4.2.1Incident Radiation at The Top of The
Atmosphere
4.2.2Variations in Insolation
Due to Earth-Sun Distance
4.2.3Variations in Solar
Insolation Due to Solar Zenith Angle
4.2.4Key Points about Radiation that
Reaches Earth's Atmosphere
4.2.5Interactions Between
Light and Matter in the Atmosphere
4.2.6Atomic Structure and the Energy of
an Atom
4.2.7Absorption and Emission of Photons by
Atoms
4.2.8The Energy of a
Molecule
4.2.9Key Points about The
Interaction of Light and Matter
4.2.10Absorption in the
Atmosphere
4.2.11Basic Ozone Photochemistry
4.2.12Atmospheric Scattering - Some
Basics
4.2.13Rayleigh Scattering and Mie
Scattering
4.2.14Single and Multiple
Scattering
4.2.15Key Points about Atmospheric
Scattering
4.2.1 Incident Radiation at The Top of The
Atmosphere
The Sun emits electromagnetic radiation in all directions, but we are
only concerned with the amount of energy that reaches Earth's
atmosphere. The amount of energy transferred to the atmosphere at a
given position depends on where the Sun is relative to the local
zenith, which is the direction directly overhead. The angle
between the Sun and zenith is known as the solar zenith angle (.), as
illustrated in Figure 11. The heating effectiveness of solar
radiation, called insolation, varies with latitude and time of
day since these factors affect the solar zenith angle. We can see
from Figure 11 how different solar zenith angles affect the amount of
solar radiation that is transferred into the atmosphere. Clearly,
during the day we get the most solar radiation at noon, when the Sun
is highest in the sky, and the least at sunset, when the solar zenith
angle is near 900.
4.2.2 Variations in
Insolation Due to Earth-Sun Distance
The amount of solar radiation that reaches Earth's atmosphere is
dependent on Earth-Sun geometry, which changes seasonally. Earth's
orbit is elliptical so the distance between Earth and Sun changes
regularly during the year. The solar irradiance, which can be thought
of as number of photons emitted per unit area on a sphere, is
expressed as the radiant flux divided by the area. At the outer
surface of the Sun, the irradiance is 6.34 x 107 W m-2. However, as
the photons travel radially outward from the Sun, the radius, and
thus the surface area of the light sphere increases. Let's say that
the radius of the Sun is r. When the light (photons) have traveled a
distance r' from the surface of the Sun, the sphere of light has an
increased area of 4" (r+r')2. The irradiance is now the radiant flux,
or number of photons, divided by the new area of the sphere. The
surface area of a sphere is proportional to the square of the radius
so the number of photons per unit area (irradiance) is inversely
proportional to the square of the distance the photons have traveled
away from the Sun. Note that the total number of photons has not
changed, they have just spread out. Thus the further Earth is from
the Sun, the fewer the number of photons that hit a particular area
of the atmosphere. Figure 12 shows the Sun-Earth distance cycle in
the F10.7 solar record. The variation in the distance between
perihelion (closest Earth -Sun alignment) and aphelion (most distant
alignment) is about 1.8%. As a result, the variation of solar
irradiance arriving at the top of Earth's atmosphere over a year is
about 3.2% (i.e. square of difference in distance from Sun to Earth).
4.2.3 Variations in Solar
Insolation Due to Solar Zenith Angle
The other factor affecting the amount of incoming solar radiation at
a given position is the changing solar zenith angle. As we saw in
Figure 11, the lower the solar zenith angle (the
higher the Sun is in the sky) the greater the incoming radiation. We
know that the solar zenith angle changes daily as Earth rotates about
the Sun. However, the induced diurnal changes in the ozone occur very
high in the stratosphere, and at most levels the ozone does not
respond to these very short-term changes. As a result, in ozone
studies we are more interested in the longer-term changes.
