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Budgets and turn-over times of atmospheric sulfur compounds
4rmorphrri, En~,rrmmm Vol IL PP. 671-6130Pcrgamon Press 1978 Prmted an Great Br~tstn
BUDGETS
AND TURN-OVER TIMES OF ATMOSPHERIC SULFUR COMPOUNDS HENNING
RODHE
Department of Meteorology, University of Stockholm, Arrhenius Laboratory, S-106 91 Stockholm. Sweden* (First received 13 June 1977 and in jinol
firm
20 September 1977)
Al&met-The paper starts by detining the time concepts ‘residence time’ ‘age’ and ‘turn-over time’ and by discussing their inter-relations briefly. Some basic comments about box models as applied to sulfur in the atmosphere are also presented. It is suggested that when using budgets lo estimate overall fluxes the optimum size for such boxes should be about four times the product of the turn-over time and an average transport velocity. A brief review is made of previous estimates of atmospheric sulfur budgets of scales ranging from global down to about 100 km. Particular emphasis is put on the implied turn-over times (i.e. average residence times) for the different sulfur compounds These estimates are compared with estimates of time scales made from observations and experiments and from the use of long range transport models Such comparisons are complicated by possible deviations from exponential residence time distributions which make, for example, rate coeficients estimated for short transport times unrepresentative for the full life cycle of the molecules in the atmosphere. Based on the presently available data an estimate is presented of the overall turn-over times in the midlatitude atmosphere of man-made SO, and SOi- and of the turn-over times with respect to the difierent transformation and removal processes. The estimated overall turn-over times of S02, SOf- and sulfur (SO, + SO:-) in this climate are roughly 25, 80 and 50 h respectively. The turn-over time with respect to the different removal and transformation processes are generally somewhat more uncertain. For SO, the dry deposition. wet deposition and transformation to SOi- correspond to turn-over tirnes of about 60, 100 and 80 h respectively. These tigures would imply that about 30% of the SO1 is transformed to SOi- before being deposited The time scales mentioned here represent average conditions for a particular type of climate and may not be applied directly to specific situations (e.g. seasons) in similar climates or to other climatic zones Most of the sulfur budgets estimates utilized in this study apply to conditions in Europe. A plea is made for similar studies to be undertaken in other parts of the world In North America there may already be enough data available for such studies I. INTRODUCTION
When describing the circulation of chemical compounds in the atmosphere it is essential to have an idea about time scales that characterize the transformation and removal processes. If such time scales are known ad if measurements of the concentration in the air are available, the amounts that are transformed or removed can be estimated In connection with dispersion calculations a knowledge of these time scales will also in principle enable us to calculate the patterns of air concentration and fallout provided the sources and the dispersive characteristics of the atmosphere are known. On the other hand, if, for example, the deposition has been measured, a knowledge of the time scale of deposition will make it possible to infer something about the amounts of this compound in the atmosphere and about a possible build up of the concentrations. There are bicW
two approaches to the problem.
of estimating the time scales of transformation and removal processes One is to study the processes themselves by measurements, either in the atmosphere * Contribution No. 350 from International Meteorological Institute in Stockholm. 671
itself or in a laboratory, or possibly by theoretical calculations The other approach, and the one I shall be mainly concerned with in this paper, is to use budget calculations to estimate the space and time averages of such time scales. The wish to assess man’s impact on the cycle of various compounds is another important reason to attempt to make budget estimates i.e. systematic comparisons of sources, sinks and mean concentrations over reasonably large portions of the atmosphere. Most previous atmospheric sulfur budgets have dealt with global totals of sources and sinks Since at least the man-made sulfur sources are very unevenly distributed ovef the globe and be-cause of the limited residence time of sulfur in the atmosphere (see below) it is obvious that possible ecological impacts of man’s interference with the sulfur cycle most likely are of a local or regional rather than global character. Consequently, it should be more logical to consider budgets of limited regions of he giobe (Granat et af., 197~
The purpose of this paper is to discuss how budget estimates (i.e. systematic comparisons of soufces. sinks and concentrations over reasonably large time and space scales) can be used to estimate the time scales that characterize transformation and removal processes of sulfur compounds in the atmosphere. The
HENNING RODHE
672
first secttons contain a general discussion about different ways of defining time scales and about some fundamental concepts of box models. In the followmg sections various sulfur budget estimates are described and the time-scales obtained are compared with other independent estimates. Finally, an attempt is made to combine the informatton available in an estimate of likely values of the various time scales associated with the circulation of sulfur in polluted regions m midlatitudes.
2. DEFINITIONS
OF TIME SCALES
The terminology used here follows largely the one used by BoIin and Rodhe (1973). Steady store condition is assumed to prevail. 1. Residence time is the time spent by a molecule from the moment of injection into or formation in the atmosphere to the moment of transformation or removal. Transit time could be used as an alternative expression for the same quantity. Particularly in cases when the sources and sinks are situated at the boundary of the reservoir (in this case at the ground) this latter expression may be preferable. Since the residence time (transit time) for individual molecules of a given compound may be quite different it is useful to introduce a frequency function &T) describing the frequency distribution of residence times If we are interested in the fate of a SO2 molecule emitted into the atmosphere we must separate between the residence time of the SO2 molecule itself, fso,, and the residence time of the sulfur atom, TV. A transformation of SO2 to SOi- implies a sink for SO, (and a source for SO:-), but not for the S atom. A sulfur atom that is introduced as SO2 and removed as SOiwill thus have a residence time rs = %oI + rso,. 2. Average residence time, 7,. is the average value of the residence times (transit times) of all molecules: I Tr =
s0
T&T)
dr
This is the quantity, often refered to simply as the ‘residence time’. commonly used to characterize the circulation of a compound in the atmosphere. If the frequency distribution of residence times is approximately exponential such a simple characterization may suffice. In other cases, it may be necessary to add more information about the frequency function such as higher order moments. 3. The age of a molecule in a reservoir is the time since it was introduced. The corresponding frequency function we denote by I&T). The age of a molecule when it leaues the reserooir is equal to the residence time of that molecule. In general, the age and residence time are of course quite different from each other. 4. The average age. 7a, is the average value of the ages of all molecules found in the reservoir at any
one ttme: T’* =
S’
rY'(r)dr.
0
5, may be larger or smaller than T, depending upon the shape of the frequency function (cf: Bolin and Rodhe, 1973). They are equal when the frequency functions have an exponential shape. 5. Turn-over time, To, is the ratio of the total mass of the compound in the reservoir to the total flux out of (or into) it: 7. = M/F. This IS a bulk quantity which contains no explicit information about the shape of &T) or Jl(r) It can be shown (Bolin and Rodhe, 1973) that fO is identical with 7r so that the turn-over time is actually a measure of the average residence time spent by molecules of the compound in the reservoir. The age concept has a natural application in problems involving radioactive material. In the foilowing discussion I will confine myself to the residence ttme concept and the turn-over time. In cases where there are two or more competing sink mechanisms one may also apply the turn-over time concept to an individual sink mechanism. As an example we can think of a pollutant that is removed either by dry or wet deposition (precipitation scavenging). Let Q be the emission rate and D and Wthe rates of dry and wet deposition respectively. If M is the steady state mass of the pollutant in the atmosphere (or in a well defined fraction of the atmosphere) we have 7. = M/(I) + W) = M/Q. The turn-over times with respect to dry and wet deposition separately may now be defined as 7or, = M/D It follows that and row = M/W respectively. l/To = (~/T~J + (l/row). In the special case when the removal process may be described by a first order reaction, the turn-over time with respect to this particular process as defined above is equal to the inverse of the rate coefficient. It is worth noting that whereas dry deposition is a process which is generally continuous in time, the wet removal is only effective during certain periods of time. Therefore the two time scales 7oD and so,,, have a somewhat different character. When discussing the physical interpretation of 7w it may be advantageous to think of it as determined by two distinct processes; (a) the frequency of occurrence of clouds or rain, (b) the scavenging process inside the cloud or the rain. Rodhe and Grandell (1972) showed that quite general conditions one may write TOW =
A+
BI-‘,
under (1)
where A and B are functions that describe the frequency of occurrence of rain and 1 is the scavenging coefficient in the rain. Thus even with very effective scavenging in rain (1-t = 0). row has a finite value (.A) corresponding basically to the time it takes to
673
Atmospheric sutfur compounds experience the first rain. It may be mentioned that in the model used by Rodhe and Grandell(l972) the frequency function of residence times (NT)) is not a simple exponential function. It is therefore not quite appropriate to use the inverse of their turn-over time as a decay constant in a first order reaction.
Before the discussion of the various sulfur budget estimates (see section 4) it may be Useful t0 clarify some basic concepts regarding box models In a box model the spatial distribution of the compound inside the box (reservoir) is not explicitly eonsidered In most cases it is rather assumed that the conditions inside the box are reasonably homogeneous This is in contrast to analytical or numerical dispersion models where the spatial (and possibly temporal) distribution is dealt with explicitly. The advantage with a box model is that it may enable an overall assessment to be made of the time scales involved and of the relative importance of various transformation and removal processes without laborious computations. As is normally done, we shall limit the discussion to steady state situations where sources and sinks balance each other. It is often useful to consider a system of reservoirs rather than a single one. This may be the case when the conditions are spatially non-uniform or when one is interested in the circulation of a compound, between different media. As an example one may take the model of the global sulfur cycle as formulated by, for example, Eriksson (1960) Another situation when a series of reservoirs may be considered is when one is considering the circulation of an element in a medium and the element occurs in the form of different chemical compounds In this case each compound may be taken as a reservoir for the element. As a simple example let us consider anthropogenic sulfur emissions into the atmosphere and let the atmospheric content of SO1 and SO:- be two sulfur reservoirs (Fig 1). In this figure Q is the emission of SO,, C the conversion of SO1 to SOi- and D and W the dry and wet deposition processes. M, and M, are the amounts of sulfur in the forms of SO, and SOirespectively. To simplify the notation we shall drop the subscript ‘0’ for the turn-over time rO.
