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A model of the phosphorus cycle and phytoplankton growth in Skaha Lake, British Columbia Fleming, William M. 1974

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A MODEL OF THE PHOSPHORUS CYCLE AND PHYTOPLANKTON GROWTH IN SKAHA LAKE, BRITISH COLUMBIA by WILLIAM M. FLEMING A.B. Dartmouth College, 1963 M.S. Colorado State University, 1966 A THESIS SUBMITTED IN PARTIAL FULFILMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY in the Department of C i v i l Engineering We accept this thesis as conforming to^he required standard THE UNIVERSITY OF BRITISH COLUMBIA June, 1974 In p r e s e n t i n g t h i s t h e s i s in p a r t i a l f u l f i l m e n t o f the r e q u i r e m e n t s f o r an a d v a n c e d d e g r e e a t t h e U n i v e r s i t y o f B r i t i s h C o l u m b i a , I a g r e e t h a t the L i b r a r y s h a l l make i t f r e e l y a v a i l a b l e f o r r e f e r e n c e and s t u d y . I f u r t h e r a g r e e t h a t p e r m i s s i o n f o r e x t e n s i v e c o p y i n g o f t h i s t h e s i s f o r s c h o l a r l y p u r p o s e s may be g r a n t e d by the Head o f my Department o r by h i s r e p r e s e n t a t i v e s . It i s u n d e r s t o o d t h a t c o p y i n g o r p u b l i c a t i o n o f t h i s t h e s i s f o r f i n a n c i a l g a i n s h a l l not be a l l o w e d w i t h o u t my w r i t t e n p e r m i s s i o n . Department o f Q / ^ ' / \ n € e f iVl ^ , The U n i v e r s i t y o f B r i t i s h C o l u m b i a V a n c o u v e r 8, Canada Date A u ^ f - °j 117*/ A B S T R A C T Phosphorus i s recognized as a key nutrient in the cultural eutro-phication of lakes. A simulation model of the phosphorus cycle in eutro-phic Skaha Lake shows total phosphorus to be a useful indicator for the prediction of trophic states. Difference equations and a daily time scale are used i n a mass balance model which accounts for the dynamic s t r a t i f i c a -tion regime of the lake. Total phosphorus movement between epilimnion, hypolimnion, and sediments i s detailed i n a series of submodels. An eddy diffusion submodel predicts loading from the hypolimnion to the epilimnion which can equal external loading for short periods of the summer. A phos-phorus sedimentation submodel predicts organic sedimentation on the basis of primary production and inorganic sedimentation from adsorption consider-ations. A regeneration submodel considers the temperature-dependent decom-position rates of sedimented phosphorus. A primary production submodel accounts for temperature, ligh t and phosphorus dependency, as well as res-piration, grazing, sinking and advection losses. Based on known phosphorus loading and three years of limnological data, reasonable agreement was found between re a l and simulated total phosphorus concentration, phytoplankton bio-mass, and hypolimnetic dissolved oxygen. Results show that three to four times more phosphorus apparently returns to the lake from deep-water sediments than possible by bacterial de-composition alone. Improved simulation of phytoplankton production could probably be achieved with the inclusion of a zooplankton submodel and exten-i i i i i sion to include the specific growth dynamics of more than one algal group. The Michaelis-Menton half-saturation constant appears to be the most sensitive coefficient in the primary production submodel. The probable effects of four phosphorus management policies are assessed using 20 years of hydrologic data (1949-69) and the eutrophic conditions of 1970 as a starting point. While no attempt i s made to pre-dict the trophic status of the lake for the next 20 years, definite trends are apparent. With no phosphorus removal and no increase in loading over the hypothetical 20-year period, phytoplankton blooms increase in intensity and hypolimnetic dissolved oxygen approaches zero. With 60 per cent removal of municipal phosphorus and conditions of either low or high economic growth in the Penticton region, the eutrophic conditions of 1970 are reached within 12 to 14 years. Algal blooms and hypolimnetic dissolved oxygen deficits are particularly serious during dry years. With 100 per cent municipal phosphorus removal, trophic conditions appear to improve significantly, with the possi-b i l i t y of minor algal blooms during only dry years. These results indicate that complete removal of the phosphorus from municipal sources appears to be the most rational long-range management policy. These conclusions demonstrate that a theoretical model to pre-dict trophic indicators in a lake can be useful as both a research tool and a practical planning aid for decision-making. TABLE OF CONTENTS Page LIST OF TABLES v i i LIST OF FIGURES ix CHAPTER I. INTRODUCTION 1 A. PROBLEM DEFINITION. 1 1. The Eutrophication Problem 1 2. Phosphorus and Eutrophication 2 3. The Need For A Predictive Model 4 B. RESEARCH OBJECTIVES ' 7 II. THE OKANAGAN BASIN AND SKAHA LAKE 9 A. THE OKANAGAN BASIN 9 1. Water Quantity and Quality Problems 9 2. Geographical Setting 10 3. Geological History 10 4. Hydrology. 12 5. Water Use 13 6. Cultural Development and Associated Phosphorus Loading. 13 B. SKAHA LAKE 15 1. Physical Limnology. . . . . . . . . . . . . . . . . . . 15 (a) The Lake Basin 15 (b) The Lake Sediments 16 2. Chemical Limnology 16 (a) Water Chemistry 16 (b) Sediment Chemistry 19 (c) Net Sedimentation Rates of Phosphorus Forms . . . . 21 3. Biological Limnology 21 (a) Phytoplankton and Periphyton 21 (b) Macrophytes . . . . . 24 (c) Zooplankton 24 (d) Fish 25 4. Trophic State 25 5. Paleolimnology. . 27 iv V CHAPTER Page I I I . PHOSPHORUS CYCLING IN LAKES AND MODELLING APPROACH 29 A. EUTROPHICATION AND THE LIMITING NUTRIENT CONCEPT 29 1. The "Law of the Minimum" 29 2. R e l a t i v e Importance of Carbon, N i t r o g e n and Phosphorus. 30 (a) Carbon 30 (b) N i t r o g e n 31 (c) Phosphorus 32 B. THE PHOSPHORUS CYCLE IN LAKES 34 1. Phosphorus Compartments i n Lake Water 35 (a) Orthophosphate Phosphorus (Soluble Reactive Phosphorus). . . 35 (b) Soluble Organic Phosphorus 36 (c) P a r t i c u l a t e Phosphorus 36 (d) T o t a l Phosphorus 37 2. Turnover Rates of Orthophosphate. 38 3. The Lake as a P r o d u c t i v i t y Chamber 44 C. MODELLING APPROACH 45 1. Si m u l a t i o n M o d e l l i n g 45 (a) Time Scale 46 (b) Approach to Mathematical Statement o f R e l a t i o n s h i p s 47 2. S i m u l a t i o n Approaches to M o d e l l i n g the Phosphorus Cycle 48 (a) The Compartment Approach 48 (b) The Mass Budget Approach 50 IV. DEVELOPMENT OF A MODEL FOR SKAHA LAKE 53 A. FUNDAMENTAL INPUT-OUTPUT EQUATION 53 1. Form of the Equation f o r the E p i l i m n i o n 53 (a) Input Terms 53 (b) Output Terms 54 (c) Combined Mass Balance 54 2. Form of the Equation f o r the Hypolimnion 55 (a) Input Terms. 55 (b) Output Terms 55 (c) Combined Mass Balance . 55 3. M o d i f i c a t i o n of Mass Balance During M i x i n g P e r i o d s . . . 56 B. MIXING BEHAVIOR OF SKAHA LAKE AND VOLUME CHANGES OF EPILIMNION AND HYPOLIMNION 56 v i CHAPTER Page C. DEVELOPMENT OF SUBMODELS 58 1. Eddy Diffusion Submodel 58 (a) Simplifying Assumptions for Eddy Diffusion 59 (b) Equation for Eddy Diffusion Transport 59 (c) Coefficient of Eddy Diffusion 60 2. Sedimentation Submodel 61 (a) Sedimentation from the Epilimnion 61 (1) Sedimentation of Inorganic Phosphorus 61 a. Precipitation of Phosphorus Minerals. . . . 61 b. Adsorption of Phosphate 63 (2) Sedimentation of Organic Phosphorus 63 (b) Sedimentation from the Hypolimnion 67 (1) Sedimentation of Inorganic Phosphorus 67 (2) Sedimentation of Organic Phosphorus 69 (3) Resulting Expression for Sedimentation from the Hypolimnion 71 3. Internal Loading Submodel.. 72 (a) Mechanisms Controlling Phosphorus Transport at the Sediment-Water Interface 73 (1) Physical Disturbance and Mixing 73 (2) Physical Diffusion 74 (3) Biological Uptake 75 (4) Anaerobic Chemical Regeneration 76 (5) Decomposition Regeneration 77 (b) Formulation of Internal Loading Submodel 79 (1) L i t t o r a l Zone Regeneration 79 (2) Deep Water Sediment Regeneration 80 4. Primary Production Submodel . 81 (a) Other Phytoplankton Models 82 (b) Basic Phytoplankton Equation 84 (c) Phytoplankton Growth 84 (1) Temperature Dependency 85 (2) Light Dependency 85 (3) Nutrient Dependency 91 (4) Final Growth Rate Expression 94 (d) Phytoplankton Losses 95 (1) Respiration Losses 95 (2) Grazing by Zooplankton 96 (3) Sinking of Phytoplankton Cells 97 (4) Advection Losses 98 5. Hypolimnetic Dissolved Oxygen Submodel. . . . 98 V. RESULTS 101 A. VERIFICATION OF THE MODEL FOR SKAHA LAKE. 101 v i i CHAPTER Page 1. Total Phosphorus Concentration 101 (a) Upper Mixed Layer 101 (b) Hypolimnion Phosphorus . 107 2. Phytoplankton Production I l l 3. Dissolved Oxygen in the Hypolimnion I l l 4. Simulation of the South Basin of Skaha Lake . . . . . 115 5. Verification for 1970-71 and 1972-73 115 B. SENSITIVITY ANALYSES 117 1. Sensitivity of Phosphorus Loading and Hydrology . . . 117 2. Sensitivity of Physical and Biological Coefficients . 120 C. EDDY DIFFUSION 123 VI. DISCUSSION 125 A. INTERPRETATIONS AND LIMITATIONS 125 1. Sedimentation from the Epilimnion 126 2. Regeneration of Phosphorus from Deep-Water Sediments. 126 3. Phytoplankton Production 127 B. APPLICATION TO MANAGEMENT OF THE EUTROPHICATION PROBLEMS OF SKAHA LAKE 130 C. SUITABILITY OF THE MODEL FOR OTHER LAKES 134 VII. SUMMARY AND CONCLUSIONS 137 LITERATURE CITED 140 APPENDIX A. INPUT DATA FOR SKAHA LAKE 152 B. COLLECTION AND ANALYSES OF LIMNOLOGICAL DATA 159 1. Total Phosphorus 159 2. Phytoplankton 160 3. Dissolved Oxygen 161 LIST OF TABLES Table Page I. PHYSICAL CHARACTERISTICS OF SKAHA LAKE 15 I I . CHEMICAL CHARACTERISTICS OF SKAHA LAKE 18 I I I . ALGAL ABUNDANCE IN SKAHA LAKE, 1969-70 22 IV. PHYTOPLANKTON IN SKAHA LAKE,. 1971 22 V. PERIPHYTON IN SKAHA LAKE, 1971 23 VI. TURNOVER TIMES OF PHOSPHORUS FLUX BETWEEN COMPARTMENTS 40 VII. SENSITIVITY OF COEFFICIENTS ON PHOSPHORUS CONCENTRATION . . . . 121 VIII. SENSITIVITY OF COEFFICIENTS ON PHYTOPLANKTON PRODUCTION . . . . 122 A - l . MIXING AND EDDY DIFFUSION DATA. 153 A-2. RADIATION AND EPILIMNION TEMPERATURE 155 A-3. ESTIMATED PERCENTAGES OF TOTAL PHOSPHORUS ENTERING SKAHA LAKE FROM KNOWN SOURCES, 1969-71 156 A-4. MONTHLY OUTFLOW HYDROLOGY FROM SKAHA LAKE, 1969-70 157 A-5. YEARLY OUTFLOW HYDROLOGY FROM SKAHA LAKE, 1949-73 158 v i i i LIST OF FIGURES Figure Page 1. Location and watershed boundary of the Okanagan Basin 6 2. Bathymetry of Skaha Lake 11 3. Hypsometric curves of the north and south basins of Skaha Lake . . 17 4. Eutrophication of lakes i n the Okanagan Basin compared to other lakes in Europe and North America 26 5. Phosphorus transformations i n s t r a t i f i e d lakes during summer; expressed in turnover times . 41 6. Adsorption of phosphorus on an oxidized calcerous sediment. . . . 70 7. Growth rate of phytoplankton as a function of temperature . . . . 86 8. Relative photosynthesis rate as a function of light intensity . . 88 9. Growth rate of a phytoplankton population as a function of phosphorus concentration 92 10. Algal respiration rate as a function of temperature 95 11. Loading rate of phosphorus to Skaha Lake, 1969-70, and phosphorus outflow rate 102 12. Phosphorus concentration in surface water of Skaha Lake, 1969-70, with no modification of original assumptions 103 13. Phosphorus concentration in surface water of Skaha Lake, 1969-70, with the sedimentation rate from the epilimnion doubled 105 14. Simulated sedimentation rate of phosphorus from the epilimnion of Skaha Lake, 1969-70, and regeneration rate from l i t t o r a l sedi-ments . 106 15. Phosphorus concentration in surface water of Skaha Lake, 1969-70, with the sedimentation rate from epilimnion doubled and the re-generation rate from deep-water sediments X 3.5 108 16. Simulated sedimentation rate of phosphorus from the hypolimnion of Skaha Lake, 1969-70, and the regeneration rate from deep-water sediments 109 ix X LIST OF. FIGURES (Continued) Figure Page 17. Simulated sedimentation rates of organic phosphorus and inorganic phosphorus from the hypolimnion of Skaha Lake, 1969-70 110 18. Simulated phosphorus concentration i n the hypolimnion of Skaha Lake, 1969-70 112 19. Phytoplankton biomass in the trophogenic layer of Skaha Lake, 1969-70 113 20. Dissolved oxygen concentration in the hypolimnion of Skaha Lake, 1969-70 114 21. Simulated phosphorus, phytoplankton and hypolimnetic dissolved oxygen with varying phosphorus loading and hydrologic discharge, Skaha Lake, 1969-70 118 22. Loading rate of phosphorus from external sources to Skaha Lake, 1969-70, and simulated "internal loading" to the epilimnion by eddy diffusion 124 23. Simulated phytoplankton growth rates showing the limiting effects of temperature, light and phosphorus, Skaha Lake, 1969-70. . . . . 129 24. Hypothetical effects of four different phosphorus management policies on the long-range eutrophication of Skaha Lake. 133 25. Predictions of the trophic status of Skaha Lake with present phosphorus loading policies, tertiary treatment for phosphorus removal, and land disposal of sewage (Stockner and Pinsent 1974) . 135 CHAPTER I INTRODUCTION A. PROBLEM DEFINITION 1 . The Eutrophication Problem Most lakes begin t h e i r existence i n a r e l a t i v e l y n u t r i e n t -scarce s t a t e , as many North American lakes d i d ten to f i f t e e n thousand years ago f o l l o w i n g the Pleistocene g l a c i a t i o n . As n u t r i e n t s leach from surrounding rocks over geologic time, they accumulate i n the water and sediments, r e s u l t i n g i n the growth of primary production (mainly algae and other photosynthetic organisms). Primary production stimulates second-ary production (or primary consumption) by small aquatic animals, which i n turn enhances secondary consumption by l a r g e r aquatic animals ( f i s h ) . This process of i n c r e a s i n g n u t r i e n t content and production i s a n a t u r a l one, generally r e f e r r e d to as eutrophication, and may continue u n t i l a lake be-comes a swamp, then a bog, and f i n a l l y a meadow. While eutrophication i s a n a t u r a l process, i t i s u s u a l l y a very slow one, and a deep lake i n a n u t r i e n t - s c a r c e watershed may take tens of thousands of years to become eutrophic. (Some deep lakes w i l l probably never become eutrophic). However, the process can be a c c e l e r -ated by the c u l t u r a l impact of man's a c t i v i t i e s which can add vast amounts of n u t r i e n t s over a very short geologic time span. The eutrophication of many North American lakes, such as Lake E r i e , has increased exponentially over the l a s t several decades. While moderate l e v e l s of eutrophication (mesotrophy) may be d e s i r a b l e to enhance such values as f i s h production, 1 2 advanced l e v e l s have severe d e t r i m e n t a l e f f e c t s . H i g h l y eutrophic l a k e s , which tend to be plagued by a l g a l blooms and g r e a t l y reduced r e c r e a t i o n -a l v a l u e s , may become anaerobic i n deeper waters. Furthermore, these waters may develop t a s t e , odour, c o l o u r and f i l t e r c l o g g i n g problems which reduce water supply v a l u e s . I t i s important to d i s t i n g u i s h between " n a t u r a l e u t r o p h i c a t i o n " , a gradual process over thousands of year s , and " c u l t u r a l e u t r o p h i c a t i o n " , an a c c e l e r a t e d process of n u t r i e n t enrichment t a k i n g p l a c e i n tens of years o r l e s s . S t i m u l a t o r y n u t r i e n t s , e s p e c i a l l y phosphorus and n i t r o -gen, have both n a t u r a l and c u l t u r a l o r i g i n s . R a i n f a l l , r u n o f f and ground water from n a t u r a l or w i l d e r n e s s watersheds normally c o n t r i b u t e only s m a l l percentages of n u t r i e n t s r e q u i r e d f o r a c c e l e r a t e d e u t r o p h i c a t i o n . N u t r i e n t s from a g r i c u l t u r a l , domestic and i n d u s t r i a l sources are g e n e r a l l y the major causes of c u l t u r a l l y e u t r o p h i c l a k e s . The e f f e c t of a drainage b a s i n on the t r o p h i c s t a t u s of l a k e s w i t h i n i t i s of prime importance. As suggested by Hutchinson (1969), i t i s u n r e a l i s t i c to conceive of o l i g o t r o p h i c or e u t r o p h i c water types, but r a t h e r of l a k e s and t h e i r drainage b a s i n s and sediments as forming o l i g o -t r o p h i c or e u t r o p h i c systems. For i n s t a n c e , the coexistence i n the same watershed of a h i g h l y p r o d u c t i v e a g r i c u l t u r a l i n d u s t r y , together w i t h a nonproductive surface water i s incompatible (Stumm and Stumm-Zollinger 1972). 2. Phosphorus and E u t r o p h i c a t i o n The key r o l e played by phosphorus, e i t h e r as a s t i m u l a t o r y n u t r i e n t or as an i n d i c a t o r of the presence of s t i m u l a t o r y n u t r i e n t s , has been g e n e r a l l y accepted by most s c i e n t i s t s . The presence and.rate of increase 3 of phosphorus con c e n t r a t i o n s i n l a k e waters i s considered to be an impor-tant i n d i c a t i o n of the t r o p h i c s t a t e of l a k e s and of the r a t e at which e u t r o p h i c a t i o n i s p r o g r e s s i n g . Consider the f o l l o w i n g o b s e r v a t i o n s : " C o n t r o l of phosphorus i n p u t to waters i s the key to the c o n t r o l of e u t r o p h i c a t i o n i n a m a j o r i t y of cases." (O.E.C.D. 1973). "A r e l a t i o n s h i p between phosphorus l e v e l s and a l g a l p r o d u c t i v i t y has been demonstrated f o r many n a t u r a l waters." (Kramer et al. 1972) . "For most i n l a n d waters phosphorus appears to p l a y a major r o l e i n i n f l u e n c i n g p r o d u c t i v i t y . Under almost a l l circumstances phosphorus i s a key element i n the f e r t i l i -z a t i o n of n a t u r a l bodies of water." (Stumm.and Stumm-Z o l l i n g e r 1972). "These, and many other observations have f o s t e r e d the widespread b e l i e f that the r a p i d e u t r o p h i c a t i o n of l a k e s throughout the world i s l a r g e l y being caused by i n c r e a s e d i n p u t of phosphorus r e s u l t i n g from human a c t i v i t i e s . " ( R i g -l e r 1973). "Of a l l the elements present i n l i v i n g organisms, phos-phorus i s l i k e l y to be the most important e c o l o g i c a l l y , be-cause the r a t i o of phosphorus to other elements i n organisms tends to be c o n s i d e r a b l y g r e a t e r than the r a t i o i n the p r i -mary sources of the b i o l o g i c a l elements. A d e f i c i e n c y i n phosphorus i s t h e r e f o r e more l i k e l y to l i m i t the earth's p r o d u c t i v i t y of any r e g i o n of the earth's surface than i s a d e f i c i e n c y of any other m a t e r i a l except water." (Hutchin-son 1957). ". . .mass balance c a l c u l a t i o n s show that i n Lake E r i e as a whole, phosphorus i s g e n e r a l l y the l i m i t i n g growth f a c -t o r , and work on many other l a k e s i n North America and Europe r e v e a l s t h a t the same i s true f o r a l a r g e number of l a k e s i n the w o r l d . " ( P r i n c e and Bruce 1972). "Phosphorus i s u s u a l l y the i n i t i a t i n g f a c t o r [ i n e u t r o -p h i c a t i o n ] w h i l e other substances. . .together w i t h organic growth f a c t o r s , probably a l s o p l a y a p a r t . " (Vollenweider 1968). 4 3. The Need For A P r e d i c t i v e Model As Vollenweider (1969) has noted, n u t r i e n t budgets of la k e s are a fundamental problem of t h e o r e t i c a l and a p p l i e d limnology. Much i s known about the gene r a l theory of n u t r i e n t c y c l i n g i n l a k e s ; t h a t i s , about the supply of n u t r i e n t s , l o s s e s through v a r i o u s mechanisms, and concentra-t i o n over time. Much i s a l s o known about the q u a l i t a t i v e r e l a t i o n s h i p be-tween n u t r i e n t c o n c e n t r a t i o n and b i o l o g i c a l p roduction i n l a k e s . Quanti-t a t i v e l y , much l e s s i s known about n u t r i e n t budgets, as very few d e t a i l e d budget s t u d i e s have been performed on l a k e s . In t h i s regard, the phos-phorus budget i s no e x c e p t i o n . The c o n c e n t r a t i o n of phosphorus i n a lake i s determined by four b a s i c f a c t o r s : (a) the r a t e of i n p u t of t o t a l phosphorus to the lake from a l l sources; (b) the sedimentation of phosphorus, or the r a t e at which exchanging phosphorus i s l o s t from f u r t h e r metabolism by i n c o r -p o r a t i o n i n t o i n o r g a n i c i n s o l u b l e p r e c i p i t a t e s and undecayed org a n i c matter i n the l a k e bottom (Hayes and P h i l l i p s 1958); (c) the morphometric p r o p e r t i e s of the l a k e , which i n f l u e n c e thermal s t r a t i f i c a t i o n and r e l a -t i v e s i z e of the ph o t o s y n t h e t i c l a y e r (Hayes and P h i l l i p s 1958); and (d) h y d r o l o g i c i n p u t which determines how q u i c k l y phosphorus i s d i l u t e d and fl u s h e d through the l a k e . Because of the importance o f phosphorus i n the e u t r o p h i c a t i o n process, i t i s o f great p r a c t i c a l importance to be able to p r e d i c t from known l o a d i n g (phosphorus i n p u t ) the f o l l o w i n g : (1) the c o n c e n t r a t i o n of phosphorus i n the e p i l i m n i o n and hypolimnion; (2) the amount of phosphorus l o s t to the sediments; (3) the amount of phosphorus regenerated by the 5 sediments to the water; (4) the amount of phosphorus l o s t by hydrologic flow-through; (5) the. amount of r e s u l t i n g a l g a l growth; (6) the e f f e c t s of reducing (or increasing) the phosphorus supply. This information would enable p r e d i c t i o n of the time necessary to reach s p e c i f i e d eutrophication l e v e l s . Q u a n t i f i c a t i o n of these f a c t o r s for p r e d i c t i o n purposes i s p o s s i b l e through the formulation of a simulation model of the phosphorus-phytoplank-ton system. There i s a need for a model which accounts f o r the dynamic s t r a t i f i c a t i o n regime of temperate lakes and which d e t a i l s phosphorus move-ment between epilimnion, hypolimnion and sediments. Such a model could be i n i t i a l l y developed by e i t h e r of two basic approaches: (a) a general model f o r a s t r a t i f i e d lake; or (b) a s p e c i f i c model d e t a i l i n g the phosphorus cycle i n a s p e c i f i c lake with eutrophication problems. The second apporach Is the one chosen i n t h i s study because of the need to v e r i f y the model with data from a s p e c i f i c lake. Generalization of the model to other temperate lakes i s considered a f t e r v e r i f i c a t i o n . Skaha Lake, one of a chain of lakes i n the Okanagan Basin of southern B r i t i s h Columbia, i s i d e a l l y s u i t e d for a study of t h i s type (Figure 1). In recent years, the lake has shown signs of i n c r e a s i n g eutrophication, p a r t i c u l a r l y i n the form of a l g a l blooms. During these blooms v i s i b i l i t y w i thin the lake has been les s than a meter, and the r e c r e a t i o n a l value of the lake has been s e r i o u s l y degraded (Coulthard and S t e i n 1967). Because of the i n c r e a s i n g r e c r e a t i o n a l , a g r i c u l t u r a l and i n d u s t r i a l use of the area, an exhaustive five-year study was recently completed to determine, i n part, Figure 1. Location and watershed boundary of the Okanag Basin. Drainage divides between lake basins shown by dotted lines. 7 present l e v e l s and causes of eutrophication i n the Okanagan lakes (Canada-B r i t i s h Columbia Okanagan Agreement 1969). Major l i m n o l o g i c a l emphasis was placed on Skaha Lake, and p a r t i c u l a r l y complete data was c o l l e c t e d on the mixing regime, phosphorus loading, sedimentation, phosphorus i n the water mass, and a l g a l biomass. These data form the base from which t h i s model i s developed and v e r i f i e d . B. RESEARCH OBJECTIVES The objectives of t h i s research are f o u r f o l d : (1) to describe the p h y s i c a l , chemical and b i o l o g i c a l processes c o n t r o l l i n g the phosphorus cycle i n Skaha Lake; (2) to formulate a simulation model which p r e d i c t s seasonal v a r i a t i o n s of t o t a l phosphorus i n the water mass; (3) to formu-l a t e a model which predicts seasonal v a r i a t i o n s i n phytoplankton b i o -mass; (4) to formulate a model which pr e d i c t s d i s s o l v e d oxygen d e p l e t i o n rates i n the hypolimnion. These objectives are pursued i n the following s i x chapters. Chapter I I describes the water quantity and q u a l i t y problems of the Okana-gan Basin, and the limnology of Skaha Lake. Emphasis i s placed on n u t r i e n t loading and biology. Chapter III discusses the r e l a t i o n s h i p between nutrients and eutrophication, and d e t a i l s the complexity of the phosphorus cycle i n lakes. Modelling approaches are evaluated and the mass balance method i s described. In Chapter IV the fundamental input-output equations f o r the epilimnion and hypolimnion of Skaha Lake are presented. The d e t a i l s of each submodel (eddy d i f f u s i o n , sedimentation, i n t e r n a l loading, primary 8 production, and hypolimnetic dissolved oxygen) are then discussed. The assumption of a strong relationship between primary production and phos-phorus sedimentation i n Skaha Lake i s stressed. In Chapter V the results of the model are presented and v e r i -fied with Skaha Lake data on phosphorus concentration, algal biomass, and hypolimnetic dissolved oxygen. Sensitivities of the major "forcing functions" (phosphorus loading and hydrologic discharge) and of the physi-cal-biological coefficients used in submodels are analyzed. Chapter VI i s a discussion of interpretations and limitations of the model; included is an application of the results to the management of the eutrophication problems of Skaha Lake. Chapter VII summarizes the major conclusions of the study, and assesses the value of the model as a research tool and planning aid. CHAPTER I I THE OKANAGAN BASIN AND SKAHA LAKE A. THE OKANAGAN BASIN 1. Water Quant i t y and Q u a l i t y Problems The Okanagan Basin i n B r i t i s h Columbia i s plagued by water problems of both q u a n t i t y and q u a l i t y . The b a s i n l i e s i n the r a i n sha-dow of an orographic p r e c i p i t a t i o n system, r e s u l t i n g i n annual p r e c i p i -t a t i o n as low as 25 cm at O l i v e r ( K e l l e y and S p i l s b u r y 1949). While the 3 2 average annual r u n o f f f o r B r i t i s h Columbia i s 118 m /hr/km , the net i n -3 2 fl o w to Okanagan Lake i s 9.8 m /hr/km (Marr 1970). Even w i t h the l a r g e storage c a p a c i t y of the l a k e s , a water shortage i n the v a l l e y has a 10 per cent chance of occurrence i n any year because of i r r i g a t i o n r e q u i r e -ments f o r 25,000 hectares of lan d (Marr 1970). Great f l u c t u a t i o n s i n run-o f f from one year to the next have created a need f o r f l o o d c o n t r o l dams on the r i v e r s connecting the l a k e s , e n a b l i n g c a r e f u l l y c o n t r o l l e d water l e v e l s to be maintained. The water q u a l i t y problems focus mainly around signs of i n -c r e a s i n g e u t r o p h i c a t i o n , p a r t i c u l a r l y a l g a l blooms. Skaha Lake has i n recent years (1968-71) e x h i b i t e d two blooms.per year — a minor one i n l a t e s p r i n g and a more s e r i o u s one i n l a t e summer or autumn. Although Osoyoos Lake has not e x h i b i t e d a l g a l blooms, signs of i n c r e a s i n g e u t r o -p h i c a t i o n are evident (Booth 1969). Okanagan Lake, much longer and deeper than e i t h e r Skaha or Osoyoos Lakes, s t i l l appears to be i n an o l i g o t r o p h i c s t a t e . 