Greenhouse 101:
How the Greenhouse Effect Works

(c) 2006 by Barton Paul Levenson



I. How Light Interacts with Matter.

Any material object not at absolute zero radiates photons according to the Stefan-Boltzmann law:

I = ε σ T4<1>

where

I is the power radiated in watts per square meter,
ε is the emissivity (ranging from 0 to 1 for various substances),
σ is the Stefan-Boltzmann constant (5.6704 x 10-8 in the SI), and
T is the temperature in degrees Kelvin.

The wavelength of maximum emission gets smaller as temperature goes up. The Sun, at an effective temperature of 5,779° K, radiates with a peak of 0.5 microns, mostly in visual wavelengths. (This isn't a coincidence with human sight capability. We evolved to see in visual light wavelengths because that was the primary source of radiant energy in our environment, at least during the daytime.) By way of contrast, the Earth's surface, at a temperature averaging only about 288° K, gives off light that peaks at 10.6 microns, in the infrared.

A material object which doesn't change its state or undergo chemical reactions when struck by light, can only react to that light in one of three ways:

It can absorb it, as when blacktop in summer heats up in the sun.
It can reflect it, as when light strikes a mirror.
It can transmit it, the way Sunlight goes through air or glass.

By conservation of energy, the three reactions have to add up to 100% of the incident energy:

A + R + T = 1<2>

where A is absorptivity, R reflectivity, and T transmissivity.

Gases are material bodies, and radiate photons and interact with light beams. The interesting thing about gases and absorption is that absorptivity varies with wavelength. A gas might absorb electromagnetic radiation (photons) very efficiently at 10 microns and fail to absorb much at all at 0.5 microns.

This is how greenhouse gases work. They have poor absorptivity for visual light (sunlight), but good absorptivity for infrared light (thermal emission from the Earth's surface).



II. How the Greenhouse Effect Works.

The greenhouse effect can be thought of as happening in several stages:

1. Sunlight passes through the atmosphere without much being absorbed.

2. The sunlight transmitted by the atmosphere heats the ground.

3. The warm ground radiates infrared light.

4. Greenhouse gases in the atmosphere absorb the IR light.

5. The greenhouse gases heat up, like any material body absorbing light energy.

6. The warmer greenhouse gases radiate IR themselves.

7. Some of the energy radiated by the atmosphere goes back to the ground.

In other words, you've got both sunshine and "atmosphere shine" heating the ground. If there were no greenhouse gases in the atmosphere, sunshine heating the Earth's surface would be the whole story. But on any planet with greenhouse gases in the atmosphere, the surface will be hotter than if there were no greenhouse gases. And the more the greenhouse gases, the higher the surface temperature. This is why loading the atmosphere with carbon dioxide from fossil fuel burning and deforestation is a bad idea.



III. Some Numbers and Calculations.

The Solar energy that passes through a unit area perpendicular to it, at a given distance from the Sun, is known as the "Solar constant." At Earth's distance, this averages 1,367.6 watts per square meter.

The flux actually absorbed by a planet can be found with this equation:

F = (S / 4) (1 - A)<3>

where S is the Solar constant and F the absorbed flux in watts per square meter. The factor of 1/4 arises because the Earth receives sunlight on its cross-section (area π r2) but is actually spherical in shape (area 4 π r2), and half in darkness.

A is the planet's "bolometric Bond albedo" -- the fraction of electromagnetic reflected away by the planet at all wavelengths. From now on I'll just call this "the albedo." The latest estimate for the Earth's albedo is 0.298 (Goode, 1998). Thus F for the Earth works out to be 240.0 watts per square meter.

The planet's "effective temperature" is defined as the temperature radiated by the planet as seen from a distance. This is related to the absorbed flux by

Te = (F / σ)0.25<4>

where σ is the Stefan-Boltzmann constant discussed in part I. From this relation, the Earth's effective temperature works out to be 255.1 degrees K.

Note that water freezes at 273.15 K. If absorption of sunlight were the whole story, the Earth would be frozen solid. But obviously it is not. Earth's mean global annual surface temperature is 288.2 K according to the NOAA/NASA US Standard Atmosphere.

The extra 33.1 K is due to Earth's greenhouse effect. The greenhouse effect is not only real, it is vital to the survival of life on Earth.

For ways to estimate the surface temperature of a planet, taking the greenhouse effect into account, try here:

Planetary Temperatures



Reference: Goode, Philip 1998. "Earthshine Measurements of Global Atmospheric Properties." http://www.bbso.njit.edu/Research/Earthshine/earthshine-proposal.html, accessed 10/13/1998.



Page created:04/18/2007
Last modified:  02/09/2011
Author:BPL