The major forcing for the climate system is energy received from the Sun. The Earth intercepts a fraction of the radiant energy emitted by the Sun. A surface perpendicular to the solar ray at the upper edge of the Earth's atmosphere and at the mean Earth-Sun distance receives 1367Wm—2 or the solar constant (Sc), but its true value is uncertain by 4Wm—2 (Hoyt and Schatten, 1997). The solar radiation spread evenly over the spherical surface of the entire globe equates to 342 W m—2. This relationship exists because the shadow area of a spherical planet is a circle with the same radius as the sphere but an area one-fourth that of the sphere. The radiant energy delivered to the upper edge of the Earth's atmosphere is available to be transmitted, reflected, or absorbed by the atmosphere and reflected or absorbed at the Earth's surface.

The Earth's radiation balance is an accounting of the disposition of the intercepted solar energy for a specified period. In its simplest form, the radiation balance tells us that the amount of solar radiation absorbed by the atmosphere and the Earth's surface is equal to the amount of thermal radiation emitted by the Earth's surface and atmosphere back to space for periods greater than one year (Burroughs, 2001). By assuming that both the Sun and Earth behave as blackbody radiant energy absorbers and emitters (see Section 2.8.2), the simplest expression of the radiation balance takes the form

which complies with the conservation of energy expressed in the First Law of Thermodynamics for a closed system. Quantitative expression of the individual solar and thermal radiant energy fluxes involved in Equation 2.3 requires familiarity with the physical laws that determine the properties of solar radiation and thermal radiation. An overview is presented in the following sections to facilitate development of the basic principles required for expanding Equation 2.3 to include the relevant radiant energy fluxes. Expanded treatments of these topics are found in Peixoto and Oort (1992), Guyot (1998), and Andrews (2000).

Any object with a temperature above absolute zero (—273.15 °C or 0K) emits radiant energy. Radiant energy in the form of electromagnetic energy travels in a wave form and has properties determined by the temperature of the emitting object. The wave is a series of adjacent crests and troughs. The energy can be characterized by the speed, wavelength, or the frequency of the waves, but the wavelength is used most often in climatology. Wavelength is the distance between two adjacent crests. However, the speed of an electromagnetic wave is a constant, and the speed must equal the product ofthe wavelength and the frequency. The frequency is the number of waves passing a given point per unit time. Thus, longer wavelengths of electromagnetic energy have lower frequencies and shorter wavelengths have higher frequencies. Electromagnetic energy requires no intervening medium for transmission.

Electromagnetic radiation can be thought of as either a wave or as a stream of particles that represents movement of energy through space. A photon is a single particle or a discrete unit of electromagnetic energy. It represents the smallest amount of energy transported by an electromagnetic wave of a specific frequency. Wave theory is commonly employed when scattering of radiation by particles and surfaces is the primary concern (Hartmann, 1994). Thinking of radiant energy as discrete parcels or photons is the common convention when radiation absorption and emission are of primary interest.

Differences in the energy levels of electromagnetic radiation are related to photon energy, Eph, which is proportional to its frequency. The relationship is expressed as he*

where h is Planck's constant (6.63 x 10—34 J s), v is the wave frequency in cycles per second, c* is the speed of light (3.00 x 108 m s—1), and l is the wavelength in micrometers, mm (1 mm = 10—6 m). The difference in photon energy is important when electromagnetic energy interacts with matter. Equation 2.4 tells us that high-frequency and short-wavelength photons have high energy. Low-frequency and long-wavelength photons have low energy. The significance of these differences is seen when the selective response of atmospheric gases to radiation is addressed in Section 2.9.

Understanding absorption and emission of radiant energy is aided by using the concept of blackbody radiation. A blackbody is a hypothetical object that emits or absorbs electromagnetic radiation with 100% efficiency. An object that emits radiation that is uniquely related to the temperature of the object is a blackbody radiator. The energy flux is known as blackbody radiation since it corresponds to emission from a surface with unit emissivity at all wavelengths. Emissivity is the ratio of the actual energy emission of an object to the black-body emission per unit area at the same temperature. The dependence of black-body emission on temperature is expressed by the Stefan-Boltzmann law as

0.1 0.15 0.2 0.3 0.5 1.0 1.5 2.0 3.0 5.0 10 15 20 30 50 100

Wavelength (microns)

0.1 0.15 0.2 0.3 0.5 1.0 1.5 2.0 3.0 5.0 10 15 20 30 50 100

Wavelength (microns)

Fig. 2.1. Normalized blackbody emission spectra as a function of wavelength for the Sun (6000 K) and Earth (255 K). (From Peixoto and Oort, 1992, Figure 6.2. Used with kind permission of Springer Science and Business Media.)

where F* is the blackbody radiative energy emission inWm-2, e is the emissiv-ity for a blackbody and is dimensionless, a is the Stefan-Boltzmann constant (5.67 x 10"8Wm"2 K~4), and T is temperature in K. The Stefan-Boltzmann law is an integral of Planck's law over all frequencies for the entire wavelength domain. Using the average flux density of the Sun's photosphere (6.4 x 107Wm~2) and rearranging Equation 2.5, the effective emission temperature of the Sun's photosphere is estimated as 6000 K. Neither the Sun nor Earth is a perfect blackbody, but they conform approximately to Planck's law.

