While the CMIP5 model outputs are provided as global ocean grids, the field values at the specific locations of tide gauges are required, as input, to both the KS and GPR analyses. Where the tide gauges are coincident with model grid points, the associated value of the model output is used. Otherwise, an inverse distance weighting interpolation scheme is used to estimate the field at the desired location.
We examined three alternative interpolation schemes to assess the sensitivity of the KS GMSL estimate to this choice: (1) a nearest-neighbour approach, selecting the value on the CMIP5 grid that is closest to the tide gauge site; (2) a Delaunay interpolant, computing a linear interpolation between the irregularly spaced model cells along the coastlines; and (3) a Gaussian process (or simple kriging) methodology. For the Gaussian process interpolation, we employed a Gaussian process prior with a mean equal to the mean of the model grid values within a 200 km radius of the tide gauge location and a Matérn covariance function with smoothness parameter equal to 5/2. Since we are interested in the variability of the ocean models immediately surrounding each tide gauge site, the length scale of the Matérn covariance function was set to 1° (∼110 km). Neither the nearest-neighbour approach nor the Delaunay interpolated altered the estimate of the GMSL rate over the time period 1901–90. The Gaussian process interpolation scheme changed the GMSL estimate by less than 2%, significantly smaller than the estimated ±0.2 mm yr−1 90% CI on the estimate.
Computation of GMSL rates and accelerations
The mean and uncertainty of GMSL rates are estimated using a generalized least squares regression of a linear trend to the reconstructed GMSL time series. While the GPR methodology outputs a full temporal covariance matrix, the KS methodology does not. For this purpose, we adopt a temporal covariance matrix Σ with elements having the form:
Σ_{i,j} = σi  σj exp(-(tj - ti)/τ
where σi and σj are the instantaneous uncertainties in GMSL at time i and j, respectively, derived in the multi-model KS analysis. To estimate the decorrelation timescale, τ, we examined the annual PSMSL tide gauge data and computed the mean temporal correlation coefficient across all tide gauges. This coefficient approaches zero after 2 years, and we set τ to 3 years. Estimates of acceleration in GMSL cited in the main text for the two probabilistic analyses are computed using a generalized least squares fit of a quadratic through the associated GMSL time series. Estimates of acceleration for the Church and White4 and Jevrejeva et al.3 time series listed in Fig. 2 are based on a weighted least squares regression through the published time series (see figure legend).
Analysis of bias introduced by using a subset of tide gauges
We used a bootstrapping technique to assess the potential biases introduced in estimates of GMSL rates when only a subset of tide gauge records is used. We randomly sampled our global sea-level reconstruction based on the Kalman smoother at a specific number of tide gauge sites in the database of 622 sites, computed the associated GMSL curve by binning the sites into 12 regions and averaging the result, and then used this curve to determine the rate of sea-level change over the time period 1901–90. The time series of the sea-level reconstruction at any given tide gauge site were sampled to match any missing data at that site in the PSMSL database. We repeated the analysis 100 times for subsets ranging in size from 25 to 600 sites. The mean sea-level rate we computed in this exercise and its associated uncertainty are shown in Extended Data Fig. 3 as a function of the number of sites. The horizontal blue line and shading is the mean rate of sea-level rise from 1901 to 1990, and its associated uncertainty, respectively, obtained from the KS-derived time series (1.2 ± 0.2 mm yr−1; Figs 2, 3).
The mean sea-level rate obtained from this analysis asymptotes towards its final value and the spread in rates decreases monotonically as the number of tide gauges used in the analysis increases. The asymptote lies ∼0.4 mm yr−1 above the KS estimate, which is consistent with the difference between the KS and ‘KS PSMSL sampling’ rate estimates for 1901–90 shown in Fig. 3. This result suggests that the combined effects of data sparsity and missing data introduce an upward bias into the estimate of GMSL. This bias is reduced in the KS (and GPR) methodologies because these techniques extract global information by using the observations, together with model-based geometries (or covariances) associated with the underlying contributions, to estimate (and sum) these contributions.
Analysis of bias introduced by an EOF analysis of altimetry records
To compare our results with EOF-based reconstructions of sea level4,43, we computed the GMSL time series following the approach adopted by Church and White4, but replacing altimetry and tide gauge observations with our KS reconstruction. The EOFs were computed using the KS sea-level reconstruction from 1993 to 2010, limited to the latitudinal observation range of satellite altimetry (65° N to 65° S). As in ref. 43, a spatially uniform EOF was added to the basis set to account for changes in mean sea level within the altimetry data (here the KS reconstruction), while the weights of the EOFs were computed using the first differences of the KS reconstruction at the tide gauge locations (sampled to reflect missing data in the PSMSL database) in order to eliminate dependence on a consistent datum. The GMSL time series was computed using an area-weighted mean of the EOF-reconstruction. To compute the uncertainty in our estimated GMSL, we sampled our distribution for each KS reconstructed tide gauge 1,000 times and computed the corresponding EOF-derived GMSL time series. We used this distribution of GMSL curves with a generalized least squares regression to compute a trend and uncertainty. This analysis yielded a linear trend of 1.4 ± 0.4 mm yr−1, demonstrating the existence of a bias since the ‘true’ underlying reconstruction has a trend of 1.2 ± 0.2 mm yr−1 (see Fig. 3, ‘KS EOF’).
Inverted barometer correction
The results in the manuscript were obtained using tide gauge observations that were not corrected for the inverse barometer (IB) effect. Previous studies (for example, refs 44 and 45) have shown that the sea-level response to atmospheric pressure changes can be non-negligible on regional scales.
In order to investigate the potential effect that atmospheric pressure changes have on our probabilistic estimate of GMSL, we repeated the KS analysis on the full tide gauge data set after we corrected these records for the IB effect. Specifically, we used the HadSLP2 global reconstructed atmospheric pressure data set46 to compute the IB correction. We next applied the correction to the observations at the 622 tide gauge sites and then re-ran the KS analysis. The 1901–90 GMSL rate of change associated with this analysis is 1.2 ± 0.2 mm yr−1, consistent with the value cited in the main text. We conclude that while the IB effect can impact regional sea-level histories, it has a negligible effect on our probabilistic estimates of GMSL.
Optimality of the Kalman smoother
Local sea levels observed by tide gauges reveal significant interannual and decadal variability. This variability can lead to temporal correlation in the sea-level time series that needs to be considered if one seeks to obtain optimal estimates of the underlying GMSL contributions. In order to test the optimality of the Kalman smoother, we investigated the properties of the innovation sequence by computing the residuals between the observations and the KS model estimate of sea level at every tide gauge site. Since every KS estimate of sea level is accompanied by its associated uncertainty, we randomly sampled from each sea-level distribution to obtain 100 time series of residuals for every site. Following the optimality test described in ref. 47, we computed the mean AR(1) coefficient across the 100 samples at each tide gauge site. An optimal Kalman smoother is characterized by a white noise innovation sequence. In practice, this means that, within uncertainty, the AR(1) coefficients of the innovation sequences will be close to zero. In the exercise above, we obtained a mean AR(1) coefficient of 0.2 ± 0.3 (90% confidence). This indicates that our innovation sequence is (within uncertainty) white noise and that the smoother is, or is close to, optimal.
Sensitivity of GMSL estimates to limitations of the CMIP5 climate simulations
The presence of unmodelled ocean dynamics can also affect the smoother performance. As described above, the limitations of the CMIP5 simulations as models for the true dynamic variability of the oceans is addressed in the GPR analysis by augmenting the covariance computed from the climate runs with two additional terms: a covariance modelled with two Matérn functions, and a white noise variance.


Optimality of the Kalman smoother
Local sea levels observed by tide gauges reveal significant interannual and decadal variability. This variability can lead to temporal correlation in the sea-level time series that needs to be considered if one seeks to obtain optimal estimates of the underlying GMSL contributions. In order to test the optimality of the Kalman smoother, we investigated the properties of the innovation sequence by computing the residuals between the observations and the KS model estimate of sea level at every tide gauge site. Since every KS estimate of sea level is accompanied by its associated uncertainty, we randomly sampled from each sea-level distribution to obtain 100 time series of residuals for every site. Following the optimality test described in ref. 47, we computed the mean AR(1) coefficient across the 100 samples at each tide gauge site. An optimal Kalman smoother is characterized by a white noise innovation sequence. In practice, this means that, within uncertainty, the AR(1) coefficients of the innovation sequences will be close to zero. In the exercise above, we obtained a mean AR(1) coefficient of 0.2 ± 0.3 (90% confidence). This indicates that our innovation sequence is (within uncertainty) white noise and that the smoother is, or is close to, optimal.
Sensitivity of GMSL estimates to limitations of the CMIP5 climate simulations
The presence of unmodelled ocean dynamics can also affect the smoother performance. As described above, the limitations of the CMIP5 simulations as models for the true dynamic variability of the oceans is addressed in the GPR analysis by augmenting the covariance computed from the climate runs with two additional terms: a covariance modelled with two Matérn functions, and a white noise variance.
To assess the sensitivity of the KS analysis to unmodelled ocean dynamics, we examined its response to (1) a known synthetic ocean dynamic signal and (2) the inclusion of the dynamic response to freshwater hosing of the North Atlantic.
We used the mean KS estimates of the ice sheet melt rates and uniform sea-level contribution, as well as the multi-model estimate of the GIA contribution, to construct synthetic sea-level observations at the 622 tide gauge sites. We then added the dynamic sea-level change associated with one of the six CMIP5 climate models and ran the multi-model KS using the five remaining climate models to obtain an estimate of the GMSL rate. We repeated this analysis for each of the CMIP5 simulations. By not including the climate model used in constructing the synthetics in the multi-model component of the KS methodology, we tested the ability of the smoother to account for unmodelled dynamics. The 1901–90 GMSL rates determined from the complete set of 6 analyses ranged from 1.1 to 1.3 mm yr−1. Five of these analyses yielded a 90% CI of 0.2 mm yr−1, while the sixth yielded a 90% CI of 0.3 mm yr−1. These values are consistent with the results for the KS analysis cited in the main text (1.2 ± 0.2 mm yr−1).
