(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
chlorophyll were determined by collecting water samples for laboratory analysis. Water samples were collected from the five areas and their designated subareas in two ways. A rather complete coverage for nutrient content was obtained on a t least two occasions for each area through week-long synoptic cruises in 1973 and 1974. Area 5 was similarly sampled intensively in 1975. In addition to the synoptic survey, regular stations were sampled on a monthly basis between 1973 and 1974 in all but area 1.In all cases, the mean values for P for an area or subarea were averaged in with the other monthly single-station or multiple-station means to obtain a seasonal (April-October) mean value. In subareas where regular stations did not exist, the mean from the synoptic surveys necessarily sufficed for the subarea mean. This is considered reasonable for these nearshore areas because of the rather low seasonal variation in P content. The one exception was area 2A, the area receiving the input from the river Tidan a t Mariestad, where observations were few and variability was great. Physical data were also most scarce and variable in area 2A. The number of regular stations sampled for P content in the nearshore areas and the subareas during 1973-1974 are as follows: area 1, none; 2A, none; 2B, one; 2C, none; 3A, one; 3B, two; 4, two; 5A, one; 5B, two; and 5C, one. The mean values and associated standard deviations for both P and chl a reflect, as near as existing data permit, the seasonal conditions. P concentrations reflect the water column content since the mean value for each observation was determined by averaging all values through the water column. In general, area 5 has the best coverage for both physical data and phosphorus and chl a content, whereas results from area 2 are not too reliable. Estimates of Residence Times. T o estimate the effects of nutrient input to lakes, it is obvious from Vollenweider (7) and Vollenweider and Dillon ( 3 )that knowing the water res-
idence time is of great importance. However, the concept of residence time can vary. The theoretical residence time is most commonly used. This is usually defined as
where Vis the volume of the lake (or part of the lake), and QI is the inflow rate of water to the lake. For simplification it is often assumed that precipitation on the lake equals the evaporation from the lake, thus, Q J = Qo (discharge from the lake). In some lakes the theoretical residence time of the input water will not be sufficiently accurate to be able to precisely determine the time available for physical, chemical, and biological agents to operate on the input of, for instance, nutrients. However, a more accurate measure is complicated to obtain even in the seemingly most uncomplicated lakes. When dealing with archipelagos, instead of the entire lake, the inflow of water from the open lake must also be considered as the other main source of water and material to the nearshore areas. Assuming that the mixing in the archipelagos is complete, it is possible to use the steady state continuity equation as suggested by Palmer (8) to calculate the inflow from the open lake. With this technique the theoretical residence times of archipelago water, for example, can be calculated for each of the five nearshore areas according to the following equation:
where CA,Cr, and Cr, are the concentrations of some conservative substance in the archipelago, input water, and lake water, respectively. (In the calculations we have used spec. conductance as a conservative substance.) Finally, the inflow of lake water to the archipelago will, under the same assumptions, be
?;
(3)
5:. 5.;
I
?
, Area
5
Oal b o s j o n
fi Area I
The comparisons between the residence times could then give some useful information for understanding the behavior of the archipelagic water and a t the same time indicate why estimated effects of nutrients on the archipelago are different from observed. P Loading. The mean annual loading rates of P into the five nearshore areas were estimated for the period 1972-1974. River input was estimated by multiplying monthly flows by monthly measured concentrations. Loadings from municipal sewage and from industrial wastes were included according to published values (9). The loading of P into subsequent subareas was estimated by multiplying the mean P content in the preceding subarea by the annual discharge either from the river, or in the case of area 2, the river combined with lake water flow through the area using a net lake flow estimate (2). Prediction of P Content. For the purpose of predicting mean P content in the various subareas, the equation of Volenweider and Dillon ( 3 )was used. That equation was derived from a steady state solution of Vollenweider’s ( 7 ) model for lake P content and is L(l
i o krn 1
Figure 1. Lake Vanern showing nearshore areas and area sections Areas are (1-5) Kinneviken, Mariestadsfjarden, Asfjorden. Kattfjorden, and Satersholmsfjarden, respectively 322
Environmental Science & Technology
-R)
ZP
(4)
where L is areal P loading in mg P m-2 yr-l, R is the retention coefficient, Z is the mean depth (m), and p is the flushing rate (yr-l). P was also predicted from Vollenweider’s ( 7 ) original steady state equation: (5)
