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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  M.S.  A.B. Dartmouth College, 1963 Colorado State University, 1966  A THESIS SUBMITTED IN PARTIAL FULFILMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY  i n the Department of C i v i l Engineering  We accept this thesis as conforming t o ^ h e required standard  THE UNIVERSITY OF BRITISH COLUMBIA June, 1974  In  presenting  an  advanced  the  Library  I further for  degree shall  agree  scholarly  by  his  of  this  this  thesis  in p a r t i a l  fulfilment  at  University  of  the  make  that  it  permission  purposes  may  representatives.  written  thesis  for  available for  It  financial  is  by  the  understood  gain  for  extensive  be g r a n t e d  shall  of  Q/^'/  The U n i v e r s i t y o f B r i t i s h V a n c o u v e r 8, Canada  Au^f-  °j  117*/  requirements  copying  that  not  reference  Head o f  be  \ n € e f iVl ^,  Columbia  the  B r i t i s h Columbia,  permission.  Department  Date  freely  of  of  I agree and this  or  allowed  without  that  study. thesis  my D e p a r t m e n t  copying  for  or  publication my  A B S T R A C T  Phosphorus i s recognized phication of lakes.  as a key nutrient i n the c u l t u r a l eutro-  A simulation model of the phosphorus cycle i n eutro-  phic Skaha Lake shows t o t a l phosphorus to be a u s e f u l i n d i c a t o r f o r the prediction of trophic s t a t e s .  Difference equations and a d a i l y time scale  are used i n a mass balance model which accounts f o r 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 d e t a i l e d i n a series of submodels.  An eddy  d i f f u s i o n submodel predicts loading from the hypolimnion to the epilimnion which can equal external loading f o r short periods o f the summer. phorus sedimentation  submodel predicts organic sedimentation  of primary production and inorganic sedimentation ations.  A phos-  on the basis  from adsorption  consider-  A regeneration submodel considers the temperature-dependent decom-  p o s i t i o n rates of sedimented phosphorus.  A primary production submodel  accounts f o r temperature, l i g h t and phosphorus dependency, as w e l l as r e s p i r a t i o n , grazing, s i n k i n g and advection l o s s e s .  Based on known phosphorus  loading and three years of l i m n o l o g i c a l data, reasonable between r e a l and simulated  agreement was found  t o t a l phosphorus concentration, phytoplankton b i o -  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 b a c t e r i a l decomposition probably  alone.  Improved simulation of phytoplankton production  could  be achieved with the i n c l u s i o n of a zooplankton submodel and extenii  iii  sion to include the s p e c i f i c growth dynamics of more than one a l g a l group. The Michaelis-Menton  h a l f - s a t u r a t i o n constant appears to be the most  s e n s i t i v e c o e f f i c i e n t i n the primary production submodel. The probable effects of four phosphorus management p o l i c i e s are assessed using 20 years of hydrologic data (1949-69) and the eutrophic conditions of 1970 as a s t a r t i n g point. While no attempt i s made to pred i c t the trophic status of the lake f o r the next 20 years, d e f i n i t e trends are apparent.  With no phosphorus removal and no increase i n loading over  the hypothetical 20-year period, phytoplankton  blooms increase i n i n t e n s i t y  and hypolimnetic dissolved oxygen approaches zero.  With 60 per cent removal  of municipal phosphorus and conditions of e i t h e r low or high economic growth i n the Penticton region, the eutrophic conditions o f 1970 are reached within 12 to 14 years.  A l g a l blooms and hypolimnetic dissolved oxygen d e f i c i t s are  p a r t i c u l a r l y serious during dry years.  With 100 per cent municipal phosphorus  removal, trophic conditions appear to improve s i g n i f i c a n t l y , with the p o s s i b i l i t y of minor a l g a l blooms during only dry years.  These r e s u l t s indicate  that complete removal of the phosphorus from municipal sources appears to be the most r a t i o n a l long-range management p o l i c y . These conclusions demonstrate that a t h e o r e t i c a l model to pred i c t trophic i n d i c a t o r s i n a lake can be useful as both a research tool and a p r a c t i c a l planning aid f o r decision-making.  TABLE OF CONTENTS Page LIST OF TABLES  vii  LIST OF FIGURES  ix  CHAPTER I.  INTRODUCTION  1  A.  PROBLEM DEFINITION.  1  1. The Eutrophication Problem 2. Phosphorus and Eutrophication 3. The Need For A Predictive Model  1 2 4  B. II.  RESEARCH OBJECTIVES  '  7  THE OKANAGAN BASIN AND SKAHA LAKE  9  A.  9  THE OKANAGAN BASIN  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.  15 15 16 16 16 19 21 21 21 24 24 25 25 27  2.  3.  4. 5.  Physical Limnology. . . . . . . . . . . . . . . . . . . (a) The Lake Basin (b) The Lake Sediments Chemical Limnology (a) Water Chemistry (b) Sediment Chemistry (c) Net Sedimentation Rates of Phosphorus Forms . . . . Biological Limnology (a) Phytoplankton and Periphyton (b) Macrophytes . . . . . (c) Zooplankton (d) Fish Trophic State Paleolimnology. . iv  V  CHAPTER III.  Page PHOSPHORUS CYCLING IN LAKES AND MODELLING APPROACH  29  A.  AND THE LIMITING NUTRIENT CONCEPT  29  The "Law o f t h e Minimum" R e l a t i v e Importance o f Carbon, N i t r o g e n and P h o s p h o r u s . (a) Carbon (b) N i t r o g e n (c) Phosphorus  29 30 30 31 32  EUTROPHICATION 1. 2.  B.  THE PHOSPHORUS CYCLE IN LAKES  34  1.  35  2. 3. C.  35 36 36 37 38 44  MODELLING APPROACH  45  1.  45 46 47 48 48 50  2.  IV.  Phosphorus Compartments i n Lake Water (a) Orthophosphate Phosphorus ( S o l u b l e R e a c t i v e Phosphorus). . . (b) S o l u b l e O r g a n i c Phosphorus (c) P a r t i c u l a t e Phosphorus (d) T o t a l Phosphorus Turnover Rates o f Orthophosphate. The Lake as a P r o d u c t i v i t y Chamber  Simulation Modelling (a) Time S c a l e (b) A p p r o a c h t o M a t h e m a t i c a l Statement o f R e l a t i o n s h i p s S i m u l a t i o n Approaches to M o d e l l i n g t h e Phosphorus C y c l e (a) The Compartment Approach (b) The Mass Budget Approach  DEVELOPMENT OF A MODEL FOR SKAHA LAKE  53  A.  FUNDAMENTAL INPUT-OUTPUT EQUATION  53  1.  53 53 54 54 55 55 55 55 56  2.  3. B.  Form o f t h e E q u a t i o n f o r t h e E p i l i m n i o n (a) I n p u t Terms (b) Output Terms ( c ) Combined Mass B a l a n c e Form o f t h e E q u a t i o n f o r the H y p o l i m n i o n (a) I n p u t Terms. (b) Output Terms (c) Combined Mass B a l a n c e . M o d i f i c a t i o n o f Mass B a l a n c e D u r i n g M i x i n g P e r i o d s . . .  MIXING BEHAVIOR OF SKAHA LAKE AND VOLUME CHANGES OF EPILIMNION AND HYPOLIMNION  56  vi  CHAPTER  Page  C.  DEVELOPMENT OF SUBMODELS  58  1.  58 59 59 60 61 61 61 61 63 63 67 67 69  2.  3.  4.  5.  V.  Eddy D i f f u s i o n Submodel (a) Simplifying Assumptions for Eddy D i f f u s i o n (b) Equation for Eddy D i f f u s i o n Transport (c) C o e f f i c i e n t of Eddy D i f f u s i o n Sedimentation Submodel (a) Sedimentation from the Epilimnion (1) Sedimentation of Inorganic Phosphorus a. P r e c i p i t a t i o n of Phosphorus Minerals. . . . b. Adsorption of Phosphate (2) Sedimentation of Organic Phosphorus (b) Sedimentation from the Hypolimnion (1) Sedimentation of Inorganic Phosphorus (2) Sedimentation of Organic Phosphorus (3) Resulting Expression f o r Sedimentation from the Hypolimnion Internal Loading Submodel.. (a) Mechanisms C o n t r o l l i n g Phosphorus Transport at the Sediment-Water Interface (1) Physical Disturbance and Mixing (2) Physical D i f f u s i o n (3) B i o l o g i c a l Uptake (4) Anaerobic Chemical Regeneration (5) Decomposition Regeneration (b) Formulation of Internal Loading Submodel (1) L i t t o r a l Zone Regeneration (2) Deep Water Sediment Regeneration Primary Production Submodel . (a) Other Phytoplankton Models (b) Basic Phytoplankton Equation (c) Phytoplankton Growth (1) Temperature Dependency (2) Light Dependency (3) Nutrient Dependency (4) F i n a l Growth Rate Expression (d) Phytoplankton Losses (1) Respiration Losses (2) Grazing by Zooplankton (3) Sinking of Phytoplankton Cells (4) Advection Losses Hypolimnetic Dissolved Oxygen Submodel. . . .  71 72 73 73 74 75 76 77 79 79 80 81 82 84 84 85 85 91 94 95 95 96 97 98 98  RESULTS  101  A.  101  VERIFICATION OF THE MODEL FOR SKAHA LAKE.  vii  CHAPTER  Page 1.  2. 3. 4. 5. B.  C.  VI.  101 101 107 Ill I l l 115 115  SENSITIVITY ANALYSES  117  1. 2.  117 120  S e n s i t i v i t y of Phosphorus Loading and Hydrology . . . S e n s i t i v i t y of Physical and B i o l o g i c a l Coefficients .  EDDY DIFFUSION  123  DISCUSSION  125  A.  INTERPRETATIONS AND LIMITATIONS  125  1. 2. 3.  126 126 127  B.  C. VII.  