Decoding the Hockey Stick – Part 1

There is a lot of discussion about climate change these days. It’s quite a polarizing topic, actually. It’s astounding to me to see how science – or a scientific result – is suddenly a taboo topic in polite company, just like politics and religion. It upsets me. Why are we not interested in the science? Why can’t I talk about it?

Well, I talk about it anyway, at least to those who are interested in listening. If people want to argue, then I usually shut down. It’s not that I don’t feel that such discussion isn’t worthwhile, and with some people I will try to be engaged, but honestly, most of the arguments stem from a fundamental misunderstanding of how science works and how scientists look at data. It’s frustrating, and it’s not something easily explained. There’s also a certain amount of mistrust of science, which I find disturbing.

Rather than trying to explain the entire body of climate science, perhaps I’ll take a moment to talk about one aspect of the climate debate. One thing that some argue is completely bunk.

The Hockey Stick.

Most everyone has heard of this. I’m not talking about the game of Hockey, here. I’m talking about the Hockey Stick. Considered by some to be the smoking gun proving global warming and by others as manipulated data. The gist of it is that if we can look at average annual temperatures over the last several hundred years, we see that there’s some fluctuations around an average, but that the last few decades have been getting warmer and warmer, more so than at any other time on record. This, then, is the rapid global warming that everybody is arguing about (but that you don’t talk about with your family at Christmas).

Well, where does this come from? When you see images of the Hockey Stick, you see time along the bottom and you expect to see temperature on the vertical axis, so that when the lines go up, you’re looking at warmer temperatures. What the vertical axis shows, however, is what’s called the “temperature anomaly” (although it is, at least, labeled in degrees). What the heck is that?

The temperature anomaly is the difference between any given year’s average annual temperature and the average of all the annual temperatures over a specified period of time (sometimes from 1951-1980, sometimes from 1902-1980, sometimes something else, always defined). During that span of time, temperatures were relatively constant. The decision to use this period of time as a baseline by which to compare everything else was arbitrary. (Or I assume, so. I wasn’t there when this decision was made!) The fact is, they just needed a ‘zero’ point against which to compare everything else. Presumably, records during that period of time were precise and accurate enough for the researchers to be confident in them.


PRECISION and ACCURACY: These are two terms that are sometimes confused for one another, but in science have very specific meanings. Accuracy is getting the right answer. It’s hitting the bullseye. In the case of temperature, it reflects how correct the temperature reading on any given thermometer is. Precision describes how well the same answer can be found. If you shoot ten arrows at a target, precision is about how close together those ten arrows are. In science, it’s about putting the same thermometer in the same freezer on different days and getting the same temperature reading, or perhaps putting ten seemingly identical thermometers in the freezer at once and seeing how similar all the readings are. Precision is shown on graphs (like the Hockey Stick) with error bars or confidence envelopes.

What’s important is to realize that something can be precise and not accurate and vice versa. I can shoot ten arrows at a target and they can all clump to the upper right of the bullseye, which I was aiming for. That’s precise, but not accurate. Or I can shoot ten arrows and have them spread out, surrounding the bullseye. In this case, they’re accurate, but not precise.

Precision and accuracy is a big deal in science, and particularly in climate science. Both of these are called into question when the legitimacy of the interpretation of the Hockey Stick is discussed.


In order to calculate a temperature anomaly, of course, one must first come up with a value for average annual temperature. For more recent years, this comes from instrumental records, aka, thermometers. One of the difficulties faced, however, is how to calculate a global average annual temperature, especially when temperatures vary all over the world, from day to day and season to season. And really, how can you compare annual temperatures in the arctic with annual temperatures on the equator? And then, throw on top of that precision issues with the thermometers themselves. Geez! How do you handle all those data?

Well, it’s complicated. The first thing you have to do is normalize everything. Normalizing means to set everything up onto the same scale so that they can be compared easily. This is where the temperature anomaly comes in. By using an average of a particular set of years and then showing all your annual weather data relative to that, it becomes possible to compare Arctic temperatures with equatorial temperatures. In the Arctic, a temperature anomaly of 1 degree might mean a change from -5 to -4 degrees, whereas on the Equator, it’s a change from 72 to 73 degrees. By normalizing using the temperature anomaly, we can easily see that the temperature went up one degree in both places.

The normalized anomalies can be averaged for specific regions (to help even out the differences between regions that have tons of thermometers and regions that don’t), and then for the whole world to get at a global temperature change. That’s what we’re really interested in.

When you calculate all these averages, you can also calculate the variation of the values. For example, in the Arctic, the anomaly could be 2 degrees, whereas on the Equator it could be 1 degree. You can calculate the average (1.5) but also calculate some statistics to represent the variation. This is where error bars come in. Your average is 1.5, but the range is from 1 to 2 degrees, so you draw a little bar on the graph representing that. (This example is not real, of course. Standard deviation or standard error would be used in a real scientific study, but you get the idea.) The error bars can also be extended (or shortened) depending upon the known precision of the thermometer used.

What you wind up with is a lovely graph of squiggly lines representing the global temperature anomaly over time. A positive anomaly means warmer temperatures than in times past. A negative anomaly means colder temperatures. The Hockey Stick shows warmer temperatures than in the past, and things seem to be getting warmer.

One of the problems with the typical image of the Hockey Stick, when it’s flashed up in the news is that it almost always lacks the error bars. The error bars are important. When looking at instrumental records (thermometers), for which we have data going back into the late 19th century, we can see that the error bars get smaller and smaller over time. This is due to improvements in the technology of temperature measurement. But the errors are still there.

Average global temperature anomalies.

Error bars give you a possible range within which the actual ‘real’ measurement might be. That is to say, that even though there’s a point on the plot, it might not be in exactly the right spot. The error bars give you a measure of how inaccurate the data point might be. It’s possible for data points to show a nice complex pattern, but to have error bars so big, that the pattern might not be real.

I like to think of error bars as bumpers. Imagine that you put a string into the plot between the error bars and pull it tight. If it can make a flat line between the error bars, then the data don’t show any pattern. If you pull the string tight and it still has bends and peaks in it, then those features probably represent true variations.

In the case of the Hockey Stick, the upturn of the temperature anomalies in the last few decades is pretty compelling. With error bars, the increase in temperature anomalies might be a little smaller, but it is still there.

Average global temperature from instrumental records. Colored lines show different possible rates of warming.

But what does this mean? We see an increase in the temperature anomaly over the last few decades, but really, this plot doesn’t look so much like the Hockey Stick you’ve seen elsewhere. The full-blown Hockey Stick goes back about 600 years, but we didn’t have thermometers way back then. How can we measure mean annual global temperatures from that far back.

Alas, that’s a topic for another post.

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