The solar zenith angle also changes as a function of season. These variations drive the seasonal cycle in temperature and atmospheric circulation. Figure 13 shows the average distribution of solar insolation as a function of latitude and season. To understand this plot, we must first remember how Earth's tilt changes as it revolves around the Sun. During northern hemisphere summer, the northern hemisphere tilts towards the Sun, causing the Sun to be higher in the sky with a smaller zenith angle and longer amounts of daylight. Summer solstice, around June 22, marks the highest point of the Sun in the northern hemisphere, and the longest amount of daylight of the year. On this day the Sun is directly overhead at Tropic of Cancer (23.5o N latitude) at noon, and the Sun never sets anywhere north of the Arctic Circle at 66.5o N latitude. At the same time, the southern hemisphere is tilted away from the Sun, and is undergoing the shortest daylight period of the year with the highest solar zenith angle. Just as the region north of the Arctic circle remains in light all day, all regions south of the Antarctic circle (66.5o S latitude) remain in darkness. This is known as polar night. The situation is reversed at the winter solstice, which occurs around December 22. In Figure 13, polar night is indicated by the shaded regions, where there is no solar insolation. Notice the maximum solar insolation occurs at the North (South) Pole at the summer (winter) solstice, due to the exceptionally long days. At the equinoxes (September 22 and March 22) the Sun is directly over the equator. The Vernal, or spring equinox, marks the end of polar night at the North Pole, and the beginning of polar night at the South Pole, with the largest amount of solar insolation occurring at the equator. The opposite scenario occurs on the Autumnal, or fall equinox. Note that the length of daylight at all latitudes is exactly 12 hours on the equinoxes. If the amount of insolation were to be added over the year, we would find more insolation in the tropics when compared to high latitudes, leading to the temperature differential between the tropics and the poles.
Figure 13. Solar Insolation as a Function of Latitude and
Season
4.2.4 Key Points about the Solar
Radiation that Reaches Earth's Atmosphere:
-The amount of energy transferred to Earth's atmosphere from the Sun
depends on the solar zenith angle (position of the Sun in the sky)
with most energy transferred when the solar rays are most direct
(smallest solar zenith angle).
-Radiation transfer depends on the Sun-Earth distance which varies
about 3.2% during the year as the Earth moves on its elliptical
orbit. Radiation intensity decreases as the square of the distance
between the Sun and Earth.
-The solar zenith angle changes seasonally depending on the Earth's
tilt toward or away from the Sun.
4.2.5 Interactions Between
Light and Matter in the Atmosphere
Now that we know about the solar radiation coming into the
atmosphere, we want to look at what happens to that radiation. Solar
radiation that penetrates Earth's atmosphere may either be: 1)
reflected back into space; 2) scattered to other parts of the
atmosphere by atoms, molecules, cloud droplets, and aerosols; 3) or
absorbed by atmospheric constituents (most notably ozone), increasing
the energy of the absorbing materials. Absorption entails the
disappearance of a photon, with all of the photon's energy being
transferred to an atom or molecule. Scattering occurs when
light interacts with an atom, molecule, or aerosol such that the
light's direction of travel is changed, but its energy, and the
energy of the scattering particle, remains the same. Radiation that
reaches the surface is either reflected back into the atmosphere or
absorbed by the surface. All of these processes involve radiative
transfer, which is defined as the exchange of energy between
photons and matter. In the following sections we are going to take a
closer look at radiative transfer through absorption and scattering
processes in the atmosphere. However, to understand these processes,
we must first understand what the energy of an atom or molecule is,
and how it can be changed.
4.2.6 Atomic Structure, and the
Energy of an Atom
An atom consists of a nucleus, which is made up of positively-charged
protons and uncharged neutrons, surrounded by a cloud of
negatively-charged electrons. To give you an idea of the scale of
things, a proton and a neutron have about the same mass, while an
electron has about 1/2000 of that mass. An electron, being so much
lighter and moving quickly, cannot occupy as small a volume as the
nucleus. You can identify the location of a (heavy) nucleus with a
certain degree of accuracy, but the uncertainty in the location of
any (light) electron belonging to the same atom is many times larger.
The best you can say is that it is very likely to be within a certain
distance of the nucleus. This is a consequence of the
Heisenberg Uncertainty Principle. The
diameter of a typical nucleus is about 10-15 meters, while the
electrons whirl about it at a typical distance of about 10-10 meters.
That's like the nucleus being the head of a pin in the middle of a
stadium, and the electrons spending most of their time out in the
cheap seats. The space between the electrons and the nucleus is
completely empty.
Why do the electrons stay with the nucleus, then? It's because of their electrical charges. The electron's negative charge is attracted to the positively charged proton(s) in the nucleus. And, while an electron can be removed from an atom (in a process called ionization), that process takes a lot of energy.
An electron in an atom has a certain, definite energy. Because the
electron is so much lighter than the nucleus, it must move around in
a much larger volume than the nucleus does. This means that an
electron is always moving, so it always has some kinetic
energy. And because it is always at some distance from the
nucleus, it always has some potential energy based on the
electrical attraction between electron and nucleus. The instantaneous
kinetic and potential energies of the electron are constant as long
as nothing is applying a force to it.
