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We present a new approach to estimate time variations in J2. Those variations are represented as the sum of contributions from individual sources. This approach uses solely Gravity Recovery And Climate Experiment (GRACE) data and the geoid fingerprints of mass redistributions that take place both at the surface and in the interior of the solid Earth. The results agree remarkably well with those based on satellite laser ranging, while estimates of the sources explain the observed variations in J2. Seasonal variations are dominated by terrestrial water storage and by mass redistribution in the atmosphere and ocean. Trends, however, are primarily controlled by the Greenland and Antarctic ice sheets and by glacial isostatic adjustment. The positive trend from surface mass variations is larger than the negative trend due to glacial isostatic adjustment and leads to an overall rising trend during the GRACE period (2002–2017).

Present-day mass redistribution increases the total ocean mass and, on average, causes the ocean bottom to subside elastically. Therefore, barystatic sea level rise is larger than the resulting global mean geocentric sea level rise, observed by satellite altimetry and GPS-corrected tide gauges. We use realistic estimates of mass redistribution from ice mass loss and land water storage to quantify the resulting ocean bottom deformation and its effect on global and regional ocean volume change estimates. Over 1993-2014, the resulting globally averaged geocentric sea level change is 8% smaller than the barystatic contribution. Over the altimetry domain, the difference is about 5%, and due to this effect, barystatic sea level rise will be underestimated by more than 0.1 mm/yr over 1993-2014. Regional differences are often larger: up to 1 mm/yr over the Arctic Ocean and 0.4 mm/yr in the South Pacific. Ocean bottom deformation should be considered when regional sea level changes are observed in a geocentric reference frame.

We investigate the effect of self-attraction and loading (SAL) induced by the projected accumulation of sea water on shallow continental shelf areas. Using output from a climate model, we compute 21st century changes in regional steric sea surface height and find that steric changes are largest over the deep ocean and relatively small on the shallow continental shelves. The resulting redistribution of sea water towards the shelf areas leads to mass accumulation on the shelves and therefore to increased gravitational attraction as well as increased loading on the sea floor. We find that, depending on the scenario and region, SAL effects may result in an additional sea level rise of 1–3 cm on the world's continental shelf areas by the end of the 21st century. These estimates are at most 15% of the combined changes in sea surface height induced by redistribution of water masses and steric expansion.

Long‐term trends and decadal variability of sea level in the North Sea and along the Norwegian coast have been studied over the period 1958–2014. We model the spatially nonuniform sea level and solid earth response to large‐scale ice melt and terrestrial water storage changes. GPS observations, corrected for the solid earth deformation, are used to estimate vertical land motion. We find a clear correlation between sea level in the North Sea and along the Norwegian coast and open ocean steric variability in the Bay of Biscay and west of Portugal, which is consistent with the presence of wind‐driven coastally trapped waves. The observed nodal cycle is consistent with tidal equilibrium. We are able to explain the observed sea level trend over the period 1958–2014 well within the standard error of the sum of all contributing processes, as well as the large majority of the observed decadal sea level variability., Key Points Regional sea level budgets at the Northwestern European shelf over the last decades are closedCorrelation between open ocean steric and shelf sea level is consistent with propagation of coastally trapped wavesVertical land motion and solid earth deformation are key to close the budget

Long-term trends and decadal variability of sea level in the North Sea and along the Norwegian coast have been studied over the period 1958–2014. We model the spatially nonuniform sea level and solid earth response to large-scale ice melt and terrestrial water storage changes. GPS observations, corrected for the solid earth deformation, are used to estimate vertical land motion. We find a clear correlation between sea level in the North Sea and along the Norwegian coast and open ocean steric variability in the Bay of Biscay and west of Portugal, which is consistent with the presence of wind-driven coastally trapped waves. The observed nodal cycle is consistent with tidal equilibrium. We are able to explain the observed sea level trend over the period 1958–2014 well within the standard error of the sum of all contributing processes, as well as the large majority of the observed decadal sea level variability.

The only vertical land movement signal routinely corrected for when estimating absolute sea-level change from tide gauge data is that due to glacial isostatic adjustment (GIA). We compare modeled GIA uplift (ICE-5G + VM2) with vertical land movement at ?300 GPS stations located near to a global set of tide gauges, and find regionally coherent differences of commonly ±0.5–2 mm/yr. Reference frame differences and signal due to present-day mass trends cannot reconcile these differences. We examine sensitivity to the GIA Earth model by fitting to a subset of the GPS velocities and find substantial regional sensitivity, but no single Earth model is able to reduce the disagreement in all regions. We suggest errors in ice history and neglected lateral Earth structure dominate model-data differences, and urge caution in the use of modeled GIA uplift alone when interpreting regional- and global- scale absolute (geocentric) sea level from tide gauge data.

