Development of the Development of the CMAQ-UCD Sectional CMAQ-UCD Sectional

Aerosol ModelAerosol ModelK. Max Zhang and Anthony S. WexlerK. Max Zhang and Anthony S. Wexler University of California DavisUniversity of California Davis

Biosketch of CMAQ-Biosketch of CMAQ-UCDUCD

19919900

19919988

1999-1999-20002000

2002-2002-20032003

8:30pm (EST) Feb 9, 8:30pm (EST) Feb 9, 2005, Atlanta2005, Atlanta

Tony Wexler wrote the Tony Wexler wrote the original AIMoriginal AIM

Sun and Wexler Sun and Wexler simulated SCAQS simulated SCAQS particle size particle size distributionsdistributions

Clegg, Brimblecombe Clegg, Brimblecombe and Wexler and Wexler developed online AIMdeveloped online AIM

CMAQ-AIM in CMAQ-AIM in VISTASVISTAS

Started CMAQ-Started CMAQ-AIM effortAIM effort

Renamed to Renamed to CMAQ-UCDCMAQ-UCD

2004 - 2004 - presentpresent

CMAQ-AIM in BRACE, CMAQ-AIM in BRACE, CRPAQSCRPAQS

20062006CMAQ-UCD public CMAQ-UCD public releaserelease

• Uses Models-3/CMAQ as platformUses Models-3/CMAQ as platform• Incoporates an aerosol module developed Incoporates an aerosol module developed

by Sun, Zhang and Wexler.by Sun, Zhang and Wexler.• The aerosol module is sectional, fully The aerosol module is sectional, fully

dynamic and computationally efficient.dynamic and computationally efficient.

CMAQ-UCDCMAQ-UCD

Gas ChemistryGas Chemistry Aerosol DynamicsAerosol Dynamics

Integration of large set of Integration of large set of stiff ODEsstiff ODEs

the calculation of rate of the calculation of rate of change for gas-phase species change for gas-phase species is is mathematically trivial: mathematically trivial:

...21 RRi ckc

dtdc

requires requires partitioningpartitioning between between gaseous and particulate phasesgaseous and particulate phases

the calculation of rate of the calculation of rate of change for particulate species change for particulate species needs needs aerosol thermodynamicsaerosol thermodynamics computationcomputation

Gas-phase chemistry vs. Aerosol Gas-phase chemistry vs. Aerosol dynamicsdynamics

Dynamic Gas-to-Particle Dynamic Gas-to-Particle TransportTransport

• UncoupledUncoupled Partitioning of each volatile species one by onePartitioning of each volatile species one by one

• CoupledCoupled (near pH independent) (near pH independent) NHNH33 and HNO and HNO33 and/or NH and/or NH33 and HCl condense and and HCl condense and

evaporate together to maintain near acid-neutralityevaporate together to maintain near acid-neutrality

• ReplacementReplacement (near pH independent) (near pH independent) HNOHNO33 condenses as HCl evaporates or vice versa condenses as HCl evaporates or vice versa

in near acid-neutrality conditionsin near acid-neutrality conditions

HNOHNO33(g)(g)UncoupUncoupledled

Calculate vapor pressure Calculate vapor pressure of HNOof HNO33 and NH and NH33 on on particle surfaceparticle surface

NHNH33(g)(g)

NONO33--

Then partition NHThen partition NH33..

NHNH33(g)(g)UncoupUncoupledled

NHNH44++

NONO33--

UncoupUncoupledled

NHNH44NONO33

HNOHNO33(g)(g) NHNH33(g)(g)CoupleCoupledd

In near acid-neutrality In near acid-neutrality conditionsconditionsNHNH44NONO33

HNOHNO33(g)(g) HCl(g)HCl(g)ReplacemReplacementent

ClCl--NONO33-- In near acid-neutrality In near acid-neutrality

conditionsconditions

  CaseCase TTAA TTNN TTCC Mechanism(s)Mechanism(s)11          No Aerosol ThermodynamicsNo Aerosol Thermodynamics

22 XX UncoupledUncoupled

33 XX UncoupledUncoupled

44 XX UncoupledUncoupled

55 XX XX Coupled NHCoupled NH33 and HNO and HNO33

66 XX XX Coupled NHCoupled NH33 and HCl and HCl

77 XX XX ReplacementReplacement

88 XX XX XX Coupled NHCoupled NH33 and HNO and HNO33, NH, NH33 and HCl and HCl

Simplified Simplified ThermodynamicsThermodynamics

• A rigorous approach is to minimize Gibbs A rigorous approach is to minimize Gibbs free energyfree energy

• What we need: equilibrium vapor pressures What we need: equilibrium vapor pressures of NHof NH33/HNO/HNO33/HCl, and water content /HCl, and water content (requiring (requiring phase state)phase state)

• Strategies:Strategies: Using phase diagrams to determine phase stateUsing phase diagrams to determine phase state Using vapor pressure cap to determine the Using vapor pressure cap to determine the existence of NHexistence of NH44NONO33(s) and NH(s) and NH44Cl(s)Cl(s)

Phase diagram of Phase diagram of HH++, NH, NH44++, SO, SO44

2-2-, NO, NO33--

2233 ANANANHNONH mKpp

ANHNONH Kpp 33

Vapor Pressure CapVapor Pressure Cap

ConstantConstant

MolalityMolality

Activity CoefficientActivity CoefficientVapor Vapor pressurepressure

0.1

1

10

100

PN

H3P

HN

O3

(ppb

2 )

0.90.80.70.60.50.4Relative Humdity

10-19

10-18

10-17

10-16

PN

H3 P

HN

O3 (atm

2)

10 oC

20 oC

30 oC

Numerical Integration Numerical Integration using ATSusing ATS

• We are developing an Asynchronous Time-We are developing an Asynchronous Time-Stepping (ATS) integration method.Stepping (ATS) integration method.

