Some aspects of the transfer of atmospheric trace constituents past the air-sea interface

am4-698117811101-2055

Armospherl~ Envrronmenr Vol. 0

12. pp. 2055-2087. Pergamon Press Ltd. 1978. Printed in Great Bntain

solDO,Kl

REVIEW PAPER SOME ASPECTS OF THE TRANSFER OF ATMOSPHERIC CONSTITUENTS PAST THE AIR-SEA INTERFACE*

TRACE

W. G. N. SUNN’, L. HASSE’, B. B. HICKS~, A. W. HOGAN’, D. LAL’, P. S. LI&, K. 0. MUNNICH’, G. A. SEHMEL~and 0. VITTORI~ LDepartment of Atmospheric Sciences, Oregon State University. Corvallis, OR 97331, U.S.A.; 2 Meteorologisches Institut der Universitat Hamburg, D 2000 Hamburg 13, Bundesstrasse 55, W. Germany; 3 Atmospheric Physics Section, Radiological and Environmental Research Division, Argonne National Laboratory, Argonne, IL 60439, U.S.A.; *State University of New York at Albany, Atmospheric Sciences Research Center, 130 Saratoga Road, Scotia, NY 12302, U.S.A.; 5Physical Research Laboratory, Navrangpura, Ahmedabad 380 009, Xndia ; ’ University of East Angha, School of Environmental Sciences, University Plain, Norwich NR4 7TJ, U.K.; ’ Institut fiir Umweltphysik der Universitiit Heidelberg, D-69 Heidelberg, Im Neuenheimer Feld 366, W. Germany ; * Atmospheric Sciences Department, Battelle, Pacific Northwest Laboratories, Richland, WA 99352, U.S.A.; a Instituto di Fisica Dell’ Atmosfera. Sezione Microfisica, C.N.R., Via de’ Castagnoli. I, 40126 Bologna, Italy. (Firs received 19 July 1977 and in~nul~rm

9 Mar 1978)

Abstract - This review addresses known and unknown aspects of wet and dry fluxes of atmospheric trace constituents past the air-sea interface. First, various methods for parameterizing these fluxes are developed from coupled continuity equations; also, the need for parameterizing various meteorological phenomena is illustrated. Next, different theoretical analyses of precipitation scavenging are outlined and data for collection efficienciesand washout ratios summarized. A resistance model for dry deposition ilhtstrates that the rat~limiting stage of dry removal can occur in different layers depending on atmospheric and oceanic conditions and on properties of the pollutants; recent results for the dry fluxes of both particles and gases are summarized. After this review of known aspects of wet and dry removal processes, an interluding section uses the reviewed material to illustrate, with a number of worked examples, present capabilities to predict air pollution fluxes past the air-sea interface. Atmospheric residence times are also estimated. The second halfof the paper emphasizes future research required to improve predictions ofatmospheric removal processes and residence times.

INTRODUCTION

Treating the oceans as the ultimate receptacle for much of man’s pollution has caused concern that some ocean resources may be jeopardized, e.g. see Assessing Potentiul Ocean Fo~futunts (U.S.A. NAS, 1975). Some of the ocean resources used by man are for fishing, shipping, recreation, oxygen production, climate regulation and, of course, for receiving much of man’s pollution. One of the pathways for pollutants to reach the ocean is via the atmosphere and it is the purpose of this paper to review some of the knowns and indicate some of the unknowns about a portion of this pathway. A review of the total pathway would necessarily include many features. Some of these features are: the characteristics of the pollutants, including their concentrations, chemical and physical properties, and possible modifications of these properties in the at* A portion of this review appears as chapter 4 entitled “Wet and Dry Removal Processes” in the U.S. National Academy of Sciences publication The Tropospheric Transport o~Poifut~ts

and Other S~sta~es

Prosper0 J. M. (cd.), 1978.

to the Oceans,

mosphere; the atmospheric processes that influence the pollutants’ concentrations, including diffusion, transport, and deposition; and the pollutants’ possible fate in the oceans, e.g. resuspension from the surface, transport to deeper layers, and concentrations in food chains. From these and other features of the total problem the scope is here restricted to focus on atmospheric removal processes, especially wet and dry removal. Of course other removal mechanisms are important for some atmospheric trace constituents (e.g. chemical transformations of gases) but, as will be seen, it is already a challenging task to review just precipitation scavenging and dry deposition. Succinctly, the problem addressed is : given the pollutants’ properties and air concentrations, find their fluxes to the ocean. Perhaps an acceptable method to outline the paper is to display here the paper’s section and subsection titles : CONTINUITY EQUATIONS AND PARAMEI’ERIZATIONS

Microscale parameterization Atmospheric residence times Global scale ~rameteri2ations Summary and comments

and reservoirs

W. G. N. SLINN et al.

20% PRECIPlTATtON SCAVENGING

Wet removal time scale Wet removal of particles Particle washout ratios Gas scavenging Summa~ and comments DRY DEPOSITION

Transfer velocities Dry deposition of perfectly absorbed gases Dry deposition of particles Dry deposition of gases Summary and commits ILLUSTRATIVE CALCULATIONS

Wet versus dry removal Some interesting special cases Summary and comments SOME CURRENT AND SUCGfBTED

RESEARCH

Radionuclide m~surements Precipitation scavenging studies Micrometeorologic factors influencing dry deposition The air-sea interface and surface-layer mixing Gas exchange across the air-sea interface Particle dry deposition to the oceans CONCLUDING REMARKS

A list of symbols used in this review is included as Appendix A; Appendices B and C contain some supporting calculations. CONTii’iUITY EQUATIONS AND PARAMETERIZATIONS

The purpose of this first section is to outline some general features of the task before us. The task is to describe parameterizations for wet and dry removal processes that can be applied at time and space scales ofinterest. Unfortunately, though, and common to any outline, it is advantageous to assume some prior knowledge of the subject matter ; for example, we have found it convenient to borrow some results from later in the review. Consequently, if the reader finds this section to ~~omplicat~ we either ask for his patience to accept some items without adequate intr~u~tiou or, failing this, invite him to skip the first section for now and return it after perusing the sections on wet and dry removal. A framework for the entire presentation is provided by coupled ~ontin~ty equations which describe the instantaneous concentrations of the trace constituent in air, x, and in the ocean, C. In generally standard notation (and see Appendix A) these convective diffusion equations are dX t+v*Vw=

- V*(-D#Vx

$+vVC=

(1)

- w3.

- V.(-D,VC

As a first step, (1)and (2) are averaged over what can be qualitatively described as microscale processes. These include not only the molecular induced motions of the trace constituent but also the motions induced by high frequency (Z 1 cycle per minute) turbulence. Let averages over these microscale processes be identified by tildes; e.g., i. Then (1) and (2) become

where the microscale average flux caused by turbulent (as well as molecular) fluctuations is -Q’,=

+ xd,) + $(x)

- L*(X)

In (1) and (2) the subscripts g and I refer to conditions in the gas phase (i.e. in the atmosphere) and in the liquid phase (ocean), respectively; the v’s are instantaneous (molecular averaged) velocities of the two fluids (assumed incompressible); D’s are molecular or Brownian diff~iviti~; d’s describe any drift velocities relative to the fluid velocities that the trace constituent might possess (e.g. caused by gravity or diffusiophoresis); and G and 15are gain and loss rates per unit volume caused by such processes as radioactive production and decay, chemical conversion, particle coagulation and pr~ipitation scavenging. To complete the specification of the problem then in addition to the governing equation (1) and (2) coupling boundary conditions at the air-sea interface must be specified. One inviolable condition is equality of normal components of the fluxes in the two media. The required second interfacial boundary condition depends on characteristics of the trace constituent; examples will be given in a subsequent paragraph. The continuity equations and coupling boundary conditions describe the entire problem of interest here but this formalism exceeds present analysis capabilities. The essence of this report is to discuss, and indeed, the essence of this field of study is to develop approximations or parameterizations for terms in the equations and boundary conditions in a form suitable for applications at space and time scales of interest. In turn, a major difficulty in this endeavor arises from the plethora of space and time scales contained in the equations; for example, Fig. f qualitatively illustrates some of the vertical space scales and associated time scales contained in the equations. In this introductory section the essentials of this parameterization will be illustrated by averaging (1) and (2) over progressively larger scales.

+ Cd,) + G,(C) (2)

4;

-ds’+OVx’

(5)

in which the prime (‘) symbolizes the portion of the variable which fluctuates on the microscale but whose microscale average is zero; the correlation between drift and concentration fluctuations, drx’, is retained for possible application to the case of sufficiently

Aspects of VER;lCAl$;;;; SC LE(

Z(

TROPOPAUSE UPPERTROPOSPHERE

ld

--

TURBULENTDIFFUSION

10' - 18

104

--

lROPOPAUSEFOi.DING

10'

lkm

ld

EKMANOR LAYER

lo1 10'

lURBULENT

DIFFUSION AND PRECIPITATION EVENTS

i

WAVEMIXING

lm

TRANSPORTACROSSAIR'SVISCOUS PARTICLE RADIUS

10 1

1 mm

SUBLAYER

a1

aoi

SEA

SPRAY SEA-

lo-)

SALT NUCLEI

1o-6

<

z

p:

SUBlAYER:

Iurn)

im

lcm viscous

am1 GASES

3

1w

L

SURFACE FlUAS

GAS REACTIONSOf

INTEREST INVlSCOUS

SUBLAYER

4

10*

10-l

- ld

lcrm TRANSPORTACROSSTHESEA'SVISCOUSSUBLAYER: PARTICLE RADIUS Igm) lm

lO-5 10

-4

viscous SUBtAYER

10-l

10

1

CAPILLARY WAVES

lit am1 GASES

GRAVITY WAVES It

16- IO6 ld - IO9 14 _ ld

CHEMICALTRANSFORMATIONS MIXING IN BOUNDARY LAYER ATTACHMENT OFREACTIVE GASES AND RADIONUCLIDESTO PARTICLES

102

CONSTANTFLUX LAYER GRAVITY WAVES t

1

TIME SCALL (SECONDSI

"REMOVAl"PROCE5.S

STRATOSPHERE

BOUNDARY

2057

the transfer of atmospheric trace constituents

EKMANOR BOUNDARYLAYER THERMOCLINE

:$ 16 1 : $ -12

WAVEANDTUREULENTMlXlNGABOVf THERMOCLINE

lD1 - lD6

SETlLINGANND DIFFUSIONOFMICRON-SIZE PARTICLES ANDGASESTOOCEANFLOOR

lD1’ - 10"

102 ld

lkm

DEEP OCEAN 104

OCEANFLOOR

Fig. 1. An indication

of the range of vertical space scales which are contained in Equations estimates for the corresponding time scales for pollutant transfer.

massive aerosol particles which do not exactly follow the fluid’s turbulent fluctuations; and, again, D is the molecular or Brownian diffusivity of the species. In analogy with this molecular diffusion term a common parameterization of the turbulent flux is -v;x’ = IK.Vi

(6)

where IK is known as the (second-order tensor) turbulent or eddy diffusivity. Much has been written about the range of validity of this parameterization (e.g. see Corrsin, 1974); its use near the air-sea interface will be discussed in a later section. Associated with these microscale-averaged continuity equations are parameterized boundary conditions. The condition for equality of normal components of fluxes at the interface (2 = :i) becomes

[kg + ;jnailJr=zi = [C, + &,~]Ir=ri’

(7)

A major thrust ofthis review will be to discuss methods used to parameterize the required second boundary

(1) and (2)and the

condition; for now, we display in Table 1 some of the many parameterizations available, each of which will be discussed later. In general, the major unsolved problems in this area of research are to interpret these parameterizations in terms of underlying microscale physical and chemical processes that dictate transfer across the interface. Atmospheric residence times

To describe the flux of atmospheric trace constituents past the air-sea interface it is usually an essential first step, as illustrated in the previous subsection, to average over and to parameterize the microscale processes. However, this is only the first step and the importance and the required accuracy of the parameterizations can be seen only by illustrating how they can be applied and what other approximations are introduced in the course of their application. In turn, this depends on the time and space scales of interest. For example, the microscale para-

t Liss and Slater (1974) fCalder (l%l) 5 Chamberlain ( 1960)

Subscripts i - interface. bulk concentration, b * Slinn (197153)

measured

at a convenient

(z=z,)

reference

height, h.

_~______

ways IO specify the second interfacial

(i.e. [P* + &a

I. Optional

(i) -[Ez + a,&, = Glil (ii) - [cz + dJ&.* = u?li, (iii) - [Fz + d,& = q,g - ~,s,

2. For particles

B. Spec$r rhe c~mm~njlux

2. For particles (i) i, = Je, (ii) & = 0

gases i, = Xc, i, = 0

concenrrations

A. Relate 1. For (i) (ii)

Table

~__~ .~

~~-~~

condition

‘1,

~5

8

k, k;

k,

’

flux is taken

= Calder’s deposition velocityt = Chamberlain’s deposition velocityg = resuspension velocity* .___

factor)

__~____

to be in the positive z direction

= gas-phase transfer velccityt = liquid-phase transfer velocity = k; ’ + .Zk; ‘, total transfer velocity

Positive

J = concentralion jump* (related to the resuspension Perfect sink (see comment for similar case for gases)

the equations)

Remarks

~. ~

(3) and (4) for dry flux past the interface

decouples

for Equations

JP = Henry’s law constant Perfect sink (this condition

boundary

.~___

Aspects of the

2059

transfer of atmospheric trace constituents

only dry deposition depleted the tracer; between ti and tl, wet deposition occurred; etc. Given these “data” for q in Fig. 2a then the first equality in (8) can be used to evaluate the (time dependent) residence time 7 shown in Fig, 2b. A histogram which shows the distribution of the different residence times of Fig. 2b is shown in Fig. 2c. In turn, it can be imagined that if this type of experiment were repeated a large number of times, then a density function for the residence time could be obtained, as shown in Fig. 2d. Finally, an (ensemble) average residence time for this type of tracer release could be defined as oc ?= 7ft7Id7 (9) j 0

Fig. 2. A schematic development (see text) of the probability density functionf(s) for the residence time, r.

meterizations could be used directly in detailed atmospheric models if it is desired to determine the outcome of a specific tracer release or for design and execution of field experiments to determine and/or test wet and dry removal parameterizations. In contrast, for the predictions of long-term average pollutant fluxes to the ocean, it is expected that coarse models of largescale meteorological processes will continue to be profitably applied and it is therefore useful to see how the microscale parameterizations are used in such schemes. One of the coarse models for large-scale meteorological processes utilizes the concept of atmospheric residence time. To introduce this concept qualitatively, consider the fate of a stable tracer released to the atmosphere and integrate (3) over the volume V occupied by the tracer at time t. If the total amount of tracer still present in the atmosphere is q, then (3)can be used to definean atmospheric residence time, 7, according to 7-1=

2 4 dr +

= ;l

y[V@

+ ;ii) + L)dl’

(8)

s where the gain term has been ignored, V is large enough so that there is no flux ofthe tracer through the volume’s surface carried by the mean wind, and the subscript g (for gas phase) on the flux and loss terms has been dropped for convenience. That the first equality in (8) defines a residence time can be seen qualitatively by considering the scenario illustrated in Fig. 2. In Fig. 2a : between t, and t, it is assumed that

which, however, masks the information that wet and dry removal processes (and possibly other removal processes for other than stable tracers) separately contribute to the residence time. What is desired now is to demonstrate the relationship between the atmospheric residence time and parameterizations for wet and dry removal processes in order that other needed ~~rnete~~tions can be displayed. Toward this goal, we first average (8) over many tracer releases or over a suitably long time during the continuous release of a single tracer. Thus we ignore any distinction between ensemble and time averaging although this point deserves further thought and discussion. The long-term average of large-scale meteorological prooesses will be denoted by an overbar, e.g. f. Next, with use of the divergence theorem, the volume integral of the divergence of the dry flux is written as a surface integral of the flux. In the case of aerosol particle removal, the dry flux can be parameterized as in Table 1, e.g. as u& where J$ is the ~llutant’s average bulk air conc~tration at a convenient reference height (e.g. 1 or 10 m) and u, is a dry deposition velocity. Also for aerosol particles, the loss rate per unit volume by precipitation scavenging can be written as r = li;i where $ is an average precipitation scavenging rate coefficient. With these parameterizations the average of (8) yields f-l=f;l

+f;'

(10)

where i; ’ XC$ and f;l= v,/& in which b,, is a parameterization of the pollutant’s long-term average vertical distribution

For example, if h;l = 3 km and v,, = 0.3 cm s-i, then id = 10d; for a monthly average rainfall rate of IO cm mo- ’ and reasonable values for other terms in t,J then it will be seen that for particles, S, is also of the order of 1Od. Although this presentation is sketchy, it is hoped that the major point can be seen. It is that, toward the goal of predicting air pollution fluxes to the oceans, obtaining microscale parameterizations of the removal processes is only the first step. Details of

W. G. N. SLINN er 01.

2060

Table 2. Average residence time of water vapor in the atmosphere as a function of latitude* Latitude range (degrees) O-10

10-20

20-30

2.7

30-40

40-50

50-60

60- 70

1.3

1.o

70-80

80-90

Average precipitable water (g cm-‘)

4.1

3.5

Average precipitation &cm-* year-‘)

186

114

82

89

91

77

42

19

11

11.2

12.0

8.7

6.4

6.2

8.7

(13.4)

(15.0)

8.1

Residence time (days)

2.1

1.6

0.7t

0.45t

l Reprinted with permission from C. E. Junge (1963) Air Chemisrryand Radiooctirit~, p. 10. Academic Press, New York. t Values extrapolated.

additional steps depend on the space and time scales of interest. For example, in the above discussion of atmospheric residence times it is seen that just as important as obtaining accurate parameterizations of the dry deposition velocity is to have accurate knowledge about average meteorological conditions such as those parameterized by i;,. Similarly, it is necessary to know some average properties about precipitation. However, although these needs are significant and will be discussed in somewhat greater detail in later sections, still there is a tendency in this review to emphasize the microscale parameterizations, leaving the macroscale topics for emphasis possibly in another review at a later time (see also U.S.A. NAS, 1978).

