The Earth's Energy Budget I -- General Radiation Laws and Solar Radiation

We will now take a look at the energy budget for the planet Earth and provide an explanation for the greenhouse effect. All of the energy into and out of the Earth's climate system is in the form of electromagnetic radiation. A detailed study of this material is too complex to cover in this class. We will go into enough detail to allow you to understand some of the basic properties of radiation and the natural emission of radiation. The laws of radiation will be used to qualitatively describe how the Earth comes to a radiative equilibrium temperature. We will then apply this material to study the global warming issue.

Universal Radiation Laws

Radiation is a form of energy transfer. Radiation energy emitted (or given off) by one object is delivered to another object when that object absorbs the radiation energy. Radiation energy travels through outer space at the "speed of light" (300,000 km/sec or 186,000 mi/hr). Visible light is just one type or classification for radiation. It is the type of radiation that can be sensed by our eyes. We cannot see other types of radiation, but they exist.

All objects in the universe emit (or give off) radiation. At a very basic level, radiation is emitted photon by photon. Billions upon billions upon billions ... of photons. Different types of radiation can be described by the energy carried by a single photon. As mentioned previously, for studies of the Earth's climate, we are mainly concerned about ultraviolet, visible, and infrared radiation (listed in order from most energetic to least energetic photons). Keep in mind that there exists a continuous spectrum of photon energies in the universe, which extends from much more energetic than ultraviolet to much less energetic than infrared.

For solids, liquids, and high density gases (like stars), we can characterize the radiation emitted using the following two rules:

The rate of energy emission (total radiation energy emitted per square meter of surface area per second) depends only on the temperature of the object. The higher the temperature of an object, the greater the rate of radiation energy emitted. Therefore, the Sun (surface temperature 5800 K [5728°C]) emits much more radiation energy than the Earth's ground surface (average temperature 288 K [15°C or 59°F]). Simply stated, hotter objects emit more radiation energy than colder objects.
The dominant type of radiation emitted by an object also depends on temperature. As the temperature of an object increases, a larger percentage of the total radiaton emitted shifts toward higher photon energies. For example, the Sun emits most of its radiation energy in the form of visible photons, while the cooler Earth emits most of its energy in the form of infrared photons. A star much hotter than the Sun, may emit most of its energy in the form of ultraviolet photons. In order to not mislead you, I should state the each object in the universe emits photons over a wide range of energies. Thus, while the Sun emits many more visible photons than ultraviolet or infrared, it does emit these as well. Simply stated, hotter objects have their peak radiation energy emission at a higher photon energy than colder objects, which have peak energy emissions at lower photon energy.

Instructive figure depicting emission curves or the spectrum of photons emitted for objects at three different temperatures: green representing the surface of the sun, red representing a heating coil on an electric stove, and black representing the surface of the Earth. This hand drawn figure is instructive only and no attempt was made to properly scale the axes.
Note the maximum emission for the sun is in the visible photon range. We see white, which is a mixture of all visible colors. The heating coil has its maximum emission in the infrared range, which is not visible to us. However, it is hot enough to emit some visible photons. These are on the red or lower energy side of the visible photon range. The coil is red since it emits more red photons than blue. The surface of the Earth is too cold to emit any visible photons, so we cannot see it in the dark. Emission curves for objects at four different temperatures. The curves are properly scaled. The bottom axis is similar to the figure on the left with higher photon energies to the left and lower photon energies to the right. The upper curve represents the surface of the sun, which has a surface temperature of about 6000 K. Because of its surface temperature, the sun emits most of its radiation energy in the form of visible photons as shown by the 6000 K emission curve. The visible radiation spectrum is shown in color. Ultraviolet photons are to the left of purple (higher energy) and infrared photons are to the right of red (lower energy). We did not discuss the wavelength of radiation in this class.