9 10 2. Geographical Setting 2 The Okanagan Basin occupies a 8100 km area i n the I n t e r i o r Plateau of southern B r i t i s h Columbia (Figure 1). The c e n t r a l v a l l e y within the basin i s a U-shaped trough with a chain of narrow, north-south trending g l a c i a l lakes — Okanagan, Skaha, Vaseux and Osoyoos ( F i g -ure 1). The v a l l e y bottom v a r i e s i n width from 2 to 13 km and r i s e s from a v a l l e y bottom e l e v a t i o n of 275 m to 2440 m i n the surrounding mountains (Marr 1970). 3. Geological Hi s t o r y According to St. John (1973), the Okanagan V a l l e y i s a s t r u c -t u r a l trench overlying a system of l i n k e d f a u l t s which separate bedrock of l a t e Paleozoic or e a r l y Mesozoic age. The east side of Skaha Lake i s underlain by Monashee metamorphic rocks and l a t e r i n t r u s i v e s , while bedrock on the west side consists of andesite and trachyte flows and agglomerates of Eocene or Oligocene age. The f a u l t trace forming the contact between these bedrock types runs along the course of McLean Creek, an eastern t r i b u t a r y to Skaha Lake (St. John 1973). The bedrock base of the Okanagan trench i s o v e r l a i n by unconsol-idated sediments p r i m a r i l y of g l a c i a l o r i g i n , which reach a thickness of 600 m i n the middle of Okanagan Lake (St. John 1973). The sediments vary i n thickness under Skaha Lake from about 370 m north of Kaleden (Figure 2) to l e s s than 30 m at the narrow point separating the lake's north and south basins. According to St. John, i t i s probable that during the P l e i s t o -cene (one m i l l i o n years ago to the present) the v a l l e y was a sedimentation trap f o r morrainal m a t e r i a l , g l a c i a l outwash, and l a c u s t r i n e and f l u v i a l sediments. inflow Figure 2. Bathymetry of Skaha Lake; contour i n t e r v a l 25 f t (from St. John 1973). C i r c l e d numbers i n d i c a t e p e riphyton s t a t i o n s . 12 The glaciers began to recede somewhat before 10,000 years ago, and Fulton (cited in St. John 1973) reports the recession to be well advanced by 9750 B.P. (before present). By 8900 B.P. a l l of the ice had melted and the glacial lakes had been drained to the level of the existing lakes. The clay and s i l t glaciolacustrine c l i f f s bordering southern Okana-gan and Skaha Lakes were probably formed during the period of glacial re-cession when glac i a l downwasting processes were shaping the basin's present topography (St. John 1973). St. John estimates that a very large per-centage of the sediments are of glacial origin, while only a few tens of meters of sediment can be attributed to sedimentation from the modem main-stem lakes. The mass wastage that has occurred from the c l i f f s bordering Skaha Lake i s v i s i b l e as landslide scars, and deposits on the lake bottom from these landslides are present (St. John 1973). 4. Hydrology The annual runoff into Okanagan Lake has been estimated to 3 3 vary between 0.099 km in 1929 to 0.918 km in 1948 (with a mean value 3 of 0.450 km (Marr 1970). To emphasize the arid condition of the area, 2 Marr has noted that the average net inflow from the 6060 km Okanagan Lake watershed amounts to a yield of only 8.26 cm. The great variation in nat-ural runoff has prompted the construction of dams at or below the outlets of a l l the mainstem lakes to control flow-through rates. The lakes now have a controlled level fluctuation of 1.3 m or less (Marr 1970). Except for 6.4 km of natural channel below Vaseux Lake, s t i l l used as a spawning area for sockeye salmon, a l l of the streambanks connecting the lakes have been a r t i f i c i a l l y channelized. 13 The contribution of water from the higher elevations of the basin i s essential to the water supply of the lakes. Marr (1970) has estimated that no runoff i s contributed from areas up to 900 m in ele-vation, 25 cm is contributed from areas at 1200 m, and 60 cm comes from areas at 1800 m. 3 The average annual inflow to Skaha Lake is 0.474 km , resulting in a theoretical hydrologic turnover of 0.89/year (inflow/lake volume = 0.474/0.54). Therefore, the theoretical retention time of water in the lake (the reciprocal of the turnover) i s 1.1 years. Okanagan Lake has a greater retention time (nearly 60 years) because of i t s much greater vol-ume. Osoyoos Lake has a retention time of about 0.4 years. 5. Water Use Marr reports that in.1966 irrigation accounted for the use of 3 0.178 km of water. Three-quarters of the irrigation water comes from over 100 storage reservoirs located in the uplands of the watershed (Russell and McNeil 1974, Marr 1970). Marr (1970) indicates that the possibility of further upland storage i s limited and the source of large future demands must come in the form of pumping from the mainstem lakes. This is one important economic reason for concern about the water quality of the lakes. 3 Domestic use of water accounts for about 0.01 km , or less than 10 per cent of agricultural consumption (Marr 1970). 6. Cultural Development and Associated Phosphorus Loading The Okanagan Valley i s one of the fastest growing regions in 14 British Columbia. From 1961 to 1971 the population increased from 75,000 to 113,000, an increase of 51 per cent (the province as a whole increased 34 per cent) (Okanagan Study Commission 1971). By 1980 the population is estimated to reach 160,000, a 41 per cent increase from 1971. Using estimates from Vollenweider (1968), Patalas and Salki (1973) have calculated that about 1.7 kg/capita/year of total phosphorus •now enters the lake system. Unless measures are taken to remove phos-phorus from water before i t enters the lakes, the loading can be expected to increase approximately proportionately to the population growth. The effect on the water quality of the lakes would, by most rational estimates, be extremely undesirable. Patalas and Salki (1973) estimate that 88 to 90 per cent of the total phosphorus load to Skaha Lake is associated with cul-tural sources (municipal sewage, agriculture and industry). If no measures were taken to remove phosphorus from effluent be-fore i t reached Skaha Lake, Patalas and Salki (1973) estimate that loading 2 2 w i l l nearly double between now and 1990 (from 2.3 g/m /year to 4.0 g/m / year). However, i f 80 per cent of the cultural or controllable phosphorus load were removed, the 1990 loading (even with the projected population growth) would decrease to about 1.0 g/m /year, or be cut by more than half. Patalas and Salki speculate that i f similar phosphorus removal took place throughout the basin, the trend of trophic changes in Okanagan Lake could be reversed from high oligotrophy or low mesotrophy to the middle range of oligotrophy, and Skaha and Osoyoos Lakes would change from high to moder-ate eutrophy. 15 B. SKAHA LAKE 1. Physical Limnology (a) The Lake Basin. Significant physical characteristics of the lake basin are shown in Table 1. TABLE I PHYSICAL CHARACTERISTICS OF SKAHA LAKE* Volume .558 km"3 2 Surface Area 20.1 km Mean Depth 28 m Maximum Depth 57 m Maximum Length 11.9 km Maximum Width 2.4 km Perimeter 29.5 km Maximum Surface Temperature 25°C Warming Rate of Hypolimnion .37°C/month Maximum Transparency (Secchi disk), 1939 12 m Maximum Transparency, 1971 7 m Data from Blanton and Ng 1972 16 A hypometric curve showing the relationship between area and depth i s shown in Figure 3. The bathymetry of the lake basin (Figure 2) shows that the lake i s divided into two basins separated by a bedrock s i l l at a depth of about 24 m (St. John 1973). A well-defined bench at a depth of 15 m exists near the mouth of McLean Creek. The fact that the southern basin i s 2 2 smaller in surface area than the northern one (3.0 km compared to 17.1 km ) and much shallower (mean depth of 15 m compared to 28 m) has important im-plications for the relative biological productivity of each basin. St. John observes that the dual basin morphology provides a terrigenous sedi-ment trap situation, with the northern basin accumulating more terrigenous material and the southern one more organic carbon. The phosphorus cycling model described in Chapter IV considers each basin separately. (b) The Lake Sediments. Core samples taken from the sediments i n -dicate that typical deep muds consist of 58.5 per cent s i l t , 41 per cent clay and 0.5 per cent sand (St. John 1973). Some of the surface sediments contain a predominance of sand, indicating recent landslides from lakeside c l i f f s . St. John reports an average sedimentation rate of about 0.21 cm/year, with an average annual net accumulation in the past 100 years of 1.5 x 10^ kg of material. 2. Chemical Limnology (a) Water Chemistry. Table II shows representative variations in chemical characteristics during the years 1968-71. It is important to note that although hypolimnetic dissolved oxygen values less than 2 mg/1 have been recorded, the hypolimnion of Skaha Lake has not, at least during the four years for which data are available, become anaerobic. Figure 3. Hypsometric curves of the north and south basins of Skaha Lake showing the relationship between area and depth. 18 TABLE I I CHEMICAL CHARACTERISTICS, SKAHA LAKE* ** Hypolimnetic Dissolved Oxygen <2 mg/1 to satu r a t i o n Hypolimnetic Oxygen D e f i c i t 0.076 mg/cm2/day 0 2 pH 8.1 to 9.2 Tota l Residue 102 to 159 mg/1 Bicarbonate 38 to 115 mg/1 S i l i c a t e 0.4 to 6.4 mg/1 Orthophosphate, epilimnion <0.002 to 0.095 mg/1 (P) Orthophosphate, hypolimnion 0.006 to 0.085 mg/1 (P) Orthophosphate, Spring Mixing 1971 0.015 mg/1 (P) Tota l Phosphorus, Epilimnion 0.007 to 0.124 mg/1 (P) Tota l Phosphorus, Hypolimnion 0.008 to 0.104 mg/1 (P) Total Phosphorus, Spring Mixing 1971 0.060 mg/1 (P) Ni t r a t e , Epilimnion <0.01 to 0.02 mg/1 Ni t r a t e , Hypolimnion <0.01 to 0.17 mg/1 Tota l Kjeldahl nitrogen, Epilimnion <0.01 to 0.75 mg/1 Total Kjeldahl nitrogen, Hypolimnion 0.08 to 0.69 mg/1 * Data from Stein and Coulthard 1971 and Williams 1972. , Patalas and S a l k i 1973, Seasonal v a r i a t i o n s i n dissolved oxygen and t o t a l phosphorus w i l l be discussed i n d e t a i l i n Chapter V. 19 (b) Sediment Chemistry. St. John (1973) reports that deep s e d i -ments from the south basin contain 1.69 times greater concentrations of organic carbon than deep sediments f rom the north basin. The increase i n the south basin i s probably due to two f a c t o r s : (1) " d i l u t i o n " of organic matter i n the north basin by more terrigenous m a t e r i a l , and (2) greater production of organic matter by the shallower south basin. Core p r o f i l e s show a sharp increase i n organic carbon i n the upper f i v e centimeters. According to St. John, t h i s f i v e centimeters represents about 23 years of sedimentation, which i s about the length of time sewage has been d i s -charged i n s i g n i f i c a n t quantity into the lake. Apatite, mainly i n the form Ca^Q (PO^)^ (OH^, appears to play a large part i n Skaha sediment composition, both s u r f i c i a l l y and at depth. In the s u r f i c i a l sediments, an average of 70 per cent of the phosphorus (by weight) i s i n the form of ap a t i t e (Williams 1973). Most of the apa-t i t e probably enters the lake when ra i n s erode the c l i f f s surrounding the lake, and t h i s process would proceed with or without man's influence (St. John, personal communication). Williams also assumes that the a p a t i t e has a terrigenous o r i g i n from the watershed, and does not form as a r e s u l t of chemical p r e c i p i t a t i o n within the lake. He fu r t h e r assumes that a p a t i t e plays l i t t l e or no r o l e i n the phosphorus c y c l e of the lake because of i t s very low s o l u b i l i t y and s i g n i f i c a n c e as a n u t r i e n t source f o r aquatic organisms. The f a c t that a p a t i t e i s concentrated near the shoreline and i n -l e t s i s fu r t h e r i n d i c a t i o n of terrigenous o r i g i n . Apatite increases with depth i n the sediment column, i n d i c a t i n g conversion from organic phosphorus to apatite within the sediment (Williams 1973). William's conclusion i s 20 supported by results showing that the increase in apatite with depth is matched by an approximately equal decline in organic phosphorus. Adsorbed phosphorus (inorganic phosphate ions associated with sediment components having a high capacity to take up orthophosphate from solution by exchange with hydroxyl groups) constitutes an average of 18 per cent of the phosphorus (by weight) in the s u r f i c i a l sediments (Williams 1973). Williams concludes that i t is l i k e l y that phosphorus adsorbed onto sediments remains essentially unaltered, and is not involved in conversion to apatite or regeneration to overlying waters. The concentration of adsorbed phosphorus increases with increasing water depth and distance from shore. A decrease in adsorbed phosphorus concentration with depth in the sediment i s probably due to loading increases in recent years (Williams 1973). Organic phosphorus makes up an average of 12 per cent of the phosphorus (by weight) in the s u r f i c i a l sediments (Williams 1973). Williams concludes that approximately 20 per cent of the sedimented organic phosphorus is converted into orthophosphate or soluble organic phosphorus and returns to the overlying water; this amount, however, is small compared with loading of phosphorus from external sources. Within the sediments further breakdown of organic phosphorus to orthophosphate occurs, but the orthophosphate is converted to apatite within the sediments and does not regenerate to overlying waters (Williams.19 73). 21 (c) Net Sedimentation Rates of Phosphorus Forms. St. John (1973) estimates a total net sedimentation rate of 1.15 x lo7 kg/yr. This e s t i -mate i s a single one, and does not account for different sedimentation rates in different parts of the lake. Combining this estimate with aver-age s u r f i c i a l concentrations of apatite, sorbed phosphorus and organic phosphorus of 635 ppm, 177 ppm and 109 ppm respectively, Williams estimates the following annual sedimentation rates: apatite 7600 kg sorbed phosphorus 2000 kg organic phosphorus 1300 kg Total 10900 kg 3. Biological Limnology (a) Phytoplankton and Periphyton. Phytoplankton have been measured in two ways, both of which are "standing stock" measurements and do not reflect productivity (rate of growth). Table III shows algal abundance during selected months in 1969-70 in cells/ml (Stein and Coulthard 1971), with percentages of four algal types. The figures represent the average of samples taken from four depths (surface to 18 m) in the north basin. The table shows that during 1969-70 a spring bloom (April) occurred, dominated by diatoms and phytoflagellates; and a summer (July) bloom occurred, dominated by blue-green algae. Blue-green algae dominated during late summer and autumn. These concentrations are averages of 36 s u r f i c i a l samples taken in shallow and deep sections in both basins of the lake. 22 TABLE I I I ALGAL ABUNDANCE IN SKAHA LAKE, 1969-70 •k ( a l g a l counts i n c e l l s / m l ) A p r i l 1970 June 1969 July 1969 Sept. : Tota l Phytoplankton 3100 ** 76 ** 2120 446 % Blue-Green Algae 2.3 19.4 59.2 91.0 % Green Algae 4.1 0 3.2 0.8 % Diatoms 40.3 69.8 18.5 3.8 % P h y t o f l a g e l l a t e s 42.2 10.8 18.6 4.2 * For greens and blue-greens, a chain of 12-15 c e l l s = 1 a l g a l " c e l l " as shown i n Table III. ** a l g a l bloom During 1971 c h l o r o p h y l l a was monitored i n surface waters to i n -dicate phytoplankton biomass. Monthly sampling shows the following v a r i -a t i o n i n the north and south basins from May to September (Williams 1972), indicated i n Table IV. TABLE IV PHYTOPLANKTON IN SKAHA LAKE, 1971 (values i n ug/1 chl o r o p h y l l d) MAY JUNE JULY AUGUST SEPT. LATE SEPT. North 8 6 12 29 26 290 South 5 10 19 10 25 140 23 The order-of-magnitude increase i n l a t e September i n d i c a t e s a large bloom, but the dominant species responsible was not determined. De-t a i l e d phytoplankton data i s presented i n Chapter V. Periphyton (attached algae) abundance during 1971 i s shown i n Table V f o r three sections of the lake (Stockner et al. 1972a). Sta t i o n 1 i s at the extreme north and near the Okanagan River inflow. S t a t i o n 2 i s on the eastern shore about midway i n the north basin, and s t a t i o n 3 i s i n the south basin near the outflow (Figure 2). TABLE V PERIPHYTON IN SKAHA LAKE, 1971 (values i n ug/1 c h l o r o p h y l l a) APRIL MAY JUNE JULY AUGUST SEPTEMBER Station 1 0.5 1.0 1.5 38.5 49.5 5.0 Station 2 0.5 1.5 1.0 1.5 1.0 Station 3 0.1 0.5 1.7 2.0 1.5 While s t a t i o n s 2 and 3 show low periphyton growth, s t a t i o n 1 i n d i -cates very pronounced growth during J u l y and August. Stockner et al. (1972a) hypothesize that the low biomass at s t a t i o n s 2 and 3 may be because of u t i l i z a t i o n of n u t r i e n t s by phytoplankton populations. High biomass at s t a t i o n 1 may i n d i c a t e that periphyton populations use a v a i l a b l e nutrients from the Okanagan River before they can be taken up by the phyto-plankton. 24 (b) Macrophytes. Macrophytes grow in the l i t t o r a l , or shallow shoreline region of Skaha Lake. The l i t t o r a l can be defined as the zone extending from the shoreline to a depth where v i s i b l e plant growth occurs, or the area above the compensation depth for photosynthesis (Stockner et I 2 al. 1972b). The l i t t o r a l zone comprises about 3.2 km or 17 per cent of the surface area in Skaha Lake. Submergent macrophytes predomi-nate in the north end, whereas extensive beds of both emergent and sub-mergent vegetation grow on the l i t t o r a l bench of the east and west shore-lines (Stockner et al. 1972b). Floating leafed plants and emergent vege-tation occurs in the south end of the lake. Macrophytes and associated epiphytic periphyton have the a b i l i t y to trap considerable quantities of nutrients before they can be u t i l i z e d by phytoplankton (Stockner et al. 1972b). Because Skaha Lake contains sig -nificantly less l i t t o r a l area than the other mainstem lakes (about 25 per cent of the surface area of Okanagan Lake and the north basin of Osoyoos Lake i s l i t t o r a l ) , nutrients may be more available for phytoplankton growth in Skaha (Stockner et al. 1972b). This may be an important factor in explaining the relatively high trophic level of Skaha Lake. (c) Zooplankton. The crustacean plankton (copepods and cladocerans) were sampled in 1969 by Patalas and Salki (1973). Four species of copepods and eight species of cladocerans were found, with Cyclops bicuspidatus and Diaptomus ashlandi dominant in a l l three lakes. Relative volumes of settled 3 2 net plankton in Okanagan, Skaha and Osoyoos Lakes were 13, 19 and 26 mm /cm respectively. The average number of crustacean zooplankton in Okanagan 2 2 Lake was 188 individuals/cm , in' Skaha Lake 238 individuals/cm and in 2 Osoyoos Lake 161 individuals/cm . 25 (d) Fish. According to Northcote et al. (1972), the contribution of salmonid species to the f i s h stock of Skaha Lake was considerably lower in 1971 than 1948 (4.6 per cent from 14.8 per cent). Numbers of mountain whitefish were much lower in 1971 than in 1948; whereas 60 were netted in 1948, only five were netted in 1971. No carp were netted in 1948, whereas 17 were collected in 1971. The apparent shift in species composition from salmonid and coregonine species to coarse f i s h i s an indication of increas-ing eutrophy (Larkin and Northcote 1969). The low average age of salmonids in Skaha, Vaseux and Wood Lakes may be indicative of advanced eutrophication (Northcote et al. 1972). Lar-kin and Northcote (1969) cite research in Europe showing that the average age of coregonids gradually decreased as eutrophication increased. Four fis h attributes used as eutrophication indices for the mainstem Okanagan lakes (relative abundance, average length, weight-length and growth rate) lead Northcote et al. (1972) to conclude that Skaha Lake i s the most eutro-phic, followed by Osoyoos and Vaseux. 4. Trophic State The word "trophic" has been defined as "the rate and ways of o supplying a lake with organic matter" (Aberg and Rodhe 1942). The adjec-tives oligotrophic, mesotrophic and eutrophic were used by Naumann (1932) and Thienemann (1931) to describe increasing levels of organic production in lakes. Figure 4 shows the trophic state (as described by annual phos-phorus loading) of the Okanagan lakes compared with other lakes in the world (from Vollenweider 1968, Patalas and Salki 1973). Skaha Lake f a l l s family of fi s h containing the whitefish and cisco (when these are not included in the Salmonidae) - 1 0 . o - i < O U . o *-3 a. c - I.OH < o < Z> z z < ^ Lake Norrviken (Sweden) OSOYOOS Greifensee — (Switzerland ) Pf dff ikersee — • ( Switzerland) , .. L a k e E r i e • Moses Lake ( C a n o d a ) ( U.S.A.) Lake MendotaQ ( U.S.A.) Lake Malare .(Sweden) Hallwillersee (Switzerland) Lake Furesrf^ '" 1 1 (Denmark )||JJ Lake Annecy, • . . r T f l l l ! ^ t r a n c e - ' ,Tiirlersee |( Switzerland ) Eutrophic Lakes SKAHA • Baldeggersee (Switzerland) O Zurichsee ( Switzerland) Lake Washington ( U . S . A . ) Lake Ontario ^(Canada)* Lake Geneva (France'^witzerland ) Lake1Constance (Austria, Germany, Switzerland) Mesotrophic Lakes (I) yOligotrophic Lakes 50 100 1 5 0 0 MEAN D E P T H ( m ) Figure 4. Eutrophication of lakes in the Okanagan Basin compared to other lakes in Europe and North America (Patalas and Salki 1973). Criteria of annual phos-phorus loading and mean depth from Vollenweider (1968, 1969) . Open circles indicate loading estimates from Haughton et a l . 1974; black circles indicate loading cal-culated by Patalas and Salki (1973) according to Vollenweider (1968) c r i t e r i a ; squares indicate 1990 loading estimates with no phosphorus removal; triangles indicate 1990 loading with 80% removal of municipal phosphorus. l% 27 w e l l w i t h i n the c l a s s i f i c a t i o n of a e u t r o p h i c l a k e f o r the f o l l o w i n g r e a -sons : 1. The t o t a l phosphorus c o n c e n t r a t i o n (at overturn) has been (1970) g r e a t e r than 0.03 mg/1 ( c r i t e r i a from Vollenweider 1968). 2 2. Phosphorus l o a d i n g i s g r e a t e r than 0.5 g/m /year, which i s considered to be i n the "dangerous" l o a d i n g category f o r a l a k e of Skaha's mean depth by Vollenweider (1968). 3. The h y g o l i m n e t i c oxygen d e p l e t i o n r a t e i s g r e a t e r than 0.05 mg/cm /day ( c r i t e r i a from Hutchinson 1957). 4. The minimum transparency i s l e s s than 2 m ( c r i t e r i a from Beeton 1965). 5. Salmonid f i s h s p e c i e s have decreased i n r e l a t i v e abundance si n c e 1948 and have a low average age ( c r i t e r i a from L a r k i n and Northcote 1969). 6. C h l o r o p h y l l a values i n d i c a t i n g phytoplankton biomass have been greater than a seasonal range of 5 - 140 mg/m ( c r i -t e r i a from Sakamoto, c i t e d i n Vollenweider 1968). 7. Dominance of blue-green algae and diatoms i s evident d u r i n g much of the growing season ( c r i t e r i a from Sawyer 1973). The c o n c l u s i o n s of S t e i n and Coulthard (1971), Stockner (1972), and P a t a l a s and S a l k i (1971) f u r t h e r support the c l a s s i f i c a t i o n of Skaha Lake as moderately e u t r o p h i c . 5. Paleolimnology According to Stockner (1972), cores taken i n the sediments of Skaha Lake i n d i c a t e g e n e r a l l y o l i g o t r o p h i c c o n d i t i o n s p r i o r to 1940. The most s i g n i f i c a n t change i n diatom assemblages has occurred i n the l a s t 25 years (the upper 7-8 cm of sediment), w i t h diatoms i n d i c a t i v e of e u t r o p h i c c o n d i t i o n s showing marked increases i n r e l a t i v e abundance. In the upper 8 cm of sediment there i s a s i g n i f i c a n t i n c r e a s e i n the diatom Fragilaria crotonensis ( i n d i c a t i v e of enriched c o n d i t i o n s ) and a corresponding decrease 28 in the diatoms C y c l o t e l l a o c e l l a t a and Melosira i t a l i c a (indicative of oligotrophic conditions). Stockner attributes this recent change in dominant diatom assemblages to sewage enrichment, mainly from the Penticton sewage treatment plant. Stockner notes that in Lake Washington (Seattle) the peak abundance of F r a g i l a r i a cvotonensis corresponded with the f i r s t occurrence of blue-green algal blooms. CHAPTER I I I PHOSPHORUS CYCLING IN LAKES AND MODELLING APPROACH A. EUTROPHICATION AND THE LIMITING NUTRIENT CONCEPT 1. The "Law of the Minimum" L i e b i g ' s "law of the minimum" ( f i r s t s t a t e d by Justus L i e b i g i n 1840) expresses the idea that the growth of a p l a n t i s dependent on the amount of e s s e n t i a l n u t r i e n t presented to i t i n minimum q u a n t i t y . How-ever, work s i n c e L i e b i g ' s time has shown th a t two c o n d i t i o n s should be s a t i s f i e d bef ore the p r i n c i p l e can be a p p l i e d (Odum 1971). The f i r s t c o n d i t i o n i s that the "law" i s only a p p l i c a b l e under steady s t a t e c o n d i t i o n s when n u t r i e n t i n f l o w equals n u t r i e n t outflow. Odum (1971) observes t h a t c u l t u r a l e u t r o p h i c a t i o n u s u a l l y produces a v e r y "unsteady s t a t e " i n which pr o d u c t i o n o s c i l l a t e s between a l g a l blooms and d i e - o f f s . Release of d i s s o l v e d n u t r i e n t s upon decomposition of the algae may i n i t i a t e another bloom. The n u t r i e n t budget of a lake i s seldom, i f ever, i n a steady s t a t e c o n d i t i o n — i n p u t of n u t r i e n t s seldom equals out-put. Because l a k e s act as n a t u r a l t r a p s f o r both sediments and n u t r i e n t s , most l a k e s e x h i b i t a n u t r i e n t g a i n over time (Sawyer 1966). In view of t h i s i n t e r p r e t a t i o n of L i e b i g ' s law, the "carbon-phosphorus con t r o v e r s y " (Vallentyne 1970; Kuenzel 1969), which attempts to decide which n u t r i e n t , carbon or phosphorus, i s the key element i n c u l -t u r a l e u t r o p h i c a t i o n , may be of o n l y academic i n t e r e s t . According to Odum (1972), the " e i t h e r / o r " argument may not be r e l e v a n t because carbon d i o x i d e , phosphorus, n i t r o g e n , and other elements may r a p i d l y r e p l a c e each other as 29 30 limiting factors during the o s c i l l a t i o n . For example, Goldman (1968) found potassium, sulfur, and molybdenum to be most limiting to growth in Castle Lake, California. The second constraint which should be applied to Liebig's law is that of "factor interaction." The a v a i l a b i l i t y of a substance other than the minimum one may modify the rate of u t i l i z a t i o n of the minimum one (Odum 1971). Rodhe (1948) found that Asterionella in a phosphorus-limiting 3 culture medium showed no growth with an addition of 10 mg P/m , whereas in phosphorus-limiting Lake Erken water the algae grew significantly with the addition of only one mg P/m (cited in Hutchinson 1957). Hutchinson specu-lates that some material, possibly a peptide Influencing the rate with which phosphorus is assimilated, i s lacking in the culture media but is present in the lake water. A complicating aspect of the concept is that different phyto-plankton populations have different nutrient requirements. For example, maximum growth of Botryococcus braunii occurs at a phosphorus concentration of 0.089 mg/1, while Nitzschia palea grows fastest at 0.018 mg/1 (Odum 1971). Green flagellates grow well when nitrogen i s in the form of urea, uric acid, and ammonia, while the diatom Nitschia requires inorganic nitrate for maximum growth (Odum 1971). 