1. 1 Mass Flux in a Horizontally Homogeneous Atmosphere A useful tool for emissions and lifetimes. Assume an atmosphere well- mixed in latitude and longitude; valid if the lifetime times wind speed is << domain size. Assume that the only sources are at the surface. Assume losses are uniform in the atmosphere. Assume steady state, i.e., Production of X = loss of X The loss over an area is the integral (over altitude) of the concentration times the rate constant. Proof? NCAR’s BAO Tower

2. 2 View from the top of the BAO tower

3. 3 For a trace species X with an exponential decay with altitude, the column content,  X, is the altitude integral. If H 0 (m) is the scale height for concentration in gm -3 then : For altitude profiles that do not follow a clean exponential decay, the column content must be measured.

4. 4 If X is in steady state then production equals loss. Production = Flux of X (g m -2 s -1 ) Loss = Where k ’ = first order rate (or pseudo first order) constant (s -1 ) X = concentration (g m -3 ) For an exponentially decaying species:

5. 5 NO Z = NO 0 e (-Z/600) Example of NO over a fertilized corn field.

6. 6 Production = Flux of X (g m -2 s -1 ) Loss Let X be NO over a large fertilized corn field at night. The only loss is reaction with O 3. NO + O 3 → NO 2 + O 2 If k = 2x10 -14 cm 3 s -1 and [O 3 ] = 50 ppb, then [O 3 ] >> [NO] and k ’ = 2x10 -14 x 50x10 -9 x 2.5x10 19 = 2.5x10 -2 s -1 Flux = k’  NO = 2.5x10 -2 s -1 x 6x10 -5 = 1.5x10 -6 g m -2 s -1. Enough to generate ozone photochemically. Production = Flux = k’  NO In the this example H 0 = 600 m and  X = 6x10 -5 g m -2.

7. 7 SO 2 has little impact on weather or climate, but sulfate aerosols do. How fast is SO 2 oxidized to sulfate? The main source of SO 2 is coal combustion for electricity generation, and the emission rates are reasonably well known. The known sinks are dry deposition, attack by OH, and oxidation to sulfate in clouds containing aqueous H 2 O 2, but the strength of these sinks remains uncertain. The effective lifetime  net is: Example 2. Profiles of SO 2 over the eastern US.

8. 8 CMAQ and aircraft SO2 The average profile measured from aircraft shows that most of the SO 2 resides below 3000 m altitude. CMAQ SO 2 column content is 1.5 times larger than the observed column content.

9. 9 CMAQ Aircraft Example comparison. The Good: Smallest 5% differences between CMAQ and aircraft.

10. 10 CMAQ Aircraft The not so bad: Median differences between CMAQ and aircraft.

11. 11 CMAQ Aircraft The Ugly: Largest 95% differences between CMAQ and aircraft.

12. 12 GOCART and Aircraft GOCART average SO 2 column content is 1.4 times larger than the aircraft column content.

13. 13 SO 2 lifetime The SO 2 profile shows a rapid decrease with altitude, nearing zero by 3000 m. If SO 2 is destroyed before it is advected away from the source, we can assume steady state conditions. Production of SO 2 = loss of SO 2 The loss over an area is the integral (over altitude) of the concentration times the rate constant. Production = Flux of SO 2 (g m -2 hr -1 )Loss k ’ = first order rate constant (hr -1 ) [ SO 2 ] = concentration of SO 2 (g m -3 )

14. 14 SO 2 lifetime Rearrange to get lifetime, . Production (Flux) = Loss

15. 15 To test this theory we used a Gaussian plume dispersion model. Gaussian plume for a single point source.

16. 16 Lifetimes and sources SO 2 lifetimes (hours) generated using Gaussian plume dispersion model. Assumed lifetime = 4 hours. SO 2 lifetimes (hours) 0 -2 2 -6 6-17 17-47 47-620 SO 2 point sources

17. 17 Boxes for flux calculation Boxes used to determine SO 2 flux from point sources. Box 1 Box 2 Box 3 Power plants

18. 18 16 hr lifetime stats Lifetimes calculated assuming a 16 hour lifetime. Add error (2 hours) and standard deviation in quadrature to get uncertainty of method = 2.8 hours

19. 19 The flux from each US state and Canadian municipality was weighted by the number of back trajectory points that crossed the area. 24 hour back trajectories

20. 20 Weighted flux from US states and Canadian municipalities (g hr -1 m -2 ). SO 2 column content (g m -2 ) Uncertainty = (.95 2 + 2.8 2 ).5 = 3 hours

21. 21 Summary The average SO 2 lifetime calculated using 180 measured profiles (from the summer in the Mid- Atlantic region) and EPA and Environment Canada emissions was 18 +/- 6 hrs (95% C.I.). CMAQ and GOCART over-predict SO 2 by 20 – 40% near the surface → The simulated lifetime is too long. Possible explanations: – Errors in cloud cover – leading to less reaction of SO 2 and H 2 O 2 in clouds. – Some unaccounted-for sink.