Total Phosphorus Concentration (a) Upper Mixed Layer (b) Hypolimnion Phosphorus . Phytoplankton Production Dissolved Oxygen i n the Hypolimnion Simulation of the South Basin of Skaha Lake . . . . . V e r i f i c a t i o n for 1970-71 and 1972-73  Sedimentation from the Epilimnion Regeneration of Phosphorus from Deep-Water Sediments. Phytoplankton Production  APPLICATION TO MANAGEMENT OF THE EUTROPHICATION PROBLEMS OF SKAHA LAKE  130  SUITABILITY OF THE MODEL FOR OTHER LAKES  134  SUMMARY AND CONCLUSIONS  LITERATURE CITED  137 140  APPENDIX A.  INPUT DATA FOR SKAHA LAKE  152  B.  COLLECTION AND ANALYSES OF LIMNOLOGICAL DATA  159  1. 2. 3.  159 160 161  Total Phosphorus Phytoplankton Dissolved Oxygen  LIST OF TABLES  Table  Page  I.  PHYSICAL CHARACTERISTICS OF SKAHA LAKE  15  II.  CHEMICAL CHARACTERISTICS OF SKAHA LAKE  18  III.  ALGAL ABUNDANCE IN SKAHA LAKE, 1969-70  22  PHYTOPLANKTON IN SKAHA LAKE,. 1971  22  PERIPHYTON  23  IV. V. VI.  IN SKAHA LAKE, 1971  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  viii  LIST OF FIGURES Figure  Page  1.  Location and watershed boundary of the Okanagan Basin  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 i n Europe and North America  26  Phosphorus transformations i n s t r a t i f i e d lakes during summer; expressed i n 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 l i g h t i n t e n s i t y . .  88  9.  Growth rate of a phytoplankton population as a function of phosphorus concentration  92  5.  6  10.  A l g a l r e s p i r a t i o n rate as a function of temperature  95  11.  Loading rate of phosphorus to Skaha Lake, 1969-70, and phosphorus outflow rate  102  Phosphorus concentration i n surface water of Skaha Lake, 1969-70, with no modification of o r i g i n a l assumptions  103  Phosphorus concentration i n surface water of Skaha Lake, 1969-70, with the sedimentation rate from the epilimnion doubled  105  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 s e d i ments .  106  Phosphorus concentration i n surface water of Skaha Lake, 1969-70, with the sedimentation rate from epilimnion doubled and the r e generation rate from deep-water sediments X 3.5  108  Simulated sedimentation rate of phosphorus from the hypolimnion of Skaha Lake, 1969-70, and the regeneration rate from deep-water sediments  109  12. 13.  14.  15.  16.  ix  X  LIST OF. FIGURES (Continued)  Figure 17.  18.  19.  20.  21.  22.  23. 24. 25.  Page Simulated sedimentation rates of organic phosphorus and inorganic phosphorus from the hypolimnion of Skaha Lake, 1969-70  110  Simulated phosphorus concentration i n the hypolimnion of Skaha Lake, 1969-70  112  Phytoplankton biomass i n the trophogenic layer of Skaha Lake, 1969-70  113  Dissolved oxygen concentration i n the hypolimnion of Skaha Lake, 1969-70  114  Simulated phosphorus, phytoplankton and hypolimnetic dissolved oxygen with varying phosphorus loading and hydrologic discharge, Skaha Lake, 1969-70  118  Loading rate of phosphorus from external sources to Skaha Lake, 1969-70, and simulated " i n t e r n a l loading" to the epilimnion by eddy d i f f u s i o n  124  Simulated phytoplankton growth rates showing the l i m i t i n g e f f e c t s of temperature, l i g h t and phosphorus, Skaha Lake, 1969-70. . . . .  129  Hypothetical e f f e c t s of four d i f f e r e n t phosphorus management p o l i c i e s on the long-range eutrophication of Skaha Lake.  133  Predictions of the trophic status of Skaha Lake with present phosphorus loading p o l i c i e s , t e r t i a r y treatment f o r phosphorus removal, and land disposal of sewage (Stockner and Pinsent 1974) . 135  CHAPTER I  INTRODUCTION  A.  PROBLEM DEFINITION 1.  The  Eutrophication  Most l a k e s b e g i n scarce  Problem their existence  in a relatively nutrient-  s t a t e , as many N o r t h American l a k e s d i d t e n t o f i f t e e n  y e a r s ago  f o l l o w i n g the P l e i s t o c e n e g l a c i a t i o n .  surrounding  thousand  As n u t r i e n t s l e a c h from  r o c k s o v e r g e o l o g i c time, t h e y accumulate i n the water  and  sediments, r e s u l t i n g i n the growth o f p r i m a r y p r o d u c t i o n  (mainly  and  stimulates  other photosynthetic  ary production  organisms).  Primary production  (or p r i m a r y consumption) by  of i n c r e a s i n g n u t r i e n t content  and  production  g e n e r a l l y r e f e r r e d t o as e u t r o p h i c a t i o n , and may comes a swamp, then a bog,  and  and  i t i s usually a  t o become e u t r o p h i c .  take  (Some deep l a k e s  However, the p r o c e s s  can be  short geologic  time span.  many N o r t h American l a k e s , such as Lake E r i e , has s e v e r a l decades.  (mesotrophy) may  The  be d e s i r a b l e to enhance such v a l u e s 1  amounts  eutrophication of  increased  While moderate l e v e l s of  will  acceler-  ated by t h e c u l t u r a l impact o f man's a c t i v i t i e s which can add v a s t  over the l a s t  be-  f i n a l l y a meadow.  never become e u t r o p h i c ) .  of n u t r i e n t s o v e r a v e r y  This  one,  u n t i l a lake  a deep l a k e i n a n u t r i e n t - s c a r c e watershed may  tens o f thousands of y e a r s probably  (fish).  i s a natural  continue  While e u t r o p h i c a t i o n i s a n a t u r a l p r o c e s s , v e r y slow one,  second-  s m a l l a q u a t i c a n i m a l s , which i n  t u r n enhances secondary consumption by l a r g e r a q u a t i c a n i m a l s process  algae  exponentially  eutrophication  as f i s h  production,  2  advanced l e v e l s have s e v e r e d e t r i m e n t a l e f f e c t s .  Highly eutrophic lakes,  w h i c h t e n d t o be p l a g u e d b y a l g a l blooms and g r e a t l y r e d u c e d r e c r e a t i o n a l v a l u e s , may become a n a e r o b i c  i n deeper w a t e r s .  Furthermore,  these  w a t e r s may d e v e l o p t a s t e , o d o u r , 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 I t i s important  values. t o 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 g r a d u a l p r o c e s s o v e r thousands o f y e a r 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 p r o c e s s o f n u t r i e n t e n r i c h m e n t t a k i n g p l a c e i n t e n s o f 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 b o t h 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 o r 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 required f o r accelerated e u t r o p h i c a t i o n . f r o m a g r i c u l t u r a l , d o m e s t i c and i n d u s t r i a l s o u r c e s  Nutrients  a r e g e n e r a l l y the major  causes o f 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  w i t h i n i t i s of prime importance.  b a s i n on t h e t r o p h i c s t a t u s o f l a k e s As s u g g e s t e d by H u t c h i n s o n (1969), i t  i s u n r e a l i s t i c t o conceive o f 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 o f l a k e s and t h e i r d r a i n a g e t r o p h i c o r e u t r o p h i c systems.  b a s i n s and s e d i m e n t s as f o r m i n g  oligo-  F o r i n s t a n c e , t h e c o e x i s t e n c e i n t h e same  watershed o f 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 S t u m m - Z o l l i n g e r  1972). 2.  Phosphorus and E u t r o p h i c a t i o n The key r o l e p l a y e d by p h o s p h o r u s , 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 o r a s an i n d i c a t o r o f t h e p r e s e n c e o f 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 a c c e p t e d  by most s c i e n t i s t s .  The p r e s e n c e a n d . r a t e  of increase  3  o f phosphorus c o n c e n t r a t i o n s i n l a k e w a t e r s i s c o n s i d e r e d  t o be an  impor-  t a n t 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 o f the r a t e a t w h i c h eutrophication i s progressing.  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 t o w a t e r s i s the key to the c o n t r o l o f 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 c a s e s . " (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 w a t e r s . " (Kramer et al. 1972) . "For most i n l a n d w a t e r s phosphorus appears t o 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 a l m o s t a l l c i r c u m s t a n c e s 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 StummZollinger 1972). "These, and many o t h e r o b s e r v a t i o n s have f o s t e r e d the widespread b e l i e f t h a t 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 t h r o u g h o u t the w o r l d i s l a r g e l y b e i n g caused by i n c r e a s e d i n p u t o f phosphorus r e s u l t i n g f r o m human a c t i v i t i e s . " (Rigler 1973). "Of a l l the elements p r e s e n t i n l i v i n g o r g a n i s m s , phosphorus i s l i k e l y t o be the most i m p o r t a n t e c o l o g i c a l l y , because the r a t i o o f phosphorus t o o t h e r elements i n o r g a n i s m s tends t o be c o n s i d e r a b l y g r e a t e r t h a n the r a t i o i n the p r i mary s o u r c e s o f the b i o l o g i c a l e l e m e n t s . 