One of the things that strikes me about discussions of climate change, especially from those who dismiss it as relatively harmless, is a widespread lack of understanding on how non-linear systems behave. Indeed, this seems to be one of the key characteristics that separate those who are alarmed at the prospect of a warming climate from those who are not.

At the AGU meeting this month, Kerry Emanuel presented a great example of this in his talk on “Hurricanes in a Warming Climate”. I only caught his talk by chance, as I was slipping out of the session in the next room, but I’m glad I did, because he made an important point about how we think about the impacts of climate change, and in particular, showed two graphs that illustrate the point beautifully.

Kerry’s talk was an overview of a new study that estimates changes in damage from tropical cyclones with climate change, using a new integrated assessment model. The results are reported in detail in a working paper at the World Bank.┬áThe report points out that the link between hurricanes and climate change remains controversial. So, while Atlantic hurricane power has more than doubled over the last 30 years, and model forecasts show an increase in the average intensity of hurricanes in a warmer world, there is still no clear statistical evidence of a trend in damages caused by these storms, and hence a great deal of uncertainty about future trends.

The analysis is complicated by several factors:

  • Increasing insurance claims from hurricane damage in the US have a lot to do with growing economic activity in vulnerable regions. Indeed, expected economic development in the regions subject to tropical storm damage means that there’s certain to be big increases in damage even if there were no warming at all.
  • The damage is determined more by when and where each storm makes landfall than it is by the intensity of the storm.
  • There simply isn’t enough data to detect trends. More than half of the economic damage due to hurricanes in the US since 1870 was caused by just 8 storms.

The new study by Emanuel and colleagues overcomes some of these difficulties by simulating large numbers of storms. They took the outputs of four different Global Climate Models, using the A1B emissions scenario, and fed them into a cyclone generator model to simulate thousands of storms, comparing the characteristics of these storms with those that have caused damage in the US in the last few decades, and then adjusting the damage estimates according to anticipated changes in population and economic activity in the areas impacted (for details, see the report).

The first thing to note is that the models forecast only a small change in hurricanes, typically a slight decrease in medium-strength storms and a slight increase in more intense storms. For example, at first sight, the MIROC model indicates almost no difference:

Probability density for storm damage on the US East Coast, generated from the MIROC model for current vs. year 2100, under the A1B scenario, for which this model forecasts a global average temperature increase of around 4.5C. Note that x axis is a logarithmic scale: 8 means $100 million, 9 means $1 billion, 10 means $10 billion, etc (source: Figure 9 in Mendelsohn et al, 2011)

Note particularly that at the peak of the graph, the model shows a very slight reduction in the number of storms (consistent with a slight decrease in the overall frequency of hurricanes), while on the upper tail, the model shows a very slight increase (consistent with a forecast that there’ll be more of the most intense storms). The other three models show slightly bigger changes by the year 2100, but overall, the graphs seem very comforting. It looks like we don’t have much to worry about (at least as far as hurricane damage from climate change is concerned). Right?

The problem is that the long tail is where all the action is. The good news is that there appears to be a fundamental limit on storm intensity, so the tail doesn’t really get much longer. But the problem is that it only takes a few more of these very intense storms to make a big difference in the amount of damage caused. Here’s what you get if you multiply the probability by the damage in the above graph:

Changing risk of hurricane damage due to climate change. Calculated as probability times impact. (Source: courtesy of K. Emanuel, from his AGU 2011 talk)

That tiny change in the long tail generates a massive change in the risk, because the system is non-linear. If most of the damage is done by a few very intense storms, then you only need a few more of them to greatly increase the damage. Note in particular, what happens at 12 on the damage scale – these are trillion dollar storms. [Update: Kerry points out that the total hurricane damage is proportional to the area under the curves of the second graph].

The key observation here is that the things that matter most to people (e.g. storm damage) do not change linearly as the climate changes. That’s why people who understand non-linear systems tend to worry much more about climate change than people who do not.


  1. Isn’t “Damage in US dollars” also related to the value or buying power of a US Dolllar? The Fed has been printing money hand over fist over the last three years, who knows what a dollar will buy in the future? Was the value of a US dollar included in those models?

  2. Klem, the “US Dollar” in the World Bank paper (Mendelsohn et al.) does not involve fluctuation of actual currency, inflation or deflation. In the description of how they used past economic data, they wrote: “Dollar values were updated to 2010 USD using GDP deflator”. “2010 USD” (at other times than the year 2010) is an imaginary concept and there is ambiguity, for inflation rate is different with respect to different goods (e.g. gold and petroleum). But the results seem relatively more robust using the imaginary concept than using the actual currency. Of course, it is a difficult problem for individuals to know how much dollars then need to keep in order to have a certain amount of “2010 USD” some time in the future.

  3. What they left out is that we are getting much better at protecting life and property from damage thanks to building codes and forecasting. When you ask people like Pielke and Emanuel to factor these in they throw up their hands and ask How? Until this is attacked you really cannot make damage estimates across years that are worth anything

  4. Pingback: Notes from Hurricane Sandy | Serendipity

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