Editing IPCC:AR6/SROCC/Chapter-4 (section)

===== 4.2.2.2.1 Thermal expansion contribution =====

The ocean thermal expansion is caused by excess heat being absorbed by the ocean, as the climate warms. Thermal expansion is estimated from ''in situ'' ocean observations and ocean heat content reanalyses that rely on assimilation of data into numerical models (Storto et al., 2017 <sup>[[#fn:r162|162]]</sup> ; Sections 1.8.1.1 and 1.8.1.4; WCRP Global Sea Level Budget Group, 2018 <sup>[[#fn:r163|163]]</sup> ) . Full-depth, high-quality and unbiased ocean temperature profile data with adequate metadata and spatio-temporal coverage are required to estimate thermal expansion and to understand drivers of variability and long-term change (Pfeffer et al., 2018 <sup>[[#fn:r164|164]]</sup> ; Section 5.2.2.2.2) .

Historically, however, observational gaps exist and some ocean regions remain under-sampled to date (Sections 1.8.1.1 and 5.2.2.2.2; Figure 1.3; Appendix 1.A, Figure 1.1). Other factors also introduce uncertainty in estimates of thermal expansion like changes in instrumentation, systematic instrumental errors, changes in the quality control of the data and the mapping method used to produce regular grids (Section 5.2.2.2.2; Palmer et al., 2010 <sup>[[#fn:r165|165]]</sup> ) . In the upper 700 m, the largest sources of uncertainty for estimates of global mean thermal expansion from 1970 to 2004 are the choice of mapping methods (Boyer et al., 2016 <sup>[[#fn:r166|166]]</sup> ) , followed by the choice of bias correction for the bathythermographic observations (Cheng et al., 2016 <sup>[[#fn:r167|167]]</sup> ; Section 5.2.2.2.2). From 2006 onwards, the uncertainty is considerably reduced (Roemmich et al., 2015 <sup>[[#fn:r168|168]]</sup> ; von Schuckmann et al., 2016 <sup>[[#fn:r169|169]]</sup> ; Wijffels et al., 2016 <sup>[[#fn:r170|170]]</sup> ) , because the Argo array reached its targeted near-global ( up to ±60° latitude) coverage for the upper 2000 m in November 2007 (Riser et al., 2016 <sup>[[#fn:r171|171]]</sup> ; Section 5.2.2.2.2) .

Since AR5, in a community effort, the (WCRP Global Sea Level Budget Group, 2018 <sup>[[#fn:r172|172]]</sup> ) revisited the global mean thermal expansion estimates based on observations only. On the basis of a full-depth 13-member ensemble of global mean thermal expansion time series developed with the latest data and corrections available, they estimated that the global thermal expansion was 1.40 (1.08 – 1.72) mm yr <sup>–1</sup> for 2006–2015, 1.36 (0.96 – 1.76) mm yr <sup>–1</sup> for 1993–2015 (see Table 4.1). While the relative contribution of the upper 300 m did not change (~70%) between 2006–2015 and 1993–2015, the 700–2000 m contribution increased around 10% over the Argo decade (2006–2015), when observations for that depth interval soared ( Figure 1.3; Appendix 1.A, Figure 1.1) . This suggests that observed changes for 700–2000 m may have been underestimated for 1993 – 2005. Before 1993, estimates are based on a smaller ensemble of 4 datasets in which no thermal expansion is assumed below 2000 m because of lack of data (see Section 5.2.2.2.2 for more details). This ensemble shows a thermal expansion linear rate of 0.89 (0.84 – 0.94) mm yr <sup>–1</sup> for 1970–2015 (see Table 4.1).

Coupled climate models simulate the historical thermal expansion (see Table 4.1). However, for models that omit the volcanic forcing in their control experiment, the imposition of the historical volcanic forcing during the 20th century results in a spurious time mean negative forcing and a spurious persistent ocean cooling related to the control climate (Gregory, 2010 <sup>[[#fn:r173|173]]</sup> ; Gregory et al., 2013 <sup>[[#fn:r174|174]]</sup> ) . Since AR5, the magnitude of this effect has been estimated from historical simulations forced by only natural radiative forcing. Then it has been used to correct the historical simulations forced with the full 20th century forcing (Slangen et al., 2016 <sup>[[#fn:r187|187]]</sup> ; Slangen et al., 2017b <sup>[[#fn:r188|188]]</sup> ) . The resulting ensemble mean of simulated thermal expansion provides a good fit to the observations within the uncertainty ranges of both models and observations (Slangen et al., 2017b <sup>[[#fn:r189|189]]</sup> ; Cheng et al., 2019 <sup>[[#fn:r190|190]]</sup> ; Table 4.1) . The spread, which is essentially due to uncertainty in radiative forcing and uncertainty in the modelled climate sensitivity and ocean heat uptake efficiency (Melet and Meyssignac, 2015 <sup>[[#fn:r191|191]]</sup> ) , is still larger than the observational uncertainties (Gleckler et al., 2016 <sup>[[#fn:r192|192]]</sup> ; Cheng et al., 2017 <sup>[[#fn:r193|193]]</sup> ; Table 4.1) . Compared to AR5, the availability of improved observed and modelled estimates of thermal expansion and the good agreement between both confirm the ''high confidence'' level in the simulated thermal expansion using climate models and the ''high confidence'' level in their ability to project future thermal expansion.

