux deficit in solar active regions. Evidence of significant total irradiance modulation by facular flux excess is cited. A persistent radiative cycle of active regions consistent with the ACRIM irradiance results and the morphology of solar active regions was found. The pattern of regularly recurrent active region maxima between April and October suggests an asymmetry in solar activity generation during this period.

Willson, R. C.↗

NASA NTRS2004

Cyclic Oxidation Modeling and Life Prediction

The cyclic oxidation process can be described as an iterative scale growth and spallation sequence by a number of similar models. Model input variable include oxide scale type and growth parameters, spalling geometry, spall constant, and cycle duration. Outputs include net weight change, the amounts of retained and spalled oxide, the total oxygen and metal consumed, and the terminal rates of weight loss and metal consumption. All models and their variations produce a number of similar characteristic features. In general, spalling and material consumption increase to a steady state rate, at which point the retained scale approaches a constant and the rate of weight loss becomes linear. For one model, this regularity was demonstrated as dimensionless, universal expressions, obtained by normalizing the variables by critical performance factors. These insights were enabled through the use of the COSP for Windows cyclic oxidation spalling program.

Smialek, James L.↗

NASA NTRS1999

Postseismic Deformation after the 1964 Great Alaskan Earthquake: Collaborative Research with Goddard Space Flight Center

The purpose of this project was to carry out GPS observations on the Kenai Peninsula, southern Alaska, in order to study the postseismic and contemporary deformation following the 1964 Alaska earthquake. All of the research supported in this grant was carried out in collaboration with Dr. Steven Cohen of Goddard Space Flight Center. The research funding from this grant primarily supported GPS fieldwork, along with the acquisition of computer equipment to allow analysis and modeling of the GPS data. A minor amount of salary support was provided by the PI, but the great majority of the salary support was provided by the Geophysical Institute. After the expiration of this grant, additional funding was obtained from the National Science Foundation to continue the work. This grant supported GPS field campaigns in August 1995, June 1996, May-June and September 1997, and May-June 1998. We initially began the work by surveying leveling benchmarks on the Kenai peninsula that had been surveyed after the 1964 earthquake. Changes in height from the 1964 leveling data to the 1995+ GPS data, corrected for the geoid-ellipsoid separation, give the total elevation change since the earthquake. Beginning in 1995, we also identified or established sites that were suitable for long-term surveying using GPS. In the subsequent annual GPS campaigns, we made regular measurements at these GPS marks, and steadily enhanced our set of points for which cumulative postseismic uplift data were available. From 4 years of Global Positioning System (GPS) measurements, we find significant spatial variations in present-day deformation between the eastern and western Kenai peninsula, Alaska. Sites in the eastern Kenai peninsula and Prince William Sound move to the NNW relative to North America, in the direction of Pacific-North America relative plate motion. Velocities decrease in magnitude from nearly the full plate rate in southern Prince William Sound to about 30 mm/yr at Seward and to about 5 mm/yr near Anchorage. In contrast, sites in the western Kenai peninsula move to the SW, in a nearly trenchward direction, with a velocity of about 20 mm/yr. The data are consistent with the shallow plate interface offshore and beneath the eastern Kenai and Prince William Sound being completely locked or nearly so, with elastic strain accumulation resulting in rapid motion in the direction of relative plate motion of sites in the overriding plate. The velocities of sites in the western Kenai, along strike to the southwest, are opposite in sign with those predicted from elastic strain accumulation. These data are incompatible with a significant locked region in this segment of the plate boundary. Trenchward velocities are found also for some sites in the Anchorage area. We interpret the trenchward velocities as being caused by a continuing postseismic transient from the 1964 great Alaska earthquake.