To assess the sensitivity of our GMSL results to ocean dynamic effects due to freshwater input (‘hosing’) from GIS melt, we used the results of a previous study48 to investigate the dynamic sea-level signal arising from North Atlantic freshwater ‘hosing’ simulations. Specifically, we computed the difference between the results of the 0.1 Sv hosing run and the control (no-hosing) simulation described in ref. 48 and scaled this difference by 0.05 to approximate a synthetic dynamic signal for a GIS melt rate equivalent to 0.5 mm yr−1 GMSL rise over the twentieth century. After subtracting a uniform 0.5 mm yr−1 from the spatial pattern, we calculated time series of this signal at all 622 tide gauge sites, added these to the observed record, and repeated the KS analysis. The presence of these unmodelled dynamics has negligible effect on our estimate of GMSL. The 1901–90 rate estimated in the above test agrees with the value presented in the manuscript (1.2 ± 0.2 mm yr−1).
While the above sensitivity tests indicate that the probabilistic analyses have quantified, with reasonable accuracy, the impact of uncertainties in CMIP5 models of ocean dynamic variability, improving such models is an important requirement in any effort to further refine estimates of GMSL rates.
Kalman smoother reconstruction of sea level at sites with no observations
To investigate how well the KS is able to estimate sea level at sites without observations, we ran the Kalman smoother using data from 450 randomly chosen tide gauge sites and estimated the sea level at the remaining 172 sites. Extended Data Fig. 4 shows the GMSL time series estimated in this new analysis as well as a comparison of the estimated and observed sea level at a representative subset of 5 of these 172 sites (the remaining sites show similar fits). We calculate a 1901–90 GMSL rate of 1.2 ± 0.2 mm yr−1, consistent with the results presented in the manuscript when all 622 tide gauge sites are used in the analysis. The consistency between the estimated and observed values at the 172 tide gauge sites also indicates that limitations of the CMIP5 simulations in modelling ocean dynamics are not degrading the ability to predict sea-level trends at sites without observations. More generally, the analysis demonstrates the power of the KS method in reconstructing sea level when the method is applied with physics-based and model-derived geometries of the underlying physical processes.
Extended data figures and tables
Extended Data Figure 1: Illustrative sea-level fingerprints. a, b, Normalized sea-level changes due to rapid melting of the Greenland Ice Sheet (a) and the West Antarctic Ice Sheet (b). The variable ‘normalized sea-level change’ on the colour scale is formally dimensionless, but may be interpreted as having the unit of metres of sea-level change per metre of the equivalent GMSL change associated with the melt event.
Extended Data Figure 2: The present-day rate of change of sea level in mm yr−1 due to GIA for a suite of Earth models. a, b, Mean sea-level change (a) and standard deviation (b) computed from the output of 161 GIA model simulations (see text). In both frames, the colour scale saturates in the near field, which includes areas of post-glacial rebound and peripheral subsidence.
Extended Data Figure 3: Bootstrapping analysis of GMSL rate for 1901–90 obtained by sampling the global reconstruction of sea level. Data points show the mean computed from a bootstrapping analysis of the 1901–90 GMSL rate as a function of the number of geographic sites used in the analysis (ranging from 25 to 600). Error bars, ±1s.d. Sites are obtained by randomly sampling the global KS reconstruction at a subset of tide gauge sites and introducing data gaps that are consistent with those that exist in the PSMSL database15. The analysis was repeated 100 times for each choice of the number of sites. Also shown (horizontal blue line and shading) is the 1901–90 rate and its 90% CI computed from the KS GMSL curve in Fig. 2 (1.2 ± 0.2 mm yr−1; Figs 2 and 3).
Extended Data Figure 4: Results of the KS analysis performed using a random subset of 450 tide gauges. a, KS-estimated GMSL curve derived using a subset of 450 of the 622 tide gauge records discussed in the main text (blue line) and the reconstruction of Church and White4 (magenta line) and Jevrejeva et al.3 (red line). The shaded regions represent the 1σ certainty range. Panels b–f show the KS reconstructions (black lines) at a representative set of 5 of the 122 sites that were not used in the estimation procedure. The observations are shown in red.


Suzuki et al. (2005)
Title:
Projection of future sea level and its variability in a high-resolution climate model: Ocean processes and Greenland and Antarctic ice-melt contributions
Corresponding author:
Tatsuo Suzuki
Citation:
Suzuki, T., Hasumi, H., Sakamoto, T. T., Nishimura, T., Abe‐Ouchi, A., Segawa, T., et al. (2005). Projection of future sea level and its variability in a high‐resolution climate model: Ocean processes and Greenland and Antarctic ice‐melt contributions. Geophysical Research Letters, 32(19), n/a-n/a. https://doi.org/10.1029/2005gl023677
URL:
https://agupubs.onlinelibrary.wiley.com/doi/full/10.1029/2005GL023677
Abstract
Using a high-resolution climate model, we projected future sea level and its variability based on two scenarios for 21st century greenhouse gas emission. The globally averaged sea level rise attributable to the steric contribution was 23 and 30 cm for the two scenarios. The results of the high-resolution model and a medium-resolution version of the same model for global and local sea level change agreed well. However, the high-resolution model represented more detailed ocean structure changes under global warming. The changes affected not only the spatial distribution of sea level rise, but also the changes in local sea level variability associated with ocean eddies. The enhanced eddy activity was responsible for extreme sea level events.
Introduction
Sea level change is an important aspect of future climate change for human societies and the environment. Estimates of the rate of globally averaged sea level change during the 20th century are in the range of 1 to 2 mm yr−1 [Church et al., 2001]. This globally averaged rise in sea level is mainly the result of the thermal expansion of seawater and land-ice melt. Future projections of sea level change have been calculated using various coupled atmosphere–ocean general circulation models (CGCMs [e.g., Gregory and Lowe, 2000; Gregory et al., 2001; Meehl et al., 2005]). Gregory et al. [2001] compared the results of the projections that followed the IS92a scenario for greenhouse gas (GHG) emissions. The rates of globally averaged sea level rise predicted by the models for the 21st century were in the range of 2.0–3.7 mm yr−1, but regional sea level change was not spatially uniform and some regions experienced more than twice the global average rate of rise. However, different models, while sharing some features, predicted different distributions. The geographical distribution of sea level change is principally determined by changes in density structure and wind stress forcing, both of which affect ocean circulation [Church et al., 2001]. Reproducing ocean structures is important for estimating the distribution of future sea level changes. However, the details of ocean structures, such as western boundary currents and fronts with pronounced horizontal gradients of water properties, have not been reproduced by existing coarse-resolution CGCMs. In this study, we compared sea level projections made by CGCMs with differing resolutions, focusing particularly on detailed features of the spatial distribution of sea level changes as predicted by a high-resolution model.
We also present global and local changes in 21st century sea level variability. Extreme changes in sea levels could severely affect human activities, and storm surges and coastal wave height have been identified in previous studies as sources of extreme sea levels [Church et al., 2001]. Unfortunately, the resolution of CGCMs has not been adequate to resolve these events. Extreme sea levels associated with ocean eddies, however, are represented by high-resolution models. Warm eddies increase the flooding risk in coastal areas. For example, Okinawa Island flooded on 22 July 2001 without the passage of an atmospheric low; rather, a warm eddy was responsible for increasing the sea level by more than 15 cm [Tokeshi and Yanagi, 2003]. Therefore, it would be advantageous to project changes in sea level variability using a high-resolution climate model that included eddies.
Models and Experiments
The CGCM used in this study was the Model for Interdisciplinary Research on Climate, version 3.2 (MIROC3.2), developed at the Center for Climate System Research, University of Tokyo, National Institute for Environmental Studies and Frontier Research Center for Global Change [K-1 Model Developers, 2004]. The ocean component explicitly represented sea surface elevation. The higher-resolution version of MIROC3.2 (MIROC3.2_hi) consisted of a T106 global atmospheric spectral model with 56 vertical levels, an eddy-permitting global ocean model in which horizontal resolution was zonally 0.28° and meridionally 0.19° with 48 vertical levels, and other components (i.e., land, river, and sea ice). In the medium-resolution version of MIROC3.2 (MIROC3.2_med), a T42 global atmospheric spectral model with 20 vertical levels was coupled with a medium-resolution OGCM in which horizontal resolution was zonally 1.4° and meridionally 0.56° around the equator, with 44 vertical levels. The same physical parameterizations were applied to these models, but resolution-dependent parameters were adjusted per model.
Both models were integrated by prescribing external conditions, including solar and volcanic forcing, GHG concentrations, aerosol emissions, and land use. MIROC3.2_hi was spun up for 109 years under the fixed external conditions of the year 1900 after coupling the atmosphere and the ocean. MIROC3.2_med was spun up for 560 years under the fixed conditions of the year 1850. For control runs, we continued the integration under the same conditions for 100 years in MIROC3.2_hi and 400 years in MIROC3.2_med. Twentieth century experiments (20C3M) were performed after the spin-up. These runs were forced by the historical external conditions from 1900 to 2000 in MIROC3.2_hi and from 1850 to 2000 in MIROC3.2_med. Future projections for the 21st century were initiated by the final states of the 20C3M runs and performed by prescribing the external conditions according to the Intergovernmental Panel on Climate Change (IPCC) special report for emission scenarios. CO2 concentrations at the end of the 21st century were 720 and 550 ppm under the A1B scenario and the B1 scenario, respectively [Intergovernmental Panel on Climate Change, 2000]. For MIROC3.2_med, three 20th century runs were performed using different initial conditions (1st, 101st, and 201st years for the control run). We used the ensemble mean of the three members in this study. The model integration was restricted by computing resource limitations, especially for the high-resolution model, and the control runs showed some trends. Therefore, we subtracted these trends from the results.
Globally Averaged Sea Level Rise
The steric contribution (thermal expansion and haline contraction) to sea level rise was estimated from the model ocean temperature and salinity. As the Boussinesq approximation was adopted in the ocean model, the globally averaged sea level rise attributable to steric factors was diagnosed indirectly from density changes as the equivalent volume change under mass conservation:
urn:x-wiley:00948276:media:grl20251:grl20251-math-0001
where ΔH is the globally averaged sea level rise, S is the surface area of the ocean, Z is the ocean depth, ρ is the in situ density, and Δρ is its difference from the reference state. Because the haline contribution was small, the globally averaged change in sea level was caused mainly by changes in ocean heat content. To validate the model, the upper ocean heat content was compared with observations [Levitus et al., 2005]. Decadal variations were not in phase, but long-term trends and the changes over the last decade for both models were similar to observations (data not shown). The 21st century steric contribution was projected to be about 30 cm for the A1B scenario and 23 cm for the B1 scenario in MIROC3.2_hi (Figure 1a). This result was similar to that for MIROC3.2_med (Figure 1b) and within the range of estimations of previous CGCMs [Gregory et al., 2001]. Both models had linear trends in the control runs: about 0.15 mm yr−1 in MIROC3.2_hi and about 0.14 mm yr−1 in MIROC3.2_med. These linear trends were subtracted from the projections.
