Extreme Weather Events: What are the Odds?

March 27, 2014

Above, graph from James Hansen illustrating the shifting bell curve of extremes as mean global temperatures rise.
Although the rise is only about a degree C for now, the shift in extreme events on the warm side means more and more occasions where human systems and infrastructure are hit by conditions not seen in human experience.

Stefan Rahmstorf in RealClimate:

Does global warming make extreme weather events worse? Here is the #1 flawed reasoning you will have seen about this question: it is the classic confusion between absence of evidence and evidence for absence of an effect of global warming on extreme weather events. Sounds complicated? It isn’t. I’ll first explain it in simple terms and then give some real-life examples.

The two most fundamental properties of extreme events are that they are rare (by definition) and highly random. These two aspects (together with limitations in the data we have) make it very hard to demonstrate any significant changes. And they make it very easy to find all sorts of statistics that do not show an effect of global warming – even if it exists and is quite large.

Would you have been fooled by this?

Imagine you’re in a sleazy, smoky pub and a stranger offers you a game of dice, for serious money. You’ve been warned and have reason to suspect they’re using a loaded dice here that rolls a six twice as often as normal. But the stranger says: “Look here, I’ll show you: this is a perfectly normal dice!” And he rolls it a dozen times. There are two sixes in those twelve trials – as you’d expect on average in a normal dice. Are you convinced all is normal?

You shouldn’t be, because this experiment is simply inconclusive. It shows no evidence for the dice being loaded, but neither does it provide real evidence against your prior suspicion that the dice is loaded. There is a good chance for this outcome even if the dice is massively loaded (i.e. with 1 in 3 chance to roll a six). On average you’d expect 4 sixes then, but 2 is not uncommon either. With normal dice, the chance to get exactly two sixes in this experiment is 30%, with the loaded dice it is 13%[i]. From twelve tries you simply don’t have enough data to tell.


In 2005, leading hurricane expert Kerry Emanuel (MIT) published an analysis showing that the power of Atlantic hurricanes has strongly increased over the past decades, in step with temperature. His paper in the journal Nature happened to come out on the 4th of August – just weeks before hurricane Katrina struck. Critics were quick to point out that the power of hurricanes that made landfall in the US had not increased. While at first sight that might appear to be the more relevant statistic, it actually is a case like rolling the dice only twelve times: as Emanuel’s calculations showed, the number of landfalling storms is simply far too small to get a meaningful result, as those data represent “less than a tenth of a percent of the data for global hurricanes over their whole lifetimes”. Emanuel wrote at the time (and later confirmed in a study): “While we can already detect trends in data for global hurricane activity considering the whole life of each storm, we estimate that it would take at least another 50 years to detect any long-term trend in U.S. landfalling hurricane statistics, so powerful is the role of chance in these numbers.” Like with the dice this is not because the effect is small, but because it is masked by a lot of ‘noise’ in the data, spoiling the signal-to-noise ratio.

Heat records

The number of record-breaking hot months (e.g. ‘hottest July in New York’) around the world is now five times as big as it would be in an unchanging climate. This has been shown by simply counting the heat records in 150,000 series of monthly temperature data from around the globe, starting in the year 1880. Five times. For each such record that occurs just by chance, four have been added thanks to global warming.

You may be surprised (like I was at first) that the change is so big after less than 1 °C global warming – but if you do the maths, you find it is exactly as expected. In 2011, in the Proceedings of the National Academy we described a statistical method for calculating the expected number of monthly heat records given the observed gradual changes in climate. It turns out to be five times the number expected in a stationary climate.

Given that this change is so large, that it is just what is expected and that it can be confirmed by simple counting, you’d expect this to be uncontroversial. Not so. Our paper was attacked with astounding vitriol by Roger Pielke Jr., with repeated false allegations about our method (more on this here).

European summer temperatures for 1500–2010. Vertical lines show the temperature deviations from average of individual summers, the five coldest and the five warmest are highlighted. The grey histogram shows the distribution for the 1500–2002 period with a Gaussian fit shown in black. That 2010, 2003, 2002, 2006 and 2007 are the warmest summers on record is clearly not just random but a systematic result of a warming climate. But some invariably will rush to the media to proclaim that the 2010 heat wave was a natural phenomenon not linked to global warming. (Graph from Barriopedro et al., Science 2011.)

