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NASA NTRS1978

Analysis of Satellite-to-Satellite Tracking (SST) and altimetry data from GEOS-C

Radar altimetry and satellite-to-satellite (SST) range and range rate tracking measurements were used to infer the exterior gravitational field of the earth and the structure of the geoid from GEOS-C metric data. Under the SST analysis, a direct point-by-point estimate of gravity disturbance by means of a recursive filter with backward smoothing was attempted but had to be forsaken because of poor convergence. The adopted representation consists of a more or less uniform grid of discrete masses at a depth of approximately 400 km from the earth's surface. The layer is superimposed on a spherical harmonics model. The procedure for smoothing the altimetry and inferring the fine-structured gravity field over the Atlantic test area is described. The local disturbances are represented by means of a density layer. The altimeter height biases were first estimated by a least squares adjustment at orbital crossover points. After taking out the bias, long wavelength contributions from GEM-6 as well as a calibration correction were subtracted. The residual heights were then represented by a mass distribution beneath the earth's surface.

Wong, L.↗

NASA NTRS1989

Reflection of solar radiation by a cylindrical cloud

Potential applications of an analytic method for computing the solar radiation reflected by a cylindrical cloud are discussed, including studies of radiative transfer within finite clouds and evaluations of these effects on other clouds and on remote sensing problems involving finite clouds. The pattern of reflected sunlight from a cylindrical cloud as seen at a large distance has been considered and described by the bidirectional function method for finite cloud analysis, as previously studied theoretically for plane-parallel atmospheres by McKee and Cox (1974); Schmetz and Raschke (1981); and Stuhlmann et al. (1985). However, the lack of three-dimensional radiative transfer solutions for anisotropic scattering media have hampered theoretical investigations of bidirectional functions for finite clouds. The present approach permits expression of the directional variation of the radiation field as a spherical harmonic series to any desired degree and order.

Smith, G. L.↗

NASA NTRS1992

COBE Differential Microwave Radiometers - Preliminary systematic error analysis

The techniques available for the identification and subtraction of sources of dynamic uncertainty from data of the Differential Microwave Radiometer (DMR) instrument aboard COBE are discussed. Preliminary limits on the magnitude in the DMR 1 yr maps are presented. Residual uncertainties in the best DMR sky maps, after correcting the raw data for systematic effects, are less than 6 micro-K for the pixel rms variation, less than 3 micro-K for the rms quadruple amplitude of a spherical harmonic expansion, and less than 30 micro-(K-squared) for the correlation function.

Kogut, A.↗

NASA NTRS2011

Comment on "An Analysis of VLF Electric Field Spectra Measured in Titan's Atmosphere by The Huygens Probe" By J. A. Morente et al.

Morente et al. have recently revisited the VLF electric field measurements made with the Permittivity, Wave and Altimetry (PWA) instrument during the descent of the Huygens Probe through the atmosphere of Titan. They assert that they have identified several harmonics of the transverse resonance mode of the surface?]ionosphere cavity, which would prove the existence of an electrical activity in the atmosphere of the largest satellite of Saturn. We refute this finding on the basis that it results from an artifact due to an improper analysis of the data set. [2] The investigators of the Permittivity, Wave and Altimetry (PWA) experiment on the Huygens Probe have reported the extremely low frequency (ELF) and very low frequency (VLF) electric signals recorded during the descent through the atmosphere of Titan. The PWA data are archived in the Planetary Science Archive (PSA) of ESA, and an extensive description of the instrument is at the disposal of the scientific community. Morente and his coworkers have revisited this data set and reported the results of their investigations in two papers. In a first paper, they claim that they have detected in the ELF range (0.100 Hz) several harmonics of a global resonance allegedly generated by lightning activity in the spherical cavity guide formed by the surface of Titan and the inner boundary of the ionosphere, a phenomenon similar to the Schumann resonance observed at EartH In the second paper dedicated to the VLF electric signal recorded by PWA, in the range 0.10 kHz, they argue that they can also bring out the transverse resonance and its harmonics, a more local phenomenon that develops around the excitation source and whose frequency is controlled by the separation between Titan?fs surface and the inner ionospheric boundary. [3] The PWA investigators have analyzed the narrowband ELF signal at about 36 Hz effectively observed during the entire descent. They have not endorsed, however, the alternative approach of Morente et al. that discloses additional ELF narrow-band signals and numerous related harmonics. Hamelin et al. and Beghin et al. have questioned the work of Morente and his coworkers and demonstrated unambiguously that their findings are mere artifacts entirely due to a faulty procedure. Morente et al. refuted this critical analysis of their ELF paper in a rebuttal. The present comment draws a parallelism between the ELF and VLF papers and demonstrates that the VLF signal carries no evidence whatever of any transverse resonance. The analyses of the ELF and VLF signals by Morente and his coworkers are flawed, and their conclusions are shown here to be invalid. A more comprehensive and thorough assessment of the numerical approaches proposed by Morente et al. is given by Berthelin et al..

