** Computer exercise 1 **

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:

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

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

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

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