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Results for “generalized spherical harmonics”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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At least 19 records
All sourcesNASA NTRSDOE OSTI
NASA NTRS1980

Spherical harmonic analysis of a synoptic climatology generated with a global general circulation model

Spherical harmonic analysis was used to analyze the observed climatological (C) fields of temperature at 850 mb, geopotential height at 500 mb, and sea level pressure. The spherical harmonic method was also applied to the corresponding "model climatological" fields (M) generated by a general circulation model, the "GISS climate model." The climate model was initialized with observed data for the first of December 1976 at 00. GMT and allowed to generate five years of meteorological history. Monthly means of the above fields for the five years were computed and subjected to spherical harmonic analysis. It was found from the comparison of the spectral components of both sets, M and C, that the climate model generated reasonable 500 mb geopotential heights. The model temperature field at 850 mb exhibited a generally correct structure. However, the meridional temperature gradient was overestimated and overheating of the continents was observed in summer.

Christidis, Z. D.↗
NASA NTRS1990

Determination of the ocean circulation using Geosat altimetry

A spherical harmonic model of the sea surface topography complete to degree and order 10 and a model of the earth's geopotential field complete to degree and order 50 have been obtained in a simultaneous solution using Geosat altimeter data and tracking data from 14 different satellites. The sea surface topography model compares well with oceanographic models computed using hydrographic data and ship drift data. Currently, errors in the estimated gravity field model limit the determination of the spherical harmonic coefficients of the general ocean circulation to degrees 10 and lower, corresponding to a minimum wavelength of 4000 km. Error analysis indicates that the correlation between the geoid and the sea surface topography model is less than 0.2, indicating good separation of the geoid and the sea surface topography at wavelengths of 4000 km or longer. Estimates of the scale factor for the significant wave height (H1/3), which is used to compute the electromagnetic bias correction and the bias for the Geosat altimeter, are obtained. The estimate of the H1/3 correction is 3.6 + or - 1.5 percent, and the height bias estimate is zero.

Nerem, R. S.↗
NASA NTRS1975

Gravity fields of the solar system

The most frequently used formulations of the gravitational field are discussed and a standard set of models for the gravity fields of the earth, moon, sun, and other massive bodies in the solar system are defined. The formulas are presented in standard forms, some with instructions for conversion. A point-source or inverse-square model, which represents the external potential of a spherically symmetrical mass distribution by a mathematical point mass without physical dimensions, is considered. An oblate spheroid model is presented, accompanied by an introduction to zonal harmonics. This spheroid model is generalized and forms the basis for a number of the spherical harmonic models which were developed for the earth and moon. The triaxial ellipsoid model is also presented. These models and their application to space missions are discussed.

Zendell, A.↗
NASA NTRS1990

A spherical harmonics method for asteroid pole determination

A new and general method is presented for determining pole orientations of unresolved solar system bodies that exhibit brightness variation with rotation. The accuracy of the method is limited only by the number of available apparitions, which imposes the degree where the Legendre expansion must be truncated. It is shown that power spectra of lightcurves provide enough information to extract pole coordinates from the data, independent of body shape and albedo variegation. The method has been tested using several computer-generated synthetic light-curves, and the accuracy is found to be about 5 deg in both the longitude and latitude of the pole, which is considerably better than that obtained from the standard triaxial ellipsoid model. Finally, the new spherical harmonics method has been applied to six well-observed asteroids: 16 Psyche, 22 Kalliope, 39 Laetitia, 44 Nysa, 45 Eugenia, and 349 Dembowska.

Lumme, K.↗
NASA NTRS1991

A unified approach to the helioseismic forward and inverse problems of differential rotation

A general, degenerate perturbation theoretic treatment of the helioseismic forward and inverse problem for solar differential rotation is presented. For the forward problem, differential rotation is represented as the axisymmetric component of a general toroidal flow field using velocity spherical harmonics. This approach allows each degree of differential rotation to be estimated independently from all other degrees. In the inverse problem, the splitting caused by differential rotation is expressed as an expansion in a set of orthonormal polynomials that are intimately related to the solution of the forward problem. The combined use of vector spherical harmonics as basis functions for differential ratio and the Clebsch-Gordon coefficients to represent splitting provides a unified approach to the forward and inverse problems of differential rotation which greatly simplify inversion.