Reservoir residence times can also be defined for unsteady conditions for the important special cases that the exchange and destruction processes are first order in Qi. Then (12) becomes

z=

1’ .fijQj j Qi + Pi - i.,Qi

where Yij and Iii are inflow and outflow (or leaving) exchange rates, li are de-cay rates, and the prime on the summation sign symbolizes no sum on i. If Pi is independent of Qi then the solution to (15) is that the steady-state concentration,

Global scale parameterirations and reserroirs

Pi + ~’ .fijQj

Still coarser parameterizations are valuable, e.g. to estimate the global fate of pollutants released from sources in the 30-60”N latitude zone. Suitable parameterizations of the removal processes can be obtained by averaging (3) over reservoirs of desired size. Toward this end, let Qi be the total amount of the trace constituent of interest in reservoir i and Fi be the net outflow through the reservoir’s surface. Further, if this net outflow is divided into an outflow, Oi, and an inflow, Ii. then clearly an average of (3) over reservoir i leads to

dQi= 1. _ dt

0, + p, _ D

’

’

’

’

where Pi and Di are the total production and destruction, respectively, of Qi in reservoir i. At steadystate conditions (12) yields the transparent result Ii + Pi = Di + Oi and at these conditions a similarly transparent servoir residence time can be defined as

Qi

Tr=p,=m.

Qi

(1%

(13) re-

(14)

Table2illustrates(14)for thecaseofprecipitablewater although it should be emphasized that these results may be inaccurate since steady-state conditions rarely prevail and since both mixing between latitude belts and “dry deposition” of water vapor has been ignored

(Qihr =

;,+‘x, ,,, * I#

I’ j

is approached with a characteristic

time constant

(17) It is noted that for steady-state conditions, then the two times (14) and (17) are equivalent. A simple example using this formalism will illustrate where further research could improve this macroscale parameterization. Thus, consider the box model of the troposphere shown in Fig. 3. The values for the reciprocals of the exchange rates shown in Fig. 3 were chosen only for illustrative purposes although they were guided by the model of Lal and Rama (1966). That the exchange rates for transfer in opposite directions between some adjacent reservoirs differ by an order of magnitude reflects the approximate, orderof-magnitude differences in air masses of the reservoirs. (Note that net transfer between reservoirs terminates when the mixing ratios, not the Q’s, are equal.) If these exchange rates are used in (16) and (17) then the results of the calculation (see Appendix B) for the case that Ai = 0 and the only source, Pi, is in the 30-60”N reservoir, are as shown in Table 3 and Fig 4. The fallouts from the reservoirs were calculated from (Fallout), = /,Qi

(18)

2061

Aspects of the transfer of atmospheric trace constituents SOUTHEAST

NORTHEAST TRADES

TRADES I

180d ,?‘

8 /

1SOd WESTERLIES

WESTERLIES

1

/ 25d> SOUTH EASTERLIES 1 9cfJs

150d

+--

Ud"/1

68

1

2506

:

/

I

30”

00

76

126

%25d

/ 250d /

WORTH EASTERLIES

150d -15d

1

1Od

IOd

300

1 600

7d

1

90%

126

Fig. 3. A schematic of the reservoirs chosen to illustrate Equations (16) and (17).The volumes of the reservoirs in each hemisphere are assumed to differ by an order of magnitude and this explains why the reciprocals of some exchange rates also differ by an order of.magnitude.

in which, for Table 3, Ii, is the removal rate from the ith reservoir found by averaging over appropriate latitude zones ofTable 2. In Fig. 4 two cases are shown : for one, the Iis of Table 2 were used ; for the other, the removal rates were assumed to be a factor of 10 slower than for water vapor. This example illustrates the importance not only of accurate parameterizations of the removal processes but also of accurate parameterization of the exchange rat= between reservoirs. Some appropriate research topics will be suggested for consideration in a later section. Summury

and

comments

In summary, hopefully these introductory remarks have demonstrated the unifying features of the continuity equations (I) and (2), the types of parameterizations needed, and the interrelations among progressively coarser descriptions of the behavior of atmospheric trace constituents. It is re-emphasized that the needed ~rameterizations are not only for the removal mechanisms themselves but, depending on the space and time scales of interest: for (1) the correlations between velocity and concentration fluctuations, vq; for (2) the turbulent (or eddy) diffusivity, IK ; for (3) the effective height i;d and average removal rate 5; or for (4) inter-reservoir exchange rates. In this paper the emphasis will be on parameterizing microstale aspects of the wet and dry removal processes. Incidentally, we cannot side with the critics who view reservoir models as outmoded and oversimplified; we are certain that these models and the

concept of reservoir residence times will continue to play an essential role in developing useful predictions of material fluxes to the oceans. It is noted from (lo), (14) and (17) that residence times are essentially the inverses of the removal rates and partitioning the atmosphere (and other geospheres) into various reservoirs essentially amounts to obtaining the first few terms in a spatial Fourier analysis of the removal rates. It is true that in the limit of infinitely many reservoirs this partitioning will return the analysis to the continuum formulation from which it originated but it is also apparent that rarely would this much detail be desired ; an exception, perhaps, is to describe the fate of a specific pollutant or tracer release. In contrast, residence time concepts can provide simple, convenient, and as accurate as desired estimates for timeaveraged fluxes to the ocean. With this said, however, we now turn to our primary task of discussing microscale parameterizations for wet and dry removal processes. The im~rtance of this task is illustrated in Fig. 4 where it is seen that if the removal rates for a pollutant injected into the 30-6O”N reservoir are reduced by an order of magnitude then the pollutant’s concentration in, for example, the south polar zone is increased by about three orders of magnitude. In the next section the emphasis is on precipitation scavenging; following that will be a description of ~rameteri~tions for dry deposition ; then some illustrative calculations will be presented ; finally there is a survey section on current and suggested future research.

Table 3. Model results for fallout rates as given in Table 2 and exchange rates as shown in Fig. 3 Reservoir

90-60”s

60-30 S

30-0’S

O-30”N

30-6O”N

60-90”N

Z, (days)

12

7

10

10

I

12

ri (days)

6.7

5.2

9.1

9.1

5.2

6.7

P, (units/day) Qi (units)

0 9.4 X 10-s

0 2.1 X 10-J

0

0

1

0

I.0 X 10-l

2.0 x lo0

5.4 x loo

2.4 x 10-l

[Fallout], (units/day)

7.9 X 10-b

3.0 X 10-b

I.0 X 10-Z

2.0 X 10-l

7.7 x 10-I

2.0 x lo-’

W. G. N. SLINNet al. snowflakes, etc.) whose gravitation terminal velocity, t‘,, exceeds local updraft speeds by about 10 cm s- ‘. Thus, the incorporation of air pollutants into cloud droplets (v, = 1 cm s- ‘) will not be described as precipitation scavenging since this stage does not insure the pollutant’s removal from the atmosphere. Indeed,

r---l

--

I

I

j

‘-1

I I

0 1I 1

even thecapture and subsequent transport of materials by precipitation may not lead to their removal if the hydrometeors evaporate en route to the earths surface; in this case+ the process is just one of many ways that substances can be redistributed in the atmosphere. In this section some theoretical considerations will first be introduced and then used to interpret some especially useful data; in a later section, some precipitation scavenging research topics will be suggested.

SOURCE

................

17.5

MbNTROPICAL"" TROmPAUSE

15.0

EAN LAR PAUSE

*a.* *. : MAN *.. WLAR .*.* TROWPAUSE :

j

Wet removal time scale

zlkml 125

la0

Fig. 4. The solutions to the set of Equations (16) and (17), see Appendix B, for the steady-state concentration of polhttant in each reservoir for the case of a unit source in the reservoir 30-6O”N. The solid curve is for the removal and transfer rates shown in Fig. 3 ; the dashed curve is for the fallout rates l/10 the rates shown in Fig. 3; the dotted curve is an indication of the mean tropopause (for January-August 1959,see Junge (1963). p. 246). With the latitude and altitude scales shown, the same area under the tropopause curve represents the same mass fraction of the atmosphere and therefore this plot supports the approximation made in formulating the problem that the air masses in the three reservoirs dilfer by about an order of magnitude.

In the previous section, an average wet removal time scale or contribution to the residence time for particles was given in (10) as ?w = I$-‘, where 3 is an average precipitation scavenging rate coefficient. The main thrust of this section will be to present parameterizations for the removal rate, $, but before doing this it may be informative to see an alternative derivation of the wet removal time scale. This can be seen by envisioning the fate of a specific, stable tracer released to the atmosphere. If dry deposition is ignored, then the total amount of tracer remaining in the atmosphere at any time t might be as shown in Fig. 5, curve (a). Thus, after a number of days (say, V-i days on the average) the tracer is presumed to interact with a precipitating storm system and a fraction ei of the tracer (say, Eon the average) is removed by the storm, leaving the fraction (1 - si) still airborne. Continuing in this manner we see that after n storms, the fraction of the tracer still airborne is

PRECIPITATIONSCAVENGING

The term precipitation scavenging is used here to describe atmospheric trace constituent removal from the atmosphere by various types of precipitation. By precipitation is meant those hydrometeors (raindrops,

The corresponding deposition pattern is shown as the broken curve, 5(d). It can be envisioned that if this type of experiment were repeated a large enough number of times, then the average curves Sb and Sc would be. obtained.

bl 9h; b) q/qq.

Il-cil

ii i-

0

erp { -2,t) Z - a25 I*l25dl -1

0

5

10

15

20

Tlmt.tldayrl

Fig. 5. A schematic development (see text) of a continuum description for precipitation scavenging.

2063

Aspects of the transfer of atmospheric trace constituents

Analytically, the average concentration found from the approximation

4w = ,Fo ” (I- - E,) = 4o

Rt ” 1- 7 2: exp{-cvttj

( >

can be

(19)

or from assuming that precipitation scavenging is a Poisson process and using known properties of Poisson processes, or from integrating the analytical statement that during At the average amount removed is -Aq = (GAt)Eq. Similarly, the average amount of tracer deposited during At is EVqAtand therefore the rate of wet deposition is Etq = .Gqoexp { -Et}.

(20)

Equations (19) and (20) describe the average curves (b) and (c) of Fig. 5 and display a second formulation for the characteristic wet removal time scale i, = $-’

= @VT-‘.

(21)

Although this simple analysis is informative there are a number of impediments to using it for quantitative descriptions of precipitation scavenging. For example, it has been implicitly assumed that the fraction of the material removed by an individual storm, E, is independent of the amount of material present. For most material this would be true but cases where it might fail include the following: if there are too many particles present which act as cloud-droplet or ice-crystal nuclei then their presence could influence the precipitation rate; for some gases, cloud droplets can become saturated with the gas and then only a certain amount, not a specific fraction, of the gas will be removed. Of more significance, however, is the present lack of knowledge about Eand V.To separate the problem into its micro- and larger-scale portions, consider the case of aerosol particles which, for reasons described later, are typically more efficiently removed from within rather than from below clouds. Then let the average fraction of the aerosol particles removed by a storm be written as E = .&, where El is the average fraction of the particles incorporated into the cloud water and E,, is the average efficiency with which cloud water is removed by a storm. Then the meteorological problems are to obtain &,, and the average time, ?-I, between encounters with precipitation storms. These parameters are not known at all well, even over land. For example, clearly E,, can vary from zero (for a nonprecipitating storm) to perhaps 90%; for precipitating storms, probably E;, 2: l/3 is accurate to within a factor of three but there is little data to support this contention. Similarly, Vcan be estimated to be the total precipitation at a site (say, 100 cm y - *) divided by the average precipitation per storm (say, 1 cm per storm) or V = (3 d)- ’ but clearly this is a crude approximation. Even the annual average precipitation to the oceans is not known well. With these crude estimates follows the equally crude estimate of the contribution of wet removal to the average re-

sidence time for water vapor: i, 2 (E,,V)-’ z 10d. This discussion illustrates the need for additional meteorological research to obtain E,, and V; the discussion in the next subsection will illustrate required research for the determination, essentially, of& Wet removal of particles

Although the above analysis is informative, fortunately there is another way to quantitatively estimate f,, i.e. ?, = $- I. For aerosol particles of radii a, irreversibly captured by precipitation, then the loss rate per unit volume in (3) varies linearly with the air concentration of the particles : t(a) = $i(a), where 4 is the microscale-average removal rate. This removal rate can be obtained from a simple analysis of collisions between particles and hydrometeors (Chamberlain, 1960; Engelmann, 1968). The familiar result (which it should be noted, is valid both within and below clouds) is J(r,t;a)

O”dlN(r, t ; I)u,(l)AE(a, 1)

= I

(22)

0

where N(l)dl is the number of hydrometeors per unit volume whose length scale (e.g. drop radius) is between 1.to I+ dl; I+(2 10 cm s- I) is the hydrometeor’s gravitational terminal velocity and A is their cross-sectional area ; and &a, I) is the collection efficiency (or AE is the effective collection cross section). In turn, the collection efficiency can be written as a product of the collision efficiency and a retention efficiency, usually

KERKERANDtWMftI19UI. l

12110+ ,*Lrll+Rd

IMPACTION

INTERCEPTION

DIFFUSION

R-l.ll)mm'

DROPJUSTRMCHEDV,

(1+ Ret

/

Re=lCt.R-,.IBmm

d 10-1 RADIUS W

IO0

10'

UN,7 DENSIT" SPHERES, I I,,",,

Fig. 6. Semi-empirical expressions for the collision efficiency between drops and particles as a function of particle size and accounting for dilfusion, interception and inertial impaction. The difksion and impaction portions of the curves have sufficient experimental support to consider them reliable to within a factor of 2 or 3. See Slinn (19761~)for a possible explanation of the scatter in the data for particles of radii - 0.5 /.nn; see Slinn (1976b) for an illustration of the importance of accounting for aerosol particle growth by attachment to plume or cloud particles or by water vapor condensation. Reprinted with permission from J. Air. Woter nnd Soil Pollution.

W. G. N. SLWNet al.

2064

loo

DIFFUSION

/

NEEDLES

~

-

‘._,’ t

AND DENDRITES?

POWDER SHOW AND TISSUEPAPER?

E

SLEn GRAUPEL

20

Ia0

RIMEDCRYSTALS 1 lo*

POWDER SNOW

ld

l&l

10'

5D

loo

1

DENDRITES

1

10

10-l

aISSUEPAPER

-

50

109

-

ICC@

ICAMERAFILM I

I

DATA:

---IITRE MfAN CURVE 11974) NATURALSNOW.LABTESTS IJ STARRAND MASON llw61 TISSUEPAPER . A.

