Estimation of concentration and fluxes of passive gases on the basis - - PowerPoint PPT Presentation

Estimation of concentration and fluxes

• f passive gases on the basis of data

assimilation system for Siberian region

• N. Kilanova,

Е. Klimova, А. Zudin

Institute of Computational Technologies

• f the Siberian Branch
• f the Russian Academy of Sciences

6 Acad. Lavrentjev avenue 630090 Novosibirsk

Passive pollution transport and diffusion model

= ∂ ∂ − + ∂ ∂ + ∂ ∂ + ∂ ∂ z s w w y s v x s u t s

g)

(

η + ∂ ∂ ∂ ∂ + ∂ ∂ ∂ ∂ + ∂ ∂ ∂ ∂

⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛ ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛ ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛

z s k z y s k y x s k x 3 2 1

The problem is considered in Dt=G×[0,T], G=S×[h,H]; S={0≤x≤X;0≤y≤Y}. Boundary conditions: s=sg

( )

s s z s − = ∂ ∂ α ν

= ∂ ∂ z s ν

z=h z=H

Scheme of the experiment for evaluation of passive pollution concentration and emission

Initial data

• n the concentration

and emission Evaluation of the concentration and emission for the model Assimilation procedure – concentration and emission evaluation Observational data

Kalman filter algorithm

1 1 1 1 1 1; 1

; ( ) ; ( ) ; ( ); 0,..., . ( )( ) ; ( )( ) .

f a k k k f a T k k k k k f T f T k k k k k k k a f k k k k a f f k k k k k k f f t f t T a a t a t T k k k k k k k k k k

x A x P A P A Q K P M M P M R P I K M P x x K y M x k K P E x x x x P E x x x x

− − − − − − −

= = + = + = − = + − = = − − = − −

The suboptimal Kalman filter algorithm

Passive pollution transport and diffusion model :

(s – passive pollution

concentration, η- emission)

k k As k s η + = +1

k k η η = +1

η η ~ 0 =

Forecast errors covariance matrix:

∑ = Δ Δ − ≅ Δ Δ = N i T i s i s N T k s k s f k P 1 ) ( 1 1 ) (

t k s f k s k s − = Δ

The concentration and emission in the data assimilation procedure

Experiment 1 - the absolute value of emissions restores. The initial approximation of the field emission is zero.

0 = f η

Forecast of concentration and emission:

f k f k 1 − =η η

f k f k As f k s 1 1 − + − = η

The concentration and emission in the data assimilation procedure

Experiment 2 - value of the correction factor restores

) 1 ( ~ f f δη η η + =

Forecast of concentration and emission:

f k f k f k 1 * 2 1 1 − − + − = χ α αδη δη f k f k As f k s 1 1 − + − = η

) 1 ( ~ f k f k δη η η + =

A.W.Heemink, A.J.Segers “Modeling and prediction of environmental data in space and time using Kalman filtering”, Stochastic Environmental Research and Risk Assessment 16 (2002), 225-240 ,Springer-Verlag 2002.

The concentration and emission in the data assimilation procedure

“True“ field of concentration and emission:

Observational data :

ξ + = t k s k M

• k

y

1 1 1 − + − + − = k ε t k t k As t k s η

η η = t

) 1 ( ~ t t δη η η + =

t k t k 1 − =η η

t k t k t k 1 * 2 1 1 − − + − = χ α αδη δη

Evaluation of the concentrations and emissions:

) ( 1 ) ( f k s k M

• k

y k R T k M f k P k M T k M f k P f k s a k s − − + + =

∑ = Δ Δ − ≅ Δ Δ = N i T i s i s N T k s k s f k P 1 ) ( 1 1 ) (

t k f k k δη δη δη − = Δ

) ( 1 ) ( ) ( f k s k M

• k

y k R T k M f k P k M T s f k a k − − + Δ Δ + = η η η

t k f k k η η η − = Δ

) ( 1 ) ( ) ( f k s k M

• k

y k R T k M f k P k M T s f k a k − − + Δ Δ + = δη δη δη

T Th he e r re eg gi io

• n

n ( (4 48 8. .9 9o

• N

N, , 8 85 5. .9 9o

• E

E; ; 7 76 6. .9 9o

• N

N, , 1 10 09 9o

• E

E) )

The initial field of CO2

http://www.gmes-atmosphere.eu/data Modeling data

each pink band is the observational data every 6 hours

C Co

• n

nc ce en nt tr ra at ti io

• n

n f fi ie el ld d, , ( (( (k kg g / / k kg g) )* *1 10 0-

• 4

4,

, h he ei ig gh ht t

• f

f 1 12 20 00 m m) )

Estimate of the concentration CO2 for 24 hours

C Co

• n

nc ce en nt tr ra at ti io

• n

n f fi ie el ld d, , ( (( (k kg g / / k kg g) )* *1 10 0-

• 4

4,

, h he ei ig gh ht t

• f

f 1 12 20 00 m m) )

R Ro

• t

t m me ea an n s sq qu ua ar re e e er rr ro

• r

r f fo

• r

r c co

• n

nc ce en nt tr ra at ti io

• n

n, , ( (( (k kg g / / k kg g) )* *1 10 0-

• 4

4)

)

Estimate of CO2 emission for 24 hours

C CO O2

2

E Em mi is ss si io

• n

n f fi ie el ld d, , ( (( (k kg g / / k kg g) )* *1 10 0-

• 4

4)

)

The initial emission field is zero 0 = f η

f k f k 1 − =η η

) ( 1 ) ( * * ) ( f k x k M

• k

y k R T k M f k P k M T x f k a k − − + Δ Δ + = η η η

t k f k k η η η − = Δ

Estimate of CO2 emission for 24 hours

R Ro

• t

t m me ea an n s sq qu ua ar re e e er rr ro

• r

r f fo

• r

r e em mi is ss si io

• n

n, , ( (( (k kg g / / k kg g) )* *1 10 0-

• 4

4)

) C CO O2

2

E Em mi is ss si io

• n

n f fi ie el ld d, , ( (( (k kg g / / k kg g) )* *1 10 0-

• 4

4)

)

The initial emission field is

η η ~ 0 =

Estimate of CO2 emission for 24 hours

R Ro

• t

t m me ea an n s sq qu ua ar re e e er rr ro

• r

r f fo

• r

r c co

• n

nc ce en nt tr ra at ti io

• n

n, , ( (( (k kg g / / k kg g) )* *1 10 0-

• 4

4)

), , R Ro

• t

t m me ea an n s sq qu ua ar re e e er rr ro

• r

r f fo

• r

r c co

• n

nc ce en nt tr ra at ti io

• n

n, , ( (( (k kg g / / k kg g) )* *1 10 0-

• 4

4)

)

η η ~ 0 =

0 = η

Conclusions

• The algorithm for the joint estimation of

the passive polution concentration and emission is suggested.

• Numerical experiments have shown that

this algorithm reduces the root mean square error estimation of the polution concentration.

• This algorithm allows to select the

emission fields according to the

• bservational data .

Thank you for your attention!