On the usefulness of atmospheric and oceanic angular momentum in recovering polar motion and gravity field variations in a unified process
Introduction
As Services within the International Association of Geodesy (IAG) the space geodetic techniques of satellite laser ranging (SLR) (e.g. Pearlman et al., 2002), Doppler Orbitography and Radiopositioning Integrated by Satellite (DORIS) (e.g. Tavernier et al., 2006), Global Navigation Satellite Systems (including GPS) (Beutler et al., 1999) and Very Long-Based Interferometry (VLBI) (e.g. Schlueter et al., 2002) are now used extensively to produce time series of station coordinates for tectonic motion etc and Earth rotational parameters for rotational dynamics. Space geodetic techniques can also be used to investigate surface mass redistribution in the oceans, atmosphere and continental water storage as the variations cause changes in the Earth’s gravity field harmonics (Wahr et al., 1998) which directly affect satellite orbits. Thus, satellite tracking to geodetic satellites provides a powerful mechanism for quantifying dynamic effects within the total Earth system.
Previous studies of surface mass redistribution from space geodetic techniques have utilized satellite laser ranging to passive geodetic satellites such as LAGEOS, Starlette, Stella or Ajisai (e.g. Dong et al., 1996, Cheng et al., 1997, Cazenave et al., 1999, Cheng and Tapley, 1999, Nerem et al., 2000, Cox and Chao, 2002, Moore et al., 2005) to investigate secular variations in the zonal harmonics and annual and semi-annual variability in the lower degree and order harmonics. Other studies (e.g. Crétaux et al., 2002) have utilized DORIS tracking of SPOT and TOPEX/Poseidon. Several of these studies have recorded good agreement between the geodetic results and geophysical models of surface mass redistribution. In addition to direct recovery from orbital perturbations, temporal variability in the gravity field can be inferred from deformation studies using the Global Positioning System (GPS) (Blewitt et al., 2001, Wu et al., 2003, Gross et al., 2004, Wu et al., 2006).
The mass redistribution, coupled with short-term motion primarily in the atmosphere and oceans and longer-term changes in the coupling between the Earth’s liquid core and mantle, cause changes in the Earth’s rotation through conservation of angular momentum. Utilizing relationships between the rotational dynamics allows recovery of degree 2 harmonics (e.g. Chen et al., 2000, Chen and Wilson, 2003, Gross et al., 2004).
Temporal variability in the geopotential is also a prime objective of the Gravity Recovery And Climate Experiment, GRACE, (Tapley et al., 2004). GRACE is producing monthly or more frequent snap-shots of the gravity field with applications to hydrology, oceanography and the cryosphere (e.g. Chen et al., 2004, Wahr et al., 2004, Chen et al., 2006). GRACE has also produced global static gravity fields (e.g. Tapley et al., 2003) of accuracy superior to those obtained over the previous two decades from satellite tracking.
Space geodetic techniques provide ERP parameters at daily intervals with the possibility of even shorter time scales with GPS. However, the typically low sensitivity of orbits to the gravity field variability or the high correlation between the harmonics means that there is little possibility of space geodetic techniques providing accurate measurements of mass change, even at low spatial resolutions, at intervals of less than a few days/weeks (e.g. SLR, GPS) or months (e.g. GRACE). However, the disparity in temporal resolutions raises the possibility of simultaneously recovering and using higher frequency degree 2 harmonics from the ERP data (on utilizing angular momentum data) within an orbital determination procedure.
The study is complementary to Moore and Wang (2003) in which annual mass variations from geophysical data were used within an orbit determination procedure to account for (i) geocentre effects, (ii) geophysical loading of station coordinates, and (iii) to increment the gravity field coefficients to degree and order 20. In that study, the observed geocentre motion was used to quantify the effects of the mass variations. The utilization of variations in the geocentre and station coordinate deformation were shown to have a positive effect. However, the gravity field variations had little effect on the geocentre results due possibly to the absorption of gravity field errors in orbital parameters (e.g. 1 cy/rev empirical along-track and cross-track accelerations) used in that study.
This paper now seeks to investigate the usefulness of atmospheric/oceanic angular momentum in recovering polar motion and gravity field variations in a unified process from LAGEOS. We start, in Section 2, by reviewing the relevant theory connecting Earth rotation, mass loads, excitation functions, angular momentum (AM) and the degree 2 harmonics. This is followed, in Section 3, by a summary of the geophysical angular momentum and mass data utilised in the study, the orbit determination procedures and geophysical parameter estimations from LAGEOS and a comparison of the LAGEOS based excitation functions and those from the geophysical data. The section also presents a comparison of the degree 2 harmonics derived directly within the orbit computation and from the ERPs utilising geophysical angular momentum data. In Section 4, we consider the hypothesis whether short-periodic variability in the degree 2 gravity field harmonics inferred from ERP parameters modified for the atmospheric and ocean angular momentum have any benefit within orbit determinations.
Section snippets
Review of rotational theory
The relationships between the Earth rotation parameters Xp, and Yp (polar motion) and the excitation functions, χi, i = 1, 2 can be concisely written in terms of the complex functionsUtilizing conservation of angular momentum principles, polar motion (Munk and MacDonald, 1960, Wahr, 1982, Gross, 1992) satisfies:where Ω is the Earth’s mean angular rotation; C and A the Earth’s polar
Geophysical angular momentum and mass data
The period of study covers the 6 years 1998–2003 inclusive. Geophysical data for the mass and motion components, as required within the excitations of (1a), (1b), (2a), (2b), (3), have been acquired from several sources. Atmospheric angular momentum and mass functions were taken from the NCEP/NCAR reanalyses inverted barometer atmospheric product (Salstein and Rosen, 1997). This atmospheric data is available every 6 h but was reduced to daily data compatible with the oceanic and hydrological
Use of AM data and gravity mass change in orbit determinations
The low sensitivity of orbits to the gravity field variability or the high correlation between the harmonics limits the time period over which mass change, even at low spatial resolutions, can be recovered from space geodesy. However, the relatively high temporal resolution of ERPs does raise the possibility of simultaneously recovering and using higher temporal frequency for the degree 2 harmonics from the ERP data within an orbital determination procedure. The methodology will require that
Discussion
This paper has examined the second degree zonal and second-degree order one harmonics as recovered directly from orbital perturbations of LAGEOS I and II and inferred from Earth rotation parameters (polar motion and length of day) estimated in the same orbit determinations. The ERP excitation functions were compared against geophysical data comprising atmospheric, ocean and hydrological mass and atmospheric and oceanic angular momentum (motion). It is seen that the excitation function χ1 is
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2015, Treatise on Geophysics: Second Edition