I thought I would just briefly mention a recent paper by Bloch-Johnson, Pierrehumbert & Abbot called Feedback temperature dependence determines the risk of high warming. As I understand it, the basic idea is to consider what would happen if the feedback response has a temperature dependence. If the feedback response is linear, then you can estimate the climate sensitivity, , at any time using
However, it is clear that feedbacks do have a temperature dependence. The Planck response () is clearly temperature dependent. What we don’t know – given all the feedbacks – is the strength of this possible non-linearity. What Bloch-Johnson et al. do is simply assume that the climate sensitivity has a non-linear term,
The figure to the right shows how different values of influences the response to a change in forcing. The dashed line is the linear response. Negative values reduce the response, while positive ones increase it. There are also combinations of and that could lead to runaway warming. Most GCMs, apparently, suggest that the linear approximation works well. There are some – as shown in the right hand panel above – that do, however, indicate a non-negligible value.
As shown in the figure above, the paper also considers the impact of a possible non-linearity on observationally-based estimates of climate sensitivity. Negative values reduce both climate sensitivity and the range, while positive values do the opposite. Something to bear in mind, though, is that most observationally based analyses assume feedbacks are linear, and so – by definition – cannot be used to determine if they’re not.
Anyway, that’s all I was going to say. As I understand it, the point of the paper is not to suggest that feedbacks will be non-linear, but to illustrate the impact of them being non-linear. Additionally it illustrates that such a non-linearity would not be evident in observationally-based studies. In a sense, it seems to be a Black swan type of argument. If feedbacks are non-negligibly non-linear, then this would not yet be evident, but could result in the probability of high climate sensitivity being much greater than we currently think. This is especially true if we do continue to follow a high emission pathway, which could ultimately much more than double atmospheric CO2.
Update : I had an email from Ray Pierrehumbert with some additional context. I’ve added it below. Bear in mind that the figure is simply illustrative of how a bifurcation might work, not from some kind of actual calculation.
Although the nonlinear term can be quite important even for mid-range IPCC type climate sensitivity, when you go out on the fat tail (say, 8C per doubling) then the nonlinearity becomes not just a modification of the story, but the WHOLE story — unless the world manages to limit radiative forcing to very small values. So, consideration of fat tails and nonlinearity/bifurcations are inseparable. Worse, when there is a bifurcation, the local analysis can tell you that you jump but it doesn’t tell you where you land — could be just a transition to a state a few degrees higher, but could be a Venus-type runaway (not that I think the latter is likely, but it can’t be settled based on the kind of local analysis people usually do). In other words, not just a black swan, but potentially a whole flock of black swans.This sketch may be a useful visualization. The vertical axis represents climate state (think global mean temperature) the horizontal represents control knob (think CO2) The arrows represent two possible jumps, compatible with the same local behavior. As one gets close to the fold, the linear analysis becomes increasingly meaningless.