GMDGeoscientific Model DevelopmentGMDGeosci. Model Dev.1991-9603Copernicus GmbHGöttingen, Germany10.5194/gmd-8-2723-2015Complementing thermosteric sea level rise estimatesLorbacherK.katja.dommenget@unimelb.edu.auNauelsA.https://orcid.org/0000-0003-1378-3377MeinshausenM.Australian-German College of Climate & Energy Transitions, School of Earth Sciences,
The University of Melbourne, Parkville 3010, Victoria, AustraliaThe Potsdam Institute for Climate Impact Research, Telegrafenberg A26, 14412 Potsdam, GermanyK. Lorbacher (katja.dommenget@unimelb.edu.au)2September201589272327349December201410February20151June201511August2015This work is licensed under a Creative Commons Attribution 3.0 Unported License. To view a copy of this license, visit http://creativecommons.org/licenses/by/3.0/This article is available from https://gmd.copernicus.org/articles/8/2723/2015/gmd-8-2723-2015.htmlThe full text article is available as a PDF file from https://gmd.copernicus.org/articles/8/2723/2015/gmd-8-2723-2015.pdf
Thermal expansion of seawater has been one of the most important contributors to
global sea level rise (SLR) over the past 100 years. Yet, observational
estimates of this volumetric response of the world's oceans to temperature
changes are sparse and mostly limited to the ocean's upper 700 m.
Furthermore, only a part of the available climate model data is sufficiently
diagnosed to complete our quantitative understanding of thermosteric SLR
(thSLR). Here, we extend the available set of thSLR diagnostics from the
Coupled Model Intercomparison Project Phase 5 (CMIP5), analyze those model
results in order to complement upper-ocean observations and enable the
development of surrogate techniques to project thSLR using vertical
temperature profile and ocean heat uptake time series. Specifically, based on
CMIP5 temperature and salinity data, we provide a compilation of thermal
expansion time series that comprise 30 % more simulations than currently
published within CMIP5. We find that 21st century thSLR estimates derived
solely based on observational estimates from the upper 700 m (2000 m) would
have to be multiplied by a factor of 1.39 (1.17) with 90 % uncertainty
ranges of 1.24 to 1.58 (1.05 to 1.31) in order to account for thSLR
contributions from deeper levels. Half (50 %) of the multi-model total
expansion originates from depths below 490 ± 90 m, with the range
indicating scenario-to-scenario variations. To support the development of
surrogate methods to project thermal expansion, we calibrate two simplified
parameterizations against CMIP5 estimates of thSLR: one parameterization is
suitable for scenarios where hemispheric ocean temperature profiles are
available, the other, where only the total ocean heat uptake is known
(goodness of fit: ±5 and ±9 %, respectively).
Introduction
Sea level rise due to anthropogenic climate change constitutes a major impact
to the world's coastlines, low-lying deltas and small island states. The
climate system is warming and during the relatively well-sampled recent
40-year period (1971–2010) the world ocean absorbed 93 % of the Earth's
radiative energy excess, whereby 70 % of the net oceanic heat gain is found
in depths above and 30 % below 700 m . As the ocean
takes up heat, the thermal expansion of seawater is a major driver behind sea
level rise (SLR). note that 40 % of the observed
global mean SLR over 1971–2010 can be attributed to thermal expansion. This
volumetric response of the ocean to temperature changes is expressed by its
thermal expansion coefficient αe.g., and
is due to nonlinearities of the thermodynamic properties (potential
temperature, Θ, salinity, S, and pressure, p) in the equation of
state of seawater density, ρe.g.,. Thus,
changes in heat fluxes at the sea surface and heat redistribution in the
ocean's interior by advection, eddies and diffusion, lead to non-zero
temperature differences altering the sea level even if the global mean
potential temperature changes equal zero
.
In turn, processes in the interior ocean cause spatial patterns of ocean heat uptake at
the sea surface which define regional and global warming rates .
Sea level is often defined as the height of the sea surface relative to the geoid –
the surface of equal gravitational potential of a hypothetical ocean at rest
– also called the geocentric sea level according to .
Therefore sea level changes integrate all volume changes of the world ocean.
Aside from thermal expansion, SLR is also induced by changes in ice-sheet as
well as glacier mass and land water storage that combined amounts to 60 % of
the observed global mean SLR over 1971–2010 . Over
the last century, these mass changes in the ocean termed
“barystatic” sea level changes by together with
ocean's thermal expansion have been the main contributors to global mean SLR. Some
other influences, such as salinity variations associated with freshwater
tendencies at the sea surface and redistributed in the ocean's interior have
a negligible effect on seawater density and thus sea level changes on the
global scale e.g.,; on regional to
basin scales, however, the role of salinity should not be neglected in sea
level studies e.g.,. In the long term, the mass
contribution might become substantially larger than thermal expansion
contribution to SLR because of the larger efficiency of land-ice melting for
a given amount of heat . However, the current
climate models of the Coupled Model Intercomparison Project Phase 5 (CMIP5)
do not include land ice-sheet discharge dynamics and their contributions to
the global mean SLR budget . Furthermore, simulating
land ice-sheet discharge dynamics from the Antarctic ice sheets might
translate into large uncertainties in climate models, since non-linear
processes may be triggered that could alter the sea level rise contribution
dramatically
e.g.,. Since
the beginning of the satellite altimetry era in 1993, the contribution of
thermal expansion to global mean SLR is estimated to be 34 % (observations)
and 47 % (simulations), respectively see Table 13.1
in. Down to the present day, the observed
SLR contribution from thermal expansion is limited in the space and time
dimension: available observed long-term (decadal) time series of thermosteric
sea level rise (thSLR) are mainly globally averaged values using different
spatio-temporal interpolation/reconstruction methods and cover the upper
2000 m at maximum
. Observed
contributions to thSLR from depths below 2000 m are assumed to increase
monotonically and linearly in time
. For details on the spatial as
well as temporal coverage and quality of oceanic temperature measurements
that underlie thSLR estimates we refer to and
references therein.