2. Relative Importance of Carbon, Nitrogen and Phosphorus (a) Carbon. Carbon has several natural sources: epilimnion waters are usually saturated with carbon dioxide from the atmosphere, and bicarbon-ates come from erosion material ubiquitous in v i r t u a l l y a l l drainage basins (Prince and Bruce 1972). In most lakes these natural sources alone are s u f f i -cient to support the observed biomass. 31 In a study of growth rates of Chlorella, Microcystist and Anabaena with respect to carbon a v a i l a b i l i t y , Morton et al. (1972) conclude that " i t i s very d i f f i c u l t to control growth by carbon dioxide control in sys-tems open to the atmosphere." They report that the atmosphere is an ade-quate source of carbon dioxide (even in the "absence of wind mixing) for depths to at least 1.7 m, permitting substantial algal production. Morton et al. further report that naturally present bicarbonate can be u t i l i z e d by algae as a source of carbon, and can provide enough carbon for large algal blooms. Mass balance carbon budget results from Lake Erie indicate that the carbon supply from natural sources is at least 25 times as much as the carbon from cultural sources (Prince and Bruce 1972). It is concluded that the carbon from sewage would be completely insufficient to account for the observed biomass In Lake Erie. (b) Nitrogen. Nitrogen enters lakes from a variety of natural and cultural sources, and has been shown in a number of cases to be one of the important limiting nutrients. If sufficient phosphorus i s in the water at the time of spring overturn before growth begins, i t has been shown that nitrogen can become a limiting factor later in the summer (Prince and Bruce 1972). Based on a study of 17 lakes in Wisconsin, Sawyer (1967) concludes that at least 0.3 mg/1 inorganic nitrogen plus at least 0.015 mg/1 inorganic phosphate are necessary at the time of spring mixing to stimulate algal blooms later in the season. Goldman (1968) reports that a sequence of limiting nutrients ranged from magnesium in the spring to nitrogen in the summer to phosphorus in the autumn In Brooks Lake, Alaska. In Lake Tahoe iron and nitrogen limited 32 phytoplankton growth. Goldman concludes that ". . .some component of the phytoplankton w i l l respond positively to almost any addition of nutrients, but the community as a whole w i l l tend to share some common deficiencies." Nitrogen has special characteristics (compared to phosphorus) which limit i t s usefulness as a controlling nutrient in cultural eutrophi-cation. The fact that some nuisance blue-green species have the a b i l i t y to f i x their own nitrogen from elemental ^ dissolved in lake water makes the control of this source d i f f i c u l t . Olsen (1970) reports that the blue-green alga Anabaena azolla can f i x up to 95 kg N/ha in one summer in small Danish lakes. Billaud (1966) reports that some species of Anabaena in Alaskan lakes f i x nitrogen accounting for 50 per cent of the assimilation at the peak of the growing season. Bacteria such as Azotobaater and Clostri-dium can also f i x nitogen in lakes. Denitrifying bacteria (e.g., Pseudomonas denitrifioans) can convert nitrates to n i t r i t e s and molecular nitrogen under anaerobic conditions, adding further d i f f i c u l t y to the quantification of the nitrogen cycle. The high solubility of nitrate in ground water causes leaching of nitrate into lakes. This input comes from agricultural sources and septic tanks in aerobic s o i l , and i s d i f f i c u l t to quantify as well as to eliminate. (c) Phosphorus. Much evidence i s available showing a direct relation-r ship between phosphorus (usually accompanied by nitrogen as well) and algal growth (Stockner 1972). The Lake Washington case (Edmondson 1970) is a striking example of an extremely high correlation between phosphate concen-tration at spring mixing and summer algal biomass for 30 years of obser-vations. Edmondson's results show clearly that the controlling factor in eliminating the lake's eutrophication problems was the reduction (by 33 about 50 per cent) of phosphorus loading. The effects of removal of phosphorus from sewage show that phos-phorus can be the most important nutrient limiting algal growth. Maloney reports (using Selenastmm as a test organism) that re-addition of phosphate to "tertiary effluent" (secondary effluent with the phosphorus removed) at levels of 0.02, 0.04 and 0.06 mg P/l resulted in c e l l counts of 213,000/ml, 314,000/ml and 644,000/ml,respectively, after 14 days of growth (cited in Vallentyne 1970). The tertiary effluent without any added phosphorus showed a growth of only 3,700 cells/ml. Vallentyne concludes that "there i s . . . no question about the effectiveness of sewage treatment for phosphate re-moval in terms of reducing algal growth." Phosphorus was shown to be the most important limiting factor in the production of the green alga Cladophora in the Great Lakes (Neil and Owen 1964). Decreases in carbon, nitrogen and phosphorus in 46 Swiss lakes during the growing season are related to i n i t i a l concentrations of the same elements in the spring (data published by Thomas 1970 and analyzed by Vollenweider 1970, cited in Prince and Bruce 1972). Significant corre-lation i s reported between spring concentration and subsequent per cent decrease during the summer (as dissolved nutrients were taken up by plants) for each nutrient, but the highest correlation i s reported for phosphorus av a i l a b i l i t y and phosphorus decrease. Cross-correlation analyses show high correlation between phosphorus a v a i l a b i l i t y and nitrogen and carbon decreases during the growing season; but they indicate insignificant or very low corre-lation between carbon or nitrogen a v a i l a b i l i t y and phosphorus decrease (Prince and Bruce 1972), Prince and Bruce conclude, on the basis of Vollenweider 1s 34 analysis, that phosphorus a v a i l a b i l i t y appears to be the dominant factor in the metabolism of the 46 Swiss lakes (which range from oligotrophic to highly eutrophic), and that phosphorus is the key nutrient governing the production of algae in these lakes. In the lakes of the world in which nutrients have been related to production, i t can be concluded that "phosphorus is most frequently the limiting element, followed in order of decreasing importance by nitrogen and carbon" (Prince and Bruce 1972). B. THE PHOSPHORUS.CYCLE IN LAKES Ponds and lakes are especially useful for the quantitative study of nutrient cycling because the interactions are relatively self-contained over short periods of time. Although he exaggerated the "closed system" properties of lakes, Forbes in 1887 appreciated the idea that a lake ". . .forms a l i t t l e world within i t s e l f — a microcosm within which a l l the elemental forces are at work and the play of l i f e goes on in f u l l , but on so small a scale as to bring i t easily within the mental grasp." The exponential increase in knowledge of the phosphorus cycle in the last 25 years is summarized by Hutchinson (1969): "It became apparent (Hutchinson 1941) that in many small lakes the nutrient elements were undergoing very rapid c y c l i c a l changes, passing from the sediments into the free water and back, in dying plankton or l i t t o r a l vegetation, over and over again. The easy a v a i l a b i l i t y of a r t i f i c i a l radioisotopes after 1945 made the detailed investigation of this kind of cycle possible (Hutchinson and Bowen 1947, 1950; Coffin et al. 1949; Hayes et al. 1952) and culminated in Rigler's extraordinary discovery (1956, 1964) that the turnover time of ionic phosphorus in the epilimnion of a lake in summer can be of the order of 1 minute." 35 1. Phosphorus Compartments i n Lake Water The " t o t a l phosphorus" determination c o n s i s t s of three types of phosphorus: soluble orthophosphate (soluble r e a c t i v e phosphorus); soluble organic phosphorus (soluble unreactive phosphorus); and p a r t i c u l a t e phos-phorus. D e f i n i t i o n s of these types and t h e i r s i g n i f i c a n c e i n the phosphorus cycle are discussed i n t h i s section. (a) Orthophosphate Phosphorus (Soluble Reactive Phosphorus). This form of phosphorus i s assumed to be the soluble, inorganic p o r t i o n (PO^ , ), 32 and i s the form i n which isotopes such as P occur. Experiments i n v o l v i n g the c y c l i n g of r a d i o a c t i v e phosphorus measure t h i s compartment (Rigler 1973). -3 Orthophosphate, or PO^ , i s generally assumed to be the quantity measured when membrane-filtered water (0.45 u f i l t e r ) i s analysed by one of the molyb-denum blue techniques.. However, Ri g l e r points out that orthophosphate i s probably g r o s s l y overestimated by universally-used a n a l y t i c a l techniques f o r the following reasons: (1) f i l t r a t i o n might damage d e l i c a t e a l g a l c e l l s and release phosphates-phosphorus or r e a d i l y hydrolysed phosphate esters i n t o the f i l t r a t e ; (2) a c i d i f i c a t i o n of the sample with s u l f u r i c acid could hydro-_3 lyse free phosphate esters and release PO^ from f u l v i c acid-metal phos-phates or from c o l l o i d a l i r o n phosphate; (3) arsenic i s one of the elements _3 that can i n t e r f e r e s e r i o u s l y with the c o l o r i m e t r i c determination of PO^ i n the molybdenum blue technique. R i g l e r concludes that there i s considerable evidence suggesting that chemically determined orthophosphate i s much -3 -3 greater than actual PO^ and assumes that "the PO^ , compartment i s very small and cannot be measured chemically." This unfortunate f a c t leads 36 Rigler to conclude that severe limitations must be imposed on the inter--3 pretation of tracer results because rate constants of.PO^ uptake cannot be converted to phosphorus fluxes (flux implies a rate constant multiplied by an amount) because the chemically determined amount i s in question. The size of the orthophosphate compartment is quite small, even by conventional estimates which are assumed to be overestimated. In a study of nine Ontario lakes which ranged from oligotrophic to eutrophic, Rigler (1964) found that only five to eight per cent of the total phosphorus was orthophosphate. (b) Soluble Organic Phosphorus. This portion of the phosphorus content of water has, by most investigators, been assumed to be the d i f f e r -ence between the "soluble phosphorus" portion and the orthophosphate portion. Soluble phosphorus i s the measure obtained when membrane-filtered (0.45 mic-rons) water i s analyzed after being digested with an oxidizing acid solution (Rigler 1973). In 1964 Rigler found that nine lakes In Ontario presumably had 12 to 32 per cent of the total phosphorus in the form of soluble organic phosphorus. However, more recent evidence demonstrates that current analytical methods do not adequately separate organic and particular phosphorus (Rigler 1973). Rigler prefers to refer to this compartment as "soluble unreactive phosphorus," arguing that analytical techniques cannot sufficiently distinguish between soluble organic and particulate phosphorus. (c) Particulate Phosphorus. This compartment is equal to the total phosphorus value minus the soluble phosphous determination. Accord-ing to Rigler (1973) , the original assumption by early workers that a l l particulate phosphorus is associated with large plankton and trypton (in-37 organic particulate phosphorus) must be rejected. Particulate phosphorus is associated with particles ranging in size from large zooplankton (and fish) down to colloids, and the choice of a 0.45 micron f i l t e r to separate particulate and "soluble unreactive" phosphorus i s quite arbitrary. Rigler maintains that much of the "soluble unreactive" part i s in particles less than 0.1 micron and much is col l o i d a l , but perhaps only a small fraction i s in solution. In 1964 Rigler found that nine Ontario lakes had 62 to 83 per cent of the total phosphorus in the form of particulate phosphorus. (d) Total Phosphorus. This compartment i s measured when an un-fil t e r e d water sample i s treated by persulfate acid digestion and analyzed. It should include a representative sampling of the phosphorus associated with the bacteria and plankton (both phyto- and zoo-) from the depth at which the sample is collected. While the assumption that the measurement includes phosphorus in phytoplankton is relatively valid, a similar assump-tion for zooplankton is questionable. At times, a significant fraction epilimnetic phosphorus may be in the form of zooplankton (Riger 1973). Because zooplankton exhibit pronounced horizontal distribution patterns ("patchiness") as well as daily v e r t i c a l migration, an adequate sample at a given depth would have to be an average of several locations at different times of the day (Rigler 1973). It i s not surprising that total phosphorus in the trophogenic layer can fluctuate greatly from day to day, as 50 or 100 ml samples are normally taken (Rigler 1973). For example, Chamberlain (1968) showed that one extra Daphnia in a 50 ml water sample would increase the total phosphorus of the sample by 4 Mg/1, very s i g n i f i -cant when the total phosphorus averaged 14 yg/1 (cited in Rigler 1973). 38 In summary, i t can be concluded that while a l l the compartments of phosphorus have measurement d i f f i c u l t i e s , orthophosphate is perhaps the least reliable and total phosphorus perhaps the most. 2. Turnover Rates of Orthophosphate Measurement of the phosphorus flux rate in lakes is the best method available for study of the cycling a c t i v i t y of phosphorus. Pomer-qy (1960) states the argument in this way: "Measurement of the concentration of dissolved phos-phate in natural waters gives a very limited indication of phosphate a v a i l a b i l i t y . Much or v i r t u a l l y a l l of the phos-phate in the system may be inside l i v i n g organisms at any given time, yet i t may be overturning every hour with the result that there w i l l be a constant supply of phosphate for organisms able to concentrate i t from a very dilute solution. Such systems may remain stable biologically for considerable periods in the apparent absence of available phosphate. The observations presented here suggest that a rapid flux of phosphate is typical of highly productive systems, and that the flux rate i s more important than the concentration in maintaining high rates of organic production." The concept of "turnover" is a useful one for comparing exchange rates of phosphorus between different compartments of an ecosystem such as a lake. After equilibrium has been reached, the "turnover rate" is the fraction of the total amount of phosphorus in a component which is released (or which enters) in a given time period. "Turnover time" is the recipro-cal of the turnover rate, or the time required to remove the phosphorus content of the considered compartment in the absence of other transferral mechanisms. A hypothetical exchange between two compartments in a lake w i l l i l l u s t r a t e the concept: 39 d i s s o l v e d P°4 i n water 10 Ug/1 5 yg/1 • day 4 yg/1 • day P i n phytoplankton 20 yg/1 In t h i s example the "turnover r a t e " between the d i s s o l v e d P0~^ compartment and phytoplankton compartment (due to uptake by algae and consequent growth) i s 5 yg/1 • day exchange * 10 yg/1 i n the water compartment = 0.5/day. The "turnover time" i s the r e c i p r o c a l of 0.5, or two days, which i s equal to the -3 time necessary f o r a complete turnover of the PO^ i n the water. Now, i f we l o o k at the opposite pathway i n which the p a r t i c u l a t e phosphorus i n the phytoplankton i s decomposed by b a c t e r i a and r e - e n t e r s the d i s s o l v e d PO. 4 compartment, the turnover r a t e i s 4/20 = 0.2/day, w i t h a turnover time of f i v e days. Turnover times between v a r i o u s phosphorus compartments are c i t e d i n Table VT> . and a s i m p l i f i e d schematic of t r a n s f o r m a t i o n s i s _3 shown i n Figure 5. The turnover time of e p i l i m n e t i c PO^ from water to o r g a n i c compartments has been measured i n a v a r i e t y of temperate l a k e s from o l i g o t r o p h i c to e u t r o p h i c , and i n d y s t r o p h i c and bog l a k e s (Chamber-l a i n 1968, R i g l e r 1964); i t i s g e n e r a l l y between one and e i g h t minutes dur-ing summer s t r a t i f i c a t i o n ( R i g l e r 1973). T h i s f l u x i s i n d i c a t e d i n F i g u r e -3 5 as being between the s o l u b l e i n o r g a n i c PO^ and p h y t o p l a n k t o n - b a c t e r i a compartments. R i g l e r notes that s i m i l a r turnover times can be expected during the p r o d u c t i v e p e r i o d i n l a k e s that have a high r a t i o of p a r t i c u -l a t e phosphorus:orthophosphate. The c o n s i d e r a b l y longer turnover time i n winter (around one day) can be a t t r i b u t e d to decreased temperature, increased 40 TABLE VI TURNOVER TIMES OF PHOSPHORUS FLUX BETWEEN COMPARTMENTS ORIGINAL COMPARTMENT RECEIVING COMPARTMENT TURNOVER TIME REFERENCE S o l u b l e i n o r g a n i c P (summer) ( w i n t e r ) S o l u b l e i n o r g a n i c P S o l u b l e o r g a n i c P P a r t i c u l a t e P P h y t o p l a n k t o n <30 u Z o o p l a n k t o n ( e x c r e t i o n ) L i t t o r a l v e g e t a t i o n (Erioaulon) L i t t o r a l v e g e t a t i o n (Sphagnum) Sediments i n u n s t r a - ' t i f i e d l a k e " " (no b a c t e r i a ) " " (wi th b a c t e r i a ) p h y t o p l a n k t o n and b a c t e r i a <30 u s o l u b l e o r g a n i c P l i t t o r a l v e g e t a t i o n (Sphagnum) l i t t o r a l v e g e t a t i o n (Eriaaulon) l i t t o r a l v e g e t a t i o n and s e d i m e n t s l i t t o r a l s e d i m e n t s s o l u b l e i n o r g a n i c P l i t t o r a l fauna (musse ls ) d e e p - w a t e r sed iments H II II II s o l u b l e i n o r g a n i c P 0 . 9 - 7 . 3 m i n u t e s R i g l e r 1964 7 m i n u t e s - 7 days 0 . 2 days 0 . 0 9 days 0 . 3 4 days 5 . 4 - 1 7 . 0 days 2 . 7 days 0 . 2 days 2 . 5 days 50 days 100 d a y s 40 - 71 days 2 . 2 days 2 . 1 days 3 days 3 . 5 days 39 - 176 days 1 5 . 5 days 3 . 6 days R i g l e r 1964 Hayes and P h i l l i p s 1958 C o f f i n et al. 1949 Hayes et al. 1952 Hayes and P h i l l i p s 1958 i t H K u e n z l e r 1961 H u t c h i n s o n 1941 R i g l e r 1956 G a c h t e r 1968 R i g l e r 1973 Haney 1970 Hayes and P h i l l i p s 1 9 5 8 C o f f i n et al. 1949 Hayes and P h i l l i p s 1958 41 0.2 days-3-8days-EPILIMNION HYPOLIMNION Phytoplankton and bacteria 2 days JL Zooplankton (herbivores and carnivores) 3-7 weeks Particulate P 3-7weeks weeks or longer Figure 5. Phosphorus transformations in stratified lakes during summer; expressed in turnover times. Dashed lines indicate no data available on rates. 42 concentration of orthophosphate and to the reduced biomass of plankton (Rigler 1973). -3 The return of PO^ from the b i o t i c pool to the dissolved ortho-form i n water i s mainly due to three mechanisms: (1) d i r e c t release by phytoplankton; (2) excretion by zooplankton: and (3) enzymatic hyd r o l y s i s of organic phosphorus compounds excreted by organisms or produced by decomp-o s i t i o n of dead plankton (Rigler 1973). While the t h i r d mechanism has not been measured with s u f f i c i e n t s o p h i s t i c a t i o n to determine a f l u x , d i r e c t r elease by small plankton has been estimated from the r a t e of r e -32 lease of P from seston (suspended p a r t i c u l a t e matter) as averaging 0.019 hr (turnover time of 53 hours or 2.2 daysj R i g l e r 1973). Excretion by zooplankton has been estimated from grazing rates to be of s i m i l a r magni-tude (0.02 h r - 1 ) to the release by small plankton (Haney 1970, R i g l e r 1973). Ri g l e r f e e l s that most of the phosphorus excreted by zooplankton i s u l t i --3 mately regenerated as PO^ , although a part of i t may be excreted i n organic phosphorus compounds. The soluble organic compartment (referred to by R i g l e r as "soluble unreactive phosphorus") a c t u a l l y c o n s i s t s of two subcompartments, but because the r e l a t i o n s h i p of the l a r g e r subcompartment ( p a r t i c l e s i z e 0.1 - 0.45u) to the cycle i s unclear, Figure 5 shows i t to be one compartment. The soluble organic and inorganic compartments appear to exchange phosphorus about two -3 orders of magnitude slower than the PO^ and phytoplankton-bacteria compart-ments, and Hayes and P h i l l i p s (1958) report a turnover time of f i v e hours. Rigl e r notes that the physical-chemical nature of t h i s compartment i s s t i l l l a r g e l y unknown, as i s i t s function in the phosphorus economy of the tropho-genic layer. While some of the soluble organic f r a c t i o n i s undoubtedly u t i l i z e d 43 directly for biologic growth, the quantity and rate have not been ascer-tained. Phytoplankton of a size greater than 30y are pictured by Rig-ler (1973) as comprising a large compartment through which phosphorus cycles relatively slowly (no rates are given) and from which phosphorus is largely regenerated by decomposition. -3 Movement between the PO^  compartment and l i t t o r a l vegetation is relatively rapid (two to eight hours, Hayes and P h i l l i p s 1958), while movement from vegetation back to the water i s much slower (three to eight days; Hayes and P h i l l i p s 1958, Confer 1969). Particulate organic phosphorus in the form of dead plankton ce l l s sediments to the bottom of lakes at rates of between 1.0 and 2.5 per cent/day, resulting in turnover times of between 40 and 100 days (Hutchinson 1941, Rigler 1956, Gachter 1968). The return of phosphorus from the sediments (or "internal load-ing") is an extremely important key to understanding the eutrophication process, and w i l l be dealt with i n considerable detail in the section on internal loading. It w i l l simply be noted here that the turnover time of this flux can vary from days to weeks or longer. Laboratory measurement -3 of the flux between sediment mud (with bacteria) and P0^ is reported by Hayes and P h i l l i p s (1958) to be about three days in both directions. With no bacteria present, the exchange between the sediment and the water was slowed to 15 days. _3 The importance of bacteria in determining rates of PO^ exchange i n aquatic ecosystems should not be underestimated. Rigler (195 6) surmised that bacteria might be the primary cause for rapid turnover times between 44 plankton and water and noted that they compete very effectively with algae _3 for PO^  . Rhee (1972) studied the competition for phosphates between a bacterium species (Pseudomonas) and an algal species (Scenedesmus), He found that algal growth was severely limited in the presence of bacteria, but the growth of bacteria was hardly affected by algae. The faster growth rate of bacteria accounted for the suppressed growth of algae in mixed cultures. 3. The Lake as a Productivity Chamber The contrast between biomass and productivity (rate of growth) is a very important one for aquatic ecosystems, and stresses the importance of turnover rate in determining organic growth. Ketchum (1967) states the contrast in this way for the marine environment: "It has been estimated by Ryther (1960) that the plant biomass in the oceans is only 0.1% of the total plant bio-mass on earth, but that this small population contributes 40% of the annual world production of organic matter. The large production which results from such a small standing crop in the marine environment i s an indication of the rapidity of the turnover of the population. Practically a l l of the photosynthesis of the sea is carried on by microscopic plants which can, under ideal conditions, double their population size daily. In contrast to this i t takes 50 years or more to develop a forest (90.5% of the earth's biomass) and the rate of annual production (25% of the total) is a small fraction of the standing crop at any one time." The total reserve of phosphorus in a body of water (i.e., the quantity of soluble, particulate, sestonic, and accessible sedimented phos-phorus), i s a pertinent gross parameter because i t indicates the ultimate capacity for biomass synthesis (Stumm and Stumm-Zollinger 1972). The authors note that stoichiometrically 1 mg of phosphorus w i l l yield (on the 45 average) about 100 mg of a l g a l biomass, which exerts a biochemical oxygen demand of approximately 140 mg. This means that secondary sewage e f f l u e n t which contains 3-8 mg phosphorus/1 can y i e l d 300-800 mg/1 organic matter i n the productive environment of a eutrophic lake such as Skaha. C. MODELLING APPROACH Modelling the phosphorus budget and phytoplankton growth i n a lake i s a simulation problem. Simulation of the ph y s i c a l and b i o l o g i c a l processes i n a lake has two major goals, one t h e o r e t i c a l and one p r a c t i c a l : (1) the model increases understanding of how the lake functions, and (2) the model enables p r e d i c t i o n of eutrophication problems as a response to varying n u t r i e n t inputs. Mathematical programming, which has the s p e c i f i c aim of maximizing or minimizing an ob j e c t i v e function subject to c o n s t r a i n t s , i s not a p p l i c a b l e to t h i s problem. At a l a t e r stage when a d e c i s i o n must be made on a minimum standard of water q u a l i t y with minimum cost, optimization techniques may be quite u s e f u l . 