Final Report for Aerosol Modeling for the Global Model

Atmospheric and

Environmental Research, Inc.

Final Report for

Aerosol Modeling for the Global Model Initiative

NAS5-99201

For the period May 25, 1999 to May 24, 2001

Principal InvestigatorDebra K. Weisenstein

Malcolm K.W. Ko

Atmospheric and Environmental Research, Inc.

131 Hartwell Avenue, Lexington, MA 02421-3126

March 28, 2001

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1. AGENCY USE ONLY (Leave b/ank) 2. REPORT DATE 3. REPORT TYPE AND DATES COVERED

March 30, 2001 Final Report, May 25, 1999 to May 24, 2001

5. FUNDING NUMBERS4. TITLE AND SUBTITLE

Aerosol Modeling for the Global Model Initiative

6. AUTHORS

Debra K. Weisenstein

Malcolm K. W. Ko

7. PERFORMING ORGANIZATION NAME(S) AND ADDRESS(ES)


131 Hartwell Avenue

Lexington, MA 02421

9. SPONSORING/MONITORING AGENCY NAME(S) AND ADDRESS(ES)

NASA Goddard Space Flight Center

Greenbelt, MD 20771

NAS5-99201

8. PERFORMING ORGANIZATIONREPORT NUMBER

P796

10. SPONSORING/MONITORING AGENCYREPORT NUMBER

11. SUPPLEMENTARY NOTES

12a. DISTRIBUTION/AVAILABILITY STATEMENT 12b. DISTRIBUTION CODE

13. ABSTRACT (Maximum 200 words)

The goal of this project is to develop an aerosol module to be used within the framework of the Global Modeling Initiative (GMI). The

model development work will be preformed jointly by the University of Michigan and AER, using existing aerosol models at the twoinstitutions as starting points. The GMI aerosol model will be tested, evaluated against observations, and then applied to assessment of

the effects of aircraft sulfur emissions as needed by the NASA Subsonic Assessment in 2001. The work includes the following tasks:

1. Implementation of the sulfur cycle within GM1, including sources, sinks, and aqueous conversion of sulfur. Aerosol modules will

be added as they are developed and the GMI schedule permits.

2. Addition of aerosol types other than sulfate particles, including dust, soot, organic carbon, and black carbon.

3. Development of new and more efficient parameterizations for treating sulfate aerosol nucleation, condensation, and coagulation

among different particle sizes and types.

4. Develonment of a 3-D database which can be used to evaluate results of the aerosol model.

14. SUBJECT TERMS

aerosol model

Global Model Initiative (GMI)

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unclassified

18. SECURITY CLASSIFICATION OFTHIS PAGE

unclassified

NSN 7540-01-280-5500

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15. NUMBER OFPAGES

52

16. PRICECODE

20. LIMITATION OF ABSTRACT

unlimited

Computer Generated STANDARD FORM 298 (Rev 2-89)Prescribed by ANSI Std 239-18298-102

Abstract

This is the final report for a project funded by the Subsonic Assessment Program of the

Atmospheric Effects of Aviation Project to implement an aerosol prognostic capability in the

Global Modeling Initiative three-dimensional model. Though the original contract period was

reduced from 3 years to 2 years and the funding was reduced by 50%, we have accomplished

many of the original goals and are prepared to continue the work under other funding. The

work involved collaboration between Atmospheric and Environmental Research, Inc. (AER)

and the University of Michigan. The main accomplishment of the contract period was a thor-

ough intercomparison of aerosol process algorithms between the AER microphysical code and

the University of Michigan microphysical code. The AER code simulates nucleation, conden-

sation, and coagulation of sulfate aerosols using a 40 bin size distribution. This approach is

not practical for use in 3-D models because of its computational demands. The University of

Michigan code calculates the mass loading and aerosol number concentration using a 2-mode

distribution. A common set of algorithms which differ only in the method of resolving the

aerosol size distribution has now been agreed to and is described in this report. Thus we are

in a position to modify the 2-mode parameterizations to provide more realistic simulations.

The AER two-dimensional aerosol model has been updated for consistency with the common

algorithms and global calculations performed.

1 Project Overview

The goal of this project was to develop an aerosol module to be used within the framework

of the Global Modeling Initiative (GMI). The motivation came from the need to assess the

atmospheric impact of sulfur compounds and particulate matter emitted by jet engines in the

upper troposphere and lower stratosphere. The model development work was performed jointly

by the University of Michigan and AER, using existing aerosol models at the two institutions

as starting points. The GMI aerosol module was to be tested, evaluated against observations,

and then applied to assessment of the effects of aircraft sulfur emissions as needed by the NASA

Subsonic Assessment in 2001. The original scope of the work included the following tasks:

1. Implementation of the sulfur cycle within GMI, including sources, sinks, and aqueous

conversion of sulfur. Aerosol modules will be added as they are developed and the GMI

schedule permits.

2. Addition of aerosol types other than sulfate particles, including dust, soot, organic carbon,and black carbon.

3. Development of new and more efficient parameterizations for treating sulfate aerosol nu-

cleation, condensation, and coagulation among different particle sizes and types.

4. Development of a 3-D database which can be used to evaluate results of the aerosol model.

Note that the contract period was shortened from 3 to 2 years, with the total funding reduced

to half of the proposed budget. Thus the performance objectives were modified over the original

statement of work. Still, we were able to address most of the issues in the original proposal,

though item (2) above was eliminated from the project scope.

Sulfur source gas production and removal rates were delivered to GMI by Joyce Penner to

begin the process of implementing the sulfur cycle in the 3-D model (Task 1). The GMI team,

however, has been too busy to implement this yet. To accomplish Task 3, we performed inter-

comparisons between tile AER and University of Michigan aerosol aerosol models, comparing

nucleation, condensation, and coagulation codes. This resulted in updates of both model codes,

as common algorithms were agreed to. The final versions of the these algorithms are presented

in this final report. We are now confident that the model differences are due only to the method

of resolving the size distribution. Results of the model intercomparison exercises were presented

at GMI meetings in January 2000 and June 2000. A 3-D database suitable for model evaluation

(Task 4) exists at the University of Michigan and is available for model comparisons when GMI

implements our aerosol modules and generates aerosol distributions.

2 Scientific Results

2.1 Approach

The AER 2-D sulfate aerosol model is described in Weisenstein et al. [1997]. It uses 40

size bins by volume doubling from 0.39 nm to 3.2 #m. Each size bin is transported separately,

2

assuminga single constant radius. Condensation rates are calculated for eachbin size, andcoagulationdeals with the interaction of each bin sizewith all others. This model has beenusedfor the calculation of supersonicaircraft perturbations to stratosphericaerosolsurfaceareadensity (IPCC [1999], Kawa et al. [1999]) and for the study of volcanic perturbations to the

stratospheric aerosol layer ( Weisenstein et al. [1997]; Weisenstein and Yue [1999]). Nucleation

previously followed the classical formulation of Zhao and Turco [1995] but has been replaced

with the Kulmala et al. [1998] parameterization for this study. The diffusion coefficient in the

condensation algorithm has been updated according to Jacobson [1999], and the Kelvin effect

has been added.

The University of Michigan 2-mode aerosol model follows Kreidenweis and Seinfeld [1988],

Harrington and Kreidenweis [1998a], and Harrington and Kreidenweis [1998b]. The term

"mode" refers to an aerosol distribution characterized by its mean radius, number concentra-

tion, and a geometric standard deviation. The mass and number concentration of each mode

are calculated prognostically in the model. The mean radius is derived from mass and number

concentration; the standard deviation ag of the lognormal distribution is assumed. The size

distributions of the two modes may overlap, though each mode is transported separately. Mode

1 generally represents fine, submicron sized particles resulting from recent nucleation events.

