Cliff Mass is at it again, trying to tell us that the recent extreme heat in the northwest is unrelated to man-made global warming. What’s surprising is that he actually had this to say in a recent blog post:



the more extreme the weather anomaly, the less likely it is to be caused by human-induced (anthropogenic) global warming.



The truth is exactly the opposite.

I have an idea where Cliff Mass might have gotten his wrong idea. Suppose the phenomenon is governed by the normal probability distribution, and that we choose our scale so that the mean is zero and the standard deviation is 1. Let’s say that we limit “extreme” to values which are at least two standard deviations above the historical mean.

Then we can consider what happens when we increase the mean, say, by 1 standard deviation. We won’t change the cutoff limit of “extreme,” we’ll just change the probability of its occurence. Here’s the probability of occurence for extremes from 2 to 6 standard deviations, for the unchanged mean (in blue) and after the mean increases (in red):

Increasing the mean makes all extremes more likely. But, as expected, as the extreme gets more and more extreme it gets less and less likely.

The relevant question is, when we increase the mean, by how much does the probability increase? Perhaps Cliff Mass is considering the difference in probability, i.e. the probability after increasing the mean, minus the probability before. Here’s a graph:

The more extreme the extreme, the less is the absolute increase in probability.

But that’s not what counts. What matters is the ratio of the probabilities, i.e. the probability after increasing the mean divided by the probability before:

Increasing the mean by 1 standard deviation will makes a 2-sigma extreme 7 times as likely. But it makes a 3-sigma extreme 17 times as likely, a 4-sigma extreme 43 times as likely, a 5-sigma extreme 110 times as likely, and a 6-sigma extreme 290 times as likely.

The truth is, that the more extreme the weather anomaly, the more likely it is to be caused by human-induced (anthropogenic) global warming.

But perhaps Cliff Mass suffers from another misconception. Maybe he’s so intent on denying the link between global warming and extremes that he limits himself to the narrowest possible definition of “caused by.” Maybe he actually believes that extreme heat cannot possibly be caused by global warming because we get our energy from the sun — so all extreme heat events are “caused” by solar radiation.

That seems like claiming that all lung cancer is “caused” by genetic defects of lung cells, so no lung cancer is “caused” by cigarette smoking.

I prefer a more relevant definition: that without man-made global warming it wouldn’t have happened. Clearly, without man-made global warming the majority of extreme heat events, and the vast majority of “extreme extreme” heat events, wouldn’t have happened.