Radiative Forcing

ACS Climate Science Toolkit | How Atmospheric Warming Works

Radiative forcing by a climate variable is a change in Earth’s energy balance between incoming solar radiation energy and outgoing thermal IR emission energy when the variable is changed while all other factors are held constant. The best understood radiative forcings are due to variations in solar energy input and changes in greenhouse gas atmospheric concentrations, because their radiative forcings can be computed using the experimentally verified concepts outlined in the multilayer atmosphere model and its application to Earth’s atmosphere.


Variation in the energy from the sun is a radiative forcing external to the Earth. In our analyses of planetary energy balance and the mechanism of atmospheric warming, we made the tacit assumption that the sun’s energy input is constant. However, there is an 11-year cycle of increase and decrease in the solar output reaching the Earth that is correlated with sunspot activity. The satellite data in the graphic show that the variation is minor, about 1 W·m–2 out of the 1366 W·m–2 (0.07% total variation) reaching the Earth. The data also show that there has been no net increase in solar input as the Earth’s temperature has increased markedly during the 30-year period shown. There is a hint of a minor periodicity in the temperature record superimposed on the overall increase, but the minor periodic variation in the sun’s input is not driving the temperature upward.

The computations to determine the radiative forcing for a greenhouse gas require a detailed knowledge of its IR absorption and emission properties. These are available from the HITRAN database. “HITRAN is an acronym for high-resolution transmission molecular absorption database. HITRAN is a compilation of spectroscopic parameters that a variety of computer codes use to predict and simulate the transmission and emission of light in the atmosphere. The database is a long-running project started by the Air Force Cambridge Research Laboratories (AFCRL) in the late 1960's in response to the need for detailed knowledge of the infrared properties of the atmosphere,” from http://www.cfa.harvard.edu/hitran/.

Intensity vs wavenumber graph

This figure simulates what would be observed looking down from 70 km above the surface as an imaginary atmospheric experiment is carried out. The blue emission curve is what would be observed when the CO2 concentration is 280 ppm. Then, without changing anything else (including the atmospheric temperature profile, all other gas concentrations, and the surface temperature), we imagine adding enough CO2 to double its concentration to 560 ppm throughout the atmosphere. The red emission curve is what would be observed from this atmosphere with the doubled CO2 concentration.

Qualitatively, you can see that the emission at the higher concentration is “fatter”. The temperatures (layers) from which emission occurs out in these “wings” are lower and, hence, the emissions are lower in energy (further toward the low end of the energy scale). The result is that there is less emission from the atmosphere with the higher amount of CO2. If there is less IR emission, the energy balance of the planet is upset with more incoming than outgoing energy and hence the planet will warm. Thus CO2 concentration is a positive forcing on the temperature.

For the particular atmospheric conditions chosen for this simulation, the doubled CO2 concentration decreases the amount of IR emission energy by 3.53 W·m–2. Thus, this imaginary CO2 concentration doubling produces a radiative forcing of +3.53 W·m–2. The consequences of such changes in radiative forcing are illustrated in this figure, a simple graphical representation of the forcing mechanism for planetary warming associated with an increased concentration of atmospheric CO2.

Credit: American Chemical Society

The decreasing concentration of CO2 with altitude is represented by the decreasing intensity of color in the diagrams and the lines on the plots show the lapse rate of atmospheric temperature. This kind of diagram is also used in the Toolkit page applying the multilayer atmosphere model to the Earth. The initial energy balance diagram here represents the atmospheric temperature and CO2 concentration profiles when the planet is in energy balance between incoming solar radiation and outgoing thermal IR emission represented by the squiggly arrow.

The middle diagram represents the situation after adding sufficient CO2 to double its concentration throughout the atmosphere, but before the temperature or any other variable has changed. That is, the lapse rate remains the same, but the top of the CO2 column, at the concentration from which emission to space occurs, is at a higher, colder altitude. Since the emission occurs from colder layers, the amount of energy emitted is decreased and the planet is no longer in energy balance. The amount of incoming solar radiation is larger than the amount of outgoing thermal IR emission. This is a positive forcing and the extra energy warms the planet and its atmosphere.

A new energy balance is reached when the warming has brought the column of CO2 to a higher temperature where its emission once again balances the incoming solar radiation. The lapse rate at this new energy balance is the same as it was initially, but moved to higher temperatures in each layer, as shown. The result of the CO2 forcing at the top of the atmosphere is a warmer surface temperature. Emission from the top of the atmosphere controls the surface temperature.

The figure in the sidebar shows that the emission from the atmosphere is inversely proportional to the logarithm of the concentration of CO2 in ppm, when other variables are held constant. Much of the contemporary interest in radiative forcing is concerned with the effects of increasing atmospheric concentrations of greenhouse gases. The baselines for comparison of the increases are usually taken as the concentrations in 1750, at the beginning of the Industrial Revolution. For CO2, the baseline value, C0, is 278 ppm. The slope of the line in the figure then gives the radiative forcing for C, another CO2 concentration, as:

radiative forcing for C ppm CO2, W·m–2 = (5.35 W·m–2) ln(C/C0)

The radiative forcing for the 2011 CO2 concentration, 393 ppm, is 1.85 W·m–2. Similar analyses can be made for the radiative forcing by other greenhouse gases and are included in the IPCC reports, summarized in this graphic.

Credit: Figure 2, FAQ 2.1, from the IPCC Fourth Assessment Report (2007), Chapter 2,
Changes in Atmospheric Constituents and in Radiative Forcing

The complete story is, however, not just one of radiative forcing by greenhouse gases. Other radiative forcings, albedo changes, for example, and feedbacks, especially from increasing water vapor, also occur. The effects of both positive and negative feedback factors have to be accounted for in determining the climate sensitivity associated with an increase in atmospheric CO2. Attaining the new energy balance involves some processes that are relatively rapid, taking place on a decadal time scale, and others that are slower, taking centuries, millennia, or longer to reach the balance.

Atmospheric Emision as a Function of CO2 Concentration
Credit: Jerry Bell