STAVITSKAYA 119723 . CIRCUAR DISK,CAMERA FILA ti. CUT STARS,CAMERA FILM

lo21

t11bl

I

,.,,I

a01

,,,I

I

81

I

, ,,

LO

10

PARTIQERADIUS,a @ml

Fig. 7. A tentative suggestion for the co&ion efficiencybetween particles and ice crystals. For discussions of theoretical analyses and experimental bases,see Slinn (1976~).Reprinted with permission from J. Air. Water and Soil Pollution.

taken to be unity. Figs 6 and 7 show semi~mpirical expressions for the colfision efficiencies between particles and raindrops (Fig. 6) or snowflakes (Fig. 7) which correlates most of the available data (Slinn, 1976b). Because of remaining uncertainties in the collection efficiencies and because of lack of c priori data on hydrometeor size dist~butions, Shnn (1976c) advanced the following approximations to (22):

p(r,t)

;a) = c- R

E(a,R,),

for rain

m _) _ $# Pht) 2 b(a,& PO %#I

(23)

rates it is easy to obtain expressions for the wet flux of aerosol particles to the earth’s surface. If the particle concentration does not vary significantly over short horizontal distances, then an integral over the average hydrometeor’s flight path can be replaced by a vertical integral. As a result, the wet flux is simply w=

ip JIidz I

with # as given in (23) or (24). For example for rain scavenging, then (23) in (25) yields w(r, t ;a) = clp,(r, t)/R,,]&(c,

for snow. (24)

These approximations were obtained, essentially, by multiplying and dividing the integrand in (22) by 1and recalling the definition of the precipitation rate. In these equations, c is a numerical factor - l/2; p(r, tf is the precipitation rate (rainwater equivalent); R, is the volume-mean drop radius, g is the acceleration of gravity; pv and p. are the mass densities of water and air, respectively; 0, is an average terminal velocity for the snowflakes and E and 8 are average collection efficiencies, evaluated using the mean drop size and characteristic length 1, see Fig. 7, respectively. From the exnressions (23) ., and (24) \, for the removal

(25)

0

R&,6

(26)

where the subscript zero refers to surface level conditions; fb (or &) is the particle air concentration at a convenient reference height ; and where the characteristic height k, from which the particles are removed has been defined via k, =

s

mP(Z)

o

PO

_

x(4

lib

&,R,,J

K~h,,Rrn,)

dz.

(27)

Similar expressions can be obtained for snow scavenging using (24). Sina, as can be seen in Figs 6 and 7, the coHeetion eiTiciency is strongly dependent on particle size and since particle growth is usually substantial within clouds either because the particle acts as a cloud-droplet or ice-crystal nucleus or because of

2065

Aspesztsof the transfer of atmospheric trace constituents particle attachment to existing cloud particles, then the range of integration in (27) can usually be restricted to the height of the active, rain-forming region within the cloud. For example, to fit data recently obtained by Gatz (1976a) and to be described below, Slinn (1976b) used c = l/2, R,, = 0.5 mm, E as given in Fig. 6 with a reasonable particle growth rate, and h, = 600 m. In the case that in-cloud scavenging is more important than below cloud scavenging then the wet flux of particles from a steady-state cloud can be derived using the simple method developed by Junge (1963). In this case, if the average fraction (Q) of the particles entering thecloud is incorporated into thecloud water, then the concentration of the captured particles is (E& units per volume or (q)/(L) units per mass of cloud water, where () represents an average value

over the height of the storm and (L) is the average condensed water content of the clouds. If this concentration (q)/(L) also appears in the precipitation from the storm (which would be true for gravitational coagulation of equally concentrated drops and for no evaporation or dilution en route to the earth’s surface) then the flux of material from the storm would be 1.

_

-

(&IX) -

CL)

APO

where pWpOis the mass flux of water from the storm. Particle washout ratios For comparisons with experimental data it is useful to define the washout ratio, r, which is the ratio of the

material’s concentration

Table 4. Some measured washout ratios, r =

in surface-level precipitation,

(K/J&

Scavenged material

r X 10-6

Notes

Fallout radionuclides

1.0 f 0.3

1957-1965 average for many radionuclides sampled at locations throughout the world; inorganic dust data from continuous measurements (Gedeonov et al., 1970).

Mass of inorganic dust Total pollen (- 15-50 pm dia.) Aerosol particles : Element mmd (rm) -0.5 Pb -1.0 Zn 5 3.0 Fe Ca -2.0 Mn 5.7 Mg K Element Cl Zn Br Na Se Sb V Pb cs Mn Cr As co Fe Al

Avg. ~1~(cm s - ‘) 0.06 0.07 0.08 0.1 0.15 0.15 0.23 0.25 0.31 0.33 0.36 0.37 0.50 0.94 1.1 1.3 1.6

3.2 0.65-3.8

0.063 0.15 0.21 0.29 0.31 0.38 0.46 1.08 0.40 0.17 0.98 0.25 0.16 0.16 0.24 0.24 0.24 0.36 0.22 0.85 0.23 0.26 0.17 0.6)

Scavenged by convective storms in Oklahoma (Gatz, 1966 and personal communications, 1976). Scavenged by convective storms near St. Louis; reported data multiplied by 106cm3m-‘/1.2 x lO’gairm_” to convert to dimensionless form; precipitation weighted mean washout ratios for all 1971-72 data (Gatz, 1976a).

Annual average values, July 1972-June 1973, at Harwell, U.K. ; reported data divided by 1.2 x 10m3g aircmW3 to convert to dimensionless form ; average dry deposition velocities deduced from dry flux to a mechanical collector; rain sampler was automatically covered during dry periods; some local contamination may explain the high value of cd for Ni. Data obtained via personal communications from P.A.Cawse, Environmental and Medical Sciences Division, B.364, Atomic Energy Research Establishment, Harwell, Oxon OX1 I ORA, U.K. Also, see Peirson er al. (1974).

Reactive gases :

CNWl/CNH,l PO;I/l?WI cso;l/c~w

0.12-0.22 0.18-0.40 0.05-0.15

Ratio taken ofreaction product massconcentration in rain to precursor-gas mass concentration in air at various locations in Europe (Junge, 1963).

0.0 1-o. 1

Estimated from available data for St. Louis Metromex Project; convective storm scavenging.

0.15-0.30

Estimated from July 72-June 73, National Air Sampling data for urban and nonurban sites, respectively, in Northeastern United States (Dana, 1976).

W. G. N.

2066

K~, to its average concentration in surface level air, & or i*, where the bulk air concentration is measured at a convenient reference height. Since the flux of precipitation to the surface is p,, then K~ = P^lp, and using (26) or (28) the washout ratio becomes =y=@”

;).

(29)

For example, for c = 0.5, R, = 0.5 mm and h, = 500m or for p, = 1 gcme3, (L) = lob6 gm-’ and (x/xb) = 0.5, then (29) becomes r =

0.5 x lo6 E. = 0.5 x lo6 (El).

rpojb

(31)

although it is noted that none of the data in Table 4 have been obtained at an ocean site. Clearly it would be useful to obtain such data and, to assist in its interpretation, it would be valuable if simultaneous measurements were obtained of particle size, the pollutant’s vertical distribution, and properties of the precipitation and’storm. Gas

scaaenging

For gases that form simple solutions in water then the term in thecontinuity equation describing loss rate per unit volume must account for the possible desorption of the gas from raindrops : L = A(i - NC)

centration in the drop (Postma, 1970; Hales, 1973) then after a drop has fallen only a few tens of meters, typically it will become saturated with the gas. Consequently, except very near the source of a gas (e.g. near a stack exit) it is usually an adequate approximation to set the surface-level concentration of an unreactive gas in raindrops equal to the equilibrium value: K. = 3F - lx0 = ax0

(32)

where A is an average rate ofgas transfer to the drops, rZis the concentration of the gas in the drop, and Jy is Henry’s law constant. However, since the transfer rate by molecular diffusion to drops is relatively rapid, and since small drop size and/or drop internal circulation promotes the rapid equilibration of the gas con-

(33)

where a z Jy- ’ is the solubility coefficient. This gives for the washout ratio and wet flux r = (K/x)~

(30)

Usually the washout ratios are reported for a particular element or compound, independent of particle size, in which case (29) should be averaged over the particle size distribution of the species. Table 4 shows some measured washout ratios and they are seen to be generally in the range lo’-106. Incidentally, some authors report dimensional washout ratios (with dimensions such as m3cmm3, kg air/I. water or m3 I.- ‘) and therefore the reader may find washout ratios in the literature near 10’ or lo3 rather than 106. The dependence of the washout ratios on mass-median size of the particles, shown in Table 4 and reported by Gatz (1976a), can be fit with the theory leading to (26) (Slinn, 1976b). Actually, the value of the washout ratio near lo6 (which is a physically real concentration factor) can be seen from a simple physical argument if one notes that the aerosol material initially distributed, say, in 106, 10 pm cloud droplets coagulate to form 1, 1 mm drop; it is this selective condensation plus coagulation which accounts for the frequently observed washout ratio (or precipitation scavenging concentration factor) of 106. With these measured washout ratios then the wet flux of aerosol particles to the ocean can be estimated to be I- =

SLINN et al.

= a;

W* = rpoXo.

(34)

In Table 5 are shown the Henry’s law constants for a number of gases. It is seen that the resulting washout ratios for low molecular weight gases are substantially smaller than the values of 105-lo6 typical for aerosol particles scavenged by either rain or snow. Snow scavenging of gases can generally be ignored unless the ice-crystal lattice is particularly accommodating for the gas molecules. Table 5 includes some gases such as CO,, SO1 and NH, which are reactive in water and the corresponding washout ratios are for the wet removal only of the dissolved gases, not their reaction products. To account for the details of the scavenging of reactive gases it is necessary to evaluate the possible chemical reactions which these gases can undertake in the presence of other dissolved gases and a host of other trace constituents, some of which could catalyze specific reactions. These complicated analyses can lead to the definition of an enhanced solubility coefficient a* (e.g. see Junge, 1963 ; Postma, 1970; Hales, 1973); the enhanced solubility coefficient for SO1 for two pH values and as a function of x is shown in the last section of Table 5 (Dana, 1976). However, for the case of wet removal to the ocean it would seem that a major simplification is available. Whereas clouds are effective “reaction vessels” for the chemical conversion of reactive gases to relatively involatile products (e.g. SO2 + SO:-) and whereas most material would be expected to be subjected to at least 10 condensation-evaporation cycles (i.e. clouds) before being deposited on the oceans (Junge, 1964) then it would seem to be acceptable to ignore the wet removal of most reactive gases and, instead, to assume that reactive pollutant gases are converted to their reaction products before they are scavenged. The appropriateness of this assumption is strengthened by the large values of the washout ratios for the reactive gases listed in the last section of Table 4; as further support for this assumption it is noted that these reactions products (i.e. NH:, NO; and SO:-) were measured in polluted atmospheres, possibly after experiencing only a single storm. Summary

and comments

In this section, three different methods have been described which can supply estimates for the wetremoval time scale. From (21) or from (10) with (23) for

Aspects of the transfer of atmospheric trace constituents Table 5. Henry’s Law constants JI”, solubility coefficients (2, and washout ratios I* J)” or a-’ (r = WX)O)

Compound I.

II.

3.73 x 3.22 x 2.57 x 1.84 x 1.72 x 6.82 x 2.19 x 1.26 x 9.30 x 8.23 x 7.85 x 4.71 x 5.0 x 4.2 x

N,d CC& (Me),S Me1 SO2 Hg

10’ 10’ 10’ 10’ 10’ 10’ 10’ 10’ 10-l 10-l 1O-3 lo-’ 10’ 10’ 5 x loo 1.6 x 10’ 1.1 x loo 3.0 x 10-l 2.4 x 10-l 3.8 x 10-l 4.8 x 10-l

Polychlorinated biphenyls: Aroclor 1260 Aroclor 1248 Aroclor 1254 Arcclor 1242

2.9 x 1.5 x 1.1 x 2.4 x

10-l 10-i 10-l 1O-2

Pesticides DDT Aldrin Lindane Dieldrin

1.6 x 5.3 x 2.0 x 7.7 x

1O-3 lo-’ 10-s 10-e

co H,S CH, NO CzH6 GH, 0, NzO CO* CzH, SO, NH, co

EiF

III.

x (ppbv) IV.

Sulfur : pH = 5.0

pH = 6.0

2061

For example, if for particles we take: E, 3: 1, EC, = 0.25 and 0 = (2.5 d)-i or R,,, = 0.25 mm, c = 0.5, PO = lOOcmy_’ and ,? = 10m2 or &, = 10km and ? = 0.3 x lo6 then (35) yields i, 2: 10 days. With these three different approaches available one would hope that the final estimates for the wet-removal time scale would be fairly reliable. Unfortunately, however, all three approaches contain significant uncertainties; none of the estimates are reliable to within a factor of 2 or 3 and they may be incorrect by as much as an order of magnitude. At present, the best available procedure to estimate the wet flux of pollutants to the ocean is probably to use the measured washout ratios shown in Table 4 and, if necessary, to extrapolate from this data using the theory presented in this section to guide extrapolations. In a later section, some recommended research to improve our knowledge of wet removal processes will bedescribed. Beforedoing this, however, it is useful to look at other important removal processes. DRY DEF’OSlTlON

In the first section, the residence times of atmospheric trace constituents were related to the wet and dry removal processes. In the previous section, the magnitude of the wet removal flux was written as 1y = rp& and expressions for the washout ratio were obtained. In this section, the focus will be on the dry flux 9, whose magnitude to a horizontal surface can be written as

r = a*

1 3 10 30

3.7 x 3.0 x 2.2, x 1.5 x

10’ 10’ 10’ 10’

1 3 10 30

9.0 x 5.5 x 3.2 x 1.9 x

10’ 10’ 10 10’

* The solubility coefficients typically decrease with increasing temperature (e.g. for 0, the solubility in water at 20°C is about 60% of its value at O’C) and typically decrease with the presence of other constituents (e.g. for O2 the solubility in sea

water is about 80% of its value in fresh water at the same temperature). The first group of data listed here, I, for freshwater at lS”C,is taken from Heines and Peters (1974); the second group, II, for seawater at an unspecified temperature is from Liss and Slater (1974) ; the third group, III, are estimates for.pure water recently reported by Junge (1975); the fourth group, IV, is the enhanced solubility coefficient, a*, in moles per unit volume of water to moles per unit volume of air for total dissolved sulfur (i.e. other than SO:-) in water of indicated pH at 20°C for the indicated air concentrations of SO, (Hales and Sutter, 1973; Dana, 1976).

rain (or (24) for snow) or with the washout ratio as given by (29) we have

where, again, P, is the z-component (positive, up) of the (turbulent and molecular) diffusive flux and a, is the positive rcomponent of any average drift velocity the material might possess, other than the drift for the material attached to precipitation. The average in (36), denoted by the tilde, is the average over the high frequency portion of the turbulence spectrum. To develop (36) to permit an evaluation of dry deposition it is clearly necessary to specify F, and 2, and to do this a number of approaches are available. For example, for the turbulence contribution to the flux, one can return to (5) and work with the defining correlation between fluctuations in the pollutant’s air concentration and the vertical component of the wind field: w7?‘.This approach, however, is more exacting than the present state-of-the-art can support for the prediction of average material fluxes to the ocean. A parameterization of the turbulent flux is to introduce the gradient-flux ansatz as in (6): - w7x’= K, d$ildz, where K, is the vertical component of the turbulent diffusivity. Some aspects of this approach will be used in the sequel. However, for now, a most illuminating analysis follows from a still coarser description. In this approximation the mean concentration gradient is replaced by a difference in mean concentrations between two adjacent layers of the atmosphere, divided by the height difference, 6, between where the mean

___

O W

: E 5

G

REACTIVE GASES

Id I

-TRANSFER

10

pP- Zgcm

-3

I 10-l

I 10-z

lo-3

18

I

coTa'.

s-l.18

Id

IO-)

h km

~U,),~3IU

lo-5

10’

ld Id _I 12 TRANSFERRESISTAI(CE,r (Icm 'I -

100

I 106

Id

lo*

I

10-L

'"dw - (u,la130

cIn2s-’

lo4

I

I

1

1-l)

I I

DIFFUSION. K b~rn~s-~).Id

~GM~IRCIRCIJLA~IDNS

a1

CALM

1

-1

Id

16

10-z 1

RI

, slpml-

(Ll

d

K- Id

10-I

MLOCITY OR CONDUCT~E.

DIFFUSIDN.iilm s“) - 1

MIXING

ld

I

MM

s-1.

1

ld

100

CRAVlTAFlOWALSElTUNG:

u-

K lcm's-'I- 10'

LNSlABlf ~~~STABlI

SUbSIDENCE

DIFFUSION U(D ij* 1Om s-'

WDRMlS

ld 1

b

I

ftScwP

1 (u,),

K

S;Gw

l 2 (1

l&-d

16

f

E

B

A

LAMI;

B ‘-i-iii

K =itT-i%

VELoClrf APPROXIMA ESTIMARS DEPniShn~

I

_

-_-r^l

_

-

_

._l,

=li

_--

.a.-

-

,^

_

._

_

I

-.

-

.

.

-

.I

__._^__

_

..___

---i

-

Fig. 8. A multilayer model for dry deposition of particles and gases to the ocean. For specific conditions in each layer, specific points in each range can be identified ; which of these points is farthest to the right in the figure, identifies the layer which impedes the dry deposition flux with greatest resistance. The alphabetical symbol at the far right of the figure identifies the symbols used in the formulae of the text.

