Ultimate understanding of t h e chemistry of toxaphene and its significance in natural waters depends on chemical identification of t h e components of t h e mixture. Acknowledgement T h e authors acknowledge the assistance of G. D. Veith of t h e University of Wisconsin Water Chemistry Program, of Vern Hacker, a n d of many others of t h e Wisconsin Department of Natural Resources. Literature Cited Boyle, H. W., Burttschell, R. H., Rosen, A. A , , in “Organic Pesticides in the Environment,” R. F. Gould, Ed., Amer. Chem. SOC.,Washington, D. C., 207-18, 1966. Buntin, G. A,, U.S. Pat. 2,565,471,August 28, 1951. Cohen, J. M., Kamphake, L. J., Lemke, A. E., Henderson, C., Woodward, R. L., J . Amer. Water Works Ass., 52, 1551-5 (1960). Faucheux, L. J., Jr., J. Ass. Offic. Anal. Chem., 48,955-9 (1965). Hemuhill. J . E., Proer. Fish Cult.. 16.41-2 (1954). Henderson, C., Pi&ering, Q. H., Tarzwell, C. M., Trans. A m . Fish. Soc , 88,23-32 (1959). Hercules Powder Co., Wilmington, Del., Hercules Toxicol. Data Bull. T-105, 9 pp, 1962. Hughes, R. A,, “Persistence of Toxaphene in Natural Waters,” MS thesis. Water Chemistrv Deuartment. Universitv of Wisconsin, Ma’dison, Wis., 135 pp, 1968. Hughes, R. A., “Studies on the Persistence of Toxaphene in Treated Lakes,” PhD thesis, ibid., 274 pp, 1970. Hughes, R. A., Veith, G. D., Lee, G. F., Water Res., 4, 547-58 (1970). Kayser, H., Ludemann. D., Neumann, H., Z . Angeu. Zool., 49, 123-48 (1962).
Koeppe, R. Z., Fischerie, 9,771-94 (1961). Lawrence, J. M., Progr. Fish Cult., 12, 141-6 (1950). Ludemann, D., Neumann, H., 2. Angew. Zool., 47, 11-33 (1960). Mahdi, M. A., U.S. Bur. Sport Fish. Wildl., Inuest. Fish Contr., 6, 10 pp, 1966. Moroney, M. J., “Facts from Figures,” Penguin Books Inc., Baltimore, Md. 472 pp 1965 rev. Poff, R. J., personal communication (Staff Supervisor), Wis. Dept. Nat. Resources, Madison, Wis., August 22,1969. Reinert, R. E.,-Pest. Monitor. J., 3, 233-40 (1970). Rose, E., Quart. Biol. Rept., Iowa State Conservation Comm., Fish and Game Div., 9,4-6 (1957). Surber, E. W., Progr. Fish Cult., 10, 125-31 (1948). Tanner, H. A,, Hayes, M. L., Colo. Cooperative Fishery Res. Unit Quarterly Rept., 1, 31-9 (1955). Terriere, L. C., Kiigemagi, U., Gerlach, A. R., Borovicka, R. L., J. Agr. Food Chem., 14,M-9 (1966). Veith, G. D., “The Role of Lake Sediments in the Water Chemistry of Toxaphene,” MS thesis, Water Chemistry Department, University of Wisconsin, Madison, Wis., 43 pp, 1968. Veith, G. D., Lee, G. F., Enuiron. Sei. Technol., 5,230-4 (1971). Workman, G. W. Neuhold, J . M., Progr. Fish Cult., 25, 23-30 (1963). Young, L. A., Nicholson, H. P., ibid., 13, 193-8 (1951). Received for reuiew Nocerizber 18, 1971. Resubmitted January 15, 1973. Accepted July 2, 1973. This project u a s supported by a contract from the Wisconsin Department of Natural Resources, Training Grant No. 2Tl-WP-22 and Research Fellouship No. 1F l - WP-26. 196-OlA1, both from the Federal Water Pollution Control Administration and by the C’niuersity of Wisconsin Research Committee. Additional support was giuen by the Unicersity of Wisconsin Engineering Experiment Station, the Department of Cicil and Encironmental Engineering, and the University of Wisconsin Water Resources Center.
