Although the global-mean sea level (GMSL) rose over the
twentieth century with a positive contribution from thermosteric and
barystatic (ice sheets and glaciers) sources, the driving processes of GMSL
changes during the pre-industrial Common Era (PCE; 1–1850 CE) are largely
unknown. Here, the contributions of glacier and ice sheet mass variations
and ocean thermal expansion to GMSL in the Common Era (1–2000 CE) are
estimated based on simulations with different physical models. Although the
twentieth century global-mean thermosteric sea level (GMTSL) is mainly
associated with temperature variations in the upper 700 m (86 % in
reconstruction and 74
Contemporary global-mean sea-level (GMSL) rise is one of the key indicators
of the earth's energy imbalance. For instance, the GMSL rise (1.2–1.5 mm yr
Recent studies have shown that more than 90 % of the observed change in GMSL during the last few decades can be explained solely by ocean thermal expansion and changes in the mass balance of continental ice storage (Leuliette and Miller, 2009; Church et al., 2013; Church and White, 2011; WCRP Global Sea Level Budget Group, 2018). Significant improvements in the understanding of changes in ocean thermal structure as well as in the continental ice and water storage (e.g. Kjeldsen et al., 2015; Marzeion et al., 2015; Zanna et al., 2019; Parkes and Marzeion, 2018; Humphrey and Gudmundsson, 2019) have indeed resulted in the closure of the GMSL budget for the entire twentieth century, pointing to the dominant role of those processes (e.g. Frederikse et al., 2020).
The GMSL was about 120 m below the current level at the Last Glacial
Maximum (about 21 ka BP). The subsequent deglaciation caused the sea level
to rise until the mid-Holocene (from
The driving processes of GMSL changes during the PCE are likely the same as those responsible for the recent sea-level rise (e.g. Gregory et al., 2006; Ortega et al., 2013), but their relative contributions are largely unknown. In particular, considering the PCE as a period with weak anthropogenic perturbations allows one to examine the processes controlling GMSL from natural forcing and internal climate variability. In addition, the response time of the climate components (oceans, glaciers and ice sheets) and the corresponding GMSL change can be of the order of several centuries (upper ocean and glaciers) or even millennia (deep oceans and ice sheets). Consequently, the understanding of current changes in GMSL calls for the analysis of past variability. For example, the cooling anomalies observed in the deep Pacific in the twentieth century were related to the Little Ice Age (LIA) cooling and were shown to offset the recent global heat gain in the upper ocean in some regions (Gebbie and Huybers, 2019).
This paper focuses on the GMSL changes in the CE by analysing the contributions of major components (ocean thermal expansion and changes in continental ice-mass balance) derived from model experiments. A comparison of model-derived GMSL with proxy-based sea-level estimates (e.g. Kopp et al., 2016) is also provided. Such an exercise is important because estimates of different contributing processes to GMSL can provide insights into potential differences in the mechanisms controlling these GMSL changes between different periods in the CE. Also, as the climate in the PCE is less impacted by the anthropogenic forcing and largely a result of natural variability, the findings place the current anthropogenic warming and sea-level rise in a broader context. Using model simulations, we mainly ask whether the GMSL changes over the CE can be explained within the uncertainty estimates and what the major sources of uncertainty are. Also, which processes determine the centennial-scale variability seen in the proxy-based GMSL reconstructions during the CE?