Ritzwoller, Michael H.↗
NASA NTRS1981

Spherical harmonic analysis of a model-generated climatology

Monthly mean fields of 850 mb temperature (T850), 500 mb geopotential height (G500) and sea level pressure (SLP) were generated in the course of a five-year climate simulation run with a global general circulation model. Both the model-generated climatology and an observed climatology were subjected to spherical harmonic analysis, with separate analyses of the globe and the Northern Hemisphere. Comparison of the dominant harmonics of the two climatologies indicates that more than 95% of the area-weighted spatial variance of G500 and more than 90% of that of T850 are explained by fewer than three components, and that the model adequately simulates these large-scale characteristics. On the other hand, as many as 25 harmonics are needed to explain 95% of the observed variance of SLP, and the model simulation of this field is much less satisfactory. The model climatology is also evaluated in terms of the annual cycles of the dominant harmonics.

Christidis, Z. D.↗
NASA NTRS2018

A New Model of Jupiter's Magnetic Field From Juno's First Nine Orbits

A spherical harmonic model of the magnetic field of Jupiter is obtained from vector magnetic field observations acquired by the Juno spacecraft during its first nine polar orbits about the planet. Observations acquired during eight of these orbits provide the first truly global coverage of Jupiter's magnetic field with a coarse longitudinal separation of ~45 deg between perijoves. The magnetic field is represented with a degree 20 spherical harmonic model for the planetary ("internal") field, combined with a simple model of the magnetodisc for the field ("external") due to distributed magnetospheric currents. Partial solution of the underdetermined inverse problem using generalized inverse techniques yields a model ("Juno Reference Model through Perijove 9") of the planetary magnetic field with spherical harmonic coefficients well determined through degree and order 10, providing the first detailed view of a planetary dynamo beyond Earth.

Connerney, J. E. P.↗
NASA NTRS1989

Plasma pressure in the environment of Jupiter, inferred from Voyager 1 magnetometer observations

A model combining the internal magnetic field with a self-consistent model of the Jovian magnetodisc was fitted to the Voyager 1 Jovian magnetic field data by means of a generalized inverse technique. The model parameters included the internal field spherical harmonic coefficients as well as with parameters describing the plasma distribution in the magnetosphere. Assuming that the pressure in the middle and outer magnetosphere is related to the unit flux tube volume V through PV exp gamma = const, the model fit yielded a value of 0.88 for gamma. If the hot (30 keV) plasma is transported adiabatically inward under the interchange instability triggered by centrifugal force of the heavy torus ions, losses are not sufficient to account for such a low value of gamma beyond L = 10. Closer to the planet, as the outer edge of the Io plasma torus is approached, PV exp gamma is found to decrease inward, as expected from the particle measurements, which identified an inner boundary of the particle fluxes in that region. With the present stage of the development of magnetodisc models, secular variations of the internal field still remain difficult to estimate.

Caudal, G.↗
NASA NTRS1992

The magnetic field of Neptune

A model is given of the planetary magnetic field of Neptune based on a spherical harmonic analysis of the observations obtained by the Voyager 2. Generalized inverse techniques are used to partially solve a severely underdetermined inverse problem, and the resulting model is nonunique since the observations are limited in spatial distribution. Dipole, quadrupole, and octupole coefficients are estimated independently of other terms, and the parameters are shown to be well constrained by the measurement data. The large-scale features of the magnetic field including dipole tilt, offset, and harmonic content are found to characterize a magnetic field that is similar to that of Uranus. The traits of Neptune's magnetic field are theorized to relate to the 'ice' interior of the planet, and the dynamo-field generation reflects this poorly conducting planet.

