Heating of earth by the sun and cooling by radiating to space are a function of the spectra of the following: incoming sunlight, sunlight reflected back to space and infrared radiation to space. Some of the incoming solar radiation is scattered in all directions, hence the blue sky (scattering strongly favors shorter wavelengths). The gases in the atmosphere effect reflection and infrared irradiation. both. This page describes these spectra and their effects. The earth’s surface absorbs the remaining solar radiation after reflection and upward scattering.
NOTE: Click images to enlarge.
Also explained is why computation of transmission of earth’s infrared to space requires use of a packaged computer program.
A spectrum shows the distribution of specific properties as a function of wavelength or frequency. Here we are discussing light (electromagnetic radiation). The full light spectrum is given below:
A nanometer (nm), also called a millimicron (mμ) is one billionth of a meter. Spectra are also presented by frequency, which is usually in units of wavenumbers (cm-1). Frequency increases as wavelength decreases. A frequency of 10,000 wavenumbers corresponds to 1 micron or 1,000 mμ wavelength. To get frequency In microns, divide wavenumber into 10,000.
BLACKBODIES
A blackbody absorbs and emits all the light it can at a specific temperature and wavelength. A perfect blackbody has an absorptivity of 1 and an emissivity of 1. Minimum value for each is 0. The spectrum of the sun at its surface is close to that of a blackbody of 5700 K. Heat leaving the earth’s surface has a spectrum corresponding to an average blackbody temperature of 15.7C. Below is a spectrum of solar light incident at the top of our atmosphere (yellow) and received by the earth’s surface (red). The visible part of the spectrum is bound by the two horizontal dotted lines. The difference in the two curves is the effect of the atmosphere:
Yellow: Spectrum of sun, Red: Spectrum of solar radiation reaching earth’s surface.
It is seen that the atmosphere absorbs some of the suns light (converting to heat) due to scattering and various gases: O2, water vapor, and CO2. These gases, and others, also absorb some of the heat radiated from the earth, contributing to the greenhouse effect. The spectrum below shows the effects of various gases to the greenhouse effect.
Emission spectra of sun and earth surface imposed on absorption spectra of atmospheric gases
Notice in the green curve (CO2) in Figure 3 above. A value of 100% means that all the light at the given wavelength is absorbed. The major absorption band at about 15 microns shows that the effect of CO2 in that band is maximized. The only CO2 bands that can effect of greenhouse effect are those small bands to the left of the large band. Notice also that water vapor (blue curve) absorbs more of the earths radiation than CO2.
BEER’S LAW AND ABSORPTION SPECTRA
The amount of incident light transmitted by a layer of a substance (T) at a given wavelength (λ) is exponentially dependent upon the path the light travels (l) and the concentration of each component (c) of the substance. Mathematically, Beer’s Law is expressed as follows:
Tλ = exp-(l * Σaiλciλ)
Where aiλ is the absorption strength of component i at wavelength λ
In the case of the atmosphere, the path L is constant, so transmission of infrared light it is a function of concentration only. In the case of a gas, the concentration is proportional to the partial pressure (p) of the gas. So the for the atmosphere, Beer’s Law can be expressed as
Tλ = exp-(Σaiλpiλ)
WHY COMPUTER COMPUTATION OF ATMOSPHERIC TRANSMISSION IS NECESSARY (ModTrantm is used herein).
Beer’s Law applies very well for solids and liquids, with moderate considerations for temperature within the medium, and is virtually independent of pressure. There is no rotation of molecules in liquids and solids, and vibration is very limited due to the restraints of intermolecular bonds. However, due its independence of each gas molecule to rotate and vibrate, the absorption of energy by gases follows only the general trend of Beer’s Law, which can’t be used if the radiation path has varying pressures and temperatures.
For the atmosphere, the partial pressure does decrease with altitude, so computation of Tλ is very difficult. Compounded with that is the absorption spectrum of gaseous CO2, typical of polyatomic gases, which looks like the following:
Infrared Spectra of Atmospheric Gases, Lower Image is Narrow Band of CO2 Asymmetric Stretching
The absorption of radiation and the re-emission of it the same at any pressure and temperature combination. However, the shape and wavelength of each line varies with temperature and pressure, which varies with earth’s longitude, latitude and altitude. So besides calculating the absorption of each of the thousands of lines, additional calculations have to include parameters of the earth’s geometry.