Theoretical Effects of Artificial Destratification on Algal Production in Impoundments Marc Lorenzen’ and Ralph Mitchell Laboratory of Applied Microbiology, Division of Engineering and Applied Physics, Harvard University, Cambridge, Mass. 021 38
~
~~
Artificial mixing is a n important tool in the management of eutrophic lakes and reservoirs. Theoretical models of phytoplankton production are briefly reviewed and a model for application to mixed impoundments is derived. T h e model considers both nutrient depletion and the balance between photosynthesis and respiration as potential biomass limiting factors. T h e results of model calculations show that nutrient limited biomass is directly proportional to the depth of mixing, whereas light-limited peak biomass decreases linearly with increased depth of mixing. It is believed t h a t in impoundments where artificial destratification is a successful control technique, nutrient limited algal blooms are replaced by light-limited blooms of smaller magnitude. T h e most important variables are the depth available for mixing and the attenuation of light in the water column. >Present address, LVater and Land Resources Department. Battelle-Xorthwest. Richland. Wash. 99352. To whom correspondence should be addressed.
Artificial destratification of lakes a n d reservoirs has received increasing attention in recent years. Primary emphasis has been on quality control in water supply reservoirs (Committee Report, American Water Works Association, 1971; Ridley and Symons. 1972; Knoppert et al., 1970; Ridley, 1970). Several benefits have been observed as a result of artificial mixing. Aerobic conditions can be maintained throughout the water column with t h e subsequent oxidation of objectionable reduced chemical species ( F e z + ,M n 2 + , S 2 - ) . In addition, it has been reported (Ridley and Symons, 1972) t h a t algal biomass can be reduced and that populations can be changed by mixing. T h e Metropolitan Water Board of London routinely uses artificial mixing as a means of controlling algal growth. Ridley (1972) has held chlorophyll a levels to 20 pg/l. in a mixed reservoir, whereas unmixed reservoirs of similar character regularly peak a t 100 pg/l. Standing crops of blue-green algae are sometimes reduced to a greater extent t h a n green algae or diatoms (Robinson et al., 1969). However, mixing does not always reduce algal productivity. There Volume 7 , Number 10, October 1973
939
are reports of no change or increased algal biomass as a result of mixing (Committee Report, American Water Works Association, 1971; Knoppert e t al., 1970; Laverty and Nielsen, 1970). Although mixing installations are increasing in number, no generally acceptable explanation for t h e changes in algal populations has been presented. Ridley and Symons (1952) have suggested mechanisms t h a t may be important in changing algal production in mixed impoundments. They suggest t h a t cooling the epilimnion could reduce algal growth rates, vertical transport of algal inhibitors could reduce productivity, induced turbulence could keep algal particles moving a t intolerable rates, increased zooplankton grazing may occur, and the changed light regime of the algae could affect the maximum algal biomass produced. I t is the purpose of this paper to develop a model of algal production in impoundments and show how it can be used to describe and predict the major effects of artificial mixing on algal biomass. It is not the goal of this model to describe t h e detailed behavior of the phytoplankton community, but rather to consider mechanisms that put upper limits on biomass production. T h e model will be used to evaluate two mechanisms as potential biomass limiting factors: nutrient depletion and light limitation. Future refinements would include algal sinking rates and predation by other microorganisms as secondary factors which could influence the upper limits of biomass production.
PreL)ious Models Patten (1968) has reviewed 23 mathematical models of plankton production. Of these, the most pertinent to this work are those of Sverdrup (1953), Murphy (1962), Talling (1957a, 1957b), and Vollenweider (1965). More recent models of Bella (1970) and Oskam (1971) are also related. All of these models consider light as a rate-controlling parameter and include no consideration of nutrients. These models have been generally used to describe rates of production. Sverdrup (1953) quantified Gran and Braarud’s (1935) suggestion that turbulent mixing could impede phytoplankton growth. Sverdrup viewed net phytoplankton growth as the balance between gross photosynthesis and plant respiration. He assumed that the distribution of phytoplankton was homogeneous, t h a t nutrients were not limiting, that the extinction coefficient was constant, and t h a t photosynthesis was directly proportional to light intensity. Using these assumptions, Sverdrup showed that there is a “critical depth” of the mixed layer. If the depth of the mixed layer exceeds this critical value, no net production should take place because total respiration would exceed total photosynthesis on a 24-hr basis. Sverdrup’s model was extremely important in introducing the concept of a critical mixed depth and showing the importance of the mixed depth in controlling the balance between photosynthesis and respiration. However, the mathematical formulations used were not realistic. Light saturation effects were not considered. Only daily average light intensities were used. and the attenuation of light due to algal cells was not included. More recent models developed to describe the relationship between photosynthesis and depth attempt to use more realistic formulations and include some refinements. Talling (1957a, 1957b) included light saturation effects. Vollenweider (1965) considered “day rates” but not respiration or decreased transparency due to the presence of algal cells. Bella (1970) considered the effect of sinking rates of algal cells on net production. Oskam (1971) modi940
Environmental Science & Technology
fied Vollenweider’s ( 1965) basic formulations to include respiration and incremental attenuation coefficients due to light absorption by the algae. Murphy (1962) used Sverdrup’s (1953) formulations with the inclusion of a n incremental attenuation coefficient.