Connerney, J. E. P.↗
NASA NTRS1994

Limits on coronal reflection using high-frequency solar oscillations

Acoustic waves in the Sun with frequencies above about 5.3 mHz can propagate in the chromosphere. We examine imaged solar intensity data for evidence of reflection of these waves in the upper chromosphere, where the temperature increases by a large factor over a short distance. Our method is to compare the observed and theoretically derived frequency spacings between peaks in the power spectrum. We find that our theoretical frequencies provide the best fit to the data when the reflection in the upper atmosphere is eliminated. In particular, the model of Kumar (1993b), which includes the source depth, and radiative damping, in the calculation of power spectra but ignores chromospheric reflection, gives peak frequencies that are in good agreement with the observations. For acoustic waves of frequency greater than 6 mHz we put an upper limit to the reflectivity of chromosphere and corona, using our method, of about 10%. At a given spherical harmonic degree, the frequency spacing between peaks in the data generally decreases with increasing frequency, because the lower turning point of the waves is moving inward. However, between 5 and 5.5 mHz the frequency spacing increases slightly. This feature is probably associated with the acoustic cutoff frequency in the solar atmosphere, i.e., it indicates a transition from trapped waves to propagating waves. We are able to reproduce the observed behavior by a crude modeling of the solar atmosphere. Further study of these peaks should provide an independent way of exploring the mean structure of the solar atmosphere, particularly around the temperature minimum region.

Kumar, P.↗
NASA NTRS2013

NASA Tech Briefs, Februrary 2013

Topics covered include: Measurements of Ultra-Stable Oscillator (USO) Allan Deviations in Space; Gaseous Nitrogen Orifice Mass Flow Calculator; Validation of Proposed Metrics for Two-Body Abrasion Scratch Test Analysis Standards; Rover Low Gain Antenna Qualification for Deep Space Thermal Environments; Automated, Ultra-Sterile Solid Sample Handling and Analysis on a Chip; Measuring and Estimating Normalized Contrast in Infrared Flash Thermography; Spectrally and Radiometrically Stable, Wideband, Onboard Calibration Source; High-Reliability Waveguide Vacuum/Pressure Window; Methods of Fabricating Scintillators With Radioisotopes for Beta Battery Applications; Magnetic Shield for Adiabatic Demagnetization Refrigerators (ADR); CMOS-Compatible SOI MESFETS for Radiation-Hardened DC-to-DC Converters; Silicon Heat Pipe Array; Adaptive Phase Delay Generator; High-Temperature, Lightweight, Self-Healing Ceramic Composites for Aircraft Engine Applications; Treatment to Control Adhesion of Silicone-Based Elastomers; High-Temperature Adhesives for Thermally Stable Aero-Assist Technologies; Rockballer Sample Acquisition Tool; Rock Gripper for Sampling, Mobility, Anchoring, and Manipulation; Advanced Magnetic Materials Methods and Numerical Models for Fluidization in Microgravity and Hypogravity; Data Transfer for Multiple Sensor Networks Over a Broad Temperature Range; Using Combustion Synthesis to Reinforce Berms and Other Regolith Structures; Visible-Infrared Hyperspectral Image Projector; Three-Axis Attitude Estimation With a High-Bandwidth Angular Rate Sensor Change_Detection.m; AGATE: Adversarial Game Analysis for Tactical Evaluation; Ionospheric Simulation System for Satellite Observations and Global Assimilative; Modeling Experiments (ISOGAME); An Extensible, User- Modifiable Framework for Planning Activities; Mission Operations Center (MOC) - Precipitation Processing System (PPS) Interface Software System (MPISS); Automated 3D Damaged Cavity Model Builder for Lower Surface Acreage Tile on Orbiter; Mixed Linear/Square-Root Encoded Single-Slope Ramp Provides Low-Noise ADC with High Linearity for Focal Plane Arrays; RUSHMAPS: Real-Time Uploadable Spherical Harmonic Moment Analysis for Particle Spectrometers; Powered Descent Guidance with General Thrust-Pointing Constraints; X-Ray Detection and Processing Models for Spacecraft Navigation and Timing; and Extreme Ionizing-Radiation-Resistant Bacterium