Figure 1: A time series of globally averaged sea level change in (a) MIROC3.2_hi and (b) MIROC3.2_med (ensemble mean). Solid lines indicate the steric contribution. Broken lines represent the Greenland ice sheet and dotted lines indicate the Antarctica ice sheet.


Globally Averaged Sea Level Rise
The steric contribution (thermal expansion and haline contraction) to sea level rise was estimated from the model ocean temperature and salinity. As the Boussinesq approximation was adopted in the ocean model, the globally averaged sea level rise attributable to steric factors was diagnosed indirectly from density changes as the equivalent volume change under mass conservation:
urn:x-wiley:00948276:media:grl20251:grl20251-math-0001
where ΔH is the globally averaged sea level rise, S is the surface area of the ocean, Z is the ocean depth, ρ is the in situ density, and Δρ is its difference from the reference state. Because the haline contribution was small, the globally averaged change in sea level was caused mainly by changes in ocean heat content. To validate the model, the upper ocean heat content was compared with observations [Levitus et al., 2005]. Decadal variations were not in phase, but long-term trends and the changes over the last decade for both models were similar to observations (data not shown). The 21st century steric contribution was projected to be about 30 cm for the A1B scenario and 23 cm for the B1 scenario in MIROC3.2_hi (Figure 1a). This result was similar to that for MIROC3.2_med (Figure 1b) and within the range of estimations of previous CGCMs [Gregory et al., 2001]. Both models had linear trends in the control runs: about 0.15 mm yr−1 in MIROC3.2_hi and about 0.14 mm yr−1 in MIROC3.2_med. These linear trends were subtracted from the projections.
Figure 1: A time series of globally averaged sea level change in (a) MIROC3.2_hi and (b) MIROC3.2_med (ensemble mean). Solid lines indicate the steric contribution. Broken lines represent the Greenland ice sheet and dotted lines indicate the Antarctica ice sheet.
The contributions of ice-sheet melt were estimated using the methods of Wild et al. [2003]. The contributions of the Greenland and Antarctic ice-sheet melts exhibited opposite tendencies in both models, as in previous estimations [Church et al., 2001]. However, the amplitude in MIROC3.2_hi was larger than that in MIROC3.2_med (Figure 1). The difference between the two models appeared to be a result of the differences in projected temperature rises in the Greenland and snowfall increases in the Antarctica. Both of these differences in arctic temperature and snowfalls are strongly related to the difference in the climate sensitivity of the MIROC3.2_hi and MIROC3.2_med, in which the A1B run induced global warming of about 4.0°C in MIROC3.2_hi and 3.4°C in MIROC3.2_med at the end of the 21st century, respectively. This different sensitivity may partly due to the difference in the control SST and sea ice distribution in the two models.
The globally averaged sea level rise in MIROC3.2_hi is similar to that in MIROC3.2_med in spite of the different sensitivity. It is because the total heat flux into the ocean for the 21st century is similar in the both models, though the net heat flux into ocean in MIROC3.2_hi is larger than that in MIROC3.2_med during the early 21st century. The upper ocean in MIROC3.2_hi also warms up more than that in MIROC3.2_med. The reasons for these differences are currently under investigation.
Regional Sea Level Change
The sea level patterns corresponding to major ocean gyres were well represented by both models (data not shown). In particular, narrow western boundary currents, such as the Kuroshio, were reproduced realistically in MIROC3.2_hi [Sakamoto et al., 2005]. The globally averaged sea level rise estimated in the previous section was added to the local sea levels calculated by each model to obtain sea level projections. Mass balance was ensured in a globally averaged sense by this procedure [Greatbatch, 1994]. Some regions experienced substantially higher sea level rise in both models than the 21st century global average (Figure 2).
Figure 2: The changes in mean sea level between 1980 and 2000 (20C3M) and between 2080 and 2100 (A1B) in (a) MIROC3.2_hi and (b) MIROC3.2_med (ensemble mean).
To distinguish sea level changes caused by global warming from background variability, such as decadal variations, we estimated area-weighted spatial standard deviations of the local sea level change with respect to the control climate. Gregory et al. [2001] assumed that sea level changes associated with global warming and background variability were not spatially correlated. Under this assumption, increased spatial standard deviation would be attributable to global warming if changes in background variability were relatively small. The spatial standard deviation increased with time for both models and reached 7–13 cm by the end of the 21st century (Figure 3), indicating that the projected sea level changes were sufficiently significant relative to background variability. There was a conspicuous signal from the last decade of the 20th century in MIROC3.2_hi.
Figure 3: The spatial standard deviation of the decadal mean field of local sea level change with respect to the control climate. Solid lines indicate MIROC3.2_hi and broken lines represent MIROC3.2_med (ensemble mean).
The regions with large sea level changes were more restricted to specific areas and the magnitudes of change were more pronounced in MIROC3.2_hi than in MIROC3.2_med (Figure 2). These results were consistent with the fact that spatial variability in MIROC3.2_hi was larger than in MIROC3.2_med at the end of the 21st century (Figure 3). The sea level variability associated with eddies was also shown in MIROC3.2_hi (Figure 4a), and this spatial distribution was consistent with satellite obsersvations. These changes were closely related to regional sea level changes and were as large as several centimeters for some regions during the 21st century (Figure 4b).
Figure 4: (a) The root-mean-square (rms) of the sea level anomaly from the 3-month running mean for the control run in MIROC3.2_hi. (b) Changes in the rms between 1980 and 2000 (20C3M) and between 2080 and 2100 (A1B) in MIROC3.2_hi.
Both models exhibited a region of large sea level rises in the North Pacific. These sea level changes were also shown in the Hadley Centre coupled atmosphere-ocean general circulation model (HadCM3), which has a horizontal resolution similar to that of MIROC3.2_med [Gregory and Lowe, 2000]. This feature has not been represented in previous coarser-resolution models [Gregory et al., 2001]. With higher resolution, as in MIROC3.2_med and HadCM3, fronts at the western boundary currents and their extensions were more sharply reproduced, so sea level changes associated with their shifting or intensification were better captured. Such features became further differentiated at higher resolution (Figure 2).
There was a reduced sea level rise north of the Kuroshio Current at approximately 150°E and an enhanced sea level rise to the south in MIROC3.2_hi. This sea level change was associated with the acceleration of the Kuroshio caused by changes in wind stress and the consequential spin-up of the Kuroshio recirculation [Sakamoto et al., 2005]. In contrast, the Kuroshio in MIROC3.2_med overshot to the north in comparison with that in MIROC3.2_hi. Therefore, the region of large sea level rises in MIROC3.2_med extended northward relative to that in MIROC3.2_hi. MIROC3.2_hi also exhibited a region of reduced sea level rises in the North Pacific subpolar gyre. We believe that this feature was related to the intensification of the Aleutian Low, which is also considered to be the cause of the Kuroshio acceleration [Sakamoto et al., 2005]. This acceleration was associated with the enhanced eddy activity in the Kuroshio and the Kuroshio extension under global warming (Figure 4b). These features were not represented in MIROC3.2_med, partly because the subpolar gyre was not well represented due to the overshooting of the Kuroshio. Similar acceleration of a western boundary current and enhanced eddy activity were also detected east of Australia.


Both models exhibited a region of large sea level rises in the North Pacific. These sea level changes were also shown in the Hadley Centre coupled atmosphere-ocean general circulation model (HadCM3), which has a horizontal resolution similar to that of MIROC3.2_med [Gregory and Lowe, 2000]. This feature has not been represented in previous coarser-resolution models [Gregory et al., 2001]. With higher resolution, as in MIROC3.2_med and HadCM3, fronts at the western boundary currents and their extensions were more sharply reproduced, so sea level changes associated with their shifting or intensification were better captured. Such features became further differentiated at higher resolution (Figure 2).
There was a reduced sea level rise north of the Kuroshio Current at approximately 150°E and an enhanced sea level rise to the south in MIROC3.2_hi. This sea level change was associated with the acceleration of the Kuroshio caused by changes in wind stress and the consequential spin-up of the Kuroshio recirculation [Sakamoto et al., 2005]. In contrast, the Kuroshio in MIROC3.2_med overshot to the north in comparison with that in MIROC3.2_hi. Therefore, the region of large sea level rises in MIROC3.2_med extended northward relative to that in MIROC3.2_hi. MIROC3.2_hi also exhibited a region of reduced sea level rises in the North Pacific subpolar gyre. We believe that this feature was related to the intensification of the Aleutian Low, which is also considered to be the cause of the Kuroshio acceleration [Sakamoto et al., 2005]. This acceleration was associated with the enhanced eddy activity in the Kuroshio and the Kuroshio extension under global warming (Figure 4b). These features were not represented in MIROC3.2_med, partly because the subpolar gyre was not well represented due to the overshooting of the Kuroshio. Similar acceleration of a western boundary current and enhanced eddy activity were also detected east of Australia.
Another important difference between the two models was found in the western tropical Pacific. In MIROC3.2_hi, there was a reduced sea level rise east of Mindanao Island that spread to the eastern tropical Pacific (Figure 2a). This feature was caused by intensification of the wind-induced Ekman upwelling under global warming. This wind-induced Ekman upwelling in this region was not well resolved in MIROC3.2_med [Suzuki et al., 2005]. The reduced sea level rise was associated with the acceleration of the North Equatorial Current (NEC) and the North Equatorial Counter Current (NECC). The acceleration of these currents and the Subtropical Counter Current increased the meridional gradient of zonal velocity, which was associated with an enhanced eddy (Figure 4b). The region stretched zonally to 120°W. These responses of the zonal flows to global warming will be investigated in future studies.
