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NASA NTRS1994

The millimeter-wave spectrum of the CaF radical (X(sup 2)Sigma(+))

The pure rotational spectrum of the CaF radical has been measured in the laboratory using millimeter/sub-mm direct absorption spectroscopy. Fourteen rotational transitions have been detected originating in the v = 0 mode of the species. Rotational lines of the vibrationally excited v = 1, 2, and 3 states have also been observed. Spin-rotation splittings, as well as hyperfine interactions arising from the nuclear spin of the fluorine atom, were resolved in the CaF spectra. Rotational, fine-structure, and in some cases, hyperfine parameters were determined for the various vibrational modes of the molecule from a nonlinear least-squares fit to the data, using a (sup 2)Sigma Hamiltonian, and are in agreement with past measurements. The newly measured rest frequencies for CaF, which are accurate to at least + or - 100 kHz, will enable astronomical searches to be conducted for the molecule in interstellar and circumstellar gas. Given the recent detection of AlF in IRC + 10216, metal fluoride species may be more abundant than previously thought.

Anderson, M. A.↗

NASA NTRS2009

Development of Jet Noise Power Spectral Laws Using SHJAR Data

High quality jet noise spectral data measured at the Aeroacoustic Propulsion Laboratory at the NASA Glenn Research Center is used to examine a number of jet noise scaling laws. Configurations considered in the present study consist of convergent and convergent-divergent axisymmetric nozzles. Following the work of Viswanathan, velocity power factors are estimated using a least squares fit on spectral power density as a function of jet temperature and observer angle. The regression parameters are scrutinized for their uncertainty within the desired confidence margins. As an immediate application of the velocity power laws, spectral density in supersonic jets are decomposed into their respective components attributed to the jet mixing noise and broadband shock associated noise. Subsequent application of the least squares method on the shock power intensity shows that the latter also scales with some power of the shock parameter. A modified shock parameter is defined in order to reduce the dependency of the regression factors on the nozzle design point within the uncertainty margins of the least squares method.

Khavaran, Abbas↗

NASA NTRS1994

FORTRAN programs to process Magsat data for lithospheric, external field, and residual core components

The FORTRAN programs supplied in this document provide a complete processing package for statistically extracting residual core, external field and lithospheric components in Magsat observations. To process the individual passes: (1) orbits are separated into dawn and dusk local times and by altitude, (2) passes are selected based on the variance of the magnetic field observations after a least-squares fit of the core field is removed from each pass over the study area, and (3) spatially adjacent passes are processed with a Fourier correlation coefficient filter to separate coherent and non-coherent features between neighboring tracks. In the second state of map processing: (1) data from the passes are normalized to a common altitude and gridded into dawn and dusk maps with least squares collocation, (2) dawn and dusk maps are correlated with a Fourier correlation efficient filter to separate coherent and non-coherent features; the coherent features are averaged to produce a total field grid, (3) total field grids from all altitudes are continued to a common altitude, correlation filtered for coherent anomaly features, and subsequently averaged to produce the final total field grid for the study region, and (4) the total field map is differentially reduced to the pole.

Alsdorf, Douglas E.↗

DOE OSTI2025

Optimized Auxiliary Functions for Robust Mitigation of Finite-Size Errors in Periodic Hybrid Density Functional Theory

When calculating properties of periodic systems at the thermodynamic limit (TDL), the dominant source of finite size error (FSE) arises from the long-range Coulomb interaction, and can manifest as a slowly converging quadrature error when approximating an integral in the reciprocal space by a finite sum. The singularity subtraction (SS) method offers a systematic approach for reducing this quadrature error and thus the FSE. Here, in this work, we first investigate the performance of the SS method in the simplest setting, aiming at reducing the FSE in exact exchange calculations by subtracting the Coulomb contribution with a single, adjustable Gaussian auxiliary function. We demonstrate that a simple fitting method can robustly estimate the optimal Gaussian width and leads to rapid convergence toward the TDL. Furthermore, we suggest new forms of the auxiliary function, whose optimal parameters could also be determined through least-squares fitting. For a range of semiconductors and insulators, the proposed auxiliary functions achieve robust, millihartree-level accuracy in hybrid density functional theory calculations, including cases with sparse k-meshes and large basis sets.

