(19) Sanders, W. N., Maynard, J. B., Anal. Chem., 40,527 (1968). (20) McEwen, D. J., ibid., 38, 1047 (1966). (21) Papa, L. J., Dinsel, D. L., Harris, W. C., J . Gas Chromutogr., 6 , 270 (1968). (22) Jacobs, E. S., Anal. Chem., 38,43 (1966). (23) Hurn, R. W., Allsup. J. R., Cox, F., “Effect of Gasoline Additives on Gaseous Emissions”, National Tech. Information Serv. Publ. No. PB-253 782, U S . Dept. of Commerce, Springfield, Va., Dec. 1974. (24) Neligan, R. E., Arch. Enuiron. Health, 5,581 (1962).
(25) Stephens, E. R., Burleson, F. R., J . Air Pollut. Control Assoc., 17,147 (1967).
(26) Stephens, E. R., Burleson, F. R., ibid., 19,929 (1969). (27) Simmons, W., Filing sheet amending Section 70200, “Table of Standards Applicable Statewide”of Title 17 of the California Administrative Code, Sacramento, Calif., May 15, 1975.
Received f o r reuieu M a y 9, 1977. Accepted September 27, 1977. Work supported by the National Science Foundation, Research Applied to National Needs Grant No. E N V 73-02904-A04. T h e contents of this paper do not necessarily reflect the uiews and policies of the National Science Foundation, nor does mention of trade names or commercial products constitute endorsement or recommendation f o r use.
Estimation of Time-Averaged Hydroxyl Radical Concentration in the Troposphere W. Brock Neely‘’ and James H. Plonka2 The Dow Chemical Co., Midland, Mich. 48640
With the global emission figures for methylchloroform, the atmospheric monitoring data, and the experimental bimolecular rate constant for hydroxyl attack, a calculation of the time-averaged hydroxyl radical concentration was made. Values of 4.8 X lo5 and 1.8 X lo6 molecules/cm3 (rt20%) for the northern and southern troposphere were necessary to satisfy the mass balance equations. These numbers agree favorably with other estimations of the hydroxyl radical concentration in the troposphere. Based on these calculations, the residence time for methylchloroform in the troposphere was in the range 2.6--4.0 years with an average value of 3.3 years.
In recent years a great deal of atmospheric monitoring data have shown that in addition to the chlorofluoromethanes, a wide variety of simple organochlorine compounds have been found in relatively unpolluted air ( I , 2 ) . These include such species as CHC13, CHSCl, CH3CC13, and CHC12CH2Cl. T o assess the future impact of these and other halocarbons in the atmosphere, it is necessary to balance the rate of production against the rate of dissipation. An important step in this problem is the discovery of sinks for the chlorocarbons in the lower atmosphere. In this connection the critical role of the hydroxyl radical as the rate-limiting step in the photodissociation reaction of the hydrogen-containing halocarbons has been receiving great attention (3-5). The general reaction is shown in Equation 1: RC1,H
+ OH*-
RC1;
+ H20
(1)
This type of bimolecular reaction has been studied by many investigators, and it is unlikely that the experimentally derived rate constants will be in serious error (7, 8). The value that becomes very critical, however, is the time-averaged concentration of hydroxyl radical assumed to be present in the troposphere. The actual hydroxyl radical concentration varies diurnally, seasonally, as well as vertically and horizontally. What is required for modeling purposes is a number that will average out these differences over a long time frame. Again this has been studied quite intensively, and values ranging from lo5 molecules/cm3 to 107 molecules/cm3 have been reported (5-11). The main source of OH. in the troposphere is the reaction shown in 2. The electronically excited
2
Environmental Sciences Research. Inorganic Product Department.
0013-936X/78/0912-0317$01.00/0
oxygen for this reaction is produced by the photolysis of ozone.
0 + HzO
-
20H.
(2)
The destruction of OH. occurs through Reactions 3 and 4 (6). OH.