Freymueller, Jeffrey T.↗

NASA NTRS1989

Data traffic reduction schemes for Cholesky factorization on asynchronous multiprocessor systems

Communication requirements of Cholesky factorization of dense and sparse symmetric, positive definite matrices are analyzed. The communication requirement is characterized by the data traffic generated on multiprocessor systems with local and shared memory. Lower bound proofs are given to show that when the load is uniformly distributed the data traffic associated with factoring an n x n dense matrix using n to the alpha power (alpha less than or equal 2) processors is omega(n to the 2 + alpha/2 power). For n x n sparse matrices representing a square root of n x square root of n regular grid graph the data traffic is shown to be omega(n to the 1 + alpha/2 power), alpha less than or equal 1. Partitioning schemes that are variations of block assignment scheme are described and it is shown that the data traffic generated by these schemes are asymptotically optimal. The schemes allow efficient use of up to O(n to the 2nd power) processors in the dense case and up to O(n) processors in the sparse case before the total data traffic reaches the maximum value of O(n to the 3rd power) and O(n to the 3/2 power), respectively. It is shown that the block based partitioning schemes allow a better utilization of the data accessed from shared memory and thus reduce the data traffic than those based on column-wise wrap around assignment schemes.

Naik, Vijay K.↗

NASA NTRS1993

Dwarf novae

Dwarf novae are defined on grounds of their semi-regular brightness variations of some two to five magnitudes on time scales of typically 10 to 100 days. Historically several different classification schemes have been used. Today, dwarf novae are divided into three sub-classes: the U Geminorum stars, the SU Ursae Majoris stars, and the Z Camelopardalis stars. Outbursts of dwarf novae occur at semi-periodic intervals of time, typically every 10 to 100 days; amplitudes range from typically 2 to 5 mag. Within certain limits values are characteristic for each object. Relations between the outburst amplitude, or the total energy released during outburst, and the recurrence time have been found, as well as relations between the orbital period and the outburst decay time, the absolute magnitude during outburst maximum, and the widths of long and short outbursts, respectively. Some dwarf novae are known to have suspended their normal outburst activity altogether for a while. They later resumed it without having undergone any observable changes. The optical colors of dwarf novae all are quite similar during outburst, considerably bluer than during the quiescent state. During the outburst cycle, characteristic loops in the two color diagram are performed. At a time resolution on the order of minutes, strictly periodic photometric changes due to orbital motion become visible in the light curves of dwarf novae. These are characteristic for each system. Remarkably little is known about orbital variations during the course of an outburst. On time-scales of minutes and seconds, further more or less periodic types of variability are seen in dwarf novae. Appreciable flux is emitted by dwarf novae at all wavelengths from the X-rays to the longest IR wavelengths, and in some cases even in the radio. Most dwarf novae exhibit strong emission line spectra in the optical and UV during quiescence, although some have only very weak emissions in the optical and/or weak absorptions at UV wavelengths.

Ladous, Constanze↗

NASA NTRS1991

Elimination of secular terms from the differential equations for the elements of perturbed two-body motion

In 1961, Sperling linearized and regularized the differential equations of motion of the two-body problem by changing the independent variable from time to fictitious time by Sundman's transformation (r = dt/ds) and by embedding the two-body energy integral and the Laplace vector. In 1968, Burdet developed a perturbation theory which was uniformly valid for all types of orbits using a variation of parameters approach on the elements which appeared in Sperling's equations for the two-body solution. In 1973, Bond and Hanssen improved Burdet's set of differential equations by embedding the total energy (which is a constant when the potential function is explicitly dependent upon time.) The Jacobian constant was used as an element to replace the total energy in a reformulation of the differential equations of motion. In the process, another element which is proportional to a component of the angular momentum was introduced. Recently trajectories computed during numerical studies of atmospheric entry from circular orbits and low thrust beginning in near-circular orbits exhibited numerical instability when solved by the method of Bond and Gottlieb (1989) for long time intervals. It was found that this instability was due to secular terms which appear on the righthand sides of the differential equations of some of the elements. In this paper, this instability is removed by the introduction of another vector integral called the delta integral (which replaces the Laplace Vector) and another scalar integral which removes the secular terms. The introduction of these integrals requires a new derivation of the differential equations for most of the elements. For this rederivation, the Lagrange method of variation of parameters is used, making the development more concise. Numerical examples of this improvement are presented.

