Journal of Geodynamics 53 (2012) 34–42 Contents lists available at SciVerse ScienceDirect Journal of Geodynamics j ourna l ho me pag e: http://www.elsevier.com/locate/jog Low-degree gravity change from GPS data of COSMIC and GRACE satellite missions Tingjung Lin a , Cheinway Hwang a,∗ , Tzu-Pang Tseng a,c , B.F. Chao b a Dept of Civil Engineering, National Chiao Tung University, 1001 Ta Hsueh Road, Hsinchu 300, Taiwan b Institute of Earth Sciences, Academia Sinica, 128, Sec. 2, Academia Road, Nangang, Taipei 115, Taiwan c SPACE Research Centre, School of Mathematical and GeoSpatial Sciences, RMIT University, 394-412 Swanson Street, Melbourne 3001, Australia a r t i c l e i n f o Article history: Received 7 March 2011 Received in revised form 12 August 2011 Accepted 12 August 2011 Keywords: FORMOSAT-3/COSMIC GPS GRACE Geoid change Zonal coefficient a b s t r a c t This paper demonstrates estimation of time-varying gravity harmonic coefficients from GPS data of COS- MIC and GRACE satellite missions. The kinematic orbits of COSMIC and GRACE are determined to the cm-level accuracy. The NASA Goddard’s GEODYN II software is used to model the orbit dynamics of COSMIC and GRACE, including the effect of a static gravity field. The surface forces are estimated per one orbital period. Residual orbits generated from kinematic and reference orbits serve as observables to determine the harmonic coefficients in the weighted-constraint least-squares. The monthly COSMIC and GRACE GPS data from September 2006 to December 2007 (16 months) are processed to estimate harmonic coefficients to degree 5. The geoid variations from the GPS and CSR RL04 (GRACE) solutions show consistent patterns over space and time, especially in regions of active hydrological changes. The monthly GPS-derived second zonal coefficient closely resembles the SLR-derived and CSR RL04 values, and third and fourth zonal coefficients resemble the CSR RL04 values. © 2011 Elsevier Ltd. All rights reserved. 1. Introduction Low earth orbit satellites (LEOs) have become a basic and effi- cient tool for determining global gravity field and its time variation. A number of satellite missions were launched for that purpose, including the CHAllenging Minisatellite Payload (CHAMP; Reigber et al., 1996), the dual-satellite Gravity Recovery and Climate Exper- iment (GRACE; Tapley, 1997), and Gravity Field and Steady-State Ocean Circulation Explorer (GOCE; ESA, 1999). At the same time, the Constellation Observing System for Meteorology, Ionosphere and Climate (COSMIC) mission, also known as FORMOSAT-3 (Chao et al., 2000; Hwang et al., 2008) is also able to yield time-varying gravity signals. Despite different measurement techniques, one common fea- ture of the missions is to use GPS (Global Positioning System) observations for precise orbit determination. Compared to the satellite laser ranging (SLR) technique that can only obtain one- dimensional (scalar) distances, GPS coordinate measurements are fully 3-dimensional and also be used for gravity recovery (Hwang et al., 2008). GPS-determined precise kinematic orbits contain all information of orbital perturbation forces, including those due to time-varying gravity changes, which can be estimated if other per- turbation forces are properly modeled. Before the launch of CHAMP ∗ Corresponding author. Fax: +886 3 5716257. E-mail address: cheinway@mail.nctu.edu.tw (C. Hwang). and GRACE, time-varying gravity fields are mainly determined by SLR. Han (2003) used about 2 years of CHAMP orbit data to recover the temporal variation of the Earth gravity fields up to degree and order 3. Four releases of monthly GRACE gravity field solutions up to degree and order 60 or higher solely from GRACE K-band ranging (KBR) and GPS measurements have been published by CSR, GFZ and JPL (see http://www.csr.utexas.edu/grace; Bettadpur, 2007). The release 4 (RL04) of GRACE solutions is based on the one- step approach to model the gravity field, i.e., to use the raw GPS measurements directly in the equations of motion for estimation of harmonic coefficients. The GGM and EIGEN series of static grav- ity field models (Tapley et al., 2004; Reigber et al., 2005; Förste et al., 2006) based on GRACE satellite-to-satellite KBR and GPS mea- surements are computed in this way. The two-step approach, i.e., computing the kinematic and reference (i.e., dynamic) orbits of LEOs first and estimating gravity fields using such orbits, is com- monly used for gravity field modeling. In the second step of this approach where the gravity recovery is carried out, four methods may be employed by combining GPS-derived orbits of LEOs with different types of space measurements: (i) Kaula’s linear perturba- tion theory (Kaula, 1966); (ii) direct numerical integration (Hwang, 2001; Visser et al., 2001; Rowlands et al., 2002); (iii) energy balance approach (Wolff, 1969; Wagner, 1983; Jekeli, 1999; Visser et al., 2003; Visser, 2005) (iv) acceleration approach (Ditmar et al., 2006). In this paper, we will experiment with 16 months of COSMIC and GRACE GPS data, from September 2006 to December 2007, to demonstrate the feasibility of gravity recovery solely from GPS 0264-3707/$ – see front matter © 2011 Elsevier Ltd. All rights reserved. doi:10.1016/j.jog.2011.08.004