Quiton, Stephen Jon [University of California, Ber↗

NASA NTRS1994

Separation of lithospheric, external, and core components of the south polar geomagnetic field at satellite altitudes

We present a new approach to producing scalar Magsat magnetic anomaly maps based on correlation coefficient filtering and the use of almost all of the available orbits. Our method differs from earlier techniques with respect to the following: (1) Passes are selected based on their variance properties rather than planetary indices such as Kp. (2) The core field model is least squares fit to individual passes and subsequently removed instead of substracting the model directly. This technique replaces band pass filtering or polynomial trend removal methods. (3) Each selected pass is sorted geographically and by local time, placed into one of four different altitude bands, and correlation coefficient filtered with the two adjacent passes. The filtering is the second step toward isolating the static lithospheric signal from the more dynamic external field signals. (4) Least squares collocation is used to grid the correlated passes; subsequently, the dawn and dusk maps are also correlation filtered providing another step toward removal of external fields. (5) The four resultant total field maps are continued to a common altitude and again correlation filtered for the static lithospheric anomalies. (6) The filtered results are then averaged together to provide a new total field map of the lithosphere south of 40 deg S latitude. Our total field map differs from previous efforts over the crustal blocks of West Antarctica. We obtained a positive anomaly over Edward VII Peninsula, extending into the Byrd subglacial basin and obtained a negative anomaly over the Ellsworth Mountains and parts of the Byrd subglacial basin. Also, a positive anomaly extending from the Ross Sea to offshore Wilkes Land is present in our map; however, this feature is absent in other maps. Positive anomalies marking the Weddell Sea in previous efforts are not present in our map. Prominent external field anomalies in the quadrant offshore of Wilkes Land are present in all previous efforts; however, these signatures are reduced in our total field map. This map significantly advances efforts for the identification and interpretation of magnetic anomalies of the south polar lithosphere.

Alsdorf, Douglas E.↗

NASA NTRS1981

Statistical model to perform error analysis of curve fits of wind tunnel test data using the techniques of analysis of variance and regression analysis

The considered research had the objective to design a statistical model that could perform an error analysis of curve fits of wind tunnel test data using analysis of variance and regression analysis techniques. Four related subproblems were defined, and by solving each of these a solution to the general research problem was obtained. The capabilities of the evolved true statistical model are considered. The least squares fit is used to determine the nature of the force, moment, and pressure data. The order of the curve fit is increased in order to delete the quadratic effect in the residuals. The analysis of variance is used to determine the magnitude and effect of the error factor associated with the experimental data.

Alston, D. W.↗

NASA NTRS1981

High-resolution laser absorption spectroscopy of ozone near 1129.4 cm (-1)

A Beer's Law experiment was performed with a tunable diode laser to determine self broadened line shape parameters of one infrared absorption ozone line in the nu1 band for ten pressures from 0.26 to 6.29 torr at 285 K. The SO2 line positions were used for wavelength calibration. Line shapes were iteratively fitted to the Voigt function at a Doppler width of 29.54 MHz (HWHM) resulting in values for the integrated line strength, (S), of (0.144 +/- 0.007) x 10 to the minus 20th/cm molecule/cu cm, line center frequency, nu sub o, of 1129.426/cm and the Lorentzian contributions to halfwidth. A linear least squares fit of (alpha sub L)5 as a function of pressure yielded a zero intercept of 15.27 +/- 0.29 MHz (rho = 0.99) and a broadening parameter, (alpha sub L)5, of 5.71 +/- 0.29 MHz/Torr. This results in a line width (FWHM) of 0.144 +/- .007/cm at 760 torr and 285 K.

Majorana, L. N.↗

NASA NTRS1990

Spectroscopic analysis of global tide gauge sea level data

Yearly and monthly global tide-gage sea-level data are fitted to numerically generated tidal data in order to search for the 18.6-yr lunar nodal tide and 14-month pole tide. Both of these tides are clearly evident, with amplitudes and phases that are consistent with a global equilibrium response. The ocean's response to atmospheric pressure is studied with the least-squares fit technique. Consideration is given to the global rise in sea level, the effects of postglacial rebound, and the possible causes of the enhanced pole tides in the North Sea, the Baltic Sea, and the Gulf of Bothnia. The results support O'Connor's (1986) suggestion that the enhanced pole tide in these regions is due to meteorological forcing rather than a basin-scale resonance. Also, the global average of the tide-gage data show an increase in sea level over tha last 80 yr of between 1.1 and 1.9 mm/yr.