1. Simulation Modelling In the simulation of a complex system such as a lake, i t i s neces-sary to make a reasonable compromise between s i m p l i c i t y and r e a l i t y . If the model i s too simple, i t may not be a u s e f u l a b s t r a c t i o n of nature. If i t i s too complex and includes too many v a r i a b l e s , more data are required than are a v a i l a b l e . Excessive complexity burdens computational f a c i l i t i e s as well as the human mind i n the i n t e r p r e t a t i o n of causal i n t e r a c t i o n s . As Russell and McNeil (1974) state, ". . .the aim i s to produce r e s u l t s of acceptable accuracy with models of minimum, complexity." 46 Considering the immense complexity of i n t e r a c t i o n s between n u t r i -ents, sediments and b i o t a i n a lake, and the d i f f i c u l t y of i d e n t i f y i n g and measuring these i n t e r a c t i o n s , i t i s not s u r p r i s i n g that a c e r t a i n amount of realism must be s a c r i f i c e d . Walters (1971) observes that i n applied e c o l o g i c a l problems i n which p r e d i c t i o n i s the goal, realism and g e n e r a l i t y are often s a c r i f i c e d f o r p r e c i s i o n . In order to p r e d i c t with some degree of p r e c i s i o n the n u t r i e n t r e l a t i o n s h i p s within a lake, s i m p l i -f y i n g assumptions must be made. The d e t a i l e d d i s c u s s i o n of the submodels ampl i f i e s the nature of the assumptions made i n t h i s model. (a) Time Scale. The next step i n model b u i l d i n g i s to decide the time scale to be considered, and the r e s o l u t i o n of the time scale. For i n i t i a l modelling of phosphorus concentration and r e s u l t i n g a l g a l growth, i t i s u s e f u l to look at a time span of one year i n order to v e r i f y the model. Model r e s u l t s are compared with a c t u a l measurements of phosphorus and algae i n the lake, and the model pr o g r e s s i v e l y r e f i n e d u n t i l actual and predicted values agree reasonably w e l l . Resolution of the time scale (or time i n t e r v a l ) i s another com-promise, i n t h i s instance between d e t a i l (a short time i n t e r v a l ) and gener-a l i z a t i o n (a long time i n t e r v a l ) . While i t has been shown i n the previous se c t i o n that phosphorus can cycle i n minutes between some compartments in a lake, t h i s i n t e r v a l i s too short f o r p r a c t i c a l use i n a model which w i l l run f o r years (and too expensive i n computer time). A weekly or bi-weekly (twice a month) i n t e r v a l would be s a t i s f a c t o r y , except that most c o e f f i c i e n t s of a l g a l metabolism are expressed i n the l i t e r a t u r e i n u n i t s per day. Therefore, a compromise i n t e r v a l of one day i s chosen. 47 (b) Approach to Mathematical Statement of Relationships. Two basic mathematical approaches have been used in modelling ecological sys-tems: (1) continuous form, with the use of d i f f e r e n t i a l equations; and (2) discrete form, with the use of difference equations. The continuous form describes changes that occur continuously over time, and while they are the most powerful way of representing general flow processes in ecolo-gical systems, they are often d i f f i c u l t to solve (Walters 1971). Further-more, Watt (1968) points out that many biological processes have variables which do not have continuous, but rather discrete values. The only practical approach in modelling the volume changes associated with lake s t r a t i f i c a t i o n i s the use of a f i n i t e time period (difference equation). The daily changes in volume occurring during the spring s t r a t i f i c a t i o n and autumn de-stratification processes cannot be practically described by a differential equation, and are more accurately represented by a difference equation. Difference equations have the advant-age of being clearer to understand, making the poss i b i l i t y of errors hidden in the complexity of d i f f e r e n t i a l equations less l i k e l y . For these reasons the discrete form (difference equations) was chosen for the equations in this model. With this form computations are performed for each time interval according to the following relationship (adapted from Walters 1971): value of variables now statement of value of variables relationships after one time period or rules for change 48 The essence of t h i s type of systems model i s the "statement of r e l a t i o n s h i p s " or " r u l e s f o r change" which d e f i n e the way v a r i a b l e s w i l l change (Walters 1971). With these r u l e s incorporated i n the inputs and outputs, the way i n which each v a r i a b l e w i l l change each day can be shown as f o l l o w s (adapted from Walters 1971): new value o l d valu e c . , , = c . i _ , + in p u t s - outputs of v a r i a b l e o f v a r i a b l e * With the use of t h i s input-output format, the problem of developing a systems model i s reduced to choosing reasonable ways to express the change of the i n f l o w s and outflows of the system over time (Walters 1971). Other s e c t i o n s of t h i s chapter d i s c u s s the d e t a i l s of these t r a n s f o r m a t i o n s . 2. S i m u l a t i o n Approaches t o M o d e l l i n g the Phosphorus Cy c l e Two b a s i c approaches have been used i n modelling the phosphorus c y c l e i n a q u a t i c systems: (a) the "compartment" approach; and (b) the "mass balance" approach. (a) The Compartment Approach. This approach uses radiophosphorus 32 t r a c i n g data ( P) as i t s b a s i s , and emphasizes the r a t e of movement of phosphorus between the compartments, as discussed i n the s e c t i o n on phos-phorus c y c l i n g and shown i n Figure 5. M o d e l l i n g s e v e r a l compartments and the i n t e r a c t i o n s between each one can be enormously complex. For example, a phosphorus model w i t h 15 compartments can have as many as 55 pathways of f l u x between compartments (Klueseher 1970). Simpler compartment models have been conceived, but even a s i x compartment phosphorus model has at l e a s t 23 Important f l u x pathways (Fleming 1971). 49 R i g l e r (1973) dis c u s s e s the problems i m p l i c i t i n the f o r m u l a t i o n of a compartment model f o r phosphorus c i r c u l a t i o n i n a l a k e . F i r s t l y , t h i s method assumes the system i s i n a steady s t a t e , and t h i s c o n d i t i o n i s r a r e -l y , i f ever, met i n a q u a t i c ecosystems (except t h a t during summer s t a g n a t i o n a pseudo st e a d y - s t a t e i s sometimes achieved i n some temperate l a k e s ) . 32 Secondly, P i s introduced o n l y i n the orthophosphate compartment, and w h i l e measurement of the r a t e of movement of the t r a c e r i s considered v a l i d , measurement of the q u a n t i t y of orthophosphate i n each compartment i s i n s e r -i ous q u e s t i o n (see previous s e c t i o n ) . T h i r d l y , the chemical and p h y s i c a l nature of s o l u b l e organic (or s o l u b l e unreactive) phosphorus i s s t i l l l a r g e l y unknown, as i s i t s r o l e i n the phosphorus economy of the trophogenic zone. F o u r t h l y , e x i s t i n g data are inadequate to provide t r u e r a t e constants of phosphorus movement out of the e p i l i m n i o n to the l i t t o r a l and hypolimnion. R i g l e r (personal communication) caut i o n s a g a i n s t the compartment approach f o r a n a l y s i s of phosphorus c i r c u l a t i o n between e p i l i m n i o n , hypolimnion and sediments because these k i n d s of f l u x data have not been q u a n t i f i e d . While no attempts have been made to formulate even a s i m p l i f i e d compartment model of phosphorus f l u x i n a freshwater system, at l e a s t one attempt (Pomeroy et al. 1969) has been made i n a s a l t water marsh. This model i n c l u d e s seven compartments (some of which are d i v i d e d i n t o subcompart-ments) and a t l e a s t 14 f l u x e s (radiophosphorus t r a c i n g ) between compartments. Because of t i d a l f l u s h i n g , routes of export from the system co u l d not be evaluated. In summary, i t can be concluded t h a t techniques of t r a c i n g phos-phorus i n a q u a t i c ecosystems have not yet reached the l e v e l of s o p h i s t i c a t i o n necessary t o enable modelling of the phosphorus c y c l e by the compartment approach. 50 (b) The Mass Eudget Approach. A more f r u i t f u l approach to the problem of nutrient budgets in lakes is proposed by Vollenweider (1969). Extending the earlier work of B i f f i (1963) and P i o n t e l l i and Tonolli (1964) Vollenweider begins with the basic mass balance assumption that the amount of a substance in a lake is essentially a function of the supply and loss (brought about by sedimentation and outflow) of the substance. B i f f i con-siders the hydrologic flow-through an essential factor, while P i o n t e l l i and Tonolli emphasize the loss through sedimentation. Vollenweider ex-tends these concepts in an analysis of the total phosphorus budgets of eight Swiss lakes, and formulates the following relationship. General form: change in mass of phosphorus = loading - sedimentation - outflow Specific form: dm W T -TT— = J - am - pm dt w w for which a steady-state solution in terms of phosphorus concentration and specific loading i s : [m_J = z L w' " (a+p) where is the mass of phosphorus in the lake (kg); J i s the loading (kg); a i s an empirically determined sedimentation coefficient (years ^~); p is the coefficient of hydrologic flow-through (years ^ ; equal to Q/V, where 3 3 Q i s the outflow discharge (m /year) and V is the lake volume, m ); [m ] is w o _ the mean concentration of phosphorus in the lake (g/m ); z is the mean depth of the lake (m); and L is the specific loading of phosphorus to the lake (g/m2). 51 Vollenweider accounts for the fact that during s t r a t i f i c a t i o n only a part of the entire lake volume i s involved in mixing and hydrologic flow-through, and has developed an expression for the "mean exchange epilim-nion" during this period. Vollenweider assumes that the loading rate is constant and that the concentration of phosphorus in the outflow i s the same as the average concentration in the lake. The most d i f f i c u l t part of the analysis is the formulation of an expression which accurately describes the sedimentation of phosphorus. Vollenweider decided that his original assumption that phosphorus sedimenta-tion Was a linear function of the amount of phosphorus in the water (c*11^) did not adequately f i t experimental data. He therefore introduced a co-efficie n t , T, which made sedimentation a function of loading as well as the amount of phosphorus in the water. The resulting equation produced a satisfactory f i t with experimental data when a mean value of 0.39 for T was used: d [mw] L t L —~— = — - a[m ] - —(1-p) - P[m] dt — w — w z z loading - sedimentation - outflow Vollenweider suggests that further development of this model should include a set of simultaneous reaction equations to describe the complexities of the sediment-water exchanges (1968 and personal communication). O'Melia (1972) extends Vollenweider's model with the division of a lake into an epilimnion and hypolimnion, and the introduction of a term to describe the eddy diffusion of phosphorus from hypolimnion to epilimnion. 52 O'Melia's mass balance formulation for the epilimnion i s : dP d[P g] d t " = W + k z A e - ^ T " s V e [ P P ] " ^ [ P T ] inflow + eddy diffusion - sedimentation - outflow With the exception of the eddy diffusion term (the second term in the equa-tion), this formulation is almost identical to Vollenweider's. Here P is the amount of total phosphorus in the epilimnion (kg); W is the rate of i n -put of total phosphorus from the land (kg/year), a l l of which is assumed to enter the epilimnion; the term k A d[P ]/dz describes the input of phosphate Z 6 S to the epilimnion by diffusion from the hypolimnion, where is the co-2 efficient of eddy diffusion or v e r t i c a l mixing (m /year), A is the area 2 of the thermocline (m ),.d[P ]/dz is the gradient of soluble phosphate s across the thermocline (mg/1); the term sVe[PP] is the sedimentation loss, where s is the sedimentation coefficient (years ^ ) , V^ is volume of the epilimnion (m ), and [PP] is the concentration of particulate phosphorus in the epilimnion (mg/1); the last term is the outflow ( a l l considered to 3 be from the epilimnion) in which Q lake discharge (m /year) and [P^] i s o the concentration of total phosphorus in the epilimnion (g/m ). O'Melia does not include a model for the mass balance of phosphorus in the hypo-limnion, which i s essential for the determination of the concentration gradient across the thermocline. CHAPTER IV DEVELOPMENT OF A MODEL FOR SKAHA LAKE The work of Voll e n w e i d e r and O'Melia forms the e s s e n t i a l base from which a mass balance model f o r an epilimnion-hypolimnion-sediment system can be formulated. In t h i s model " t o t a l phosphorus" i s considered the b a s i c measure f o r the element. The n o r t h and south basins of Skaha Lake are considered s e p a r a t e l y , and h o r i z o n t a l homogeneity i s assumed In each b a s i n . Separate equations are formulated f o r the e p i l i m n i o n and hypolimnion. The b a s i c form of these equations i s described i n t h i s s e c t i o n , w h i l e the d e t a i l s of submodels are described i n a l a t e r s e c t i o n . A. FUNDAMENTAL INPUT-OUTPUT EQUATION 1. Form of the Equation f o r the E p i l i m n i o n I f steady s t a t e c o n d i t i o n s p r e v a i l e d i n the n u t r i e n t budget of a l a k e , the f o l l o w i n g r e l a t i o n s h i p would be t r u e : Input - Output = 0 or Input = Output However, most l a k e s a c t as n a t u r a l t r a p s f o r sediments ( i n c l u d i n g phosphorus) and e x h i b i t a n u t r i e n t g a i n over time. In order to understand the dynamics of t h i s n u t r i e n t i n c r e a s e , i n p u t s and outputs must be described i n d e t a i l . A l l terms are r a t e s i n kg/day. (a) Input Terms. Input of phosphorus can be des c r i b e d by the f o l l o w i n g equation: 53 54 input = P L E + P E + P v + P R E where P i s external loading from a l l sources (kg/day), P is eddy diffusion from the hypolimnion (kg/day), P^ is a volume gain of phosphorus (kg/day) as the epilimnion forms and develops following spring mixing, and P R E is regeneration of organic phosphorus from bacterial decomposition in the l i t t o r a l zone (kg/day). The loading term, PT _, is the summation of natural and cultural sources of phosphorus. Natural sources come from dustfall and precipitation on the lake surface, streamflow from vi r g i n watersheds, and ground water i n -flux from natural sources. Cultural sources include municipal waste, storm sewer flows, industrial waste, agricultural return flow, agricultural ground water, septic tank ground water, and inputs from disturbed watersheds (e.g. logging and mining). The collection and r e l i a b i l i t y of these data are dis-cussed in Appendix B. (b) Output Terms. Output of phosphorus from the epilimnion is described by the following equation: Output = P S E + P Q where P^E is the sedimentation to the hypolimnion (kg/day) and P^ i s the outflow (kg/day). (c) Combined Mass Balance. The combined mass balance equation for the epilimnion becomes: P =P +P + P + P + P - P - P TE IE LE E V RE SE 0 where P^g is the resulting amount of total phosphorus (kg) in the epilim-nion at the end of each time period (day) and P is the i n i t i a l amount of 55 phosphorus (kg) a t the beginning of each p e r i o d . The outflow of phosphorus from the l a k e , P_, i s equal to QC , 0 e 3 where Q i s the discharge of water from the l a k e (m /day) and C i s the e 3 c o n c e n t r a t i o n of phosphorus i n the e p i l i m n i o n (kg/m ). 2. Form of the Equation f o r the Hypolimnion As i n the e p i l i m n i o n , a mass balance f o r the hypolimnion c o n s i s t s of i n p u t and output terms expressed as r a t e s i n kg/day. (a) Input Terms. Input to the hypolimnion can be d e s c r i b e d by the f o l l o w i n g equation: Input - P L R + P r h where P i s l o a d i n g by sedimentation from the e p i l i m n i o n (kg/day) and P L H RH i s r e g e n e r a t i o n from the sediments (kg/day), or " i n t e r n a l l o a d i n g . " (b) Output Terms. Output from the hypolimnion can be described by the f o l l o w i n g equation: Output = P S H + P E + P v + P Q where P i s the sedimentation l o s s (kg/day), P_ i s the eddy d i f f u s i o n l o s s on h to the e p i l i m n i o n (kg/day), P^ i s a l o s s to the e p i l i m n i o n as s t r a t i f i c a t i o n occurs a f t e r s p r i n g m i xing (kg/day), and P^ i s an o u t f l o w l o s s which occurs d u r i n g complete mixing when the e n t i r e l a k e i s t r e a t e d as a hypolimnion i n the model (kg/day). (c) Combined Mass Balance. The combined mass balance equation f o r the hypolimnion becomes: P = P + P + P - P - P - P - P TH IH LH RH SH E V 0 where P_ i s the r e s u l t i n g amount of t o t a l phosphorus (kg/day) i n the hypo-In 56 / limnion at the end of each day and P i s the i n i t i a l amount (kg/day) at the beginning of the daily period (equal to P for the previous day). TH 3. Modification of Mass Balance During Mixing Periods During months when the lake is completely mixed (mid-November to mid-April) the hypolimnion model w i l l be used to describe the balance of phos-phorus in the entire lake. The fact that slight inverse s t r a t i f i c a t i o n occurs in winter when an ice cover forms on at least part of the lake is not taken into account, except by adjustment of coefficients as described in another section. With the advent of autumn mixing phosphorus i s brought from the hypolimnion (where i t has been accumulating during summer stagnation) to the trophogenic layer. This phosphorus increase may stimulate an autumn phytoplankton bloom. B. MIXING BEHAVIOR OF SKAHA LAKE AND VOLUME CHANGES OF EPILIMNION AND HYPOLIMNION No attempt i s made to predict the thermal regime (and consequent-ly the mixing behavior) of the lake. Instead, thermal data describing the mixing behavior of the lake in 1969-70 are used to calculate volumetric changes of the epilimnion, metalimnion (thermocline) and hypolimnion in each basin (Table A-l in Appendix A). Area-depth relationships from the hypsometric curve (Figure 2) and thermal data are used for the calculations. The end of the complete mixing period occurs in mid-April when the formation of the epilimnion begins. As the total volume of the lake re-mains constant, growth of the volume of the epilimnion i s at the expense of the hypolimnion. Therefore, as the epilimnion increases In volume, the 57 hypolimnion correspondingly decreases in volume. Computation of these volume changes takes into account changes in volume of the metalimnion (thermocline). As the volume of the epilimnion grows with increasing s t r a t i f i c a t i o n , phosphorus within such volume is lost from the hypolim-nion and added to the epilimnion (W. K. Oldham, personal communication). This phosphorus exchange i s included in the mass budget as and is calculated according to the following equation: V x h where P v is the mass of phosphorus lost from the hypolimnion and added to the epilimnion (kg), is the volume of water lost from the hypolim-3 nion and added to the epilimnion (m ) and C^ is the concentration of total 3 phosphorus in the hypolimnion (kg/m ). Thermal records show that the inverse s t r a t i f i c a t i o n of winter is completely absent by mid-March, and vigorous mixing takes place from mid-March to mid-April. The starting point chosen for the model is mid-March which could be termed the beginning of the "spring overturn." The period of complete mixing in the autumn ("autumn overturn") begins in mid-November and lasts u n t i l mid-December when the inverse s t r a t i f i c a t i o n of winter begins. During some years an ice cover begins to form in mid-Decem-ber, and can remain on at least part of the lake u n t i l March. Dissolved solids data collected during two winters (Stein and Coulthard 1971) i n d i -cate l i t t l e v e r t i c a l variation and relatively complete mixing during the period of ice cover. For validation purposes mixing data for 1969-70 is used, and for prediction purposes an "average mixing year" is developed by computing 58 mean mixing volume variations for the years 1967-71. These are shown in Table A-l of Appendix A. C. DEVELOPMENT OF SUBMODELS The detailed development of five submodels i s described in this section: eddy diffusion, sedimentation, internal loading, primary production, and dissolved oxygen. 1. Eddy Diffusion Submodel Eddy diffusion i s commonly regarded as the main mechanism of vertical heat transport through the water column of a thermally s t r a t i -fied lake (Mortimer 1942, Hutchinson 1957). The same mechanism i s con-sidered by Lerman and S t i l l e r (1969) and O'Melia (1972) to be responsible for the transport of dissolved substances, including phosphorus, through the water column. Upward transport of soluble phosphorus from hypolimnion to epi-limnion can produce high concentrations of phosphorus in the euphotic zone (O'Melia 1972). O'Melia calculates that the ver t i c a l flux of phos-phate to the epilimnion of the Vierwaldstatersee (Switzerland) can exceed inputs of phosphorus from land runoff during summer stagnation. For this 2 calculation O'Melia assumes an eddy diffusion coefficient of 0.05 cm /sec in a thermocline 5 m thick with a concentration gradient of 0.02 mg/1 of 2 inorganic phosphorus across the thermocline. The result (0.6g/m »year) is equal to the estimated total phosphorus loading from the land to the lake, and exceeds the "permissible loading" level proposed by Vollenweider (1968) for a lake of the Vierwaldstatersee's mean depth (104 m). 59 (a) Simplifying Assumptions for Eddy Diffusion. Three major processes are considered to dominate the eddy diffusion process in s t r a t i -fied lakes: (1) turbulence is the driving force which determines the i n -tensity and rate of eddy diffusion; (2) temperature differences between epilimnion and hypolimnion cause thermal s t r a t i f i c a t i o n which inhibits eddy diffusion; (3) the concentration gradient of dissolved substances between s t r a t i f i e d layers determines the net transport between the layers. Turbulence is caused mainly by wind which mixes the epilimnion to varying degrees. Attempts to model thermocline development from wind data have not been very satisfactory (Hutchinson 1957), making turbulence a d i f f i -cult process to quantify in lakes. Furthermore, in order to verify a model for turbulence effects, detailed temperature records are necessary. Unfortunately, ve r t i c a l temperature profiles from Skaha Lake are available only twice a month. For these reasons, turbulence i s assumed to be con-stant in the eddy diffusion model, and the epilimnion is considered to be continually mixed to the thermocline. Thermal s t r a t i f i c a t i o n and the phos-phorus concentration gradient are the processes considered in this submodel. (b) Equation for Eddy Diffusion Transport. An expression describ-ing transport of soluble phosphorus between hypolimnion and epilimnion is : P = k C A E e g t where P is the rate of phosphorus movement by eddy diffusion (kg/day); k 2 is the coefficient of eddy diffusion (a function of temperature, m /day); C i s the concentration gradient of soluble and colloidal phosphorus across 3 2 the thermocline (kg/m *m); and A is the area of the thermocline (m ). The 60 simplifying assumption is made that turbulence caused by wind mixing is con-stant during the strati f i e d period, and that complete mixing occurs within the epilimnion. Colloidal and soluble phosphorus involved in eddy d i f f u -sion amount to approximately 30% of the total phosphorus content in Skaha Lake (calculated from Stein and Coulthard 1971 and Williams 1972). (c) Coefficient of Eddy Diffusion. Estimation of this coefficient is the major theoretical consideration of this submodel. Lerman and S t i l l e r (1969) review three methods for the estimation of the coefficient, of which the f i n i t e difference method is the most applicable for modelling on a sea-sonal basis. The method i s used extensively in studies of diffusion and heat movement, and is based on replacing the differentials by differences between the temperature values in two profiles recorded at times t and t+1 (Lerman and S t i l l e r 1969). The following equation expresses the relationship in terms of six temperatures: three at time t at depths z-1, z, and z+1, and three at time t+1 at the same depths (Lerman and S t i l l e r 1969): k e = x l 2K t/x 2D where M is the thickness of the metalimnion (thermocline) (m); D i s the time period chosen (day); x = T - T 1 z,t+l z,t X2 = ( T z - l , t + T«-l it+l ) = 2 ( T z , t + + (Vl,t + Vu.t+l* where T is temperature (°C). Coefficients for the s t r a t i f i c a t i o n period of 1969-70 are calcu-lated from temperature profiles and presented in Table A-l in Appendix A. The values are in the same range of magnitude and variation as those calculated by 61 O'Melia for the Vierwaldstattersee (1972) and by Lerman and S t i l l e r for Lake Tiberias (1969). 