Q__
C
I
1 4
’
MI + Ml
” = D1 -I- D2 +
M2 I
W, + W, =
The turn-over times for SO, and SOi=
Ml
-
Q
=
MI + Ml Q
’
(2)
are
MI D,+W,+C
It follows that rS =
~SO, + aTso,
(5)
where a = C/Q is the fraction of the sulfur that is converted to sulfate before being deposited when applying a box model to study the sulfur budget of a portion of the atmosphere the choice of an appropriate box size, L, is not a trivial matter. On the one hand, a sulfur budget,for the global or hemispheric. atmosphere entails an averaging over very different conditions: highly polluted industrial areas and more or less clean remote areas Evidently such an average will be representative neither for the polluted regions nor for the clean. On the other hand if too small a box size is chosen the fluxes across the boundaries will be so large that it may be impossible to make any meaningful estimates of the importance of emissions, transformations and removal mechanisms In principle, it is of course possible to keep track of the fluxes across the lateral boundaries of the box, but in practice the estimates of such fluxes may be so uncertain that subsequent deductions are of limited value if the box size is small. For studies of the fate of man-made emissions of a compound like sulfur the optimum box size should be such that the distance from the major source region to the edge of the box is somewhat larger, by a factor 2, say, than the scale of decay of the sulfur in the atmosphere (R = r. x v where v is an average transport velocity). If we let L,,,,, denote the diameter of an appropriately chosen circular box with a point source near the center we then have
I&, 5 4 T*V.
(6)
Since rs is a quantity which may not be known u priori but which one wants to determine from the budget estimate it follows that the choice of L may have to be done through trial and error. It goes without saying that other factors of a practical nature, such as the availability of measurements, also influence the choice of box size.
so,-s
,
Ml
by
TS02
3. BOX MODELS
so,-s
The turn-over time of sulfur in this model is given
1’
Wl 02 w2 Fig. 1. Simplified diagram of atmospheric cycle of manmade sulfur. Q represents the emission of S02, C the conversion of SO2 to SOi- and D and W the dry and wet deposition respectively. M, and M2 are the amounts of SOI-S and SOi--S present in the atmosphere.
4. PREVIOUSLY PUBLISHED ATMOSPHERIC SULFUR BUDGETS
No attempt is made to make a complete review of all previous estimates I will rather limit myself to making a few comments about some of these esti-
HENNING RODHE
674
mates, partly in the light of what was said about time scales in the foregoing sections. I will also try to discuss the reasons for some of the differences between various estimates 4.1 G/&l
budgets
sition on soil, vegetation and water surfaces by the former authors. The low sulfur budget presented by Granat et al. (1976) is actually based on two independent estimates both of which show similar low values
I. The first one (due to Hallberg) assumes that there was a pre-industrial balance for the sulfur in the soil and that the emission of H,S (or any other volatile reduced sulfur compound) from land areas is small (this assumption was based on the work by Hitchcock, 1976). From estimates of weathering, volcanism and (a) What are the sources (natural and man-made). river run-off the pre-industrial (natural) deposition of sinks and residence times of sulfur compounds in the sulfur on land was derived and subsequently the atmosphere-ocean-soil system‘! required emission from coastal and ocean areas This (b) How do man’s activities compare with nature’s budget does not rely explicitly on any atmospheric in determining the overall budget of atmospheric suideposition data. It is, however, critically dependent fur compounds? on the assumption about small H,S emission from The determination-directly or indirectly--of the land areas If such emissions can be shown to be annual fluxes is normally the starting pomt in these larger, this budget must be revised to account for a budgets (Eriksson. 1960, 1963; Junge, 1960, 1963; larger turn-over. Robinson and Robbins, 1970; Kellogg et al., 1972; 2. The second estimate (due to Granat) is based Friend, 1973; Granat et al.. 1976). entirely on atmospheric data. The low flux of HIS The turn-over time is either determined by a comis mainly a result of a downward revision of the gloparison with estimated burdens or it is taken from bal wet deposition. Earlier estimates relied almost enindependent estimates and used to calculate the tirely on data from Europe and the U.S. which were burdens Of all global fluxes, only the man-made probably not unaffected by man-made emissions. emissions into the atmosphere can be considered Therefore, the extrapolation of those deposition known with a sufficient accuracy: maybe +250/, The values to a global figure might have given too large wet deposition, extrapolated from measurements pri- values. Although this second budget estimate of marily in Europe and the U.S.. has generally been Granat et al. took into account more recent deposiconsidered also to be reasonably well known. Howtion measurements from remote areas than previous ever, a critical review of all available data made by authors, the data base is still very inadequate and Granat (Granat et a/., 1976) indicated that the global the global deposition estimate accordingly quite unwet deposition might have been overestimated in all certain. The interpretation of the data in this case earlier estimates The dry depositjon cannot be was deliberately slightly biased towards the low side. measured directly but is normally estimated with the The difference between the budgets by Granat et aid of (a few) measurements of the background surface al. (1976) and the three previous ones may possibly air concentrations and a deposition velocity. The be taken as a measure of the uncertainty involved most uncertain post in the atmospheric part of these in such estimates. budgets is the flux of volatile reduced sulfur comThe following comments may serve as concluding pounds (H& dimethylsulfide, etc.) from land or sea remarks to this subsection. surfaces. This flux is generally derived as a balance Estimates of the global sulfur budget are very unfor the atmospheric reservoir. There is little indepencertain and will remain so until much more data is dent quantitative evidence to support estimates of this available on deposition and air concentrations of difflux. ferent sulfur compounds. The most uncertain part is A comparison between the different authors’ esti- the emission of reduced volatile sulfur compounds mate of this flux is given in Table 1. The difference into the atmosphere. between the first two estimates and the following five Because of these uncertainties, global budgets will is mainly due to a likely overestimate of the dry deponot give much useful information about turn-over times of atmospheric sulfur. Because of the uneven spatial distribution of manTable I. Estimates of the annual global emission of made sulfur sources and of the relatively short resireduced volatile sulfur compounds into tbe atmosphere by dence time of sulfur in the atmosphere global avernatural processes. ages will not give a fair description of the magnitude Flux I” Tg sulfur ) ’ Author of the human intervention in the sulfur cycle in different parts of the world. x7 Enkrson. 1960 The basic purpose for making estimates of the global sulfur budget can be formulated as seeking answers to the following questions (cf: Kellogg er al., 1972):
Jun@. 1963 Robmson and Robbms. 1970 Kello~ er 01. 1972 Frmd 1973 Granal et al. 1916
210 98 n9 IO6 33 and 37
4.2 Regional suljirr budgets In this section I will consider sulfur budgets made for more limited parts of the atmosphere, from con-
Atmospheric sulfur compounds
tinental scales down to one or a few hundred kilometers. Areas chosen for such budgets have generally been those significantly affected by man-made sulfur emissions This is, of course, due to the interest in the fate of the pollution sulfur and to the availability of concentration and deposition measurements in such areas Many attempts have been made to establish the balance of sulfur compounds on even smaller space scales such as in cities or in chimney plumes. Interesting as they may be these studies are normally representative for very special conditions and must not be extrapolated to represent a full life cycle of the sulfur in the atmosphere. An early attempt to establish a sulfur balance on a continental scale was made by Junge (1960) Based on measurements of wet deposition in the US and estimates of the man-made emission in the same area he concluded that the turn-over time of the pollution sulfur with respect to wet deposition ((T&,) was about 6 days With an estimated dry deposition a total tumover time 7, of 34 days was derived (Junge, 1963) By applying similar arguments to an area in northem Europe Rodhe (1972) arrrived at a figure of 24 days for the same quantity (7s) It seems likely that, primarily because of a rather high estimate of the background sulfur deposition in the area and an underestimate of the dry deposition, this value of the turn-over time is slightly high. Another budget estimate for northern Europe, based on the more detailed information then available, was presented by Rodhe (Granat et 01.. 1976) The area studied is bounded by latitudes 45”N and 65”N and by longitudes 1O”W and 20”E and has a characteristic horizontal dimension of about 2CQOkm (Fig. 2) The input data included the source inventory and measurements of surface air concentrations performed within the LRTAP-project (Eliassen and Salt-
Fig. 2. The area used by Rodhe (in Granat et al., 1976) to study the atmospheric sulfur budget,
675
Table 2. Balance sheet for atmospheric sulfur over NW Europe around the year 1973 (Granat et al., 1976) (unit, Ts Y-‘)
by prcap~~~uon by dwect uptake Total Net export of pollution
of emlsslO”
41 2.9-5 9 7.0-10.0
OS 0 2X1.3 07-08
4.6 3 l-62 77-108
23-46
bones, 1975) and wet deposition data from the European Air Chemistry Network (Granat, 1978). By comparing the mass of sulfur in the air with the total man-made emissions, a turn-over time of 2-3 days was derived The net export of pollution sulfur from the area was estimated to 2346% of the emission (see Table 2). In view of the comments about a suitable box size made in section 3 (Lop, 3 47,,v), the results show that it would have been advantageous to study a somewhat larger area. With 7. 55 50 h and V s 25 km h-i &,, would be about So00 km. A similar area was used by Garland (1977) in a study of the sulfur balance over western Europe. This estimate was based on essentially the same data and the conclusions are not very different: a net export out of the area equal to about 30% of the man-made emissions implying a turn-over time of this sulfur of roughly 2 days. The estimate of the total dry deposition was slightly higher and that of the total wet deposition slightly lower than the corresponding estimates made by Rodhe (1976) It should be stressed here that this type of budget estimate depends critically on average values of a few key parameters notably the deposition velocity, v,+ and the scale height, H. of atmospheric sulfur, none of which can be considered very accurately determined. The value of the deposition of sulfur from natural sources and from man-made sources outside the area is also an uncertain quantity. Several budgets on a smaller scale such as for individual countries have been presented. The first attempt in this direction seems to have been made by Meetham (1950) who estimated the balance of soot and SO2 over Great Britain. His estimate of the tumover time of SO2 was very low (about 10 h) essentially because of an incorrect assumption about its vertical distribution. Garland and Branson (1976) used much more reliable data including measurements of the vertical distribution of SO, to set up a SOI balance for Great Britain. Their study shows that the deposition within the country is well below 50% of the emitted amounts (see also Garland, 1977) No attempt was made to determine a turn-over time of sulfur over the country but it was suggested that the dry deposition alone would limit the mean life time of SO, to about 2 days With our notation (see Table 3) this corresponds to (r,,b 5 2 days.
