Heat Waves and Global Warming

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A new scientific report says that extreme heat waves will likely become much more common in the future, due to global warming. For instance, the sort of extremely hot day that used to occur only once in twenty years will likely become an every-other-year event by the end of the 21st century.

This may seem rather surprising. We have heard that Earth's average temperature will likely rise over the next century, but the amount sounds modest: only a few degrees, small compared to the 30 degree (Fahrenheit) swing in temperatures between day and night, or the 60 degree swing between winter and summer.

While rigorous climate modeling is very technical, it turns out that we can get a basic understanding of the reason for the dramatic increase in extremes using some very simple calculations, which are the focus of today's post.

The Associated Press ran a story summarizing thenew report from the Intergovernmental Panel on Climate Change.The report uses careful language to clarify the strength of the evidencefor each of its conclusions. The relevant quote for us is:

It is very likely that the length, frequency and/orintensity of warm spells, or heat waves, will increase over most landareas. Based on the A1B and A2 emissions scenarios, a 1-in-20 yearhottest day is likely to become a 1-in-2 year event by the end of the21st century in most regions, except in the high latitudes of theNorthern Hemisphere, where it is likely to become a 1-in-5 yearevent.

The report covers other weather phenomena besides heat waves, but Iwant to stick to heat extremes so that we do not get sidetracked bydiscussions about the physical mechanisms that might connect highertemperatures to more precipitation, more drought, or more storms.

Here's the basic idea for understanding how extremes get magnified:

• We start with a "bell shaped curve" representing the variety of temperatures we see in today's climate.
• We shift the curve to the right by a small amount, representing the rise in Earth's average temperature over the next century.
• We examine what happens to the high temperature part of the curve, i.e. to the frequency of heat extremes.

First, let's look at a picture.

I have labeled the vertical scale "hypothetical" frequency toemphasize that this is not a plot of real temperature data.It is just a "bell shaped curve" designed to illustrate the ideas.

The black line represents the original 20th century climatefor some hypothetical location, with an average temperature of 40degrees. The taller parts of the graph correspond to the more commontemperatures: in this location, most temperatures are between 0 and80, with temperatures as low as -40 or as high as +120 extremely rare.

The red line represents the climate at some future point whenthe average temperature has risen 5 degrees, to 45. In this example,we have not changed the shape of the curve at all: we have simplyshifted it five units to the right (real climate modeling alsoattempts to understand how the shape might change). This makes thetypical temperature range 5 to 85. Temperatures over 100 arerare, since both curves are close to zero near the righthand side of the chart.

Now let's now zoom in on the right-most part of the curve: the"right tail", representing the very hottest days.

Look at the blue line. Days over 110 are quite rare (about one in 12years for the black line), but they happen more than twice asoften under the red curve (about one in 5 years). So even a small shift inthe curve (5 degrees out of a typical spread of 80 is about a 6%shift) can produce a large change in extreme conditions (2.5 times asoften, in this example).

My example curves were drawn using a "normal" distribution,which is the widely used "bell-curve" shape of classical statistics,but there is no particular reason that real temperature data needs tobe shaped that way. Let's now look at some actual temperature data,and see if we can illustrate a 1-in-20 year event becoming a 1-in-2year event.

You can get real temperature readings from many sources. Somecountries make it particularly easy to download large amounts data for free.Australiahas a particularly user friendly site. I downloaded the daily maximumtemperature (degrees Celsius) in Melbourne, station number 086071, forthe years 1868 through 2010, inclusive, which provide 52,230 qualitychecked daily values with no missing values.

We will use the following R code to make the graphs. Asdiscussed in many previous posts, you can follow along by downloadingyour own completely free copy of the open source, high quality,statistical programming language R fromThe Comprehensive R Archive Network.

ds <- read.table("melbourne.tab", header=TRUE, sep="\t")dc <- 3.5 # shift in degrees Cpng('melbourne.png', 800, 500)par(mar=c(5, 5, 1, 1), cex=1.5, lwd=2)plot(density(ds$maxDayTempDegrC+dc), col="red",     xlab='Temperature (F)', ylab='Actual Frequency (%)')lines(density(ds$maxDayTempDegrC))dev.off()z <- rev(sort(ds$maxDayTempDegrC))[7] # 44.1 Cpre <- sum(ds$maxDayTempDegrC >= z)post <- sum((ds$maxDayTempDegrC+dc) >= z)print(c(pre, post, post/pre))png('melbourne2.png', 800, 500)par(mar=c(5, 5, 1, 1), cex=1.5, lwd=2)plot(density(ds$maxDayTempDegrC+dc), col="red",     xlim=c(40,50), ylim=c(0,0.006),     xlab='Temperature (F)', ylab='Actual Frequency (%)')lines(density(ds$maxDayTempDegrC))lines(c(z, z), c(0,0.005), col='blue')dev.off()

First, we plot the temperature distribution from 1868 through 2010 inblack, then overlay a shifted version of the curve in red, based onadding 3.5 degrees C to all the temperatures.

Next, we zoom in on the section above 40 Celsius (104 Fahrenheit):

The sample sizes for extreme events are by definition low,so by nature this sort of prediction isvery sensitive to the exact nature of the shift in the curve(i.e. does it also change its shape, not just slide over), as well asto where we draw the line to denote "extremes".

If we choose 42 C (108 F) as out threshold, days that hot orhotter would be expected to occur ten times more often in future thanin the past, because while only 40 past observations were that hot,400 future ones are.

If we want to look for a 1-in-20 year event in the historicaldata, we need a temperature threshold that is reached or exceeded only7 times among the 52,230 observations. That is 44.1 C in this data set(the vertical blue line in the last chart). Temperatures reach or exceed thisin the hypothetical future data set 109 times, which is 16 times moreoften, making it an almost every year occurrence!

Climate change is a complex subject, and careful data analysisand modeling require great technical sophistication. Nonetheless,these examples illustrate the simple point that while we may not knowthe exact amount of the impact, a relatively small shift in theaverage value of the temperature distribution can indeed produce verylarge increases in the relative frequency of rare events like heat waves.

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If you enjoyed this topic, you may also like Tracking Hurricane Irene.

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