The TCR-to-ECS ratio

Something I’ve been interested in is whether or not the ratio between the Transient Climate Response (TCR) and the Equilibrium Climate Sensitivity (ECS) best estimates from most of Nic Lewis’s work makes sense. Typically his TCR best estimate is around 1.35^oC, while his ECS best estimate is around 1.65^oC; giving a TCR-to-ECS ratio bigger than 0.8. For climate models, the ratio is typically below 0.8 and, most likely, below 0.7. I did ask Nic Lewis if he could explain his rather high TCR-to-ECS ratio, and he responded in his normal charming fashion. His argument, I think, is simply that you take the energy balance forms of the equations that describe TCR and ECS

and

and you simply plug in the values for the change in temperature (), change in forcing (), and change in system heat uptake rate () and out pops an answer. My question, however, was trying to delve slightly deeper into this issue, which I’ll try to explain below.

As discussed in Section 4 of this paper (Earth’s energy imbalance and implications by Hansen et al.) for a given climate sensitivity, the climate response function (defined as the fraction of the fast-feedback equilibrium response to a climate forcing) depends on the rate at which energy is mixed into the deep ocean. If energy is mixed into the deep ocean slowly, then most of the energy will heat the upper ocean, land and atmosphere, and the climate response will be fast. If, however, it is rapidly mixed into the deep ocean, then the climate response will be slow (the upper ocean, land and atmosphere will warm more slowly). This will manifest itself as a difference in the magnitude of the planetary energy imbalance that can be sustained; if the climate response is fast, we’d expect the typical planetary energy imbalance to be small; if it is slow, we’d expect it to be larger.

This is illustrated in the figure below, which shows examples of 3 different climate response functions, all of which can match the historical surface temperature record, but which produce different planetary energy imbalances. If the climate response is slow, we might expect a planetary energy imbalance today of around 1Wm^-2. If it is fast, we might expect it to be less than 0.5Wm^-2. Given that, today, it is probably somewhere between 0.6 and 0.8Wm^-2, Hansen et al. (2011) suggest that an intermediate response is more realistic and that most climate models possibly mix energy into the deep ocean too rapidly (they tend to have slow climate response functions). However, is this sufficient to explain the discrepancy between a TCR-to-ECS ratio of 0.6 to 0.7 – suggested by most climate models – and a value in excess of 0.8, as suggested by Nic Lewis’s work?

Credit : Hansen et al. (2011)

Credit: Miller et al. (2015)

In trying to understand this better, I came across a paper called Model structure in observational constraints on transient climate response, by Miller et al. It includes the figure on the right that shows the TCR-to-ECS ratios for Perturbed Physics Ensembles (PPE), CMIP5 models, and also includes the AR4 and AR5 ranges for TCR and ECS. Judging by this figure, it would seem that a TCR-to-ECS ratio between 0.8 and 0.9 is possible, but would seem to require that the TCR be quite low; less than 1.5^oC, which is indeed consistent with Nic Lewis’s best estimate. However, this still doesn’t really indicate that a TCR-to-ECS ratio greater than 0.8 is consistent with the planetary energy imbalance being greater than 0.6Wm^-2.

I’m not quite sure where to go with this. This post is really just some thoughts on this. It seems that a TCR-to-ECS ratio above 0.8 is possible if the TCR is sufficiently low. Given how much we’ve now warmed, however, a low TCR is becoming less likely. Also, if the system can sustain a planetary energy imbalance of between 0.6Wm^-2 and 0.8Wm^-2 might also suggest that a TCR-to-ECS ratio above 0.8 is unlikely, because the potential amount of committed warming could then be larger than 20% of a low TCR.

I should say that I think Nic Lewis’ work is very interesting and makes a valuable contribution to our understanding of climate sensitivity. However, it does suggest some things that are at odds with other estimates; such as a much larger probability of the ECS being below 2^oC, and a higher TCR-to-ECS ratio. Also, there is the possibility that feedbacks are time-dependent in such a way that observationally-based estimates of climate sensitivity may suggest that climate sensitivity is lower than it actually is.

I should also add that focusing only on climate sensitivity can be a bit misleading, as how much we will actually warm will depend on climate sensitivity and on carbon cycle feedbacks. These can be combined into a single quantity called the transient response to cumulative emissions, which is thought to be between 0.8^oC and 2.5^oC per 1000GtC. Since we’ve warmed by almost a degree after emitting just under 600GtC might suggest that the lower end of this range is rather unlikely. I’ll stop there. Comments welcome.