Both models showed a narrow band of enhanced sea level rise in the Southern Ocean. Under global warming in our models, the westerlies shifted southward and strengthened. These changes in the wind field contributed to the southward shift and the intensification of the circumpolar fronts, which are linked to sea level change. These changes were also connected with a couple of narrow bands of enhanced and reduced eddy activity that stretched east from Argentina to the south of Australia in MIROC3.2_hi.
A dipole pattern of sea level change in the North Atlantic Ocean, i.e., an enhanced rise north of the Gulf Stream extension and a reduced rise to the south, was recognized in both models. Bryan [1996] suggested that this pattern was consistent with weakening of the upper branch of the Atlantic Meridional Overturning Circulation (AMOC). The AMOC was weakened from 14 Sv (1 Sv = 106 m3 s−1) to 9 Sv in MIROC3.2_hi and from 19.5 Sv to 12.5 Sv in MIROC3.2_med during the 21st century.
Discussion and Conclusions
The dynamic effect of sea level pressure was not included in either of the ocean components. The change in spatial standard deviation estimated from model sea level pressure during the 21st century was less than 2 cm. These changes, while not negligible, were small in comparison to the spatial variability caused by ocean structure changes (Figure 3). Therefore, we did not indicate the contribution of sea level pressure in this study.
The strengthening of eddy activity was recognized in a globally averaged sense. The global average of the root-mean-square (rms) increased from 4.8 to 5.1 cm in the A1B scenario and from 4.8 to 5.0 cm in the B1 scenario during the 21st century. These changes were small compared to levels of globally averaged sea level rise. However, enhanced eddy activity was confined to specific areas, and those areas overlapped with the areas of enhanced sea level rise around some coastal regions and islands, suggesting that the frequency of extreme sea levels may increase in those regions during the 21st century.
We have described future sea level changes as projected by MIROC3.2_hi according to the 21st century scenarios for GHG emissions and compared them with the results of MIROC3.2_med. The globally averaged sea level rise during the 21st century predicted by the two models was similar. The distribution of sea level changes in MIROC3.2_hi also resembled that in MIROC3.2_med on a large scale. However, MIROC3.2_hi presented more detailed ocean structure changes under global warming. The changes in the ocean structure affected not only the spatial distribution of sea level rise, but also changes in local sea level variability. Therefore, it is critical to consider changes in sea level variability when assessing the possible effects on human activities.


Welcome to SeaLevelDocs’s documentation!
Contents:
Suzuki et al. (2005)
Hughes et al. (2010)
Church and White (2011)
Kuhlbrodt and Gregory (2012)
Church et al. (2013)
Hallberg et al. (2013)
Kopp et al. (2014)
Hay et al. (2015)
DeConto and Pollard (2016)
Chen et al. (2017)
Chen and Tung (2018)
Horton et al. (2018)
Little et al. (2019)
Bamber et al. (2019)
Gregory et al. (2019)
Hamlington et al. (JGR, 2020)
Sadai et al. (2020)
Palmer et al. (2020)
Yin et al. (2020)
Yuan and Kopp (2021)
Couldrey et al. (2021)
Dangendorf et al. (2021)
Zika et al. (2021)
DeConto et al. (2021)
Li et al. (2022)
Slangen et al. (2022)
van de Wal et al. (2022)
Bamber et al. (2022)
Wickramage et al. (2023)
Li et al. (2023)
Park et al. (2023)
Indices and tables
Index
Module Index
Search Page


Hamlington et al. (JGR, 2020)
Title:
Understanding of contemporary regional sea-level change and the implications for the future
Key Points:
An overview of the current state of understanding of the processes that cause regional sea-level change is provided
Areas where the lack of understanding or gaps in knowledge inhibit the ability to assess future sea-level change are discussed
The role of the expanded sea-level observation network in improving our understanding of sea-level change is highlighted
Corresponding author:
Hamlington
Citation:
Hamlington, B. D., Gardner, A. S., Ivins, E., Lenaerts, J. T. M., Reager, J. T., Trossman, D. S., et al. (2020). Understanding of contemporary regional sea-level change and the implications for the future. Reviews of Geophysics, 58, e2019RG000672. https://doi.org/10.1029/2019RG000672
Abstract
Global sea level provides an important indicator of the state of the warming climate, but changes in regional sea level are most relevant for coastal communities around the world. With improvements to the sea-level observing system, the knowledge of regional sea-level change has advanced dramatically in recent years. Satellite measurements coupled with in situ observations have allowed for comprehensive study and improved understanding of the diverse set of drivers that lead to variations in sea level in space and time. Despite the advances, gaps in the understanding of contemporary sea-level change remain and inhibit the ability to predict how the relevant processes may lead to future change. These gaps arise in part due to the complexity of the linkages between the drivers of sea-level change. Here we review the individual processes which lead to sea-level change and then describe how they combine and vary regionally. The intent of the paper is to provide an overview of the current state of understanding of the processes that cause regional sea-level change and to identify and discuss limitations and uncertainty in our understanding of these processes. Areas where the lack of understanding or gaps in knowledge inhibit the ability to provide the needed information for comprehensive planning efforts are of particular focus. Finally, a goal of this paper is to highlight the role of the expanded sea-level observation network - particularly as related to satellite observations - in the improved scientific understanding of the contributors to regional sea-level change.
Plain Language Summary
This review paper addresses three important questions: (1) What do we currently know about the processes contributing to sea level change? (2) What observations do we use to gain this knowledge? and (3) Where are these gaps in our knowledge and the need for further improvement in our understanding of the drivers of regional sea level? By answering these specific questions in a focused manner, this paper should be a useful resource for other scientists, sea-level stakeholders, and a broader audience of those interested in sea level and our changing climate.
Introduction
Global mean sea level (GMSL) is an important indicator of a warming climate (Church & White, 2011; Milne et al., 2009; Stammer et al., 2013), but changes in regional sea level are most relevant to coastal communities around the world (Kopp et al., 2015; Nicholls, 2011; Woodworth et al., 2019). The regional variability of the processes driving sea-level change (SLC), along with their uncertainties and relative importance over different time scales, pose challenges to planning efforts. Available observations of sea level show clear spatial and temporal inhomogeneity. From satellite altimeter observations covering the time period from 1993 to present, regional rates of rise can be more than double the global average in some locations while near zero at other locations (Cazenave & Llovel, 2010). Furthermore, as a result of internal variability, the pattern of linear trends in regional sea level has shifted or reversed in many regions from the first half of the altimeter record to the second (e.g., Han et al., 2017; Peyser et al., 2016; Figure 1). Over longer time periods (i.e., hundreds of years), tide gauge records also show regional differences in the rates of SLC, owing in part to the vertical motion of the land upon which the gauges sit (e.g., Church et al., 2004; Church & White, 2006; Hay et al., 2015; Kleinherenbrink et al., 2018; Santamaroa-Gomez et al., 2014, 2017; Thompson et al., 2016). Understanding and accounting for these regional differences are critical first steps in providing information that is useful for planning efforts at the coast.
Figure 1: Satellite altimeter-measured regional sea-level trend patterns from (top) 1993–2005, (middle) 2006–2018, and (bottom) 1993–2018. Black contours and gray shading denote areas where the estimated trend is not significant at the 95% confidence level.
Due in large part to improvements in the sea.level observing system, the processes contributing to recent SLC are now well known. The uncertainty in the budget of GMSL rise over the last decade has been reduced (Cazenave et al., 2018), allowing for an assessment of the relative contributions of different processes that are important on global scales. While more challenging on regional levels, satellite observations, along with in situ measurements, have also led to a dramatically improved understanding of the processes causing regional differences in SLC. Fundamentally, the drivers that dominantly impact GMSL have a regional signature, and no process will result in a change that is uniform across the ocean (Milne et al., 2009; Stammer et al., 2013). Similarly, no contributor to SLC is constant in time, and the time scales upon which the processes vary can differ dramatically. Separating the contributors temporally and geographically can be useful when considering a particular planning horizon, although the range of variability inherent to the individual contributors can make this difficult. Additionally, it is the combined impact of several factors operating on these different scales that is of direct importance.
The causes of global and regional SLC have been the focus of recent review papers, with regional change most comprehensively discussed and summarized in Stammer et al. (2013), Kopp et al. (2015), and Slangen et al. (2017). The understanding of these processes has progressed in recent years, and the outstanding gaps in knowledge and remaining uncertainties have shifted accordingly. The intent of the present paper is to provide an overview and update of the current state of understanding of the processes that cause regional SLC and to identify and discuss limitations and uncertainty in our understanding of these processes. Although the focus is on contemporary SLC, we do include discussion of projections of future SLC. In particular, we are concerned with areas where lack of understanding or gaps in knowledge inhibit comprehensive planning efforts at the regional level. While we do not make explicit connections to planning efforts, we expect that a detailed discussion of uncertainties could be useful to those translating science into actionable plans (e.g., Horton et al., 2018). This paper is a resource for those interested in particular aspects of regional SLC by giving a detailed presentation of the most recent estimates of their contributions and a discussion of where improvement may be made in the coming years. Finally, a goal of this paper is to highlight the potential role of the expanded sea-level observation network - particularly as related to satellites - to understanding the contributors to regional SLC.
This paper is organized according to the individual processes of regional relative SLC, with each process covered in a section. In section 2, we provide a brief summary of how the contributors to regional sea level are separated and we present definitions for the terminology adopted in the remainder of the paper. Sections 3 through 8 discuss the individual processes contributing to regional SLC, with each section broken into two components: (1) a summary of the current state of knowledge, and (2) an overview of current limitations or areas of uncertainty and a discussion of where progress will likely be made in the coming years. In section 9, we summarize advances toward overcoming these limitations or reducing uncertainties that may be expected through recent and future additions to the sea-level observational network, with particular emphasis on satellite-based observations.
Processes Contributing to Regional SLC


The causes of global and regional SLC have been the focus of recent review papers, with regional change most comprehensively discussed and summarized in Stammer et al. (2013), Kopp et al. (2015), and Slangen et al. (2017). The understanding of these processes has progressed in recent years, and the outstanding gaps in knowledge and remaining uncertainties have shifted accordingly. The intent of the present paper is to provide an overview and update of the current state of understanding of the processes that cause regional SLC and to identify and discuss limitations and uncertainty in our understanding of these processes. Although the focus is on contemporary SLC, we do include discussion of projections of future SLC. In particular, we are concerned with areas where lack of understanding or gaps in knowledge inhibit comprehensive planning efforts at the regional level. While we do not make explicit connections to planning efforts, we expect that a detailed discussion of uncertainties could be useful to those translating science into actionable plans (e.g., Horton et al., 2018). This paper is a resource for those interested in particular aspects of regional SLC by giving a detailed presentation of the most recent estimates of their contributions and a discussion of where improvement may be made in the coming years. Finally, a goal of this paper is to highlight the potential role of the expanded sea-level observation network - particularly as related to satellites - to understanding the contributors to regional SLC.