HENNING RODHE
676
This estimate was based on a value of the SO, scale height of about 1200m measured over rural Great Britain. Since the scale height would probably increase by diffusion as the sulfur is transported away from the country it is probable that (T~*)~ is somewhat larger than 2 days when a full life cycle is considered (cJ: discussion of the paper by Garland and Branson, 1977). Sulfur balance estimates have recently been presented for Hungary (Virhelyl, in press) and for an area covering parts of Austria, Czechoslovakia and Hungary (MCsziros and Virhelyi, 1977). No attempt was made lo derive any turn-over time. In the latter study the authors used the balance equation to estlmate the emissions inside that area. Because of the small size of these areas the fluxes across the boundaries become the dominant terms in the balance and the inferences about the remaming flux terms become more uncertain. Smith and Jeffrey (1975) used aircraft measurements of SO2 and SOi- off the east coast of England to make a sulfur balance for an area roughly 200 km wide covering the major source region upwind over the country. They found that within 24 h about 30% of the SO2 had been deposited and IO-207; converted to SO:-. The remaining 5@-60% was observed as an export of SO1 from the area The implied deposition velocity for SO2 was around 0.8 cm s-‘. No number for the transformation rate was given but It was suggested that most of the transformation nught occur very rapidly after the emission and that the subsequent transformation was small. 5. OTHER
WAYS OF ESTIMATING TIME SCALES
ASSOCIATED WITH THE TRANSFORMAnON DEPOSITION
AND
OF SULFUR COMPOUNDS
We have seen that budgets can be used to estimate the importance of different transformation and deposition processes. On the other hand. independent estimates of the importance of these physical and chemical processes are often used as important input parameters in the budgets. It is therefore of interest to discuss briefly some other evidence about such processes 5.1 Observations and experiments It IS beyond the scope of this paper to make a review of the large amount of work on the transformation and removal of sulfur compounds that has been performed The reader is referred to the other review papers in this volume. Only some brief comments will be made. (a) Dry deposition. Measurements of dry deposition of SO2 by the profile method and by some other methods have been made mainly for grass and water surfaces. Deposition velocities-defined as the ratio of the ffux and the surface air concentration-normally lie in the range 0.5 to 2 cm s- ’ with an average value of slightly less than 1 cm s-’ (Garland. 1978).
With a scale height of 1.5 km. a depositron velocity of 0.8 cm s- ’ corresponds to a turn-over time with respect to dry deposition of roughly 50 h. It is not yet clear how effective forests are in removmg SO, under different conditions and the extrapolation of the measured deposition values to large areas with different surface characteristics is far from straight forward. Furthermore. most deposition measurements have been made in temperate climate and may not be representative for other climatic regimes. Some measurements indicate that the deposltion of SO, on snow might be as low as 0.1 cm s- ’ (Dovland and Eliassen, 1976). Regarding the dry deposition of sulfate particles it is generally believed (e.g. Garland and Branson. 1976) that it is small compared to the wet deposition. Deposition velocities for submicron particles of less than 0.1 cm s-’ have been mentioned (Chamberlain. 1967). were Somewhat larger values (0.2-0.5 cm s-‘) reported by Van der Hoven (1975). (b) Wet deposition. As was pointed out in section 3 the average rate of removal by precipitatron is determined both by the frequency of OOcurrence of precipitation events and by the scavenging coefficient during the precipitation. The former quantity is evidently highly dependent on the prevailing climatic condition. Based on a very limited amount of data Rodhe and Grandell (1972) found that the lower limit of the turn-over time with respect to precipitation seavenging-i.e. the term A in Equation l-was about 35 h in winter and 90 h in summer for Scandinavian climate. As an annual average this lower limit may be set at about 50 h for the climate of northern Europe. The incorporation of sulfur into the rain-drop can take place either inside the cloud during the formatlon of raindrops or when the raindrop is falling through the cloud-free air below the cloud. For details of the physical processes involved in the scavenging of gases and particles. reference is made to papers by Hales (1972) and Slinn (1977). Data on the distribution of radioactive compounds have been used by several authors to estimate the removal rate. A review of such studies made by Martell and Moore (1974) concluded that the average residence time for tropospheric aerosols was less than or about equal to one week. Presumably. wet removal has been the dominant removal mechanism in these cases. Generally. estimates of the scavenging coefficients for gases and particles vary widely (see e.g. McMahon et al., 1976). As far as sulfur compounds are concerned there does not even seem to be a consensus about the relative importance of SO2 and sulfate scavenging for the wet removal of sulfur from the atmosphere. (c) The rate of tranSformation SO, to SO:- If the experimental evidence for removal rates was quite mconclusive, this is even more true for the transformation rates. Estimates of the inverse of transformation rates vary from a few hours to at least hundred hours (EPA. 1975).
617
Atmospheric sulfur compounds There are reasons to believe that the transformation rates vary not only between different climatic conditions but also depending upon the concentrations of various other man-made compounds It may therefore not be possible to compare rates deduced from studies made in chimney plumes with rates applicable to large scale budgets (see section 6.1) Husar er al. (1978) reported detailed studies of the sulfur budget of a power plant plume in the St Louis area in the U.S. performed as part of the MISTT Project. The plume was sometimes identified up to a distance of about 300 km (Gillani et al., 1978). Reaction rates for the conversion of sulfur dioxide to sulfate were found to be typically 0.01-0.04 h-’ during noon hours and less than 0.005 h-’ at night. Similar values have been reported from measurements in the plume from the Sudbury Smelter Plant in Canada (Lusis and Wiebe, 1976; Forrest and Newman, 1977) Alkezweeny and Powell (1977) report somewhat higher values (around 0.10 h- ‘) in the urban plume of St Louis for travel times up to a few hours
5.2 Long-range
transport
models
Provided that the description of the transport and dispersion processes in such models is trustworthy, a comparison between calculated and observed concentrations can give useful information about transformation and/or removal processes. Since such a condition is not always fulfilled a certain amount of scepticism about interpreting model parameters as physical parameters is well motivated. A further complication arises in those cases when attempts are made to determine more than one parameter at the same time. It is then not enough to find a set of parameters which gives a reasonable agreement between calculated and observed values. One has to show that such a set is unique i.e. that other sets may not also give a fair agreement. This problem was encountered and commented upon by Eliassen and Saltbones (1975). In their study, these authors compare the measurements of surface air concentrations (daily means) obtained in the LRTAP network with values calculated with the aid of a dispersion model based on trajectories. The data were taken from 6 stations in northern Europe and covered two periods of each two months’ duration. Three parameters were estimated by regression analysis: the decay rate of SO2 (including dry removal, wet removal and conversion to sulfate), the conversion rate SO2 to sulfate and the mixing height. Eliassen and Saltbones found average values of these parameters around 0.07 h-l, 0.007 h-’ and 12OOm respectively. Because of the neglect in the model of any removal of sulfate by precipitation the derived conversion rate is likely to be smaller than the real value. The decay rate of SO, is more likely to have some physical significance, but the comments made above must be kept in mind. In the calculations referred to in the LRTAP report
(Eliassen, 1978) the values of the parameters are partly based on the above estimates by Eliassen and Saltbones (1975) If, in the model, precipitation scavenging were allowed to act on sulfate particles instead of on SO2 higher values of the transformation rate and of the decay rate for SO:- would have been implied. A similar type of model was used in the SURE experiment in the U.S.A. (EPRI, 1976) to calculate SO, and SO$- concentrations for comparison with observed 24-h values Transformation rates (SO2 to SO:-) in the range 0.02 h-i-O.01 h-’ seemed to give a fair agreement but the limited amount of data prevented any firm conclusions from being drawn. Prahm et al. (1976) applied a simple trajectory box model to study the transport of SO1, SOi- and trace metals from the British Isles to the Fames where measurements had been made. Values of the deposition velocities for SO, and SOi- (2 and 0.4 cm s-l, respectively) and of the transformation rate (0.011 h-‘) were derived. These values are. however, dependent on several assumptions the most critical probably being a ‘dilution factor’ and they are there fore uncertain to at least 50% For example, a larger dilution would decrease the deposition velocity and at the same time increase the transformation rate. Omstedt and Rodhe (1978) used a simple onedimensional (height) dispersion model to study the ratio of SO, to SOi- in a polluted region. By comparison with observations of this ratio they concluded that the average conversion rate is likely to be in the range 0.04-0.007 h-’ for European conditions. They further found that it was difficult to explain the observed wet deposition pattern if all sulfur had to be transformed to SOi- in the air before being scavenged by precipitation. In order to have a rapid enough wet removal of sulfur the scavenging of SO1 is likely to be significant. 6. DlSCU!WON