The objective of the present study is both to complement observed and
existing simulated thSLR estimates in a number of ways and to enable the
development of surrogate techniques for long-term thSLR projections. We begin
by introducing the observed and simulated data sets as well as the method to
arrive at thSLR estimates. Subsequently, we calculate the simulated thermal
expansion over the entire ocean grid for a number of CMIP5 models that have
not published those time series yet. Sections 3 and 4 present both the
extended CMIP5 thSLR (zostoga) data set and depth-dependent results
that can complement upper ocean layer observations. Sections 5 and 6
investigate hemispheric and global averages of calibrated thSLR mimicking
CMIP5 estimates. In Sect. 7 we discuss and summarize our results focussing on
the extent to which the observations might underestimate the contribution to
thSLR from depths below the main thermocline.
Methods and models
The volumetric response to changes in the ocean's heat budget, the
thermosteric sea level, ηΘ, at any horizontal grid point and any
arbitrary time step is defined by the vertically integrated product of the
thermal expansion coefficient, α, and the potential temperature
deviation from a reference state, Θexp-Θref,
ηΘ(x,y,t)=∫-H0α(Θexp-Θref)dz,
where the spatial 3-D thermal expansion coefficient, α is defined by
α=-1ρ(Sref,Θref,p)ρ(Sref,Θexp,p)-ρ(Sref,Θref,p)(Θexp-Θref).
CMIP5 publishes time series of global mean (0-D) ηΘ, called
zostoga and represents the integral value of ocean's thermal expansion, α (Θexp-Θref), at each grid
point, over the entire ocean volume. For the majority of the fully coupled
climate models, sea level changes due to net gain of heat need to be
diagnosed offline as a result of using the Boussinesq approximation,
conserving ocean's volume and not mass . Here, we
derive global mean yearly depth profiles of thermal expansion by using
independent Θ and S prognostics of CMIP5 model simulations in
Eq. (2).
In order to derive thermal expansion estimates, and zostoga, from
hemispherically or globally averaged vertical temperature profiles, rather
than from sparsely observed and computationally expensive spatial 3-D fields
of temperature, salinity and pressure, we use a simplified parameterization
of a thermal expansion coefficient, α1.5, as a polynomial of
Θ and p:
α1.5=(c0+c1Θ0(12.9635-1.0833p)-c2Θ1(0.1713-0.019263p)+c3Θ2(10.41-1.1338p)+c4p-c5p2)×10-6,
with Θ0=Θexp, Θ1=Θ02 and Θ2=Θ03/6000 and calibration parameters cn=0-5. This polynomial
algorithm is based on a simplification of the equation of state of seawater
given in , assuming a constant salinity of 35 PSS-78. It is,
for example, included in the reduced-complexity Model for the Assessment of
Greenhouse-gas Induced Climate Change (MAGICC)
. The depth profile,
z, is expressed by the pressure profile p=0.0098(0.1005z+10.5exp((-1.0)z/3500)-1.0),
assuming a mean ocean depth of 3500 m and a mean maximum ocean depth of
6000 m in Eq. (3). As a first step, we use time-dependent vertical global
and hemispheric profiles of Θ from the CMIP5 models to test the
reliability of thermal expansion estimates based on this simplified approach
(Eq. 3). With these time series of vertical temperature profiles we calibrate
α1.5 in Eq. (3) with calibration parameters cn against globally
and hemispherically averaged vertical profiles of α in Eq. (2) (using
squared differences as goodness-of-fit statistic).
We name this parameterization the 1.5-D simplification, as it uses two
hemispherically averaged depth profiles. In addition, we use the CMIP5 data
to estimate the zero-dimensional (0-D) thermal expansion coefficient
α0. Divided by ocean's specific heat capacity, reference density and
area, it gives the “expansion efficiency of heat” (in m YJ-1,
1 YJ ≡ 1024 J) and allows the comparison of thermal expansion
from models with different spatial dimensions . This
constant quantifies the proportionality between global mean thSLR and ocean
heat uptake (OHU) cf..
We examine a broad range of CMIP5 scenarios, namely the historical
(post-1850) climate simulations, the idealized 1 % CO2 per year increase
(1pctCO2) and the response to abrupt 4 × pre-industrial
CO2 increase (abrupt4xCO2). But as we aim to complement observed
and existing simulated thSLR estimates and to design surrogate techniques to
project long-term thSLR, we focus on the four scenarios defining future
change in radiative forcing, namely rcp2.6, rcp4.5,
rcp6.0 and rcp8.5. These scenarios specify four greenhouse
gas concentration trajectories and their Representative Concentration
Pathways (RCP). They are named after the amount of radiative forcing (in
W m-2) realized in the year 2100 relative to values of the
pre-industrial (pre-1850) control scenario (piControl) for
details seeand Table S1 in the Supplement.
However, recent literature suggests that the rapid adjustment primarily due
to clouds generates forcing variations that cause differences in the
projected surface warming among the CMIP5 models even if radiative forcing is
equally prescribed for each individual CMIP5 model .
Independent of the model and estimation method, a “full linear drift” is
removed from all simulated thermosteric sea level time series,
zostoga and temperature time series by subtracting a linear trend
based on the entire corresponding (piControl) scenario in order to
allow for comparison with observational time series. For our globally and
hemispherically averaged thSLR time series the sensitivity to the method of
drift correction is less than 1% due to small low-frequency (inter-annual to
inter-decadal) variability present in the evolution of this integral oceanic
property. This contrasts the large low-frequency variability, e.g. in the
sea surface temperature evolution . For details about
methods of climate drift correction in CMIP5 models see
, and the supplementary by
. Additionally, we correct the historical
time series by adding the suggested thSLR trend of
0.1 ± 0.05 mm yr-1 by to take into
account that the CMIP5 piControl scenario might be conducted without
volcanic forcing and thus underestimate the oceanic thermal expansion in the
historical scenario . The adjustment of
global mean SLR to changes in ocean mass is fast and linear
; thus in the longer term, impacts of changing ocean
mass on SLR may well become the primary contribution to the trend in SLR. For
projected time series beyond the historical simulations, we use the
rcp4.5 simulations consistent with .
