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  • View in gallery

    Time series of radiative forcing due to the change of atmospheric CO2 and climate response. (a) Evolution of radiative forcing due to the atmospheric CO2 change in the simulations (W m−2), (b) evolution of the global mean surface air temperature anomaly (°C), (c) evolution of the global mean thermosteric sea level anomaly (m), and (d) evolution of the time integral of the radiative forcing (W m−2 yr−1). The anomalies are between the simulation and the control.

  • View in gallery

    Sea level change (m) as a function of the global mean ocean temperature change (°C). Slope = 0.66 m °C−1, for the 4×CO2, 2%CO2, and 1%CO2 simulations. The dashed lines indicate the results for the corresponding 0.5×CO2 simulations described in Fig. 1.

  • View in gallery

    Time series of the climate response to the same radiative forcing change as in Fig. 1 with the two-layer model. (a) Evolution of the upper ocean layer temperature anomaly (°C), (b) evolution of the lower ocean layer temperature anomaly (°C), and (c) lower ocean layer temperature change (°C) as a function of the integral of the radiative forcing during the phase with high CO2 (solid lines) and continuing under 0.5×CO2 (dashed lines).

  • View in gallery

    (a),(b) Atmospheric CO2 (ppm), (c),(d) global mean surface air temperature (°C) and (e),(f) global mean oceanic temperature (°C) evolution in additional simulations in which CO2 is either (left) raised to 4×CO2 and held constant for 140 yr or (right) ramped up at 1% yr−1 for 140 yr, and in either case lowered to 0.5×CO2 at different times between 10 and 140 yr and then held constant.

  • View in gallery

    Relations between (a) the time for the global mean ocean temperature change To to return to its initial value under 0.5×CO2 and To at the time when CO2 is lowered to 0.5×CO2, (b) the time for To to return to its initial value under 0.5×CO2 and the time integral of the radiative forcing during the phases with high CO2 (F-up), and (c) the integral of the radiative forcing during the phases with high CO2 (F-up) and during the phase with the low CO2 (F-down) up to the time at which To returns to 0°C. Each symbol is the result of one of the simulations in Fig. 3. The dotted line indicates where the symbols would align if the warming and cooling were symmetrical. The solid line is the linear fit with a slope of −0.58. (d) Results from the simulations of Fig. 1 for global mean ocean temperature change (°C) as a function of the integral of the radiative forcing during the phase with high CO2 and stabilization (solid lines) and continuing under 0.5×CO2 (dashed lines).

  • View in gallery

    Results for the climate response of the AOGCM and the step model in response to 1%CO2 for 140 yr, then 0.5×CO2. (top) Time series of (a) global mean surface air temperature and (b) global mean oceanic temperature. (c)–(f) zonal mean ocean temperature at (left) t = 140 yr and (right) t = 224 yr (when the mean oceanic temperature change is back to 0°C), for (c),(d) the AOGCM and (e),(f) the step model.

  • View in gallery

    Global mean ocean temperature change (°C) as a function of the integral of the radiative forcing during the phase with high CO2 (1%CO2, solid lines) and continuing under 0.5×CO2 (dashed lines).

  • View in gallery

    Zonal-mean ocean temperature anomaly (°C) as a function of depth after 70 yr of simulation, (a) under 4×CO2 (warming) and (b) under 0.25×CO2 (cooling). Both simulations start from the same initial state. The anomaly is with respect to the control simulation.

  • View in gallery

    Thermosteric sea level change (m) when the global mean ocean temperature is back to its initial value at t = 224 yr. The scenario followed is 1%CO2 for 140 yr, then 0.5×CO2.

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The Reversibility of Sea Level Rise

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  • 1 NCAS-Climate, University of Reading, Reading, United Kingdom
  • | 2 NCAS-Climate, University of Reading, Reading, and Met Office Hadley Center, Exeter, United Kingdom
  • | 3 Met Office Hadley Center, Exeter, United Kingdom
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Abstract