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 t o l i m i t the e a r t h ' s p r o d u c t i v i t y o f any r e g i o n o f the e a r t h ' s s u r f a c e t h a n i s a d e f i c i e n c y of any o t h e r m a t e r i a l e x c e p t w a t e r . " (Hutchinson 1957). ". . .mass b a l a n c e c a l c u l a t i o n s show t h a t i n Lake E r i e as a w h o l e , phosphorus i s g e n e r a l l y t h e l i m i t i n g growth f a c t o r , and work on many o t h e r l a k e s i n N o r t h A m e r i c a and Europe r e v e a l s t h a t the same i s t r u e 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 B r u c e 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 , p r o b a b l y a l s o p l a y a p a r t . " (Vollenweider 1968).  4  3.  The Need F o r A P r e d i c t i v e Model As V o l l e n w e i d e r  (1969) has n o t e d , n u t r i e n t budgets o f l a k e s  a r e a f u n d a m e n t a l p r o b l e m o f t h e o r e t i c a l and a p p l i e d l i m n o l o g y . known about t h e g e n e r a l the supply  t h e o r y o f 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  o f n u t r i e n t s , l o s s e s t h r o u g h v a r i o u s mechanisms, and  t i o n o v e r time.  Much i s  concentra-  Much i s a l s o known about t h e 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 production  i n lakes.  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 b u d g e t s , as v e r y few d e t a i l e d budget s t u d i e s have been p e r f o r m e d on l a k e s . phorus budget i s no  In t h i s regard,  t h e phos-  exception.  The c o n c e n t r a t i o n four basic f a c t o r s : l a k e from a l l sources;  o f phosphorus i n a l a k e i s d e t e r m i n e d by  (a) t h e r a t e o f i n p u t o f t o t a l phosphorus t o t h e (b) t h e s e d i m e n t a t i o n  o f phosphorus, or the r a t e  a t w h i c h e x c h a n g i n g phosphorus i s l o s t f r o m f u r t h e r m e t a b o l i s m 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  organic  m a t t e r i n t h e l a k e b o t t o m (Hayes and P h i l l i p s 1958); (c) t h e morphometric p r o p e r t i e s o f t h e l a k e , w h i c h i n f l u e n c e t h e r m a l 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 photosynthetic  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 w h i c h d e t e r m i n e s how q u i c k l y phosphorus i s d i l u t e d and flushed through the l a k e . Because o f t h e i m p o r t a n c e o f phosphorus i n t h e e u t r o p h i c a t i o n process,  i t i s o f g r e a t p r a c t i c a l i m p o r t a n c e t o be a b l e t o p r e d i c t from  known l o a d i n g (phosphorus i n p u t ) t h e f o l l o w i n g :  (1) t h e c o n c e n t r a t i o n o f  phosphorus i n t h e e p i l i m n i o n and h y p o l i m n i o n ; (2) t h e amount o f phosphorus l o s t t o t h e s e d i m e n t s ; (3) t h e amount o f phosphorus r e g e n e r a t e d by t h e  5  sediments to the water; flow-through; of reducing  (4) the amount of phosphorus l o s t by  (5) the. amount of r e s u l t i n g a l g a l growth; (or i n c r e a s i n g ) the phosphorus s u p p l y .  e n a b l e p r e d i c t i o n o f the time n e c e s s a r y levels.  Q u a n t i f i c a t i o n o f these  (6)  hydrologic the  effects  T h i s i n f o r m a t i o n would  to r e a c h s p e c i f i e d  eutrophication  f a c t o r s f o r p r e d i c t i o n purposes i s p o s s i b l e  through the f o r m u l a t i o n o f a s i m u l a t i o n model o f the phosphorus-phytoplankton system. There i s a need f o r a model which accounts f o r the dynamic stratification  regime o f temperate l a k e s and which d e t a i l s phosphorus move-  ment between e p i l i m n i o n , h y p o l i m n i o n and be  initially  developed by e i t h e r of two  model f o r a s t r a t i f i e d cycle i n a s p e c i f i c Is  the one  l a k e ; or  b a s i c approaches:  (a) a  lake. after  Skaha Lake, one  The  second apporach  particularly  o f a c h a i n o f l a k e s i n the Okanagan B a s i n  the l a k e has  i n the form o f a l g a l blooms.  been s e r i o u s l y degraded  f i v e - y e a r study was  of  of t h i s type  (Figure  shown s i g n s o f i n c r e a s i n g e u t r o p h i c a t i o n , During  (Coulthard  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 an e x h a u s t i v e  temperate  verification.  w i t h i n the l a k e has been l e s s than a meter, and the l a k e has  the model w i t h  G e n e r a l i z a t i o n o f the model to o t h e r  B r i t i s h Columbia, i s i d e a l l y s u i t e d f o r a study  In recent years,  general  (b) a s p e c i f i c model d e t a i l i n g the phosphorus  chosen i n t h i s study because o f the need to v e r i f y  lakes i s considered  1).  Such a model c o u l d  l a k e w i t h e u t r o p h i c a t i o n problems.  d a t a from a s p e c i f i c  southern  sediments.  these blooms  visibility  the r e c r e a t i o n a l v a l u e and  Stein  1967).  i n d u s t r i a l use  r e c e n t l y completed  of  Because o f the  area,  to d e t e r m i n e , i n p a r t ,  Figure 1. Location and watershed boundary of the Okanag Basin. Drainage divides between lake basins shown by dotted l i n e s .  7  present l e v e l s  and causes o f e u t r o p h i c a t i o n i n the Okanagan l a k e s  B r i t i s h Columbia Okanagan Agreement  1969).  p l a c e d on Skaha Lake, and p a r t i c u l a r l y  (Canada-  Major l i m n o l o g i c a l emphasis  complete d a t a was  collected  was  on the  m i x i n g regime, phosphorus l o a d i n g , s e d i m e n t a t i o n , phosphorus i n the water mass, and a l g a l b i o m a s s .  These d a t a form the base from which  this  model i s developed and v e r i f i e d .  B.  RESEARCH OBJECTIVES The o b j e c t i v e s o f t h i s r e s e a r c h a r e f o u r f o l d :  (1) t o d e s c r i b e  the p h y s i c a l , c h e m i c a l and b i o l o g i c a l p r o c e s s e s c o n t r o l l i n g the phosphorus c y c l e i n Skaha Lake; (2) to f o r m u l a t e a s i m u l a t i o n model which p r e d i c t s s e a s o n a l v a r i a t i o n s of t o t a l phosphorus i n the w a t e r mass; (3) to formul a t e a model which p r e d i c t s s e a s o n a l v a r i a t i o n s i n p h y t o p l a n k t o n mass; (4) t o f o r m u l a t e a model which p r e d i c t s  d i s s o l v e d oxygen  bio-  depletion  r a t e s i n the h y p o l i m n i o n . These o b j e c t i v e s a r e pursued i n t h e f o l l o w i n g s i x c h a p t e r s . Chapter I I d e s c r i b e s t h e water q u a n t i t y and q u a l i t y problems o f t h e Okanagan B a s i n , and the l i m n o l o g y o f Skaha Lake.  Emphasis  i s p l a c e d on n u t r i e n t  l o a d i n g and b i o l o g y . Chapter I I I d i s c u s s e s t h e r e l a t i o n s h i p between n u t r i e n t s  and  e u t r o p h i c a t i o n , and d e t a i l s the c o m p l e x i t y o f the phosphorus c y c l e i n lakes.  M o d e l l i n g approaches are e v a l u a t e d and the mass b a l a n c e method  is described.  I n Chapter IV the fundamental i n p u t - o u t p u t e q u a t i o n s f o r  the e p i l i m n i o n and h y p o l i m n i o n o f Skaha Lake a r e p r e s e n t e d . of each submodel  The  details  (eddy d i f f u s i o n , s e d i m e n t a t i o n , i n t e r n a l l o a d i n g , p r i m a r y  8  production, and hypolimnetic dissolved oxygen) are then discussed.  The  assumption of a strong r e l a t i o n s h i p between primary production and phosphorus sedimentation i n Skaha Lake i s stressed. In Chapter V the results of the model are presented and v e r i f i e d with Skaha Lake data on phosphorus concentration, a l g a l biomass, and hypolimnetic dissolved oxygen.  S e n s i t i v i t i e s of the major "forcing  functions" (phosphorus loading and hydrologic discharge) and of the physic a l - b i o l o g i c a l c o e f f i c i e n t s used i n submodels are analyzed.  Chapter VI  i s a discussion of i n t e r p r e t a t i o n s and l i m i t a t i o n s of the model; included i s an a p p l i c a t i o n of the r e s u l t s 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 a i d .  CHAPTER I I  THE OKANAGAN BASIN AND SKAHA LAKE  A.  THE OKANAGAN BASIN 1.  Water Q u a n t i t y and Q u a l i t y Problems The Okanagan B a s i n i n B r i t i s h Columbia i s p l a g u e d by w a t e r  problems o f b o t h 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 t h e r a i n s h a -  dow o f an o r o g r a p h i c 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 a n n u a l p r e c i p i t a t i o n as l o w as 25 cm a t O l i v e r ( K e l l e y and S p i l s b u r y 1 9 4 9 ) .  