This paper is organized according to the individual processes of regional relative SLC, with each process covered in a section. In section 2, we provide a brief summary of how the contributors to regional sea level are separated and we present definitions for the terminology adopted in the remainder of the paper. Sections 3 through 8 discuss the individual processes contributing to regional SLC, with each section broken into two components: (1) a summary of the current state of knowledge, and (2) an overview of current limitations or areas of uncertainty and a discussion of where progress will likely be made in the coming years. In section 9, we summarize advances toward overcoming these limitations or reducing uncertainties that may be expected through recent and future additions to the sea-level observational network, with particular emphasis on satellite-based observations.
Processes Contributing to Regional SLC
As we discuss in the sections to follow, changes in sea level arise from a diverse set of physical processes. As a result, scientists from a range of disciplines are working on different questions related to sea level. The need to address the impacts of ongoing and future SLC, along with associated policy considerations, further increases the breadth of those studying or interested in SLC. This diversity and broad interest have led to inconsistency in sea-level terminology that can hinder progress in research, communication, and policy. To address this issue, Gregory et al. (2019) have provided guidelines and clearly defined terminology for discussing SLC. In Gregory et al. (2019), SLC refers to the geocentric SLC, specifically  the change in the height of sea level with respect to the terrestrial reference frame. When including the movement of the land at the coast, the phrase relative SLC is used, which is the change in the height of the mean sea surface relative to the solid surface, and thus includes the effects of vertical land motion (VLM). Given that relative SLC encompasses both geocentric SLC and VLM, and to simplify the discussion in this paper, we have chosen to use SLC to refer to changes in relative sea level for the remainder of this paper. The definition of spatial scales is separated by regional and global. The term “regional” is used to refer to processes that are considered properties of regions, with spatial of hundreds of kilometers and less. Unless specified, this includes local changes that occur at a specific geographic location. Processes are said to be of “global” scale if they contribute to variability in GMSL. The global mean refers specifically to the area-weighted mean of SLC for the entire connected surface of the ocean.
There are several ways to separate and distinguish between the different processes contributing to regional SLC. Here, we separate the contributors into six different sections. Regional and global SLC associated with ice mass changes is divided into contributions from ice sheets (section 3) and contributions from glaciers (section 4), recognizing that the observational and measurement considerations can differ between the two. Further changes arising from variability in land water storage are presented in a separate section (section 5). Each of these three contributors are discussed first in terms of their impact on GMSL, and then in terms of their regional signature through changes in Earth Gravitation, Rotation, and Deformation (GRD), caused by redistributions of land ice and water (discussed in more detail below). The primary intent of this paper is to discuss regional SLC, but the magnitude of the regional contributions of these factors is related to the size of their GMSL contribution. These three contributors are also intentionally covered first due to the similarity of the mechanism that impacts regional SLC. Regional SLC associated with steric variability and ocean dynamics (also referred to as sterodynamic SLC) is combined into a single discussion (section 6), which includes both natural and anthropogenic contributions. This section also covers dynamic SLC that may occur as a result of freshwater input into the ocean associated with the contributors in sections 3 through 5. Given its large contribution to the SLC at the coast, a section is included on VLM, covering a range of temporal and spatial scales (section 7). Finally, as the goal here is to cover a wide range of time scales that impact regional and local SLC, a section on higher-frequency variability is provided that includes variations in sea level associated with astronomic tides, storm surges, ocean swell, wave setup, and wave run-up (section 8).
We use the term sea level in this paper to refer to both the lower-frequency variations described in sections 3 through 6, and the higher-frequency variations in section 8. Pugh and Woodworth (2014) define sea level as the sum of four main components: mean sea level, astronomical tides, a meteorological component, and waves. Using this description, sections 3 through 6 largely discuss changes in mean sea level, while section 8 covers the other higher-frequency components. As a summary of the contributing factors covered in this paper, Table 1 provides an overview of the relevant time scales of each process in addition to the magnitude of its associated contribution on a yearly basis. One of the main takeaways from this breakdown is the wide range of time scales and subcomponents associated with each factor, and the degree to which each needs to be accounted for within any particular time frame of interest.
Table 1: Components of Regional Sea-Level Rise Covered in This Paper, Along With Their Relevant Time Scales and Potential Magnitude
Component
Dominant temporal
scales
Potential magnitude
(yearly)
Ice sheets
years to centuries
millimeters to
centimeters
Glaciers (outside of ice sheets)
months to centuries
millimeters to
centimeters
Steric and dynamic sea-level change
months to decades
millimeters to
meters
Land water storage
months to decades
millimeters to
centimeters
High-frequency water level
variability
minutes to years
centimeters to
meters
Solid earth deformation/vertical
land motion
years to centuries
millimeters to
meters
Contributions From Ice Sheets
Current State of Knowledge


We use the term sea level in this paper to refer to both the lower-frequency variations described in sections 3 through 6, and the higher-frequency variations in section 8. Pugh and Woodworth (2014) define sea level as the sum of four main components: mean sea level, astronomical tides, a meteorological component, and waves. Using this description, sections 3 through 6 largely discuss changes in mean sea level, while section 8 covers the other higher-frequency components. As a summary of the contributing factors covered in this paper, Table 1 provides an overview of the relevant time scales of each process in addition to the magnitude of its associated contribution on a yearly basis. One of the main takeaways from this breakdown is the wide range of time scales and subcomponents associated with each factor, and the degree to which each needs to be accounted for within any particular time frame of interest.
Table 1: Components of Regional Sea-Level Rise Covered in This Paper, Along With Their Relevant Time Scales and Potential Magnitude
Component
Dominant temporal
scales
Potential magnitude
(yearly)
Ice sheets
years to centuries
millimeters to
centimeters
Glaciers (outside of ice sheets)
months to centuries
millimeters to
centimeters
Steric and dynamic sea-level change
months to decades
millimeters to
meters
Land water storage
months to decades
millimeters to
centimeters
High-frequency water level
variability
minutes to years
centimeters to
meters
Solid earth deformation/vertical
land motion
years to centuries
millimeters to
meters
Contributions From Ice Sheets
Current State of Knowledge
Using measurements from the joint NASA (US) /DLR (Germany) Gravity Recovery and Climate Experiment (GRACE) twin satellite mission, the Greenland and Antarctic Ice Sheets lost mass and collectively contributed around 1.17 ± 0.17 mm yr^{-1} to GMSL (Figure 2) from 2002 to 2017, about one third of the total GMSL rise (Dieng et al., 2017). This rate has been steadily increasing since the 1990s (Bamber et al., 2018). The Greenland Ice Sheet holds enough water to raise GMSL by 7.4 m, while the Antarctic Ice Sheet has the potential to increase GMSL by 58 m (Fretwell et al., 2013; Morlighem et al., 2017). Although both ice sheets are currently losing mass, they do so at different rates via different mechanisms. The Antarctic Ice Sheet mass loss has increased threefold from 2002-2007 (0.2 ± 0.1 mm yr^{-1} sea-level equivalent) to 2012-2017 (0.6 ± 0.1 mm yr^{-1}) (Shepherd et al., 2018) and is mostly attributed to an increase in ice sheet discharge from glacier acceleration in West Antarctica (Gardner et al., 2018; Mouginot et al., 2014; Rignot et al., 2011). This increase is driven by a combination of an intrinsic geometric instability associated with marine-based ice sheets grounded on bedrock that deepens toward the center of the ice sheet and changes in the availability of warm, circumpolar deep water under floating ice shelves due to decadal atmospheric variability (Jenkins et al., 2016). Warm ocean water acts in tandem with atmospheric warming to thin and break up foating ice shelves (Khazendar et al., 2016; Liu et al., 2015; Paolo et al., 2015), leading to acceleration and retreat of the glaciers they buttress (Shepherd et al., 2018; Wouters et al., 2015). In contrast, the Greenland Ice Sheet mass loss is dominated by changes in surface mass balance (SMB, precipitation minus sublimation and meltwater runoff), with a smaller contribution caused by increased discharge from marine terminating outlet glaciers (Enderlin et al., 2014; Shepherd et al., 2018). Increase in runoff along the entire Greenland Ice Sheet margin is predominantly caused by atmospheric warming which promotes the intensification of ice sheet surface melt (Van den Broeke et al., 2016) and in turn rates of frontal (ocean) melting (Carroll et al., 2016).
Figure 2: Time series and spatial patterns of ice sheet mass changes as measured by GRACE (2002-2017, Wise et al., 2018). In the upper plot, the solid lines show the GRACE mass balance from Antarctica (blue) and Greenland (red), with uncertainties contoured in the same color, and the three dotted lines show the lower, middle, and upper estimates of ice sheet mass loss in the business-as-usual, high-emissions RCP8.5 future scenario (IPCC, 2013). The numbers in the upper plot give the best linear Þt for each ice sheet. The lower plots show the linear trend in units of cm water equivalent per year squared over the 2002-2017 period.
