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High-Order DDM Sensitivity Analysis of Particular Matter in CMAQ
Wenxian Zhang, Shannon Capps, Yongtao Hu, Athanasios Nenes, and Armistead Russell
Georgia Institute of TechnologyOct 11, 2010
PM has the potential to affect
- Visibility- Human health- Climate…
Sensitivity Analysis
• A tool to quantify the response of pollutant concentrations to the changes in source emissions or other parameters
• Sensitivity can be calculated by different methods, depending on the focus of application.
- Brute Force Method (BFM) - Decoupled Direct Method (DDM) - Adjoint
Air QualityModel
Input:E, T, RH, U, R…
Output:Ci
Sensitivity
What’s the response?
Decoupled Direct Method
Air QualityModel
E C(E)Base Run
Air QualityModel
E - ΔE C(E - ΔE)Third Run
Air QualityModel
E + ΔE C(E + ΔE)Second Run
(1) ( ) ( )
2BFM
C E E C E ES
E
First Order
(2)2
( ) 2 ( ) ( )
( )BFM
C E E C E C E ES
E
Second Order
Air Quality Model
C aerosol C transportC gas
S aerosol S transportS gas
S0
C
S
C0
First Order
(1),
( )
( )i
i pp
ConcentraitonS
Emission
1 2
2(2), ,
1 2
( )ii p p
ConcentrationS
Ep Ep
Second Order
BFM DDM-PM
Brief History of DDM Sensitivity in Air Quality Models
• 1980’s: Dunker developed for air quality modeling
- Gas phase, first order• 1997+: Implementation in CIT, URM, CMAQ, CAMx• 2002+: First order aerosol phase (eg., Boylan et al., 2002 in
URM; Napelenok et al., 2006 in CMAQ; Koo et al., 2007 in CAMx)
• 2003: High order gas phase (eg., Hakami et al. 2003 in CMAQ)
- Use for source apportionment and uncertainty analysis
Implementing HO DDM-PM in CMAQ:
( ) ( )ii i i i
CuC K C R E
t
(2)(2) (2) (2) (1) (1)( ) ( ) '( , , )ijkijk ijk ijk i ij ik
SuS K S JS f C S S
t
(1)(1) (1) (1)( ) ( ) ( )ijij ij ij i
SuS K S JS f C
t
(Solve using the same algorithm for concentrations)
First Order
Second Order
ISORROPIA
H2SO4, NH3, HNO3, HCl, H2Ov
H+, NH4+, Na+, Cl-, SO4
=, HSO4-,
NO3-, OH-, H2O,
NH3(aq) , HNO3(aq) , HCl(aq)
Salts
,( ) ( )i j
ii
a K j
RH, temperatureTotal concentrations
Sulfate-ammonium-nitrate-chloride-sodium system
i i ia x
i ia p
Equilibrium equations
Calculating Second-Order (and higher)DDM Sensitivities
3 3 3 2
3 3 2
2 2 2 223 3 3 2
1 2 3 1 2 3 1 2 1 2 2 1 2
21
[ ] [ ] log [ ]1 [ ] 1 1 22ln10 0
[ ] [ ] [ ] [ ]
[ ] [ ] log [ ]1 [ ] 1 1 22ln10
[ ] [ ] [ ] [ ]
1 [ ] [
[ ]
HNO
HNO
NO HNO H OH
H p NO p HNO p p H O p
NO HNO H OH
H p p NO p p HNO p p p p H O p p
H
H p
3 3 3 3 2 2
2 2 22 3 1 2 3 1 2 2 1 2
[ ] [ ] [ ] [ ] [ ] [ ]] 1 1 2
[ ] [ ] [ ]
NO NO HNO HNO H O H OH
p NO p p HNO p p H O p p
3
23
4 23 2
[ ][ ]
[ ][ ]HNOH NO
KHNO H O RT
Equilibrium Equation
First-Order Sensitivity Equation
Second-Order Sensitivity Equation
Second-Order Sensitivities;Higher order found from similar
Processes (eqs. very similar to 1st order)
263
1
log_ ( ) 1( )HNO
i
coef i S ip
2621
[ ]_ ( ) 1( )
i
H Ocoef w i S i
p
2 263
11 2
log_ ( ) 2( )HNO
i
coef i S i RHSp p
2
2621
1 2
[ ]_ ( ) 2( )
i
H Ocoef w i S i
p p
Available from 1st order
Evaluation of DDM Performance: First Order • RH = 95% T = 298K• Total Sulfate: 0.1~10μmol/m3
• Total Ammonium: 0.1~10μmol/m3
• Total Nitrate: 0.1~10μmol/m3
• Total Sodium: 0.5μmol/m3
• Total Chloride: 1.0μmol/m3
[ ]A
p
H+ NH4+ SO4
= HSO4- NO3
- Ap
TS
TA
TN
Brute Force Sensitivities (mol/mol)
DD
M S
ensi
tiviti
es (m
ol/m
ol)
Evaluation of DDM Performance: Second Order • RH = 95% T = 298K• Total Sulfate: 0.1~10μmol/m3
• Total Ammonium: 0.1~10μmol/m3
• Total Nitrate: 0.1~10μmol/m3
• Total Sodium: 0.5μmol/m3
• Total Chloride: 1.0μmol/m3
2
2
[ ]A
p
H+ NH4+ SO4
= HSO4- NO3
- Ap
TS
TA
TN
DD
M S
ensi
tiviti
es (m
ol/m
3)-1
Brute Force Sensitivities (mol/m3)-1
Accuracy: DDM versus BFM
• Noisy BFM second-order sensitivities
- Perturbation (Δ) - Convergence criteria (ε)
10
0.01
1 10
10
0.001
1 10
3
0.01
1 10
First Order Sensitivity of AS to SOx Second Order Sensitivity of AS to SOx
Performance of HO DDM-PM in CMAQ Aerosol Sulfate (AS)
- Episode: Jan1 – Jan 7, 2004- Grid resolution: 36km, 13 vertical layers- Meteorology: MM5- Emissions: SMOKE
Evaluation of HO DDM-PM in CMAQ Aerosol Sulfate (AS)
First Order Sensitivity of AS to SOx Second Order Sensitivity of AS to SOx
Date: Jan 2, 2004Emission change for BFM: 50%
Summary
• High-order DDM-PM has been developed and implemented in CMAQ.
• HO DDM-PM appears to perform better than BFM. - Need better way to test as BFM is subject to noise
• Results from CMAQ captures the features of physical and chemical processes.
• Future Applications - Source Apportionment - Emission inventory assessment - Air quality model uncertainty analysis
• Advisor: Dr. Armistead Russell• Funding Source: Conoco-Phillips• Support from CAMx modeling group
Acknowledgements