While the  3 2 average a n n u a l r u n o f f f o r B r i t i s h Columbia i s 118 m /hr/km , t h e n e t i n 3 2 f l o w t o Okanagan Lake i s 9.8 m /hr/km  (Marr 1970).  Even w i t h t h e l a r g e  s t o r a g e c a p a c i t y o f t h e l a k e s , a w a t e r s h o r t a g e i n t h e v a l l e y h a s a 10 p e r c e n t chance o f o c c u r r e n c e i n any y e a r because o f i r r i g a t i o n ments f o r 25,000 h e c t a r e s o f l a n d (Marr 1 9 7 0 ) .  require-  Great f l u c t u a t i o n s i n run-  o f f from one y e a r t o t h e n e x t have c r e a t e d a need f o r f l o o d c o n t r o l dams on t h e r i v e r s c o n n e c t i n g t h e 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 w a t e r l e v e l s t o be m a i n t a i n e d . The w a t e r q u a l i t y problems f o c u s m a i n l y around s i g n s o f 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  r e c e n t y e a r s (1968-71) e x h i b i t e d two blooms.per y e a r —  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 o r autumn.  Although  Osoyoos Lake has n o t e x h i b i t e d a l g a l blooms, s i g n s o f i n c r e a s i n g p h i c a t i o n a r e evident (Booth 1969).  eutro-  Okanagan L a k e , much l o n g e r and  deeper t h a n e i t h e r Skaha o r Osoyoos L a k e s , s t i l l appears t o be i n an oligotrophic  state.  9  10  2.  Geographical  Setting  The Okanagan B a s i n o c c u p i e s a 8100 P l a t e a u o f s o u t h e r n B r i t i s h Columbia  km  2  (Figure 1).  a r e a i n the The  Interior  central valley  w i t h i n the b a s i n i s a U-shaped t r o u g h w i t h a c h a i n of narrow, n o r t h south trending g l a c i a l l a k e s — ure 1).  Okanagan, Skaha, Vaseux and  Osoyoos  (Fig-  The v a l l e y bottom v a r i e s i n w i d t h 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 o f 275 m t o 2440 m i n the s u r r o u n d i n g mountains (Marr 1970).  3.  Geological History A c c o r d i n g t o S t . John (1973), t h e Okanagan V a l l e y i s a  t u r a l t r e n c h o v e r l y i n g a system  o f l i n k e d f a u l t s which s e p a r a t e  of l a t e P a l e o z o i c o r e a r l y M e s o z o i c  age.  strucbedrock  The e a s t s i d e o f Skaha Lake  i s u n d e r l a i n by Monashee metamorphic r o c k s and  later intrusives,  while  bedrock on the west s i d e c o n s i s t s o f a n d e s i t e and t r a c h y t e f l o w s and agglomerates  o f Eocene o r O l i g o c e n e age.  c o n t a c t between t h e s e bedrock  The  fault  t r a c e forming  the  t y p e s runs a l o n g the course o f McLean  Creek, an e a s t e r n t r i b u t a r y t o Skaha Lake ( S t . John 1973). The bedrock base of the Okanagan t r e n c h i s o v e r l a i n by i d a t e d sediments  unconsol-  p r i m a r i l y of g l a c i a l o r i g i n , which r e a c h a t h i c k n e s s o f  600 m i n the m i d d l e o f Okanagan Lake ( S t . John 1973). i n t h i c k n e s s under Skaha Lake from about  The  sediments  370 m n o r t h o f Kaleden  vary  ( F i g u r e 2)  to l e s s than 30 m a t the narrow p o i n t s e p a r a t i n g the l a k e ' s n o r t h and s o u t h b a s i n s . A c c o r d i n g t o S t . John, cene (one m i l l i o n y e a r s ago  i t i s p r o b a b l e t h a t d u r i n g the P l e i s t o -  to the p r e s e n t ) the v a l l e y was  a sedimentation  t r a p f o r m o r r a i n a l 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 sediments.  fluvial  inflow  F i g u r e 2. Bathymetry o f Skaha Lake; c o n t o u r i n t e r v a l 25 f t (from S t . John 1973). C i r c l e d numbers i n d i c a t e p e r i p h y t o n s t a t i o n s .  12  The g l a c i e r s began to recede somewhat before 10,000 years and Fulton (cited i n St. John 1973) advanced by 9750 B.P.  ago,  reports the recession to be well  (before present).  By 8900 B.P.  a l l of the i c e had  melted and the g l a c i a l lakes had been drained to the l e v e l of the e x i s t i n g lakes.  The clay and s i l t g l a c i o l a c u s t r i n e c l i f f s bordering southern Okana-  gan and Skaha Lakes were probably formed during the period of g l a c i a l recession when g l a c 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 g l a c i a l o r i g i n , while only a few tens of meters of sediment can be attributed to sedimentation stem lakes.  from the modem main-  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 l a n d s l i d e scars, and deposits on the lake bottom from these landslides are present 4.  (St. John 1973).  Hydrology The annual runoff into Okanagan Lake has been estimated to  vary between 0.099 km  3  i n 1929  to 0.918  km  3  i n 1948  (with a mean value  3 of  0.450 km  (Marr 1970).  To emphasize the a r i d condition of the area, 2  Marr has noted that the average net inflow from the 6060 km watershed amounts to a y i e l d of only 8.26  cm.  Okanagan Lake  The great v a r i a t i o n i n nat-  u r a l runoff has prompted the construction of dams at or below the o u t l e t s of a l l the mainstem lakes to c o n t r o l flow-through have a controlled l e v e l f l u c t u a t i o n of 1.3 for  rates.  The lakes  m or l e s s (Marr 1970).  now Except  6.4 km of natural channel below Vaseux Lake, s t i l l used as a spawning  area f o r 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 e s s e n t i a l to the water supply of the lakes.  Marr (1970) has  estimated that no runoff i s contributed from areas up to 900 m i n e l e vation, 25 cm i s contributed from areas at 1200 m, and 60 cm comes from areas at 1800 m.  3 The average annual inflow to Skaha Lake i s 0.474 km , r e s u l t i n g i n a t h e o r e t i c a l hydrologic turnover of 0.89/year (inflow/lake volume = 0.474/0.54).  Therefore, the t h e o r e t i c a l retention time of water i n the  lake (the r e c i p r o c a l 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 v o l ume.  Osoyoos Lake has a retention time of about 0.4 years. 5.  Water Use Marr reports that in.1966 i r r i g a t i o n accounted f o r the use of  3 0.178 km  of water.  Three-quarters of the i r r i g a t i o n water comes from  over 100 storage reservoirs located i n the uplands of the watershed (Russell and McNeil 1974, Marr 1970).  Marr (1970) indicates that the p o s s i b i l i t y of  further upland storage i s l i m i t e d and the source of large future demands must come i n the form of pumping from the mainstem lakes.  This i s one  important economic reason f o r concern about the water quality of the lakes.  3 Domestic use of water accounts f o r about 0.01 km , or l e s s than 10 per cent of a g r i c u l t u r a l consumption (Marr 1970). 6. C u l t u r a l Development and Associated Phosphorus Loading The Okanagan V a l l e y i s one of the fastest growing regions i n  14  B r i t i s h 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). estimated  By 1980  to reach 160,000, a 41 per cent increase from  Using estimates from Vollenweider (1973) have calculated that about 1.7 •now enters the lake system.  the population i s 1971.  (1968), Patalas and  kg/capita/year  Salki  of t o t a l phosphorus  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  e f f e c t on the water q u a l i t y of the lakes would, by most r a t i o n a l estimates, be extremely undesirable.  Patalas and S a l k i (1973) estimate that 88 to 90  per cent of the t o t a l phosphorus load to Skaha Lake i s associated with c u l t u r a l sources  (municipal sewage, a g r i c u l t u r e and i n d u s t r y ) .  If no measures were taken to remove phosphorus from effluent  be-  fore i t reached Skaha Lake, Patalas and S a l k i (1973) estimate that loading 2 w i l l nearly double between now year).  and 1990  (from 2.3 g/m  2 /year to 4.0 g/m  /  However, i f 80 per cent of the c u l t u r a l or c o n t r o l l a b l e 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 h a l f .  Patalas and S a l k i speculate that i f s i m i l a r phosphorus removal took place throughout the basin, the trend of trophic changes i n 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 moderate eutrophy.  15  B.  SKAHA LAKE 1.  Physical Limnology (a) The Lake Basin.  S i g n i f i c a n t physical c h a r a c t e r i s t i c s of the  lake basin are shown i n 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 d i s k ) , 1939  12 m  Maximum Transparency, 1971 Data from Blanton and Ng 1972  7m  16  A hypometric curve showing the r e l a t i o n s h i p between area and depth i s shown i n 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 e x i s t s  near the mouth of McLean Creek.  The f a c t that the southern basin i s  smaller i n surface area than the northern one and much shallower  (3.0 km 2 compared to 17.1 km 2 )  (mean depth of 15 m compared to 28 m) has important  p l i c a t i o n s for the r e l a t i v e b i o l o g i c a l p r o d u c t i v i t y of each basin.  