Extended CMIP5 zostoga data set
For CMIP5 models that report zostoga, we calculate the RMSE
between published zostoga values and our recalculated values based
on the provided Θ and initial S depth profiles. Averaged over all
CMIP5 models and scenarios and normalized by the mean zostoga value,
the RMS-error amounts to ±1 %, providing confidence that our 3-D
equation of state implementation is consistent with those of CMIP5 modelling
groups. As not all CMIP5 models that provide Θ and S also provide
zostoga, our recalculated data set comprises 30 % more modelled
zostoga time series than currently published within CMIP5 (compare
Table S1 and Fig. 1a, e.g., to Fig. 13.8 in ). These
complementing zostoga time series contribute 50 % more CMIP5
models to multi-model ensemble thSLR estimates than previously used by
; they are available at
http://climate-energy-college.net/complementing-thermosteric-sea-level-rise-estimates and as Supplement.
Time series of zostoga published by the individual model groups are
available, e.g., here http://pcmdi9.llnl.gov/esgf-web-fe.
Median and its 90 % confidence interval for projections of global
mean thSLR (in m) in 2046–2065 and 2081–2100 relative to 1986–2005 as well
as in year 2100 relative to year 1900 for the four RCP scenarios.
Period1986–20052046–20652081–210021002081–2100scenarioIPCC-AR5Historical0.04 [0.01 to 0.07]rcp2.60.10 [0.06 to 0.13]0.15 [0.10 to 0.20]0.19 [0.14 to 0.24]0.14 [0.10 to 0.18]rcp4.50.11 [0.08 to 0.14]0.19 [0.14 to 0.24]0.24 [0.19 to 0.29]0.19 [0.14 to 0.23]rcp6.00.11 [0.08 to 0.14]0.20 [0.15 to 0.25]0.26 [0.21 to 0.32]0.19 [0.15 to 0.24]rcp8.50.13 [0.10 to 0.16]0.28 [0.22 to 0.34]0.36 [0.29 to 0.42]0.27 [0.21 to 0.33]
For the RCPs, our extended data set implies a maximum thSLR of 0.4 m for the
21st century. For rcp8.5 in 2081–2100 relative to 1986–2005, the
projected model median thSLR and its 90 % confidence interval amounts to
0.28 ± 0.06 m (see Table 1 for more scenario
results). The corresponding thSLR published by is
0.27 ± 0.06 m. For all four RCP scenarios, our
results indicate that previous CMIP5 multi-model ensemble estimates by
have been robust, despite being based on 30 % less
models than used here (Tables 1, S1 and Table 13.5 in
). The idealized scenarios reveal a concave thSLR up
to 0.4 m in 1pctCO2 and a convex sea level rise up to 0.8 m in
abrupt4xCO2 over the first 100 years.
Complementing observations
For the upper 700 m, our extended CMIP5 multi-model median rate of thSLR and
its standard deviation globally amounts to 0.57 ± 0.03 mm yr-1
from 1971 onward to 2010 (Figs. 1b and S3b in the Supplement) and is similar
to the observed arithmetic mean 0.53 ± 0.02 mm yr-1 of the three
individual trends 0.63 ± 0.02 mm yr-1,
0.45 ± 0.02 mm yr-1 and
0.50 ± 0.03 mm yr-1cf. Fig. 13.4
in. For the same period, around half of the models
underestimate the ocean's thermal expansion in simulations, even after the
correction for missing volcanic forcing in the piControl scenario
. Nevertheless, the majority of the
historical scenarios capture the main volcanic eruptions in the
years 1963 (Agung), 1982 (El Chichón) and 1991 (Pinatubo) with a sea level
drop 1–2 years later. Generally, differences in the observed and interannual
variability suggest that the underlying spatial patterns of interannual
thermosteric sea level variability are different . For
the altimetry period (1993–2010), our multi-model median is
1.45 mm yr-1, with 1.02 to 1.97 mm yr-1 as 90 % uncertainty,
taking into account the contribution of thermal expansion to the global mean
SLR from the entire ocean depth. This rate of thSLR equals the corresponding
rate of 1.49 mm yr-1 and its uncertainty range of 0.97 to
2.02 mm yr-1 listed in Table 13.1 by and
confirms again the robustness of simulated thSLR estimated presented by
with 30 % less models for a multi-model estimate
than used here.
Time series of observed and simulated global mean yearly thSLR (in
cm). (a) Simulated thSLR (zostoga) relative to year 1900 for seven
CMIP5 scenarios: historical (31/47), 1pctCO2 (19/32),
abrupt4xCO2 (17/30), rcp2.6 (18/26), rcp4.5
(27/40), rcp6.0 (13/20), rcp8.5 (27/40); the ratio in
brackets indicates the number of models of published (solid lines)
zostoga and recalculated (dashed lines) zostoga in this
study based on simulated temperature and salinity fields. Bars indicate the
thSLR of the four RCP scenarios in year 2100 (see also Table 1).
(b) Observed contribution to yearly thermosteric sea level of the upper 700 m by
, and
relative to year 1961 and corresponding simulated
time series of the historical and rcp4.5 scenarios, whereby
the solid light (dark) grey lines represent the model mean (median). Observed
contribution to yearly thermosteric sea level (in cm) from layers
(c) between 700 and 2000 m by and
and (d) below 2000 m by
relative to year 1993 (indicating the start of
the satellite sea level altimetry period). Corresponding simulated time
series are shown as in (b).
The model median contribution to thSLR from the layer between 700 and 2000 m
suggests a slight underestimation of the observational data for the period
2005–2013 (Figs. 1c and S3c). For ocean depths below 2000 m, the model
median trend for the years 1990–2000 of 0.11 mm yr-1 in the
historical scenario seems to reliably represent the thSLR
contribution which estimated (Figs. 1d and S3d).
For an ocean warming occurring at a depth below 3000 m
estimate a similar thSLR over a 40-year period;
based on observed and assimilated data it amounts to 0.10 and
0.13 mm yr-1, respectively. For the upper 2000 m, the depth profiles
of thermodynamic properties across CMIP5 models are largely aligned with
observational depths profiles for Θ and S of the modern day
(2005–2013) ocean provided by the Argo program
; the same is true for the derived thermal
expansion coefficient see Fig. 2 and depth profiles of potential
temperatures in the piControl scenario
by. The simulated salinity profile shows the
observed maximum at around 200 m that reflects evaporation zones and a
minimum at around 500 m that reflects mode water regions. For depths below
500 m, the model spread of Θ and S amounts to
2 ∘C and 0.4 PSS-78, with only a few
model outliers. Independent of the model and scenario, the thermal expansion
coefficient α at the sea surface decreases from
4 × 10-4∘C-1 in tropical to near zero in polar
regions and, globally averaged, shows the familiar concave vertical profile
e.g., with a minimum around 1500 m (Fig. 2). The
minimum global mean climatological value of α amounts to
1.3 × 10-4∘C-1 for the historical
scenario and agrees well with the observed one. Averaged over the entire
water column, α (1.56 × 10-4∘C-1)
compares well with the corresponding value from ocean-only simulations
1.54 × 10-4∘C-1,. In
the Northern Hemisphere, α is 1 % higher than in the Southern
Hemisphere because average temperatures tend to be higher above 2000 m in
the Northern Hemisphere (not shown). For details on the horizontal and
vertical behaviour of α see, e.g., and
.