where the net sedimentation coefficient (T is used (yr-l). Mean sedimentation coefficients were obtained for this equation from the ratio of observed mean sedimentation rates for the five areas [L. Hakanson (Dept. of Physical Geography, Univ. of LJppsala, Uppsala, Sweden), written communication] in g P yr-l to the observed amount of P in the various areas in g P m-2. The most difficult parameter in the first equation to obtain is R , the retention coefficient. R was estimated in two ways: R,,, the observed coefficient, was estimated in the various areas and subareas from
P load in - P load out P load in
(6)
and R, was calculated from an equation by Kirchner and Dillon ( 1 0 ) :
R = 0.426 exp(-O.271qs)
+ 0.574 exp(-0.00949
ys) (7)
where ys is determined from Q/A-inflow over area. Prediction of Chlorophyll Content. Chl a was predicted from the P content with the aid of the empirical equation of Dillon and Rigler ( 4 ) : loglo chl I I = 1.449 logiJ't,,t
- 1.136
(8)
Dillon and Rigler developed this equation from observations on a number of North American lakes-46 data points in all. The equation defines the relationship between pregrowth period total phosphorus concentration and mean summer chl a content. The correlation coefficient was 0.95, although the confidence interval for a given estimate is quite large because the relationship is log-log. Although Dillon and Rigler used the pregrowth period P content, the spring-summer mean was used from the Lake Vanern nearshore areas because of the relatively small seasonal variability in the values. Also, Dillon and Rigler stated that their equation was valid only if P could be considered the most limiting nutrient as indicated by an N:P ratio greater than 12. This was always the case in Lake Vanern.
Results and Discussion Water Movement. Residence times and the transport of water from the lake t.o the archipelago ( Q L ) , calculated with Equations 1-3, are listed in Table I for the archipelagic areas. Comparison between the residence times shows that in all areas the theoretical residence times for surface water input alone are much longer than those t h a t also take into account the inflow of lake water. A general feature of the values for Ql, is that they almost always indicate smaller amounts of transported water compared with the actual volume transported when physically measured, due to the fact that complete mixing never occurs. This has been shown for area 5 where several direct current measurements were performed (2). Here, the mean water transport was estimated t o be a t least three times the value shown in Table I. The same phenomenon has been ohserved for the exchange of water between the two main basins of Lake Vanern and in Asfjorden (area 3) where extremely high values of water transport were shown by others ( 11). Also, a number of instantaneous observat,ions in areas 1 and 2 indicate t h a t very large volumes of' water are transported from the lake to the archipelago. In Kattfjorden (area 4), however, the estimated transport (QL) should be fairly close t o a physically measured transport of water. Thus. note that the physically transported volumes of water through R cross-sectional area, representing the outer limits of the archipelago, do not always represent the exchanged water volumes that are needed to estimate a water quality condition. Furthermore, even if the open lake water is well
mixed in the archipelago, the river input may not be; e.g., if the surface water entering the archipelago has the character of a jet, it will not mix significantly. This condition exists to some extent in all areas except area 2 . In area 5 the river Klaralven (main input) behaves like a jet thorugh the archipelago for part of the year. The inflow (Qr) may then be too high a value if one wants t o use water residence time t o estimate the movement of a substance. The result of the incomplete mixing of the input river water will often tend to offset the effects from excessive lake water inflow, which means that the theoretical residence times ( Ttr) are more realistic for purposes of estimating substance residence times. From our experiences ( 2 ) ,it is rather obvious that in Vanern neither the estimated volumes of water entering from the open lake nor the theoretical residence times ( T t ~are ) entirely adequate. Because data on water movement are insufficient, the conventional estimate of theoretical residence time was used as a first approximation in the following calculations, although calculations including lake water inflow and other more sophisticated residence time concepts based on the salt budget would no doubt improve agreement between observed and predicted values. Phosphorus. Phosphorus loading and the physical characteristics in the five nearshore areas are shown in Table 11. Industry contributes a sizable amount of P to areas 2-4, most of this coming from pulp mills. These are mean values for the three-year period 1972-1974. Interestingly enough, the input to area 5 during that period dropped by 87% because of the initiation of secondary treatment in 1973 and tertiary treatment in 1974. Thus, the present input of P to area 5 is only 21% of the 1972-1974 mean value shown in Table 11. Note that areal P loading appears rather high in all the nearshore areas, ranging from over 1 g P m-2 yr-' to 0.7. The loading to the total area of Varmlandssjon is only 0.14 g P m-2 yr-l. While the areal loading is rather high in the nearshore Table I. Calculated Residence Times in Days in Five Nearshore Areas of Lake Vanern a Area
1
r,,
605 2 QL 5800 TtA
2 (A
+ B)
181 6.7 555
+
2 (A B C)
+
510
3
4
5 (A
157 715 38 305
B
74.8 38 147
a t = theoretical. / = surface water inflow, A = archipelago water, of lake water in m3/s. Not possible to calculate.
