EGM96 Gravity Model Research Articles

Fast Height Conversion Method for BDS Receivers

In order to apply the positioning results of BDS receiver into engineering practice, geodetic height obtained from positioning calculation of receiver should be converted into normal height, therefore it is needed to calculate height anomaly. Also in order to meet the meter level height conversion demand, reduce the memory space consumption by height conversion program and accelerate the program running speed, this paper shows one fast height conversion computation method with the reduced order spherical harmonic coefficients of the gravity model, namely that the height anomaly computed respectively with spherical harmonic coefficients of EGM96 gravity model extending to degree 360 and order 360 and EGM08 earth gravity field extending to degree 2190 and order 2159 is deemed as benchmark, and summarizes the time consumption and relative accuracy of the fast height conversion method. According to the test and comparative analysis of height anomaly computed between world-wide grid points and Asia-Pacific region grid points, test results indicate that this height anomaly computation method with reduced-order spherical harmonic coefficients of EGM96 gravity model can meet the height conversion accuracy and speed demand for positioning results of BDS receivers all over the world or in Asia-Pacific region.

Application of numerical integration techniques for orbit determination of state-of-the-art LEO satellites

Classical numerical integration methods have been tested for determining the orbit of most recent Low Earth Orbiter (hereafter LEO) satellites. In general, numerical integration techniques for orbit determination are commonly used to fill the gap between two discrete, observed epochs. In this study orbits have been determined using the EGM96 gravity model by the Euler, Runge-Kutta, Bulirsch-Stoer and Adams-Moulton numerical integration techniques among others. This analysis is performed for a LEO, the GOCE, and for medium altitude satellite, one GPS satellite. The orbits are integrated under different assumptions on the roughness of the force model, considering effects of the ellipticity, high order gravity and non-static Earth generated accelerations on the orbit.

Variational solution about over-determined geodetic boundary value problem and its related theories

Abstract A new solving method is studied by minimizing the quadratic functional in the paper. At first, the so-called calculus solution of over-detemined gedetic boundary value problem is introduced with help of variation principle, and various theoretical properties of it are discussed. Then the general way to compute it is given, and particularly, we can obtain its analytical expression under the case that boundary are all spheres. At last, an arithmetic example is constituted with EGM96 gravity model and computive result illustrates that the method can

Spectral analysis of quasi-stationary sea surface topography from GRACE mission

During the last two decades satellite altimetry has offered an abundance of measurements of the sea surface resulting in the improvement of global mean sea surface height (MSSH) and marine geoid determination. On the other hand, with the launching of new generation gravity satellites, some high accuracy long-wavelength gravity models are available. These breakthroughs give us a great opportunity for new estimation of quasi-stationary sea surface topography (QSST). In this paper, the new gravity model GGM01C derived from GRACE mission is briefly presented, and a new global high precision and high-resolution QSST is determined based on the GGM01C model and the global MSSH. The spectral features of the QSST estimated by GGM01C and EGM96 gravity model to degree/order 200 are discussed by spectral analysis. As a result, the QSST is mainly composed of long waves, medium waves partially and short waves scarcely, its power spectral structures are different between the zonal direction and the meridional direction, there are great differences between the two models, which maybe explain why the ocean currents derived from the two gravity models by Tapley show different patterns.

LAGEOS-type satellites in critical supplementary orbit configuration and the Lense–Thirring effect detection

In this paper we analyse quantitatively the concept of LAGEOS-type satellites in critical supplementary orbit configuration (CSOC) which has proved capable of yielding various observables for many tests of general relativity in the terrestrial gravitational field, with particular emphasis on the measurement of the Lense–Thirring effect. By using an entirely new pair of LAGEOS-type satellites in identical, supplementary orbits with, e.g., semimajor axes a = 12 000 km, eccentricity e = 0.05 and inclinations iS1 = 63.4° and iS2 = 116.6°, it would be possible to cancel out the impact of the mismodelling of the static part of the gravitational field of the Earth to a very high level of accuracy. The departures from the ideal supplementary orbital configuration due to the orbital injection errors would yield systematic gravitational errors of the order of a few per cent, according to the covariance matrix of the EGM96 gravity model up to degree l = 20. However, the forthcoming, new gravity models from the CHAMP and GRACE missions should greatly improve the situation. So, it should be possible to measure the gravitomagnetic shifts of the sum of their nodes ΣLT with an accuracy level perhaps less than 1%, of the difference of their perigees ΔLT with an accuracy level of 5% and of ẊLT ≡ ΣLT − ΔLT with an accuracy level of 2.8%. Such results, which are due to the non-gravitational perturbations mismodelling, have been obtained for an observational time span of about 6 years and could be further improved by fitting and removing from the analysed time series the major time-varying perturbations which have known periodicities.

Determination of gravity anomaly using satellite altimeter data in the Great Lakes

In this paper, the determination of gravity anomalies in the Great Lakes using satellite altimeter data of GEOSAT Geodetic Mission (GM) and TOPEX/Poseidon is discussed. The seasonal change of lake level was observed from TOPEX/Poseidon satellite altimeter data. This analysis of lake level change was made to determine the mean lake surface profiles along the TOPEX/Poseidon repeat tracks. The least squares collocation was used to predict gravity anomalies. The gravity anomalies are determined by using mean lake surface profiles derived from TOPEX altimeter data and along-track slopes and azimuth derived from lake surface heights measured by the GEOSAT altimeter. To remove influences of the cycle-to-cycle time variation of lake level, along-track slopes of altimeter height are used. These results are compared to the exisiting surface gravit data measured in the Great Lakes. The gravity anomaly in the Lake Huron derived from the altimeter data using the least squares collocation shows slightly better comparison with the surface gravity anomaly than that implied by the EGM-96 gravity model.

