1. ATS 621 Fall 2012
Lecture 3

2. Includes semipermanent high and low pressure areas that reside over oceans & continents
Affects pollutant long-range transport
Includes migratory high and low pressure fronts
Affects urban and regional pollutant transport
Examples: meandering & dispersion of chimney plume, flows around a building

3. idealized
reality

4. Idealized general circulation
Midlatitudes:
westerlies caused by Coriolis force on winds moving across the subtropical latitudinal belts, and requirement of thermal wind balance (equator-to-pole T gradient)
at low levels, semi-stationary subtropical high P regions pump anti-cyclonically moving air into the midlatitudes
Coriolis force pushes air toward east, producing westerly flow

5. Idealized general circulation
Midlatitudes:
Thermal wind invigorates westerly flow at midlats, esp in the winter hemisphere (equator-to-pole T gradient largest)
in NH, higher T in subtropics imply higher P and anti-cyclonic motion; lower T at high lats imply lower P and cyclonic motion
converge at midlats -- westerly flow strongthen -- e.g. jet stream
Westerlies play large role in re-distribution of anthropogenic emissions from NH mid-lats: jet stream disperses to all parts of hemisphere

6. Idealized general circulation

7. Idealized general circulation
Tropics:
Hadley Cell moves warm, moist air upwards into the tropical upper atmospheres and transports it across latitudinal belts to higher lats in both hemispheres
Sustained by solar input to equatorial lats - results in strong, persistent convection
winter hemisphere is most vigorous
Inter-tropical Convergence Zone (ITCZ) is a band of low P, migrates seasonally (NH summer: closer to Northern midlats; NH winter, closer to, but somewhat north of, equator)

8. Idealized general circulation
Ferrel Cell is weaker - transports cold air upward near poles and warm air downward near midlats (opposite of natural tendency)
Monsoonal flow occurs in low-latitude regions around the globe due to T gradients bewteen land and sea (solar heating during summer)
drives moist flow from ocean to land - strong convective currents induced by hot land surface lift air -- precipitation
currents typically oriented north-south - strong localized cross-equatorial flow
Interact with other features of the general circ (e.g. E. Pac. SST)
Ferrel
Hadley

9. Side view
Note how species might get mixed;
mixing relatively slow between hemispheres

10. Characteristic mixing times
Lower stratosphere
2 years
Troposphere
50 years
1 year
1 month
Planetary boundary layer
1 hour
Surface mixed layer of ocean, 10 hours year years
POLE
POLE
EQUATOR

11. Aside: What about diffusion?

12. Mixing time scales + chemical lifetimes
How do we compute these “temporal scales”?

13. Species lifetimes sources sinks Soluble species; ~ week These can be:
Wet deposition
Dry deposition
Chemical reaction
Need to consider main reaction pathways, e.g., reaction with OH

14. (notes are wrong here, this is correct)
Consider example of CO
Not very soluble
Low dry deposition rate
Main sink is reaction with OH
For averaged [OH] of 1 × 106 molecules cm-3, this calculation yields a chemical lifetime estimate for CO of about 50 days
(notes are wrong here, this is correct)
Pseudo-first-order reaction

15. How would you expect CO to be distributed in the atmosphere?
Surface mixed layer of ocean, 10 hours year years
Planetary boundary layer
POLE
EQUATOR
Lower stratosphere
Troposphere
1 year
1 hour
50 years
2 years
1 month

16. CO is “moderately long lived”

17. http://www. esrl. noaa. gov/gmd/dv/iadv/graph. php

18. The view from space (January 2011, from MOPITT)
Check out the multiyear animation with commentary:

19. The Box Model
Flux: amount of material transferred, per unit time and per unit area
Reservoir, M (called “burden” if there are boundaries, e.g., “column burden”)
Source(s), Q
Sink(s), S
Turnover time (average time spent in the reservoir):
Budget:

