Detecting a forced signal in satellite-era sea-level change

In this study, we compare the spatial patterns of simulated geocentric sea-level change to observations from satellite altimetry over the period 1993–2015 to assess whether a forced signal is detectable. This is challenging, as on these time scales internal variability plays an important role and may dominate the observed spatial patterns of regional sea-level change. Model simulations of regional sea-level change associated with sterodynamic sea level, atmospheric loading, glacier mass change, and ice-sheet surface mass balance changes are combined with observations of groundwater depletion, reservoir storage, and dynamic ice-sheet mass changes. The resulting total geocentric regional sea-level change is then compared to independent measurements from satellite altimeter observations. The detectability of the climate-forced signal is assessed by comparing the model ensemble mean of the ‘historical’ simulations with the characteristics of sea-level variability in pre-industrial control simulations. To further minimize the impact of internal variability, zonal averages were produced. We find that, in all ocean basins, zonally averaged simulated sea-level changes are consistent with observations within sampling uncertainties associated with simulated internal variability of the sterodynamic component. Furthermore, the simulated zonally averaged sea-level change cannot be explained by internal variability alone—thus we conclude that the observations include a forced contribution that is detectable at basin scales.


Introduction
During the altimetry period  global mean sea level (GMSL) has been rising at a rate of about 3 mm yr −1 (WCRP Global Sea Level Budget Group 2018). This is about double the rate of 20th century GMSL rise, depending on the tide-gauge based reconstructions used White 2011, Ray andDouglas 2011, Jevrejeva et (Dieng et al 2017, Legeais et al 2018 agrees with the sum of the observed contributions (WCRP Global Sea Level Budget Group 2018), as well as with the sum of simulated contributions from CMIP5 climate models (Slangen et al 2017).
Over the altimetry period, GMSL rise is about 40% due to thermal expansion (i.e. 'global-mean thermosteric sea-level rise') and 60% due to mass contributions (changes in land ice and terrestrial water storage, i.e. 'barystatic sea-level rise') (WCRP Global Sea Level Budget Group 2018, Gregory et al 2019). The spatial pattern of change, however, is mainly related to ocean dynamic sea-level change, which dominates over the barystatic fingerprints (e.g. Spada and Galassi 2016) that result from changes in Earth gravity, rotation and viscoelastic solid-Earth deformation (GRD, Gregory et al 2019) due to shrinking land ice from glaciers and ice sheets as well as changes in terrestrial landwater storage.
Several studies have shown that the total GMSL change (Dangendorf et al 2015, Slangen et al 2016 as well as the component contributions (Marcos and Amores 2014, Slangen et al 2014 are partly driven by external climate forcings (e.g. increasing greenhouse gas concentrations). These studies usually consider time periods of at least 40 years or more. Detecting a forced trend in sea level becomes more challenging on smaller space-and shorter time-scales as regional modes of internal variability have a larger influence on sea level at these scales. Here, we refer to internal variability as sea-level changes originating from inherent climate variability, particularly in the coupled ocean-atmosphere system. This includes climate modes such as El Nino-Southern Oscillation (ENSO), Pacific Decadal Oscillation and North Atlantic Oscillation (e.g. Roberts et al 2016). Conversely, a forced signal is related to external drivers, both natural (e.g. volcanic eruptions) as well as anthropogenic (e.g. greenhouse gas emissions).
The large contribution of internal variability in sterodynamic sea-level change (changes in ocean density and circulation) complicates the detection of a forced regional sea-level signal on decadal time scales. Richter et al (2017) showed that extensive spatial averaging is necessary to detect a forced signal in sterodynamic sea-level change for period lengths similar to the altimetric record (i.e. 25 years). To assess whether a forced signal can be detected regionally in total sea level over this short period of time, we compare the simulated total sea-level trend patterns with the observed trends from altimetric observations over the period 1993-2015 while also taking simulated internal variability into account.
The dataset used in our analysis originates from two recent studies that compared global and regional sea-level change as observed and derived from tide gauges with model-simulated changes over the 20th century (Slangen et al 2017, Meyssignac et al 2017a) Meyssignac et al (2017a showed that observed (coastal) multidecadal variability is well reproduced by the model ensemble and mainly originates from the sterodynamic sea-level contribution. We will therefore focus on the sterodynamic contribution when quantifying internal variability.