+ CO
OH. + CH4
--*
+
+ COn HzO + CH; H
(3) (4)
The work in this paper represents a different approach from previous studies in deriving a time-weighted average value for the OH- concentration. The study is based on the use of the production history of methylchloroform (l,l,l-trichloroethane) and matching it against the monitoring data collected over the past few years, summarized recently by Lovelock (12),and shown in Figure 1.In this figure the low tropospheric values for the halocarbon in the early 1970’s with the subsequent rise to the present values would argue that no significant natural source for this volatile gas exists. Hence, the assumption that what is present in the atmosphere is due to man-made emission is probably valid. Accepting this assumption it is possible to carry out a mass balance study of the production data in a manner similar to our previously reported studies on trichlorofluoromethane and carbon tetrachloride (13).The problem then reduces to estimating what hydroxyl radical concentration in the troposphere is required to satisfy the mass balance equations. Note that both Lovelock (12) and Singh (14) have used a simplified compartmental analysis study, and their results will be discussed in a later section.
The Model We have recently worked out a mass budget model for the distribution of volatile gases in the various compartments of the biosphere ( 1 3 ) .The model shown in Figure 2 was developed for trichlorofluoromethane and partially validated using carbon tetrachloride data. This model requires an estimate of worldwide emission as input plus a knowledge of the chemical and physical properties of the agent under question. Production Data. The global production and emission figures for methylchloroform were estimated by the Corporate Product Department of the Dow Chemical Co. and are shown in Table I. Chemical a n d Physical Properties. The key properties are shown in Table 11. Henry’s constant and the transfer constants between air and water were calculated (15) using the method originally described by Liss and Slater (16).Since
0 1978 American Chemical Society
Volume 12, Number 3, March 1978
317
the parameters used by Liss and Slater were based on observations made in the North Atlantic, the derived rate constants for methylchloroform will be suitable for estimating the flux in an ocean environment. Material Balance Equation. The equations relating to the four main compartments of Figure 2 are given below:
Northern ocean:
Northern troposphere:
where N , S , A, and B represent concentrations of the chemical in the respective compartments. The various symbols and rate constants are shown in Table 111. The two unknowns are the values for kg and k 7 , the rate constants for photodegradation in the northern and the southern troposphere, respectively. The above equations were programmed to run on the Continuous System Modeling Program of the IBM 370 computer. Values for k6 and k7 in reciprocal years were adjusted to obtain the best fit to the experimental data of Lovelock shown in Figure 1.
dNldt = ko/V1- k f l - kgN - kGN - klh'
+ k4S + k 2 ( VgIV1)A
Southern troposphere:
+ kz(V41V2)B - kdS - k4S - k7S - k l S
dSldt = kaN
'g[:
T
1
Southern ocean: dBldt = k l ( VzIV4)S - k2B
Results
nI
Lovelock's Monitoring Data
dAldt = kl(V1/VB)N - k2A
North
60 -
South
Figure 1 shows the actual monitoring data collected over the years and summarized by Lovelock (12). In addition, the recent measurements of Rasmussen are also included. The Rasmussen data were collected between March 5 and March 20, 1976, on a trip down the coast of California and into the Southern Hemisphere (20).The continuous curves in Figure
Table 1. Worldwide Global Production of Methylchloroform in Millions of Pounds Year
I
1
1971
I
I
I
I
1973
1974
1975
1976
1972
1951 1952 1953 1954 1955 1956 1957 1958 1959 1960 1961 1962 1963 1964 1965 1966 1967 1968 1969 1970 1971 1972 1973 1974 1975 1976
Years
Figure 1. Computer simulation of tropospheric concentrations of
methylchloroform Bars: uncertainty associated with monitoring data. Range in photodegradation rate constant shown at left of simulation curves
I
4
A ~
k5
Vl
k3
vz
k
6 Troposphere
4
b A
kl
Stratosphere
k5
k6
k0
I
N k2
k4
A S kl
k2
1;;".1
Total
Released to atmosphere
0.3 0.5 2.1 6.0 17.6 27.4 43.2 45.7 66.8 79.6 83.8 124 112 125 161 240 288 320 327 34 1 368 508 750 800 804 917 6558
Produced
0.3 0.5 2.2 6.4 18.5 30.4 45.5 48.1 70.3 83.8 88.1 131 128 142 182 256 32 1 349 370 400 422 589 772 859 825 965 7105
Cumulative release
0.8 2.9 8.9 26.5 53.9 97.1 142.8 209.8 289.2 373 497 609 734 895 1135 1423 1743 2070 241 1 2779 3287 4037 4837 5641 6558
Ocean
North
Where
0 0 0 0
South
rate constants have been described in text. V,, V,, V3 and V, are t h e volume3'of the respective compartments. N , S, A and B represent concentrations. ko annual production vented into northern troposphere.
