TL;DR: Assuming everything can be fit with a linear trend completely overwhelms the importance of working out what that trend is in these extreme cases, so while instructive for median behaviour, I don’t believe this approach is sufficient to assert anything about tail probabilities.
It’s good to see so much work summarised in one page, but the cost of this is rigour. I agree with the problems with using ECS as mentioned above, and add that, since these trajectories do not result in net 0 CO$_2$ emissions at 2100, it’s not even a good approach to estimate the temperature in 4100 (in the imaginary world where really slow and hard-to-model things stay the same, but easy-to-model things don’t, except CO$_2$ [1]). It’s also worth noting that TCRE normally assumes a linear CO$_2$-T relationship rather than logarithmic, although this is disputed [2], and not really designed for changes of many degrees. A similar problem exists for carbon intensity. You assume an exponential decay, but so far we’ve seen a pretty linear one. (This would imply negative emissions will eventually happen on their own!) While it’s good that you put so much effort into probability distributions of these values, it doesn’t help if you’re wrong about the equation they go in.
Regarding constant carbon intensity improvements (geometric, linear or otherwise) and extra effort, I’m not really clear what you’re proposing needs conserved – a conservation of the current level of effort into decarbonisation, or a conserved rate of change of effort into decarbonisation (since we’ve clearly been putting more effort in recently). It feels like you’re implying a constant effort derivative, i.e. slowly increasing carbon price and legislation.
You (and many others) complain the IPCC does not report extremes of the ECS PDF, then complain about what they are. The IPCC specifically makes a point of not quoting values for these extremes because there isn’t any consensus on it. We do not have > 95% confidence that the full simulations aren’t missing some big factor, in the same way we missed the breakdown of the ozone layer until after it was observed. The presence of the ozone hole, and various other weird new atmospheric chemistries, places similar limits on our confidence in paleoclimate data, as does the unprecedented rate of CO$_2$ release [3]. This does indeed increase the importance of the priors, which is why the fact we can’t agree on them is so problematic. By this point I don’t think it’s possible to disentangle true priors from decades of simulations, back-of-the-envelope calculations and climate history, and since we want to use all of these factors later, none of them can be considered truly prior. The degree of agreement between old and new estimates of ECS is interesting but irrelevant, since it doesn’t include those tails.
Your final point, that the ‘median view’ is that Earth system feedbacks are less important, is inconsistent with the degree of rigour shown elsewhere in the article. You aren’t interested in the median view of these, you’re interested in the 95th percentile views. And that should feature some of these ZOMG WE’RE GOING TO DIE!!!1 papers.
[2] Implications of non-linearities between cumulative CO2 emissions and CO2 -induced warming for assessing the remaining carbon budget, Nicholls et al.
TL;DR: Assuming everything can be fit with a linear trend completely overwhelms the importance of working out what that trend is in these extreme cases, so while instructive for median behaviour, I don’t believe this approach is sufficient to assert anything about tail probabilities.
It’s good to see so much work summarised in one page, but the cost of this is rigour. I agree with the problems with using ECS as mentioned above, and add that, since these trajectories do not result in net 0 CO$_2$ emissions at 2100, it’s not even a good approach to estimate the temperature in 4100 (in the imaginary world where really slow and hard-to-model things stay the same, but easy-to-model things don’t, except CO$_2$ [1]). It’s also worth noting that TCRE normally assumes a linear CO$_2$-T relationship rather than logarithmic, although this is disputed [2], and not really designed for changes of many degrees. A similar problem exists for carbon intensity. You assume an exponential decay, but so far we’ve seen a pretty linear one. (This would imply negative emissions will eventually happen on their own!) While it’s good that you put so much effort into probability distributions of these values, it doesn’t help if you’re wrong about the equation they go in.
Regarding constant carbon intensity improvements (geometric, linear or otherwise) and extra effort, I’m not really clear what you’re proposing needs conserved – a conservation of the current level of effort into decarbonisation, or a conserved rate of change of effort into decarbonisation (since we’ve clearly been putting more effort in recently). It feels like you’re implying a constant effort derivative, i.e. slowly increasing carbon price and legislation.
You (and many others) complain the IPCC does not report extremes of the ECS PDF, then complain about what they are. The IPCC specifically makes a point of not quoting values for these extremes because there isn’t any consensus on it. We do not have > 95% confidence that the full simulations aren’t missing some big factor, in the same way we missed the breakdown of the ozone layer until after it was observed. The presence of the ozone hole, and various other weird new atmospheric chemistries, places similar limits on our confidence in paleoclimate data, as does the unprecedented rate of CO$_2$ release [3]. This does indeed increase the importance of the priors, which is why the fact we can’t agree on them is so problematic. By this point I don’t think it’s possible to disentangle true priors from decades of simulations, back-of-the-envelope calculations and climate history, and since we want to use all of these factors later, none of them can be considered truly prior. The degree of agreement between old and new estimates of ECS is interesting but irrelevant, since it doesn’t include those tails.
Your final point, that the ‘median view’ is that Earth system feedbacks are less important, is inconsistent with the degree of rigour shown elsewhere in the article. You aren’t interested in the median view of these, you’re interested in the 95th percentile views. And that should feature some of these ZOMG WE’RE GOING TO DIE!!!1 papers.
[1] Beyond equilibrium climate sensitivity, Knutti et al 2017 http://iacweb.ethz.ch/staff/mariaru/BeyondEquilibriumClimateSensitivity/KnuttiRugensteinHegerl17.pdf
[2] Implications of non-linearities between cumulative CO2 emissions and CO2 -induced warming for assessing the remaining carbon budget, Nicholls et al.
https://iopscience.iop.org/article/10.1088/1748-9326/ab83af/pdf
[3] Anthropogenic carbon release rate unprecedented during the past 66 million years, Zeebe et al.
https://www.nature.com/articles/ngeo2681