Atmospheric Radiation and Photochemistry

Solar Power Design Manual

Do It Yourself Solar Energy

Get Instant Access

4.1 RADIATION

Basically all the energy that reaches the Earth comes from the Sun. The absorption and loss of radiant energy by the Earth and the atmosphere are almost totally responsible for the Earth's weather on both global and local scales. The average temperature on the Earth remains fairly constant, indicating that the Earth and the atmosphere on the whole lose as much energy by reradiation back into space as is received by radiation from the Sun. The accounting for the incoming and outgoing radiant energy constitutes the Earth's energy balance. The atmosphere, although it may appear to be transparent to radiation, plays a very important role in the energy balance of the Earth. In fact, the atmosphere controls the amount of solar radiation that actually reaches the surface of the Earth and, at the same time, controls the amount of outgoing terrestrial radiation that escapes into space.

Radiant energy, arranged in order of its wavelengths X, is called the spectrum of radiation. The electromagnetic spectrum is shown in Figure 4.1. The Sun radiates over the entire electromagnetic spectrum, although, as we will see, most of the energy is concentrated near the visible portion of the spectrum, the narrow band of wavelengths from 400 to 700 nm (0.4-0.7 pm). Our interest will be confined to the so-called optical region, which extends over the near ultraviolet, the visible, and the near infrared, the wavelength range from 200 nm to 100 pm. This range covers most of the solar radiation and that emitted by the Earth's surface and atmosphere. Three interrelated measures are used to specify the location in the electromagnetic spectrum, the wavelength X, the frequency v, and the wavenumber v = X""1. Frequency v and wavelength X are related by v = c/X, where c is the speed of light. In the ultraviolet and visible portion of the spectrum it is common to characterize radiation by its wavelength, expressed either in nanometers (nm) or micrometers (nm). In the infrared part of the spectrum, the wavenumber (cm-1) is frequently used.

Radiation is emitted from matter when an electron drops to a lower level of energy. The difference in energy between the initial and final level, Ae, is related to the frequency of the emitted radiation by

Atmospheric Chemistry and Physics: From Air Pollution to Climate Change, Second Edition, by John H. Seinfeld and Spyros N. Pandis. Copyright © 2006 John Wiley & Sons, Inc.

Low Frequency

High Frequency (Radio)'

Very High Frequency (Television)

Ultra-high Frequency' (Radar)

Infrared

Visible | Ultraviolet \

X-Rays

Gamma Rays <

Cosmic Rays

104m

102 m

in"1 m

10"2cm p^

10"4cm

10 6cm

10 cm

1012cm

FIGURE 4.1 Electromagnetic spectrum.

where Planck's constant, h = 6.626 x 10 34 J s, and the speed of light in vacuum, c = 2.9979 x IO8 m s 1 (see Table A.6). When the energy difference As is large, the frequency of the excited photon is high (very small wavelength) and the radiation is in the X-ray or gamma-ray region. Equation (4.1) also applies to the absorption of a photon of energy by a molecule. Thus a molecule can absorb radiant energy only if the wavelength of the radiation corresponds to the difference between two of its energy levels. Since the spacing between energy levels is, in general, different for molecules of different composition and shape, the absorption of radiant energy by molecules of differing structure occurs in different regions of the electromagnetic spectrum.

The amount of energy radiated from a body depends largely on the temperature of the body. It has been demonstrated experimentally that at a given temperature there is a maximum amount of radiant energy that can be emitted per unit time per unit area of a body. This maximum amount of radiation for a certain temperature is called the blackbody radiation. A body that radiates, for every wavelength, the maximum possible intensity of radiation at a certain temperature is called a blackbody. This maximum is identical for every blackbody regardless of its constituency. Thus the intensity of radiation emitted by a blackbody is a function only of the wavelength, absolute temperature, and surface area. The term "blackbody" has no reference to the color of the body. A blackbody can also be characterized by the property that all radiant energy reaching its surface is absorbed.