im-  St.  John observes that the dual basin morphology provides a terrigenous s e d i ment trap s i t u a t i o n , with the northern basin accumulating  more terrigenous  material and the southern one more organic carbon. The phosphorus c y c l i n g model described i n Chapter IV considers each basin separately. (b) The Lake Sediments.  Core samples taken from the sediments i n -  dicate that t y p i c a l deep muds consist of 58.5 clay and 0.5 per cent sand (St. John 1973).  per cent s i l t , 41 per cent Some of the surface sediments  contain a predominance of sand, i n d i c a t i n g recent l a n d s l i d e s from lakeside cliffs.  St. John reports an average sedimentation  with an average annual net accumulation  rate of about 0.21  cm/year,  i n the past 100 years of 1.5 x 10^ kg  of m a t e r i a l . 2.  Chemical Limnology (a) Water Chemistry.  Table II shows representative v a r i a t i o n s i n  chemical c h a r a c t e r i s t i c s during the years 1968-71.  It i s important  that although hypolimnetic dissolved oxygen values l e s s than 2 mg/1  to note have been  recorded, the hypolimnion of Skaha Lake has not, at least during the four years for which data are a v a i l a b l e , 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  D i s s o l v e d Oxygen  <2 mg/1 t o s a t u r a t i o n  Hypolimnetic  Oxygen D e f i c i t  0.076 mg/cm /day 0 2  pH  8.1 t o 9.2  T o t a l Residue  102  Bicarbonate  38 to 115 mg/1  Silicate  0.4 t o 6.4 mg/1  2  t o 159 mg/1  Orthophosphate,  epilimnion  <0.002 t o 0.095 mg/1 (P)  Orthophosphate,  hypolimnion  0.006 t o 0.085 mg/1 (P)  Orthophosphate,  S p r i n g M i x i n g 1971  0.015 mg/1 (P)  T o t a l Phosphorus,  Epilimnion  0.007 t o 0.124 mg/1 (P)  T o t a l Phosphorus,  Hypolimnion  0.008 t o 0.104 mg/1 (P)  T o t a l Phosphorus,  Spring Mixing  1971  0.060 mg/1 (P)  Nitrate,  Epilimnion  <0.01 t o 0.02 mg/1  Nitrate,  Hypolimnion  <0.01 to 0.17 mg/1  Total Kjeldahl nitrogen,  Epilimnion  Total Kjeldahl nitrogen,  Hypolimnion  <0.01 t o 0.75 mg/1 0.08 t o 0.69 mg/1  *  Data from S t e i n and C o u l t h a r d 1971 , P a t a l a s and S a l k i 1973, and W i l l i a m s 1972.  Seasonal v a r i a t i o n s i n d i s s o l v e d oxygen and t o t a l phosphorus w i l l be d i s c u s s e d i n d e t a i l i n Chapter V.  19  (b) Sediment Chemistry.  S t . John (1973) r e p o r t s t h a t deep  sedi-  ments from t h e south b a s i n c o n t a i n 1.69 times g r e a t e r c o n c e n t r a t i o n s o f o r g a n i c c a r b o n than deep sediments f rom the south b a s i n i s p r o b a b l y  the north basin.  due t o two f a c t o r s :  The i n c r e a s e i n  (1) " d i l u t i o n " o f o r g a n i c  m a t t e r i n the n o r t h b a s i n by more t e r r i g e n o u s m a t e r i a l , and (2) g r e a t e r production  o f o r g a n i c m a t t e r by t h e s h a l l o w e r  south b a s i n .  show a sharp i n c r e a s e i n o r g a n i c c a r b o n i n the upper f i v e According  t o S t . John, t h i s f i v e c e n t i m e t e r s  of s e d i m e n t a t i o n ,  represents  Core p r o f i l e s centimeters.  about 23 y e a r s  which i s about the l e n g t h o f time sewage has been d i s -  charged i n s i g n i f i c a n t q u a n t i t y i n t o t h e l a k e .  A p a t i t e , m a i n l y i n the form Ca^Q (PO^)^ ( O H ^ , l a r g e p a r t i n Skaha sediment c o m p o s i t i o n ,  appears t o p l a y a  b o t h s u r f i c i a l l y and a t depth.  In t h e s u r f i c i a l sediments, an average of 70 p e r cent o f the phosphorus (by w e i g h t ) i s i n the form o f a p a t i t e ( W i l l i a m s 1973). t i t e probably  e n t e r s t h e l a k e when r a i n s erode t h e c l i f f s s u r r o u n d i n g t h e  l a k e , and t h i s p r o c e s s would proceed w i t h o r w i t h o u t John, p e r s o n a l has  Most o f t h e apa-  communication).  Williams  man's i n f l u e n c e ( S t .  a l s o assumes t h a t t h e a p a t i t e  a t e r r i g e n o u s o r i g i n from t h e watershed, and does n o t form as a r e s u l t  of c h e m i c a l  precipitation within the lake.  He f u r t h e r assumes t h a t a p a t i t e  p l a y s l i t t l e o r no r o l e i n t h e phosphorus c y c l e o f t h e l a k e because o f i t s v e r y 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 organisms.  The f a c t t h a t a p a t i t e i s c o n c e n t r a t e d  near the s h o r e l i n e and i n -  l e t s i s further indication of terrigenous o r i g i n .  Apatite increases  depth i n the sediment column, i n d i c a t i n g c o n v e r s i o n to a p a t i t e w i t h i n the sediment  ( W i l l i a m s 1973).  f o r aquatic  from o r g a n i c  William's  with  phosphorus  conclusion i s  20  supported by results showing that the increase i n apatite with depth i s matched by an approximately equal decline i n organic phosphorus. Adsorbed phosphorus  (inorganic phosphate ions associated  with sediment components having a high capacity to take up orthophosphate from s o l u t i o n by exchange with hydroxyl groups) average of 18 per cent of the phosphorus sediments (Williams 1973).  constitutes an  (by weight) i n the s u r f i c i a l  Williams concludes that i t i s l i k e l y  that  phosphorus adsorbed onto sediments remains e s s e n t i a l l y unaltered, and i s not involved i n conversion to apatite or regeneration to overlying waters.  The concentration of adsorbed phosphorus increases with  increasing water depth and distance from shore.  A decrease i n adsorbed  phosphorus concentration with depth i n the sediment i s probably due to loading increases i n recent years (Williams 1973). Organic phosphorus makes up an average of 12 per cent of the  phosphorus  (by weight) i n 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 i s converted into orthophosphate or soluble organic phosphorus and returns to the overlying water;  this amount, however,  i s small compared with loading of phosphorus from external sources. Within the sediments further breakdown of organic phosphorus to orthophosphate occurs, but the orthophosphate i s 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 t o t a l net sedimentation rate of 1.15 x lo7 kg/yr. mate  This e s t i -  i s a single one, and does not account f o r d i f f e r e n t sedimentation  rates i n d i f f e r e n t parts of the lake. age s u r f i c i a l concentrations  Combining t h i s estimate with aver-  of apatite, sorbed phosphorus and organic  phosphorus of 635 ppm, 177 ppm and 109 ppm respectively, Williams estimates the following annual sedimentation rates:  3.  apatite  7600 kg  sorbed phosphorus  2000 kg  organic phosphorus  1300 kg  Total  10900 kg  B i o l o g i c a l Limnology (a) Phytoplankton and Periphyton.  Phytoplankton have been measured i n  two ways, both of which are "standing stock" measurements and do not r e f l e c t p r o d u c t i v i t y (rate of growth). Table I I I shows a l g a l abundance during selected months i n 1969-70 i n c e l l s / m l (Stein and Coulthard 1971), with percentages of four a l g a l types.  The figures represent the average of samples taken from  four depths (surface to 18 m) i n 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 l a t e  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 i n both basins of the lake.  22  TABLE I I I ALGAL ABUNDANCE (algal  •k  counts i n c e l l s / m l )  A p r i l 1970 T o t a l Phytoplankton % % % %  IN SKAHA LAKE, 1969-70  June 1969  3100 **  Blue-Green A l g a e Green A l g a e Diatoms Phytoflagellates  2.3 4.1 40.3 42.2  J u l y 1969  Sept. :  **  76  2120  446  19.4 0 69.8 10.8  59.2 3.2 18.5 18.6  91.0 0.8 3.8 4.2  * For greens and b l u e - g r e e n s , a c h a i n o f 12-15 c e l l s = 1 a l g a l " c e l l " as shown i n T a b l e III.  ** a l g a l bloom  D u r i n g 1971 c h l o r o p h y l l a was m o n i t o r e d d i c a t e p h y t o p l a n k t o n biomass.  Monthly  i n s u r f a c e waters to i n -  sampling shows the f o l l o w i n g  vari-  a t i o n i n t h e n o r t h and south b a s i n s from May t o September ( W i l l i a m s 1972), indicated  i n T a b l e IV. TABLE IV PHYTOPLANKTON IN SKAHA LAKE, 1971 ( v a l u e s i n ug/1 c h l 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  o r d e r - o f - m a g n i t u d e i n c r e a s e i n l a t e September i n d i c a t e s a  l a r g e bloom, but  the dominant s p e c i e s r e s p o n s i b l e was  t a i l e d phytoplankton Periphyton Table V  data  i s presented  not  determined.  i n Chapter V.  ( a t t a c h e d a l g a e ) abundance d u r i n g 1971  f o r t h r e e s e c t i o n s o f the l a k e  (Stockner et al.  i s shown i n  1972a).  