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![Page 1: Air quality decision support under uncertainty (case study analysis) Piotr Holnicki Systems Research Institute PAS 01-447 Warszawa, Newelska 6 holnicki@ibspan.waw.pl.](https://reader036.fdocuments.in/reader036/viewer/2022062500/56649f1f5503460f94c373e4/html5/thumbnails/1.jpg)
Air quality decision support under uncertainty(case study analysis)
Piotr Holnicki
Systems Research Institute PAS01-447 Warszawa, Newelska 6
![Page 2: Air quality decision support under uncertainty (case study analysis) Piotr Holnicki Systems Research Institute PAS 01-447 Warszawa, Newelska 6 holnicki@ibspan.waw.pl.](https://reader036.fdocuments.in/reader036/viewer/2022062500/56649f1f5503460f94c373e4/html5/thumbnails/2.jpg)
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.
![Page 3: Air quality decision support under uncertainty (case study analysis) Piotr Holnicki Systems Research Institute PAS 01-447 Warszawa, Newelska 6 holnicki@ibspan.waw.pl.](https://reader036.fdocuments.in/reader036/viewer/2022062500/56649f1f5503460f94c373e4/html5/thumbnails/3.jpg)
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
![Page 4: Air quality decision support under uncertainty (case study analysis) Piotr Holnicki Systems Research Institute PAS 01-447 Warszawa, Newelska 6 holnicki@ibspan.waw.pl.](https://reader036.fdocuments.in/reader036/viewer/2022062500/56649f1f5503460f94c373e4/html5/thumbnails/4.jpg)
iiki
zihhii EqccR
z
cK
zcKc
t
c
),,( 1 u
The basic processes of air pollution dispersion
![Page 5: Air quality decision support under uncertainty (case study analysis) Piotr Holnicki Systems Research Institute PAS 01-447 Warszawa, Newelska 6 holnicki@ibspan.waw.pl.](https://reader036.fdocuments.in/reader036/viewer/2022062500/56649f1f5503460f94c373e4/html5/thumbnails/5.jpg)
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)
![Page 6: Air quality decision support under uncertainty (case study analysis) Piotr Holnicki Systems Research Institute PAS 01-447 Warszawa, Newelska 6 holnicki@ibspan.waw.pl.](https://reader036.fdocuments.in/reader036/viewer/2022062500/56649f1f5503460f94c373e4/html5/thumbnails/6.jpg)
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:
![Page 7: Air quality decision support under uncertainty (case study analysis) Piotr Holnicki Systems Research Institute PAS 01-447 Warszawa, Newelska 6 holnicki@ibspan.waw.pl.](https://reader036.fdocuments.in/reader036/viewer/2022062500/56649f1f5503460f94c373e4/html5/thumbnails/7.jpg)
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)()(
),()()(
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'
1000001
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'
1
![Page 8: Air quality decision support under uncertainty (case study analysis) Piotr Holnicki Systems Research Institute PAS 01-447 Warszawa, Newelska 6 holnicki@ibspan.waw.pl.](https://reader036.fdocuments.in/reader036/viewer/2022062500/56649f1f5503460f94c373e4/html5/thumbnails/8.jpg)
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
![Page 9: Air quality decision support under uncertainty (case study analysis) Piotr Holnicki Systems Research Institute PAS 01-447 Warszawa, Newelska 6 holnicki@ibspan.waw.pl.](https://reader036.fdocuments.in/reader036/viewer/2022062500/56649f1f5503460f94c373e4/html5/thumbnails/9.jpg)
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
![Page 10: Air quality decision support under uncertainty (case study analysis) Piotr Holnicki Systems Research Institute PAS 01-447 Warszawa, Newelska 6 holnicki@ibspan.waw.pl.](https://reader036.fdocuments.in/reader036/viewer/2022062500/56649f1f5503460f94c373e4/html5/thumbnails/10.jpg)
Impact of the input data – meteorology
(wind field, mixing height, temperature, cloudeness, precipitation, …)
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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
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Case study example – regional scale
Domain – 110 x 56 kmDiscretization – 2km x 2kmEulerian model RGFOR3
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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
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Concentration map for nominal emissions
Season-averaged (Winter) distribution of SO2 in the domain
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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
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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
![Page 17: Air quality decision support under uncertainty (case study analysis) Piotr Holnicki Systems Research Institute PAS 01-447 Warszawa, Newelska 6 holnicki@ibspan.waw.pl.](https://reader036.fdocuments.in/reader036/viewer/2022062500/56649f1f5503460f94c373e4/html5/thumbnails/17.jpg)
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%
Rec. 1 Rec. 2 Rec. 3 Rec. 4 Rec. 5
+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%
Rec. 1 Rec. 2 Rec. 3 Rec. 4 Rec. 5
+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%
Rec. 1 Rec. 2 Rec. 3 Rec. 4 Rec. 5
+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
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Uncertainty in decision support due toair quality forecast uncertainty
![Page 19: Air quality decision support under uncertainty (case study analysis) Piotr Holnicki Systems Research Institute PAS 01-447 Warszawa, Newelska 6 holnicki@ibspan.waw.pl.](https://reader036.fdocuments.in/reader036/viewer/2022062500/56649f1f5503460f94c373e4/html5/thumbnails/19.jpg)
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;
![Page 20: Air quality decision support under uncertainty (case study analysis) Piotr Holnicki Systems Research Institute PAS 01-447 Warszawa, Newelska 6 holnicki@ibspan.waw.pl.](https://reader036.fdocuments.in/reader036/viewer/2022062500/56649f1f5503460f94c373e4/html5/thumbnails/20.jpg)
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
![Page 21: Air quality decision support under uncertainty (case study analysis) Piotr Holnicki Systems Research Institute PAS 01-447 Warszawa, Newelska 6 holnicki@ibspan.waw.pl.](https://reader036.fdocuments.in/reader036/viewer/2022062500/56649f1f5503460f94c373e4/html5/thumbnails/21.jpg)
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
![Page 22: Air quality decision support under uncertainty (case study analysis) Piotr Holnicki Systems Research Institute PAS 01-447 Warszawa, Newelska 6 holnicki@ibspan.waw.pl.](https://reader036.fdocuments.in/reader036/viewer/2022062500/56649f1f5503460f94c373e4/html5/thumbnails/22.jpg)
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)
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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
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Application of Monte Carlo method
Optimization algorithm
↓
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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
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Optimal selection of emission reduction technologies initial index - Ji=2.63.107
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 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
a) uncertain (fuzzy) solution b) reference solution
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Optimal selection of emission reduction technologies initial index - Ji=3.92.107
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 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
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Histogram of the optimal emission; initial index - Ji=3.24.107
reference solutionuncertain (fuzzy) solution
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Histogram of the optimal emission; initial index - Ji=2.63.107
uncertain (fuzzy) solution reference solution
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Histogram of the optimal emission; initial index - Ji=3.92.107
uncertain (fuzzy) solution reference solution
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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.
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Thank You for attention