• Similar concepts have been applied in Similar concepts have been applied in molecule dynamics and solid mechanics.molecule dynamics and solid mechanics.

• With ATS, each variable is integrated based With ATS, each variable is integrated based on its intrinsic time scale.on its intrinsic time scale.

• CPU time can be saved by reducing number CPU time can be saved by reducing number of integrations for slow variables and of integrations for slow variables and avoiding inversion of large Jacobian. avoiding inversion of large Jacobian.

ε1c1

c2

c3

. . .

cn

tcurr tnew

ε2

ε3

εn

“pass”

“scan”……

……

……

……

……

. . .

t1,local

t2,local

t3,local

fastest

slowest

tn,local

ATS vs. GEAR for typical ATS vs. GEAR for typical TampaTampa conditions conditions

Condensation caseCondensation case Evaporation caseEvaporation case

10-8

10-7

10-6

10-5

10-4

10-3

10-2

10-1

100

RM

S

0.12 3 4 5 6

12 3 4 5 6

102 3

CPU time (s)

Gear ATS

(a)

10-8

10-7

10-6

10-5

10-4

10-3

10-2

10-1

100

RM

S

0.012 3 4 5 6

0.12 3 4 5 6

12

CPU time (s)

Gear ATS

(b)

10-8

10-7

10-6

10-5

10-4

10-3

10-2

10-1

100

RM

S

0.0012 3 4 5 6

0.012 3 4 5 6

0.12 3

CPU time (s)

Gear ATS

(c)

10-8

10-7

10-6

10-5

10-4

10-3

10-2

10-1

100

RM

S

0.0012 4 6 8

0.012 4 6 8

0.12 4

CPU time (s)

Gear ATS

(d)

ATS vs. GEAR for typical ATS vs. GEAR for typical BakersfieldBakersfield conditions conditions

Condensation caseCondensation case Evaporation caseEvaporation case

ATS vs. GEAR for typical ATS vs. GEAR for typical Los AngelesLos Angeles conditions conditions

Condensation caseCondensation case Evaporation caseEvaporation case

2

46

0.001

2

46

0.01

2

46

0.1

RM

S

0.1 1 10CPU time (s)

(e)

Gear ATS

10-6

10-5

10-4

10-3

10-2

RM

S

5 6 7 8 90.1

2 3 4 5 6 7 8 91

CPU time (s)

(f)

Gear ATS

ATS vs. GEAR for typical ATS vs. GEAR for typical RiversideRiverside conditions conditions

Condensation caseCondensation case Evaporation caseEvaporation case

2

3

456

0.01

2

3

4

RM

S

5 60.1

2 3 4 5 61

2 3 4 5 610

2

CPU time (s)

(g)

Gear ATS

68

0.001

2

4

68

0.01

2

4

68

0.1

RM

S

4 5 60.1

2 3 4 5 61

2 3 4 5 610

CPU time (s)

Gear ATS

(h)

ATS BenchmarkATS BenchmarkTest Test CasesCases

EPS = 0.1EPS = 0.1 EPS = 0.01EPS = 0.01

RMSRMSCPU CPU time time (s)(s)

RMSRMS CPU time CPU time (s)(s)

TampaTampa Cond.Cond. 4.74.71010-2-2 0.230.23 8.68.61010-4-4 0.470.47

Evap.Evap. 1.71.71010-2-2 0.040.04 1.31.31010-3-3 0.140.14

BakersfieBakersfieldld

Cond.Cond. 1.01.01010-2-2 0.00240.0024 1.31.31010-3-3 0.0130.013

Evap.Evap. 1.21.21010-2-2 0.00240.0024 5.85.81010-4-4 0.0190.019

Los Los AngelAngeleses

Cond.Cond. 4.34.31010-3-3 0.030.03 2.92.91010-3-3 0.140.14

Evap.Evap. 5.45.41010-3-3 0.050.05 1.11.11010-3-3 0.180.18

RiversideRiverside Cond.Cond. 8.08.01010-3-3 0.050.05 2.92.91010-3-3 0.180.18

Evap.Evap. 8.08.01010-3-3 0.040.04 3.63.61010-3-3 0.120.12

SDASDA 1.91.9 2.72.7

Summary• We developed a sectional, dynamic partitioning and We developed a sectional, dynamic partitioning and

computationally efficient aerosol module in CMAQ-computationally efficient aerosol module in CMAQ-UCD.UCD.

• CMAQ-UCD adopts three gas-to-particle partitioning CMAQ-UCD adopts three gas-to-particle partitioning schemes: Uncoupled, Coupled and Replacement.schemes: Uncoupled, Coupled and Replacement.

• CMAQ-UCD applies simplified thermodynamic CMAQ-UCD applies simplified thermodynamic schemes to determine the vapor pressures of volatile schemes to determine the vapor pressures of volatile species and particle phase states.species and particle phase states.

• CMAQ-UCD employs a novel asynchronous time-CMAQ-UCD employs a novel asynchronous time-stepping (ATS) integration technique to solve stiff stepping (ATS) integration technique to solve stiff ODE problems in aerosol dynamics.ODE problems in aerosol dynamics.

AcknowledgementAcknowledgement• USEPA• California Air Resources Board• VISTAS• Dr. Robin Dennis, Dr. Ajith Kaduwela and

Dr. Gail Tonnesen