4.1.1 Solar and Terrestrial Radiation

The Sun is a gaseous sphere of radius about 6.96 x 10s km and of mass about 1.99 x 1030kg. It is made up of approximately three parts hydrogen and one part helium. In the core of the Sun energy is produced by nuclear reactions (fusion of four H atoms into one He atom, with a small loss of mass). It is believed that energy is transferred to the outer layers mainly by electromagnetic radiation. The outer 500 km of the Sun, called the photosphere, emits most of the radiation received on the Earth. Radiation emitted by the photosphere closely approximates that of a blackbody at about 6000 K. The energy spectrum of the Sun as compared with that of a blackbody at 5777 K as received at the top of the Earth's atmosphere is shown in Figure 4.2. The maximum intensity of incident radiation occurs in the visible spectrum at about 500 nm (0.5 pm). In contrast, Figure 4.3 shows the emission of radiant energy from a blackbody at 300 K, approximating the Earth. The peak in radiation intensity occurs at about 10 pm in the invisible infrared.

The monochromatic emissive power of a blackbody FB(A,)(Wm~2 m_1) is related to temperature and wavelength by

2nc2hX~5

where k is the Boltzmann constant (Table A.6). (In Chapter 3 we used kg to represent the Boltzmann constant to avoid confusion with the reaction rate coefficient.)

As can be seen from Figures 4.2 and 4.3, the higher the temperature, the greater is the emissive power (at all wavelengths). We also see that, as temperature increases, the maximum value of FB(h) moves to shorter wavelengths. The wavelength at which the maximum amount of radiation is emitted by a blackbody is found by differentiating (4.2) with respect to X, setting the result equal to zero, and solving for X. The result is approximately hc/5kT and with X expressed in nm and Tin kelvin units is

2000

fc 6 1500

1000

o 00

1000

Atmospheric Chemistry

FIGURE 4.2 Solar spectral irradiance (WrrT2 nm"1) at the top of the Earth's atmosphere compared to that of a blackbody at 5777 K (dashed line) (Iqbal 1983). There is a reduction in total intensity of solar radiation from the Sun's surface to the top of the Earth's atmosphere, given by the ratio of the solar constant, 1370Wm~2, to the integrated intensity of the Sun [see (4.4)]. That ratio is about 1/47,000. (Reprinted by permission of Academic Press.)

Wavelength, |0,m

FIGURE 4.2 Solar spectral irradiance (WrrT2 nm"1) at the top of the Earth's atmosphere compared to that of a blackbody at 5777 K (dashed line) (Iqbal 1983). There is a reduction in total intensity of solar radiation from the Sun's surface to the top of the Earth's atmosphere, given by the ratio of the solar constant, 1370Wm~2, to the integrated intensity of the Sun [see (4.4)]. That ratio is about 1/47,000. (Reprinted by permission of Academic Press.)

Thus hot bodies not only radiate more energy than cold ones, they do so at shorter wavelengths. The wavelengths for the maxima of solar and terrestrial radiation are 480 nm and ~ 10,000 nm, respectively. The Sun, with an effective surface temperature of ~6000K, radiates about 2 x 105 more energy per square meter than the Earth does at 300 K.

If (4.2) is integrated over all wavelengths, the total emissive power Fg (W m~2) of a blackbody is found to be poo

Jo where ct = 5.671 x 10~8 Wm~2K-4, the Stefan-Boltzmann constant.

4.1.2 Energy Balance for Earth and Atmosphere

The Earth's climate is controlled by the amount of solar radiation intercepted by the planet and the fraction of that energy that is absorbed. The flux density of solar energy, integrated a

Atmospheric Chemistry

FIGURE 4.3 Spectral irradiance (W m 2 |im 1) of a blackbody at 300 K.

20 30 40 50 60 Wavelength, (im

FIGURE 4.3 Spectral irradiance (W m 2 |im 1) of a blackbody at 300 K.

over all wavelengths, on a surface oriented perpendicular to the solar beam at the Earth's orbit is about 1370 Wm"2. This is called the solar constant} Let the solar constant be denoted by 50 = 1370Wm~2. The cross-sectional area of the Earth that intercepts the solar beam is nR1, where R is the Earth's radius. The surface area of the Earth that receives the radiation is 4jiR2. Thus the fraction of the solar constant received per unit area of the Earth is (nR2/4nR2) = \ of the solar constant, about 342 Wm"2. Of this incoming solar radiation, a fraction is reflected back to space; that fraction, which we can denote by Rp, is the global mean planetary reflectance or albedo. Rp is about 0.3 (Ramanathan 1987; Ramanathan et al. 1989).2 Contributing to Rp are clouds, scattering by air molecules,

'Since the late 1970s, regular satellite measurements of the solar constant have been performed (Mecherikunnel et al. 1988). Maximum differences in the value of S0 among the instruments is about 2 W irT2, corresponding to a little more than 0.1% of the value of S0. Over the period 1980-1986 the so-called SMM/ACRIM instrument measured an average value of S0 of about 1386Wm~2, whereas that on NIMBUS-7 reported an average S0 of about 1370Wm~2.

