## PROBLEMS

12. 1 NO x - and hydrocarbon-limited regimes for ozone production

We model the lower troposphere over the eastern United States as a well-mixed box of height 2 km extending 1000 km in the east-west direction. The box is ventilated by a constant wind from the west with a speed of 2 m s -1 . The mean NO x emission flux in the eastern United States is 2x10 11 molecules cm -2 s -1 , constant throughout the year. Let PHOx represent the production rate of HOx in the region. As seen in this chapter, we can diagnose whether O 3 production in the region is NO x - or hydrocarbon-limited by determining which one of the two sinks for HOx, (1) or (2), is dominant:

(1)

(2)

We present here a simple approach for making this diagnosis.

1. The NO x emitted in the eastern United States has a lifetime of 12 hours against oxidation to HNO 3 by reaction (2). Assume reaction (2) to be the only sink for NOx (a fair approximation during summer). Calculate the fraction of emitted NO x that is oxidized within the region (vs. ventilated out of the region). You should find that most of the NO x emitted in the eastern United States is oxidized within the region.

2. A photochemical model calculation indicates a 24-hour average HOx production rate PHOx = 4x10 6 molecules cm -3 s -1 over the eastern United States in July. Compare this source of HOx to the source of NO x . Conclude as to whether O 3 production over the eastern United States in July is NO x - or hydrocarbon-limited.

3. The same photochemical model calculation indicates a 24-hour average HOx production rate PHOx = 1.0x10 6 molecules cm -3 s -1 in October.

3.1. Why is the HOx production rate lower in October than in July?

3.2 Conclude as to whether ozone production over the eastern United States in October is NO x - or hydrocarbon-limited.

4. As temperatures decrease in the fall, NO x may be increasingly removed by

(3)

where RO 2 NO 2 is an organic nitrate such as PAN (in summer, the organic nitrates decompose back to NO x because of the high temperatures). Consider a situation where reaction (3) represents the main HOx sink.

4.1 Write an equation for the O 3 production rate as a function of PHOx, [NO], and [NO 2 ].

4.2 Assuming that the [NO]/[NO 2 ] ratio is a constant, show that O 3 production is neither NO x - nor hydrocarbon-limited.

[To know more: Jacob, D.J., et al., Seasonal transition from NOx- to hydrocarbon-limited O3 production over the eastern United States in September, J. Geophys. Res., 100, 9315-9324, 1995.]

12. 2 Ozone titration in a fresh plume

We generally think of NO x as a source of ozone in urban air. However, ozone can be titrated in a fresh NO x plume, causing some difficulty in interpreting urban ozone data. Consider a point source at the surface releasing NO continuously at a rate Q (moles s -1 ). The pollution plume is transported by the mean wind with a constant wind speed U (m s -1 ). As the plume dilutes it entrains background air containing negligible NO x and an ozone concentration [O 3 ]b. We assume that the crosswind extent of the plume at a distance x (m) downwind of the source is a half-disk with radius R = ax, where a is a fixed coefficient. We further assume that the plume is well-mixed across its cross-sectional area, and that the only reactions taking place in the plume are

(4)

(5)

These two reactions are sufficiently fast that they can be assumed at equilibrium:

1. Show that the NO x concentration in the plume at a distance x downwind from the source is given by:

where [NO x ](x) is in units of ppbv, and b = 40x10 -9 is a conversion factor from moles m -3 to ppbv; we will use 1 ppbv = 40x10 -9 moles m -3 in what follows .

2. Show that:

[O 3 ](x) = [O 3 ] b - [NO 2 ](x)

3. You now have three equations relating [NO](x), [NO 2 ](x), and [O 3 ](x). Solve for [O 3 ](x). Plot [O 3 ](x) for the following typical values: Q = 5 moles s -1 , U = 5 m s -1 , K = 10 ppbv, a = 0.05, and [O 3 ]b = 50 ppbv. How far downwind of the source will the ozone concentration have recovered to 90% of its background value?

[Epilogue: once ozone in the plume has recovered to background levels, further O 3 production takes place in the plume by peroxy+NO reactions followed by reaction (2). Thus the emission of NO x represents a sink for ozone near the point of emission and a source further downwind.]