SIO 217C: Climate
Spring 2014
Radiative Transfer Discussion Questions
1. Consider pure absorption of solar radiation along a path where the absorbing molecule is
uniformly distributed. Physically explain why solar radiation decreases exponentially with
increasing path length.
2. Consider radiation going along a path in some particular direction. Describe two processes
that could decrease radiation along the path in the particular direction. Describe two
processes that could increase radiation along the path in the particular direction. Provide a
specific example for each process.
3. Consider an atmosphere with some particles. What are all of the factors contributing to
absorption optical thickness between point A and point B?
4. Consider an atmosphere in which an absorber of solar radiation has uniform mixing ratio and
density decreases exponentially with height. Let optical thickness be zero at the top of the
atmosphere and increase downwards. If the Sun is directly overhead, GPC Eq. 3.22 indicates
that the maximum rate of energy absorption occurs at the height where optical thickness is
unity. At what height in the atmosphere is downwelling solar radiation largest? At what
height in the atmosphere is downwelling solar radiation smallest? At what height in the
atmosphere is absorber density largest? At what height in the atmosphere is absorber density
smallest? Why is the rate of solar radiation absorption small where optical thickness is much
smaller than unity? Why is the rate of solar radiation absorption small where optical
thickness is much larger than unity?
5. Consider an atmosphere in which an absorber of solar radiation has uniform mixing ratio and
density decreases exponentially with height. Let optical thickness be zero at the top of the
atmosphere and increase downwards. At what height in the atmosphere is rate of temperature
change largest? Is this the same height where the rate of energy absorption is largest? Why?
6. Consider two different fluids in which an absorber of solar radiation has uniform mixing
ratio. Fluid A has density that is uniform with height and Fluid B has density that is
exponentially decreasing with height. Let optical thickness be zero at the top of the fluid and
increase to a value of five at the bottom of the fluid, and assume the Sun is directly overhead.
Sketch how downwelling solar radiation varies with height for each fluid (height is the
vertical coordinate). Sketch how downwelling solar radiation varies with pressure for each
fluid (pressure is the vertical coordinate). Explain your reasoning.
7. Consider two types of particles. Type A purely absorbs solar radiation and Type B purely
scatters solar radiation. Assume the Sun is directly overhead and the total extinction optical
depth of the atmospheric column is the same for both types. Will downwelling solar radiation
at a particular level in the atmosphere be larger, smaller or the same for an atmosphere with
only Type A particles compared to an atmosphere with only Type B particles? Why?
8. Consider an atmosphere with uniform temperature, density decreasing exponentially with
height, and uniform mixing ratio of a gas that absorbs at thermal infrared wavelengths. Let
optical thickness be zero at the top of the atmosphere and increase downwards, and let the
total optical thickness of the atmosphere be much larger than unity. Does a thin atmospheric
layer near the top of the atmosphere emit more, less, or the same amount of radiation
upwards as a thin atmospheric layer near the surface? Why? Is the amount of radiation
escaping to space that is emitted by a thin atmospheric layer near the top of the atmosphere
more, less, or the same as the amount of radiation escaping to space that is emitted by a thin
atmospheric layer near the surface? Why? What is the approximate value of optical thickness
(as a vertical coordinate) with the largest amount of radiation escaping to space that is
emitted by a thin atmospheric layer? Explain your reasoning. Would your answer to the
previous question be larger, smaller, or the same if atmospheric temperature monotonically
decreased with height? Why? What if atmospheric temperature monotonically increased with
height?
9. Total atmospheric optical thickness varies as a function of wavelength. Will optical thickness
be large or small for a wavelength in the: a) water vapor absorption band near 6 µm, b) water
vapor window, but not near the ozone absorption band, and c) CO2 absorption band near 15
µm? Explain your reasoning. Would your answers above vary with location on Earth? Why
or why not?
10. Let optical thickness be zero at the top of the atmosphere and increase downwards. Using
optical thickness as a vertical coordinate, let τλ be the optical thickness with the largest
amount of radiation escaping to space that is emitted by a thin atmospheric layer. Does τλ
vary with wavelength strongly, weakly, or not at all? Explain your reasoning.
11. Let optical thickness be zero at the top of the atmosphere and increase downwards. Using
optical thickness as a vertical coordinate, let τλ be the optical thickness with the largest
amount of radiation escaping to space that is emitted by a thin atmospheric layer.
Qualitatively, at what height in the atmosphere does τλ occur for a wavelength in the: a)
water vapor absorption band near 6 µm, b) water vapor window, but not near the ozone
absorption band, and c) CO2 absorption band near 15 µm? Explain your reasoning. Would
your answers above vary with location on Earth? Why or why not?
12. For simplicity, let the optical thickness of the atmosphere be uniform across all thermal
infrared wavelengths (i.e., a “gray” atmosphere). Let optical thickness be zero at the top of
the atmosphere and increase downwards. Using optical thickness as a vertical coordinate, let
τmax be the optical thickness with the largest amount of radiation escaping to space that is
emitted by a thin atmospheric layer. Assuming this atmosphere has the same average
characteristics as Earth’s atmosphere, at what approximate height does τmax occur? What is
the approximate temperature at this height? Imagine that the concentration of greenhouse
gases instantaneously increases to a new value in the atmosphere but the atmosphere has not
yet had time to return to radiative equilibrium. Is the total optical thickness of the atmosphere
larger, smaller, or the same as before? Is the approximate height at which τmax occurs higher,
lower, or the same as before? Is the approximate temperature at this height warmer, colder, or
the same as before? Is the amount of upwelling thermal radiation at the top of Earth’s
atmosphere larger, smaller, or the same as before? Does the height at which τmax occurs
change as the atmosphere returns to radiative equilibrium? Does the temperature change?
Does the amount of upwelling thermal radiation change? Explain your reasoning for all
answers.
Difficult Question
13. Imagine a planet where the primary emitting molecule is uniformly distributed in the
atmosphere, the molecule emits equally well at all thermal infrared wavelengths, atmospheric
temperature is horizontally uniform, and atmospheric temperature decreases with height. A
telescope measures how emission temperature varies with location on the planetary disk, as
seen through the telescope. Is the measured emission temperature at the center of the disk
warmer, colder, or the same as the measured emission temperature at the edge of the
planetary disk? Why?