Freshman Seminar: Introduction to the Science of Climate Change Prof. Jordi Miralda-Escudé, F 9:30

Lecture 2: The Earth's atmosphere and the greenhouse effect.

What determines the height of the atmosphere?

We know that on the surface of the Earth, gravity pulls objects to the ground. Why does the air not fall to the ground?

Pressure determines the height of the atmosphere. The gravity force is balanced by pressure. As we go higher in the atmosphere, there is progressively less air, so pressure decreases with height. Air tends to go to where pressure is lower, and the force caused by this change in pressure with height balances gravity.

• You experience pressure decreasing with height when you get more tired hikinp up a very high mountain. Pressure drops by about a factor of 2 from sea-level to 5.5 km, or 17000 feet. so at 17000 feet you are only getting half the oxygen into your lungs for a fixed rate of breathing, and at 8000 feet you get only about three quarters compared to sea-level.
• You can understand how the height of the atmosphere is determined if you think that molecules of air are moving constantly at a speed that is about the speed of sound, or 300 meters per second, a little faster than the speed of a modern passenger airplane. If a molecule were moving up at this speed from the surface of the Earth and did not collide with any other molecules, it would reach a height of about 5 to 10 km before gravity would slow it down and make it fall. In reality molecules are constantly colliding among themselves and changing their direction and speed, but the effect is the same: gravity confines most molecules to within 10 km, given the random motions of the molecules. The atmosphere continues to much higher altitudes, but with ever decreasing densities, the density dropping roughly by a factor 2 every 5 km.

The Earth's atmosphere is divided into four regions at increasing heights, in which the temperature changes differently (see the figure in page 3 of Graedel and Crutzen, or here to see a plot .

• Troposphere : this is the layer between 0 and 10 km, which contains most of the air (air density rapidly goes down above the troposphere). Temperature drops with height.

  Why? The reason why temperature drops with height lies in where the energy from the Sun is absorbed: most sunlight is absorbed on the ground, and so it is the surface that gets heated. The air tends to scatter some of the light, but scattering does not cause any heat: the energy of the light is just sent back to space if the light is reflected out. The atmosphere also absorbs some light, but relatively little of it (as we see later when we talk about the energy budget).

  The air, on the other hand, can cool by emitting infrared radiation out to space. With little heating from the Sun, that is why the air at high altitude gets so cold. In fact, air in the troposphere would be much colder if it were only heated by sunlight. Actually, the troposphere also gets heated by transport of heat from the hotter surface of the Earth. This transport of heat occurs in two ways:

  • Convection of air: convection occurs when the bottom layers of air are sufficiently warmer than the top layers. Hot air is less dense than cold air at the same pressure, so hot air tends to rise and carry heat upwards with it. You see the same phenomenon in a pot of water on the stove: heating from below causes the convective motion you see when the water boils because hot water tends to rise above colder water. You also see that in your house in winter: if you heat the lower floor, the upper floor will also warm up as the air convects, but if you heat the upper floor, the lower floor will stay cold.
  • Latent heat of water vapor: the warmth of the ground causes water to evaporate from the sea and the wet land. Evaporation of water requires a lot of energy. The water vapor then flow upward with the convective movements. At a high altitude, the water vapor condenses again into little water droplets, forming clouds. When the water condenses, the energy that was taken from the ground when it evaporated is released back, warming up the air at high altitudes.
  Convection in the troposphere causes, among other things, the beatiful shapes of cumulus clouds when water condenses as air rises.
• Stratosphere : this layer is between 10 km and 50 km, and the temperature increases with height.

  The reason is that the stratosphere contains ozone molecules that absorb ultraviolet radiation from the Sun. In fact, this ozone layer in the stratosphere protects us from the damaging effects of ultraviolet radiation on our skin and eyes. The energy of this ultraviolet light heats the stratosphere. At higher altitude in the stratosphere, cooling by infrared emission decreases but heating by ozone is still strong, and that is why temperature increases with altitude.

  When warmer air lies above colder air, there can be no convection, so the stratosphere is a very quiet layer of the atmosphere, with very little vertical mixing. All weather phenomena occur in the troposphere only.

  The top of the troposphere, which separates it from the stratosphere, is marked by the maximum height reached by convective movements, and is called the tropopause.

• Mesosphere : this layer is between 50 km and 100 km. Temperatures decline again with altitude as heating by ozone diminishes.
• Thermosphere : above 100 km, the atmosphere is very thin. Molecules start being broken up into individual atoms by very short wavelength ultraviolet light from the Sun, and further up the atoms are ionized. These processes make the thermosphere very hot at high altitudes (although with very little energy content because the density is so low). The thermosphere eventually merges with the interplanetary plasma as one moves away from the Earth.

