Air quality decision support under uncertainty (case study analysis) Piotr Holnicki Systems Research Institute PAS 01-447 Warszawa, Newelska 6 [email protected]

Air quality decision support under uncertainty(case study analysis)

Piotr Holnicki

Systems Research Institute PAS01-447 Warszawa, Newelska 6

[email protected]

mailto:[email protected]



Applications of air pollution transport models

– air quality analysis and forecast,

– exceedance of critical levels for concentration or

critical loads for deposition ,

– assessment of environmental impact of emission sources,

– selection of emission reduction technology,

– selection of new investments location,

– analysis of new technologies of energy generation,

– IAM – Integrated Assessment Models.

Emission

Population

Terrain coverage

Emission reductiontechnologies

Roads

Orography

Industry

Topography

Land use

Meteo forecast

Effects

Visualization

Economy

Decisions

Emission model

Meteorological fields

Meteorological model

Chemical transformations

Numerical model

Distribution of air pollution

Service

Integrated system of air quality management

iiki

zihhii EqccR

z

cK

zcKc

t

c

),,( 1 u

The basic processes of air pollution dispersion

QccKct

ch

0|),0( na nT Sbcc

0|),0( na0

nT Sn

cKh

Initial conditions cc w0)0(

Notation: – domain considered,

c – pollution concentration,

n

hK

Q – total emission field.

)(),(1

),,(),,( tiqyxN

iityxqtyxQ

(2

)

– wind field vector,

– outward normal vector,

– horizontal diffusion coefficient,

– pollution reduction coefficient,

(1a)

(1b)

),0( T

Boundary conditions

Transport equation

Mathematical model of air pollution dispersion

(1)

2

2

2

2

2

2

2exp

2exp

2exp

2),,(

zzyzy

HzHzy

u

Qzyxc

x

cK

xx

cu x

Gaussian trail model (local scale)

z

cK

zy

cK

yx

cu zy

Assumptions:

Pollutant concentration:

http://www.arl.noaa.gov/slides

Regional and urban scale pollution dispersion models

Eulerian model

Lagrangian model

./transformdepositionemissiondiffusionadvection

t

c

ations/transformdepositionemissiondiffusion td

cd

tttxtxtxttx

ttxtxttx

),(),(5,0)()(

),()()(

0

'

1000001

00000

'

1

Main sources of modeling uncertainty

1) Input data a) emission sources (point – energy sector, heavy industry; area – housing, industry; linear – transportation system)

b) meteorological data (wind field, atmospheric stability, mixing height, temperature, humidity, precipitation,…..)

2) Model parametersa) model type (Lgrangian, Eulerian, other, temporal & spatial scale)b) simplifications of mathematical descriptionc) parameterization of some processes (horizontal & vertical diffusion,

dry & wet deposition, chemical transformations, …..)d) numerical implementation (approximation of transport equations,

time & space discretization step, numerical diffusion effect, ….)

3) Physical description of the domaina) orographyb) topography c) terrain coverage

Impact of the input data – emission sources

Categories of emission sources

a) high point sources (energy sector) – relatively low uncertainty, necessary analysis of initial puff formation b) intermediate point sources (other industry) – higher uncertainty and imprecision of emission data

(technological parameters and fuel are not known)

c) area sources (industry, housing) – high uncertainty – emission data are assessed basing on

some aggregated information

d) linear sources (transportation systems) – high uncertainty -- emission depends on the traffic, car parameters, fuel use and characteristics

Impact of the input data – meteorology

(wind field, mixing height, temperature, cloudeness, precipitation, …)

Impact of the input data – meteorology (atmospheric stability)

Category Stability class

A strongly unstable

B unstable

C slightly unstable

D neutral

E slightly stable

F stable

– unstable conditions

– neutral conditions

– stable conditions

Pasquill stability categories

Case study example – regional scale

Domain – 110 x 56 kmDiscretization – 2km x 2kmEulerian model RGFOR3

No Source Coordinates He[m]

Emisson (Winter)SO2 [t/d]

Emission (Summer)SO2 [t/d]

