Introduction
Global sea level has increased by around 0.2 m since the beginning of the
20th century and will continue to rise during the 21st century and far beyond
. This will have wide-ranging impacts for
coastal regions around the globe and therefore requires careful monitoring.
The total sea level signal is the sum of several individual sea level
components, the main ones being thermal expansion, global glacier melt,
Greenland and Antarctic ice-sheet mass loss, and land water storage changes
. Over the coming centuries, the magnitude of total sea level rise (SLR)
will strongly depend on the amount of anthropogenic greenhouse gases (GHGs)
emitted to the atmosphere during the 21st century and the corresponding
physical responses of the major SLR drivers . Future GHG
emissions are therefore a main uncertainty source when trying to project SLR
trajectories. SLR uncertainties are further increased by structural
differences of the underlying process-based models for the individual SLR
contributions and limited process understanding, like the behavior of polar
ice shelves in a warming world . To assess major parts
of these scenario and model uncertainties, we extend the widely used simple
carbon-cycle climate model MAGICC
to
comprehensively model global SLR. This MAGICC sea level model has
been designed to emulate the behavior of process-based sea level projections
presented in the fifth IPCC Assessment Report , with
thorough calibrations for each major sea level component. It is intended to
serve as an efficient and flexible tool for the assessment of
multi-centennial global SLR. In the following section, we motivate
and explain the key concepts underlying the MAGICC sea level model.
Section covers the detailed model description and
Sect. provides key results. In Sect. , we discuss
the capabilities of the presented sea level emulator and shine a first light
on potential applications.
Motivation
Future sea level is modeled with varying degrees of complexity.
Process-based modeling represents the physically most comprehensive but also
computationally most expensive approach to project SLR. It is based on
Atmosphere–Ocean General Circulation Models (AOGCMs) and specialized glacier,
ice-sheet and groundwater models that dynamically simulate sea level changes
resulting from natural and anthropogenic forcings. The main sea level output
from AOGCMs is the thermosteric ocean response, mostly diagnosed with
post-simulation adjustments to compensate Boussinesq approximation effects
. Process-based glacier and ice-sheet models are
generally run separately or “offline” and receive important boundary
conditions either from observational data, AOGCMs, or regional climate model
input . Due to the complexity of the physical
processes required to capture the dynamical response of each individual
component, this SLR modeling approach is not feasible for efficient
multi-centennial and multi-scenario research designs. It is mainly used to
improve our physical understanding of the individual SLR components. The need
for more efficient tools to project long-term SLR has led to the development
of alternative approaches.
In the 1980s, first semi-empirical models (SEMs), which estimate global sea
level changes based on the evolution of global-mean temperature, were
introduced together with early approaches to model thermal expansion based on
simplified ocean processes . Generally, SEMs establish
statistical relationships between observed/reconstructed global-mean
temperature or radiative forcing changes and observed/reconstructed global-mean sea level changes. Assuming that such relationships do not change in the
future, they are used to estimate future SLR from projected global
temperature/forcing changes . Therefore, these SEMs do not calculate sea level by
resolving the underlying physical processes. This approach generated
considerable scientific debate and was not included in latest IPCC estimates
. The computational efficiency of
this method, however, made it attractive to applied research questions, like
investigating the global-mean SLR response for different climate targets
. Recently, this method has been developed further and
was applied to individual sea level components . SLR projections are also provided based on expert elicitations
. Furthermore, sea level expert judgments have been
combined with statistical models synthesizing sea level projections for
individual components . Other studies have used an extended
suite of methods, analyzing paleoclimatic archives, modeling parts of the SLR
response with a reduced complexity model, and deriving future projections for
land-ice contribution-based semi-empirical considerations .
The growing efforts in the sea level modeling community to provide fully
transparent and freely available model code are reflected by the recent
introduction of a transparent, simple model framework to estimate regional
sea levels . Previous MAGICC versions also provided SLR estimates based on simplified parameterizations for selected components
.
Here, we adopt an approach of deriving a total sea level response by
emulating existing process-based projections for individual sea level
components . Future sea level dynamics
is synthesized by calibrating simplified parameterizations to the selected
complex model projections for all major sea level contributions. Progress in
the understanding of individual sea level processes and the availability of
revised future sea level contributions require sea level emulators to be
updated regularly. With this study, we are able to complement the existing
sea level projection emulators with a platform based on a comprehensive set
of individual sea level components that allows for projections consistent
with IPCC AR5 estimates. The MAGICC sea level model represents the first
efficient sea level emulator that dynamically calculates thermal expansion
with a hemispheric upwelling-diffusion model based on full hemispheric ocean
temperature profiles calibrated with data from phase 5 of the Coupled Model
Intercomparison Project (CMIP5) . It mimics process-based
sea level responses for the seven main sea level components with thoroughly
calibrated parameterizations that extend global sea level projections to
2300. Integration of the sea level model into MAGICC ensures a consistent
treatment of future SLR and its uncertainties along the full chain
from emissions to atmospheric composition, to temperature to sea level. With
the option to run large ensembles in a probabilistic setup, the MAGICC sea
level model allows one to explore the scenario and model uncertainty space and
directly investigate SLR responses associated with mitigation pathways that
are not covered by the standard RCP scenarios . In addition,
the MAGICC global SLR projections could be used for calculating regional SLR
information by using them as input for pattern scaling approaches
.
Schematic of the MAGICC sea level model structure and the driving
MAGICC hemispheric upwelling-diffusion energy balance core. Heat is
transported through the oceans by downwelling and corresponding layer
entrainment, upwelling, diffusion, and the exchange between the hemispheres.
Ocean mixed layer is denoted MXL, depth-dependent ocean areas are shown by
smaller ocean layers towards the ocean bottom. Illustrative potential ocean
temperature warming profiles that feed into the layer-dependent thermal
expansion module are sketched for both hemispheres. Ocean and air temperature
fluxes (TOCN, TGL) relevant for the sea level model
as well as other major energy fluxes are shown as arrows. Figure adapted from
.
Model description
The MAGICC sea level emulator (Fig. ) has been developed as an
extension to the widely used MAGICC model version 6 . The MAGICC ocean model has been revised and calibrated
with available CMIP5 ocean temperature and thermal expansion data. The
updated MAGICC ocean provides the basis for our thermal expansion
parameterization based on . Parameterizations for global
glacier, Greenland surface mass balance (SMB), Antarctic SMB, and Greenland
solid ice discharge (SID) have been calibrated against selected process-based
projections for the corresponding SLR components. The linear response
function approach for the Antarctic SID component presented in
was adapted to satisfy MAGICC model specifications. In
addition, we have implemented the option to include land water SLR
contribution estimates based on , with an extension
until 2300.
MAGICC ocean model update and thermal expansion
MAGICC is based on a hemispheric upwelling-diffusion entrainment ocean model
with depth-dependent areas for each of its 50 ocean layers
. In this study, we provide a first series of updates
for MAGICC version 7, which will be consistent with the ensemble output of
CMIP5 . The upwelling velocity is variable in MAGICC and
the model conserves the upwelling mass flux through layer-specific
entrainment which is proportional to the area decrease from the top to the
bottom of each layer. To avoid overestimation of ocean heat uptake for higher
warming scenarios, the ocean routine includes a warming-dependent vertical
diffusivity term which leads to reduced heat uptake efficiency for higher
warming . In MAGICC6, the air temperature increases
were assumed proportional to the mixed-layer ocean temperatures. A
proportionality constant α (default value: 1.25) is used in earlier
versions of MAGICC to account for diminishing sea-ice extent in the Arctic,
exposing a larger area of the (relatively warm) surface ocean waters as
warming progresses with time. Here, we replace this constant factor by a term
that takes into account the fact that this amplifying effect will itself
diminish as the Arctic sea-ice retreat is bound by the limit of a sea-ice-free ocean in summer. The chosen functional form initially assumes a simple
linear amplification (as in MAGICC6), and then progresses asymptotically
towards a constant offset between the surface air temperature and top ocean-layer warming. This new exponential adjustment term relates hemispheric air
temperature change ΔTxA to hemispheric mixed-layer ocean
temperature change ΔTxO,1 as follows:
MAGICC ocean model calibration results with optimal sets of ocean
and thermal expansion calibration parameters for the available CMIP5 models.
Calibration parameters are introduced in Sect. . Goodness-of-fit
(GOF) results are given as weighted residual sum of squares (RSS) divided by
the number of calibrated model years (weight potential ocean temperature [K]:
10; weight thermal expansion [mm]: 0.001). The optimal set for the mean
response of the calibration data is given at the bottom of the
table.