Model Derivation Previous models are not directly applicable to analyzing the effects of artificial mixing on algal production in impoundments. However, some of the basic principles delineated in the models discussed will be used to provide a straightforward derivation of a simplified model which considers both nutrient depletion and light limitation as biomass limiting factors. The purpose of the model developed is to show the manner in which different circumstances put different maximum limits on biomass levels. It will be shown how two mechanisms, nutrient depletion and light limitation, can be considered independently and then combined to evaluate the potential algal biomass t h a t can be produced in an impoundment. T h e results will show t h a t nutrient limited biomass is directly proportional to the depth of the mixed layer, whereas light-limited biomass decreases linearly with iccreased depth of mixing. Nutrient limitation will be considered as the capacity of the system to produce biomass prior to some essential nutrient(s) being exhausted. Light limitation will be evaluated by considering the balance between photosynthesis and respiration in a water column. Nutrient Limitation. The role of nutrients as rate or biomass limiting factors should be clearly distinguished. Kinetic data relating nutrient concentrations to algal uptake and growth rates accumulated in recent years (Fuhs, 1972; Pearson et al., 1969; Pearson and Huang 1972) indicate that low nutrient concentrations are required before algal growth rates are limited by available nutrients. By the time nutrients are depleted to a low enough level to affect rates of production, the system may have little capacity left to produce additional biomass because nutrient(s) would already be essentially exhausted. The relative importance of a nutrient as a rate or capacity limiting factor can be evaluated by considering the ratio of initially available nutrients (Co) to the half-saturation constant ( K , ) from a typical Monod nutrientgrowth rate function. The higher the initial nutrient concentration ( C O ) .the more biomass can be produced before the nutrient is depleted to such a level that the rate function is affected. T h e larger CoIK, is, the more reasonable it is to consider nutrients as only biomass limiting. For eutrophic impoundments in which nutrient concentrations are high, nutrient depletion can be considered as a capacity-limiting factor where some concentration, X , of algae can be produced before nutrient depletion limits further growth. T h e total nutrient-limited biomass t h a t can be produced in a water column can then be expressed as:
cz
xz
= (1) where C = algal concentration, mg/l. Z = depth of uniform algal distribution. meters X = capacity of system to produce algal biomass before nutrient(s) is (are) depleted, mg/l.
This formulation is written to apply to mixed reservoirs in which uniform distributions of phytoplankton can be maintained throughout the water column or well-stratified lakes in which uniform algal distributions can be maintained in the epilimnion. Appropriate modifications and more complex formulations could be used when nonuniform distributions occur.
Light Limitation. Available light can limit maximum biomass as well as the rate of algal growth. However, to demonstrate t h a t light can limit maximum biomass, rate functions must be written and the factors affecting the rate functions determined. T h e conditions can then be evaluated t h a t result in the rate of change of algal biomass being zero. If we assume lateral variations across the system are negligible, the rate of change of algal concentration in any element can be written as
in which the first term on the right-hand side gives turbulent mixing, the second algal settling, the third algal growth, the fourth algal respiration, and the fifth predation. where
To describe K for a water column, the variation of light intensity must be considered as a function of depth. T h e light intensity a t any depth can be approximated by
Id
=
I , exp[-(cy
+ PC)dl
(5)
where I d = light intensity a t depth, d, lux I , = surface light intensity, lux a = attenuation coefficient of light in medium, meter-1 fl = incremental attenuation coefficient of light due to algae, m-1/mI-z/1. If Equations 4 and 5 are substituted into Equation 3, then t h e instantaneous rate of net production at any depth is
For the case when the phytoplankton concentration is uniform through some depth Z, the integral of Equation 6 over this depth, the instantaneous rate of net production in the water column is given by Equation 7 .