Global mean vertical profiles for all models of historical
in year 1900 (upper panels, a–c), historical in year 2005
relative to year 1986 (d), rcp8.5 in year 2100 relative to the
historical mean over 1986 to 2005 (lower panels, e–g) and
abrupt4xCO2 within the first year (h): (a) potential temperature
(in ∘C, 0 to 20), (b) salinity (in PSS-78, 32 to 36) and (c) thermal
expansion coefficient α (in 10-4∘C-1, 1.2 to 2.8);
(d) thermal expansion per layer (in mm m-1, -0.1 to 0.2), (e) temperature
deviation (in ∘C, -1 to 5), (f) thermal expansion per layer (in mm m-1, -0.2
to 1.2) and (g) thermal expansion coefficient α (in
10-4∘C-1, 1.0 to 2.8), (h) thermal expansion per layer (in mm m-1, -0.2 to
1.2). Observed profiles (grey lines) are based on the Argo data as an average
over the period 2005 to 2013, except for the thermal expansion in (d). Model
outliers are indicated in (a).
Model median percentage contribution to global mean thSLR for the
entire water column from depths below 700 m (light grey) and below 2000 m
(dark grey) for the historical scenario, for projections for the
four RCP scenarios and the two idealized CO2 scenarios derived from
Eq. (2). Whisker plots quantify the temporal average distribution of the
contribution to thSLR of the first 20 years, the entire time series and the
last 20 years, respectively: 2006–2025/2006–2100/2081–2100 for
RCPs (a–d); 1901–1920/1900–2005/1981–2005 for the
historical scenario (e); and 1–20/1–100/81–100 for the
1pctCO2 and abrupt4xCO scenarios (f, g).
Bars and whiskers represent the 25–75 and 5–95 % uncertainties of the
median, respectively; the central mark of the bar indicates the model median,
the asterisk the model mean.
Observed thSLR estimates with a vertical integration limit that is not the
entire ocean depth due to data sparsity will need to be complemented by an
approximation for the thSLR contributions originating by changes in deeper
layers. Our CMIP5 analysis derives those deeper layer contributions as
percentage shares of total thSLR across our range of scenarios (see
multi-model median in Fig. 3). The contributions relevant to a global sea
level budget clearly depend on the scenario and hence the atmospheric
forcing. The higher the radiative forcing gradient of the scenario, the lower the contribution is from depths below 2000 m. The stronger the warming
signal in the ocean's upper layers the more enhanced the stratification is in
the upper layers. The abrupt4xCO2 scenario is noticeable where
90 % of the thermal expansion is confined to the upper 700 m in the first
20 years and that the evolution of thSLR contributions from a depth below
2000 m (as share of total thSLR) shows an opposing trend compared to the
21st century evolution of the multi-gas scenarios. Firstly, the idealized
experiments are started from pre-industrial control equilibrium conditions
and hence miss the initial stratification and upper layer expansion between
historical's start year (usually 1850) and the start year of our
analysis (1900 for the historical and 2006 for the RCP scenarios)
cf.. Secondly, the initial warming pulse in
abrupt4xCO2 is extreme: already within the first year of the model
scenario, thermal expansion in the upper 300 m shows a clear increase in the
global mean, for all CMIP5 models, and amounts to a magnitude of thermal
expansion corresponding to the last 20 years (1986–2005) of the
historical scenario (Figs. 2d, h and S3a). After 20 years, the
thermal expansion for the abrupt4xCO2 scenario in this upper layer
equals almost the thermal expansion of the rcp2.6 scenario at the
end of the 21st century (not shown). Both characteristics of
abrupt4xCO2 define a large vertical temperature gradient between
surface and deeper water almost instantaneously. Mixing and advection erodes
this large vertical temperature gradient, so that after 90 years the
contribution below 700 m increased to 33 % and below 2000 m to 7 %. At
the beginning of the 21st century, the initial thSLR contribution for the
four RCP scenarios shows high levels around 40 % (20 %) for depth below
700 m (2000 m) and then decreases in layers below 2000 m. For the lower
and intermediate forcing scenarios, rcp2.6 and rcp4.5, the
700 m upper layer's proportion decreases, too. In all multi-gas scenarios,
the middle layer's share of total thSLR, i.e., between 700 and 2000 m (light-grey band in Fig. 3), tends to increase over the 21st century. The
explanation for this tendency of middle and deeper layer thSLR contributions
to the total thSLR is likely related to multiple effects. The warming induced
intensified stratification in the upper 700 m seems the obvious effect for
the decreasing contributions from layers below 2000 m. Additionally, we
propose the effect of the cessation of sporadic volcanic forcing in the RCP
scenarios compared to the historical simulations. Towards the end of
the historical scenario, i.e., the start of the RCP scenarios, the
volcanic forcing in historical might suppress the thermal expansion
of middle layers (700–2000 m) and might therefore lead to a certain rebound
effect of the middle layer thSLR contributions in the mid-21st century (cf.
Fig. S3). However, for the multi-gas scenarios, the overall 21st century
multi-model median thSLR contribution of the deep ocean is 39% from depth
below 700 m with 24 to 58 % as 90 % uncertainty and 17 % from depths
below 2000 m with 5 to 31 % as 90 % uncertainty (see Fig. 3a–d). The
contributions for the RCP reference period (1986–2005, Church et al., 2013a)
taken from the historical simulations are 46 % [21 to 73 %] (and
21 % [4 to 44 %]) (Fig. 3e).