2. Sedimentation Submodel This submodel considers only the downward movement of particulate phosphorus by sedimentation. Regeneration back from lake sediments is con-sidered in the succeeding submodel (internal loading). Sedimentation processes from the epilimnion and hypolimnion are considered to be different, and are dealt with separately. (a) Sedimentation from the Epilimnion. Sedimentation of phosphorus from the epilimnion occurs in both inorganic and organic forms. Different mechanisms predominate in the sedimentation of each form. (1) Sedimentation of Inorganic Phosphorus. There are two major mechanisms responsible for the sedimentation of inorganic phosphorus in lakes: (1) chemical precipitation of phosphorus minerals; and (2) adsorp-tion of phosphate onto the surface of the lake sediment. a. Precipitation of Phosphorus Minerals. There are three phosphorus mineral groups which may be involved in inorganic precipitation: the calcium phosphates, the iron phosphates, and the aluminum phosphates. The mineralogy and stoichiometry of a l l these groups are complicated (Kramer et al. 1972). It is possible to calculate the equilibrium s t a b i l i t y relationships of the apatites, variscite, and strengite using pK values, assuming average con-centrations of the cations (Ca, Fe, Al), and knowing the pH of the water and concentration of soluble phosphate (Kramer et al. (1972). Modelling the sea-sonal variation of these variables Is beyond the scope of this investigation. Furthermore, in eutrophic lakes such as Skaha, the sedimentation of organic phosphorus is considered quantitatively more important than inorganic 62 phosphorus. However, an understanding of the pathways of chemical p r e c i p i -t a t i o n of phosphates i n l a k e s i s p e r t i n e n t to t h i s d i s c u s s i o n . Stumm (1964) concludes that hydroxyapatite may l i m i t phosphate _3 (PO^ ) co n c e n t r a t i o n s i n l a k e s t o 0.03 mg/1; he computes from t h e o r e t i c a l e q u i l i b r i u m r e l a t i o n s h i p s that the e q u i l i b r i u m c o n c e n t r a t i o n of phosphate i n contact w i t h hydroxyapatite i s 0.03 mg/1 at a pH of 7, and th a t a d d i -t i o n s of phosphate beyond t h i s l e v e l would cause p r e c i p i t a t i o n of hydroxy-a p a t i t e i n the sediments. However, Lee (1970) p o i n t s o u t t h a t l a b o r a t o r y and f i e l d o b s e r v a t i o n s i n d i c a t e t h a t ". . . i t i s d o u b t f u l t h a t hydroxyapatite p l a y s an important r o l e i n the environmental chemistry of phosphate i n n a t u r a l waters." Lee observes t h a t there are many eutrophic l a k e s where the concen-t r a t i o n of phosphate g r e a t l y exceeds 0.03 mg/1 (the Madison, Wisconsin l a k e s t y p i c a l l y have 10 to 50 times t h i s amount), and hydroxyapatite i s not a domi-nant form of sediment phosphorus. P o r c e l l a et al. (1971) conclude t h a t w h i l e Stumm's hypothesis may be a p p l i c a b l e to o l i g o t r o p h i c l a k e s , i t i s i n c o n s i s t e n t w i t h the ob s e r v a t i o n i n eutrophi c l a k e s t h a t phosphate con c e n t r a t i o n s decrease during a l g a l a c t i v i t y and do not i n c r e a s e again u n t i l autumn mixing occurs. They note t h a t b i o l o g i c a l growth and decomposition, as w e l l as the secondary e f f e c t s of m i c r o b i a l r e a c t i o n s on pH, b e t t e r e x p l a i n the observed c y c l i n g of n u t r i e n t s i n eutrophic l a k e s . Experiments i n a h e t e r o t r o p h i c b i o l o g i c a l r e a c t o r (a tank s i m u l a t i n g a e u t r o p h i c l a k e ) i n d i c a t e that removal of phosphorus by the sedimentation of dead a l g a l c e l l s i s q u a n t i t a t i v e l y more important than the chemical p r e c i p i -t a t i o n of phosphates (Tenney et at. (1972). I t was found that no phosphate removal occurs i f the biomass i s removed from the suspension and continued 63 aeration proceeds, even at relatively high pH values. It is concluded that chemical conditions in Skaha Lake (maximum recorded pH of 9.2) are not con-ducive to significant chemical precipitation of insoluble phosphates. While Williams (1973) reports that the majority of the phosphorus in the s u r f i c i a l sediments of Skaha Lake is in the form of hydroxyapatite (70%), he concludes that the apatite comes directly from the s o i l and rocks of the watershed, not from chemical precipitation within the lake. The min-eralogical composition of the bedrock supports this hypothesis. The depofii-tional pattern of apatite sedimentation shows that the highest concentrations occur in the northern basin near the inflow of the Okanagan River. Locally high apatite concentrations exist near areas of probable erosion and trans-port from the watershed. Williams concludes that the hydroxyapatite plays l i t t l e or no role in the phosphorus cycle of the lake waters, either before or after deposition. Personal communication with Williams confirms that stream input estimates of phosphorus probably do not include apatite, as i t is a relatively heavy mineral not normally sampled with conventional stream sampling techniques. These findings support the hypothesis that chemical precipitation of hydroxyapatite has l i t t l e , i f any, effect on the phosphorus budget of Skaha Lake water. b. Adsorption of Phosphate. Since this sedimentation mechanism is assumed to be significant only during the mixing period (Novem-ber to March) when the epilimnion does not exist, i t w i l l be discussed in the section on sedimentation from the hypolimnion. (2) Sedimentation of Organic Phosphorus. Seasonal variation in the sedimentation of organic phosphorus is assumed to be a function of p r i -64 mary production in the epilimnion, which results in the sedimentation of organic matter. Evidence supporting this assumption comes from many inves-tigators. In a study of oxygen-nutrient relationships in the central basin of Lake Erie, Eurns and Ross (1972) report that high rates of oxygen deple-tion occur in the same areas as profuse primary productivity. They conclude that since approximately 88 per cent of the hypolimnetic oxygen was consumed in the decay of organic materials during the summer of 1970, i t is probable that a massive algal bloom was the major cause of anaerobic conditions that subsequently developed in the hypolimnion. The bloom caused "algal rains" (the sedimentation of dead algal cells from the epilimnion to the hypolimnion, and then to the sediment) which formed a f l u f f y green layer on the bottom, 2 to 3 cm thick. Much phosphorus accompanied the sedimentation of these algal c e l l s , a portion of which was regenerated back to the hypolimnion following decomposition (details of this process are discussed in the next section on internal loading). Williams and Mayer (1972) summarize the significance of this elegant study: "We now know that the summer months have been marked by a tremendous increase in the deposition of phos-phorus on the sediment-water interface, in the form of a l -gal remains, and that a high proportion of this algal-derived phosphorus is retained by the sediments during [the aerobic portion of] this period." Hutchinson (1957) describes an experiment by Elnsele (1941) in which phosphatewas a r t i f i c i a l l y added to the eutrophic Schleinsee to study the uptake of soluble orthophosphate by organisms and subsequent sedimentation. The total organic (soluble and particulate) phosphorus increased almost as much as the inorganic phosphorus decreased, and i t was evident that phosphate 65 was being taken up very rapidly and sedimented as particulate organic phosphorus. Sedimentation rates of phosphorus have been measured in eutrophic lakes during extreme summer st r a t i f i c a t i o n in two ways: (1) radiophosphorus tracing; and (2) actual measurement with sediment traps. Using the former method, Hutchinson (1950) found that about two per cent of the total phos-phorus in the trophogenic layersedimented daily, while Rigler (1964) reports a daily loss of about one per cent. These values are similar to those ob-tained by Bosch for the Vierwaldstattersee from analyses of the phosphorus content of sediment traps (Gachter 1968). Bosch found that 1.4 to 2.5 per cent of the phosphorus in the trophogenic layer ended up in the sediments daily. Seasonal variation, and especially the response to algal blooms, is not reported in these investigations. Rigler (1973) observes that these rates of phosphorus loss are consistent with Hutchinson' s results (1938) showing the hypolimnetic oxygen d e f i c i t in four lakes to be directly pro-portional to the amount of particulate organic matter in the water. The following expression describes sedimentation of organic phos-phorus from the epilimnion to l i t t o r a l sediments and the hypolimnion: POT. = B k k SE s pb re c where P is the rate of organic phosphorus sedimentation from the epilim-SE nion (kg/day), B is the rate of sedimentation of phytoplankton cells (bio-s mass) from the epilimnion (kg/day), k ^ Is the coefficient of phosphorus in phytoplankton biomass (kg phosphorus/kg dry weight phytoplankton), and k is the coefficient of phosphorus recycling within the epilimnion (dimensionless). 66 This i s a c o n s e r v a t i v e estimate of organic phosphorus sedimentation, as i t i s o u t s i d e of the scope of t h i s r e s e a r c h to account f o r sedimentation l o s s e s of zooplankton and higher t r o p h i c l e v e l s . While t h i s e xpression d e s c r i b e s the amount l o s t from the e p i l i m n i o n , i t i s important t o note t h a t about 17 per cent of t h i s amount ends up i n l i t t o r a l sediments and 83 per cent goes to the hypolimnion (based on a survey of the l i t t o r a l area of Skaha Lake, Stockner et al. 1972b). This Information i s used i n the f o l l o w i n g s e c t i o n on i n t e r n a l l o a d i n g , or reg e n e r a t i o n from the sediments. The biomass of phytoplankton s i n k i n g from the e p i l i m n i o n each day (B ) i s estimated by the f o l l o w i n g r e l a t i o n s h i p : B S p where B i s the biomass of phytoplankton i n the trophogenic l a y e r ( k g ) and Sp i s the r a t e of s i n k i n g as c e l l s sediment out of the trophogenic layer (day "*"). Both B and Sp are estimated by the primary production submodel i n a f o l l o w i n g s e c t i o n of t h i s chapter. The c o e f f i c i e n t of phosphorus i n phytoplankton biomass (k^^) I s c a l c u l a t e d from the assumption t h a t phytoplankton have, on the average, a f i x e d composition of the major elements. R e d f i e l d et at. (1963) have de-f i n e d an average organism s t o i c h i o m e t r y of ^^06^16^1^263^110 t* i e o c e a n s « This r a t i o i s v e r y s i m i l a r to a C:N:P r a t i o i n the p a r t i c u l a t e organic matter i n the water above the thermocline i n Lake E r i e of 122:18:1 (Burns and Ross 1972). Although analyses of organisms do not always agree w i t h t h i s composi-t i o n and can vary due to " l u x u r y " uptake of a v a i l a b l e phosphorus (Kramer et al. 1972) i t i s a reasonable approximation f o r m o d e l l i n g purposes. The mole-c u l a r weight of t h i s average molecule (dry weight) of org a n i c matter i s 3551 67 g-atoms, and the phosphorus portion weighs 31 g-atoms; the resultant frac-tion of phosphorus in a mass of organic matter is 31/3551, or 0.0090. There-fore, the coefficient of phosphorus in plankton (by weight) i s approximated as 0.009 mg P/mg dry weight of phytoplankton. Strickland (1965) reports a slightly higher figure of 0.011 for diatoms in the ocean. The coefficient of recycling, k » I s estimated according to the quantity of organic matter decomposed within the epilimnion, thereby releas-ing soluble phosphate for reuse by plankton and preventing this portion of epilimnion phosphorus from sedimenting to the hypolimnion. Kajak et al. (1970) found that 63 per cent of total primary production in several Polish lakes was decomposed in the epilimnion, therefore never sedimenting to the hypolim-nion. Of the remaining 37 per cent which reached the hypolimnion as seston, 19 per cent was decomposed in the hypolimnion and 18 per cent was decomposed in the sediments. It is estimated from these results that approximately 60 per cent of the phosphorus in organic matter remains and is decomposed in the epilimnion, and that the coefficient of recycling (which indicates that percentage reaching the hypolimnion) is approximately 0.4. (b) Sedimentation From the Hypolimnion. Sedimentation losses from the hypolimnion result from two major mechanisms: (1) inorganic sedi-mentation by adsorption on the bottom sediments; and (2) organic sedimentation of algal c e l l s . (1) Sedimentation of Inorganic Phosphorus. While phos-phorus sedimentation during the growing season is assumed to be dominated by organic forms, the assumption is not valid during the period of complete mixing when low water temperatures and decreased solar radiation cause organic 68 production to be minimal. During this period (mid-November to mid-April) soluble inorganic forms of phosphorus are not rapidly taken up by organisms and the concentration of dissolved orthophosphate (or soluble reactive phos-phorus) increases. It i s suggested that during this six-month period the dominant mechanism of phosphorus sedimentation is adsorption of orthophos-phate by the sediments. Relatively complete mixing takes place during this period (except for slight inverse s t r a t i f i c a t i o n in mid-winter), resulting in a reasonably uniform distribution of soluble phosphorus throughout the water column and enabling sediment-water contact at a higher rate than possible dur-ing s t r a t i f i c a t i o n . Adsorption reactions are important in controlling the exchange of phosphorus between sediments and the overlying water, and many studies i n -dicate that phosphate tends to be readily adsorbed to lake sediments (Lee 1970, Golterman 1973, Williams and Mayer 1972). Williams and Mayer (1972) report that sorbed phosphorus accounts for up to 50 per cent of the total phos-phorus in the s u r f i c i a l sediments of Lake Erie. Eighteen per cent of the phosphorus in the s u r f i c i a l sediments of Skaha Lake i s composed of sorbed phosphorus, which i s the most abundant form after apatite (which accounts for 70 per cent)(Williams 1973). The adsorption of phosphorus by lake muds has been quantified with radiophosphorus experiments by Olsen (1958). For oxidized sediments, Olsen found that phosphate equilibrium between sediments and water is described as the difference between gross adsorption (a) and release back to the water (r). The gross adsorbed amount follows the Freundlich adsorption isotherm, v expressed as k C where k and v are constants for the particular type of a a a 69 sediment and C i s the concentration of orthophosphate in the water. Arm-strong and Gloyna (1967) used a similar form of the Fr.eundlich adsorption isotherm to describe the adsorption of radionuclindes to aquatic sediments. Olsen (1958) found that release back to the water i s expressed as -v k C where k and v are constants for the sediment and C i s the concentra-r r r tion of orthophosphate in the water (mg/1). The expression for net adsorp-tion (loss from the water to the sediment) i s : net adsorption = gross adsorption - release (a-r) v -v = k C a - k C r a r where adsorption i s in mg P/kg of sediment (dry weight) (Figure 6)« It is assumed that approximately the upper one mm of sediment is involved in the adsorption process (Olsen 1958), which means that 1.7 x 10^ kg of sediment 2 are involved (assuming the area of the north basin to be 17 km and the speci-f i c gravity of the sediment i s 0.1). For a calcerous lake sediment, Olsen found the constants to be: k = 171, k = 13.5, v =0.17, and v =0.5. a ' r ' a ' r (2) Sedimentation of Organic Phosphorus. Sedimentation of orga-nic phosphorus from the hypolimnion can be described by the following expression k ,(0.83)?,^ rh SE where k ^  is the recycling coefficient for organic phosphorus within the epi-limnion (day "^), 0.83 is the proportion of phosphorus sedimenting from the epilimnion which reaches the hypolimnion, and P is the rate of sedimentation SE of phosphorus from the epilimnion (kg/day). It is assumed that a percentage of the organic phosphorus which sediments to the hypolimnion from the epilimnion w i l l decompose in lower waters 70 Figure 6. Adsorption of phosporus on an oxidized calcerous sediment (Olsen 1958). 71 before reaching the sediment. The recycling coefficient, ^ r n» reflects the proportion of organic phosphorus which f i n a l l y reaches the bottom of the lake. Kajak et al. (1970) found that of 37 per cent of the organic matter in the epilimnion which reached the hypolimnion, 19 per cent was decomposed in hypolimnetic water and 18 per cent reached the bottom of the lake. These results indicate that about half of the organic matter reaching the hypolim-nion is decomposed in the water before f a l l i n g to the sediment, and thus the recycling coefficient for the hypolimnion is approximated as 0.5/day. Not a l l of the phosphorus sedimenting from the epilimnion reaches the hypolimnion. Assuming horizontal homogeneity of total phosphorus in the water, a percentage equal to the area of the l i t t o r a l zone w i l l sediment in the l i t t o r a l . Since the area of the l i t t o r a l zone is 17 per cent of the total area (Stockner et al. 1972b), 17 per cent of phosphorus sedimenting from the epilimnion w i l l end up in the l i t t o r a l and the remainder (83 per cent) w i l l reach hypolimnetic waters. Therefore, 83 per cent of P w i l l reach the hypo-SE limnion. (3) Resulting Expression for Sedimentation From the Hypolimnion. The following expression describes sedimentation of inorganic and organic phos-phorus from the hypolimnion: P = adsorption loss + organic sedimentation SH - ( k a C V a - k r C V r ) S d + k r h ( 0 . 8 3 ) P S E where P i s the sedimentation of phosphorus from the hypolimnion (kg/day) on and Sj is the dry weight of sediment involved in adsorption (kg). 72 3. Internal Loading Submodel Internal loading of phosphorus i n a lake i s the amount regenerated from the sediments following the i n i t i a l gross sedimentation process. Net sedimentation could be conceptualized as gross sedimentation minus i n t e r n a l loading (regeneration). Although net sedimentation i s the amount of import-ance to "eutrophication l i m n o l o g i s t s " , the mechanisms involved i n gross sedimentation and subsequent regeneration are quite d i f f e r e n t and must be modelled separately i f an accurate estimate of net sedimentation i s to be achieved. The importance of i n t e r n a l loading to the phosphorus budget of lakes can be great, e s p e c i a l l y during anaerobic conditions when the sediments may r e -generate more phosphorus to the lake than incoming streams and groundwater (ex-t e r n a l loading) contribute. During two summers of hypolimnetic conditions, the eutrophic Baldeggersee (Switzerland) gained four times as much phosphorus from sediment regeneration than from external surface loading (Bachofen, c i t e d i n Vollenweider 1968). The s i t u a t i o n reversed during aerobic conditions when more phosphorus was taken up (on a d a i l y rate) by the sediments than had been released during anaerobic conditions. In the c e n t r a l basin of Lake E r i e i n t e r n a l phosphorus loading during anaerobic conditions contributed 1.1 times the amount from external loading (Burns and Ross 1972). During aerobic conditions the sediments s t i l l l o s t phos-phorus to the overlying water, but the amount was only 25 per cent of the ex-t e r n a l loading during the same period. The percentage of sedimented organic phosphorus which returned to the water under aerobic conditions was 25 per cent (a f i g u r e c o i n c i d e n t a l with the preceeding 25 per cent). During the two months 73 of anaerobic conditions, 1.7 times the sedimented organic phosphorus returned to the water. Burns and Ross suggest that a possible explanation for the low per-centage of phosphorus regeneration (25 per cent) during aerobic conditions is that most of the orthophosphate regenerated from bacterial decomposition is produced on the lake bottom in close proximity to precipitated f e r r i c hydro-xides. This situation would lead to the formation of insoluble f e r r i c hydroxy-phosphate complexes. While these complexes would l i k e l y dissolve i f conditions subsequently became anaerobic, they would remain insoluble while the hypolimnion remained aerobic (Burns and Ross 1972). (a) Mechanisms Controlling Phosphorus Transport at the Sediment- Water Interface. Five major mechanisms control the transfer of nutrients from sediments to the hypolimnion: (1) physical disturbance and mixing; (2) physical diffusion; (3) biological uptake; (4) anaerobic chemical regeneration; and (5) decomposition regeneration. (1) Physical Disturbance and Mixing. In his cl a s s i c a l papers on the exchange of dissolved substances between mud and water, Mortimer (1941, 1942) observed that ordinary processes of molecular diffusion were extremely slow in transmitting material between sediments and water. Physical processes that speed up transmission are mixing during overturn periods, horizontal move-ment of water over the benthos (which increases eddy diffusion), convection currents under winter ice cover, and movement of benthic organisms (Mortimer 1941). Seiche action would also contribute to eddy diffusion at the inter-face (T.G. Northcote, personal communication). These losses are d i f f i c u l t to quantify. 74 Following a period of high winds on Lake Erie, Kramer et al. (1970) report increases in soluble orthophosphate and suspended mineral material in the water. In the l i t t o r a l area of the Bodensee Siessegger (1968) reports that agitation of the sediment after storms caused a 100-fold orthophosphate increase in the overlying water. Uithin 18 hours of the storm the orthophos-phate concentration was halved. Regeneration of phosphorus by this mechanism is of more significance for l i t t o r a l zones and shallow.lakes than for deep lakes because of greater effects on the sediments due to wind, wave and current action. Activity by benthic organisms, such as tub i f i c i d worms, results in phosphorus loss from sediments (Whitten and Goodnight 1967). Bottom-feeding f i s h such as carp and perch species deplete the sediment of organic forms of phosphorus. The significance of these losses from the sediments, although not quantified, i s probably not great (Williams and Mayer 1972). (2) Physical Diffusion. Regeneration to the water can occur as a result of diffusion of soluble phosphorus out of the sediments due to a difference in concentration of soluble phosphorus between the i n t e r s t i t i a l water of the sediment and the overlying water (Williams and Mayer 1972). The soluble phosphorus regenerated may form through diagenesis of sedimented par-ticulate phosphorus within the sediments. The rate of diffusion depends on the concentration difference between the sediment i n t e r s t i t i a l water and the overlying water, the porosity of the sediment, and the circulation of water over the mud surface (Williams and Mayer 1972). These variables have not been determined for Skaha Lake. According to Williams and Mayer (1972), the role of the oxidized microzone at the interface in controlling regeneration has not been adequately 75 evaluated. Although i t has been suggested that the microzone acts as a barrier to the exchange of phosphorus across the interface because of the presence of f e r r i c iron, i t i s questionable whether the barrier is effective when the microzone is unconsolidated. Diagenetic formation of hydroxyapatite within sediments (an important process in the sediments of Skaha Lake) is a mechanism which acts in opposition to the diffusion of soluble phosphate into overlying water (Williams and Mayer 1972). For Lake Erie and Lake Ontario sediments, the concentration of soluble +2 -3 Ca , PO^  , and OH ions in the i n t e r s t i t i a l water of the sediments corresponds very closely to the solubility product of hydroxyapatite (Sutherland et al. 1966, Williams and Mayer 1972). Hydroxyapatite, once formed, is very unlikely to participate in regeneration reactions. Due to the d i f f i c u l t y in modelling the diffusion process, the lack of necessary data (especially the phosphorus concentration of i n t e r s t i t i a l sedi-ment water), and the lack of knowledge concerning i t s quantitative role in the nutrient budget of lake sediments, modelling this mechanism w i l l not be attempted. (3) Biological Uptake. Radiophosphorus studies show that l i t t o r a l vegetation (especially macrophytes) can take up phosphorus from sediments direct-ly , without f i r s t entering the water phase (Pomeroy et al. 1967). Pomeroy finds a rapid turnover time of several days between phosphorus in the s u r f i c i a l sedi-ments of a salt water marsh and Spavtina (marsh grass). Uptake of solubilized sediment phosphorus by macrophytes and epiphytic algae probably takes place in the l i t t o r a l zone of Skaha Lake (Stockner et al. 1972a), thereby preventing a percentage of solubilized phosphorus from organic decomposition from entering the water mass. However, movement of phosphorus from epiphytic and macrophytic 76 vegetation to the water also occurs, and this process would tend to diminish the amount of net uptake by the vegetation (Hayes and Phillips 1958, Confer 1969). For modelling purposes i t w i l l be considered that net movement of phosphorus from sediments to water through biological uptake is not s i g n i f i -cant in the overall phosphorus budget of the lake. (4) Anaerobic Chemical Regeneration. Mortimer (1941, 1942) re-ported that when iron changes from the f e r r i c form (under aerobic conditions) to the ferrous form (under anaerobic conditions), i t changes from an insoluble to a soluble state. This means that phosphorus previously precipitated as i n -soluble f e r r i c phosphate under aerobic conditions at the sediment-water inter-face, becomes soluble when the oxygen is depleted in the hypolimnion. The re-sult of the change to anerobic conditions can be a massive increase in soluble phosphate in the hypolimnion of a lake (e.g. Lake Erie, Burns and Ross 1972). Although much of this soluble phosphate may reprecipitate when autumn mixing reoxygenates the hypolimnion, i t may be only a portion of the phosphorus lost from the sediments during the anaerobic period. Burns and Ross (1972) report that the soluble reactive phosphorus decreased by approximately 10 per cent during the overturn, whereas the decrease would have been approximately 53 per cent i f a l l the anaerobic soluble reactive phosphorus had converted to the particulate form. These results indicate that a significant part of the so l -uble phosphorus (both organic and inorganic) regenerated under anaerobic con-ditions ultimately re-enters the biological cycle of Lake Erie. Although anaerobic hypolimnetic conditions have not yet occurred in Skaha Lake, the Lake Erie study indicates that a change to anaerobic conditions could result in a phosphorus release of more than four times the amount released under aerobic conditions. 