ZN

DIFFUSIGN~D cwEcTlDN Fo ll#RMDCUNE

-

I

I

I

SIMPLI SOLLIFIDNS

PARTICLES

WAVtSmD WECHHCAL FURBUltHCE

t

:

::

V

FILM

-5%

I

PARTICIES

E II

L A Y

; N

:

s

:

D E

CfJNSTrnT w=xOR MCHIU(ICALTURBUIINCEUVER

BOWDARY OR MIXEDlAYER

ALOFI LAm

Id

-

Aspects of the

concentrations

2069

transfer of atmospheric trace constituents

are measured : (37)

where kr = K,/6, and therefore kl is a net velocity at which the material is transferred by turbulence across the Ith layer. As will be seen later, similar approximations can be introduced for transfer by processes other than turbulence. The major advantage of this simple approach is that with it, it is relatively easy to identify the rate-limiting stage of the dry deposition process. Transfer velocities

To utilize the parameterization shown on the righthand side of (37) it is first necessary to develop estimates for the transfer velocities within various atmospheric (and similarly, oceanic) layers. To obtain these transfer velocities consider the atmospheric layers shown in Fig. 8. On the extreme right-hand side of Fig. 8 the atmospheric layers are identified with letters A through D; in the second column from the right-hand side are shown approximate layer depths and these lead to the transfer velocity estimates shown in the next column. Finally, these velocity estimates are plotted as horizontal bars in the middle of Fig. 8 : the appropriate abscissa is at the top of the figure; the horizontal spread of the bars is derived by accounting for the variation in environmental conditions shown. As explanatory notes to Fig. 8 the following should be mentioned. Far from the interface and for trace constituents of interest, the dominant transfer mechanism is almost invariably turbulence. In the constant flux layer, the mixing velocity is approximately su+ where x is von Karman’s constant and u. = (r/p,)“’ is the friction velocity (in which r is the shear stress and pa is the density of air); this result can most easily be obtained using K, 2 z-u,z and 6 = z in (37). The approximation u* 5 3% U is based on experimental data discussed later. For high molecular weight gases the reduction of the transfer velocity within the deposition layer by the factor !Scz’3,where Sc is the Schmidt number, purports to account for both the reduced layer thickness and the decrease in diffusivity but it is an approximation even for flow over a smooth, solid surface (see Appendix C). Finally, the transfer velocity for particles includes the gravitational settling term, v,,,and any other slip velocity, v, such as might be caused by gradients in turbulent fluctuations or diffusiophoresis. The similar transfer velocities in the ocean, given in the lower half of Fig. 8, and the dependence on the Henry’s law constant, Z”, and effective solubility coeflicient, a*, will be described in subsequent paragraphs. Dry deposition of perfectly absorbed gases

A formalism is now developed which uses these transfer velocities and can display the rate-limiting stage of the dry deposition process. Consider, first, transfer through the atmosphere of low molecular

weight gases which are completely adsorbed by the ocean; as will be seen later, an example of this case is SO*. Then the drift velocity 2, of (36) can be ignored. If the remaining gradient terms (for turbulent and molecular diffusion) are approximated as in (37) then for steady-state conditions (and therefore continuous flux through all layers) the flux can be approximated -F,

= k&

- x’e)= kn($ - ic) = kc& - X’tJ= MD

- x’o) (38)

where jr is the mean gas concentration at the top of the Ith layer. For this case of a perfectly absorbed gas, i. could be taken as zero but retaining the symbol is convenient for the subsequent development. Alternatively, an overall atmospheric transfer velocity could be defined via -F,

= k.(iA - io)

(39)

or, identically, -F,

= k.[(L

- &) + (L - 2 +(L - X’D)+ (X’D- x’o)]. (4)

The advantage of (40) is that if (iA - ie), etc., are substituted from (38) into (40) and F, is cancelled from the result then we obtain 1 1 1 -=k,+g+c+& k,

1

1 (41)

As a final step, if we set rt = kl’ then (41) becomes r,,=rA+rB+rc+rD=xrJ

(42)

which is the desired result since it sets the overall atmosphere “resistance” (the reciprocal of the overall transfer velocity or”conductance” k,) equal to the sum of the transfer resistances in the individual layers. These transfer resistances, the inverses of the transfer velocities, are plotted in Fig. 8 with the appropriate abscissa at the bottom of the figure. The horizontal spread of each “resistance bar” in Fig. 8 shows the range of resistances that “typically” occurs in the appropriate layer as environmental conditions range over the values shown. For specific conditions in each layer, specific points in each range can be identified. Which of these points is farthest to the right in the figure identifies the layer which impedes the dry deposition flux with greatest resistance. Thus, if the resistance in layer 1 is greatest, then transfer through the Ith layer is the rate-limiting stage of the overall dry deposition process and the overall atmospheric transfer rate, k,, can be set as approximately equal to k,. However it is seen in Fig. 8 that, at least for low molecular weight gases, the resistances in the atmospheric layers are typically of comparable magnitude (about 1 s cm- ‘) and unless there is a very stable layer aloft or the wind speeds are low, then there is not a clearly defined rate-limiting stage; typically, then, for low-molecular weight perfectly absorbed gases, k, = lcms-‘. The transfer velocity for high mol. wt gases can be

W. G. N. SLINN et al.

2070

substantially smaller than 1 cm s-i. For example, for high mol. wt gases which are highly soluble in water (e.g. see Table 5 for the solubility coefficients of some pesticides) then as seen in Fig 8, the rate-limiting stage appears to be within the atmosphere’s viscous sublayer. If the transfer across this viscous sublayer can be modeled as in Appendix C then this gives k, 2 kD = x (~*~~/(SC)~‘~

(43)

where Sc = v/D, v is the kinematic viscosity of air, and D is the molecular diffusion coefficient for the gas species in air. It must be emphasized, however, that this estimate is tentative until further research on the air-sea interface is performed. Mentioning specific research topics that recommend themselves will be deferred until a later section. Dry

deposition

of particles

For particles, the magnitude of the dry flux can be parameterized as

in which u. is the gravitational settling speed and v, is the (positive, down) component of any other slip velocity the particles might possess, e.g. caused by diffusiophoresis or gradients in turbulent fluctuations. As it stands, (44) can not be conveniently recast into a form similar to (37) displaying differences in concentrations. However, above the deposition layer usually turbulent transport dominates the transfer of particles of interest and therefore in these layers, the other terms in (44) are usually ignorable. Then, in the deposition layer where the turbuient fluctuations are damped, the downward flux can be parameterized (see Table 1) by the difference 9 =

U&Zi)

-

C,C(Zi) = Ud[iD - i*]

leads to (481 In other words, the overall resistance is the sum of resistances in the individual layers, with r;’ the resistance to particle transfer across the deposition layer. As can be seen from Fig. 8. for particles (just as for high molecular weight, highly soluble gases} most of the atmospheric transfer resistance occurs in the deposition layer; but for both these types of atmospheric trace constituents, the resistances in this layer are not known at all well For particles of radii, a, in the range 0.001 5 a 6 0.1 pm, the transfer velocity would be given by (43) for transfer to a smooth, solid surface, ignoring electrical and phoretic effects ; in other words, these particles can effectively beconsidered as largegas molecules and Brownian diffusion dominates the transfer across the deposition layer. The resulting resistance bar is shown as the upper of the two parallel bars shown in the row labelled “particles” in Fig. 8. Depending on the wind speed (i.e. on u,), the transfer velocity would begin to increase again for particles with a c 0.1 pm because of the more substantial particle mass; the resulting resistance bar is shown as the lower of the parahel bars, resistance decreasing to the left in Fig. 8. The dotted bar to the right is included in Fig. 8 to emphasize the importance of resuspension. However it should be reiterated that these resistances are not known well; some recommended further research will be mentioned in a later section. For now, the best information available for particle deposition velocities is that obtained from water/wind

(45)

where cd and L’, are deposition and resuspension velocities, respectively, and i, = (r,/r,)?(zi) is the average air concentration which, when resuspension occurs, would be in balance with the pollutant’s concentration in the ocean. For example, for NaCI seasalt particles

- u

pl!E m3

”

( ) lms-’

where n is about 3 and could be deduced more accurately from available data (e.g. see Junge, 1963). For SOi- particles, C'(Zi)is about a factor of 5 smaller than for Na; for Sr, C!(q) is about 3 orders of magnitude smaller, and then so would be the corresponding &‘s, ignoring fractionization. With these approximations, then the flux can be written as 2 = k&

- Xs) = k&a - 2

= k&c - in)

= L.,(,?, - i,) = ko(L - i,).

(47)

Proceeding as in the development

of (41), then (47)

Fig. 9. Deposition velocity as a function of particle size as measured by Sehmel and Sutter (1974) for particles of density 1.5 g cm- 3 depositing on a water surfacein a wind tunnel, and by MGlier and Schumann (1970) for similar conditions using

polystyrene latex spheres, sodium chloride particles, and purified-water residual nuclei.

2071

Aspects of the transfer of atmospheric trace constituents

tunnel measurements and shown in Fig. 9. For particles smaller than 0.1 pm these results suggest that the increase in cd with increasing diffusivity given by a SC-~,’ dependence may be correct; however, waves, “sea spray”, and induced motion of the water surface in the wind tunnel possibly did not adequately simulate conditions at sea. For particles larger than about 1 pm it is seen that r,, is substantially larger than the gravitational settling speed, re; indeed, it appears to be larger than the corresponding inertial impaction contribution to cd for deposition to a smooth surface (Sehmel, 1973 ; Caporaloni et ul., 1975 ; Slinn, 1976d). Possibly this is caused by an increase in inertial impaction on waves; if so, then failure to simulate ocean waves in the wind tunnel should limit generalizations from the data. Finally, for particle diameter in the range 0.1 to 1 pm, the deposition velocity shown in Fig. 9 appears to be Laused simply by the two effects : gravitational settling and Brownian diffusion. However, as will be discussed in more detail later, for conditions over the ocean, diffusiophoresis would be expected to decrease and thermophoresis, increase, the deposition to an evaporating ocean.

mated in a manner similar to the atmospheric case. In

particular it is noted that by equating stresses at the interface, then (pu,),,. = (pw,), which provides an estimate for (u*),. Also, it should be noted that since the molecular diffusion of gases in water is slow (typically D - 1 cm2 day-‘) whereas \I,,,~0.01 cm2 -* number is typically s 7 then the Schmidt very much larger than unity. The appropriate k, to use in (50) depends on the depth to where the “bulk” concentration, c, is measured, usually a few meters below the surface. We now return to (49) and (50) for the case of gases which form simple solutions in the ocean. Then Henry’s law prevails at the interface: ii = NC:, If the flux is also written as 9 = Ux’b - ii,,

9 = kg[(,& - ii) + ‘%‘(cSi - I;&)]

For the case of gases which are not perfectly absorbed by the ocean then it is imperative to account for their flux back to the atmosphere. To simplify the analysis in this case it is convenient to reformulate the problem and develop only a two-layer model. In the atmospheric layer, all transfer rates are lumped into a single overall gas-phase transfer rate, k,, between the air-sea interface and a convenient height in the atmosphere where a bulk concentration, ,&, is measured. Then (49)

In the ocean layer, similarly, 9 = k,(Ci - C,)

(501

where k, is the transfer velocity in the liquid between the surface and the depth for convenient measurement of the bulk concentration, ?,. The two expressions for the dry flux, (49) and (50), can now be equated and lead to an estimate for the total transfer rate. Before describing this, however, it is useful to discuss transfer processes in the ocean. In the above discussion the emphasis has been on developing parameterizations for transfer processes in the atmosphere, starting from the continuity equation. (1). Clearly. though, a similar parameterization for (2) could have been described and would lead to an overall transfer

velocity in the ocean

where the subscripts f-f label the layers in the ocean shown in Fig. 8. There. too, are shown estimates for the transfer velocities through the individual layers, esti-

(53)

where k, is an overall or total transfer velocity and X, = .#“?* is the air concentration which would be in equilibrium with the existing bulk concentration of the gas in the ocean, then algebra similar to that used earlier leads to

Dry depositionqf yuses

9 = k,(;i, - ii).

(52)

(541

or 1

_.i,”

k, - k,

k,

(551

which relates the total transfer velocity to the transfer velocities in the two media. Incidentally, instead of (53). sometimes it is convenient to write the flux in terms of liquid phase concentrations ; viz., GJ = K&/.X

- ?,I

(56)

from which it is seen that I(, = .Xk, In (55) the tolai resistance to transfer, r, = k;’ appears as the sum of a gas-phase resistance re = k; * and a liquid-phase resistance r, = .;Yk; * : rl = rv + rp

(57)

Fig. 8 shows that for solubility coefficient a = X - 1 2_ 100, then the liquid phase transfer resistance dominates; Table 5 shows that many low mol. wt gases fall in this category. Some pesticides and herbicides fall in the intermediate range, 10’ 5 NV’ 5 10’ and the resistances in the atmosphere and the ocean are comparable in magnitude (Munnich, 1971). For highly soluble gases or gases which react in the ocean to form relatively involatile products, then their transfer is gas phase controlled. Actually, for the case of reactive gases such SO, it is necessary to strain the formalism somewhat, in an attempt to account for gas “transfer” to reaction products. For example, for a first order reaction with reaction rate constant /I then averaging (2) over highfrequency turbulence and accounting only for vertical

W. G. N. SLINNet al.

2072

ILLUSTRATIVE CALCULATIONS

diffusion, leads to

One way to modify the formalism to account for this case is first to identify the rate-limiting stage of the transfer process in the ocean. If this is the viscous sublayer, then from (58) an effective flux “through” this layer can be identified as -F,

= kF(& - Z,) + /IS,(& - Cc)

(59)

where kF = [K,, + &J/6,, in which 6, is the thickness of the layer, and where the introduction of a nonzero Cc in the last term of (59) can not be justified except on the basis of mathematical convenience. The convenience is that (59) then leads to an effective transfer velocity k? = kF + BJ,,

(60)

i.e., enhanced by the chemical reactivity of the gas. In turn, if (60) is used in (55) then the total transfer velocity can be written as 1 1 H c=k,+ol*k,

In the previous sections we have reviewed some of the basic information on wet and dry removal processes. In this section, a few worked cases will be presented to illustrate how this information can be used to estimate these removal fluxes and corresponding atmospheric residence times. The specific cases demonstrated are chosen because of their interest and because, in some cases, confirming experimental data is available. Wet versus dry deposition

A recurring request is to estimate the relative importance of wet vs dry deposition; it is difficult to give an unequivocal response, however, since the relative importance of these two processes depends on many factors. To prepare to illustrate this statement, we take the wet flux, W = KP = rpxb and for the dry flux 9 = k,(Xb - x,). If these fluxes are multiplied by time T during which they operate and if, for the moment, we consider the case x+ = 0 (perfect sink) then the ratio of total wet to total dry deposition is Wr

-=-

(61)

where x* is an effective enhancement of the solubility of the gas in water. As is shown in Fig. 8, a* z 1 for CO1 and a* 2r lo3 for SO2 (Liss and Slater, 1974). These considerations lead to the prediction that for highly soluble or reactive gases then their transfer, at least to the upper layers of the oceans, is controlled by transfer through the atmosphere. These restrictive comments about the ocean’s upper layers follow from observing the bottom resistance bar in Fig. 8 which shows that transfer to the deep ocean and ultimately to the ocean floor is orders-of-magnitude slower than other transfer processes and therefore is the ratelimiting step of the final deposition of most airborne material. Summary and comments A summary of this section cannot be presented here that is better than the summary shown in Fig. 8. It may be useful to emphasize, however, that this development has restricted value since clearly it is based on crude parameterizations of the governing equation and crude approximations for the transfer velocities. In contrast, if short-term estimates are desired, e.g. to predict the fate of a specific pollutant or tracer release or to support limited-duration field experiments, then it probably would be necessary to retain the gradientflux parameterization of the turbulence flux or return to the correlation WAX’, depending on the accuracy with which other factors are known. On the other hand, for long-term average estimates ofdry flux of pollutants to the ocean, the type of parameterization developed in this section is probably the best available. Methods for making such estimates will be illustrated in the next section.

