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S ELECTEDl 'MA, 2 6 i981

D

An Analysis of Surface Production

ofSea-Salt AerosolsIC. W. Fairall

BDM/NPS

Monterey, California 93940

Ir3!T!BU' 1ON :,&A ,/.i;T ,l

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) C..Farl Project Enine NI00014-78-C-0204

9 pgAkOEmwI.GORGANIZATION dAimi-N AND OONI91 to. PNOORAM ELEMENT. PROJECT. TASKA 9A & WORK UN IT NUM411NS1

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Monterey, CA 93940 214 MONITONING AGEN"cv NME &R&OO*Es""ed" 7II 1. Cantoiidmg 1fte)j #11. ICURITY' CLASS. (at thi le ,mr

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10 SUPPLEMENTARY NOTES

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5ECUN01TV CLASSIFICATION OF T"1% PAGE (6 0 1.000

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I FOREWORD

This report was prepared under Work Order Number 422 of Contract

N00014-78-C-0204 in support of the U.S. Naval Postgraduate School researchproject supported by the Naval Air Systems Command (Air 370) and the Naval

J Material Command (EO/MET). The work was performed in support of the Envi-

ronmental Physics Group at NPS under the direction of Professors G. E.

Schacher and K. L. Davidson.

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ITABLE OF CONTENTS

FOREWORD ii

TABLE OF CONTENTS iii

LIST OF FIGURES iv

LIST OF TABLES v

ABSTRACT vi

A. INTRODUCTION 1

B. AEROSOL SPECTRUM 2

C. FLUX SPECTRUM ANALYSIS 5

D. FLUX SPECTRUM AND WIND SPEED 10

E. NON-EQUILIBRIUM 16

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ILIST OF FIGURES

Figure Page

1 Ensemble average total aerosol volume 4spectra from JASIN. The number to theright of the spectrum is the wind speedcategory in meter/second.

2 Time series of atmospheric 222Rn activity 7(solid line, Larsen, Kasemir and Bressan,1979) ai.: continental aerosol coefficient(dashed line), A'.

3 Time series of the Lerms of Equation 9 8for 2 pm radius and 15 pm radiusparticles. The dashed line is theaverage contribution of the surface pro-duction term and should be the sum ofthe other three terms.

4 The ensemble average surface flux spectrum, 9F (r), for the CEWCOM-78 analysis period(verage wind speed, 8 m/sec).

5 Ensemble average contribution of entrain- 11ment (W^), Stokes fallout (W ) and surfaceflux W F1 F/V s assuming a slate of dynamicequii ri u m.

6 Ensemble average equilibrium sea salt volume 12spectra from JASIN. The number to the rightof the spectrum is the wind speed category inmeters/second.

7 Ensemble average surface flux spectra de- 14duced from Equation 11 and Table II. Thenumber to the right of the spectrum is thewind speed in meters/second,

8 Changes in aerosol spectral density (dV /dt) 18versus changes in mixing volume (-dh/dti.This graph illustrates thr dominance ofthese terms in Equation 9 for short timeperiods.

vii

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II LIST OF TABLES

Table Page

I CEWCOM-78 meteorological and aerosol data 6for the time period analyzed for thisreport. The aerosol volume spectra densityV(R) is given in each radius, R, in pm.

II Equilibrium sea-salt aerosol-spectra in 13pm2/cm 3 as a function of radius (pm) andwind speed (m/sec).

III Surface sea-salt aerosol flux, F (r), 15(m:m 2/cm/sec) as a function of p~rticleradius (pm) and wind speed (m/sec).

IV The equilibrium time constant for aerosols 16at S 0.8, h 400 m and We = 0.4 cm/sec.

IIII

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ix

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i ABSTRACT

iThe rate of production of sea water droplets by bubble bursting at

the ocean surface is virtually impossible to measure directly. Laboratory

simulations are also difficult. However, the surface flux can be inferred

from measurements of the rate of change of aerosol densities and changes in

the height of the marine boundary mixed layer. Data from CEWCOM-78 has

been analyzed to produce the aerosol surface flux volume spectrum from 0.5

to 15 pro radius at a wind speed of 8 m/sec. Using this flux spectrum and

equilibrium aerosol spectra from JASIN, similar flux spectra are calculated

for sind speeds from 5 to 15 m/sec.