Mode 2 represents coarse particles which sediment rapidly. The prognostic equations for massand number concentration include terms related to homogeneous nucleation of new sulfuric

acid/water particles, condensation of H2SO4 on preexisting sulfate aerosol, and coagulation of

sulfate aerosol particles.

It was decided at the beginning of this project that the modal approach, currently used by

the University of Michigan model, would be applied to the GMI model. The reason for this is the

efficiency of the scheme, which makes it practical for three-dimensional modeling. Only aerosol

mass and number in each mode need to be transported. The size-resolving approach used by

AER requires that the number density in each of 40 bins be transported. Adding non-sulfate

aerosol types would require an additional 40 bins for each type. The size-resolving approach does

have the advantage of more accurately dealing with aerosol sizes and the interactions among

particles. This would be particularly important in regions of nucleation and in regions suchas aircraft wakes where aerosols are added to the atmosphere. To address this issue, we have

performed model intereomparisons to analyze and improve the performance and accuracy of the

modal scheme. We also have the option of increasing the number of modes for situations where

more accuracy is required.

Because the AER and University of Michigan models differ in dimensionality and transport

parameterizations, a meaningful direct comparison was not possible. Therefore we chose to com-

pare individual aerosol processes within a box model. Realistic initial conditions were chosen,

some including an initial aerosol distribution and some initialized with only gas phase H2SO4.

Analysis of these process model intercomparisons allowed us to determine differences between

the AER and University of Michigan microphysical modeling approaches. Differences due to

nucleation, condensation, and coagulation algorithms were resolved, so that the remaining dif-

ferences are due only to the different methods of resolving the size distribution. The common

algorithms agreed to are described below.

2.2 Microphysical Algorithms

2.2.1 Nucleation

The fornmlation of homogeneousnucleation follows the parameterizationof Kulmala et al.

[1998], with the nucleation rate J (particles cm -3 s -1) given by:

J = exp(25.1289Ns,al - 4890.8Ns_gI/T - 1743.3/T

-2.24795Ns,aIRH + 7643.4xat/T - 1.9712z_JRH) (1)

with

N,u,: = ln(Na/N.,.) (2)

T - 273.15

5 = 1+ 273.15 (3)

Here Na is the ambient sulfuric acid vapor concentration, Na,c is the sulfuric acid vapor con-

centration needed to produce a nucleation rate of 1 cm-3s -1, T is temperature (K), x_z is acid

mole fraction of the embryo, and RH is fractional relative humidity. N,,c is parameterized as:

N_,_ = exp(-14.5125 + 0.1335T - 10.5462RH + 1958.4RH/T). (4)

The H2SO4 mole fraction in the critical nucleus is given by

0.0154RA

xa_ = 1.2233 RA + RH + 0.0102 In N,v - 0.0415 In Nwv + 0.0016T (5)

where RA denotes fractional relative acidity, and N,. and Nwv are sulfuric acid and water vapor

concentration (cm-a), respectively. The embryo radius r* is obtained by solving

20"?2 w

-o (6)T*

where

A#w

Vw

= -kBTln(N_v/N_,so_) (7)

= 18( + dX_ )/A, (8)

after the composition (x_t) is known. Here X_ is the mass fraction of acid in the embryo, A.

is Avogadro's number, kB is the Boltzmann constant, and p and a are the density and surface

tension of the droplet. N_:og is the equilibrium concentration of water vapor over the surface

of a solution with composition xal. The parameterizations are valid over the temperature range

from 233 K to 298 K and from 10 to 100% relative humidity. For use near the tropopause and

in the lower stratosphere, we are awaiting an updated parameterization from Kulmala.

2.2.2 Condensation

The condensation rate Gi onto Ni particles of radius ri is given by

Gi = 47r/3Ds(Ns- NSsat)riNi (9)

with

[ (1.33Kni + 0.71 4(1 - a)) ]-1 (10)

Kni = --.As (11)ri

Ds is the diffusion coefficient for HeS04 molecules in air. Ns and N sat denotes the number

density of H2S04 in the gas phase and the equilibrium H2S04 number density over the surface

of sulfate aerosol particles, respectively. N sat includes solution and curvature (Kelvin) effects

[Jacobson, 1999]. fl is the correction factor for non-continuum effects and imperfect surfaceaccommodation. Two different values for the accommodation coefficient a are currently tested:

a=l and c_=0.04. As in the equation for the Knudson number Kni denotes the mean free path

for H2SO4 molecules in air.

In the two mode model, the particle volume mean radius, r,,ol, times a correction factor is

substituted for ri above

' ri = rvotexp(-ln2cra). (12)

This corrects for the effect of the size distribution on the condensation rate of the mode. However,

the size dependence of the Knudson number Kni and of the supersaturation over a curved surface

are ignored. Potential improvements to the two mode treatment of condensation could include

a new parameterization of the correction factor or performing the condensation calculation for

multiple bins within each mode.

2.2.3 Coagulation

We only consider Brownian coagulation. For the coagulation kernel Kij between a particles

of radius ri and a particle of radius rj, we apply the interpolation formula of Fuchs [1964]:

Kij = 47r(Di+ Dj)(ri+ri)

( r_+rj 4(Di+Dj) )-1a2'_a/2 + (13)r i Ac rj -4- (g2 _[_ YJ; (C 2 "_ C2) 1/2 (r i At rj)

0.87 ]kBT 1 + Kna,i(1.249+0.42 exp(-K-_,/)) j (14)with Di - 6 zr r/, ri

Kna,i = --Aa (15)ri

gi = 2 (ri -4- li) 3 -- (r/2 nt- /2)3/2 _ 2ri (16)3 rili

4 Dili = --

7r c i

C i = ....

k Trmi ]

1/2

(17)

(18)

ku and T denote the Boltzmann constant and the temperature. Aa is the mean free path of air

molecules, r/a the dynamic viscosity, and mi the mass of a particle of radius ri.

In the 40 bin model, coagulation between two particles in the same bin results in one particle

in the next larger bin. Coagulation between one particle and another particle from a smaller

bin results in a fraction of the combined particle mass in the original larger bin and the next

larger bin. In the two mode model, coagulation between two particles in the same mode results

in a reduction in number density in that mode, but no mass change in that mode. Coagulation

between particles in different modes results in mass transfer to the larger mode. A scheme to

shift mass between modes as coagulation occurs has been implemented but needs further testingand refinement.

2.3 Box Model Intercomparison

The most important milestone in the first year of our project involved a model intercompar-

ison of the two mode model and the 40 bin model. We first performed the comparisons using

four sets of initial conditions, designated Box 1 through Box, 4. Relative humidities varied from

0.66% to 95%, temperatures from 208 K to 263 K, and pressure levels were either 200 or 500

mb. Each model used these initial conditions without transport and reported initial tendencies

and time evolution of the aerosol distribution for a 24 hour period. Tables 1-4 show the initial

conditions and initial rates for nucleation, condensation, and coagulation (Boxes 1 and 2 have

no initial condensation or coagulation because there was no initial aerosol). This exercise re-

sulted in many algorithm updates for both models as standard formulations were agreed to and

differences resolved. We are now confident that the differences between model results derive

solely from the different ways of treating the size distribution.

The Figures 1-4 represent the time evolution of aerosol mass, number, nucleation rate, and

condensation rate over 24 hours for each of the four initial conditions. Results from the two

mode model (labeled UMICH) and the 40 bin model (labeled AER) are shown with values

of a in the condensation equation of 1.0 and 0.04. The value of a used in the condensation

equation has generally been 1.0, which implies that all collisions between gas phase H2SO4 and

aerosol particles result in particle growth. With a value of c_ of 0.04, the condensation rate is

dramatically reduced and the time required for gas-to-particle transfer is increased from 1 hour

to 30 hours in Box 1 and from 1 hour to 12 hours in Box 4. Differences in the treatment of

condensation (because of the different ways of representing the size distribution) are apparent

and result in different number concentrations after integration.