Figure 2. Schematic representations of distribution of methylchloroform in major compartments of environment ke in south troposphere should be k, 318
Environmental Science & Technology
Table II. Chemical and Physical Properties of Methylchloroform
Vapor pressure Water solubility Henry's constant Transfer air to water Transfer water to air a
96 mm Hg at 20 O C 480 ppm at 20 " C 1.41a 1.51 (calcd)b 7.54 cm/hb 1 1.4 cmlh
Ref. 17. Calculated according to ref. 75
2 are the result of the computer simulation where k 6 was varied from 0.08 to 0.15 yr-1 and k7 was varied from 0.4 to 0.5 yr-1. This represents the best fit generated by the model t o the actual measurements of methylchloroform in the troposphere. Watson et al. (7) reported a value of 3.72 X exp (-1627/T) for the bimolecular rate constant between methylchloroform and the hydroxyl radical. This constant is very similar to the value of 3.50 X exp (-1562/T) determined by NASA (8);hence, an average value of 3.61 X exp (-1600/T) was estimated, Since the rate constant is temperature dependent, it becomes important to select a value that will reflect average tropospheric conditions. Temperature in the troposphere ranges from 15 "C a t sea level to -45 "C a t 10 km (18).This yields an average value of --12 "C, which will be used in the calculation. I t could be argued that a value closer to 15 "C would be a better choice since this is the region where the bulk of the reaction takes place. However, our main interest is in deriving a tropospheric average value for the hydroxyl radical concentration; consequently, a temperature of -12 "C is more suitable for our objective. With these considerations in mind, the hydroxyl radical concentration can then be estimated from Equation 5: [OH.] = hP2.48 X
(molecules/cm3)
estimated the latitudinal and vertical distribution, which varied seasonally and diurnally. They determined that approximately 71% of the OH. is contained in the band 30"s30°N, and 97% is contained between 60"s and 60"N with 1.5 times as much in the south as in the north. Their values ranged from 5 X lo6 molecules/cm3 a t the equator to lo5 molecules/ cm3 above 60"N. Davis et al. ( 1 0 ) experimentally found 1-3 X lo6 molecules/cm3 a t 34"N a t 7 km and projected a 24-h average of 5 X IO5 molecules/cm3. Levy (22, 23) calculated values of 1.5 X lo6 to 4.1 X lo6 molecules/cm3. Warneck (9) calculated the hydroxyl production rates in the northern troposphere and estimated a yearly average of 7.5 X lo5molecules/cm3. More recently, Crutzen and Fishman ( 2 5 ) presented data to support their earlier observation of an average OH- in the Northern Hemisphere in the range of 3-5 X lo5 molecules ~ m - Furthermore, ~ . they estimated a ratio of 2.7 between the Northern and Southern Hemisphere, with the higher value
Table 111. Parameters for Model Shown in Figure 1 Description
where h is the estimated rate constant in reciprocal years derived from the simulation ( k 6 for the northern and k7 for the southern compartment). Using average values for k 6 and h; of 0.12 and 0.45 yr-I in Equation 5 , the average hydroxyl radical concentration in the north is estimated to be 4.84 X 105 and 1.82 X lo6 molecules/ cm3 in the south within &20%. From the temperature dependence of the bimolecular rate constant as shown in the Arrhenius expression, it was determined that for every increase of 1 "C there would be a 2% decrease in the estimated hydroxyl radical concentration. A summary of the simulation results using the values for h6 and k7 of 0.12 and 0.45 yr-l is shown in Table IV for the last five years. The only validation possible was comparing the calculated concentration of methylchloroform in water in the North Atlantic with experimental observations by Lovelock. In a personal communication Professor Lovelock provided a range of sea concentrations taken in the North Atlantic in November 1973 (48N 01W to 21N 06W). The results of eight