About 70% of the sunlight reaching Earth is absorbed, the other 30% is reflected back to space. Of the 70% absorbed, 50% is absorbed in the ground, the other 20% is absorbed in the atmosphere and clouds.

The surface cools by convection and latent heat, transmitting this heat to the atmosphere. It also cools by emitting infrared radiation, but only a small fraction of this radiation escapes directly to space. Most of the infrared radiation from the surface is absorbed in the atmosphere. The atmosphere can then return a lot of infrared radiation back to the surface, keeping the surface much warmer than it would be if no infrared radiation were returned. This warming by the return of infrared radiation from the atmosphere to the ground is called the greenhouse effect. Click here for a diagram showing the Earth energy budget, and see also page 17 of Graedel and Crutzen.

The greenhouse effect is made possible by two important properties of the atmosphere:

• The atmosphere is opaque to a lot of the infrared radiation that is emitted from the ground. Opacity measures the degree to which a medium absorbs radiation at some wavelength. For example, a piece of glass is transparent to visual light, so it has very small opacity. But you can't see through a piece of wood, so wood is highly opaque, it has a high opacity. Opacity varies with wavelength. The atmosphere of the Earth is transparent to some wavelengths, but for most of the radiation emitted by the Earth surface (with wavelength between 5 and 30 micrometers), the atmosphere is highly opaque. This means that the surface radiation will typically be absorbed somewhere in the atmosphere before it has a chance to escaping to space. The atmosphere itself will also be emitting infrared radiation. A lot of this will be again absorbed at some other point in the atmosphere. But at sufficiently high elevation, where the atmosphere is thin enough, the radiation emitted from there will eventually be able to escape to space.

• The upper atmosphere is generally colder than the Earth surface. This implies that the radiation emitted from the upper atmosphere to space will be less than the radiation that is emitted from the surface. The result is that, overall, less radiation is emitted to space, so the surface can be kept warmer by the presence of the atmosphere.

  If the atmosphere were everywhere at the same temperature as the surface, then the top of the atmosphere would emit as much radiation to space as the emission from the surface of the Earth. So, no matter how opaque the atmosphere was, there would be no greenhouse effect.

Of all the infrared radiation emitted from the surface of the Earth, only 10% escapes directly to space. The other 90% is absorbed by the atmosphere, and 80% of it is emitted back downwards from the atmosphere to the ground. The other 10% is used to heat the atmosphere, adding to the heat provided by convection and latent heat, and absorption of sunlight in the atmosphere. This heating of the atmosphere is balanced by the cooling due to the infrared emission from the atmosphere to space. This emission from the atmosphere to space is only about half of what was originally emitted by the surface.

The rate at which energy is emitted in infrared radiation from the surface is larger than the rate at which the surface absorbs energy from the Sun. The reason why the surface can stay at its warm temperature despite of this is because it gets additional energy from the infrared radiation emitted downwards by the atmosphere.

Therefore, you can say the atmosphere acts like a blanket that keeps the Earth surface warmer. The way that a blanket helps your body stay warm when you are in a cold place is analogous: the best blankets conduct the least possible heat (which is analogous to the atmosphere creating a greater greenhouse effect if it is more opaque, because infrared radiation will be less able to go through the atmosphere). At the same time, the reason the blanket keeps you warm is because its outer surface is colder than the surface of your body, so less radiation is emitted outwards from the outer surface of the blanket than the radiation that is emitted from your body surface to the inner surface of the blanket. The inner surface of the blanket returns a lot of the infrared radiation back to your body, keeping it warm.

Note an important difference between this blanket analogy and the Earth atmosphere. When you keep your body warm with a blanket, the energy keeping your body warm comes from inside the body (from your biological metabolism). For the Earth, the energy keeping it warm comes in externally with the sunlight. Greenhouse gases in the atmosphere are opaque to long-wave radiation emitted by the Earth surface (longer than 5 micrometers). But they are highly transparent to short-wave radiation (shorter than about 1 micrometer). Most of the energy from sunlight comes in at short wavelengths, so it is not blocked by greenhouse gases.

The gases in the Earth atmosphere that are opaque to long-wave infrared radiation, and therefore contribute a greenhouse effect, are water vapor, carbon dioxide, methane, and nitrous oxide. There are also various complex molecules called halocarbons that are of human origin and did not exist in nature before industrialization, which contribute to the total greenhouse effect.

Note that the most abundant molecules in the atmosphere, oxygen and nitrogen, are totally transparent to infrared radiation. The molecules able to absorb and emit long-wave radiation constitute a very small fraction of the atmosphere.

The next lecture explains how much each gas contributes to the greenhouse effect and how these gases have been changed by human activities.