Physics, Economics, and Hurricane Arguments

I just finished an interview, via Skype, that will eventually be up on the web. One question I was asked was how knowledge of one field feeds into thinking about another. It occurred to me that I had an interesting example, a case where two unrelated fields, both of which I have worked in, showed that two different arguments for a conclusion in a third field were both wrong.

The three fields are physics, economics, and climate science. The conclusion, widely repeated, is that global warming will result in either more frequent or more violent hurricanes, or both. The conclusion may, for all I know, be correct. Two common arguments for it, however, are both wrong.

The first argument is that hurricanes get their energy from heat, so can be expected to be more violent or more frequent if there is more heat to feed them. That sounds plausible—provided you don't know the relevant physics. A hurricane is a heat engine, converting thermal energy to mechanical energy in the form of moving air. A heat engine does not, indeed cannot, simply convert thermal energy to work—one that did that and nothing else, say a ship that ran without fuel on the heat of the ocean, would be what is called a perpetual motion machine of the second kind and is impossible because it violates the second law of thermodynamics.

A heat engine works by taking heat from a high temperature source, turning some of it into work, and dumping the rest into a lower temperature sink. The amount of work it can get out depends not simply on the temperature of the source but on the temperature difference (if my memory from long ago studies is correct, actually the difference in 1/T) between source and sink. So if you warm both source and sink, air and sea in the case of a hurricane, there is no particular reason to expect that more work will be available, hence no particular reason to expect hurricanes to get either more frequent or more violent.

The second argument is empirical. It is claimed—I presume correctly—that on average you get more hurricanes in hot weather. The obvious conclusion is that if earth's climate gets warmer, we will have more (or more powerful) hurricanes. This time it is economics, in particular the history of ideas in economics, that points out the mistake.

Quite a long time ago, William Phillips, an economist from New Zealand, noticed an interesting empirical relation—on average, when inflation was high, unemployment was low. The relation got labeled the "Phillips Curve." The obvious conclusion was that one could hold down unemployment at the cost of tolerating some inflation. A variety of governments tried to implement such policies. Their failure in the U.S. got labeled "stagflation," a situation with both high unemployment and high inflation.

What was wrong with the Phillips Curve was not the empirical evidence but the causal conclusion. What was really going on, as the evidence is now widely interpreted, was that unemployment tended to be low when inflation was higher than people expected. That makes sense on a fairly simple model. If workers underestimate inflation, they will see wage offers as more attractive than they really are and so be more willing to accept them, less willing to wait for a better job, than they would be if they correctly estimated future inflation. If employers underestimate inflation, they will observe high demand for their products at current prices and see that as a reason to hire more workers and expand production.

Times when inflation is high are also, on average, times when it is higher than people expect, giving you the empirical relation Phillips had observed. But if a government tries to exploit the relation by maintaining an inflation rate of (say) five percent a year, after a while people adjust their expectations accordingly and the unemployment rate goes back up. Raise it to ten percent, unemployment falls briefly, people adjust their expectations, and unemployment goes back up again.

The same argument applies in the case of temperature and hurricanes. On average, times when air temperature are higher than normal are also times when the temperature difference between air and sea is larger than normal—the sea, after all, has enormous heat capacity, and so tends to average out short term fluctuations in air temperature. So the observation that hurricanes are more likely in hot weather does not imply that they would be more likely if both sea and air got warmer, as, in a global warming scenario, they do. 

None of this implies that global warming does not make hurricanes more frequent or more violent. I have seen empirical claims in both directions—both that hurricanes are and are not increasing—and do not know enough about the field to evaluate them. But it does mean that two apparently persuasive arguments for why we should expect such a relation are wrong. 

And in each case, I spotted the error because of my background in a different, in one case entirely unrelated, field.