Data and methods
The data sets used in this study are described in detail by Slangen et al (2017) and Meyssignac et al (2017a). This section summarizes the most important methodological details. Regional sea-level change was estimated using output from 12 climate models (supplementary material, table 1) contributing to phase 5 of the Climate Model Intercomparison Project (CMIP5, Taylor et al 2012) over the period 1900-2015. The output of the climate model simulations was used to calculate the components of sea-level changes associated with sterodynamic sea level, atmospheric loading, glacier mass changes, and ice-sheet surface mass balance contributions. The contribution from groundwater depletion, reservoir storage, and dynamic ice-sheet mass changes was estimated from observations as they are not simulated by climate models.
Annual mean values were computed from the monthly mean output from CMIP5 historical simulations (1993-2005 here) and the Representative Concentration Pathway 8.5 scenarios (RCP8.5, 2006(RCP8.5, -2015. The choice of CMIP5 scenario and models was based on maximum data availability to ensure a consistent model dataset. We note that RCPs remain similar during the first part of the 21st century, and our results are not sensitive to the choice of RCP. Ocean dynamic sea level was taken directly from the CMIP5 models. As most models employ the Boussinesq approximation and conserve volume rather than mass, the global mean was removed from those fields. Global-mean thermosteric sealevel change was then obtained from integrating the three-dimensional temperature field using the United Nations Educational, Scientific and Cultural Organization (UNESCO) 1980 international equation of state (IES80). Combining dynamical sea level with the global thermosteric change gives the total sterodynamic sea-level change.
Changes in atmospheric mass and surface pressure distribution result in regional sea-level changes. Those changes have been computed using CMIP5 data, following Stammer and Hüttemann (2008). Though small over most of the ocean area, they can make a significant contribution regionally.
Glacier mass change and the SMB contribution from the ice sheets are derived from model output as follows. The glacier model by Marzeion et al (2012) is forced with CMIP5 temperature and precipitation to model the SMB of the worlds glaciers while taking changes in hypsometry into account. Greenland SMB is computed by forcing the regional climate model MAR with CMIP5 temperature and precipitation from the extended historical CMIP5 simulations (Fettweis et al 2013, Meyssignac et al 2017b. The Antarctic SMB is computed as the average of two estimates: the first method approximates the SMB from the CMIP5 change in precipitation minus evaporation in each model over the Antarctic ice sheet, scaled to fit the best estimate of the Antarctic SMB for the period 1985-2010 from the regional climate model RACMO2.1 forced by ERA-Interim reanalysis data (Lenaerts et al 2012). The second method assumes a linear relationship between the SMB change and CMIP5 Antarctic surface temperature of 6% K −1 , consistent with observations of the last deglaciation based on ice-core data (Frieler et al 2015). Both methods yield similar results over the 20th century.
For the contribution from ice-sheet mass changes due to dynamic ice flow, we use the estimate by Shepherd et al (2012) from 1992 to 2011. The ice dynamical time series are then extended to 2015 using the assumption that the West Antarctic discharge was slightly above the 2008-2012 average (Sutterley et al 2014) according to a constant mass loss rate, the East Antarctic and Antarctic Peninsula discharge followed the 2001-2010 average, and the Greenland ice sheet discharge was constant at the 2010 value (Enderlin et al 2014).
As with the dynamical ice-sheet mass change, the sea-level contribution from groundwater depletion and reservoir storage is not represented in the climate models used in this study and is therefore based on observations. The groundwater contribution was taken from Döll et al (2014), while the contribution from artificial reservoirs was taken from Chao et al (2008). The latter data was available until 2008. The average rate of the last 5 years of available data was used thereafter to extend the data to 2015.
The regional sea-level changes associated with the transfer of mass between ocean and land described above (i.e. changes in land ice and landwater storage) were computed using the average of two different sealevel equation solvers. One is based on an updated version of SELEN (Spada et al 2012) and the other one on Schotman (2008). Both include the effects of Earth rotation. In contrast to Slangen et al (2017) and Meyssignac et al (2017a), geocentric instead of relative GRD fingerprints were computed in order to compare modelled sea level with altimetric (geocentric) sea level.
Lastly, we account for the ongoing response of the sea surface to the last deglaciation (glacial isostatic adjustment, GIA). As before, we are interested in geocentric instead of relative sea-level changes. Therefore, we only include the present-day rate of sea-surface variation (e.g. Tamisiea 2011, Spada 2017 as provided by Peltier (2004). The model uses the ICE-5G ice chronology and includes the feedback on sea level caused by Earth rotation. Note that the GIArelated geocentric sea-level trend patterns are very different from their relative sea-level counterpart (compare e.g. Figures 2(a) and (c) in Spada 2017) with opposite sign in regions close to the former ice sheets.