Model
Kz
dKztopdT
η
γ
β
w0
Δwtwt
Twt
ϕ
GOF
ACCESS1.0
4.3846
-1.3441
2.4191
0.2954
0.1997
0.0678
0.9999
1.9021
1.1141
0.11
ACCESS1.3
0.1792
-0.0249
4.5743
0.0806
0.0598
9.959
0.2044
3.0533
1.1277
0.08
BCC-CSM1.1
1.3457
0.0701
2.223
0.2245
0.2348
0.0100
0.9506
16.417
1.0303
0.11
BNU-ESM
1.9336
-0.4034
3.5734
0.2422
0.6824
2.9546
0.0010
4.5004
1.2220
0.13
CanESM2
0.9065
0.2868
5.0000
0.1132
0.1259
1.171
0.7481
8.1589
1.0857
0.16
CCSM4
1.1155
0.2327
1.6218
0.3368
0.0132
1.2702
0.3359
1.5202
1.0321
0.15
CESM1-BGC
1.1713
-0.0654
3.2018
0.1302
0.1024
9.986
0.223
3.8928
1.0533
0.03
CESM1-CAM5
0.1000
0.8004
2.5411
0.2834
0.0767
1.9277
0.7618
16.873
1.0993
0.13
CMCC-CESM
0.4599
-0.0209
1.8620
0.2551
0.0100
10.000
0.4610
9.4486
1.1590
0.13
CMCC-CM
1.4137
-0.4317
1.0552
0.9129
0.2519
1.9925
0.9999
19.599
0.9382
0.10
CMCC-CMS
0.1000
-0.7989
4.9992
0.0807
0.1531
9.9999
0.2939
4.7474
0.9858
0.05
CNRM-CM5
0.1377
0.1547
3.2070
0.1776
0.4134
0.5078
0.8680
1.3343
1.0254
0.20
CNRM-CM5-2
1.3200
-0.2081
5.0000
0.1146
0.1037
0.6386
0.8098
1.7782
1.4547
0.05
CSIRO-Mk3.6.0
2.0085
-0.0361
3.7756
0.1510
0.0137
0.0117
0.1865
17.812
1.0633
0.49
EC-EARTH
2.5850
-0.6157
4.9892
0.1077
0.2489
2.4364
0.0720
19.999
1.0624
0.05
GFDL-CM3
0.1000
0.3796
5.0000
0.1638
0.0599
2.9073
0.3461
2.3735
1.1692
0.18
GFDL-ESM2G
2.6329
-1.4040
2.1535
0.2304
1.0000
2.2037
0.8837
20.000
1.3555
0.15
GFDL-ESM2M
2.9547
1.0000
4.9372
0.1387
0.1479
0.0101
0.5316
7.4830
1.1790
0.11
GISS-E2-H
1.2987
0.3002
1.5682
0.4334
0.0334
0.5996
0.9527
2.4943
1.1256
0.07
GISS-E2-HCC
0.1000
1.0000
1.4129
0.6907
0.3571
3.7715
0.9091
17.974
1.0928
0.11
GISS-E2-R
0.9151
0.9383
1.6601
0.4458
0.1069
1.0556
1.0000
1.5897
1.0861
0.17
GISS-E2-RCC
4.9680
-1.0529
1.484
0.5898
0.1609
1.3509
0.2843
1.3137
1.1696
0.12
HadGEM2-CC
0.4727
-0.0493
2.8069
0.1638
0.5988
4.6183
0.0246
1.2449
1.3297
0.07
HadGEM2-ES
0.6165
0.0620
3.4649
0.2123
0.3212
2.9456
0.2779
2.3299
1.1488
0.39
IPSL-CM5A-LR
1.0928
-0.0191
3.1337
0.1181
0.2414
1.8789
0.3740
11.705
1.0677
0.10
IPSL-CM5A-MR
1.0047
-0.0643
1.5549
0.3573
0.9473
0.7214
1.0000
15.414
1.0472
0.09
IPSL-CM5B-LR
1.6262
0.0318
5.0000
0.1234
0.0262
6.5424
0.1259
12.950
1.2550
0.05
MIROC5
2.2396
0.5792
4.9999
0.0961
0.4486
0.0100
0.1234
2.8327
1.1048
0.15
MIROC-ESM
0.6896
0.1877
2.0219
0.4933
0.2884
1.4103
0.9501
3.6729
1.1383
0.12
MIROC-ESM-CHEM
0.9997
-0.5891
1.1388
1.1193
0.0254
9.6999
0.3022
4.4868
1.1277
0.05
MPI-ESM-LR
1.7898
-0.0385
3.2976
0.2319
0.8504
1.1209
0.2792
2.1975
1.2154
0.33
MPI-ESM-MR
2.0752
-1.2640
1.4401
0.5752
0.0510
10.000
0.5349
8.2459
1.1122
0.06
MPI-ESM-P
1.3946
-0.4808
4.4931
0.0898
0.0389
10.000
0.2498
3.9468
1.2927
0.07
MRI-CGCM3
1.4610
0.2543
4.2439
0.1300
0.1760
5.9552
0.0071
2.4876
1.1478
0.05
NorESM1-M
1.3714
0.4972
1.404
0.4805
1.0000
3.0676
0.2752
2.5603
1.1744
0.11
NorESM1-ME
2.8281
0.6425
2.8026
0.1382
0.2966
10.000
0.0266
15.706
1.1203
0.08
Mean
1.3547
-0.7115
1.7022
0.3602
0.5515
9.9876
0.2469
4.2944
0.8823
0.05
ΔTxA=ΔTxO,1+η1-e-γΔTxO,1.
For large γΔTxO,1, the new sea-ice adjustment term
moves towards a constant offset η between surface air temperature
warming ΔTxA and mixed-layer ocean warming ΔTxO,1. However, the surface air temperature warming initially
approximates ΔTxA=ΔTxO,1(1+ηγ) for small γΔTxO,1, with
(1+ηγ) representing the old MAGICC6 proportionality coefficient
α. The sea-ice adjustment parameters η and γ are optimized
together with other selected parameters for every CMIP5 model included in the
MAGICC ocean model calibration (see Sect. ). The parameter sets
are optimized to represent the depth-dependent potential ocean temperature
(thetao) responses from 36 CMIP5 models (see Table ). The tuned model captures ocean-layer-specific
thetao change and related vertical redistribution characteristics of
individual CMIP5 models, both indicators for overall ocean heat uptake
behavior. Net ocean heat uptake can be robustly translated into thermal
expansion . Therefore, we can define the thermosteric
response as the vertical sum of the layer-specific thetao anomalies
multiplied by a corresponding thermal expansion coefficient α which is
weighted by the specific ocean-layer area. The thermal expansion coefficient
α captures all relevant properties of seawater (potential seawater
temperature, salinity, and pressure) that determine the corresponding sea
level response . For MAGICC, a simplified thermal
expansion coefficient representation was developed, which is solely based on
thetao and pressure . Recently,
have updated this parameterization to match CMIP5
thermal expansion behavior. We build our parameterization on
and calculate the thermal expansion coefficients for
every MAGICC depth with the following polynomial of θ and p:
α=(c0+c1θ0(12.9635-1.0833p)-c2θ10.1713-0.019263p+c3θ2(10.41-1.338p)+c4p-c5p2)10-6.
The hemispheric layer-specific thetao values θz are
processed for every time step with θ0=θz, θ1=θ02, and θ2=θ036000, assuming a mean
maximum ocean depth of 6000 m. The ocean depth profile, z, is translated
into the pressure profile p=0.0098(0.1005z+10.5exp-1.0z3500-1.0, with 3500 m as the mean ocean
depth. For each of the 36 MAGICC CMIP5 ocean parameter sets, the
corresponding calibration parameters c0-5 are taken from Table S2 in
. It is the combination of the CMIP5 MAGICC ocean update
with the matching thermal expansion parameters that allows us to estimate
36 unique thermal expansion responses based on the selected ensemble of CMIP5
models. Our method does not cover all the spatial heterogeneity effects of
thermal expansion that are seen in the three-dimensional CMIP5 fields.
Therefore, we apply a model-specific scaling coefficient ϕ to the
thermosteric estimates for each ocean layer to further improve the fit
between the aggregated thermal expansion from the calibrated MAGICC ocean
model and the CMIP5 thermosteric SLR (zostoga) estimates (see
Sect. for more details).
Global glaciers
Mountain glaciers superseded thermal expansion as the biggest single
contribution to SLR by the middle of the 20th century .