Figures 5-8 show the initial aerosol size distributions as a function of radius and those calcu-

lated by each model during and at the end of the model integration for the case where c_=l.0.

Box 1 results show that the two mode model accurately reproduces the size distribution in the

situation where all aerosols are nucleated within the first minute and condensation ceases after

2 minutes due to depletion of gas phase H2SQ. A single-mode log-normal distribution results

after 1 hour due to coagulation, though the width of the distribution is somewhat narrower in

6

the 40 bin model than the two mode model. In Box 2, nucleation continues for 5 hours and

the final aerosol mass is reached after 10 hours. In this case, the 40 bin model shows a skewed

distribution after 1 and 5 hours due to continued particle generation in the smallest size bin,

while the two mode model shows the same peak number density, but a symmetrical distribution.

Box 3 was initialized with a three-mode size distribution, and subsequent changes in total

aerosol mass were minor. Both models show no change in the size distribution over 24 hours,

but the two mode model fits the initial distribution into a single mode, so the initial shape is

not preserved. Box 4 had an initial aerosol distribution along with nucleation and condensation

for the first hour, though the total aerosol mass increased by only 1% in the 24 hour period.

The two mode model fit the initial aerosols into mode 2 and the newly nucleated aerosols into

mode 1. The particle number densities in mode 1 after 1 and 5 hours are much less than in the

40 bin model, and by 24 hours all mode 1 particles have been shifted into mode 2.

We repeated the Box 4 calculations using a single lognormal distribution (rather than a

superposition of three lognormals) as the initial condition. Figure 9 shows results of the Box

4 calculation of aerosol mass, number concentration, nucleation rate, and condensation rate

with the revised initialization. The AER results shown in red used the original initial aerosol

distribution, which assumed 90% of the initial particles in a lognormal distribution with mode

radius of 0.021 #m, 10% of the initial particles in a lognormal distribution with mode radius

of 0.069 #m, and 0.04% of the initial particles in a lognormal distribution with mode radius

of 0.351 #m. The green line represents a calculation performed with a single lognormal initial

distribution with mode radius of 0.043 #m. The UMICH model, since it fits the initial aerosol

distribution into the larger of its two modes, can only represent the initial distribution as a

single lognormal. Aerosol number concentration differs most between the models. AER model

results using a single lognormal initial distribution (green lines) are considerably closer to the

UMICH values than the standard AER results (shown in red). We find better agreement since

the 2-mode model now accurately represents the initial distribution. However, compared to the

AER model, the 2-mode model often overestimate condensation and underestimates coagulation

rates. Some of this difference is likely due to the different timestepping schemes employed by

the two models: an explicit scheme for AER and an implicit scheme for UMICH.

An additional intercomparison exercise involved using a range of actual zonal mean and

extreme conditions for January and performing 24 hour aerosol integrations. The calculations

are for four altitudes (850, 500, 200, and 50 mb) and a range of latitudes. Figure 10 shows a

scatter diagram of AER results vs. UMICH (labeled Bimodam) results as originally calculated

in November 1999. Total particle number, nucleation over 24 hours, and condensation over 24

hours are shown. The plots show that agreement between the models was reached only for a

limited subset of conditions. Figure 11 shows current results after the models were updated to

similar microphysics. Agreement is much improved and falls within reasonable limits for all but

a few conditions. These results were presented at the International Conference on Nucleation

and Atmospheric Aerosols by Michael Herzog.

2.4 Enhancements to the AER 2-D Sulfate Aerosol Model

Updates to the AER aerosol model have included implementation of new microphysical

algorithms to match those agreed to for GMI and improvements to the 2-D transport and

chemistry. The AER 2-D sulfate aerosol model and the AER 2-D chemistry transport model have

7

beencombinedinto one model. Previously thesewere separatemodels,with the sulfate modelusing input OH and Oafrom the chemistrymodel and the chemistry modelusing input surfacearea density from the sulfatemodel. With the modelscombined,perturbation calculations canbe done with a singlecalculation rather than a seriesof two or moredifferent calculations. Forexample,a Mt. Pinatubo calculation cancalculatechangesin sulfatesurfaceareadensity whichwill impact ozonein the samecalculation. While this currently haslittle effecton model results,it will allow for greater interactivity of sulfateand other trace gasesin the future. For example,wecould allow HNOa to condenseonto sulfateaerosolsand generatePSCsof STScomposition.This developmentwork on the AER 2-D sulfateaerosolmodel was fundedlargely through ourSAGE II contract (NAS1-99096)but is of benefit to this contract also.

Convectionhas beenadded to the AER 2-D model, using codeand data filesobtained fromVictor Dvortsov [Dvortsov et al., 1998] and based on CCM3 convective fluxes. We found the

convection to work well with the transport circulation of the GSFC 2-D model, as this transport

is based on observational data. With the AER transport, which includes an enhanced Kzz

term to partially account for convection, inclusion of the convective parameterization results in

too much tracer transport between the surface and the upper troposphere. Figures 12 and 13

show model-calculated aerosol extinction at 1.02 ttm and aerosol surface area density without

(panel a) and with (panel b) convection. The calculated extinction with convection agrees well

with SAGE observations for nonvolcanic periods. Aerosol surface area density is considerably

enhanced by convection in the lower stratosphere, and may be somewhat too large compared toobservations.

The time stepping scheme in our 2-D aerosol model uses time splitting and performs nu-

cleation before condensation. In cases with both large nucleation and condensation rates, the

gas phase H2SO4 may be used up by nucleation and none left for condensation. Observational

results indicate that under conditions with ample available surface area for condensation, the

effects of nucleation are limited [Kulmala et al., 2000]. We have explored this issue in the global

2-D model by modifying the time stepping scheme. Figure 14a shows the annual average aerosol

surface area density calculated by the model in its normal mode, where the nucleation step is

performed before the condensation step. Figure 14b shows results with the condensation step

performed first. Performing nucleation first results in 20-30% greater aerosol surface area density

in the upper tropical troposphere. To help assess the accuracy of these schemes, we have subdi-

vided the 1 hour time step into 40 substeps doing condensation and nucleation in sequence. The

calculated surface area density with this scheme is shown in Figure 14c and falls between those

shown in Figures 14a and 14b. This should represent a fairly accurate time-stepping scheme,

though the computational time required is prohibitive. A new scheme has been devised which

calculates the rate of change of gas phase H2SO4 due to nucleation and condensation (before

modifying the aerosol number densities) and subdivides the time step if nucleation and/or con-

densation will deplete all H2SO4 within a single time step. Results of this scheme are shown

in Figure 14d. The computer time required for this scheme is quite modest because only grid

points with large aerosol changes will perform a maximum of 50 substeps.

Tile condensation and nucleation routines of the model have also been updated. Updates to

the condensation rate include correction of the effective mean free path and diffusion coefficient

according to Jacobson [1999], introduction of the Kelvin effect, and use of saturation vapor

pressures from Ayers et al. [1980] and sulfuric acid activity coefficients from Taleb et al. [1996]

as parameterized in Kulmala et al. [1998]. Tile impact of these changes on calculated annual

8

averagesurfaceareadensity for nonvolcanicconditions is shownin Figure 15,where15ausestheold condensationroutine and 15bthe newroutine. The most obviousimpact is due to the Kelvineffectand results in a smaller surfacearea density at high latitudes and high altitudes. Useofupdatedvapor pressuresin the condensationschemehasvery little effecton calculated surfaceareadensity. It doeshavean impact, however,on nucleationrates. Figure 15cshowssurfaceareadensity calculated with the new vapor pressuresused in the Zhao and Turco [1995] nucleation

scheme. Surface area density increases by 30-40% in the tropical upper troposphere with use of

the updated vapor pressures. Figure 15d shows a calculation using the Kulmala et al. [1998]

nucleation parameterization for grid points where the relative humidity is greater than 10%

and the classical nucleation approach for all other cases. The Kulmala et al. parameterization

includes the effects of hydration, which our classical approach does not. The nucleation rate

in the troposphere is smaller with the Kulmala et al. parameterization, and thus surface area

densities are smaller.

