Evolution in time of fluxes at the top of the atmosphere (TOA) in several GCMs running the standard scenario in which CO2 is increased at the rate of 1%/yr until the concentration has quadrupled.
A classic way of comparing one climate model to another is to first generate a stable control climate with fixed CO2 and then perturb this control by increasing CO2 at the rate of 1%/yr. It takes 70 years to double and 140 years to quadruple the concentration. I am focusing here on how the global mean longwave flux at the TOA changes in time.
For this figure I’ve picked off a few model simulations from the CMIP5 archive (just one realization per model), computed annual means and then used a 7 yr triangular smoother to knock down ENSO noise, and plotted the global mean short and long wave TOA fluxes as perturbations from the start of this smoothed series. The longwave () and shortwave () perturbations are both considered positive when directed into the system, so is the net heating. The only external forcing agent that is changing here is CO2, which (in isolation from the effects of the changing climate on the radiative fluxes) acts to heat the system by decreasing the outgoing longwave radiation (increasing ). But in most of these models, L is actually decreasing over time, cooling the atmosphere-ocean system. It is an increase in the net incoming shortwave () that appears to be heating the system – in all but one case. This qualitative result is common in GCMs. I have encountered several confusing discussions of this behavior recently, motivating this post. Also, the ESM2M model that is an outlier here is very closely related to the CM2.1 model that I have looked at quite a bit, so I am interested in its outlier status.
Since the radiative forcing due to CO2 is logarithmic over this range, the radiative forcing increases linearly in time. Global mean surface temperatures also increase roughly linearly in time, as does the heat uptake , as seen in the following:
Another reason that I am interested in this comparison is that ESM2M has a low transient climate response ( warming at the time of doubling) that I like for a variety of reasons.
When thinking about this sort of thing, I tend to start with the energy balance of the ocean mixed layer, the surface layer of the ocean that is well-mixed by turbulence generated at the surface. Globally averaged we can think of this layer as being something like 50m deep, providing a heat capacity that is more than an order of magnitude larger than the atmosphere. Ignoring the latter, we can think of as heating this layer directly. This surface layer is cooled by transfer of heat to deeper layers of the ocean:
On the time scales of interest here the heat capacity of this layer is itself negligible and we can ignore the time-derivative in this equation, so that . For small perturbations, I’ll assume that where is the CO2 forcing and is the sensitivity of the longwave flux to temperature. We could also write in general, but in this case of CO2 forcing only , is small and we can think of as pure feedback.
Importantly for this discussion, I am also going to write . is referred to as the efficiency of the heat uptake — the heat uptake per unit global warming. This allows us to define a transient climate response very easily — solving for :
In previous posts, I have referred to the time scales of the forcing for which this is a useful first approximation as the intermediate regime (this hasn’t caught on — maybe I should try something else) — intermediate between the faster time scales (due to volcanoes for example) for which the heat capacity of the mixed layer is important and the slower time scales over which the deeper ocean starts to equilibrate.
With these sign conventions, and are positive, while is negative if shortwave feedback is positive (sorry). If all of these coefficients are constant in time over these 140 years of simulation, and given our other approximations, we expect and to both increase linearly in time, as is roughly the case in these models. (Actually, is typically a bit concave upwards while is a bit concave downwards, but I think the simplest model is adequate here even if it can only fit these curves to the extent that they are linear in time.) Solving for ,
Whether increases or decreases in time — that is, whether the forcing wins or the response to increasing temperatures wins — depends on the sign of . If the positive shortwave feedback is larger in magnitude than the efficiency of the heat uptake, decrease as increases. To create this counterintuitive behavior the short wave feedback does not have to compete with . It need only compete with . Averaging over the models (leaving aside ESM2M), and looking at the values averaged over years 60-80, at the time of doubling, I get . It is closer to 0.9 in ESM2M. The corresponding mean value of is about -0.85 (and -0.3 in ESM2M). Assuming that at the time of doubling is 3.5 W/m2, I get (with ESM2M roughly 2.2, so nothing special there.)
Most of the spread among models in the shortwave feedback is undoubtedly due to clouds, but there is a non-cloud related background positive shortwave feedback –partly due to surface (snow and ice) albedo feedback and partly due to positive short wave water vapor feedback. The latter does not get mentioned much because it is often lumped together with the larger infrared feedback, but it accounts for something like 15% of the total water vapor feedback (water vapor absorbs solar radiation, reducing the amount of solar radiation reaching the surface, so more vapor mean means less reflection from the surface and less loss of energy to space through this reflection.) The surface albedo and water vapor shortwave feedbacks are probably enough in themselves to compete with . In ESM2M negative short wave cloud feedbacks bring the magnitude of down and is relatively large, resulting in the intuitive response – the outgoing longwave decreasing with time with increasing CO2.
(The following paragraph corrected on June 1, 2014.) Although it is not directly relevant to the simulations described above, it is interesting to consider the special case in which there is some positive solar forcing added to the positive longwave forcing. For simplicity, let’s just assume that there is no shortwave feedback, so (we still have long wave feedback of course). The temperatures will increase if is positive, and this warming must be due to positive in our simple model (assuming once again that we are in the intermediate regime). But is it or that looks like it is causing the warming? A manipulation similar to that above shows that .So if the shortwave forcing is larger than times the longwave forcing — this ratio is something like 25% in the main group of models that we looked at above — the system is being heated by the shortwave rather than the longwave flux even though the shortwave forcing might be much smaller than the longwave forcing.
I guess the moral here, if there is one, is that it is useful to have an explicit model in mind, however simple, when thinking about the Earth’s energy balance and its relationship with surface temperature.
[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.]