The global mass balance of glaciers likely turned negative in the 19th
century, e.g., ; 20th century glacier mass loss
contributed around 0.1 m of global sea level , with an
increasing fraction of the glacier mass loss related to anthropogenic
climatic warming, reaching around 70 % in recent years
. Analyses of the remaining glacier mass susceptible to
melt vary from around 0.35 m sea level equivalent (SLE)
to almost 0.5 m SLE , with both studies including
peripheral glaciers of the ice sheets. The latter study is based on a glacier
surface mass balance model forced with regional monthly precipitation and
temperature data. Changes in glacier volume are derived with the help of
volume–area scaling methods. In the follow-up study ,
2300 estimates of transient glacier mass dynamics forced by 15 CMIP5
temperature and precipitation fields were complemented by equilibrium global
glacier projections in response to long-term warming levels from 1 to 10 ∘C. These two experimental setups projecting transient and
equilibrium glacier SLR contributions form the basis of the glacier component
that has been implemented in the MAGICC sea level model. We include Randolph
Glacier Inventory 4.0 (RGI 4.0) updates on regional glacier mass loss
. The selected parameterization is based on the assumption
that global glacier melt is proportional to the remaining volume susceptible
to melt (at the current global temperature) times the melt forcing. This melt
forcing is expressed by the temperature difference between current
temperature and the temperature that would be expected if the currently
remaining glacier volume was in equilibrium. Thus, we apply the following
functional form to relate the global glacier SLR response GLt to the
remaining global glacier volume as well as the temperature forcing:
GLt=GLt-1+κVeq-VcumTt-Teqν
with calibration parameters κ and ν and Veq being the
equilibrium glacier volume change that would result from warming level Tt.
This value is interpolated from the glacier equilibrium
response data. Vcum is the cumulative glacier volume change since the
year 1850. Teq is the inverse function of the equilibrium glacier
response Veq to Tt and gives the temperature that would lead to the
glacier volume change Vcum in terms of a theoretical equilibrium
response.
Greenland ice sheet
The Greenland contribution to SLR increased rapidly during the last decades
of the 20th century . Regional atmospheric and ocean
warming has triggered widespread surface melt and solid
ice discharge . An increasingly negative SMB and a growing
SLR contribution from SID, which captures accelerating ice stream flow and
more frequent calving events due to warmer ocean temperatures, have been
identified to be responsible for about half of the observed mass loss each
. The Greenland ice sheet is expected to become
one of the largest SLR contributions in the future ,
with potentially irreversible ice-sheet loss for scenarios of persistent and
strong warming . In the following, we
present SMB and SID parameterizations that have been implemented and
calibrated in the MAGICC sea level model.
Surface mass balance
The mass balance at the surface of the Greenland ice sheet is predominantly
determined by the accumulation of snowfall in winter and runoff through
melting in summer. Continuing global warming will influence the SMB through
both increased snowfall and increased melting . As melting
is expected to increase more strongly than snowfall, SMB losses will likely
dominate future Greenland contributions to SLR
. Regional surface air temperatures are the
primary driver of these projected SMB changes if we assume future
precipitation changes over Greenland to be scalable with rising temperatures
. Regional atmospheric temperatures are
closely linked to the global-mean surface air temperature tas. We
utilize this link for our sea level component by relating two tas-dependent terms to capture the long-term SMB sea level response. In the
parameterization, the SMB response to tas can vary from either being
approximated as scaling linearly, or nonlinearly with exponent φ, or
as a combination of both. The calibration procedure chooses the optimal
balance of the linear and nonlinear terms. Furthermore, the surface melt
contribution is damped by diminishing ice availability for high warming
scenarios and eventually becomes zero when all available ice is melted.
Hence, the cumulative Greenland SMB SLR contribution GIStSMB at time
step t can be written as
GIStSMB=GISt-1SMB+υχTt+(1-χ)Ttφ1-GISt-1SMBGISmaxSMB0.5.
The maximum Greenland ice volume available for surface melt GISmaxSMB
is about 7.36 m . The overall temperature sensitivity is
denoted by υ and the choice of φ sets the degree of
nonlinearity, while χ determines the relative magnitude of the linear
and nonlinear terms. We calibrate the three parameters υ, χ,
and φ with reference data from . Their
process-based Greenland SMB projections until 2100 are based on the regional
climate model Modele Atmospherique Regional (MAR), which is coupled to the
soil-ice-snow-vegetation-atmosphere transfer scheme. The MAR model
is forced by CMIP5 data for temperature, wind, humidity, and surface
pressure. Comparing the MAGICC Greenland SMB response to millennial
projections of Greenland ice-sheet sea level contributions
indicates that the functional form of our
SMB parameterization will hold for multi-centennial projections at least
until 2300.
Solid ice discharge
Future ocean warming is expected to reduce the frontal stress of the
Greenland outlet glaciers while increased melt water from atmospheric warming
can reduce the friction at the bottom of these glaciers. Both processes lead
to the speed-up and thinning of these glaciers, with increased discharge of
solid ice into the oceans . Even though the SMB contribution
is projected to dominate the Greenland contribution to SLR, the SID component
has the potential to contribute significantly to SLR
. Recent attempts to quantify the
future ice-dynamic SLR contribution for Greenland vary widely, mainly due to
different methodologies . We select
one of the key approaches presented in the latest IPCC assessment for our
reference data ; used flow line modeling to
project mass loss from Greenland's four main outlet glaciers, Helheim,
Jakobshavn Isbrae, Kangerdluqssuaq and Petermann, until 2200. Their model is
forced with ocean and atmosphere data from SRES A1B and RCP8.5 scenario runs
conducted with the CMIP3 model ECHAM5-OM. As the four main outlet glaciers
drain about 20 % of the entire Greenland ice-sheet area, the sum of the
individual glacier contributions has been multiplied by a factor of 5 to
estimate the SID sea level contribution of the whole ice sheet
. We use the same approach to emulate the
response of , with the cumulative Greenland SID SLR
contribution GIStSID at time step t being:
GIStSID=sGISmaxoutlet-GISVdis(t)outlet
with GIStSID defined as the difference of the initial maximum ice
volume susceptible to discharge and the remaining ice volume available for
discharge at time step t. Maximum ice volume, GISmaxoutlet, and
remaining ice volume at time step t, GISVdis(t)outlet, are
determined for the four main Greenland outlet glaciers. By applying the
scaling factor s=5, the sea level contribution is then scaled up to the
entire Greenland ice sheet. For t=0, GISVdis(t=0)outlet=GISmaxoutlet. The remaining ice volume susceptible to discharge at
time step t, GISVdis(t)outlet, has the following function form:
GISVdis(t)outlet=GISVdis(t-1)outlet-max0,ϱGISVdis(t-1)outleteϵT(t-1)
with the annual discharge being the product of the discharge sensitivity
ϱ, the SID volume GISVdis(t-1)outlet available at time step
t-1, and an exponential tas term, which is dependent on a
temperature sensitivity ϵ. We have calibrated ϱ, ϵ,
and the maximum SID outlet glacier volume GISmaxoutlet based on the
projected minimum and maximum contributions for dynamic retreat and thinning
for scenarios SRES A1B and RCP8.5, shown in Fig. 3e of . An
upper limit of the potential Greenland SID discharge contribution has not
been clearly defined yet . We include the
maximum SID outlet glacier volume susceptible to discharge
GISmaxoutlet in our calibration. Applying the scaling suggested by
, our total Greenland SID maximum ice discharge volumes
amount to around 180 and 268 mm SLE for the minimum and maximum cases
presented in . For comparison,
obtained 420 mm for the ice-dynamic Greenland sea level contribution,
indicating, however, that the actual amount might be significantly smaller.
For high warming scenarios, our SID projections deplete GISmaxoutlet
before the year 2300, which causes the annual Greenland SID sea level
contribution to drop to zero.
Antarctic ice sheet
Air temperatures over the Antarctic ice sheet are generally much colder than
over the Greenland ice sheet. They will be too low to cause wide-spread
surface melting, even under strong global warming . Only
peripheral, low-lying glaciers, especially around the Antarctic Peninsula are
susceptible to retreat through increased ablation . A
warmer atmosphere over Antarctica will however hold more moisture, leading to
higher snowfall. This effect is expected to lead to a positive SMB through
snow accumulation and, thus, a slightly negative SLR contribution
. The main driver of Antarctic ice loss and
a resulting positive sea level contribution is the increased melting of ice
shelves through warmer ocean waters . SID
will be the dominant SLR contribution of Antarctica, with increasing ocean
temperatures causing basal melt in marine-based ice-sheet sectors,
potentially even triggering marine ice-sheet instabilities and irreversible
ice loss . We implemented parameterizations
capturing both the Antarctic SMB and the SID contributions to SLR in the
MAGICC SLR mode. They are presented below.