II

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ITHE BDM CORPORATION

IA. INTRODUCTION

There are two compone nts to aerosols in the marine boundary layer:

1) continental (background) and 2) locally generated sea-spray droplets.

The sea-spray droplets are generated primarily by the bursting of bubbles

Iat the sea surface. The bubble are produced by biological activity,

chemical reaction and breaking waves (white caps). At wind speeds greater

than about 3 meters per second, white caps are the primary contributor

to the bursting bubbles. Thus, the sea surface is a continuous source of

sea-salt aerosols in the marine boundary layer. These surface produced

aerosols can be characterized by a surface flux spectrum, Fs(r), which

represents the volume of aerosol produced per square centimeter of ocean

I surface each second as a function of aerosol particle radius. This quantity

is a function of wind speed.

The continuous production of sea-salt aerosols is balanced by several

removal mechanisms. One obvious mechanism is the loss of particles as they

fall back to the surface. This settling under gravity is called "Stokes

fallout" and is characterized by the Stokes velocity. The particles are

transported vertically by turbulence in the marine boundary layer and main-

tained at a uniform density throughout the mixed layer. The growth of the

height of the layer constitutes another loss mechanism called "entrainment."

IThe final loss mechanism is "rainout," which occurs when the particles

become condensation nuclei in the formation of clouds.

IGiven the surface flux spectrum and a parameterization of the removalmechanisms, one could predict evolutions of the aerosol density spectrum.

Unfortunately, the surface flux spectrum is not known. However, we can

reverse the process--that is, use parameterizations of the removal processes

and evolutions of the aerosol spectrum--to obtain estimates of the surface

I flux spectrum. This-report describes the calculation of F s(r) from data

taken by the NPS Environmental Physics Group during CEWCOM-78 and JASIN.

I

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B. AEROSOL SPECTRUM

The first step to analyzing the evolution of the aerosol spectrum is

to remove those variations due to changes in the ambient relative humidity.

This is done by transforming each spectrum to a reference relative humidity

(RH 80% or a saturation ratio S = 0.8). We make the usual assumption

that the particle radius a saturation S is given by:

r = r0 g(s) (1)

where r0 is the radius at S = 0.8 and g(s) = 0.81 exp [0.066S/(1.058 - S)].

If we have a measured aerosol number density spectrum, n(r), then the

transformed spectrum at standard saturation, n'(ro ), is:

dn' '( ) = n (r g(s)) g(s) (2)

0

Since we prefer to work with the volume spectrum V(r) r3 n(r), the

corresponding relationship is:

dV _V(r V(r g(s))/g(S) (3)dr 0o

We now must separate the measured spectrum into its two basic components:

1) the background continental aerosol of nonlocal origin, Vc, which

is present above and within the marine layer; and

2) the sea-salt aerosol locally generated at the sea surface, V5.

which is well-mixed throughout the marine layer (Z < h).

Thus, we assume:

V(r) Vc (r) + V s(r) Z < h (4a)

V(r) = Vc (r) Z > h (4b)

2

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The continental aerosol component is represented with a Junge typedistribution,

f V (r) = A/r (5)

where A is the continental coefficient. Since there is very little sea-

salt volume production for r < 0.3 pm, we can use the small size rarvge of

the spectrum to calculate the continental coefficient (A' = ro V'(r )).

This is docuwented in Figure 1 where ensemble averages of volume spectra

indicated that V'(r ) is essentially independent of wind speed at r = 0.1 pim.0 0

At low level wind speeds, the r = 0.1 inl and r = 0.3 pim ensemble average

spectra are described quite accurately by Equation 5. The claim that A'

is an accurate index of continental influence is nicely validated by com-

parison with atmospheric Radon activity from CEWCOM-78 (Figure 2). Thus,

locally generatod sea-salt component can be calculated using:

V'(ro) = V'(ro) - A'/r 0 (6)

Time remainder oi this report will deal exclusively with the volume

spectra transformed to standard humidity, V'(ro). However, to simplify

t!,e notation we will drop the prime and sub-zero with the understanding the

VS now refers to the spectrum at RH = 801, with radius, r, an implied

variable.