t = time, days
d = depth, meters
D d = vertical diffusion coefficient, mz/sec C r = algal sinking velocity, m / d a y K = specific algal growth rate, dayR = specific algal respiration rate, dayP = predation rate, mg/l./day Equation 2, with specified D d and appropriate boundary conditions, generally describes the concentration distribution with depth and time. However, in a perfectly mixed zone, uniform vertical algal distributions can be maintained so ( a C / d d ) = 0. Under this condition, Equation 2 simplifies such t h a t algal growth and decay become the rate-limiting processes. Although zooplankton grazing and bacterial degradation can quickly reduce algal biomass, it is not clear that such predation limits peak biomass levels. In this model, predation will not be considered in placing an upper limit on peak biomass. In the mixed zone, Equation 2 then reduces to
ln[AI, exp[-(a
(1
+
+
PO21
(AI, exp[-(cu
+
+ BC)Z]\’)i’*]) -
RCZ ( 7 )
The depth 2, is the mixed depth. For a stratified lake, Z will be considered the depth of the thermocline and for a n artificially mixed lake, Z is the depth to which mixing is accomplished. Because light varies considerably over a 24-hr day, it is useful to integrate Equation 7 over one day to yield a “day rate.” Vollenweider (1965) has suggested the use of the “standard light day” (Equation 8) for the photosynthesis portion of the net growth rate function. Respiration is integrated over 24 hr.
~dC - K C - R C
(3) cl t Although there is some evidence t h a t the specific respiration rate. R, is not constant at different light intensities (Hoch and Owens, 1963), there are not sufficient d a t a to improve on the common assumption (Shelef et al., 1968) that R is constant for any alga. T h e functional dependence of K , the specific growth rate, on environmental parameters is not well defined and varies among different algal species. The specific growth rate should depend on light, temperature, nitrogen, and phosphorus as well as other factors. However, for eutrophic impoundments where nutrient concentrations are initially high, the specific growth rate will be considered to be only a function of available light. Changes in euphotic zone temperatures are small and would not appreciably affect algal growth rates. T h e functional dependence of K on light intensity has been shown by S m i t h (1936) and others to fit a function such as
k ’ = [l where
KrnaxAI
+
where I o ( t ) = surface light intensity a t time t t = time, plus or minus from solar noon = noon surface light intensity Io X = the number of hours of daylight T o calculate a day rate, the values of I o ( t ) may be calculated either from Equation 8 for each hourly period, or any observed values of incident radiation may be used. T h e instantaneous net column production rate (Equation 7) is then evaluated a t each of the appropriate I o ( t ) values and averaged over the day. This integration yields a daily rate of net column production. The daily rate is:
(3)
K,,,
= specific algal growth rate a t light saturation and temperature of interest, day-I A = a constant proportional to rate a t low light intensities, luxI = light intensity, lux
The value of A can be considered as a measure of adaptation to low light intensities (Vollenweider, 1965).
where AT is the time interval chosen for evaluation, hours. This day rate can be integrated to calculate biomass as a function of time; or, by setting the rate equal to zero, a Volurne7, Number 10, October 1973
941
steady state value of C can be calculated for various algal characteristics (K,,,, A , R, P ) and physical conditions (I, 2, a , A). T h e value of C calculated in this manner is t h e peak light-limited algal concentration.
Calculations and Results T o illustrate t h e results of model calculations, algal growth parameters are needed. Because it is not the purpose of this paper to describe laboratory studies, assumed values will be used for illustration. Table I summarizes t h e values used for the calculations. Biomass vs. T i m e , Figure 1 shows t h e calculated concentration of algal biomass as a function of time for differ-
Table 1. Summary of Parameters Used in Calculations Parameter
P
Value Used 0.53 day-' 0.10 day-' 0.054 lux 0.20 m - ' / m g / l .