DT

rP

(62)

4T

where, for example, if P is the total annual precipitation then T = 3.15 x 10’s y-’ is the number of seconds per year. As an illustration of (62), consider the case of aerosol particles with mass-mean dry deposition velocities v,, 2 k, = 1, 0.1 cm s- ’ (which might be appropriate for Fe and Pb particles, respectively, removed from a well-mixed atmosphere). Then, for a washout ratio r = 0.3 x lo6 for both these aerosols (cf. Table 4) and for P = 1OOcm y-l, (62) gives

w,/% = l,

vd = lcms-’

wT/gT=

vd=o.lcms-’

10,

(63)

J

which suggests that the wet deposition of particles is typically more important than their dry deposition although it should not be overlooked that the estimates for the dry deposition velocities are uncertain and that the same air concentration x = xs was used to estimate both processes (it is easy to envision cases where this would be inappropriate). As a second illustration of (62) consider the case of gases which form simple solutions in rain water and in the ocean and, further, the case of gases whose dry deposition is controlled by transfer in the ocean. In this case (cf. Fig. 8) then k, z X’- ’ k, and the washout ratio r ‘YX’-‘. Actually these two Henry’s law constants (for sea water and for rain) are different but ignoring this and substituting these expressions into (62) gives wT

p

9T

k,T

-=-_;

soluble gases, dry transfer liquid-phase controlled

(64)

which is independent of the gases’ solubility coefficients. Further, if the dry transfer is assumed to be

controlfed in the ocean‘s viscous subIayer and ifwe use the estimate for the transfer velocity shown in Fig. 8, viz.

foi reasonable v&es of the parameters, then for P (64) gives #‘,@r z 10e3. This rest& = Imy-t, indicates that wet removal of these may be ignored gases compared with their dry removal_ However it is to be noted that dry removal could not continue ~nde~n~te~ywith kr as in (65) since the top fayers of the ooean would soon become saturated with such gases, When this occurs it would no longer be appropriate to ignore _Y*,ds was done to obtain (62); then the fIux of the gas back to the atmosphere would be important and k, would decrease to a value consistent with the transfer ofthe gas across the thermochne into the deep ocean Or consistent with the gases ultimate conversion to a less volatile form. Two other illustrations off62) are for highly ma&we or highly soluble gases (cf. Fig. 8 for thecases t(* = lo3 arid._??-’ = i03). Then dry transfer can be rate limited in the atmos~h~e~ & I k,, and if most of the transfer resistance occurs in the atmosphere‘s viscous sublayer, then kBz.p (~,)~/(Sc)i’~. Substituting this into (S2)and using r = .@ - 2 yields *

‘T

P(Sc),2 3

soluble gases, dry transfer

9 =H.rfu.jeT’ T. gas-phase

(66)

controt&zd.

Whether or not wet or dry removal is dominant depends on the vafues for the gases’ parameters displayed in j66); some specific cases will be described later. Actually, for highly reactive gases the competition is not so much between wet and dry removal. as it is between the rate of conversion of the gas to its reaction product in the atmosphere vs in the ocean However, such a gas must first reach the ocean and if, e.g. for S02, it is transferred through theatm~s~here at arateofabout lcms-’ then the dry removal contribution to the residence time fd = k&h “c I kmi I cm 2-t 2 10s s. This t~me~nstant~ ofabout a day, is the time constant to be compared with the rate of conversion of the reactive gas in the atmosphere; for SO2 the twa rates are probably comparable.

Triaiated water vapor is a particuhrly j~t~r~ting gas. fts washout ratio P = c( f: .@ -I is about 10s and its dry transfer velocity is about I cm s-‘. Consequently, from (62), it is seen that dry removal ofNT0 is two or three times more important than wet removal when P fl IO0 cm y- ’ (Eriksson, I%_!$. One can also see this from the following crude argument. Annual pracipitatiotl is approximately equal to nclt evaporation. Nrrt evaporation, however, is controkd by relative humidity over the oceans. Therefore, if we crudely estimate the average humidity to be abaut two

thirds ofthe saturation value, this means that twice as many water molecules art exchanged between the sea and the atmosphere as is given by the net eva,poration Rux, and since the tatter equals rainfall, the: molecular transfer of F-ET0 (i.e. water moIecufes) is twice the transfer by rain. Similarly, ifthe ~ontr~butjo~ from dry transfer is included in the estimate for water vapor’s atrnos~~~ri~ residence time shown in Table 2, then the values shown there should be corres~~~i~gly reduced. However, ifwet removal of particles dominates, then the wet removal contribution to their residence time would remain near the values shown in Tabte 2. viz., about $0 days. Carbon-14 as “CO, is another interesting case especially because much of our knowledge of air-sea gas exch&nge on the global scale has been derived from information on its distribution. Contrary to the situation with tritiated water vapor, CO2 is, afthough more sofubb than most other gases, ~~~t~~~~~insoluble in water compared with water itself. From Fig. 8 (or see Munnich, 1971) it can be seen that there exists a critical value of the effetive soiubiiity coefficient I+@ - ’ in the range f0’ to fO_’beyond which the transfer resistance of the liquid becomes negligible corners with the resistance in the gas phase. Tritiated water vapor and SOa faI1in this latter category and their dry deposition is controlled by the resistance in the atmosphere. CC++, on the other hand, with a,-H - ’ n 1 is wetl below the critical value and its transfer is exch~sive~y liquid-phase ~ontro~~~~ This is similar to the ease for most gases. An estimate for the remova! flux for “CO2 (see (65)) is then lit& 2: IO-’ iizb where here the back flux of ?XI, (but not COz) can be ignored. The resulting atmospheric residence time for 14CQz can be estimated as S,, = fip!kl cc to3 me of 5-N years. As calt be seen from Table 5, some pesticides and FCBs h~~esoiubi~~tyc~f~~ie~ts near thecritical value between IO2 and lo3 and therefore their dry removal are borderline cases between gas- and liquid-phase control. Consistent with (62), the wet removal of such gases is genera& neg~~g~b~~.Xnthe case of DDT, with -y -* * S x f@‘,it might be estimated that its overali tE3t&ir

velocity

is

approximatefy

k, I .X-I

(W5UI) 2 0.5cms-’ if transfer in the atmosphere were assumed to be about 1 cm s - I. This, however, ignores the fact that if the atmospheric transfer is ~on~ro~~~dwithin the atmosphere’s viscous sublayer, then the de~sjtion vefocity must be reduced rough+ by the factor (I$D)“~. For a diffusivity of DDT in air of about 8 X foe3 cm2 s-l, then (v/D)' ' 2 X and therefore ka “v O,I cm s- ’ (~~~~~ch, 1971). ~~~s~quently the dominant resistance for DDT tends to be in the atrnos~ber~ (The crudeness of the anaiysis can not justify a more definite statement.) The ~orres~ffd~ng atmospheric residence time for DDT is about one month, For some ofthe PC&, with x - t - 1tY to 10~ then k, *I 10v2 to 10-r cm s-t, and their dry removaf is fiquid-phase controllect. It should be rn~~tion~~ though, that the attachment of substances such as

W. G. N. SLINN a al.

2074

DDT to aerosol particles and their subsequent removal by precipitation may be an important removal mechanism. Summary and comments

In summary, it can be seen that a controlling property of a substance in atmosphere-ocean transfer is its equilibrium partition between the gas and liquid phases. This is true for the removal of all substances present in the atmosphere in the molecularly dispersed form (gases and vapors) and also for aerosol particles. For the case of particles, we can assume that their equilibrium partition is entirely on the liquid phase side since a particle in the gas phase will eventuaiiy enter the liquid phase and stay there. In the same context, the DDT example might teach a further lesson by the way this partition factor can be derived if it is not known directly (Munnich, 1971). Under equihbrium conditions in the presence of the pure substance (= phase A = solid DDT) the product of all three partition factors between phase A and B (where Bis the solution phase), Band C (where C is the vapor phase) and C and A, namely, ([4]/[Bf). @J/fcl). ([C]/[Af) = 1, and in this way the gas/liquid partition can always be derived from the other two partition factors The general conclusion is that a substance even if it is very “insoluble” in water has a gas/liquid partition quite on the liquid side if only its vapor pressure is sufficiently low. SOME CURRENT AND SUGGESTED RESEARCH

In the previous sections a framework has been presented for the prediction of atmospheric trace constituent fluxes past the air-sea interface and a few worked examples have been demonstrated. In the presentation a number of weaknesses in the framework have been noted but little attention was paid to how these weaknesses might be strengthened. In this section the emphasis will be on current and suggested future research which might strengthen prediction capabilities. The ordering of topics will generally follow the order in which the topics appeared in previous sections. Radionuclide measurements

Measurements and analyses of natural and anthropogenic radi~nuclide concentrations can provide valuable information on mixing, inter-reservoir transfer, and on wet and dry removal processes. For the analysis of much of this data it is assumed that nongaseous radionuchdes rapidly attach to atmospheric aerosol particles and therefore from this data, inferences can be made about the behavior of atmospheric aerosols. Because this is a fundamental assumption, further studies of this attachment process and its variability would be welcome, e.g. along the lines developed by Lassen et al. (1960, 1961) and Brock (1970). To illustrate the importance of this type of analysis it is noted that in their recent critical review,

Marteli and Moore (1974) conclude that the best estimates of tropospheric aerosol residence times are those based on 210Bi to ‘rOPb activity ratios as well as those based on the average 210Pb concentrations vs altitude in the troposphere over central continental areas. Each of these methods indicate an average tropospheric aerosol residence time of less than one week. However, as reported by these authors, size distribution measurements have indicated that 90% of the 210Pb and 210Bi activity can be associated with particles smaller than 0.3 pm dia. (Gillette et al., 1972) and the presentation in the previous sections would suggest that such particles would have a relatively longer residence time than larger particles. Consequently, to increase the utility of radionuchde data, further research to characterize the radionuclides and their hosts would be welcome. Extensive data are available for wet and dry fallout ofradionuclides, particularly to the land and for fission products. Technological breakthroughs are required to measure deposition rates to the ocean and in some cases, even to the land (e.g. for ’ “Pb and “‘Bi). Some data are, however, available for the sea-surface for fission products (~humann, 1975). The ratio of dry to wet deposition for 9*Sr was found to be about 20% and independent of latitude inIO”S to 45”N; similar values were found for zloPb. These values, which represent upper limits, are similar or even lower than the values observed in the case of land for fission products and trace elements (Cambray et al., 1973; Cawse, 1974). However, to generalize from these results the relative importance of wet and dry removal to the oceans would ignore the different source functions, the particle sizes to which the radionuclides are attached, and the differences for dry deposition to mechanical vs natural collectors. The observations of higher integrated “Sr activity in the oceans by Bowen and his colleagues have led to speculations of possible mechanisms which may be responsible for higher fall-out over oceans (Bowen and Sugihara, 1960; Volchok et al., 1971; Volchok, 1974). From the information presented in the previous paragraph some authors have concluded that dry deposition can be ruled out as an important contributing factor. Several other factors such as higher rainfall over oceans, land run-off, etc., have been considered_ but at present there exists no firm resolution of this problem. From the above paragraphs one can see that, whereas it is a relatively simple matter to estimate the total radionuclide fallout at a specific place, it is nevertheless difficult to extrapolate from available measurements to estimate the global values for fallout, over oceans or lands. As a further example, it is now well documented that for several land sites, the specific activity in rams is relatively independent of total rainfall. Thus, Crooks et al. (1960) found that for five stations in the U.K. where annual rainfall varied between 50 and 320~~1, the specific activity of 90Sr remained between 5.7 and 6.5 pCi I.-‘. However, the

2075

Aspects of the transfer of atmospheric trace constituents results for some coastal stations show a very good inverse correlation (La1 et al., 1976) and in some C+EXS, a.weak positive dependence has been found, e.g. for 2’QBh data in Hokkaido, Japan (Fukuda and Tsuonogai, 1975). It can therefore be seen that considerable ~cert~nty remains in estimating both the globalaverage values or relative land/ocean values of fallout. In order to improve prediction capabilities, better and more complete data are needed. Especially useful would be more information on air-concentrations, attachment processes, and wet/dry fallout of the r~jonuc~id~ 7Be, zloPo, ‘loBi, “‘Pb and trace elements such as Hg, As, Pb, Zn, etc. The fallout studies should seek relationships between the concentrations in air and in precipitation for oceanic, coastal and inland stations. In view of the inadequacy of mechanical dry deposition samplers, the obvious solution should not be overlooked to study in detail the actual flux of radionuclides to the ocean itself, and the fate of the radionuciides in the ocean. Precipitation

scavenging studies

A good compilation of current activities in wet removal research is available in the conference proceedings Precipitation Scavenging - 1974 (Beadle and Semonin, 1976). Much of the current research is focused on evaluating the collection efficiency between particles and various types of precipitation (for a review, see Siinn, 1976c), determining the deposition patterns of tracers released into pr~jpitating storms (for a review, see Gatz, 1976b), and determining the deposition downwind of specific sources. Rain scavenging of gases has been extensively investigated by Hales and his coworkers (e.g. see Dana et al., 1975). Earlier precipitation scavenging conference proceedings are those edited by Engelmann and Siinn (1970) and Styra et al. (1970). To assist in quantifying the wet flux of pollutants to the oceans, the washout ratio measurements for a number of pollutants by Gatz (1976a), Peirson et al. (1974), and Cawse (1974) are especially valuable. Some of their data were used earlier in this report to form Table 4. The theoretical analyses of washout ratios outlined earlier in this report may be able to explain many of the observed variations of washout ratios, for example, with particle size, rain intensity, drop size, storm type, and with the vertical profiles of the pollution. Measurements of washout ratios over the oceans (in fact, at any location) coupled with vertical profiles of the trace constituents ingested by the storms and with details about the precipitation and trace constituents would be most welcome contributions. A series of research projects that could greatly improve our knowledge of precipitation scavenging is to perform budget studies on progressively more

complicated storm systems. It is envisioned that these projects would start with simple wave and cap clouds, progress to orographic and cumulus clouds, and finally study budgets in cumulonimbus and frontal storms. The difference between inflow and outflow of

material (including water vapor) should be compared with their removal by precipitation. Budgets should be performed for water vapor, trace elements, simple compounds, ions, and for inorganic and organic gases. Particle size distribution measurements in the inflow and outflow air could yield info~ation on the modification of the aerosols by clouds, and similar studies could yield information about clouds as sources and sinks of cloud droplet and ice crystal nuclei. There are indications that studies such as these may soon be performed in the northeastern United States as a part of regional air ~llution studies. More statistical information about storms is desired such as average duration, total precipitation, cloud water removal efficiencies, and frequency of occurrence. Over the oceans, even the total rainfall is uncertain : 90Sr fallout may represent the best available rain gauge! Marwitz (1972) and Browning and Foote (1976) have discussed the dramatic (-order of magnitude) decrease in precipitation efficiency of convective storms as the wind directional shear from cloud base to cloud top increases by an order of magnitude, but there is little data available for the cioud water removal efficiency for frontal storms. In addition to field projects described in the previous paragraph, perhaps further development of remote sensing from satellites will yield valuable statistical information on storms ; probably much information could also be obtained from existing global circulation models. Micrometeorobgicalfctors

ir#uencing dry deposition

Since the turbulent motions that generally control thedry transfer ofatmospheric pollution to the vicinity of the sea surface are precisely those that contribute to the vertical fluxes of sensible heat, moisture, and momentum, studies ofthese latter fluxes can be used to infer information about the turbulent transfer of pollutants. Considerable experimental effort has resuited in a fairly good knowledge of the oceanic case, at least in wind speeds below about 15ms-*. Present understanding can be summarized by the observations that (a) a surface layer in which fluxes are rapidly equilibrated (-minutes) extends up to 20-50 m typically (see, however, Deacon, 1973), (b) empirical descriptions, obtained over land, of flux-gradient relationships apply equally well over water, and (c) the wind drag at the surface T is well-described by a simple drag coefficient relationship involving the air density p and the mean wind speed U: T = cdpu*

(67)

where Cd is found to be approx 1.3 x lo- 3 in moderate winds and in near-neutral stratification and approx 1.4 x 10V3 for slightly unstable conditions, typical at sea. However, variations in C, with wind speed have been suggested although as a dimensionless quantity, Cd should not depend only on the mean wind but possibly on some dimensionless characteristic of the wave spectrum. A dependence of C, on c/u,, where c is

W. G. N.

2076

the phase speed of the significant waves and U, is the friction velocity, has been suggested although such a dependence should be expected only for an equilibrium wave spectrum. The experimental evidence is perhaps fortuitous since relations between C, = u2ti2 and c/u, are influenced by experimental errors in II,. The friction velocity u* = (r/p)“* is a convenient and useful measure of the turbulence intensity. For cases where the wind speed is measured directly (usually at a height of 10 m), the simple proportionality u+ = 0.037 Is,, is compatible with the drag coefficient given in (67) for typical conditions at sea. For those situations in which a direct measurement of the velocity is not available, it is possible to estimate u+ from the geostrophic wind speed ug based on surface pressure gradients (Deacon, 1973 ; Hasse, 1974) u* 5 0.025 U#.

(69)

Errors involved in the evaluation of u* from these relatively simple relationships are likely to be of the order of *200/,. Similar errors can arise from the neglect of atmospheric stability; corrections for stability can be derived from the relationships recommended by Dyer (1974) and Hasse (1974). However, it is unlikely that stability corrections are important for contaminant profiles if the controlling resistance to dry deposition is associated with heights below a few decimeters, provided the proper u+ is used. A number of reports have recently focused on strengthening the electrical analogy for trace constituent transport through the constant flux layer. A later subsection will address the case of particle transport ; for gases, the analogy can be developed by integrating the gradient-flux ansatz -F&K(z)2

(70)

where the diffusivity K contains both turbulent and molecular contributions. In general, if the dry flux is constant, then integration of (70) from the interface z = z, leads to (71) where k,

’

z

re =

c =

J 21

dz’/K(z’).

