Tutorial on Radiative Transfer

1) Energy transfer mechanisms

CONDUCTION by molecular motions, the dominant mechanism is solids and
also important in the upper layers of the atmosphere (above 100 km)
where molecules are relatively far apart.

CONVECTION by fluid motions, the dominant mechanism in the oceans and
important in the lower atmosphere.  We'll talk about it next week.

RADIATION consisting of electromagnetic waves traveling at the speed
of light: the only mechanism capable of transferring energy through a
vacuum (e.g., between the earth and the rest of the universe).

The units of energy transfer are energy per unit time per unit area.
Energy per unit time is also called 'power' and has the unit watts
(abbreviated by W)  Hence the rate of energy transfer (e.g., by
radiation) is expressed in watts per square meter.  We call this the
'flux' of radiation.  The flux of solar radiation incident on a flat
horizontal surface when the sun is directly overhead and the sunlight
is undepleted by the atmosphere is 1368 watts per square meter.  1368
watts is roughly equivalent to the electrical power consumed by a
hair dryer.
 

2) The Electromagnetic Spectrum

Radiation comes in a spectrum  (continuous range) of wavelengths, all
traveling at the speed of light.  The longer the wavelength of the
radiation, the longer it takes a wave to pass a fixed point.  The
number of waves that pass a fixed point in a fixed amount of time
like a second is called the 'frequency' of the radiation.  Hence,
wavelength and frequency are inversely proportional: the longer the
wavelength the lower the frequency and vice versa.  Wavelength is
expressed in microns (millions of a meter) for radiation with short
wavelengths and centimeters or even meters for radiation with very
long wavelengths

Names for ranges of the electromagnetic spectrum (in order of
increasing wavelength):

X-RAY- (< 0.01 microns) passes through living tissue, lethal in high doses
ULTRAVIOLET (UV)- capable of causing sunburn and skin cancer
VISIBLE- (0.3-0.7 microns)  the narrow range that human eyes are sensitive to
INFRARED (IR) (0.7-100 microns) important for energy emitted by planets
MICROWAVE- (beyond 100 microns) carry radio and television signals

Of all the ranges, x-rays have the highest frequencies, radio waves the lowest.
 

3) Radiation as packets of energy

Radiation can also be thought of as consisting of tiny packets of
energy called photons.  The more energy in a packet, the more
powerful its effects when it collides with matter.  The energy
carried by photons is directly proportional to their frequency (or
inversely proportional to their wavelength).

Absorbed radiation, regardless of its frequency (or wavelength)
produces heating.  If the frequency of the radiation is higher than
some threshold, it can facilitate 'photochemical reactions' as well.
For example, the familiar photosynthesis reaction in which plants
make chlorophyll requires visible radiation.  Still higher frequency
(more energetic) radiation can break molecules apart: a process
referred to as 'photo-dissociation'.  For example radiation with
wavelengths shorter than 0.31 microns (in the UV, just beyond the
visible) can break up ozone (O3) molecules into 0 (atoms) and O2
(molecules).  O2 molecules are more tightly bound together than O3
molecules so it takes more energy to split them-- the threshold
wavelength for photo-dissociation of O2 is 0.24 microns.  X-rays
carry enough energy to strip electrons off atoms, thereby creating
electrically charged particles or ions.  This process, referred to as
'photo-ionization', is important at levels of the earth's atmosphere
above 60 km.
 

4) Emitted radiation: the Stefan-Boltzmann law

All matter emits radiation at all wavelengths. The maximum amount
of radiation that a body can emit, summed over all wavelengths, is
proportional to its temperature (expressed in degrees Kelvin) raised
to the fourth power.  This relationship is the so called
Stefan-Boltzmann law.

A body that emits the maximum possible amount of radiation, given its
temperature (i.e., the amount prescribed by the Stefan-Boltzmann law)
is called a 'black body'.  Hence, if we know the flux of radiation
emitted by a body, we can use the Stefan-Boltzmann law to calculate
the temperature a black body would have to be at in order to emit the
equivalent amount of radiation.  The temperature calculated in this
manner is known as the 'effective radiating temperature' or the
'equivalent black body temperature'.  The radiometer (or 'infrared
thermometer') demonstrated in class exploits this principle--- based
on the Stefan-Boltzmann law, the radiation scale in its digital
circuitry is replaced by a temperature scale.
 

5) Emitted Radiation: Wien's Law

The wavelength at which the emission from a body is strongest is
inversely proportional to its absolute temperature-- that is, the
higher its temperature, the shorter the wavelength at which it emits
radiation most strongly. This relationship is referred to in the text
as Wien's law.  Bodies the temperature of planets (i.e., hundreds of
degrees K) emit virtually all their radiation in the infrared range
(around 10 microns).  The 'photosphere' of the sun (the layer from
which the sun emits ~99% of its radiation) has a temperature of ~6000
K.  Most of its radiation is in the visible and 'near infrared' parts
of the spectrum between 0.3 and 2 microns.  The thin ionized gases in
the sun's corona are much hotter than the photosphere.  They're
responsible for the x-rays emitted by the sun. Fortunately for us,
these gases are so thin that they don't emit very much radiation.
 

6) Absorption spectra of gases

Not all materials behave as black bodies.  It was demonstrated in
class that  ice emits less radiation than a black body-- that's why
the radiometer gave a reading of -3 C instead of 0 C for the
temperature of the ice.  A thin layer of a gas also behaves in a
manner different from a black body.  Instead of absorbing all the
radiation incident on it and emitting its own radiation almost as a
black body, it absorbs and emits radiation in narrow ranges of
wavelengths referred to as absorption bands.  At wavelengths of the
electromagnetic spectrum that lie in between between their absorption
bands, these layers of gas are transparent.  Each kind of gas
molecule has its own characteristic 'absorption spectrum'.  Gases
like ozone (O3) water vapor (H2O) and carbon dioxide (CO2), whose
molecules are comprised of three or more atoms, have more and
stronger absorption bands in the infrared part of the spectrum than
N2 and O2 have.

Figure 3-13 in the text shows the absorption spectrum (the infrared
part only) for the earth's atmosphere.  The important absorption
bands in the spectrum are labeled.  Most of the radiation emitted by
the earth's surface in the the narrow 'window region' centered near
10 microns is able to escape directly to space, without being
absorbed on its way through the atmosphere. In contrast, radiation at
the wavelength of the major absorption bands will be absorbed and
re-emitted many times on its way through the atmosphere. The earth's
atmosphere is also nearly transparent to radiation in the visible and
near infrared range of the spectrum-- i.e., the wavelengths of
incoming solar radiation.  Hence it lets most of the solar radiation
in, but blocks most of the outgoing infrared radiation emitted by the
earth's surface