determinations gave a 95% confidence range of 3.01 X to 5.05 X g/mL ( 2 1 ) .Our calculation yielded a value of 2.0 X g/mL. If we consider the assumption used in deriving the calculated number, the agreement with the experimental numbers is most reassuring. Figure 3 illustrates the rate of disappearance of methylchloroform from the troposphere with time, assuming no further input after 1976. From this graph a residence time for the halocarbon of 3.3 years (f20%) was estimated. Note that 3.3 years is a high value since it is based on the reported emissions of the chlorinated hydrocarbon. If the actual worldwide emissions were greater, a shorter residence time would be necessary to keep the model in balance.
Discussion Time-averaged hydroxyl radical concentrations have been estimated by other investigators. A brief summary of these results will be presented, and the values compared with those derived from the study. Crutzen and Isaken (6) calculated average OH. concentration based on CO/CH4 tropospheric profile data. Their results start with values of 1.3 X 106 molecules/cm3 a t ground level and reach a minimum of 2 X lo5 molecules/cm3 a t the tropopause for an average value of 3.5 X lo5 molecules/cm3. Chang and Wuebbles (11)produced a theoretical model of global tropospheric OH. distribution and
Value
Ref
Weight of air in of 2 X loz1 g troposphere assuming height of 10 km Area of water north of 1.54X loi8 equator cm2 2.09 X loi8 Area of water south of equator cm2 Transfer from troposphere 0.03 yr-' to stratosphere Transfer between 0.9yr-' northern and southern troposphere Mixing depth of ocean 100 m Mixing depth of 10 km troposphere Weight of water in north 1.54X 10" g (depth X area) Weight of water in south 2.09 X '01 g Flux between ocean and 9.98=yr-' air Flux between air and 0.066byr-' ocean
(5)
a 9.98 = 11.4 cmih (24 X 365idepth of ocean) yr-', (24 X 365/depth of troposphere) yr-'.
18
19 19 13 13
13 13
0.066 = 7.54 cm/h
Table IV. Summary Printout of Computer Simulation of Methylchloroform in Various Compartments of Figure 1
Year
Concn in troposphere (PPI ) North South
1970 1971 1972 1973 1974 1975 1976
28 31 37 49
1977 1978 1979 1980 1981
49 36 26 19 15
58
64 73
17 22 22 27 34 39 44
Concn in ocean
g/mL) North
South
1.15 1.25 1.5 2.0 2.3 2.6 3.0
0.52 0.57 0.65 0.81 0.99 1.1 1.3
Annual release to stratosphere ( X 1O'O g )
1.3 1.5 2.0 2.4 2.8 3.1
Production assumed to be terminated in 1976 39 29 22 16 12
2.1 1.6 1.11 0.82 0.52
1.2 0.96 0.68 0.51 0.38
2.9 2.2 1.7 1.2 0.9
Volume 12,Number 3,March 1978
319
being in the south. Singh (26)has used the methylchloroform data to make an estimate of average hydroxyl radical concentrations, and their results yield values of 2.6 X lo5 molecules/cm3 in the north and 7.8 X lo5 molecules/cm3 in the south with a ratio of 3.0. These results along with the estimation from this study are given in Table V. Our value for the northern troposphere is in good agreement with some of the other calculations, particularly, Warneck (9),Davis et al. (IO), Crutzen and coworkers (6,24,25),and Singh (26).We project a higher differential between the north and the south than was estimated by other investigators (11, 25, 26). I t appears obvious that whatever the absolute number may be, there must be a higher concentration of OH- in the south. This is probably due to a combination of higher water vapor and a lower CO level in the south as compared to the north. Both of these factors would contribute to the lower value of OH. in the north. The model predicts a flux of 2.8 X 1O1O g of methylchloroform into the stratosphere in 1975 (see Table IV). This converts to a flux of 2.32 X lo6 atoms of C1 cm-2 s-l. Crutzen and Isaken ( 6 )in their calculation estimated a flux of about twice this value. The difference is probably attributed to the higher hydroxyl radical concentration in the southern troposphere
Concentration in
Northern Troposphere
\.Southern
3