More specifically the rules above can be written as mathematical equations, that is, given the temperature of an object, the rate of photon emission over the entire range of photon energies can be computed. See the instructive figure of emission curves shown above on the left. The figure is not drawn to scale because if it were the radiation energy emitted by the Earth would be too small to see next to the much larger radiation energy emitted by the hotter surface of the sun. The figure does show the two radiation laws, though. There are curves for objects at three different temperatures. Although not drawn to scale, the higher temperature objects emit much more total radiation energy (area under each curve) than lower temperature objects. In addition, notice that the peak of each curve, which corresponds to the energy where the object emits most of its photons or radiation, moves toward higher photon energy as the temperature increases. Objects emit radiation energy (photons) over a range of energies around the peak. Objects near the temperature of the Earth's surface are not hot enough to emit any visible radiation and thus can only be seen by reflected light. The electric heating coil is hot enough to emit some visible radiation. It is mostly the lowest energy visible radiation (the color red), so it is visible to us as glowing red. The sun emits all colors of visible photons and we perceive this mixture as white light. The sun is hot enough to emit some ultraviolet photons, which are potentially harmful to life on Earth. The figure above on the right shows emission curves for 3000 K to 6000 K bodies. (K denotes temperature in Kelvin units. Conversion K = °C + 273). Note that the Sun, with a temperature near 6000 K, has its peak emission in the visible radiation range, while cooler objects have peak emissions at lower photon energies. These curves are also drawn on the same scale, which indicates that total radiation energy emitted falls rapidly as the temperature of the emitting object lowers. Here is a figure that shows the emission curves for the Earth and Sun with proper units for radiation energy, which indicates that the hotter Sun, with a temperature near 6000 K (5728°C), emits over 1 million times more radiation energy per square meter of surface area than the cooler Earth at a temperature of 288 K (15°C). The labels below the emission curves indicate that for climate studies, the spectrum of radiation is broken into two components: shortwave radiation (high energy visible and near visible photons from the Sun) and longwave radiation (lower energy infrared photons from the Earth's surface, clouds, and gases in the atmosphere). Shortwave and longwave refer to the wavelength of the electromagnetic radiation, which is not discussed in this class.

The mathematical radiation laws can also be used backwards: by measuring the radiation energy emitted by an object, we can determine its temperature. For example, if I point an infrared detector toward you, I will measure radiation characteristic of a 98°F object. If I point the detector at a colder wall in the room, I will measure less radiation energy, which is the amount characteristic of an object with a temperature of about 75°F. Because the infrared detector is measuring radiation emitted by objects on Earth (rather than normal vision which works by seeing visible light that is reflected from an object), the infrared detector can sense the difference between you and the cold wall even in the dark. This is how passive military night vision works. The presence of people (at night) can be detected by measuring the higher amount of infrared energy emitted by warm bodies compared to colder surroundings. Differences in the infrared energy measured are then displayed as a false color visible images that can be seen by human eyes. The two figures below are false color infrared images. One before the boy bounces a ball and one after the ball has been bounced. Because the ball gets hotter after being bounced it emits more infrared radiation. The scale on the right relates the displayed false color with temperature. Similarly, the temperature of the Earth can be determined by satellite measurements of infrared radiation emitted from the surface of the Earth and the atmosphere.

False color infrared image of boy before bouncing ball. Temperature color scale shown right of image. False color infrared image of boy after bouncing ball.

Remember radiation is one of the ways that energy can be transferred from one object to another. The actual energy transfer takes place when an object absorbs the radiation energy that was emitted by another object. Absorption can be said to occur photon by photon. Once a photon is absorbed, it ceases to exist, and its energy is delivered to that object. In the case of the Earth and Sun, the Earth heats up when it absorbs radiation energy (photons) that were emitted from the Sun.

Radiative Equilibrium Temperature of the Earth

Radiation is the only form of energy transfer that can move through the vacuum of outer space. Thus, radiation is the only way for energy to be transfered into or away from the planet Earth. The original source of nearly all of the energy for the physical and biological processes that take place on Earth is radiation energy that came from the Sun. The Earth continuously emits radiation energy off to space. The net effect of these two processes (absorption of radiation energy from the Sun and emission of radiation energy to space) determines the average temperature for the planet.