Grard, Rejean↗

DOE OSTI2022

Fingerprinting Brownian Motions of Polymers under Flow

Here, we present a quantitative approach to the self-dynamics of polymers under steady flow by employing a set of complementary reference frames and extending the spherical harmonic expansion technique to dynamic density correlations. Application of this method to nonequilibrium molecular dynamics simulations of polymer melts reveals a number of universal features. For both unentangled and entangled melts, the center-of-mass motions in the flow frame are described by superdiffusive, anisotropic Gaussian distributions, whereas the isotropic component of monomer self-dynamics in the center-of-mass frame is strongly suppressed. Spatial correlation analysis shows that the heterogeneity of monomer self-dynamics increases significantly under flow.

36 MATERIALS SCIENCE↗

NASA NTRS1984

Continental and oceanic crustal magnetization modelling

Inversion of magnetic data from the MAGSAT satellite, to arrive at intensities of magnetization of the Earth's crust, was performed by two different methods. The first method uses a spherical harmonic model of the magnetic field. The coefficients believed to represent sources in the Earth's crust can then be inverted to arrive at vertical dipole moments per unit area at the Earth's surface. The spherical harmonic models contain coefficients of degrees of harmonics up to 23. The dipole moment per unit area for a surface element can then be determined by summing the contribution for each individual degree of harmonic. The magnetic moments were calculated for continental and oceanic areas separately as well as over certain latitudinal segments. Of primary concern was to determine whether there are any differences between continental and oceanic areas. The second analysis with magnetization intensities was made using narrower ranges of degrees of harmonics, assuming that higher degrees are present in the core field signal.

Harrison, C. G. A.↗

NASA NTRS2004

Magsat to CHAMP: Magnetic Satellite Explorations of Lithospheric Anomalies over Kursk, Bangui and the Antarctic

We compare crustal magnetic anomaly maps over the Kursk (Russia) and Bangui (Central African Republic) isolated anomalies and the Antarctic derived from the Magsat, \Orsted and CHAMP satellite fields. We wish to demonstrate how progress in satellite magnetic missions has improved the recovery of the crustal magnetic field. The 6-month long Magsat mission of 25 years ago generated two major methods of processing satellite magnetic anomaly data for lithospheric studies. The first was a global perspective using spherical harmonics that emphasize the more regional and global lithospheric fields. However, these fields commonly do not resolve local anomaly features in any detail. Therefore a second procedure involved the use of the individual satellite orbit or track data to recover small-scale anomalies on a regional scale. We present results over prominent magnetic anomalies such as Kursk, Bangui and the large Antarctic continent that demonstrate how the various analysis methods affect the recovery of crustal anomalies. The more recent \Orsted and CHAMP missions are successfully recording data with an improved accuracy and with full spatial and temporal coverage. We show and interpret the total magnetic intensity anomaly maps over these areas from all three satellite magnetometer data sets.

Kim, H.↗

NASA NTRS2014

The Gravity Field, Orientation, and Ephemeris of Mercury from MESSENGER Observations After Three Years in Orbit

We have analyzed three years of radio tracking data from the MESSENGER spacecraft in orbit around Mercury and determined the gravity field, planetary orientation, and ephemeris of the innermost planet. With improvements in spatial coverage, force modeling, and data weighting, we refined an earlier global gravity field both in quality and resolution, and we present here a spherical harmonic solution to degree and order 50. In this field, termed HgM005, uncertainties in low-degree coefficients are reduced by an order of magnitude relative to the earlier global field, and we obtained a preliminary value of the tidal Love number k(sub 2) of 0.451+/-0.014. We also estimated Mercury's pole position, and we obtained an obliquity value of 2.06 +/- 0.16 arcmin, in good agreement with analysis of Earth-based radar observations. From our updated rotation period (58.646146 +/- 0.000011 days) and Mercury ephemeris, we verified experimentally the planet's 3: 2 spin-orbit resonance to greater accuracy than previously possible. We present a detailed analysis of the HgM005 covariance matrix, and we describe some near-circular frozen orbits around Mercury that could be advantageous for future exploration.