During the last century, global climate has been warming, and projections indicate that such a warming is likely to continue over coming decades. Most of the extra heat is stored in the ocean, resulting in thermal expansion of seawater and global mean sea level rise. Previous studies have shown that after CO2 emissions cease or CO2 concentration is stabilized, global mean surface air temperature stabilizes or decreases slowly, but sea level continues to rise. Using idealized CO2 scenario simulations with a hierarchy of models including an AOGCM and a step-response model, the authors show how the evolution of thermal expansion can be interpreted in terms of the climate energy balance and the vertical profile of ocean warming. Whereas surface temperature depends on cumulative CO2 emissions, sea level rise due to thermal expansion depends on the time profile of emissions. Sea level rise is smaller for later emissions, implying that targets to limit sea level rise would need to refer to the rate of emissions, not only to the time integral. Thermal expansion is in principle reversible, but to halt or reverse it quickly requires the radiative forcing to be reduced substantially, which is possible on centennial time scales only by geoengineering. If it could be done, the results indicate that heat would leave the ocean more readily than it entered, but even if thermal expansion were returned to zero, the geographical pattern of sea level would be altered. Therefore, despite any aggressive CO2 mitigation, regional sea level change is inevitable.

Corresponding author address: Nathaelle Bouttes, NCAS-Climate, Meteorology Department, University of Reading, Reading, RG66BB, United Kingdom. E-mail: n.bouttes@reading.ac.uk

Abstract

During the last century, global climate has been warming, and projections indicate that such a warming is likely to continue over coming decades. Most of the extra heat is stored in the ocean, resulting in thermal expansion of seawater and global mean sea level rise. Previous studies have shown that after CO2 emissions cease or CO2 concentration is stabilized, global mean surface air temperature stabilizes or decreases slowly, but sea level continues to rise. Using idealized CO2 scenario simulations with a hierarchy of models including an AOGCM and a step-response model, the authors show how the evolution of thermal expansion can be interpreted in terms of the climate energy balance and the vertical profile of ocean warming. Whereas surface temperature depends on cumulative CO2 emissions, sea level rise due to thermal expansion depends on the time profile of emissions. Sea level rise is smaller for later emissions, implying that targets to limit sea level rise would need to refer to the rate of emissions, not only to the time integral. Thermal expansion is in principle reversible, but to halt or reverse it quickly requires the radiative forcing to be reduced substantially, which is possible on centennial time scales only by geoengineering. If it could be done, the results indicate that heat would leave the ocean more readily than it entered, but even if thermal expansion were returned to zero, the geographical pattern of sea level would be altered. Therefore, despite any aggressive CO2 mitigation, regional sea level change is inevitable.

Corresponding author address: Nathaelle Bouttes, NCAS-Climate, Meteorology Department, University of Reading, Reading, RG66BB, United Kingdom. E-mail: n.bouttes@reading.ac.uk

1. Introduction

Model-based studies have explored the evolution of climate in scenarios where atmospheric CO2 concentrations rise at various rates, following which CO2 is stabilized or the emissions are stopped (Meehl et al. 2005; Plattner et al. 2008; Solomon et al. 2009; Frölicher and Joos 2010; Gillett et al. 2011). In the latter case, global mean surface air temperature subsequently stays approximately constant or declines slowly as CO2 is removed from the atmosphere by natural processes. In some scenarios, including the later part of the policy-relevant Representative Concentration Pathway 2.6 (RCP2.6; Moss et al. 2010), which will be assessed in the next report of the Intergovernmental Panel on Climate Change (IPCC), CO2 is assumed to be artificially removed from the atmosphere at greater rates than natural uptake, producing a faster reduction in forcing and a faster cooling. However, sea level from thermal expansion continues to rise for many centuries following a stabilization of CO2 concentration in the atmosphere or a cessation of CO2 emissions (Meehl et al. 2005; Lowe et al. 2006; Plattner et al. 2008; Solomon et al. 2009; Frölicher and Joos 2010; Gillett et al. 2011). This raises the question of what it would take to reverse sea level rise.

In this work, we use a 3D atmosphere–ocean general circulation model (AOGCM) to explore how the emissions pathway affects the peak sea level and the subsequent decline. For simplicity, we consider CO2-only scenarios, since CO2 is the dominant forcing. We consider only the global mean thermosteric sea level, and not the additional component from glaciers and the ice sheets of Greenland and Antarctica (Charbit et al. 2008; Ridley et al. 2009; Vizcaíno et al. 2010; Huybrechts et al. 2011). The thermosteric term is influenced by ocean interior transport processes, including large-scale oceanic circulations such as the Atlantic meridional overturning circulation (AMOC). In the deep ocean, temperature changes caused by these processes occur on a hundred- to thousand-year time scale. Although this is slow, the thermosteric sea level change may be reversed more quickly than ice sheet mass loss, which would require a longer time scale of thousands of years (Charbit et al. 2008; Ridley et al. 2009). Likewise, reversing the sea level change induced by glaciers and ice caps would be a slower process. Thermosteric sea level change is subject to less (though still substantial) scientific uncertainty than ice sheets and glaciers, and is sufficient alone to cause significant sea level rise impacts for many centuries into the future.

