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NASA NTRS1990

Resolution of the 1D regularized Burgers equation using a spatial wavelet approximation

The Burgers equation with a small viscosity term, initial and periodic boundary conditions is resolved using a spatial approximation constructed from an orthonormal basis of wavelets. The algorithm is directly derived from the notions of multiresolution analysis and tree algorithms. Before the numerical algorithm is described these notions are first recalled. The method uses extensively the localization properties of the wavelets in the physical and Fourier spaces. Moreover, the authors take advantage of the fact that the involved linear operators have constant coefficients. Finally, the algorithm can be considered as a time marching version of the tree algorithm. The most important point is that an adaptive version of the algorithm exists: it allows one to reduce in a significant way the number of degrees of freedom required for a good computation of the solution. Numerical results and description of the different elements of the algorithm are provided in combination with different mathematical comments on the method and some comparison with more classical numerical algorithms.

Liandrat, J.↗

NASA NTRS1990

Maximum likelihood estimates of polar motion parameters

Two estimators developed by Jeffreys (1940, 1968) are described and used in conjunction with polar-motion data to determine the frequency (Fc) and quality factor (Qc) of the Chandler wobble. Data are taken from a monthly polar-motion series, satellite laser-ranging results, and optical astrometry and intercompared for use via interpolation techniques. Maximum likelihood arguments were employed to develop the estimators, and the assumption that polar motion relates to a Gaussian random process is assessed in terms of the accuracies of the estimators. The present results agree with those from Jeffreys' earlier study but are inconsistent with the later estimator; a Monte Carlo evaluation of the estimators confirms that the 1968 method is more accurate. The later estimator method shows good performance because the Fourier coefficients derived from the data have signal/noise levels that are superior to those for an individual datum. The method is shown to be valuable for general spectral-analysis problems in which isolated peaks must be analyzed from noisy data.

Wilson, Clark R.↗

NASA NTRS1993

Gravity wave forcing in the middle atmosphere due to reduced ozone heating during a solar eclipse

We present an analysis of the gravity wave structure and the associated forcing of the middle atmosphere induced by the screening of the ozone layer from solar heating during a solar eclipse. Fourier integral techniques and numerical evaluation of the integral solutions were used to assess the wave field structure and to compute the gravity wave forcing of the atmosphere at greater heights. Our solutions reveal dominant periods of a few hours, characteristic horizontal and vertical scales of about 5000 to 10,000 km and 200 km, respectively, and an integrated momentum flux in the direction of eclipse motion of about 5.6 x 10 exp 8 N at each height above the forcing level. These results suggest that responses to solar eclipses may be difficult to detect above background gravity wave and tidal fluctuations until well into the thermosphere. Conversely, the induced body forces may penetrate to considerable heights because of the large wave scales and will have significant effects at levels where the wave field is dissipated.

Fritts, David C.↗

NASA NTRS2000

The intensities of methane in the 3-5 mu m region revisited

The analysis of the linestrengths of the infrared spectrum of methane (12 and 13) in the 3-5 mu m region has been revisited onthe basis of new measurements from Fourier transform spectra recorded at Kitt Peak under various optical densities.

Methane High resolution Infrared Absolute intensit↗

NASA NTRS2013

Optical Properties of Iron Silicates in the Infrared to Millimeter as a Function of Wavelength and Temperature

The Optical Properties of Astronomical Silicates with Infrared Techniques (OPASI-T) program utilizes multiple instruments to provide spectral data over a wide range of temperature and wavelengths. Experimental methods include Vector Network Analyzer (VNA) and Fourier Transform Spectroscopy (FTS) transmission, and reflection/scattering measurements. From this data, we can determine the optical parameters for the index of refraction, n, and the absorption coefficient, k. The analysis of the laboratory transmittance data for each sample type is based upon different mathematical models, which are applied to each data set according to their degree of coherence. Presented here are results from iron silicate dust grain analogs, in several sample preparations and at temperatures ranging from 5-300 K, across the infrared and millimeter portion of the spectrum (from 2.5-10,000 μm or 4,000-1 cm(exp −1).