+ C+)
5 (A
+ B)
241
QL
= input
Table II. Phosphorus Loading and Physical Characteristics in Five Nearshore Areas in Lake Vanern, Sweden, During 1972-1974 Physical characteristics from Lindell (7) Areas
1
2
3
4
5
37.5 4.2 39.2 80.9
9.9 76.0 11.0 47.6 25.0 , . , 45.9 123.6
P load in tons
River Sewage Industry
Total P load in g m-' yr-' Mean river inflow m3 s-l Mean detention time in days Mean depth (2) in m Area in km'
78.3 25.5
51.8 44.4 ... 18.7 103.8 114.9 0.92 19 605 8.6 112.9
0.80 25
1.09 75
0.85 17
0.70 147
510 157 715 241 7.7 20.6 19.5 11.3 143.2 74.1 54.0 177.3
Volume 12,Number 3,March 1978 323
areas, Tables 111-VI1 show that the predicted and observed concentrations are not proportionately as high. That is due to the relatively high flushing rates in the nearshore areas (mean of 7.0 yr-l). The amount of P measurable a t any one time and available for algal uptake is relatively low in highly flushed areas ( 5 ) . The agreement between predicted and observed P is quite good if the observed retention coefficient (R,) from Equation Table 111. Physical Characteristics, P Loading, and Predicted and Observed P and Chlorophyll Content in Kinneviken, Area 1 P loading from 1972-1974, and observed values from 1973-1974 for P and 1973 for Chl a except where indicateda Whole area
Area, km2 Z,m Volume,. km3 P , yr-’ L, g P m+ yr-’
Lake
112.9 8.6 0.997 0.60 0.92 0.47 0.65 0.0 94.5 62.4 178.3 11.0 f 2.1 ( n = 10) 54.0 4.96 ( n = 3)
RO
Rc
u,yr-’ Pp(Ro), p p m , Kl/L PpC J), PLg/L Po, pg/L f SD Chl ap, pg/L Chl a,, pg/L
6 is used. This is clearly represented by the solid circles in Figure 2. The striking anomaly is the highest predicted value in area 1 (Table 111), which is relatively easy to explain. The flushing rate is greatly underestimated (residence time overestimated) if only theoretical residence time for the surface water input is used. A pattern of rapid inflow of water from the open lake into area 1,described earlier, effectively carries the external supply of nutrients into the open lake; therefore, they are not observed in the nearshore area. If this is taken into account, then the predicted P level is much closer to the observed value of 11 pg/L. There is also a slight difference between predicted and observed values in areas 3B and 5A. The cause of the higher observed values in 3B could be an influence from the open lake, due to inflow of lake water, but data are not available
Table V. Physical Characteristics, P Loading, and Predicted and Observed P and Chlorophyll Content in Designated Sections of Asfjorden, Area 3 P loading from 1972-1974, and observed values from 1973-1974 for P and 1974 for Chi a. See legend from Table Ill Section
8.4 f 1.6 ( n = 11) 1.5 f 0.37 ( n = 6)
p = flushing rate, L = loading rate of P, I?, = retention coefficient observed, Rc = retention coefficient calculated ( IO), u = sedimentation rate, P, = pre-
dicted phosphorus content using respective correction for sedimentation, Po = observed mean f standard deviation (seasonal), Chl a, = observed mean f standard deviation (seasonal), Chi a, = predicted mean. Data from 1970, 1971, and 1973 ( 1 ) . Chl a,, pg/L Chl a,, pg/L f SD
Table IV. Physical Characteristics, P Loading, and Predicted and Observed P and Chlorophyll Content in Designated Sections of Mariestadsfjarden,Area 2 P loading from 1972-1974, and observed values from 1973-1974 except where indicated. See legend from Table 111 A
Area, km2 -z, m Volume, km3 P , yr-’ L, g P rn+ yr-’ RO Rc
u,yr-‘ Pp(Roh p p m ,W L Pp(d, Po, pg/L f SD Chi a,, pg/L Chl a,, pg/L f SD
28.0 4.3 0.119 8.64 2.95 0.61 0.41 3.86 31.0 46.8 55.1 29.5 f 12 ( n = 4) 10.5 10.5 f 2.4a ( n = 3)
Section B
46.6 4.6 0.214 3.55 0.911 0.77 0.50 9.35 12.8 27.9 15.4 11.4 f 3.5 ( n = 9) 3.0 1.g6
C
Lake
