The Inescapable Implication of Uncertainty

By Stephan Lewandowsky
Professor, School of Experimental Psychology and Cabot Institute, University of Bristol
Posted on 26 March 2012
Filed under Cognition

In a previous post, we saw that uncertainty is not your friend. In a nutshell, if there is uncertainty, things could be worse than anticipated as well as better.

The previous post encapsulated this in a figure, which I show again below because it serves as a departure point for our next installment of our uncertainty analysis:

The figure shows synthetic distributions of climate sensitivity (if you don’t know what that is, begin by reading the previous post). The means of the four distributions in the above figure are identical but their standard deviations differ considerably, from .49 in the top left to 2.6 in the bottom right. The spread of each distribution characterizes the extent of uncertainty surrounding the mean estimate of 3 degrees.

The consequences of this increase in uncertainty are as obvious as they are inescapable: As uncertainty increases, the probability of a truly catastrophic outcome (defined as climate sensitivity exceeding the highly conservative 5°C mark; indicated by red lines in the figure) increases from a small .07% in the top left panel to a concerning 14% in the bottom right. In other words, increasing the standard deviation of our distribution fivefold, from .5 to 2.5, increases the likelihood of catastrophe by a factor of 200. (The word “catastrophe” has been over-used in the climate arena, but a 5°C increase would be truly catastrophic by most accounts, and most climate scientists are very concerned even about the possibility of considerably lower increases.) See update below.

The first conclusion about the climate system therefore has to be that the greater the uncertainty, the greater the potential for catastrophe.

That said, another aspect of the above figure appears to offer comfort at first glance. As uncertainty increases, from the top left to the bottom right panel, the proportion of the distribution towards the lower end of sensitivity also increases as a trivially necessary consequence of keeping the mean constant. The proportion of low estimates (< 2°C) reaches a whopping 42% when the uncertainty is greatest (bottom-right panel in the figure). This seemingly invites an alternative interpretation: With nearly half of all estimates of sensitivity below the ostensibly-safe “guardrail” of 2°C, perhaps one could legitimately ignore the upper tail, however fat it gets with increasing uncertainty? See update below.

Whether this gamble is advisable might at first glance appear to be a matter of subjective preference—some people may legitimately think that a 40%+ chance of being safe outweighs a 14% likelihood of catastrophe. As it turns out, however, we can push our analysis further and show that the lower end of the climate sensitivity distribution does not offer the comfort it implies at first glance.

From Sensitivity to Cost

To understand the reasons for this, we must first relate climate sensitivity to the likely damage associated with climate change. Common sense dictates that greater sensitivity translates into greater cost: For example, if sensitivity is low and sea levels rise by only 2 cm, damage will be relatively minimal (i.e., we lose a few meters of beach). If sensitivity turns out to be higher, and sea levels rise by 60 cm, the damage is considerable (i.e., we need to build dams and levees or move people out of harm’s way, all at great cost).

What is even more important than the fact that damage cost increases with climate sensitivity is to ascertain the functional form of that increase: Will a .5°C increase of sensitivity from 2.5°C to 3°C incur the same additional cost as an increase from 3°C to 3.5°C? What about an increase from 4.5°C to 5°C?

It turns out that the precise form of this damage function is subject to debate. However, what does not appear to be subject to debate among economists is the fact that the damage function is convex (e.g., Nordhaus, 2010; Tol, 2011; Weitzman, 2010). “Convex” means that the rate at which damages are increasing with increasing climate sensitivity is itself increasing. This is illustrated in the figure below, using a highly convex (quadratic) function for illustrative purposes.

Consider first the top panel of the figure (Panel A). The panel itself contains three smaller panels, and the largest one in the top-right quadrant displays the cost function used for this example. The horizontal panel at the bottom shows the climate-sensitivity distribution from before, with the mean (3°C) highlighted by a vertical blue line. The left vertical panel shows the distribution of expected damage costs.

The damage-cost distribution was obtained by taking each observation in the sensitivity distribution and “reflecting” it onto the vertical axis using the convex damage-cost function. Units on the damage-cost axis are omitted because the figure is not seeking to convey actual dollar values (although economists believe that they can compute those values for future anticipated warming).

The most important message from the above figure arises from comparison of panels A and B.

The only difference between the two panels is the degree of uncertainty associated with climate sensitivity: The mean sensitivity is identical, but the spread (standard deviation) of the sensitivity distribution is greater in Panel B (standard deviation 2.5) than in Panel A (standard deviation .5).