2. Method

We run simulations with the Fast Met Office/UK Universities Simulator (FAMOUS) AOGCM (Smith et al. 2008). FAMOUS is a low-resolution version of the third climate configuration of the Met Office Unified Model (HadCM3) AOGCM (Gordon et al. 2000): its atmosphere component runs on a 5° latitude by 7.5° longitude grid with 11 levels and its ocean component on a 2.5° latitude by 3.75° longitude grid with 20 levels. It is structurally almost identical to HadCM3 and produces climate and climate-change simulations that are reasonably similar to HadCM3, but runs about 20 times faster and is hence particularly useful for investigations involving many long integrations. Despite the coarse resolution, the present-day climatology of FAMOUS is adequate without flux correction.

The simulations employ idealized scenarios in which atmospheric CO2 is first increased and then either held constant or abruptly decreased. The increase follows three pathways (Fig. 1a): an instantaneous increase of CO2 to 4 times the preindustrial value (4×CO2; the preindustrial value is 280 ppm), a 1% increase of CO2 yr−1 (1%CO2) for 140 yr, and a 2% increase of CO2 yr−1 (2%CO2) for 70 yr. Both the 1%CO2 and 2%CO2 ramps end at 4 times the preindustrial value. Thus, at t = 140 yr the CO2 concentration is the same in all scenarios, but the three pathways that have led to that level differ. Beyond t = 140 yr the CO2 concentration is either kept constant at this value or instantaneously reduced, to either the preindustrial value (1×CO2) or half of it (0.5×CO2), and then held constant at the reduced value; in section 4c we also consider a scenario in which CO2 is ramped down. We consider these idealized scenarios because they give a clear demonstration of the qualitative behavior of sea level. In particular, this is the reason for choosing the 0.5×CO2 concentration (140 ppm), which is of course unrealistic for natural carbon sinks, being lower than the concentration at glacial maxima such as during the Last Glacial Maximum (atmospheric CO2 concentration of around 190 ppm approximately 21 000 yr ago).

Fig. 1.
Fig. 1.

Time series of radiative forcing due to the change of atmospheric CO2 and climate response. (a) Evolution of radiative forcing due to the atmospheric CO2 change in the simulations (W m−2), (b) evolution of the global mean surface air temperature anomaly (°C), (c) evolution of the global mean thermosteric sea level anomaly (m), and (d) evolution of the time integral of the radiative forcing (W m−2 yr−1). The anomalies are between the simulation and the control.

Citation: Journal of Climate 26, 8; 10.1175/JCLI-D-12-00285.1

As the CO2 concentrations scenarios are idealized, they are not evaluated in terms of feasibility or corresponding emissions. For the latter, a coupled carbon–climate model would be needed, which would include the fact that if emissions are cut to zero, the biosphere and ocean would progressively take up less carbon as they saturate. This would suggest that to achieve the assumed rates of CO2 reduction, actively removing CO2 from the atmosphere by artificial means may be needed, since the CO2 would otherwise stay in the atmosphere for a long time (several thousand years; Eby et al. 2009). The reduction of forcing does not necessary requires CO2 reduction and could possibly be obtained by other suggested geoengineering mechanisms (Shepherd et al. 2009), but the feasibility of this is not further discussed here.

We calculate sea level rise due to thermal expansion from ocean temperature change diagnosed from the model. As found previously (Russell et al. 2000), global mean thermosteric sea level rise η and global mean ocean temperature rise To (equivalent to the increase in ocean heat content) are in a nearly linear relationship (Fig. 2) and so we speak of them interchangeably. In the following sections, we interpret the qualitative features of results of the AOGCM for surface air temperature and sea level change using a range of simpler models (summarized in Table 1).

Fig. 2.
Fig. 2.

Sea level change (m) as a function of the global mean ocean temperature change (°C). Slope = 0.66 m °C−1, for the 4×CO2, 2%CO2, and 1%CO2 simulations. The dashed lines indicate the results for the corresponding 0.5×CO2 simulations described in Fig. 1.