The GMSL varies either due to changes in the ocean mass (
The GMTSL is estimated using the 3-D field of ocean temperature and salinity
from
Computations covered 1–2000 CE for LOVECLIM and 850–2005 CE for
PMIP3 and CMIP5 models and CESM1. We used the equation of sea-water state of
Jackett and McDougall (1995) for the thermosteric sea-level computations
rather than the recent equation (IOC, SCOR and IAPSO, 2010), as most of the climate models considered in this study
employ the former equation in their formulation. For GMTSL computations
using simulations from the PMIP3
The contribution from ice sheet mass variations (Antarctic and Greenland) is
estimated from the finite-difference ice sheet model
The model for Greenland is set up at 16 km horizontal resolution and uses the shallow ice approximation. Floating ice is not considered and is removed when it occurs. In the absence of (i) useful constraints on marine-terminating outlet glacier evolution over the CE, (ii) applicable forcing and (iii) sufficient process understanding, the model does not consider explicit ice-ocean interactions and is driven by SMB forcing alone. The model initialization builds on earlier work and starts from an existing thermodynamically coupled steady state with constant, present-day boundary conditions (IMAUICE1 in Goelzer et al., 2020). From here, the model is relaxed for 10 kyr with a fixed ice temperature to the PDDM SMB forcing with a surface temperature anomaly of zero degrees to produce a nominal initial state for CE simulations.
For simulations forced using PMIP3 GCM outputs, the initial state is
assigned to the year 850 CE, and the model is run forward with GCM-derived
spatially constant 2 m air temperature anomalies as input to the PDDM.
Simulations using output from LOVECLIM are set up similarly but cover the
entire CE, with the initial state assigned to 1 CE. The same is true for
forcing derived from the last millennium reanalysis data version 2 (LMR;
Tardif et al., 2019). The GCM-forced experiments are complemented by
simulations driven with spatially constant temperature anomalies derived
from an ice core record (Kobashi et al., 2011) spanning 1–2000 CE. We have
introduced two types of perturbations to test uncertainty in the initial
state. In the first case, the initial state is perturbed for 500 years
before the start of the simulations with a constant temperature offset
between
The model for Antarctic simulations is run at a 32 km horizontal resolution
and uses a combination of shallow ice and shallow shelf approximations, with
velocities added over grounded ice to model basal sliding (Bueler and Brown,
2009). We use the Schoof flux boundary condition (Schoof, 2007) at the
grounding line with a heuristic rule, following Pollard and DeConto (2012).
Model initialization again builds on an existing present-day ice sheet
steady state (IMAUICE2 in Seroussi et al., 2020), which is first relaxed
with fixed ice temperature for 10 kyr to the PDDM SMB and zero subshelf
basal melting. We then continue for another 5 kyr with background subshelf
basal melt rates estimated for the modelled ice draft using the shelf melt
parameterization of Lazeroms et al. (2018) with a thermal forcing based on
the World Ocean Atlas (WOA; Garcia et al., 2019) at 400 m depth. Assuming a
colder ocean for the first millennium CE, and since we could not find stable,
steady-state grounding line positions for the original thermal forcing, we
introduced an offset of
Subshelf basal melt rate anomalies for the transient GCM-forced experiments
are derived using spatially uniform ocean temperature anomalies averaged
over 400–600 m from models in combination with a high subshelf melt
sensitivity of 11 m yr
The glacier volume change estimates are made using the Open Global Glacier Model (OGGM, Maussion et al., 2019) version 1.4 (Maussion et al., 2021). The OGGM is an open-source model which couples a surface mass balance model with a model of glacier dynamics. The OGGM is used to model the annual rate of glacier mass change for 18 of the 19 glaciated regions defined in the Randolph Glacier Inventory (RGI; Pfeffer et al., 2014), with the Antarctic and sub-Antarctic region not modelled due to limitations of the baseline climatology dataset. We used gridded monthly temperature and total precipitation records from the last millennium reanalysis (LMR) data version 2 (Tardif et al., 2019) to drive the model. The OGGM determines the temperature and precipitation at each glacier location by applying these as anomalies to a reference climate. We have not used PMIP climate model results because of the potential biases in those models that would require specific corrections before adequately driving OGGM, and deriving those corrections is out of the scope of the present study (Parkes and Goosse, 2020).