Heat records can teach us another subtle point. Say in your part of the world the number of new heat records has been constant during the past fifty years. So, has global warming not acted to increase their number? Wrong! In a stationary climate, the number of new heat records declines over time. (After 50 years of data, the chance that this year is the hottest is 1/50. After 100 years, this is reduced to 1/100.) So if the number has not changed, two opposing effects must have kept it constant: the natural decline, and some warming. In fact, the frequency of daily heat records has declined in most places during the past decades. But due to global warming, they have declined much less than the number of cold records, so that we now observe many more hot records than cold records. This shows how some aspects of extreme events can be increased by global warming at the same time as decreasing over time. A curve with no trend does not demonstrate that something is unaffected by global warming.


Drought is another area where it is very easy to over-interpret statistics with no significant change, as in this recent New York Times opinion piece on the serious drought in California. The argument here goes that man-made climate change has not played “any appreciable role in the current California drought”, because there is no trend in average precipitation. But that again is a rather weak argument, because drought is far more complex than just being driven by average precipitation. It has a lot to do with water stored in soils, which gets lost faster in a warmer climate due to higher evaporation rates. California has just had its warmest winter on record. And the Palmer Drought Severity Index, a standard measure for drought, does show a significant trend towards more serious drought conditions in California.

The cost of extreme weather events

If an increase in extreme weather events due to global warming is hard to prove by statistics amongst all the noise, how much harder is it to demonstrate an increase in damage cost due to global warming? Very much harder! A number of confounding socio-economic factors clouds this issue which are very hard to quantify and disentangle. Some factors act to increase the damage, like larger property values in harm’s way. Some act to decrease it, like more solid buildings (whether from better building codes or simply as a result of increased wealth) and better early warnings. Thus it is not surprising that the literature on this subject overall gives inconclusive results. Some studies find significant damage trends after adjusting for GDP, some don’t, tempting some pundits to play cite-what-I-like. The fact that the increase in damage cost is about as large as the increase in GDP (as recently argued at FiveThirtyEight) is certainly no strong evidence against an effect of global warming on damage cost. Like the stranger’s dozen rolls of dice in the pub, one simply cannot tell from these data.

The emphasis on questionable dollar-cost estimates distracts from the real issue of global warming’s impact on us. The European heat wave of 2003 may not have destroyed any buildings – but it is well documented that it caused about 70,000 fatalities. This is the type of event for which the probability has increased by a factor of five due to global warming – and is likely to rise to a factor twelve over the next thirty years. Poor countries, whose inhabitants hardly contribute to global greenhouse gas emissions, are struggling to recover from “natural” disasters, like Pakistan from the 2010 floods or the Philippines and Vietnam from tropical storm Haiyan last year. The families who lost their belongings and loved ones in such events hardly register in the global dollar-cost tally.

It’s physics, stupid!

While statistical studies on extremes are plagued by signal-to-noise issues and only give unequivocal results in a few cases with good data (like for temperature extremes), we have another, more useful source of information: physics. For example, basic physics means that rising temperatures will drive sea levels up, as is in fact observed. Higher sea level to start from will clearly make a storm surge (like that of the storms Sandy and Haiyan) run up higher. By adding 1+1 we therefore know that sea-level rise is increasing the damage from storm surges – probably decades before this can be statistically proven with observational data.

There are many more physical linkages like this – reviewed in our recent paper A decade of weather extremes. A warmer atmosphere can hold more moisture, for example, which raises the risk of extreme rainfall events and the flooding they cause. Warmer sea surface temperatures drive up evaporation rates and enhance the moisture supply to tropical storms. And the latent heat of water vapor is a prime source of energy for the atmosphere. Jerry Meehl from NCAR therefore compares the effect of adding greenhouse gases to putting the weather on steroids.