The evolution of the aerosol spectrum is described by the following

equation:

h dV-S F - (We + Ws) Vs (7)

3

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102;RH=85%

JASIN20 min u ave

20

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10 0- x7

h3

1 01 0, , ,.,,111 I I ,1 10.1 1 10

Radius (pm)Fi.,ire 1 Ensemble averacle total aerosolol lul;ie spectra from JASIN.

The number to the rigjht of the spectrum is the wind speedcatejory in weter/second.

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where h is the height of the boundary layer, W the entrairment velocityeand 1W is the Stokes velocity:S

W 1.57 x 10- ( + 12 0.81 3 2 2 (8)

s (I+10. (-)-T) )r g (s)()

where r is in pm and Ws is cm/sec. In this equation we have left out the

cloud formation removal mechanism because it acts on a much longer time

scale.

C. FLUX SPECTRUM ANALYSIS

The CEWCOM-73 data have been used to evaluate the surface flux term

of Equation 7. Since the other terms of the expression were measured, one

simply calculates Fs using a rearrangement of the terms.

A period was chosen from CEWCOP.1-78 where all data were available,

the synoptic conditions were fairly stable, the wind speed was reasonably

constant and a good mixed layer was present (Table 1). There was a slowly

decreasing continental influence indicative of steady NW winds (A' in Table

I and Figure 2). Subsidence was assumed to be negligible so that We = dh/dt.

Thus, the final expression used is:

Fs = h + (h -W ) V (9)dt (d--W v

The scatter and uncertainty of the aerosol and mixed layer depth mea-

surements introduces certain trade-offs between averaging times and statisti-

cal validity. For short averaging times, the random scatter of the

individual terms is considerable leading to large variations in the time

derivative terms. By increasing the averaging time to four hours, the FIs "signal-to-noise" becomes more reasonable. A time series of the individual

termms of Equation 9 is shown in Figure 3 for two different particle sizes.

The average surface production flux spectrum is shown in Figure 4. This

flux spectrum applies to [he average surface conditions for the entire 20

hour period (average wind speed was about 3 m/sec).

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IFi gure 4. The ensemble average surface flux spectru. F (r) for the C,,- .

analysis period (average wind speed, 8 m/sec).

II9I

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The relative Contributions of entrainment, graviational fallout and

sur~tic pruduction .iW nilly illustrated by defining an equivalent surface

prJu1ULtiun vertical eloity, W F s/V so that in equilibium (dVs/dt = 0)r 5 5

I,4 F ' ,. U + t (10)

For, the avergje conditions found in the analysis period, the entrain-

r.ent and Stokes terms were roughly equal at a particle radius of 5 ,m

(Fi ,re 5).

U. FLUX: A',r .... l". ....~ FEF-L ,' , ,Z: ,! .. ... ',4 1 i D ', PF ED

:-J .... I the roudsonably constant wind speeds during the 20 hour

,G,".,-7., pr i , ,-twre aule to improve the statistical certainty for the

Fs Icu1iti,: L cbining all the data from the period, assuming that the

t1,l ,qoul; be a r|ea-,onable representation for U = 8 m/sec wind speed. Thus,

.H.OW fldw ?Idv tha ,_ surface flux spectrum at a single wind speed. In order to

ucl il it. Lhu fl-ax it other wind speeds, we note that the right hand side of

L;i,ition 10 is ,uirly independent of wind speed for equilibrium conditions.

Sr~ref ore, the flux at one wind speed can be r' it,.d to the flux at other

,.-iri speeds it ttoe equilibrium volume spectra are known.

Vs ( U)

F ( ' ) : F ( ) V 1s {U 2) (21)

We have available from JASI'N a large set of ensemble averages of

aerosol volume spectra at different wind speeds (Figure 6 and Table I).

It is a simple matter to apply this data to Equation 11, using the

CEW'CUM-74 aerosol flux and equil ibrium spectrum to generate the surface

volur,e flux spectra as a function of wind speed (Figure 7 and Table III).

10

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101C EWCOM -78

X-- WF

EU

~i 0

UX

01

Radius (pm)

Figure 5. Enseii;ble average contrib~tion of entrainment (W ),Stokes fallout(WS) and surface flux W F F s /V s assuming a stste of dynamiccq i Ii br ium.