i s a t the extreme n o r t h and near the Okanagan R i v e r i n f l o w . on the e a s t e r n shore about midway i n the n o r t h b a s i n , and the south b a s i n near the o u t f l o w  De-  Station 1  Station 2 i s  station 3 is in  (Figure 2).  TABLE V PERIPHYTON IN SKAHA LAKE, ( v a l u e s i n ug/1  1971  c h l o r o p h y l l a)  APRIL  MAY  JUNE  JULY  AUGUST  SEPTEMBER  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  Station 1  While s t a t i o n s 2 and  3 show low p e r i p h y t o n growth, s t a t i o n 1  c a t e s v e r y pronounced growth d u r i n g J u l y and August. hypothesize  t h a t t h e low biomass a t s t a t i o n s 2 and  u t i l i z a t i o n o f n u t r i e n t s by p h y t o p l a n k t o n biomass a t s t a t i o n 1 may  3 may  populations.  et al.  (1972a)  be because o f High  i n d i c a t e t h a t p e r i p h y t o n p o p u l a t i o n s use a v a i l a b l e  n u t r i e n t s from the Okanagan R i v e r b e f o r e plankton.  Stockner  indi-  they can be taken up by the  phyto-  24  (b) Macrophytes.  Macrophytes grow i n 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 al.  1972b).  for photosynthesis (Stockner et  I The l i t t o r a l zone comprises about 3.2 km  cent of the surface area i n Skaha Lake.  2  or  17 per  Submergent macrophytes predomi-  nate i n the north end, whereas extensive beds of both emergent and submergent vegetation grow on the l i t t o r a l bench of the east and west shorel i n e s (Stockner et al. 1972b).  F l o a t i n g leafed plants and emergent vege-  t a t i o n occurs i n 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 s i g -  n i f i c a n t l y 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 a v a i l a b l e f o r phytoplankton growth i n Skaha (Stockner et al. 1972b).  This may be an important factor  in explaining the r e l a t i v e l y high trophic l e v e l of Skaha Lake. (c) Zooplankton. The crustacean plankton (copepods and cladocerans) were sampled i n 1969 by Patalas and S a l k i (1973).  Four species of copepods  and eight species of cladocerans were found, with Cyclops bicuspidatus Diaptomus ashlandi  dominant i n a l l three lakes.  and  Relative volumes of s e t t l e d 3  net  plankton i n Okanagan, Skaha and Osoyoos Lakes were 13, 19 and 26 mm  respectively.  The average number of crustacean zooplankton i n Okanagan  2 2 Lake was 188 individuals/cm , in' Skaha Lake 238 individuals/cm and i n 2 Osoyoos Lake 161 individuals/cm .  2 /cm  25  (d) F i s h . of salmonid in 1971  According to Northcote et al.  species to the f i s h stock of Skaha Lake was  than 1948  (4.6 per cent from 14.8  whitefish were much lower i n 1971 1948,  (1972), the contribution  than i n 1948;  only f i v e were netted in 1971.  17 were c o l l e c t e d i n 1971.  per cent).  considerably lower  Numbers of mountain  whereas 60 were netted i n  No carp were netted i n 1948, whereas  The apparent s h i f t i n species composition  from  salmonid and coregonine species to coarse f i s h i s an i n d i c a t i o n of increasing eutrophy (Larkin and Northcote 1969). The low average age of salmonids i n Skaha, Vaseux may  and Wood Lakes  be i n d i c a t i v e of advanced eutrophication (Northcote et al. 1972).  Lar-  kin and Northcote (1969) c i t e research i n Europe showing that the average age of coregonids gradually decreased  as eutrophication increased.  Four  f i s h a t t r i b u t e s used as eutrophication indices f o r the mainstem Okanagan lakes  ( r e l a t i v e abundance, average length, weight-length  lead Northcote et al.  and growth rate)  (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-  t i v e s o l i g o t r o p h i c , mesotrophic and eutrophic were used by Naumann (1932) and Thienemann (1931) to describe increasing l e v e l s of organic production i n lakes.  Figure 4 shows the trophic state (as described by annual phos-  phorus loading) of the Okanagan lakes compared with other lakes i n the world  (from Vollenweider  1968,  Patalas and S a l k i 1973).  Skaha Lake f a l l s  family of f i s h containing the whitefish and cisco (when these are not included i n the Salmonidae)  -  10.o-i  Eutrophic Lakes <  ^ Lake Norrviken (Sweden)  O  OSOYOOS  SKAHA  U.  o *3a. c-  < o < Z> z z <  •  I.OH  Greifensee — (Switzerland ) Pf dff ikersee — • ( Switzerland) .. • Moses ,Lake  Mesotrophic Lakes (I)  Baldeggersee (Switzerland) O Zurichsee ( Switzerland)  Lake Washington (U.S.A.) Lake Ontario ( U.S.A.) ^(Canada)* Lake Geneva Lake Malare (France'^witzerland ) .(Sweden) Lake MendotaQ Hallwillersee Lake Constance ( U.S.A.) (Switzerland) (Austria, Germany, Switzerland) Lake F u r e s r f ^ ' " (Denmark )||JJ Lake Annecy, • . . r T f l l l ! ^ t r a n c e -' ,Tiirlersee |( Switzerland ) L  a  (  k  C  e  a  E  n  o  d  r  i  a  e  )  1  yOligotrophic Lakes  11  50 100 500 MEAN D E P T H ( m ) Figure 4. Eutrophication of lakes i n the Okanagan Basin compared to other lakes i n Europe and North America (Patalas and Salki 1973). C r i t e r i a of annual phosphorus loading and mean depth from Vollenweider (1968, 1969) . Open c i r c l e s indicate loading estimates from Haughton et a l . 1974; black c i r c l e s indicate loading c a l 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. % 1  l  27  w e l l w i t h i n t h e c l a s s i f i c a t i o n o f 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 o v e r t u r n ) has been (1970) g r e a t e r than 0.03 mg/1 ( c r i t e r i a from V o l l e n w e i d e r 1968).  2 2. Phosphorus l o a d i n g i s g r e a t e r t h a n 0.5 g/m / y e a r , w h i c h i s c o n s i d e r e d t o be i n t h e "dangerous" l o a d i n g c a t e g o r y f o r a l a k e of Skaha's mean depth by V o l l e n w e i d e r (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 t h a n 0.05 mg/cm /day ( c r i t e r i a from H u t c h i n s o n 1957). 4. The minimum t r a n s p a r e n c y i s l e s s t h a n 2 m f r o m Beeton 1 9 6 5 ) .  (criteria  5. Salmonid f i s h s p e c i e s have d e c r e a s e d i n r e l a t i v e abundance s i n c e 1948 and have a low a v e r a g e age ( c r i t e r i a f r o m L a r k i n and N o r t h c o t e 1969). 6. C h l o r o p h y l l a v a l u e s i n d i c a t i n g p h y t o p l a n k t o n biomass have been g r e a t e r t h a n a s e a s o n a l range o f 5 - 140 mg/m (crit e r i a f r o m Sakamoto, c i t e d i n V o l l e n w e i d e r 1968). 7. Dominance of b l u e - g r e e n a l g a e and d i a t o m s i s e v i d e n t d u r i n g much o f t h e growing s e a s o n ( c r i t e r i a f r o m Sawyer 1973). The  c o n c l u s i o n s of  S t e i n and C o u l t h a r d (1971), S t o c k n e r  (1972),  and P a t a l a s and S a l k i (1971) f u r t h e r support t h e c l a s s i f i c a t i o n o f Skaha L a k e as m o d e r a t e l y 5.  eutrophic.  Paleolimnology According to Stockner  (1972),  c o r e s t a k e n 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 t o 1940.  The  most s i g n i f i c a n t change i n d i a t o m assemblages has o c c u r r e d i n t h e l a s t  25  y e a r s ( t h e u p p e r 7-8 cm of s e d i m e n t ) , w i t h diatoms i n d i c a t i v e o f e u t r o p h i c c o n d i t i o n s showing marked i n c r e a s e s i n r e l a t i v e abundance. cm  In t h e upper 8  of sediment t h e r e i s a s i g n i f i c a n t i n c r e a s e i n t h e d i a t o m  crotonensis  Fragilaria  ( i n d i c a t i v e of e n r i c h e d c o n d i t i o n s ) and a c o r r e s p o n d i n g  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 oligotrophic  conditions).  Stockner a t t r i b u t e s  italica  ( i n d i c a t i v e of  t h i s recent change i n  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 the f i r s t occurrence of blue-green a l g a l blooms.  corresponded with  CHAPTER I I I  PHOSPHORUS CYCLING IN LAKES AND  A.  EUTROPHICATION AND 1.  The  "Law  THE  MODELLING APPROACH  LIMITING NUTRIENT CONCEPT  o f t h e Minimum"  L i e b i g ' s "law o f the minimum" ( f i r s t s t a t e d by J u s t u s 1840)  Liebig in  e x p r e s s e s the i d e a t h a t the growth of a p l a n t i s dependent on  amount o f e s s e n t i a l n u t r i e n t p r e s e n t e d t o i t i n minimum q u a n t i t y . e v e r , work s i n c e L i e b i g ' s t i m e has  shown t h a t two  s a t i s f i e d bef ore t h e p r i n c i p l e can be a p p l i e d The  conditions  the How-  should  be  (Odum 1 9 7 1 ) .  f i r s t c o n d i t i o n i s t h a t the "law"  i s o n l y a p p l i c a b l e under  s t e a d y 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 e q u a l s n u t r i e n t  outflow.  Odum (1971) o b s e r v e s 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 w h i c h p r o d u c t i o n die-offs. may  R e l e a s e of d i s s o l v e d n u t r i e n t s upon d e c o m p o s i t i o n o f the  i n i t i a t e a n o t h e r bloom.  