In a recent post I made some crude estimates of projected global mean surface temperature (GMST) change to year 2090, based on the estimates of transient climate response/sensitivity (TCR/TCS) values taken from the AR5. The numbers I got were at the very low end of the AR5 90% confidence intervals and I couldn’t understand why. As mentioned there, my working assumption was that my numbers were most likely the indefensible ones. And that does indeed appear to be exactly the case, and fortunately the discrepancy between my values and the AR5’s was not too hard to spot. So, this post is to explain the mistake I made and provide a little associated discussion.
The very short version is that I forgot to account for the temperature time delay(s) in the earth system whenever an increasing RF is imposed over a number of years. Stupid mistake, but good learning experience. As a quick review, I got these median and mean GMST values, using the means and medians respectively of the 52 TCR values given in AR5 WG1 (45 are from Chapter 9, Tables 9.5 and 9.6). I applied the standard RF linear pro-rating to account for differences in delta RF from a doubling, the latter being how TCR is defined. For total anthro (TA) forcings, using the midpoints of the AR5 time intervals, I got these numbers:
Period RCP dT.med dT.mean AR5.mid 1 1995-2090 rcp26 0.433 0.444 1.0 2 1995-2090 rcp45 1.145 1.176 1.8 3 1995-2090 rcp60 1.632 1.676 2.2 4 1995-2090 rcp85 2.726 2.799 3.7
Let’s call it ~2.75 deg C for the RCP 8.5 scenario, or almost a degree below the AR5 midpoint.
TCR is clearly defined–the GMST change expected from a 1% per year increase in
RF CO2 (or an equivalent RF from all sources, CO2eq), once 2x RF CO2/CO2eq has been reached. A 1.0 percent increase always takes ~70 years to reach doubling [log(2, base=1.01)], so the time span–and hence the intensity–of the imposed RF change, is clearly defined. The longer it takes for a given increase in RF, the greater the T change by the end of the interval, relative to that at some future time beyond it (i.e., when equilibrium is reached). Due to ocean heating and large scale mixing, only some fraction of the RF-induced T effects can manifest in 70 years, which is why the Equilibrium Climate Senstivity (ECS) is always quite a bit higher than the TCR is. The AR5 reference time period midpoints (1995-2090, 95 years) give an interval just a little longer than the defined TCR 70 year period, not enough to matter hugely it would seem.
The lagged temperature increase in the system depends on several factors, but the AR4 (2007) best estimate was for an additional increase of 0.6 degrees C by year 2100. For the RCP 8.5 scenario, adding that value to 2.75 brings the estimate to 3.35, so now we’re definitely in the ball park just by that adjustment alone. But that 0.6 does not include any lagged response(s) that might originate in say the earlier decades of the 21st century but not be manifest until toward the end thereof. Trying to estimate that value requires a close look at the CMIP5 model outputs. I’ll look again in the AR5 for any such estimates (any help on the issue appreciated!), but it’s not hard at all to see that another 0.35 degrees, or more, could arise therefrom, giving a midpoint estimate of 3.7 degrees C, for the RCP 8.5.
The topics of time lags and slow feedbacks are very interesting ones IMO (in any field of science) and the fact that these are substantial in global T responses to rapid RF changes is of major importance. The fact that the mean/median TCR estimates declined between AR4 and AR5 is not necessarily a good thing, given that ECS estimates did not change much with them*. From a strict predictability perspective, forcing the system hard and fast is not a good thing, and you surely don’t want a big gap between TCR and ECS estimates, because it will tend to increase the difficulty of identifying and communicating cause and effect relationships. And since the scientific understanding on climate change and its attribution certainly affects policy, that’s not a good situation to be in.
* On reflection, one should also consider the fact that TCR estimates based on observational data have more confidence attached to them, than do ECS estimates from same, making the whole topic that much more intriguing.
1. Edited several times for clarity.
2. The xkcd cartoon that spurred my original post is +/- unaffected by these considerations, i.e. still biased high, (but not by as much as I’d originally thought either). This is because that cartoon uses (presumably), the middle 20th century as its baseline point, and the lagged 0.6 degree C addition to the year 2100 T estimate, and whatever might be due to RF increases from 2000 to ~2030, are already +/- included in any estimate of T change from 1950 to 2100. Most GHG-induced warming is post-1950, when [CO2] was about 310 ppm.