MESSENGER↗

DOE OSTI2022

Multiview Incomplete Knowledge Graph Integration with application to cross-institutional EHR data harmonization

Objective: The growing availability of electronic health records (EHR) data opens opportunities for integrative analysis of multi-institutional EHR to produce generalizable knowledge. A key barrier to such integrative analyses is the lack of semantic interoperability across different institutions due to coding differences. We propose a Multiview Incomplete Knowledge Graph Integration (MIKGI) algorithm to integrate information from multiple sources with partially overlapping EHR concept codes to enable translations between healthcare systems. Methods: The MIKGI algorithm combines knowledge graph information from (i) embeddings trained from the co-occurrence patterns of medical codes within each EHR system and (ii) semantic embeddings of the textual strings of all medical codes obtained from the Self-Aligning Pretrained BERT (SAPBERT) algorithm. Due to the heterogeneity in the coding across healthcare systems, each EHR source provides partial coverage of the available codes. MIKGI synthesizes the incomplete knowledge graphs derived from these multi-source embeddings by minimizing a spherical loss function that combines the pairwise directional similarities of embeddings computed from all available sources. MIKGI outputs harmonized semantic embedding vectors for all EHR codes, which improves the quality of the embeddings and enables direct assessment of both similarity and relatedness between any pair of codes from multiple healthcare systems. Results: With EHR co-occurrence data from Veteran Affairs (VA) healthcare and Mass General Brigham (MGB), MIKGI algorithm produces high quality embeddings for a variety of downstream tasks including detecting known similar or related entity pairs and mapping VA local codes to the relevant EHR codes used at MGB. Based on the cosine similarity of the MIKGI trained embeddings, the AUC was 0.918 for detecting similar entity pairs and 0.809 for detecting related pairs. For cross-institutional medical code mapping, the top 1 and top 5 accuracy were 91.0% and 97.5% when mapping medication codes at VA to RxNorm medication codes at MGB; 59.1% and 75.8% when mapping VA local laboratory codes to LOINC hierarchy. When trained with 500 labels, the lab code mapping attained top 1 and 5 accuracy at 77.7% and 87.9%. MIKGI also attained best performance in selecting VA local lab codes for desired laboratory tests and COVID-19 related features for COVID EHR studies. Compared to existing methods, MIKGI attained the most robust performance with accuracy the highest or near the highest across all tasks. Conclusions: The proposed MIKGI algorithm can effectively integrate incomplete summary data from biomedical text and EHR data to generate harmonized embeddings for EHR codes for knowledge graph modeling and cross-institutional translation of EHR codes.

Zhou, Doudou↗

NASA NTRS1974

Analysis of acoustic radiation in a jet flow environment

The analysis of sound fields from arbitrary source distributions in terms of Legendre and spherical Hankel functions is well known. The purpose of this paper is to extend this classical method of analysis to environments such as jet flows where flow and flow gradients are inherently present. The wave-equation governing the radiation of sound in such an environment is derived. The steady state flow and flow gradients in the axial and transverse directions appear as coefficients in the terms of the wave-equation. A semi-numerical method is used to solve the wave-equation in terms of modified spherical harmonics yielding the phase velocities and the directivities of an infinite set of modes. The directivity of each mode is obtained in terms of modified Legendre functions by numerical integration. Some results of these directivity and phase-velocity calculations are presented for a limited number of frequency and flow parameters. Both convective and shear refraction are shown to be important.

Mungur, P.↗

NASA NTRS1984

Infrared parameterization and simple climate models

The geographical distribution of the annual mean and the annual cycle in surface temperature and satellite-observed IR is examined, and the spherical harmonic representation of the data fields is exploited to demonstrate how variances and covariances are dominated by the largest space and time scales. The geographical distribution of the annual cycle in the T and IR fields is explored; the strong imprint of the continents in both is clearly evident. The influence of the cloudiness of seasonal precipitation regimes on the IR annual cycle is also quite striking, especially over the subtropics. Analysis of the data shows that the simple form IR = A+BT (with A = 204 W/sq m and B = 1.93 W/sq m/K) explains 90 percent of the area-weighted variance in the annual mean and annual cycle of the zonally averaged IR field.