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 o v e r t i m e (Sawyer  (Vallentyne  1970;  the  phosphorus, n i t r o g e n , and  be o f o n l y academic i n t e r e s t .  element i n c u l -  A c c o r d i n g t o Odum  n o t be r e l e v a n t because c a r b o n d i o x i d e ,  o t h e r elements may  29  "carbon-  K u e n z e l 1969), w h i c h a t t e m p t s  t o d e c i d e w h i c h n u t r i e n t , c a r b o n o r p h o s p h o r u s , i s t h e key  (1972), t h e " e i t h e r / o r " argument may  nutrients,  1966).  I n v i e w o f 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,  t u r a l e u t r o p h i c a t i o n , may  algae  i n p u t o f n u t r i e n t s seldom e q u a l s o u t -  Because l a k e s a c t as n a t u r a l t r a p s f o r b o t h sediments and  phosphorus c o n t r o v e r s y "  and  The n u t r i e n t budget of a l a k e i s seldom, i f  ever, i n a steady s t a t e c o n d i t i o n — put.  o s c i l l a t e s between a l g a l blooms  r a p i d l y replace  each o t h e r  as  30  l i m i t i n g factors during the o s c i l l a t i o n .  For example, Goldman (1968)  found potassium, s u l f u r , and molybdenum to be most l i m i t i n g to growth in Castle Lake, C a l i f o r n i a . The second constraint which should be applied to Liebig's law i s that of "factor i n t e r a c t i o n . " The a v a i l a b i l i t y of a substance other than the minimum one may (Odum 1971).  modify the rate of u t i l i z a t i o n of the minimum one  Rodhe (1948) found that Asterionella  in a  phosphorus-limiting 3  culture medium showed no growth with an addition of 10 mg P/m phosphorus-limiting  , whereas i n  Lake Erken water the algae grew s i g n i f i c a n t l y with the  addition of only one mg P/m  (cited i n Hutchinson 1957).  Hutchinson specu-  lates that some material, possibly a peptide Influencing the rate with which phosphorus i s assimilated, i s lacking i n the culture media but i s present  i n the lake water. A complicating aspect of the concept i s that d i f f e r e n t phyto-  plankton populations  have d i f f e r e n t nutrient requirements.  maximum growth of Botryococcus  braunii  of 0.089 mg/1,  palea  while Nitzschia  For example,  occurs at a phosphorus concentration grows f a s t e s t at 0.018  mg/1  (Odum 1971).  Green f l a g e l l a t e s grow w e l l when nitrogen i s i n the form of urea, u r i c a c i d , and ammonia, while the diatom Nitschia  requires inorganic n i t r a t e for maximum  growth (Odum 1971). 2.  Relative Importance of Carbon, Nitrogen and Phosphorus (a) Carbon.  Carbon has several natural sources:  epilimnion waters  are u s u a l l y saturated with carbon dioxide from the atmosphere, and ates come from erosion material ubiquitous (Prince and Bruce 1972).  bicarbon-  i n v i r t u a l l y a l l drainage basins  In most lakes these natural sources alone are  cient to support the observed biomass.  suffi-  31  In a study of growth rates of Chlorella, with respect to carbon a v a i l a b i l i t y , Morton et al.  Microcystis  t  and Anabaena  (1972) conclude that  " i t i s very d i f f i c u l t to control growth by carbon dioxide c o n t r o l i n systems open to the atmosphere."  They report that the atmosphere i s an ade-  quate source of carbon dioxide (even i n the "absence of wind mixing) f o r depths to at l e a s t 1.7 m, permitting substantial a l g a l production.  Morton  et al. further report that n a t u r a l l y present bicarbonate can be u t i l i z e d by algae as a source of carbon, and can provide enough carbon f o r large a l g a l blooms. Mass balance carbon budget r e s u l t s from Lake E r i e indicate that the carbon supply from natural sources i s at l e a s t 25 times as much as the carbon from c u l t u r a l sources (Prince and Bruce 1972).  I t i s concluded  that the carbon from sewage would be completely i n s u f f i c i e n t to account for the observed biomass In Lake E r i e . (b) Nitrogen.  Nitrogen enters lakes from a v a r i e t y of n a t u r a l and  c u l t u r a l sources, and has been shown i n a number of cases to be one of the important l i m i t i n g nutrients.  If s u f f i c i e n t phosphorus i s i n the water at  the time of spring overturn before growth begins, i t has been shown that nitrogen can become a l i m i t i n g f a c t o r l a t e r i n the summer (Prince and Bruce 1972).  Based on a study of 17 lakes i n Wisconsin, Sawyer (1967) concludes  that at l e a s t 0.3 mg/1  inorganic nitrogen plus at l e a s t 0.015 mg/1  phosphate are necessary at the time of spring mixing to stimulate  inorganic algal  blooms l a t e r i n the season. Goldman (1968) reports that a sequence of l i m i t i n g nutrients ranged from magnesium i n the spring to nitrogen i n the summer to phosphorus i n 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 p o s i t i v e l y to almost any a d d i t i o n of nutrients, but the community as a whole w i l l tend to share some common d e f i c i e n c i e s . " Nitrogen has s p e c i a l c h a r a c t e r i s t i c s (compared to phosphorus) which l i m i t i t s usefulness as a c o n t r o l l i n g nutrient i n c u l t u r a l eutrophication.  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 ^ the control of t h i s source d i f f i c u l t . blue-green alga Anabaena azolla small Danish lakes.  Olsen (1970) reports that the  can f i x up to 95 kg N/ha i n one summer i n  B i l l a u d (1966) reports that some species of Anabaena  i n Alaskan lakes f i x nitrogen accounting at the peak of the growing season. dium can also f i x nitogen i n lakes. denitrifioans)  dissolved i n lake water makes  f o r 50 per cent of the a s s i m i l a t i o n  Bacteria such as Azotobaater  and  Clostri-  D e n i t r i f y i n g bacteria (e.g., Pseudomonas  can convert n i t r a t e s 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 q u a n t i f i c a t i o n of the nitrogen c y c l e . The high s o l u b i l i t y of n i t r a t e i n ground water causes leaching of n i t r a t e into lakes.  This input comes from a g r i c u l t u r a l sources and septic  tanks i n 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 a v a i l a b l e showing a d i r e c t relation-r  ship between phosphorus (usually accompanied by nitrogen as well) and a l g a l growth (Stockner 1972).  The Lake Washington case (Edmondson 1970) i s a  s t r i k i n g example of an extremely high c o r r e l a t i o n between phosphate concent r a t i o n at spring mixing and summer a l g a l biomass for 30 years of observations.  Edmondson's r e s u l t s show c l e a r l y that the c o n t r o l l i n g factor  in eliminating the lake's eutrophication problems was the reduction (by  33  about 50 per cent) of phosphorus loading. The e f f e c t s of removal of phosphorus from sewage show that phosphorus can be the most important nutrient l i m i t i n g a l g a l growth. reports (using Selenastmm  Maloney  as a test organism) that re-addition of phosphate  to " t e r t i a r y e f f l u e n t " (secondary e f f l u e n t with the phosphorus removed) at l e v e l s of 0.02, 0.04 and 0.06 mg P / l resulted i n c e l l counts of 213,000/ml, 314,000/ml and 644,000/ml,respectively, a f t e r 14 days of growth (cited i n Vallentyne 1970).  The t e r t i a r y e f f l u e n t without any added phosphorus showed  a growth of only 3,700 c e l l s / m l .  Vallentyne concludes that "there i s . . .  no question about the effectiveness of sewage treatment f o r phosphate r e moval i n terms of reducing a l g a l growth." Phosphorus was shown to be the most important l i m i t i n g f a c t o r i n the production of the green alga Cladophora  i n the Great Lakes (Neil and  Owen 1964). Decreases i n carbon, nitrogen and phosphorus i n 46 Swiss lakes during the growing season are related to i n i t i a l concentrations of the same elements i n the spring (data published by Thomas 1970 and analyzed by Vollenweider 1970, cited i n Prince and Bruce 1972).  Significant corre-  l a t i o n 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 c o r r e l a t i o n i s reported f o r phosphorus a v a i l a b i l i t y and phosphorus decrease.  Cross-correlation analyses show high  c o r r e l a t i o n 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 i n s i g n i f i c a n t or very low correl a t i o n 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 s 1  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 o l i g o t r o p h i c to  highly eutrophic), and that phosphorus i s the key nutrient governing the production of algae i n these lakes. In the lakes of the world i n which nutrients have been related to production,  i t can be concluded that "phosphorus i s most frequently the  l i m i t i n g element, followed  i n order of decreasing  importance by nitrogen  and carbon" (Prince and Bruce 1972).  