Now consider the consequences of increasing uncertainty on damage costs: Although mean sensitivity is the same across both panels, the average expected damage increases with uncertainty—the mean damage in Panel A is lower than in Panel B. The comparison is made easy by comparing the lengths of the two vertical double-headed arrows, which point to the mean damage in each panel. It is quite clear that the arrow is longer—representing greater expected cost—in Panel B than in Panel A.

In a nutshell, if we expect X°C warming, the expected damage cost associated with that degree of warming is a function not (only) of X but also of the uncertainty associated with our estimate of X—and the greater that uncertainty, the greater the expected damage.

Not only is uncertainty not your friend, but greater uncertainty translates into greater expected loss.

And There is More

And this is just the beginning, because there are a few more points worth making about the above figure: First, not only does increasing uncertainty about climate sensitivity increase the mean expected damage cost (i.e., best mean prediction), but it also increases the uncertainty around that expected damage cost—and that increase in uncertainty is particularly dramatic. Of course, uncertainty surrounding expected damages is highly relevant because it must be taken into account when assessing the total expected risk from climate change. To illustrate, whereas expected (mean) damage increases by “only” around 50% between the two panels, the associated standard deviation (uncertainty) of the damage increases 10-fold.

Another point worth making about the figure is that greater values of climate sensitivity likely translate into quicker evolution of the climate, all other things being equal (e.g., Bahn et al., 2011, Fig. 2). In other words, greater uncertainty about sensitivity (Panel B) not only translates into greater expected damage, but that damage is also likely to arrive sooner rather than later because the rate of temperature increase is greater with greater sensitivity. (This must not be confused with the fact that greater sensitivity may entail a longer asymptotic response time of the climate system; e.g. Hansen et al., 1985. That is, with greater sensitivity the climate system warms more quickly, but because it ultimately reaches a higher temperature, getting to that asymptote may take longer than with lesser sensitivity.)

This is an important point to bear in mind because if the greater damage were delayed, rather than accelerated, economists could claim that its absolute value should be temporally discounted (as all economic quantities typically are; see Anthoff et al., 2009). But if greater damage arrives sooner, then any discounting would only further exacerbate the basic message of the above figure: Greater uncertainty means greater real cost.

To sum up, uncertainty is no one’s friend. Greater uncertainty means things can be worse than you think. And greater uncertainty means you’ll pay more for the damages arising from climate change than if there were less uncertainty. In fact, you may end up paying much more than anticipated.

Uncertainty is no one’s friend.

The next post in this series we will examine how uncertainty affects the likely cost of mitigation.

Update 28/3/12: It has been drawn to my attention that the 5°C cutoff for an outcome to be labeled "catastrophic" was too conservative; that is, temperature increases considerably less than that would be associated with outcomes that most people would consider catastrophic. Conversely, limiting temperature increases to 2°C may not be "safe."

I do not necessarily disagree, but those issues are not central to the point made here: Wherever one places a cutoff above or below the mean, the implications of the fat tails are identical, and it does not matter where exactly the "catastrophe" lurks. The crucial fact is that greater uncertainty translates into greater likelihood of catastrophic (or bad or terrible) outcomes, all other things being equal.


Anthoff, D.; Tol, R. S. J. & Yohe, G. W. Discounting for Climate Change Economics: The Open Access Open Assessment E-Journal, 2009, 3.

Bahn, O.; Edwards, N. R.; Knutti, R. & Stocker, T. F. Energy policies avoiding a tipping point in the climate system Energy Policy, 2011, 39, 334-348.

Hansen, J.; Russell, G.; Lacis, A.; Fung, I.; Rind, D. & Stone, P. Climate Response Times: Dependence on Climate Sensitivity and Ocean Mixing Science, 1985, 229, 857-859.

Nordhaus, W. D. Economic aspects of global warming in a post-Copenhagen environment Proceedings of the National Academy of Science, 2010, 107, 11721-11726.

Weitzman, M. L. What is the ``Damages Function'' for Global Warming – and What Difference Might it Make? Climate Change Economics, 2010, 1, 57-69.

Tol, R. S. J. The Social Cost of Carbon Annual Review of Resource Economics, 2011, 3, 419-443.