Citation: Journal of Climate 26, 8; 10.1175/JCLI-D-12-00285.1

Table 1.

Summary of the main results from the models.

Table 1.

3. Surface air temperature change

During the first part of the simulations (the “high-CO2 phase”), while the atmospheric CO2 concentration is increasing, the change of global mean surface air temperature Ts tracks the CO2 concentration (Figs. 1a,b). In the case where the CO2 concentration is instantaneously increased, Ts takes a couple of decades to respond. After 140 yr, Ts is the same in the three simulations. It has similarly been shown that, under scenarios in which emissions peak and decline, the peak warming attained depends only on the cumulative CO2 emission and is largely insensitive to the emissions pathway up to the time of maximum temperature (Allen et al. 2009a; Matthews et al. 2009; Zickfeld et al. 2009; Bowerman et al. 2011).

The second part of the simulations (the “low-CO2 phase”) begins at year 141, when the CO2 concentration is either stabilized or lowered. After CO2 stabilizes, the rate of surface air temperature increase is greatly reduced (Fig. 1b). If the radiative forcing abruptly returns to zero, Ts falls most of the way to zero within around two decades. If CO2 is set to a value smaller than the initial one, the radiative forcing becomes negative, and Ts falls below its initial value. It is apparent that Ts depends roughly linearly on the forcing (Figs. 1a and 1b are similar in form), as can be understood from simple “zero-layer” heat balance equations for time-dependent climate change (Gregory and Mitchell 1997; Raper et al. 2002; Gregory and Forster 2008; Held et al. 2010; see Table 1):
e1
where α is the climate feedback parameter, κ is the ocean heat uptake efficiency, and the radiative forcing F depends roughly linearly (actually logarithmically) on the atmospheric CO2 concentration C. In this zero-layer model, there is no feedback of ocean temperature on the rate of heat uptake and the ocean is effectively infinitely deep (i.e., it can absorb heat indefinitely).

C is equivalent to the increase in the CO2 burden of the atmosphere (1 GtC ≡ 0.47 ppm). Hence C is determined uniquely at each time by the cumulative CO2 emissions E through the relationship C = AE, provided the airborne fraction A is constant. Observations indicate that A has been approximately constant during recent decades (Knorr 2009), but it could change in the future (Friedlingstein et al. 2006). How much it might change appears to depend on both the emissions scenario (Gloor et al. 2010) and the behavior of the carbon cycle (Friedlingstein et al. 2006), which is uncertain. For the shapes of scenario considered here, and assuming that a linear model provides a reasonable first-order representation of the carbon cycle (Joos et al. 1996), then we would expect a constant value of A to also be an acceptable approximation. If so, Ts will track E (Matthews et al. 2009; Gregory et al. 2009).

4. Sea level change

a. Dependence of sea level rise on the pathway of emissions

Sea level behaves qualitatively differently from Ts. The evolution of sea level rise due to thermal expansion depends on the pathway of emissions (Stouffer and Manabe 1999; Zickfeld et al. 2012) and reaches different values at 140 years despite the CO2 concentration and Ts being the same at that time (Fig. 1c). Comparing Figs. 1c and 1d, we see that sea level rise depends almost linearly on the integral of the radiative forcing while the forcing is positive (high-CO2 phase). This is consistent with the zero-layer model, in which the rate of ocean heat uptake N is proportional to Ts,
e2
and hence the rate of sea level depends on F. However, the actual sea level rise is given by
e3
provided κ and α are constant (Gregory and Forster 2008).

Thus, because the thermosteric sea level is proportional to the time integral of the radiative forcing, the longer the forcing lasts, the bigger the change in thermosteric sea level rise (and oceanic temperature). The sea level change is the largest in the simulation where the largest fractional increase in the atmospheric burden of CO2 occurs the earliest, which implies where CO2 has been emitted the earliest. Because of a focus on impacts related to peak warming, it has been proposed that policy targets for avoiding dangerous climate change might be set in terms of cumulative CO2 emission (Allen et al. 2009b). However, if we are concerned with mitigating sea level impacts, targets must be set on the rate of emission as well.