If an atom has more than one electron, we can call the total energy of the atom the sum of all of the individual electron energies. It turns out that an electron in an atom is only allowed to have certain definite values for its total energy. We call these definite values energy levels. Each of the electrons in an atom has a set of allowed energies. The total energy of the atom, then, can only have certain values, equal to the sums of all the possible electron energies.
When an atom's energy changes, it may only go from one allowed energy level to another allowed energy level. The atom's energy can change in any of a number of processes, including collisions with other atoms, and by absorbing or emitting photons.
4.2.7 Absorption and Emission of Photons
by Atoms
Any atom has definite allowed energy levels. The energies of the
levels are different from one another so if an atom is to go from one
energy level to another, it must either transfer energy to something
else (to go to a lower level), or acquire energy from something else
(to move to a higher level). If an atom is in a very hot medium where
particles have a lot of kinetic energy (like in the solar
atmosphere), it may exchange energy with other atoms in collisions.
The energy of an atom may also be changed if it absorbs or emits a
photon.
Let's consider a hydrogen atom. It is the most abundant and
simplest atom in the universe with one proton in its nucleus and a
single electron. The lone electron has certain definite energy levels
it can sit in, but one in particular, called the ground state,
is the lowest energy level. We can assign a whole number n to each of
the energy levels, with n=1 being the ground state. It turns out that
the electron's energy is expressed as:
En = -Rñ/n2
where Rñ is a constant called the Rydberg constant. So if
the electron is in some initial state ni , and it is moving to some
final state nf, then the energy ( E ) it must acquire is:
E = Rñ(l/ni2 - 1/nf2).
One of the more important ways it can change levels is by
absorbing a photon whose energy, E=hf, is exactly the same as E.
In ordinary absorption, photons are swallowed whole. What if a photon whose energy is greater than the required E comes by? Could the atom absorb energy from it, and leave the rest? The answer is, in general, no. If a photon comes by that has an energy that does not correspond to a E for some transition between levels, it does not interact with the atom. This is exactly what we see in the spectrum of hydrogen in Figure 14. For most wavelengths (or photon energies) there is no absorption, but for a set of well-defined wavelengths corresponding to the exact energy between certain electron energy levels, the hydrogen atoms absorb light, leaving very narrow dark lines on the spectrum.
Figure 14. Absorption Spectrum of Hydrogen
But what if the photon has an energy greater than the amount
needed for any of the transitions between levels? Looking back at the
equation that defines the energy level of an atom we see that En is
negative for all n values (levels) and that for n=ñ,
Eñ=0. The situation where n=ñ corresponds to the
complete removal of the electron from the nucleus. We call this
process ionization. If the electron is promoted from some
level to n=ñ by the absorption of a photon, the process is
called photoionization. In fact, if an atom in some state n
(with an energy E= -Rñ/ n2) encounters a photon whose energy
(hf) exceeds +Rñ/n2, the photon may disappear, ionizing the
atom. The excess energy the photon had before the encounter shows up
in the kinetic energy (motion) of the electron as it departs from the
atom.
Hydrogen is the simplest of the atoms with a single electron and its spectrum is correspondingly simple. What about multi-electron elements? Electrons have electromagnetic properties so besides being affected by the positively-charged nucleus, electrons in an atom are affected by the presence of other electrons in the same atom. The spectroscopy of multi-electron atoms is somewhat more complicated than that of hydrogen, but the basic ideas are the same. At any instant of time, the electrons are in a definite state, with a definite energy level. Only photons with energies corresponding to the difference between some pair of energy levels may he absorbed by the atom. Thus, the absorption spectra of these atoms shows the absorption of very narrow bands of light wavelength while the emission spectra show the release of these same wavelengths as the electrons "fall back" to their ground states.