20. TYPES OF SOURCES Natural Surface: terrestrial and marine
highly variable in space and time, influenced by season, T, pH, nutrients…
eg. oceanic sources estimated by measuring local supersaturation in water and using a model for gas-exchange across interface =f(T, wind velocity….)
Natural In situ:
eg. lightning (NOx) N2 NOx, volcanoes (SO2, aerosols)
 generally smaller than surface sources on global scale but important b/c material is injected into middle/upper troposphere where lifetimes are longer
Anthropogenic Surface:
eg. mobile, industry, fires
 good inventories for combustion products (CO, NOx, SO2) for US and EU
Anthropogenic In situ:
eg. aircraft, tall stacks
Secondary sources: tropospheric photochemistry
Injection from the stratosphere: transport of products of UV dissociation (NOx, O3) transported into troposphere (strongest at midlatitudes, important source of NOx in the UT)

21. TYPES OF SINKS
Wet Deposition: falling hydrometeors (rain, snow, sleet) carry trace species to the surface
in-cloud nucleation (depending on solubility)
scavenging (depends on size, chemical composition)
Soluble and reactive trace gases are more readily removed
Generally assume that depletion is proportional to the conc (1st order loss)
Dry Deposition: gravitational settling; turbulent transport
particles > 20 µm  gravity (sedimentation)
particles < 1 µm  diffusion
 rates depend on reactivity of gas, turbulent transport, stomatal resistance and together define a deposition velocity (vd)
In situ removal:
chain-terminating rxn: OH+HO2  H2O + O2
change of phase: SO2  SO42- (gas  dissolved salt)
Typical values vd:
Particles:0.1-1 cm/s
Gases: vary with srf and chemical nature (eg. 1 cm/s for SO2)

22. RESISTANCE MODEL FOR DRY DEPOSITION
Deposition Flux:
Fd = -vdC
Vd = deposition velocity (m/s)
C = concentration
Concentration at a reference height
Use a resistance analogy, where rT=vd-1 C3
For gases at steady state can relate overall flux to the concentration differences and resistances across the layers:
Aerodynamic resistance = ra C2
Quasi-laminar layer resistance = rb C1
Canopy (surface) resistance = rc
C0=0
Uptake (absorb, adsorb, into stomata, into liquid layer…)
For particles, assume that canopy resistance is zero (so now C1=0), and need to include particle settling (settling velocity=vs) which operates in parallel with existing resistances. End result:
Reference: Seinfeld & Pandis, Chap 19

23. Typical values for dry deposition velocities
Nitric acid has a high deposition velocity because of its reactivity and solubility
Ozone and SO2 are lower, e.g., typical average for SO2 is ~1 cm/s
Ma and Daggupaty, J. Appl. Met., 39, , 2000.

24. Particles have lower dry deposition velocities than gases
Ma and Daggupaty, J. Appl. Met., 39, , 2000.

25. Wet deposition
Simplified approach in early models was to define large-scale (stratiform) and convective precipitation scavenging coefficients
Done in different ways now with more sophisticated modeling approaches
A “wet deposition velocity” was defined via the washout ratio, wr : where p0 is the precipitation intensity, ~0.5 mm hr-1 for drizzle and 25 mm hr-1 for heavy rain, and where wr is the ratio of the concentration of the species in surface-level precipitation to the concentration in surface-level air

26. Example values (1994 reference)

27. Back to the Box Model….
Example: strat-trop exchange

29. How are sinks represented?
Wet and dry deposition:
Chemistry:
Notice these are all first-order losses (rate = constant x M)

30. The simplified box modelQ S
(assumes first order loss process)
If not in steady state, and if we have an initial condition, we can solve the equation and examine approach to new steady state

32. SPECIAL CASE: SPECIES WITH CONSTANT SOURCE, 1st ORDER SINK
Steady state solution (dm/dt = 0)
Initial condition m(0)
Characteristic time t = 1/k for
reaching steady state
decay of initial condition
If S, k are constant over t >> t, then dm/dt g 0 and mg S/k: "steady state"

33. EXAMPLE: GLOBAL BOX MODEL FOR CO2 reservoirs in PgC, flows in Pg C yr-1
atmospheric content (mid 80s)
= 730 Pg C of CO2
annual exchange land = 120 Pg C yr-1
annual exchange ocean= 90 Pg C yr-1
(now ~816 PgCO2)
Human Perturbation
IPCC [2001]

