The glacial isostatic adjustment (GIA) signal at present day is
constrained via the joint inversion of geodetic observations and GIA
models for a region encompassing northern Europe, the British Isles,
and the Barents Sea. The constraining data are Global Positioning
System (GPS) vertical crustal velocities and GRACE (Gravity Recovery
and Climate Experiment) gravity data. When the data are inverted
with a set of GIA models, the best-fit model for the vertical motion
signal has a
Glacial isostatic adjustment (GIA) is the process by which the Earth's
crust and underlying mantle deform in response to surface loading and
unloading by large ice sheets and glaciers (e.g. Peltier and Andrews,
1976; Wu and Peltier, 1982). Glacial isostatic deformation at present day can include contributions from both recent (annual,
decadal) variations in ice cover as well as contributions from
millennial-scale variations in ice cover during Pleistocene and
Holocene glaciation cycles, although in this study GIA refers to the
latter paleo-signal, specifically from the last glaciation. Ongoing
GIA is usually the dominant present-day deformation signal in formerly
glaciated areas (for example, up to approximately
1
In Scandinavia, the GIA process has been studied extensively and constrained with data including relative sea-level indicators, Global Positioning System (GPS) measurements and satellite gravity data (e.g. Lambeck et al., 1998; Milne et al., 2001; Steffen et al., 2010; see also Steffen and Wu, 2011, for a review). While the GIA process in the region of the former Fennoscandian Ice Sheet is probably more extensively studied than anywhere else in the world, GIA in the Barents Sea is by comparison less well understood due in part to the lack of observational evidence left behind by a marine-based ice sheet. Auriac et al. (2016) provide a recent summary of GIA models in the Barents Sea region. Studies have also focussed on the smaller British Isles region, which experiences GIA deformation in response to deglaciation of both the local British Isles Ice Sheet and the larger adjacent Fennoscandian Ice Sheet (Bradley et al., 2011; Kuchar et al., 2012). The ice sheet evolution of the region as a whole was recently summarized by Patton et al. (2017). These studies and many others have provided valuable insight into regional GIA processes. The majority of GIA models are, however, forward models which can be limited by uncertainties in both the ice sheet model and Earth model. Furthermore, because a best-fit forward GIA model is generally a single Earth–ice model combination, their predictions of GIA deformations are typically provided without uncertainties.
This paper constrains the GIA signal in northern Europe through the simultaneous inversion of vertical land motion rates from GPS and gravity change rates from GRACE (Gravity Recovery and Climate Experiment). The semi-empirical method also estimates corresponding uncertainties for the preferred model(s), which, relative to forward model studies, is a notable advantage of semi-empirical or data-driven methodologies. Similar empirical and semi-empirical approaches have been implemented to estimate regional long-term GIA signals in Antarctica (Riva et al., 2009; Gunter et al., 2014), North America (Sasgen et al., 2012; Simon et al., 2017), Alaska (Jin et al., 2016), and Fennoscandia (Hill et al., 2010; Müller et al., 2012; Zhao et al., 2012). Here, our methodology is based on that of Hill et al. (2010); relative to their previous work, we update both the GPS and GRACE datasets, incorporate a second model ice sheet history into the a priori input, and expand the study area to include regions south and west of Scandinavia, including the British Isles, as well as the Barents Sea to the north. Rather than focus on model parameter estimation, we focus on the constraint on the GIA signal at present day. There are three main goals: (i) to model the paleo-GIA signal at present day in a continuous region between Scandinavia and the British Isles; (ii) to estimate empirically the uncertainty of the modelled signal; and (iii) to assess the importance of applying an elastic correction to the vertical land motion data.