1976
1
1
1978
1980
1
I
1982 1984 Years
I
Tropofphere
1986
1988
Figure 3. Simulation of disappearance of methylchloroform in troposphere, assuming no further input after 1976
Table V. Summary of OH* Concentrations in Northern Troposphere Author
Ref
Crutzen & lsaken Crutzen Davis et al. Warneck Levy Levy Levy Chang & Wuebbles
6 24 10
9 22 23 23 11
Av [OH.] concn (mo1ecu1es/cm3)
3.5 x 105 5.0 x 105 5.0 x 105 7.5 x 4.1 X 3.3 x 1.5 X 2.0 x
105
Literature Cited
IO6 106
(1) Yung, Y. L., McElroy, M. B., Wofsy, S. C., Geophys. Res. Lett.,
lo6 106
Ratio southhorth -1.5 Crutzen & Fishman
25
Singh
26
3.0-5.0 X lo5
Ratio southhorth 2.7 This work
320
2.6 x 105
Ratio southhorth 3.0 4.8 x 105
Ratio southhorth 3.75
Environmental Science & Technology
that was used in this study as compared with the constant value of 3.5 X IO5 molecules/cm3 used by Crutzen and Isaken (6).By way of comparison the estimated flux of chlorofluoromethane is in the range of 12 X lo6 atoms C1 ern+ sdl ( 6 ) . As Crutzen and Isaken ( 6 ) state, methylchloroform is not nearly as serious as the alleged chlorofluoromethane problem; however, the future growth of this chlorocarbon should be watched carefully. An examination of the simulation results in Table IV and Figure 3 illustrates another reason for not being overly concerned with methylchloroform in the stratosphere. As the data demonstrate, if at some future time a problem is perceived, the troposphere will cleanse itself much more rapidly than in the case of the chlorofluoromethanes. The residence time for methylchloroform is in the range of 2-4 years as compared with trichlorofluoromethane where the time is measured in decades ( 1 3 ) .I t is reassuring to note that our residence time is in agreement with the value of 3 years estimated by Yung et al. ( 1 ) . Using a budget analysis on methylchloroform production, Singh (14,26)predicts a residence time of about eight years. In addition to the many uncertainties in the data base, one of the reasons for the discrepancy between our results and Singh’s must be related to the average global concentrations of methylchloroform that were used in the two calculations. Singh uses a value of 90 ppt (26),whereas our estimation is 76 ppt. The lower estimate results from using all the past monitoring data and fitting the best curve through the points by means of adjusting the dissipating reaction constants k6 and k 7 . Another problem between the two studies is that Singh uses a continuous exponential growth function to represent input of methylchloroform into the troposphere. This function is fitted with an annual growth rate of 16%in the halocarbon (14).Our model uses the actual production history that has been assembled for methylchloroform over the years. Examination of this data (Table I) indicates a fast growth in the early years followed by a steady growth of about 16-18%. T o fit an exponential curve to the production data starting in 1951 and ending in 1976 with an accumulated total of 6.5 X lo9 lb, a growth constant of 0.36 would be required instead of 0.16 used by Singh. Finally, the suggestion was made by one of the reviewers that the discrepancy in the residence time might be due to the uncertainties in the interhemispheric exchange rates ( k 3 and k 4 ) . A sensitivity analysis on these parameters indicated that a f10% change in k3 and k 4 caused only a 1-2% change in the predicted methylchloroform concentration. In addition, the value of 0.9 used for this exchange rate is in agreement with what other investigators are using (26). Regardless of the discrepancies in the absolute number, it is apparent that the hydroxyl radical concentration in the Northern Hemisphere is in the range of 3-5 X lo5 molecules cm-3 and that there is about three times this amount in the south. It now becomes important to determine if this ratio is becoming larger with the passage of time as suggested by Wofsy (27)and Singh (26).
