Earth’s gravity field modelling based on satellite

Authors: X Guo P Ditmar Q Zhao R Klees H H Farahani

Publish Date: 2017/02/25

Volume: 91, Issue: 9, Pages: 1049-1068

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Abstract

GPS data collected by satellite gravity missions can be used for extracting the longwavelength part of the Earth’s gravity field We propose a new data processing method which makes use of the ‘average acceleration’ approach to gravity field modelling In this method satellite accelerations are directly derived from GPS carrier phase measurements with an epochdifferenced scheme As a result no ambiguity solutions are needed and the systematic errors that do not change much from epoch to epoch are largely eliminated The GPS data collected by the Gravity Field and SteadyState Ocean Circulation Explorer GOCE satellite mission are used to demonstrate the added value of the proposed method An analysis of the residual accelerations shows that accelerations derived in this way are more precise with noise being reduced by about 20 and 5 at the crosstrack component and the other two components respectively as compared to those based on kinematic orbits The accelerations obtained in this way allow the recovery of the gravity field to a slightly higher maximum degree compared to the solution based on kinematic orbits Furthermore the gravity field solution has an overall better performance Errors in spherical harmonic coefficients are smaller especially at low degrees The cumulative geoid height error is reduced by about 15 and 5 up to degree 50 and 150 respectively An analysis in the spatial domain shows that large errors along the geomagnetic equator which are caused by a high electron density coupled with large shortterm variations are substantially reduced Finally the new method allows for a better observation of mass transport signals In particular sufficiently realistic signatures of regional mass anomalies in North America and southwest Africa are obtainedGPSbased highlow satellitetosatellite tracking hlSST is a wellestablished method to map the Earth’s gravity field since the launch of the CHAllenging Minisatellite Payload CHAMP satellite mission Reigber et al 1998 Later on hlSST was also exploited by the Gravity Recovery And Climate Experiment GRACE Tapley et al 2004 and the Gravity Field and SteadyState Ocean Circulation Explorer GOCE Drinkwater et al 2006 satellite missions This technique is particularly useful to map the longwavelength part of the Earth’s gravity field Reigber et al 2003Until now gravity field is typically modelled on the basis of satellite kinematic orbits computed as an intermediate product eg Baur et al 2014 In the last decade several techniques have been developed to exploit the kinematic orbits for gravity field modelling eg Baur et al 2014 In the context of this study we will focus on the average acceleration approach Ditmar and van Eck van der Sluijs 2004 This approach has been successfully applied in the compilation of a number of gravity field models including the DEOS CHAMP01C 70 model derived from CHAMP data Ditmar et al 2006 and the DGM1S model which is based on data from the GRACE and GOCE satellite gravity missions Farahani et al 2013 These models use kinematic orbits that were derived from GPS hlSST data by a precise point positioning approach Švehla and Rothacher 2005 followed by a threepoint doubledifferentiation scheme Hereafter this approach is referred to as the ‘orbit method’ In this approach the quality of the gravity field model critically depends on the quality of the kinematic orbitsIn general kinematic orbits are sensitive to the observation geometry and various systematic errors eg mismodelling of the antenna phase centre variations PCV and the highorder ionosphereinduced errors In recent years dedicated algorithms were developed to mitigate the impact of those errors on the kinematic orbits and corresponding gravity field solutions Jäggi et al 2009 2011 2015 Bock et al 2011 However the kinematic orbits may still suffer from some unknown or mismodelled systematic errors as well as artefacts that are difficult to be modelled for Low Earth Orbiters LEO eg hardware delays from both the GPS satellites and GPS receivers nearfield multipath effects etcThe GPS carrier phase measurements were already applied to derive relative vehicle accelerations in airborne gravimetry Jekeli and Garcia 1997 In this research we propose to use a somewhat similar approach in gravity field modelling from GPS data collected by satellites The basic idea is to estimate average satellite accelerations directly from the GPS carrier phase measurements using an epochdifferenced scheme Hereafter this approach is referred to the ‘phase method’ The main benefit of this approach is that no phase ambiguity solutions are needed and that systematic errors which do not change much from epoch to epoch are largely eliminated It is worth mentioning that the phase method still requires knowledge of the satellite orbit as will be shown later However this orbit only plays a supporting roleWe demonstrate the added value of the proposed approach using GPS data collected by the GOCE mission The GOCE satellite was equipped among others with two 12channel dualfrequency Lagrange GPS hlSST instruments Intelisano et al 2008 each consisting of a geodeticquality GPS receiver and a helix antenna In this study GPS data collected in the nominal phase of the GOCE mission spanning the time interval from November 2009 to July 2012 are used and the days with data problems are excluded as proposed in Visser et al 2014 The average satellite accelerations derived both from the kinematic orbits and directly from GPS phase measurements are exploited to recover the gravity field In order to demonstrate the strength of the proposed method more convincingly we consider two variants of kinematic orbits One is the officially provided kinematic orbit ie the SST PKI 2 product EGGC 2010 Bock et al 2014 hereafter denoted as the ESA European Space Agency orbit and the orbit method in this case is denoted as the ‘orbitESA method’ The other one is computed in house by the PANDA Position And Navigation Data Analyst software Liu and Ge 2003 which was developed at Wuhan University hereafter this orbit is denoted as the WHU orbit and the orbit method in this case is denoted as the ‘orbitWHU method’ To ensure a fair comparison of the orbit method and the phase method the carrier phase data and measurement models used in the latter one are identical to those adopted when deriving the WHU kinematic orbitTo assess the quality of the obtained gravity solutions the gravity field model DGM1S is used It is based on GRACE KBand Ranging KBR and GOCE gradiometry data Farahani et al 2013 and therefore has a much higher accuracy than the hlSSTbased solutions obtained with either method In addition we make an attempt to identify some mass transport signals in the obtained solutionsThe outline of the paper is the following In Sect 2 we provide a review of the average acceleration approach and present the functional model of deriving average accelerations from kinematic orbits and GPS phase measurements In addition we discuss in that section the inversion of average accelerations into gravity field parameters with a focus on the data weighting scheme In Sect 3 noise in the average satellite accelerations obtained with both the phase and the orbit method is analysed In Sect 4 we assess the quality of the derived gravity field models Finally Sects 5 and 6 are left for discussion and conclusions respectively

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