2The average value of the albedo, the incoming radiation that is reflected or scattered back to space without absorption, is usually taken to be somewhere in the range of 30-34%. It is important to note that the albedo varies considerably, depending on the surface of the Earth. For example, in the polar regions, which are covered by ice and snow, the reflectivity of the surface is very high. On the other hand, in the equatorial regions, which are covered largely with oceans, the reflectivity is low, and most of the incoming energy is absorbed by the surface.

FIGURE 4.4 The Earth's annual and global mean energy balance (Kiehl and Trenberth 1997). Of 342 Wm~2 incoming solar radiation, 168 Wm~2 is absorbed by the surface. That energy is returned to the atmosphere as sensible heat, latent heat via water vapor, and thermal infrared radiation. Most of this radiation is absorbed by the atmosphere, which, in turn, emits radiation both up and down. (Reprinted by permission of the American Meteorological Society.)

FIGURE 4.4 The Earth's annual and global mean energy balance (Kiehl and Trenberth 1997). Of 342 Wm~2 incoming solar radiation, 168 Wm~2 is absorbed by the surface. That energy is returned to the atmosphere as sensible heat, latent heat via water vapor, and thermal infrared radiation. Most of this radiation is absorbed by the atmosphere, which, in turn, emits radiation both up and down. (Reprinted by permission of the American Meteorological Society.)

scattering by atmospheric aerosol particles, and reflection from the surface itself, the surface albedo (the surface albedo is denoted as Rs). The fraction 1 — Rp represents that fraction of solar shortwave radiation that is absorbed by the Earth-atmosphere system. For Rp = 0.3, this corresponds to about 235 Wm-2. This amount is matched, on an annual and global average basis, by the longwave infrared radiation emitted from the Earth-atmosphere system to space (Figure 4.4). The infrared radiative flux emitted at the surface of the Earth, about 390Wm-2, substantially exceeds the outgoing infrared flux of 235 W m~2 at the top of the atmosphere. Clouds, water vapor, and the greenhouse gases (GHGs) both absorb and emit infrared radiation. Since these atmospheric constituents are at temperatures lower than that at the Earth's surface, they emit infrared radiation at a lower intensity than if they were at the temperature of the Earth's surface and therefore are net absorbers of energy.

The equilibrium temperature of the Earth can be estimated by a simple model that equates incoming and outgoing energy (Figure 4.5). Incoming solar energy at the surface of the Earth is

For an average blackbody temperature of the Earth-atmosphere system Te defined on the basis of (4.4), the longwave emitted flux averaged over the globe is

Blackbody Temperature Earth

Equating Fs and FL yields the following expression for Te:

For Rp = 0.30, this equation gives Te ~ 255 K. If the Earth were totally devoid of clouds, then the global albedo would be about Rp = 0.15. With this value of Rp, the equilibrium temperature Te = 268 K. This simple equation predicts that Te varies about 0.5 K for a lOWm"2 (0.7%) variation in the solar constant, or for a reflectance variation around Rp = 0.3 of ARp = 0.005.

In summary, the net outgoing radiative flux of about 235 Wm"2 corresponds to a blackbody temperature of 255 K (—18°C). The surface emission of 390 W m 2 corresponds to a blackbody temperature of 288 K. Therefore, the surface temperature is about 33°C warmer than it would be if the atmosphere were completely transparent (and the planetary albedo were still 0.3).