Bond, Victor R.↗

NASA NTRS1998

Empirical correction for earth sensor horizon radiance variation

A major limitation on the use of infrared horizon sensors for attitude determination is the variability of the height of the infrared Earth horizon. This variation includes a climatological component and a stochastic component of approximately equal importance. The climatological component shows regular variation with season and latitude. Models based on historical measurements have been used to compensate for these systematic changes. The stochastic component is analogous to tropospheric weather. It can cause extreme, localized changes that for a period of days, overwhelm the climatological variation. An algorithm has been developed to compensate partially for the climatological variation of horizon height and at least to mitigate the stochastic variation. This method uses attitude and horizon sensor data from spacecraft to update a horizon height history as a function of latitude. For spacecraft that depend on horizon sensors for their attitudes (such as the Total Ozone Mapping Spectrometer-Earth Probe-TOMS-EP) a batch least squares attitude determination system is used. It is assumed that minimizing the average sensor residual throughout a full orbit of data results in attitudes that are nearly independent of local horizon height variations. The method depends on the additional assumption that the mean horizon height over all latitudes is approximately independent of season. Using these assumptions, the method yields the latitude dependent portion of local horizon height variations. This paper describes the algorithm used to generate an empirical horizon height. Ideally, an international horizon height database could be established that would rapidly merge data from various spacecraft to provide timely corrections that could be used by all.

Hashmall, Joseph A.↗

NASA NTRS1982

Measurement of total electron content of midlatitude ionosphere and protonosphere via Faraday rotation and group relay techniques using transmission from geostationary satellites ATS-3 and ATS-6

Measurement of integrated columnar electron content and total electron content for the local ionosphere and the overlying protonosphere via Faraday rotation and group delay techniques has proven very useful. A field station was established having the geographic location of 31.5 deg N latitude and 91.06 deg W longitude to accomplish these objectives. A polarimeter receiving system was set up in the beginning to measure the Faraday rotation of 137.35 MHz radio signal from geostationary satellite ATS 3 to yield the integrated columnar electron content of the local ionosphere. The measurement was continued regularly, and the analysis of the data thus collected provided a synopsis of the statistical variation of the ionosphere along with the transient variations that occurred during the periods of geomagnetic and other disturbances.

Paul, M. P.↗

NASA NTRS1994

Steps toward determination of the size and structure of the broad-line region in active galactic nuclei. 5: Variability of the ultraviolet continuum and emission lines of NGC 3783

We report on the results of intensive ultraviolet spectral monitoring of the Seyfert 1 galaxy NGC 3783. The nucleus of NGC 3783 was observed with the International Ultraviolet Explorer satellite on a regular basis for a total of 7 months, once every 4 days for the first 172 days and once every other day for the final 50 days. Significant variability was observed in both continuum and emission-line fluxes. The light curves for the continuum fluxes exhibited two well-defined local minima or 'dips,' the first lasting is less than or approximately 20 days and the second is less than or approximately 4 days, with additional episodes of relatively rapid flickering of approximately the same amplitude. As in the case of NGC 5548 (the only other Seyfert galaxy that has been the subject of such an intensive, sustained monitoring effort), the largest continuum variations were seen at the shortest wavelengths, so that the continuum became 'harder' when brighter. The variations in the continuum occurred simultaneously at all wavelengths (delta(t) is less than 2 days). Generally, the amplitude of variability of the emission lines was lower than (or comparable to) that of the continuum. Apart from Mg II (which varied little) and N V (which is relatively weak and badly blended with Ly(alpha), the light curves of the emission lines are very similar to the continuum light curves, in each case with a small systematic delay or 'lag.' As for NGC 5548, the highest ionization lines seem to respond with shorter lags than the lower ionization lines. The lags found for NGC 3783 are considerably shorter than those obtained for NGC 5548, with values of (formally) approximately 0 days for He II + O III), and approximately 4 days for Ly(alpha) and C IV. The data further suggest lags of approximately 4 days for Si IV + O IV) and 8-30 days for Si III + C III). Mg II lagged the 1460 A continuum by approximately 9 days, although this result depends on the method of measuring the line flux and may in fact be due to variability of the underlying Fe II lines. Correlation analysis further shows that the power density spectrum contains substantial unresolved power over timescales of is less than or approximately 2 days, and that the character of the continuum variability may change with time.

Reichert, G. A.↗