b. Long-term commitment to sea level rise

If CO2 is stabilized, ocean temperature and sea level continue to rise (Fig. 1c), in contrast to Ts (Fig. 1b). After the CO2 concentration is stabilized, because Ts is approximately the same in the three stabilization simulations (Fig. 1b; ~5.5°C), the rate of thermosteric sea level rise is nearly the same in all three. That is, the three solid lines in Fig. 1c are nearly parallel; the rate is ~4 mm yr−1, much higher than the recent rate of 0.9 mm yr−1 for 1993–2008 (Church et al. 2011). Thus the zero-layer model still explains the evolution of both temperature and sea level in the AOGCM for at least a century after stabilization of the CO2 concentration.

c. Reversibility of sea level rise

The experiments with stabilized CO2 may give an impression that sea level rise is irreversible, but if CO2 is returned instantaneously to its initial value, sea level immediately falls, albeit at a slow and decreasing rate so that after 160 years it has fallen only half the way to its initial level. Any practical measures to remove CO2 from the atmosphere would produce a gradual rather than an instantaneous decrease; if CO2 is ramped down, the oceanic temperature initially continues to rise, then gradually stabilizes, and then begins to fall. This is illustrated by a simulation in which CO2 increases at 1% yr−1 for 140 yr and then decreases at 1% yr−1 for the next 140 yr (cyan lines in Fig. 1). In this experiment the time-integral forcing is the same as in the scenario of 4×CO2 followed by 1×CO2 (dotted red lines); the later reduction in CO2 means that sea level is higher following the ramp-down. If the radiative forcing becomes negative (dashed lines), sea level falls back more rapidly to its initial value. Thus, sea level rise is in principle reversible, provided that the radiative forcing is reduced sufficiently. A long-term multicentury commitment to rising thermal expansion is not physically inevitable, although it may be practically so.

However, the zero-layer model fails to explain the sea level reversibility in the AOGCM. Since the sea level rise is proportional to the integral of the forcing F, it predicts that sea level will remain constant if the forcing is returned to zero, and will fall only if a negative forcing is applied. The zero-layer model assumes heat loss into an infinite heat sink that does not warm up and therefore does not give back heat spontaneously. It cannot account for sea level falling under zero forcing because it neglects changes happening below the ocean surface layer. In reality, the ocean is finite and more than one time scale is relevant. The rapid time scale of one or two decades relates to the ocean surface layer and accounts for most of the response of surface air temperature to the radiative forcing following abrupt change in CO2. The time scale of the “recalcitrant” response (Held et al. 2010) is another time scale that applies to the evolution of sea level.

This can be illustrated with a two-layer model (Gregory 2000; Held et al. 2010; Table 1). The two-layer model is composed of an ocean with an upper layer of thickness du (100 m) and temperature Tu, and a deep layer of thickness dl (2000 m) and temperature Tl, where both temperature are perturbations from an equilibrium with zero surface heat flux. The upper layer has little heat capacity and plays the role of a regulator; it absorbs the forcing, determines the radiation of heat to space, and is thermally coupled to the lower layer, which has large heat capacity and provides inertia. The heat flux between the two is proportional to their temperature difference. The temperatures thus follow the two equations
eq1
eq2
with being the volumetric heat capacity, the surface heat flux, the thermal diffusivity, and the climate feedback parameter.

When the radiative forcing F changes abruptly, Tu rapidly reaches a new near-equilibrium (Fig. 3a), in which F is nearly balanced by transfer of heat to or from the lower layer. If F reverts to zero, the upper layer rapidly becomes cooler than the lower layer, which therefore loses heat (Fig. 3b, dotted lines). If a negative forcing is applied, the upper layer gets still colder, the temperature difference between the two layers is greater, the transfer of heat from the lower to the upper ocean is faster, and the lower layer cools down more rapidly (Fig. 3b, dashed lines). Unlike the zero-layer model, the two-layer model reproduces remarkably well these features of the evolution of surface temperature and thermosteric sea level in the much more complex AOGCM (Figs. 3a and 3b are qualitatively very similar to Figs. 1b and 1c). The two-layer model thus accounts for the reversibility of sea level rise when the radiative forcing diminishes because it has a finite ocean and the model is able to distinguish surface temperature from heat content so that it can lose heat spontaneously.

Fig. 3.
Fig. 3.

Time series of the climate response to the same radiative forcing change as in Fig. 1 with the two-layer model. (a) Evolution of the upper ocean layer temperature anomaly (°C), (b) evolution of the lower ocean layer temperature anomaly (°C), and (c) lower ocean layer temperature change (°C) as a function of the integral of the radiative forcing during the phase with high CO2 (solid lines) and continuing under 0.5×CO2 (dashed lines).