Whisker plots of percentage thermal expansion from the layers
between 700 and 2000 m, below 700 m and below 2000 m, respectively, relative
to the total thermal expansion integrated over the entire water column, for
seven scenarios. Thermal expansion estimates are derived from Eq. (2) (left
bar) and Eq. (3) (right bar) used in simpler climate models (here with the
optimized calibration parameters in Table S2) and are based
on (a) globally, (b) northern and (c) southern
hemispherically averaged vertical potential temperature profiles, followed by
a temporal averaging over the entire time series (see Fig. 3). Bars and
whiskers represent the 25–75 and 5–95 % uncertainties of the median,
respectively; the central mark of the bar indicates the model median, the
asterisk the model mean. The number of models available for these statistical
estimates are crosses on the left of the box, at which crosses above and
below the whiskers indicate model outliers.
The 1.5-D parameterization
We obtain six calibration parameters cn for each CMIP5 model through our
optimization scheme that minimizes the RMS errors from iteration to
iteration. When comparing our extended set of CMIP5 thSLR (zostoga)
time series with the thSLR time series obtained by using potential
temperatures and standard pressure profiles with Eq. (3), we then obtain an
average error of ±5 %, ranging between 1 and 17 % across the CMIP5
model suite (see Table S2). The hemispherically averaged percentage
contributions to thSLR based on the 1.5-D simplified thermal expansion
coefficient (Eq. 3) for all seven scenarios compare well with our extended
CMIP5 data set (Fig. 4). The thSLR contribution from depths below 2000 m is
larger in the Southern Hemisphere than in the Northern Hemisphere. This might
be due to model-dependent mixing rates forming Antarctic bottom water, that
assigned to CMIP5 model biases in the Southern Ocean's
sea surface temperature. Strong outliers (values far outside the whiskers and
the 90 % confidence interval) are found in the depth range below the main
thermocline between 700 and 2000 m independent of the scenario and spatial
averaging.
The 0-D parameterization
Our findings complement who analyzed the
“expansion efficiency of heat” as constant of proportionality between thSLR
and OHU for the 1pctCO2 scenarios and concluded that model
differences in the stratification below the main thermocline largely explain
the differences between the individual models. Based on the original CMIP5
ensemble with 30 % less CMIP5 models than used here, the constant for
global mean (0-D) time series estimated by
amounts to 0.11 ± 0.01 m YJ-1. Our median and its 90 %
confidence interval amounts to 0.12 m YJ-1 [0.10 to 0.14] as integral
over the entire water depths, 0.14 m YJ-1 [0.12 to 0.15] for the upper
700 m and 0.10 m YJ-1 [0.08 to 0.11] below 700 m (Table S4.1). The
constant depends on the 3-D pattern of heat redistribution with the main
contribution arising from the upper 700 m. This pattern depends in equal
measure on the individual model and on the scenario for a given model (see
Table S4.1 and S4.2). Our 0-D approach results in a normalized difference
between thSLR estimates based on a 3-D (in Eq. 2) and spatially constant
(0-D) thermal expansion coefficients of 9 %.
Discussion and summary
The present study aims to complement our quantitative understanding of thSLR
using CMIP5 results. Firstly, based on CMIP5 temperature and salinity data
for a range of scenarios, we calculate a compilation of thermal expansion
time series that comprise 30 % more simulations than currently published
within CMIP5. This accounts for 50 % more models in the multi-model
ensemble estimates than used by . However, our results
confirm the robustness of these previous CMIP5 multi-model thSLR estimates.
CMIP5 multi-model mean depth and standard deviation (in m) where the
individual model mean (left bar) and median (right bar) depth of thSLR
originates for the four RCP scenarios, as well as the historical scenario and
the two idealized CO2-forcing scenarios. Thermal expansion estimates are
derived from Eq. (2) based on (a) globally, (b) northern
and (c) southern hemispherically averaged vertical potential
temperature profiles, followed by a temporal averaging over the last 20 years (see Figs. 3 and 4). Table S5 summarizes the estimates. The horizontal
solid (dashed) line indicates the mean (median) depth of thSLR based on
climatological temperature and salinity profiles .
Secondly, we quantify the thSLR contribution from the entire ocean depth in
order to complement observational estimates that are primarily available for
the upper ocean layers down to 700 m cf..
Sparse observational evidence points to non-significant contributions to
global mean thSLR from depths below 2000 m during 2005 to 2013
. Our results suggest that 21st century thSLR estimates
derived solely based on observational estimates from the upper 700 m would
have to be multiplied by a factor of 1.39 (with a 90 % uncertainty range of
1.24 to 1.58) in order to be used as approximation for total thSLR
originating from the entire water column. Correspondingly, our CMIP5 model
analysis suggests that partial thSLR contribution based on hydrographic
measurements from the upper 2000 m can be expected to account already for
around 85 % of the total thSLR and consequently have to be multiplied only
by 1.17 (with a 90 % uncertainty range of 1.05 to 1.31). In fact, our
results indicate that half (50 %) of the thSLR contributions can come from
depths below 570 m in the historical simulations and from slightly
shallower levels (490 ± 90 m) in the future RCP scenarios, when
averaged across the last 20 years of the scenario period (Fig. 5 and
Table S5). Here, we define “half-depth” as the median of the depths
distribution of OHU and thSLR contributions. We find that those
“half-depths” are located within the thermocline. The OHU half-depth is
around 100 m deeper than the thSLR half-depth due to nonlinearities in the
seawater equation of state (not shown). Furthermore, those half-depths seem
to be deeper in the Southern than in the Northern Hemisphere because the
layers above 2000 m are warmer in the Northern Hemisphere and less
stratified below the main thermocline. The recent study by
corroborates the relevance for hemispheric
partitioning of model results to adjust for the poor sampling of the Southern
Hemisphere's upper ocean temperatures. The mean depths are 100 (300) m lower
than the medians for the idealized (RCP) scenarios and 400 m for the
historical scenario (Table S5). This indicates a positive skewness
of the vertical distribution of thermal expansion because of its long tail
towards depths below 700 m. For climatological temperature and salinity
profiles , the difference between the mean (1200 m) and
median (700 m) depth is even greater compared to our model diagnostic
results of the historical scenario. This can be explained by a
reduced vertical temperature gradient within the main thermocline and a
weaker stratification above the main thermocline induced by the absent end of
20th-century warming in the climatological profiles. In case of the
historical scenario, the difference between mean and median depth of
thermal expansion shows that the amount of thSLR due to the externally forced
warming during the period 1986–2005 is small compared to the underlying
interannual variability that is generated by the internal variability of
ocean dynamics . However, these findings
highlight the importance of the thSLR contribution from deeper ocean layers
e.g.,. Present and projected thSLR is not
predominantly (> 50 %) attributable to the layers above the depth of 700 m,
the depth most observational based estimated are still limited to
.