Surface mass balance
Positive Antarctic SMB anomalies under all warming scenarios lead to
consistently negative contributions to global sea level for the 21st century.
Similar to Greenland, a strong (but different) link exists between future
Antarctic SMB and global-mean surface air temperature tas. Several
studies confirmed the Clausius–Clapeyron equation-based exponential
relationship between atmospheric warming and SMB accumulation. The values
range from 3.7 % ∘C-1 up to around 7 % ∘C-1 , with most recent estimates
based on a large ensemble of climate models pointing to about 5 % ∘C-1 . has been one
of the few studies using regional climate simulations to assess Antarctic SMB
changes beyond 2100, without accounting for climate–ice-sheet feedbacks
however. Their assessment is based on the regional atmospheric climate model
RACMO2 and the two global climate models ECHAM5
and HadCM3 that have been forced by
two comparably moderate emission scenarios (SRES A1B and ENSEMBLES E1),
leading to a 2200 Antarctic warming of 2.4–5.3 ∘C. Results show SMB
increases of 8–25 %, which translate into a global sea level drop of
73–163 mm. We select these projections as reference for our SMB
parameterization. Due to the expected strong SMB link to tas, we
have chosen a simple functional form that relates the annual Antarctic SMB
sea level contribution to this primary driver:
AIStSMB=AISt-1SMB+ξρTt+(1-ρ)Ttσ.
The annual change in the Antarctic SMB contribution to SLR is derived from
the sum of a linear and nonlinear tas term, calibrated with the
three parameters ξ, ρ, and σ. The transfer from global-mean
tas to regional surface air temperature changes as well as the
translation of air temperatures into snowfall accumulation is captured in
ξ, while ρ controls the nonlinearity of the parameterization. The
calibrated parameterization is then used to extend Antarctic SMB SLR
estimates until 2300 presuming that the rationale behind the projections
presented in hold for another 100 years. This is
consistent with findings from up to 3000-year-long Antarctic SMB simulations
that are forced by idealized scenarios doubling or quadrupling atmospheric
CO2 concentration levels . Results from
these studies show ice mass gains due to additional snowfall for more than
500 years after the start of the experiments, e.g., see Fig. 7 in
.
Solid ice discharge
Improved process understanding has allowed for a first assessment of the
Antarctic dynamic ice-discharge contribution to SLR in the fifth IPCC
Assessment Report . Antarctic SID has the potential to
supersede all other sea level contributions because of the vast ice masses
accessible for warm ocean waters and susceptible to self-amplified retreat
. Loss of these ice masses alone would eventually lead to
several meters of global SLR . Recent observations and
modeling suggests that the process of self-sustained retreat has already
begun and will dominate over the slower adjustments to tas and
precipitation changes across the Antarctic continent on decadal to centennial
timescales .
convolved the responses from five different Antarctic ice-sheet models to
basal melt forcing as used in the SeaRISE project
with a large set of MAGICC temperature projections for the full suite of RCP
scenarios. In their study, the projected global-mean tas signal is
converted into subsurface ocean temperatures that are translated into basal
melt forcing. The melt forcing is then convolved with individual response
functions for the Amundsen Sea, Ross Sea, Weddell Sea, and East Antarctic
sectors. This approach is well-suited for the MAGICC sea level model
implementation because it relates the ice-sheet response directly to
tas. We implement a step-wise convolution routine in the MAGICC SLR
model, which allows us to process the response functions for the different
sectors. The total SLR contribution from Antarctic SID, AISSID, can be
written as the sum of the contributions from the individual sectors:
AISSID=∑n=14∫0tFn(τ)Rn(t-τ)dτ.
The sector-specific basal melt forcing Fn is the product of the basal
melt sensitivity ψ and the sector-specific subsurface ocean temperature
anomaly dTOCN. The region-specific ice-sheet response function Rn(t-τ) is based on linear response theory . The basal
melt forcing F is the product of the basal melt sensitivity ψ and the
sector-specific subsurface ocean temperature anomaly dTOCN. Starting in
1850, derived the latter from the projected annual
MAGICC global-mean tas anomalies via ocean temperature scaling and a
time delay between surface and ocean subsurface warming. We adopt all
relevant melt forcing parameters from . They determined
these parameters either through calibrations against 19 CMIP5 models or
adopted them from the existing literature, such as the basal melt sensitivities
ranging from 7 to 16 m a-1 K-1
. The response functions are derived
for 500 years and cover the time frame of their source experiments described
in . We provide Antarctic SID projections up to the
year 2300. For the MAGICC component, it is only response functions from the
three ice-sheet models that have an explicit representation of ice-shelf
dynamics that is included, namely PennState-3D , PISM
, and SICOPOLIS . The
response functions presented by and implemented here do
not account for all ice-sheet processes and feedbacks. Thus, the Antarctic
SID estimates provided by the MAGICC sea level model may underestimate the
actual Antarctic SID sea level response.
Land water storage
The assessment of the observed and projected anthropogenic land water
contribution to SLR is subject to ongoing discussions
. Associated
uncertainties are high, mainly due to sparse data coverage and incomplete
process understanding. Two major processes drive changes in land water
storage: the depletion of groundwater resources, which positively contributes
to SLR, and water impoundment which damps the SLR signal. Analyses show that
the latter contribution has been shrinking since the late 20th century
, which leaves groundwater depletion as the main
human-driven land water storage (LWS) SLR contribution throughout the 21st
century and beyond. We include the option to provide LWS sea level estimates
based on the approach introduced by . They forced the
hydrological model PCR-GLOBWB with climate projections
from AOGCMs to derive estimates for future groundwater depletion until 2100.
Original estimates had to be revised because only roughly 80 % of
annually depleted groundwater ends up in the oceans . We
adapt our time series accordingly, reducing the sea level
contribution estimates from groundwater depletion by 20 %. We use the
30-year average annual depletion rate for the period 2071–2100 to extend the
projections beyond the 21st century. We assume that projected rates of human
water use and groundwater abstraction, which show more constant rates towards
the end of the 21st century , will persist beyond 2100. The
fraction of non-renewable groundwater to total groundwater abstraction is
projected to increase to around 50 % by 2100 . This
indicates that, ultimately, the total amount of groundwater available for
abstraction is limited. To account for such an upper bound of the LWS sea
level contribution, we use a term that relates the cumulative LWS
contribution to a theoretical maximum LWS volume that can be depleted. No
distinction is made between different climate scenarios for the post-2100 LWS
extension due to the limited process understanding and the associated large
uncertainties . Hence, we implement the revised
estimates until 2100 and apply the following post-2100 LWS
parameterization:
LWSt=LWSt-1+LWSconst1-LWSt-1-LWS2100LWSmax-LWS21000.5.
The maximum LWS volume LWSmax has not been quantified yet
. However, quantified the amount of
modern groundwater, which is defined as less than 50-year-old groundwater
located in the top 2 km of the continental crust. This type of groundwater
dominates the interaction with general hydrological cycle and the climate
system. It is also the most accessible for land use . We
here define LWSmax as the total amount of available modern groundwater,
which has been estimated to be around 350 000 km3, roughly translating to
1000 mm SLE.
Model calibration
For the MAGICC ocean model calibration, we use two CMIP5 variables for our
reference dataset: ocean potential temperatures (thetao) and
thermal expansion (zostoga). Ocean-depth-specific thetao
time series are extracted for a total of 36 CMIP5 models, which have been
running pre-industrial control (pictrl), historical, some or all of
the RCP experiments as well as the idealized 1 % CO2 per year increase
(1pctCO2) experiments. Each individual model output is converted
into hemispheric annual-mean thetao depth profile time series that
are then vertically interpolated to match the MAGICC ocean-layer depths. We
combine historical and RCP runs to create layer-specific time series from
1850 to 2100 or 2300 depending on the experiment lengths of the individual
CMIP5 model runs. Ocean temperature data available from the CMIP archives are
subject to drift because the time scales for the ocean to adjust to external
forcing are much longer than the length of the control experiments
. Individual model drifts have been identified
based on the respective pictrl runs. The full linear trend from the
pictrl experiments has been removed from the historical plus RCP and
1pctCO2 scenario time series.
The initial thetao profiles are prescribed for every CMIP5 model
calibration as well as the respective depth-dependent ocean area fractions.
