Homework 4  Spectral Lines

Radiation objective:
To become familiar with lines shape dependence on temperature and pressure.
MATLAB objective:
We will use this routine to investigate remote sensing the atmosphere.

A)  Download the following Matlab function to calculate the Lorentz line shape, given temperature (T) and pressure (P).

Choose 3 pairs of temperature and pressure that are representative of the range of these parameters in the troposphere and stratosphere.  Record these values in your lab report and justify your choices.  Calculate the Lorentz line shape using these values.  Plot the resulting line shape on one graph; wavenumber versus line shape.  You will probably need to use a linear-log plot (semilogy) for this graph.  Explain how the Lorentz line shape depends on your choices of temperature and pressure.  What happens to the center of the line as opposed to the wings of the line as the pressure increases?

B)  The absorption of an individual Lorentz spectral line, k(v), is equal to the line shape, f(v), times the strength of the line, S.

k(v) = S * f(v)

The transmission, T(v), is given by

T(v) = exp(-k(v) * u)

where u is the amount of absorbing gas.  u is the integral of the density of the gas (kg/m3) along the atmospheric path (meters), so that it has units of kg/m2.  Since the line shape is dimensionless, the line strength, S, must have units of m2/kg.

Assume that the line strength is equal to 1 m2/kg.  Calculate the transmission of a Lorentz line at a temperature of 300 K and pressure 1000 mb for u = 0.1, 1.0, 10.0 kg/m2.

Plot these three transmission vectors as a function of wavenumber, all on the same graph.  Use linear axes for both x and y.  Explain how the transmission varies as a function of the gas concentration, u.  What happens to the center of the line as opposed to the wings of the line as the concentration increases?  Are the wings of spectral lines important in an atmosphere where the concentrations of greenhouse gases are increasing?