Optical↗

NASA NTRS2013

Optical Properties of Iron Silicates in the Infrared to Millimeter as a Function of Wavelength and Temperature

Methods: laboratory↗

NASA NTRS2015

Fuel Distribution Estimate via Spin Period to Precession Period Ratio for the Advanced Composition Explorer

The spin period to precession period ratio of a non-axisymmetric spin-stabilized spacecraft, the Advanced Composition Explorer (ACE), was used to estimate the remaining mass and distribution of fuel within its propulsion system. This analysis was undertaken once telemetry suggested that two of the four fuel tanks had no propellant remaining, contrary to pre-launch expectations of the propulsion system performance. Numerical integration of possible fuel distributions was used to calculate moments of inertia for the spinning spacecraft. A Fast Fourier Transform (FFT) of output from a dynamics simulation was employed to relate calculated moments of inertia to spin and precession periods. The resulting modeled ratios were compared to the actual spin period to precession period ratio derived from the effect of post-maneuver nutation angle on sun sensor measurements. A Monte Carlo search was performed to tune free parameters using the observed spin period to precession period ratio over the life of the mission. This novel analysis of spin and precession periods indicates that at the time of launch, propellant was distributed unevenly between the two pairs of fuel tanks, with one pair having approximately 20% more propellant than the other pair. Furthermore, it indicates the pair of the tanks with less fuel expelled all of its propellant by 2014 and that approximately 46 kg of propellant remains in the other two tanks, an amount that closely matches the operational fuel accounting estimate. Keywords: Fuel Distribution, Moments of Inertia, Precession, Spin, Nutation

Moment of Inertia↗

NASA NTRS1998

On the Buckling of Imperfect Anisotropic Shells with Elastic Edge Supports Under Combined Loading Part I:: Theory and Numerical Analysis - Pt. 1

A rigorous solution is presented for the case of stiffened anisotropic cylindrical shells with general imperfections under combined loading, where the edge supports are provided by symmetrical or unsymmetrical elastic rings. The circumferential dependence is eliminated by a truncated Fourier series. The resulting nonlinear 2-point boundary value problem is solved numerically via the "Parallel Shooting Method". The changing deformation patterns resulting from the different degrees of interaction between the given initial imperfections and the specified end rings are displayed. Recommendations are made as to the minimum ring stiffnesses required for optimal load carrying configurations.

Arbocz, Johann↗

NASA NTRS1992

Analysis of satellite-derived ozone and water vapor measurements

Research under this grant has involved analyses of satellite-derived measurements of water vapor and total ozone. Upper tropospheric water vapor data from the Nimbus 7 temperature-humidity infrared radiometer (THIR) 6.7 micron channel were analyzed by Fourier transformation to provide wavenumber spectra for a case of an upper level system over Europe. The power law spectrum for horizontal scales from 60 to several hundred km suggests that when convective cloud energy sources are not present, the enstrophy-cascading process (with variance proportional to the minus three power of wavenumber) may hold to much smaller scales than previously thought. Several investigations of the middle atmosphere (stratosphere and mesosphere) were also conducted. Slow atmospheric oscillations with periods of 1-2 months were investigated in total ozone measurements and in ionospheric data. Using one-point correlation maps and total ozone mapping spectrometer (TOMS) data, strong statistical evidence was found for the planetary-scale oscillations at these periods. A dipole-like pattern in the tropical equatorial Indian ocean-western Pacific region was documented, along with wavetrain-like patterns emanating into the extratropics. While attempting to follow the oscillations upward above stratosphere, oscillations were studied in ionospheric data (D-region radio wave absorption, in the upper mesosphere, around 80-90 km altitude). Cross-spectral analyses with solar flux data revealed that much of the observed 1-2 month variance in the ionospheric D-region was well correlated to solar variations. Further research has involved investigations of the photochemical lifetime of greenhouse gases methane and nitrous oxide. Using Nimbus 7 satellite data, a new analysis technique was employed to determine the lifetime of these gases in situ in the upper stratosphere. The lifetimes are found to be in good agreement with theoretical estimates.

