The great challenge of understanding climate is its complexity. Everything influences everything else. Retreating glaciers, deforestation of the Amazon, El Nino and ocean currents, desertification and shrinkage of the Aral and Caspian Seas, it’s one big baffling and ever-changing ball of string that no one, it seems, can authoritatively unravel.
But the power of the maximum entropy principle lies in doing what seems impossible on a detail level, finding a reliable rule in the chaos. When a system is viewed from the right perspective, the MEP can reduce an insanely complex problem to a smooth distribution of a single variable.
I have followed the debate about global warming (and other kinds of climate change) for a number of years. Like most people, I felt that the technical details were largely outside my domain of expertise. However, in fields like epidemiology, I have been shocked at how easily a new approach could be found. The power of the MEP is tremendous! So I was keen to see if something similar might be attempted in climatology, and for years kept a lookout for relevant papers.
Starting in November 2009, I investigated a paper by a Hungarian physicist, Ferenc Miskolczi, which invoked the MEP and promised a radically new view of climate. Miskolczi argued that maximum entropy considerations would prevent water vapor from being taken up in the huge quantities that the modelers predicted. Global warming would be averted by the MEP.
Miskolczi’s paper was focused on radiation physics, a highly technical approach. When he was discouraged by NASA, his employer, from publishing it, he quit and did so anyway. His argument was not well received by mainstream climatologists, and has not so far changed very many minds. But there were hints in the ensuing debate of some simpler possibilities not considered by either side. Miskolczi argued that the maximum entropy principle imposes a strict balance in the atmosphere between kinetic energy and gravitational potential energy, and maintaining this balance limits water vapor uptake. This particular application of the MEP is known as the ‘virial theorem’.
What piqued my curiosity was that in the midst of the debate, a senior NASA climatologist remarked that he had never seen the virial theorem applied to Earth’s atmosphere. Here was an application of the maximum entropy principle crying out for further investigation!
The result, after months of effort and more months of logistical delays, is my own paper on the subject. I have come to realize that Miskolczi was right in at least one of his claims. Maximum entropy considerations do limit the atmosphere’s ability to absorb more water vapor. The challenge is to show it in a simple way. By comparison with Miskolczi’s approach, my argument is almost absurdly straightforward.
All global circulation models (GCM) rely on a kind of physics short-cut, something called the hydrostatic approximation. After trying to re-create the basic model rules on a spreadsheet, I realized that this short-cut is inappropriate for use in global warming studies. It makes them fatally flawed, exaggerating the amount of warming caused by greenhouse gases by a factor of 3 to 5.
Here is the chief symptom that something has gone wrong. The modelers all report that if CO2 is added to the model atmosphere, then after several decades, temperatures go up everywhere — at the poles and the equator, both at sea level and high up in the atmosphere.
The hydrostatic approximation imposes a strict proportionality between temperature and air density. If temperatures go up, air density must go down. So if temperatures go up everywhere, air density goes down everywhere. But then where exactly did the air go in the model? And where should it go? I believe the virial theorem, the maximum entropy principle, and some common sense, together provide the answer.
Readers not familiar with the power of the MEP will no doubt be tempted to label this just more crazy ‘denialism’. But sometimes a very simple answer gets overlooked. Please read the paper and judge for yourself.