Combination of geodetic observations and models for glacial isostatic adjustment fields in Fennoscandia

We demonstrate a new technique for using geodetic data to update a priori predictions for Glacial Isostatic Adjustment (GIA) in the Fennoscandia region. Global Positioning System (GPS), tide gauge, and Gravity Recovery and Climate Experiment (GRACE) gravity rates are assimilated into our model. The technique allows us to investigate the individual contributions from these data sets to the output GIA model in a self-consistent manner. Another benefit of the technique is that we are able to estimate uncertainties for the output model. These are reduced with each data set assimilated. Any uncertainties in the GPS reference frame are absorbed by reference frame adjustments that are estimated as part of the assimilation. Our updated model shows a spatial pattern and magnitude of peak uplift that is consistent with previous models, but our location of peak uplift is slightly to the east of many of these. We also simultaneously estimate a spatially averaged rate of local sea level rise. This regional rate (similar to 1.5 mm/yr) is consistent for all solutions, regardless of which data sets are assimilated or the magnitude of a priori GPS reference frame constraints. However, this is only the case if a uniform regional gravity rate, probably representing errors in, or unmodeled contributions to, the low-degree harmonic terms from GRACE, is also estimated for the assimilated GRACE data. Our estimated sea level rate is consistent with estimates obtained using a more traditional approach of direct "correction" using collocated GPS and tide gauge site

Impact of self-attraction and loading on Earth rotation

The impact of self-attraction and loading (SAL) on Earth rotation has not been previously considered except at annual timescales. We estimate Earth rotation excitations using models of atmospheric, oceanic, and land hydrology surface mass variations and investigate the importance of including SAL over monthly to interannual timescales. We assess SAL effects in comparison with simple mass balance effects where net mass exchanged with the atmosphere and land is distributed uniformly over the global ocean. For oceanic polar motion excitations, SAL impacts are important even though mass balance impact is minor except at the annual period. This is true of global (atmosphere + land + ocean) polar motion excitations as well, although the SAL impacts are smaller. When estimating length-of-day excitations, mass balance effects have a dominant impact, particularly for oceanic excitation. Although SAL can have a significant impact on estimated Earth rotation excitations, its consideration generally did not improve comparisons with geodetic observations. This result may change in the future as surface mass models and Earth rotation observations improve

Stochastic filtering for determining gravity variations for decade-long time series of GRACE gravity

We present a new stochastic filter technique for statistically rigorous separation of gravity signals and correlated “stripe” noises in a series of monthly gravitational spherical harmonic coefficients (SHCs) produced by the Gravity Recovery and Climate Experiment (GRACE) satellite mission. Unlike the standard destriping process that removes the stripe contamination empirically, the stochastic approach simultaneously estimates gravity signals and correlated noises relying on covariance information that reflects both the spatial spectral features and temporal correlations among them. A major benefit of the technique is that by estimating the stripe noise in a Bayesian framework, we are able to propagate statistically rigorous covariances for the destriped GRACE SHCs, i.e. incorporating the impact of the destriping on the SHC uncertainties. The Bayesian approach yields a natural resolution for the gravity signal that reflects the correlated stripe noise, and thus achieve a kind of spatial smoothing in and of itself. No spatial Gaussian smoothing is formally required although it might be useful for some circumstances. Using the stochastic filter, we process a decade-length series of GRACE monthly gravity solutions, and compare the results with GRACE Tellus data products that are processed using the “standard” destriping procedure. The results show that the stochastic filter is able to remove the correlated stripe noise to a remarkable degree even without an explicit smoothing step. The estimates from the stochastic filter for each destriped GRACE field are suitable for Bayesian integration of GRACE with other geodetic measurements and models, and the statistically rigorous estimation of the time-varying rates and seasonal cycles in GRACE time series

Dynamic adjustment of the ocean circulation to self-attraction and loading effects

