Schematic of three different idealized global warming scenarios. The time period is roughly 1,000 years and each scenario starts with the CO2 increase and warming from the anthropogenic pulse of emission in the 20th and 21st centuries. On the left, emissions are slowed so that CO2 is maintained at the level reached at the end of this pulse. In the center, emissions are eliminated at the end of the pulse, resulting in slow decay of CO2. On the right, CO2 levels are abruptly returned to pre-industrial levels –perfect geoengineering – a scenario useful for isolating the recalcitrant component of warming discussed in post #8.
If we stop emitting CO2 at some future time how would surface temperature evolve over the ensuing decades and centuries — ignoring all other forcing agents? This question (or closely related questions) has been looked at using a number of models of different kinds, including Allen et al, 2009, Matthews et al, 2009, Solomon et al, 2009, and Frolicher and Joos, 2010. These models agree on a simple qualitative result: global mean surface temperatures stay roughly level for as long as a millennium, at the value achieved at the time at which emissions are discontinued, as illustrated schematically in the middle panels above.
This simple result emerges from a cancellation between the climate response to CO2 perturbations and the CO2 response to emissions. If the CO2 in the atmosphere remained at the level attained at time , then the surface would continue to warm as the deep ocean equilibrated and the heat uptake by the ocean relaxed to zero. This increase from a transient response with substantial heat uptake to a response with an equilibrated deep ocean is the fixed-concentration commitment.
However, when emissions are eliminated, the CO2 in the atmosphere does not stay fixed, rather it decays slowly. This decay does not take the system back to pre-industerial CO2 levels, since full equilibration requires transfer of carbon to sediments and crustal rocks, which requires far more than a millennium. We can imagine the airborne fraction of the emitted carbon as evolving in time, from a larger value before , perhaps comparable to that observed in recent decades (about 45%), and then asymptoting, after roughly 1000 years, to a smaller non-zero value.
The papers listed above suggest that the reduction of airborne fraction from the current value to this equilibrated value more or less compensates for the additional warming that would be experienced with fixed CO2. Additionally, the time scale of the adjustment of this airborne fraction and of the relaxation of the ocean heat uptake to zero are roughly the same — they are both controlled in large part by the physical mixing of shallow oceanic waters into the deeper oceans. This similarity in the slow adjustment time scale, and the coincidence of the rough cancellation of the fixed concentration warming commitment with the reduction in airborne fraction, combine to make plausible the relatively flat surface temperature response.
One could make a long list of things that could upset this picture, dramatic changes in land surface carbon uptake/release being an excellent example. In any case, it will be interesting to see what emerges from new generations of Earth System Models when applied to this idealized scenario.
It is worth keeping in mind that sea level, for example, will respond very differently in this zero-emission scenario – the component due to thermal expansion continues to rise on these time scales, in all of these models, as the surface warming penetrates further into the ocean. It is also worth keeping in mind that the temperature response to short-lived forcing agents, such as methane, would look more like the right panel in the figure, with the temperature response peaking at the time at which emissions are curtailed.
To the extent that the response of climate to emissions is linear, as it presumably is for small enough emissions, we could write an expression for the response of any climate index to CO2 emissions, :
where is the climate response at time for unit emissions between the times and . ( is a time before which anthropogenic emissions are negligible.) If the problem can also be assumed stationary in time, then is a function only of the time elapsed between forcing and response, . The claim is not that this linear perspective is the final story, of course, but only that it may be a useful point of reference. combines the response of climate to CO2 and the response of CO2 to emissions.
What might look like? Following the discussion above, for the global mean surface temperature we can imagine it looking as simple as
The fast relaxation time is the time required for both the temperature of the ocean surface layer and its CO2 concentration to equilibrate, treating the deeper ocean layers as infinite reservoirs of heat and carbon. A single relaxation time might not be adequate, but as long as the relaxation takes place fast enough, it would have little effect on the big picture except to smooth out the response to the high frequency component of the emissions. Might this response function actually be more robust than the physical climate CO2 or carbon cycle CO2 responses separately? If your model does not represent the time scale of the equilibration of the deep ocean adequately, this might, as mentioned above, have compensating effects on the shapes of the CO2 and CO2 response functions, leaving the response with the same relatively flat shape.
Ignoring the relaxation time , the implication of this simple form for the response is that the global mean surface temperature at time can be thought of as simply the linear response to the sum total of past emissions
The implications of this result can be looked at as a glass half empty or half full. From a pessimistic perspective it says that, in the absence of geoengineering, we are committed for the next millennium to the warming that we have already created by past emissions. More optimistically, we could say that future surface temperature increases are due to future emissions — that is, it is not the climate system that has committed us to additional warming, but rather the inertia in the society and infrastructure producing the emissions themselves.
To the extent that this picture holds, we can also say that the emissions trajectory over time is not particularly important for where we end up – the climate in the year 2100, say, would depend on the total emissions between now and 2100 and not on how these emissions were distributed over the 21st century.
The ease of communicating this result is also worth emphasizing. Only one number is needed — — the warming per unit cumulative emissions. Typical central estimates for in the papers listed above are in the range 1.5-2 degrees C per trillion tons of carbon emitted. Clearly, it is pretty important to know whether this simple picture is useful or misleading.
One final point. For the idealized scenario pictured in the central panel at the top of the post, the warming never approaches the value consistent with the equilibrium response to the maximum CO2 at the end of the anthropogenic pulse. To relate the sustained temperature response to the maximum CO2 we need to use the transient climate response (TCR). (See posts #4-6 for discussion of the TCR). I think this is another good reason to place more emphasis on the TCR in discussions of climate sensitivity.
[note added on Feb. 25, to make contact with some previous posts and to address an e-mailed comment:]
As the system equilibrates the spatial structure of the warming will presumably change, even if the global mean temperature does not. In particular, you would expect more polar amplification with time, especially in the Southern Ocean, where temperatures are very slow to warm (see figure at the top of post #11). On the other hand, tropical temperatures, which are more equilibrated, might cool over time. You can’t infer a whole lot from global mean temperature about things like the temperature of the oceans around the Antarctic ice sheet. See Gillett et al 2011.
[The views expressed on this blog are in no sense official positions of the Geophysical Fluid Dynamics Laboratory, the National Oceanic and Atmospheric Administration, or the Department of Commerce.]