If it is assumed that the dominant contribution to K above the aerodynamic roughness height z,, is from turbulent diffusion then in the constant flux layer and for neutral density stratification K 3: xu,z,

we have

z 2 zo,

in which x is von Karman’s constant. (73) into (72) leads to

s

I0 dz’

rp=

-

ri K(z)

Z

+

(x14,)-’

(73) Substituting

In - E r, + r, zo

(74)

SLINN et al.

in which an aerodynamic resistance, r, = (XI,)- ’ ln(z/zo) = ii/u:, and an atmospheric surface layer resistance where molecular diffusion dominates, r,, have beeen identified separately. Many expressions for this surface layer resistance have been suggested in an attempt to account comdy for pollutant-dependent heights at which molecular diffusion dominates and to compensate for the lack of an equivalent to form (or pressure) drag (Owen and Thompson, 1963; Dipprey and Sabersky, 1963; Sherrif and Gumley, 1966; Dawson and Trass, 1972; Garratt and Hicks, 1973; Yaglom and Kader, 1974; Brutsaert, 1975; Roth, 1975). Generally these expressions are of the form u,r_ E B- ’ =oReb,W

-d

(75)

where a, b, c, and d are constants, Re, = u,zo/v is the surface Reynolds number and Sc = v/D is the Schniidt number. For example, Dipprey and Sabersky (1963) gave a = 10.25, b = 0.2, c = 0.44 and d = 8.5. If this formalism is adequate for gases then it should -also apply for particles smaller than about 0.1 pm since typically inertial effects for such particles are negligible compared with their molecular (or Brownian) diffusion. However, it should be noted that expressions such as (75) have never been advanced specifically for the case of air-sea transfer and therefore further research (e.g. see Shepherd, 1974) to test their adequacy in this case would be appropriate. One of the difficulties in the application of these formulae to the case of dry deposition to the oceans is that the roughness length has no direct physical meaning at sea but rather, z. is a function of the sea state and the relative speed of the wind and waves. For example, in a recent review paper, Gifford (1976) quoted the suggestion by Kitaigorodskii (1970) that the “equivalent sand roughness” of the sea, h,, depends on u, (or U) relative to the peak phase velocity of gravity waves, co, according to h, =

6’ ti * co ( 0.38 u:/g, u+ <
(76a) VW

where r~ is the r.m.s. wave height and g is the acceleration of gravity. Thus during early stages of wave development, with II+ >>co, (76) suggests that the waves behave essentially as immobile roughness ela ments; later in the wave development, u2 <
Aspects of the transfer of atmospheric trace constituents uncertain but also the mean wind profile itself. Thus, although it has been found that atmospheric turbulence spectra above the waves in general do not show strong influences of wave motion, wind profiles in the trade wind regime were distorted below the wave heights in the sense that da/& was increased (Dunckel er al., 1974). This probably is a feature typical for swell only (that is, peak wave speed c,, greater than wind speed). An interpretation is that waves take stress from, or feed stress to, the atmosphere depending on the relative speeds cc, and U. The slope of the profile should reflect the fraction of stress transported by turbulence in contrast to momentum uptake via pressure forces. The stress uptake by waves as a fraction of total stress is between 20% and 80% (Dobson, 1971; Hasselmann et al., 1973 ; Snyder, 1974). Considering that the wave field initially adjusts fairly rapidly (of the order of an hour) to changes in the wind field and that the drag coefficient seems to be fairly independent from the sea state, it seems reasonable to assume the fraction going into waves to be at the lower margin (20%) in most cases, except shortly after rapid change. The consequences for material transfer would be proportional in that a reduction of turbulence intensity would cause a corresponding reduction in turbulent transfer of pollutants but with momentum uptake by pressure on waves there could be corresponding increases in inertial impaction of particles and convective transport of gases. The air-sea interface and surface-layer mixing

The analysis in earlier sections suggest, however, that the most important details to study may be of the air-sea interface itself and of mixing in the oceans. Thus, it was seen from simple analyses that in many cases dry transfer would be controlled in the viscous sublayers at the interface or by mixing in the top layers of the ocean (cf. Fig. 8). It is therefore important to learn more about these layers, especially to determine if mechanisms exist to “short-circuit” the high transfer resistances predicted by simple theories. Here a few comments are made about relevant facets of the interface and mixing in the ocean’s surface layer. The momentum boundary layers, themselves, are probably not strongly influenced by waves and the slip of the surface. Typically the slip of the sea surface is a few percent of tiiO. Gravity waves are not expected to strongly influence the aqueous interfacial layer because their wave length is large compared with the characteristic viscous length ; capillary waves may be more important because of their smaller size. Waves may affect transports by their periodic stretching and compressing the interracial layer. If this et&t is proportional to the change in surface area, then variations in thickness of about 15% could be expected. However, although the momentum boundary layers may not vary significantly, the deposition layer thicknesses and the corresponding flux through these layers of high-mol. wt gases and particles whose transfer is controlled by Brownian diffusion can be

2077

significantly altered. Analysis of this problem, e.g. along the lines developed by Zimin (1964) and Slinn (1976c) for the similar problem of transport to raindrops with internal circulation, are desirable. The physics of waves and wave breaking certainly should be investigated from the point of view of pollutant transport. The increase in surface area by waves is modest since wave steepness is limited. A typical steepness of longer gravity waves is l/17 and if to this are added capillary waves with a steepness of, say, l/7, then the increase in surface area would be about 15%. Cox and Munk (1955) give for the relative increase in surface area AA = 0.0015 + 0.0026 U k 0.002 A

(77)

with the masthead velocity, Is, given in m s- ‘. Waves begin to break at Beaufort 3 and spray blown from the crest of breaking waves start to become noticeable at Beaufort 6. With higher wind speeds the amount of spray in the air increases rapidly ; at hurricane speeds it is said that the sea surface. is no longer defined : the air is filled with spray. Increase of effective surface area with spray, capture of aerosol particles by spray drops, trapping of gas by breaking waves are some of the processes that deserve further investigation since all would effectively bypass the slow transport across the interfacial layers. In contrast, interfacial resistance can be increased by surface films, a subject recently reviewed by Liss (1975, 1976). Natural and artificial surface films can potentially influence gas exchange either directly, i.e. by acting as an additional barrier to transfer, or indirectly by affecting some interfacial property which is important for gas transfer, e.g. by damping capillary waves. However, any effect will be severely reduced if the film material does not form a continuous layer at the interface. It has been argued (Garrett, 1972; Liss, 1975 and 1976) that because the material found at the sea surface is generally of very mixed chemical composition, has low in situ film pressure, and can be considerably compressed before exhibiting any ap preciable rise in film pressure, then it is unlikely to form a continuous layer and so will not play a significant role in retarding gas exchange. Exceptions may occur in coastal and other areas of high biological production, in the vicinity of oil spills or, possibly, in shipping lanes. It is further noted that although no systematic census is known to us, it is usually reported that oil slicks at sea break up at wind speeds 3 m s-i and higher. The absence of capillary waves (which become damped when a continuous film is present) is probably a sensitive indicator of areas where exchange retardation might be significant. Mixing within the oceans is complicated and deserves further study. Near the interface the turbulence intensity in the water is determined by the stress transmitted past the interface and by the velocity profile. Compared to a layer of, say, 1 cm depth at the interface, the orbital motions of most wave com-

W. G. N. SUNNet al.

2078

ponents decay on a larger depth scale (of order l/271 where 1 is the wave length) and thus do not contribute to the velocity profile adjacent to the interface. For such a small layer, the velocity profile may be modeled as a logarithmic (constant stress) profile assuming the stress in the water to be equal to the part of the total stress transferred to the interface as shearing stress (compared to pressure forces on waves). Logarithmic profiles have been reported by Shemdin and Lai (1970) in the water layer ofa wind/water tunnel. However, it is difficult to infer what the fraction of momentum taken by the waves will do for the turbulent transports in the near surface water layers. If the wave energy is fed by wave-wave interactions to higher frequencies, then the energy taken up by longer waves would also be available for turbulence generation. This argument is based on the assumption that dissipation occurs mainly in the thin layers of orbital motions of the small waves ; ifit is correct, then small errors should be made in estimating pollution fluxes by assuming the total stress to pass through the interface as tangential stress. Mixing to deeper layers may be dominated by buoyancy (cooling of the surface due to evaporation and effective net radiation enhances mixing; heating of the surface due to strong insolation is only in rare cases strong enough to produce stable stratification and inhibit mixing) but certainly ocean currents contribute to vertical mixing. The ultimate deposition of materials to the ocean floor depends, ofcourse, on mixing past the thermocline and in the deep ocean, about which the authors have limited knowledge. Gas exchange

across

the air-sea

interface

Some aspects of the exchange processes requiring further investigation to strengthen the prediction capabilities for gas transfer will be mentioned in this subsection. Earlier, in Equations (53) and (56), the exchange flux was written in terms of an overall transfer velocity expressed on a gas (k,) or liquid (K,) phase concentration basis, with K, = %‘k,. In turn, the overall transfer velocity is 1 _=‘+Z k,

k,

a*k,

(78)

where the first term represents the resistance presented by the gas phase rp = k; ’ and the second term, the resistance from the liquid phase, r,. In (78), a+ is an effective enhancement of the gas solubility coefficient caused by chemical reactivity. In this subsection, current research and research needs to determine re and r, will be discussed. It is of course true that measurements of gas transfer will yield only the total resistance, k,-’ or K;‘. However, in common with the evaporation/condensation of any appreciably pure liquid, the aqueous phase resistance should be negligible for water molecules crossing the air-sea interface; i.e. r, = 0 (Whitney and Vivian, 1949). Consequently, by measuring the exchange of water molecules, along with the transfer of other gases, it is possible to divide the overall re-

sistance to exchange into its gas and liquid phase components. A mean value for k, for Hz0 over the oceans is approx 3000 cm h-i or 0.8 cm s- 1(Schooley, 1969). Direct measurements using the radon deficiency method (Broecker, 1965) together with results from studies of natural and bomb produced ‘*CO2 (Broecker and Peng, 1974) yield a value for K, of about 20 cm h - ’ ; as will be seen later, these results essentially yield k, N 20cm h-l. For gases which are chemically reactive in water, a* will be greater than one and the liquid phase transfer velocity higher than for a gas which is inert in the aqueous phase. Exchange enhancement has been observed in the laboratory for COz and SOI (Hoover and Berkshire, 1969; Liss, 1973; Brimblecombe and Spedding, 1972; Slater, 1974). and a number of equations proposed which are reasonably successful in accounting for the magnitude of the effect (Hoover and Berkshire, 1969; Quinn and Otto, 1971; Emerson, 1975). The equations predict that under typical marine conditions the value of a* for CO2 is very close to unity (1.02-1.03) so that exchange enhancement due to chemical reactivity is only a few percent. In contrast, under similar conditions, values of a* for SOr can be several thousand, which means that chemical reaction greatly increases the rate of exchange for this gas. The very large difference between a* for CO, vs SOz arises because therateofhydration for SO1 (3.4 x IO6 s-i) is about 10’ times faster than the hydration rate for CO, (3 x lo-zs-1). Using the values fork, and K, given above, together with data for X and calculated values for a*, Equation (78) can be used to split the overall resistance to transfer for any gas into its gas and liquid phase components. It is found that for gases of low solubility which are chemically unreactive in seawater (a* z l.O), then r, >> rl (e.g. N,, O,, CO,, CH.+, NrO, noble gases). In the case of gases of high solubility and/or rapid aqueous phase chemistry rs >> r, (e.g. H20, S02, Nor, NHJ, HCI, HF). These transfer velocities are average values for the whole ocean surface. They are satisfactory for calculating overall gas fluxes and have been used, along with average values for air-sea concentration differences, to obtain fluxes of the following gases across the sea surface: SO,, N,O, CO, CH,, CCL,, CCI,F, MeI, (Me)rS (Liss and Slater, 1974). In order to refine these flux calculations it is necessary to have a better knowledge of the concentrations of the gases of interest in seawater and in the marine atmosphere as well as more accurate values for the gas and liquid phase transfer velocities. Since many of the gases of interest occur at very low levels (down to 1 part in 10” by volume) their determination in seawater and marine air must be carried out with great care. The reliability and small number of measurements of the air-sea concentration differences are probably the most important factors presently limiting the accuracy of these calculations. However, for quite a number of gases, the methodology for

Aspects of the transfer of atmospheric trace constituents making such measurements is available so that there is no major technological barrier to obtaining concentration data on whatever temporal and spatial sampling grid is required. In order to obtain better values for k, a considerable amount of micromet~rological knowledge is available although, as discussed in the previous subsections, further research is required. M~crometeorological techniques for the measurement of water vapor fluxes, such as eddy correlation and the profile method, may be applicable to the direct determination of fluxes of other gases whose air-water exchange is under gas phase control. However, profile methods cannot be used to find the flux of gases for which the principal resistance to transfer is in the water phase. For these gases most of the concentration change will take place across the larger resistance, so that vertical gradients in the air will be very small. When it comes to estimating values for the liquid phase transfer velocity very few in situ techniques are available. The radon deficiency method (Broecker, 1965) which involves measurement of the decrease in the Rn2**/RazZ6 ratio in near surface waters due to loss of Rn to the atmosphere, is presently the most useful. AIthough the method gives an overall transfer velocity, viz., K,, see (56) nevertheless, since for Rn r, >>rs, then the values obtained will, for all practical purposes, be equal to the transfer velocity of the liquid phase (k,). In contrast to k,, which from both theoretical (Hicks and Liss, 1976) and experimental studies (Liss, 1973) increases linearly with wind velocity, laboratory wind tunnel experiments indicate that k, increases approx as the square of the wind speed (Downing and Truesdale, 1955; Kanwisher, 1963; Liss, 1973). Although some recent results (Broecker, personal communication), obtained using the radon deficiency method on the GEOSECS cruises in the Atlantic, do show an increase in k, with wind speed, the rate of increase is considerably less than that expected from the laboratory studies. This discrepancy may be because in the laboratory tunnel a full wave field is unable to build up due to the very limited fetch. Alternatively, it has been suggested (Quinn and Otto, I971) that the square law relationship found in the laboratory may not be a direct result of wind stress. Instead the effect of wind may be to increase the rate of evaporation of water molecules; the resultant evaporative cooling of the surface water leading to convective mixing in the liquid near the interface. If such an effect is important in promoting gas exchange, then in the environment, it will depend on many processes other than wind velocity (e.g. air-water temperature difference, humidity). This could explain why laboratory results are apparently poor predictors of gas exchange rates at sea. Various models have been developed which potentially allow k, to be calculated indirectly, such as the simple result used earlier in this paper (cf. Fig. 8). More complicated models are the surface renewal model of

2079

Higbie (1935) and later developments of it (Danckwerts, 1951; Munnich, 1963). In these, the liquid near the interface is replaced intermittently by fluid from the bulk. Another class of models are those in which the surface water is described in terms of a regular system of eddies whose size is determined by the scale length of the turbulence in the underlying fluid (Fortescue and Pearson, 1967; Lamont and Scott, 1970). The main difficulty in applying all these models to environmental air-water interfaces, and especially the sea surface, is in specifying the necessary input parameters, e.g. the residence time of elements of fluid at the interface in the surface renewal models and the scale length and rate of turbulent dissipation of energy in the eddy models. In order to gain a better understanding of k, for calculating gas exchange rates across the air-sea interface the following experiments are of prime importance : (a) Detailed, precise measurements of k, using the radon deficiency method in order to establish the relationship between the liquid phase transfer velocity and meteorological parameters, such as wind speed. These measurements are probably best carried out from a weathership and determination of the concentration of various gases in surface seawater and marine air should be performed at the same time. (b) Careful laboratory wind tunnel experiments should becarried out in order to identify the important factors controlling liquid phase exchange m~hanisms for gas transfer (eva~rationl~onden~tion. waves, spray, bubbles, wind, surface films, etc.). Another, but possibly less important problem connected with gas transfer across the air-sea interface is whether values for the Henry’s law constant determined at relatively high partial pressure in the gas phase (often one atmosphere of pure gas) are approp riate in environmental situations. There is some evidence for carbon monoxide (Meadows and Spedding, 1974) that this is not the case and laboratory determinations of X at environmental concentrations should be carried out for gases whose air-sea exchange is important. Particle dry deposition

to the oceans

Our knowledge of particle dry deposition to the oceans is severely restricted both experimentally and theoretically. Essentially the only relevant data available for deposition velocities as a function of particle size were shown in Fig. 9 and this data was obtained from wind tunnel studies (Sehmel and Sutter, 1974; Moller and Schumann, 1970). Under some conditions wind tunnel data is valuable, especially if the controlling resistance is in the deposition layer next to the surface; however, extrapolations from wind tunnel data to estimates of the fluxes to the oceans must be suspect if, as was the case for the data of Fig. 9, the state of the sea surface (including waves and spray) is not adequately duplicated, On the other hand, although some recent modeling studies are beginning to de-