The oceanic response to surface loading, such as that related to atmospheric pressure, freshwater exchange, and changes in the gravity field, is essential to our understanding of sea level variability. In particular, so-called self-attraction and loading (SAL) effects caused by the redistribution of mass within the land–atmosphere–ocean system can have a measurable impact on sea level. In this study, the nature of SAL-induced variability in sea level is examined in terms of its equilibrium (static) and nonequilibrium (dynamic) components, using a general circulation model that implicitly includes the physics of SAL. The additional SAL forcing is derived by decomposing ocean mass anomalies into spherical harmonics and then applying Love numbers to infer associated crustal displacements and gravitational shifts. This implementation of SAL physics incurs only a relatively small computational cost. Effects of SAL on sea level amount to about 10% of the applied surface loading on average but depend strongly on location. The dynamic component exhibits large-scale basinwide patterns, with considerable contributions from subweekly time scales. Departures from equilibrium decrease toward longer time scales but are not totally negligible in many places. Ocean modeling studies should benefit from using a dynamical implementation of SAL as used here

Concepts and terminology for sea level: mean, variability and change, both local and global

Changes in sea level lead to some of the most severe impacts of anthropogenic climate change. Consequently, they are a subject of great interest in both scientific research and public policy. This paper defines concepts and terminology associated with sea level and sea-level changes in order to facilitate progress in sea-level science, in which communication is sometimes hindered by inconsistent and unclear language. We identify key terms and clarify their physical and mathematical meanings, make links between concepts and across disciplines, draw distinctions where there is ambiguity, and propose new terminology where it is lacking or where existing terminology is confusing. We include formulae and diagrams to support the definitions

Using a spatially realistic load model to assess impacts of Alaskan glacier ice loss on sea level

Ice loss from glaciers results in highly nonuniform patterns of sea level change due to the effects of self-attraction and loading. To quantify these spatial effects, it is necessary to obtain an ice load model that is both spatially realistic and regionally complete. We demonstrate a technique to produce such a model for the Alaskan glaciers by combining mass balance rates from a Gravity Recovery and Climate Experiment (GRACE) mascon solution with realistic glacier geometries. This load model can be used to solve the “sea level equation” to determine gravitationally self-consistent sea level and gravity rates. The model predicts a significant drop in relative sea level in the near field of the glaciers, with coastal rates of around −9 mm/yr (compared to a global average rise of 0.2 mm/yr) and significant differences to those predicted by a coarser model. The magnitude and sensitivity of these near-field rates imply that the near-field tide gauge records could contain significant information about the spatial distribution of ice loss. Comparison of model gravity rates with an independently produced, spherical harmonic, GRACE solution verifies that our technique can successfully capture the mass changes estimated in the mascon solution within our higher-resolution model. Finally, we use our ice load model to examine the possibility of detecting the effects of ice loss in estimates of ocean bottom pressure (OBP) from GRACE. We use the model to simulate the effects of GRACE signal leakage and show that the OBP signal from leakage has a similar pattern to, but larger amplitude than, the sea level “fingerprint” expected from ice los

Effects of self-attraction and loading on annual variations of ocean bottom pressure

The impact of self-attraction and loading (SAL) on ocean bottom pressure xi, an effect not previously considered, is analyzed in terms of the mean annual cycle based on decade long estimates of changes in land hydrology, atmospheric pressure, and oceanic circulation. The SAL-related changes in xi occur as a result of deformation of the crust due to loading and self-gravitation of the variable fluid loads. In the absence of SAL, net freshwater input and changes in mean atmospheric pressure over the ocean give rise to a spatially constant xi annual cycle with an amplitude similar to 1-2 cm in equivalent water thickness. Consideration of SAL physics introduces spatial variations that can be significant, particularly around continental boundaries, where the amplitude of deviations can exceed 1 cm. For the spatial variability induced by SAL effects, changes in both land hydrology and atmospheric pressure are important. Effects related to the changing ocean circulation are relatively weaker, apart from a few shallow coastal regions. Comparisons with a few in situ, deep ocean observations indicate that for the most accurate xi estimates, one needs to consider spatially varying SAL-related signals, along with the effects of mean atmospheric pressure and net freshwater input into the oceans. Nevertheless, the most complete estimates, including also effects of ocean circulation, are able to account for only similar to 1/3 of the observed annual variances. Sources of the remaining contribution remain unclea