68.6 11.2 0.767 1.68 0.23 0.07 0.48 3.92 11.4 6.4 3.7 11.2 f 2.9 8.8 f. 1.3 ( n = 7) 2.5 2.56 2.2 f 0.7‘ ( n = 6)
a Data from 1970, 1971, and 1973 ( I ) . Data from 1973 in vivo ( I). Data from 1973 ( 7).
324
Environmental Science &. Technology
B
A
a
28.4 20.6 0.586 4.04 2.85 0.46 0.26 1.44 18.5 25.3 25.1 18.6 f 8.6 ( n = 8) 5.1 2.2 f 0.5 ( n = 3)
20.4 20.6 0.420 5.63 1.23 0.43 0.19 2.52 6.1 8.6 7.3 10.6 f 2.2 ( n = 9) 1.o 2.8 f 0.7 ( n = 3)
Lake
10.0 f 2.2 ( n = 11) 2.2 f 2.2’ ( n = 5)
Data from 1973.
Table VI. Physical Characteristics, P Loading, and Predicted and Observed P and Chlorophyll Content in Kattfjorden, Area 4 ’
P loading from 1972-1974, and observed values from 1973-1974 for P and 1974 for Chl a. See legend from Table 111 Whole fjorden
Area, km2 z, m Volume, km3 P , yr-’ L, g P m-* yr-‘ RO
RC
u,yr-’ Pp(Ro), Pp(Rc), P p l d Pg/L Po, pg/L f SD Chl a,, pg/L Chl a,, pg/L f SD
54.0 19.5 1.05 0.51 0.85 0.88 0.55 3.87 10.3 38.5 10.0 10.2 f 1.2 ( n = 13) 2.1 21 f 0.6 (n= 9
Lake
10.9 f 3.7 ( n = 11) 10.9 f 3.7 ( n = 6)
from 3B. If 1974 loading values are used for 5A, instead of the 1972-1974 mean, loading is reduced from 5.6 to 3.9 g P m-2 yrl, and the predicted value comes out equal to the observed: 16 pglL. Clearly, if the loading and flushing rates are reasonably accurate, the expected concentration will be very close to the observed when R, is used. The use of retention coefficients (R,) from Equation 7 gave a much poorer fit between observed and predicted P, as expected, than the observed values (R,) (Figure 2). In most cases the R, values were greater than the R, values, which were a function of surface hydraulic loading (10). R, values would be independent of the lake water movement into the nearshore areas and tend to predict the fractional retention if the river inflow were the only water inputs to each system. For those lake inflows that have lower concentrations of P than within the areas, the area P content would be diluted and cause the R,, values to appear greater than they would be without any lake inflow. The relatively good agreement between observed and expected P may be due in part to that phenomenon. The comparison of the two methods of estimating retention coefficient is shown in Figure 3. The method of predicting P using the sedimentation coefficients and Vollenweider’s original model (Equation 5) was less accurate in most cases than by the R, method (Tables 111-VII). That was also more or less expected since the sedimentation rates reported by L. Hakanson (written communication) were means for the entire nearshore area in question. The one case (area 4, Table VI) where the entire fjord was used and not subdivided, the predicted P using the sedimentation coefficient was very close to the observed, 10 vs. 10.2 pg/L. Chlorophyll a . The data on chl a were not as numerous as that for P. Many of the observed values (chl a ) are based on as few as two or three calculated area means. Of course, each area mean determined at one time was often a result of more than one observation throughout the area. Because of the sparse data, the relative agreement between observed and predicted chl a can only indicate a general trend. Chl a predicted by Equation 8 agreed reasonably well with observed values, even when predicted instead of measured P was used (Figure 4). The 95 and 50% confidence intervals reported by Dillon and Rigler’s results were included in Figure 4 to indicate how well the prediction in Vanern agreed with