1 Jaworzno III (21,24) 250 303.2 227.2

2 Rybnik (1,20) 200 225.2 167.6

3 Siersza A (30,23) 150 104.0 88.0

4 SierszaB (30,23) 260 91.8 68.0

5 Skawina (43,11) 120 90.1 58.6

6 Łaziska I (8,20) 200 78.0 55.6

7 Będzin B (18,31) 200 65.0 15.2

8 Łęg (46,12) 250 52.0 37.2

9 Katowice (13,25) 250 52.0 37.2

10 Będzin A (18,31) 160 45.1 30.2

11 Łaziska II (8,20) 160 34.7 23.1

12 Łaziska III (8,20) 100 33.8 23.5

13 Jaworzno IIA (21,24) 120 29.9 19.2

14 Jaworzno IIB (21,24) 100 25.1 17.7

15 Halemba (8,25) 110 26.0 17.3

16 Bielsko-Biała (14,2) 140 18.7 11.2

17 Bielsko-Km. (15,1) 250 16.9 7.5

18 Chorzów (12,27) 100 15.1 7.5

19 Jaworzno I (20,23) 152 12.3 6.8

20 Tychy (13,19) 120 11.6 8.6

Parameters of emission sources

Concentration map for nominal emissions

Season-averaged (Winter) distribution of SO2 in the domain

Parameter Uncertainty range(for 95% of data)

Distribution

Emission [g/s] ± 20% N / L-N

Outlet gas velocity [m/s] ± 15% N / L-N

Outlet gas temperature [oK] ± 15% N / L-N

Mixing height [m] ± 25% N / L-N

Components of geostrophic wind [m/s] ± 25% N / L-N

Components of anemometric wind [m/s] ± 25% N / L-N

Temperature [oC] ± 25% N / L-N

Precipitation intensity [mm/h] ± 25% N / L-N

Atmospheric stability class [ - ] ± 1 -

Uncertainty range of the input data

Application of Monte Carlo method

REGFOR3 – regional, three-layer Eulerian model

↓

1000 input data sets

Uncertainty distribution in receptors

sets of concentration of pollutant in receptors

Concentration forecast

Pollution transport model

Em

iss

ion

in

ten

sity

: (n

) so

urc

es

s 1 1 1 1 1

2 2 2 2 2

n n5 5 5

10

20

30

40

50

90

60

70

80

100

mean

meanmean

mean

mean

95%

5%

95%

95% 95%

95%

5%

5%

5%

5%

75%

25%

75%

75%

75%

75%

25%

25%25%

25%

Rec. 1 Rec. 2 Rec. 3 Rec. 4 Rec. 5

+14% -11%15.7

+10% -10%57.3

+7%

-7% 42

+12% -12%59.6

+14% -15%42

10

20

30

40

50

90

60

70

80

100

mean

meanmean

mean mean

95%

5%

95%

95%95%

95%

5%

5%5%

5%

75%

25%

75%

75%

75%

75%

25%

25% 25%

25%


+17% -16%16.3

+16% -15%58.5

+11%

-11% 41.3

+28% -20%59.0

+18% -17%41.6

10

20

30

40

50

90

60

70

80

100

mean

mean

mean

mean

mean

95%

5%

95%

95%

95%

95%

5%

5%5%

5%

75%

25%

75%

75%

75%

75%

25%

25%25%

25%


+30% -21%17.5

+26% -18%60.1

+29%

-27% 41.3

+26% -21%63.7

+34% -25%43.7

10

20

30

40

50

90

60

70

80

100

mean

mean

mean

mean

mean

95%

5%

95%

95%

95%

95% 5%

5%5%

5%

75%

25%

75%

75%

75%

75%

25%

25%

25%

25%


+47% -29%17.8

+84% -76%58.2

+53%

-55% 41

+65% -61%63.3

+57% -57%37

Concentration uncertainty due to input data uncertainty

emission intensity

source parameters

basic meteo data

atmospheric stability class

Uncertainty in decision support due toair quality forecast uncertainty

Optimal strategy of emission abatement – notation

Quality functional

Current concentration

Current emission

dcyxcyxwcJ ad )),(,0(max),(2

1)( 2

– admissible level of concentration),( yxw

),(,),(),(),(1

yxuyxAyxcyxcN

iiio

),( yxAi

adc

,1},1,0{,1,)1(),(11

0 Nixxxeuyxu ji

M

jji

M

jjijii

,)(1

21

1

0

11

0

1ji

M

jjiji

N

iiji

M

jji

N

ii

N

iiT xffuxfucC

Emission reduction cost

Notation

– source —> receptor transfer matrix

– admissible level of concentration

],,,[ 21 Nuuuu

],,,[ 21 Meeee

MNjifF }{

MNjixX }{

N – number of controlled sources, M – number of desulphurization technologies,

– „0-1” control variable matrix

– effectiveness of emission reduction– emission vector

– matrix of the unit costs

oc – background concentration;

Discrete problem (DP) of the optimal abatement strategy Find the optimal solution of the following problems