Source record↗
NASA NTRS1997

Modeling of the Coupled Magnetospheric and Neutral Wind Dynamos

Over the past four years of funding, SRI, in collaboration with the University of Texas at Dallas, has been involved in assessing the influence of thermospheric neutral winds on the electric field and current systems at high latitudes. The initial direction of the project was to perform a set of numerical experiments concerning the contribution of the magnetospheric and neutral wind dynamo processes, under specific boundary conditions, to the polarization electric field and/or the field-aligned current distribution at high latitudes. To facilitate these numerical experiments we developed a numerical scheme that relied on using output from the NCAR Thermosphere-Ionosphere General Circulation Model (NCAR-TIGCM), expanding them in the form of spherical harmonics and solving the dynamo equations spectrally. Once initial calculations were completed, it was recognized that the neutral wind contribution could be significant but its actual contribution to the electric field or currents depended strongly on the generator properties of the magnetosphere. Solutions to this problem are not unique because of the unknown characteristics of the magnetospheric generator, therefore the focus was on two limiting cases. One limiting case was to consider the magnetosphere as a voltage generator delivering a fixed voltage to the high-latitude ionosphere and allowing for the neutral wind dynamo to contribute only to the current system. The second limiting case was to consider the magnetosphere as a current generator and allowing for the neutral wind dynamo to contribute only to the generation of polarization electric fields. This work was completed and presented at the l994 Fall AGU meeting. The direction of the project then shifted to applying the Poynting flux concept to the high-latitude ionosphere. This concept was more attractive as it evaluated the influence of neutral winds on the high-latitude electrodynamics without actually having to determine the generator characteristics of the magnetosphere. The influence of the neutral wind was then determined not by estimating how much electric potential or current density it provides, but by determining the contribution of the neutral wind to the net electromagnetic energy transferred between the ionosphere and magnetosphere. The estimate of the net electromagnetic energy transfer and the role of the neutral winds proves to be a more fundamental quantity in studies of magnetosphere- ionosphere coupling also showed that by using electric and magnetic field measurements from the HILAT satellite, the Poynting flux could be a measurable quantity from polar-orbiting, low- altitude spacecraft. Through collaboration with Dr. Heelis and others at UTD and their expertise of the electric field measurements on the DE-B satellite, an extensive analysis was planned to determine the Poynting flux from the DE-B measurements in combination with a modeling effort to help interpret the observations taking into account the coupled magnetosphere-ionosphere.

Thayer, Jeffrey P.↗
NASA NTRS2013

Region Spherical Harmonic Magnetic Modeling from Near-Surface and Satellite-Altitude Anomlaies

The compiled near-surface data and satellite crustal magnetic measured data are modeled with a regionally concentrated spherical harmonic presentation technique over Australia and Antarctica. Global crustal magnetic anomaly studies have used a spherical harmonic analysis to represent the Earth's magnetic crustal field. This global approach, however is best applied where the data are uniformly distributed over the entire Earth. Satellite observations generally meet this requirement, but unequally distributed data cannot be easily adapted in global modeling. Even for the satellite observations, due to the errors spread over the globe, data smoothing is inevitable in the global spherical harmonic presentations. In addition, global high-resolution modeling requires a great number of global spherical harmonic coefficients for the regional presentation of crustal magnetic anomalies, whereas a lesser number of localized spherical coefficients will satisfy. We compared methods in both global and regional approaches and for a case where the errors were propagated outside the region of interest. For observations from the upcoming Swarm constellation, the regional modeling will allow the production a lesser number of spherical coefficients that are relevant to the region of interest

Modeling↗
NASA NTRS1974

Error enhancement in geomagnetic models derived from scalar data

Models of the main geomagnetic field are generally represented by a scalar potential gamma expanded in a finite number of spherical harmonics. Very accurate observations of F were used, but indications exist that the accuracy of models derived from them is considerably lower. One problem is that F does not always characterize gamma uniquely. It is not clear whether such ambiguity can be encountered in deriving gamma from F in geomagnetic surveys, but there exists a connection, due to the fact that the counterexamples of Backus are related to the dipole field, while the geomagnetic field is dominated by its dipole component. If the models are recovered with a finite error (i.e. they cannot completely fit the data and consequently have a small spurious component), this connection allows the error in certain sequences of harmonic terms in gamma to be enhanced without unduly large effects on the fit of F to the model.