Citation: Journal of Climate 26, 8; 10.1175/JCLI-D-12-00285.1

d. Asymmetry of sea level evolution

In the zero-layer model, the ocean temperature and sea level change should be back to zero when the integral of F returns to zero (i.e., after a negative forcing of the same time integral as the one during the high-CO2 phase). For example, for the 1×CO2 scenario followed by 0.5×CO2, this is at 280 yr, but actually the sea level in the AOGCM reaches zero sooner, at 224 yr.

To quantify better the link between the ocean temperature change and the radiative forcing, we have run additional AOGCM simulations (Fig. 4), beginning with a high-CO2 phase of either constant 4×CO2 or a 1%CO2 ramp-up. In these simulations, CO2 is reduced abruptly to 0.5×CO2 after various times between 10 and 100 yr (instead of 140 yr as in the scenario of Fig. 1).

Fig. 4.
Fig. 4.

(a),(b) Atmospheric CO2 (ppm), (c),(d) global mean surface air temperature (°C) and (e),(f) global mean oceanic temperature (°C) evolution in additional simulations in which CO2 is either (left) raised to 4×CO2 and held constant for 140 yr or (right) ramped up at 1% yr−1 for 140 yr, and in either case lowered to 0.5×CO2 at different times between 10 and 140 yr and then held constant.

Citation: Journal of Climate 26, 8; 10.1175/JCLI-D-12-00285.1

During the low-CO2 phase, the time for the oceanic temperature to cool down to its initial value depends linearly on the oceanic warming achieved during the high-CO2 phase (Fig. 5a), and hence on the integral of the forcing during that phase (Fig. 5b). However, it takes less negative integral radiative forcing F (or less time with a symmetrical forcing evolution) for the oceanic temperature to go back to its initial value (Fig. 5c) . Thus, the relationship between the oceanic temperature change and the integral of the forcing is different during the high-CO2 and low-CO2 phases (Fig. 5d). The amount of negative radiative forcing needed for the sea level to go back to its initial value is linearly related to the amount of positive radiative forcing:
eq3
The numerical factor depends on the scenario and model.
Fig. 5.
Fig. 5.

Relations between (a) the time for the global mean ocean temperature change To to return to its initial value under 0.5×CO2 and To at the time when CO2 is lowered to 0.5×CO2, (b) the time for To to return to its initial value under 0.5×CO2 and the time integral of the radiative forcing during the phases with high CO2 (F-up), and (c) the integral of the radiative forcing during the phases with high CO2 (F-up) and during the phase with the low CO2 (F-down) up to the time at which To returns to 0°C. Each symbol is the result of one of the simulations in Fig. 3. The dotted line indicates where the symbols would align if the warming and cooling were symmetrical. The solid line is the linear fit with a slope of −0.58. (d) Results from the simulations of Fig. 1 for global mean ocean temperature change (°C) as a function of the integral of the radiative forcing during the phase with high CO2 and stabilization (solid lines) and continuing under 0.5×CO2 (dashed lines).

Citation: Journal of Climate 26, 8; 10.1175/JCLI-D-12-00285.1

Although it exhibits reversibility, the two-layer model cannot explain why the ocean cools down more effectively than it warms up. In the two-layer model, the relationship between ocean temperature and is the same in the high-CO2 and low-CO2 phases (Fig. 3c), unlike in the AOGCM (Fig. 5d). The lower layer is a very large well-mixed heat capacity that sets the long time scale for approach to a steady state. Consequently, the lower layer warms much less than the upper layer in the high phase (at 140 yr in the 1% scenario, Tu = 4.4°C in Fig. 3a and Tl = 0.4°C in Fig. 3b). Because Tu closely tracks F, and , the heat flux between the layers has roughly the same time profile as F, and . Because the single lower layer has too much heat capacity and does not warm up very much, the heat flux depends almost entirely on the upper temperature and hence on the integral of the radiative forcing. More layers would be needed to explain the faster loss of heat during the low-CO2 phase.