Rates of vertical land motion measured by GPS are taken from both Kierulf
et al. (2014) and the Nevada Geodetic Laboratory (Blewitt et al., 2016)
(Fig. 1). The Kierulf et al. (2014) dataset has relatively dense coverage
within the region of the former load centre of the Fennoscandian Ice Sheet
(FIS), particularly in Norway, but sparse coverage elsewhere. The data from
Blewitt et al. (2016) are thus used for the region outside the former ice
sheet margin. The Kierulf et al. (2014) dataset has 150 stations with time
series lengths of at least 3 years. The data from Blewitt et al. (2016) span
1996–2016 and have been limited to sites which have at least 10 years of
data. To avoid spatial overlap of sites, the data from Blewitt et al. (2016)
have been additionally filtered to include only one site within
a 30
Rates of vertical land motion (
As further described in Kierulf et al. (2014), their rates were
derived using the GAMIT/GLOBK GPS analysis software (Herring
et al., 2011) and have uncertainties that assume a combination of
white noise and flicker noise, while the data from the Nevada Geodetic
Laboratory were calculated using the MIDAS trend estimator, an
algorithm that is less sensitive to discontinuities in GPS time series
(Blewitt et al., 2016). Although the processing technique differs for
each dataset, the two datasets are combined in order to achieve the
best possible spatial coverage in the study area. Common sites in the
two datasets compare within the observational uncertainties at all but
2 of 31 sites, and no apparent bias is observed between the
differences at the shared sites (Fig. A1). Because the uncertainties
are consistently larger for the data from the Nevada Geodetic
Laboratory than for the data from Kierulf et al. (2014), we use the
common sites to determine an average uncertainty scaling factor (
The GRACE data are processed as in Simon et al. (2017). Rates of
gravity change for a 10.5-year period from February 2004 to June 2014
are estimated using 113 GRACE Release-05 (RL05) monthly solutions from
the University of Texas at Austin Center for Space Research (CSR). The
coefficients are truncated at degree and order 96. Part of the GIA
signal may also be lost during the filtering, particularly at higher
orders; the typical spatial resolution of the signal is
Changes in terrestrial hydrology as well as present-day ice mass loss from Greenland and glaciers and ice caps in Svalbard, the Russian Arctic, and Scandinavia may form a significant contribution to the total measured gravity change and vertical motion rates within the study area.
In the continental region and south of approximately 71.5
Estimates of present-day mass changes in Scandinavia, the Russian
Arctic, and Svalbard are summarized in Table 1 for various studies,
and vary considerably depending on estimation method and time
period. Ice mass loss in Scandinavia originates from glaciers in
western Norway and is consistently small with estimated rates between
In the Russian Arctic, glaciological estimates of mass change are
consistent within uncertainties for the different time periods and
suggest mass change between
In Svalbard, estimated mass change rates are more discrepant. Again,
glaciological estimates are the largest, but two estimates of
Estimates of present-day mass change for Svalbard, the Russian
Arctic, and Scandinavia for different time periods and from different
sources. Letters in parentheses indicate estimation method: gl –
glaciological; I – IceSat; G – GRACE; C – CryoSat. All rates are in
GRACE measures total mass changes (solid Earth plus cryosphere), and
thus a correction for one needs to be applied in order to isolate the
other. While the glaciological values and the altimetry estimates
(which are corrected for crustal uplift due to GIA) are both intended
to represent changes to the cryosphere, the differing mass change
estimates among measurement techniques for the Russian Arctic and
Svalbard raise the question of which value to use when applying
a correction to the total GRACE trend shown in Fig. 2a. Relative to
GRACE, the glaciological and altimetry methods both consistently infer
larger mass losses, suggesting that GRACE contains a significant mass
gain signal from the solid Earth, either from glacial isostatic
adjustment from the last glaciation or from the Little Ice Age
(LIA). For both Svalbard and the Russian Arctic, we choose to apply an
estimate that averages the ICESat and CryoSat estimates over the
years 2003–2014 (Table 1). Subtracting these averaged rates from the
total GRACE estimates for a similar time period (2003–2013; Schrama
et al., 2014; Table 1) infers a reasonably consistent total solid
Earth or GIA signal of
However, applying the averaged ice melt corrections to Svalbard and the Russian Arctic creates a large mass gain signal over these two areas and a relatively smaller signal in the central Barents Sea; this pattern is generally inconsistent with ice coverage in the Barents Sea region suggested by several different Pleistocene ice sheet reconstructions (Auriac et al., 2016), and it is therefore inconsistent with the paleo-GIA signal that the input signal should represent. Possible explanations for this inconsistency are as follows: (i) models of LGM ice cover in the region require thicker ice over Svalbard and the Russian Arctic than in the Barents Sea; (ii) there is a large Little Ice Age GIA signal over these two regions; and/or (iii) the Wiener filter applied to the GRACE data too aggressively filters signal in these small regions. The first explanation is unlikely because glacial margin chronology suggests that Svalbard and the Russian Arctic were located on or near the margin of the Barents Ice Sheet where ice cover would have been thinnest. To counteract the effect of either of the latter two explanations (LIA rebound or signal loss in GRACE), we apply ad hoc scaling factors of 0.25 and 0.2 to the ice mass loss estimates in Svalbard and the Russian Arctic (Table 1), so that their removal from the total GRACE signal results in a spatial pattern in the residual (i.e. paleo-GIA) signal that is approximately consistent with thicker LGM ice cover over the Barents Sea than around its margins (Fig. 2e). Such a scaling factor approach is certainly not ideal but serves to provide a GRACE input signal in the Barents Sea region that has a spatial pattern broadly consistent with expectations of the paleo-GIA response to loading and unloading from the Barents Ice Sheet.
