THE I NVERSE PROBLEM FOR ESTI MATI ON OF AEROSOL FALLI NG FI ELDS - PowerPoint PPT Presentation

THE I NVERSE PROBLEM FOR ESTI MATI ON OF AEROSOL FALLI NG FI ELDS FROM AREA SOURCES RAPUTA V.F. Institute of Computational Mathematics and Mathematical Geophysics of SB of RAS, Novosibirsk

Problem setting ∂ ( ) ∂ ∂ ∂ u r C C C ( ) + ∇ − = + ∇ ∇ VC w K K C ( 1 ) z ∂ ∂ ∂ ∂ t z z z ∂ ∂   C C + = s ( 2 )   K wC z ∂ ∂   z t = z 0 ∂ C = − α s ( 3 ) V C C g s s ∂ = z 0 t = = C C ( , , ) x y z , C C ( , ) x y ( 4 ) = = 0 s s 0 t 0 t 0 1

I. Estimation of concentration fields of local gauge Point source ∂ ∂ ∂ ∂ ∂ ∂ q q q q ( ) ( ) ( ) − = + u z w k z v z , ∂ ∂ ∂ ∂ ∂ ∂ ( 5 ) x z z z y y ∂ + q ( ) ( ) = → = δ δ − k wq q q M y z H 0, 0, , r →∞ = ( 6 ) ∂ x x 0 z = z 0 n m     z z ( ) ( ) ( ) ( ) = = = ( 7 )     u z u , k z k , v z k u z 1 1 0     z z 1 1 3       2 x x 3 y ( ) 2 ( 8 ) = ⋅ − − max max   q x y q     , ,0 exp 1 , max       x 2 x 4 k x   0 2

3 1 θ = ⋅ θ = θ = 3 2 3 2 e q x , x , , ( 9 ) 1 max max 2 max 3 2 4 k 0 Light impurity   θ θ θ 2 ( ) r y r θ = − −  3  ( 1 0 ) 1 2 q x , exp .   3/ 2 x x   x Polydisperse aerosol θ   θ w θ θ θ 2 ( r ) K p y 4 i r  ∑ θ = − − ⋅ ( 1 1 ) i 1  2 3  2 q x , exp ,   ( ) θ w + θ w 3/2 Г x x  x 1 w x 4 i = i 1 i 4 1 θ = . ( ) 4 + k 1 n 1 3

Area source   ( ) 2 ( ) N r θ y-y ∑ ( ) 2   ⋅ i q x,y, θ = θ 2 exp - - x-x   1 ( ) i ( 1 2 ) 2 ϕ 2 x-x 2 x-x   i i=1 i 1+n M u H θ = θ = 1 , ( ) ( 1 3 ) 1 2 ( ) ϕ 2 2 π 1+n k 1+n k 1 1 LS method – estimate of parameters ( r ) r = θ + ξ r q x , , k k k ( 1 4 ) [ ]   ξ = ξ ξ = δ σ = 2 E E k j N 0 , , , 1, .   n k j kj k ( ) ( ) N r r 2 ∑ r −   θ = σ − θ 2 ( 1 5 ) J r q x , .   N k k k = k 1 4

II. Numerical modeling of processes of distribution sulphate aerosol in a neighbourhood of lake Selitrennoe Fig. 1. The plan of air samples Fig. 2. The calculated field of and the recovered field of countable concentration of countable concentration 0.3-0.4 microns light fraction, (thousands of particles per litre) of formed with south wind 0.3 – 0.4 microns fraction of sulphate aerosol 5

The analysis of the observation data of countable concentration Fig. 3. The measured and calculated values of countable concentration of an aerosol for fraction 0.3-0.4 microns 6

Estimates of parameters of the model (12) according to observation data 1997 г . 2004 г . Размер θ θ ⋅ ⋅ R max, R max, 6 6 частиц 10 10 / / 1 1 км км 0,3 – 1,25 4,24 0,7 1,01 0,4 мкм 0,4 – 1,15 3,51 0,5 0,81 0,5 мкм 0,5 – 1 0,6 0,91 0,4 0,25 мкм 7

The analysis of the observation data of mass concentration (A linear source model) Fig. 4. The measured and calculated values of sulphate aerosol mass concentration 8

III. Interpretation of density data of dropouts of plant pollen а ) Leban Fig. 5. The measured and recovered density values of dropout of leban pollen 9

b) Birch Fig. 6. The calculated density curve of dropout of birch pollen, recovered on the points had on distances 10

IV. Methods of estimation of regional pollution of territories ⋅ ϕ M g ( ) Point source ϕ = q r ( , ) , ( 1 6 ) π ⋅ ⋅ ⋅ 2 u h r θ ⋅ ϕ g ( ) ( ) Φ ϕ = θ = λ ⋅ π ⋅ ⋅ r , ), M u h ( 1 7 ) /(2 r Замечание 1. ( ) λ ⋅ ϕ ′ ′ ′⋅ θ ϕ Mg B u h ( , ) g ( ) ( ) ∫∫ Φ ϕ = Ω = ( 1 8 ) r , d ′ ′ π ⋅ 2 r u h r Ω ′ ′ λ ⋅ M B u h d ( , ) ∫∫ ′ = θ Ω ′ ′ π ⋅ 2 u h Ω ′ ′ B u h d ( , ) 1 1 ∫∫ ∫∫ ′ ′ Ω = Ω = ( 1 9 ) B u h d ( , ) ′ ′ ⋅ ⋅ ⋅ u h u h u h Ω Ω 11