Short, D. A.↗

DOE OSTI2021

Performance Improvements for the Griffin Transport Solvers

Griffin is a Multiphysics Object-Oriented Simulation Environment based reactor multiphysics analysis application jointly developed by Idaho National Laboratory and Argonne National Laboratory. Griffin includes a variety of deterministic radiation transport solvers for fixed source, k-eigenvalue, adjoint, and subcritical multiplication, as well as transient solvers for point-kinetics, improved quasi-static, and spatial dynamics. A code assessment performed in FY-20 identified two significant issues with the transport solvers in Griffin: first, the primary heterogeneous SN (discrete ordinates) transport solver based on continuous finite element methods required significant mesh refinement and higher memory usage compared to solvers based on the method of characteristic for equivalent accuracy. Second, the homogeneous PN (spherical harmonics expansion) transport solver did not adequately support polynomial refinement, which is a feature usually required for problems with spatial homogenization and pronounced streaming, typical in fast or gas-cooled reactor systems. To address the first issue, the development effort focused on the more promising discontinuous finite element method (DFEM)-based SN transport solver in Griffin. The addition of an asynchronous parallel transport sweeper and coarse mesh finite difference (CMFD) acceleration have rendered a superior heterogeneous SN transport capability for multiphysics problems that requires far less computing resources in terms of both CPU time and memory usage. This is demonstrated with typical thermal- and fast-spectrum reactor benchmark problems, including 2D Transient Reactor Test, 3D Advanced Burner Test Reactor (ABTR), and 2D and 3D Empire microreactor. For the second issue, the development effort focused on a new transport solver based on the hybrid finite element PN method (HFEM-PN), equivalent to the variational nodal method, as well as a new diffusion solver based on HFEM-Diffusion. This solver is intended for homogenized domains with multiphysics coupling (i.e., supports mesh displacement, seamless temperature feedback, etc.). Initial calculations with the HFEM-Diffusion implementation show very good parallel efficiency for the residual evaluations with the 2D ABTR benchmark. A future development effort will be centered on further improvements to the CMFD, HFEM-PN, and DFEM diffusion solvers to ensure Griffin meets performance and software quality assurance requirements for advanced reactor design and analysis.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

NASA NTRS1978

Determination of some dominant parameters of the global dynamic sea surface topography from GEOS-3 altimetry

The 1977 altimetry data bank is analyzed for the geometrical shape of the sea surface expressed as surface spherical harmonics after referral to the higher reference model defined by GEM 9. The resulting determination is expressed as quasi-stationary dynamic SST. Solutions are obtained from different sets of long arcs in the GEOS-3 altimeter data bank as well as from sub-sets related to the September 1975 and March 1976 equinoxes assembled with a view to minimizing seasonal effects. The results are compared with equivalent parameters obtained from the hydrostatic analysis of sporadic temperature, pressure and salinity measurements of the oceans and the known major steady state current systems with comparable wavelengths. The most clearly defined parameter (the zonal harmonic of degree 2) is obtained with an uncertainty of + or - 6 cm. The preferred numerical value is smaller than the oceanographic value due to the effect of the correction for the permanent earth tide. Similar precision is achieved for the zonal harmonic of degree 3. The precision obtained for the fourth degree zonal harmonic reflects more closely the accuracy expected from the level of noise in the orbital solutions.

Mather, R. S.↗

NASA NTRS1994

Evidence for active hotspots on Venus from analysis of Magellan gravity data

The 500-Myr average crater retention age for Venus has raised questions about the present-day level of tectonic activity. In this study we examine the relationship between the gravity and topography of four large volcanic swells, Beta, Atla, Bell, and Western Eistla Regiones, for clues about their stage evolution. The Magellan line-of-sight gravity data are inverted using a point mass model of the anomalous mass to solve for the local vertical gravity field. Spectral admittance calculated from both the local gravity inversions and a spherical harmonic model is compared to three models of compensation: local compensation, a 'flexural' model with local and regional compensation of surface and subsurface loads, and a 'hotspot' model of compensation that includes top loading by volcanoes and subsurface loading due to a deep, low density mass anomaly. The coherence is also calculated in each region, but yields an elastic thickness estimate only at Bell Regio. In all models, the long wavelengths are compensated locally. Our results may indicate a relatively old, possibly inactive plume.