Bookmark and Share


1  2  Next

Comments 1 to 50 out of 55:

  1. George.Laking at 11:55 AM on 31 March, 2012
    Thank you for continuing the series. I'm presuming you will bring in something about Value of Information analysis in the next installment. Such an analysis would, I expect, imply the realignment of pretty much all scientific effort towards CC mitigation. If only funding bodies could see that.
  2. I found this is an informative and interesting post so i think so it is very useful and knowledgeable. I would like to thank you for the efforts you have made in writing this article.
    facebook auto liker
    youtube views
  3. You know your projects stand out of the herd. There is something special about them. It seems to me all of them are really brilliant!
    hochzeit musik dj
  4. japan.comp234 at 20:24 PM on 6 October, 2015
    it was a wonderful chance to visit this kind of site and I am happy to know. thank you so much for giving us a chance to have this opportunity..
    things to do in phuket
  5. japan.comp234 at 19:56 PM on 14 October, 2015
    Great post, you have pointed out some fantastic points , I likewise think this s a very wonderful website.
    wedding planner phuket
  6. japan.comp234 at 16:39 PM on 15 October, 2015
    I’ve been searching for some decent stuff on the subject and haven't had any luck up until this point, You just got a new biggest fan!..
    fat diminisher system review
  7. japan.comp234 at 18:47 PM on 23 October, 2015
    Thanks, that was a really cool read!
    car title loans Los Angeles
  8. This was really an interesting topic and I kinda agree with what you have mentioned here!
    The Venus Factor Review
  9. Please continue this great work and I look forward to more of your awesome blog posts.
    MintsApp Review
  10. japan.comp234 at 19:39 PM on 31 October, 2015
    I am very much pleased with the contents you have mentioned. I wanted to thank you for this great article.
    Venus Factor Review
  11. brad.haddon234 at 21:13 PM on 2 November, 2015
    Your blog provided us with valuable information to work with. Each & every tips of your post are awesome. Thanks a lot for sharing. Keep blogging..
    ecom premier academy bonus
  12. japan.comp234 at 18:55 PM on 5 November, 2015
    Thanks, that was a really cool read! Build my list 2.0 review
  13. japan.comp234 at 23:34 PM on 5 November, 2015
    Interesting topic for a blog. I have been searching the Internet for fun and came upon your website. Fabulous post. Thanks a ton for sharing your knowledge! It is great to see that some people still put in an effort into managing their websites. I'll be sure to check back again real soon. how to get lots of followers on twitter how to get youtube subscribers fast
  14. japan.comp234 at 19:09 PM on 6 November, 2015
    I recently came across your blog and have been reading along. I thought I would leave my first comment. I don't know what to say except that I have enjoyed reading. Nice blog. I will keep visiting this blog very often. Build my list 2.0
  15. japan.comp234 at 20:30 PM on 9 November, 2015
    Thanks, that was a really cool read! Genius marketing pro
  16. This is a good post. This post gives truly quality information. I’m definitely going to look into it. Really very useful tips are provided here. Thank you so much. Keep up the good works. itunes alternative mac
  17. Thank you for very usefull information.. the founder of Google Larry.Christians Pope Francis
  18. Love what you're doing here guys, keep it up!..
  19. Thank you very much for writing such an interesting article on this topic. This has really made me think and I hope to read more.
    original site
  20. japan.comp234 at 18:58 PM on 3 December, 2015
    Good focuses you composed here..Great stuff...I think you've made some really intriguing points.Keep up the great work. bali promo
  21. japan.comp234 at 20:04 PM on 3 January, 2016
    These are some great tools that i definitely use for SEO work. This is a great list to use in the future.. Smart Member 2.0
  22. Only aspire to mention ones content can be as incredible. This clarity with your post is superb and that i may think you’re a guru for this issue. High-quality along with your concur permit me to to seize your current give to keep modified by using approaching blog post. Thanks a lot hundreds of along with you should go on the pleasurable get the job done.
    online Casinos mit Startguthaben ohne einzahlung
  23. brad.haddon234 at 16:06 PM on 7 January, 2016
    Its an extraordinary delight perusing your post.Its loaded with data I am searching for and I want to post a remark that "The substance of your post is marvelous" Great work. Spring Web Design
  24. japan.comp234 at 22:27 PM on 7 January, 2016
    A debt of gratitude is in order for sharing the information, keep doing awesome... I truly delighted in investigating your site. great asset... Venus Factor Review
  25. japan.comp234 at 19:56 PM on 8 January, 2016
    Awesome article! I want people to know just how good this information is in your article. It’s interesting, compelling content. Your views are much like my own concerning this subject. Tang Group of Companies Redhill Condo
  26. japan.comp234 at 19:17 PM on 11 January, 2016
    I was reading your article and wondered if you had considered creating an ebook on this subject. Your writing would sell it fast. You have a lot of writing talent. seriöse Online Casino
  27. japan.comp234 at 18:23 PM on 12 January, 2016