Evolution of the Earth's principal axes and moments of inertia: the canonical form of solution

Harmonic coefficients of the 2nd degree are separated into the invariant quantitative (the 2nd-degree variance) and the qualitative (the standardized harmonic coefficients) characteristics of the behavior of the potential V2(t). On this basis the evolution of the Earth's dynamical figure is described as a solution of the time-dependent eigenvalues–eigenvectors problem in the canonical form. Such a canonical quadratic form is defined only by temporal variations of the harmonic coefficients and always remains finite, even within an infinite time interval. An additional condition for the correction or the determination of temporal variations of the 2nd degree is obtained. Temporal variations of the fully normalized sectorial harmonic coefficients are estimated in addition to ˙C¯20, ˙C¯21, and ˙S¯21 of the EGM96 gravity model. In addition, a non-linear hyperbolic model for C¯2m(t), S¯2m(t) is constructed. The trigonometric form of the hyperbolic model leads to the consideration of the potential V2(ψ) instead of V2(t) within the closed interval −π/2≤ψ≤+π/2. Thus, it is possible to evaluate the global trend of V2(t), the Earth's principal axes and the differences of the moments of inertia within the whole infinite time interval.

GEOID AND SEA SURFACE TOPOGRAPHY DERIVED FROM ERS-1 ALTIMETER DATA BY THE ADJOINT METHOD

A method for splitting sea surface height measurements from satellite altimetry into geoid undulations and sea surface topography is presented. The method is based on a combination of the information from altimeter data and a dynamic sea surface height model. The model consists of geoid undulations and a quasi-geostrophic model for expressing the sea surface topography. The goal is the estimation of those values of the parameters of the sea surface height model that provide a least-squares fit of the model to the data. The solution is accomplished by the adjoint method which makes use of the adjoint model for computing the gradient of the cost function of the least-squares adjustment and an optimization algorithm for obtaining improved parameters. The estimation is applied to the North Atlantic. ERS-1 altimeter data of the year 1993 are used. The resulting geoid agrees well with the geoid of the EGM96 gravity model.

GEOIDAL GEOPOTENTIAL AND WORLD HEIGHT SYSTEM

The geoidal geopotential value of W 0 = 62 636 856.0 ± 0.5m 2 s −2 , determined from the 1993 –1998 TOPEX/POSEIDON altimeter data, can be used to practically define and realize the World Height System. The W 0 -value can also uniquely define the geoidal surface and is required for a number of applications, including General Relativity in precise time keeping and time definitions. Furthermore, the W 0 -value provides a scale parameter for the Earth that is independent of the tidal reference system. All of the above qualities make the geoidal potential W 0 ideally suited for official adoption as one of the fundamental constants, replacing the currently adopted semi-major axis a of the mean Earth ellipsoid. Vertical shifts of the Local Vertical Datum (LVD) origins can easily be determined with respect to the World Height System (defined by W 0 ), in using the recent EGM96 gravity model and ellipsoidal height observations (e.g. GPS) at levelling points. Using this methodology the LVD vertical displacements for the NAVD88 (North American Vertical Datum 88), NAP (Normaal Amsterdams Peil), AMD (Australian Height Datum), KHD (Kronstadt Height Datum), and N60 (Finnish Height Datum) were determined with respect to the proposed World Height System as follows: −55.1 cm, −11.0 cm, +42.4 cm, −11.1 cm and +1.8 cm, respectively.

Precise ERS-2 orbit determination using SLR, PRARE, and RA observations

The second European Remote Sensing satellite ERS-2, launched in 1995, is supported by satellite laser ranging (SLR), the German precise range and range-rate equipment (PRARE) microwave tracking system, and radar altimetry (RA). SLR, PRARE and crossover RA observations (XO/RA) from May, June, and July 1996 have been analyzed using the GEOSAT software developed at Forsvarets forskningsinstitutt (FFI, The Norwegian defence research establishment). Orbits computed with the JGM3 gravity model and the more recent EGM96 gravity model have been compared with orbits from other analysis centers. Based on these comparisons in addition to the post-fit observation residuals, and results from internal orbital overlaps, we conclude that the radial component of the ERS-2 orbit can be determined with a precision of 6 cm.

Global derivation of marine gravity anomalies from Seasat, Geosat, ERS-1 and TOPEX/POSEIDON altimeter data

SUMMARY Marine gravity anomalies over the area 82s to 82N and 0E to 360E on a 2' x 2' grid have been derived from Seasat, Geosat, ERS-1 and TOPEX/POSEIDON altimeter data. The inverse Vening Meinesz formula with a 1-D FFT method was used to compute gravity anomalies from gridded north-south and west-east geoid gradients, in a remove-restore procedure with the EGM96 gravity model as the reference field. This paper presents a new gridding technique and an altimeter data management system that help to extract data efficiently. In the 12 areas where ship-measured gravity and satellite-derived gravity were compared, rms agreements of 5-14 mgal were obtained. Special discussions of the gravity anomalies over selected inland seas, the Arctic, Antarctica and coastal waters are presented. The derived gravity anomalies show detailed tectonic structures of the world ocean. The global data set will be continuously updated with more altimeter data included in the derivation.