MOMENT-BASED REPRESENTATIONOF SULFATE AEROSOL

IN THE EASTERN UNITED STATESAND COMPARISON WITH OBSERVATIONSS. Yu, P. S. Kasibhatla,

D. L. WrightS. E. Schwartz,

R. McGrawA. Deng

http://www.ecd.bnl.gov/steve/schwartz.html

Prepared for presentation atDOE Atmospheric Sciences Program Meeting

Albuquerque, NM19-21 March 2002

OUTLINE

• Introduction: Key aerosol processes and properties

• Moments of the aerosol particle size distribution

• Obtaining aerosol properties from the moments

• Representing aerosol evolution by the Method of Moments

• Application in a regional scale chemical transport model and comparisonwith observations

• Summary

NUCLEATION AND GROWTH PROCESSESOF ATMOSPHERIC AEROSOLS AND CLOUDS

REPRESENTATIONS OF AEROSOL SIZE DISTRIBUTION

Whitby, Atmos. Environ., 1978

SIZE MATTERSLight scattering efficiency of ammonium sulfate vs. radius

1 0

8

6

4

2

0

Sca

tte

rin

g

Eff

icie

ncy

, m

2/g

(SO

42

- )

0 . 0 1 0 . 1 1Radius, µm

5

Data of Ouimette and Flagan, Atmos. Environ., 1982

MOMENTS OF THE PARTICLE SIZE DISTRIBUTION

µkkr

dN

drdr≡ ∞

∫ ( )0

(not normalized)

Moment Physical Interpretation Unit

µ0 Particle number concentration cm-3

µ1 Total radius per unit volume cm cm-3

µ2 ( )4 1π − × Area per unit volume cm2 cm-3

µ3 ( )43

1π − × Volume per unit volume cm3 cm-3

EVALUATING AEROSOL PROPERTIESFROM THE MOMENTS

Aerosol physical or optical properties are an integral over the sizedistribution, requiring integrals of the form

P r f r dr=∞

∫ σ ( ) ( )0

where the kernel function σ ( )r describes the property of interest.

Problem: How to evaluate integrals over the aerosol size distributionwhen only the lower-order moments of the distribution are known???

. . .cont'd

EVALUATING AEROSOL PROPERTIESFROM THE MOMENTS (cont'd)

Solution: Gaussian quadrature

σ σ( ) ( ) ( )r f r dr r wii

N

i≈=

∞ ∑∫1

0

Here σ ( )r is the known kernel function and f r( ) is the unknown sizedistribution.

The N abcissas { ri} and N weights { wi } are determined from 2N momentsof f r( ) by inversion of

µkk

ik

i

N

ir f r dr r w≡ ==

∞ ∑∫ ( )1

0 k = 0, 1, …, 2N-1.

Aerosol properties (e.g., light scattering coefficient) evaluated in this wayare accurate typically to a few percent. Other approaches can yieldaccuracies several-fold better.

REPRESENTATION OF AEROSOL DYNAMICSBY THE METHOD OF MOMENTS

The method of moments is an approach to describing aerosol propertiesand dynamics in terms of the moments µk of the radial number sizedistribution f r( ).

µkk

r f r dr= ∞∫0 ( )

Aerosol dynamics can be represented by growth laws (differentialequations) in the moments.

The moments advect and mix just like chemical species--they areconserved and additive.

Hence representing aerosol properties and dynamics in 3-D transportmodels is equivalent to representing a small number of additionalchemical species -- the low order moments.

METHOD OF MOMENTSHeuristic Description

Consider accretion of monomer by existing aerosol.

This can be considered a reaction between monomer (m) and aerosolsurface area (A)

m A

kmA

+ → slightly larger distribution

Rate =

Aerosol surface area density is

A r f r dr= ∫ =∞ 4 420 2π πµ( )

So accretion of monomer by existing aerosol is a reaction betweenmonomer and second moment.

MOMENT EVOLUTION BY THE METHOD OF MOMENTS

Consider the growth law for particles of radius r:

dr

dtr r ( ) = φ( )

The corresponding moment evolution equation is:

1 10k

d

dtr r f r drk

kµ φ= −∞∫ ( ) ( )

But this set of equations is generally not closed!

QUADRATURE METHOD OF MOMENTSThe quadrature method of moments evaluates the moment evolutionequation

d

dtk r r f r drk

kµ φ= −∞∫ 10

( ) ( )

by Gaussian quadratures:

d

dtk r r wk i

k

ii iµ φ≅ −

=∑ 1

1

3( )

This approach is completely general and highly accurate.

R. McGraw, Aerosol Sci. Technol. (1997)

KEY PUBLICATIONS ON MOMENT METHODSMcGraw R. Description of atmospheric aerosol dynamics by the quadrature moment of

methods. Aerosol Sci. Tech. 27, 255-265 (1997).

McGraw, R., Nemesure, S., and Schwartz, S. E. Properties and evolution of aerosols withsize distributions having identical moments. J. Aerosol. Sci. 29, 761-772 (1998).