Trupin, A.↗

NASA NTRS2017

Kepler Uniform Modeling of KOIs: MCMC Notes for Data Release 25

This document describes data products related to the reported planetary parameters and uncertainties for the Kepler Objects of Interest (KOIs) based on a Markov-Chain-Monte-Carlo (MCMC) analysis. Reported parameters, uncertainties and data products can be found at the NASA Exoplanet Archive . The codes used for this data analysis are available on the Github website (Rowe 2016). The relevant paper for details of the calculations is Rowe et al. (2015). The main differences between the model fits discussed here and those in the DR24 catalogue are that the DR25 light curves were used in the analysis, our processing of the MAST light curves took into account different data flags, the number of chains calculated was doubled to 200 000, and the parameters which are reported are based on a damped least-squares fit, instead of the median value from the Markov chain or the chain with the lowest 2 as reported in the past.

DR25↗

NASA NTRS1977

Reduction of polarizing radiometer data

High-precision polarizing radiometers have been constructed for the measurement of the angular dependence of the intensity and polarization for atmospheric and ground-reflected radiation. When the data are fit with a form containing constant, first harmonic, second harmonic, and slope terms, excellent agreement with data taken with a polarizing radiometer may be obtained. A technique has been derived for rapid data reduction by using a single matrix which, when multiplied by the data values, produces the reduced values in the sense of a least-squares fit.

Walraven, R. L.↗

NASA NTRS1983

Fitting of satellite and in-situ ocean surface temperatures Results for polymode during the winter of 1977-1978

For the period considered, December 1977 through February 1978, bivariate Gaussian discriminant function cloud identification revealed that more than 93 percent of the 8-km resolution GOES infrared pixels were cloud contaminated. Cloud-free in-situ calibration points were distributed in nonrandom groups; this resulted in systematic errors when using least squares techniques. Surfaces and regression lines were least squares fitted between satellite and in-situ data; use was also made of differences and ratios. The best results were achieved with a regression in the form of the infrared radiative transfer equation; but this was no better than + or - 0.9 K. Because of extensive cloudiness, the linear regressions were seldom useful, and temperature ratios with + or - 1.3 K experimental errors best represent the applicability of GEOS data to sea surface temperatures.

Maul, G. A.↗

NASA NTRS1993

Statistical fitting accuracy in photon correlation spectroscopy

Continuing our experimental investigation of the fitting accuracy associated with photon correlation spectroscopy, we collect 150 correlograms of light scattered at 90 deg from a thermostated sample of 91-nm-diameter, polystyrene latex spheres in water. The correlograms are taken with two correlators: one with linearly spaced channels and one with geometrically spaced channels. Decay rates are extracted from the single-exponential correlograms with both nonlinear least-squares fits and second-order cumulant fits. We make several statistical comparisons between the two fitting techniques and verify an earlier result that there is no sample-time dependence in the decay rate errors. We find, however, that the two fitting techniques give decay rates that differ by 1 percent.

Shaumeyer, J. N.↗

NASA NTRS1974

Post-flight differential correction analysis using Vinti's spheroidal method for the small astronomy satellite orbit

The results of an intensive analysis of a differential orbit improvement method utilizing observational data for a 550-kilometer altitude, near-circular, near-equatorial satellite orbit are presented. Observations of the Small Astronomy Satellite (SAS-1) are in the form of direction cosines as measured at two ground interferometer tracking stations near the Equator during the first 22 orbital revolutions (approximately 37 hours) after launch of the spacecraft. Numerical results, in both tabular and graphical form, are displayed for numerous iterated fittings of various observational arcs by differential correction of the orbital elements. Parameters varied in these comparative cases include the time duration of the observational data block, the number of pairs of direction cosine data and the number of tracking station passes included in the solution, the distribution of such passes between the two available tracking stations, and the acceptance criterion for the observational residuals in the least squares fitting procedure. It was found that three observational pairs of direction cosine data, the minimum number possible for a uniquely determined solution in theory, are sufficient to promote covergence to an accurate solution, if properly selected.