Runs with two different reference climatic conditions are performed: one
using CRU TS 4.01 (Climatic Research Unit gridded Time Series 4.01; Harris
et al., 2020) mean climate from 1951–1980 (glacier simulation covers the
period 1–2000 CE), and the other using ERA5 (covers 850–2000 CE),
which is a recent update of the ERA-interim data as documented in Hersbach
et al. (2020). Temperature and precipitation at the reference grid
elevation for each of the two datasets are scaled to the glacier surface at
each OGGM grid point using a default temperature lapse rate of
The contributions of positive degree-months for ablation and solid
precipitation for accumulation are combined to calculate mass balance, which
is used to update glacier geometry annually. In this study, frontal ice
ablation of tidewater glaciers is not explicitly simulated. The initial
state of mountain glaciers at the beginning of the millennial simulations is
unknown: we therefore use the year
The simulated volume (
The GMSL derived from proxy-based sea-level reconstructions for the CE from Kopp
et al. (2016), Kemp et al. (2018) and Walker et al. (2022) are considered
for comparison with our model GMSL. Those GMSL reconstructions are
iterations of a spatiotemporal statistical model applied to a growing
database of the CE proxy reconstructions. In this spatiotemporal model
framework, the GMSL is an estimate from the signal “common” to all sea-level
records in the CE proxy database. As the GMSL is the “globally uniform”
term among sites in the spatiotemporal model, the method could give a true
estimate of GMSL in the presence of spatially complete data. Consequently,
the quality of the estimate depends on the geographic distribution of proxy
records, which is very uneven (however, some sensitivity tests to explore
the effect of the geographic distribution of proxy records have been done in
Kopp et al., 2016). As the Walker et al. (2022) reconstruction is based on
the latest update of the proxy sea-level database, and the Kemp et al. (2018) and Kopp et al. (2016) curves do not differ much over the CE, we show the GMSL from Walker et al. (2022) and Kemp et al. (2018) in our model
comparison. Also, in Kemp et al. (2018), the GMSL during
We also compare our model GMTSL with the reconstructed GMTSL estimates from Zanna et al. (2019) over 1870–2018. Since Zanna et al. (2019) already compared their reconstruction to different observation-based oceanic heat content estimates (e.g. Levitus et al., 2012; Ishii et al., 2017), we do not show all those available products in this paper for the twentieth century comparison. Reconstructions of ocean temperatures over the CE are limited to either sea surface temperature derived from palaeoceanography (proxy) data (e.g. PAGES2k Consortium, 2017; McGregor et al., 2015) or spatially averaged oceanic heat content estimates generated through inverse modelling and using available instrumental and palaeo-data (Gebbie and Huybers, 2019). Although such datasets have helped to understand certain key features of ocean climate variability during the CE, they do not provide a direct estimate of the contribution of ocean changes to GMSL. Hence, we do not attempt to compare our model thermosteric variability with any of those datasets in this paper. Also, as the GMSL reconstruction from Walker et al. (2022) and Kemp et al. (2018) already incorporated the tide-gauge based twentieth century GMSL (e.g. Hay et al., 2015), we do not show those available twentieth century GMSL reconstructions in this paper.
As described in the previous sections, our model experiments span two
distinct periods (either 1–2000 or 850–2000 CE) depending on the
input fields used to run the ice-sheet model or the reference climate used
in our glacier model. Our thermosteric estimates also cover these two
periods depending on the model (1–2000 CE for LOVECLIM and 850–2000
for the rest of the models). Hence, we present our model-derived sea-level
components and the final GMSL estimates as two groups, namely
Details of the two groups of model experiments presented in this
study. The columns are split into two rows for the barystatic components for
EXP-I and EXP-II, highlighting the physical model used (top row) and the
input used to run the model (bottom row). The numbers in square brackets show
the number of independent simulations made either using different models
(e.g. PMIP model simulations) or based on the input field given to the
physical model (ice sheet/glacier model run with different input fields) for
each component. Abbreviations (for the variables used) are:
To estimate model uncertainty for the glacier contribution, we combined the
impacts of intraregional and interregional uncertainty. It should be noted
that since all samples (regional glacier volume simulations) are taken from
a
Interregional uncertainty is also estimated with a “leave X out” method by creating a set of global volume reconstructions, each leaving out three top level RGI regions. The contribution of each region is then perturbed according to the regional standard deviation calculated as above. For each region in the sample of regions, a single value is sampled from a normal distribution with a mean of 0 and a standard deviation of 1. Then the standard deviation time series for the region is multiplied by that single value and added to the regional time series. Perturbing regional time series in this way results in a more realistic range than simply adding (a likely underestimate) or normalized multiplying (a likely overestimate) the independent uncertainty ranges from the intraregional and interregional samples. The sample of perturbed regional time series (with the three top level regions removed) is then added together and scaled to match the total (including all modelled RGI regions) global volume in 2001. We did this for 1000 independently sampled leave-3-out sets of regions and formed the confidence interval for combined intraregional and interregional uncertainty as to the 1 standard deviation.