2.5 Future Directions

Implementation of a prognostic aerosol scheme for GMI should continue to be a high priority.

The GMI model in the future will have the capability to adequately handle problems involv-

ing both stratospheric and tropospheric chemistry and transport. Many problems involving

atmospheric sulfate and aerosols (volcanic effects, aircraft impacts) will require both a realistic

troposphere and a realistic stratosphere. If GMI funding continues, we are prepared to imple-

ment the 2-mode aerosol module within GMI. The algorithms described here are the appropriate

first step, but can be improved by increasing the number of modes (after model analysis to de-

termine the optimum number), adding other aerosol types (dust, soot, black carbon, organic

carbon), and developing parameterizations for the interaction of these aerosol types.

3 Deliverables

Source emission rates and chemical rate constants required to calculated gas phase sulfur

chemistry were delivered to GMI by Joyce Penner. An aerosol database which will be used to

compare three-dimensional calculated aerosol distributions with observations is available at the

University of Michigan. Aerosol microphysical parameterizations are available as fortran code

and can be delivered to the GMI team at Lawrence Livermore National Laboratory on short

notice.

The following presentations were related to this contract:

1. given by Joyce Penner at the January 2000 GMI Meeting in Washington, DC [Penner et

al., 2000];

2. given by Debra Weisenstein at the June 2000 GMI and AEAP Meeting, Snowmass, CO

[ Weisenstein et al., 2000];

3. given by Michael Herzog at the International Conference on Nucleation and Atmospheric

Aerosols, Rolla, MO [Herzog et al., 2000a; 2000b].

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spheric particles, Nature, _0_, 66-69, 2000.

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for the Global Modeling Initiative, GMI Science Team Meeting, Washington, DC, Jan. 4-6,2000.

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25,977, 1996.

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December 13-17, 1999.

10

Weisenstein,D. K., M. K. W. Ko, J. E. Penner, and M. Herzog, An aerosolmodule for theGlobal Modeling Initiative, presentedat the Atmospheric Effects of Aviation Conference,Snowmass,CO, June 5-9,2000.

Zhao, J., and R. P. Turco, Nucleation simulations in the wakeof a jet aircraft in stratosphericflight, J. Aerosol Sci., 26, 779-795, 1995.

11

Table 1: Initial Conditions and Initial Rates for Box 1

Quantity Units UMich Value AER Value

Initial Conditions

Pressure [mb] 500

Temperature [K] 262.96

Rel. humidity [%] 86.57

Rel. acidity [%] 13.10

H20 gas [molec/cm 3] 6.719 x 1016

H2SO4 gas [molec/cm 3] 7.097 x 10 °s

Aerosol mass [molec/cm 3] 0.0

H2SO4 mass fraction 0.2078

Aerosol density [g/cm 3] 1.1632

Nucleation

Nucleation rate [molec/cm3/s] 8.705x 10 °4

Density of nucleus [g/cm 3] 1.562

Radius of nucleus [#m] 5.006 x 10 -°4

Size of nucleus [molec/particle] 3.199

500

262.96

86.57

13.11

6.723x 1016

7.100 x 10 °s

0.0

0.2078

1.1632

8.722 x 10 o4

1.562

5.001 × 10 -04

3.192

12



Pressure

Temperature

Rel. humidity

Rel. acidity

H20 gas

H2SO4 gasAerosol mass

H2SO4 mass fraction

Aerosol density

Nucleation rate

Density of nucleus

Radius of nucleus

Size of nucleus

Initial Conditions

[rob] 200 200

[K] 233.93 233.93

[%] 0.66 0.66

[%] 27.89 27.89

[molec/cm 3] 4.197x 1013 4.299x 2013

[molec/cm 3] 2.407 × 1007 2.408 × 20 07

[molec/cm a] 0.0 0.0

0.7486 0.7486

[g/cm 3] 1.6992 1.727

Nucleation

[molec/cm3/s] 0.590 0.591

[g/cm 3] 1.805 1.806

[pin] 4.272 X 10 -04 4.267 x 10 .04

[molec/particle] 3.199 2.946

13



Pressure

Temperature

Rel. humidity

Rel. acidity

H20 gas

H2SO4 gas

Aerosol mass

Aerosol number

Aerosol avg. radius

H2SO4 mass fraction

Aerosol density

Nucleation rate

Density of nucleus

Radius of nucleus

Size of nucleus

H2SO4 saturation

Mean free path

H2SO4 gas diff. coeff.

Condensation rate

Particle velocity

Coag. Kernel

Number Change

Initial Conditions

[mb] 500

[K] 208.12

[%] 6.366

[%] 100

[molec / cm 3] 2.206 x 1013

[molec/cm 3] 2.603× 10 o5

[molec/cm 3] 3.850× 10 °7

[cm -3] 8.503

[#m] 5.670x 10 .02

0.6168

[g/cm a] 1.541

Nucleation

[molec/cm3/s] 6.102x10 -°s

[g/cm 3] 1.7905

[#m] 3.064 x 10 -04

[molec/particle] 1.032

Condensation

[mo lec / cm 3] 3.056 x 10 -03

[cm] 3.328 x 10 -°5

[cm2/s] 9.119x10 -°2

[molec / cm3/s] 7.1213

Coagulation

[cm/s] 7.823

[cm 3] 1.137 × 10 .9

[cm -3 s -1] -8.224x 10 -s

500

208.12

6.366

i00

2.206x 1013

2.603x 1005

3.851x 10 07

8.259

5.701× 10 -02

0.6168

1.587

6.102× I0-°s

1.766

3.061×10 -04

1.030

3.051×I0 -o3

3.327× 10-06

9.124x 10 -02

3.659

7.707

1.301x10 -09

-9.121x10 -0s

14



Pressure

Temperature

Rel. humidity

Rel. acidity

H20 gas

H2SO4 gas

Aerosol mass

Aerosol number

Aerosol avg. radius

H2304 mass fraction

Aerosol density

Nucleation rate

Density of nucleus

Radius of imcleus

Size of nucleus

H2SO4 saturation

Mean free path


Condensation rate

Particle velocity

Coag. Kernel

Number Change

Initial Conditions

[rob] 200 200

[K] 218.05 218.05

[%] 95.43 95.43

[%] 100 100

[molec/cm a] 1.110xl015 1.110×1015

[molec/cm 3] 2.293 x 10 °_ 2.293 x 10 (/_

[molec/cm a] 2.484 x 10 °s 2.485 x 10 °s

[cm-3] 411.08 402.99

[#m] 5.700 x 10 -°_ 5.701 x 10 -()2

0.1163 0.1163

[g/cm a] 1.091 1.113

Nucleation

[molec/cm3/s] 3.688 3.689

[g/cm a] 1.650 1.636

[#m] 3.609× 10 -°4 3.606× 10 -4

[molec/particle] 1.346 1.343

Condensation

[molec/cm 3] 1.458× 10 -ll 1.457× 10 -ll

[cm] 8.718 x 10 -06 8.715 x 10 -()6

[cm2/s] 0.244 0.245

[molec/cm3/s] 4432 2431

Coagulation

[cm/s] 9.517 9.419

[cm a] 2.122 x 10 -0 2.408 x 10 -o9

[cm -a s -1] -3.587x 10 -4 -3.678x 10 -04

15

Aerosol Mass Aerosol Number Concentration

800 .... I .... r .... r r I r _ P I [ ....