4.2.8 The Energy of a
Molecule
When we look at atmospheric composition we see that most of the
constituents are not atoms but molecules. A molecule is an assembly
of atoms held together by the mutual attraction of the positively
charged nuclei to electrons that are shared between them. For all
practical purposes, the nuclei define where the atoms are. Typical
distances between atoms in molecules are on the order of 10E-10 m;
however, the nuclei are constantly in motion with respect to each
other. Even in a molecule consisting of just two atoms, like oxygen
(O2), the nuclei may never come to rest relative to each other. There
are kinetic and potential energies associated with this nuclear
motion. Like the electron energies in an atom, the nuclear motions in
a molecule may only have certain definite energy values. Thus, the
total energy of a molecule is the total of the electron energies plus
the total of the energies associated with the nuclear motions. Energy
levels associated with the nuclear motions are called vibrational or
rotational energy levels, depending on the type of motion. For
simplicity we will only refer to vibrational energy levels in this
discussion.
The differences between allowed vibrational energy levels are much smaller than differences between allowed electron energy levels so it takes less energy to make a transition between these states. For example, to excite an electron in a typical free atom generally requires a photon with a wavelength that's in the visible or ultraviolet part of the electromagnetic spectrum, while to promote a molecule from one vibrational level to another (with no other change) requires a photon that's in the infrared part of the spectrum. Many molecules absorb visible and/or ultraviolet light as well as infrared light. You can think of the energy levels of a typical molecule as looking like the following diagram in Figure 15.
Figure 15. Electronic and Vibrational/Rotational Levels
Molecules can make purely electronic transitions (symbolized by A on Figure 15) and purely vibrational transitions (as in B). But molecules can simultaneously change both electronic and vibrational states (as in C). There are many, many such transitions possible with energy changes that are very, very near each other. Additionally, a photon with enough energy can break a molecule apart into smaller molecules or individual atoms. This process is called photodissociation. Photodissociation can occur over a range of wavelengths because any excess energy is transferred to the segments produced in the form of kinetic energy. The result of this process is that instead of a single, sharply defined wavelength at which photons are absorbed, molecules absorb photons over a fairly wide band of wavelengths.
4.2.9 Key Points about the
Interaction of Matter and Light:
1. An electron in an atom at any instant of time is characterized by
its energy.
2. There are only certain energies that an electron is allowed to
have.
If a photon comes by that just happens to have an energy that
corresponds to the difference between two of the allowed energies, it
may be absorbed. The electron winds up in a higher energy level and
the photon ceases to be.
Since electron energy levels are well defined, so are their
differences. If you shine white light (with all visible wavelengths)
through a sample containing these atoms, most of the photons that go
in will come out. However, photons having certain wavelengths
(energies) will be absorbed by some of the atoms and they won't come
out.
We call the pattern of light absorption as a function of
wavelength the absorption spectrum of an atom.
If an atom encounters a photon with enough energy to tear its
electron free from the nucleus, the atom becomes ionized, and any
excess energy is transferred from the photon to the free electron in
the form of kinetic energy.
Molecules have nuclear vibrational and rotational levels that add
to the energy states of a molecule. Transitions between these states
take less energetic photons than electronic transitions.
4.2.10 Absorption in the
Atmosphere
Absorption of solar radiation in the atmosphere serves two purposes:
1) it is a heat source [see radiative
heating] for Earth-atmosphere system; and, 2) it prohibits
high-energy radiation from reaching Earth's surface. Solar radiation
at wavelengths shorter than about 0.31 m, which covers a portion of
the ultraviolet region (UV-B) through the X-ray region, can be
extremely dangerous to the biosphere if it is subjected to exposure
for extended periods of time. Figure 16 shows how this potentially
dangerous solar radiation is absorbed in the atmosphere.
Specifically, it shows the altitude at which the radiation has been
reduced by a factor of e (about 2.7) from its value at the top of the
atmosphere and the species responsible for the absorption. For these
wavelengths, nearly all of the radiation is absorbed before it
reaches the surface. In fact, only a small portion of radiation of
the least energetic of these wavelengths ever reaches the ground
(Gordon- % of UV-B reaching the ground?).
Figure 16. Solar Radiation Absorption as a Function of
Altitude
Solar radiation at wavelengths shorter than 0.1 m contains enough
energy to photoionize the atomic constituents of the far upper
atmosphere (altitudes above about 90 km), including oxygen and
nitrogen (O and N), and photodissociate molecular oxygen and nitrogen
(O2 and N2). We can recall that in the process of ionization
(photodissociation), the excess energy is transferred from the photon
to the free electron (atom) in the form of kinetic energy. This
ultimately results in increased heat in the layer. More absorption
takes place at the top of the layer so the temperature of the layer
increases with altitude. This atmospheric layer is the
thermosphere [click to temperature structure of the
atmosphere], also known as the ionosphere because of the high
percentage of ionized particles. The radiation responsible for
maintaining the ionosphere is emitted primarily from the Sun's
chromosphere, which is the second hottest portion of the Sun's
atmosphere. The temperature of the thermosphere varies significantly
depending on the amount of solar activity. The temperature in this
altitude region varies from 500 K during periods of low solar
activity to 2000 K during periods of high solar activity.