77 (5) Decomposition Regeneration. The importance of bacteria in returning soluble nutrients to the water in lakes is stressed by McCoy and Sarles (1969): "Bacteria are the prime agents of the return of dead organic matter (plant and animal bodies) to the soluble state." This is accomplished by the mineralization of organic nitrogen as NH* or NO^ , -3 and organic phosphorus as PO^ . McCoy and Sarles point out that a well-balanced mixture of bacteria is present in temperate lakes to carry out degra-dation of chitin, cellulose, pectins, proteins and other complex organic com-pounds. Measurement of the flux between sediment mud (including bacteria) and soluble phosphate is reported by Hayes and Ph i l l i p s (1958) to be about three days in both directions. With no bacteria present the exchange between sediment and water was slowed to 15 days. Although phosphorus can be regenerated from phytoplankton cells by autolysis in addition to bacterial decomposition, the relative importance of the processes has not been adequately evaluated (Hooper 1973). Therefore, the assumption is made that most of the regeneration occurs through bacterial decomposition. The assumption is made that bacterial growth is proportional to algal growth, and that bacterial growth is limited by the same factors of temperature and nutrients that l i m i t primary production; therefore i t w i l l be assumed that as algal populations increase during the growing season, bacterial populations w i l l increase proportionally and w i l l have the capability, under optimum temperature conditions, of decomposing much of the organic matter pro-duced by primary production. Evidence for this assumption comes from the work 78 bf Thomas (1969) showing that in the Swiss Ziirichsee the same growth factors that stimulate most freshwater algae also stimulate bacteria associated with them. Thomas shows that increases in bacterial density are directly propor-tional to the phosphate content of the water at 20°C. As w i l l be shown in the submodel on primary production, similar relationships are true for algal production and phosphorus. On the sediment surface of an aerobic lake with an abundant supply of dead organic matter ( a reasonable assumption in a eutrophic lake such as Skaha), temperature w i l l probably be the most important factor controlling the decomposition process. McCoy and Sarles state that in a northern temp-erate climate a low rate of bacterial activity i s maintained by relatively cold water temperatures for about two-thirds of the year; during the summer months, however, there i s a "flush" of bacterial activity which noticeably increases the bacterial decomposition of organically held phosphorus. The relationship between temperature and bacterial decomposition processes i s reported for the bacterial community in the sediments of eutro-phic Lake Wingra, Wisconsin (Boylen and Brock 1973). The results show that the heterotrophic bacteria i n Lake Wingra sediments do not adapt to the low temper-atures (1.0 - 1.5°C) which prevail in winter. Using the rate of glucose uptake and CO2 evolution as a measure of the difference i n decomposition rate, Boylen and Brock (1973) show that at the optimum temperature (25° C) under aero-bic conditions, decomposition rates were four-fold to 14-fold higher than at the low temperature. The authors conclude that a consequence of this i s that bacterial decomposition processes should occur at a much slower rate during winter than during summer (and in the colder sediments of the hypolimnion), 79 and plant material that had not decomposed before cold weather set in w i l l decompose at least four times more slowly than in warm sediments. The results of Boylen and Brock indicate a nearly linear relation-ship between decomposition rates at 5°C and 25°C, and typical curves i n d i -cate that decomposition occurs approximately four times faster at the higher temperature than at the lower. The linearity of the relationship makes possible the mathematical formulation of a coefficient of decomposition, k .^ If we assume that k^ = 1 at 25°C, we can relate k^ to temperature by: k, = .04T where T i s sediment temperature , d in o C Now i t i s possible to say that in the summer when the epilimnion water and l i t t o r a l sediments have a temperature of 20 - 25°C, organic matter w i l l de-compose four times faster than in the hypolimnetic sediments where the temp-erature i s 4 - 6°C. The fact that the average concentration of organic phos-phorus i n the deep sediments of Skaha Lake i s 3.2 times the average concen-tration in the l i t t o r a l sediments supports this assumption (Williams 1973). (b) Formulation of Internal Loading Submodel. The assumption i s made that in a eutrophic lake such as Skaha Lake, regeneration of phosphorus from the sediments i s best reflected in a submodel describing the decomposition of organic matter. Since decomposition i s a function of sediment temperature, and since the l i t t o r a l zone in summer has a much higher temperature than the deep water sediments, separate submodels are developed for the two zones. (1) L i t t o r a l Zone Regeneration. The assumption i s made that at summer temperatures in the l i t t o r a l (20 - 25°C) bacterial decomposition of sedimented phosphorus i s returned either to l i t t o r a l vegetation or the water 80 mass. This assumption i s supported by an intensive f i e l d survey of the l i t t o r a l sediments which showed the s u r f i c i a l sediments to be v i r t u a l l y de-void of organic matter i n the summer (J. G. Stockner, personal communica-tion). The conclusion drawn' from this evidence i s that the organic phos-phorus which accumulates in the l i t t o r a l sediments does so during the winter when decomposition rates are much lower. With the information that the l i t t o r a l area of Skaha Lake occupies 17 per cent of the total area of the lake, the following submodel i s proposed: PRL = °' 1 7 PSE kd where P D T is the regeneration of phosphorus from the l i t t o r a l (kg/day); P RL SE i s the sedimentation of phosphorus from the epilimnion (kg/day), and k^ i s the coefficient of decomposition which i s temperature dependant. (2) Deep Water Sediment Regeneration. Regeneration of phos-phorus from deep water sediments occurs at a slower rate than from the warmer l i t t o r a l sediments. The lower temperature results in a lower c o e f f i -cient of decomposition. The following expression describes regeneration from deep water sediments: P = k P RH d SHorg where P i s the regeneration of phosphorus from hypolimnetic sediments (kg/day); k, i s the coefficient of decomposition, and P„„ i s the amount of organic d r SHorg & phosphorus sedimenting to the bottom of the hypolimnion (kg/day; according to the sedimentation submodel, equal to 0.83 P O T :,k_ u). 81 4. Primary Production Submodel The primary production submodel is formulated for the prediction of the biomass of phytoplankton in the trophogenic layer, or the upper 8 m of the lake. In addition to being of great interest in the study of the eutrophication problem, the prediction of phytoplankton i s a necessary v a r i -able i n the sedimentation submodel. Marked seasonal variation i n population density i s a characteris-t i c feature of phytoplankton in northern temperate lakes (Odum 1971). Odum gives the following description of a typical phytoplankton growth season, and the relationship with temperature, light and nutrients: "Very high densities which appear quickly and persist for a short time are called "blooms" or phyto-plankton "pulses." In the northern United States ponds and lakes often exhibit a large early spring bloom and another, usually smaller, pulse in the autumn. The spring pulse, which limnologists sometimes c a l l the "spring flower-ing", typically involves the diatoms and is apparently the result of the following combination of circumstances. During the winter, low water temperatures and reduced light result i n a low rate of photosynthesis so that regenerated nutrients accumulate unused. With the advent of favorable temperature and light conditions the phytoplankton organ-isms, which have a high biotic potential, increase rapidly since nutrients are not limiting for the moment (i. e . , the spring bloom). Soon, however, nutrients are exhausted and the bloom disappears. When nutrients again begin to accumu-late, nitrogen-fixing blue-green algae, such as Anabaena, often are responsible for autumn blooms, these organisms being able to continue to increase rapidly despite a reduc-tion of dissolved nitrogen — that i s , u n t i l phosphorus, low temperature, or some other factor becomes limiting and halts the population growth." As the combination of temperature, light and nutrient supply changes seasonally, phytoplankton populations change qualitatively as well as quanti-tatively. Pearsall (cited in Hutchinson 1967) attributes the spring maxima of diatoms in English lakes to a temporarily high concentration of Si which 82 comes with the spring freshet. He concludes that individual species have different nutrient requirements, and succeed each other as the waxing popu-lation reduces the available supply. The interactions of changing light and temperature conditions along with changes in nutrient supply result in a very complex situation. Dinobryon divergens often replaces diatoms at the end of the spring bloom when Ca and Si levels drop and the N:P ratio rises. In Douglas Lake, Michigan, A s t e r i o n e l l a bloomed during the autumn overturn because of phosphorus-rich hypolimnetic waters (anaerobic in summer) mixing with epilimnetic waters (Tucker 1957, cited in Hutchinson 1967). (a) Other Phytoplankton Models. An early model by Fleming, formu-lated in 1939, i s described by Patten (1968). Fleming emphasized grazing losses in the following equation to describe the spring diatom bloom in the English Channel: ^ | = P [a - (b+ct)] where P i s phytoplankton concentration; a i s a constant growth rate; and (b+ct) i s a death rate resulting from zooplankton grazing. The work of Riley and his co-workers (1946, 1949, 1963, 1965) in modelling plankton populations in the ocean represents the f i r s t r e a l i s t i c attempt to deal quantitatively with the problem. According to Patten (1968), Riley, Stommel and Bumpus (1949) produced the f i r s t systems model, a set of simultaneous d i f f e r e n t i a l equations containing negative feedback loops. In simplified form, Riley's formulation i s : HP ~ = (PH - R - G - S + T)P dT where P i s the rate of change in phytoplankton density; PH i s the rate of 83 photosynthesis (growth); R i s the rate of respiration; G i s the grazing rate (loss to zooplankton); S i s the sinking rate of dead c e l l s ; and T is the rate of upward movement due to turbulent eddies. Riley's contribution i s to relate the growth rate, respiration rate and grazing rate to basic en-vironmental variables — temperature, radiation, the extinction coefficient of light in water, and nutrient concentration. This results in time-variable coefficients, as the environmental components change throughout the year. Respiration i s determined by temperature, and photosynthesis i s limited by temperature, light and phosphate concentration. In general, Riley found that observed values for phytoplankton density were within 25 per cent of the calculated values during one annual cycle in the waters at Georges Bank off the coast of New England. Steele (1956, 1964) proposed similar models to predict plankton production in the Gulf of Mexico and Fladen Ground. He reports that a steady state assumption does not exist for shallow and deep layers i n the ocean, and considers each of the two layers to have differing inputs and outputs. Steele uses a different expression than Riley to describe light penetration and introduces a v e r t i c a l eddy diffusion term, but rel i e s on the same type of mass balance formulation. More recent models consider three major interdependent systems: nutrients, phytoplankton and zooplankton (Chen 1970, Di Toro et al. 1971). External environmental parameters considered are temperature, radiation and advective flow. Parker (1972) adds f i s h as a fourth major component to his model of Kootenay Lake, but uses the same mass balance approach as Chen and Di Toro. 84 (b) Basic Phytoplankton Equation. A diffe r e n c e equation i s pro-posed to describe phytoplankton dynamics on a d a i l y b a s i s . Many published rate c o e f f i c i e n t s for plankton growth are d a i l y rates, making the choice of a d a i l y time scale p a r t i c u l a r l y u s e f u l . The following generalized ex-pression describes the biomass of phytoplankton i n the trophogenic zone: B = B T + (G - R — Z — S — 0 )B I p p p p p I vesultinq i n i t i a l ,, . , . . . , . , ~, biomass = biomass a v o w t } l ~ r>esp%vat%on - grastng - stnHng - outflow where B i s biomass of phytoplankton (kg); B^ i s the i n i t i a l biomass of phytoplankton at the beginning of the time period (kg); G^ i s the d a i l y growth rate of phytoplankton, dependent on temperature, nutrients and r a d i -a t i o n (day ^ ) ; R^  i s endogenous r e s p i r a t i o n rate which r e s u l t s i n a loss of organic carbon i n the phytoplankton population (day ^ ) ; Z^  i s the grazing rate of zooplankton (day "*"); i s the rate of s i n k i n g as c e l l s sediment out of the trophogenic layer(day ^ ) ; and 0^  i s the rate of advective loss from the outlet of the lake (day ^ ) . Each of these terms i s discussed i n d e t a i l . (c) Phytoplankton Growth. A basic problem i n modelling phyto-plankton dynamics i s the fact that d i f f e r e n t species react d i f f e r e n t l y to the three most important environmental v a r i a b l e s : temperature, n u t r i e n t s , and l i g h t . As Di Toro et al. (1971) point out: "The a v a i l a b l e information i s not s u f f i c i e n t l y d e t a i l e d to spec i f y the growth k i n e t i c s f or i n d i v i d u a l phytoplankton species i n n a t u r a l environments." Therefore, the pragmatic approach of Di Toro et al. i s adopted, which i s to 85 ignore the problem of differing species requirements for temperature, nut-rients, and li g h t . The basic unit of kg of dry weight of phytoplankton in the trophogenic zone (computed from concentrations in mg/1) i s used for the entire population, and average coefficients for growth and loss are taken from the literature. (1) Temperature Dependency. If nutrients and light are not limiting, the temperature of the water i s the significant parameter limiting the growth rate of phytoplankton (Di Toro et al. 1971). Di Toro et al. have reviewed 22 experiments i n the literature which examine maximum growth rates as a function of temperature, and conclude that a straight-line f i t i s a reasonable approximation of the data relating the maximum growth rate K^day to temperature T(°C)(Figure 7): K T = k l T where k^ has values in the range 0.10±0.025/day • °C. The coefficient k^ indicates an approximate doubling of the saturated growth rate for a temperature change from 10 to 20°C, which i s consistent with the generally accepted temperature-dependence of biological growth rates (Di Toro et al. 1971). The upper water temperature range in Skaha Lake (near freezing to 25°C) f i t s in this range well enough for modelling purposes. (2) Light Dependency. The relationship between light and photosynthesis i n water is well known: photosynthesis i s limited by light at low intensity (e.g. during the winter), whereas the optimum i n -tensity photosynthetic production i s limited by other factors (e.g. temper-ature and nutrients) (Vollenweider 1965). Vollenweider (1965) has reviewed 86 o •o Temperature ° C Figure 7. Growth rate of phytoplankton as a function of temperature ( a f t e r Di Toro et a l . 1971). 87 s e v e r a l s i m i l a r models f o r c a l c u l a t i n g photosynthesis i n the trophogenic layer on the basis of primary production and l i g h t measurements (Steemann Nielson 1952, T a i l i n g 1957, Ryther and Yentsch 1957, Vollenweider 1958, 1960). These 2 models c a l c u l a t e the rate of primary production (g carbon/m ) with the 3 following information: production rate at l i g h t optimum (g carbon/m • day) obtained from in situ experiments); a function of the photosynthetically active incident l i g h t (dimensionless); and the attenuation c o e f f i c i e n t of l i g h t f l u x i n water (m "*") . Steele (1964, 1965) uses a somewhat more e m p i r i c a l formulation to describe the r e l a t i o n s h i p between l i g h t and photosynthesis, which seems appropriate f o r t h i s model because i t requires l e s s data and accounts for growth i n h i b i t i o n at high l i g h t i n t e n s i t y (Figure 8): I I K L = — exp(l - — ) m m where i s the r e l a t i v e rate of photosynthesis when nutrients are not l i m i t -ing (a c o e f f i c i e n t between 0 and 1, day ; I i s the average l i g h t i n t e n s i t y a. i n the trophogenic layer(explained i n the following s e c t i o n , langleys/day); and I i s the l i g h t i n t e n s i t y at which phytoplankton growth i s maximum (langleys/day). Steele assumes that I i s approximately 0.5 I i n winter in a and 0.3 I i n summer, while Ryther (1956) considers h a l f of t o t a l i n c i d e n t a. s o l a r r a d i a t i o n to be photosynthetically active (making I = 0.5 I ). Di m a Toro et al. (1971) use a figure of 300 langleys/day for I m . 88 tn in d> si — 100 200 300 400 500 600 700 800 Light Intensity ( ly/day) Figure 8. Relative photosynthesis rate (percent of maximum) as a function of light intensity (langleys/day). Theoretical curve from equation by Steele (1956) and data points from Manning and Juday (the response of a variety of phytoplankton populations; cited in Edmonson 1956). 89 The preceding equation includes the symbol I , which represents the average light intensity in the trophogenic layer. The well-known Beer-Lambert relation describes the decrease of light intensity with depth in water: 1 = 1 exp(-k z) z o v e where I is the light intensity (langleys/day) at depth z(m); I is the i n -z o cident incoming radiation (langleys/day); k& is the extinction coefficient (m \ explained below); and z is the depth (m). This relation has been in-tegrated for the photosynthetic layerby Riley (1946) to produce an expression describing the average photosynthetic light intensity in the trophogenic layer: I I =c-2"(l " exp(- k z)) a kgz r v e where I is the average light intensity in the trophogenic layer (langleys/ a. day) and z is the depth of the trophogenic layer (8 m in this case). This expression i s also used by Parsons and Takahashi (1973) in comparing growth rates of two phytoplankton species of differing c e l l aize. The extinction coefficient, k g, i s a function of two major fac-tors: (1) dissolved coloured material and particulate inorganic matter, and (2) phytoplankton c e l l s , both of which reduce light intensity, thereby i n -hibiting photosynthesis (Chen 1971, Di Toro et al. 1971). If the phytoplank-ton concentration i s large, the extinction coefficient is mainly a function of this concentration, and the phytoplankton shade themselves from further growth (Di Toro et al. 1971). 90 The follov;ing expression describes the extinction coefficient as a function of these two causes (Chen 1970, Di Toro et al. 1971): k = k + k e ew ep where k i s the result of extinction from coloured dissolved and particu-ew late inorganic matter (m "*") and k i s a result of phytoplankton shading (m /^mg/1 phytoplankton). While i t is d i f f i c u l t to completely separate the two factors, a measurement of light absorption during the winter (not under ice cover) when production i s minimal i s a good indication of k ew Edmondson (1956) describes a method for converting Secchi-disk measurements to extinction coefficients: ew D where C i s an empirically determined dimensionless constant of 1.7 and D is the Secchi-disc transparency (m). The maximum Secchi-disc transparency in Skaha Lake in 1971 was 7 m, which indicates an extinction coefficient of 1.7/7 = 0.24/m. The relationship between algal c e l l density and light absorption i s reported by Azad and Borchardt (1969). These results are interpreted by Chen (1970) and Di Toro et al. (1971) in the following formulation of k : k = 0.17 B ep c where B^ is the concentration of phytoplankton in mg/1. The extinction co-eff i c i e n t , k e, therefore has been given the following form: k = 0.24 + 0.17 B e c 91 The biomass of phytoplankton in the trophogenic layer(B, kg) is 3 converted to concentration (B^, kg/km ) through division by the volume of 3 3 the trophogenic layer(km ). (Concentration in kg/km is converted to con-* , -6 centration in mg/1 through multiplication by the conversion factor 10 ). The trophogenic layer of Skaha Lake i s calculated to have a depth of 8 m, 2 based on an estimate of the l i t t o r a l area of the north basin of 2.9 km (Stockner et al. 1972b). The hypsometric curve of the north basin (Figure 3) indicates that the upper 8 m of water has a volume of approximately 0.124 km3. (3) Nutrient Dependency. The relationship between phyto-plankton growth and nutrient concentration i s most often expressed by a Michaelis-Menton (or Monod growth kinetics) expression (Ketchum 1939, Ketchum 1967, Dugdale 1967, Eppley et al. 1969, Chen 1970, Di Toro et al. 1971, Kramer et al. 1972, Parsons and Takahashi 1973). The Michaelis-Menton expression takes the following form: - K ( [ N ] ^ . y " S \ + [N] ) where y i s the average daily growth rate (day ^ ) ; K^ , i s the maximum daily growth rate (dependent on temperature and defined i n a previous section, day ^ ) ; [N] i s the concentration of the limiting nutrient i n the trophogenic layer (mg/1); and K^ is the Michaelis-Menton, or half-saturation constant for phyto-plankton growth with the limiting nutrient (Figure 9). The half-saturation constant is defined as the nutrient concentration at which growth is half of the maximum growth rate. 92 - 2 . 0 0 1 2 3 4 5 Phosphate concentration,y.q/litre Figure 9. Growth rate of a phytoplankton population as a function of phosphorus concentration when phosphorus is the limiting nutrient (Fuhs e_t a l . 1972). Growth rates are shown at varying p^ values with a half-saturation con-stant of approximately 1 ug/1 phosphate. 93 According to Di Toro et al. (1971), "There exists an increasing body of experi-mental evidence to support the use of this func-tional form IMichaelis and Menton] for the dependence of the growth rate on the concentration of either phosphate, nitrate, or ammonia i f only one of these nutrients i s i n short supply." It w i l l be assumed that phosphorus is the nutrient i n short supply in Skaha Lake, and that approximately half of the supply of total phosphorus in the trophogenic layer is "biologically active," and therefore potentially available for growth (Gachter 1971 makes a similar assumption for several Swiss lakes). According to J. G. Stockner (personal communication), the assumption that phosphorus is the limiting nutrient for most of the season in Skaha Lake is a reasonable one. Although bioassay results (Stockner et al. 1972c) show nitrogen to be more limiting than phosphorus during two per-iods of 1971, phosphorus probably became limiting later in the summer during a bloom of blue-green algae {Gleotrichia'). It i s unlikely that blue-green algae, of which many species possess the capability to fix nitrogen directly from the molecular form in the trophogenic layer, would be limited by nitro-gen. High rates of nitrogen fixation have been correlated with high produc-tion rates of blue-green algae, primarily Anabaena, G l e o t r i c h i a , and Aphanizo-menon (Brezonik 1972). Phosphorus, there fore, is generally regarded to be the most important limiting nutrient to the growth of blue-green algae. F i t z -gerald (1972) notes that: ". . . i f bioassays are carried out with mixtures of nitrogen-fixing and nonnitrogen-fixing phytoplankton, i t might be d i f f i c u l t to interpret the results, since the nitrogen-fixing species could be phosphorus limited and the nonfixing algae could be nitrogen limited but have surplus phosphorus. . . 94 tests with in situ algae must be frequent enough so that trends can be followed and careful scrutiny given to the species composition of samples tested at different times." The Michaelis-Menton coefficient for phytoplankton growth with phosphorus as the limiting nutrient i s known to vary for different algal species. Di Toro et al. (19 71) have interpreted the results of six investigations, and report a variation between 0.006 and 0.025 mg/1 phosphorus. Fuhs et al. (1972) report lower values near 0.001 mg/1 for two species of diatoms. (4) Final Growth Rate Expression. The growth rate of phyto-plankton i s assumed to depend on temperature, light, and nutrients, and the preceeding formulations separately describe the effects of these three limiting factors. Each of the three formulations can be considered a "reduction factor" since each one reduces the theoretical maximum growth rate. Therefore, i t is rational to multiply the three formulations to-gether to arrive at a f i n a l growth rate expression. The same rationale is followed by Ketchum (1939) in dealing with two nutrients, and by Riley (1965), Chen (1970) and Di Toro et al, (1971) in dealing with temperature, light and nutrients. Following this procedure, the growth rate expression becomes: I I [P] G P x j — exp(l - ~ ) x maximum t h e o r e t i c a l growth rate depend-ent on temperature m m reduction factor for light reduction factor for phosphorus 95 where [P] is the concentration of "biologically active" phosphorus (mg/1). Other terms have been defined previously. (d) Phytoplankton Losses. The loss of phytoplankton cells from the trophogenic layer can be attributed to four major mechanisms: respira-tion, grazing by zooplankton, sinking of dead c e l l s , and advection from the outflow of the lake (Chen 1970, Di Toro et al. 1971). (1) Respiration Losses. Endogenous metabolism of algae re-sults in degradation of algal protoplasm to supply energy for survival (McKinney 1962). The chemistry of endogenous metablism i s the same as the familiar one for respiration: c c 7 Ho <A> Q N + 6.25 0 o 5.7 C0 o + NH. + 3.4 H„0 McKinney notes that the demand for oxygen in the absence of sunlight for photosynthesis can be as great as the photosynthetic production of oxygen. Using data from Riley et al. (1949), Di Toro et al. (1971) have established the following relationship for algal respiration as a function temperature: 0 5 10 15 20 25 Temperature °C Figure 10. Algal respiration rate as a function of temperature (data from Riley, cited in Di Toro et a l . 1971). 