In this section I shall first make some comments about the comparison between the various time scales referred to in the previous two sections When making such comparisons it is essential to be very clear about the definitions and significances of the time scales used I finally summarise the information about turnover times available from the budget estimates and attempt an estimate of likely values as applied to a European type climate. 6.1 The relation
between reaction
rates and turn-over
times One of the first things to consider is to which extent it may be justified to equate the inverse of estimated rate coefficients with turn-over times (i.e. average residence times) Almost all estimates of reaction rates from measured data are based on the assumption that the reaction is of first order with a constant coe.fRcient and that therefore the decay corrected for the disper-
HENNING RODHE
678
have been transformed or removed. the inverse of the estimated rate coefficients may be much smaller than the real turn-over time. When modelling a situation like this a decay proportional to the square of the concentration might be considered (b) This is the exponential case when k,,’ = Q. (c) The rate of removal is slow in the beginning and increases later on. Here the Inverse of the rate coefficient estimated close to the source may be larger than the turn-over time (k,, > TV). A physlcal situation when this may apply is decay due to wet removal during a precipitation situation if the pollutant has to disperse up to cloud levels before it is being significantly removed. Measurement of SO1 oxidation rates in a power plant plume reported by Husar et a/. (1978) indicate a variation of the rate coefficient during the first few hours which would give rise to a similar distribution of residence times. 6.2 Summary of turn-over %I
‘I:
Fig. 3. Three examples of distribution functions for residence times. The turn-over time rO (the average residence time) is about equal in the three cases. If rate coefficients are determined from measurements close to the source (i.e. short times) the inverse of such rate coefficients may differ very markedly from the turn-over time (see text)
sive dilution is exponential. If this is not valid the inverse of the estimated rate coefficient may be a poor measure of the turn-over time. In order to exemplify such situations let us consider the distribution function, F(T), for the residence times of individual molecules (Bolin and Rodhe, 1973). F(r) is thus the fraction of all molecules that have a residence time less than T and 1 - F(7) is the fraction which is still in the air the time T after they have been enutted Figure 3 shows three different examples of such distribution functions. (a) The rate of removal is rapId in the beginning but decreases later so that a substantial fraction of the molecules have a long residence time. This situation may occur for example when high concentration of other pollutants near the source contribute to a rapid reaction. The values of SO2 oxidation rates quoted in Table 8 in the review by McMahon et al. (1976) indicate that this is a normal situation. Removal by dry deposition at the surface may also give rise to a similar shape. This is because the proportion of the molecules that quickly get in contact with the surface will decrease as the pollutant is spread to higher elevations If situations such as these apply, a rate coefficient estimated from measurements made at short distances from the source may seriously underestimate the real turn-over time (k,: < T,,). Even if measurements are extended up to a point when 50% of the molecules
time
estimates
Table 4 summarizes the information about tumover times obtained from the budget estimates discussed in section 4. All estimates discussed here refer to pollution sulfur, emitted mainly as S02, in a temperature climate (Europe or U.S.A.). The definition of the various time scales used in Table 4 are given in Table 3. Since the time scales in the table are interrelated there is actually more information about each time scale than indicated by the numbers in the particular column. These interrelations follow from the definitions of the different time scales as given in Table 3. For example, we have 1
1 7so*
= (z,o, 1
1 -=GO,
1
@SO,
1 )D +
(Kx’
1
1 1 _=-+‘5s
(fS)D
1
+ (Qo,)w + (G&
(&’
and ss = 7s02 + cttSo, where LXIS the fraction of the emitted sulfur that is transformed to sulfate before Table 3. Definitions The symbols of the
of the turn-over times used in Table 5. right hand sides are defined in Fig. 1.
679
Atmospheric sulfur compounds Table 4. Summary of estimates of turn-over times of sulfur compound in the atmosphere (unit. hours) Authors I50
Jun~e. 1960. 1963 Rodhc. 1972 Crnnat CI 01.. 1976 Gwland. 1977 El~asscn and Saltbonn. 1975 EPRI.
Omstdt
14cw
75-100 5&w 50 70 5n
IS
50 loo
1976
and Rodhe.
197x
90
Prnhm VI rd.. 1976
Smnh JeRrc). 1975
Garland and Bramon 1976
Husar t, ul.. 197x
25. I so
lb1
I?
70
ldl
IC)
40
hased on plume budgels no preclpltallo” scarengn*
35
Martell and Moore. 1974
deposition. LXis related to the time scales involved by the relation
Taking into account such relations and the comments made in Section 4 about the various estimates we may make a rough guess of likely values of the different time scales for the particular conditions prevaiiing in northern Europe. Such an estimate is given at the bottom of Table 4. This estimate is of course uncertain (no attempt is made to estimate any ranges) but at least it gives an internally consistent picture. The figures imply that about 30% of the SO, is transformed to SOi- before being deposited None of the estimated values seems to disagree too much with the data given in the table Minor differences are by and large within the uncertainty ranges of the different estimates (cf: section 4) The major uncertainties in the set of values given at the bottom of Table 4 seem to be associated with the three turn-over times (r&., (rso,)c and (rsoJv. For example, from the arguments presented here there is no serious contradiction in assuming a (Q&, value well below 100 h. Similarly (rsoJv may be taken to be somewhat less or larger than 80 h. It should again be emphasized that the time scales estimated here represent average conditions for a particular type of climate. For specific situations (e.g. seasons) in the same region or for other climatic zones the values may be quite different,
7. CONCLUDING
REMARKS
Budget estimates may be useful for tying together various pieces of information into a consistent picture. They may also help in identifying the most significant uncertainties in our knowledge about the circulations of the various compounds Global sulfur budgets have the common weakness that they form an average over extremely different conditions in different parts of the globe. Furthermore, concentration and deposition data are only available from very limited areas. These factors point to the advantages of making sulfur budgets over regions where data are available and where the conditions (climatewise and emissionwise) may be reasonably homogeneous It has been shown that such regional budgets-most of them applied to European conditions-may produce some useful estimates of the importance of those processes that transform and remove sulfur compounds from the atmosphere. It is recommended that similar studies be undertaken in other parts of the world In particular, North American may offer an interesting possibility in view of the large man-made emissions and of the measurements already available. One may also caution against the use of annual averages in budget estimates Pronounced seasonal variations in the rates of emission, transformation and/or removal may make such averages quite misleading In the discussion above it has become apparent
680
HENNINGRODHE
that there are definite problems associated with a comparison between time scales derived from budgets and those derived in other ways. In particular, the difference between turnover times (i.e. average resi-
dence times) and the inverse of rate coeficients should be kept in mind A need for careful definitions of the time scales used is obvious This paper is an attempt to formulate a basis for the discussion of associated problems. Acknowledgement-This work was done under contract No G3922-003 of the Swedish Natural Sctence Research Council. 1 wish to thank L. Granat for useful discussions. REFERENCES Afkezweeny A. J. and Powell D. C. (1977) Estimation of tr~sfor~tion rate of SO, to SO6 from atmospheric concentration data. Amwspherrr Environment il. 179-182.
Bofin B. and Rodhe H. (1973) A note on the concepts of age distribution and transit time m natural reservoirs. Telfus 2S. 58-62. Chamberlain A. C. (1967) Transport of Lycopodium spores and other small particles to rough surfaces. Proc. R. Sot. 296, 45-70. Dovfand H. and Ehassen A. (1976) Dry deposition on a snow surface. Atmospheric Environment 10, 783-785. Efiassen A. (1978) The’ OECD study of long range transport of air pollutants. Long range transport modelfing. Atmospheric Environment 12. 479-487.
Efiassen A. and Saltbones J. (1975) Decay and transformation rates of’ SO2 as estimated from emission data, trajectories and measured concentrations. Atmospheric Environment 9. 425-429.
EPA (1975) Position paper on regulation of atmospheric sulfates U.S. Environmental Protection Agency, Research Triangfe Park U.S.A. EPRI (1976) Design o/ the surfate regumal experiment (SURE). Final rewrt ofresearch protect 485. Vol. 1: SUP parting dota andbnalysis. Electric power Research Insb-
tute. California, U.S.A. Eriksson E. (1960) The yearly circulation of chtoridc and sulfur in nature; meteorological. geochemical and pcdological implications-Part II. Tel/us 12, 63-109. Eriksson E. (1963) The yearly circulation of sulfur in nature. J. geophys. Res. 68, 40014008. Forrest J. and Newman L. (1977) Oxidation of sulfur dioxide in the Sudbury smelter plume. Atmospheric Environment 11. 517-520. Friend J. P. (1973) The global sulfur cycle. In Chemistry of the Lower Atmosphere. (Edited by Rasoof S. I.) pp. 177-201. Plenum Press, New York Garland J. A. (1977) The dry deposition of sufphur dioxide to land and water surfaces. Proc. R. met. Sot. Lend. A 354. 245-268. Garland J. A. (1978) Dry and wet removal of sufphur from the atmosphere. Atmospherjc Envrronment 12, 349-362. Garland J. A. and Branson J. R. (1976) The mixing height and mass balance of SO, in the atmosphere above Great Britain. Atmospheric Environment 10, 353-362. Discussion of this paper by H. Rodhe. Atmospheric Environment It,
659-661.
Giffani N. V., Husar R. B., Husar J. D. and Patterson D. E. (1978) Prqect MISTT: Kinetics of particulate suf-
fur for~~on
m a power plant plume out to 300 km
Atmospheric Environment 12, 589-598.