Three independent observational methods are used to calculate current ice sheet mass loss rates: gravimetry, altimetry, and the inputÐoutput method (Shepherd et al., 2018). Each method has various strengths and weaknesses, with differing sensitivities to necessary corrections. Mass loss estimates from gravimetry (Velicogna & Wahr, 2006) provide the only direct measure of mass change of the ice sheets, but require a correction due to glacial isostatic adjustment (GIA) processes, which dominates the uncertainty in derived mass-loss rates. GIA uncertainties are largest for Antarctic Ice Sheet, and while estimates vary among studies, a recent study (Caron et al., 2018) estimates Antarctic Ice Sheet GIA uncertainty to be ~40 Gt (Gigaton = 10^{12} kg) per year, which is approximately 30% of the mass trend. Greenland, on the other hand, has a GIA uncertainty of ~13 Gt/yr, which is less than 5% of the Greenland Ice Sheet mass loss trend. Repeated satellite and airborne laser and radar altimetry provide detailed surface height change observations over ice sheets, but conversion from surface height to mass loss requires knowledge of spatial and temporal variability in firn density, a parameter that is poorly constrained due to sparse observations within the ice sheet interior (Pritchard et al., 2009). The input-output method (Gardner et al., 2018; Rignot et al., 2011, 2019; Shirzaei & Bgmann, 2012, 2018) - the only method that gives a longer time series of ice sheet mass balance (Kjeldsen et al., 2015; Rignot et al., 2019; Mouginot et al., 2019) - combines observations of ice flux across the grounding line from satellite remote sensing with modeled SMB estimates. In general, most observational time series are less than 20 years old, making the detection of mass loss acceleration in the presence of large natural variability challenging, especially in ice sheet SMB (Wouters et al., 2013). Radar altimetry from CryoSat-2 (launched in 2010), as well as new gravimetry (GRACE Follow-On, GRACE-FO) and laser altimeter (ICESat-2) missions launched in 2018, will extend the time series and provide continuous monitoring of ice sheet changes in the coming years.
We depend on a suite of numerical models to project future ice sheet changes, and these models also contribute to constraining past and present behavior. These models are traditionally used in a stand-alone framework but are increasingly “coupled” to represent the full spectrum of ice sheet-climate interactions. Atmospheric (surface climate and SMB) and oceanic (e.g., temperature, salinity, circulation, sea ice) forcings to the ice sheet are supplied by a variety of climate models, which are either produced for the full globe (global circulation models and climate reanalysis) or spatially limited to one particular ice sheet and surroundings (regional climate models). While circulation models historically focused on coupled ocean-land-atmosphere processes, modern earth system models also include the carbon cycle through dynamic atmospheric chemistry, as well as forcing of the ocean and atmosphere by the ice sheets. Regional climate models have become a preferred tool in representing ice sheet surface climate and SMB because they incorporate surface energy and snow hydrology processes and have the spatial resolutions (~5 km) necessary to accurately model the Greenland Ice Sheet and individual Antarctic Ice Sheet basins (Agosta et al., 2019; Lenaerts et al., 2017; Noel et al., 2018; Van Wessem et al., 2018), often with steep topographic slopes around ice sheet margins. However, the accuracy of any regional climate model depends on the quality of the atmospheric forcing at the model domain boundaries, and observations necessary to evaluate climate and SMB over extensive areas of northern Greenland and Antarctica are lacking.


We depend on a suite of numerical models to project future ice sheet changes, and these models also contribute to constraining past and present behavior. These models are traditionally used in a stand-alone framework but are increasingly “coupled” to represent the full spectrum of ice sheet-climate interactions. Atmospheric (surface climate and SMB) and oceanic (e.g., temperature, salinity, circulation, sea ice) forcings to the ice sheet are supplied by a variety of climate models, which are either produced for the full globe (global circulation models and climate reanalysis) or spatially limited to one particular ice sheet and surroundings (regional climate models). While circulation models historically focused on coupled ocean-land-atmosphere processes, modern earth system models also include the carbon cycle through dynamic atmospheric chemistry, as well as forcing of the ocean and atmosphere by the ice sheets. Regional climate models have become a preferred tool in representing ice sheet surface climate and SMB because they incorporate surface energy and snow hydrology processes and have the spatial resolutions (~5 km) necessary to accurately model the Greenland Ice Sheet and individual Antarctic Ice Sheet basins (Agosta et al., 2019; Lenaerts et al., 2017; Noel et al., 2018; Van Wessem et al., 2018), often with steep topographic slopes around ice sheet margins. However, the accuracy of any regional climate model depends on the quality of the atmospheric forcing at the model domain boundaries, and observations necessary to evaluate climate and SMB over extensive areas of northern Greenland and Antarctica are lacking.
The relation between ice sheets and climate is defined by a two-way connection: While ice sheets respond to atmospheric and oceanic conditions, they also influence the surrounding climate, for example, via the discharge of freshwater into oceans (Bronselaer et al., 2018; Schloesser et al., 2019) and changes in topographic geometries (e.g., Fyke et al., 2018). To this end, the ice sheet modeling community has increasingly focused on simulations that are fully coupled to climate models. The ongoing intercomparison of climate models (Sixth Coupled Model Intercomparison Project; CMIP6) includes several models that couple to dynamical ice sheet models for the first time (Nowicki et al., 2016). The initial development has been associated with atmosphere/ice sheet coupling over the Greenland Ice Sheet (e.g., Lipscomb et al., 2013). Major, ongoing challenges of such models include matching the temporal and spatial scales of the ice sheet model with the global models, providing accurate initial conditions for the ice sheet model, and allowing for the variable extent of the ice-covered surface. Initial improvements have been made in the representation of SMB in earth system models guided by lessons from regional climate models (e.g., Vizcaino et al., 2013). Advances in the coupling of ocean and ice sheet models (e.g., Goldberg et al., 2018) will continue to improve our ability to model the Antarctic Ice Sheet, particularly in West Antarctica, where oceanic forcings are likely to play a pivotal role in future ice sheet mass loss. Recent studies have demonstrated the impact of ice-ocean coupling on such sub-ice-shelf melt rates and grounding line migration (Golledge et al., 2019; Jordan et al., 2017; Seroussi et al., 2017).
The ice-sheet mass loss to the ocean strongly influences regional sea level, as associated changes in Earth’s GRD responses dictate the spatial distribution of water across the global ocean (Farrell & Clark, 1976; Milne & Mitrovica, 1998; Mitrovica et al., 2001). These so-called “sea-level fingerprints” are crucial to determining regional SLC (Figures 3a and 3b). In general, mass loss causes a sea level fall in the near field, a reduced sea-level rise at intermediate distances, and a greater-than-global-mean sea-level rise at larger distances. Sea-level fingerprints can be computed for specific portions of ice sheets, enabling accurately quantified sensitivities of basin-scale ice mass loss to local sea-level rise at any coastal cities. The collapse of Petermann Glacier in Greenland, for example, would lead to 38% lower sea-level rise at New York and 20% higher sea-level rise at Tokyo relative to the global mean (Larour et al., 2017; Mitrovica et al., 2018). Estimating the current and projecting future contributions from the two ice sheets - including spatial variability in the contribution across each ice sheet - is thus critical to understanding regional SLC. Updated assessments of the regional impact on coastal cities will continue to be made as our understanding of mass loss from ice sheets advances and projections are improved.
Uncertainties and Future Outlook
While significant progress has been made in recent years as described above, estimating future ice sheet contributions to sea level relies on models, which contain large uncertainties. These uncertainties exist in every stage of modeling ice sheets in future climates, from fundamental understanding of ice sheet physical processes (e.g., DeConto & Pollard, 2016), initialization (Goelzer et al., 2018), parameter, and boundary condition choices (e.g., Larour et al., 2012; Nias et al., 2016; Schlegel et al., 2015), to the quality of atmospheric and ocean forcings, which in turn rely on climate models with all their associated uncertainties (Nowicki & Seroussi, 2018; Robel et al., 2019); all of these uncertainties can limit the quality of model projections. For example, climate model-driven projections reported in the Fifth Assessment Report of the Intergovernmental Panel on Climate Change (IPCC) underestimated mass loss from 2006 to present, especially in the case of the Greenland Ice Sheet, including in the strongest warming (business-as-usual) RCP8.5 scenarios (Figure 2). This example highlights the need for extensive evaluation of present-day model performance, careful selection of model forcing, and, on the longer term, a focus on earth system model development to improve high-latitude atmospheric (e.g., clouds, radiation, precipitation) and oceanic processes, horizontal resolution and/or statistical downscaling (Lenaerts et al., 2019). Multimodel ensembles and intercomparisons (e.g., the Ice Sheet Model Intercomparison Project, ISMIP6; Nowicki et al., 2016) will also provide critical contributions to uncertainty quantifications.
Figure 3: Contribution to relative sea.level rise (mm/year) from 2002 to 2015 from (a) Antarctica Ice Sheet mass loss, (b) Greenland Ice Sheet mass loss, (c) terrestrial water storage variability, and (d) glacier mass loss. Adapted from Adhikari and Ivins (2016).
Ice sheet contributions are especially important when planning for future SLC (e.g., Garner & Keller, 2018; Oppenheimer & Alley, 2016; Sriver et al., 2018; Sweet et al., 2017). The research community is increasingly employing probabilistic approaches when making projections of future sea-level contributions from ice sheets (Edwards et al., 2019; Little et al., 2013; Ritz et al., 2015; Schlegel et al., 2018), which are necessary for holistic probabilistic projections of sea-level rise (e.g., Kopp et al., 2014, 2017; Perrette et al., 2013, Slangen et al., 2014). Probabilistic projections, however, are subject to the same limitations as the models or structured expert judgements (e.g., Bamber & Aspinall, 2013; Bamber et al., 2019) used to construct them. There is some utility in turning to past analogs of high sea-level contributions from ice sheets (e.g., the last interglacial or Pliocene) to calibrate ice sheet models and improve probabilistic projections (e.g., Edwards et al., 2019), but these too are impacted by prior model uncertainties, as well as by the uncertainties in paleo-reconstructions. Furthermore, the efficacy of using modern ice sheet trends for constraining future contributions remains an active area of research (Kopp et al., 2017). As these deep uncertainties in ice sheet contributions are elucidated and probabilistic projections continue to improve, they will inform policy decisions that are based on projected probabilities that regional- and global-scale sea levels will exceed critical levels (e.g., Bakker et al., 2017; Buchanan et al., 2016; Rasmussen et al., 2018; Sweet et al., 2017).


Figure 3: Contribution to relative sea.level rise (mm/year) from 2002 to 2015 from (a) Antarctica Ice Sheet mass loss, (b) Greenland Ice Sheet mass loss, (c) terrestrial water storage variability, and (d) glacier mass loss. Adapted from Adhikari and Ivins (2016).