Solar radiation with wavelengths from 0.1 m to 0.2 m is strongly
absorbed by molecular oxygen at altitudes of 50-110 km, which is in
the mesosphere and lower thermosphere. In the case of O2,
photodissociation is the absorption process in operation. The atomic
oxygen produced in this process is a primary constituent of the upper
atmosphere. Between 0.2 and 0.31 m, the photodissociation of ozone in
the stratosphere is the important process. These reactions maintain
the ozone layer, and are discussed in more
detail in the next section, and in the Ozone Photochemistry
Chapter.
Of the radiation reaching the top of the atmosphere, more than 98%
is at wavelengths longer than 0.31m which includes the near
ultraviolet (0.32-0.40 m, known as UV-A), visible, and infrared
regions of the spectrum. At these wavelengths, there is very little
absorption in the atmosphere. Ozone has a weak absorption band in the
visible region due to vibrational-electronic transitions of the
molecule. Molecular oxygen has weak absorption at red light
wavelengths, CO2 has a number of weak absorption bands in the near
infrared, and ozone also displays weak absorption in the infrared.
However, these IR bands are more important to the radiative transfer
of longwave radiation. The most significant absorber of
longer-wavelength solar radiation is tropospheric water vapor.
Tropospheric water vapor concentrations are highly variable, and the
amount of light that penetrates to the surface is highly dependent on
the local amount of water vapor in the troposphere. It also depends
on the amount of cloud and aerosol present in the troposphere, which
can scatter the radiation back towards space.
4.2.11 Basic Ozone Photochemistry
Stratospheric ozone is created and destroyed primarily by ultraviolet
radiation. The chemical reactions that control the gas-phase
photochemical production and destruction of ozone are summarized in
Figure 17. When high energy ultraviolet photons (about 0.1 - 0.2 m)
strike molecular oxygen (O2) they split the molecule into two single
oxygen atoms by photodissociation (Eqn. A). The free oxygen atoms can
then combine with molecular oxygen in a three-body collision (M being
the third body) to form ozone (O3) molecules (Eqn. B). Note that in
this reaction M can be any atom or molecule. Its presence is
necessary to conserve energy and angular momentum.
Figure 17. Ozone Photochemical Reactions
Ozone is a very important absorber of UV-B radiation (0.29-0.32 m). When an ozone molecule is exposed to a UV photon with a wavelength in the 0.2-0.31 m range, it may photodissociate back into O2 and O (Eqn. C). During dissociation, the atomic and molecular oxygen gain kinetic energy which produces heat and causes an increase in atmospheric temperature. The free oxygen atom may then combine with an oxygen molecule, creating another ozone molecule, or it may collide with an existing ozone molecule and break it apart, creating two oxygen molecules. Whenever O and O2 recombine, there is no change in the amount of either constituent, but only an increase in heat due to the absorption of a photon. This is why ozone is capable of absorbing most of the incident UV radiation, despite the low concentrations of ozone in the stratosphere (average of 3 ozone molecules per 1 million molecules air). While most of the UV photons are absorbed high in the stratosphere by some form of oxygen (O, O2, or O3), longer wavelength photons can penetrate deeper into the atmosphere because they are not energetic enough to react with O or O2 and are only weakly absorbed by O3. Although weak, ozone does absorb radiation at visible wavelengths and this absorption can lead to ozone photodissociation, creating regions of ozone production and destruction lower in the stratosphere. The processes of ozone creation and destruction through interactions with UV and visible photons are known as Chapman Reactions.
[ sentence on why ozone layer is at
particular altitude]
Most ozone is destroyed through catalytic chemical processes rather than Chapman Reactions. Ozone is a highly unstable molecule that readily gives up its extra oxygen atom to free species such as nitrogen, hydrogen, bromine, and chlorine ( Eqns. E, F on Figure 17). The net reaction converts an ozone molecule to two oxygen molecules. Note that the catalyst in the reaction (denoted by X) is recycled and can go on to destroy more ozone. These catalytic compounds occur naturally in the stratosphere, released from sources such as soil, water vapor, biological processes, and the oceans. Several of these species also have man-made contributions from fertilizer, pesticides, fire extinguishers, refrigerants, Styrofoam, and solvents. These have consequences for the rate of ozone destruction in the stratosphere. Less stratospheric ozone may lead to increases in the amount of UV-B radiation reaching the Earth's surface. For more details on current results concerning ozone decreases and UV-B increases see the information in Ozone Variability and Trends [CLICK TO CHAPTER 8]. If you would like more details on reactions involving ozone in the stratosphere, see Ozone Photochemistry [CLICK TO CHAPTER 5].