Granat L. (1978) Sulfate in precipitation as observed by the European Atmospheric Chemistry Network Atmospheric Environmenr 12, 413424. Granat L., Hal&erg R. 0. and Rodhe H. (1976) The global sulphur cycle. in Nirrogen. Phosphorus and SuiphurGlobal Cycles. (Edited bv Svensson B. H. and Siiderlund R.) SCOPE report 7, Ecbl. Bull, (Stockholm) 22, 89-134. Hales J. M. (1972) Fundamentals of the theory of gas scavenging by rain. Armospkerrc ~n~)ironment. 6, 6355659 Hitchcock D. R. (1976) Microbiofoaical contributions to the atmosphenc’ load of particulate sulfate. In Enoironmental Biochemistry (edited by Nriagu J. 0.) pp. 351-367 Ann Arbor Science, Ann Arbor. Husar R. B., Patterson D. E.. Husar J. D.. Gillam N. V and Wilson W. E. (1978) Sulfur budget of a power plant plume. Atmospheric Environment 12. 549-568. Junge C. E. (1960) Sulfur m the atmosphere. I yeophys. Res. 65. 227-237. Junge C. E. (1963) Au Chemistry and R~Ioact~~ir~. pp 70-74. Academic Press, New York. Kellogg W. W.. Cadfe R. D., Allen E. R., Lazrus A. L. and Marteff E. A. (1972) The sulfur cycle. Science 175, 587-596. Lusts M. A. and Wiebe H. A. (1976) The rate of oxidation of sulfur dioxide in the plume of a nickel smelter plant. Atmospheric Environment 10, 793-798.
Marteff E. A. and Moore H. E. (1974) Tropospheric aerosol residence times: a critical revtew. J. Rechs. atmos. 8, 903-910.
McMahon T. A., Denison P. J. and Fleming R. (1976) A long-distance air pollution transportation model incorporating washout and dry deposttion components. Atmospheric Environment 10, IS l-761 Mee~am A. R. (19X)) Natural removal of ~ifu~on from the atmosphere. Q. JI. R. met. Sot. 76. 359-371. Mtslaros E. and Varhefvi G. f 1977) An attemot to estimate the continental sufphur emissions on the basts of atmospheric measurements Atmospheric Environment 11. 169-172. Omstedt G. and Rodhe H. (1978) Transformation and removal process for sulfur compounds m the atmosphere as described by a one-dimensional timedependent diffusion model. Atmospheric Enrironment 12, 503-509. Prahm L. P., Torp U. and Stern R. M (1976) Deposition and transformation rates of sufphur oxides during atmospheric transport over the Atfants. TeNus 28, 355-372. Robinson E. and Robbins C. (1970) Gaseous sulfur polfutants from urban and natural sources. J. Air Pofiut Control. Ass. 20, 233-235.
Rodhe H. (1972) A study of the sulfur budget for the atmosphere over northern Europe. Tellus 24, 128-138. Rodhe H. and Grandell J. (1972) On the removal time of aerosol particles from the atmosphere by precipitation scavenging. Tellus 24, 442-454. Slinn W. G. N. (1977) Some approximations for the wet and dry removal of particles -and gases from the atmosphere. War. Air. Soil Pollut. 7, 513-543.
Smith F. B. and Jeff’rey G. H. (1975) Airborne transport of sufphur dioxide from the U.K. Atmospheric Environment 9, 643659.
Van der Hoven 1. (1975) Deposition of particles and gases. USAEC TfD-24190, Clearinghouse FSTI, Springfield, Va. Varhelyi G. An attempt to estimate the sulfur budget over Hungary. Atmospheric Environment 12, (in press).
BUDGETS
AND TURN-OVER TIMES OF ATMOSPHERIC SULFUR COMPOUNDS HENNING
RODHE
Department of Meteorology, University of Stockholm, Arrhenius Laboratory, S-106 91 Stockholm. Sweden* (First received 13 June 1977 and in jinol
firm
20 September 1977)
Al&met-The paper starts by detining the time concepts ‘residence time’ ‘age’ and ‘turn-over time’ and by discussing their inter-relations briefly. Some basic comments about box models as applied to sulfur in the atmosphere are also presented. It is suggested that when using budgets lo estimate overall fluxes the optimum size for such boxes should be about four times the product of the turn-over time and an average transport velocity. A brief review is made of previous estimates of atmospheric sulfur budgets of scales ranging from global down to about 100 km. Particular emphasis is put on the implied turn-over times (i.e. average residence times) for the different sulfur compounds These estimates are compared with estimates of time scales made from observations and experiments and from the use of long range transport models Such comparisons are complicated by possible deviations from exponential residence time distributions which make, for example, rate coeficients estimated for short transport times unrepresentative for the full life cycle of the molecules in the atmosphere. Based on the presently available data an estimate is presented of the overall turn-over times in the midlatitude atmosphere of man-made SO, and SOi- and of the turn-over times with respect to the difierent transformation and removal processes. The estimated overall turn-over times of S02, SOf- and sulfur (SO, + SO:-) in this climate are roughly 25, 80 and 50 h respectively. The turn-over time with respect to the different removal and transformation processes are generally somewhat more uncertain. For SO, the dry deposition. wet deposition and transformation to SOi- correspond to turn-over tirnes of about 60, 100 and 80 h respectively. These tigures would imply that about 30% of the SO1 is transformed to SOi- before being deposited The time scales mentioned here represent average conditions for a particular type of climate and may not be applied directly to specific situations (e.g. seasons) in similar climates or to other climatic zones Most of the sulfur budgets estimates utilized in this study apply to conditions in Europe. A plea is made for similar studies to be undertaken in other parts of the world In North America there may already be enough data available for such studies I. INTRODUCTION
When describing the circulation of chemical compounds in the atmosphere it is essential to have an idea about time scales that characterize the transformation and removal processes. If such time scales are known ad if measurements of the concentration in the air are available, the amounts that are transformed or removed can be estimated In connection with dispersion calculations a knowledge of these time scales will also in principle enable us to calculate the patterns of air concentration and fallout provided the sources and the dispersive characteristics of the atmosphere are known. On the other hand, if, for example, the deposition has been measured, a knowledge of the time scale of deposition will make it possible to infer something about the amounts of this compound in the atmosphere and about a possible build up of the concentrations. There are bicW
two approaches to the problem.
of estimating the time scales of transformation and removal processes One is to study the processes themselves by measurements, either in the atmosphere * Contribution No. 350 from International Meteorological Institute in Stockholm. 671
itself or in a laboratory, or possibly by theoretical calculations The other approach, and the one I shall be mainly concerned with in this paper, is to use budget calculations to estimate the space and time averages of such time scales. The wish to assess man’s impact on the cycle of various compounds is another important reason to attempt to make budget estimates i.e. systematic comparisons of sources, sinks and mean concentrations over reasonably large portions of the atmosphere. Most previous atmospheric sulfur budgets have dealt with global totals of sources and sinks Since at least the man-made sulfur sources are very unevenly distributed ovef the globe and be-cause of the limited residence time of sulfur in the atmosphere (see below) it is obvious that possible ecological impacts of man’s interference with the sulfur cycle most likely are of a local or regional rather than global character. Consequently, it should be more logical to consider budgets of limited regions of he giobe (Granat et af., 197~
The purpose of this paper is to discuss how budget estimates (i.e. systematic comparisons of soufces. sinks and concentrations over reasonably large time and space scales) can be used to estimate the time scales that characterize transformation and removal processes of sulfur compounds in the atmosphere. The
HENNING RODHE
672
first secttons contain a general discussion about different ways of defining time scales and about some fundamental concepts of box models. In the followmg sections various sulfur budget estimates are described and the time-scales obtained are compared with other independent estimates. Finally, an attempt is made to combine the informatton available in an estimate of likely values of the various time scales associated with the circulation of sulfur in polluted regions m midlatitudes.
2. DEFINITIONS
OF TIME SCALES
The terminology used here follows largely the one used by BoIin and Rodhe (1973). Steady store condition is assumed to prevail. 1. Residence time is the time spent by a molecule from the moment of injection into or formation in the atmosphere to the moment of transformation or removal. Transit time could be used as an alternative expression for the same quantity. Particularly in cases when the sources and sinks are situated at the boundary of the reservoir (in this case at the ground) this latter expression may be preferable. Since the residence time (transit time) for individual molecules of a given compound may be quite different it is useful to introduce a frequency function &T) describing the frequency distribution of residence times If we are interested in the fate of a SO2 molecule emitted into the atmosphere we must separate between the residence time of the SO2 molecule itself, fso,, and the residence time of the sulfur atom, TV. A transformation of SO2 to SOi- implies a sink for SO, (and a source for SO:-), but not for the S atom. A sulfur atom that is introduced as SO2 and removed as SOiwill thus have a residence time rs = %oI + rso,. 2. Average residence time, 7,. is the average value of the residence times (transit times) of all molecules: I Tr =
s0
T&T)
dr
This is the quantity, often refered to simply as the ‘residence time’. commonly used to characterize the circulation of a compound in the atmosphere. If the frequency distribution of residence times is approximately exponential such a simple characterization may suffice. In other cases, it may be necessary to add more information about the frequency function such as higher order moments. 3. The age of a molecule in a reservoir is the time since it was introduced. The corresponding frequency function we denote by I&T). The age of a molecule when it leaues the reserooir is equal to the residence time of that molecule. In general, the age and residence time are of course quite different from each other. 4. The average age. 7a, is the average value of the ages of all molecules found in the reservoir at any
one ttme: T’* =
S’
rY'(r)dr.