As shown in Table 1, our independent estimates of thermosteric and ice sheet
contributions are limited to less than 10 cases and not consistent for
these 2 processes. On the other hand, we have generated 1000 synthetic
curves and derived confidence levels for the glacier sea-level simulations,
as described in the previous section. To have a consistent set of estimates
for thermosteric and ice sheet contribution, we employed a Monte Carlo
method by generating 1000 realizations of available estimates in each
contributing process. Ensemble members are generated by randomly selecting
and perturbing one of the available estimates at a time. Specifically, we
perturbed the estimate by drawing random numbers (white noise) from a
Gaussian distribution using the a priori standard deviation (which is taken as the
RMSE between the ensemble mean and the randomly selected estimate) and
adding those random numbers to the selected estimate. Note that this method
does not include any other specific process that misses in our modelling
experiments but acknowledges the remaining uncertainty (e.g. uncertainty
arises from model initialization, different input data, or differences in
model physics) and propagates the overall uncertainty to the final GMSL
curve in a consistent way. An additional remark here is that for
thermosteric estimates from EXP-II, for which the computation is restricted
to the top 700 m owing to the deep layer temperature drift, we added a
Global-mean thermosteric sea level from LOVECLIM climate model
simulations (orange; 1–2000 CE) and Zanna et al. (2019) reconstruction
(green; 1870–2018) for
Figure 1 shows the GMTSL computed over the entire depth (Fig. 1a), top 700 m (Fig. 1b), and below 700 m (Fig. 1c) from the LOVECLIM model for
the CE. Our primary goal here with Fig. 1 is to illustrate the relative
contribution of the
Contributing components to GMSL.
Over the period 1900–2000 CE, 86 % and 74
However, the relative contribution of the oceanic upper and lower layers to
the total GMTSL changes varies significantly over the PCE, as shown in
Fig. 1a. For instance, the upper layer cooling contributes only half of
the total GMTSL decrease during 1500–1750 (LIA). An increase in the upper
layer GMTSL during 1250–1500 was offset by a deep layer cooling (Fig. 1b,
c) and resulted in a weak total GMTSL rise over that period (Fig. 1a). The
contribution of the upper layer to the GMTSL fall during 250–500 (500–750) is about 56 % (59 %), suggesting that the cooling below 700 m
has an equally important role over those periods. The lag in the lower layer
thermosteric rise compared to the recent warming of the upper ocean
(
The GMTSL estimates from all the available simulations show that the
amplitude of GMTSL changes in the PCE is small compared to the
twentieth century rise (Figs. 1 and 2a). The GMTSL does not vary more than
Figure 2a shows that the GMTSL increased during the first three centuries of
the CE (so-called Roman Warm Period) and then declined to 700 CE, a period
characterized by cold and dry climatic conditions, referred to as the Late
Antique Little Ice Age (Helama et al., 2017). The GMTSL then rose about 1 cm
toward the Medieval Warm Period (
The 250-year moving rate of sea level for each of the components shown
in Fig. 2.