We incorporate zostoga estimates for each of the 36 CMIP5 ensemble
members by detrending the times series with the full linear trend of the
pictrl runs. To ensure a full CMIP5-consistent calibration setup, we
constrain MAGICC for every CMIP5 model optimization by prescribing the
corresponding model-specific annual global-mean surface air temperature
tas. Previous studies have shown that calibration methods for highly
parameterized simple models do successfully show global convergence, even
with a large number of free parameters
. Here, we select all MAGICC
parameters, which directly determine the ocean-layer-specific potential ocean
temperature and corresponding thermal expansion responses. These nine
parameters drive the band routine of the hemispheric upwelling-diffusion
ocean model. The vertical thermal diffusivity, Kz, its sensitivity to
global-mean surface temperatures at the mixed-layer boundary,
dKztopdT, the sea-ice adjustment
parameters η and γ described above, the initial upwelling rate
w0, the ratio of changes in the temperature of the entraining waters to
those of the polar sinking waters β, the ratio of variable to fixed
upwelling Δwtwt, and the corresponding threshold
temperatures that lead to constant upwelling rates, namely Twt, and the
global thermal expansion scaling coefficient ϕ. The minimum vertical diffusivity Kz,min
is set to 0.1 cm2 s-1, as stated in . This
value represents the lower bound for the calibration of
Kz. More
details on the individual parameters can be found in
except for the sea-ice adjustment variables described in Sect. . For
every CMIP5 model, this suite of calibration parameters is optimized based on
the scenario-specific CMIP5 thetao data for the representative
layers 1 (30 m layer-mean depth), 2 (110 m), 3 (210 m), 8 (710 m), 15
(1410 m), 30 (2910 m), and 40 (3910 m), and the corresponding
zostoga time series. The eight calibration layers have been selected
to allow the MAGICC ocean model to emulate the key features of the CMIP5
ocean temperature profiles, with the majority of calibration layers set in
the upper ocean to ensure sufficient coverage of the stronger temperature
gradients. The number of reference layers is not increased further to
preserve computational efficiency; 5000 random parameter sets are drawn prior
to each model optimization procedure. The number of initial random runs has
been determined through iterative testing to ensure convergence to a global
optimum. The resulting best fit is subsequently used for the initialization
of the automated Nelder–Mead simplex optimization routine
with a termination tolerance of 10-8 and
a maximum iteration number of 10 000. We use weighted residual sum of
squares (RSS) for goodness-of-fit (GOF) diagnostics during the optimization
process . The ocean calibration also takes into
account the available CMIP5 zostoga time series. The
zostoga optimization component is given 4 orders of magnitude less
relative weight than the thetao component in order to prioritize the
accurate layer-by-layer emulation of the respective CMIP5 model
thetao time series. The GOF values are then divided by the number of
calibrated model years, accounting for the varying amount of scenario data
available for each model. This allows us to compare the GOFs of the
calibrations for all 36 CMIP5 models.
The calibration procedures for the other SLR components also optimize the
specific parameters listed in Tables to
based on the Nelder–Mead Simplex method with a termination tolerance of
10-8 for a change in RSS during the last iteration. For an overview of
all relevant variables and calibration parameters please see Table . All the remaining SLR components use reference SLE contributions
in millimeters for the respective optimizations. For the glacier
contribution, the MAGICC sea level response is fitted to the transient
projections. The free parameters κ and ν are
calibrated for each of the 14 CMIP5 reference models and their respective
combined historical and RCP simulations, starting in 1850. Corresponding
CMIP5 global-mean tas projections are prescribed in the MAGICC model
to ensure consistency with CMIP5. We use a subset of the model-specific
1965–2100 projections made available by to calibrate the
parameterization for the Greenland SMB contribution. In total, 24 CMIP5 models are
selected based on the availability of CMIP5 tas projections for the
scenarios RCP4.5 and RCP8.5. We then prescribe these global-mean tas
time series for the calibration procedure of the three parameters υ,
χ, and φ. Calibration data for the Greenland SID component is
only available for one GCM, ECHAM5. For the optimization of the parameters
ϱ, ϵ, and GISmaxoutlet, global-mean tas
runs for SRES A1B and RCP8.5 are used with 2200 extensions, repeating the
last decade of the 21st century 10 times . The calibration
of the Antarctic SMB component is based on process-based SLR responses forced
by two GCMs . In this reference study, ECHAM5 and
HadCM3 model output was applied for scenarios SRES A1B and ENSEMBLES E1. We
replicate these GCM responses and use the provided Antarctic SMB sea level
contributions starting in 1980 to determine the optimal parameters ξ,
ρ, σ. The Antarctic SID as well as the LWS components are not
subject to calibration procedures as they apply the same method of the
reference study in the case of Antarctic SID or simply include and extend the
reference data for LWS.
Glacier sea level component calibration results with parameter sets
for the available CMIP5 models. Calibration parameters are introduced in
Sect. . GOF is given as weighted RSS divided by the number of
calibrated model years (weight glacier SLE contribution [mm]: 1). The optimal
set for the mean response of the calibration data is given at the bottom of
the table.
Model
κ
ν
GOF
BCC-CSM1.1
0.0131
0.1551
51.88
CanESM2
0.0098
0.1742
27.22
CCSM4
0.0104
0.2743
6.935
CNRM-CM5
0.0101
0.2217
122.8
CSIRO-Mk3.6.0
0.0088
0.2963
120.1
GFDL-CM3
0.0125
0.1932
6.061
GISS-E2-R
0.0116
0.0955
11.81
HadGEM2-ES
0.0114
0.2961
50.19
IPSL-CM5A-LR
0.0091
0.2260
33.82
MIROC5
0.0126
0.1198
12.77
MIROC-ESM
0.0099
0.1402
23.91
MPI-ESM-LR
0.0079
0.4451
25.04
MRI-CGCM3
0.0081
0.1885
13.10
NorESM1-M
0.0106
0.1126
34.04
Mean
0.0106
0.0788
6.10
Greenland SMB sea level component calibration results with optimal
parameter sets for the available CMIP5 models. Calibration parameters are
introduced in Sect. . GOF is given as weighted RSS divided by the
number of calibrated model years (weight Greenland SMB SLE contribution [mm]:
1). The optimal set for the mean response of the calibration data is given at
the bottom of the table.
Model
υ
χ
φ
GOF
ACCESS1.0
0.2190
0.9748
3.2749
0.74
ACCESS1.3
0.2021
0.2490
1.2781
0.46
BCC-CSM1.1
0.0664
0.2398
2.3731
0.56
BNU-ESM
0.1290
0.0000
1.9068
0.89
CanESM2
0.0656
0.0000
2.2971
1.96
CCSM4
0.0186
0.0000
2.7122
1.17
CESM1-BGC
0.0618
0.0000
1.9517
1.06
CMCC-CM
0.0830
0.0000
1.9688
1.57
CNRM-CM5
0.1009
0.0000
1.8283
0.36
CSIRO-Mk3.6.0
0.1459
0.4702
1.8740
0.60
GFDL-CM3
0.3347
0.7326
2.2962
0.56
GFDL-ESM2M
0.1077
0.0000
2.0794
0.90
GISS-E2-R
0.1302
0.0000
1.9605
0.26
HadGEM2-CC
0.2308
0.9594
2.9988
0.27
HadGEM2-ES
0.1974
0.8354
2.2872
0.55
IPSL-CM5A-LR
0.1762
0.4514
1.8847
0.25
IPSL-CM5A-MR
0.0802
0.0000
2.0480
0.67
IPSL-CM5B-LR
0.0531
0.0000
2.4263
0.99
MIROC5
0.2168
0.0000
1.8440
1.11
MIROC-ESM-CHEM
0.1557
0.3454
2.1621
1.51
MIROC-ESM
0.1549
0.5188
2.3107
1.10
MPI-ESM-LR
0.0333
0.0000
2.6372
1.49
MRI-CGCM3
0.0645
0.0000
2.2958
0.59
NorESM1-M
0.0969
0.0000
2.0000
0.50
Mean
0.1148
0.0000
2.0169
0.47
Greenland SID sea level component calibration results with optimal
parameter sets for the low and high cases introduced by .
Calibration parameters are introduced in Sect. . GOF is given as
weighted RSS divided by the number of calibrated model years (weight
Greenland SID SLE contribution [mm]: 1).
Case
ϱ
ϵ
GISmaxoutlet
GOF
[mm]
Low
9.062×10-4
0.3891
35.98
0.81
High
7.933×10-4
0.4722
53.63
1.62
Antarctic SMB sea level component calibration results with optimal
parameter sets for the CMIP3 models ECHAM5 and HadCM3. Calibration parameters
are introduced in Sect. . GOF is given as weighted RSS divided by
the number of calibrated model years (weight Antarctic SMB SLE contribution
[mm]: 1). The optimal set for the mean response of the calibration data is
given at the bottom of the table.