0
5, may be larger or smaller than T, depending upon the shape of the frequency function (cf: Bolin and Rodhe, 1973). They are equal when the frequency functions have an exponential shape. 5. Turn-over time, To, is the ratio of the total mass of the compound in the reservoir to the total flux out of (or into) it: 7. = M/F. This IS a bulk quantity which contains no explicit information about the shape of &T) or Jl(r) It can be shown (Bolin and Rodhe, 1973) that fO is identical with 7r so that the turn-over time is actually a measure of the average residence time spent by molecules of the compound in the reservoir. The age concept has a natural application in problems involving radioactive material. In the foilowing discussion I will confine myself to the residence ttme concept and the turn-over time. In cases where there are two or more competing sink mechanisms one may also apply the turn-over time concept to an individual sink mechanism. As an example we can think of a pollutant that is removed either by dry or wet deposition (precipitation scavenging). Let Q be the emission rate and D and Wthe rates of dry and wet deposition respectively. If M is the steady state mass of the pollutant in the atmosphere (or in a well defined fraction of the atmosphere) we have 7. = M/(I) + W) = M/Q. The turn-over times with respect to dry and wet deposition separately may now be defined as 7or, = M/D It follows that and row = M/W respectively. l/To = (~/T~J + (l/row). In the special case when the removal process may be described by a first order reaction, the turn-over time with respect to this particular process as defined above is equal to the inverse of the rate coefficient. It is worth noting that whereas dry deposition is a process which is generally continuous in time, the wet removal is only effective during certain periods of time. Therefore the two time scales 7oD and so,,, have a somewhat different character. When discussing the physical interpretation of 7w it may be advantageous to think of it as determined by two distinct processes; (a) the frequency of occurrence of clouds or rain, (b) the scavenging process inside the cloud or the rain. Rodhe and Grandell (1972) showed that quite general conditions one may write TOW =
A+
BI-‘,
under (1)
where A and B are functions that describe the frequency of occurrence of rain and 1 is the scavenging coefficient in the rain. Thus even with very effective scavenging in rain (1-t = 0). row has a finite value (.A) corresponding basically to the time it takes to
673
Atmospheric sutfur compounds experience the first rain. It may be mentioned that in the model used by Rodhe and Grandell(l972) the frequency function of residence times (NT)) is not a simple exponential function. It is therefore not quite appropriate to use the inverse of their turn-over time as a decay constant in a first order reaction.
Before the discussion of the various sulfur budget estimates (see section 4) it may be Useful t0 clarify some basic concepts regarding box models In a box model the spatial distribution of the compound inside the box (reservoir) is not explicitly eonsidered In most cases it is rather assumed that the conditions inside the box are reasonably homogeneous This is in contrast to analytical or numerical dispersion models where the spatial (and possibly temporal) distribution is dealt with explicitly. The advantage with a box model is that it may enable an overall assessment to be made of the time scales involved and of the relative importance of various transformation and removal processes without laborious computations. As is normally done, we shall limit the discussion to steady state situations where sources and sinks balance each other. It is often useful to consider a system of reservoirs rather than a single one. This may be the case when the conditions are spatially non-uniform or when one is interested in the circulation of a compound, between different media. As an example one may take the model of the global sulfur cycle as formulated by, for example, Eriksson (1960) Another situation when a series of reservoirs may be considered is when one is considering the circulation of an element in a medium and the element occurs in the form of different chemical compounds In this case each compound may be taken as a reservoir for the element. As a simple example let us consider anthropogenic sulfur emissions into the atmosphere and let the atmospheric content of SO1 and SO:- be two sulfur reservoirs (Fig 1). In this figure Q is the emission of SO,, C the conversion of SO1 to SOi- and D and W the dry and wet deposition processes. M, and M, are the amounts of sulfur in the forms of SO, and SOirespectively. To simplify the notation we shall drop the subscript ‘0’ for the turn-over time rO.
Q__
C
I
1 4
’
MI + Ml
” = D1 -I- D2 +
M2 I
W, + W, =
The turn-over times for SO, and SOi=
Ml
-
Q
=
MI + Ml Q
’
(2)
are
MI D,+W,+C
It follows that rS =
~SO, + aTso,
(5)
where a = C/Q is the fraction of the sulfur that is converted to sulfate before being deposited when applying a box model to study the sulfur budget of a portion of the atmosphere the choice of an appropriate box size, L, is not a trivial matter. On the one hand, a sulfur budget,for the global or hemispheric. atmosphere entails an averaging over very different conditions: highly polluted industrial areas and more or less clean remote areas Evidently such an average will be representative neither for the polluted regions nor for the clean. On the other hand if too small a box size is chosen the fluxes across the boundaries will be so large that it may be impossible to make any meaningful estimates of the importance of emissions, transformations and removal mechanisms In principle, it is of course possible to keep track of the fluxes across the lateral boundaries of the box, but in practice the estimates of such fluxes may be so uncertain that subsequent deductions are of limited value if the box size is small. For studies of the fate of man-made emissions of a compound like sulfur the optimum box size should be such that the distance from the major source region to the edge of the box is somewhat larger, by a factor 2, say, than the scale of decay of the sulfur in the atmosphere (R = r. x v where v is an average transport velocity). If we let L,,,,, denote the diameter of an appropriately chosen circular box with a point source near the center we then have
I&, 5 4 T*V.
(6)
Since rs is a quantity which may not be known u priori but which one wants to determine from the budget estimate it follows that the choice of L may have to be done through trial and error. It goes without saying that other factors of a practical nature, such as the availability of measurements, also influence the choice of box size.
so,-s
,
Ml
by
TS02
3. BOX MODELS
so,-s
The turn-over time of sulfur in this model is given
1’
Wl 02 w2 Fig. 1. Simplified diagram of atmospheric cycle of manmade sulfur. Q represents the emission of S02, C the conversion of SO2 to SOi- and D and W the dry and wet deposition respectively. M, and M2 are the amounts of SOI-S and SOi--S present in the atmosphere.
4. PREVIOUSLY PUBLISHED ATMOSPHERIC SULFUR BUDGETS
No attempt is made to make a complete review of all previous estimates I will rather limit myself to making a few comments about some of these esti-
HENNING RODHE
674
mates, partly in the light of what was said about time scales in the foregoing sections. I will also try to discuss the reasons for some of the differences between various estimates 4.1 G/&l
budgets
sition on soil, vegetation and water surfaces by the former authors. The low sulfur budget presented by Granat et al. (1976) is actually based on two independent estimates both of which show similar low values
I. The first one (due to Hallberg) assumes that there was a pre-industrial balance for the sulfur in the soil and that the emission of H,S (or any other volatile reduced sulfur compound) from land areas is small (this assumption was based on the work by Hitchcock, 1976). From estimates of weathering, volcanism and (a) What are the sources (natural and man-made). river run-off the pre-industrial (natural) deposition of sinks and residence times of sulfur compounds in the sulfur on land was derived and subsequently the atmosphere-ocean-soil system‘! required emission from coastal and ocean areas This (b) How do man’s activities compare with nature’s budget does not rely explicitly on any atmospheric in determining the overall budget of atmospheric suideposition data. It is, however, critically dependent fur compounds? on the assumption about small H,S emission from The determination-directly or indirectly--of the land areas If such emissions can be shown to be annual fluxes is normally the starting pomt in these larger, this budget must be revised to account for a budgets (Eriksson. 1960, 1963; Junge, 1960, 1963; larger turn-over. Robinson and Robbins, 1970; Kellogg et al., 1972; 2. The second estimate (due to Granat) is based Friend, 1973; Granat et al.. 1976). entirely on atmospheric data. The low flux of HIS The turn-over time is either determined by a comis mainly a result of a downward revision of the gloparison with estimated burdens or it is taken from bal wet deposition. Earlier estimates relied almost enindependent estimates and used to calculate the tirely on data from Europe and the U.S. which were burdens Of all global fluxes, only the man-made probably not unaffected by man-made emissions. emissions into the atmosphere can be considered Therefore, the extrapolation of those deposition known with a sufficient accuracy: maybe +250/, The values to a global figure might have given too large wet deposition, extrapolated from measurements pri- values. Although this second budget estimate of marily in Europe and the U.S.. has generally been Granat et al. took into account more recent deposiconsidered also to be reasonably well known. Howtion measurements from remote areas than previous ever, a critical review of all available data made by authors, the data base is still very inadequate and Granat (Granat et a/., 1976) indicated that the global the global deposition estimate accordingly quite unwet deposition might have been overestimated in all certain. The interpretation of the data in this case earlier estimates The dry depositjon cannot be was deliberately slightly biased towards the low side. measured directly but is normally estimated with the The difference between the budgets by Granat et aid of (a few) measurements of the background surface al. (1976) and the three previous ones may possibly air concentrations and a deposition velocity. The be taken as a measure of the uncertainty involved most uncertain post in the atmospheric part of these in such estimates. budgets is the flux of volatile reduced sulfur comThe following comments may serve as concluding pounds (H& dimethylsulfide, etc.) from land or sea remarks to this subsection. surfaces. This flux is generally derived as a balance Estimates of the global sulfur budget are very unfor the atmospheric reservoir. There is little indepencertain and will remain so until much more data is dent quantitative evidence to support estimates of this available on deposition and air concentrations of difflux. ferent sulfur compounds. The most uncertain part is A comparison between the different authors’ esti- the emission of reduced volatile sulfur compounds mate of this flux is given in Table 1. The difference into the atmosphere. between the first two estimates and the following five Because of these uncertainties, global budgets will is mainly due to a likely overestimate of the dry deponot give much useful information about turn-over times of atmospheric sulfur. Because of the uneven spatial distribution of manTable I. Estimates of the annual global emission of made sulfur sources and of the relatively short resireduced volatile sulfur compounds into tbe atmosphere by dence time of sulfur in the atmosphere global avernatural processes. ages will not give a fair description of the magnitude Flux I” Tg sulfur ) ’ Author of the human intervention in the sulfur cycle in different parts of the world. x7 Enkrson. 1960 The basic purpose for making estimates of the global sulfur budget can be formulated as seeking answers to the following questions (cf: Kellogg er al., 1972):
