METR 104: Our Dynamic Weather (Lecture w/Lab) Some Notes on Topics Covered in the Weeks of March 12 and 26, 2012 Dr. Dave Dempsey Dept. of Geosciences SFSU, Spring 2012

A Puzzle

1. In Thought Questions on the Earth's Average Temperature, you learned that:

• Averaged over the whole globe and over a number of years, satellite measurements show that 342 Watts/m2 of solar radiative energy reaches the earth from the sun. (That is, for each square meter at the top of the earth's atmosphere, 342 Joules of energy arrive each second.)

• On the average, the earth (atmosphere and surface combined) reflects about 31% of this energy back to space and absorbs the rest (69%). Hence, the global, long-term average intensity of solar radiation absorption is 0.69 × 342 Watts/m2 = 236 Watts/m2.

• Satellites have measured a global, long-term average intensity of radiation emitted by the earth to space of about 235 Watts/m2. Hence, the earth as a whole loses heat (by emitting radiative energy to space) about as fast as it gains heat (by absorbing solar radiation). That is, the long-term, global average heat budget for the planet is very nearly balanced.

• A basic law of radiation says that most things emit radiative energy all the time. Another basic law of radiation says that the warmer an object is, the more intensely it emits radiative energy. In fact, there is a quantitative relation between the temperature of an object and the intensity with which it emits radiative energy. Based on the fact that the earth emits about 235 Watts/m 2to space (on the average), we can determine the effective temperature that the earth as a whole (atmosphere and surface combined) must be to emit radiative energy with that intensity. It turns out to be about −3°F (−20°C).

• In contrast, we can measure the earth's global, long-term average surface temperature (using both thermometers and measurements of radiation that it emits), and it turns out to be about 59°F (15°C). That is, the earth's surface is more than 60°F (35°C) warmer than the earth as a whole! Why?

• Using the same relation between an object's temperature and the intensity with which it emits radiative energy, we determine that the earth's surface emits about 391 Watts/m2, much more than the earth as a whole emits to space (235 Watts/m2).

• These results (based on observations and the well-established basic laws of radiation) raise several questions:
• Why is the earth's surface so much warmer than the earth as a whole (as seen from space, based on the radiative energy that the earth emits to space)?
• The earth's surface emits much more radiative energy than the earth as a whole emits to space. What happens to much of the radiative energy that the earth's surface emits?
• Since the global average earth's surface temperature doesn't change dramatically from year to year (typically no more than a few tenths of a degree up or down), we conclude that the heat budget for the earth's surface must be nearly balanced. (Otherwise, the temperature would change more than we observe it to. That insight comes from the principle of conservation of energy, a fundamental physical principle that the observable physical world obeys.) However, the earth's surface emits quite a bit more radiative energy (and hence loses quite a bit more heat: 391 Watts/m2) than the earth as a whole, much less the surface, absorbs from the sun (236 Watts/m2). (And the surface must absorb less than this, since the atmosphere absorbs at least some of it.) If the heat budget for the surface is nearly balanced, then there must be at least one more major source of heat for the surface besides the sun. What could that be?

2. In class, we performed a couple of experiments. They involved shining a 150 Watt light bulb equally through three, essentially identical, transparent, unsealed glass bottles containing slightly different mixtures of gases (basically air), and recording the temperature of the air inside. We considered three bottles in particular:

• One containing ordinary air from the room, starting out at the temperature of the air in the room.
• One containing a little room-temperature tap water at the bottom, a little of which evaporated into the air in the bottle, adding more water vapor than was already present in the air in the room. It also started out the same temperature as air in the room.
• One containing air from the room plus extra carbon dioxide added when put some ordinary baking soda (sodium bicarbonate) into the bottle and then poured some hydrochloric acid onto it. (The two react to produce a noticeable fizz, which is carbon dioxide gas being released.)
3. What we noticed first was that when we turned on the light bulb, we could still see right through the bottles. That is, the gases inside neither absorbed nor reflected significant amounts of visible light—they were essentially transparent to visible light. As a result, the visible light would have little or no effect on the temperature of the air inside the bottles.

However, the temperature inside all three bottles went up significantly (several degrees Fahrenheit or more). Moreover, the temperatures didn't go up at the same rate in each bottle—the temperature in the bottle containing ordinary air rose less than it did in the bottles containing extra water vapor or extra carbon dioxide.

Why would the temperature rise in each bottle at all, since the gases inside didn't noticeably absorb visible light? Several possibilities:

1. The thermometer itself was absorbing visible light from the bulb and warming up. However, I had rigged a piece of white (and hence reflective) paper to shield the temperature sensor from the direct light from the bulb, so this doesn't seem like a very satisfying explanation. Besides, why would the temperature rise by different amounts in the three bottles if this were the main explanation?
2. The glass of the bottle absorbed radiation from the light (though it couldn't have been much of the visible light, because the glass was nearly transparent), and the warmed glass then warmed the air inside by conduction. Although this might have happened to some degree, it would have occurred to the same extent in all three bottles, yet the temperature rose by different amounts in the three bottles, so this doesn't seem like a very satisfying explanation, either.
3. The extra water vapor in one bottle and the extra carbon dioxide in another were absorbing more radiation from the light bulb than the ordinary air in the third bottle was—just not visible light. This is possible because the light bulb doesn't emit just visible light, it also emits shorter wavelengths of infrared radiation (like the sun) and, since it isn't as hot as the sun, it also probably emits significant amounts of longwave infrared radiation (like the earth and most things in the classroom do, though at lower intensities because they weren't as warm as the bulb was).