96 Di Toro et al. conclude that a straight line adequately f i t s these data, which can be formulated as: R = K_T P 2 where R^  i s the endogenous respiration rate (day "*"), i s a constant which is approximately 0.005 ± 0.001, and T is °C. (2) Grazing by Zooplankton. Loss of phytoplankton by graz-ing can be the most significant factor reducing phytoplankton biomass. An in s i t u method of measuring the grazing rate of the zooplankton community (excluding animals less than 70 u) in a eutrophic lake is reported by Haney (1970; cited in Rigler 1973). Results show that organisms such as bacteria (.Pseudomonas), yeast (Rhodotorula), and small algae (Chlamydomonas) were eaten by zooplankton at approximately equal average rates of 0.033/hour i n the trophogenic layer during summer s t r a t i f i c a t i o n (Rigler 1973). This rate corresponds to 0.79/day (the fraction of small algae eaten each day) i f zooplankton are 100 per cent efficient at assimilating their food. Based on studies of the assimilation efficiency of zooplankton (Marshall and Orr 1953, Corner et al. 1967, and Conover 1964, 1966; cited in Rigler 1973), Rigler (1973) assumes that a reasonable estimate of e f f i -ciency i s approximately 60 per cent. The assimilation efficiency is probably lower i f blue-green algae make up a significant part of the total algal pop-ulation. The resistance of blue-green algae to grazing i s one reason for large blue-green blooms (Odum 1971). It is suggested that the assimilation efficiency i s half (30 per cent) when blue-green algae dominate the popula-tion. The following expression describes the loss of algae by grazing: Z p = ( K G ) ( K A ) where Z p is the rate of grazing loss by zooplankton (day K is the grazing rate with 100 per cent efficiency (0.79 day "*"), and K is the coefficient of assimilation efficiency (0.3 to 0.6). (3) Sinking of Phytoplankton Cells. Sinking rates of dead cells vary according to the size, shape, and chemical composition of the cel l s , and are therefore a function of the characteristics of the algal spe-cies. For example, some species of blue-green algae contain gas vacuoles which slow their sinking rates (Morris 1967, Bella 1970), and some diatom species sink faster than others because of a higher proportion of s i l i c a (Lund 1959). Estimates of sinking rates of marine phytoplankton include 3 m/day (Steele 1958), 3 to 6 m/day (Riley 1965),0.5 to 2.0 m/day (Smayda 1970), and 0.29 to 0.73 m/day (Walsh and Dugdale 1971). Bella (1970) re-ports an average sinking rate of 0.75 to 1.0 m/day for a l l freshwater a l -gae excpet blue-greens, which he assumes sink very slowly. Lund (1959) reports the sinking rates of freshwater diatoms to vary between 0.19 m/day for A s t e r i o n e l l a species to 0.91 m/day for Melosira species. From these data i t appears that a reasonable estimate of the sinking rate i s between 0.5 and 1.0 m/day. Using this estimate, the daily loss of algae from the tropho-genic layerby sinking would be six to 12 per cent (e.g. 0.5 m/day * 8 m = 0.06/day). An expression describing the rate of sinking losses i s : S = V IT p s' t 98 where S is the rate of sinking losses (day ), V is the velocity of phy-p s toplankton sinking (m/day), and T i s the thickness of the trophogenic layer(m) . (4) Advection Losses. Because of the relative non-motility of phytoplankton, some loss w i l l occur through hydrologic flow at the out-let of the lake (Uhlmann 1972). The following expression describes this rate of loss: Where Op is the rate of outflow loss of phytoplankton (day ), Q is the 3 daily discharge from the outlet of the lake (m /day), and V is the volume 3 of the Crophogenic layer(m ). 5. Hypolimnetic Dissolved Oxygen Submodel Although i t i s not necessary to predict dissolved oxygen in the hypolimnion in order to model phosphorus and phytoplankton, this infor-mation serves as a useful check on other parts of the model. The oxygen status of hypolimnetic water has great importance i n regulating the phosphorus retention capacity of the sediments (see regeneration submodel). Therefore, i t i s of value to be able to predict the approximate number of years before the hypolimnion becomes anaerobic ( i f present phosphorus loading rates conr tinue). Through other submodels, enough information is available to formu-late a simplified oxygen depletion model for the hypolimnion. This submodel describes oxygen conditions during the s t r a t i f i e d period of the year, and the assumption i s made that the entire lake is saturated with dissolved oxygen during mixing periods. Since the "modelling 99 year" begins at spring mixing, the hypolimnion w i l l be saturated with dissolved oxygen for the i n i t i a l conditions. Except for a minor amount of eddy diffusion of oxygen from the epilimnion (ignored in this submodel), the beginning of str a t i f i c a t i o n isolates the hypolimnion from receiving additional dissolved oxygen u n t i l the autumn mixing period. The hypolim-nion w i l l gradually undergo oxygen depletion during summer s t r a t i f i c a t i o n , and the assumption i s made that the rate of depletion i s a direct function of the amount of organic matter sedimenting into the region below the thermo-cline. The conclusion of Burns and Ross (1972) that approximately 88 per cent of the hypolimnetic oxygen of Lake Erie was consumed i n the decay of organic matter supports this assumption. Decomposition of organic matter is assumed to proceed according to the following reaction (Fogg 1953): C 5 ?H Q g 0 2 3N + 6.25 0 2 -> 5.7 C0 2 + NK^ + 3.4 H20 Therefore, for each 5.7 moles of C decomposed (equivalent to 68.5 g-atoms C), 6.25 moles of 0 2 are used (200 g-atoms). With the information that phytoplankton are 53 per cent by dry weight carbon (on the average, Fogg 1953), i t i s concluded that for each 129 g-atoms of phytoplankton de-composed, 200 g-atoms of oxygen are used. Converting to a simpler ratio, for each gram of phytoplankton decomposed, 1.55 g of oxygen i s used. The following formulation describes the use of oxygen through decomposition in the hypolimnion: 100 DO dc (.4 B S .83) C F (1.55) phytoplankton sinking from epilimnion c o e f f i c i e n t of oxygen use c o e f f i c i e n t of decomposition where D0^c i s the dissolved oxygen used i n decomposition (mg/1 • day); .4 i s the proportion of phytoplankton not recycled within the epilimnion, and therefore reaching the hypolimnion and l i t t o r a l sediments; B^ is the con-centration of phytoplankton biomass in the epilimnion (mg/1); S p is the rate of sinking of phytoplankton c e l l s (day * ) ; .83 i s the proportion of lake area involved i n hypolimnetic sedimentation; 1.55 is the stoichiometric coefficient of oxygen use per mg of phytoplankton decomposed; k^ is the temperature-dependent coefficient of decomposition (defined i n the regener-ation submodel); and is the temperature of the hypolimnion (°C). CHAPTER V RESULTS A. VERIFICATION OF THE MODEL FOR SKAHA LAKE* Three trophic indicators are considered the most important for verification of the model: (1) the total phosphorus concentration in the upper mixed layer of the lake (the whole lake during mixing); (2) the phytoplankton concentration in the trophogenic layer; and (3) the minimum dissolved oxygen concentration in the hypolimnion. Collec-tion and analysis of these limnological data are discussed in Appendix B. During the year of simulation (March 1969 to March 1970), the total input phosphorus from a l l known sources was 24,500 kg (see Table A-3) of Appendix A for percentages of different sources). Variations of input and output of phosphorus to and from Skaha Lake during the simulation year are shown i n Figure 11. The i n i t i a l phosphorus concen-tration in March 1969 was 27 yg/1 (conditions of complete mixing; Stein and Coulthard 1971). 1. Total Phosphorus Concentration (a) Upper Mixed Layer. In the process of mathematically simulating a natural system, the modeller generally learns something about the validity of his basic assumptions. While the i n i t i a l simulation of the phosphorus concentration in the upper mixed layer (Figure 12) indicates a reasonable The following results pertain to the north basin, except where the south basin i s specifically discussed. 101 102 500 120 180 240 T I M E ( D A Y S ) 300 360 Figure 11. Loading rate of phosphorus to Skaha Lake, 1969-70 (upper curve) and phosphorus outflow rate (lower curve). 103 0 60 120 180 240 300 360 T I M E ( D A Y S ) Figure 12. Phosporus concentration i n surface water of Skaha Lake, 1969-70, with no modification of o r i g i n a l assumptions ( c i r c l e s i n d i c a t e observed values and s o l i d l i n e simulated va l u e s ) . 104 f i t to the shape of the real data, there are two significant discrepancies. The f i r s t i s that minimum simulated concentrations in midsummer are consis-tently too high, and the second i s that the f i n a l simulated concentration is too low. The f i r s t discrepancy could be caused by: (1) the sedimenta-tion rate of phosphorus loss from the epilimnion is underestimated; or (2) the rate of eddy diffusion of phosphorus from the hypolimnion to the epilimnion is overestimated. To evaluate the f i r s t , the coefficient of eddy diffusion was reduced by 20 per cent (a maximum reasonable margin of error), but no appreciable difference was observed in the simulated phosphorus concen-tration. However, when the sedimentation of phosphorus from the epilim-nion was doubled (Figure 13), the f i t was considerably improved for the midsummer minimum values. Doubling the phosphorus sedimentation i s a reasonable change in the original assumption for the following reasons. The sedimentation submodel i s directly dependent on the biomass of phyto-plankton in the trophogenic layer (Chapter IV). As stated in Chapter IV, this i s a conservative estimate of sedimentation loss because other organ-isms (bacteria, zooplankton, fish) also sediment to the bottom and decrease the amount of phosphorus in the upper layer. Therefore, losses occurring from the sedimentation of other organisms would tend to increase losses from the epilimnion. In addition, losses may occur by mechanisms not modelled, such as the chemical precipitation of inorganic phosphorus minerals like apatite (Golterman 1973). (Rates of phosphorus loss by sedimentation from the epilimnion are shown in Figure 14. The lower curve represents regener-ation from l i t t o r a l sediments by bacterial decomposition). 105 100 Q_ CO o zn CL. 0 60 120 180 240 300 360 TIME(DAYS] Figure 13. Phosphorus concentration in surface water of Skaha Lake, 1969-70, with the sedimentation rate from the epilimnion doubled (circles indicate observed values and sol i d line simulated values). 106 500 o 200 | 150 1 P 100 t Q_ 120 180 240 TIME(DRYS) 360 Figure 14. Simulated sedimentation rate of phosphorus from the epilimnion of Skaha Lake, 1969-70 (upper curve) and regeneration rate from l i t t o r a l sediments (lower curve). 107 The second discrepancy apparent i n the simulated results of Figure 13 shows the lake losing phosphorus between the mixing period of March 1969 (day 1) and the same period in March of 1970 (day 360). The simulated curve shows the lake with a f i n a l concentration of 26 yg/1, whereas analytical data showed that the lake actually increased in con-centration to 33 yg/1. A plausible explanation for this discrepancy i s that the estimated regeneration rate of sedimented phosphorus from the sediments to the hypolimnion i s too low. By increasing the regeneration rate three times, a f i n a l concentration of 31 yg/1 was simulated, while an increase of four times resulted in a f i n a l concentration of 35 yg/1. A correct simulated concentration of 33 yg/1 was achieved by increasing the regeneration rate 3.5 times (Figure 15). Apparently, bacterial decom-position rates are greater than expected, or there are other factors acting to increase the rate of phosphorus regeneration from the sediments. Several possible mechanisms, such as diffusion, turbulent mixing, and chemical re-generation are discussed in Chapter IV. Estimated sedimentation losses from the hypolimnion and regener-ation are shown i n Figure 16 (estimates according to revised assumptions). The sedimentation losses are divided into organic and inorganic components in Figure 17. Organic sedimentation is a dynamic function of phytoplank-ton production, while inorganic sedimentation by adsorption i s shown as a relatively constant process. (b) Hypolimnion Phosphorus. During 1969-70 phosphorus determinations were made to a depth of only 20 m in Skaha Lake, which has a maximum depth of 57 m. As phosphorus concentrations often tend to increase in the hypo-108 100 120 180 240 300 360 T I M E ( D R Y S ) Figure 15. Phosphorus concentration in surface water of Skaha Lake, 1969-70, with the sedimentation rate from the epilimnion doubled and the regeneration rate from deep-water sediments X 3.5 (circles indicate observed values and s o l i d line simulated values). 109 Figure 16. Simulated sedimentation rate of phosphorus from the hypolimnion of Skaha Lake, 1969-70 (upper curve) and the regeneration rate from deep-water sediments (lower curve). 110 Figure 17. Simulated sedimentation rates of organic phos-phorus (upper curve) and inorganic phosphorus (lower curve) from the hypolimnion of Skaha Lake, 1969,-70. I l l limnion of deep lakes during summer st r a t i f i c a t i o n (Golterman 1973), the measurements from Skaha are not considered sufficient for validation pur-poses. Simulated averages for the entire hypolimnion (Figure 18) i n d i -cate a maximum concentration of over 50 pg/1. 2. Phytoplankton Production Simulation of phytoplankton biomass' (Figure 19) indicates that the timing of peaks could not be precisely predicted. The simulated peak of the f i r s t bloom lagged 20 to 30 days behind the real peak, and could not be modified by manipulation of growth coefficients (within limits reported i n the literature). The low growth period around day 90 after the f i r s t bloom was not simulated accurately, and was probably due to the omission of a dynamic zooplankton grazing model. With the assumption of a constant grazing rate, losses from grazing are underestimated at high phytoplankton production. 3. Dissolved Oxygen in the Hypolimnion According to the submodel i n Chapter IV, dissolved oxygen i n the hypolimnion i s directly dependent on phytoplankton production, and the lag of 20 to 30 days between real and simulated values (Figure 20) i s a reflec-tion of the lag in the phytoplankton simulation. Agreement between real and simulated values at the end of summer stagnation (about 6 mg/1) is rela-tively close. Because oxygen use i n the hypolimnion is an indirect mea-sure of the amount of organic matter produced in the lake and sedimented to the hypolimnion, the values at the end of summer stagnation are an approximate indication of the sum of organic productivity during the grow-ing season. 112 CD o cx o CO m o_ co o IE CL 100 90 I 80 70 • 60 •• y 501 40 -30 •• g 20} 10 0 0 — — I 1 1 1 1 1 h—i 1 1 1 1— 60 120 180 240 TIME(DAYS) H 1 1 1 ( -300 360 Figure 18. Simulated phosphorus concentration in the hypolimnion of Skaha Lake, 1969-70. 113 Figure 19. Phytoplankton biomass in the trophogenic layer of Skaha Lake, 1969-70 (dashed line indicates observed values and so l i d line simulated values). 114 Figure 20. Dissolved oxygen concentration i n the hypo-limnion of Skaha Lake, 1969-70 ( c i r c l e s i n d i c a t e observed values and s o l i d l i n e simulated values). 115 4. Simulation of the South Basin of Skaha Lake The model i s programmed so that the outflow of phosph6rus from the north basin is equal to the inflow to the south basin. The smaller 3 south basin with a volume of 0.041 km and a mean depth of 15 m (the same 3 figures for the north basin are 0.517 km and 28 m), has greater eutrophic potential than the north basin. In addition, prevailing north winds in summer bring floating algal matter from the north basin to the south. Verification of simulated values for the south basin was simi-lar to verification for the north basin (no figures are presented). More eutrophic conditions in the south basin are evidenced by more measured phosphorus at the end of the year (37 yg/1 compared to 33 yg/1 for the north basin), a higher phytoplankton peak (5.5 mg/1 compared to 4.6 mg/1 for the north basin), and less hypolimnetic dissolved oxygen at the end of stagnation (5.4 mg/1 compared to 6.6 mg/1 for the north basin). 5. Verification for 1970-71 and 1972-73 During the next year (March 1970 to March 1971), quite different hydrologic conditions occurred. While 1969-70 was nearly an average hydro-logic year (11 per cent higher than the average discharge from Skaha Lake; Table A-4 in Appendix A), 1970-71 was an exceptionally dry year, with only 47 per cent of the average discharge (48 years of record). With this hydro-logic flow and a phosphorus loading of 25,000 kg (a two per cent increase over the previous year), the model predicts a substantial phosphorus i n -crease: from 33 yg/1 in March 1970 to 53 yg/1 in March 1971. This predic-tion i s within 12 per cent of the measured concentration of 60 yg/1 for April 1971 (Williams 1972). No phytoplankton or dissolved oxygen data are 116 available for the summer of 1970. No data i s available for the spring and summer of 1972, making i t impossible to verify the model for 1971-72. During this period hydro-logic conditions were average (14 per cent higher than 1969-70), and phos-phorus loading was approximately the same as in the previous two years. During the period March 1972 to March 1973 significant changes occurred in both phosphorus loading and hydrologic flow. This was the f i r s t year the phosphorus removal system in the Penticton sewage treatment plant was operating effectively, resulting in 50 to 60 per cent removal of phosphorus from municipal sources (Haughton et al. 1974). This resulted in an overall loading decrease of approximately 33 per cent from the previous year. An unusually heavy snowpack resulted in the highest yearly flow on 8 3 record through Skaha Lake: 10.4 X 10 m (884,000 acre-ft), or approxi-mately twice the flow of 1969-70 (an average year). With these new loading and hydrologic conditions, the model predicts a total phosphorus concentration of 16 yg/1 for the spring of 1973 in the north basin, a large decrease from 42 yg/1 the previous spring. Lake data for the spring of 1973 indicates a concentration of 13 yg/1 i n the north basin (B.C. Pollution Control Branch, courtesy of E. R. Haughton). The modelled value is therefore within 23 per cent of the analytical value. Based on this low spring phosphorus concentration, the model predicts s i g -nificantly lower phytoplankton growth during the summer of 1973 (peak of 2.9 mg/1), probably not in the bloom category. A. M. Thomson (personal com-munication) confirms that there were no serious algal problems in Skaha Lake during 1973. 117 B. SENSITIVITY ANALYSES Two types of sensitivity are important in this simulation. The f i r s t i s the sensitivity of the model to the major "forcing functions": phosphorus loading and hydrologic discharge. The second is the sensitivity of the model to changes in the 15 physical and biological coefficients (con-stants) used in the submodels. 1. Sensitivity of Phosphorus Loading and Hydrology Simulation results of the three trophic indicators (phosphorus, phytoplankton, and hypolimnetic dissolved oxygen) are shown i n Figure 21a. For comparison with subsequent simulations, a key value of each indicator i s chosen: (1) the concentration of total phosphorus at the end of the year; (2) the peak value of phytoplankton biomass; and (3) the minimum concentration of dissolved oxygen in the hypolimnion. For 1969-70 (Figure 21a) these values are: phosphorus 33 yg/1, phytoplankton 4.6 mg/1, and dissolved oxygen 6.6 mg/1. Simulations at varying loading and hydrologic discharge are pre-sented in Figures 21b - 21f. Figure 21b shows the indicators with the phos-phorus loading doubled (49,000 kg/year). The effect of this hypothetical loading i s to increase the phosphorus concentration to 64 yg/1 (from 33), to increase the phytoplankton peak to 6.3 mg/1 (from 4.6), and to decrease the hypolimnetic dissolved oxygen to 1.9 mg/1 (from 6.6). Simulation at half of the original loading (12,250 kg/yr) (Figure 21c) indicates quite different trophic conditions. Phosphorus concentration decreases to 19 yg/1 by the end of the year, the phytoplankton peak is 3.2 118 (a) Loading and discharge for 1969-70 Q_ tn o X Q. 60 120 180 240 300 TIME(DflYS) (b) Loading doubled 60 120 180 240 300 360 TIME(DAYS) (c) Loading halved (d) Discharge doubled 60 120 180 240 300 360 TIME(DAYS) 60 120 180 240 300 360 TIME(DAYS) (e) Discharge halved o u cn ZD ce o X Q-in o X 0--I 15 60 120 180 240 300 360 TIME(DAYS) (f) Loading halved and discharge doubled 15 60 120 180 240 300 360 TIME(DAYS) Figure 21. Simulated phosphorus (solid l i n e ) , phytoplankton (short dashes) and hypolimnetic dissolved oxygen (long dashes) with varying phosphorus loading and hydrologic discharge, Skaha Lake, 1969-70. 119 mg/1, and hypolimnetic dissolved oxygen decreases only to 9.4 mg/1. Trophic conditions similar to effects of halving the loading are simulated by doubling the hydrologic discharge (Figure 21d; the original loading of 24,500 kg i s maintained). Phosphorus concentration decreases to 22 yg/1, the phytoplankton peak i s 3.5 mg/1, and the hypolimnetic dissolved oxygen minimum is 9.0 mg/1. Halving the discharge (while maintaining o r i g i -nal loading) produces simulated conditions similar to the effects of doubling the loading (Figure 21e): phosphorus increases to 47 yg/1, phytoplankton concentration peaks at 5.3 mg/1, and hypolimnetic dissolved oxygen reaches a minimum of 4.6 mg/1. Doubling the discharge and halving the loading simultaneously produce significantly lower trophic conditions (Figure 21f): phosphorus decreases to 12 yg/1, phytoplankton peaks at 3.0 mg/1, and dissolved oxygen reaches a minimum of 11.6 mg/1. It i s significant that large changes i n trophic status may theore-t i c a l l y occur in only one year as a result of variations i n hydrology and phosphorus loading. This theory was tested during 1972-73 (as described in the previous section), and the results show that although significant changes did occur during the year of high runoff and decreased loading, an even larger impact was evident during the following year. Hence, the hydrologic and loading condit ions occurring from March 1972 to March 1973 resulted In a decrease in spring phosphorus concentration of 26 yg/1 (from 42 to 16). The lower phosphorus concentration resulted in significantly lower phytoplank-ton production during the summer of 1973, and no serious algal blooms. 120 2. Sensitivity of Physical and Biological Coefficients The sensitivity of 15 physical and biological coefficients on the simulation of phosphorus concentration at the end of the year (March 1970) i s shown i n Table VII. The range of each coefficient as reported in the literature (Chapter IV) is shown in column 2, and the value used i n the simulation is shown i n column 3. The simulated phosphorus concentra-tion (using the coefficient values i n column 3) is shown i n column 4. The resulting phosphorus concentration when the coefficient i s set at i t s mini-mum value (with a l l other coefficients remaining the same) is shown in column 5, and the concentration with the coefficient at i t s maximum value i s shown in column 6. The maximum per cent deviation from the simulated concentration (33 yg/1) is shown in column 7. The analysis shows the coefficient of decom-position (k^) to be the most sensitive, with a maximum positive deviation of 15 per cent. This simplified sensitivity analysis does not explore the interactive sensitivity of the 15 coefficients as they vary with respect to each other, but i t does give an approximate index of relative s e n s i t i v i -ties . Table VIII explores the sensitivities of the same coefficients with respect to the phytoplankton peak, and indicates much greater deviations than with respect to phosphorus concentration. The most sensitive c o e f f i -cient appears to be the Michaelis-Menton half-saturation constant (K^), which can cause an increase of 56 per cent in simulated phytoplankton biomass when the minimum value reported in the literature i s used in the model. The sink-ing velocity (Vg) i s apparently the second most sensitive coefficient, caus-ing a maximum positive deviation of 39 per cent in phytoplankton biomass. TABLE VII SENSITIVITY OF COEFFICIENTS ON PHOSPHORUS CONCENTRATION COEFFICIENT I RANGE REPORTED VALUE IN LITERATURE USED SIMULATED CONCENTRATION FOR VALUES IN COLUMN 3 CONCENTRATION USING MINIMUM VALUE CONCENTRATION USING MAXIMUM VALUE MAXIMUM PECENTAGE DEVIATION FROM COLUMN 4 k d .03 - .05 .04 33 29 38 +15 k d 80 - 120 100 33 36 30 + 9 k r h .4 - .6 • .5 33 34 32 + 3 ±20% 33 34 33 + 3 V .15 - .19 .17 33 32 34 ± 3 Tpb .007-.015 .009 33 33 32 - 3 150-300 200 33 32 33 - 3 .4 - .7 .6 33 32 33 - 3 KG .6 - .9 .79 33 33 33 0 v s .5 - 1.5 1.0 33 33 33 0 k2 .004- .006 .005 33 33 33 0 k Z .15 - .25 .20 33 33 33 0 «H .001 -.03 .01 33 33 33 0 k l .075 -.125 .10 33 33 33 0 k 1 re .3 - .5 .4 33 33 33 0 DEFINITION OF COEFFICIENTS k^ = c o e f f i c i e n t of decomposition k = c o e f f i c i e n t of adsorption cl k = c o e f f i c i e n t of r e c y c l i n g i n hypolimnion k = c o e f f i c i e n t of eddy d i f f u s i o n v = c o e f f i c i e n t of adsorptive release k , = c o e f f i c i e n t of phosphorus i n biomass 1^ = l i g h t i n t e n s i t y of maximum growth K A = c o e f f i c i e n t of zooplankton a s s i m i l a t i o n K G re c o e f f i c i e n t of grazing v e l o c i t y of sinki n g of phytoplankton c e l l s c o e f f i c i e n t of r e s p i r a t i o n c o e f f i c i e n t of l i g h t e x t i n c t i o n f o r plankton biomass Michaelis-Menton h a l f - s a t u r a t i o n c o e f f i c i e n t c o e f f i c i e n t of maximum growth c o e f f i c i e n t of r e c y c l i n g i n epilimnion TABLE VIII SENSITIVITY OF COEFFICIENTS ON PHYTOPLANKTON PRODUCTION SIMULATED ' MAXIMUM CONCENTRATION CONCENTRATION CONCENTRATION PERCENTAGE RANGE REPORTED VALUE FOR VALUES USING MINIMUM USING MAXIMUM DEVIATION COEFFICIENT IN LITERATURE USED IN COLUMN 3 VALUE VALUE FROM COLUMN 4 1 ? 3 4 5 6 7 .001 - .03 .01 4.56 7.13 2.51 +56 .5 - 1.5 1.0 4.56 6.35 3.39 +39 A .4 - .7 .6 4.56 5.99 4.12 +31 hi 150 - 300 200 4.56 5.24 3.29 -28 k l .075 - .125 .10 4.56 3.62 5.69 +25 kpb KG .007 - .015 .009 4.56 5.04 3.55 -22 .6 - .9 .79 4.56 5.56 4.18 +22 k k e p . re .15 - .25 .20 4.56 5.26 4.01 +15 .3 - .5 .4 4.56 5.11 4.11 +12 k ±20% 4.56 4.09 4.13 -10 k d .03 - .05 .04 4.56 4.34 4.78 ±5 k2 .004 - .006 .005 4.56 4.69 4.43 ±3 k a 80 - 120 100 4.56 4.65 4.47 ±2 k r h .4 - .6 .5 4.56 4.60 4.52 ±1 v n a .15 - .19 .17 4.56 4.52 4.60 ±1 123 C. EDDY DIFFUSION Eddy diffusion of phosphorus from the hypolimnion to the epi-limnion cannot be verified, as this movement cannot be directly measured. According to the eddy diffusion submodel (Chapter IV), "loading" of phos-phorus to the epilimnion by eddy diffusion from the hypolimnion can, during a short part of the summer s t r a t i f i c a t i o n period, contribute nearly as much phosphorus as external loading (Figure 22). The figure shows that for a few days of the summer, the model simulates a supply of 250 kg/day to the epilimnion by eddy diffusion. During this time the predicted concentration difference between the epilimnion and hypolimnion reached a maximum of AO yg/1. 