observed values within a variability expected from the equation. Interestingly enough, six of the values fall within the 50% limits, and all except the value from area 1 are close to or within the 95% limits. The extreme width of Dillon and Rigler’s cohfidence intervals is a result of plotting the data on an arithmetic scale while their relationship is log-log. Although it is very useful as a management tool to predict chl a to within 50%probability, the log-log relationship gives too much error at the 95% level to be very useful within a narrow range of chl a like that in Lake Vanern. Open Lake. The loading of P to the open water in Varmlandssjon was considered from the standpoint of determining the role of the nearshore areas in retaining P and the response in terms of algal biomass in the open lake. Because the cal-
50
-
40
-
-.
t=6 2 X
X
0)
a
3
n
30-
X
a w c
;
20-
a n
V
1
10
I
I
20
30 OBSERVED P t d pgll
I 50
I
40
Figure 2. Observed vs. predicted total phosphorus content in five nearshore areas of Lake Vanern Predicted values using Ro and Rc indicated by solid circles and crosses, respectively
Table VII. Physical Characteristics, P Loading, and Predicted and Observed P and Chlorophyll Content in Designated Sections of Satersholmsfjarden, Area 5 P loading from 1972-1974 and 1973-1975 for observed values. See legend from Table ill
0.8
Secllon A
Area, km2
21.9 6.8 0.149 31.1 5.64 RO 0.27 RC 0.077 (T, yr-’ 13.6 Pp(Ro), 19.5 Pp(Rc), Pg/L 24.6 Pp(d3 CCglL 22.9 16.0 f 2.1 Po pg/L f SD ( n = 6) Chl a,, bg/L 4.3 Chi a,, pg/L f SD 6.0 f 2.0 ( n = 2)
-
z, m Volume, km3 c,yr-’ L, g P m-* yr-’
B
63.2 12.8 0.81 5.72 1.17 0.24 0.29 9.49 12.1 11.3 9.9 12.2 f 1.6 ( n = 16) 2.7 3.7 f 1.2 ( n = 12)
C
92.2 23.0 2.12 2.17 0.61 0.28 0.36 7.33 8.8 7.8 5.4 8.8 f 2.0 ( n = 7) 1.7 2.2 f 0.9 ( n = 12)
Lake
0.6 0
a
0.4
*SA 0.2
9.5 f 1.9 ( n = 17)
0
0.2
0.8
0.4
0.8
1.0
RC
1.8 f 0.7 ( n = 11)
Figure 3. Comparison of retention coefficients Ro and nearshore areas in Lake Vanern
Rc for
Volume 12, Number 3, March 1978
five
325
culated retention coefficient, R,, is more independent, it was used to estimate the quantity of P retained in the nearshore areas. Also, R, is the only value obtainable for the entire lake. Thus, a weighted retention coefficient for the nearshore area was obtained (0.38). R, values were used for each area, except no retention was assumed to occur in area 1. Therefore. all P
10-
8-
-
ii 6-
0’
6 0 W I-
o0
4-
W
a a
0
2
6
4
OBSERVED ChlQ
pg/l
rb
0
Figure 4. Observed chl a content vs. chl a predicted from calculated P using Dillon and Rigler’s 1974 equation Confidence intervals are those from Dillon and Rigler ( 4 )
0.81
i’ 0.5
EUTROPHY 0.4
N
cn
\
E
0.3
a
0.E
94
*X
0.1
/
I
I
I
I
5
10
15
20
i
25 m
i Figure 5. Phosphorus loading, corrected for retention and flushing, vs. mean depth (9,showing limits for eutrophy and mesotrophy and distribution of 10 subareas in Lake Vanern
326 Environmental Science & Technology
from the river Lidan was considered to enter the lake. Otherwise, the mean nearshore R, values were weighted to the P load into each area. The R, value for the total area of Varmlandssjon was 0.75. The difference, 0.37, is the retention coefficient that can logically be applied to the open water area, whereas 0.38 can be applied to the nearshore areas. The predicted P content for the open water is 139 mg P m-2 yr-’ (1 - 0.75) = 10.0 pg/L P 0.115 yr-’. 30 m The observed mean value for the open lake is 9.5 pg/L. A chl a content of 2.1 pg/L can be predicted from the P value of 10 pg/L, and the observed mean chl a is 2.0 pg/L. The similarity of observed and predicted values to some extent validates the use of an R , value for the whole lake. It would appear that the nearshore areas have about an equal role in removing P as the open water area. The role of the nearshore areas would be relatively greater than the open water if R, values had been used, but this was not done for this purpose as indicated before, because dilution effects from inflowing lake water probably caused an unrealistic raising of the R, values. The equally