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

Lecture 1: What determines the temperature of the Earth?

The Energy Flux from the Sun.

Earth is heated by the Sun. The rate of heating depends on the flux of radiation energy that reaches the Earth from the Sun.

What is flux? Flux is the amount of energy that reaches the Earth per unit of area and per unit of time, or power reaching per unit of area.

What does the flux from the Sun depend on?

• The more luminous the Sun, the greater the flux.
• The greater the distance from the Sun, the lower the flux.
• More quantitatively, the flux increases in proportion to the luminosity of the Sun and inversely proportional to the square of the distance from the Sun.

How does the Earth cool down?

If the energy coming from the Sun into the Earth was the only exchange of energy that the Earth had with outer space, what would happen to the Earth?

• Because energy is conserved (neither created nor destroyed), the energy coming from the Sun would keep accumulating as heat in the Earth. The Earth would need to get hotter and hotter.

So what is necessary for the Earth to maintain a constant temperature?

• The Earth also needs to cool down, losing the same energy to space as it gains from the Sun, so that its temperature is in balance.

How does the Earth cool down?

• All material objects are continuously emitting radiation from their surfaces. The higher their temperature, the more radiation they emit. The Earth emits radiation to space.
• This radiation emitted by all objects, sometimes called thermal radiation, has a characteristic wavelength that depends on the temperature. At the temperature of the Earth surface, thermal radiation is at infrared wavelengths, about 10 microns. The human eye cannot detect this radiation. As the temperature of an object increases, the wavelength of the emitted radiation shortens. If you heat a piece of iron or coal, it starts glowing with a red color. The red color is the longest wavelength radiation our eyes can see. As the temperature is further increased, the color would change to yellow and then white (as the characteristic wavelength gets shorter). The Sun is very hot and its light is the thermal radiation from its surface, with a white color. An even hotter object than the Sun would become blue, and emit also a lot of ultraviolet light (at even shorter wavelengths).
• If you look at a piece of iron that is cold, it looks black and it seems not to emit radiation. However, it is still emitting, although the amount of radiation is much less than when it is hot, and has a long wavelength that your eye does not see. At room temperature objects emit only infrared radiation.
• Similarly the Earth emits infrared radiation to space. If you have an infrared camera in space, the Earth would look like an object glowing in the darkness of space. This infrared glow comes both from the day side and the night side. The glow increases with temperature, so it would be brightest from the equator where the Earth is warmer, and dimmest at the poles.
• This thermal emission is totally different than the reflected light from the Sun, which is what the visual images of the Earth from space show. Reflection has nothing to do with the temperature of an object, it simply occurs because the incident light from the Sun does not all get absorbed by the Earth, some of it is reflected back, the same way the light from a bulb is reflected off the objects around it.

Earth's balance of energy

In order for the temperature of the Earth to be at equilibrium, there needs to be a balance between the energy coming in from the Sun and the energy getting out as infrared emission to space . If more energy is coming in as sunlight, the Earth will heat. If more energy is getting out as infrared emission, the Earth will cool.

• To be more precise, some energy is actually generated in Earth's interior and continuously flows to the surface. This is because the interior of the Earth is very hot, and its heat is maintained by long-lived radioactive decays of uranium and other radioactive elements. The power flowing from Earth's interior is much smaller (about 10000 times smaller) than the power the Earth receives from the Sun. So the energy emitted by the Earth needs to balance both the energy input from the Sun and from Earth's interior. But of course, the sum of the two is just a tiny little bit larger than the energy input from the Sun alone.

The Orbit of the Earth, the Inclination of its Rotation Axis, and the reason for the seasons.

The Earth spins about its own axis, and it also revolves around the Sun. What causes the seasons?

• The orbit of the Earth is not exacly circular, but an ellipse with a small eccentricity. At its closest distance from the Sun, the Earth is about 147 million kilometers, and at its furthest distance it is about 152 million kilometers away. Can this be the reason for the seasons?
• When it is summer in North America, is it summer everywhere on Earth? No, in the Southern hemisphere it is then Winter!

The axis of rotation of the Earth is tilted, relative to the plane of its orbit around the Sun. The tilt angle is 23.5 degrees. This causes the seasons.

• The axis of rotation stays pointing in the same direction as the Earth revolves around the Sun. When the North pole is tilted towards the Sun, the Northern hemisphere gets a much larger amount of sunlight than the Southern hemisphere, and it is summer in the North. Half a revolution later, the North pole is tilted away from the Sun and the South pole towards it. Then it is summer in the Southern hemisphere.
• Note: the summer in the Northern hemisphere is actually the season after June 21 (the summer solstice). On June 21, the amount of sunlight received is maximum in the North. During spring, the amount of sunlight received in the North is just the same as in summer. But summer is hotter than spring because it takes some time for the surface of the Earth to warm up. The same thing happens in the Winter solstice: the minimum insolation in the northern hemisphere occurs on December 21, but the coldest days occur later around January, because the Earth surface takes some time to cool down to its minimum temperature. This is an example of the response time of the climate to a driving force (in this case, the driving force is the amount of sunlight received in each hemisphere).

Summary:

• The Earth is heated by the flux of energy it receives from the Sun, and cools down by emitting infrared radiation to space.
• The rates of incoming and outgoing energy have to be in balance if the Earth temperature is to remain constant.
• The eccentricity of Earth's orbit causes the distance to the Sun to slightly change (being largest in July and shortest in January). The seasons, however, are caused by the tilt of the axis of rotation of the Earth.
• The maximum temperature in summer is reached some time after the maximum insolation, on June 21, because of the response time of the climate.