# Calculate and plot the blackbody emission at ? = 10 µm for each pressure level from the Planck…

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,

MatLab, …).

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

kg-1

.

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

kg-1

. 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

observed changes.

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