Ice sheet contributions are especially important when planning for future SLC (e.g., Garner & Keller, 2018; Oppenheimer & Alley, 2016; Sriver et al., 2018; Sweet et al., 2017). The research community is increasingly employing probabilistic approaches when making projections of future sea-level contributions from ice sheets (Edwards et al., 2019; Little et al., 2013; Ritz et al., 2015; Schlegel et al., 2018), which are necessary for holistic probabilistic projections of sea-level rise (e.g., Kopp et al., 2014, 2017; Perrette et al., 2013, Slangen et al., 2014). Probabilistic projections, however, are subject to the same limitations as the models or structured expert judgements (e.g., Bamber & Aspinall, 2013; Bamber et al., 2019) used to construct them. There is some utility in turning to past analogs of high sea-level contributions from ice sheets (e.g., the last interglacial or Pliocene) to calibrate ice sheet models and improve probabilistic projections (e.g., Edwards et al., 2019), but these too are impacted by prior model uncertainties, as well as by the uncertainties in paleo-reconstructions. Furthermore, the efficacy of using modern ice sheet trends for constraining future contributions remains an active area of research (Kopp et al., 2017). As these deep uncertainties in ice sheet contributions are elucidated and probabilistic projections continue to improve, they will inform policy decisions that are based on projected probabilities that regional- and global-scale sea levels will exceed critical levels (e.g., Bakker et al., 2017; Buchanan et al., 2016; Rasmussen et al., 2018; Sweet et al., 2017).
As ice sheet models improve in their resolution, initialization procedures, and process implementation, they become increasingly reliant on observations to both force their behavior and validate their performance. Accurate reproduction of ice sheet dynamics, especially near grounding lines, requires high-resolution surface and bed topography (Aschwanden et al., 2016, 2019; Morlighem et al., 2014; Nias et al., 2018), estimates of basal shear stress (Parizek et al., 2013), and sub-ice shelf bathymetry (Schodlok et al., 2012). Geometric constraints on outlet glacier dynamics have improved dramatically in recent years (e.g., Greenbaum et al., 2015; Morlighem et al., 2017; Vaughan et al., 2012), but technological advancements (e.g., radar tomo.graphy; Al-Ibadi et al., 2018) and geophysical methods development (toward observational validation of sub-surface model parameters such as basal shear stress (Brisbourne et al., 2017), temperature (MacGregor et al., 2015; Schroeder et al., 2016), and englacial velocity (Holschuh et al., 2017, 2019; Leysinger Vieli et al., 2007) could drive significant improvement in model projections. Importantly, new aerogeophysical campaigns and satellite missions will be required to collect data optimized for these new techniques, as well as to fill gaps in existing subsurface observations. Ice sheet model development should focus on including geophysical observations directly, and extending the data assimilation capabilities from the inclusion of snapshot surface observations to the inclusion of time series data (Goldberg & Heimbach, 2013; Larour et al., 2014) to take full advantage of the abundance of remote sensing observations now available.
Contributions From Glaciers
Current State of Knowledge
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Figure 4: Time series of cumulative mass anomalies from GRACE for all primary glacier regions of the Randolph Glacier Inventory, except the Greenland and Antarctic periphery, covering the time period from 2002 to 2017. From Wouters et al. (2019).
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Uncertainties and Future Outlook
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Contributions From Changes in Land Water Storage
Current State of Knowledge
[…]
Uncertainties and Future Outlook
[…]
Steric Sea-Level and Ocean Dynamics
Current State of Knowledge
[…]
Uncertainties and Future Outlook
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VLM/Solid Earth Deformation
Current State of Knowledge
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Uncertainties and Future Outlook
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Contributions From High-Frequency Water Level Variability
Current State of Knowledge
[…]
Uncertainties and Future Outlook
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Near-Term Outlook of Regional Relative Sea-Level Understanding
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Summary
Changes in GMSL provide an integrative measure of the state of the climate system, encompassing both the ocean and cryosphere and may be viewed as an important indicator of what is currently happening to the climate in the present and what may happen in the future. While an increase in GMSL portends an increase in sea level of some magnitude along the world’s coastlines, the response on regional levels is not uniform. Water that is added to the ocean from land will not be distributed evenly everywhere (sections 3-5) and changes in ocean dynamics add to the regional variability in sea-level rise (section 6). Using observations from tide gauges and satellite altimetry, the extent of the spatial variability in the rate of sea-level rise can be understood. With the recent improved understanding of GRD effects on sea level, and the suite of VLM effects outlined here, it has become clear that the use of a single global rate to describe sea level around the globe is problematic, and improved assessment of sea-level rise on regional levels is required from a planning perspective.
Over the past century, coastal sea levels have risen over the majority of the globe. The effect of increasing sea level relative to land is a significant reduction in the elevation gap between typical high tides and a threshold elevation at which flooding begins (Sweet et al., 2018). Coastal communities were established with this gap in mind, recognizing flooding might occur under the most extreme of conditions. Recent reports (e.g., Sweet et al., 2017, 2018) have detailed the rapidly declining gap along the coastlines of the world, and the accelerated effect this has had on flood frequencies in many coastal locations. One important implication of these analyses is that the narrowed gap between high tide and flooding conditions can now be overcome by sea-level variability on a range of time scales. Subsequently, from a decision-making perspective, improved projections of future regional SLC are needed over a variety of time horizons, not simply the longest.
As discussed here, sea level varies on time scales from short-term (section 8), to seasonal-to-decadal (sections 5 and 6) or longer (sections 3-5). When considered in tandem with the movement of land relative to the ocean (section 7), contributions to sea level at each of these time scales can combine constructively, increasing sea levels and high-tide flood frequencies over both the short and long terms. The gap described above is known in many locations, and time horizons can be generated over which high-tide flood frequency will begin to increase rapidly. When considering only the long-term trend, this time horizon is usually found to be on the order of decades. However, when combined with the other contributors to sea-level variability, it is highly likely that in the short term (on the order of years) the cumulative effect of high-tide flooding will extend beyond “nuisance” levels and becomes too frequent for business as usual in coastal areas. As such, there is a strong need for improved information regarding future sea-level rise across a range of time scales.
While understanding the long-term contributions from melting glaciers and ice-sheets is essential, so too is understanding, quantifying, and possibly predicting the variability that will occur on seasonal to decadal time scales. Recent studies suggest that these contributors are becoming distinguishable with the records available (e.g., Fasullo & Nerem, 2018; Nerem et al., 2018). With the observations that are available - or will become available soon - coupled with improved data analysis and modeling efforts, our understanding of future regional SLC will continue to advance in the coming years. Knowing that planning efforts are underway and that sea-level rise is already impacting many parts of the world’s coastlines, it is worth taking inventory of the current state of understanding and clearly identifying areas of uncertainty that are impacting our ability to provide complete, accurate, and actionable information at the coast. Such assessments should be undertaken frequently to update relevant information in light of new science results, and to assist those tasked with translating current scientific understanding into plans that can be put into action at the coast.


Wickramage et al. (2023)
Title:
Sensitivity of MPI-ESM Sea Level Projections to Its Ocean Spatial Resolution
Corresponding author:
Chathurika Wickramage
Keywords:
Ocean, Sea level, Climate models, Mesoscale models, Model comparison
Citation:
Wickramage, C., Köhl, A., Jungclaus, J., & Stammer, D. (2023). Sensitivity of MPI-ESM Sea Level Projections to Its Ocean Spatial Resolution, Journal of Climate, 36(6), 1957-1980. doi:10.1175/JCLI-D-22-0418.1
URL:
https://journals.ametsoc.org/view/journals/clim/36/6/JCLI-D-22-0418.1.xml
Abstract
The dependence of future regional sea level changes on ocean model resolution is investigated based on Max Planck Institute Earth System Model (MPI-ESM) simulations with varying spatial resolution, ranging from low resolution (LR), high resolution (HR), to eddy-rich (ER) resolution. Each run was driven by the shared socioeconomic pathway (SSP) 5-8.5 (fossil-fueled development) forcing. For each run the dynamic sea level (DSL) changes are evaluated by comparing the time mean of the SSP5-8.5 climate change scenario for the years 2080–99 to the time mean of the historical simulation for the years 1995–2014. Respective results indicate that each run reproduces previously identified large-scale DSL change patterns. However, substantial sensitivity of the projected DSL changes can be found on a regional to local scale with respect to model resolution. In comparison to models with parameterized eddies (HR and LR), enhanced sea level changes are found in the North Atlantic subtropical region, the Kuroshio region, and the Arctic Ocean in the model version capturing mesoscale processes (ER). Smaller yet still significant sea level changes can be found in the Southern Ocean and the North Atlantic subpolar region. These sea level changes are associated with changes in the regional circulation. Our study suggests that low-resolution sea level projections should be interpreted with care in regions where major differences are revealed here, particularly in eddy active regions such as the Kuroshio, Antarctic Circumpolar Current, Gulf Stream, and East Australian Current.
Significance Statement
Sea level change is expected to be more realistic when mesoscale processes are explicitly resolved in climate models. However, century-long simulations with eddy-resolving models are computationally expensive. Therefore, current sea level projections are based on climate models in which ocean eddies are parameterized. The representation of sea level by these models considerably differs from actual observations, particularly in the eddy-rich regions such as the Southern Ocean and the western boundary currents, implying erroneous ocean circulation that affects the sea level projections. Taking this into account, we review the sea level change pattern in a climate model with featuring an eddy-rich ocean model and compare the results to state-of-the-art coarser-resolution versions of the same model. We found substantial DSL differences in the global ocean between the different resolutions. Relatively small-scale ocean eddies can hence have profound large-scale effects on the projected sea level which may affect our understanding of future sea level change as well as the planning of future investments to adapt to climate change around the world.
Introduction
Rising sea levels are among the largest threats of anthropogenic global warming to society, with far-reaching consequences for many coastal and island populations around the globe (Church et al. 2011; Fox-Kemper et al. 2021). Our understanding of the global mean sea level trends has improved significantly over the past decades based on coordinated modeling efforts, such as the Coupled Model Intercomparison Project (CMIP) and the analysis of past observations (e.g., Church et al. 2011; Fox-Kemper et al. 2021). However, a quantitative understanding of processes that lead to regional to local-scale sea level changes is still pending, which affects the ability to accurately forecast future coastal changes (Church et al. 2013a). Although the quantitative budget of the global sea level rise is understood, insufficient data hampers the understanding on regional and coastal scale, which makes improving modeling efforts essential for closing the gaps.
Physically, regional to local-scale sea level change is a global problem as it depends on processes taking place locally as well as remotely. As such, it is directly or indirectly affected by all components of the climate system as well as contributions originating from the solid Earth such as vertical seafloor movement or changes in gravity (Stammer et al. 2013). However, the relative contribution of individual processes or forcing components to the regional or local sea level changes is strongly dependent on the spatial and temporal scales under consideration and might also change under global warming conditions.
