On Bayesianism—this is an important point. The very heavy tailed estimates all use a “zero information” prior with an arbitrary cut-off at eg 10 degrees or 20 degrees. (I discuss this in my write-up). This is flawed and more plausible priors are available which thin out the tails a lot.
However, I don’t think you need this to get to there being substantial tail risk. Eyeballing the ECS estimates that use plausible priors, there’s still something like a 1-5% chance of ECS being >5 degrees, which means that from 1.5 doublings of GHG concentrations, which seems plausible, there’s a 1-5% of ~7 degrees
My understanding is there are two somewhat separate issues, one being the improper use of uniform priors and the other being a failure to give estimates that take all evidence (GCMs, recent temperatures, paleoclimate, etc) into account, with probability distributions from mostly-independent evidence sometimes having wrongly been taken as confirmation of the same uncertainty range instead of being combined into a narrower one. Do the estimates that you’re eyeballing update on every line of evidence? Annan and Hargreaves under some assumptions find numbers like a 95% upper probability bound of 3.6 degrees, which would imply virtually no risk of ECS>5. (Structural uncertainty may, of course, weaken such conclusions.)
As you explain in your writeup, the 7 degrees here represents an eventual temperature increase that will only be attained in centuries, and the increase over the 21st century would be significantly less (though still major), which makes the scenario less extreme than it sounds.
Your writeup uses Wagner and Weitzman’s interpretation of the IPCC’s uncertainty range for sensitivity. If I remember correctly, AR5 does discuss the issues of priors and combined evidence, but bases the 1.5-4.5 degree range on subjective judgment, so it’s hard for me to be sure that bad Bayesianism is what’s causing this interval to be as wide as it is, but Annan seems to think people aren’t taking his points into account enough.
I’ve found it hard to find good information on the questions most directly relevant to estimating the pdf of the size of the effects of climate change (with your writeup as one of the main exceptions) and may be getting things wrong.
Yes I think you are in fact right that plausible priors do seem to exclude ECS above 5 degrees.
You pick out a major problem in drawing conclusions about ECS—the IPCC does not explain how they arrive at their pdf of ECS and the estimate seems to be produced somewhat subjectively from various current estimates from instrumental and paleoclimatic data and from their own expert judgement as to what weight to give to different studies. I think this means that they give some weight to pdfs with a very fat tail, which seems to be wrong, given their use of uniform priors. This might mean that their tail estimate is too high
Intuitively I’m inclined to agree that the probability of very high or low climate sensitivities is overestimated due to the existence of a few separate lines of evidence that give us similar estimates, and because some studies have used inappropriate priors.
But I’ve heard climate science experts say it’s harder to “nail down” the upper end of the ECS range, IIUC because of the multiplicative nature of positive feedbacks. A simple blackbody model of Earth with no feedbacks says that doubling CO2 would give us about 1.1°C of warming (IIRC) but there are several feedbacks in which a temperature increase causes a larger temperature increase: water vapour, ice albedo, permafrost melt (not technically included in ECS, but worth considering along with the effect of destabilizing shallow clathrates, if any), cloud feedback (thought to be small), a potential increase in drought leading to higher albedo, changes to the oceanic depth-temperature gradient / changes to ocean currents (which reminds me, global warming could ultimately cause cooling in Europe which implies that if the ECS is X, the typical warming would be above X outside Europe, and as I have noted elsewhere in this discussion, the land will warm more than the ocean surface at equilibrium).
When you stack the PDF of all the feedbacks together, the tail of the distribution gets uncomfortably long. (I didn’t read much of Annan & Hargreaves so if their analysis specifically addresses the “stacking” of feedbacks, let me know.) [Overall, there have been new papers suggesting we can constrain ECS below 4° and others saying we can’t, so I think we need to give the dust some time to settle—while still looking for tractable things we can do in this area.]
Note that the historical data on the ECS doesn’t help much to constrain the upper end of the temperature range because ECS is likely not independent from initial temperature; we’ll be reaching temperature zones Earth hasn’t had for many millions of years, and we don’t have very solid data going back beyond 800,000 years.