4,.i\/ t

400 a f I UMICH 8

=c ia / i "" '_' UMICH (_=0.04) Itl / / _ AER t 6

= II /J ---- AER (o[=0.04) /

20"ilg I 4

0 0

0 5 10 15 20 25 30 0 5 10 ! 5 20 25 30

time [mini time [mini

Nucleation Rate (10s averages) Condensation Rate (10s averages)

25

20

0.2 .]"E

i ) ,o

00 5 10 15 0 5 10 15

time [min] time [rain]

Figure 1: Model calculations of aerosol evolution for Box 1 initial conditions fl'om the UMICH

(lflack lines) and the AER (red lines) models. The change in aerosol mass. aerosol number

concentration, nucleation rate, and condensation rate are shown over 12 hours. Solid lines

represent vahls of _ in the condensation equation of 1.0, while dashed lines repI'eSellt (_=0.04.

16

10

C

5

Aerosol Mass

UMICH

UMICH (_--0.04)AER

AER (c_--0.04)

3t)000

,., 20000E

0

Aerosol Number Concentration

.... I .... L .... [ ' ' • I '

0 5 10 15 20 0 5 10 15 20

time [h] time [h]

Nucleation Rate (10s averages) Condensation Rate (10s averages)2.0 1000

[email protected]

i mm_ !.0

"_ i 41)0

0.5200

0.0 00 5 10 15 20 0 5 10 15 20

time [hi time [h]

Figure 2: Model (:alculati(ms of aerosol evolution fi)r Box 2 initial (-(mditions from the U._IICH

(black lines) and the AER (red lines) nm(Ms. The ('hange in aerosol mass, aerosol numbm'

concentration, nuch'ation rate. an(l condensation rate are shown over 2=1 hours. Solid lines

tel)resent valus of :_ in the ctmdensati<m equation t)f 1,0. while dashed lines represent e_=().()4.

17

38.7

2_ 38.6

E%

38.5

38.4

Aerosol Mass

8.6

8.5

8.3

8.20 5 10 15 20 0

time [hi


.... [ , r i .... _ .... r r r

I I I [ I I I h [ I I I I [ I I h I I I I I

5 10 15 20

time [hi

E

8e-08

6e -08

4e-08

2e-08

0e+00

Nucleation Rate (10s averages)8

E34

E

o 5 l0 15 2O o 5

time [h]

Condensation Rate (10s averages)

10 15 20

time [hi

Figure 3: Model calculations of aerosol evolution for Box 3 initial conditions ff()m the UMICH

(black lines) and the AER (red lines) models. The change in aerosol mass, aerosol tmmt)er('()ncentratioll. nu(:leation rate, and condensation rate are shown over 24 hours. Solid lines

tel)resent valus of (_' in the (,ondensation equation of 1.0, while (lashed lines ret)resent _=0.04.

18

251

250E

E%"_ 249

248

Aerosol Mass

0 3 6 9 12

time [hi


40000

300O0

10t_)

00 3 6 9 12

time [hi

Nucleation Rate (10s averages) Condensation Rate (10s averages)5 5000

4 4(NX)

1 1000

0 00 3 6 0 3

time [h] time [h]

Figure 4: Model (:ah:ulations of aerosol evohltion fl)r Box 4 initial conditions fr()m the U_IICH

l])]ack li)w.s) _)_1 tJw AEt_ (red ]ine,,Q models. The change i_ aero.so] mas,s, aero.sr)l )))m_l)('r

('()nt'entrati()n, ml(:h,ati()n rate, a Il(t (:on(h,nsation rate at(' shown ov(,r 12 hours. Solid lines

rol)ro._(')It vahl,_ (_f () iz_ tho (:ondensatio)i (,quation ()f 1.0, whih' da._ho(i ]i))(,s r('l)resent ()=0.04.

19

Ix 10'_

lxlO:'

E

e-

._ 1×10 4

¢)

e--

1×10 3

lxlO-

lxlO ('

1xlO 5

E:J

e--

.z._ Ixl() 4

e,.,

C

Ix 10 3

:1 iiii I , , ,,1,, I i i , , ,,_,| , . . . i,,, I

AER Model __ Initial

I hour

5 hours24 hours

. .,.,I , ,,,.I , , , , J,J,l

O.(X) 1 0.01 O, I 1

:1 Illl[

=

IIIll

().(X) I

Radius (gm)

........ I ........ I ........ I

UMICH Model [-- Initial t

l- I hour ]5 hours [

24 hours]

lxlO z ........ I10.01

Radius (_tm)

Figure 5: Model ('alculati()ns of t,h(, evolution of the aerosol size distribution for Box 1 initial

(,on(litions from t h(, AE1R (top panel) and the UMICH (bottom panel) models. Results areshown after 1 horn'. 5 hours, and 24 hours.

2O

1IX)()()

E

IO()()

I00

iO,

1

0.10.001 0.01 O.] 1

Radius (lam)

I0000 : ..... t ........ I ........ i '

I(XX)

"_" 1O0

I0

5

1

O.l

UMICH Model

O.(X)1 0.01

| | i IIll i

Initial

I hour [

5 hour,,

24 hours

I i _,,Jl j , , i ,,,,I

O.I I

Radius (Urn)

Figure 6: Model calculations of tile evolution of the aerosol size distribution fi)r Box 2 initial

conditions from the AER (top panel) and the UMICH (bottom panel) models. Results are

sh_>xvn after 1 hour, 5 hours, and 24 hours.

21

100i,

10 L

=_

c-

O

¢-O. 1

¢-

0.01

0.001

1(X)

10

E

I

O. 1

0.0 I

0.001

i |1_[

i i lIB I

' ' ' ''"1 ' ' ' ' ''"1

AER Model

| i w i i iii] i ._

JInitial ]

I hour [

5 hours24 hours

| | |

0.01 O.I

Radius (tam)

ii1|[

!

....... I ........ I

UMICH Model

i i i , i |it[

Initial1 hour

5 hours24 hours

0.00 ! 0.01 O. I I

Radius (tam)

Figure 7: Model cal(:ulations of the evolution of the aerosol size distribution for Box 3 initial

(:()n(litions fi'om the AER (top panel) an(l the UMICH (bottonl t)anel) mo(l(,ls. Results ar(,

shown after 1 hour, 5 hours, and 24 hours, along with the initial aerosol size (listril)uti()n.

22

jl

AER Model

0.01

UMICH Model

23

251

250

E

E%-_ 249

2480 3

Box 4 no gas sourceAerosol Mass

UMICH

_--, UMICH (or=0.04)

AER

---- AER (t_=0.04)

AER (one mode)

6 9

time [h]

40000

30000

"_ 20000

10000

012


0 3 6 9 12

time [hi

Nucleation Rate (10s averages)

5

4

2

1

00 3 6

time [hi

5000

4000

._ 3o00

=_ 2000

1000


0 3 6

time [hi

Figure 9: Model calculations of aerosol evolution for Box 4 initial conditions from the UMICH

(black lines) and the AER (red lines) models. The change in aerosol mass. aerosol tmmber

concentration, mu,leation rate, and condensation rate are shown over 6 or 12 hours. Solid lines

represent values of, in the condensation equation of 1.0, while dashed lines represent ,.=0.04.

Ih,sults from the AER model using only one lognormal mode for the initial condition are shown

in green.

