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Light flux in

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Ground state

FIGURE 14.6 Schematic diagram of radiative transfer in the atmosphere: (a) between vertical layers in the atmosphere; (b) within a volume element; (c) on a molecular level. The filled circles on the energy levels portray qualitatively the much larger populations in the ground state.

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Ground state

FIGURE 14.6 Schematic diagram of radiative transfer in the atmosphere: (a) between vertical layers in the atmosphere; (b) within a volume element; (c) on a molecular level. The filled circles on the energy levels portray qualitatively the much larger populations in the ground state.

In a particular layer of air in the atmosphere, the net change in energy of the layer is a result of the total fluxes crossing its boundaries from above and below. For example, in Fig. 14.6a for the layer between altitudes z, and z2, if the net flux into the layer F"ct is larger in magnitude than the net flux out, F"el, the difference (F,ncl — F2ncl) must go into heating the layer.

There are a variety of radiative transfer models for the atmosphere that incorporate all of the emission, absorption, and scattering processes as a function of altitude. These are used to predict the total radiance as a function of wavelength as well as the effect of changes in atmospheric gases, aerosol particles, and clouds on it. For details, see the books by Liou (1980), Goody and Yung (1989), and Lenoble (1993) as well as the article by Clough et al. (1992) for a typical line-by-line radiative transer model.

b. Molecular-Level View

On a molecular level, absorption of terrestrial infrared radiation of the appropriate wavelength corresponding to the energy-level splittings in the molecule causes vibrational-rotational excitation or, in the case of HzO, pure rotational transitions as well. Vibration-rotation transitions occur if there is an oscillating dipole moment in the molecule, a requirement not met by homonuclear diatomics such as N2 and 02. Recall from Chapter 3.A.1 that the vibrational energy spacing is typically sufficiently large that at room temperature ( ~ 298 K), most molecules are in the lowest vibrational energy level, and hence absorption of infrared radiation occurs from this v' = 0 state. The selection rules dictate that Au = 1 transitions are by far the most likely, giving vibrationally excited molecules in v" = 1 upon absorption of infrared radiation emitted by the earth's surface. (Of course, associated rotational transitions occur simultaneously, and overtone and combination bands can also be important.)

Take the simplified case of transitions between the ground state (energy E{)) and one higher energy level (£,) shown in Fig. 14.6c. Most molecules reside in the ground vibrational state at atmospheric temperatures and can therefore absorb energy corresponding to Et - E{). Once a molecule has made the transition to the upper state, it can undergo spontaneous emission of light (shown as hv^"'u), induced emission of light (shown as hv™^), or deactivation back to E() through collisions with other molecules. Induced emission is not important in the atmosphere due to the low light levels. In the troposphere, the total gas densities are sufficiently high that the collision frequency is large. In addition, the radiative lifetime for vibration-rotation transitions is typically quite long, of the order of 1-100 ms for most molecules (Lambert, 1977). As a result, collisional deactivation of the excited molecules is their major fate (see Problem 1).

Another consequence of the high gas concentrations in the troposphere and most of the stratosphere is that it is collisions, rather than radiative processes, that control the population of molecules in various vibrational and rotational energy levels. As a result, excited molecules in E[ are formed primarily by collisions (shown as "collisional activation" in Fig. 14.6c), not by absorption of radiation. Under these conditions, in the simplest (hypothetical) case of a molecule with ground-state energy E() of degeneracy g„, and one in excited-state energy of degeneracy g,, the ratio of the number of molecules in to that in the ground (£„) state is given by the Boltzmann distribution:

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Thus, gas collisions lead to a small equilibrium population of excited states. A small fraction of molecules in the excited states emit radiation rather than being collisionally deactivated. Based on the Boltzmann distribution, the population of the emitting states and hence the intensity of such radiation would be expected to decrease with decreasing temperature.

This situation with thermal equilibrium, where the population of the excited states and hence emission intensity is determined by collisions, is known as "local thermodynamic equilibrium" (LTE) and holds in the atmosphere up to altitudes of ~ 50-60 km (Lenoble, 1993). Above this altitude, non-LTE models must be used (e.g., see López-Puertas et al., 1998a, 1998b).

