How long does it take for the atmosphere to mix? If I release a say, one litre of gas, at a particular point on the planet, how soon, on average, would it take to be distributed evenly (mixed) across the entire earth's atmosphere?
The time scale of interhemispheric tropospheric transport is in the order of one year (Chapter 4 of the book Introduction to Atmospheric Chemistry written by Daniel J Jacob). This is not an exact answer to your question, but might be a fair enough number for the problem you have in mind.