## Problems

1. Imagine that the Brewer-Dobson circulation and the horizontal eddy transport both speed up.

(a) What will happen to the mean age of air in the stratosphere?

(b) What will happen to the total amount of Clv, NO,, and Br,, in the stratosphere?

2. Water vapor budget of the stratosphere.

(a) What is the mass of the stratosphere?

(b) Assuming a lifetime of stratospheric air of 2 years, what is the mass flow out of the stratosphere (in kg s ')'.'

(c) The "small comet" hypothesis. Virtually all of the hydrogen in the stratosphere is transported there from the troposphere. However, it was suggested at one point that 20 comets hit the Earth every minute, and that each comet contained 30 tonnes of H20. If this water is deposited in the stratosphere (and then well mixed throughout the stratosphere), then how much water vapor in the stratosphere would be attributable to this source?

(d) Tropospheric sources of total hydrogen match the observed stratospheric total hydrogen abundance to within a few percent. How much of a missing source of water vapor can therefore be accommodated? Is the small-comet hypothesis consistent with this uncertainty? How could one modify the small-comet hypothesis to be consistent with these calculations?

3. DIY ("debunk it yourself')- Explain why this is wrong:

A new study reports measurements by a satellite that indicate a localized and natural source of BrO, a known ozone-depleting substance, in the Arctic troposphere, especially over the Hudson Bay area. The measurements show a springtime "plume" of bromine, which destroys ozone in the Arctic troposphere. If this naturally produced chemical mixes into the polar stratosphere it could be the source of the stratospheric "ozone hole", found in polar regions during springtime, instead of man-made refrigerant chemicals (as is currently believed).

4. Help Mark S. calculate column O,:

(a) Given the O, VMR as a function of pressure, derive an expression for the column abundance in Dobson units.

(b) Assuming that the VMR of O, is zero in the troposphere and 5 ppmv in the stratosphere, what is the column abundance? Assume the tropopause is at 200 hPa.

(c) Now assume that a weather system causes the tropopause to rise to 150 hPa. What is the column abundance?

(d) Franco asks Mark to explain why the column changes. Help Mark out.

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