Stern, D. P.↗
NASA NTRS2016

Normalization and Implementation of Three Gravitational Acceleration Models

Unlike the uniform density spherical shell approximations of Newton, the consequence of spaceflight in the real universe is that gravitational fields are sensitive to the asphericity of their generating central bodies. The gravitational potential of an aspherical central body is typically resolved using spherical harmonic approximations. However, attempting to directly calculate the spherical harmonic approximations results in at least two singularities that must be removed to generalize the method and solve for any possible orbit, including polar orbits. Samuel Pines, Bill Lear, and Robert Gottlieb developed three unique algorithms to eliminate these singularities. This paper documents the methodical normalization of two of the three known formulations for singularity-free gravitational acceleration (namely, the Lear and Gottlieb algorithms) and formulates a general method for defining normalization parameters used to generate normalized Legendre polynomials and Associated Legendre Functions (ALFs) for any algorithm. A treatment of the conventional formulation of the gravitational potential and acceleration is also provided, in addition to a brief overview of the philosophical differences between the three known singularity-free algorithms.

Eckman, Randy A.↗
NASA NTRS1985

The magnetic field at the core-mantle boundary

Models of the geomagnetic field are, in general, produced from a least-squares fit of the coefficients in a truncated spherical harmonic expansion to the available data. Downward continuation of such models to the core-mantle boundary (CMB) is an unstable process: the results are found to be critically dependent on the choice of truncation level. Modern techniques allow this fundamental difficulty to be circumvented. The method of stochastic inversion is applied to modeling the geomagnetic field. Prior information is introduced by requiring that the spectrum of spherical harmonic coefficients to fall-off in a particular manner which is consistent with the Ohmic heating in the core having a finite lower bound. This results in models with finite errors in the radial field at the CMB. Curves of zero radial field can then be determined and integrals of the radial field over patches on the CMB bounded by these null-flux curves calculated. With the assumption of negligible magnetic diffusion in the core; frozen-flux hypothesis, these integrals are time-invariant.

Bloxham, J.↗
NASA NTRS2011

Normalization of Gravitational Acceleration Models

Unlike the uniform density spherical shell approximations of Newton, the con- sequence of spaceflight in the real universe is that gravitational fields are sensitive to the nonsphericity of their generating central bodies. The gravitational potential of a nonspherical central body is typically resolved using spherical harmonic approximations. However, attempting to directly calculate the spherical harmonic approximations results in at least two singularities which must be removed in order to generalize the method and solve for any possible orbit, including polar orbits. Three unique algorithms have been developed to eliminate these singularities by Samuel Pines [1], Bill Lear [2], and Robert Gottlieb [3]. This paper documents the methodical normalization of two1 of the three known formulations for singularity-free gravitational acceleration (namely, the Lear [2] and Gottlieb [3] algorithms) and formulates a general method for defining normalization parameters used to generate normalized Legendre Polynomials and ALFs for any algorithm. A treatment of the conventional formulation of the gravitational potential and acceleration is also provided, in addition to a brief overview of the philosophical differences between the three known singularity-free algorithms.

Eckman, Randy A.↗
NASA NTRS1981

Voyager 1 assessment of Jupiter's planetary magnetic field

An estimate of Jupiter's planetary magnetic field is obtained from the Voyager 1 observations of the Jovian magnetosphere. An explicit model for the magnetodisc current system is combined with a spherical harmonic model of the planetary field with both sets of parameters determined simultaneously using a nonlinear generalized inverse methodology. The resulting model fits the observations extremely well throughout the analysis interval (r 20 Jovian radii). The Jovian internal field model obtained from the Voyager 1 data is very similar to the octopole Pioneer 11 models. The best fitting magnetodisc lies in the centrifugal equator, 2/3 of the way between the rotational and magnetic equators, as appropriate for centrifugal loading of the magnetosphere by a cold plasma.

Connerney, J. E. P.↗