Robin Lamboll, studies climate change science and policy.
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$_2$ ). It’s also worth noting that TCRE normally assumes a linear CO$_2$-T relationship rather than logarithmic, although this is disputed , 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 . 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.
 Beyond equilibrium climate sensitivity, Knutti et al 2017 http://iacweb.ethz.ch/staff/mariaru/BeyondEquilibriumClimateSensitivity/KnuttiRugensteinHegerl17.pdf
 Implications of non-linearities between cumulative CO2 emissions and CO2 -induced warming for assessing the remaining carbon budget, Nicholls et al.
 Anthropogenic carbon release rate unprecedented during the past 66 million years, Zeebe et al.
I did a crude calculation in DICE2016R, which doesn't take into account a wide range of effects nor most of the points in my comment below about elasticity. In terms of damage to the economy, the social cost of carbon for 10 years, 20 years and 30 years is about $5, $10 and $14, verses a current total social cost of carbon of $37. This is just taking the social cost of carbon now minus the discounted social cost of carbon in the future for the optimised development pathway. It's about an order of magnitude lower in the non-optimised (baseline) pathway for DICE. General disagreement over the social cost of carbon between models may make this vary over orders of magnitude and the DICE model is low compared to models like PAGE.
Something that the authors of this book perhaps should have highlighted is that DICE's main virtue is its simplicity: it is far from being either the only or the best IAM for most analyses. However, to appreciate how badly calibrated the damage function is, here's a note from the documentation:
"However, current studies generally omit several important factors (the economic value of losses from biodiversity, ocean acidification, and political reactions), extreme events (sea-level rise, changes in ocean circulation, and accelerated climate change), impacts that are inherently difficult to model (catastrophic events and very long term warming), and uncertainty (of virtually all components from economic growth to damages). I [Nordhaus] have added an adjustment of 25 percent of the monetized damages to reflect these non-monetized impacts. "
(Quote is from the manual of DICE 2013R, http://www.econ.yale.edu/~nordhaus/homepage/homepage/documents/DICE_Manual_100413r1.pdf , still valid for 2016R version as per https://www.pnas.org/content/114/7/1518/tab-figures-data .)
For most reasonable emissions pathways, temperature and linked physical effects depend only on cumulative emissions*. Delaying a given emission by some time therefore does not impact the amount of climate change it causes, so from a climate-focused perspective we don’t see any change in the harm of emissions with time (this may not be true at very low net emissions rates but is at rates similar to present-day). This would mean that the only time delaying emissions would have any climatic benefit would be if they are delayed until a time when net emissions are negative (in which case the world experiences a lower peak cumulative emissions than it would do when emitting without the delay, which we assume is less bad). It’s not clear if and when this will happen, and climate-based discounting would be 0 before that point.
This suggests that for all climatic 'badness functions' (effects on humans/ecology) no discounting is needed, however this may depend on the rate of change as well as the state of the system, and human impacts may also depend human development, equality and preparation for climate change. As we hope that the rate of emission will begin to decrease soon, this would mean that delayed emissions might be less impactful in the future. It’s going to be very assumption/IAM-dependent as to how much though. It's also not clear that this generates a positive discount rate - it's possible that people seeing more climate change sooner incentivises more research/investment in averting it, which takes time to pay off.
It’s important to distinguish two different factors that could be relevant when discussing this – one is the social cost of carbon (potentially measured in money lost, or in more egalitarian DALY losses), the other is the carbon market value of carbon. If one assumes the existence of a well-functioning global carbon market, then emissions at times after this may be largely absorbed by elasticity. However at times prior to this/if the market is not comprehensive, the ‘offsetting’ may be just displacing consumption.
A lower limit on the discount rate could come from the probability of catastrophic events (which may be a function of pure time, carbon concentration and derivative of concentration). In the event of a nuclear war, meteorite impact etc. our climate may no longer be determined primarily by emissions concentrations, hence carbon released after this period is of lower importance.