4.2.12 Atmospheric Scattering -
Some Basics
When light encounters some material, whether as a gas in the
atmosphere, a liquid or solid, the light can interact with molecules
of that material in such a way that the light's direction of travel
is changed but its energy remains the same (or is modified very
slightly). We call such an interaction scattering. Unless we
are looking directly at a light source, almost all of the light that
enters our eyes has been scattered by the atmosphere or solid objects
around us.
While absorption is best explained in terms of the particle nature of light (photons), scattering is a wave phenomena of light. In the last section we saw how a molecule can only absorb photons of certain energies, depending on the electronic and vibrational levels of the molecule. However, molecules can interact with electromagnetic radiation of any energy in the scattering process. Even when absorption does not occur, electrons are still somewhat free to move around in a molecule and, in particular, to respond to electric oscillating field of the light. To illustrate the wave nature of light and its scattering interaction, think of a seagull sitting on the water when a boat passes nearby. The wake of the boat (a group of waves in the water) moves toward the bird and eventually passes under it. As it does so, the bird moves up and down following the surface of the wave under it. Now think of a molecule with an electromagnetic wave (light) approaching it from some direction. Since the wave is an oscillation of an electrical field it will be a force felt by a charged particle in the vicinity of another charged particle. So a negatively charged electron will feel a force applied to it by the passing wave, just as the seagull felt the vertical force applied by the passing boat wake. Of course, electrons in a molecule are also under the influence of their electrostatic attraction for the positively charged nuclei. They are going to be pulled only so far before their attraction for the nucleus takes over.
So, as the sinusoidal oscillation of the electric field pass the
molecule, the electrons are forced back and forth in a direction that
is perpendicular to the direction the light is traveling. This
process entails increasing the kinetic and potential energies of the
electrons, which means that some of the energy that the
electromagnetic wave carries must be transferred to the oscillating
electrons.
Now here's the tricky part. Newton's First Law, F = ma, tells us
that since a force F is being applied to the electron which has a
small mass m, the electron accelerates. It is also a fact that
electromagnetic radiation is generated by accelerating charged
particles. So, an oscillating force (from the incident light) is
applied to the electron, which therefore accelerates, emitting
electromagnetic radiation. Since the electron is oscillating back and
forth along a line, the electromagnetic radiation it emits is a
regular, sinusoidal oscillation at a frequency the electron is
oscillating with, which is just the same frequency that the incident
radiation had!
Let's summarize the process. An incident electromagnetic wave
interacts with a molecule forcing the electrons to oscillate back and
forth and removing some energy from the incident wave in the process.
Just by oscillating back and forth, the electron emit electromagnetic
radiation of the same frequency (and energy) it interacted with in
all directions. If the incident wave is only present for a finite
amount of time, a certain amount of energy will be lost from the
field but by the time the electron is finished oscillating, it will
have emitted the same amount of energy as had been lost. The energy
of the molecule itself will not have changed, only the direction of
the radiation is altered which gives rise to the term scattering.
Scattering is called elastic scattering if the energy of the
re-emitted radiation is exactly identical to the incident radiation.
If the emitted radiation is slightly greater or less, we refer to it
as inelastic scattering.
The radiation may have come in one direction but the re-emitted radiation leaves in all directions away from the scattering particle. Radiation from a scattering particle leaves in all directions but it is greatest in the plane perpendicular to the line along which the particle is accelerating. It falls off as the square of the cosine of the angle away from this plane. We can illustrate this in Figure 1?. The coordinate system is selected with the positive z axis in the direction of the propagation of the incident wave, the origin at the center of the molecule, and the x axis lined up with the direction of the electric field vector of the incident wave. In general, the light that is scattered by a particle is scattered more in some directions than others. The phase function P(,.) tells us what fraction of light is scattered in different directions. Here, and . are angles that express the direction of scattered light relative to the incident light, as seen in the figure. The angle that the out-going light's direction makes with the z-axis is . If the light leaves going in the same direction then =0 and if it is scattered back toward the same direction as the incident light came from, =". The angle . expresses the azimuth of the outgoing light measured from some direction. If the particle is spherical, there will be no .-dependence in the phase function. If the particle is not spherical, . can be measured from some special geometrical axis of the scattering particle.
