Radon-222 is widely used as a tracer of vertical transport in the troposphere. It is emitted ubiquitously by soils and is removed from the atmosphere solely by radioactive decay (k = 2.1x10 -6 s -1 ). We consider in this problem a continental atmosphere where 222Rn concentrations are horizontally uniform. Vertical transport is parameterized by a turbulent diffusion coefficient Kz.
2. An analytical solution to the continuity equation can be obtained by assuming that Kz is independent of altitude, that 222Rn is at steady state, and that the mixing ratio C of 222Rn decreases exponentially with altitude:
Observations show that this exponential dependence on altitude, with a scale height h = 3 km, provides a reasonably good fit to average vertical profiles of 222Rn concentrations. Show that under these conditions
4. The mean residence time of water vapor in the atmosphere is 13 days ( See Concept of lifetime ). Using the same assumptions as in question 2, estimate a scale height for water vapor in the atmosphere.