Lastly, in order to support the development of surrogate methods to project
thermal expansion, we calibrate two simplified parameterizations against
CMIP5 estimates of thSLR: one parameterization is suitable for scenarios
where hemispheric ocean temperature profiles are available (1.5-D approach),
the other, where only the total OHU (0-D approach) is known. Generally,
expanding a mass of warm, salty subtropical water is more efficient for a
given temperature increase than a mass of cold, fresh subpolar water for the
same temperature increase. In upper tropical waters a warming signal persists
longer than in upper high-latitude waters due to the weaker, temperature-dominated stratification in higher latitudes, except in the Southern Ocean
around Antarctica where salinity changes play a fundamental role in
determining the strength of stratification
. Our diagnosis of CMIP5 profiles
confirms the large variations in α, the 3-D thermal expansion
coefficient, due to strong meridional (not shown) and vertical density
gradients originating from strong temperature gradients (see Eq. 2 and
Fig 2). These strong vertical as well as meridional gradients in the thermal
expansion efficiency raise the question whether simplified approaches that
collapse either the meridional component (our 1.5-D simplification) or both
dimensions (the 0-D approach) are sufficiently reliable. The introduced
errors of ±5 % (1.5-D) and ±9 % (0-D) compared to the CMIP5 data
based on the entire ocean grid, suggest that the simplifications are
sufficiently accurate for long-term SLR projections, when other uncertainties
(land ice-sheet response, climate sensitivity or radiative forcing
e.g., dominate the final result.
The Supplement related to this article is available online at doi:10.5194/gmd-8-2723-2015-supplement.
All authors contributed to designing and writing the text.
K. Lorbacher conducted the analysis and drafted the manuscript.
Acknowledgements
We thank Dimitri Lafleur for his valuable and helpful comments on the
manuscript. 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 (listed in Table S1 of this paper and based on
http://cmip-pcmdi.llnl.gov/cmip5/docs/CMIP5_modeling_groups.pdf) for
producing and making available their model output. For CMIP the US Department
of Energy's Program for Climate Model Diagnosis and Intercomparison provides
coordinating support and led development of software infrastructure in
partnership with the Global Organization for Earth System Science Portals.
Observational data by , ,
and are provided at
http://www.cmar.csiro.au/sealevel/sl_data_cmar.html,
https://atm-phys.nies.go.jp/~ism/pub/ProjD,
http://www.nodc.noaa.gov/OC5/3M_HEAT_CONTENT/basin_tsl_data.html and
http://sio-argo.ucsd.edu/RG_Climatology.html,
respectively. Edited by: R. Marsh
ReferencesAbraham, J. P., Baringer, M., Bindoff, N. L., Boyer, T., Cheng, L. J.,
Church, J. A., Conroy, J. L., Domingues, C. M., Fasullo, J. T., Gilson, J.,
Goni, G., Good, S. A., Gorman, J. M., Gouretski, V., Ishii, M., Johnson, G.
C., Kizu, S., Lyman, J. M., Macdonald, A. M., Minkowycz, W. J., Moffitt, S.
E., Palmer, M. D., Piloa, A. R., Reseghetti, F., Schuckmann, K., Trenberth,
K. E., Velicogna, I., and Willis, J. K.: A Review of Global Ocean Temperature
Observations: Implications for Ocean Heat Content Estimates and Climate
Change, Rev. Geophys., 51, 450–483, 10.1002/rog.20022, 2013.Bindoff, N. L. and Hobbs, W. R.: Oceanography: Deep ocean freshening, Nature
Climate Change, 3, 864-865, 10.1038/nclimate2014, 2013.Boyer, T. P., Antonov, J. I., Baranova, O. K., Coleman, C., Garcia, H. E.,
Grodsky, A., Johnson, D. R., Locarnini, R. A., Mishonov, A. V., O'Brien, T.
D., Paver, C. R., Reagan, J. R., Seidov, D., Smolyar, I. V., and Zweng, M.
M.: World Ocean Database 2013, NOAA Atlas NESDIS 72, edited by: Levitus, S.,
Technical Editor: Mishonov, A., Silver Spring, MD, 209 pp.,
10.7289/V5NZ85MT, 2013.
Church, J. A., Clark, P. U., Cazenave, A., Gregory, J. M., Jevrejeva, S.,
Levermann, A., Merrifield, M. A., Milne, G. A., Nerem, R. S., Nunn, P. D.,
Payne, A. J., Pfeffer, W. T., Stammer, D., and Unnikrishnan, A. S.: Sea Level
Change, in: Climate Change 2013: The Physical Science Basis. Contribution of
Working Group I to the Fifth Assessment Report of the Intergovernmental Panel
on Climate Change, edited by: Stocker, T. F., Qin, D., Plattner, G.-K.,
Tignor, M., Allen, S. K., Boschung, J., Nauels, A., Xia, Y., Bex, V., and
Midgley, P. M., Cambridge University Press, Cambridge, United Kingdom and New
York, NY, USA, 1137–1216, 2013a.Church, J. A., Monselesan, D., Gregory, J. M., and Marzeion, B.: Evaluating
the ability of process based models to project sea-level change, Environ.
Res. Lett., 8, 014051, 10.1088/1748-9326/8/1/014051, 2013b.Domingues, C. M., Church, J. A., White, N. J., Gleckler, P. J., Wijffels, S.