Walden, H.↗

NASA NTRS1990

A case study of the Thunderstorm Research International Project storm of July 11, 1978. I - Analysis of the data base

The data obtained at the time of the Thunderstorm Research International Project storm at the Kennedy Space Center on July 11, 1978 are analyzed in a model-independent manner. The data base included data from three Doppler radars, a lightning detection and ranging system and a network of 25 electric field mills, and rain gages. Electric field measurements were used to analyze the charge moments transferred by lightning flashes, and the data were fitted to Weibull distributions; these were used to estimate statistical parameters of the lightning for both intracloud and cloud-to-ground flashes and to estimate the fraction of the flashes which were below the observation threshold. The displacement and the conduction current densities were calculated from electric field measurements between flashes. These values were used to derive the magnitudes and the locations of dipole and monopole generators by least squares fitting the measured Maxwell current densities to the displacement-dominated equations.

Nisbet, John S.↗

NASA NTRS1988

Observations of the 8 December 1987 occultation of AG+40 deg 0783 by 324 Bamberga

The occultation of AG+40 deg 0783 by 324 Bamberga on 8 December 1987 was observed at 13 sites in the United States, Japan, and China. At four sites the event was observed photoelectrically; the other observations were visual. A least-squares fit of a circular limb profile to the data gives a diameter of 227.6 + or - 1.9 km. However, this solution is inconsistent with a negative visual observation near the northern edge of the ground track. The inconsistency cannot be removed by assuming an elliptical profile. The data suggest that Bamberga, despite its low-amplitude lightcurve, may depart significantly from a spherical or ellipsoidal shape. The asteroid also appears to be at least 10 percent smaller than indicated by infrared radiometry.

Millis, R. L.↗

NASA NTRS1989

Observations of the 8 December 1987 occultation of AG +40 deg 0783 by 324 Bamberga

Millis, R. L.↗

NASA NTRS2003

A New Fitting Procedure for the Blended He I 1083 nm Multiplet

The He I 1083 nm multiplet is a powerful tool for observing the outer solar atmosphere but is difficult to analyze because the lines are weak, highly variable, and spectrally blended, both internally and with other neighboring solar and telluric lines. After separation from nearby spectral features, two components of the He I multiplet are resolved. Fitting these lines with two unconstrained Gaussian profiles always gives a ratio of major to minor component of less than half the value which would be expected for optically thin lines. One possibility for explaining the discrepancy between the weakness of the lines and the ratio of the spectral components is to assume that the line formation regions are concentrated in laterally unresolved, optically thick structures with small filling factor. However, we present here a least-squares fitting technique using cubic splines with fixed breakpoints with the constraint that the blend is the sum of three identically shaped profiles shifted in wavelength according to the atomic structure of the blend and weighted by the corresponding statistics weights, in agreement with optically thin line formation. The basis functions for the fitting procedure have no built-in spectral symmetry or shape. The resulting underlying profiles tend to be asymmetric with excess absorption to the blue, consistent with formation by "hot" and "cool" spatial elements within the observed volume, with the hotter regions having differential motion toward the observer. The results agree well with NASA/XSO Spectromagnetograph observations in quiet sun and coronal holes. Partial funding of this research was provided through the NASA Sun-Earth Connection SR&T program.

Jones, H. P.↗

NASA NTRS1997

A Model-Based Approach for the Measurement of Eye Movements Using Image Processing

This paper describes a video eye-tracking algorithm which searches for the best fit of the pupil modeled as a circular disk. The algorithm is robust to common image artifacts such as the droopy eyelids and light reflections while maintaining the measurement resolution available by the centroid algorithm. The presented algorithm is used to derive the pupil size and center coordinates, and can be combined with iris-tracking techniques to measure ocular torsion. A comparison search method of pupil candidates using pixel coordinate reference lookup tables optimizes the processing requirements for a least square fit of the circular disk model. This paper includes quantitative analyses and simulation results for the resolution and the robustness of the algorithm. The algorithm presented in this paper provides a platform for a noninvasive, multidimensional eye measurement system which can be used for clinical and research applications requiring the precise recording of eye movements in three-dimensional space.

Sung, Kwangjae↗