The net radiative energy input, Fna = Fs — Fi, is zero at equilibrium. If a perturbation occurs then the change in net energy input is related to the changes in both solar and longwave components by

To reestablish equilibrium, a temperature change ATe results, which can be related to AFnet by a parameter Xq where Xo, having units K(Wm 2) ', is the climate sensitivity factor. If we neglect any feedbacks in the climate system, Xo can be estimated as (dFe/cTef1

and Xo ~ 0.3 K (Wm-2)-1. A doubling of the C02 abundance from the preindustrial (pre-Industrial Revolution) level is estimated to produce AFL = 4.6Wm~2. With Xo = 0.3 K (W m~2)-1, this would lead to an increase in the global mean temperature of A Te — 1.4K. This temperature increase is less than what climate models predict because of feedbacks that act to enhance warming. As noted earlier, such feedbacks include, for example, the fact that a warmer atmosphere contains more water vapor, and hence an enhanced infrared absorption.

Global climate change is induced by a forcing that disturbs the equilibrium and leads to a nonzero average downward net flux at the top of the atmosphere (TOA):

It is customary to write (4.11) in terms of downward flux, — Fnet, at the TOA; an increase of -f nel corresponds to heating of the planet. Primary forcing can occur as a result of changes of So, Rp, or F). Changes in incoming solar radiation have resulted from changes in the Earth's orbit and from variations in the Sun's output of energy. Changes in the planetary albedo Rp can result from changes in surface reflectance from human activity (agriculture, deforestation), from changes in the aerosol content of the atmosphere from both natural (volcanoes) and anthropogenic (industrial emissions, biomass burning) causes, and to a lesser extent from changes in levels of gases that absorb solar wavelengths (e.g., ozone). Changes in the emitted longwave flux FL result primarily from changes (increases) of absorbing gases in the atmosphere and to a lesser extent from changes in aerosols.

We return to this in Chapter 23.

4.1.3 Solar Variability

The amount of solar radiation reaching Earth and Earth's changing orientation to the Sun have been the major causes for climatic change throughout its history. If the Sun's radiation intensity declined by 5-10% and there were no other compensating factors, ice would engulf the planet in less than a century. Although no theory exists to predict future changes in solar output, the effect of changes in Earth's orbit as it travels around the Sun is beginning to be understood. During the past million years, Earth has experienced 10 major and 40 minor episodes of glaciation. All appear to have been controlled by three so-called orbital elements that vary cyclically over time:

1. Earth's tilt changes from 22° to 24.5° and back again every 41,000 years.

2. The month when Earth is closest to the Sun also varies over cycles of 19,000 and 24,000 years. Currently, Earth is closest to the Sun in January. This month-of-closest-approach factor can make a difference of 10% in the amount of solar radiation reaching a particular location in a given season.

3. The shape of Earth's orbit varies from being nearly circular to being more elliptical with a period of 100,000 years.

The climatic cycles caused by these orbital factors are called Milankovitch cycles after the Serbian mathematician Milutin Milankovitch, who first described them in 1920. Superimposed on the Milankovitch cycles are changes in the Sun that occur over days or months or a few years.

Even though studies of ocean cores have shown that these orbital changes are the principal determinant of the times of glaciation, the exact mechanisms by which Earth responds to the orbital changes have not been established. Orbital changes alone appear not to have caused the vast climate shifts associated with glaciation and déglaciation. Feedbacks, such as changes in Earth's reflectivity, amount of particles in the atmosphere, and the carbon dioxide and methane content of the atmosphere, act together with orbital changes to enhance global warming and cooling. The levels of carbon dioxide and methane, as shown in ice core measurements, decrease during times of glaciation and increase during warming periods, although it is not known exactly how or why their concentrations rise and fall. (See Chapter 23.)

The radiative forcing resulting from changing solar output can be obtained by multiplying the change in total solar irradiance by (1 — Rp)/4, where Rp is the Earth's albedo. For Rp = 0.3, (1 - #p)/4 = 0.175. A 0.1% change in total solar irradiance (1.4 Wm~2) would be equivalent to a radiative forcing of about 0.2 W m

Was this article helpful?

0 0
Getting Started With Solar

Getting Started With Solar

Do we really want the one thing that gives us its resources unconditionally to suffer even more than it is suffering now? Nature, is a part of our being from the earliest human days. We respect Nature and it gives us its bounty, but in the recent past greedy money hungry corporations have made us all so destructive, so wasteful.

Get My Free Ebook


Post a comment