To check on the third possibility above, we considered a figure showing atmospheric absorption spectra for several gases found in the atmosphere, including water vapor, carbon dioxide, oxygen and ozone (combined), nitrogen oxide, and methane. This figure shows how well each gas, at its present concentrations in the atmosphere, absorb each of a range of wavelengths of radiation, including wavelengths of solar radiation (ultraviolet, visible, and short wavelengths of infrared radiation) and terrestrial radiation (longwave infrared radiation). The absorption spectra figure shows that water vapor doesn't absorb visible light (it's invisible) but it does absorb some short wavelengths of infrared radiation and longwave infrared radiation, both of which were probably emitted by the light bulb, and carbon dioxide absorbs some longwave infrared radiation. Hence, we might expect that adding either of these gases to the bottles would cause them to absorb more of the (non-visible) wavelengths of radiative energy emitted by the light bulb and hence produce a bigger increase in temperature than would ordinary air.

Gases that are largely transparent to solar radiation but absorb at least some wavelengths of longwave infrared radiation are called greenhouse gases. Water vapor and carbon dioxide are leading examples, but there are others, too (such as nitrous oxides, methane, chlorofluorocarbons [CFCs, which are created only by humans], and others.) As we'll see, greenhouse gases are crucial to understanding how the earth's energy budget works.

These experiments and the atmospheric absorption spectra give us additional information that can help us try to resolve some of the questions raised in Section I above as a result of our attempts to answer Thought Questions on the Earth's Average Temperature.

4. To try to address the questions (in Section I above) raised by our attempts to answers to Thought Questions on the Earth's Average Temperature, we considered in more detail the global, long-term budget of energy for the atmosphere, the earth's surface, and (combining the two) for the earth as a whole (see Figure: The Earth's Long-Term, Global Average Energy Budget). This budget is based on observations recorded by satellites and ground-based measurement instruments. In particular, we worked through Thought Questions on the Earth's Long-Term, Global Average Energy Budget. (See Responses to Thought Questions on the Earth's Average Temperature.)

It is worth repeating that without greenhouse gases and clouds, the earth's surface would average over 60°F colder than we observe it to be (about −3°F vs. 59°F). And yet, greenhouse gases represent a small fraction of all gases in air: the most abundant greenhouse gases, water vapor and carbon dioxide, represent only about 1% and 0.04% (respectively) of all air molecules.

How much do water vapor, clouds, and carbon dioxide each contribute to the total greenhouse effect? Water vapor makes the biggest contribution (about 50%). Clouds are next (about 25%), and carbon dioxide contributes most of the rest (about 20%). Other, lesser greenhouse gases make up the other 5%.

It's worth noting that the analogy of the earth's greenhouse effect to the way in which an actual greenhouse works is only partly correct. It's true that both greenhouse gases and the glass in a greenhouse are transparent to visible light (that is, they don't absorb or reflect much sunlight). As a result, sunlight reaches the earth's surface, where plants, soil, etc. absorb most of it and warm up. With or without a greenhouse, the plants, soil, etc. emit longwave infrared (LWIR) radiation. With or without a greenhouse, air next to the earth's surface doesn't absorb much visible light and hence doesn't warm much by radiative absorption. At this point the similarity ends. The glass in a greenhouse is transparent not only to visible light but also to longwave infrared radiation, so most of the LWIR radiation emitted by plants, soil, etc. enters the lower atmosphere, just as it does without a greenhouse. However, as the plants, soil, etc. on the surface warm by solar absorption, they become warmer than the air in direct contact with them. As a result, heat conducts out of the plants, soil, etc. into the air next to the surface, warming it. The warmed air expands and becomes less dense. At this point, the similarity ends.

1. Without a greenhouse, the warmed, less dense air rises away from the surface, taking its heat with it. (This transport of heat upward in warm, rising air is called convection.) Cooler, unwarmed air from farther above the surface sinks to replace the departed, rising air. The net effect is to reduce the increase in temperature recorded next to the surface: convection transports heat away from the atmosphere next to the surface.

2. In contrast, inside a greenhouse, the warmed, less dense air can't rise—it is trapped there by the roof and walls of the greenhouse. The heat in the warmed air is therefore trapped there, too, and so temperatures increase more inside of a greenhouse than they do outside. This is not how the "greenhouse effect" works! (For an explanation of how the greenhouse effect works, see Responses to Thought Questions on the Earth's Average Temperature.)

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