124 500 450 I H 1 1 1 1 1 1 1 1 H 120 180 240 T I M E ( D A Y S ) 300 360 Figure 22. Loading rate of phosphorus from external sources to Skaha Lake, 1969-70 (upper curve) and simulated "internal loading" to the epilimnion by eddy diffusion (lower curve). CHAPTER VI DISCUSSION A. INTERPRETATIONS AND LIMITATIONS The sedimentation submodel assumes a d i r e c t r e l a t i o n s h i p be-tween phytoplankton production and phosphorus sedimentation (Chapter IV). This r e l a t i o n s h i p i s evident i n midsummer when the sedimentation of dead organic matter r e s u l t s i n low values of t o t a l phosphorus con-centration i n the epilimnion during the peak of the growing season (Figure 13). Because t o t a l phosphorus rather than dissolved orthophos-phate i s modelled, these low values must r e f l e c t sedimentation of par-t i c u l a t e phosphorus, and not simply losses through uptake of soluble phosphate by organisms. The low values during the summer appear to describe a lake which receives phosphorus i n a form a v a i l a b l e f or growth (or makes incoming p a r t i c u l a t e phosphorus a v a i l a b l e through decomposition), uses the phosphorus i n the production of organic matter, and then s e d i -ments a po r t i o n of the dead p a r t i c u l a t e organic phosphorus. In t h i s sense, the t o t a l phosphorus curve (Figure 13) i s s i m i l a r to the curve for soluble orthophosphate, which usually reaches non-detectable l e v e l s during the growing season i n a productive lake (Hutchinson 1957, R i g l e r 1973); But the f a c t that t o t a l phosphorus remains at detectable l e v e l s during the height of the growing season may make i t a more useful i n d i -cator than orthophosphate of p o t e n t i a l primary production. 125 126 1. Sedimentation From the Epilimnion Simulated phosphorus sedimentation from the epilimnion appears to have been i n i t i a l l y underestimated by a factor of approximately two (Chapter V). This discrepancy can be interpreted in several possible ways. F i r s t , i t could be assumed that sedimentation of phosphorus by algal organisms accounts for only half of the actual amount, and that sedimentation by other organisms (bacteria, zooplankton, fish) must at least double the amount. This assumption was made in f i t t i n g the simulated curve to the real data (Chapter V). Secondly, i t i s possible that other mechanisms are responsible for sedimentation of particulate phosphorus from the epilimnion. One possibility i s that precipitation of phosphorus minerals such as apatite takes place. Because no chemical precipitation submodel was formulated (for the reasons discussed in Chapter IV), this possibility cannot be quantitatively explored. Adsorption losses from the epilimnion to sedi-ment muds are probably not great, as only 17 per cent of the area of the epilimnion (the l i t t o r a l ) i s in contact with sediments. 2. Regeneration of Phosphorus from Deep-water Sediments A surprising finding of the simulation analysis was that three to four times the amount of phosphorus was apparently released from the sediments than could be explained by processes of bacterial decomposition. Several explanations are possible, the most obvious one being that much of the phosphorus sedimenting through the hypolimnion did not reach the sediments in the f i r s t place, and was decomposed en route by biological or chemical mechanisms. This explanation would mean that the coefficient 127 of recycling for the hypolimnion (k j) 1 S considerably higher than the 0.5/day value (±0.1) reported in the literature (Chapter IV). A second explanation is that sedimented phosphorus is regener-ated three to four times faster to the water than can be explained by processes of bacterial decomposition. Other mechanisms, such as d i f f u -sion, physical disturbance by benthic organisms, turbulence during mixing periods, and chemical solubilization are po s s i b i l i t i e s (discussed in detail i n Chapter IV). Regeneration through turbulence during mixing periods does not appear l i k e l y , however, as real data does not show a marked concentration increase at the beginning of these periods (Figure 12). 3. Phytoplankton Production Simulated phytoplankton growth (Figure 19) does not begin u n t i l about day 70 when the growth rate (a function of temperature, light and nutrient conditions) exceeds the loss rate (a function of grazing, respir-ation, sinking, and advection losses from the south end of the lake). The i n i t i a l exponential growth phase is temporarily reversed around day 90 by phosphorus deficiency caused by sedimentation of phosphorus-bearing algal c e l l s , and by self-shading effects. The major probable reason that the simulated reversal is not as great as the real data indicates is the omis-sion of a dynamic zooplankton submodel which would increase grazing losses during high algal growth. The lack of adequate zooplankton data for Skaha Lake precludes the validation of such a submodel. The second simulated growth phase (peak at day 100) is terminated again by^phosphorus sedimentation and self-shading, but at this higher 128 growth level the effects are more severe. A third peak occurs around day 150 because of continuing favorable conditions of temperature, light and nutrients. Losses by sinking and advection exceed growth after this peak, and no net growth occurs after day 210 when temperature and light conditions become unfavorable. The effects of phosphorus on the growth rate are separated from those of temperature and light in Figure 23. This analysis excludes the effects of losses (grazing, respiration, sinking and advection) on the net growth rate, and focuses on only the growth factors. The upper curve represents the simulated daily growth rate as a function of only temperature and light, while assuming that there i s an abundance of avail-able phosphorus. The lower curve represents the growth rate with a l l three limiting factors included. If the assumption is accepted that phosphorus i s the limiting nutrient for most of the growing season, the difference between the two curves indicates the specific effect of phos-phorus limitation on phytoplankton growth. Several simplifying assumptions have been made in the formula-tion of the primary production submodel which limit i t s accuracy of pre-diction. Different rates of phosphorus uptake, sinking, and grazing pre-ference by zooplankton for different phytoplankton species have not been modelled. Data from Skaha Lake (Stein and Coulthard 1971) show that the f i r s t phytoplankton peak was dominated by diatoms and phytoflagellates, while the second was dominated by blue-green species. Differences in the Michaelis-Menton half-saturation constant for phosphorus uptake, sinking rate, and grazing rate can be significant between diatoms and 129 Figure 23. Simulated phytoplankton growth rates showing the limiting effects of temperature and ligh t (upper curve) and the limiting effects of temperature, light and phos-phorus (lower curve), Skaha Lake, 1969-70. 130 blue-green algae (Chapter IV), and these differences have been averaged i n the model. A better f i t between real and simulated values could probably be achieved by modelling the two algal groups separately. Given these limitations and simplifying assumptions, the results indicate that total phosphorus can be used as a measure of the most li m i t -ing nutrient i n the simulation of phytoplankton production i n Skaha Lake. The assumption that approximately half of the total phosphorus i s available for growth (Gachter 1971) appears to be reasonable. In order to investigate the effects of other possible limiting nutrients on phytoplankton production (e.g. nitrogen, carbon), additional models would have to be formulated. B. APPLICATION TO MANAGEMENT OF THE EUTROPHICATION PROBLEMS OF SKAHA LAKE In this section an assessment is made of the hypothetical long-range (20-year) effects of four different phosphorus management policies on the eutrophication of Skaha Lake. The four management policies are: I. No phosphorus removal and no growth in the Penticton region II. 60 per cent phosphorus removal (approximately the removal with chemical precipitation at the Penticton sewage treatment plant i n 1972-73; Haughton et al. 1974) and a "high" population growth projection of three per cent per year (Okanagan Basin Agreement Final Report 1974) III. 60 per cent phosphorus removal and "low" growth (approximately 1.5 per cent per year) IV. Complete removal of a l l phosphorus from municipal waste (equivalent to a spray irrigation system of municipal waste disposal) Policy IV assumes that 60 per cent of the phosphorus loading to Skaha Lake is from Penticton municipal wastes (Haughton et a l . 1974), and 131 that the remaining 40 per cent from agricultural and natural sources re-mains at a constant level. The annual population growth estimates of three per cent and 1.5 per cent result in a yearly increase in phosphorus input of approximately two per cent and one per cent, as only 60 per cent of the annual input comes from municipal sources. As reported in the Canada-British Columbia Okanagan Basin Agreement Final Report (1974), the growth estimates are considered linear rather than exponential for the 20-year period. In order to approximate the type of hydrologic v a r i a b i l i t y typi-cal of the Okanagan Basin, outflow discharges from Skaha Lake for the 20-year period preceeding the year of simulation (1949-1969) are used. During this O O Q period yearly flows varied from 2.29 X 10 m (187,000 acre-ft) to 7.95 X 10 m (646,000 acre-ft) (see Table A-5 of Appendix A). The 20-year simulations of the four management policies are not i n -tended to be predictions of the trophic state of Skaha Lake 20 years from now. F i r s t , the hydrologic variations of the next 20 years are impossible to predict. Secondly, the simplifying assumptions and limitations inherent in the submodels make future predictions a risky exercise. These simulations are, therefore, only an attempt to show general trends that might be ex-pected in the trophic indicators with the hydrologic variation that occurred from 1949 to 1969. The i n i t i a l conditions chosen for each of the four sim-ulations are the trophic conditions for the modelling year 1969-70: a f i n a l phosphorus concentration of 33 yg/1, a phytoplankton peak of 4.6 mg/1, and a hypolimnetic dissolved oxygen minimum of 6.6 mg/1. These same trophic i n d i -cators are then modelled for a 20-year period with each of the four manage-ment policies. 132 The results of policy I (no treatment and no growth) appear to keep the lake in as high or higher trophic state than i t was in 1970 (Figure 24). Except during relatively wet years (e.g. years 3 and 11), the phosphorus concentration fluctuates around the i n i t i a l value of 33 yg/1 until the occurrence of four relatively dry years (years 12 - 15). The low flow causes the modelled concentration to exceed 60 yg/1, with associ-ated high phytoplankton biomass (over 6 mg/1) and low hypolimnetic dissolved oxygen (nearly 1 mg/1, dangerously close to anaerobic conditions). Using the serious bloom conditions of 1969 as a reference point (Stein and Coult-hard 1971), phytoplankton peaks appear to indicate bloom conditions during each of the 20 years. The results of policy II (high growth and 60 per cent removal; Figure 24) show at f i r s t an improvement in trophic conditions, but by year 12 the situation returns to the i n i t i a l eutrophic state. By year 20 conditions have become nearly the same as the trophic state in year 20 for policy I. Under policy III (low growth and 60 per cent removal; Figure 24), there i s again improvement at f i r s t , but by year 14 the situation i s back to the i n i t i a l trophic state. The dry period does not appear to affect the lake as seriously as with the higher loading rates of policy II, but algal growth appears to remain in the bloom category. To investigate the effects of removing a l l of the phosphorus from municipal sources (e.g. spray irrigation), a 20-year period with a 60 per cent reduction (no growth) was simulated (Figure 24). Trophic con-133 I NO PHOSPHORUS REMOVAL AND NO GROWTH I 60% PHOSPHORUS REMOVAL AND HIGH GROWTH A -P h o s p h o r u s P h v t o o l a n h t o n A Di s o l v e d o x y g e n \ / \ V'/ > — — V * v / \ / V e 14 ^ 70 o E 12 g — 60 Iroli | O 8 S o 4 0 x> 6 | •6 4 ^ 8 3 0 I 2 o °" 10 >• o a 0 i i i P h o s p h o f u S — • P h y t o p l a n k t o n D i s s o l v e d o x y g e n ,'\ A 1 / s A K \ / y v A — — \ , V ' \ 8 10 12 14 n T i m * t n y . a r i 6 IB 20 10 12 14 IS 18 i n y t a r t Figure 24. Hypothetical effects of four different phos-phorus management policies on the long-range eutrophication of Skaha Lake. 134 ditions show significant improvement: no low dissolved oxygen conditions occur and phytoplankton growth appears to remain at a tolerable level during most of the period. Even during an exceptionally dry year (15) when the phytoplankton peak reaches a level that could be considered a minor bloom, the peak i s only half of the i n i t i a l value. These simulations support the predictions of Stockner and Pinsent (1974) concerning the relationship between future phosphorus loading and the trophic state of Skaha Lake (Figure 25). Stockner and Pinsent have established trophic c r i t e r i a on the basis of hydrologic retention time, mean depth, phytoplankton and periphyton production, dis-solved oxygen depletion, and other limnological data. Values within and above the " c r i t e r i a " area indicate a moderate to high trophic state, and the probability of moderate to serious algal blooms during most years. With phosphorus removal by advanced ("tertiary") treatment, Stockner and Pinsent predict the probability of frequent algal blooms for moderate, high, and low population growth rates (I, II, and III) after 1980. With complete removal of municipal phosphorus ("land treatment"), an acceptable trophic state with infrequent algal blooms is predicted. This "steady state" situa-tion could, however, be upset i f phosphorus loading from Okanagan Lake i n -creased significantly. C. SUITABILITY OF THE MODEL FOR OTHER LAKES The model has been formulated for a lake with relatively high primary production, making i t more suitable for eutrophic than oligotrophic lakes. The key assumption of the sedimentation submodel is that sedimenta-135 O I I I 1 : I I I 1970 1980 1990 2 0 0 0 2010 2 0 2 0 YEAR Figure 25. Predictions of the trophic status of Skaha Lake with present phosphorus loading policies, tertiary treatment for phosphorus removal, and land disposal of sewage. Each policy is considered for three projected growth scenarios. The area within and above the " c r i t e r i a " zone is considered moderately to highly eutrophic (from Stockner and Pinsent 1974). 136 tion of phosphorus i s a direct function of primary production in the tropho-genic layer, thus ignoring possible sedimentation by chemical precipitation. While i t seems reasonable to assume that much of the soluble phosphorus in a eutrophic lake such as Skaha i s uti l i z e d in . the production of organic matter, this may not be the case in oligotrophic lakes such as Okanagan or Kalamalka. Chemical precipitation of phosphorus minerals such as apatite probably plays a greater role in the phosphorus cycle of such lakes (Por-cella et al. 1972, Lee 1970). Therefore, this model appears to be more suited to eutrophic lakes such as Osoyoos. A chemical precipitation sub-model would probably be a necessary addition for application of the model to an oligotrophic lake such as Kalamalka. CHAPTER VII SUMMARY AND CONCLUSIONS A simulation model of the phosphorus cycle in eutrophic Skaha Lake shows total phosphorus to be a useful indicator for the prediction of trophic states. Difference equations and a daily time scale are used in a mass balance model which accounts for the dynamic s t r a t i f i c a t i o n regime of the lake. Total phosphorus movement between epilimnion, hypolimnion, and sediments is detailed in a series of submodels. An eddy diffusion submodel predicts loading from the hypolimnion to the epilimnion which can equal external loading for short periods of the summer. A phosphorus sedi-mentation submodel predicts organic sedimentation on the basis of primary production and inorganic sedimentation from adsorption considerations. A regeneration submodel considers the temperature-dependent decomposition rates of sedimented phosphorus. A primary production submodel accounts for temperature, light and phosphorus dependency, as well as respiration, grazing, sinking and advection losses. Although many simplifying assump-tions were necessary in the formulation of detailed submodels, the model succeeded i n simulating three key trophic indicators reasonably well. Based on known phosphorus loading and three years of limnological data, reasonable agreement was found between real and simulated total phosphorus concentra-tion, phytoplankton biomass, and hypolimnetic dissolved oxygen. 137 136 The model i s considered applicable to other eutrophic lakes, but not to oligotrophic lakes without the inclusion of a submodel describ-ing sedimentation losses from phosphorus mineral precipitation. The i n -clusion of a submodel describing regeneration of phosphorus by diffusion from sediments could improve predictability, as results show that three to four times more phosphorus apparently returns to the lake from deep-water sediments than possible by bacterial decomposition alone. This find-ing shows the model to be a useful research tool for indicating areas need-ing further research. Improved simulation of phytoplankton production could probably be achieved with the inclusion of a zooplankton submodel and extension to include the specific growth dynamics of more than one algal group. The Michaelis-Menton half-saturation constant appears to be the most sensitive coefficient in the primary production submodel. The probable effects of four phosphorus management policies are assessed using 20 years of hydrologic data (1949-69) and the eutrophic conditions of 1970 as a starting point. While no attempt is made to pre-dict the trophic status of the lake for the next 20 years, definite trends are apparent. With no phosphorus removal and no increase i n loading over the hypothetical 20-year period, phytoplankton blooms increase in intensity and hypolimnetic dissolved oxygen approaches zero, while phosphorus concen-trations are greater than 60 yg/1. With 60 per cent removal of municipal phosphorus and conditions of either low or high economic growth in the Pen-ticton region, the eutrophic conditions of 1970 are again reached within 12 to 14 years. Algal blooms and hypolimnetic dissolved oxygen deficits are particularly serious during dry years. With 100 per cent municipal phospho 139 removal, trophic conditions appear to improve significantly, with the possi-b i l i t y of minor algal blooms during only dry years. These results indicate that complete removal of the phosphorus from municipal sources appears to be the most rational long-range management policy. Percentage removals associated with advanced waste treatment appear to be only a temporary solution. These conclusions demonstrate that a theoretical model to pre-dict trophic indicators in a lake can be useful as both a research tool and a practical planning aid for decision-making. LITERATURE CITED Aberg, B. and W. Rodhe. 1942. 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APPENDIX A INPUT DATA FOR SKAHA LAKE TABLE A-l MIXING AND EDDY DIFFUSION DATA (North Basin) EPILIMNION HYPOLIMNION THERMOCLINE THERMOCLINE COEFFICIENT OF D A T E VOLUME VOLUME VOLUME THICKNESS EDDY DIFFUSION (km3) (km3) (kin ) (m) (cm2/sec) 15 March 1969 0 .517 1 April 1969 0 .517 15 April 1969 .024 .459 1 May . 1969 .048 .415 15 May 1969 .070 .377 1 June 1969 .080 .35 7 15 June 1969 .090 .337 1 July 1969 .106 .315 15 July 1969 .114 .307 1 August 1969 .120 .303 15 August 1969 .125 .302 1 September 1969 .144 .285 15 September 1969 .160 .273 1 October 1969 .184 .253 15 October 1969 .210 .233 1 November 1969 .280 .187 15 November 1969 .517 0 .1 December 1969 0 .517 15 December 1969 0 . .517 1 January 1970 0 .517 15 January 1970 0 .517 1 February 1970 0 .517 15 February 1970 0 .517 1 March 1970 0 .517 0 0 0 0 0 0 .034 2.0 .077 .054 3.0 .077 .070 5.0 .051 .080 5.0 .077 .090 6.0 .020 .096 5.0 .077 .096 5.0 .077 .094 5.0 .077 .090 5.0 .077 .088 7.0 .154 .084 7.0 .077 .080 7.0 .077 .074 6.0 .077 .050 2.0 .077 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 \ TABLE A-l (Continued) MIXING;DATA (South Basin) EPILIMNION HYPOLIMNION THERMOCLINE THERMOCLINE VOLUME VOLUME VOLUME THICKNESS D A T E (km ) (km3) (km3) (m) 15 March 1969 0 .041 0 0 1 April 1969 0 .041 0 0 15 April 1969 .002 .036 .003 1.0 1 May 1969 .014 .022 .013 2.0 15 May 1969 .014 .016 .011 4.0 1 June 1969 .014 .016 .011 6.0 15 June 1969 .014 .016 .011 6.0 1 July 1969 .014 .016 .011 6.0 15 July 1969 .014 .016 .011 6.0 1 August 1969 .014 .016 .011 6.0 15 August 1969 .014 .016 .011 6.0 1 September 1969 .014 .016 .011 6.0 15 September 1969 .018 .012 .011 6.0 1 October 1969 .024 .008 .009 6.0 15 October 1969 .030 .006 .005 3.0 1 November 1969 .036 .003 .002 2.0 15 November 1969 .041 0 0 0 1 December 1969 0 .041 0 0 15 December 1969 0 .041 0 0 1 January 1970 0 .041 0 0 15 January 1970 0 .041 0 0 1 February 1970 0 .041 0 0 15 February 1970 0 .041 0 0 1 March 1970 0 .041 0 0 155 TABLE A-2 RADIATION AND EPILIMNION TEMPERATURE D A T E NET RADIATION* (langleys/day; average for month) EPILIMNION TEMPERATURE (°C) 15 March 1969 315 1.8 1 April 1969 3.0 15 April 1969 361 5.8 1 May 1969 8.4 15 May 1969 553 11.3 1 June 1969 14.8 15 June 1969 569 18.6 1 July 1969 20.2 15 July 1969 579 20.4 1 August 1969 20.6 15 August 1969 500 20.6 1 September 1969 18.4 15 September 1969 312 15.2 1 October 1969 13.0 15 October 1969 203 11.2 1 November 1969 9.6 15 November 1969 89 7.8 1 December 1969 5.8 15 December 1969 47 4.0 1 January 1970 3.0 15 January 1970 82 2.4 1 February 1970 1.8 15 February 1970 163 1.2 1 March 1970 1.4 1 langley = 1 g calorie/cm^; measured,with Eppley 180 Pyranometer at Summerland, B.C.; reported in Monthly Radiation Summary, Dept. Transport, Meteorol. Branch, Gov. of Canada, 1969-1970. Stein and Coulthard 1971. 156 TABLE A-3 ESTIMATED PERCENTAGES OF TOTAL PHOSPHORUS ENTERING SKAHA LAKE FROM KNOWN SOURCES, 1969-71* S O U R C E PERCENTAGE Municipal sewage (Penticton) Okanagan Lake (via Okanagan River) Tributary streams (natural sources) Septic tanks (via ground water) Dustfall and precipitation Agriculture (via streams) Septic tanks (via streams) Ground water (natural sources) Industry Storm sewers Ground water (other sources) 59.7 21.9 7.6 5.3 3.5 0.7 0.4 0.3 0.3 0.2 0.1 TOTAL 100.0% (24,500 kg from March 1969 to March 1970) Haughton et al. 1974 (includes estimates of storm sewer loading from Hendren and Oldham 1972 and ground water loading from Kennedy et al. 1972) TABLE A-4 MONTHLY OUTFLOW HYDROLOGY FROM SKAHA LAKE, March 1969 to March 1970* MONTH DISCHARGE (Acre-ft) 15 March - 31 March 32,800 April 51,300 May 85,000 June 40,600 July 37,200 August 34,800 September 34,100 October 31,700 November 22,900 December 19,800 January 15,100 February 14,300 1 March - 15 March 4,800 TOTAL 426,000 Although monthly values are shown here, daily values were used in computing inflow and outflow of phosphorus (from Surface Water Summary for British Columbia, Gov. of Canada, Dept. Transport). The average discharge for 48 years of record is 386,000 acre-ft/yr. 158 TABLE A-5 YEARLY OUTFLOW HYDROLOGY FROM SKAHA LAKE, 1949 to 1973 (15 March to 15 March of the following year) YEAR DISCHARGE (acre-ft/yr) 1949 450.2 1950 524.0 1951 635.6 1952 417.3 1953 416.8 1954 530.9 1955 456.2 1956 436.6 1958 408.4 1959 646.0 1960 337.1 1961 341.6 1962 286.8 1963 187.2 1964 446.2 1965 432.2 1966 243.6 1967 313.0 1968 418.2 1969 426.0 1970 182.9 1971 486.1 1972 844.0 * From Surface Water Summary for British Columbia, Gov. of Canada, Dept. Transport APPENDIX B COLLECTION AND ANALYSES OF LIMNOLOGICAL DATA During 1969-70 sampling of phosphorus, phytoplankton and dissolved oxygen in Skaha Lake was bimonthly from 1 May to 15 September and monthly the remainder of the year (Stein and Coulthard 1971). Water samples for chemical and biological analyses were taken in two transects: one across the north basin and one across the south basin. For use in the model, data from each transect was averaged to give one value for each basin. At each point on the transects water samples and measurements were taken at 0, 3, 6, 12, and 18 m (Stein and Coulthard 1971). Depending on the thickness of the epilimnion, values from the surface, 3 m and 6 m were averaged for an epilimnion concentration. 1. Total Phosphorus Total phosphorus i n the lake was determined according to the method described by Gales et al. (1966). This method involves a colouri-metric determination after treatment with sulfuric acid and persulfate. A similar method was used to determine total phosphorus i n the Okanagan River inflow to Skaha Lake. This method i s described by Fee (1971): 11. . .a colourimetric determination on an auto-analyser with ammonium molybdate and stannous chloride after 30 minutes i n an autoclave with sulfuric acid and potassium persulfate; determination done on shaken sample." 159 160 2. Phytoplankton Water samples for algal analyses were counted with a Sedgwick-Rafter counting chamber and 100X magnification with a compound microscope (Coulthard and Stein 1969). Algal biomass was reported in units of cells/ml. For colonial or filamentous algae i t was not feasible to count individual ce l l s , and the following scale was used (Coulthard and Stein 1969): Bacillariophyceae (diatoms) A s t e r i o n e l l a formosa Hass 8 cells = 1 unit C y o l o t e l l a glomevata Bachm. 1 c e l l = 1 unit Cymbella sp. 1 c e l l = 1 unit Melosira spp. 1 c e l l = 1 unit Naviaula sp. 1 c e l l = 1 unit Pinnularia sp. 1 c e l l = 1 unit Stephanodisous sp. 1 c e l l = 1 unit T a b e l l a r i a sp. 1 c e l l = 1 unit Chlorophyceae (green algae) Mougeotia sp. Chrysophyceae (chrysophtes) Dinobryon sp. Cryptophyceae (cryptomonads) Cryptomonas ovata Ehrbg. Cyanophyceae (blue-green algae) Anabaena flos-aquae (lyngb.) Breb. Bos toe sp. O s c i l l a t o r i a acutissima Kuff Dinophyceae (dinoflagellates) Certa-ium k i v u n d i n e l l a (O.F. Mull.) Duj. 12-15 cells = 1 unit 1 c e l l = 1 unit 1 c e l l = 1 unit 12-15 cells 12-15 cells 1 unit 1 unit 12-15 cells = 1 unit 1 c e l l = 1 unit Phytoplankton biomass was converted from cells/ml to dry weight concentration i n mg/1. This conversion can be variable depending on the species of phytoplankton, and an average value of 100 cells/ml =0.3 mg/1 161 dry weight was used (Chen 1970, Di Toro et al. 1971). 3. Dissolved Oxygen Dissolved oxygen values were obtained with a membrane electrode oxygen/temperature probe (YSI-54) (Stein and Coulthard 1971). For compara-tive purposes, at least one set of determinations in each transect was made using the modified Winkler method. 

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