(DP-A) – minimization of environmental cost

(DP-B) – minimization of technological cost

The set of admissible solutions

},1,1,11

,1

)1(:}1,0{{ MjNijixM

j

M

jjixjeo

iuiujixadX

min))(( xcJ

MAXCN

iTC ic

1

subject to the total cost constraint

minimize the environmental cost function

MAXJxcJ ))((

min1

N

iTC ic

subject to the constraint of environmental standard

minimize the cost of emission abatement

adXijx

min))(( adXcJ

MAXCN

iiTC c

1

MAXJadXcJ ))((

min1

N

iicTC

Find the optimal solution of the following problems

(MP-A) – minimization of environmental cost

subject to the total cost constraint

minimize the environmental cost function

(MP-B) – minimization of technological cost

subject to the constraint of environmental standard

The set of admissible solutions

adij Xx

},1,1,1,)1(:0{ 2

11

2 MjNixxeuuxX ji

M

j

M

jjij

oiijiad

Modified problem (MP) of the optimal abatement strategy

minimize the cost of emission abatement

1) "doing nothing" technology (e = 0 ),

2) low sulfur fuel (e = 0.30 ),

3) dry desulphurization method (e = 0.35 ),

4) low sulfur fuel + dry desulphurization method (e = 0.545 ),

5) half-dry desulphurization method (e = 0.75 ),

7) wet desulphurization method (e = 0.85 ),

8) Low sulfur fuel + wet desulphurization method (e = 0.895 ),

6) low sulfur fuel + half-dry desulphurization method (e = 0.825 ),

The real data case study – desulphurization technologies

Computational domain

Efficiency of abatement technologies

Location of emission sources

110 km x 76 km – rectangle domain

20 – power plants (emission sources)

Characteristics of the controlled emission sources

NoSource Coord. Stack

[m]Emiss[t/d]

