GLOBAL WARMING MADE SIMPLE A. E. Snyder, Version 1.0

Complicated? The models that predict global warming are complicated. They do something very hard – predict how the climate will evolve in detail over hundreds of years. Like all models, they are subject to error, they are never complete, and not all their many predictions work out. Those opposed to doing anything about global warming exploit these inevitable flaws to confuse the public and delay action. There is, however, no serious disagreement among the scientist (climatologists) who work on the problem that global warming is happening. Why is that?

Simple Because the basic science that underlies global warming is simple, not radical and not new. In 1824, Fourier calculated the-the earth would be much cooler without any carbon dioxideA. Without some global warming, we might not be around to worry about it. Thermodynamics is the basic science used in global warming calculations. It too is old with roots going back to the 1600s, but its modern form was already in place in the mid-1800sB. The basic process is an equilibrium between the incoming radiation from the sun and the outgoing radiation from the earth. The radiation from the sun on the relevant, short time scale is nearly constant while the outgoing radiation from the earth varies rapidly with temperature like this: FOURIER

=

(1)

where is the flux of radiation emitted by the earth and is the Stefan-Boltzmann’s constantC. Note the very rapid fourth power dependence of the flux on temperature. In the absence of absorption or reflection (albedo) the equilibrium point is determined by the eq1uation = where is the solar radiation incident on the surface. On the average just as much radiation is emitted by the earth as is absorbed from the sun.

1

There is a flux of about 1400 / incident on the earth which results in about = 350 / hitting the earth’s surface when we average over day and night and allow for the fact that earth is not flatD. So it follows that

=

(2)

Plugging in the numbers we find the average temperature is ~ − 17 ̊ …burr … day time temperatures would be a bit higher. It would be a bit lower, if I accounted for albedo. A slightly more complicated modelE that accounts for albedo, absorption of outgoing infrared by greenhouse cases and separate temperatures for the atmosphere and the surface yields the following formula for the surface temperature:

=

(

)

where α is the albedo and ε is the emissivity of the atmosphere. If effect.

(3) = 0 there is no greenhouse

How does the surface emperature change when ε is changed? Well, doubling the equivalent concentration changes ε from 0.78 to 0.8 which plugged into equation (3) yields a temperature increase of Δ = 1.2 ̊ (2 ̊ ). The more complex General Circulation ModelsF that include all sorts of feedback effects, predict somewhat bigger increases, typically ~3 ̊ . That’s in the same ballpark. The simple calculation based on the simple underlying physics gives a big enough increase to be worrying. Even, if you distrust the models, the size of Δ says, “we should not do this experiment.” Here I’ve pretty much adopted the Wikipedia discussion of a simple model. In 1967 at NASA summer school at Columbia, I did a similar, but even simpler calculation as a homework problem. We in the summer school did not know about global warming at the time, but in retrospect, it taught me how simple the concept of global warming is.

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Models Wrong? Unknown unknownsG

In ~1994 my wife Margaret heard Dixy Lee RayH speak about global warming at the Hoover InstitutionI. Dr. Ray had previously been chairman of the Atomic Energy CommissionJ and was a real scientist though not a climatologist. I haven’t been able, even in the age of Google, to find anything about what she said at “the Hoov.”. Likely there is something similar in her bookK “Environmental Overkill.”. I did find an interview about the book she did on CSPANS book notes that you can see and read here.

DIXY LEE RAY

The gist of her thesis was that as the global warming science was uncertain and the cost of doing something about it certain and large, we should do nothing. It was Margaret’s description of what Dr. Ray said that got me thinking about my simple homework problem from 1967 and its implications for global warming.

The science is less uncertain now than ‘94, but it was never that uncertain. The cost of doing something about it has risen dramatically and is rising still. Science is never, of course, perfectly certain. If somebody is certain, they’re talking about religion, not science. So Dr. Ray was right that the science is uncertain, but her conclusion that we should do nothing is wrong. The simple energy balance calculation, well known in ’67 much less ’94, shows that we are increasing the emissivity of our atmosphere enough to have serious consequences. Given the uncertainty in even the most sophisticated models, we should NOT dump carbon in the air anymore! Model uncertainty could go either way. Things could be better or things could be worse. A miracle could happen, and some unknown negative feedback could just cancel the effect of our greenhouse gas emissions, and all will be OK. That’s not very plausible. Depending on phase (time delay) and size an unknown feedback could push us into an ice age. That’s not better, nor is it plausible. At the other extreme, an unknown positive feedback could cause runaway heating. It’s those ‘unknown unknowns’ that get you. Let’s hope the models are right! There is some comfort from the earth’s history; over billions of years it has suffered some huge climate shifts (like the rise of oxygen in the atmosphere, asteroid impacts) and life has managed to hang on. However, a lot of species died out.