    Wow i can say that this is another great article as expected of this blog.Bookmarked this site..
  28. japan.comp234 at 21:32 PM on 18 January, 2016
    I found your this post while searching for information about blog-related research ... It's a good post .. keep posting and updating information. how to get followers on instagram
  29. japan.comp234 at 19:14 PM on 21 January, 2016
    This is very interesting content! I have thoroughly enjoyed reading your points and have come to the conclusion that you are right about many of them. You are great. hampton bay lighting
  30. amsbosstoolsmobi at 18:08 PM on 23 January, 2016
    You have a very inspiring way of exploring and sharing thoughts. Really Motivating.
    startup investment platform
  31. amsbosstoolsmobi at 16:47 PM on 25 January, 2016
    I really love the quality writing as offered on this post, cheers to the writer.
    Buy High Pagerank Backlinks
  32. japan.comp234 at 18:59 PM on 29 January, 2016
    You know your projects stand out of the herd. There is something special about them. It seems to me all of them are really brilliant! internet marketing agency
  33. japan.comp234 at 19:45 PM on 30 January, 2016
    Great Information sharing .. I am very happy to read this article .. thanks for giving us go through info.Fantastic nice. I appreciate this post. geniux supplement review - bonuses
  34. The best part, most of them will be available gain free twitter followers instantly to you through the MOOC for free! Those purchasing the MOOC will receive special tools, templates, and videos to enhance your learning buy quality twitter followers experience.
  35. In completing this course you will buy real twitter followers review develop a fuller understanding of the data and will be able to increase the effectiveness of your content strategy by making better decisions and spotting crises before they get real twitter followers fast happen!
  36. MOOC 2 bonus content in the paid toolkit includes track followers twitter access to Semantria's analytics engine to extract some data on the markets you are developing and have how to get more real twitter followers it analyzed.
  37. By enrolling in this course, you will be given how to get targeted twitter followers access to IBM's Bluemix technology for one month for free as well as Lexalytics' Semantria check followers twitter tool.
  38. For those earning a Course Certificate, you will be given an track number of twitter followers additional five months of Bluemix and three months of Semantria at no cost with a special key buy twitter followers instantly code generated only for your email address.
  39. japan.comp234 at 22:48 PM on 2 February, 2016
    I appreciate this article for the all around examined substance and incredible wording. I got so included in this material that I couldn't quit perusing. I am inspired with your work and ability. Much thanks to you to such an extent. marco
  40. amsbosstoolsmobi at 18:46 PM on 3 February, 2016
    Thank you, I've been seeking for info about this subject matter for ages and yours is the best I have discovered so far.
    lettre en bois
  41. japan.comp234 at 17:55 PM on 4 February, 2016
    This was a really great contest and hopefully I can attend the next one. It was alot of fun and I really enjoyed myself.. ageless male
  42. There is so much in this article that I would never have thought of on my own. Your content gives readers things to think about in an interesting way. Thank you for your clear information.
  43. including reasonable comments here... aftermarket car parts
  44. japan.comp234 at 20:17 PM on 3 March, 2016
    I have read a few of the articles on your website now, and I really like your style of blogging. I added it to my favorites blog site list and will be checking back soon. Please check out my site as well and let me know what you think. Holiday
  45. japan.comp234 at 19:04 PM on 7 March, 2016
    I know your expertise on this. I must say we should have an online discussion on this. Writing only comments will close the discussion straight away! And will restrict the benefits from this information. los angeles varicose vein center
  46. It proved to be Very helpful to me and I am sure to all the commentators here!
    auto insurance quotes without personal information
  47. japan.comp234 at 19:50 PM on 9 March, 2016
    Only aspire to mention ones content can be as incredible. This clarity with your post is superb and that i may think you’re a guru for this issue. High-quality along with your concur permit me to to seize your current give to keep modified by using approaching blog post. Thanks a lot hundreds of along with you should go on the pleasurable get the job done. This Site
  48. japan.comp234 at 19:22 PM on 10 March, 2016
    Good post but I was wondering if you could write a litte more on this subject? I’d be very thankful if you could elaborate a little bit further. Appreciate it! 100k Factory Ultra Edition review
  49. Thanks for the nice blog. It was very useful for me. I'm happy I found this blog. Thank you for sharing with us,I too always learn something new from your post.
    Weight Loss For Women
  50. japan.comp234 at 20:14 PM on 11 March, 2016
    Positive site, where did u come up with the information on this posting? I'm pleased I discovered it though, ill be checking back soon to find out what additional posts you include. Salesenvy Review

1  2  Next

Comments Policy

Post a Comment

You need to be logged in to post a comment. Login via the left margin or register a new account.