Radiative Exchange

Absorption, reflection, and emission of radiation are critical processes that shape the global energy balance and its regional variations. To understand these variations, the nature of radiation, the processes that reflect and absorb it, as well as the resulting latitudinal variation of radiative fluxes for the present-day climate are explained in the following.

Electromagnetic Radiation

Electromagnetic radiation is characterized by its wavelength A, or alternatively by its frequency v. The two variables are related by A x v = c, with c being the speed of light (c = 3 x 108 km s in vacuum). Climatically relevant are mainly the following wavelength ranges: (1) ultraviolet radiation, corresponding to wavelengths of less than 400 nm; (2) visible light, ranging from 400 nm (blue light) to 750 nm (red light); and (3) infrared radiation, referring to wavelengths longer than 750 nm. Radiation with shorter wavelengths is generally referred to as more energetic.

The peak of emission of solar radiation is about 550 nm (green light), while the Earth with its much lower emission temperature has its peak emission at about 11 mm (infrared). The peak of emission is described by Wien's law (Apeak = 0.2898 x 10- mK/TR). Since these peak wavelengths and the associated distributions are well separated, electromagnetic radiation in climatology is generally classified into two types: solar (or shortwave) radiation that is emitted by the Sun, and terrestrial (or longwave) radiation associated with emission ofradiation within the Earth system.

Solar Radiation

In order to understand spatial and temporal variations in temperature, one needs to consider the causes of variability in the heating and cooling terms of the energy balance. The main factor in this variaibility is the variations of solar radiation that can result from three aspects:

1. The amount of emitted radiation by the Sun (solar luminosity L0). The typical value of the solar luminosity is L0 = 3.9 x 1026 W, corresponding to a surface emission temperature of= 5760 K. The actual value of L0 varies, for instance, on decadal timescales through the sunspot cycle (11 years, by less than 1.5 Wm-2), and increases over geologic time (L0 was about 70% of the present-day value 4.5 billion years ago).

2. The distance dEarth of the Earth to the Sun. The flux of solar energy remains constant through any surface around the Sun, but the density decreases quadratically with distance, so that at the mean distance of the Earth's orbit of about dEarth = 150 x 106 km, an average amount of I0 = L0/4^d|arth = 1367 Wm-2 illuminates the Earth.

The value of I0 is referred to as the solar constant. Considering that the Sun illuminates the Earth's cross section of size ^«Earth2, but the surface area of the Earth is 4^dEarth, the mean solar radiation used above is obtained by Io,mean = Io/4 = 342 Wm~2. The mean distance of the Earth varies between 147 x 106 and 152 x 106km throughout the year, due to Earth's slightly eccentric orbit (Figure 2). The location of the Earth's path that is closest (farthest) to the Sun is called the perihelion (aphelion). The perihelion currently occurs in early January, so that the Earth in total receives about 7% more sunlight in January than it does in July. These orbital parameters - perihelion, eccentricity, and obliquity (or tilt) - vary on longer timescales and relate to the timing of ice ages. Even though the direct impacts of solar radiation are well understood, the indirect effects and feedbacks that amplify the Earth system response to these orbital changes are not yet fully understood.

3. the orientation of the surface toward the Sun, as characterized by the solar zenith angle 8: The amount of incident solar radiation for a given region depends on latitude and time within the year. It is calculated from the zenith angle 8, which measures the position of the Sun to the vertical, and the declination angle 6, which characterizes the relation of the Earth's tilt to the direction of sunlight (Figure 3). Integration yields a global mean solar radiation Io,mean = Io/4.

Reflection of Radiation

Reflection of radiation is mainly due to scattering. The size of the scattering particle plays an important role and affects the amount of radiation of a certain wavelength A that is scattered, resulting in three forms of scattering:

1. Rayleigh scattering applies to very small particles with diameters of 0.1-1 nm, such as electrons. The intensity of scattering varies with A~ , therefore affecting primarily radiation of short wavelength. This process of scattering results in blue skies since blue light is scattered much more strongly than red light.