Observed sea-level anomalies were obtained from the European Space Agency (ESA) sea level climate change initiative (http://www.esa-sealevel-cci.org). The data set covers the period 1993-2015 and merges all the available altimeter measurements together on a regular grid with a ¼ • spatial resolution (Quartly et al 2017, Legeais et al 2018. Model simulations as well as observations have been re-gridded to a regular 1 × 1 • grid using bilinear interpolation. Internal variability is expected to govern spatial patterns of sea-level change at decadal time periods through ocean dynamic processes. Internal variability in free running coupled climate models is not constrained to be in phase among models or with observations. Thus, by taking the multi-model ensemble mean over 12 climate models, we are able to reduce the internal variability and better isolate the forced signal common to all models. Additionally, the magnitude and spatial pattern of internal variability in sterodynamic sea-level change is quantified for each model by computing linear trends over running 20-year periods for each grid box using the last 500 years (if available) of the fixed-forcing pre-industrial control simulation of each model. We characterise the trends that could be induced by internal variability using the 5th and 95th percentile of the resulting trend distribution and compare these percentiles to observed and ensemble-mean trends in total sea level over the period 1993-2015.
In this way, we assess whether the observed trends lie within the range of simulated sterodynamic sea-level trends expected from internal variability .

Results
In this section, we compare observed and simulated regional trends in total sea-level change, and subsequently present the individual simulated contributions and their characteristics.
The observed trend in GMSL over 1993-2015 is 2.91 ± 0.34 mm yr −1 while the multi-model mean trend is 2.70 ± 0.43 mm yr −1 (figure 1). The spatial variability in the observed trend pattern is much higher than in the multi-model mean (spatial standard deviation of 1.90 vs 0.58 mm yr −1 ; table 1) because the internal variability is strongly reduced due to the averaging over 12 models. The spatial standard deviation of the total trend pattern based on the individual models is closer to the observed value (table 1, last column) but still underestimates the spatial variability (though within uncertainties). Common to the observed and simulated trend pattern is a larger than average rise in the mid-latitude of the western south Atlantic Ocean, east of Australia in the southern Pacific Ocean and southwest of Greenland. The spatial pattern of the residual sea-level change (observed minus modelsimulated, figure 1(c)) is dominated by the observed pattern, with similar spatial variability (table 1). Over about three quarters (73%) of the world's oceans, the residual sea-level trends are within the range of internal variability in sterodynamic height, with notable exceptions in the eastern and western tropical Pacific Ocean, the southern Indian Ocean, as well as  Global mean sea-level trends for contributions and total sea level, spatial standard deviation of regional trend pattern for ensemble mean and mean over standard deviation of regional trend pattern from individual models (for simulated contributions). The uncertainty (in brackets) represents the standard deviation of the multi-model mean for the modelled estimates and is taken from WRCP 2018 for the observations. GSMB/ASMB Greenland/Antarctic surface mass balance, GIA glacial isostatic adjustment.

Standard deviation of
Mean over standard deviation Global mean (mm/yr) (ensemble-mean) regional of regional trend pattern for The sterodynamic contribution represents the largest global contribution and dominates the spatial variability (figure 2 and table 1) away from the sources of changing land ice in the polar regions. The ensemble mean (figure 2(a)) shows distinct spatial features, e.g. a large positive sea-level trend anomaly in a zonal band between 30-60 • S and a smaller than average trend south of 60 • S. A larger than global-average sea-level rise is also simulated in the northern North Atlantic region. Similar to the total trend patterns, the spatial variability of the sterodynamic ensemble mean (figure 2(a)) is less than half the spatial variability of the observed sea-level trend pattern (table 1). A strong reduction is to be expected as the internal variability partly averages out in the ensemble mean. The spatial variability of individual models (fourth column in table 1) is closer to the observed variability but still underestimates it. This may be because climate models do not represent mesoscale eddies which tend to enhance sterodynamic sea-level variability (e.g. Penduff et al 2010).
Glacier mass change and ice sheet dynamics constitute the second and third largest contributions to GMSL rise for the period 1993-2015. However, they contribute little to the spatial variations, except close to the changing ice masses in the polar regions. In contrast, GIA and changes in atmospheric mass loading contribute little to GMSL change but have a slightly larger effect on regional sea-level trends. The latter shows a distinct sea-level rise in the Southern Ocean along the coast of Antarctica. The regional variability of the ice sheet SMB and landwater contributions (reservoir storage and groundwater extraction) are an order of magnitude smaller than the sterodynamic contributions. Their global contributions are, however, not negligible.