Smrekar, Suzanne E.↗

NASA NTRS1986

The onset of time-dependent convection in spherical shells as a clue to chaotic convection in the earth's mantle

This work presents a detailed numerical study of the dynamical behavior of convection in a spherical shell, as applied to mantle convection. From both two-dimensional (120 radial and 360 tangential points) and three-dimensional (60 radial levels and spherical harmonics up to order and degree L = 33, m = 33), it is shown that for a spherical shell (with inner-to-outer radii ratio eta = 0.62) convection becomes time-dependent, with l = 2 dominating, at a Rayleigh number of about 31 times supercritical for a constant-viscosity, base-heated configuration. This secondary instability is characterized by oscillatory time dependence, with higher frequencies involved, at slightly higher Rayleigh numbers. In illustrating the onset of time dependence, the analysis is extended to show that the onset of weak turbulence in spherical-shell convection takes place at about 60 times the critical Rayleigh number via a quasi-periodic mode.

Machetel, Philippe↗

NASA NTRS1993

New Mars free-air and Bouguer gravity: Correlation with topography, geology and large impact basins

Free-air and Bouguer gravity anomalies from a 50x50 field (MGM635), derived at the Goddard Space Flight Center, with global topography, geology, and the distribution of large impact basins was compared. The free-air gravity anomalies were derived from re-analysis of Viking Orbiter and Mariner 9 tracking data and have a spatial resolution of 250-300 km. Bouguer anomalies were calculated using a 50x50 expansion of the current Mars topography and the GSFC degree 50 geoid as the equipotential reference surface. Rotational flattening was removed using a moment of inertia of 0.365 and the corrections from Table B2 of Sleep and Phillips. Crustal density and mean density were assumed to be 2.9 and 3.93 gm/cm(sup 3). The spherical harmonic topography used has zero mean elevation, and differs from the USGS maps by about 2 km. Comparisons with global geology use a simplified map with about 1/3 the number of units on the current maps. For correlation with impact basins, the recent compilation by Schultz and Frey was used.

Frey, Herbert↗

NASA NTRS1996

Distortion Representation of Forecast Errors for Model Skill Assessment and Objective Analysis

We study a novel characterization of errors for numerical weather predictions. In its simplest form we decompose the error into a part attributable to phase errors and a remainder. The phase error is represented in the same fashion as a velocity field and will be required to vary slowly and smoothly with position. A general distortion representation allows for the displacement and a bias correction of forecast anomalies. In brief, the distortion is determined by minimizing the objective function by varying the displacement and bias correction fields. In the present project we use a global or hemispheric domain, and spherical harmonics to represent these fields. In this project we are initially focusing on the assessment application, restricted to a realistic but univariate 2-dimensional situation. Specifically we study the forecast errors of the 500 hPa geopotential height field for forecasts of the short and medium range. The forecasts are those of the Goddard Earth Observing System data assimilation system. Results presented show that the methodology works, that a large part of the total error may be explained by a distortion limited to triangular truncation at wavenumber 10, and that the remaining residual error contains mostly small spatial scales.

Hoffman, Ross N.↗

DOE OSTI2025

Window convolution of the galaxy clustering bispectrum

In galaxy survey analysis, the observed clustering statistics do not directly match theoretical predictions but rather have been processed by a window function that arises from the survey geometry including the sky footprint, redshift-dependent background number density and systematic weights. While window convolution of the power spectrum is well studied, for the bispectrum with a larger number of degrees of freedom, it poses a significant numerical and computational challenge. In this work, we consider the effect of the survey window in the tripolar spherical harmonic decomposition of the bispectrum and lay down a formal procedure for their convolution via a series expansion of configuration-space three-point correlation functions, which was first proposed by Sugiyama et al. (2019). We then provide a linear algebra formulation of the full window convolution, where an unwindowed bispectrum model vector can be directly premultiplied by a window matrix specific to each survey geometry. To validate the pipeline, we focus on the Dark Energy Spectroscopic Instrument (DESI) Data Release 1 (DR1) luminous red galaxy (LRG) sample in the South Galactic Cap (SGC) in the redshift bin 0.4 ≤ z ≤ 0.6. We first perform convergence checks on the measurement of the window function from discrete random catalogues, and then investigate the convergence of the window convolution series expansion truncated at a finite of number of terms as well as the performance of the window matrix. This work highlights the differences in window convolution between the power spectrum and bispectrum, and provides a streamlined pipeline for the latter for current surveys such as DESI and the Euclid mission.

79 ASTRONOMY AND ASTROPHYSICS↗