Jun@. 1963 Robmson and Robbms. 1970 Kello~ er 01. 1972 Frmd 1973 Granal et al. 1916
210 98 n9 IO6 33 and 37
4.2 Regional suljirr budgets In this section I will consider sulfur budgets made for more limited parts of the atmosphere, from con-
Atmospheric sulfur compounds
tinental scales down to one or a few hundred kilometers. Areas chosen for such budgets have generally been those significantly affected by man-made sulfur emissions This is, of course, due to the interest in the fate of the pollution sulfur and to the availability of concentration and deposition measurements in such areas Many attempts have been made to establish the balance of sulfur compounds on even smaller space scales such as in cities or in chimney plumes. Interesting as they may be these studies are normally representative for very special conditions and must not be extrapolated to represent a full life cycle of the sulfur in the atmosphere. An early attempt to establish a sulfur balance on a continental scale was made by Junge (1960) Based on measurements of wet deposition in the US and estimates of the man-made emission in the same area he concluded that the turn-over time of the pollution sulfur with respect to wet deposition ((T&,) was about 6 days With an estimated dry deposition a total tumover time 7, of 34 days was derived (Junge, 1963) By applying similar arguments to an area in northem Europe Rodhe (1972) arrrived at a figure of 24 days for the same quantity (7s) It seems likely that, primarily because of a rather high estimate of the background sulfur deposition in the area and an underestimate of the dry deposition, this value of the turn-over time is slightly high. Another budget estimate for northern Europe, based on the more detailed information then available, was presented by Rodhe (Granat et 01.. 1976) The area studied is bounded by latitudes 45”N and 65”N and by longitudes 1O”W and 20”E and has a characteristic horizontal dimension of about 2CQOkm (Fig. 2) The input data included the source inventory and measurements of surface air concentrations performed within the LRTAP-project (Eliassen and Salt-
Fig. 2. The area used by Rodhe (in Granat et al., 1976) to study the atmospheric sulfur budget,
675
Table 2. Balance sheet for atmospheric sulfur over NW Europe around the year 1973 (Granat et al., 1976) (unit, Ts Y-‘)
by prcap~~~uon by dwect uptake Total Net export of pollution
of emlsslO”
41 2.9-5 9 7.0-10.0
OS 0 2X1.3 07-08
4.6 3 l-62 77-108
23-46
bones, 1975) and wet deposition data from the European Air Chemistry Network (Granat, 1978). By comparing the mass of sulfur in the air with the total man-made emissions, a turn-over time of 2-3 days was derived The net export of pollution sulfur from the area was estimated to 2346% of the emission (see Table 2). In view of the comments about a suitable box size made in section 3 (Lop, 3 47,,v), the results show that it would have been advantageous to study a somewhat larger area. With 7. 55 50 h and V s 25 km h-i &,, would be about So00 km. A similar area was used by Garland (1977) in a study of the sulfur balance over western Europe. This estimate was based on essentially the same data and the conclusions are not very different: a net export out of the area equal to about 30% of the man-made emissions implying a turn-over time of this sulfur of roughly 2 days. The estimate of the total dry deposition was slightly higher and that of the total wet deposition slightly lower than the corresponding estimates made by Rodhe (1976) It should be stressed here that this type of budget estimate depends critically on average values of a few key parameters notably the deposition velocity, v,+ and the scale height, H. of atmospheric sulfur, none of which can be considered very accurately determined. The value of the deposition of sulfur from natural sources and from man-made sources outside the area is also an uncertain quantity. Several budgets on a smaller scale such as for individual countries have been presented. The first attempt in this direction seems to have been made by Meetham (1950) who estimated the balance of soot and SO2 over Great Britain. His estimate of the tumover time of SO2 was very low (about 10 h) essentially because of an incorrect assumption about its vertical distribution. Garland and Branson (1976) used much more reliable data including measurements of the vertical distribution of SO, to set up a SOI balance for Great Britain. Their study shows that the deposition within the country is well below 50% of the emitted amounts (see also Garland, 1977) No attempt was made to determine a turn-over time of sulfur over the country but it was suggested that the dry deposition alone would limit the mean life time of SO, to about 2 days With our notation (see Table 3) this corresponds to (r,,b 5 2 days.
HENNING RODHE
676
This estimate was based on a value of the SO, scale height of about 1200m measured over rural Great Britain. Since the scale height would probably increase by diffusion as the sulfur is transported away from the country it is probable that (T~*)~ is somewhat larger than 2 days when a full life cycle is considered (cJ: discussion of the paper by Garland and Branson, 1977). Sulfur balance estimates have recently been presented for Hungary (Virhelyl, in press) and for an area covering parts of Austria, Czechoslovakia and Hungary (MCsziros and Virhelyi, 1977). No attempt was made lo derive any turn-over time. In the latter study the authors used the balance equation to estlmate the emissions inside that area. Because of the small size of these areas the fluxes across the boundaries become the dominant terms in the balance and the inferences about the remaming flux terms become more uncertain. Smith and Jeffrey (1975) used aircraft measurements of SO2 and SOi- off the east coast of England to make a sulfur balance for an area roughly 200 km wide covering the major source region upwind over the country. They found that within 24 h about 30% of the SO2 had been deposited and IO-207; converted to SO:-. The remaining 5@-60% was observed as an export of SO1 from the area The implied deposition velocity for SO2 was around 0.8 cm s-‘. No number for the transformation rate was given but It was suggested that most of the transformation nught occur very rapidly after the emission and that the subsequent transformation was small. 5. OTHER
WAYS OF ESTIMATING TIME SCALES
ASSOCIATED WITH THE TRANSFORMAnON DEPOSITION
AND
OF SULFUR COMPOUNDS
We have seen that budgets can be used to estimate the importance of different transformation and deposition processes. On the other hand. independent estimates of the importance of these physical and chemical processes are often used as important input parameters in the budgets. It is therefore of interest to discuss briefly some other evidence about such processes 5.1 Observations and experiments It IS beyond the scope of this paper to make a review of the large amount of work on the transformation and removal of sulfur compounds that has been performed The reader is referred to the other review papers in this volume. Only some brief comments will be made. (a) Dry deposition. Measurements of dry deposition of SO2 by the profile method and by some other methods have been made mainly for grass and water surfaces. Deposition velocities-defined as the ratio of the ffux and the surface air concentration-normally lie in the range 0.5 to 2 cm s- ’ with an average value of slightly less than 1 cm s-’ (Garland. 1978).
With a scale height of 1.5 km. a depositron velocity of 0.8 cm s- ’ corresponds to a turn-over time with respect to dry deposition of roughly 50 h. It is not yet clear how effective forests are in removmg SO, under different conditions and the extrapolation of the measured deposition values to large areas with different surface characteristics is far from straight forward. Furthermore. most deposition measurements have been made in temperate climate and may not be representative for other climatic regimes. Some measurements indicate that the deposltion of SO, on snow might be as low as 0.1 cm s- ’ (Dovland and Eliassen, 1976). Regarding the dry deposition of sulfate particles it is generally believed (e.g. Garland and Branson. 1976) that it is small compared to the wet deposition. Deposition velocities for submicron particles of less than 0.1 cm s-’ have been mentioned (Chamberlain. 1967). were Somewhat larger values (0.2-0.5 cm s-‘) reported by Van der Hoven (1975). (b) Wet deposition. As was pointed out in section 3 the average rate of removal by precipitatron is determined both by the frequency of OOcurrence of precipitation events and by the scavenging coefficient during the precipitation. The former quantity is evidently highly dependent on the prevailing climatic condition. Based on a very limited amount of data Rodhe and Grandell (1972) found that the lower limit of the turn-over time with respect to precipitation seavenging-i.e. the term A in Equation l-was about 35 h in winter and 90 h in summer for Scandinavian climate. As an annual average this lower limit may be set at about 50 h for the climate of northern Europe. The incorporation of sulfur into the rain-drop can take place either inside the cloud during the formatlon of raindrops or when the raindrop is falling through the cloud-free air below the cloud. For details of the physical processes involved in the scavenging of gases and particles. reference is made to papers by Hales (1972) and Slinn (1977). Data on the distribution of radioactive compounds have been used by several authors to estimate the removal rate. A review of such studies made by Martell and Moore (1974) concluded that the average residence time for tropospheric aerosols was less than or about equal to one week. Presumably. wet removal has been the dominant removal mechanism in these cases. Generally. estimates of the scavenging coefficients for gases and particles vary widely (see e.g. McMahon et al., 1976). As far as sulfur compounds are concerned there does not even seem to be a consensus about the relative importance of SO2 and sulfate scavenging for the wet removal of sulfur from the atmosphere. (c) The rate of tranSformation SO, to SO:- If the experimental evidence for removal rates was quite mconclusive, this is even more true for the transformation rates. Estimates of the inverse of transformation rates vary from a few hours to at least hundred hours (EPA. 1975).