a
0.70 meter-'
x
12 hr 54,000 lux
Kmax
R A
10 max
Definition Maximum specific growth rate Specific rate of respiration Adaptation to low light Incremental attenuation coefficient Attenuation coefficient of water Length of daylight Maximum surface light intensity
i
/ 35
40
45
M
TIME I O A Y S I
Figure 1. Calculated algal concentration as a function of time for different values of the mixed depth. Initial algal concentration was the same for each depth of mixing
i
5
0
,
,
5
10
I
15
1
20
25
1
I
30
35
40
45
50
TIME I D A Y S I
Figure 2. Calculated algal biomass in the water column as a function of time for different values of the mixed depth. Initial algal biomass was the same for each depth of mixing 942
Environmental Science & Technology
ent values of a uniformly mixed depth. These curves were calculated for a n initial algal concentration of 1.0 mg/l. The effect of the mixed depth in limiting maximum algal concentrations is seen to be very important, particularly a t shallow depths. Because t h e initial concentration of algal biomass was t h e same for each depth of mixing, the total initial biomass in the water column was not the same for each depth of mixing. Figure 2 shows the total biomass in the water column as a function of time for different.depths of mixing. In this figure, the initial total biomass in t h e water column was the same for each depth of mixing ( 5 g/mZ). This means t h a t the initially assumed algal concentration decreased as the mixed depth was increased. Figure 2 illustrates t h a t if the initial total biomass in the water column is t h e same, the total biomass at any time should decrease as the depth of mixing increases. An important point t h a t can be illustrated with the use of Figure 2 is t h a t even though lower peak biomass levels may be predicted as a result of increasing the mixed depth, algal biomass may still increase following destratification. Assume, for example, t h a t Figure 2 is based on the appropriate constants for a lake stratified a t a depth of two meters and a bloom has progressed to a level of 10 g/m2. If this lake were completely mixed to a depth of 5 meters, the total biomass would be the same as immediately prior to mixing. The 5-meter line starting at 10 g/m2 in Figure 2 would describe the subsequent course of a light-limited bloom. T h e total biomass continues to increase following destratification. However, the peak value is much lower than would have resulted if the lake had remained stratified at 2 meters. T h e 5-meter water column would have a lower peak biomass and a much lower algal concentration because the total biomass would be distributed over 5 meters rather t h a n 2 meters. P e a k Biomass. T o illustrate the importance of the physical parameters a and 2 (attenuation coefficient and depth of mixed layer), it is useful to calculate only the peak biomass. T h e light-limited peak biomass in the water column can be found by setting Equation 9 equal to zero and solving for C.Z. Nutrient-limited peak biomass is given by Equation 1. Such calculations were carried out using the variables summarized in Table I. Figure 3 shows the results of the calculations. The maximum light-limited biomass is plotted as a function of mixed depth for two values of the attenuation coefficient a . Nutrient-limited peak biomass is plotted for various values of X (see Equation 1).I t is apparent t h a t the light-limited peak biomass is strongly dependent on the attenuation coefficient, N. and on the depth of mixing. T h e nutrient-limited peak biomass can be considered to be independent of optical characteristics, although the time required to deplete nutrients will depend on the rate function which is dependent on the light intensity. In evaluating these calculations it was observed t h a t the calculated light-limited peak biomass was a linear function of mixed depth. This observation suggests t h a t the second term in Equation 9 is negligible in comparison to t h e first term when peak biomass is to be calculated. The negligible value of the second term in Equation 9 is to be expected when calculating peak biomass. Physically, the small value of the second term means t h a t the algal concentration has reached a maximum value to utilize optimally the available light in the mixed depth chosen. Therefore, integration of Equation 9 to infinite depth would add very little production because little light would penetrate beyond the chosen mixed depth. T h e value of the second term when evaluated at infinite depth is zero.
When algal densities are not near t h e maximum lightlimited value, light does penetrate beyond the chosen depth and neglecting the second term in Equation 9 would overestimate net production. For the peak biomass case, Equation 9 can now be simplified to
I
'
I
I
I
L I G H T LIMITED ALGAL BIOMASS
-
Equation 10 can then be solved for '2.2, the peak lightlimited biomass in the water column. MIXED DEPTH, z (METERS)
+
I1
[Al,(t)]21'~z)dt) - (cu/P)Z (11)
Light-limited peak biomass can be represented by plotting C.2 against 2. This line has a slope of - a l p and an intercept of
The importance of the various terms in Equation 11 are illustrated in Figure 4. Only the ratio of the maximum photosynthetic rate, K,,,, to the respiration rate, R, affects peak light-limited biomass. This result may help to generalize the model because the ratio of photosynthesis to respiration may not be as variable between taxonomic groups as either value separately. T h e effects of light intensity (I,) and adaptation to low light ( A ) are damped by the natural log term. T h e incremental attenuation of light due to the algae ( p ) affects both the intercept and the slope of the light-limited biomass line. Since the two effects on biomass are in the opposite direction, the result is t h a t p is most important a t shallow mixing depths where light limitation would not normally be important because nutrients would be controlling. The significance of the water transparency is very important. T h e term fi is not likely to vary greatly between different algal species and hence different impoundments, b u t C Y , which depends on
1
,
35
0
I
I
1
I
I
1
I
I
1
8
10
12
14
16
18
2C
X = 10mgiY.