In this context a caveat of previous CMIP projections is that underlying climate models are of relatively low spatial resolution, thereby intrinsically excluding the impact of resolved ocean eddies on the solution. To what extent existing sea level projections are thus biased toward large-scale climate mode responses as opposed to regional dynamical balances remains therefore to be understood, making it difficult to provide quantitative information about future sea level projections in specific regions, such as coastlines. This situation now gradually changes as climate projections from eddy-resolving models are becoming available accounting for the dynamical processes associated with boundary or coastal current dynamics, which are important for accurate small-scale sea level change information (e.g., van Westen et al. 2020; van Westen and Dijkstra 2021; Li et al. 2022). Given these new opportunities, it is now timely to test previous CMIP sea level change projections against novel eddy-rich climate projections.
Against this background, the aim of this paper is to provide an understanding of the sensitivity of CMIP type sea level projections to model resolution and, thus, to define an uncertainty level in CMIP previous projections resulting from the lack of small-scale processes and eddy mechanisms. Specifically, we aim to quantify differences in the resulting sea level projections obtained under shared socioeconomic pathway (SSP) 5-8.5 forcing (O’Neill et al. 2017) with respect to lower-resolution simulations using a hierarchy of spatial resolutions. The respective work will be based on the eddy-rich Max Planck Institute Earth System Model (MPI-ESM-ER) experiments (Gutjahr et al. 2019), which have been performed as part of the CMIP6-endorsed HighResMIP (Haarsma et al. 2016). At the same time, we aim to identify causes for those changes in terms of mechanisms, which can result from differences in the ocean dynamics and differences in the air–sea exchange of heat, freshwater, or momentum. Geographically, our work focuses on the North Atlantic, the North Pacific, and the Southern Ocean, where large-scale effects from mesoscale eddies can be expected, given the presence of strong and eddy-rich western boundary currents.
The structure of the remaining paper is as follows: Section 2 describes the model and the evaluation methods used. Common characteristics of sea level change in the models are described in detail in section 3. In section 4, we compare the ocean model projection in each basin. We conclude and summarize with section 5.
Materials and methods
Climate model simulations with MPI-ESM
Our study is based on climate projections obtained with the MPI-ESM1.2 and performed under the protocol of the CMIP phase 6 (CMIP6; Eyring et al. 2016). The MPI-ESM is a fully coupled climate model, using ECHAM6 (Stevens et al. 2013) for the atmosphere and MPIOM (Jungclaus et al. 2013) for the ocean. Details on the CMIP6 version in comparison with its predecessor can be found in Mauritsen et al. (2019). Our study considers three versions of the same model configuration, including the low-resolution (LR), high-resolution (HR), and eddy-rich (ER) models, all driven by the SSP5-8.5 (fossil-fueled development) (O’Neill et al. 2017) forcing. From each model simulation monthly mean fields are available. Configurations for all experiments evaluated here are summarized in Table 1.
Table 1: Summary of MPI-ESM projections used in this study.


The structure of the remaining paper is as follows: Section 2 describes the model and the evaluation methods used. Common characteristics of sea level change in the models are described in detail in section 3. In section 4, we compare the ocean model projection in each basin. We conclude and summarize with section 5.
Materials and methods
Climate model simulations with MPI-ESM
Our study is based on climate projections obtained with the MPI-ESM1.2 and performed under the protocol of the CMIP phase 6 (CMIP6; Eyring et al. 2016). The MPI-ESM is a fully coupled climate model, using ECHAM6 (Stevens et al. 2013) for the atmosphere and MPIOM (Jungclaus et al. 2013) for the ocean. Details on the CMIP6 version in comparison with its predecessor can be found in Mauritsen et al. (2019). Our study considers three versions of the same model configuration, including the low-resolution (LR), high-resolution (HR), and eddy-rich (ER) models, all driven by the SSP5-8.5 (fossil-fueled development) (O’Neill et al. 2017) forcing. From each model simulation monthly mean fields are available. Configurations for all experiments evaluated here are summarized in Table 1.
Table 1: Summary of MPI-ESM projections used in this study.
The coupled control simulations were initialized and forced following the CMIP6 protocol for HR and LR. The reference year for the preindustrial control simulation (piControl) is 1850, and it is conducted under conditions that have been selected to be typical of the time before the start of large-scale industrialization. A control simulation typically begins after an initial spinup phase, during which the climate system reaches a state close to an equilibrium (Eyring et al. 2016). For ER, the coupled control simulation was however initialized following the CMIP6-HighResMIP protocol (Haarsma et al. 2016). The ER control run was initialized after 30 years of spinup initialized from the averaged state of the Met Office Hadley Centre EN4 observational dataset from 1950 to 1954 (Good et al. 2013) for the ocean and ER atmosphere initialized from HR atmospheric state (Gutjahr et al. 2019). The length of control run is 1000 years for LR, 500 years for HR, and 200 years for ER.
The low-resolution version of MPI-ESM (MPI-ESM-LR) approximately has a 1.9° horizontal resolution for the atmosphere (spectral truncation at T63; 210 km at the equator; 192 × 96 longitude/latitude) and 47 hybrid sigma pressure level extending to a 0.01 hPa top level. The ocean component has a bipolar 1.5° horizontal resolution (GR1.5; approximately 150 km near the equator; 256 × 220 longitude/latitude) and 40 vertical levels with layer thickness ranging from 12 m near the surface to several hundred meters at depth. The horizontal grid spacing varies from 185 km in the tropical Pacific to 22 km around Greenland. The poles of the ocean model are over Greenland and Antarctica (coast of the Weddell Sea). The LR version cannot capture mesoscale ocean processes and dynamics (for more details, Mauritsen et al. 2019).
The high-resolution configuration, MPI-ESM-HR (Müller et al. 2018), uses a 0.9° horizontal resolution (T127; 384 × 192 longitude/latitude) for the atmosphere, which is approximately 100 km around the equator. HR has a relatively highly resolved stratosphere extending to a 0.01 hPa top level with 95 vertical levels (L95). A tripolar grid 0.4° horizontal resolution (TP04; 802 × 404 longitude/latitude) is used for the ocean component. Two poles are placed in the Northern Hemisphere over central Asia (Siberia) and Canada, providing quasi-homogeneous resolution of a approximately 40 km in the Arctic Ocean. In the Southern Hemisphere, grid distances decrease with increasing latitude. South of the Antarctic Circumpolar Current (ACC) at around 60°S the resolution is 20 km. HR comprises 40 unevenly spaced vertical levels, allocating 20 levels within the upper 700 m. HR is permitting eddies in the tropics but not resolving the Rossby radius in the higher latitudes. Even though HR fails to resolve the Rossby radius length scales, key for the representation of boundary currents and fronts, it still can capture reasonable eddy-like structures (see Jungclaus et al. 2013; Müller et al. 2018).
The Gent–McWilliams (GM) parameterization (Gent and McWilliams 1990) of mesoscale eddies is used in LR and HR. The GM coefficients in HR and LR are constant and quite small. They are scaled with the grid spacing. The GM parameterization decreases linearly with increasing resolution, and a value of 250 m−2 s−1 was chosen for a grid cell that is 400 km wide (Gutjahr et al. 2019).
The eddy-rich MPI-ESM-ER (Gutjahr et al. 2019) has the same T127/L95 atmospheric component as HR. However, the horizontal resolution of the ocean component is on a tripolar 6-min (TP6M) horizontal grid (approximately 0.1° or 10 km) in both latitude and longitude, and has 80 vertical levels. ER has three poles over North America, Russia, and Antarctica. In the eddy-rich-resolution model simulations, the GM parameterization for mesoscale eddies is disabled, and eddy effects are resolved according to the ratio of the first baroclinic deformation radius to the horizontal grid spacing. Eddies are not resolved at higher latitudes and over shallow/shelf regions. The grid resolution is smaller south of 50°S (Table 1; for more details, check Mauritsen et al. 2019; Putrasahan et al. 2021). The ER model has nominal horizontal resolution of ∼10 km which means that the large-scale (order of 1000 km) and oceanic mesoscale eddies (order of 10 and larger) are resolved almost everywhere; however, the ocean submesoscale eddies are typically less than 10 km are not included in the ER simulation. In addition, the air–sea interactions from processes such as mesoscale storms are not resolved by the atmospheric component of ER model.
As part of our analysis, we compare results from all model version described above under the SSP5-8.5 climate forcing scenario covering 2080–99, to their historical simulations during 1995–2014. In all cases we consider ensemble means using all available members, which are 10 members in LR, 2 in HR, and 3 in ER to minimize the impact of climate variability. Prior to analyzing the model output, we interpolated it onto the same grid of 1° horizontal resolution. As the development of ER was computationally expensive, it has not been tuned and spun up according to the standard of HR and LR (Mauritsen et al. 2019). Therefore, the linear trend obtained from the only member of the control run was removed from the historical and scenario data. While we focus mostly on effects of ocean resolution, we note that LR features also considerably lower resolution in the atmosphere. Therefore, we put particular emphasis in the discussion on changes we diagnose in the ER configuration, which was run with the same atmosphere as the HR model.
Analyzing model output
This study considers the dynamic sea level (DSL), which is defined as the mean sea level above the geoid due to ocean dynamics (Gregory et al. 2019):
ζ = η − η′. (1)
Here ζ is the variable “zos” according to the CMIP terminology (Griffies et al. 2016), η, which is named “sterodynamic sea level,” is the sea surface height relative to a reference geopotential surface, and η′ denotes a global mean (Gregory et al. 2019). Hence, DSL change (Δζ) should have a zero global mean by definition. We therefore subtracted the global mean from each input field.
As we are interested in future sea level change, our work focuses on the dynamic sea level change (Δζ) pattern, which is calculated from the difference between the DSL change in SSP5-8.5 forcing scenario (Δηs) relative to the DSL change in the historical simulation (Δηh):
Δζ = Δηs − Δηh. (2)
Considering that changes in circulation and changes in wind stress in principle are the key drivers of these changes, we also calculated changes in the barotropic streamfunction ψ, changes in surface wind stress, and variation in the meridional overturning circulation and analyzed their differences as function of model resolution.