24

Box Model Comparison: ]first try

Total Particle Number

$

ee

.<

106

lO s

104

10 -_

102

10 I

10"

10"11

after 24h, January, extreme values

_///

O 50mb <>_

O I"1200mb J: @1_ <>500mb /_ll_v"

A850mb .///

/

' '_ l'_ "i'o_ 10' "i'_" lo' io"Bimodam [#/cm _]

10 u

!0 _

,_ 10 7

ce

10 5

I IIs

10 _

IO'10 a_"L'iOf_i'O' "'_10 "_v "t'O 7

Bimodam [molec/cm _ day ]

Nucleation

over 24h, January. extreme values

0 50m ill[_idl[

[] 200m b

:= :f/j//'

/ i/

I0" 10 N

$

Condensation

lO u

10 7

i0 -_

10 _

!0 _

I0 -_iO l

over 24h, January. extreme values

.................. %!ii

'0 50m'b i

1-1200mb .It_W',_

0500mb ,.fi_._

A850mb ,_/"<_ '_

I0""_ "'5o'_ Io_ l."t

Bimodam [molec/cm day]

Figure 10: Scatter diagrani of total particle nunlt)er, nucleation rate, and condensation rate after

it 324 }lOllr calculation with the AER and UXIICH models. Results represent Iiio ill'st coniparis<in

of flit' iIlodol,_ in N()VOlll})(_l' 1999.

25

I0 tl

lO _

._ 10 7

E

l0 s

E

_e 10 _

Box Model Comparison Today [after corrections and improvements I

Total Particle Number

l0 s

104

i0 -_

102

c_.<

10'

10"

10 "i

I0"

after 24h, January, extreme values

O 50mb <> /_/

n200mb X/_ /

Y. °0:by

//f °10° 10' 102 10"_ 104 10"_

UMICH [#/cm _]

10'

10 -I10'

Nucleation

over 24h, January, extreme values

...................... /_^///

O 50mb A Z///_/_

[] 200m b ////_/

<> 500m b _.t//A850mb •

10' 10 _ 10 _ 107 10" 10"

UMICH [molec/cm 3 day]

lO II

10 _

-.N 10 7

_ 10 5

l0 s

lO tI0'

Condensation

over 24h, January, extreme values

- :i ........2C] 200mb

O500mb

A 850mb

to, to-_ ,;"'- ,;"- ,o,,UMICH [molec/cm _ day]

Figure 11: Scatter diagram of total particle number, uucleation rate, and condensation rate after

a 24 hour calculation with the AER and UMICH models. Results represent a comparison of the

current models after corrections and improvement to synchronize the microphysical treatment.

26

(a)

3O

4o 1(b) -o1_ °1_-°1-

a

_" --6.o--__ <..z:z__,_c.o •20 -:, -10. _U.o _-----8.0-"el

90as 60os 30°S EQ 30 °N 60°N )O°NLaLitude

Figure 12: Calculated 1.02 /,m aerosol extinction (10 -s km-1) for April under nonvolcanic

conditions. The GSFC transport is used within the AER 2-D sulfate model, and panel (b) also

includes the convective parameterization of Dvortsov et al. [1998].

27

35

(a)SO

_" 25

,__20

G9

15.Wll_

,.+..a

•_ 10

__0 -_ _0.2-

____o.__° __o.4_•0.6____0 "6-

--°8_-_.o_o_-_.o_

--i.__ (__ ----

\@

90°S 60°S S0°S EQ SOON 60°N 90°NLatitude

(b)35

3O

"_" 25

20(D

15

<_ 10

5

90°S

i ' ' I ' ' I ' ' I ' ' I ' ' I ' ' l

0. _- __---Z-7-----_.

• o.6---_2__I

• 3.0-

) S] )1 & '_"\\ 'e_bo c6 _

60°S 30°S EQ 30°N 60°N 90°NLaf.if.ude

Figure 13: Calculated annual average aerosol surface area density (#m 2 cm-3) under nonvol-

canic conditions. The GSFC transport is used within the AER 2-D sulfate model, and panel

(b) also includes the convective parameterization of Dvortsov et el. [1998].

28

40_'' ''' I '_---1-_' , ,--r--

oLot-_" o__t_-- .4 0.4-

_0.6 _06-

1.5--------_.0_

_--77/_c___7 ---

20

i0

90os 60os 30°S EQ 30 °N 60°N 9°°NLatitude

40 _ I ' _ 1 ' ' I ' ' I ' ' I ' '

.---. 30 --0.2" _0.4______________0.4.--------0.4 _

_0 6 .6-

20 -_i o_---/----_-_-i.°--

<_o.__.o f't _7 -_I

i ¢_1"1 I

90°S 60os 30°S EQ 30 °N 60°N 90°NLatitude

40 , i i , , i i i i , , i i , i , ,

.._/

30 --0.2__-_. _ ,,_0. 4---------.------_0.4-

_o 6_°6---

,._,.o--/<....._o/...----,,j___,

IlL, I ,90os 60os 30°S EQ 30°N 60°N 90°N

Latitude

40

(d)3O

_) 2O

I0

_ _0. i-O. 1_0.2__

--0.2________0.4_/---0" g----------_ 0.4 -

_0.6 0.6-

.__'*,t°_./,..___-_..______.___-

_\',,, /% <_.<_(_\\ I J "-'-" "r....e CO

o o o ,_-

90os 60oS 30°S EQ 30 °N 60°N 90°NLatitude

Figure 14: Calculated annual average aerosol surface area (#m2/cm 3) from the AER 2-D model

using GSFC transport parameters and convection. Panel (a) is with nucleation performed before

condensation, panel (b) is with condensation performed first, panel (e) is with condensation and

then nucleation performed consecutively in a substep loop 40 times per hourly advective step,

and panel (d) is with the new time stepping scheme.

29

40 _ _ I _ ' I _ _ I ' i I i _ 1 _

(a) -o.1_ _o.i.0. t _ 0.2-

.---, 30 --0.2_--------0,4-----_0" "/--------_0 •4 -

_06 06-

Q) 20-

< lo- -__---_--_:°x_ -_

90°S 60°S 30°S Eq 30°N 60°N 90°NLatitude

40 ' ' I ' ' I _ ' I ' ' I J _ I ' '

(b)

3O

E

Q) 2O

10

-o4_;2__-_-__o 4/

90°S 60°S 30°S EQ 30°N 60°N 90°NLatitude

40 , _ I i _ I ' t I i , I ' L I t ,

(c) I

< _o __-'_'--__4"o o • " --I

/ ,.\\?(, I, , , , ,oZ ,,II90°S 60°S 30°S EQ 30°N 60°N 90°N

Latitude

4O

(d)

3O

20

.<10

/-----o._ .e--_C_t--o 4__o ,

90°S 60°S 30°S EQ 30°N 60°N 90°NLatiLude

Figure 15: Calculated annual average aerosol surface area (#m2/cm a) from the AER 2-D model

using GSFC transport parameters and convection. Panel (a) is with our normal condensation

scheme, panel (b) is with the updated condensation scheme, panel (c) is with the nucleation

scheme updated with new saturation vapor pressures, and panel (d) is with the nucleation

parameterization of Kulmala et al. [1998] used for relative humidities greater than 10%.

3O

Appendix A:

Poster Presented at GMI Meeting

June 6, 2000

Snowmass, Colorado

An Aerosol Module for the

Global Modeling Initiative

Debra Weisenstein

Malcolm Ko


Joyce Penner

Michael Herzog

University of Michigan

Atmospheric Effects of Aviation Conference

Snowmass, Colorado

June 5-9, 2000

Project Overview

A joint project between AER and the University of Michi-

gan is underway to provide aerosol predictive capability in

the Global Modeling Initiative (GMI) 3-D model. This

project leverages off of the 3-D tropospheric two moment

aerosol model at the University of Michigan and the 2-D

stratospheric arosol model with 40 size bins at AER. The

GMI aerosol module will initially operate with two aerosol

modes for efficiency, but may later use 4 or more modes.

