V2100 - The Climate System

Solar Radiation, Earth's Atmosphere, and the Greenhouse Effect.

Take away ideas and understandings:

  1. You should understand the different ways radiant energy can interact with matter.
  2. How energy is transferred from radiant energy to matter and visa versa.
  3. What processes control the shape of the vertical temperature profile of the atmosphere between the ground surface and 100 km above the surface.
  4. Why the sky is blue and Sunsets are red.

I. Interaction of electromagnetic radiation with matter.

  1. Radiant energy can interact with matter in three extreme modes. Most often its behavior is a combination of two or more of these modes, but for the sake of explanation we will look at them individually. If matter does not interact with the incident radiation, that is, there is no change in the matter because of the radiant energy that strikes it and it does not let the energy pass through it (i.e. it is opaque to the radiant energy), then it reflects the energy. Reflection only changes the direction of the beam of radiant energy, not its wavelength or amplitude. If matter allows radiant energy to pass through it unchanged, the matter is described as transparent to the incident radiation. Again, as with reflection, there is no change in any of the properties of the radiant energy. On the other hand, if there is some interaction between the incident radiation and the matter (eg. some energy is transferred from the radiant beam to the matter resulting in an increase in molecular energy of the matter), then we describe this transfer of energy from the radiant beam to the matter as absorption.

  2. Black bodies by definition absorb and re-radiate radiant energy equally and completely at all wavelengths they intercept. Thus, as a perfect reflector reflects all radiation it intercepts, and a perfectly transparent substance transmits unchanged all radiant energy striking it, so a black body absorbs all radiation that it intercepts. Gases on the other hand are not black bodies; they absorb and re-radiate only at very specific wavelengths. Our atmospheric gases absorb different narrow bands of incoming solar radiation. Each absorption band is a response to a different mechanism of energy transfer. The smaller molecules of oxygen and nitrogen absorb very short wavelengths of solar radiation while the larger molecules of water vapor and carbon dioxide absorb primarily longer infrared radiant energy.

II. Earth's limb (Figures 2, 3, 4).

III. Effect of Earth's atmosphere on incoming solar radiation.

  1. Reflectivity: 35% of incoming solar radiation is reflected back to space).

    1. Clouds; Twenty-four percent of incoming solar radiation is reflected by clouds, 4% by the Earth's surface.

    2. Scattering; Seven percent of incoming solar radiation is scattered back to space. Particles in the atmosphere can scatter incoming solar radiation. This process works as follows: a particle momentarily traps some part of the solar spectrum that strikes it and then releases that same energy in all directions. Consequently one half of the radiation scattered is returned to space and the other half is sent down to the Earth's surface.

      The wavelengths scattered depends on the size of the scattering particle. Haze and smog particles are relatively large and they scatter all wavelengths. The presence of particles of smog and haze (small water droplets) gives the sky a milky appearance. Contrast the color of the sky on a hot humid summer day with its appearance on a cold clear winter day.

      Small particles, such as air molecules (molecules of nitrogen or oxygen), scatter a larger proportion of short wavelength light (blue and violet) rather than longer wavelengths (red). This preferential scattering of blue light is what gives the sky its blue color. This effect is also responsible for red Sunsets. At Sunset, if you look directly at the Sun, the Suns rays have traveled through a much greater thickness of the Earth's atmosphere than they do when the Sun is directly overhead at noon. Consequently, because of the preferential scattering of blue light by the atmosphere, only red and yellow light reach your eyes, hence red Sunsets.

  2. Absorption: about 17% of incoming solar radiation is absorbed at various levels in the atmosphere. While reading this refer to figures 6 and figure 7.

    Absorption is the process by which radiant energy is transferred to matter. If the matter is a gas, radiation can effect it in a number of ways. The ways it can absorb energy depends on the size and complexity of the gas molecule. The gas molecule can be rotated and a variety of vibratory modes can be excited depending on the nature of the molecule. If the energy is strong enough the molecule can be broken apart. Each mode of energy absorption occurs at a specific narrow band of the solar spectrum. Gases, therefore, are not like black bodies that absorb equally and completely at all wavelengths. Rather, they absorb only at specific, often narrow ranges of wavelengths. Diatomic molecules such as nitrogen and oxygen (most of our atmosphere) can absorb energy by increasing the vibration of the bond between the two atoms. If the energy absorbed is great enough it may break the bond resulting in two free wheeling oxygen or nitrogen atoms traveling at high speeds.

    O2 + ultraviolet light = O + O

    This occurs in the uppermost regions of the atmosphere, above one hundred kilometers (refer to figure 8). The most energetic (shortest wavelength) part of the solar spectrum is involved in this process. Nitrogen absorbs only in the extreme ultraviolet of which there is very little in the Sun's radiation. Oxygen absorbs more strongly than nitrogen and over a wider range of wavelengths in the ultraviolet. Oxygen molecules are therefore broken into oxygen atoms in the highest regions of the atmosphere. By an altitude of about 100 kilometers much of the radiation that is energetic enough to do this breaking of molecular bonds is used up and this process diminishes. Hence their is heating of the uppermost atmosphere (fast moving atoms of nitrogen and oxygen) and as the altitude decreases to about one hundred kilometers the atmosphere cools. For some distance above and below 80 kilometers there is little absorption of solar energy and consequently little heating of the atmosphere so the temperature reaches a minimum.

