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.

1. Write a one-dimensional continuity equation (Eulerian form) for the 222Rn concentration in the atmosphere as a function of altitude.

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

where H is the scale height of the atmosphere.

3. The mean number density of 222Rn measured in surface air over continents is n(0) = 2 atoms cm-3. Using the assumptions from question 2, calculate the emission flux of 222Rn from the soil.

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.

[To know more: Liu, S.C., et al., Radon 222 and tropospheric vertical transport, J. Geophys. Res., 89, 7291-7297, 1984.]