Model
ξ
ρ
σ
GOF
ECHAM5
-0.11028
0.0000
1.2435
0.70
HadCM3
-0.13869
0.0000
1.3910
9.61
Mean
-0.12082
0.0000
1.5234
0.70
Potential ocean temperature depth profiles for MAGICC and reference
CMIP5 warming under RCP2.6, RCP4.5, RCP6.0, and RCP8.5 scenarios, 2081–2100
anomalies with respect to 1986–2005. Interpolated CMIP5 90 % model
ranges and corresponding median profiles are shown in colors, with circles
indicating the individual MAGICC ocean layers. MAGICC median ocean-warming
profiles given as black lines with open circles indicating selected layers
for ocean calibration. Model outliers not covered by the respective 90 %
ranges are shown for both CMIP5 reference data and MAGICC calibration
results. Potential ocean temperature residuals of the calibration are
provided for every MAGICC ocean layer in Fig. .
MAGICC sea level model calibration results for thermal
expansion (a–d), global glaciers (e–h), Greenland surface
mass balance (j–k) and solid ice discharge (l–m),
Antarctic surface mass balance (n–o), and solid ice
discharge (p–s), as well as land water (t). The panels
show scenario-specific calibrated MAGICC sea level responses as colored
lines, with underlying reference data as thin dark lines. Antarctic solid ice
discharge reference 90 % range plus corresponding median are provided as
thin dashed lines. Climate-independent land water projections are identical
to the reference data until 2100 (see Sect. ). Please note that x
and y axis ranges differ for individual panels.
Results
The MAGICC ocean model update yields optimal parameter sets for every CMIP5
model used in the calibration procedure outlined above. Those sets are listed
in Table . In Fig. , we show both the 90 %
model range and the median for the reference CMIP5 global potential ocean
temperature anomalies as well as the median MAGICC global ocean warming
profile averaged over 2081 to 2100 relative to the reference period 1986 to
2005. The figure also provides information on individual model outliers for
reference data and calibration results. Corresponding potential ocean
temperature residuals are shown in Fig. . MAGICC is able to
capture the key CMIP5 features for all RCP scenarios. The median model
response either matches or is close to the median of the CMIP5 responses. The
updated MAGICC ocean deviates from the CMIP5 data in a few cases. Generally,
there appears to be less warming in the mid-ocean between around 1500 m and
2500 m than in the CMIP5 reference data. Also, there is a tendency for the
MAGICC bottom layers to warm more than the CMIP5 reference data. However, it
is only for two of the 36 CMIP5 models used that calibration results show a
major bottom layer warming bias. The GISS-E2-R reference data show strong
mid-layer warming combined with actual bottom layer cooling, while the
HadGEM2-CC data show cooling in the upper 500 m over the historical period
(see Fig. ). In both cases, the MAGICC hemispheric
upwelling-diffusion ocean model cannot fully capture these characteristics.
For the HadGEM2-CC emulation, MAGICC overcompensates the surface cooling with
strong bottom layer warming. Apart from these anomalies, the calibrated
MAGICC ocean component captures the hemispherically averaged CMIP5 ocean
warming for the different RCP scenarios well (Figs. and
). We derive CMIP5-consistent thermal expansion estimates based on
the optimal ocean parameter sets and the additional thermal expansion scaling
parameter ϕ (see Table ).
In Fig. , we synthesize the calibration results for all sea level
contributions captured by the MAGICC sea level model. Panels (a) to (d) show
the model-specific global thermal expansion responses and the corresponding
CMIP5 zostoga reference data for the four RCP scenarios. The number
of available reference runs differs for each scenario as does the length of
the simulations. The updated MAGICC ocean component is able to mimic the
CMIP5 thermal expansion time series. Relative to 1850, the calibration yields
a 2100 thermosteric SLR range of 104 to 238 mm (CMIP5: 113 to 231 mm) for
RCP2.6, 151 to 307 mm (161 to 290 mm) for RCP4.5, 166 to 331 mm (174 to 309 mm) for RCP6.0, and 219 to 491 mm (261 to 445 mm) for RCP8.5. The
corresponding 1850 to 2300 thermosteric SLR responses range from 192 to 335 mm for RCP2.6 (CMIP5: 180 to 288 mm), 348 to 709 mm
for RCP4.5 (345 to 707 mm), 586 to 717 mm for RCP6.0 (635 to 658 mm), and 1040 to 1794 mm for RCP8.5
(1040 to 1909 mm). In contrast to some detrended zostoga CMIP5 model
time series, the MAGICC thermal expansion projections do not show negative
slopes in the 20th century, which is consistent with observations
.
The calibrated global glacier SLR response and the corresponding reference
data are shown in panels (e) to (h), while the specific calibration results
are listed in Table . The MAGICC projections show good
agreement with the updated data (Fig. e to h). Relative to 1850, the estimated glacier SLE contributions in
2100 are 145 to 259 mm (: 134 to 256 mm) for RCP2.6, 162 to
276 mm (159 to 277 mm) for RCP4.5, 163 to 276 (163 to 276 mm) for RCP6.0, and
188 to 302 mm (198 to 308 mm) for RCP8.5. For 2300, projected SLR from
glaciers amounts to a SLE range of 177 to 298 mm (: 188 to 305 mm) for RCP2.6, 255 to 374 mm (254 to 366 mm) for RCP4.5, and 325 to 439 mm
(338 to 444 mm) for RCP8.5.
In panels (j) and (k), we cover the Greenland SMB contribution, both the
reference data from and the sea level model estimates
based on the optimal parameter sets shown in Table . Our
model shows high agreement with the reference data. For 2100, we project SLE
ranges from 18 to 117 mm (: 17 to 114 mm) based on RCP4.5 and
SLE ranges from 49 to 208 (48 to 206 mm) based on RCP8.5. Projections start
in 1965, being the first year of the calibration data. The Greenland SID
calibration results are depicted in Fig. l and m. We
show MAGICC sea level model estimates based on the calibration results listed
in Table . As presented by , we show
projections of the minimum and maximum cases for the combined contribution
from the four major outlet glaciers prior to up-scaling to the entire
Greenland ice sheet. Estimates are provided relative to the year 2000. For
the SRES A1B scenario, the SLE projections range from 17 to 28 mm (: 14 to 25 mm) for the last year of the available reference data in 2190.
For the same year, we project 24 to 42 mm (26 to 43 mm) based on the RCP8.5
scenario.
Calibration results for the Antarctic SMB component, which negatively
contributes to future SLR, are listed in Table .
Corresponding output is shown in panels (n) and (o). Starting in 1980, the
reference data from provides projections that go
beyond 2100 only for the model HadCM3. For the ENSEMBLES E1 scenario, the two
model-specific 2100 SLE responses range from -29 to -18 mm (: -27 to -20 mm). The 2200 estimate lies at -67 mm (-73 mm) based on the
HadCM3 parameter set. The 2100 values for the SRES A1B scenario span from -51
to -33 mm (: -44 to -32 mm), while the 2200 Antarctic SMB
SLE response is projected to be -158 mm (-163 mm). As we model the Antarctic
SID sea level component with the linear response function approach presented
by , it is not calibrated against any reference data.
The MAGICC component utilizes the responses from the three ice-sheet models
of that study, which include an explicit representation of ice-shelf dynamics.
As the sea level responses for this subset of ice-shelf models are not
available, we show the 90 % model range and the median of all five
ice-sheet models from in Fig. p to s. CMIP5 model-specific parameter sets have been determined for
the three different ice-shelf models (, Tables 2–5). For
1850 to 2100, the 90 % ranges of the MAGICC responses based on the
ice-shelf model subset correspond to 33 to 253 mm SLE (: 15
to 227 mm) for RCP2.6, 39 to 319 mm (17 to 267 mm) for RCP4.5, 42 to 338 mm
(17 to 277 mm) for RCP6.0, and 53 to 448 mm (20 to 365 mm) for RCP8.5. For
1850 to 2300, 90 % of the MAGICC projections lie within 115 and 874 mm
SLE (: 69 to 635 mm) for RCP2.6, 209 and 1435 mm (119 to 1182 mm) for RCP4.5, 282 and 1860 mm
(161 to 1719 mm) for RCP6.0, and 505 and 3173 mm (300 to 3535 mm) for RCP8.5, respectively. The MAGICC Antarctic SID
estimates, which are based on the physically more complex ice-shelf models
only, mostly lie within the 90 % range of Antarctic SID sea level
contributions provided by .