34. TWO-BOX MODEL defines spatial gradient between two domains
Mass balance equations:
(similar equation for dm2/dt)
If mass exchange between boxes is first-order:
e system of two coupled ODEs (or algebraic equations if system is assumed to be at steady state)

35. Illustrates long time scale for interhemispheric exchange; can use 2-box model
to place constraints on sources/sinks in each hemisphere

36. TWO-BOX MODEL (with loss)
mo = m1+m2 Q T m1 m2 S1 S2
Lifetimes:
If at steady state sinks=sources, so can also write:
Now if define: α=T/Q, then can say that:
Maximum α is 1 (all material from reservoir 1 is transferred to reservoir 2), and therefore turnover time for combined reservoir is the sum of turnover times for individual reservoirs. For other values of α , the turnover time of the combined reservoir is reduced.

37. EXTRA SLIDES (not part of “official” course materials) : More on Models from Prof. Colette Heald

38. ASIDE: LIFETIME VS RADIOACTIVE HALF-LIFE
Both express characteristic times of decay, what is the relationship?
½ life:

39. ONE-BOX MODEL, including transport
Atmospheric “box”;
spatial distribution of X within box is not resolved
Chemical
production
Chemical
loss
Inflow Fin
Outflow Fout P X L D E
Flux units usually
[mass/time/area]
Emission
Deposition
(turnover time)
Lifetimes add in parallel:
(because fluxes add linearly)
Loss rate constants add in series:

40. CHAPTER 3: SIMPLE MODELS
The atmospheric evolution of a species X is given by the continuity equation
deposition
emission
transport
(flux divergence;
U is wind vector)
local change in concentration
with time
chemical production and loss
(depends on concentrations
of other species)
This equation cannot be solved exactly e need to construct model (simplified representation of complex system)
Improve model, characterize its error
Design model; make assumptions needed
to simplify equations and make them solvable
Design observational system to test model
Define problem of interest
Evaluate model with observations
Apply model:
make hypotheses, predictions

41. EULERIAN RESEARCH MODELS SOLVE MASS BALANCE EQUATION IN 3-D ASSEMBLAGE OF GRIDBOXES
The mass balance equation is then the finite-difference approximation of the continuity equation.
Solve continuity equation for individual gridboxes
Models can presently afford
~ 106 gridboxes
In global models, this implies a horizontal resolution of km in horizontal and ~ 1 km in vertical
Drawbacks: “numerical diffusion”, computational expense

42. EULERIAN MODEL EXAMPLE
Summertime Surface Ozone Simulation
Here the continuity equation is solved for each 2x2.5 grid box.
They are inherently assumed to be well-mixed
[Fiore et al., 2002]

43. IN EULERIAN APPROACH, DESCRIBING THE EVOLUTION OF A POLLUTION PLUME REQUIRES A LARGE NUMBER OF GRIDBOXES
Fire plumes over
southern California,
25 Oct. 2003
A Lagrangian “puff” model offers a much simpler alternative

44. PUFF MODEL: FOLLOW AIR PARCEL MOVING WITH WIND
[X](x, t)
In the moving puff,
wind
[X](xo, to)
…no transport terms! (they’re implicit in the trajectory)
Application to the chemical evolution of an isolated pollution plume:
[X]b
[X]
In pollution plume,

45. COLUMN MODEL FOR TRANSPORT ACROSS URBAN AIRSHED
Temperature inversion
(defines “mixing depth”)
Emission E
In column moving across city,
Solution:
[X] L x

46. LAGRANGIAN RESEARCH MODELS FOLLOW LARGE NUMBERS OF INDIVIDUAL “PUFFS”
C(x, to+Dt)
Individual puff trajectories
over time Dt
ADVANTAGES OVER EULERIAN MODELS:
Computational performance (focus puffs on region of interest)
No numerical diffusion
DISADVANTAGES:
Can’t handle mixing between puffs a can’t handle nonlinear processes
Spatial coverage by puffs may be inadequate
C(x, to)
Concentration field at time t defined by n puffs

47. FLEXPART: A LAGRANGIAN MODEL
Retroplume (20 days):
Trinidad Head, Bermuda x
Emissions Map (NOx) =
Region of Influence
But no chemistry, deposition, convection here
[Cooper et al., 2005]