GPS-measured rates of vertical land motion before and after
the applied elastic correction (
Vertical land motion rates may likewise be affected by present-day ice
mass loss and the terrestrial hydrology cycle. As with the GRACE data,
the GPS data are corrected for changes to terrestrial hydrology south
of 71.5
Finally, in addition to present-day ice mass loss signals,
a correction of 4.33
Last Glacial Maximum (LGM) ice cover in Scandinavia, the
Barents Sea, and the British Isles from ICE-5G
The prior model covariance matrix contains predictions from a set of forward GIA models that varies ice sheet history and mantle viscosity and is constructed as described in Hill et al. (2010) and Simon et al. (2017). Here, two different ice sheet histories are coupled to a suite of three-layer Earth models with an elastic lithosphere and varying upper and lower mantle viscosities.
The first ice sheet model is the global ICE-5G model (Peltier, 2004). We later compare the data-driven predictions to the more recent ICE-6G forward model (Peltier et al., 2015) (Sect. 3.3); without ICE-6G in the a priori information, the compared predictions are independent to the extent possible. In the second ice sheet model, the glacial history over Fennoscandia and the British Isles is described by the model(s) from the Australian National University (ANU; Lambeck et al., 2010). This second version of the ice sheet model contains ICE-5G coverage over Greenland and Antarctica and the model of North American coverage presented in Simon et al. (2015, 2016). Tests indicate that varying the ice sheet history over North America has little impact on the predictions in Fennoscandia, although this variation is useful for studies that wish to expand the study area outside of the current study area. Relative to ICE-5G, LGM ice cover in the ANU model is thinner over the Barents Sea, thicker over Svalbard and Scotland, and discontinuous between Scandinavia and the British Isles (Fig. 4).
Previous GIA modelling studies can be used to infer a range of
reasonable Earth model parameters for the a priori model set. Steffen
and Wu (2011) reviewed the results of several GIA modelling studies of
the Fennoscandian region and indicated that these analyses suggest
regional upper mantle viscosities of between 0.1 and
Averaged a priori rates of the Earth–ice model
set.
Prediction of present-day vertical land motion
Considering these three regions as a whole gives minimum to maximum
ranges for upper and lower mantle viscosity and lithospheric thickness
of 0.2–
The least-squares adjustment method is based on the methodology of Hill et al. (2010) and extended by Simon et al. (2017). The method simultaneously inverts the data constraints (GPS, GRACE, or both) with the a priori GIA model information and minimizes the misfit to both input types. As in Simon et al. (2017), variance component estimation (VCE) is also used to weight the input uncertainties. The prior models are combined with the data in three scenarios: inversion with the GPS data alone (D1), inversion with the GRACE data alone (D2), and inversion with both datasets (D3).
The predicted GIA response and uncertainties for the D1–D3 scenarios
are shown for vertical land motion (Fig. 6). The incorporation of the
GPS data in scenarios D1 and D3 leads to a similar pattern of regional
uplift although relative to D1, the D3 scenario predicts slightly
lower rates of uplift over the northern British Isles and in the
Barents Sea. D1 and D3 have respective peak uplift rates of 9.8 and
9.2
The predicted gravity change rates for D1–D3 are comparable to the
predicted vertical motion rates in both the spatial pattern and
relative magnitude (not shown). The peak mass change rates are again
centred over the northern Gulf of Bothnia, and are 33.7, 24.3, and
32.3
Results of the variance component analysis.
For both
Fractional
Figures 8 and 9 summarize the spatial residuals for the best-fit D3 model and the binned residuals for all models. The vertical motion residuals are unbiased and generally small. Regionally, the D3 model underpredicts vertical motion in Scotland and conversely overpredicts vertical motion along parts of the southern Norwegian coast and the Netherlands. The gravity residuals for D3 are relatively low for much of the study area, although there is noticeable overprediction in central Scandinavia and in the Barents Sea.
Spatial residuals for the D3 model for vertical motion
Histogram of residuals for models D1–D3, for prediction of
vertical motion
We compare the vertical motion prediction of D1 to two other models. The first model is the forward GIA model ICE-6G (Peltier et al., 2015), which is constrained by a global dataset of vertical land motion measurements. The majority of the these data are GPS measurements from the global solution of JPL; within the study area of Scandinavia and northern Europe, additional measurements come from the BIFROST GPS network as well as a small number of satellite laser ranging (SLR), Doppler orbitography and radiopositioning integrated by satellite (DORIS), and very long baseline interferometry (VLBI) measurements (Argus et al., 2014; Peltier et al., 2015). The second model is the semi-empirical land uplift model NKG2016LU (Vestøl et al., 2016) designed by several researchers in collaboration with the Nordic Geodetic Commission (NKG). This model is constrained with GPS-measured vertical land motion rates updated from the dataset of Kierulf et al. (2014), levelling measurements, and GIA model predictions and provides a semi-empirical estimate of total present-day vertical land motion.