2,397 (1975). (2) Lovelock, J. E., Maggs, R. J., Wade, R. J., Nature, 241, 194 (1973). (3) Niki, H., Dahy, E. E., Weinstock, B., Adu. Chern. Ser., 113, 16 (1972). (4) Demerjian, K. L., Kerr, J. A., Calvert, J. G., Adu. Enuiron. Sci. Technol.. 4, 1 (1974). (5) Darnall, K. R., Lloyd, A. C., Winer, A. M., Pitts, Jr., J. N., Enuiron. Scz Technol., 10,692 (1976). (6) Crutzen. P. J.. Isaken. I.S.A.. “The ImDact of the Chlorocarhon Industry on the Ozone Layer”, preprint, Nat. Center for Atmospheric Research, Boulder, Colo., 1975.
(7) Watson, R. T., Machado, G., Conaway, B., Wagner, S., Davis, D. D., J . Chem. Phys., 81,256 (1977). (8) NASA, Chlorofluoromethane Assessment Workshop Rep., NASA Goddard Space Flight Center, Mar. 1977. (9) Warneck, P., Planet. Space Sei., 23,1507 (1975). (10) Davis, D. D., McGee, T., Heaps, W., “Direct Tropospheric OH Radical Measurements via an Aircraft Platform: Laser Induced Fluorescence”, 12t,h Int. Symp. on Free Radicals, Laguna Beach, Calif., Jan. 1976. (11) Chang, J. S., Wuebbles, D. J., “A Theoretical Model of Global Tropospheric OH Distributions”, preprint, University of California, Livermore, Calif., 1976. (12) Lovelock, J . E., Nature, 267,32 (1977). (13) Neely, W. B., Sei. Total Enuiron., 8, 267 (1977). (14) Singh,H. B., Geophys. Res. Lett., 4,101 (1977). (15) Neely, W. B., Proc. of 1976 Nat. Conf. on Control of Hazardous Material Spills, p 197, New Orleans, La., 1976. (16) Liss, P. S., Slater, 1’. G., Nature, 247,181 (1974). (17) McConnell, G.. Ferguson, D. M., Pearson, G. R., Endeauour, p 13 (1975).
(18) Hodgman, C. D., Weast, R. C., Selby, S. M., “Handbook of Chemistry and Physics”, 42nd ed., Chemical Rubber Publ., 1960. (19) Esponshade, E. B., “Goode’s World Atlas”, Rand McNally, Chicago, Ill., 1957. (20) Rasmussen, R. A,, Pierotti, D., Krasnec, J., Halter, B., “Trip Report on the Cruise of the Alpha Helix Research Vessel”, submitted to N. Andersen, National Science Foundation, Washington, D.C., 1976. (21 ) Lovelock, d. E., Bowerchalke, Salishury, Wiltshire, LJK, private communication, Feh. 1977. (22) Levy, H., Planet. Space Sci., 21,575 (1972). (23) Levy, H., Adu. Photochrm., 9,369 (1974). (24) Crutzen. P. J., Telius, 26,47 (1974). (25) Crutzen. P. J., Fishman, .I., Grophys. Res. L r t t . , 4, 321 (1977). (26) Singh, H. B., ibid., submitted for publication. (27) Wofsy, S. C., Ann. Reu. Earth PlaneL. Sci., 4,441 (1976).