The GMSL changes due to Antarctic mass balance variations over the instrumental period (Church et al., 2013; Frederikse et al., 2020) and future projections (Moore et al., 2013; Palmer et al., 2020; Seroussi et al., 2020) are highly uncertain. The uncertainties are also prominent over the PCE, with the uncertainty range (shading around the mean) of our estimate of the Antarctic ice sheet's contribution to sea-level changes (Fig. 2b) and its rate (Fig. 3b) including both positive and negative values for the majority of the period. The range of probabilities at the beginning of the first millennium in EXP-I (Fig. 2b) indicates either a sea-level fall or rise, depending on the initial state. The central estimate (ensemble mean) of the Antarctic sea-level contribution, however, shows a long-term fall over the first millennium (1–1000 CE) and a reversal in sign further until the early twentieth century (Fig. 2b). The positive sea-level contribution during the second half of the PCE (1000–1900 CE) is further supported by the PMIP-based simulations (EXP-II). However, the uncertainty is even larger in this case (Fig. 2b). EXP-II indicates a weak positive mass balance (negative sea-level contribution) during the twentieth century, while the twentieth century change is nearly zero in EXP-I (Fig. 2b).
The inferred uncertainties are also evident in the rate of sea-level change, as seen in Fig. 3b. The central estimate of the rate (from EXP-I and EXP-II) over the entire period is in line with the sea-level or mass balance change described above. The rate is negative during 1–1000 CE and then becomes positive for the rest of the period (Fig. 3b). The twentieth century decline in sea level is reflected in the sea-level rate as the rate decreases towards the end of the period (the rate is still positive as our window of rate computation is 250 years). The surface temperature over Antarctica in the past 2 millennia (Stenni et al., 2017) exhibits an inverse relationship to sea level over multicentennial periods (Fig. 2b). Our experimental design can explain this relationship as a warmer climate generally enhances precipitation over Antarctica and decreases the GMSL (Frieler et al., 2015; Medley and Thomas, 2019).
Greenland's contribution to GMSL exhibits substantial centennial-scale
variability with a positive long-term trend (
Results from the OGGM (Fig. 2d) suggest that the GMSL, as a response to global
glacier mass balance changes, rose gradually over 1–500 CE (with a sea-level
equivalent of
Figure 4a compares our model-based GMSL (i.e. the sum of the contributing
processes shown in Fig. 2) with the GMSL from proxy-based reconstructions.
An apparent difference between the GMSL reconstructions of Kemp et al. (2018) and Walker et al. (2022) at the beginning of the CE (solid and dashed green
curves i Fig. 4a) is due to an imposed methodological constraint in the Kemp et al. (2018) reconstruction as noted in Sect. 2.4. The model GMSL exhibits a broad
agreement with proxy-based reconstructions, despite a few inconsistencies
and large uncertainty in the first millennium. Our model GMSL indicates a
steady rise of about 5–10 cm during the first 5 centuries of the CE.