617
Atmospheric sulfur compounds There are reasons to believe that the transformation rates vary not only between different climatic conditions but also depending upon the concentrations of various other man-made compounds It may therefore not be possible to compare rates deduced from studies made in chimney plumes with rates applicable to large scale budgets (see section 6.1) Husar er al. (1978) reported detailed studies of the sulfur budget of a power plant plume in the St Louis area in the U.S. performed as part of the MISTT Project. The plume was sometimes identified up to a distance of about 300 km (Gillani et al., 1978). Reaction rates for the conversion of sulfur dioxide to sulfate were found to be typically 0.01-0.04 h-’ during noon hours and less than 0.005 h-’ at night. Similar values have been reported from measurements in the plume from the Sudbury Smelter Plant in Canada (Lusis and Wiebe, 1976; Forrest and Newman, 1977) Alkezweeny and Powell (1977) report somewhat higher values (around 0.10 h- ‘) in the urban plume of St Louis for travel times up to a few hours
5.2 Long-range
transport
models
Provided that the description of the transport and dispersion processes in such models is trustworthy, a comparison between calculated and observed concentrations can give useful information about transformation and/or removal processes. Since such a condition is not always fulfilled a certain amount of scepticism about interpreting model parameters as physical parameters is well motivated. A further complication arises in those cases when attempts are made to determine more than one parameter at the same time. It is then not enough to find a set of parameters which gives a reasonable agreement between calculated and observed values. One has to show that such a set is unique i.e. that other sets may not also give a fair agreement. This problem was encountered and commented upon by Eliassen and Saltbones (1975). In their study, these authors compare the measurements of surface air concentrations (daily means) obtained in the LRTAP network with values calculated with the aid of a dispersion model based on trajectories. The data were taken from 6 stations in northern Europe and covered two periods of each two months’ duration. Three parameters were estimated by regression analysis: the decay rate of SO2 (including dry removal, wet removal and conversion to sulfate), the conversion rate SO2 to sulfate and the mixing height. Eliassen and Saltbones found average values of these parameters around 0.07 h-l, 0.007 h-’ and 12OOm respectively. Because of the neglect in the model of any removal of sulfate by precipitation the derived conversion rate is likely to be smaller than the real value. The decay rate of SO, is more likely to have some physical significance, but the comments made above must be kept in mind. In the calculations referred to in the LRTAP report
(Eliassen, 1978) the values of the parameters are partly based on the above estimates by Eliassen and Saltbones (1975) If, in the model, precipitation scavenging were allowed to act on sulfate particles instead of on SO2 higher values of the transformation rate and of the decay rate for SO:- would have been implied. A similar type of model was used in the SURE experiment in the U.S.A. (EPRI, 1976) to calculate SO, and SO$- concentrations for comparison with observed 24-h values Transformation rates (SO2 to SO:-) in the range 0.02 h-i-O.01 h-’ seemed to give a fair agreement but the limited amount of data prevented any firm conclusions from being drawn. Prahm et al. (1976) applied a simple trajectory box model to study the transport of SO1, SOi- and trace metals from the British Isles to the Fames where measurements had been made. Values of the deposition velocities for SO, and SOi- (2 and 0.4 cm s-l, respectively) and of the transformation rate (0.011 h-‘) were derived. These values are. however, dependent on several assumptions the most critical probably being a ‘dilution factor’ and they are there fore uncertain to at least 50% For example, a larger dilution would decrease the deposition velocity and at the same time increase the transformation rate. Omstedt and Rodhe (1978) used a simple onedimensional (height) dispersion model to study the ratio of SO, to SOi- in a polluted region. By comparison with observations of this ratio they concluded that the average conversion rate is likely to be in the range 0.04-0.007 h-’ for European conditions. They further found that it was difficult to explain the observed wet deposition pattern if all sulfur had to be transformed to SOi- in the air before being scavenged by precipitation. In order to have a rapid enough wet removal of sulfur the scavenging of SO1 is likely to be significant. 6. DlSCU!WON
In this section I shall first make some comments about the comparison between the various time scales referred to in the previous two sections When making such comparisons it is essential to be very clear about the definitions and significances of the time scales used I finally summarise the information about turnover times available from the budget estimates and attempt an estimate of likely values as applied to a European type climate. 6.1 The relation
between reaction
rates and turn-over
times One of the first things to consider is to which extent it may be justified to equate the inverse of estimated rate coefficients with turn-over times (i.e. average residence times) Almost all estimates of reaction rates from measured data are based on the assumption that the reaction is of first order with a constant coe.fRcient and that therefore the decay corrected for the disper-
HENNING RODHE
678
have been transformed or removed. the inverse of the estimated rate coefficients may be much smaller than the real turn-over time. When modelling a situation like this a decay proportional to the square of the concentration might be considered (b) This is the exponential case when k,,’ = Q. (c) The rate of removal is slow in the beginning and increases later on. Here the Inverse of the rate coefficient estimated close to the source may be larger than the turn-over time (k,, > TV). A physlcal situation when this may apply is decay due to wet removal during a precipitation situation if the pollutant has to disperse up to cloud levels before it is being significantly removed. Measurement of SO1 oxidation rates in a power plant plume reported by Husar et a/. (1978) indicate a variation of the rate coefficient during the first few hours which would give rise to a similar distribution of residence times. 6.2 Summary of turn-over %I
‘I:
Fig. 3. Three examples of distribution functions for residence times. The turn-over time rO (the average residence time) is about equal in the three cases. If rate coefficients are determined from measurements close to the source (i.e. short times) the inverse of such rate coefficients may differ very markedly from the turn-over time (see text)
sive dilution is exponential. If this is not valid the inverse of the estimated rate coefficient may be a poor measure of the turn-over time. In order to exemplify such situations let us consider the distribution function, F(T), for the residence times of individual molecules (Bolin and Rodhe, 1973). F(r) is thus the fraction of all molecules that have a residence time less than T and 1 - F(7) is the fraction which is still in the air the time T after they have been enutted Figure 3 shows three different examples of such distribution functions. (a) The rate of removal is rapId in the beginning but decreases later so that a substantial fraction of the molecules have a long residence time. This situation may occur for example when high concentration of other pollutants near the source contribute to a rapid reaction. The values of SO2 oxidation rates quoted in Table 8 in the review by McMahon et al. (1976) indicate that this is a normal situation. Removal by dry deposition at the surface may also give rise to a similar shape. This is because the proportion of the molecules that quickly get in contact with the surface will decrease as the pollutant is spread to higher elevations If situations such as these apply, a rate coefficient estimated from measurements made at short distances from the source may seriously underestimate the real turn-over time (k,: < T,,). Even if measurements are extended up to a point when 50% of the molecules
time
estimates
Table 4 summarizes the information about tumover times obtained from the budget estimates discussed in section 4. All estimates discussed here refer to pollution sulfur, emitted mainly as S02, in a temperature climate (Europe or U.S.A.). The definition of the various time scales used in Table 4 are given in Table 3. Since the time scales in the table are interrelated there is actually more information about each time scale than indicated by the numbers in the particular column. These interrelations follow from the definitions of the different time scales as given in Table 3. For example, we have 1
1 7so*
= (z,o, 1
1 -=GO,
1
@SO,
1 )D +
(Kx’
1
1 1 _=-+‘5s
(fS)D
1
+ (Qo,)w + (G&
(&’
and ss = 7s02 + cttSo, where LXIS the fraction of the emitted sulfur that is transformed to sulfate before Table 3. Definitions The symbols of the
of the turn-over times used in Table 5. right hand sides are defined in Fig. 1.
679
Atmospheric sulfur compounds Table 4. Summary of estimates of turn-over times of sulfur compound in the atmosphere (unit. hours) Authors I50
Jun~e. 1960. 1963 Rodhc. 1972 Crnnat CI 01.. 1976 Gwland. 1977 El~asscn and Saltbonn. 1975 EPRI.
Omstdt
14cw
75-100 5&w 50 70 5n
IS
50 loo
1976
and Rodhe.
197x
90
Prnhm VI rd.. 1976
Smnh JeRrc). 1975
Garland and Bramon 1976
Husar t, ul.. 197x
25. I so
lb1
I?
70
ldl
IC)
40
hased on plume budgels no preclpltallo” scarengn*
35
Martell and Moore. 1974
deposition. LXis related to the time scales involved by the relation
Taking into account such relations and the comments made in Section 4 about the various estimates we may make a rough guess of likely values of the different time scales for the particular conditions prevaiiing in northern Europe. Such an estimate is given at the bottom of Table 4. This estimate is of course uncertain (no attempt is made to estimate any ranges) but at least it gives an internally consistent picture. The figures imply that about 30% of the SO, is transformed to SOi- before being deposited None of the estimated values seems to disagree too much with the data given in the table Minor differences are by and large within the uncertainty ranges of the different estimates (cf: section 4) The major uncertainties in the set of values given at the bottom of Table 4 seem to be associated with the three turn-over times (r&., (rso,)c and (rsoJv. For example, from the arguments presented here there is no serious contradiction in assuming a (Q&, value well below 100 h. Similarly (rsoJv may be taken to be somewhat less or larger than 80 h. It should again be emphasized that the time scales estimated here represent average conditions for a particular type of climate. For specific situations (e.g. seasons) in the same region or for other climatic zones the values may be quite different,
7. CONCLUDING
REMARKS
Budget estimates may be useful for tying together various pieces of information into a consistent picture. They may also help in identifying the most significant uncertainties in our knowledge about the circulations of the various compounds Global sulfur budgets have the common weakness that they form an average over extremely different conditions in different parts of the globe. Furthermore, concentration and deposition data are only available from very limited areas. These factors point to the advantages of making sulfur budgets over regions where data are available and where the conditions (climatewise and emissionwise) may be reasonably homogeneous It has been shown that such regional budgets-most of them applied to European conditions-may produce some useful estimates of the importance of those processes that transform and remove sulfur compounds from the atmosphere. It is recommended that similar studies be undertaken in other parts of the world In particular, North American may offer an interesting possibility in view of the large man-made emissions and of the measurements already available. One may also caution against the use of annual averages in budget estimates Pronounced seasonal variations in the rates of emission, transformation and/or removal may make such averages quite misleading In the discussion above it has become apparent
680
HENNINGRODHE
that there are definite problems associated with a comparison between time scales derived from budgets and those derived in other ways. In particular, the difference between turnover times (i.e. average resi-
dence times) and the inverse of rate coeficients should be kept in mind A need for careful definitions of the time scales used is obvious This paper is an attempt to formulate a basis for the discussion of associated problems. Acknowledgement-This work was done under contract No G3922-003 of the Swedish Natural Sctence Research Council. 1 wish to thank L. Granat for useful discussions. REFERENCES Afkezweeny A. J. and Powell D. C. (1977) Estimation of tr~sfor~tion rate of SO, to SO6 from atmospheric concentration data. Amwspherrr Environment il. 179-182.
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m a power plant plume out to 300 km
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