Stanford, John L.↗

NASA NTRS1972

Development of spectral analysis math models and software program and spectral analyzer, digital converter interface equipment design

Spectral analyses of angle-modulated communication systems is studied by: (1) performing a literature survey of candidate power spectrum computational techniques, determining the computational requirements, and formulating a mathematical model satisfying these requirements; (2) implementing the model on UNIVAC 1230 digital computer as the Spectral Analysis Program (SAP); and (3) developing the hardware specifications for a data acquisition system which will acquire an input modulating signal for SAP. The SAP computational technique uses extended fast Fourier transform and represents a generalized approach for simple and complex modulating signals.

Hayden, W. L.↗

NASA NTRS1985

The utilization of satellite data and dynamics in understanding and predicting global weather phenomena

A two layer spectral quasi-geostrophic model is used to simulate the effects of topography on the equilibria, the stability, and the long term evaluation of incipient unstable waves. The flow is forced by latitudinally dependent radiational heating. The nature of the form drag instability of high index equilibria is investigated. The proximity of the equilibrium shear to a resonant value is essential for the instability, provided the equilibrium occurs at a slightly stronger shear than resonance. The properties of the steady Hadley and Rossby required for a thermally forced rotating fluid on a sphere are further explained. An objective parameterization technique is developed for general nonlinear hydrodynamical systems. The typical structure is one in which the rates of change of the dependent variables depend on homogeneous quadratic and linear forms, as well as on inhomogeneous forcing terms. Also documented is a steady, axisymmetric model of the general circulation developed as a basis for climate stability studies. The model includes the effects of heating, rotation, and internal friction, but neglects topography. Included is further research on cloud street phenomena. Orientation angles and horizontal wavelengths of boundary layer rolls and cloud streets are determined from an analysis of a truncated spectral model of three dimensional shallow moist Boussinesq convection in a shearing environment is further explained. Relatively broadly spaced roll clouds have orientations for which the Fourier component of the roll perpendicular shear is nearly zero, but the second corresponds to narrowly spaced rolls having orientations for which the Fourier coefficients of both the perpendicular and the parallel components of the shear are nearly equal.

Shirer, H. N.↗

NASA NTRS1986

FTIR characterization of advanced materials

This paper surveys the application of Fourier transform infrared spectroscopy to the characterization of advanced materials. FTIR sampling techniques including internal and external reflectance and photoacoustic spectroscopy are discussed. Representative examples from the literature of the analysis of resins, fibers, prepregs and composites are reviewed. A discussion of several promising specialized FTIR techniques is also presented.

Young, P. R.↗

NASA NTRS1988

FTIR characterization of thermally cycled PMR-15 composites

Chemical characterization results are presented for a variety of PMR-15/graphite composites, differentiated according to prepreg types and cure cycles, which were subjected to 1000 thermal cycles between 0 and 450 F. Fourier transform IR spectroscopy was used in conjunction with diffuse reflectance sampling to examine whether changes in the matrix resin chemistry due to environmental exposure may have contributed to microcracking. Analysis based on compound spectra revealed behavior associated with the oxidation of methylene groups to carbonyl groups on the composite surface; evidence of crosslinking also emerged, although the two phenomena do not appear to be related.

Young, Philip R.↗

NASA NTRS1992

A regularization method for extrapolation of solar potential magnetic fields

The mathematical basis of a Tikhonov regularization method for extrapolating the chromospheric-coronal magnetic field using photospheric vector magnetograms is discussed. The basic techniques show that the Cauchy initial value problem can be formulated for potential magnetic fields. The potential field analysis considers a set of linear, elliptic partial differential equations. It is found that, by introducing an appropriate smoothing of the initial data of the Cauchy potential problem, an approximate Fourier integral solution is found, and an upper bound to the error in the solution is derived. This specific regularization technique, which is a function of magnetograph measurement sensitivities, provides a method to extrapolate the potential magnetic field above an active region into the chromosphere and low corona.

