Global Warming I

Wayne,

When I presented my sermon to my Physics 125 students at the University of Tampa, we happened to be reading and learning about climate change. It was easy for those classes to find material for my Science in the News section. Pro and con, of course.

On Capitol Hill, both Senator Cruz, Chair of the Senate’s relevant science committee, and Congressman Lamar Hunt, Chair of the House’s committee, have been holding hearings. Both of these guys are Texas Republicans, and it is both astonishing and disgraceful that such men are in their positions of power over American science. Senator Cruz’s hearings mostly had to do with witnesses and Republican Senators denouncing the world-wide conspiracy among climate scientists, environmental alarmists, and left-wingers intending to destroy the American economy and install socialism. Congressman Hunt’s hearings have to do with his suspicions, so he says, that some government scientists have cheated by cooking the books so as to demonstrate that the supposed global warming pause did not exist. Of course, there is no such conspiracy, and the global warming pause did not and does not exist, and the scientists didn’t cook the books.

One thing that’s astonishing about the Republican Party’s denial of the results of years of climate research is that the fundamental aspects of the theory and data are elementary and not in dispute among scientists. What scientific fussing there is within the climate science community has to do with details, and those scientists are in remarkable agreement that the climate is warming and that we are causing it.

As I am testing my new connection from Word to WordPress, I thought I would explain these basics, as I did to my students. These students are not science majors, but are taking a required natural science course. The course is more a great ideas of Western Civilization course than a regular course for physics students. Thus I based my presentation to them upon the First Law of Thermodynamics or the idea of Conservation of Energy. Of course I had to include some facts, observations, and ancillary principles.

For this purpose, the amazing First Law of Thermodynamics is not different than a business’s accounts, with energy properly defined in place of dollars. Thus there is a balance sheet that shows stocks or amounts of energy in various accounts, and an income statement, that shows flows between accounts and into and out of the system.

Consider this figure, showing the Earth’s energy income statement.

This simplified chart is from a NASA web site. You can see the average incoming radiation flux, which is in Watts/meter2, that is power flowing through a given area. Some of the incoming radiation, which is nearly entirely in the visible and short-wavelength infrared, reflects from the atmosphere and the Earth’s surface. The Earth’s surface absorbs the rest. This absorbed energy increases the total energy account of the Earth, and it shows up in the random thermal part of the Earth’s internal energy. It shows up as an increase in the temperature of the Earth.

Everything radiates energy more or less as a so-called black body. This black body radiation has a broad spectrum, and the wavelength of the peak of that spectrum is proportional to the inverse of the (absolute) temperature of the object. Absolute temperature is in Kelvins. One degree Kelvin is the same size as a degree Celsius. But 0 C is 273 K, the freezing or melting temperature of water, and 100 C is 373 K, the boiling or condensation temperature of water. The Sun’s surface temperature is about 6000 K, and the wavelength of the peak of the Sun’s spectrum is about 0.5 micrometer, 0.5 X 10-6 m, in the green. For the sake of this discussion, consider the Earth’s temperature (averaged over everything we can think of: night and day, latitude, seasons, and so on) as 300 K, about 20 times cooler than the Sun’s surface. Thus the wavelength of the peak of the spectrum of the radiation emitted by the Earth is about 20 times longer than that of the Sun’s spectrum: 20 micrometers, 20 X 10-6 m, in the long infrared.

Furthermore, the intensity of a blackbody’s radiation is proportional to the 4th power of the temperature, T4. Roughly speaking, therefore, the Sun’s surface emits (6000 K/ 300 K)4 = 204 = 16 X 104 times as much radiation per square meter as the Earth’s surface does.

Some of the Earth’s outgoing, long wavelength radiation goes right to outer space, but certain molecules absorb some of the radiation. These are the greenhouse gases, and those molecules re-emit this radiation in all directions, including back to the Earth.