2. Mie scattering involves particles with diameters of 0.01-1 mm, such as aerosols. The intensity of scattering varies with A_1, so that the intensity of scattering is more evenly spread across wavelengths. This scattering process results, for example, in hazy skies at a windy day at the beach due to sea spray, or over cities due to air pollution (i.e., aerosol production by traffic).

3. Geometric scattering applies to large particles with sizes ranging from 10 to 100 mm, such as cloud droplets. Intensity of scattering does not vary with wavelength. This form of scattering makes clouds appear white.

Typical values of albedo (or reflectivity) of different surfaces are summarized in Table 4. The reflectivity also depends on other factors, such as the zenith angle, and wavelength. For instance, vegetated surfaces are generally

Sun Zenith Angle

equinox

Figure 2 The orbit of the Earth around the Sun and its relation to seasons. The orbit of the tilted Earth around the Sun results in the seasons, as indicated for the Northern Hemisphere (NH). In the NH winter, the Earth's axis of rotation is pointed away from the Sun, resulting in less incident solar radiation and the polar night at latitudes above the Arctic Circle. This situation is reversed in the summer.

equinox

Figure 2 The orbit of the Earth around the Sun and its relation to seasons. The orbit of the tilted Earth around the Sun results in the seasons, as indicated for the Northern Hemisphere (NH). In the NH winter, the Earth's axis of rotation is pointed away from the Sun, resulting in less incident solar radiation and the polar night at latitudes above the Arctic Circle. This situation is reversed in the summer.

Solar Zenith Polar Night

Earth

Figure 3 Effects of the orientation of the Earth's surfaces toward the Sun on the amount of incident solar radiation at different locations of the Earth's surface. Left: The amount of solar radiation that reaches the surface at a given latitude depends on the declination angle 8. The declination angle measures the angle between the Earth's axis of rotation and the vertical plane of the orbit, or, alternatively, the angle between the direction of solar radiation and the Earth's equator. The declination angle defines Earth's major regions: the tropics (latitudes -8 to +8) and the polar regions (90° - 8 to pole). Earth's declination angle is currently at 23.45°. Right: At a given location on Earth, the zenith angle measures the angle between the vertical and the Sun. It depends on hour, latitude, and time of year. In the situation shown on the left (Northern Hemisphere winter solstice), the zenith angle at location A at noon is 90°, that is, the Sun does not rise above the horizon and no solar radiation is incident at the surface. At location B, the zenith angle is in between 0° and 90°. At location Cat the tropic of Capricorn, the zenith angle is 0° at noon, and the incoming solar radiation is vertical to the surface. In sloped terrain, a correction needs to be applied for the calculation of incident radiation to correct for the slope.

Earth

Figure 3 Effects of the orientation of the Earth's surfaces toward the Sun on the amount of incident solar radiation at different locations of the Earth's surface. Left: The amount of solar radiation that reaches the surface at a given latitude depends on the declination angle 8. The declination angle measures the angle between the Earth's axis of rotation and the vertical plane of the orbit, or, alternatively, the angle between the direction of solar radiation and the Earth's equator. The declination angle defines Earth's major regions: the tropics (latitudes -8 to +8) and the polar regions (90° - 8 to pole). Earth's declination angle is currently at 23.45°. Right: At a given location on Earth, the zenith angle measures the angle between the vertical and the Sun. It depends on hour, latitude, and time of year. In the situation shown on the left (Northern Hemisphere winter solstice), the zenith angle at location A at noon is 90°, that is, the Sun does not rise above the horizon and no solar radiation is incident at the surface. At location B, the zenith angle is in between 0° and 90°. At location Cat the tropic of Capricorn, the zenith angle is 0° at noon, and the incoming solar radiation is vertical to the surface. In sloped terrain, a correction needs to be applied for the calculation of incident radiation to correct for the slope.

much more reflective (30-50%) in the near infrared (at wavelengths of 0.8-1.0 mm) but absorbent in the red part of the spectrum at about 0.6 mm, with a low reflectivity of around 5%. This difference in absorptive characteristics is used for the remote sensing of vegetation greenness.