Area source ( ) ( ) ξ η ϕ λ m , g ( ) ∫∫ = ξ η ( 2 0 ) Q x y , d d π uh d 2 S   − η y ( ) ( ) ( ) 2 2 ϕ ξ η = = = − ξ + − η   , , , x y arctg , d M M x y 1 − ξ   x 1 1 = ( 2 1 ) d + α − αµ 2 r 1 2 uuuu r r = = α = µ = θ 1 r OM , r OM , , cos 1 1 r ∞ 1 1 ∑ ( ) = α µ n P ( 2 2 ) n d r = n 0 12

∞ c ∑∫∫ ( ) ( ) ( ) ( ) = α µ ξ η ξ η ξ η = + + + = n Q x y , P m , g , , , x y d d Q Q Q ... n 1 2 3 r = n 0 S ( 2 3 ) c c c ( ) ( ) ∫∫ ∫∫ ∫∫ = µ ξ η + µ ξ η + µ ξ η + 2 mgP ( ) d d mgrP d d mgr P d d K 0 1 1 1 2 2 3 r r r S S S ( ) ( ) ( ) ′ ϕ ≅ ϕ + ϕ ψ y g g g ϕ = ψ = ϕ − ϕ arctg x , 0 0 ( 2 4 ) 0 0 ( ) ( ) − ξ + − η − ξ − η 2 x x y y r x y ψ = = cos rd rd π   x y ( ) ( ) ( ) ′ ϕ ≅ ϕ + ϕ − − ξ − η g g g 1 ( 2 5 )   0 0   2 2 2 r r 13

 π      c x y ( ) ( ) ( ) ( ) ( ) ∫∫ ′ ′ = ξ η ϕ + − ϕ − ϕ ξ + η ξ η =       Q x y , m , g 1 g g d d 1 0 0 0     2 2   r 2 r r S π   ′ ( ) ( ) ϕ + − ϕ   g 1 g ( ) ( ) ′ ′ ϕ ϕ 0 0   g x g y 2 = θ + θ + θ 0 0 ( 2 6 ) 1 2 3 3 3 r r r ( ) ( ) ( ) ∫∫ ∫∫ ∫∫ θ = ξ η ξ η θ =− ξ ξ η ξ η θ =− η ξ η ξ η c m , d d , c m , d d , c m , d d . 1 2 3 S S S ( ) ′ ( 2 7 ) g ϕ = Замечание 2. 0 14

V. Experimental researches Fig. 7. The plan of snow samples selection in neighbourhoods of Novosibirsk 15

VI. The Numerical analysis of the observation data ФЛУОРЕН ФЕНАНТРЕН 60 120 50 100 40 80 нг / л 30 нг / л 60 20 40 10 20 0 0 0 10 20 30 40 50 60 70 0 10 20 30 40 50 60 70 км км НАФТАЛИН БЕНЗ ( а ) ПИРЕН 45 45 40 40 35 35 30 30 25 нг / л 25 нг / л 20 20 15 15 10 10 5 5 0 0 0 10 20 30 40 50 60 70 0 10 20 30 40 50 60 70 км км Fig. 8. PAH concentration in a direction on northeast from 16 Novosibirsk (2006)

Zn Cr 3 25 2,5 20 2 15 мкг / л мкг / л 1,5 10 1 5 0,5 0 0 0 10 20 30 40 50 60 70 0 10 20 30 40 50 60 70 км км Осадок пыли Fe 250 70 60 200 50 150 мкг / л 40 мг / л 30 100 20 50 10 0 0 0 10 20 30 40 50 60 70 0 10 20 30 40 50 60 70 км км Fig. 9. Concentration of heavy metals and dust in northeast direction from Novosibirsk (2007) 17

Fig. 10. The field of benzapyrene aerosol dropouts recovered by model (11) in neighbourhoods of Novosibirsk (ng/l) 18

Fig. 11. The plan of samples selection in neighbourhoods of Irkutsk 19

Fig. 12. Levels of beryllium fallout on a route Irkutsk – Listvyanka for a winter continuance 20

Fig. 13. Levels of beryllium fallout on a route Irkutsk – Bayandai for a winter continuance 1994-1995 гг . ( а ), 1995-1996 гг . ( б ) . 21

Fig. 14. The plan of samples selection in neighbourhoods of Tomsk: 1 – 1974 г ., 2 – 1976 г ., 1 – 1979 г ., 4 – country standing facility 22

Conclusion 1. Few-parametric models of reconstruction of concentration fields of impurity in a neighbourhood area sources are constructed within the limits of statements of inverse problems settings of conduction of impurity in ground and boundary layers of an atmosphere. 2. On the basis of these models and in-situ data the quantitative patterns of creation of local and regional dropouts of aerosols fields for some concrete natural and anthropogenous sources are erected. 3. The select of reference points should be spent by methods of experiment planning mathematical theory. 23

4. Possibility of economical monitoring systems making, obtaining of state estimates of the long-term of a city air contamination and definition of emission of the characteristic impurities from its territory is shown. 24

Спасибо за внимание