At this point, consider the Earth’s energy balance account. Suppose that incoming solar radiation power flux plus that sent back down by the greenhouse gases is greater than the sum of the outgoing power fluxes. The Earth is absorbing more energy than it is sending out. It will, therefore, increase in temperature. If its temperature increases, it will emit more radiation. This is identical to your bank balance. If your income is greater than your expenditures, your balance will increase. If your income is less than your expenditures, your balance will decrease. Income and expenditures are flows, measured as amounts in some time period, say, $/year or Joules/second, which are Watts. Balance is a stock or quantity, measured in, say, dollars or Joules.

Consider the rightmost upward arrow, the Earth’s long wavelength radiation. Part way along that arrow splits, and some returns to the ground. The gases that cause this, the greenhouse gases, are mostly water vapor, which is the most important, and carbon dioxide. These molecules absorb some of the long wavelength infrared and radiate it away in all directions, including back to the ground. Indeed, the natural amounts of these gases warm the Earth significantly and are the reason for our generally pleasant temperatures. Without them, the Earth would be a frozen planet.

The amount of water vapor in the air varies widely, but about 1% near the ground and about 0.5% throughout the atmosphere, would be reasonable average values. Carbon dioxide used to be about 280 parts per million or 0.018%, more than two centuries ago, but now it is about 400 parts per million or 0.04%. There is a natural carbon cycle is usually in equilibrium, not changing much, but in the distant past various processes have caused the carbon dioxide to fluctuate. The recent increase, over the past 150 years, however, is the result of burning hydrocarbon fuels, coal and oil.

Consider this graph, the Keeling Curve, which is famous in the climate science community.

Dr. Charles Keeling began hiking up Mauna Loa volcano in Hawaii in 1958, and he made measurements in Antarctica and in California. He observed fluctuations in concentration each day, from plant action, each season, as you can see in this graph, and a yearly general increase. Keeling showed that the long term rate of increase was related to the amount of fossil fuels burned each year.

As the concentration of carbon dioxide increases, the fraction of the Earth’s outgoing, long wavelength infrared radiation that gets turned around and sent back to the ground increases, and the fraction that makes it to outer space decreases. If the incoming short wavelength solar radiation exceeds the outgoing long wavelength radiation, the Earth’s energy content must increase.

If the Earth’s energy content increases, its temperature increases (unless funny stuff such as phase changes occur) and its outward long wavelength radiation increases. The increase of the Earth’s energy content will continue until, once again, the incoming radiation and the outgoing radiation are equal.

Now there are subtleties that researchers must check out and account for. Better accounting would have separate balances for the Earth as a whole, including land and sea, and for the atmosphere as a whole, for example. Also, researchers have to concern themselves about various possible feedback loops, positive or negative. Perhaps the warming Earth evaporates more water, which form more clouds, which reflect more of the incoming radiation. Perhaps the warming Earth melts more snow and ice, which darkens the Earth’s surface, which leads to absorbing more of the Sun’s radiation. The professionals are on these and other matters, and they have improved their data and knowledge over many years.

Since the demonstrated carbon dioxide increase must reduce the outgoing radiation, skeptics of climate change have to explain why the Earth’s temperature doesn’t respond. But they cannot. Indeed, the Earth’s temperature response has been measured, and the suitably averaged temperature has increased along with, and with a lag, the increase in carbon dioxide. Skeptics will have to explain why the 1st Law doesn’t apply in this case.

I’m going to stop here, and continue in further posts on this subject. It is interesting that one of the responses of skeptics has been to attack the temperature data. Indeed, Dr. Muller, the author of the textbook I used was one such skeptic. He organized the Berkeley Earth Surface Temperature project, BEST, to review and check the climate scientists’ work. I’ll explain the results in one of these future posts.

3 Comments

Filed under Climate Change, Natural Science, Physics, Science in the News

3 responses to “Global Warming I

  1. Pingback: Global Warming II | two heads are better

  2. Pingback: Global Warming IV | two heads are better

  3. Pingback: Global Warming VII – Carbon Dioxide History | two heads are better

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