In panel (t), we show SLE responses for the scenario-independent land water
SLE component. From 1900 to 2100, we include the net land water SLE
contribution as presented in Fig. 3 of , corrected by the
20 % fraction of land water that does not reach the global ocean
. Post-2100, we assume a constant annual contribution based
on the assumptions outlined in Sect. . 2100 estimates span a global
sea level contribution of 39 to 77 mm. The extended land water projections
range from 156 to 261 mm SLE for 2300.
With the individual SLR components calibrated, we can project total SLR as
the combination of the individual SLE responses from each of the seven sea
level components. Two different MAGICC setups are used to project global SLR
until 2100 and 2300 based on the four RCP scenarios and their extensions. The
ocean model update is not sufficient to make the MAGICC model fully CMIP5
consistent because other crucial climate system components such as the carbon
cycle have not been updated yet. To overcome this issue, we constrain the
MAGICC model with available CMIP5 global-mean tas time series.
Together with the corresponding calibrated MAGICC ocean model parameter sets,
we are able to create a CMIP5 environment that allows us to compare our 2100
global SLR projections to the latest IPCC estimates. Beyond 2100, the number
of available CMIP5 simulations is much smaller, with only two 2300 model runs
available for RCP6.0, for example. In order to also provide a sufficiently
large number of model runs for 2300, we use 600 historically constrained
parameter sets that have been derived using a probabilistic
Metropolis–Hastings Markov chain Monte Carlo method .
This approach has been extended to also reflect carbon-cycle uncertainties
and the climate sensitivity range of the latest
IPCC assessment . For this second
setup, MAGICC is not forced to match CMIP5 global-mean tas, allowing
us to provide consistent ensemble projections out to 2300. For this ensemble,
we randomly draw from the CMIP5 ocean model parameter sets and the
calibration results for each sea level model component. Random samples are
also sourced between the minimum and maximum realizations for the Greenland
SID and LWS component as well as between the empirical basal melt
sensitivities for the Antarctic SID contribution . For
consistency, we adopt the same ensemble size for the CMIP5 constrained MAGICC
setup and randomly select the specific CMIP5 global-mean tas time
series in addition to the other randomized parameter sets from the individual
sea level components.
The 2081–2100 median values and 66 % ranges for global SLR
projections relative to 1986–2005 in meters, resolved by sea level
components for the four RCP scenarios. Estimates are provided based on the
CMIP5-consistent MAGICC setup. IPCC median projections and likely ranges are
given as a reference.
2081–2100
RCP2.6
RCP4.5
RCP6.0
RCP8.5
Total
MAGICC
0.41 [0.32 to 0.51]
0.49 [0.41 to 0.60]
0.49 [0.40 to 0.62]
0.67 [0.55 to 0.83]
IPCC
0.40 [0.26 to 0.55]
0.47 [0.32 to 0.63]
0.48 [0.33 to 0.63]
0.63 [0.45 to 0.82]
Thermal Expansion
MAGICC
0.12 [0.08 to 0.17]
0.16 [0.12 to 0.22]
0.17 [0.12 to 0.23]
0.26 [0.19 to 0.34]
IPCC
0.14 [0.10 to 0.18]
0.19 [0.14 to 0.23]
0.19 [0.15 to 0.24]
0.27 [0.21 to 0.33]
Glaciers
MAGICC
0.11 [0.09 to 0.14]
0.13 [0.11 to 0.15]
0.13 [0.10 to 0.15]
0.15 [0.13 to 0.17]
IPCC
0.10 [0.04 to 0.16]
0.12 [0.06 to 0.19]
0.12 [0.06 to 0.19]
0.16 [0.09 to 0.23]
Greenland SMB
MAGICC
0.03 [0.01 to 0.04]
0.04 [0.02 to 0.05]
0.03 [0.02 to 0.05]
0.06 [0.04 to 0.09]
IPCC
0.03 [0.01 to 0.07]
0.04 [0.01 to 0.09]
0.04 [0.01 to 0.09]
0.07 [0.03 to 0.16]
Greenland SID
MAGICC
0.03 [0.03 to 0.04]
0.03 [0.03 to 0.04]
0.03 [0.03 to 0.04]
0.05 [0.04 to 0.06]
IPCC
0.04 [0.01 to 0.06]
0.04 [0.01 to 0.06]
0.04 [0.01 to 0.06]
0.05 [0.02 to 0.07]
Antarctica SMB
MAGICC
-0.02 [-0.03 to -0.01]
-0.03 [-0.03 to 0.02]
-0.03 [-0.04 to -0.02]
-0.04 [-0.05 to -0.03]
IPCC
-0.02 [-0.04 to -0.00]
-0.02 [-0.05 to -0.01]
-0.02 [-0.05 to -0.01]
-0.04 [-0.07 to -0.01]
Antarctica SID
MAGICC
0.07 [0.04 to 0.14]
0.08 [0.06 to 0.16]
0.08 [0.05 to 0.16]
0.11 [0.06 to 0.21]
IPCC
0.07 [-0.01 to 0.16]
0.07 [-0.01 to 0.16]
0.07 [-0.01 to 0.16]
0.07 [-0.01 to 0.16]
Land water storage
MAGICC
0.06 [0.05 to 0.07]
0.06 [0.05 to 0.07]
0.06 [0.05 to 0.07]
0.06 [0.05 to 0.07]
IPCC
0.04 [-0.01 to 0.09]
0.04 [-0.01 to 0.09]
0.04 [-0.01 to 0.09]
0.04 [-0.01 to 0.09]
Global sea level projections until 2100 based on CMIP5 constrained
MAGICC runs as anomalies relative to 1986–2005 in panels (a) to
(d); 90 % ensemble range in light colors, 66 % ensemble
range in darker colors, median as solid line. The 2081–2100 anomalies with
respect to 1986–2005 as vertical bars for CMIP5 constrained MAGICC setup
(MAGICC CMIP5), historically constrained probabilistic MAGICC setup (MAGICC
PROB), and IPCC reference projections. The 2300 sea level projections in
panel (e) are showing 66 % ranges for all RCP extensions based
on MAGICC PROB; median estimates as solid lines.
The 2100 and 2300 median values as well as 66 % ranges for total
global SLR projections relative to 1986–2005 based on the MAGICC CMIP5 and
MAGICC PROB experimental designs. IPCC median projections and likely ranges
are given as a reference.
2100
2300
RCP2.6
MAGICC CMIP5
0.45 [0.35 to 0.56]
–
MAGICC PROB
0.48 [0.37 to 0.59]
1.02 [0.80 to 1.35]
IPCC
0.44 [0.28 to 0.61]
–
RCP4.5
MAGICC CMIP5
0.55 [0.45 to 0.67]
–
MAGICC PROB
0.61 [0.48 to 0.74]
1.76 [1.29 to 2.30]
IPCC
0.53 [0.36 to 0.71]
–
RCP6.0
MAGICC CMIP5
0.56 [0.46 to 0.71]
–
MAGICC PROB
0.65 [0.52 to 0.79]
2.38 [1.72 to 3.20]
IPCC
0.55 [0.38 to 0.73]
–
RCP8.5
MAGICC CMIP5
0.79 [0.65 to 0.97]
–
MAGICC PROB
0.89 [0.68 to 1.09]
4.73 [3.41 to 6.82]
IPCC
0.74 [0.52 to 0.98]
–
Global-mean tas projections until 2300 for all RCP
extensions based on the historically constrained probabilistic MAGICC setup;
90 % ensemble range in light colors, 66 % ensemble range in darker
colors, medians as solid lines. Available global CMIP5 tas reference
time series are shown as thin black lines. All temperature projections are
given relative to 1850.
In Table , we show median SLR estimates for the 2081–2100
average relative to 1986–2005 and 66 % ranges for every individual
component, with corresponding IPCC reference estimates and likely ranges. The
individual MAGICC sea level contributions are in good agreement with the IPCC
estimates. Figure shows the full suite of MAGICC SLR projections
for the RCP scenarios. The smaller panels (a) to (d) give 90 and
66 % ranges as well as median responses for all RCP scenarios until 2100
based on the CMIP5-consistent setup. Additional bars are provided for the
IPCC reference data and the probabilistic MAGICC setup, which is not
constrained to CMIP5. For the CMIP5-consistent MAGICC setup, 2100 median SLR
is projected to be 0.45 m (66 % range: 0.35 m to 0.56 m) for RCP2.6,
0.55 m (0.45 to 0.67 m) for RCP4.5, 0.56 m for (0.46 to 0.71 m) for
RCP6.0, and 0.79 m (0.65 to 0.97 m) for RCP8.5 (see also Table ). All SLR projections are provided relative to the
reference period 1986 to 2005. MAGICC SLR estimates for 2100 are generally
higher than the IPCC projections. CMIP5-consistent projections of average
2081 to 2100 SLR lie well within the IPCC range, with median estimates on
average 0.02 m higher than the corresponding IPCC values .
