Improvement of the Earth's gravity field from terrestrial and satellite data

The determination of the Earth's gravitational potential can be done through the analysis of satellite perturbations, the analysis of surface gravity data, or both. The combination of the two data types yields a solution that combines the strength of each method: the longer wavelength strength in the satellite analysis with the better high frequency information from surface gravity data. Since 1972, Ohio State has carried out activities that have provided surface gravity data to a number of organizations who have developed combination potential coefficient models that describe the Earth's gravitational potential

Spherical harmonic expansions of the Earth's gravitational potential to degree 360 using 30' mean anomalies

Two potential coefficient fields that are complete to degree and order 360 have been computed. One field (OSU86E) excludes geophysically predicted anomalies while the other (OSU86F) includes such anomalies. These fields were computed using a set of 30' mean gravity anomalies derived from satellite altimetry in the ocean areas and from land measurements in North America, Europe, Australia, Japan and a few other areas. Where no 30' data existed, 1 deg x 1 deg mean anomaly estimates were used if available. No rigorous combination of satellite and terrestrial data was carried out. Instead advantage was taken of the adjusted anomalies and potential coefficients from a rigorous combination of the GEML2' potential coefficient set and 1 deg x 1 deg mean gravity anomalies. The two new fields were computed using a quadrature procedure with de-smoothing factors. The spectra of the new fields agree well with the spectra of the fields with 1 deg x 1 deg data out to degree 180. Above degree 180 the new fields have more power. The fields have been tested through comparison of Doppler station geoid undulations with undulations from various geopotential models. The agreement between the two types of undulations is approximately + or - 1.6 m. The use of a 360 field over a 180 field does not significantly improve the comparison. Instead it allows the comparison to be done at some stations where high frequency effects are important. In addition maps made in areas of high frequency information (such as trench areas) clearly reveal the signal in the new fields from degree 181 to 360

The Development of a Degree 360 Expansion of the Dynamic Ocean Topography of the POCM_4B Global Circulation Model

This paper documents the development of a degree 360 expansion of the dynamic ocean topography (DOT) of the POCM_4B ocean circulation model. The principles and software used that led to the final model are described. A key principle was the development of interpolated DOT values into land areas to avoid discontinuities at or near the land/ocean interface. The power spectrum of the POCM_4B is also presented with comparisons made between orthonormal (ON) and spherical harmonic magnitudes to degree 24. A merged file of ON and SH computed degree variances is proposed for applications where the DOT power spectrum from low to high (360) degrees is needed

The Ohio State 1991 geopotential and sea surface topography harmonic coefficient models

The computation is described of a geopotential model to deg 360, a sea surface topography model to deg 10/15, and adjusted Geosat orbits for the first year of the exact repeat mission (ERM). This study started from the GEM-T2 potential coefficient model and it's error covariance matrix and Geosat orbits (for 22 ERMs) computed by Haines et al. using the GEM-T2 model. The first step followed the general procedures which use a radial orbit error theory originally developed by English. The Geosat data was processed to find corrections to the a priori geopotential model, corrections to a radial orbit error model for 76 Geosat arcs, and coefficients of a harmonic representation of the sea surface topography. The second stage of the analysis took place by doing a combination of the GEM-T2 coefficients with 30 deg gravity data derived from surface gravity data and anomalies obtained from altimeter data. The analysis has shown how a high degree spherical harmonic model can be determined combining the best aspects of two different analysis techniques. The error analysis was described that has led to the accuracy estimates for all the coefficients to deg 360. Significant work is needed to improve the modeling effort

Comparisons of global topographic/isostatic models to the Earth's observed gravity field