To account for the asymmetry, we apply the step-response model of Good et al. (Good et al. 2011; Table 1). In this model, the evolution of any climate variable X(t) is estimated by regarding it as the linear superposition of the responses to a succession of small instantaneous step-forcing changes in forcing, such that . We carry out a single AOGCM experiment in which CO2 is quadrupled at t = 0, giving forcing F(4×CO2), and then held constant. If X = X4(t) in this experiment, we estimate that —that is, a convolution of the response to the 4×CO2 step with the forcing time series. Good et al. (2011) show that this method is accurate for surface temperature and has skill at reproducing ocean heat uptake. We use the step model to study the experiment with 1%CO2 followed by 0.5×CO2 as an example.

The step model successfully reproduces the evolution of the surface air temperature Ts and ocean temperature To during the high-CO2 phase (Figs. 6a,b). (Note that Ts from the step model lacks the variability of the AOGCM because the convolution tends to smooth it out.) The step model estimate of the ocean temperature change latitude–depth distribution is also very good (cf. Figs. 6c,e), showing the warming spreading downward from the surface, with deeper penetration at high latitudes.

Fig. 6.
Fig. 6.

Results for the climate response of the AOGCM and the step model in response to 1%CO2 for 140 yr, then 0.5×CO2. (top) Time series of (a) global mean surface air temperature and (b) global mean oceanic temperature. (c)–(f) zonal mean ocean temperature at (left) t = 140 yr and (right) t = 224 yr (when the mean oceanic temperature change is back to 0°C), for (c),(d) the AOGCM and (e),(f) the step model.

Citation: Journal of Climate 26, 8; 10.1175/JCLI-D-12-00285.1

The step model gives a better approximation of the evolution during the low-CO2 phase than the zero- and two-layer models (Table 1). In particular, it correctly predicts that To returns to its initial value before year 280; it is qualitatively superior to the two-layer model in partly reproducing the asymmetry between the warming and cooling phases (Fig. 7). This is because the step model, like the AOGCM, has many layers and time scales. Unlike in the two-layer model, the ocean below the surface is not well mixed. The shallower layers have relatively small heat capacity and warm substantially during the high-CO2 phase, and as time passes the warming spreads to deeper layers. During the low-CO2 phase, the shallow layers likewise cool rapidly. In the AOGCM, this causes a large temperature contrast between the newly cooled surface and previously warmed subsurface layers, which forces heat out of the ocean more rapidly than it entered. In the step model, the large temperature contrast and rapid heat loss are predicted as a consequence of the large negative step in forcing from 4×CO2 to 0.5×CO2. In both models, as a consequence of the high-CO2 phase, additional heat is still being transported to deeper layers during the low-CO2 phase at the same time as the cooling penetrates into the surface. In the global mean, similar qualitative behavior would be obtained from a vertical diffusion model of ocean temperature (e.g., Marčelja 2010). The advantages of the step model are that it can be applied in 3D, and that it emulates the AOGCM without any tuning of parameters being required.

Fig. 7.
Fig. 7.

Global mean ocean temperature change (°C) as a function of the integral of the radiative forcing during the phase with high CO2 (1%CO2, solid lines) and continuing under 0.5×CO2 (dashed lines).

Citation: Journal of Climate 26, 8; 10.1175/JCLI-D-12-00285.1

However, the step model shows some inaccuracies. In particular, Ts falls too quickly at the start (Fig. 6a), and after about 30 years the step model underestimates the oceanic cooling progressively more seriously (Fig. 6b). These phenomena can be linked: both are related to an insufficient heat flux from lower layers toward the surface. Correspondingly, the cooling anomaly does not penetrate as deeply at high latitudes in the step model as in the AOGCM simulation, while in middle and low latitudes the thermocline does not cool as quickly (cf. Figs. 6d and 6f). The asymmetry between high-CO2 and low-CO2 phases is thus not as pronounced as in the AOGCM (Fig. 7).

We infer that these remaining discrepancies arise from nonlinear behavior of the AOGCM that the step model does not capture. In particular, the responses of the AOGCM to positive and negative step changes in forcing of equal magnitude are not equal and opposite (Fig. 8). This asymmetry cannot be captured by the step model, which is constructed by using the response to a positive step only, and presumably arises from the dependence of vertical heat transport on stability in the AOGCM (Stouffer and Manabe 1999). In particular, for the same absolute value of radiative forcing, the warming penetrates relatively deeper in the Arctic whereas the cooling goes deeper in the Southern Ocean (Fig. 8). This different penetration of the heat anomaly during warming and cooling simulations has previously been described by Manabe et al. (1991), with similar results in the Southern Ocean but slightly different penetration of heat in the North Atlantic. After a sequence of warming (1%CO2 experiment) followed by a cooling (0.5×CO2 experiment), this different penetration of the heat anomaly results in a warmer Arctic and cooler Southern Ocean (except in the surface) in the AOGCM than in the step model at the time (224 years) when To in the AOGCM is back to its initial value.

