[1] Apparent seasonal site position variations are derived from 4.5 years of global continuous GPS time series and are explored through the ''peering'' approach. Peering is a way to depict the contributions of the comparatively well-known seasonal sources to garner insight into the relatively poorly known contributors. Contributions from pole tide effects, ocean tide loading, atmospheric loading, nontidal oceanic mass, and groundwater loading are evaluated. Our results show that $40% of the power of the observed annual vertical variations in site positions can be explained by the joint contribution of these seasonal surface mass redistributions. After removing these seasonal effects from the observations the potential contributions from unmodeled wet troposphere effects, bedrock thermal expansion, errors in phase center variation models, and errors in orbital modeling are also investigated. A scaled sensitivity matrix analysis is proposed to assess the contributions from highly correlated parameters. The effects of employing different analysis strategies are investigated by comparing the solutions from different GPS data analysis centers. Comparison results indicate that current solutions of several analysis centers are able to detect the seasonal signals but that the differences among these solutions are the main cause for residual seasonal effects. Potential implications for modeling seasonal variations in global site positions are explored, in particular, as a way to improve the stability of the terrestrial reference frame on seasonal timescales.

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[1] Analysis of satellite laser ranging (SLR) data indicates that the Earth's dynamic oblateness (J 2 ) has undergone significant variations during the past 28 years. The dominant signatures in the observed variations in J 2 are (1) a secular decrease with a rate of approximately À2.75 Â 10 À11 yr À1 , (2) seasonal annual variations with a mean amplitude of 2.9 Â 10 À10

[1] For over three decades, satellite laser ranging (SLR) has recorded the global nature of the long-wavelength mass change within the Earth system. Analysis of the most recent time series of 30 day SLR-based estimates of Earth's dynamical oblateness, characterized by the gravitational degree-2 zonal spherical harmonic J 2 , indicates that the long-term variation of J 2 appears to be more quadratic than linear in nature. The superposition of a quadratic and an 18.6 year variation leads to the "unknown decadal variation" reported by Cheng and Tapley (2004). Although the primary trend is expected to be linear due to global isostatic adjustment, there is an evident deceleration ( € J 2 ¼ 18 AE1 ð Þ Â 10 À13 =yr 2 ) in the rate of the decrease in J 2 during the last few decades, likely due to changes in the rate of the global mass redistribution from melting of the glaciers and ice sheets as well as mass changes in the atmosphere and ocean.

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remains static in an inertial frame. Without loss of generality we define an inertial frame (CM frame) with CM as its origin and let the CM, CE and CF coincide before mass redistribution. In CM frame, the coordinates of CE, CF and mass load are denoted as rCE, rCF and rload respectively. We define the coordinates of CF and mass load in an Earth-fixed reference frame (CE frame) with CE as its origin as rCF and rload. There are simple geometric and mass balance relations rload = rCE + rload, rCF = rCE + rCF (1)

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