The 2011 great Tohoku-Oki earthquake, apart from shaking the ground, perturbed the motions of satellites orbiting some hundreds km away above the ground, such as GRACE, due to coseismic change in the gravity field. Significant changes in inter-satellite distance were observed after the earthquake. These unconventional satellite measurements were inverted to examine the earthquake source processes from a radically different perspective that complements the analyses of seismic and geodetic ground recordings. We found the average slip located up-dip of the hypocenter but within the lower crust, as characterized by a limited range of bulk and shear moduli. The GRACE data constrained a group of earthquake source parameters that yield increasing dip (7-16 degrees plus or minus 2 degrees) and, simultaneously, decreasing moment magnitude (9.17-9.02 plus or minus 0.04) with increasing source depth (15-24 kilometers). The GRACE solution includes the cumulative moment released over a month and demonstrates a unique view of the long-wavelength gravimetric response to all mass redistribution processes associated with the dynamic rupture and short-term postseismic mechanisms to improve our understanding of the physics of megathrusts.

Bedrock uplift in Antarctica is dominated by a combination of glacial isostatic adjustment (GIA) and elastic response to contemporary mass change. Here, we present spatially extensive GPS observations of Antarctic bedrock uplift, using 52% more stations than previous studies, giving enhanced coverage, and with improved precision. We observe rapid elastic uplift in the northern Antarctic Peninsula. After considering elastic rebound, the GPS data suggests that modeled or empirical GIA uplift signals are often over?estimated, par t icularly the magnitudes of the signal maxima. Our observation that GIA uplift is misrepresented by modeling (weighted root?meansquares of observation?model differences: 4.9–5.0 mm/yr) suggests that, apart from a few regions where large ice mass loss is occurring, the spatial pattern of secular ice mass change derived from Gravity Recovery and Climate Experiment (GRACE) data and GIA models may be unreliable, and that several recent secular Antarctic ice mass loss estimates are systematically biased, mainly too high.

Variations in the Earth's water cycle are commonly quantified by their effect on global mean sea?level. However, the interaction between passive adjustment of the ocean to changes in gravitational attraction due to mass redistribution, the related deformation of the solid Earth and disturbances in the Earth's rotation vector will yield a distribution that is more complicated than a uniform rise or fall of the ocean's surface. In this study, we present the first estimates of seasonal changes in passive sea?level (which we define as the height difference between the sea surface at rest and ocean floor, excluding steric and dynamical effects) based on direct observations of surface mass redistribution, made by the Gravity Recovery and Climate Experiment (GRACE) between 2003 and 2010. We show that this “selfgravitation?effect” causes seasonal variations of the sea?level of up to 1 cm – comparable to the amplitude of the long?period tides – and that inclusion in numerical ocean models results in a better agreement between observed and modelled ocean bottom pressure variations, particularly in coastal zones.

The Gravity Recovery and Climate Experiment satellites (GRACE) provide, for the first time, a method to directly measure mass exchange between the land and oceans over time. The dominant components of this exchange are due to continental ice loss/gain and land hydrology. Here, we determine the secular trend in these two components during the GRACE measurement era: 2003–2009. For each component, we model the distinct regional signatures or fingerprints of relative sea?level (RSL) change, obtaining maxima at low latitudes between ±40° N/S, but with particularly strong regional patterns. We estimate that the total ice and water mass loss from the continents is causing global mean sea?level to rise by 1.0 ± 0.4 mm/yr. Isolating the ice and hydrological signals, we find that the former is the sole net contributor to the global mean, while the latter dominates regional RSL changes in many coastal areas.

[1] We combine aftershock strain mapping, GPS measurements and leveling profiles with forward modeling of viscoelastic relaxation to study the postseismic deformation of the 1997 Umbria-Marche (Central Apennines) earthquake sequence. We explore the feasibility of GPS monitoring of postseismic transients, for the first time in Italy, generated by shallow and moderate sources. Our data allow us to distinguish a preferred coseismic faulting model as well as insight into the rheology of the Central Apennines Earth's crust. The faulting model requires a listric geometry with most of the energy released in the lower half part of the elastic crust. The rheological model consists of an elastic thin upper crust, a transition zone of about 1018 Pa s underlain by a low-viscosity lower crust, ranging from 1017 to 1018 Pa s. The postseismic deformation is, both distributed in the transition zone - lower crust and confined to the fault zone.