Unit abatement cost

1 Jaworzno III (21,24) 250 303.2 0.00 0.102 0.097 0.389 0.434

2 Rybnik (1,20) 200 225.2 0.00 0.183 0.174 0.638 0.743

3 Siersza A (30,23) 150 104.0 0.00 0.045 0.092 0.377 0.449

4 SierszaB (30,23) 260 91.8 0.00 0.051 0.104 0.427 0.510

5 Skawina (43,11) 120 90.1 0.00 0.108 0.182 0.740 1.157

6 Łaziska I (8,20) 200 78.0 0.00 0.122 0.196 0.770 0.872

7 Będzin B (18,31) 200 65.0 0.00 0.131 0.185 0.726 0.863

8 Łęg (46,12) 250 52.0 0.00 0.357 0.291 1.258 1.529

9 Katowice (13,25) 250 52.0 0.00 0.103 0.162 0.648 0.757

10 Będzin A (18,31) 160 45.1 0.00 0.142 0.200 0.785 0.933

11 Łaziska II (8,20) 160 34.7 0.00 0.136 0.220 0.866 0.981

12 Łaziska III (8,20) 100 33.8 0.00 0.065 0.105 0.415 0.470

13 Jaworzno IIA (21,24) 120 29.9 0.00 0.172 0.200 0.802 1.045

14 Jaworzno IIB (21,24) 100 25.1 0.00 0.152 0.178 0.715 0.933

15 Halemba (8,25) 110 26.0 0.00 0.115 0.229 0.933 1.207

16 Bielsko-Biała (14,2) 140 18.7 0.00 0.110 0.247 1.071 1.301

17 Bielsko-Km. (15,1) 250 16.9 0.00 0.161 0.366 1.581 1.921

18 Chorzów (12,27) 100 15.1 0.00 0.183 0.400 1.628 2.106

19 Jaworzno I (20,23) 152 12.3 0.00 0.318 0.368 1.500 1.939

20 Tychy (13,19) 120 11.6 0.00 0.274 0.600 2.439 3.154

Application of Monte Carlo method

Optimization algorithm

↓

Optimal selection of emission reduction technologies initial index - Ji=3.24.107

src abatement technologies emit. abatement technologies emit. 1 2 3 4 5 6 7 8 1 2 3 4 5 6 7 8 1 .0 .0 .0 .0 .0 .0 1 .0 45.6 .0 .0 .0 .0 .0 .0 1 .0 45.5 2 .4 .0 .6 .0 .0 .0 .0 .0 175.1 .0 .0 1 .0 .0 .0 .0 .0 146.3 3 .0 .0 .0 .7 .0 .0 .3 .0 38.0 .0 .0 .0 1 .0 .0 .0 .0 47.3 4 .0 .0 .0 .0 .0 .0 1 .0 14.3 .0 .0 .0 .0 .0 .0 1 .0 13.7 5 .0 .0 .0 .0 .0 .0 .0 1 9.5 .0 .0 .0 .0 .0 .0 .0 1 9.5 6 .0 .0 .0 1 .0 .0 .0 .0 35.8 .0 .0 .0 1 .0 .0 .0 .0 35.5 7 .0 .6 .0 .4 .0 .0 .0 .0 38.4 .0 1 .0 .0 .0 .0 .0 .0 45.5 8 .0 1 .0 .0 .0 .0 .0 .0 35.9 .0 1 .0 .0 .0 .0 .0 .0 36.4 9 .0 .4 .0 .6 .0 .0 .0 .0 29.2 .0 .1 .0 .9 .0 .0 .0 .0 24.2 10 .1 .0 .9 .0 .0 .0 .0 .0 31.3 .0 .0 1 .0 .0 .0 .0 .0 29.3 11 .0 .1 .0 .9 .0 .0 .0 .0 16.9 .0 .0 .0 1 .0 .0 .0 .0 15.8 12 .0 .0 .0 .0 .0 .0 .1 .9 3.7 .0 .0 .0 .0 .0 .0 .0 1 3.5 13 .0 .0 .0 .0 .0 .0 .0 1 3.1 .0 .0 .0 .0 .0 .0 .0 1 3.1 14 .0 .0 .0 .0 .0 .0 .0 1 2.6 .0 .0 .0 .0 .0 .0 .0 1 2.6 15 .0 .0 .0 .3 .0 .5 .0 .2 6.5 .0 .0 .0 .2 .0 .8 .0 .0 5.7 16 .0 .0 .0 .6 .4 .2 .0 .0 6.2 .0 .0 .0 .4 .6 .0 .0 .0 6.2 17 .0 .0 .5 .5 .0 .0 .0 .0 9.5 .0 .0 .6 .4 .0 .0 .0 .0 9.7 18 .0 .0 .0 .0 .0 .2 .0 .8 1.8 .0 .0 .0 .0 .0 .0 .0 1 1.6 19 .0 .0 .0 1 .0 .0 .0 .0 5.6 .0 .0 .0 1 .0 .0 .0 .0 5.6 20 .0 .0 .0 .8 .0 .2 .0 .0 4.4 .0 .0 .0 1 .0 .0 .0 .0 5.3

a) uncertain (fuzzy) solution b) reference solution


src abatement technologies emit. abatement technologies emit. 1 2 3 4 5 6 7 8 1 2 3 4 5 6 7 8 1 .0 .0 .0 .0 .0 .0 1 .0 41.5 .0 .0 .0 .0 .0 .0 1 .0 40.9 2 .7 .0 .3 v .0 .0 .0 .0 178.7 .9 .0 .1 .0 .0 .0 .0 .0 131.8 3 .0 .0 .0 1 .0 .0 .0 .0 40.1 .0 .0 .0 1 .0 .0 .0 .0 42.6 4 .0 .0 .0 .1 .0 .0 .9 .0 14.5 .0 .0 .0 .0 .0 .0 1 .0 12.4 5 .0 .0 .0 .0 .0 .0 .0 1 8.5 .0 .0 .0 .0 .0 .0 .0 1 8.5 6 .0 .0 .0 1 .0 .0 .0 .0 33.0 .0 .0 .0 1 .0 .0 .0 .0 31.9 7 .0 .9 .0 .1 .0 .0 .0 .0 39.1 .0 1 .0 .0 .0 .0 .0 .0 40.9 8 .0 1 .0 .0 .0 .0 .0 .0 33.2 .0 1 .0 .0 .0 .0 .0 .0 32.8 9 .0 .8 .0 .2 .0 .0 .0 .0 30.1 .0 1 .0 .0 .0 .0 .0 .0 21.8 10 .3 .0 .7 .0 .0 .0 .0 .0 31.2 .0 .0 1 .0 .0 .0 .0 .0 26.4 11 .0 .4 .0 .6 .0 .0 .0 .0 16.9 .0 .0 .0 1 .0 .0 .0 .0 14.2 12 .0 .0 .0 .0 .0 .0 .2 .8 3.5 .0 .0 .0 .0 .0 .0 .0 1 3.2 13 .0 .0 .0 .0 .0 .0 .0 1 2.8 .0 .0 .0 .0 .0 .0 .0 1 2.8 14 .0 .0 .0 .0 .0 .0 .0 1 2.4 .0 .0 .0 .0 .0 .0 .0 1 2.8 15 .0 .0 .0 .6 .0 .4 .0 .0 8.2 .0 .0 .0 .3 .0 .7 .0 .0 5.1 16 .0 .0 .0 .8 .2 .0 .0 .0 6.9 .0 .0 .0 .9 .1 .0 .0 .0 5.5 17 .0 .1 .7 .2 .0 .0 .0 .0 9.6 .0 .05 .9 .05 .0 .0 .0 .0 8.7 18 .0 .0 .0 .0 .0 .4 .0 .6 1.8 .0 .0 .0 .0 .0 .0 .0 1 1.4 19 .0 .0 .0 1 .0 .0 .0 .0 5.1 .0 .0 .0 1 .0 .0 .0 .0 5.0 20 .0 .0 .0 1 .0 .0 .0 .0 4.6 .0 .0 .0 1 .0 .0 .0 .0 4.8