This rise is in line with Kemp et al. (2018; although the amplitude is
smaller in reconstruction). However, the Walker et al. (2022) reconstruction
shows a nearly steady GMSL over the same period (Fig. 4a). The reconstructed sea level shows a PCE maximum (
Those salient features of GMSL evolution over the CE are also evident in
Fig. 4b, which shows a moving 250-year rate for GMSL (model and
reconstructions) and global-mean surface temperature. The GMSL trend is
positive during 1–500 CE in both the model and reconstructions, and the rate
varies between
The ensemble mean thermosteric and barystatic (sum of ice-sheet and glacier
contributions) sea levels over the CE is separately shown in Fig. 5a and
b, respectively. In general, the thermosteric changes are much weaker than
barystatic changes during the PCE (note that the scale is different for
panels a and b in Fig. 5). However, the twentieth century model GMSL change is mainly attributed to thermosteric sea-level rise. Also, while the barystatic
changes occur mostly over millennial time scales,
multidecadal to centennial changes are evident in thermosteric variability
(Fig. 5a). As noted in Sect. 3.1, the multicentennial GMTSL changes are
linked to the regional climate epochs during the PCE. For example, the
GMTSL was nearly down to the reference level (1841–1860 CE level) during 600 CE (Late Antique Little Ice Age – LALIA) and then rose by
Global-mean thermosteric
Figure 5c–f illustrate that different processes contribute variable amounts (in terms of both rate and sign) to the GMSL change in different periods, with glaciers as the dominant source throughout the PCE. The histograms in Fig. 5c–f represent the ratio of the rate of individual contributions to the net GMSL rate (in %) over the selected period. For instance, the GMSL rise during the first 600 years and GMSL fall during 1200–1800 CE are driven mainly by glacier mass-balance changes (Fig. 5c and e). Figure 5d also shows that the weak GMSL changes during 600–1200 CE (Fig. 4a) result from opposing contributions from its components. While the thermosteric and Greenland ice sheet exhibit a positive contribution (i.e. GMSL rise), the GMSL associated with changes in glaciers and the Antarctic ice sheet shows a negative contribution (Fig. 5d) and resulting in a net GMSL change which is nearly zero over this period (600–1200; Fig. 4a). Note that the uncertainties are large for all the components except the glacier contribution during this period. All the GMSL components except the Antarctic ice sheet have a positive contribution to the net GMSL fall during 1200–1800 CE. As shown in Fig. 5a, the model GMSL rise since 1800 CE is mainly linked to the thermosteric rise with a weak contribution from barystatic sea-level components (Fig. 5b and f). Figure 5c–f indicates that the changes in the GMSL centennial rate (Fig. 4b) could be because the respective contributions to GMSL vary over such time scales.
From instrumental records and models, it is virtually certain that the GMSL
rose during the twentieth century with a mean rate of
There are some notable differences between the formulation of our
model-based estimates covering the entire CE and other estimates (some of
which are mentioned above) focused on the twentieth century barystatic GMSL
rise. For example, Frederikse et al. (2020) accounted for the GMSL
contribution from missing and disappeared glaciers (Parkes and Marzeion,
2018) and assumed a constant positive rate of Antarctic mass loss (0.05
The GMTSL rise as a response to industrial climate warming started in the mid-nineteenth century in LOVECLIM (Figs. 1, 2a), following the global-mean surface temperature curve, but there is a lag of nearly half of a century in the PMIP ensemble mean (Fig. 2a) and probably in the reconstruction (Zanna et al., 2019; Fig. 1). This lag could be one of the reasons for a relatively weak twentieth century GMTSL rise in PMIP models. The relatively weak ocean thermal expansion in PMIP could have a link with the strong volcanic eruption of Krakatoa in 1883, as reported before in Gleckler et al. (2006), and possibly those eruptions earlier in the nineteenth century (See Fig. S2). The LOVECLIM is able to capture these episodic GMTSL falls in response to strong volcanic eruptions over the last millennium. However, the impact of the nineteenth century volcanos seems weaker than some earlier ones in LOVECLIM (Fig. 1). LOVECLIM is a model of intermediate complexity, and the ocean's response to volcano-induced aerosol cooling in the background of anthropogenically induced warming might be more complex. A correct ocean thermal response representation would strongly depend on the model physics and experimental design.