Absorption of Radiation

Radiation is absorbed by different processes and at different intensities, depending on material characteristics and the wavelength of incident radiation A:

1. Photoionization refers to highly energetic radiation with wavelengths of less than 100 nm; it can remove electrons from atoms, resulting in ionized atoms. This process can be found in the higher atmosphere at heights of 100 km and above in the so-called ionosphere.

2. Photodissociation applies to highly energetic radiation of short wavelengths, where the energy of the radiation is absorbed by breaking up molecular bonds. This process occurs in the atmosphere mainly for wavelengths shorter than visible light. An example is the absorption of ultraviolet radiation by molecular oxygen and ozone in the stratosphere.

3. Electronic absorption is relevant to the absorption of visible light. Here, radiation is absorbed by raising electrons into excited states. While this form of absorption has little relevance in atmospheric absorption, it is essential for photosynthesis, where electronic absorption is used to separate hydrogen ions from the water molecule.

4. Molecules can absorb radiation if the electronic charge is unevenly distributed in the molecule, causing a dipole moment. The absorption results in rotation or vibration of the molecule. This mechanism of absorption is relevant for radiation with low energy and long wavelengths (near infrared and longer).

In the atmosphere, water vapor (H2O) absorbs very well by rotational and vibrational modes due to the architecture of the molecule, where the oxygen atom attracts the electrons more than the two hydrogen atoms. Other climatically relevant gases that absorb by this mechanism are carbon dioxide (CO2), methane (CH4), and nitrous oxide (N2O).

Because the Earth's surface emits radiation mainly in the infrared, gases that absorb in these wavelengths are called greenhouse gases. Water vapor and clouds are by far the most important contributors to the strength of the

Table 4 Range and typical values of reflectivity of clouds and surface albedo for different surfaces

Range Typical

Table 4 Range and typical values of reflectivity of clouds and surface albedo for different surfaces

Atmosphere

Cirrus clouds

21

Cumulus clouds

48

Stratus clouds

69

Ice, snow, and water

Deep water, small zenith angle

3-10

7

Deep water, large zenith angle

10-100

Sea ice

30-45

30

Snow, fresh

70-95

80

Snow, old

35-65

50

Snow, forested

11-35

25

Bare land surfaces

Sand, wet

20-30

25

Sand, dry

30-45

35

Clay, wet

10-20

15

Clay, dry

20-40

30

Humus soil, moist

5-15

10

Desert

20-45

30

Concrete

15-35

20

Asphalt pavement

5-10

7

Vegetated surfaces

Tundra

18-25

15

Grassland

16-26

19

Coniferous forest

5-15

12

Deciduous forest

10-20

17

Evergreen forest

12-25

13

Cropland

18

present-day greenhouse effect. The special role of carbon dioxide originates from two facts: (1) water vapor absorbs poorly at the peak of the Earth's surface emission at about 11 mm, where the CO2 molecule has a dominant absorption peak nearby at 15 mm and therefore absorbs very well; and (2) the concentration of water vapor in the atmosphere is constrained to at or below its saturation level, which in turn depends on the ambient air temperature. Hence, the concentration of water vapor reacts to other prevailing conditions and by itself does not act as a driver for change. For instance, cold air is unable to hold large amounts of water vapor, and consequently water vapor plays a less important role, for example, in cold regions of the atmosphere, and in winter seasons in polar regions.

Zonal Distribution of Radiative Fluxes

The zonal distribution of solar and terrestrial radiation for the present day are shown in Figure 4 for the top of the atmosphere and at the surface. The imbalance of net fluxes at the top of the atmosphere, where the tropics absorb more solar radiation than is emitted as terrestrial radiation, reflect overall heat distribution within the climate system that is governed by atmospheric and ocean dynamics.

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