2080

W. G. N. SLINN

monstrate understanding of particle dry deposition to rigid surfaces (Caporaloni et ol., 1975; Slinn, 1976b, d) it appears that no one has yet successfully modeled the intricacies of particle dry deposition to the oceans. Thus, much future research is required both experimentally and theoretically; current research in both dry deposition and resuspension is well summarized in the recent conference proceedings edited by Engelmann and Sehmel (1976). From Fig. 8 and from the recent studies of Sehmel and Hodgson (1976) it does appear that the dominant resistance to particle dry deposition should occur in the last centimeter or so above the air-sea interface. For the case of dry deposition to rigid surfaces, Sehmei and Hodgson’s calculations indicate that the resistance in this lowest layer is up to 3 orders of magnitude larger (for 0.1 pm particles) than the resistance in the layer from 1 cm to lOcm, almost regardless ofatmospheric stability. A similar result can be deduced from Fig. 8. Since the corresponding airborne concentrations of particles varies little above about 1 m, it would b-e convenient to report experimental deposition velocities as the ratio of the surface flux divided by the concentration at a 1 m or a 10m reference height. Some inferences about mass-average dry deposition velocities from radionuclide measurements are available but are not entirely satisfactory. Young and Silker’s (1974) deposition velocities to the ocean of 0.7 to 2.2cm s- ’ for ‘Be (presumably attached to maritime aerosol particles) may have been influenced by precipitation scavenging. Van der Hoven’s (1968) review of the deposition velocities for various radionuclides to water surfaces are specific neither with respect to particle size nor details of the water surface. Results reported are 3s follows: 13’Cs, 0.9cms-‘; ‘03Ru, 2.3cm s-l ; 9sZr and 95Nb, 5.7 cm s- l, which are all substantially larger than corresponding values given for soil, grass, or sticky paper. Particle deposition to the ocean would be expected to increase with increasing wave height. This inference is made from Sehmel and Hodgson’s (1976)correlation of wind tunnel data on the increase in deposition to solid surfaces 3s the roughness length increases. Figure 10 shows the results of this correlation, for I(+= 30cm S - 1 and a 1 m reference height. However, it must be reemphasized that the roughness height z. is not related simply to the wave height (cf. earlier remarks or, e.g. see Businger, 1972; Giflord, 1976). Any theoretical model of particle dry deposition to the oceans must include the effect of turbulence and surface roughness, and probably should account for influences on particle motion from water vapor condensation and evaporation, particle growth by water vapor condensation, the induced motion of the sea surface, and particle capture by spray drops. To illustrate, in particular, the potential influence of water vapor evaporation from the sea surface, consider an evaporating surface of water which remains at z = 0 in

er al.

the x-y plane; the restriction that the water plane remains at z = 0 bypasses difficulties associated with the motion of the water surface. Further, consider a fixed control volume, say of base area 1 cm’ and height extending from z = - 1 to z = + 1 cm, and let the water vapor mass flux through this control volume be ri16 (positive for evaporation, negative for condensation). With this water vapor flux there can, of course, be identified a drift velocity of rhe wafer molecules, ti;‘/p, where pv is the water vapor density. With this directed motion of water molecules it can be expected that a drag force will act on the air molecules and on any particles within the control volume. The motion of the air molecules is not of much interest because after 3 short time (with characteristic velocity approximately the speed of sound) 3 density gradient of the air molecules will be established. The result will be compensating fluxes of air molecules (one flux dragged with the vapor; the opposite flux diffusing down the air’s density gradient) with the total pressure (from the air plus the water vapor) 3 constant. However, there will be 3 net flux of particles caused by the diffusion of the water vapor (Vittori and Prodi, 1967). This is known 3s Stefan flow or diffusiophoretic flux (“phoresis” = force). To determine the resulting velocity of the particles it is noted first that the directed velocity ti&‘/p,is not the velocity of the whole fluid, but only of the water molecules. After the density gradient in the air is established, the net velocity of the air molecules is zero. Consequently the velocity of the

10

k ’ I”‘l’%STABLE

/ N”t”;

ATMOSPHRI

WITH

lo-3

lV1 PARTICLE

1 DIANYlER.

10 urn

Fig. 10. Correlation of experimental data by Sehmel and Hodgson (1976) for dry deposition of particles to various solid surfaces.The data encompassed roughness heights only up to about 0.1 cm and therefore the extrapolation to greater roughness heights is tentative. The deposition velocity plotted is the flux divided by the extrapolated concentration at 1 m; v, is the gravitational settling speed for particles of indicated density;thecasewithu, = 3Ocms-‘isshown(ilOms-‘); cases with other friction velocities can be found in the referenced publication.

Aspects

fluid and, it is assumed, the velocity of any particles imbedded in the fluid, is the weighted mean of the two velocities, The resulting drift (or Stefan) velocity of the particles is

L’,=

0.A + (KlP”).P” P” + P”

2081

of the transkr of atmospheric trace constituents

h E - P,

(79)

where the approximation to ignore pV is acceptable since for cases of interest, p, <
tially completely terminate the dry deposition of some small particles. There are many other simultaneous processes which complicate the above simple picture. One factor is thermophoresis: the directed motion of a particle in the direction ofany heat flux. On the one hand, it might be argued that if the evaporation flux were rh’;over a synoptic scale region of the ocean, then after the tem~rature of the sea surface had dropped substantially, a significant portion of the latent heat required for evaporation would be supplied by the atmosphere. The result would be a thermophoretic drift of the particles in the direction opposite to the diffusiophoretic drift which, at least for submicron particles and the case of all latent heat supplied by the atmosphere, can overwhelm diffusiophoresis (Slinn and Hales, 1973). On the other hand, though, it is probably necessary to consider the microscale aspects

of the evaporation process, wherein individual “eddies” sporadically are in contact with the surface, evaporation imagined lo be intense only in some of these eddies, and the corresponding required heat for evaporation conducted from nearby regions of water which, in turn, may receive heat with a less intense flux from a larger, neighboring region of the ocean and ultimately from solar radiation. To this picture must be added the turbulent impulses to the particles which carry them across the viscous dominated region of the atmosphere (Caporaloni er nf., 1975 ; Slinn, 197639)and a consideration of where in the “eddies” these impulsive forces act on the particles compared with where diffusiophoresis and thermophoresis act. To explore these concepts, measurements of particle deposition to wet surfaces should be accompanied by temperature and humidity profiles, roughness parameters, and heat and moisture fluxes, as well as the usual turbulence characterizations. Models such as these must be explored if an understanding of particle deposition to the sea surface is to be developed, and if the discussion above has been incomplete and unsatisfactory, this, in itself, is a good indication of our present knowledge. In spite of this, considerable information can be derived from measurements of the existing aerosol particles in the near surface level, above the oceans. During the last few years, several thousand such observations have been made from islands, oceanographic ships and merchant ships of opportunity. Figure 11 shows the resulting geographic distribution of mean, total aerosol concentrations. It can be seen (Hogan, 1976a) that the concentration isopleths gen-

60

0

Ml

60

40

20 0 20

40 MEAN DATA,

I NAND

60

MARITIME CONCENTRATION 1966-1974

BRACKETED h+EDIAN

Fig.

11.

Geographic distribution of surface-level condensation nuclei t 9x3).

measured

AEROSO -)5 in cm I OFAVAI LABlf

AND WEATHER iXXX b VALUES

over

SHIP

BRACED

the

oceans

VALUES [XXX]

(Hogan,

W. G. N. SIJNN et al.

2082

erally mimic dominant meteorological regimes : cloudy areas such as the Icelandic low have relatively low mean concentrations; high pressure regions have high concentrations. Continental tongues of higher concentration are found in some monsoons1 areas, but in general the continental to maritime aerosol transition is quite rapid, as off the coast of North America. It should however be noted that these data are for total aerosol number densities, part of whose “removal” is probably caused by interparticle coagulation. There are indications that the rates of concentration changes for pollution aerosoi particles of size near 0.1 pm is not nearly so rapid as the case illustrated in Fig. 11 (Kojima and Sekikawa, 1974; Kojima et al., 1974; Misaki et al., 1975 ; Hogan, 1976b). However these conclusions, too, must beconsidered as tentative until complete evaluation is made of the contributions to the particle concentrations from air which has overridden the air adjacent to the sea surface. From the presentations in this subsection presumably it is clear that much is unknown, both from the experimental and theoretical viewpoints, about particle dry deposition to the oceans. Tracer studies of particle de~sition to the oceans or to lakes could be very productive; both Eulerian (or grid) and “Lagrangian” (or air mass) studies should be considered. In lieu of ocean measurements, further research would be useful in wind tunnels and new studies over large Ponds could yield valuable data, especially if wave generation could be controlled and the resulting variations in deposition velocity studied. Much can also be learned from measurements of the existing maritime aerosol, especially if measurements were made, for example, following the evolution of both gases and particles as a polluted air mass propagated out from a continent, over an ocean. More effort should also be devoted to model development and to investigating the validity of extrapolations from laboratory results to predictions about behavior in the ocean environment.

The wet flux can be estimated to be W = rp&

w

with the washout ratios as given in Tables 4 and 5. For scavenging of gases which form simple solutions in rain water, then r = a; reactive pollutant gases are probably converted to their reaction products before being scavenged ; the washout ratios for particles is as given in (29) using the removal rates in (23) or (24). From these relations and from the definitions of the average height from which ~llution is removed by dry processes, as in (1 l), then reservoir residence times of a pollutant can be estimated. For dry deposition from a layer of height & and with a deposition velocity $, the residence time is fd = iidk,

(83)

The rain scavenging contribution is as in (35); e.g.

to the residence time

fW = i&&z

(84)

To obtain these results, use has been made ofsimplifications which would be inappropriate for use near a specific pollutant source. If, in ad~tion to wet and dry cleansing processes, other chemicaf or physical processes contribute to a pollutant’s removal from the atmosphere then the residence time is given by

(85)

in words, the separate removal paths are like resistances in parallel. As an example of the use of (85), if for aerosol particles t,, = 10d, T, z IOd, and other processes (e.g. interparticle coagulation) proceed at a negiigibly slow rate (TV+ 5) then (85) gives f r 5 d. At a number of places in this report the potential importance of other removal processes has appeared but their details have been ignored. Examples include the oxidation of SO2 to SO:-, the coagulation of Aitken nuclei, and the attachment of radionuclides, pesticides, and other vapors to aerosol particles with their subsequent removal by precipitation. All these subject areas require further investigation; recently CONCLUDING REMARKS Junge (1975) discussed the attachment of some pesThe purposes of this paper have been to de- ticides and PCB’s to aerosols but much remains yet to monstrate some of the knowns and unknowns about be done. In the case of low mol. wt halogenated the wet and dry fluxes of atmospheric trace conhydrocarbons it may be that the only important stituents past the air-sea interface. Under the re- “removal” mechanism is by their (photo-) chemical strictions which have been discussed, the knowns can destruction in the atmosphere. It is therefore to be be summarized as follows. The dry flux for gases can be emphasized that the focus in this paper on wet and dry estimated as removal processes reflects more the authors’ purposeful restriction on the scope of the paper rather than 9 = k(& - X”c,) (80) their opinions on the relative importance of various with the total transfer velocity given by removal mechanisms. Many unknowns and corresponding needs for fu1 ture work have been identified. Ideally, perhaps, a (81) k, - k, a+k, prioritized list of recommended research topics would with k, and kl roughly as given in Fig. 8. The dry have been presented. Yet, by application of a well deposition of particles can only be qualitatively esti- established principle, to do this would require us to mated, using the deposition velocities shown in Fig. 9. discern the priorities within the overall objective of

_‘+T-

2M)3

Aspects of the transfer of atmospheric trace constituents predicting poilution fluxes to the ocean : priorities for any system can not be established until after the system objectives are established. Consequently, the authors are again aware of their limited capabilities - this time, to discern the relative values of the oceans for shipping, fishing, recreation, oxygen production, climate regulation, etc. We are also aware that man’s anthropocentric view of nature can lead him to the paradoxical conclusion that his polluting the oceans may jeopardize one of the most important ocean resources : as the ultimate sink for much of man’s pollution. TO circumvent these probIems, the authors have presented the recommended research topics generally in the form : if it desired to know... , then...is what presently impedes our understanding. In spite of our plan not to provide a prioritized list of recommended research topics, it may be convenient if we review here some of the unknowns that have been identified and some of the suggested ways to overcome these impediments to understanding wet and dry removal processes. The ordering of these topics generally follows the order the topics have appeared in the text: (i) Inter-reservoir exchange rates for large scale reservoirs are not known to within a factor of at least 2 or 3. Thorough measurements of concentrations and fallouts of various radionuclides could reduce this uncertainty. (ii) Inferences about the behavior of aerosol particles from the measured fallout of radionuclides rely on incomplete knowledge of the aerosol particles to which the radionuclides are attached. Obvious remedies suggest themselves. (iii) It is not known how dry deposition of aerosol particles to mechanical collectors is related to dry deposition to natural cohectors. Ifcontrolled (e.g. wind tunnel) studies could resolve this question then a wealth of dry deposition data could be immediately available. (iv) Information about precipitation is lacking. Desired information includes storm heights, frequency of storm occurrences, storm duration and precipitation, and cloud water removal efficiencies. (v) Much could be learned about scavenging efficiencies and modification of substances within clouds by performing budget studies for progressively more complex non-precipitating and precipitating clouds and storms. (vi) Much is unknot about the air-sea interface and these uncertainties are detrimental to our understanding of dry deposition and resuspension of particles and gases. Concerted scientific studies on the turbulence above and below the interface, wave mixing, the physics of wave breaking, gas and particle entrainment, particle resuspension, and thermally driven circulations above the thermocline would be welcome. (vii) For many gases the dominant resistance to transfer occurs in the Iiquid phase and probably in the viscous subiayer. Wind tunnel studies could help

establish the importance of evaporation sation, waves, spray, bubbles,

and conden-

wind speed and surface

films; the radon deficiency method holds most promise for determining the liquid phase resistance in the ocean. (viii) Particle dry deposition and resuspension are probably the most glaringly deficient aspects of our knowledge of pollutant transfer to the ocean: the deposition velocity for 0.1 pm particles is expected to be somewhere between IO-’ and 1O’cm s-‘! TO remove the uncertainties, studies on all fronts are r~ommended, controlled wind tunnef studies, theoretical developments, semi~ontro~~ed deposition to ponds and lakes, and budget studies using both grid (Eulerian) and air-mass ~Lagrangian”) frames over the open oceans. Acknowledgements - The authors wish to express their appreciation for the stimulating involvement of J. M. Prospero, suggestions for improvements to an earlier draft by E. F. Danielsen, Permissions to use quoted results from P. A. Cawse, M. T. Dana, D. F. Gatz and C. E. Junge, patient application of secretaria skills by R. G. Ellis, and the amiable contributions from I. C. Usage. Fiaanciai support was obtained &rough the U.S. National Academy of Sciences and the authors’ respective organixations and research contractors. Special acknowledgement of financial support to the senior author is due Batteile Memorial Institute, grant B-38?402, and the Energy Research and Development Administration, contract E(45-1).1830 and EY-76-S-2227 ‘IA 27.

REFERENCES Adam J. R. and Semonin R. G. (1970) Collection efficiency of raindrops for submicron particulates. Ibid., Engeimann and Slinn (1970). Beadle R. W. and Semonin R. G. ft976) f~eci~frat~~ Scu~~j~ - 1974. Proceedinp of a scrip held at Champagne, IL, 14-18 October 1974; ERDA Symposium Series; to be available as CONF-741014 from NTIS, Springfield, VA. Bowen V. T. and Sugihara T. T. (1960) Strontiumgo in the “mixed-layer” of the Atlantic Ocean. Nature l&I, 71-72. Brimblecombe P. and Spedding D. J. (1972) Rate of solution of gaseous sulphur dioxide at atmospheric concentrations. Nature 236, 225-229. Brock J. R. (1970) Attachment of trace substances on atmospheric aerosols. Ibid., Engelmann and Slimt (1970) Brocks K. and Kriigermeycr L. (1972) The hydrodynamic roughness of the sea surface.Stud. pkys. Oceumgr. 1,75-92. Broecker W. S. (1965) An application of natural radon to problems in ocean circulation. In Symp. on df@i&on fn oceans and fresh waters, (Edited by Icbiye T.) 116-145, Columbia University, NY. Broecker W. S. and Peng T. H. (1974) Gas exchange rates between air and sea. Tellus 26,21-35. Broecker W. S. (1976) Personal communication. Browning K. A. and Foote G. B. (1976) Airflow and bail growth in superccil storms and some implications for hail suppression. Q. II. R. met. Sot. 105499-533. Brutsaert W. (1975) The roughness length for water vanor. sensible heat, and other- scalars. J. armos. Sci. ‘3% 2028-203 1. Businger J. A. (1972) Turbulent transfer in the atmospheric surface layer. Workshop ori micrometeorology, August 14-18, 1972, American Met. Sot., Boston, MA. Calder K. L. (1961) Atmospheric diffusion of particulate

2084

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Aspects of the transfer of atmospheric trace constituents phys. Inst., Johannes Gutenberg Univcrsitiit, Contract DA-91-591.EVC 2979, available from NTIS, Springfield, VA.