Aerosol mass density and number density in each of the

modes will be transported parameters, with condensation,

nucleation, and coagulation modeled explicitly. Parameter-

izations will be developed to account for the aerosol size dis-

tribution in the condensation and coagulation calculations,

using the 40-bin model as a guide. Eventually aerosol types

other than sulfate could be added to the model, such as

organic carbon, black carbon, dust, and sea salt. Modeling

the interaction of aerosols with cirrus clouds and providing

climate impact predictability are long-term goals.

Microphysical Model Descriptions

The basic concept of the UMICH Aerosol Model follows

Kreidenweis and Seinfeld [1988], Harrington and Krei-

denweis [1998a], and Harrington and Kreidenweis [1998b].

The term "mode" refers to an aerosol subpopulation char-

acterized by its mean size which is distinguished from a

separately treated subpopulation of a different mean size;

both are present in the same volume sample. Each mode is

described by its mass and number concentration. For the

size distribution within each mode, a lognormal distribu-

tion with constant geometric standard deviation is assumed.

The prognostic equations for mass and number concentra-

tion include terms related to homogeneous nucleation of

new sulfuric acid/water particles, condensation of H2SO4

on preexisting sulfate aerosol, and coagulation of sulfate

aerosol particles.

The AER 2-D sulfate aerosol model is described in Weisen-

stein et al. [1997]. It used 40 size bins by volume dou-

bling from 0.39 nm to 3.2 #m. Each size bin is transported

separately, assuming a single constant radius. Condensa-

tion rates are calculated for each bin size, and coagulation

deals with the interaction of each bin size with all others.

This model has been used for the calculation of supersonic

aircraft perturbations to stratospheric aerosol surface area

density (IPUU [1998], Kawa et al. [1999]).

Nucleation

The formulation of homogeneous nucleation follows the pa-

rameterization of Kulmala et al. [1998]"

J = exp(25.1289N_i - 4890.8N_if/T - 1743.3/T

-2.24796N_IRH + 7643.4Xa_/T- 1.9712Xa_/RH)

with

N_IS -lnNa/N_,_T- 273.15

6-i+273.15

Na is the ambient sulfuric acid vapor concentration, Na,c

is the sulfuric acid vapor concentration needed to produce

a nucleation rate of 1 cm-3s -1, T is temperature (K), Xal

is acid mole fraction of the embryo, and RH is relative

humidity. Na,c and Xal are also parameterized

Condensation

The condensation rate Gi onto Ni particles of radius ri is

given by

with

(1.33Kni + 0.71_-- 1 + l+Kn_

Kni -- --.ri

+

-i

Ds is the diffusion coefficient for H2S04 molecules in air.

Ns and N_sat denotes the number of H2SO4 molecules in

the gas phase and the equilibrium H2S04 molecules over

the surface of sulfate aerosol particles, respectively. N_sat

includes solution and curvature (Kelvin) effects [Jacobson,

1999]. /3 is the correction factor for non-continuum effects

and imperfect surface accommodation. Two different values

for the accommodation coefficient c_ are currently tested:

c_=l and c_=0.04. As in the equation for the Knudson num-

ber Kni denotes the mean free path for H2S04 molecules

in air.

In the two mode model, the particle volume mean radius,

4

rv, times a correction factor is substituted for ri above

ri -- rvexp(-ln2ag)

This corrects for the effect of the size distribution on the

condensation rate of the mode. However, the size depen-

dence of the Knudson number Kni and of the supersatura-

tion over a curved surface are ignored.

Coagulation

We only consider Brownian coagulation. For the coagu-

lation kernel we apply the interpolation formula of Fuchs

[19641 •

ri + rj+

4 (Di ÷ Dj) )-1

(C 2 ÷ C2) 1/2 (I" i ÷ rj)

withkBT

Di = 6 7r ?]ari 1 + Kna,i(1.249 + 0.42 exp(

/_a

I_na,i --Ti

3 ri li--2ri

4Dili-

7r c i

0.87 ]Kna,i ))

5

SkBTI1/2Ci .....

\ _mi /

kB and T denote the Boltzmann constant and the temper-

ature, la is the mean free path of air molecules and r/a the

dynamic viscosity.

In the two mode model, coagulation between two par-

ticles in the same mode results in a reduction in number

density in that mode, but no mass change in that mode.

Coagulation between particles in different modes results in

mass transfer to the larger mode. In the 40 bin model, co-

agulation between two particles in the same bin results in

one particle in the next larger bin. Coagulation between

one particle and another particle from a smaller bin results

in a fraction of the combined particle mass in the original

larger bin and the next larger bin.

Box Model Intercomparison

The first step in our project involved a model intercompar-

ison of the two mode model and the 40 bin model. Four

sets of initial conditions were chosen and designated Box 1

through Box 4. Each model used these initial conditions

without transport and reported initial tendencies and time

evolution of the aerosol distribution for a 24 hour period.

6

Tables 1-4 show the initial conditions and initial rates for

nucleation, condensation, and coagulation. This exercise

resulted in many algorith updates for both models as stan-

dard formulations were agreed to. The differences between

model results now derive solely from the different ways of

treating the size distribution.

The figures represent the time evolution of aerosol mass,

number, nucleation rate, and condensation rate over 24

hours for each of the four initial conditions. Results from

the two mode model (labeled UMICH) and the 40 bin model

(labeled AER) are shown with values of c_ in the condensa-

tion equation of 1.0 and 0.04. Differences in the treatment

of condensation (because of the different ways of represent-

ing the size distribution) are apparent. Also shown are the

initial aerosol size distributions as a function of radius and

those calculated by each model during and at the end of the

model integration.

References

Fuchs, N. A., Mechanics of aerosols, Pergamon Press, New York, 1964.

Harrington, D. Y., and S. M. Kreidenweis, Simulations of sulfate aerosol dy-

namics - I. Model description, Atmos. Env., 32, 1691-1700, 1998a.

Harrington, D. Y., and S. M. Kreidenweis, Simulations of sulfate aerosol dy-

namics - II. Model intercomparisons, Atmos. Env., 32, 1701-1709, 1998b.

Intergovernmental Panel on Climate Change (IPCC), Aviation and the Global

Atmosphere, Cambridge University Press, 1999.

Jacobson, M. Z., Fundamentals of Atmospheric Modeling, Cambridge University

Press, Cambridge, U. K., 1999.

Kawa, S. R., et al., Assessment of the Effects of High-Speed Aircraft in the

Stratosphere: 1998, NASA//TP-1999-209237, 1999.

Kreidenweis, S. M. and J. H. Seinfeld, Nucleation of sulfuric acid-water and

methane sulfonic acid-water solution particles: Implications for the atmo-

spheric chemistry of organosulfur species, Atmos. Env., 22, 283-296, 1988.

Kulmala, M., A. Laaksonen, and L. Pirjola, Parameterizations for sulfuric acid/water

nucleation rates, J. Geophys. Res., 103, 8301-8307, 1998.

Weisenstein, D. K., G. K. Yue, M. K. W. Ko, N.-D. Sze, J. M. Rodriguez, and C.

J. Scott, A two-dimensional model of sulfur species and aerosols, J. Geophys.

Res., 102, 13,019-13035, 1997.