E., Barker, P. M., and Dunn, J. R.: Improved estimates of upper-ocean warming
and multi-decadal sea level rise, Nature, 453, 1090–1093,
10.1038/nature07080, 2008.Durack, P. J., Wijffels, S. E., and Gleckler, P. J.: Long-term Sea-level
Change Revisited: The Role of Salinity, Environ. Res. Lett., 9, 114017,
10.1088/1748-9326/9/11/114017, 2014a.Durack, P. J., Gleckler, P. J., Landerer, F. W., and Taylor, K. E.:
Quantifying underestimates of long-term upper-ocean warming, Nature Climate
Change, 4, 999–1005, 10.1038/nclimate2389, 2014b.Forster, P. M., Andrews, T., Good, P., Gregory, J. M., Jackson, L. S., and
Zelinka, M.: Evaluating adjusted forcing and model spread for historical and
future scenarios in the CMIP5 generation of climate models, J. Geophys.
Res.-Atmos., 118, 1139–1150, 10.1002/jgrd.50174, 2013.Fyfe, J. C., Gillett, N. P., and Thompson, D. W. J.: Comparing variability
and trends in observed and modelled global-mean surface temperature, Geophys.
Res. Lett., 37, L16802, 10.1029/2010GL044255, 2010.
Gill, A. E.: Atmosphere-Ocean Dynamics, Acadamic Press, San Diego,
California, USA, 662 pp., 1982.
Greatbatch, R. J.: A note on the representation of steric sea level in models
that conserve volume rather than mass, J. Geophys. Res., 99, 12767–12771,
1994.Gregory, J. M., White, N. J., Church, J. A., Bierkens, M. F. P., Box, J. E.,
van den Broeke, M. R., Cogley, J. G., Fettweis, X., Hanna, E., Huybrechts,
P., Konikow, L. F., Leclercq, P. W., Marzeion, B., Oerlemans, J., Tamisiea,
M. E., Wada, Y., Wake, L. M., and van de Wal, R. S. W.: Twentieth-century
global-mean sea level rise: is the whole greater than the sum of the parts?,
J. Climate, 26, 4476–4499, 10.1175/JCLI-D-12-00319.1, 2013a.Gregory, J. M., Bi, D., Collier, M. A., Dix, M. R., Hirst, A. C., Hu, A.,
Huber, M., Knutti, R., Marsland, S. J., Meinshausen, M., Rashid, H. A.,
Rotstayn, L. D., Schurer, A., and Church, J. A.: Climate models without
volcanic preindustrial volcanic forcing underestimate historical ocean
thermal expansion, Geophys. Res. Lett., 40, 1600–1604,
10.1002/grl.50339, 2013b.Griffies, S. M., Yin, J., Durack, P. J., Goddard, P., Bates, S. C., Behrens,
E., Bentsen, M., Bi, D., Biastoch, A., Böning, C. W., Bozec, A.,
Chassignet, E., Danabasoglu, G., Danilov, S., Domingues, C., Drange, H.,
Farneti, R., Fernandez, E., Greatbatch, R. J., Holland, D. M., Ilicak, M.,
Large, W., Lorbacher, K., Lu, J., Marsland, S. J., Mishra, A., Nurser, A. J.
G., Salas y Miélia, D., Palter, J. B., Samuels, B. L., Schröter, J.,
Schwarzkopf, F. U., Sidorenko, D., Treguier, A.-M., Tseng, Y., Tsujino, H.,
Uotila, P., Valcke, S., Voldoire, A., Wang, Q., Winton, M., and Zhang, X.: An
assessment of global and regional sea level for years 1993–2007 in a suite
of interannual CORE-II simulations, Ocean Modell., 78, 35–89,
10.1016/j.ocemod.2014.03.004, 2014.Hallberg, R., Adcroft, A., Dunne, J. P., Krasting, J. P., and Stouffer, R.
J.: Sensitivity of Twenty-First-Century Global-Mean Steric Sea Level Rise to
Ocean Model Formulation, J. Climate, 26, 2947–2956,
10.1175/JCLI-D-12-00506.1, 2013.Ishii, M. and Kimoto, M.: Reevaluation of Historical Ocean Heat Content
Variations With An XBT depth bias Correction, J. Oceanogr., 65, 287299,
10.1007/s10872-009-0027-7, 2009.Jackett, D. R., McDougall, T. J., Feistel, R., Wright, D. G., and Griffies,
S. M.: Algorithms for density, potential temperature, conservative
temperature, and the freezing temperature of seawater, J. Atmos. Ocean.
Technol., 23, 1709–1728, 10.1175/JTECH1946.1, 2006.Joughin, I., Smith, B. E., and Medley, B.: Marine Ice Sheet Collapse
Potentially Under Way from the Thwaites Glacier Basin, Science, 344,
735–738, 10.1126/science.1249055, 2014.
Kouketsu, S., Doi, T., Kawano, T., Masuda, S., Sugiura, N., Sasaki, Y.,
Toyoda, T., Igarashi, H., Kawai, Y., Katsumata, K., Uchida, H., Fukasawa, M.,
and Awaji, T.: Deep ocean heat content changes estimated from observations
and reanalysis product and their influence on sea level change, J. Geophys.
Res., 116, C03012, dio:10.1029/2010JC006464, 2011.Kuhlbrodt, T. and Gregory, J. M.: Ocean heat uptake and its consequences for
the magnitude of sea level rise and climate change, Geophys. Res. Lett., 39,
L18608, 10.1029/2012GL052952, 2012.Levitus, S., Antonov, J. I., Boyer, T. P., Baranova, O. K., Garcia, H. E.,
Locarnini, R. A., Mishonov, A. V., Reagan, J. R., Seidov, D., Yarosh, E. S.,
and Zweng, M. M.: World ocean heat content and thermosteric sea level change
(0–2000 m), 1955–2010, Geophys. Res. Lett., 39, L10603,
10.1029/2012GL051106, 2012.Llovel, W., Willis, J. K., Landerer, F W., and Fukumori, I.: Deep-ocean
contribution to sea level and energy budget not detectable over the pa st
decade, Nature Climate Change, 4, 1031–1035, 10.1038/nclimate2387, 2014.Lorbacher, K., Marsland, S. J., Church, J. A., Griffies, S. M., and Stammer,
D.: Rapid barotropic sea level rise from ice sheet melting, J. Geophys. Res.,
117, C06003, 10.1029/2011JC007733, 2012.Lowe, J. A. and Gregory, J. M.: Understanding projections of sea level rise
in a Hadley Centre coupled climate model, J. Geophys. Res., 111, C11014,
10.1029/2005JC003421, 2006.Meinshausen, M., Raper, S. C. B., and Wigley, T. M. L.: Emulating coupled
atmosphere-ocean and carbon cycle models with a simpler model, MAGICC6 –
Part 1: Model description and calibration, Atmos. Chem. Phys., 11,
1417–1456, 10.5194/acp-11-1417-2011, 2011.Mengel, M. and Levermann, A.: Ice plug prevents irreversible discharge from
East Antarctica, Nature Climate Change, 4, 451–455,
10.1038/nclimate2226, 2014.Moss, R. H., Edmonds, J. A., Hibbard, K. A., Manning, M. R., Rose, S. K., van
Vuuren, D. P., Carter, T. R., Emori, S., Kainuma, M., Kram, T., Meehl, G. A.,
Mitchell, J. F., Nakicenovic, N., Riahi, K., Smith, S. J., Stouffer, R. J.,
Thomson, A. W., Weyant, J. P., and Wilbanks, T. J.: The next generation of
scenarios for climate change research and assessment, Nature, 463, 747–756,
10.1038/nature08823, 2010.Palmer, M. D., Good, S. A., Haines, K., Rayner, N. A., and Stott, P. A.: A
new perspective on warming of the global oceans, Geophys. Res. Lett., 36,
L20709, 10.1029/2009GL039491, 2009.Palmer, M. D., McNeall, D. J., and Dunstone, N. J.: Importance of the deep
ocean for estimating decadal changes in Earth's radiation balance, Geophys.