Figure 10 compares the vertical land motion predictions of D1, ICE-6G, and
NKG2016LU. The ICE-6G comparison is made relative to the vertical motion
dataset presented in this paper, although as stated above, it was constrained
with a different variant of regional vertical land motion data. In addition,
NKG2016LU predictions are available on a smaller grid and provide the
best fit to data from Scandinavia and the Baltic countries; thus, we limit our comparison with this
model to north of 55
With no significant bias and a
Spatial
To assess the effect of GIA on regional sea-level change, we remove
model D1's predictions of long-term GIA from mean sea-level trends at
13 tide gauge sites along the coast of the North Sea and 7 tide gauge
sites along the Norwegian coast (Figs. 11 and 12). The sea-level
trends are taken from Frederikse et al. (2016), who estimated the rates
at Permanent Service for Mean Sea Level (PSMSL) sites over the time
interval 1958–2014. We also compare the effect of removing the
modelled relative sea-level rates of ICE-6G at the same PSMSL
locations. For both the North Sea and the Norwegian coastline,
application of the D1 long-term sea-level trends to the total
sea-level trends reduces the interstation variability and infers
a similar rate of non-GIA sea-level change (1.89 and
1.84
When corrected for the D1 long-term GIA trends, which are assumed to be
linear over decadal timescales, the standard deviation (SD) of the trends decreases somewhat from 0.81 to
0.71
Comparison of mean total, long-term GIA, and non-GIA sea-level trends (grey boxes, triangles, circles) for 13 tide gauge stations in the North Sea. Long-term GIA trends are from model D1 and ICE-6G; mean sea-level trends are from Frederikse et al. (2016).
The average sea-level trend for the seven sites along the Norwegian coast
is
Same as caption for Fig. 11, except for tide gauge locations along the Norwegian coastline.
We generate a data-driven prediction of the long-term GIA response at present
day in Scandinavia, northern Europe, and the Barents Sea through the
simultaneous inversion of GPS-measured vertical motion rates, GRACE-measured
gravity change rates, and a priori GIA model information. In models D1–D3,
we predict GIA motions for the inversion of the vertical motion data, the
gravity data, and both datasets. In both the
In general, prediction of the gravity signal is problematic, with
larger
The vertical motion signal is overall better predicted than the
gravity signal. Both the D1 and D3 models have
The prediction of vertical land motion has a small but non-negligible
sensitivity to the application of an elastic correction. The elastic
correction applied in this study is between
0.2 and 0.5
Therefore, the presence of such a difference in the vertical motion prediction suggests that while long-term GIA is the dominant contributor to vertical motion in central Scandinavia, it is still worthwhile correcting GPS land motion rates for present-day elastic signals, so long as these signals are adequately approximated (e.g. Riva et al., 2017). This conclusion, however, highlights a fundamental assumption that underpins the data-driven methodology: that the input data can be adequately “cleaned” for processes not arising from long-term GIA. Even with applied corrections for hydrology and contemporary ice mass loss, this assumption may not always be adequate, especially in regions where model misfits relative to the data are spatially coherent. Thus, the success of data-driven GIA predictions is evaluated by two criteria: (i) the estimation of realistic a posteriori uncertainties that are smaller than those associated with a priori knowledge and measurement uncertainty and (ii) the ability of the final model to provide a good fit to the data. The vertical motion predictions of models D1 and D3 satisfy both criteria for most of the study area and can thus provide a useful tool with which to separate long-term GIA signals from shorter-term forcing.
Gridded vertical land motion predictions for the D1 model
are available at the 4TU Centre for Research Data repository:
The 31 GPS measurements that are common to the Kierulf et al. (2014) and Nevada Geodetic Laboratory (Blewitt et al., 2016) datasets are shown in Fig. A1. The individual anthropogenic hydrology and glacial mass change contributions to the GRACE correction are shown in Fig. A2.
Vertical land motion measurements at 31 sites common to both datasets used in this study.
Individual and combined contributions to the correction applied to the GRACE data (combined is the same as Fig. 2c).
The authors declare that they have no conflict of interest.
We would like to thank Anthony Purcell for providing the ANU ice sheet model for Europe and the British Isles, Yoshihide Wada for making the PCR-GLOBWB hydrology model available, and Bert Wouters for providing altimetry estimates of recent mass loss for Svalbard and the Russian Arctic. We also thank two anonymous reviewers for comments that improved the manuscript. This work is part of the project for a Multi-Scale Sea-Level model (MuSSeL), funded by the Netherlands Organization for Scientific Research, VIDI Grant No. 864.12.012. Edited by: Simon McClusky Reviewed by: two anonymous referees