On Bayesianism—this is an important point. The very heavy tailed estimates all use a “zero information” prior with an arbitrary cut-off at eg 10 degrees or 20 degrees. (I discuss this in my write-up). This is flawed and more plausible priors are available which thin out the tails a lot.
However, I don’t think you need this to get to there being substantial tail risk. Eyeballing the ECS estimates that use plausible priors, there’s still something like a 1-5% chance of ECS being >5 degrees, which means that from 1.5 doublings of GHG concentrations, which seems plausible, there’s a 1-5% of ~7 degrees
My understanding is there are two somewhat separate issues, one being the improper use of uniform priors and the other being a failure to give estimates that take all evidence (GCMs, recent temperatures, paleoclimate, etc) into account, with probability distributions from mostly-independent evidence sometimes having wrongly been taken as confirmation of the same uncertainty range instead of being combined into a narrower one. Do the estimates that you’re eyeballing update on every line of evidence? Annan and Hargreaves under some assumptions find numbers like a 95% upper probability bound of 3.6 degrees, which would imply virtually no risk of ECS>5. (Structural uncertainty may, of course, weaken such conclusions.)
As you explain in your writeup, the 7 degrees here represents an eventual temperature increase that will only be attained in centuries, and the increase over the 21st century would be significantly less (though still major), which makes the scenario less extreme than it sounds.
Your writeup uses Wagner and Weitzman’s interpretation of the IPCC’s uncertainty range for sensitivity. If I remember correctly, AR5 does discuss the issues of priors and combined evidence, but bases the 1.5-4.5 degree range on subjective judgment, so it’s hard for me to be sure that bad Bayesianism is what’s causing this interval to be as wide as it is, but Annan seems to think people aren’t taking his points into account enough.
I’ve found it hard to find good information on the questions most directly relevant to estimating the pdf of the size of the effects of climate change (with your writeup as one of the main exceptions) and may be getting things wrong.
Yes I think you are in fact right that plausible priors do seem to exclude ECS above 5 degrees.
You pick out a major problem in drawing conclusions about ECS—the IPCC does not explain how they arrive at their pdf of ECS and the estimate seems to be produced somewhat subjectively from various current estimates from instrumental and paleoclimatic data and from their own expert judgement as to what weight to give to different studies. I think this means that they give some weight to pdfs with a very fat tail, which seems to be wrong, given their use of uniform priors. This might mean that their tail estimate is too high
Intuitively I’m inclined to agree that the probability of very high or low climate sensitivities is overestimated due to the existence of a few separate lines of evidence that give us similar estimates, and because some studies have used inappropriate priors.
But I’ve heard climate science experts say it’s harder to “nail down” the upper end of the ECS range, IIUC because of the multiplicative nature of positive feedbacks. A simple blackbody model of Earth with no feedbacks says that doubling CO2 would give us about 1.1°C of warming (IIRC) but there are several feedbacks in which a temperature increase causes a larger temperature increase: water vapour, ice albedo, permafrost melt (not technically included in ECS, but worth considering along with the effect of destabilizing shallow clathrates, if any), cloud feedback (thought to be small), a potential increase in drought leading to higher albedo, changes to the oceanic depth-temperature gradient / changes to ocean currents (which reminds me, global warming could ultimately cause cooling in Europe which implies that if the ECS is X, the typical warming would be above X outside Europe, and as I have noted elsewhere in this discussion, the land will warm more than the ocean surface at equilibrium).
When you stack the PDF of all the feedbacks together, the tail of the distribution gets uncomfortably long. (I didn’t read much of Annan & Hargreaves so if their analysis specifically addresses the “stacking” of feedbacks, let me know.) [Overall, there have been new papers suggesting we can constrain ECS below 4° and others saying we can’t, so I think we need to give the dust some time to settle—while still looking for tractable things we can do in this area.]
Note that the historical data on the ECS doesn’t help much to constrain the upper end of the temperature range because ECS is likely not independent from initial temperature; we’ll be reaching temperature zones Earth hasn’t had for many millions of years, and we don’t have very solid data going back beyond 800,000 years.