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102RH=87% JASIN

12 hr uave

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x 9

101 1 10

Radius (pm)Figure G. Ensemble average equilibrium sea salt volume spectra from JASIN.

The number to the right of the spectrum is the wind speed categoryin meters/second.

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TABLE 11. Equilibrium sea-salt aerosol-spectrain Pm2/cm3 as a function of radius (Gm)and wind speed (misec).

r- 0.8 2 5 10 15

5 2.8 3.4 3 0.3 0.05

7 10 10 5 1 0.35

9 18 25 13 6.4 4.2

11 20 30 20 15 15

13 24 33 22 22 22

16, 28 35 28 28 28

8* 9 11 2 0.2 0.4

*CEWCOM-78 Analysis Period

11

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TABLE III. Surface sea-salt aerosol flux,F (r), (pm2/cm n/sec) as a function ofparticle radius (pm) and wind speedI (m/sec)

0.8 2 5 10 15

5 1.3 1.1 2.5 1.0 0.33

7 4.5 3.1 4.2 3.3 2.3

9 8.2 7.7 11 21 27

11 9.1 9.2 17 49 48

13 11 10 19 72 140

16 17 11 24 92 180

3* 4.1 3.4 1.7 2.3 2.6

* CEWCOM-78 Analysis Period

1II

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E. NON-EQUILIBRIUM

For time periods of a few hours, the aerosol spectrum may not be in astate of dynamic equilibrium. If we rewrite Equation 7 in the following

form:

dVs + I - (12)dt T h

where the time constant, Tp, is

Tp = h/(We + Ws) (13)

then we see the analogy of aerosols and a capacitor charged by an applied"voltage," Fs, through a "resistance," h. In this analogy, the "capacitance,"

is (We + Ws) - .The response time of the aerosol density is a strong function of

particle radius because Ws - r2 . Values of Tp for S = 0.8 and h = 400 m

are given in Table IV.

TABLE IV. The equilibrium time constant for aerosolsat S = 0.8, h = 400 in and We = 0.4 cm/sec.

0.5 1 5 10 15

Tp, hours 23 22 11 3.5 0.5

The boundary layer mixing time, TIi, which represents the time required

for changes in aerosol density to be evenly distributed throughout the

marine layer is:

T= h/W (14)

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I THE BDM CORPORATION

For the analysis period (h = 400 m and W * 0.6 m/sec) we find Tm = 0.16

hours. Therefore, short term variations in mixing volume (dh/dt) will

is much slower than the mixing time. Thus, for time periods on the order

of one hour, changes in the aerosol density (h dVs/dt) will be highly cor-

related with the mixing volume term (Vs dh/dt).

This effect, which is particularly noticeable for smaller particles

(see Figure 3 and Table III) is shown in Figure 8.

17

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1.5- CEWCOM-78o r =.8 pm

1.0 x r=214m 0

00 5 x- 0.5

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-10-0.5-0

-1 .0 -x x

-1.5I II I

-1.5 -1.0 -0.5 0 0.5 1.0 1.5

-dh/dt (cm/sec)

Figure 3. Changes in aerosol spectral density (dV /dt) vers us changes inmixing volume (-dh/dts). This graph ilustrates the dominanceof these terms in Equation 9 for short time periods.

18

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DODAAD Code No. of Copies

1. Defense Documentation Center S47031 12Cameron Station, Building 5Alexandria, Virginia 22314

2. Library, Code 0212 2Naval Postgraduate SchoolMonterey, California 93940

3. Dean of Research, Code 012 N62271Naval Postgraduate SchoolMonterey, California 93940

4. C. W. Fairall, The BDM Corporation 5Naval Postgraduate SchoolMonterey, California 93940

5. Assoc. Professor K. L. DavidsonCode 63DsNaval Postgraduate SchoolMonterey, California 93940

6. Professor G. SchacherCode 61sqNaval Postgraduate SchoolMonterey, California 93940

7. Director, Naval Research Laboratory N00173 6Attn: Code 2627Washington, D.C. 20375

8. Office of Naval Research N62879Branch Office1030 East Green StreetPasadena, California 91106

9. Mr. Robin Simpson, ONR RepresentativeStanford University, Room 165Durond Aeronautics BuildingStanford, California 94305

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