High-Order DDM Sensitivity Analysis of Particular Matter in CMAQ Wenxian Zhang, Shannon Capps, Yongtao Hu, Athanasios Nenes, and Armistead Russell Georgia.

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