Lecture 2 Global and Zonal-mean Energy Balance

Lecture 2 Global and Zonal-mean Energy Balance

A zero-dimensional view of the planet s energy balance

RADIATIVE BALANCE Roughly 70% of the radiation received from the Sun at the top of Earth s atmosphere is absorbed by the land and ocean surfaces, and to a smaller extent, the atmosphere. This absorbed solar energy provides the fuel for atmospheric and oceanic motion, and the flows of energy determine the planet s temperature distribution. When averaged over a period of several years and over all latitudes and longitudes, Earth as a whole loses approximately as much radiant energy to space as it gains from the sun. When this condition is satisfied, we say the planet is in a state of radiative balance.

Recall that objects constantly emit radiation according to their temperature. Objects that emit with 100% efficiency are called blackbodies, and have a distribution of wavelengths of emitted radiation is given by the Planck function, which has a characteristic shape: This curve is for an object with a temperature of about 5800K, the approximate temperature of the sun.

the distribution s peak wavelength... is inversely proportional to the temperature of the object (=2898/T, Wien s law). The hotter the object, the shorter the typical emission wavelengths

The total energy emitted by the object is the area under the curve... and is proportional to the fourth power of the object s temperature (=σt 4 ). This relationship is known as the Stefan-Boltzmann law. So the energy emitted increases very quickly as the object s temperature increases.

The wavelength distributions of the radiation emitted by the sun and the earth are very different, because the sun is so much hotter than the earth. The Planck functions for temperatures characteristic of the sun and the earth. The peak wavelength of the sun s distribution is at about 0.5 microns (green light), while the peak wavelength for the earth s distribution is at about 10 microns (infrared radiation).

Solar versus Terrestrial Radiation For studies of Earth s climate, we consider two parts of the electromagnetic spectrum: 1) short-wave radiation emitted by the sun, 0.1 µm < λ < 4.0µm (ultraviolet, visible, near infrared), often called solar radiation, and 2) long-wave radiation emitted by Earth, 4.0µm λ < 60 µm (near infrared, infrared, far infrared), often referred to as terrestrial radiation. The atmosphere is relatively transparent to solar radiation, and is nearly opaque to terrestrial radiation. This arrangement is the basis of the planet s greenhouse effect, and simplifies radiative transfer calculations.

Absorption by Atmospheric Gases Certain trace gases absorb electromagnetic radiation at specific frequencies. The absorption lines are broadened by Doppler and Lorentz effects, creating large swaths of the spectrum where the clear-sky atmosphere strongly absorbs radiation. (figs from Hartmann)

Absorption spectra of radiation in the Earth s atmosphere (a) (b) (c) (a) for the entire vertical extent of Earth s atmosphere, (b) for the portion absorbed above the tropopause (11 km), and (c) individual absorption spectra for various radiatively active gases in Earth s atmosphere.

The greenhouse effect of Venus From geometry, we can calculate the average solar flux over the surface of Venus. It is approximately 661 W/m 2. Venus is very reflective of sunshine. In fact, it has a reflectivity (or albedo) of 0.8, so the planet absorbs approximately 661 X 0.2 = 132 W/m 2. By assuming that the incoming radiation equals the outgoing radiation (energy balance), we can convert this into an effective radiating temperature by invoking the Stefan-Boltzmann law (total energy = σt 4 ). We find that T=220K. But Venus surface has a temperature of 730K!!! The explanation for this huge discrepancy is the planet s greenhouse effect.

The greenhouse effect of Earth From geometry, we can calculate the average solar flux over the surface of Earth. It is approximately 343 W/m 2. The earth has a much lower albedo than Venus (0.3), so the planet absorbs approximately 343 X 0.7 = 240 W/m 2. By assuming that the incoming radiation equals the outgoing radiation, we can convert this into an effective radiating temperature by invoking the Stefan-Boltzmann law (total energy = σt 4 ). We find that T=255K. Earth s surface has a temperature of 288K While much smaller than Venus greenhouse effect, earth s is crucial for the planet s habitability.

Meridional Energy Flows

In the annual and zonal mean, the local imbalances of net heating imply that energy must be transported from equator to the poles by the atmosphere and oceans.

The radiative imbalances of the preceding figure can be used to calculate the implied energy transport from equator to pole in each hemisphere. Further calculations with atmospheric and oceanic circulation data can be used to calculate the energy transport within the atmosphere and ocean. RT: Top of atmosphere (TOA) radiation (from satellites) AT: Atmospheric heat transports OT: ocean heat transports