1. A Statistical Model of Atmospheric Transport of Contamination over A Long Distance
Yahui Zhuang

2. U

3. Development of the Atmospheric Transport Model
Identify the controlling processes
Determine statistical relationships among the processes
Formulate the model mathematically
Demonstrate the model simulations for a hypothetical source
Summary

4. Processes Controlling Long-Term Atmospheric Transport
3. Resuspension caused by wind erosion
4. Soil fixation due to physical, chemical and biological
interactions, and downward leaching
1. Time-averaged regional wind rose (wind speed and direction)
2. Statistics on wet and dry synoptic regions and the associated
wet and dry deposition velocities
Processes Controlling Long-Term Atmospheric Transport

5. Physical processes included in the model
Total Air Concentration
Primary X
Resuspended X r
Ground Concentration X g
Deposition (V w +V d ) X
Resuspension RX
Soil fixation a
Physical processes included in the model

6. Parameters and their most likely values used in the atmospheric transport model
Description t d
(46 h)
Expected length of time from an arbitrary moment in a dry period
until precipitation begins w
(7 h)
Expected length of time from an arbitrary moment in a wet period
until dry period begins l
(10 -5 s)
Dry scavenging rate -4
Wet scavenging rate
R (10 -9
Resuspension rate a
(3x10 -8
Soil fixation rate

7. Environmental Compartments?
Dry Air
Wet Air
Ground
Soil
Environmental Compartments

8. U Q
Concentration = Release rate x Residence time per unit volume

9. ò Model Formulation C Q P n( ) ( r = t dt , | Q(r0) release rateò t dt , |
Q(r0) release rate
Pn(r,t|r0) probability density function
Model Formulation

10. Pn(r,t|r0) = Gn(t|r0)Dn(r|r0)
Gn(t|r0) Gain or loss probability
Dn(r|r0) Distribution function

11. Modeling the gain or loss probabilityw g s 1/ t l R a
Dry air
Wet air
Surface
Soil

12. Modeling the gain and loss probability functionsdG 1 dt G RG R d w s g = + - t l a ( )
Modeling the gain and loss probability functions

13. Temporal evolutions of the gain and loss probabilities
Time (hour) 20 40 60 80
100
Probabilities 10 -6 -5 -4 -2 -1 -3 G s
(t) a g =G d
(t)+ G w
Temporal evolutions of the gain and loss probabilities
Initial condition: Gd(0)= 1, Gw(0) = Gg(0) = Gs(0) = 0

14. Temporal variations of gain and loss probabilities
Time (year) 20 40 60 80
100
Probabilities 10
-10 -9 -8 -7 -6 -5 -4 -3 -2 -1 G d
(t)+ G w
(t) s g a
(t)=
Initial condition: Gg(0) = 1, Gd(0) = Gw(0) = Gs(0) = 0

15. Modeling the distribution functions
1. Air
D(r|r0) = PV(r|r0) PH (r|r0)
PV(r|r0) = 1
PH (r|r0) = f(u, q)/2pr
where f(u, q) describes relative frequency with which
the wind blows from q direction at a speed u.

16. Modeling the distribution functionsdC dt P V C R g d w a = + - ( ) s
where t /(
and
are the local probabilities of dry and wet
states, respectively.
2. ground and soil

17. Variations of concentrations with time at 10 km from the source
Release time (years) 20 40 60 80
100
Normalized concentrations 10 -8 -7 -6 -5 -4 -3 -2
air
ground
soil
Variations of concentrations with time at 10 km from the source

18. Normalized air concentration Ca/Q [a km-3]
West - East (km)
-100
-80
-60
-40
-20 20 40 60 80
100
South - North (km)
6E-10
7E-10
4E-9
2E-9
1E-9 N
Normalized air concentration Ca/Q [a km-3]

19. Normalized ground concentration Cg/Q [a km-2]
West - East (km)
-100
-80
-60
-40
-20 20 40 60 80
100
South - North (km)
8e-8
1e-7
6e-7
4e-7
2e-7
6e-8
4e-8
Normalized ground concentration Cg/Q [a km-2]
T = 100 years

20. Normalized soil concentrations Cs/Q [a km-2]
South - East (km)
-100
-80
-60
-40
-20 20 40 60 80
100
3e-5
5e-4
7e-5
5e-5
4e-5
2e-5
West - East (km)
South - North (km)
0.003
0.05
0.01
0.007
0.005
(a)
(b)
T=100 years
T=1000 years

21. Summary
A statistical long-term atmospheric transport model for assessing
environmental impact has been developed
The model emphasizes the role of the atmosphere in redistributing
contamination between the air and the underlying surfaces
It explicitly accounts for dispersion, deposition and resuspension of
contaminated tracer material, using a set of statistical parameters
The model is time-dependent, and is best suited for long-term
environmental assessments of air and ground contamination