src abatement technologies emit. abatement technologies emit. 1 2 3 4 5 6 7 8 1 2 3 4 5 6 7 8 1 .0 .0 .0 .0 .0 .0 1 .0 50.0 .0 .0 .0 .0 .0 .0 1 .0 50.0 2 .2 .0 .8 .0 .0 .0 .0 .0 174.7 .0 .0 1 .0 .0 .0 .0 .0 161.1 3 .0 .0 .0 .3 .0 .0 .7 .0 27.8 .0 .0 .0 1 .0 .0 .0 .0 28.0 4 .0 .0 .0 .0 .0 .0 1 .0 15.2 .0 .0 .0 .0 .0 .0 1 .0 15.1 5 .0 .0 .0 .0 .0 .0 .0 1 10.4 .0 .0 .0 .0 .0 .0 .0 1 10.4 6 .0 .0 .0 1 .0 .0 .0 .0 39.2 .0 .0 .0 1 .0 .0 .0 .0 39.0 7 .0 .3 .0 .7 .0 .0 .0 .0 37.3 .0 1 .0 .0 .0 .0 .0 .0 32.5 8 .0 .8 .0 .2 .0 .0 .0 .0 37.6

40.0 .0 1 .0 .0 .0 .0 .0 .0 40.0

9 .0 .2 .0 .8 .0 .0 .0 .0 28.6 .0 .1 .0 .9 .0 .0 .0 .0 26.0 10 .0 .0 1 .0 .0 .0 .0 .0 32.8 .0 .0 1 .0 .0 .0 .0 .0 32.2 11 .0 .0 .0 1 .0 .0 .0 .0 17.8 .0 .0 .0 1 .0 .0 .0 .0 17.3 12 .0 .0 .0 .0 .0 .0 .0 1 4.0 .0 .0 .0 .0 .0 .0 .0 1 3.9 13 .0 .0 .0 .0 .0 .0 .0 1 3.5 .0 .0 .0 .0 .0 .0 .0 1 3.5 14 .0 .0 .0 .0 .0 .0 .0 1 2.9 .0 .0 .0 .0 .0 .0 .0 1 2.9 15 .0 .0 .0 .1 .0 .4 .0 .5 5.0 .0 .0 .0 .2 .0 .8 .0 .0 5.0 16 .0 .0 .0 .2 .3 .4 .1 .0 5.3 .0 .0 .0 .4 .6 .0 .0 .0 5.0 17 .0 .0 .3 .7 .0 .0 .0 .0 9.5 .0 .0 .6 .4 .0 .0 .0 .0 8.7 18 .0 .0 .0 .0 .0 .1 .0 .9 1.8 .0 .0 .0 .0 .0 .0 .0 1 1.7 19 .0 .0 .0 1 .0 .0 .0 .0 6.2 .0 .0 .0 1 .0 .0 .0 .0 6.2 20 .0 .0 .0 .5 .0 .4 .0 .1 3.8 .0 .0 .0 1 .0 .0 .0 .0 5.8

Histogram of the optimal emission; initial index - Ji=3.24.107

reference solutionuncertain (fuzzy) solution

–


uncertain (fuzzy) solution reference solution


uncertain (fuzzy) solution reference solution

General conclusions

• limited impact of the model uncertainty on accuracy of the optimal problem solution,

• mainly qualitative character of environment-oriented decisions,

• final accuracy of numerical test – sufficient for decision support in environmental policy,

• application of sophisticated and time-consuming methods in such applications is (due to uncertainty) rather unfounded,

• simpler and computationally efficient heuristic algorithms are more motivated in such decision tasks.

Thank You for attention

Documents

Air quality decision support under uncertainty (case study analysis) Piotr Holnicki Systems Research Institute PAS 01-447 Warszawa, Newelska 6 [email protected]