Res. Lett., 38, L13707, 10.1029/2011GL047835, 2011.Palter, J. B., Griffies, S. M., Samuels, B. L., Galbraith, E. D.,
Gnanadesikan, A., and Klocker, A.: The Deep Ocean Bouyancy Budget and Its
Temporal Variability, J. Climate, 27, 551–573,
10.1175/JCLI-D-13-00016.1, 2014.Piecuch, C. G. and Ponte, R. M.: Mechanisms of Global-Mean Steric Sea Level
Change, J. Climate, 27, 824–834, 10.1175/JCLI-D-13-00373.1, 2014.
Purkey, S. and Johnson, G. C.: Warming of Global Abyssal and Deep Southern
Ocean Waters between the 1990s and 2000s: Contributions to Global Heat and
Sea Level Rise Budgets, J. Climate, 23, 6336–6351, doi:101175/2010JCL3682.1,
2010.
Raper, S. C. B., Wigley, T. M. L., and Warrick, R. A.: Global Sea-level Rise:
Past and Future, in: Sea-Level Rise and Coastal Subsidence: Causes,
Consequences and Strategies, edited by: Milliman, J. and Haq, B., Kluwer,
Dordrecht, the Netherlands, 11–45, 1996.
Rhein, M., Rintoul, S. R., Aoki, S., Campos, E., Chambers, D., Feely, R. A.,
Gulev, S., Johnson, G. C., Josey, S. A., Kostianoy, A., Mauritzen, C.,
Roemmich, D., Talley, L. D., and Wang, F.: Observations: Ocean, in: Climate
Change 2013: The Physical Science Basis. Contribution of Working Group I to
the Fifth Assessment Report of the Intergovernmental Panel on Climate Change,
edited by: Stocker, T. F., Qin, D., Plattner, G.-K., Tignor, M., Allen, S.
K., Boschung, J., Nauels, A., Xia, Y., Bex, V., and Midgley, P. M., Cambridge
University Press, Cambridge, United Kingdom and New York, NY, USA, 2013.Rignot, E., Mouginot, J., Morligem, M., Serossi, H., and Scheuchl, B.:
Widespread, rapid grounding line retreat of Pine Island, Thwaites, Smith and
Kohler glaciers, West Antarctica from 1992 to 2011, Geophys. Res. Lett., 41,
3502–3509, 10.1002/2014GL060140, 2014.Roemmich, D. and Gilson, J.: The 2004–2008 mean and annual cycle of
temperature, salinity, and steric height in the global ocean from the Argo
Program, Prog. Oceanogr., 82, 81–100, 10.1029/2011GL047992, 2009.Rose, B. E. J., Armour, K. C., Battisti, D. S., Feldl, N., and Knoll, D. D.
B.: The dependence of transient climate sensitivity and radiative feedbacks
on the spatial pattern of ocean heat uptake, Geophys. Res. Lett., 41,
1071–1078, 10.1002/2013GL058955, 2014.
Russell, G. L., Gornitz, V., and Miller, J. R.: Regional sea level changes
projected byb the NASA/GISS Atmosphere Ocean Model, Clim. Dynam., 16,
789–797, 2000.Rye, C. D., Naveira Garabato, A. C., Holland, P. R., Meredith, M. P., Nurser,
A. J., Hughes, C. W., Coward, A. C., and Webb, D.: Rapid sea-level rise along
the Antarctic margins in response to increased glacial discharge, Nat.
Geosci., 7, 732–735, 10.1038/ngeo2230, 2014.Sen Gupta, A., Jourdain, N. C., Brown, J. N., and Monselesan, D.: Climate
Drift in the CMIP5 Models, J. Climate, 26, 8597–8615,
10.1175/JCLI-D-12-00521.s1, 2013.Taylor, K. E., Stouffer, R. J., and Meehl, G. A.: An Overview of CMIP5 and
the scenario design, B. Am. Meteorol. Soc., 93, 485–498,
10.1175/BAMS-D-11-00094.1, 2012.Trenberth, K. E. and Fasullo, J. T.: Tracking Earth's Energy, Science, 238,
316–317, 10.1126/science.1187272, 2010.Wang, C., Zhang, L., Lee, S.-K., Wu, L., and Mechoso, C. R.: A global
perspective on CMIP5 climate model biases, Nature Climate Change, 4,
201–205, 10.1038/nclimate2118, 2014.Wigley, T. M. L., Clarke, L. E., Edmonds, J. A., Jacoby, H. D., Paltsev, S.,
Pitcher, H., Reilly, J. M., Richels, R., Sarofim, M. C., and Smith, S. J.:
Uncertainties in climate stabilization, Climatic Change, 97, 85–121,
10.1007/s10584-009-9585-3, 2009.Yin, J.: Century to multi-century sea level rise projections from CMIP5
models, Geophys. Res. Lett., 39, L17709, 10.1029/2012GL052947, 2012.