In this project, you are asked to calculate the intensity of infrared radiation through the
atmosphere as defined by a real sounding taken at Melbourne airport at 23 UTC (9 am
Melbourne time) on 10th March 2018 (use the text file provided). The calculations can readily
be done as you see fit using a computer program of your choice (Python, R, Excel, IDL,
The Schwarzschild equation may be expressed as dI? = (B?(T) – I?)k??aw1ds, where ?a is the air
density and w1 is the mixing ratio of water vapour (note, k??aw1 = ßa). All other symbols are
as in the lecture notes. For simplicity only consider the monochromatic intensity at the
wavelength of 10 µm. We will be highly idealistic and assume that the only greenhouse gas of
interest is water vapour. Assume the zenith angle is 0° and k? is 0.2 m2
Break the sounding up into slabs of 50 hPa, starting at 1000 hPa and stopping at 200 hPa.
1. Calculate and plot the blackbody emission at ? = 10 µm for each pressure level from the
Planck function. Assume that the surface is a perfect blackbody at 1000 hPa in the
sounding and that there is no emission from the stratosphere, assumed to start at 200
hPa (i.e., no external source of I? above 200 hPa). Provide a table with your calculated
emission at each pressure level and at the surface (i.e., at 1000 hPa).
2. Calculate and plot the monochromatic intensity through the free troposphere, both
upwards and downwards (i.e., sum the Schwarzschild equation from the surface to 200
hPa and down, too.) You will need to convert from pressure to height for this
calculation. Use the hydrostatic approximation. Provide a table with the upward and
downward intensities as well as the height (in m) at each pressure level.
3. Calculate and plot the vertical profile of downward transmittance starting from the top
of the troposphere (i.e., 200 hPa) and upward transmittance starting from the surface.
Provide a table.
4. Estimate the upward and downward weighting functions. Provide a table. Which layer
of the atmosphere experiences the maximum absorption for upward and downward
radiation? Provide a short explanation.
5. Repeat questions 1 and 2 for ? = 20 µm. What is the percentage change in the upward
intensity emitted into the stratosphere and the downward intensity at the surface?
Provide a short explanation for the observed changes.
6. Repeat questions 1 and 2 for k? equal to 0.02 m2
. What is the percentage change in
the upward intensity emitted into the stratosphere and the downward intensity at the
surface? Provide a short explanation for the observed changes.
7. Consider the longwave transmission at night. Repeat questions 1 and 2, only lower the
surface temperature by 10 degrees. What is the percentage change in (i) the upward
intensity emitted from the surface, (ii) the upward intensity emitted into the stratosphere,
and (iii) the downward intensity at the surface? Provide a short explanation for the