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

Estimating the sea-level highstand during the last interglacial: a probabilistic massive ensemble approach

Essential to understanding sea-level change and its causes during the last interglacial is the quantification of uncertainties. In order to estimate the uncertainties, we develop a statistical framework for the comparison of paleao-climatic sea-level index points and GIA model predictions. For the investigation of uncertainties, as well as to generate better model predictions, we implement a massive ensemble approach by applying a data assimilation scheme based on particle filter methods. The different runs are distinguished through varying ice sheet reconstructions based on oxygen-isotope curves and different parameter selections within the GIA model. This framework has several advantages over earlier work, such as the ability to examine either the contribution of individual observations to the results or the probability of specific input parameters. This exploration of input parameters and data leads to a larger range of estimates than previously published work. We illustrate how the assumptions that enter into the statistical analysis, such as the existence of outliers in the observational database or the initial ice volume history, can introduce large variations to the estimate of the maximum highstand. Thus, caution is required to avoid over-interpreting results. We conclude that there are reasonable doubts whether the datasets previously used in statistical analyses are able to tightly constrain the value of maximum highstand during the last interglacial (LIG)

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

On seasonal signals in geodetic time series

We explore implications for modeling and noise analysis of stochastic seasonal processes of climatic origin in geodetic time series. Seasonal signals are generally modeled as sinusoids with annual periods (and harmonics thereof), each with constant amplitude and phase. However, environmental noise that underlies the seasonal signal in geodetic time series has a reddened power spectral density (PSD). We investigate the form of the PSD of a time series having a stochastic seasonal component and find that for frequencies greater than the nominal seasonal frequency, the PSD of the time series reflects the PSD of the seasonal amplitudes. For example, if the PSD of the seasonal amplitudes can be expressed as an inverse power law, then the PSD of the time series will behave as an inverse power law for high frequencies. Stochastic seasonal variability will also induce a peak near the nominal seasonal frequency in addition to that of the mean seasonal signal and will be relatively flat below this frequency. It is therefore possible that some of the noise in Global Navigation Satellite Systems (GNSS) time series reported by others may be associated with neglecting the stochastic component of the seasonal signal. We use a GNSS time series from site ZIMM as an example to demonstrate the existence of a variable seasonal signal (without attributing its cause), and we use an example Gravity Recovery and Climate Experiment (GRACE) time series from Alaska to demonstrate that use of a nonstochastic seasonal model can have a significant impact on the value and uncertainty of time-variable rates estimated from the time serie

Weighing the ocean: Using a single mooring to measure changes in the mass of the ocean

Combining ocean and earth models, we show that there is a region in the central Pacific ocean where ocean bottom pressure is a direct measure of interannual changes in ocean mass, with a noise level for annual means below 3 mm water equivalent, and a trend error below 1 mm/yr. We demonstrate this concept using existing ocean bottom pressure measurements from the region, from which we extract the annual cycle of ocean mass (amplitude 8.5 mm, peaking in late September), which is in agreement with previous determinations based on complex combinations of global data sets. This method sidesteps a number of limitations in satellite gravity-based calculations, but its direct implementation is currently limited by the precision of pressure sensors, which suffer from significant drift. Development of a low-drift method to measure ocean bottom pressure at a few sites could provide an important geodetic constraint on the earth system

The moving boundaries of sea level change: understanding the origins of geographic variability

As ice sheets gain or lose mass, and as water moves between the continents and the ocean, the solid Earth deforms and the gravitational field of the planet is perturbed. Both of these effects lead to regional patterns in sea level change that depart dramatically from the global average. Understanding these patterns will lead to better constraints on the various contributors to the observed sea level change and, ultimately, to more robust projections of future changes. In both of these applications, a key step is to apply a correction to sea level observations, based on data from tide gauges, satellite altimetry, or gravity, to remove the contaminating signal that is due to the ongoing Earth response to the last ice age. Failure to accurately account for this so-called glacial isostatic adjustment has the potential to significantly bias our understanding of the magnitude and sources of present-day global sea level rise. This paper summarizes the physics of several important sources of regional sea level change. Moreover, we discuss several promising strategies that take advantage of this regional variation to more fully use sea level data sets to monitor the impact of climate change on the Earth syste