Because the Sun is much hotter than the Earth, it emits much more radiation energy than the Earth. Since the temperature of the Sun is about 5800 K [5728°C], the majority of the radiation energy it emits is in the form of visible radiation. Similarly, since the temperature of the Earth is about 288 K [15°C], the majority of the radiation energy it emits is in the form of infrared radiation. So the Earth heats up by absorbing mostly visible radiation energy from the Sun (with smaller amounts of energy in the form of ultraviolet and infrared radiation), and cools down by emitting infrared radiation out to space. Over time these two processes come into balance, i.e., radiation energy absorbed equalling radiation energy emitted, and the planet Earth reaches a steady average temperature (as described below):

If there were no atmosphere (and assuming that there were no change in the amount of energy that the Earth absorbs from the sun), the average temperature of the Earth's surface would be equal to the radiative equilibrium temperature of -18°C (0°F). But the atmosphere acts to warm the surface through what is called the atmospheric greenhouse effect. The average surface temperature of the Earth is about 15°C (59°F). We will explain more about the greenhouse effect on the next reading page. You should understand that the average temperature at the Earth's surface does not have to be equal to the average temperature of the planet as a whole. For instance, we know that the temperature of the atmosphere near the tropopause is much colder than the temperature at the Earth's surface.

Interaction Between the Earth and Radiation from the Sun

Before describing the greenhouse effect, let us take a look at what happens to the radiation from the Sun that hits the planet Earth.

The Earth's Absorption of Energy from the Sun

To determine the average temperature of the planet Earth, what is important to know is how much radiation energy from the Sun is absorbed by the planet. The amount of radiation energy that hits the planet can be calculated using the temperature of the Sun, the distance from the Sun to the Earth and the size of the Earth. However, not all of this radiation is absorbed. Some is scattered back to space. Only the absorbed radiation goes into heating the Earth. The following figure illustrates this pictorially.

We will follow a beam of solar energy and study its interaction with the atmosphere and the Earth's surface. Assume the beam contains 100 units of energy as it hits the top the atmosphere:

The arrows pointing away from the Earth indicate the portion of the solar energy from the Sun that is reflected away by the Earth. It is 30 of the 100 units that hit the top of the atmosphere or 30%. The largest part of the reflection is from clouds. The remaining 70 units (or 70%) of the radiation from the Sun is absorbed by the Earth. Most of this absorption of radiation energy from the Sun happens at the Earth's surface. Thus, when there are no clouds, the atmosphere allows a majority of the visible radiation energy from the sun to pass right through where it gets absorbed by objects on the Earth's surface.

To summarize this information, of all the solar radiation that hits the planet Earth (at the top of the atmosphere):

30% is scattered back to space (reflected away)

20% by clouds
6% by air molecules and aerosols
4% by the Earth's surface

70% is absorbed

50% by the Earth's surface
16% by air molecules and aerosols
4% by clouds

The concept of radiative equilibrium for the Earth is shown in this hand drawn figure for radiative equlibrium. The above numbers and the figure represent a global average for the planet Earth. At any one location and time, the numbers vary considerably. It is most common that a particular location is not in radiative equilibrium, with one result being that the temperature will be changing with time at that location, which include daily and seasonal temperature changes.

In locations where there are thick clouds, a large fraction of the incoming solar energy is reflected back to space, much more than the global average of 30%. But clouds only cover slightly more than half of the Earth's surface at any given time, so in places where it is clear, much less than 30% of the incoming solar energy is reflected back to space. Obviously, any change in the global amount of cloud cover will have a large impact on the amount of radiation energy the Earth absorbs from the Sun and thus will impact the average temperature of the Earth.

In principle anything that causes a change in the amount of solar energy that the Earth absorbs from the sun should result in a climate change that changes the radiative equilibrium temperature to restore the radiation energy balance. This includes but is not limited to

Changes in the energy output of the Sun
Changes in cloud cover and changes in the radiation properties of clouds, i.e., some clouds better reflect radiation from the Sun than other clouds. Any climate change that results in changes in the global amount of cloud cover, whether that climate change is natural or human-related, will have a large impact on the temperature of the Earth. This is a very important consideration since it is difficult for current climate models to correctly simulate cloud cover and cloud properties, which makes predictions of future climate change uncertain.
Changes in the concentration of aerosols in the atmosphere, which can absorb and scatter radiation from the sun. There are natural and human-caused changes in aerosol concentrations and properties.
Changes in the reflective properties of the Earth's surface, e.g., when humans convert forest to crop lands.


False color infrared image of boy before bouncing ball. Temperature color scale shown right of image.	False color infrared image of boy after bouncing ball.