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'''Table 4.1'''
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Global mean sea level (GMSL) budget over different periods from observations and from climate model base contributions. All values are in mm yr–1. Values in brackets in 4.2 are uncertainties ranging from 5–95%. The climate model historical simulations end in 2005; projections for Representative Concentration Pathway (RCP)8.5 are used for 2006–2015. The modelled thermal expansion, glacier and ice sheet surface mass balance (SMB) contributions are computed from the Coupled Model Intercomparison Project Phase 5 (CMIP5) models as in Slangen et al. (2017b). For the model contributions, uncertainties are estimated from the spread of the ensemble of model simulations following Slangen et al. (2017b), see the footnotes for the details on the uncertainty propagation. GIS is Greenland Ice Sheet.
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Notes:

# (a)  The number is built from WCRP Global Sea Level Budget Group (2018) estimate of the 0–700 m depth thermal expansion, assuming no trend below 2000 m depth before 1992 and the mean value from Purkey and Johnson (2010), and Desbruyères et al. (2017) afterwards.
# (b)  The number is calculated as the mean between the estimate from a reconstruction of glacier mass balance based on glacier length (update of Leclercq et al. (2011)) and the estimate from a mass balance model forced with atmospheric observations (Marzeion et al., 2015). The uncertainty is assumed to be a gaussian with a standard deviation of half the difference between the two estimates.
# (c)  The number is calculated as the sum of the Greenland Ice Sheet (GIS) contribution from Kjeldsen et al. (2015) and the peripheral glaciers’ contribution. The peripheral glaciers’ contribution and the associated uncertainty are computed from a mass balance model forced with atmospheric observations (Marzeion et al., 2015). The total uncertainty is computed assuming that both uncertainties from the GIS contribution and from the peripheral glaciers’ contribution are independent.
# (d)  Numbers from Bamber et al. (2018). See Section 3.3.1 for more details.
# (e)  These numbers are the weighted average of the numbers from Bamber et al. (2018) and from The Imbie team (2018). The weights in the average are based on the uncertainty associated to each estimate. See Section 3.3.1 for more details.
# (f)  Only direct anthropogenic contribution, from Wada et al. (2016).
# (g)  Land water storage estimated from Gravity Recovery and Climate Experiment (GRACE) excluding glaciers, from WCRP Global Sea Level Budget Group (2018).
# (h)  Direct estimate of ocean mass from GRACE from WCRP Global Sea Level Budget Group (2018).
# (i)  Sum of the thermal expansion and the contributions from glaciers, GIS, Antarctica Ice Sheet (AIS) and land water storage. Uncertainties in the different contributions are assumed as independent.
# (j)  Sea level reconstructions that end before 2015 have been extended to 2015 with the satellite altimetry record from Legeais et al. (2018). The uncertainty is derived from the uncertainty of individual sea level reconstructions over the longest period available that start in 1970. The uncertainty from different sea level reconstructions are assumed as independent.
# (k)  The mean estimate is from the satellite altimetry estimate in WCRP Global Sea Level Budget Group (2018) corrected for GIA and for the elastic response of the ocean crust to present day mass redistribution (Frederikse et al., 2017; Lickley et al., 2018). The uncertainty is computed using the updated error budget of Ablain et al. (2015).
# (l)  Land water storage is estimated from Wada et al. (2016) and ice discharge is deduced from Shepherd et al. (2012). The ice discharge contribution is assumed to be zero before 1992. The uncertainties in the different contributions from coupled climate models are assumed independent.
# (m)  The uncertainties in the observed GMSL and the coupled climate models’ estimate of GMSL are assumed independent for the computation of the uncertainties in the residuals.
# (n)  Numbers taken from Appendix 2.A.
# (o)  Numbers taken from Zemp et al. (2019), see Sections 2.2.3 and 3.3.2 for more details.
# (p)  The Number is calculated as the mean of the estimates of Zemp et al. (2019) and Bamber et al. (2018). The uncertainties of the two estimates are assumed to be independent of each other to obtain the uncertainty estimate of the mean.

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