I’ve written a number of times about energy balance models. I think these are nice ways to estimate effective climate sensitivity (both transient and equilibrium) but they are quite simple and do suffer from some issues. For example, they are largely incapable of accounting for inhomgeneities in the forcings and cannot account for possible non-linearites.
To be clear, this doesn’t mean that I think energy balance estimates are wrong, or not useful; simply that one has to be slightly careful as to how one interprets the results. There are, however, a couple of other things that typical energy balance models cannot incorporate. We’re fairly certain that internal variability can influence that rate at which the surface warms. Energy balance models typically consider the change in various quantities (temperature, radiative forcing, system heat uptake rate) across some time interval. Internal variability could, therefore, influence the value of these changes. For example, it is largely agreed that we’ve undergone a surface warming slowdown in the last 10 years or so. Therefore, one might expect that the change in temperature today, relative to some earlier time, will be slightly smaller than if internal variability was not playing a role.
Something else that energy balance models do not consider is that there is a small lag between a change in forcing and the resulting warming. Now, I’m not talking about the time it takes for the entire system to reach equilibrium, but the time it would take for the upper ocean, atmosphere and land to reach a quasi-equilibrium (i.e., all attain the same temperature). This is relativly quick, but still probably a few years. This does mean, however, that if you consider the temperature and forcings at the same time, you may be slightly over-estimating the change in forcing.
The reason I’m writing this is because there is a recent paper by Cawley et al. (2014) called On a minimal model for estimating climate sensitivity. It’s partly a response to a paper by Craig Loehle, but I don’t really want to discuss that. What I was wanting to discuss is the model they present. Their model is basically
and is essentially the NINO3.4 ENSO index and represents internal climate variability. You don’t even really need to define what the parameters are, but they’re essentially an offset (), climate sensitivity (), a factor representing the strength of the influence of ENSO events () and a lag time (). Note also that the forcings, , are convolved with the function , which means that the forcing response isn’t instantaneous, but rather rises and then decays with a timescale set by .
My understanding of how they apply this (and the authors can correct me if I’m wrong) is that they have a forcing dataset (with a range for each forcing) and a temperature dataset (HadCRUT3v-gl). For a particular choice of forcings, they vary the parameters so as to get a best fit to the temperature dataset. Then, using the same values, they determine the transient climate response (TCR) by doubling atmospheric CO2 through an annual increase of 1% per year, over a period of 70 years. This is then repeated with different possibly forcings so as to produce a range and best estimate for the TCR. The result is shown in the figure below. The top left is the forcings, the top right is a comparison of the model and the observations, bottom left is the anthropogenic forcing, CO2 only forcing, and natural forcings, and the bottom right is the probability distribution function (PDF) for the TCR.
What Cawley et al. (2014) find is that the TCR has a 95% credible range of 1.3-2oC with best estimate (peak of the PDF) of 1.66oC. The range is similar to many other estimates, but the best estimate is higher than that obtained using energy balance models. Energy balance estimates typically get a best estimate for the TCR of between 1.3 and 1.4oC (see, for example, Otto et al. 2013, and Lewis & Curry 2014). I suspect there are a number of reasons for this. By explicitly including internal variability (through the ENSO index) and by fitting to the entire time series (rather than just the beginning and the end) Cawley et al. have probably reduced the influence of internal variability on the TCR estimate. Cawley et al. (2014) have also determined the TCR by doubling CO2 at a 1% per year increase, over a period of 70 years, which is the formal way of estimating TCR. Energy balance models cannot do this, and simply estimate it from the change – across the time interval – in the various quantities. Given that there are climate models that match the 20th century warming, but which have higher TCRs than energy balance models suggest, this may not be all that surprising.
This post has actually got rather longer than I intended, and I don’t really have any major conclusions to draw from this. It seems like an interesting paper that attempts to estimate climate sensitivity using a fairly simple model, but one that includes various factors that energy balance models are unable to incorporate. The result is broadly consistent with other estimates (TCR of somewhere between 1.3 and 2oC) but has a best estimate that is a little more consistent with climate model estimates than is typically the case for energy balance estimates. That doesn’t make it right, though, but it may indicate that the simplicity of basic energy balance models might mean that they have a tendency to under-estimate TCR, since they can’t incorporate factors that would tend to produce a larger estimate. As usual, feel free to add your own thoughts through the comments and if anyone thinks I’ve got something wrong, or misunderstood the paper, feel free to point it out.