In panel (e), we provide 2300 SLR projections for the RCP extensions based on
the probabilistic MAGICC setup, which is not constrained to CMIP5. For RCP2.6,
the median SLR response is 1.02 m (66 % range: 0.80 to 1.35 m). We
project a median of 1.76 m (1.29 to 2.30 m) for RCP4.5, 2.38 m (1.72 to
3.20 m) for RCP6.0, and up to 4.73 m (3.41 to 6.82 m) for RCP8.5 (see also
Table ). In Fig. , we provide MAGICC SLR hindcast
results and three comparison datasets for the period 1900 to 2000. The MAGICC
sea level model shows good agreement with the observational datasets based on
and . The global 1900–2300 SLR responses
are provided for all RCPs and each sea level component in the Appendix
Figs. to .
Figure shows the global-mean tas responses based on the
historically constrained, probabilistic MAGICC setup, which is used for the
2300 SLR projections. Each panel also includes the available CMIP5
global-mean tas time series; 2300 MAGICC median global-mean
tas fall well within the available CMIP5 range for RCP4.5, RCP6.0,
and RCP8.5. The MAGICC median global-mean tas response is at the
lower end of 2300 CMIP5 temperatures for RCP2.6. For this scenario, the
projected cooling over 22nd and 23rd centuries is consistent with previous
MAGICC studies, e.g., . The
overall historically constrained, probabilistic MAGICC global-mean
tas response for the 21st century is stronger than in the CMIP5
reference data for RCP4.5, RCP6.0, and RCP8.5 scenarios. This slightly
steeper 21st century global-mean tas slope is also reflected in the
corresponding probabilistic MAGICC 2100 SLR estimates, given the strong air
temperature dependence of the sea level model (see Fig. a to d).
Discussion
The MAGICC sea level model presented here synthesizes long-term sea level
projections for seven sea level components and provides up-to-date and
efficient representations of the individual SLR contributions, validated
against process-based model results (see Fig. and Sect. ). Thermal expansion is calculated with an updated version of the
MAGICC hemispheric upwelling-diffusion ocean model and an ocean-layer-specific thermal expansion parameterization by . We are
therefore able to directly account for ocean heat uptake effects, which is an
advantage over other contribution-based approaches that simply derive thermal
expansion from global-mean air temperature changes . The
MAGICC ocean thermal expansion component is calibrated to be fully consistent
with CMIP5. The glacier component parameterization accounts for both
transient projections of glacier mass loss and
equilibrium glacier responses based on . The SMB and SID
parameterizations for both ice sheets reflect available process-based
reference data . In
addition, new process understanding has been included in the land water
component . The full MAGICC model, including the sea level
module, can be run in less than 1 s for 100 model years on a single
core. This makes it an efficient platform to provide large ensembles of
global sea level projections.
Projecting SLR beyond 2100 and providing physically consistent global
estimates out to 2300 has been one of the key motivations for the development
of the MAGICC sea level model. For five of the seven sea level components,
the reference data used for calibrating the individual contributions extend
beyond 2100. For thermal expansion, global glacier, and Antarctic SID
contributions, the reference calibration period spans from 1850 to 2300. The
remaining components are based on physically plausible assumptions, which
allow us to also provide 2300 estimates, assuming that the calibrated
parameterizations for each sea level component remain valid. Our sea level
model transparently emulates and combines long-term sea level projections
from process-based models. It is also in line with observed past total sea
level change (see Fig. ). The close reproduction of selected
reference data (Figs. and ), together with the
consistent translation of climate forcing into a SLR response within the
MAGICC model, and the comprehensive representation of relevant processes
(e.g., the thermal expansion contribution produced by the CMIP5-consistent
MAGICC ocean model and the inclusion of the land water storage sea level
component) make the MAGICC sea level model a powerful addition to the
existing sea level emulators.
Both CMIP5 ocean and air temperatures serve as input for the presented sea
level model. Other published sea level emulators only utilize air temperature
projections, also provided by MAGICC, either based purely on available CMIP3
calibration results or an updated
historically constrained probabilistic MAGICC setup that reflects the latest
IPCC climate sensitivity estimates . We
here provide the first major step to making MAGICC fully CMIP5 consistent,
with the ocean model now emulating 36 CMIP5 hemispheric potential ocean
temperature and thermal expansion responses. However, other crucial elements
of the MAGICC model, like the atmosphere and the carbon cycle, are not yet
calibrated to CMIP5. When combining the CMIP5-calibrated ocean with the older
atmosphere and carbon-cycle calibrations, the resulting 21st century warming
is slightly stronger than CMIP5 (see Fig. ). To ensure a robust
MAGICC sea level model, the individual components were either calibrated with
prescribed CMIP5 temperatures, or with CMIP3-consistent time series whenever
the reference data was based on the older generation of SRES and ENSEMBLES
scenarios. The quality of the sea level model calibration is therefore not
affected by the warmer MAGICC air temperature response. Our primary 2100 SLR
projections are based on a MAGICC ensemble that is constrained by CMIP5
global-mean tas. These projections can therefore be directly
compared to recent IPCC estimates. For our 2300 projections, we run MAGICC in
the historically constrained, probabilistic setup described above. The
resulting MAGICC air temperature responses mostly reflect the available CMIP5
reference data, although they show a shorter response time scale (see
Fig. ). These differences to CMIP5 translate into the corresponding
SLR projections due to the strong air temperature dependence of the sea level
model. Hence, the MAGICC sea level module will only be able to provide fully
CMIP5-consistent SLR responses for 2300 once the remaining components of the
MAGICC model have been updated.
Sea level emulators complement the comprehensive but computationally
expensive, process-based sea level models due to their flexible and efficient
design. They can be quickly adapted to, e.g., incorporate previously unknown
uncertainties from newly quantified ice-sheet processes
. Being directly coupled to MAGICC, our sea
level model can also account for additional climate system response
uncertainties and provide consistent projections for a wide range of climate
change scenarios beyond the standard IPCC pathways. The latter aspects
describe key strengths of the MAGICC sea level model and make it a useful
tool to assess SLR for scenarios that are not covered by larger, more
comprehensive models. The emulated MAGICC sea level projections reflect,
independently, the reference responses of the calibration data for each
individual sea level component, assuming that the implemented
parameterizations fully capture the process-based simulations. Underlying
model uncertainties differ substantially for the individual sea level
components . In 2300, the three largest model response
uncertainties captured by the MAGICC sea level model for RCP8.5 are the
Greenland SMB component with 66 % range estimates of 0.74 to 2.51 m,
the thermal expansion component with a 66 % range of 1.07 to 2.65 m,
and the Antarctic SID component with 0.65 to 1.85 m. Emulators, as
presented here, can only cover the uncertainty ranges that are reflected in
the emulated process-based models. Even though there have been substantial
advances in process understanding over the last years, the physical
representation of some sea level contributions remains incomplete. The
Antarctic ice-sheet response, for example, could be subject to more rapid,
nonlinear dynamics that is not captured by current process-based
projections. Only recently, have revised potential future
Antarctic contributions to global sea level based on indicators from
paleoclimatic archives. For RCP8.5, they suggest 2100 contributions of around
1m from Antarctica alone, with 2300 contributions reaching up to around
10 m. The MAGICC sea level model projections for the Antarctic SID
contribution are based on and only yield up to around
0.35 m in 2100 and 2.68 m in 2300 for the upper bound of the 90 %
range. As the more recent research suggests, these estimates may be too low,
indicating that the Antarctic contribution to future SLR is subject to
additional uncertainties. This illustrates the need to handle long-term SLR
projections with care and to note the corresponding methodological caveats;
in particular, those surrounding the representation of Antarctic ice-sheet
changes.
The MAGICC sea level model assesses long-term global SLR trajectories by
synthesizing available process-based projections for the individual sea level
drivers and applying them to the available set of RCP scenarios and their
extensions until 2300. The current version shows 2100 estimates that are well
within the range of the latest IPCC assessment (see Fig. ). The
structure of the emulator makes the MAGICC sea level model a computationally
much more efficient tool compared to the comprehensive and complex
process-based models. The calibration routines for the individual components
have been flexibly designed to allow for timely updates whenever
new robust modeling results become available. The
presented MAGICC sea level model, together with the MAGICC ocean model
update, are new elements of MAGICC model version 6 .
The implementation of the new sea level model initiates the development of
MAGICC model version 7 to comprehensively emulate CMIP5 projections. The full
potential of the MAGICC sea level model will be unlocked once this MAGICC
model upgrade has been completed.