Global Environmental Problems

Spring 2006

Problem Set #10

Due: 26 April

1.

Recall that the average ozone content of the atmosphere is about 300 Dobson Units (DU), and that 1 DU = 2.7×10¹⁶ molecules/cm². Calculate the average concentration of ozone in the atmosphere in ppmv.

2.

Recall that the residence time of ozone in the stratosphere is about 1 week. If the residence time of ozone is so short, why wouldn’t the ozone layer recover quickly if we stopped CFC emissions?

3.

Recall that chlorine atoms liberated from CFCs are the main destroyers of ozone.

A.

In 1985, about 300,000 t of CFCl₃ (CFC-11) were produced. At what rate would ozone be destroyed, in molecules per year, if emissions of CFC-11 continued indefinitely at this rate?

Assume that all CFC–11 that is produced is ultimately released into the atmosphere, where it migrates to the stratosphere; that all the Cl atoms are separated from each CFC molecule by UV radiation in the stratosphere; and that each free chlorine atom destroys 30,000 ozone molecules before it is scavenged out of stratosphere.

HINT: think about the steady-state situation, in which the number of chlorine molecules entering the stratosphere equals the number exiting the stratosphere. Find this steady-state flow rate, then relate it to a steady-state rate of ozone destruction.

B.

The potential of various compounds to destroy ozone is measured relative to CFC-11; this is the so-called “ozone depletion potential,” or ODP. A table of steady-state ODPs and emission rates for various compounds in 1985 (before controls on emissions were adopted) is given below. For example, 1 t of CFC–12 would destroy as much ozone as 0.8 t of CFC-11. Given your answer to part A, at what rate would ozone be destroyed by the all of these compounds taken together (including CFC-11)?

Chemical

ODP

Emissions (t/y)

CFC-12

0.86

440,000

CFC-113

0.90

140,000

Halon-1211

5.1

2,600

Halon-1301

12.5

2,600

HFHC-33

0.05

81,000

Methyl chloroform

0.12

500,000

Carbon tetrachloride

1.2

70,000

C.

By roughly what percentage would average steady-state ozone concentrations drop if ozone was destroyed at a constant rate given by part B?  How does your answer compare with the results of sophisticated models that predicted a 15–20 percent decrease in average ozone levels from continuing production at 1985 levels?

HINT:  The stock of ozone, S, can be described by a simple box model (see class notes), where the rate of production, F_in, depends only on solar radiation and is equal to P = 2×10³⁹ molecules/y. The natural rate of destruction is proportional to the stock of ozone: F_out = S/t. In the absence of CFCs, F_in = F_out and P = S_o/t, where S_o and t_o are the natural stock and residence time. Adding CFCs increases F_out by an amount F_CFC.  Assume that the rate of ozone destruction is constant at the rate given in part B, and that the natural residence time remains unchanged. Solving for (S/S_o) gives the fractional decrease in ozone.

D.

EXTRA CREDIT.  In part C you assume that the rate of destruction of ozone by CFCs is constant, regardless of the ozone concentration.  A more reasonable assumption is that the rate of destruction is proportion to ozone concentration, in which case F_CFC = (S/S_o)D, where D is the rate given in part B. Redo part C using this assumption.