high retention of P in the open lake compared to the nearshore areas is largely a result of a much smaller surface hydraulic loading (also longer retention time) in the open lake. Loading Concept and Management. As pointed out by Dillon ( 5 ) ,the use of loading rates to predict the trophic state of lakes is more meaningful if the parameters of flushing rate and retention coefficient are considered. A given relationship between L ( l - R ) / p and Z should indicate a steady state P concentration. In addition, Vollenweider and Dillon ( 3 )argue that the resulting concentration is the important variable that determines the lake response. As shown in Figure 5, if the two above-mentioned parameters (L(1 - R ) / p and Z) are plotted, given straight lines indicate potential steady state concentrations. If a P concentration greater than 30 lg/L indicates eutrophy and less than 15 pg/L is oligotrophy, then three areas in Vanern could be considered mesotrophic, none is eutrophic (2A is on the line), and the remainder are oligotrophic. Placement of area 1 in the eutrophic range is, of course, in error because flushing from the lake water was not considered. The use of T t instead ~ of Ttl would place area 1 in the oligotrophic range. Note also, as would be expected, the A’s or more shoreward subareas are mesotrophic. If we use Dillon and Rigler’s equation, the predicted chl a concentrations from those steady state P concentrations in Figure 5 are 10 and 3.7 pg/L chl a . Those values agree very well with earlier suggested limits for chl a (12),10 and 4 pg/L, respectively. Furthermore, the value of 30 pg/L total P is not too different from Sawyer’s “critical” value of 15 pg/L for soluble P in Wisconsin lakes (13), if one assumes that soluble P is about one half of total. If we included Secchi disk depth, that along with chl a and phosphorus do not provide all the needed information for management nor the precision desired. Obviously, even if the process itself is very simple, the physical behavior of the lake is very difficult to include in an elementary model of the type discussed above. Prediction of a lake response from changes in loading of about 10-30% are not predictable with much confidence even with modifications of the methods discussed here. For that, a much better understanding of the specific lake in question is required. Literature Cited (1) Welch, E. B., “The Water Quality of Nearshore Areas in Lake Vanern-Causes and Prospects”, NLU Rapport No. 7 7 , 28 pp, National Swedish Environmental Protection Board, 1974.
(2) Lindell, T., “Water Movements and Exchange Processes Within Five Nearshore Areas in Lake Vanern”, NLU Rapport No. 85,84 pp, ibid., 1976. (3) Vollenweider, R. A., Dillon, P. J., “The Application of the Phosphorus Loading Concept to Eutrophication Research”, NRC Tech. Rep. 13690,42 pp, 1974. (4) Dillon, P. J., Rigler, F. H., Limnol. Oceanogr., 19, 767-73 (1974). (5) Dillon, P. J., ibid., 20,28-39 (1975). (6) Lemming, T., Lindell, T., Kvarnas, H., Mobilt Instrument for Vattenkvalitematning i n situ, Naturvardsverket Limnologiska Undersokning, Rapport No. 61,1973. (7) Vollenweider, R. A,, Arch. Hydrobiol., 66, 1-36 (1969). (8) Palmer, M. D., J . Great Lakes Res., I , 130-41 (1975). (9) Knuttson, H., Fororeningstillforensentill Vanern f r b anlaggnigar
V., Statens Naturvardsverket, Rapport, SNV P M 631, 7 pp, 1974. (10) Kirchner, W. B., Dillon, P. J., Water Resour. Res., 11, 182-3 (1975). (11) Sveriges Meterologiska och Hydrologiska Institut, “Hydrologiska forhallanden i Asfjorden”, 1968. (12) National Academies of Science and Engineering, U.S. Environmental Protection Agency, “Water Quality Criteria-1972”, GPO, Washington, D.C., 1974. (13) Sawyer, C. M., New England Water Works Assoc., 61, 109-27 (1947).