Gary, G. A.↗

NASA NTRS1999

Determination of Spectral Line Parameters in Selected Portions of the Infrared Spectrum of Water Vapor

Pressure broadening and pressure-induced shift coefficients due to water and nitrogen have been determined for water vapor transitions in the CO2 region of interest to Project HALOE. The temperature dependences of the widths and shifts have also been determined for selected transitions in this region. Results have been compared with values available in the literature. The line parameters have been obtained from the analysis of room temperature recordings of the spectrum of pure water and recordings of the spectra of heated water/nitrogen mixtures. The recordings of the water vapor spectrum were obtained with Fourier Transform Spectrometers at Kitt Peak and at the Justus-Liebig-Universitat Giessen. Up to eighteen spectra have been fitted simultaneously with a multispectrum nonlinear least-squares fitting technique developed by Dr. D. Chris Benner and colleagues.

Albert, Karen Keppler↗

NASA NTRS1995

The 1995 Atmospheric Trace Molecule Spectroscopy (ATMOS) Linelist

The Atmospheric Trace Molecule Spectroscopy (ATMOS) experiment uses a Fourier transform spectrometer on board the space shuttle to record infrared solar occultation spectra of the atmosphere. Described are the current version of the molecular spectroscopic database used for the analysis of the data obtained during three Space Shuttle missions between 1992 and 1994.

molecular database↗

NASA NTRS2013

The Relation Between Atmospheric Humidity and Temperature Trends for Stratospheric Water

We analyze the relation between atmospheric temperature and water vapor-a fundamental component of the global climate system-for stratospheric water vapor (SWV). We compare measurements of SWV (and methane where available) over the period 1980-2011 from NOAA balloon-borne frostpoint hygrometer (NOAA-FPH), SAGE II, Halogen Occultation Experiment (HALOE), Microwave Limb Sounder (MLS)/Aura, and Atmospheric Chemistry Experiment Fourier Transform Spectrometer (ACE-FTS) to model predictions based on troposphere-to-stratosphere transport from ERA-Interim, and temperatures from ERA-Interim, Modern Era Retrospective-Analysis (MERRA), Climate Forecast System Reanalysis (CFSR), Radiosonde Atmospheric Temperature Products for Assessing Climate (RATPAC), HadAT2, and RICHv1.5. All model predictions are dry biased. The interannual anomalies of the model predictions show periods of fairly regular oscillations, alternating with more quiescent periods and a few large-amplitude oscillations. They all agree well (correlation coefficients 0.9 and larger) with observations for higherfrequency variations (periods up to 2-3 years). Differences between SWV observations, and temperature data, respectively, render analysis of the model minus observation residual difficult. However, we find fairly well-defined periods of drifts in the residuals. For the 1980s, model predictions differ most, and only the calculation with ERA-Interim temperatures is roughly within observational uncertainties. All model predictions show a drying relative to HALOE in the 1990s, followed by a moistening in the early 2000s. Drifts to NOAA-FPH are similar (but stronger), whereas no drift is present against SAGE II. As a result, the model calculations have a less pronounced drop in SWV in 2000 than HALOE. From the mid-2000s onward, models and observations agree reasonably, and some differences can be traced to problems in the temperature data. These results indicate that both SWV and temperature data may still suffer from artifacts that need to be resolved in order to answer the question whether the large-scale flow and temperature field is sufficient to explain water entering the stratosphere.

Fueglistaler, S.↗

NASA NTRS1984

Opening of an interface flaw in a layered elastic half-plane under compressive loading

A static analysis is given of the problem of an elastic layer perfectly bonded, except for a frictionless interface crack, to a dissimilar elastic half-plane. The free surface of the layer is loaded by a finite pressure distribution directly over the crack. The problem is formulated using the two dimensional linear elasticity equations. Using Fourier transforms, the governing equations are converted to a pair of coupled singular integral equations. The integral equations are reduced to a set of simultaneous algebraic equations by expanding the unknown functions in a series of Jacobi polynomials and then evaluating the singular Cauchy-type integrals. The resulting equations are found to be ill-conditioned and, consequently, are solved in the least-squares sense. Results from the analysis show that, under a normal pressure distribution on the free surface of the layer and depending on the combination of geometric and material parameters, the ends of the crack can open. The resulting stresses at the crack-tips are singular, implying that crack growth is possible. The extent of the opening and the crack-top stress intensity factors depend on the width of the pressure distribution zone, the layer thickness, and the relative material properties of the layer and half-plane.

Kennedy, J. M.↗