2
4
6
MIXED DEPTH.ZiMETERS1
Figure 3. Calculated peak algal biomass as a function of mixed depth limited by nutrient depletion (upward sloping lines) and available light (downward sloping lines) for different values of X , Z, and a . Parameters summarized in Table I were used for calculations
Figure 4. Generalized plot of peak algal biomass as a function of mixed depth for both nutrient and light limitation
t h e water transparency, may range from 0.01 m - 1 to 1.0 m - 1 or more. Examination of Figure 4 reveals several interesting points. Total light-limited algal biomass (g/m2) decreases linearly with the depth of the mixed layer, whereas nutrient-limited biomass ( g / m 2 ) is directly proportional to the depth of mixing. The values plotted on the ordinate of Figure 4 are the total biomass ( g / m 2 ) in the water column. T h e light-limited concentration of algae (g/m3) decreases much more rapidly with mixed depth. The point of intersection of the nutrient limitation and light limitation lines defines the mixed depth for production of maxim u m total biomass (g/m2) in the water column. T h a t depth zoPt can be shown to be
where
i
PAT
As the depth of mixing is increased from zero to ZuPt,the peak biomass ( g / m 2 ) increases and is limited by nutrient depletion. As the mixed depth is further increased above Zopt,the peak biomass ( g / m 2 ) decreases and is limited by available light. T h e concentration (g/m3) of algae remains constant as the mixed depth increases to Zopt and then rapidly decreases with increased depth. T o illustrate the change from a stratified to a destratified situation, some depth of stratification must be assumed. If the stratified depth is 21, then, to cause a decrease in peak algal concentration, (g/m3). the depth available for mixing 2 2 must exceed Z,,,, defined in Equation 12. T o cause a decrease in total biomass in the water column, ( g / m 2 ) the depth 2 2 available for mixing must be greater t h a n
A more generalized approach to representing light and nutrient limitation is to consider a dimensionless plot. If Equation 11 is multiplied by
RP K n l . I x [ R A I,,,,,/AT/X , 11 Volume 7 , Number 10, October 1973 943
mass control, the mechanism which imposes the lower limit can be ascertained from a diagram such as Figure 4. Figure 5 provides a general diagram which can be used to compare theoretical and observed peak biomass levels.
Acknowledgment Discussions with John Ridley and Alan Steel of the Metropolitan Water Board, London, which stimulated part of this work, are gratefully acknowledged. L i t e r a t u r e Cited
RaZ Kmax F ( A I o m a x , AT / A ) DIMENSIONLESS DEPTH
Figure 5. Dimensionless plot of nutrient and light-limited peak biomass the resulting equation is
Zcu R (CZIRP - 1 K ma F( AI, maxiATI X 1 KmaxRAIo rnaiATlA ) (14) Equation 14 can then be plotted in dimensionless form to describe light-limited biomass for all situations. Figure 5 illustrates such a dimensionless plot. T h e line plotted has both intercepts of 1 and a slope of -1. In this figure, nutrient-limited biomass is represented by a line passing through the origin and having a slope of X(P/cu). Figure 5 does not delineate t h e importance of various parameters, but the diagram does provide an excellent method for evaluating the model predictions. If the appropriate constants are known, field measurements of peak biomass levels can be plotted. Field measurements should fall within the triangle defined by the nutrient-limited and light-limited lines as a function of mixed depth. The proximity of the d a t a points to either line should reflect the importance of either mechanism in controlling peak biomass.