Except for the polar regions, most of the simulated variability in zonally averaged sea level originates in the sterodynamic contribution while the other components contribute fairly evenly to the trend across latitudes (figure 3). In particular, the GRD fingerprints tend to represent broad spatial scales away from the source regions of ice melt. The signature of the western boundary currents is still present in the Atlantic Ocean just north of 40 • N and at 40 • S. In the Pacific Ocean, the variability is strongly reduced through the zonal averaging with a minimum just south of 20 • N. The GRD effects lead to a reduced sealevel contribution of land ice in the polar regions: the relative importance of glacier mass change decreases significantly from the equator towards the Arctic (Antarctic peripheral glaciers are not considered), while the dynamic ice loss primarily from the Antarctic ice sheet leads to reduced trends in the Southern Ocean. GIA (geocentric part only) decreases sea level particularly in the North Atlantic as well as in the southern Indian Ocean.
Compared to the observed trends there is relatively little latitudinal variation in the simulated trends of zonally averaged sea-level change (bold black versus red line in figure 4). For the global ocean, simulated and observed zonally-averaged sea-level trends agree well, and are both outside of what would be expected from the 90% confidence interval of the simulated internal variability in sterodynamic sea level (grey envelope), except in the polar regions. The same holds for individual ocean basins (figures 4(b)-(d)) at most latitudes, confirming the presence of a forced signal in zonally averaged total sea-level change, globally as well as basin-wide.
Residual (the difference between the observed and modelled, thin lines in figure 4) trends are mostly within the range of internal variability. Simulated and observed sea-level trends agree best in the South Atlantic Ocean. The largest disagreement is found in a narrow band in the North Pacific Ocean associated with the Kuroshio extension and in a broad stretch in the Southern Indian Ocean where simulated and observed zonal trends disagree by up to 3 mm yr −1 and the difference cannot be attributed to internal variability in sterodynamic sea level.
To test whether the forced signal originates from the GMSL rise, we removed the latter from the zonally averaged trends (figure 5). Except for localized regions in the subtropical North Pacific and southern Indian Ocean, observed as well as simulated zonal trend anomalies with respect to GMSL mostly lie within the range of internal variability. That is, the bulk of the forced signal is from the GMSL rise and regional variations in the forced signal are not detectable above the natural variability over the period 1993-2015. The spread around the ensemble mean is within the range of internal variability over the preindustrial period with an exception in the mid-latitude South Atlantic Ocean.
The analysis presented in this study has been carried out over the altimetry period 1993-2015. Recent literature has shown that the altimetry observations are subject to a bias/instrument drift in the early period during the TOPEX A mission (Watson et al 2015, Dieng et al 2017, Beckley et al 2017. We therefore repeated the analysis for the shorter period 1998-2015 thus excluding the TOPEX A data (supplementary material, figures 1-4 (available online at stacks.iop.org/ERL/15/094079/mmedia)). Over this shorter period of time, the discrepancy between the ensemble mean and the observations is larger as internal variability is even stronger in the observations. However, the general result is essentially the same: simulated as well as observed trends are larger than trends potentially generated from ocean internal variability.

Discussion
We found that the simulated spatial variability of regional sea-level trends over the period 1993-2015 is dominated by the sterodynamic contribution. Over 73% of the ocean area (unhatched area in figure 1(c)), the residual sea-level trends are within the range of estimated internal variability. This corresponds to 84% of the data (which is on a 1 × 1 • grid, such that the area represented by one grid point depends on the latitude), thus the disagreement constitutes only slightly more than would be expected from a 90% confidence interval (internal variability is defined as 5th to 95th percentile range). However, the individual models agree on the location of the disagreement (supplementary material figure 5) between residual sea-level trends (figure 1(c)) and internal variability. This leads to the conclusion that the disagreement is not due to pure chance but to either the inability of the models to simulate internal variability properly in some locations (mostly the tropical Pacific) or to some missing external forcing (see below).
Observed regional trends are strongly governed by internal variability over such a short time period. In this study, only internal variability originating from sterodynamic sea level is taken into consideration. Note that on the relatively short time scale considered here (decadal to just multi-decadal), internal variability generated in the ocean and the climate system is expected to be the dominant contribution to the spatial variability of sea-level change (Little et al 2015).
Regional sea-level residuals are unlikely to be explained by changes in the mass transfer between land and ocean because of the large spatial scales of the associated GRD fingerprints (Spada and Galassi 2016). In the regions of the western boundary currents, mesoscale-eddy activity can give rise to regional sea-level trends of several mm/yr (Sérazin et al 2016) on multi-decadal time scales. This variability comes in addition to the internal variability simulated by climate models, as mesoscale eddies are not resolved by the current CMIP5 climate models (for the representation of internal variability in individual models see e.g. Landerer et al 2014, Palmer et al 2018. The two distinct regions that show residuals that cannot be accounted for by simulated internal variability in sterodynamic sea level are the western tropical Pacific Ocean and the southern Indian Ocean. Typically, ENSO dynamics cause a see-saw trend pattern in the tropical Pacific with large sea-level rise in the western part and simultaneous sea-level drop in the eastern part and vice versa. However, the large observed sea-level rise in the western tropical Pacific Ocean cannot be accounted for by the combination of a forced signal (figure 1(b)) and internal variability in dynamic sea level. Decadal variability in the tropical Pacific Ocean is not reproduced by the models adequately (Bilbao et al 2015) possibly as a result of inaccurate representation of realistic wind forcing.