Received for review January 24, 1977. Accepted September 30, 1977.
NOTES
Quantum Yields for Reaction of Pollutants in Dilute Aqueous Solution Richard G. Zepp Environmental Research Laboratory, U S . Environmental Protection Agency, College Station Road, Athens, Ga. 30605
Procedures are reported for determining quantum yields for direct photolysis of pollutants a t low concentrations in water. Quantum yields are used tp compute half-lives for direct photolysis of aquatic pollutants under sunlight.
and 1 is the light pathlength. When light is weakly absorbed by the system (Fsh < O . l ) , F s xvery nearly equals 2.303 ( a ~ txC)l, and Equation 2 simplifies to a first-order rate expression:
+
Rate = 2.303 l o x In a recent report, Zepp and Cline ( 1 ) described equations and parameters required to compute direct photolysis rates of pollutants in the aquatic environment. Photolysis rates ( - d C / d t ) can be computed by Equation 1 where k , is the specific rate of light absorption, 4 is the quantum yield for reaction, and C is the pollutant concentration.
Usually, the quantum yield for a reaction is determined under conditions in which all the incident light or a directly measurable fraction is absorbed by the system (2). The concentrations of substrate employed in these experiments typically range from to greater than 0.1 M. The extremely low solubilities of most organic pollutants in water preclude measurement of quantum yields under conditions of complete light absorption. In this communication a technique that can be used to determine quantum yields in very dilute solution is described. An explicit description of the use of quantum yields to compute sunlight photolysis half-lives is also included. The general rate expression for photolysis in a cell containing volume V of solution and having exposed area A is:
where l o x is the incident light intensity a t wavelength, A; Fsh is the fraction of light absorbed by the system; and Fcx is the fraction of absorbed light that is absorbed by the photoreactive substance (3).The terms F,x and Fcx are expressed by: Fsx= 1 - 10-(OA + fAc)l (3) (4)
txl&
(5)
Thus, when the light intensity, extinction coefficient, and pathlength are known, the quantum yield may be computed from the slope of a first-order plot of In C vs. exposure time:
4=
dC
- - = k,$C dt
(e)
-Slope 2.303 l o x (A/V)tAl
Procedures that can be used to determine these parameters are outlined below. Monochromatic light isolated by filters (2) is usually employed in these experiments. The intensity term, I,x(A/V), can be directly determined by exposing a solution of an appropriate reference compound, i t . , a chemical actinometer, to light in exactly the same fashion as the pollutant. The same or an identical reaction cell should be used, and the cell should be filled with the same volume. The chemical actinometer should photoreact with a well-defined quantum yield at wavelength A. When all of the incident light is absorbed by the actinometer, i.e., F,x is unity, the intensity term, Iox(A/V),equals the rate of photoreaction of the actinometer divided by its quantum yield. The potassium ferrioxalate actinometer is reliable and easy to analyze (4). The average pathlength of the photolysis cell can be determined experimentally by the following procedure. If the concentration of the light absorbing substance, C, in a photoreactive system is sufficiently high that Fcx (Equation 4) is close to unity, then Equation 2 reduces to: (Rate)c = $ l o x
($) (1- 10-f~’c)
(7)
In the special case in which txlC exceeds 2, essentially all of the light is absorbed, and Equation 7 further simplifies to Equation 8.
where ax is the absorption coefficient of the solvent, tx is the molar extinction coefficient of the photoreactive substance, This article not subject to US. Copyright. Published 1978 American Chemical Society
Volume 12, Number 3, March 1978
327
