CHAPTER 3ABSORPTION, EMISSION, REFLECTION, AND SCATTERING3.1 Absorption and Emission3.2 Conservation of Energy3.3 Planetary Albedo3.4 Selective Absorption and Emission3.5 Absorption (Emission) Line Formation3.6 Vibrational and Rotational Spectra3.7 Summary of the Interactions between Radiation and Matter3.8 Beer's Law and Schwarzchild's Equation3.9 Atmospheric Scattering3.10 The Solar Spectrum3.11 Composition of the Earth's Atmosphere3.12 Atmospheric Absorption and Emission of Solar Radiation3.14 Atmospheric Absorption Bands in the Infrared Spectrum3.15 Atmospheric Absorption Bands in the Microwave Spectrum3.16 Remote Sensing RegionsReflectance (in percent) of various surfaces in the spectral range of solar radiationCHAPTER 3ABSORPTION, EMISSION, REFLECTION, AND SCATTERING3.1 Absorption and EmissionAs we noted earlier, blackbody radiation represents the upper limit to the amount ofradiation that a real substance may emit at a given temperature. At any given wavelength λ,emissivity is defined as the ratio of the actual emitted radiance, Rλ, to that from an idealblackbody, Bλ,λ = Rλ / Bλ .It is a measure of how strongly a body radiates at a given wavelength, and it rangesbetween zero and one for all real substances. A gray body is defined as a substance whoseemissivity is independent of wavelength. In the atmosphere, clouds and gases have emissivitiesthat vary rapidly with wavelength. The ocean surface has near unit emissivity in the visibleregions.For a body in local thermodynamic equilibrium the amount of thermal energy emittedmust be equal to the energy absorbed; otherwise the body would heat up or cool down in time,contrary to the assumption of equilibrium. In an absorbing and emitting medium in which Iλ is theincident spectral radiance, the emitted spectral radiance Rλ is given byRλ = λBλ = aλIλ ,where aλ represents the absorptance at a given wavelength. If the source of radiation is inthermal equilibrium with the absorbing medium, thenIλ = Bλ ,so thatλ = aλ .This is often referred to as Kirchhoff's Law. In qualitative terms, it states that materialswhich are strong absorbers at a given wavelength are also strong emitters at that wavelength;similarly weak absorbers are weak emitters.3.2 Conservation of EnergyConsider a slab of absorbing medium and only part of the total incident radiation Iλ isabsorbed, then the remainder is either transmitted through the slab or reflected from it (seeFigure 3.1). In other words, if aλ, rλ, and λ represent the fractional absorptance, reflectance, andtransmittance, respectively, then the absorbed part of the radiation must be equal to the totalradiation minus the losses due to reflections away from the slab and transmissions through it.HenceaλIλ = Iλ - rλIλ - λIλ ,oraλ + rλ + λ = 1 ,which says that the processes of absorption, reflection, and transmission account for all theincident radiation in any particular situation. This is simply conservation of energy. For blackbodyaλ = 1, so it follows that rλ = 0 and λ = 0 for blackbody radiation. In any window regionλ = 1, and aλ = 0 and rλ = 0.3-2Radiation incident upon any opaque surface, λ = 0, is either absorbed or reflected, sothataλ + rλ = 1 .At any wavelength, strong reflectors are weak absorbers (i.e., snow at visiblewavelengths), and weak reflectors are strong absorbers (i.e., asphalt at visible wavelengths). Thereflectances for selected surfaces for the wavelengths of solar radiation are listed in Table 3.1.From Kirchhoff's Law we can also writeλ + rλ + λ = 1 ,which says emission, reflection, and transmission account for all the incident radiation for mediain thermodynamical equilibrium.3.3 Planetary AlbedoPlanetary albedo is defined as the fraction of the total incident solar irradiance, S, that isreflected back into space. Radiation balance then requires that the absorbed solar irradiance isgiven byE = (1 - A) S/4.The factor of one-fourth arises because the cross sectional area of the earth disc to solarradiation, r2, is one-fourth the earth radiating surface, 4r2. Thus recalling that S = 1380 Wm-2, ifthe earth albedo is 30 percent, then E = 241 Wm-2. 3.4 Selective Absorption and EmissionThe atmosphere of the earth exhibits absorptance which varies drastically withwavelength. The absorptance is small in the visible part of the spectrum, while in the infrared it islarge. This has a profound effect on the equilibrium temperature at the surface of the earth. Thefollowing problem illustrates this point. Assume that the earth behaves like a blackbody and thatthe atmosphere has an absorptivity aS for incoming solar radiation and aL for outgoing long-waveradiation. Let Ya be the irradiance emitted by the atmosphere (both upward and downward); Ysthe irradiance emitted from the earth's surface; and E the solar irradiance absorbed by the earth-atmosphere system. Then, at the surface, radiative equilibrium requires(1-aS) E - Ys + Ya = 0 ,and at the top of the atmosphereE - (1-aL) Ys - Ya = 0 .Solving yields (2-aS) Ys = E , (2-aL)and (2-aL) - (1-aL)(2-aS) Ya = E . (2-aL)Since aL > aS, the irradiance and hence the radiative equilibrium temperature at the earth surfaceis increased by the presence of the atmosphere. With aL = .8 and aS = .1 and E = 241 Wm-2,3-3Stefans Law yields a blackbody temperature at the surface of 286 K, in contrast to the 255 K itwould be if the atmospheric absorptance was independent of wavelength (aS = aL). Theatmospheric gray body temperature in this example turns out to be 245 K.A gas in a planetary atmosphere that is a weak absorber in the visible and a strongabsorber in the infrared contributes toward raising the surface temperature of the planet. Thewarming results from the fact that incoming irradiance can penetrate to the ground with relativelylittle absorption, while much of the outgoing long-wave irradiance is "trapped" by the atmosphereand emitted back to the ground. In order to satisfy radiation balance, the surface mustcompensate by emitting more radiation than it would