The Earth's gravitational potential, as described by a spherical harmonic expansion to degree 180, was compared to the potential implied by the topography and its isostatic compensation using five different hypothesis. Initially, series expressions for the Airy/Heiskanen topographic isostatic model were developed to the third order in terms of (h/R), where h is equivalent rock topography and R is a mean Earth radius. Using actual topographic developments for the Earth, it was found that the second and third terms of the expansion contributed 30 and 3 percents, of the first of the expansion. With these new equations it is possible to compute depths (D) of compensation, by degree, using 3 different criteria. The results show that the average depth implied by criterion I is 60 km while it is about 33 km for criteria 2 and 3 with smaller compensation depths at the higher degrees. Another model examined was related to the Vening-Meinesz regional hypothesis implemented in the spectral domain. Finally, oceanic and continental response functions were derived for the global data sets and comparisons made to locally determined values

Geometric Geodesy part 2

The University Archives has determined that this item is of continuing value to OSU's history.File Rapp_Geom_Geod_ Vol_II.pdf is replaced by File Rapp_Geom_Geod_ Vol_II_rev.pdf. Typos have been corrected on pages 50, 53, 54

Consideration of permanent tidal deformation in the orbit determination and data analysis for the Topex/Poseidon mission

The effects of the permanent tidal effects of the Sun and Moon with specific applications to satellite altimeter data reduction are reviewed in the context of a consistent definition of geoid undulations. Three situations are applicable not only for altimeter reduction and geoid definition, but also for the second degree zonal harmonic of the geopotential and the equatorial radius. A recommendation is made that sea surface heights and geoid undulations placed on the Topex/Poseidon geophysical data record should be referred to the mean Earth case (i.e., with the permanent effects of the Sun and Moon included). Numerical constants for a number of parameters, including a flattening and geoid geopotential, are included

Report of the panel on geopotential fields: Gravity field, section 8

The objective of the Geopotential Panel was to develop a program of data acquisition and model development for the Earth's gravity and magnetic fields that meet the basic science requirements of the solid Earth and ocean studies. Presented here are the requirements for gravity information and models through the end of the century, the present status of our knowledge, data acquisition techniques, and an outline of a program to meet the requirements

Simulation of the Mars Surface Solar Spectra for Optimized Performance of Triple-Junction Solar Cells

The unparalleled success of the Mars Exploration Rovers (MER) powered by GaInP/GaAs/Ge triple-junction solar cells has demonstrated a lifetime for the rovers that exceeded the baseline mission duration by more than a factor of five. This provides confidence in future longer-term solar powered missions on the surface of Mars. However, the solar cells used on the rovers are not optimized for the Mars surface solar spectrum, which is attenuated at shorter wavelengths due to scattering by the dusty atmosphere. The difference between the Mars surface spectrum and the AM0 spectrum increases with solar zenith angle and optical depth. The recent results of a program between JPL and Spectrolab to optimize GaInP/GaAs/Ge solar cells for Mars are presented. Initial characterization focuses on the solar spectrum at 60-degrees zenith angle at an optical depth of 0.5. The 60-degree spectrum is reduced to ~1/6 of the AM0 intensity and is further reduced in the blue portion of the spectrum. JPL has modeled the Mars surface solar spectra, modified an X-25 solar simulator, and completed testing of Mars-optimized solar cells previously developed by Spectrolab with the modified X-25 solar simulator. Spectrolab has focused on the optimization of the higher efficiency Ultra Triple-Junction (UTJ) solar cell for Mars. The attenuated blue portion of the spectrum requires the modification of the top sub-cell in the GaInP/GaAs/Ge solar cell for improved current balancing in the triple-junction cell. Initial characterization confirms the predicted increase in power and current matched operation for the Mars surface 60-degree zenith angle solar spectrum

Efimov physics from the functional renormalization group

Few-body physics related to the Efimov effect is discussed using the functional renormalization group method. After a short review of renormalization in its modern formulation we apply this formalism to the description of scattering and bound states in few-body systems of identical bosons and distinguishable fermions with two and three components. The Efimov effect leads to a limit cycle in the renormalization group flow. Recently measured three-body loss rates in an ultracold Fermi gas $^6$Li atoms are explained within this framework. We also discuss briefly the relation to the many-body physics of the BCS-BEC crossover for two-component fermions and the formation of a trion phase for the case of three species.Comment: 28 pages, 13 figures, invited contribution to a special issue of "Few-Body Systems" devoted to Efimov physics, published versio