    Descending below eighty kilometers the atmosphere is heated by another process. Here the atmosphere gets denser (thicker) with decreasing altitude; the molecules of oxygen and nitrogen are closer together. Now if the bond of an oxygen molecule is broken and the two atoms go flying off, there is a higher likelihood that one of these atoms will strike an oxygen molecule. If it does it may form an ozone molecule. Above 50 kilometers the heating is primarily due to the break up of oxygen molecules by ultraviolet radiation with wavelengths between .12 and .18 microns, while between 50 kilometers and 10 kilometers the heating is due to the absorption by ozone of ultraviolet radiation with wavelengths between .18 and .34 microns.

    O + O2 = O3

    Ozone can in turn be broken up by ultraviolet light resulting in this reaction:

    O3 + ultraviolet light = O2 + O

    Both the breaking up of oxygen molecules above fifty kilometers and ozone molecules at fifty kilometers and below causes heating of the atmosphere that peaks at about 50 kilometers (the stratopause). Between 50 and 10-15 kilometers (the stratosphere) the solar energy energetic enough to break up ozone (ultraviolet radiation) is used up and the atmosphere cools.

IV. Effect of atmosphere on Earth radiation.

  1. Below ten kilometers the atmosphere warms in a linear way to the Earth's surface. This final heating is dominated not by solar radiation but rather by radiation from the Earth's surface. The Earth, being much cooler than the Sun, emits much longer wavelength radiation. At a solar temperature of nearly 6000 Kelvin, the peak of solar output is in the visible (light) part of the electromagnetic spectrum while the Earth, at a temperature of 278 Kelvin, emits most of its energy in the infrared (heat) portion of the electromagnetic spectrum (figure 7). Energy of this wavelength cannot be absorbed by tiny oxygen and nitrogen molecules, but it can be absorbed by the larger and more complex molecules of water vapor (H2O) and carbon dioxide (CO2). These complex molecules have a number of vibratory and rotational modes which absorbs energy in the infrared portion of the electromagnetic spectrum (figure 7). These together with other so called greenhouse gasses (methane CH4, and nitrous oxide N2O) cause the Troposphere to warm as the Earth's surface is approached (greenhouse effect). Man can and probably is enhancing this effect by adding to the atmospheric concentration of these greenhouse gasses. Most notably we are enhancing carbon dioxide, which has natural sources in the decay of plant and animal remains, through the burning of fossil carbon. Methane, which has natural sources in swamps and grazing ruminant animals, is being enhanced through the proliferation of rice paddies (artificial swamps) and cattle herds (cattle burp methane, more on that later). The atmosphere, heated by the absorption of Earth radiation by these greenhouse gasses, in turn radiates heat back to the Earth's surface increasing the Earth's surface temperature.

  2. Transparency: The Earth's atmosphere is effectively transparent to solar radiation between .34 and .7 microns. Consequently 22.5 percent of incoming solar radiation goes directly to the surface of the Earth and is absorbed.

  3. Transfer of radiation through a planet's atmosphere.

    1. A planet and its atmosphere, in our solar system, can radiate back to space only as much energy as it absorbs from incoming solar radiation.

      The solar constant x (1 - the albedo)

    2. The amount of radiation it radiates back to space is determined by its effective temperature.

      Planetary radiation = σTe4

    3. The wavelength of this planetary radiation is determined by the planet's effective temperature.

      λ = a/Te Wein's Law

    4. How strongly a planet's atmosphere absorbs the planet's radiation depends on the optical properties of its atmosphere and the nature of the planet's radiation.

    5. A planet's atmosphere has a bottom and a top; it radiates both upward and downward.

    6. Some atmosphere's are so strongly absorbing that some fraction of the atmospheric thickness can absorb all radiation received from the ground or adjacent atmospheric layers. From now on we will assume the planet does not absorb any incoming solar radiation i.e. the atmosphere is transparent to it.

      1. We can divide such a planet's atmosphere into a series of layers, each layer being just thick enough to absorb all the radiation received from adjacent layers. In this kind of atmosphere, each layer is heated by the overlying and underlying layers or the ground below the lowest layer (figure 9).

      2. The topmost layer must radiate to space the same amount of energy it receives from the Sun. If this were not the case and the topmost layer radiated less, the planet would heat up, or if it radiated more, the planet would cool off. As a consequence, the planet's temperature will change until it radiates as much as it receives.

      3. The topmost layer will radiate downward as much energy as it radiates upward. Consequently, it must receive from the layer below, or the ground, if it is the lowermost layer, twice as much energy as it radiates to space (remember, we are assuming this atmosphere is transparent to incoming solar radiation). Think about this. Lets assume that the ground lies below the second layer. How much energy must this second layer receive from the ground? Remember it is receiving energy from the layer above and from the ground below. Keep in mind the conservation of energy law; it makes the problem a lot easier than if energy were not conserved.

      4. Think about the surface temperature of a planet that has an atmosphere so strongly absorbing that it can be divided into 5 layers.


The budget of solar radiation is as follows:
Reflected 35
Absorbed by atmosphere 17.5
Scattered to the Earth from blue sky 10.5
Scattered to the Earth from clouds 14.5
Radiation going directly to Earth's surface 22.5