## Incoming Radiation from the

The discussion on the general circulation of the atmosphere in Chapter 2 presupposed that most of the heating of the earth's surface comes from solar radiation. The total solar energy reaching the surface of the earth each year is about 2 x 1021 kj (5 x 1020 kcal). Heat generated by radioactive processes in the earth and conduction from the core contribute 8 x 1017 kj (2 x 1017 kcal), and human activities contribute about 4 x 1017 kj (1017 kcal) per year. This means that less than 0.1% of the total energy reaching the earth's surface each year comes from processes other than direct solar radiation. For the purposes of this chapter, therefore, we may treat the energy input to the earth as if it all came from the sun.

The sun is almost a blackbody radiator (with superimposed line spectra); a perfect blackbody is one that absorbs all radiation impinging on it; it also emits the maximum possible energy at any given temperature. The energy emitted from unit area of the blackbody per unit wavelength per unit solid angle in unit time, BX (T), is given by Planck's blackbody equation:

where k = 1.38 x 10-23 J molecule-1 K-1 is Boltzmann's constant (the gas constant per molecule), h is Planck's constant, 6.63 x 10-34 J-s, c is the speed of light in vacuum, 3.00 x 108m/s, X is the wavelength of interest in meters, and T is the absolute temperature in kelvin.

Since the sun is emitting radiation mostly from its surface, and since we shall also wish to consider blackbody radiation from the surface of the earth, we shall rewrite equation (3-1) in the form

where I(X) is the radiation intensity emitted by each square meter of surface of the blackbody at wavelength X, T is the absolute temperature, Cj = 3.74 x 10-16 W-m2, and C2 = 1.438 x 10-2 m-K (the symbol W refers to watts). The total intensity of radiation emitted by a blackbody at any temperature is given by the Stefan-Boltzmann law,

where a = 5.672 x 10-8 W m-2 K-4 = 8.22 x 10-11 cal cm-2 min-1K-4.

The relative distribution of energy, proportional to equation (3-2), is plotted in Figure 3-1 as a function of wavelength for two temperatures. One may see that there is a wavelength of maximum emission Xmax that shifts to lower wavelengths as the temperature is increased. Most commonly, the wavelength of maximum blackbody emission is encountered in the infrared (e.g, the 3300 K curve in Figure 3-1 corresponds approximately to the output of a 200-W tungsten filament lamp). However, at 6000 K (roughly the blackbody temperature of the sun), Xmax is in the visible region (480 nm). Ninety percent of the solar radiation is in the visible and infrared, from 0.4 to 4.0 ^m, with almost constant intensity (but see Section 3.3.1). The other 10% of the solar radiation intensity varies somewhat with time in the ultraviolet region and becomes extremely variable in the x-ray region of the spectrum. The wavelength at which maximum emission of radiation occurs at any temperature is given by Wien's displacement law,

Solar radiation is emitted in all directions from the sun, and very little of this reaches earth. In fact, earth is so far away from the sun that it picks up only about 2 x 10-9 of the total solar energy output. At a distance from the sun

Wavelength (nm)

FIGURE 3-1 Distribution of energy from a blackbody radiator at 3300 K (curve A) and 6000 K (curve B).

Wavelength (nm)

FIGURE 3-1 Distribution of energy from a blackbody radiator at 3300 K (curve A) and 6000 K (curve B).

equal to the average radius of the earth's orbit, the solar energy passing any surface perpendicular to the solar radiation beam is 1.367 ± 4kW/m2 (1.95 cal cm-2 min-1); this is called the solar constant for the earth. Since the earth does not consist of a plane surface perpendicular to the path of the solar radiation but presents a hemispherical surface toward the sun, a recalculation of the solar constant must be made for radiation falling on this hemispherical surface. Actually, since we wish to use an average radiation intensity averaged over the total surface of the earth, we must compare the surface area of the whole earth, 4wr2, where r is the radius of the earth, with the area that the earth projects perpendicular to the sun's rays, wr2 (see Figure 3-2). Thus, the earth's surface has four times the area of the circle it projects on a plane perpendicular to the sun's rays, if these rays are assumed parallel at such large distances from the sun. Therefore, the solar radiation that comes in toward the earth's surface is one-fourth of the solar constant, or approximately 343 W/m2, averaged over the whole surface. These numbers indicate

Projection of Earth on perpendicular plane has area = nr2

Solar radiation, assuming parallel rays

FIGURE 3-2 Comparison of earth's surface area with the area of earth's projection on a plane perpendicular to the sun's rays.

Earth's surface area = 4nr2

Projection of Earth on perpendicular plane has area = nr2

Plane perpendicular to sun's rays

Solar radiation, assuming parallel rays

Plane perpendicular to sun's rays the total amount of solar radiation coming in to the top of the earth's atmosphere; some of this radiation is absorbed in the atmosphere and some is reflected.

The solar radiation that actually penetrates to the surface of the earth below the atmosphere no longer has the spectral distribution of black body radiation from a body at 6000 K (Figure 3-1). Figure 3-3 shows that no solar radiation with wavelength below 0.28 ^m (280 nm) reaches the surface of the earth. We already knew this, from the discussion of absorption by oxygen in the thermosphere and by ozone and oxygen in the stratosphere (Section 2.5). The absorption of solar infrared radiation has not been discussed yet, but a large portion of the sun's infrared radiation is absorbed by water vapor, carbon dioxide, and trace gases in the atmosphere. Figure 3-4 specifically shows the absorption of solar radiation by water and carbon dioxide in the atmosphere; one can see that this absorption is complete at some wavelengths.

The absorption of solar infrared radiation by various constituents of the atmosphere is not very important because comparatively little of the solar radiation is in the infrared (Figures 3-1 and 3-3). These absorptions become much more important when we consider radiation emitted by the earth. It should be fairly obvious that the earth is emitting radiation because, on the average, the earth is in thermal equilibrium. It is in the path of 2 x 1021 kj of solar radiation each year, and it is necessary that 2 x 1021 kj per year leave the earth. If less energy than that leaves the earth, it will become hotter. Some of the solar energy, as we shall see, is immediately reflected, but some is absorbed and must be reemitted.

Ultraviolet

Infrared

Frequency (Hz)lO1 1.0

Sub-mm

Microwave

101'

0.0 ^m 0.1 ^m 1.0 ^m 10 ^m 100 ^m 0.1 cm 1.0 cm 10 cm 100 cm

Wavelength, X

FIGURE 3-3 The transmission spectrum of the upper atmosphere: low transmission means high absorption. Redrawn from J. E. Harries, Earthwatch, The Climate from Space. Horwood, New York, Copyright © 1990.

FIGURE 3-3 The transmission spectrum of the upper atmosphere: low transmission means high absorption. Redrawn from J. E. Harries, Earthwatch, The Climate from Space. Horwood, New York, Copyright © 1990.

FIGURE 3-4 Spectral distribution of solar irradiation at the top of the atmosphere and at sea level for average atmospheric conditions for the sun at zenith. Shaded areas represent absorption by various atmospheric gases. Unshaded area between the two curves represents the portion of the solar energy backscattered by the air, water vapor, dust, and aerosols and reflected by clouds. Redrawn from J. P. Peinuto and A. H. Oort, Physics of Climate. American Institute of Physics, New York. Copyright © 1992 by Springer-Verlag GmbH & Co. Used by permission of the publisher.

## Post a comment