Evolution of global mean near-surface air temperature in GFDL’s CM2.1 climate model in simulations designed to separate the fast and slow components of the climate response in simulations of future climate change, as described in Held et al, 2010.
Continuing our discussion of transient climate responses, I want to introduce a simple way of probing the relative importance of fast and slow responses in a climate model, by defining the recalcitrant component of global warming, effectively the surface manifestation of changes in the state of the deep ocean.
The black curve in this figure is the evolution of global mean surface air temperature in a simulation of the 1860-2000 period produced by our CM2.1 model, forced primarily by changing the well-mixed greenhouse gases, aerosols, and volcanoes. Everything is an anomaly from a control simulation. (This model does not predict the CO2 or aerosol concentrations from emissions, but simply prescribes these concentrations as a function of time.) The blue curve picks up from this run, using the SRES A1B scenario for the forcing agents until 2100 and then holds these fixed after 2100. In particular, CO2 is assumed to approximately double over the 21st century, and the concentration reached at 2100 (about 720ppm) is held fixed thereafter. The red curves are the result of abruptly returning to pre-industrial (1860) forcing at different times (2000, 2100, 2200, 2300) and then integrating for 100 years. The thin black line connects the temperatures from these four runs averaged over years 10-30 after the abrupt turn-off of the radiative forcing.
One can think of the red lines as simulations of what we might call instantaneous perfect geoenginering, in which one somehow contrives to return the CO2 (and all of the other forcing agents in these simulations) to pre-industrial values. Perfect geoengineering so defined must be clearly distinguished from two other simple hypothetical scenarios discussed in the literature. (Let’s simplify things by just thinking of CO2 as the only relevant forcing agent.) One such scenario consists of just holding the CO2 fixed after a certain time, as in the A1B scenario after 2100 (the blue line) in the figure. The warming that occurs after 2100 as the system approaches its final equilibrium is referred to as the “committed warming” but it might be better to refer to it as the fixed concentration commitment. A second, in many ways more interesting, simple scenario (e.g. Solomon et al, 2009; Matthews and Weaver, 2110) consists of abruptly setting the emissions to zero. This is another definition of commitment, which we might call the past emissions commitment, the study of which requires a coupled carbon-climate model. Unlike the fixed concentration commitment, it often results in temperatures that stay roughly unchanged for centuries — the warming due to the reduction in ocean heat uptake is roughly balanced by the ocean uptake of CO2. Perfect geoenginering is much harder than even setting emissions to zero, of course, since one would have to take enough CO2 out of the atmosphere to return to its pre-industrial value. Needless to say, we are not interested in this scenario because of its practical relevance but rather as a convenient probe of climate models.
There are similarities in the evolution after the turnoff of the radiative forcing for the 2100, 2200, and 2300 cases (these all have the same radiative forcing before the turn-off). At first the temperature decays exponentially, with an e-folding time of 3-4 years. An exponential fit yields a cooling in this fast phase of 2.6-2.7K in each case, leaving behind what we refer to as the recalcitrant warming. The spatial structure of the fast response is very similar in these three cases as well, and differs substantially from the spatial structure of the recalcitrant remnant. These are single realizations so some of the slow evolution after the turnoff of radiative forcing could be due to background internal variability. See Held et al (2010) for some further discussion of these simulations. Wu et al (2010) discuss aspects of the response of the hydrological cycle in similar model setups.
In thinking about the recalcitrant warming, it is useful to return once again to our two box model (post #4, ignoring the limitations of this model discussed in post #5)
On time scales long compared to the fast relaxation time of the surface box with temperature , we have
When the forcing is turned off, The solution relaxes on the fast time scale to
so the response is the sum of the recalcitrant part and fast response proportional to the forcing
An important implication of this plot, taking it at face value, is that the recalcitrant component of surface warming is small at present, implying that the response up to this point can be accurately approximated by the fast component of the response in isolation, which simply consists of rescaling the TCR with the forcing.
Another implication is that acceleration of the warming from the 20th to the 21st century is not primarily due to saturation of the heat uptake (this only accounts for the 0.4K growth of the recalcitrant component), but is primarily just due to acceleration of the growth of the radiative forcing.
It is important to keep in mind the limitations of this idealized picture. There is no reason to expect the slow response to be characterized by one time scale. But more importantly for this line of argument, there is no obvious reason why intermediate time scales, related to sea ice or the relatively shallow circulations that maintain the structure of the main thermocline, could not play more of a role in the transient response of surface temperature, filling in the spectral gap between our fast and slow time scales, and requiring a more elaborate analysis of the linear response in the frequency domain.
[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.]