Although the GMSL rose over the twentieth century with positive contributions
from major sources, as shown in this study (except for a weak negative
sea-level contribution from Antarctica in EXP-II) and elsewhere, the
individual contributions to GMSL in the PCE varied in sign and magnitude
depending on the period considered (Fig. 5). Barystatic sea level dominates
the GMSL variations throughout the PCE, with the largest (least)
contribution from glaciers (Antarctica). This result is in fact identical
to the relative contributions over the twentieth century (e.g. Frederikse et
al., 2020). The amplitude of sea-level change due to glacier mass balance
changes in the PCE (2.8
The glacier contributions to sea-level change are broadly associated with the glacier area-weighted global-mean surface temperature evolution, as seen in Fig. 2. For example, the surface temperature cooling during 1000–1800 CE is associated with a worldwide net glacier advance and a corresponding GMSL decrease (Figs. 2d and 3d). Note that the glacier advance and surface temperature cooling during the second millennium are not globally uniform as there is considerable regional variability in the history of both glaciers and surface temperature throughout the PCE (Fig. 6). This is consistent with Neukom et al. (2019b) finding that, unlike the twentieth century global surface temperature rise, temperature variability during the pre-industrial period is not spatially uniform. Linking surface temperature more precisely with regional glacier changes would be difficult without further diagnostics. Nevertheless, we suggest that the changes in surface temperature and glaciers might occur over distinct time scales. For instance, while the surface temperature over glacier regions shows strong decadal to multidecadal variability, the large-scale glacier changes in the CE are mostly a centennial to multicentennial response, for which the spatial coherency might appear relatively high (Figs. 6 and 2d). As evident from Fig. 6, not all glacier regions contributed equally to the GMSL changes in the CE, but a few areas (e.g. Greenland periphery, Russian Arctic) dominate the others (e.g. North Asia, low latitudes). The distribution of glacier sea-level contribution in the CE seems to relate to the glacier initial volume distribution (which is the twentieth century glacier volume distribution as given in Farinotti et al., 2019). Going further on regional changes and the link between temperature and glacier changes is out of the scope of this present paper, which is focused on globally averaged signals (similarly, we refrain from describing the regional contributions of thermal expansion in different oceanic basins). A similar association between GMSL and regional surface temperature is also evident for Greenland and Antarctica (Figs. 2b, c and 3b, c). In the context of semi-empirical sea-level models (e.g. Oerlemans, 1989; Grinsted et al., 2010; Jevrejeva et al., 2009; Kemp et al., 2011), the millennium-scale GMSL components presented in this paper, combined with regional and global surface temperature, may potentially be helpful to resolve semi-empirical constants and response periods in a better way and can lead to useful hindcasts and projections.
Sea-level equivalent of glacier volume changes in the CE for the 18 RGI regions considered in the glacier model (orange) and the glacier area-weighted surface temperature (LMR) over each of the glacier regions in the RGI (grey). The number on the top left of each panel indicates the corresponding RGI region. Note that a 31-year low-pass filter is applied on surface temperature, but the original yearly simulation is shown for the glacier sea-level contribution. All curves are referenced to the 1841–1860 CE mean (dashed blue line). Glacier regions, as listed in RGI, are (1) Alaska, (2) western Canada and the USA, (3) Arctic Canada north, (4) Arctic Canada south, (5) Greenland periphery, (6) Iceland, (7) Svalbard, (8) Scandinavia, (9) Russian Arctic, (10) North Asia, (11) Central Europe, (12) Caucasus and Middle East, (13) Central Asia, (14) South Asia West, (15) South Asia East, (16) low latitudes, (17) Southern Andes, (18) New Zealand.
On the other hand, the thermosteric sea level varies not more than
The model and proxy-based reconstruction show some centennial-scale GMSL variability in the PCE (Fig. 4a). For example, the GMSL varies up to 5–10 cm during 1–500 and 1300–1800 CE, and those figures are nearly half of the observed GMSL change over the twentieth century. The GMSL centennial changes over the PCE could primarily result from the slow and integrated response of sea-level components to surface perturbations and reflect the long-term persistence of oceanic thermal field and long response periods of barystatic components. Our results also suggest that some of those centennial-scale changes are comparable to the twentieth century GMSL rise, for example, the sea-level change associated with Greenland variability during 1–500 CE (Fig. 2c). These centennial-scale changes during the PCE indicate that the twentieth century GMSL rise may also include a response to such natural variations. The offset of recent anthropogenic ocean warming by deep-layer cooling originating from the LIA in the Pacific, as reported by Gebbie and Huybers (2019), is an example. We suggest that a similar influence of past variability can also be expected for barystatic sea level owing to its long response time scales, so that the recent GMSL change might be linked to variability in the past. Climate forcing integration can manifest as a lower frequency change in the ocean, which can partly be misinterpreted as trends associated with deterministic forcing, as reported earlier in Ocaña et al. (2016). However, with the current simulations and analyses, it is hard to make firm conclusions on these aspects. Resolving the response time scales empirically and dedicated sensitivity experiments can provide more insights.