8

Table 1: Initial Conditions and Results for Box 1


Initial Conditions

Pressure [mb] 500 500

Temperature [K] 262.96 262.96

Rel. humidity [%] 86.57 86.57

Rel. acidity [%] 13.10 13.11

H20 molecules [molec/cm 3] 6.719E+16 6.723E+16

H2SO4 gas [molec/cm 3] 7.097E+08 7.100E+08

Aerosol mass [molec/cm 3] 0.0 0.0

H2804 mass fraction 0.2078 0.2078

Aerosol density [g/cm 3] 1.1632 1.1632

Nucleation

Nucleation rate [molec/cma/s] 8.705E+04 8.722E+04

Density of nucleus [g/cm 3] 1.562 1.562

Radius of nucleus [#m] 5.006E-04 5.001E-04

Size of nucleus [molec/part] 3.199 3.192

9



Initial Conditions

Pressure

Temperature

Rel. humidity

Rel. acidity

H20 molecules

H2SO4 gas

Aerosol mass

H2SO4 mass fraction

Aerosol density

Nucleation rate

Density of nucleus

Radius of nucleus

Size of nucleus

[mb] 200

[K] 233.93

[%] 0.66

[%] 27.89

[molec/cm 3] 4.197E+ 13

[molec/cm 3] 1.407E+07

[molec/cm 3] 0.0

0.7486

[g/cm a] 1.6992

Nucleation

[molec/cm3/s] 0.590

[g/cm a] 1.805

[#m] 4.272E-04

[molec/part] 3.199

200

233.93

0.66

27.89

4.199E+13

1.408E+07

0.0

0.7486

1.727

0.591

1.806

4.267E-04

2.946

10



Pressure

Temperature

Rel. humidity

Rel. acidity

H20 molecules

H2SO4 gasAerosol mass

Aerosol number

Aerosol avg. radius

H2SO4 mass fraction

Aerosol density

Nucleation rate

Density of nucleus

Radius of nucleus

Size of nucleus

H2SO4 saturation

Mean free path


Condensation rate

Particle velocity

Coag. Kernel

Number Change

Initial Conditions

[mb] 500

[K] 208.12

[%] 6.366

[%] 100

[molec/cm 3] 2.206E+ 13

[molec/cm 3] 2.603E+05

[molec/cm 3] 3.850E+07

[cm -3] 8.503

[#m] 5.670E-02

0.6168

[g/cm 3] 1.541

Nucleation

[molec/cm3/s] 6.102E-08

[g/cm 3] 1.7905

[,urn] 3.064E-04

[molec/part] 1.032

Condensation

[molec/cm3] 3.056E-03

[cm] 3.328E-05

[cm2/s] 9.119E-02

[molec/cm3/s] 7.1213

Coagulation

[cm/s] 7.823

[cm 3] 1.137E-9

[cm -3 s -1] -8.224E-8

500

208.12

6.366

100

2.206E+13

2.603E+05

3.851E+07

8.259

5.701E-02

0.6168

1.587

6.102E-08

1.766

3.061E-04

1.030

3.051E-03

3.327E-06

9.124E-02

3.659

7.707

1.301E-09

-9.121E-08

11

Table 4 Initial Conditions and Results for Box 4


Pressure

Temperature

Rel. humidity

Rel. acidity

H20 molecules

H2SO4 gas

Aerosol mass

Aerosol number

Aerosol avg. radius

H2SO4 mass fraction

Aerosol density

Nucleation rate

Density of nucleus

Radius of nucleus

Size of nucleus

H2SO4 saturation

Mean free path

H2SO_ gas diff. coeff.

Condensation rate

Particle velocity

Coag. Kernel

Number Change

Initial Conditions

[rob] 200

[K] 218.05

[%] 95.43

[%] 100

[molec/cm 3] 1.110E+ 15

[molec/cm 3] 2.293E+06

[molec / cm 3] 2.484E+08

[cm -a] 411.08

[#m] 5.700E-02

0.1163

[g/cm a] 1.091

Nucleation

[lnolec/cm 3/s] 3.688

[g/cm 3] 1.650[ttm] 3.609E-04

[molec/part] 1.346

Condensation

[molec/cm 3] 1.458E- 11

[cm] 8.718E-06

[cm2/s] 0.244

[molec/cma/s] 4432

Coagulation

[cm/s] 9.517

[cm 3] 2.122E-9

[tin -a S-1] -3.587E-4

200

218.05

95.43

100

1.110E+15

2.293E+06

2.485E+08

402.99

5.701E-02

0.1163

1.113

3.689

1.636

3.606E-4

1.343

1.457E-11

8.715E-06

0.245

2431

9.419

2.408E-09

-3.678E-04

12

Box 1 no gas sourceAerosol Mass Aerosol Number Concentration

14

6o0 /_s S

-_ 40o / / ---- uMxcH fi8

I / ---- UMICH (_=0.04) . =

11 I / _ Arg t -_ 6- II I/ ---- AER (0_--'0.04) / 4

0 I0 5 10 15 20 25 30 0 0 5 10 15 20 25 30

time [mini time [mini

__ Nucleation Rate (lOs averages) 2s[/i°ndensati°nRate(lOsaverage_i_ r , , , .... I .... ",02 ,-., 20 ]

loo.1 '°lAt

0.0 0 5 101L=_=I====*'I_$ 0 5 10 15

time [minl time [mini

13

Box 2 no gas sourceAerosol Mass Aerosol Number Concentration

14

38.7

38.6

E

38.5

38.4

Box 3 no gas source

Aerosol Mass

0 5 l0 15 20

time [hi

8.6

8.5

8.4

8.3

8.2


i I I I I I I I I I I I I I I I I I I I I I I i

5 10 15 20

time [h]

7

m

8e-08

6e-08

4e-08

2e-08

0e+00

Nucleation Rate (10s averages)

0 5 10 15 20

time [h]

E


5 10 15 20

time [h]

15

251

250

r_

E

" 249

248

Box 4 no gas sourceAerosol Mass

UMICH

-_-- UMICH let=0.04)

AER

_--- AER (t_=0.04)

0 3 6 9 12

time [hi


40000

300(X)

20000

100(H)

00 3 6 9 12

time [h]

Nucleation Rate (10s averages)5 5000

4 4000

_ i 2000

1 1000

0 00 3 6 0

time [h]


i

3

time [hi

16

lxlO 6

_. lx105r_j

E

0 4* _,,-I,-- lxlO

e-

¢J

0L)

1xlO 3

lxlO 2

Ixl06

1xlO 5

E

©

"_ Ixl04

e-,(D¢Je..o

L)lxl03

IxlO 2

•- I I I I l]

I a I Ill

0.001

ii I I I I l I

| | | I|l

0.001

Box 1 Size Distribution Evolution

........ I ........ I ........ I

AER Model

i I Jill

0.01 0.1

Radius (gm)

........ I ........ I

UMICH Model

0.01 0.1

Radius (_m)

m Initialm I hour

5 hours24 hours

I I I I I IIII

1

I I I I I III I

i_ Initial ]

I hour I5 hours24 hours

i i I I IIII

1

17

10000

1000

10000

1000


AER Model -- lnilial ]

-- I hour I-- 5 hours-- 24 hours

0.001 0.01 0.1 1

Radius (l-tm)

UMICH Model -- Initial-- ] hour-- 5 hours-- 24 hours

0.001 0.01 0.1 1

Radius (lam)

18


E

e-,

.o

t.,

1

0.1

©

0.01

0.001 ..... I0.001

100 1 ..... I

lOt--

0.1

¢3

0.01

0.001

...... I ........ I

AER Model

! ! ! ! ! I|| I

-- InitialI hour5 hours24 hours

I I

0.01 0.1

Radius (pm)

I IIII

1

...... I ........ I ........ I ' "

UMICH Model -- Initial

-- 1 hour

-- 5 hours

-- 24 hours

0.001 0.01 0.1 I

Radius (lam)

19

10000

1000


AER Model Initial I

I hour ]

5 hours

24 hours

0.010.001 0.01 0.1 1

Radius (Bm)

,:iOoli,............., ........, ........,,UMICH Model _ InitialI hour

m 5 hours I

I _ 24 hours I

-loo

i 10

=

0.1

0010.001 0.01 O. 1 1

Radius (lam)

2O

Documents

Final Report for Aerosol Modeling for the Global Model