Wright Jr., D. L. Retrieval of optical properties of atmospheric aerosols from momentsof the particle size distribution. J. Aerosol Sci. 31, 1-18 (2000).

Wright D. L., McGraw R., Benkovitz C. M., and Schwartz S. E. Six-momentrepresentation of multiple aerosol populations in a sub-hemispheric chemicaltransformation model. Geophys Res. Lett. 27, 967-970 (2000).

Wright D. L., P. S. Kasibhatla, R. McGraw and S. E. Schwartz. Description andevaluation of a six-moment aerosol microphysical module for use in atmosphericchemical transport models. J. Geophys. Res. 106, 20275-20291 (2001).

Wright D. L., McGraw R. and Rosner D. E., Bivariate extension of the quadraturemethod of moments for modeling simultaneous coagulation and sintering of particlepopulations, J. Coll. Interface Sci. 236, 242-251 (2001).

Wright Jr., D. L., Yu, S., Kasibhatla, P. S., McGraw, R., Schwartz, S. E., Saxena, V. K.,and Yue, G. K. Retrieval of aerosol properties from moments of the particle sizedistribution for kernels involving the step function: Cloud droplet activation. J.Aerosol Sci. 33, 319-337 (2002).

McGraw R. and Wright D. L., Chemically-resolved aerosol dynamics for internalmixtures by the quadrature method of moments. J. Aerosol Sci. submitted, 2002.

INCORPORATION OF QMOM IN REGIONALSCALE MODEL

Host model: MAQSIP - Multiscale Air Quality Simulation Platform -prototype of US EPA Models-3 Community Multiscale Air Quality(CMAQ) Modeling System

Model domain: 72 by 74 square, 36-km grid cells, 22 layers, sigmacoordinate, from the surface to ~160 hPa.

Meteorological driver: MM5 meteorological model.

Emissions: 1990 EPA National Emissions Trends (NET90) Inventory.

Chemistry: SO2 oxidation by OH in air and oxidation by H2O2 in clouddroplets.

Clouds: Sub-grid convective (precipitating and non-precipitating) andgrid-scale resolved.

Particle activation, wet and dry deposition: Dependent on particle size.

APPLICATION TO SULFATE IN EASTERNNORTH AMERICA

Simulations: 40 days, 19 July to 28 August 1995.

Comparison with observations: Sulfate mass concentration, aerosolnumber concentration and size distributions at the Great SmokyMountains National Park during SEAVS (Southeastern Aerosol andVisibility Study Andrews et al., JAWMA, 2000; Ames et al., JAWMA,2000).

Limitation: Model is for sulfate only; size measurements are for entireaerosol, not just sulfate.

TIME SERIES COMPARISON FOR SULFATECONCENTRATION

Great Smoky Mountains during SEAVS

0.0

0.1

0.2

0.3

0.4

0.5

7/19 7/23 7/27 7/31 8/4 8/8 8/12 8/16 8/20 8/24

Date (1995)

[SO

42-],

µmol

m-3

Observations50% scavenging100% scavenging

TIME SERIES COMPARISON FOR AEROSOL MOMENTSLook Ridge, Great Smoky Mountains TN (84˚ W, 36˚ N; 900 m) during SEAVS

40

30

20

10

0 µ2,

µm

2 cm

-3

300

200

100

0 µ1,

µm

cm

-3

6000

4000

2000

0

µ0,

cm

-3 Model Observation

2.0

1.5

1.0

0.5

0.0 µ5,

µm

5 cm

-3

Date (1995)7/21 7/26 7/31 8/05 8/10 8/15 8/20 8/25

2.0

1.5

1.0

0.5

0.0 µ4,

µm

4 cm

-3

8

6

4

2

0 µ3,

µm

3 cm

-3

TIME SERIES COMPARISON FOR AEROSOL MOMENTSBlack Mountain, Mount Mitchell State Park NC (82˚ W, 36˚ N; 951 m)

40

30

20

10

0 µ2,

µm

2 cm

-3

300

200

100

0 µ1,

µm

cm

-3

6000

4000

2000

0

µ0,

cm

-3 Model

Observation

0.250.200.150.100.050.00 µ

5, µ

m5 c

m-3

Date (1995)7/21 7/26 7/31 8/05 8/10 8/15 8/20 8/25

1.0

0.8

0.6

0.4

0.2

0.0 µ4,

µm

4 cm

-3

543210 µ

3, µ

m3 c

m-3

SUMMARY

The Method of Moments (MOM) provides an accurate and efficientrepresentation of aerosol evolution and microphysical properties inchemical transport models.

MOM does not provide the particle size distribution, but it tells you(almost) everything else you want to know about the aerosol.

This method is becoming sufficiently mature that it can be used in regionalscale simulations.

Comparisons with observations for sulfate are favorable.

Improvements are needed in representing other key aerosol species.