Predicted Planetary Temperatures
ACS Climate Science Toolkit | Energy Balance
In order for a planet to maintain a constant average temperature, the amount of energy it radiates must equal the amount of solar energy radiation it absorbs, as shown schematically in the diagram. In our discussion of Energy from the Sun, we found that the radiative energy flux reaching the atmosphere (if any) of the inner, rocky planets of our solar system can be calculated. However, not all this radiation is absorbed by the planet’s atmosphere and surface, because part of it gets reflected back into space by clouds and surface features.
The ratio of the amount of radiation reflected from a surface compared to the amount of radiation that strikes it is called the surface albedo. The word “albedo” is derived from the Latin word for “white,” and indicates the “whiteness” of the surface doing the reflecting. A pure white surface, approximated on Earth by freshly fallen snow, has an albedo of unity (or 100%), indicating that all the incident radiation is reflected. A black body has an albedo of zero (or 0%), since all the incident radiation is absorbed.
Different features on a planet will have different albedos and they change over time. For example, the clouds in this photograph have a relatively high albedo as they are white and reflective and the sea below them has a rather low albedo because water is a good absorber of radiation. Later the clouds may disappear so their reflectivity will be lost. The albedo of a planet is an average over time and accounts for the various planetary features. The table below gives the average albedos, α, for the inner planets of the solar system.
To calculate the actual amount of the solar energy flux that is absorbed by the atmosphere and surface of a planet, we have to account for the albedo by reducing the incoming flux by a factor of 1 – α. For a low albedo, as on Mercury, the factor is near unity and most of the incoming energy is absorbed. For a high albedo, as on Venus, the factor is closer to zero and a good deal of the incoming energy is reflected away.
Assuming that the planets act like black bodies, the incoming and outgoing energies are balanced by equating the energy flux that is absorbed to the energy flux that the black body would emit, σTP4, from the Stefan-Boltzmann law, with TP equal to average planetary temperature.
Save(1 – α) = σTP4
TP = (Save(1 – α)/σ)1/4
The predicted planetary temperatures, based on this equation, are given in the table.
Also given in the table are the experimentally observed average temperatures, Tobs, at the surface of the planets derived from astronomical and planetary probe data and direct thermometric data for Earth. For Mercury and Mars, the agreement between observation and prediction is reasonable. But the agreement between observation and prediction is not good for the Earth and is spectacularly bad for Venus. These planets are both warmer than predicted by this simple model. To find the source of the difference between the observed and predicted temperatures see Atmospheres and Planetary Temperatures.