It is this emission from the Boltzmann population of excited states that is the thermal emission shown in Fig. 14.6b as well as the upward and downward emission shown in Fig. 14.2c. It is also responsible for the positive bands to to C02 and 03 observed in Fig. 14.4c. For a detailed discussion of emission (the source function), see Goody and Yung (1989), Liou (1980, 1992), and Lenoble (1993).

c. From Molecules to the Global Atmosphere

Overall, then, there is absorption of infrared terrestrial radiation by the greenhouse gases, collisional deactivation to convert this energy to heat, and emission of infrared radiation but at the lower temperatures characteristic of higher altitudes. As a result, the energy input into the troposphere is increased. This is clearly going to be a function of the concentrations of absorbing gases, their infrared absorption cross sections, the flux of terrestrial radiation, and the total gas pressure, which determines the rate of collisional deactivation.

However, simultaneously there is emission of infrared radiation from the Boltzmann distribution of molecules in excited states, which leads to a negative energy component. This emission process depends not only on the concentration of the gas but very sensitively on the temperature since this determines the population of the excited states that emit (Eq. (A)). As we shall see in some specific cases below, it is the balance between these two at any given altitude that determines the changes in fluxes and the ultimate impact of a change in a greenhouse gas concentration.

Because of efficient trapping of specific wavelengths of infrared radiation at lower altitudes by gases such as H20, C02, and 03, radiation emitted to space by such infrared-active species generally originates from molecules at higher altitudes, where the temperature is lower. Because of the Boltzmann population temperature dependence, the relative proportion of excited states that are the source of the emission is lower. This leads to smaller total energy emission out to space compared to what would be the case for a higher temperature.

Recall that 235 W m~2 must be emitted to space to balance the net energy absorbed from incoming solar radiation (Fig. 14.2). While a small part of this (40 W m~2) comes from direct emissions from the earth's surface in the atmospheric window where strong absorptions do not occur, the larger portion (195 W m~2) comes from the lower temperature emissions from the greenhouse gases and the tops of clouds (see Fig. f4.2c). Since by the Stefan-Boltzmann law, 235 W m~2 corresponds to a temperature of 254 K, the emission of infrared radiation to space can then be thought of as occurring from an altitude where the temperature is 254 K, which is approximately 5.5 km above the earth's surface.

In effect, then, infrared emission out to space by the greenhouse gases and clouds occurs at lower temperatures than the corresponding absorptions. The 235 W m~2 of incoming solar radiation that is absorbed at the surface and in the atmosphere (Fig. 14.2b) is ultimately balanced by the outgoing radiation from the upward emission (at lower temperatures) of approximately 195 W m~2 from atmospheric constituents, including the greenhouse gases and clouds, and of 40 W m"2 from the surface that occurs in the atmospheric window between the strong absorptions due to C02, H20, and 03.

The difference of 155 W m-2 between the 390 W m~2 emitted by the earth's surface (Fig. f4.2c) and the 235 W m~2 escaping from the atmosphere represents the amount of "trapped" radiation, the "greenhouse effect."

As seen in Fig. 14.2c, in addition to the 350 W m~2 absorbed in the atmosphere by the greenhouse gases and clouds, energy is also deposited in the atmosphere by convective, vertical mixing of surface heat through thermals (24 W m~2), through the release of the latent heat of evaporation of water when it condenses into liquid water (78 W m~2), and by direct absorption of light (Fig. 14.2b, 67 W m"2). This total of 519 W m"2 (350 + 24 + 78 + 67 = 519 W nT2) is balanced by emission of infrared radiation by gases and the tops of clouds upward into space (195 W m~2) as well as downward (324 W m~2), where it is absorbed by the surface and heats it.

In summary, in a hypothetical world unperturbed by anthropogenic emissions, the presence of H20, C02, and, to a lesser extent, 03, CH4, and N20 in the atmosphere leads to a natural greenhouse effect that results in an average surface temperature of about 288 K, rather than 254 K, which is expected in the absence of these gases.

It is important to emphasize that because the greenhouse effect originates in radiative transfer processes in the earth-atmosphere system, the net effect of a

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