Receiwd /or reiieu. April 29, 1977. Accrpted Srptenzbrr 26, 1977.
Phosphorus Loading and Response in Lake Vanern Nearshore Areas Eugene B. Welch’’ and L. Tommy Lindell National Swedish Environmental Protection Board, University of Uppsala, Uppsala, Sweden
Phosphorus retention in five archipelagic areas of Lake Vanern, Sweden, was estimated, and the observed local impact on trophic state was compared with that predicted from steady state considerations. Only theoretical residence times for water were used to define changes, but other more precise methods are discussed. Five archipelagic areas of Varmlandssjon retained about 38%of the P load, and the open lake retained a similar fraction. Thus, one-half of the incoming P was retained in nearshore areas. Predicted P content agreed reasonably well with observed, and even estimates of chlorophyll a content from predicted P fell largely within the confidence intervals of chlorophyll a previously predicted from observed P concentrations for whole lake systems. Thus, with reasonably good data on P loading, retention coefficient, and flushing rate, a t least crude predictions of trophic state changes and retention capacity are possible in archipelagic areas of large lakes.
Lake Vanern, Sweden, may as a whole be considered an oligotrophic lake. However, some of the archipelagic nearshore areas have reached a mesotrophic or even eutrophic state in terms of chlorophyll and phosphorus content. Five nearshore areas of the lake were studied during 1973-75 to determine present trophic state, their effect on whole lake P retention, and effects of changed nutrient loading. The five nearshore areas shown in Figure 1 were designated largely according to earlier work (I), but with some modification of physical measurements according to Lindell (2). In addition to measurements of nutrient input to and the concentration of algae and nutrient within the areas, considerable emphasis was placed on the movement of water within and through the areas (2). The approach to this problem was similar to that proposed by Vollenweider and Dillon ( 3 ) ,Dillon and Rigler ( 4 ) ,and Dillon ( 5 ) , but applied to the lake subbasins. That is, phosphorus concentration was predicted from known P loading,
flushing rate, water distribution, and estimated retention coefficients in the different parts of five nearshore areas. The conventional concept of theoret,ical residence time or flushing rate (reciprocal of residence time) was used. While reasonably good agreement was obtained between predicted and observed P content, agreement would improve with more precise estimates of flushing rate. Predicted P content was compared to observed values and estimated values for chlorophyll u were calculated from predicted P according to Dillon and Rigler ( 4 ) and compared to the observed values. The procedure was the same for the open lake in addition to partitioning the quantity of P retained in the nearshore areas and the amount retained and sedimented in the open lake. Such an approach not only allows one to explain the present P loading-trophic state relation in the different areas of Vanern, but also represents a procedure to judge the effect of future loading on the trophic state of the open lake as well as its nearshore areas. The Vollenweider-Dillon approach allows one to judge the trophic state of a lake by tying the predicted concentration of P, the factor that determines the plankton algae biomass, to the loading rate. Thus, a loading can have a real meaning transferable to concentration and ultimately to the lake response in terms of algal biomass, water transparency, and possibly other variables such as zooplankton biomass. The approach works rather well in Vanern’s nearshore environments. The problem, of course, is the wide variability in the results when rather simple relationships are used. The counteracting advantage, however, is its simplicity, general applicability, and straightforward usefulness to management. In summary, the purposes of the research described here were threefold: Determine the predictability of P concentration and in turn chl a in nearshore areas of a large lake using retent,ion and loading rate of P Compare the relative retention of P in five nearshore areas of a large lake with that in the open water Evaluate methods for determining retention coefficient in nearshore archipelagic regions. S a m p l i n g a n d A n a l y t i c a l Methods
1 Present address, Department of Civil Engineering, University of’ Washington FX-10, Seattle, Wash. 98195.
0013-936X/78/0912-0321$01.00/0 @ 1978 American Chemical Society
Lake Data. Sampling for physical variables was performed by an automatic in situ instrument (61,whereas nutrients and Volume 12, Number 3, March 1978 321