As a general rule, the larger the scattering particle is relative to the wavelength of the incident radiation, the more energy is scattered in a forward direction. Although light is scattered in all directions, it is useful to characterize what fraction is scattered in more or less forward direction compared to what is scattered in a more or less backward direction. This is because????????? [Need a statement here about why direction is important]. One measure of the directional scattering is the forward asymmetry parameter (g). A particle that scatters equally as much energy in the forward and backward directions has a value g=0. A particle that scatters light only in the forward direction has g=1 while a particle that scatters only in backward direction has g=-1. Among the constituents of our atmosphere, g typically ranges from 0 for molecules to about 0.85 for cloud water droplets. The value of g is generally larger for larger particles.
4.2.13 Rayleigh Scattering and Mie
Scattering
In the Earth's atmosphere, particles responsible for scattering range
from atoms (about 10E-10 m) to raindrops (about 10E-2 m). The physics
of the interaction between light and particles is greatly affected by
the size of the particle relative to the wavelength of light. A
convenient measure of the particle size is the size parameter
x, defined as:
x = 2"r/w
where r is the radius of the particle and w is the wavelength of
light. Some typical values for important atmospheric constituents are
given in Table 3.
Table 3. Size Parameters for Typical Atmospheric Particles
|
Particle Type |
Smallest-Largest Radii (m) |
Size Parameter Range in Visible Region |
|
Atoms |
10E-10 - 10E-9 |
10E-3 - 10E-2 |
|
Haze particles |
10E-8 - 10E-6 |
10 E-1 - 10E1 |
|
Cloud/rain droplets |
10E-4 - 10E-2 |
10E3 - 10E5 |
If we have a collection of N molecules per unit volume, then the
rigorous mathematical rendition of the scattering process we have
just described allows us to calculate the Rayleigh scattering
cross-section:
NEED EQUATION HERE
where n is the index of refraction ...missing text... is very nearly independent of the physical state of the gas, that is, its pressure, temperature, and density, because (n2-1) is nearly proportional to N. The very interesting feature of ...missing text... is its -4 dependence. The shorter the wavelength, the greater the cross-section for Rayleigh scattering. In fact, since the wavelength range of visible light runs from 0.4 m (blue) to 0.7 m (red), nearly nine times as much blue light is scattered by this process as red light.
Because of the physics of light scattering by molecules, nearly
nine times as much blue light is dispersed by Rayleigh scattering as
red light. This accounts for two everyday occurrences. First, if you
look straight up at a clear sky it looks blue. The reason the sky is
blue is that the light from the Sun travels through the atmosphere,
and some of it passes the atmosphere directly overhead. The molecules
up there scatter far more blue light than red, so you see the blue.
Second, sunsets are red because at the time the Sun sets, light
coming from the Sun travels through a more atmosphere to reach the
observer, and as a result has much of the blue light scattered out of
the direct beam from the Sun to you. What is left is perceived as
reddish-orange by your eye.
Larger atmospheric particles, such as aerosols, are always condensed (liquid or solid) aggregates of atoms and molecules. When an electromagnetic wave strikes an aerosol particle, electrons behave as we have described before. However, in these condensed states, the distances between molecules, and therefore the oscillating electrons, are small compared to the wavelength of light. This gives rise to interference (some constructive, some destructive) between out-going electromagnetic waves. This greatly complicates scattering calculations for these particles. Gustav Mie performed these calculations for special cases and so scattering of light by particles larger than the wavelength of incoming radiation is called Mie scattering. Figure 18 summarizes the type of scattering that can occur depending on the particle size and incoming radiation.
Figure 18. Scattering as a Function of Particle Size and
Wavelength
4.3.14 Single
and Multiple Scattering
NEED MATERIAL HERE
4.3.15 Key Points about Atmospheric
Scattering
-During scattering, particles absorb light from one direction and
re-emit the radiation in all directions.
-The amount and angle of scattering depends on the size of the
scattering particle and the wavelength of radiation that interacts
with the particle.
-Generally, no energy is lost or gained by a particle in the
scattering process.