Although some earlier studies have discussed GMSL changes, either based on
proxy-based sea-level reconstructions or semi-empirical methods (Kemp et
al., 2011, 2018; Kopp et al., 2016; Grinstead et al., 2010; Walker et al.,
2021), no attempt has been made to describe those changes using process-based modelling
over the entire Common Era. This paper estimates the GMSL changes over the
Common Era (1–2000 CE) by combining contributions from land ice (glaciers
and ice sheets) mass variations and ocean thermal expansion simulated from
different physical models. The GMSL contribution from different sources
(thermosteric and barystatic) varies considerably over periods during the
PCE. Despite the large uncertainties, our model results suggest that the
glacier contribution is higher than the contribution from other sources to
GMSL changes in the CE. The GMSL contributions from the Antarctic and Greenland
ice sheets tend to cancel each other out during the PCE owing to the differing
response of the two ice sheets to atmospheric conditions. Thermosteric
contributions to GMSL changes during the PCE do not reach more than
Our model-based estimates are broadly consistent with the proxy-based GMSL
reconstructions from earlier studies, despite a few disagreements combined
with large uncertainties in the first millennium. For example, model results
suggest that the GMSL does not vary more than
All new model outputs discussed in this
paper are available on request from the corresponding author or at
The supplement related to this article is available online at:
GN and HuG designed the study. GN analysed the data and prepared the manuscript. HeG performed ice sheet simulations. Glacier simulations were performed by DP and FM. All authors contributed to the discussions and writing of the manuscript.
The contact author has declared that none of the authors has any competing interests.
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This work was supported by the Fonds National de la Recherche Scientifique (F.R.S.-FNRS-Belgium) within the framework of the project “Evaluating simulated centennial climate variability over the past millennium using global glacier modelling” (grant agreement PDR T.0028.18). Hugues Goosse is Research Director within the F.R.S.-FNRS. We acknowledge the World Climate Research Programme's Working Group on Coupled Modelling, which is responsible for CMIP, and we thank the climate modelling groups for producing and making available their model output. For CMIP, the US Department of Energy's Program for Climate Model Diagnosis and Intercomparison provided coordinating support and led the development of software infrastructure in partnership with the Global Organization for Earth System Science Portals. We thank Jennifer Walker for providing reconstructed sea-level data on request. Computational resources have been provided by the supercomputing facilities of the Université catholique de Louvain (CISM/UCL) and the Consortium des Equipements de Calcul Intensif en Fédération Wallonie Bruxelles (CECI) funded by the Fond de la Recherche Scientique de Belgique (F.R.S.-FNRS) under convention 2.5020.11. Ice sheet simulations were performed on resources provided by UNINETT Sigma2 - the National Infrastructure for High Performance Computing and Data Storage in Norway through projects NN8006K, NN9560K, NS5011K, NS8006K and NS9560K. Heiko Goelzer acknowledges support from the Research Council of Norway through projects 270061, 295046 and 324639. Fabien Maussion acknowledges support from the Austrian Science Fund (FWF) grant P30256. We thank Christopher Piecuch and the two anonymous reviewers for providing critical comments and suggestions during the revision of this paper.
This research has been supported by the Fonds National de la Recherche Scientifique (F.R.S.-FNRS Belgium; grant agreement PDR T.0028.18).
This paper was edited by Jadranka Sepic and reviewed by Piecuch Christopher and two anonymous referees.