Fig. 8.
Fig. 8.

Zonal-mean ocean temperature anomaly (°C) as a function of depth after 70 yr of simulation, (a) under 4×CO2 (warming) and (b) under 0.25×CO2 (cooling). Both simulations start from the same initial state. The anomaly is with respect to the control simulation.

Citation: Journal of Climate 26, 8; 10.1175/JCLI-D-12-00285.1

e. Regional sea level changes

Impacts of sea level change arise from its regional distribution. As shown in Fig. 6, even when the global mean ocean temperature is back to its initial value, heat in the ocean is distributed differently, with some areas warmer and others colder. This means that there is a still a regional pattern of thermosteric sea level change when To returns to 0°C (Fig. 9). Although the global mean η is 0 m, sea level is higher than in the initial state in the Arctic and Atlantic south of 45°N, and lower in the North Atlantic and southern Indian Ocean. This distribution is likely to be model dependent as the regional sea level change changes from model to model (Pardaens et al. 2011), but the same qualitative point would hold. Thus, even if it were practical to eliminate the commitment to global thermosteric sea level change by negative radiative forcing, the commitment to regional sea level change would be yet more recalcitrant.

Fig. 9.
Fig. 9.

Thermosteric sea level change (m) when the global mean ocean temperature is back to its initial value at t = 224 yr. The scenario followed is 1%CO2 for 140 yr, then 0.5×CO2.

Citation: Journal of Climate 26, 8; 10.1175/JCLI-D-12-00285.1

5. Conclusions

We have studied the future evolution of global mean sea level rise due to thermal expansion (i.e., not including contributions from ice sheets and glaciers) with an AOGCM under idealized CO2 scenarios. Unlike surface temperature change, sea level change depends not only on the cumulative emission of CO2 but also on the emission pathway. A greater rise in sea level results from earlier emissions than from later, for the same cumulative emission. Hence, targets to limit sea level rise would need to refer to rates of emissions as well as the total.

Thermal expansion will continue for many centuries if CO2 emissions cease or if CO2 concentration is stabilized. However, it is in principle reversible. Reducing the radiative forcing sufficiently would halt or reverse it, and a negative forcing would reverse it more quickly. Of course, reducing the forcing would require removal of CO2 from the atmosphere or other geoengineering, which is not yet technologically feasible and might have side effects, while a large negative forcing would produce a climate colder than the preindustrial. Even if sea level returned to its preindustrial global mean, the geographical pattern would be different from the initial one because the penetration of heat is different during warming and cooling.

We have interpreted the behavior of thermal expansion in the AOGCM by comparison with a range of simpler models. The important qualitative difference between surface temperature and sea level is that the former depends on the prevailing radiative forcing and hence the cumulative CO2 emission, while the latter depends on the time integral of radiative forcing and hence the time profile of CO2 emission. The reversibility of thermal expansion cannot be explained without this distinction, which arises because surface temperature relates to the temperature of the upper ocean only, and thermal expansion to the full depth of the ocean. The AOGCM shows that sea level rise and fall are not symmetrical with respect to forcing. When the radiative forcing is reduced, heat leaves the ocean more readily than it entered. This is partly due to the vertical profile of the ocean temperature change, which retains a memory of the time profile of radiative forcing, and partly due to the dependence of vertical heat transport processes on temperature gradients. The success of the step-response model in largely reproducing the AOGCM results indicates that this method could be a useful way to continue investigations into AOGCM ocean heat uptake in a scenario-independent way although consideration of the nonlinear behavior may be necessary.

Acknowledgments

We thank A. Pardaens and P. Good for helpful discussion, and three anonymous reviewers for their constructive comments that helped improve the manuscript. J A. Lowe acknowledges support from the AVOID programme (DECC and Defra) under contract GA0215. The research leading to these results has received funding from the European Research Council under the European Community’s Seventh Framework Programme (FP7/2007-2013), ERC Grant Agreement 247220, project “Seachange.”

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