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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
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View from the top of the BAO tower
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and )/(0
0HZZ eXX
XHZ
Z XHeXdzX
00
0
)/(0
0
0
For a trace species X with an exponential decay with altitude, the column content, X, is the altitude integral.
If H0 (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.
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If X is in steady state then production equals loss.
0
')(' XkdzzXk
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:
0
)(' dzzXk
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Exponental Loss with Alt.0.6 km scale height
0
500
1000
1500
2000
2500
3000
3500
0 20 40 60 80 100 120
Concentration NO (ng/m3)
Alt
(m
)
NOZ = NO0e(-Z/600)
Example of NO over a fertilized corn field.
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Production = Flux of X (g m-2 s-1) Loss
0
)(X' dzzk
Let X be NO over a large fertilized corn field at night. The only loss is reaction with O3.
NO + O3 → NO2 + O2
If k = 2x10-14 cm3 s-1 and [O3] = 50 ppb, then [O3] >> [NO] and
k’ = 2x10-14 x 50x10-9 x 2.5x1019 = 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 H0 = 600 m and X = 6x10-5 g m-2.
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• SO2 has little impact on weather or climate, but sulfate aerosols do. How fast is SO2 oxidized to sulfate?
•The main source of SO2 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 H2O2, but the strength of these sinks remains uncertain.
• The effective lifetime net is:
Example 2. Profiles of SO2 over the eastern US.
?H2O2OHddnet
11111
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CMAQ and aircraft SO2
Aircraft and CMAQ SO2 profiles
2002 (118 profiles)
0
500
1000
1500
2000
2500
3000
3500
0 1 2 3 4 5 6 7 8
Median SO2 (ppb)
Alt
itu
de
(m a
bo
ve s
ea l
evel
)
CMAQ
Aircraft
CMAQ/aircraft SO2 ratio
0
500
1000
1500
2000
2500
3000
3500
0 1 2 3 4 5
CMAQ/aircraft SO2 ratio
Alt
itu
de
(m a
bo
ve s
ea le
vel)
The average profile measured from aircraft shows that most of the SO2 resides below 3000 m altitude.
CMAQ SO2 column content is 1.5 times larger than the observed column content.
Column
content (g m-2) Aircraft CMAQaverage 0.009 0.014
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CMAQ
Aircraft
Example comparison.The Good: Smallest 5% differences between CMAQ and aircraft.
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CMAQ
Aircraft
The not so bad: Median differences between CMAQ and aircraft.
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CMAQ
Aircraft
The Ugly: Largest 95% differences between CMAQ and aircraft.
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GOCART and Aircraft
GOCART/aircraft SO2 ratio
0
200
400
600
800
1000
1200
1400
1600
1800
2000
0 0.5 1 1.5 2 2.5
GOCART/aircraft SO2 ratio
Alt
itu
de
(m a
bo
ve g
rou
nd
leve
l)
GOCART average SO2 column content is 1.4 times larger than the aircraft column content.
Column content
(g m-2) Aircraft GOCARTaverage 0.012 0.018
GOCART and aircraft median SO2
2000 - 2003 (223 flights)
0
200
400
600
800
1000
1200
1400
1600
1800
2000
0 2 4 6 8 10 12 14 16 18 20 22 24
SO2 (g/m3)
Alt
itu
de
(m a
bo
ve g
rou
nd
leve
l)
aircraft
GOCART
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SO2 lifetime•The SO2 profile shows a rapid decrease with altitude, nearing zero by 3000 m.
• If SO2 is destroyed before it is advected away from the source, we can assume steady state conditions.
• Production of SO2 = loss of SO2
• The loss over an area is the integral (over altitude) of the concentration times the rate constant.
Production = Flux of SO2 (g m-2 hr-1) Loss
0 2 ](z)dz[SOk'
k’ = first order rate constant (hr-1)
[SO2] = concentration of SO2 (g m-3)
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SO2 lifetime
Rearrange to get lifetime, .
0 2 ][
1
'
1dzSO
Fk
0 2 ][' dzSOkProduction (Flux) = Loss
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To test this theory we used a Gaussian plume dispersion model.
Gaussian plume for a single point source.
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Lifetimes and sources
SO2 lifetimes (hours) generated using Gaussian plume dispersion model. Assumed lifetime = 4 hours.
SO2 lifetimes (hours)
0 -2
2 -6
6-17
17-47
47-620
SO2 point sources
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Boxes for flux calculation
Boxes used to determine SO2 flux from point sources.
Box 1
Box 2
Box 3
Power plants
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16 hr lifetime stats
Lifetimes calculated assuming a 16 hour lifetime.
SO2 lifetime for different groups
0
5
10
15
20
1C 1N 1S 1W 1E 2C 2N 2S 2W 2E 3C 3N 3S 3W 3E
Group name
SO
2 li
feti
me
(hr)
Mean 14.05Standard Deviation 2.13
Add error (2 hours) and standard deviation in quadrature to get uncertainty of method = 2.8 hours
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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
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Weighted flux from US states and Canadian municipalities (g hr-1m-2) .
SO2 column content (g m-2)
0 2 ][
11dzSO
Fk
SO2 lifetime generated from 24 hr back
trajectories
05
10152025303540
0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75
SO2 lifetime (hours)
Fre
qu
ency
Uncertainty =
(.952 + 2.82).5 = 3 hours
Lifetime (hours) statistics
Mean 18.24Standard Error 0.95Standard Deviation 12.81
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Summary
• The average SO2 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 SO2 by 20 – 40% near the surface → The simulated lifetime is too long. Possible explanations:
– Errors in cloud cover – leading to less reaction of SO2 and H2O2 in clouds.
– Some unaccounted-for sink.