Complementing thermosteric sea level rise estimates

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 upperocean 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).

Abstract. 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 upperocean 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  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 (Rhein et al., 2013). As the ocean takes up heat, the thermal expansion of seawater is a major driver behind sea level rise (SLR). Church et al. (2013a) 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 α (e.g., Griffies et al., 2014) and is due to nonlinearities of the thermodynamic properties (potential temperature, , salinity, S, and pressure, p) in the equation of state of seawater density, ρ (e.g., Jackett et al., 2006). 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 (Lowe and Gregory, 2006;Piecuch and Ponte, 2014). 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 (Rose et al., 2014). 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 Church et al. (2013a). 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. Over the last century, these mass changes in the ocean (termed "barystatic" sea level changes by Gregory et al., 2013a) 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., Lowe and Gregory, 2006); on regional to basin scales, however, the role of salinity should not be neglected in sea level studies (e.g., Durack et al., 2014a). 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 (Trenberth and Fasullo, 2010). 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., Joughin et al., 2014;Rignot et al., 2014;Mengel and Levermann, 2014). 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 Church et al., 2013a). 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 (Domingues et al., 2008;Ishii and Kimoto, 2009;Levitus et al., 2012). Observed contributions to thSLR from depths below 2000 m are assumed to increase monotonically and linearly in time (Purkey and Johnson, 2010;Kouketsu et al., 2011). For details on the spatial as well as temporal coverage and quality of oceanic temperature measurements that underlie thSLR estimates we refer to Abraham et al. (2013) 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 ex-tended 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, η , 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, exp − ref , where the spatial 3-D thermal expansion coefficient, α is defined by CMIP5 publishes time series of global mean (0-D) η , called zostoga and represents the integral value of ocean's thermal expansion, α ( exp − ref ), 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 (Greatbatch, 1994). Here, we derive global mean yearly depth profiles of thermal expansion by using independent 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, α 1.5 , as a polynomial of and p: with 0 = exp , 1 = 2 0 and 2 = 3 0 /6000 and calibration parameters c n=0−5 . This polynomial algorithm is based on a simplification of the equation of state of seawater given in Gill (1982), assuming a constant salinity of 35 PSS-78. It is, for example, included in the reducedcomplexity Model for the Assessment of Greenhousegas Induced Climate Change (MAGICC) (Raper et al., 1996;Wigley et al., 2009;Meinshausen et al., 2011). 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 timedependent vertical global and hemispheric profiles of 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 α 1.5 in Eq. (3) with calibration parameters c n 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 α 0 . Divided by ocean's specific heat capacity, reference density and area, it gives the "expansion efficiency of heat" (in m YJ −1 , 1 YJ ≡ 10 24 J) and allows the comparison of thermal expansion from models with different spatial dimensions (Russell et al., 2000). This constant quantifies the proportionality between global mean thSLR and ocean heat uptake (OHU) (cf. Kuhlbrodt and Gregory, 2012).
We examine a broad range of CMIP5 scenarios, namely the historical (post-1850) climate simulations, the idealized 1 % CO 2 per year increase (1pctCO2) and the response to abrupt 4 × pre-industrial CO 2 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 see Taylor et al., 2012;Moss et al., 2010, and 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 (Forster et al., 2013). 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 (pi-Control) 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 tem-perature evolution (Palmer et al., 2009). For details about methods of climate drift correction in CMIP5 models see Taylor et al. (2012), Sen Gupta et al. (2013) and the supplementary by Church et al. (2013a). Additionally, we correct the historical time series by adding the suggested thSLR trend of 0.1 ± 0.05 mm yr −1 by Church et al. (2013b) 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 (Lorbacher et al., 2012); 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 Church et al. (2013a).

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 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 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 Church et al., 2013a). These complementing zostoga time series contribute 50 % more CMIP5 models to multi-model ensemble thSLR estimates than previously used by Church et al. (2013a); 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.
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 Church et al. (2013a) 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 Church et al., 2013a). 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.  Church et al., 2013a). 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 (Fyfe et al., 2010). For the altimetry period (1993)(1994)(1995)(1996)(1997)(1998)(1999)(2000)(2001)(2002)(2003)(2004)(2005)(2006)(2007)(2008)(2009)(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 (Roemmich and Gilson, 2009); the same is true for the derived thermal expansion coefficient (see Fig. 2 and depth profiles of potential temperatures in the piControl scenario by Kuhlbrodt and Gregory, 2012). 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 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., Griffies et al., 2014) 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 , Griffies et al., 2014). 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., Griffies et al. (2014) and Palter et al. (2014).
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 preindustrial 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. Russell et al., 2000). 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)(1987)(1988)(1989)(1990)(1991)(1992)(1993)(1994)(1995)(1996)(1997)(1998)(1999)(2000)(2001)(2002)(2003)(2004)(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 multigas 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 (Fig. 3e).

The 1.5-D parameterization
We obtain six calibration parameters c n 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 ( 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.
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 Wang et al. (2014) 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 Kuhlbrodt and Gregory (2012) 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 Kuhlbrodt and Gregory (2012) amounts to 0.11 ± 0.01 m YJ −1 . Our median and its 90 % confidence 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.
terval 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. 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  Table S5 summarizes the estimates. The horizontal solid (dashed) line indicates the mean (median) depth of thSLR based on climatological temperature and salinity profiles  down to 700 m (cf. Domingues et al., 2008). Sparse observational evidence points to non-significant contributions to global mean thSLR from depths below 2000 m during 2005 to 2013 (Llovel et al., 2014). 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 Durack et al. (2014b) 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 (Palmer et al., 2009;Palter et al., 2014). However, these find-ings highlight the importance of the thSLR contribution from deeper ocean layers (e.g., Palmer et al., 2011). 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 (Domingues et al., 2008;Ishii and Kimoto, 2009;Levitus et al., 2012). 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 (Bindoff and Hobbs, 2013;Rye et al., 2014). 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., Hallberg et al., 2013) dominate the final result.
The Supplement related to this article is available online at doi:10.5194/gmd-8-2723-2015-supplement.
Author contributions. All authors contributed to designing and writing the text. K. Lorbacher conducted the analysis and drafted the manuscript.