Geoengineering

We are running out of time to do something about global warmingL. If we fail to take adequate measures now, we’ll be faced with the scary prospect of geoengineeringM. If you don’t believe the climate models, you should be especially wary of geoengineering. Engineering depends on science. If the science is bad, the engineering will be bad. In trying to modify deliberately our climate, the General Climate Models would be deployed to estimate the effects of a given intervention. If there are ‘unknown unknowns,’ the impacts you miss could be catastrophic.

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It would be better not to muck about with the climate in the first place, but in a few years, we may have no choice. Here’s a possible engineering solution that Edward TellerN would have loved. He was always big on massive engineering projects using bombs. Set off large H-bombs on the ground in some remote location to inject dust into the upper atmosphere, thus, increasing the Earth’s albedo and cooling the planet. The effect would be like a modest nuclear winterO. Teller would be happy; Carl SaganP appalled. The Russians could do this. They have lots of space, they have big bombs, and the prevailing Siberian winds won’t take the local fallout over Las Vegas. EDWARD TELLER

This idea has the advantage that it is more or less controllable; the atmosphere clears and the effects wear off after a few years. If you didn’t like the results, you could stop. Unless the modeling is wrong and we just push ourselves into an ice age … There are, of course, side-effects of this ‘cure’, e.g., Strontium 90. It’s not even a complete cure. The oceans would continue to absorb carbon dioxide and acidify which may be a worse problem than warmingQ’R. Of course, H-bomb engineering is absurd, but other proposals don’t seem much better S. It would be better not to need them.

Consensus There is a consensus among the scientists, who know what they are talking about, that global warming is real and human-causedT. The critics point out that there have been incorrect scientific consensuses. There is certainly a long list of superseded theories. See Superseded Scientific Theories on Wikipedia. Often the older generation or those with a vested interest in their own theory have clung to discredited theory, and a ‘consensus’ remains for a while. But science is a process not a fixed body of knowledge or an immutable doctrine; the theory with the better evidence in the end wins. Global warming is not in the same category as these, so called ‘failed theories.’ They are mostly more fundamental and involve big paradigm shifts: Newton replaces Aristotle, Einstein replaces Newton and so forth. Global warming models are the application of thermodynamics. They do not depend on any radical, fundamental changes. Thermodynamics has been around for a long time; it is well tested (think steam engines); it works. The climate models may make errors on occasion. You can cherry pick them if you like, but the fundamental underlying theory is not disputed outside of perpetual motion nuts.

Conclusion The basic, simple thermodynamic calculations that undergird global warming calculations are solid and not rationally disputable. They tell us that that injecting greenhouse gasses into our atmosphere at the rate we are doing is going to have serious, perhaps catastrophic consequences.

∴ We should NOT do that! Messing with our planet is NOT a good idea! 4

A

https://www.aip.org/history/climate/simple.htm#S1e https://en.wikipedia.org/wiki/Thermodynamics#History C https://en.wikipedia.org/wiki/Boltzmann_constant D http://www.itacanet.org/the-sun-as-a-source-of-energy/part-2-solar-energy-reaching-the-earths-surface/#2.1.The-Solar-Constant E https://en.wikipedia.org/wiki/Idealized_greenhouse_model#The_model F https://en.wikipedia.org/wiki/General_Circulation_Model G http://www.brainyquote.com/quotes/quotes/d/donaldrums148142.html H https://en.wikipedia.org/wiki/Dixy_Lee_Ray I http://www.hoover.org/library-archives J https://en.wikipedia.org/wiki/United_States_Atomic_Energy_Commission K Ray, Dixy Lee; Louis R. Guzzo (1994). Environmental Overkill. New York: Harper Perennial. ISBN 0-06-0975989. L http://www.ipcc.ch/pdf/assessment-report/ar5/syr/SYR_AR5_FINAL_full_wcover.pdf M http://www.geoengineering.ox.ac.uk/what-is-geoengineering/what-is-geoengineering/ N https://en.wikipedia.org/wiki/Edward_Teller O https://en.wikipedia.org/wiki/Nuclear_winter P https://en.wikipedia.org/wiki/Carl_Sagan Q http://science.time.com/2013/08/26/ocean-acidification-will-make-climate-change-worse/ R https://www.skepticalscience.com/ocean-acidification-global-warming-intermediate.htm S https://www.bostonglobe.com/magazine/2013/10/19/geoengineering-schemes-from-cloud-brightening-spacemirrors/Dw9xmqdbtdV8cGv4K93cJN/story.html T https://www.skepticalscience.com/global-warming-scientific-consensus-intermediate.htm B

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