Junge C. E. (1975) Basic considerations about trace constituents in the atmosphere as related to the fate of global pollutants. Prof. ACS Symposium on the Fate of Pollutants in the Air and Water Environment; to be published in Advances in Environmental Science and Technology, Wiley-Interscience. Kanwisber J. (1963) On the exchange of gases between the atmosphere and the sea. Deep-Sea Res. 10, 195-207. Kerker M., Hampl V., Cooke D. D. and Matijevic E. (1974) Scavenging of aerosol particles by a falling water droplet. J. atmos. Sci. 28, 1211-1221. Kitaigorodskii S. A. (1970) The Physics of Air-Sea Interaction. Translated from Russian and published by Israel Program for Scientific Translations, Ltd., Jerusalem ; available as TT72-50062 from NTIS, Springfield, VA. Kojima H. and Sekikawa T. (1974) Some characteristics of background aerosols over the Pacific Ocean. J. met. Sot., .lap. 52,499-504. Kojima H., Sekikawa T. and Tanaka F. (1974) On the volatility of large particles in the urban and oceanic atmosphere. J. met.Sot.,Jap. 52, 90-92. Lal D. and Rama (1966) Characteristics of global tropospheric mixing based on man-made CL4, H3, and Sr9’. J. geophys. Res. 71,2865-2874. La1 D., Nijampurkar V. N., Rajagopalan G. and Somayajulu B. L. K. (1976) Observations of fallout of natural radioisotopes at tropical latitudes (in preparation). Lamont J. C. and Scott D. S. (1970) An eddv cell model of mass transfer into the surfke of’a turb&t liquid. Am. Inst. them. Engng J. 16, 513-519. Lassen et al. (1960,1%1) For an English language review of this work, see Junge (1963). Liss P. S. (1973) Processes of gas exchange across an air-water interface. Deep-Sea Res. 26, 221-238. Liss P. S. (1975) Chemistry of the sea surface microlayer. In Chemical Oceanography, (Edited by Riley J. P. and Skirrow G.) Vol. 2, pp. 193-243. Academic Press, New York. Liss P. S. (1976) Effect of surface films on gas exchange across the air-sea interface. ICES Rapp. Prti Verb. (in press). Liss P. S. and Slater P. G. (1974) Flux of gases across the air-sea interface. Nature 247, 181-184. Martell E. A. and Moore H. E. (1974) Tropospheric aerosol residence times: a critical review. J. R&s. atmos. III, 903-910. Manvitz J. D. (1972) Precipitation efficiency of thunderstorms on the High Plains. Preprints 3rd conf. weath. modification, Rapid City, S.D. Available from the American Meteorological Society, Boston, Mass., 245-247. McAlister E. D., McLeish W. and Dorduan E. A. (1971) Airborne measurements of the total heat flux from the sea during BOMEX. J. geophys. Res. 76,4172-4180. Meadows R. W. and Spedding D. J. (1974) The solubility of very low concentrations of carbon monoxide in aqueous solutions. Tellus 26, 143-150. Misaki M., Ikegami M. and Kanazawa I. (1975) Deformation of the size distribution of aerosol particles dispersing from land to ocean. J. me?. Sot., Jap. 53, 11I- 120. Miiller U. and Shumann G. (1970) Mechanisms of transport from the atmosphere to the earth’s surface. J. geophys. Res. 75, 3013-3019. Munnich K. 0. (1963) Der Kreislauf des Radiokohlenstoffs in der Natur. Na&rwissenschfien 50, 211-218. Munnich K. 0. (1971) Atmosphere-ocean relationships in global environmental pollution. Special Envr. Rept. No. 2, Meteorology as Related to the Human Environment, WMO-No. 312; available from the Secretariat of the World Meteorological Organization, Geneva. Owen P. R. and Thomson W. R. (1963) Heat transfer across rough surfaces. J. Fluid Mech. 15, 321-334. Peinon D. H., Cawse P. A. and Cambray R. S. (1974)

2085

Chemical uniformity of airborne particulate material, and a maritime effect. Notwe 251,675-679. Postma A. K. (1970) E&t of solubilities of gases on their scavenging by raindrops. Ibid., Engelmann and Slinn (1970). Quinn J. A. and Otto N. C. (1971) Carbon dioxide exchange at the air-sea interface: Flux augmentation by chemical reaction. J. geophys. Res. 76, 1539-1549. Roth R. (1975) Der vertikale Transport van Luftbeimengungen in der Prandtl-Schicht und die DepositionVelocity. Meteorol. Rdsch. 28, 65-71. Schumann G. (1975) The process of direct deposition of aerosols at the sea surface (preprint). Schooley A. H. (1969) Evaporation in the laboratory and at sea. .I. marit. Res. 27, 335-338. Sehmel G. A. (1973) Particle eddy dii&ivitities and deposition velocities for isothermal flow over smooth surfaces. J. Aerosol Sci. 4, 125-133. Sehmel G. A. and Sutter S. L. (1974) Particle deposition rates on a water surface as a function of particle diameter and air velocity. J. Rechs atmos. III, 911-918. Sehmel G. A. and Hodgson W. H. (1976) Particle dry deposition velocities. Ibid.. Engelmann and Sehmel(l976). Shemdin 0. H. and Lai R. J. (1970) Laboratory Investigation of Wave-Induced Motion Above the Air-Sea Interface. Dept. of Coastal and Oceanogr. Engr., U. of Florida Tech. Rept. 6, 87 pp. Shepherd J. G. (1974) Measurements of the direct deposition of sulphur dioxide onto grass and water by the profile method. Atmospheric Environment 8, 69-74. Sheriff N. and Gumley P. (1966) Heat transfer and friction properties of surfaces with discrete roughnesses. Znt. J. Heat Mass Transfer 9, 1297-1319. Slater P. G. (1974) The exchange ofgases across an air-water interface. Thesis, University of East Anglia, 205 pp. Slinn W. G. N. (1976a) Formulation and a solution of the diffusion, deposition, resuspension problem. Atmospheric Environment 10, 763-768. Slinn W. G. N. (1979) Some approximations for the wet and dry removal of particles and gases from the atmosphere. .Z. Air Wat. Soil Pollut. 7, 513-543. Slinn W. G. N. (1976~) Precipitation scavenging: some problems, approximate solutions, and suggestions for future research. Ibid., Beadle and Semonin (1976). Slirm W. G. N. (1976d) Dry deposition and resuspension of aerosol particles - a new look at some old problems. Ibid., Engelmann and Sehmel (1976). Stinn W. G. N. and Hales J. M. (1973) A reevaluation of the role of thermophoresis as a mechanism of in- and belowcloud scavenging. J. atmos. Sci. 28, 1465-1471. Snyder R. L. (1974) A field study of wave-induced pressure fluctuations above surface gravity waves, J. Marine Res. 32.497-531.

Sood S. K. and Jackson M. R. (1972) &avenging Study of Snow and Ice Crystals. Repts. IITRE C6105-9, 1969, and 1lTR1 C6105-18, 1972, ITT Research Institute, Chicago, IL. Starr J. R. and Mason B. J. (1966) The capture of airborne particles by water drops and simulated snow crystals. Q. JI R. met. Sot. 92,490-497. Stavitskaya A. V. (1972) Capture of water-aerosol drops by flat obstacles in the form of star shaped crystals. Zzv., Akad. Nauk. Atmos. Oceanic Phys. 8, 768-774.

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W. G. N. S~INNer al.

2086

Voichok H. L., Bowen V. T., Folsom T. R., Broecker W. S.. Schuert E. A. and Bien G. S. (1971) Oceanic distribution of radionuclides from nuclear explosions. Radioclctiriry in rhe Marine Enoironment, U.S. National Academy of Sciences, Washington, D.C. Volchok H. L. (1974) Is there excess SRPO fallout in the oceans? U.S. Health and Safety Laboratory, Rept. No. HASL-286, Vol. I, 82-88. Waldmann L. and Schmitt K. H. (1966) Thermophoresis and diffusiophoresis of aerosols. Aerosol Science, (Edited by Davies C. N.), pp. 137-162. Academic Press, New York. Whitney R. P. and Vivian J. E. (1949) Absorption of sulfur dioxide in water. Chem. Engr. Prog. 45, 323-337. Yaglom A. M. and Kader B. A. f 1974) Heat and mass transfer between a rougb wall and turbulent fluid flow at high Reynolds and Peclet numbers. J. fluid Mech. 62,601-623. Young J. A. and Silker W. B. (1974) The determination of air-sea exchange and oceanic mixing rates using ‘Be during BOMEX. J. geophps. Res. 79,4481-4493. Zimin A. G. (1964) Mechanisms of capture and precipitation of atmospheric contaminants by clouds and precipitation. Probiems of Nuclear ~eteo?oi~~ (Edited by Karol 1. L. and Malakov S. G.), trans. of “Voprosy Yader Meteorologii,” State Pub. House for Lit. in the Field of Atomic Science and Engr., pp. 139-182. USAEC Rept. AEC-tr6128, available from NTIS, Springfield, VA.

APPENDIX A The following is a list ofsymbols used frequently in the text, their dimensions and, in case of multiple use of a single symbol, the equation numbers in which the symbol appears. u= A= c= c0 = C= = C, = d=

particle radius, L hydrometeor cross-sectional area, L” empirical constant z 0.5, Equation (23) peak phase velocity of gravity waves, LT- t pollutant concentration in ocean, units L-” parameter defined in Fig. 6, dimensionless drag coefficient, dimensionless pollutant drift (or slip) vehxity. LT- ’ D = coefficient of Brownian or molecular diffusivity, LZT_’ D, = total rate of destruction within reservoir i, units T-l D = magnitude of .the dry deposition flux, units L-“T-l

E = collection efficiency of particies by drops 8 = collaction efficiencv of narticles bv ice crvstals F = diffusive flux, units L-*T- t s ’ F, = flow from reservoir i, units T- * g = acceleration of gravity, LT-’ G = source (or gain) term, units L-‘T-t hd = height from which the poliutant is removed by dry deposition at rate k,, L h, = effective height from which the pollutant is removed by wet processes, L Xc = Henry’s law constant, X/K or dC, dimensionless Ii = inflow of pollutant to reservoir i, units T-t -I,, = rate of inflow to reservoir i from reservoir j, T- ’ k = exchange rate or conductance., LT-’ h: = exchange rate in terms of liquid phase concentrations Jl”k, LT-t IK = turbulent or eddy dilfusivity, L’T-t 1y, = z-component of turbulent dilTusivity, L’T”‘t x = von Karman’s constant LI:0.4 L = sink (or loss) term, units L-‘T-t, Equation (1) L = liquid or solid water content in cloud, ML-‘, -. tquatton (Zg)

I = hydrometeor size parameter /,, = rate of outflow from reservoir i to reservoir j, T- ’ r$t = water vapor mass flux, ML-‘T-’ N = hydrometeor number density function 0, = outflow of pollutant from reservoir i, units T-i p = precipitation rate, LT-* or volume flux of precipitation, L3LezT-’ P = total precipitation during time ‘I, L Pe = Peclet number = Re SC. dimenstonless P, = total rate of production within reservoir i, units T-’ q = total amount of tracer still present in the atmosphere, units pi = quantity of pollutant in reservoir i, units r = washout ratio, (IC/& dimensionless, Equation (29) r = resistance = k- ‘, TL-t, Equation (42) R = drop radius, L Re = Reynolds number. dimensionless S = Stokes number, defined in Fig. 6, dimensionless S, = critical Stokes number, Fig. 6 SC = v/D, Schmidt number, dimensionless T = total time removal processes are acting, T ti = mean wind speed, LT- ’ a* = friction velocity, LT-’ I’ = ~,,./~~= ratio of dynamic viscosities, dimensionless, Fig. 6 v = fluid velocity, LT- ’ r,, = deposition velocity, LT- ’ rg = gravitational settling speed, LT- t t; = resuspension velocity, LT-’ 1; = magnitude of other slip velocities, e.g. Stefan velocity, LT- ’ W = magnitude of the wet flux. units L-zT-t z = vertical coordinate, L z0 = roughness height, L a = .#- ‘, soIubility coellicient, ~rn~ion~ a* = effective solubility coefficient, accounting for irreversible reactions, dimensionless /I = first-order reaction rate constant, T- * 6 = thickness of atmospheric or oceanic layers E = fractional amount of pollutant removed by a storm h’ = pollutant concentration in precipitation, units L-j, Equation (29) L = u/R, interception parameter, dimensionless, Fig. 6 i. = decay rate for a particular radionuclide, T-i A = average gas transfer rate to drops, T- 1 p = mass density, MLs3 n = r.m.s. wave height, L 7 = pollutant residence time, T, Equation (8) r = particle stopping time, T. Fig. 6 r., = residence time if only dry removal processes are acting, T '1,= lifetime, residence time, or turnover time of pollutant in reservoir i, T rr * residence time if only wet removal processes are acting, T Y= frequency with which pollutant encounters a pr~ipitating storm, T-t, Equation (IQ) v = kinematic viscosity coefficient, L*T- t, Equation (43) ti = precipitation scavenging rate coefficient, T-t x = pollutant concentration in air, units L-’ x1 = near-surface air concentration for dynamic equilibrium of deposition and resuspension, units L-J Subscripts a = air, atmosphere, aerodynamic A,B,..,l = layer identification h = bulk

2087

Aspects of the transfer of atmospheric trace constituents

solutions for the quantity of pollutant in each reservoir:

cw = cloud water d = dry y = gas phase i = interface, ith reservoir, initial I = liquid phase m = molecular. volume- or mass-mean n = normal o = surface level. ocean r = rain F= surface, snow ss = steady state f = total T = total during time interval T r = vapor w = water, wet z = vertical component

Q, = R,R2R3R,R8 Q2 = - R:R,R,R, Qj = [R$,R,R,

PADet) P/Wet) - R,R,R,R,RB]P/f=t)

Q4 = -R,RS[R,tR& Qs = R,[IR:

- R,R,)

- R:t(R,R,

(8.4) - R~R~R,l~/(De[~

- R,R,I - R,R,R,R,]P/iDW

Q6 = (- WR,)Q,. The fallout from each reservoir is given by (18) with the

removal rates shown in Fig. 3. If these removal rates are varied not only do thefalloutschange, but so also do R,, R, and R,,in accordance with (17). Thus, for example, if the removal rates are decreased by an order of magnitude. then -1

=R;’

(B.5)

1 and similarly for RI and R. r,r = position vector. time < = average i over microscale processes i = average < over large scale meteorological processes (i> = average 5 over height of storm 5’ = the fluctuating component of 5 which has zero microscale average r = sum of j with no sum on i

APPENDIX

For viscous Ilow at high Reynolds num&r past a smooth solid surface, the deceleration of the fluid is given essentially by the viscous drag : A4 “?x

APPENDIX

(

&I ‘c \‘----. w

(C.1)

With the nondim~siona~~tion u = Van’, x = Lx’, and _P = SJ’ where U, is the free-stream velocity, L is the distance along the surface from an arbitrary point, and 6, is the thickness of the viscous sublayer, then for comparable nondimensional derivatives, (Cl) yields

B

In matrix form, the steady-state equations for the reservoir model [cf. Equation (1611with a source only in 30-60’N are

R* R, R, R, 0 R, 0 0 0 0 0 0

C

0

0

0

0

Q,

0

R,

0

0

0

0

R,

RB

0

0

R,

R7

R,

0

0

R,

R,

R3

0

0

Rz

RI )(

Q2 Q, Q4 Q% Q6 )o

=

S, 1 LRe-I”

(C.3)

0 0 P

0

(C.2)

where the Reynolds number is Re = L’,L/v. Further. the convective diffusion equation within the boundary layer is approximately

and if in (C.3) we use u = (r/6,)U,, ,r = &..Y*,x = Lx’, and x = x00x*then for approximate equality of the terms, we obtain the estimate for the thickness of the diffusion layer

@.I)

(C.4)

where. from Equation (17)and Fig 3. the exchange rates are: R;’

= 6.67 (I,

R,’

Upon substituting (C.2) into (C.4) there results

= - ISOd,

R;’

= - ISti,

R;’

= 5.22r1, R,’

= -2SOrl

R;’

= -2Stt.

R;’

=9.33d,

R,’

= -180d.

(B.2) where the Schmidt number, SC = v/D. Finally, this develop ment gives as an estimate for the transfer velocity

The determinant of the coefficients in (B.1) is (net) = (R,R,R- R;(R,R,

- R,RsR, - R,R,)*

- R,R,R,)* (C.6)

(B.3)

and, upon using Cramer’s rule, one finds the following

which is the expression used in Fig. 8.