Yesterday the World Meteorological Organisation published its Annual Statement on the Climate, finding that “2013 once again demonstrated the dramatic impact of droughts, heat waves, floods and tropical cyclones on people and property in all parts of the planet” and that “many of the extreme events of 2013 were consistent with what we would expect as a result of human-induced climate change.”

With good physical reasons to expect the dice are loaded, we should not fool ourselves with reassuring-looking but uninformative statistics. Some statistics show significant changes – but many are simply too noisy to show anything. It would be foolish to just play on until the loading of the dice finally becomes evident even in highly noisy statistics. By then we will have paid a high price for our complacency.


15 Responses to “Extreme Weather Events: What are the Odds?”

  1. Andy Lee Robinson Says:

    We’re not just seeing more sixes, but it’s the sevens that’ll get us!

  2. One problem with this data. The public generally can’t read even simple graphs. Only 15 percent could read a bus schedule. So this article is way over the heads of the 99 percent.

    I’d say stick to simple probabilities for the general public. The likelihood that we can get all of these “once in a century” weather events in any given year strictly by chance with no real change in the climate is less than one in a million. You’re going to bet your kid’s future on winning the lottery with those odds?

  3. The problem is very few understand the math in two particular areas, probability and statistics and compound growth and exponentials. Ask anyone how to predict the probability of an event when the mean is shifted. Ask how many years remaining until half of starting amount x is gone when consuming y percent per period. This is math. Then there are errors understanding data. A tornado researcher knows tornado data errors. A drought researcher knows drought. A political scientist I’d equipped to know neither. Proceeding without caution in an unknown field is foolhardy. Witness Muller.

  4. redskylite Says:

    “The evidence is irrefutable” – Quite a good video from National Geographic for those who dislike reading graphs:


  5. […] Above, graph from James Hansen illustrating the shifting bell curve of extremes as mean global temperatures rise.Although the rise is only about a degree C for now, the shift in extreme events on the warm side means more and more occasions where human systems and infrastructure are hit by conditions not seen in human experience.  […]

  6. The problem is not (only) statistics. The problem is physics – understanding how global warming will affect of extreme events (two processes with different signs: increased energy, decrease gradient).

    1. The main controversy is between eminent scientists such as Rahmstorf, Emanuel – versus Knutson, Landsea (not Pielke Jr.). Changes can be exponential and logarithmic but even bell shaped …

    Knutson (http://yosemite.epa.gov/ee/epa/eerm.nsf/vwAN/EE-0566-103.pdf/$file/EE-0566-103.pdf):
    “These damage potential projections do not include important influences such as sea level rise, coastal development, and societal adaptation.”

    “One reason this approach is often favored in the case of climate change is that one assumes that the fundamental laws are more likely to be applicable in a changed climate than empirical relations derived by training a statistical model on past climate data alone.”

    “However, it is possible that more dramatic future changes could occur over the 21st century. While, in my opinion, these more dramatic changes remain speculative, they are at least plausible enough to merit discussion here.”

    “First, it is possible that 21st century changes in tropical cyclones will be less potentially damaging than the scenarios outlined in the projections section. For example, some studies suggest that TC activity in some basins, such as the NW Pacific and North Atlantic, could shift eastward away from current landfalling regions and thus perhaps reduce the percentage of storms that make landfall in major population regions. Global climate transient sensitivity or sea level rise could be at the low end, or even lower than, the range shown in IPCC …”

    “ Alternatively, it is also possible that the reverse could be true in these cases, i.e., that transient climate sensitivity, future greenhouse gas concentrations, sea level rise, and so forth could be higher than expected, or even that storm tracks could shift systematically more toward major landfalling regions, in contrast to a number of current projections.”

    “… intensity projected for the Atlantic basin showed relatively small changes in some studies, ranging even to negative values for some individual models that were analyzed….”

    2. Hasegawa et al. 2013., Drastic shrinking of the Hadley circulation during the mid-Cretaceous Supergreenhouse (http://www.clim-past.net/8/1323/2012/cp-8-1323-2012.pdf). n this work it was found that as a result of a strong warming instead of Hadley circulation has developed Farrell circulation – a warm temperate climate zone – with dominant maritime climate (deficient in hurricanes) also strongly reducing the frequency and magnitude of heat waves.

