Geometrical Model of the Earth’s Geocenter Based on Temporal Gravity Field Maps

Abstract

We demonstrate that GRACE gravity field maps could be used to derive annual amplitudes and secular rates in the geocenter z-coordinate from the low-degree odd coefficients (“pear-shaped”), i.e., from the C30, C50 and C70, although degree 1 gravity field coefficients are not estimated. This is because “pear-shaped” coefficients are not symmetrical with the equator like even zonnals C20, C40 and C60, and they are big enough relative to other low-degree “pear-shaped” coefficients to absorb any translation rate present when degree 1 gravity field coefficients are not estimated. If degree 1 gravity field coefficients are derived together with all other gravity field coefficients, degree 1 absorbs systematic effects associated to space geodesy techniques and reference frame realization. Therefore, when degree 1 coefficients are not estimated, any rate in the geocenter z-coordinate is reflected in the translation of the “pear-shaped” harmonics. This also follows from the translation of spherical harmonics. We derived the secular rate and annual amplitudes in geocenter z-coordinate from the low-degree odd coefficients (“pear-shaped”) over the last 10 years (GRACE RL05) and compared it with results from the global GPS and SLR solutions, tide-gauge records over the last 100 years and the limited data set of geocenter z-coordinates estimated from the combined orbit determination for the Jason-2 satellite and the GPS constellation. We confirm the initial assumption that temporal gravity field maps provided by the GRACE mission contain an information on the geocenter z-coordinates and estimated annual amplitudes are very close to results from GPS/SLR/LEO solutions. In addition, this approach reveals an interesting information that the asymmetrical mean sea lever rise between the Northern and the Southern hemispheres could be reflected in the rate of asymmetric surface spherical harmonics (“pear-shaped”). Following (Cazenave and Llovel 2010), satellite altimetry observations suggest that the mean sea level has been rising faster over the Southern than over the Northern Hemisphere, whereas recently (Woppelmann et al. 2014) using selected tide-gauges measurements corrected with the glacial isostatic adjustment (GIA) and GPS velocities report the opposite sign, i.e. the mean sea level rise of 2.0 ± 0.2 mm/yr for the Northern hemisphere and 1.1 ± 0.2 mm/yr for the Southern hemisphere. Based on the 10 years of GRACE gravity field models (GRACE RL05), we can draw the conclusion that difference in the mean sea level rise between the Northern and the Southern hemispheres is reflected in the rate of the z-coordinate of the geocenter and that the mean sea level has been rising faster over the Southern than over the Northern hemisphere (confirmed Church priv. com.). At the end we derive similar approach from the rates in the even degree zonal spherical harmonics and derive a rate in the scale of GRACE gravity fields of -0.5 ppb/10 yr. This shows that GRACE gravity field maps represented by spherical harmonics contain a scale and one can use temporal gravity field maps to monitor its variations over time.