Sum mar? and Conc 1 usions Previous models of plankton production have been briefly reviewed. For a more detailed discussion, the reader is referred to P a t t e n (1968). Because none of the models were directly applicable to the prediction of biomass levels in impoundments, a model was derived from basic principles. Since the literature (Fuhs 1972; Pearson et al., 1969; Pearson and Haung, 1972) suggests t h a t rates of algal growth are not affected by nutrient concentrations until very low levels are reached, nutrients were considered to limit only the total capacity of the system to produce biomass. Available illumination was considered as the only rate-controlling parameter. By considering the basic equations describing algal growth, an expression for net daily production was developed (Equation 9). This expression was used to calculate changes in biomass over time as well as maximum levels as a function of environmental parameters. Nutrient limited biomass is directly proportional to the depth of mixing, whereas light-limited biomass decreases linearly with the depth of mixing. It is believed t h a t in situations where artificial mixing has been shown to be a successful algal control technique t h a t a nutrient-limited algal crop is probably changed to a light-limited crop of smaller magnitude. By considering nutrients and light to be independent mechanisms of bio944
Environmental Science 8 Technology
Bella, D. A , , J . Water Pollut. Contr. Fed., 42, 140-52 (1970). Committee Report, J . Amer. Water Works Assoc., 63, 597-604 (1971). Fuhs, G . W., “Nutrients and Eutrophication,” G. E. Likens, Ed., Amer. SOC.Limnology and Oceanography, pp 113-33. 1972. Gran, H. H., Braarud, T., J. Biol. Bd. Can., 1, 279-467 (1935). Hoch, G. 0: H.. Owens, 0. H.. Arch. Biochem. Biophys.. 101, 171-80 (1963). Knoppert. P. L., Rook, J . J., Hofker. T., Oskam, G. J., Jour. Amer. Water Works Assoc., 62, 448-54 (1970). Laverty, G. L., Nielsen, H. L., ibid., pp 711-14. Murphy, J. F.. Trans. Amer. Fish S o c . . 91,69-76 (1962). Oskam, G. J., Int. Symp. M a n Made Lakes, Knoxville, Tenn., 1971. Patten, B. C . , Int. Rev. Gesamten Hydrobioi, 52, 357-408 (1968). Pearson. E. A , . Huang, C. H.. Amer. Inst. Biol. Sci., American SOC.Liminology and Oceanography, Minn., 1972. Pearson. E. A , , Middlebrooks, E. J., Tunzi, M., Adinarayana, A,. McGauhey, P. H., Rohlich, G. A , , Proc., Eutrophication Biostimulation Workshop, Berkeley, Calif.. 56-79. 1969. Ridley, J. E., Metropolitan Water Board, London, private communication, 1972. Ridley, J. E., Water Treat. Exam.. 19, 374-99 (1970). idlev. J. E., Symons. J. M . , .Jr.. in “Water Pollution Microbiolo“g?,“ R. Mitchel. Ed., pp 389-4.12 Wiley. 1972 Robinson. E. L., Irwin, W. H.. Symons. J . M.,Trans. K y , Acad. Sci.. 30, 1-18 (1969). Shelef, G., Oswald, W . J., Golueke, C. G., “Kinetics of Algal Systems in Waste Treatment.” SERL Rept. S o . 68-4, University of Calif., Berkeley, 1968. Smith, E. L.. Proc. S a t . Acad. Sei., Washington, D.C. 22, 504-10 (1936). Sverdrup, H. V., J . Con. Expior. Mer, 18,287-95 (1953). Talling, J. F., “Veu Phvtoi.. 5 6 , 29-50 (1957a). Talling, J. F. ibid., 133-49 (1957b). Vollenweider, R. A , , in “Primary Productivity in Aquatic Environments,” C . R. Goldman. Ed., pp 425-57, Univ. of Calif. Press. 1965. Submitted February 22. 1972. Resubmitted Aprii 13, 19i.3 Accepted Jul? 19. 1973. This u,ork was supported in part bi. E n i i ron m ental Protect ion Agenc) Research Fell oii’ship L.9 1004.
CORRECTION T h e figures for Figures 1 and 2 have been interchanged in the paper by Aubrey P. Altshuller, “Atmospheric Sulfur Dioxide and Sulfate. Distribution of Concentration a t Urban and Nonurban Sites in United States” [Enuiron. Sci. T e c h n o l . , 7 (8), 709-12 (1973)]. T h e captions remain the same. A. P. Altshuller