    3. California is not the whole United States. I remind you:

    (http://scienceblogs.com/gregladen/2014/03/01/a-letter-from-john-holdren-regarding-roger-pielke-jrs-statements/) :
    “Similarly, long-term trends (1925–2003) of hydrologic droughts based on model derived soil moisture and runoff show that droughts have, for the most part, become shorter, less frequent, and cover a smaller portion of the U.S. over the last century (Andreadis and Lettenmaier, 2006). The main exception is the Southwest and parts of the interior of the West, where increased temperature has led to rising drought trends (Groisman et al., 2004; Andreadis and Lettenmaier, 2006).”

  7. P.S. But California makes me think (most) to this paper:
    Dev Niyogi, Yongkang Xue, Sethu Raman, North Carolina State University, University of California at Los Angeles (http://ams.confex.com/ams/pdfpapers/38448.pdf):
    “Often, despite dramatic leaf level impacts due to climate changes, the natural ecosystem tends to buffer and does not show a dramatic response. Our analysis suggests that the interactions between the biotic and abiotic changes tend to have a compensatory /antagonistic response. This reduces the effect of the variable change on the overall system response.”

  8. Dan Pangburn Says:

    The warming trend since the depths of the Little Ice Age, and why the warming stopped in 2001, are accurately (95% correlation since before 1900) explained by only two drivers.

    CO2 is not one of them.

    Search AGWunveiled to see what they are.

    • dumboldguy Says:

      “Nothing better than the smell of napalm burning in the morning”. Ooops, sorry—-that’s the line from Apocalypse Now. What I meant to say was “Nothing better than the smell of another denier troll brain frying in the morning”.

      Yes, yet another ENGINEER denier troll (mechanical), has popped out from under the bridge. He is a signer of the discredited Oregon Petition and a poster of the usual cherry-picked data (with distorted interpretations) that we have dealt with so many times on Crock. Ho-hum. He is easy to google, and apparently thinks posting comments and cherry-picked data on denier sites means they are somehow true.

      Perhaps one of the best links is this one, in which Dan displays a persistence in the face of truth that is reminiscent of our unlamented and departed daveburton.

      whatsupwiththatwatts.blogspot.com/…/open-letter-to-dan-pangburn-et-al-re. html‎

    • dumboldguy Says:

      I had composed a lengthier reply, but it disappeared somehow. Dan’s comment is not worth taking the time to reconstruct my original reply, so let me just summarize.

      Pangburn is a denier troll—-an engineer (mechanical) and a signer of the discredited Oregon Petition. He does much posting on denier sites, and anyone who googles his “stuff” will see the same old cherry-picked and distorted horsepucky that we have dealt with on Crock so many times. Ho-Hum. Here’s a good link to some debunking of Pangburn, and it’s reminiscent of the kind of “thinking” that we got from daveburton. The mindless energizer bunnies of AGW denial are legion.

      whatsupwiththatwatts.blogspot.com/…/open-letter-to-dan-pangburn-et-al-re. html‎

    • dumboldguy Says:

      Don’t waste your time looking at AGWunveiled. Pangburn is a denier troll, a mechanical ENGINEER who signed the discredited Oregon Petition. He is a prolific commenter on denier sites and has nothing to offer but the same old cherry-picked date and distorted interpretations that we have seen so many times before on Crock.

      • I looked at one reference from semczys, the first. It’s an Atlantic hurricane study. He picked every quote he could to downplay huuricane impacts. He didn’t quote the line that says their is an increase in category 4 and higher hurricanes. This study is consistent with what CC has reported. Less weak huuricane frequency, higher strong hurricane frequency. Cherry picking.

        • dumboldguy Says:

          Cherry picking is all I’ve ever found when looking at his “stuff” in the past. that’s why I no longer bother—-he’s just another troll with nothing to say.

      • greenman3610 Says:

        fresh meat

  9. […] 2014/03/27: PSinclair: Extreme Weather Events: What are the Odds? […]

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