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

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

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

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 (

The volumetric response to changes in the ocean's heat budget, the
thermosteric sea level,

In order to derive thermal expansion estimates, and

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

We examine a broad range of CMIP5 scenarios, namely the

Independent of the model and estimation method, a “full linear drift” is
removed from all simulated thermosteric sea level time series,

For CMIP5 models that report

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.

For the RCPs, our extended data set implies a maximum thSLR of 0.4 m for the
21st century. For

For the upper 700 m, our extended CMIP5 multi-model median rate of thSLR and
its standard deviation globally amounts to 0.57

Time series of observed and simulated global mean yearly thSLR (in
cm).

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

Global mean vertical profiles for all models of historical
in year 1900 (upper panels,

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 CO

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

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

We obtain six calibration parameters

Our findings complement

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

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 CO

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

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

All authors contributed to designing and writing the text. K. Lorbacher conducted the analysis and drafted the manuscript.

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