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A Statistical Model of Atmospheric Transport of Contamination over A Long Distance

This study presents a statistical model for long-term atmospheric contamination transport, focusing on dispersion, deposition, and resuspension of contaminated material. It analyzes processes and relationships, formulates mathematical models, and simulates a hypothetical scenario for air and ground contamination assessment.

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A Statistical Model of Atmospheric Transport of Contamination over A Long Distance

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  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 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 3. Resuspension caused by winderosion 4. Soil fixation due to physical, chemical and biological interactions, and downward leaching

  5. Physical processes included in the model Total Air Concentration Primary X Resuspended X r 0 RX Deposition Resuspension Deposition g X (V +V ) X w d (V +V ) 0 w d r Ground Concentration X g a X Soil fixation g

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

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

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

  9. Model Formulation ¥ ò C n( r ) = Q ( r ) P n( r , t | r ) dt 0 0 0 Q(r0) release rate Pn(r,t|r0) probability density function

  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 probability 1/ t d G (t) G (t) d w Dry air Wet air 1/ t w l l w d R G (t) g Surface a G (t) s Soil

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

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

  14. Temporal variations of gain and loss probabilities 0 10 G (t) s -1 10 G (t) -2 10 g -3 10 G (t)= -4 10 a G -5 10 (t)+ G d Probabilities (t) -6 10 w -7 10 -8 10 -9 10 -10 10 0 20 40 60 80 100 Time (year) 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 functions 2. ground and soil dC g = ( P V + P V ) C - ( R + a ) C d d w w a g dt dC s = a C g dt where P = /( + ) and P = /( + ) are the local probabilities of dry and wet t t t t t t d d d w w w d w states, respectively.

  17. Variations of concentrations with time at 10 km from the source 10 -2 soil ground 10 -3 10 -4 Normalized concentrations 10 -5 10 -6 air 10 -7 10 -8 0 20 40 60 80 100 Release time (years)

  18. Normalized air concentration Ca/Q [a km-3] 100 N 80 60 6E-10 1E-9 40 20 7E-10 South - North (km) 4E-9 0 2E-9 -20 7E-10 -40 6E-10 -60 -80 -100 -100 -80 -60 -40 -20 0 20 40 60 80 100 West - East (km)

  19. Normalized ground concentration Cg/Q [a km-2] 100 80 4e-8 60 40 20 6e-8 0 8e-8 6e-7 South - North (km) 4e-7 1e-7 -20 2e-7 -40 1e-7 -60 8e-8 -80 -100 -100 -80 -60 -40 -20 0 20 40 60 80 100 West - East (km) T = 100 years

  20. Normalized soil concentrations Cs/Q [a km-2] 100 (a) 80 4e-5 T=100 years 60 40 South - East (km) 5e-5 20 0 3e-5 5e-4 7e-5 2e-5 -20 -40 3e-5 -60 5e-5 -80 4e-5 -100 100 (b) 80 60 T=1000 years 40 South - North (km) 0.005 20 0 0.003 0.05 0.01 -20 0.007 -40 0.003 -60 0.005 -80 -100 -100 -80 -60 -40 -20 0 20 40 60 80 100 West - East (km)

  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

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