A second characteristic of blackbody radiant energy that is a corollary of Planck's law is that the wavelength most strongly emitted by an object is inversely proportional to its absolute temperature. This relationship is known as Wien's displacement law and is expressed as

where Amax is the wavelength of maximum energy emission in mm, k is a constant (2898 mmK), and T is the absolute temperature in K. An important characteristic evident from Wien's law is the hotter an object, the smaller the wavelength of maximum emission. Conversely, the cooler an object, the longer the wavelength of maximum emission. In Wien's law we find the basis for distinguishing between solar and planetary radiation in the electromagnetic spectrum. Solar radiation emitted from the photosphere at a temperature of about 6000 K has a peak emission at 0.5 mm in the visible portion of the spectrum. Earth's radiation with a temperature of 255 K peaks at 10 mm in the far-infrared portion of the spectrum. Ideal Planck curves (Fig. 2.1) for the Sun and Earth integrated over the Earth's surface and all solid angles show the solar and terrestrial fluxes are equal when normalized according to their maximum values. These conditions are typical of the mid-latitudes, a solar elevation of 40°, and diffuse terrestrial radiation (Goody and Yung, 1989). The emission peaks and their related curves establish a physical basis for distinguishing between solar radiation as shortwave radiation and terrestrial radiation as longwave radiation.

Much of the Sun's ultraviolet radiation is absorbed by ozone and oxygen in the upper atmosphere as solar radiation penetrates the Earth's atmosphere (Fig. 2.2). Water vapor and carbon dioxide in the lower atmosphere absorb much of the infrared radiation beyond 1.2 to 2 mm. This accounts for the solar radiation reaching the Earth's surface being reduced to a range from 0.3 to 2 mm (Burroughs, 2001). Section 2.9 treats the selective reduction of solar radiation in the atmosphere.

It is important to recognize that about 30% of the incident solar radiation at the upper edge of the Earth's atmosphere is not available to be absorbed. This energy is reflected back to space by the atmosphere and the Earth's surface and constitutes the Earth's albedo (ap) or reflectivity (see Fig. 1.4). The left side of Equation 2.3 can then be stated as

where Sc is the solar constant of 1367 Wm—2, ap is the planetary albedo of 0.30, and rp is the Earth's radius of 6370 km. The globally averaged absorbed solar radiation at the top of the Earth's atmosphere is about 235 Wm—2. This is the amount of radiant energy that must be returned to space by terrestrial and atmospheric thermal radiation for the system to remain in thermal equilibrium.

Ultraviolet Visible Near-IR Infrared Far-Infrared Microwave

Ultraviolet Visible Near-IR Infrared Far-Infrared Microwave

Fig. 2.2. Absorption spectra for the total atmosphere and for selected atmospheric gases between the top of the atmosphere and the Earth's surface. (From Peixoto and Oort, 1992, Figure 6.2. Used with kind permission of Springer Science and Business Media.)

The Earth's radiation is complicated because the land, oceans, and atmosphere are all emitters of thermal radiation. In general, most land surfaces and the oceans can be regarded as blackbody radiators. They radiate across a continuous spectral interval approaching a constant emissivity. The radiative properties of the atmosphere are dominated by a small number of trace gases that constitute a relatively small proportion of the total atmospheric volume. Water vapor, carbon dioxide, and ozone are the primary trace gases of concern for their radiatively reactive properties. These gases absorb specific wavelengths of radiant energy, and they radiate only at specific wavelengths that give them variable emissivities.

As a result of the multiple emitters, terrestrial radiation at any given point is proportional to the fourth power of the surface temperature and the characteristics of the intervening atmosphere. The eventual emitted radiation is different from the radiation emitted by the surface because the surface radiation is absorbed and reemitted by the atmospheric trace gases whose temperatures are different from the underlying land or ocean surface temperature (Burroughs, 2001). The emitted thermal radiation is called terrestrial radiation even though it comes from both the surface and the atmosphere. Another distinctive characteristic of terrestrial radiation is that emission occurs during both the day and night.

A first approximation expressing emitted terrestrial radiation is achieved by symbolic representation of the right side of Equation 2.3. By assuming the

\107N

Reflected Solar

Reflected Solar

\107N

Outgoing Longwave Radiation. 235 W m f/40 Atmosphere Window

Greenhouse Gases

Absorbed by Surface

Thermals Evapotranspiration

Absorbed by Surface

Thermals Evapotranspiration

Outgoing Longwave Radiation. 235 W m f/40 Atmosphere Window

Greenhouse Gases

Absorbed by Surface

Fig. 2.3. Earth-atmosphere annual global mean radiation balance. Units in Wm~2. (From Kiehl and Trenberth, 1997, Fig. 7. Used with permission of the American Meteorological Society.)

terrestrial emission is like that of a blackbody and that the emission occurs over the surface area of a sphere, the terrestrial radiation emission is

Earth radiation emitted = aT44prp (2.8)

where a is the Stefan-Boltzmann constant defined for equation 2.5, Te is the Earth's blackbody emission temperature in K, and rp is defined for Equation 2.7. The net thermal radiation lost to space from the surface and the atmosphere depicted by solving Equation 2.8 approximates the 235 Wm—2 of outgoing longwave radiation shown in Figure 2.3.

Terrestrial radiation ranges across the spectral range of 4 to 200 mm with a peak emission at about 10 mm (see Fig. 2.1). Nearly 99% of the terrestrial infrared radiation occurs in the spectral range from 4 to 80 mm. However, a majority of terrestrial radiation is concentrated between 8 and 30 mm.

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