One of the most dangerous effects of climate change is its impact on extreme events. The extra energy that’s present on a warmer world doesn’t distribute itself uniformly – it can come out in large bursts, manifesting itself as heat waves, floods, droughts, hurricanes, and tornadoes, to name a few. Consequently, warming the world by an average of 2 degrees is a lot more complicated than adding 2 to every weather station reading around the world.

Scientists have a difficult time studying the impacts of climate change on extreme events, because all these events could happen anyway – how can you tell if Hurricane Something is a direct result of warming, or just a fluke? Indeed, for events involving precipitation, like hurricanes or droughts, it’s not possible to answer this question. However, research is advancing to the point where we can begin to attribute individual heat waves to climate change with fairly high levels of confidence. For example, the recent extended heat wave in Texas, which was particularly devastating for farmers, probably wouldn’t have happened if it weren’t for global warming.

Extreme heat is arguably the easiest event for scientists to model. Temperature is one-dimensional and more or less follows a normal distribution for a given region. As climate change continues, temperatures increase (shifting the bell curve to the right) and become more variable (flattening the bell curve). The end result, as shown in part (c) of the figure below, is a significant increase in extremely hot weather:

Now, imagine that you get a bunch of weather station data from all across the world in 1951-1980, back before the climate had really started to warm. For every single record, find the temperature anomaly (difference from the average value in that place and on that day of the year). Plot the results, and you will get a normal distribution centred at 0. So values in the middle of the bell curve – i.e., temperatures close to the average – are the most likely, and temperatures on the far tails of the bell curve – i.e. much warmer or much colder than the average – are far less likely.

As any statistics student knows, 99.7% of the Earth’s surface should have temperatures within three standard deviations of the mean (this is just an interval, with length dependent on how flat the bell curve is) at any given time. So if we still had the same climate we did between 1951 and 1980, temperatures more than three standard deviations above the mean would cover 0.15% of the Earth’s surface.

However, in the past few years, temperatures three standard deviations above average have covered more like 10% of the Earth’s surface. Even some individual heat waves – like the ones in Texas and Russia over the past few years – have covered so much of the Earth’s surface on their own that they blow the 0.15% statistic right out of the water. Under the “old” climate, they almost certainly wouldn’t have happened. You can only explain them by shifting the bell curve to the right and flattening it. For this reason, we can say that these heat waves were caused by global warming.

Here’s a graph of the bell curves we’re talking about, in this case for the months of June, July, and August. The red, yellow and green lines are the old climate; the blue and purple lines are the new climate. Look at the area under the curve to the right of x = 3: it’s almost nothing beneath the old climate, but quite significant beneath the new climate.

Using basic statistical methods, it’s very exciting that we can now attribute specific heat waves to climate change. On the other hand, it’s very depressing, because it goes to show that such events will become far more likely as the climate continues to change, and the bell curve shifts inexorably to the right.

References:

• Hansen, Sato, and Ruedy. (2012). Perceptions of Climate Change:
  The New Climate Dice. In press at PNAS, currently available on arXiv.
• Coumou and Rahmstorf. (2012). A decade of weather extremes. Nature Climate Change (advance online publication).
• See also discussion of the latter paper by the authors.