The misrepresentation of variability in the Pacific region might also inhibit the correct simulation of the large sea-level rise in the southern Indian Ocean. Indian Ocean sea level is subject to strong decadal variability that is governed by changes in wind stress and by changes in the Indonesian Throughflow (Han et al 2014), and therefore tightly related to changes in the tropical Pacific Ocean. Heat transport from the Pacific to the Indian Ocean started to increase abruptly in the late 1990s and is also linked to anomalous wind patterns during that period (Lee et al 2015).
Zonal averaging of regional sea level reduces the signature of internal variability associated with largely zonal oscillations (such as ENSO) and uncovers a distinct forced signal in model simulations as well as in observations. Particularly, in the tropical Pacific Ocean, the observed regional trends of opposite directions cancel each other, and simulated and observed trends in zonally averaged sea level are in good agreement. As in regional sea-level trends, there is a notable exception in the southern Indian Ocean in zonally averaged sea level. Regional sea-level trends are underestimated by climate models over the altimetry period, and the discrepancy cannot be explained by simulated internal variability in sterodynamic sea level. It is also unlikely that internal variability in the remaining contributors (land ice, land water and atmospheric pressure) has the potential to explain the large observed sea-level rise in that region.
Little is known about the internal variability of the Greenland and Antarctic ice sheet. For glaciers, Richter et al (2017) showed, using a slightly different subset of CMIP5 models, that the (modelled) contribution of glacier mass change to internal relative sealevel variability is small on the time scales considered here. Averaged over all latitudes, the glacier contribution to relative sea-level variability did not add more than 5% to the 20-yr linear trends originating from internal variability in the sterodynamic contribution for zonal averages. In narrow latitudinal bands in the northern North Atlantic, the contribution increases to 10% (supplementary figure 6, which is for relative sea level and based on a slightly different subset of models used in Richter et al 2017). To estimate the magnitude of internal variability in the mass contribution based on data used in this study, we calculated the ensemble spread of the zonally averaged mass terms around the ensemble mean over moving 22-yr windows in the simulated data over the period 1900-2015 (supplementary figures 7-9). Particularly for glaciers, the spread depends strongly on the period in time that is considered. It is generally in the order of 0.1 mm yr −1 but increases towards 0.2 mm yr −1 towards the end of the record. It is questionable whether this spread truly represents the magnitude of internal variability as decadal trends at this point in time depend strongly on the remaining glacier mass given their relatively small total mass. This is different for the large ice sheets as changes in the SMB during 1900-2015 hardly changed their total mass. Therefore, changes in the spread are also smaller. For the Antarctic SMB contribution, the spread is at most 0.075 mm yr −1 at 40 • S and mostly around or below 0.05 mm yr −1 elsewhere. The spread due to the Greenland SMB is several orders of magnitudes lower. Wouters et al (2013) showed that the reported observed trends for the Greenland and Antarctic ice sheets (combined SMB and dynamic changes) reported by Shepherd et al (2012) for the period 1992-2011 are well outside the range expected from internal variability.
Recent estimates of ice-sheet mass changes show an acceleration in the contribution to sea-level change from both ice sheets (Shepherd et al 2018, Meredith et al 2019, and it is possible that we underestimate the ice sheet contribution to sea-level change with our dataset. This, however, does not affect our main conclusion that a forced signal in sea-level change can be detected at almost all latitudes in each major ocean basin.

Conclusion
We have compared total observed and simulated geocentric sea-level change over the period 1993-2015 on regional scales. We found that model-simulated and observed trends in zonally-averaged total sea level are well above what would be expected from internal variability alone. This holds for the ocean globally and for the individual ocean basins. We conclude that a forced signal can be detected at all latitudes in each major ocean basin. Further analysis shows that the forced signal stems from the global-mean sea-level rise. That is, over the period 1993-2015 the global-mean sealevel rise, up to 90% of which has been attributed to anthropogenic emissions (Slangen et al 2016), is detectable at each latitude in each basin. Departures from the global mean, expressed as zonal-averages, are still within simulated sterodynamic internal variability.