I’ve written a number of posts about the energy balance models (EBMs) used by Nic Lewis and thought I might write one more (sorry SB 🙂 ). In a previous post, Victor asked what I thought the reasons were for the difference between EBM climate sensitivity estimates and the GCM estimates. Quite why a climate scientist would ask me I don’t know, but that didn’t stop me from attempting to answer.
One possible reason is that EBMs assume that feedbacks are linear. In other words, they assume that the radiative response to changes in temperature will be the same in the future as its been in the past (or, rather, that the relationship between the change in temperature and the change in feedback is fixed). GCMs make no such assumptions and I became aware today (H/T Richard Betts) of a paper that attempts to quantify how feedbacks vary with time in GCMs. The paper is The dependence of radiative forcing and feedback on evolving patterns of surface temperature change in climate models by Andrews, Gregory & Webb. What they did was to do a suite of GCMs runs in which CO2 is instantaneously quadrupled and then held constant while the simulation evolves for a time of 150 years. The abstract nicely summaries the basic result
Experiments with CO2 instantaneously quadrupled and then held constant are used to show that the relationship between the global-mean net heat input to the climate system and the global-mean surface-air-temperature change is nonlinear in Coupled Model Intercomparison Project phase 5 (CMIP5) Atmosphere-Ocean General Circulation Models (AOGCMs). The nonlinearity is shown to arise from a change in strength of climate feedbacks driven by an evolving pattern of surface warming. ………. We also demonstrate that the regression and fixed-SST methods for evaluating effective radiative forcing are in principle different, because rapid SST adjustment when CO2 is changed can produce a pattern of surface temperature change with zero global mean but non-zero change in net radiation at the top of the atmosphere (~ -0.5 Wm-2 in HadCM3).
So, in models where the sea surface temperature (SST) is allowed to change, the SST can change in such a way that the feedbacks are nonlinear. If I understood the paper properly, this was primarily due to changes in cloud feedback. The figure below illustrates the main result, where the term is determined using the equation
with the radiative imbalance, and the change in external forcing. Since this is a quadrupling of CO2 experiment, ECS would then be with – unlike other similar studies – here being negative. The top panels and bottom left panel in the figure below illustrates how the temperature changes as the system returns to equilibrium. It is clear that it is not linear. Similar when you compare estimates for during the first 20 years of the simulations with estimates using the last 130 years of the simulation, they’re clearly not the same (smaller – and hence higher ECS – in the latter period than in the former).
Similarly – as shown in the figure below – if you compare ECS estimates using the first 20 years of the simulation with estimates using the last 130 years, you find that estimates using the latter period tend to produce higher estimates than determined when using the earlier period.
So, what does this all mean? Well, one thing is that it may give a reason why climate sensitivity estimates using EBMs are different to those using GCMs (well, there are additional reasons, but I’ll ignore that here). The former assume that feedbacks are linear, while that latter indicates that they might not be. Does this means that feedbacks are non-linear? Not necessarily, but it does indicate that they might be. Since EBMs assume that they’re linear, they certainly cannot be used to argue that they aren’t.
As Richard Betts pointed out on Twitter, it also illustrates why EBMs are not really a method that can be used to narrow the uncertainty in future warming. If they assume that feedbacks are linear and they turn out not to be, then the EBM estimate will be wrong, however narrow one has managed to make the uncertainty interval. This doesn’t mean that EBMs are not useful, but does mean that anyone arguing that we should use them because they believe that they’re more robust than other estimates, is ignoring that they rely on an assumption that may not be correct. If anything, we have evidence to suggest that this assumption will indeed not be correct, and so it would seem that anyone discussing EBM estimates should at least be willing to acknowledge this.