Computer exercise 1

Problem statement

Extended from Exercise 3-3 in Jacob (1999).

The mass balance for the photolysis of CFC-12 is given by:

$$ \frac{d m}{dt} = E - k\,m $$

$m$ is the atmospheric mass of CFC-12, $E$ is the rate of emission, and $k$ is the rate of photolysis.

The atmospheric lifetime of CFC-12 is 100 years. Starting from an initial concentration of $m_0=400$ pptv in 1987, assume two scenarios:

  1. "business as usual": E = $4.2 \times 10^8$ kg/yr
  2. "zero emissions": E = 0 kg/yr

For this exercise, solve the ordinary differential equation using Octave's LSODE solver.

  1. Plot concentrations from 1987 to 2087 under the two scenarios.
  2. What is the change in concentration (in percent) of relative to 1987? Report values for years 2017 and 2087. Check against analytical solution.
  3. For a substance with a photolysis lifetime of 100 years, why is the concentration after 100 years not zero after emissions are turned off?

References

Jacob, D. J. (1999): Introduction to Atmospheric Chemistry. Princeton University Press.