The Hockey Stick

The significance for climate models and science communication

The climate scientist Michael Mann just won a protracted libel suit against people who called him dishonest and much worse. Mann is best known for his work on the “hockey stick”, a reconstruction of the past thousand years or so of global average temperature, estimated based on a variety of physical measurements used as proxies for temperature. It’s been disconcerting to see that many of my new-found fellow doubters of the zoonotic account of Covid origins are outraged about the verdict and, even worse, convinced that man-made climate change is a hoax. I’ll try here to explain the role played by the hockey stick and its uncertainties, in the hope that one or two minds may change.

The basic physics of why CO₂ emissions cause global warming has been known since at least 1896. In 1906 Svante Arrhenius* made a simple calculation of the magnitude that has held up well, both for predicting the warming that has already occurred and for agreement with the much more elaborate detailed models that have been made recently. The common impression that the predictions stem from the fancy models is just the opposite of the actual situation. The fancy models are used to check if something is wrong with Arrhenius’ simple prediction based on familiar physics and to predict features beyond global average temperature.

The fancy models have a number of approximate parameters in them. To get them to make realistic predictions they have to be trained on some actual temperature history. That training constrains the ranges of the parameters. Accurate temperature records are known for enough decades to allow that training.

What then is the role of the hockey stick— estimating temperatures in the past, outside the range used to train the models? There can be changes of either sign in temperature that occur fairly quickly for reasons not captured by the models. Any such random-looking effects spanning a few decades could throw the model-training off, either to over-estimate or underestimate future changes. The hockey stick represents a search for any such few-decade effects. If they were present it would imply that the error bars on the model estimates should be increased because there would be important noise in the training set. The proxy-based reconstructions don’t find much of anything along those lines.

Some of the most difficult parts of the reconstruction are essentially irrelevant. Any long-time drift over the last millennium is not part of the features affecting the model training set so it doesn’t really matter whether the reconstruction gets that accurately. It’s the decade-scale effects that matter.

Since I first posted this, I’ve been surprised to hear that highly educated quantitative people don’t know that the models have worked quite well at prediction, not just fitting old data. The key thing to test is how well the models predict temperature as a function of future changes in CO₂ and other “forcing” terms. Here are some key results from a comprehensive review. Given the striking increase in temperature in the last year, I think an updated figure would show the observation points increased compared to those shown here.

The attacks on Mann have often focused on a scandal over an email sent by a member of a research team that Mann was in, mentioning an attempt to “hide the decline”. The incident has been discussed in detail here. The “decline” was not a decline in temperature either recently or in the more distant past. It was a decline in a tree-ring proxy caused by stress when the the temperature increased too rapidly. (Tree-ring thickness usually increased with increasing temperature.) In other words, tree rings can sometimes fail to serve as good proxies. In principle if they were the only proxy that would increase the chances that some relevant previous change would have been missed. That would then mean that the error bars on the model predictions would be underestimated.

The key point here is that we are talking about slight effects on the already fairly large uncertainties in the predictions. We are not talking about a systematic error of either sign. So far as we can tell from recent changes the consensus models have probably somewhat underestimated the warming effect of our greenhouse emissions.

Still, the scandal provides a cautionary lesson for scientists. Trying to hide any effect, no matter how peripheral to the core question, is bad practice. If tree rings aren’t a consistent proxy it’s best to just be frank about that. The basic climate science stands without them. If it didn’t, it would still be right to be as open as possible.

*Arrhenius is not some minor figure fished out of obscurity for a special purpose. I am pretty sure that “Arrhenius” is by far the most commonly used personal name in my own regular publications, none of which concern climate. The typical temperature dependence of reaction rates is described by the Arrhenius form.