B.  THE PHOSPHORUS.CYCLE IN LAKES Ponds and lakes are e s p e c i a l l y u s e f u l f o r the quantitative study  of nutrient c y c l i n g because the i n t e r a c t i o n s are r e l a t i v e l y self-contained over short periods of time.  Although he exaggerated the "closed system"  properties of lakes, Forbes i n 1887  appreciated  ". . .forms a l i t t l e world within i t s e l f —  the idea that a lake  a microcosm within which a l l  the elemental forces are at work and the play of l i f e goes on i n f u l l , but on so small a scale as to bring i t e a s i l y within the mental grasp." The exponential  increase i n knowledge of the phosphorus cycle i n the l a s t  25 years i s summarized by Hutchinson (1969): "It became apparent (Hutchinson 1941) that i n 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, i n 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 a f t e r 1945 made the d e t a i l e d i n v e s t i g a t i o n of t h i s kind of cycle possible (Hutchinson and Bowen 1947, 1950; C o f f i n et al. 1949; Hayes et al. 1952) and culminated i n R i g l e r ' s extraordinary discovery (1956, 1964) that the turnover time of i o n i c phosphorus i n the epilimnion of a lake i n summer can be of the order of 1 minute."  35  1.  Phosphorus The  phosphorus:  " t o t a l phosphorus" d e t e r m i n a t i o n c o n s i s t s o f t h r e e types o f s o l u b l e orthophosphate  o r g a n i c phosphorus phorus.  Compartments i n Lake Water  ( s o l u b l e r e a c t i v e phosphorus);  ( s o l u b l e u n r e a c t i v e phosphorus); and p a r t i c u l a t e  D e f i n i t i o n s o f t h e s e types and t h e i r s i g n i f i c a n c e  cycle are discussed  i n this  (a) Orthophosphate form o f phosphorus  soluble  i n t h e phosphorus  section. Phosphorus  ( S o l u b l e R e a c t i v e Phosphorus).  i s assumed t o be t h e s o l u b l e , i n o r g a n i c p o r t i o n  and i s t h e form i n which  phos-  32 P occur.  isotopes such as  Experiments  the c y c l i n g o f r a d i o a c t i v e phosphorus measure t h i s compartment  This  (PO^, ) , involving  (Rigler  1973).  -3 Orthophosphate,  o r PO^ , i s g e n e r a l l y assumed t o be the q u a n t i t y measured  when m e m b r a n e - f i l t e r e d water  (0.45 u f i l t e r )  i s a n a l y s e d by one o f the molyb-  denum b l u e t e c h n i q u e s . . However, R i g l e r p o i n t s o u t t h a t o r t h o p h o s p h a t e i s p r o b a b l y g r o s s l y o v e r e s t i m a t e d by u n i v e r s a l l y - u s e d a n a l y t i c a l t e c h n i q u e s f o r the f o l l o w i n g reasons:  (1) f i l t r a t i o n might  phosphates-phosphorus filtrate;  o r r e a d i l y h y d r o l y s e d phosphate  (2) a c i d i f i c a t i o n  l y s e f r e e phosphate  damage d e l i c a t e a l g a l c e l l s and r e l e a s e esters into the  o f the sample w i t h s u l f u r i c _3  e s t e r s and r e l e a s e PO^  phates o r from c o l l o i d a l i r o n phosphate;  a c i d c o u l d hydro-  from f u l v i c a c i d - m e t a l phos-  (3) a r s e n i c i s one o f the elements _3  t h a t can i n t e r f e r e s e r i o u s l y w i t h t h e c o l o r i m e t r i c d e t e r m i n a t i o n o f PO^ the molybdenum b l u e t e c h n i q u e .  R i g l e r concludes that  in  there i s considerable  e v i d e n c e s u g g e s t i n g t h a t c h e m i c a l l y d e t e r m i n e d orthophosphate i s much -3 -3 g r e a t e r than a c t u a l PO^ and assumes t h a t " t h e PO^, compartment i s v e r y s m a l l and cannot be measured c h e m i c a l l y . " This unfortunate f a c t leads  36  Rigler to conclude that severe l i m i t a t i o n s must be imposed on the i n t e r -3 pretation of tracer r e s u l t s 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 i n question. The s i z e of the orthophosphate compartment  i s 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 f i v e to eight per cent of the t o t a l phosphorus was orthophosphate. (b) Soluble Organic Phosphorus.  This portion of the phosphorus  content of water has, by most i n v e s t i g a t o r s , 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 microns) water i s analyzed a f t e r being digested with an o x i d i z i n g acid s o l u t i o n (Rigler 1973).  In 1964 R i g l e r found that nine lakes In Ontario presumably  had 12 to 32 per cent of the t o t a l phosphorus i n the form of soluble organic phosphorus. However, more recent evidence demonstrates that current a n a l y t i c a l methods do not adequately separate organic and p a r t i c u l a r phosphorus (Rigler 1973).  R i g l e r prefers to refer to this compartment  as "soluble unreactive  phosphorus," arguing that a n a l y t i c a l techniques cannot s u f f i c i e n t l y d i s t i n g u i s h between soluble organic and p a r t i c u l a t e phosphorus. (c) P a r t i c u l a t e Phosphorus.  This compartment  i s equal to the  t o t a l phosphorus value minus the soluble phosphous determination.  Accord-  ing to Rigler (1973) , the o r i g i n a l assumption by early workers that a l l p a r t i c u l a t e phosphorus i s associated with large plankton and trypton ( i n -  37  organic p a r t i c u l a t e phosphorus) must be rejected.  P a r t i c u l a t e phosphorus  i s associated with p a r t i c l e s ranging i n size from large zooplankton (and f i s h ) down to c o l l o i d s , and the choice of a 0.45 micron f i l t e r to separate p a r t i c u l a t e and "soluble unreactive" phosphorus i s quite a r b i t r a r y .  Rigler  maintains that much of the "soluble unreactive" part i s i n p a r t i c l e s less than 0.1 micron and much i s c o l l o i d a l , but perhaps only a small f r a c t i o n i s i n solution. In 1964 Rigler found that nine Ontario lakes had 62 to 83 per cent of the t o t a l phosphorus i n the form of p a r t i c u l a t e phosphorus. (d)  Total Phosphorus.  This compartment i s measured when an un-  f i l 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 i s c o l l e c t e d .  While the assumption that the measurement  includes phosphorus i n phytoplankton i s r e l a t i v e l y v a l i d , a s i m i l a r assumpt i o n f o r zooplankton i s questionable.  At times, a s i g n i f i c a n t f r a c t i o n  epilimnetic phosphorus may be i n the form of zooplankton (Riger 1973). Because zooplankton exhibit pronounced horizontal d i s t r i b u t i o n patterns ("patchiness") as well as d a i l y 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 a t d i f f e r e n t times of the day (Rigler 1973).  I t i s not surprising that t o t a l  phosphorus i n the trophogenic layer can f l u c t u a t e 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 i n a 50 ml water sample would increase the t o t a l phosphorus of the sample by 4 Mg/1, very s i g n i f i cant when the t o t a l phosphorus averaged 14 yg/1 (cited i n R i g l e r 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 i s perhaps the least r e l i a b l e and t o t a l phosphorus perhaps the most. 2.  Turnover Rates of Orthophosphate Measurement of the phosphorus f l u x rate i n lakes i s the best  method a v a i l a b l e f o r study of the c y c l i n g a c t i v i t y of phosphorus. qy (1960) states the argument i n t h i s  Pomer-  way:  "Measurement of the concentration of dissolved phosphate i n natural waters gives a very l i m i t e d i n d i c a t i o n 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 phosphate i n the system may be i n s i d e l i v i n g organisms at any given time, yet i t may be overturning every hour with the r e s u l t that there w i l l be a constant supply of phosphate f o r organisms able to concentrate i t from a very d i l u t e solution. Such systems may remain stable b i o l o g i c a l l y for considerable periods i n the apparent absence of a v a i l a b l e phosphate. The observations presented here suggest that a rapid f l u x of phosphate i s t y p i c a l of highly productive systems, and that the f l u x rate i s more important than the concentration i n maintaining high rates of organic production." The concept of "turnover" i s a useful one f o r comparing exchange rates of phosphorus between d i f f e r e n t compartments of an ecosystem such as a lake.  A f t e r equilibrium has been reached, the "turnover r a t e " i s the  f r a c t i o n of the t o t a l amount of phosphorus i n a component which i s released (or which enters) i n a given time period.  "Turnover time" i s the r e c i p r o -  c a l of the turnover rate, or the time required to remove the phosphorus content of the considered compartment i n the absence of other t r a n s f e r r a l mechanisms.  A hypothetical exchange between two compartments i n a lake  w i l l i l l u s t r a t e the  concept:  39  dissolved °4 i n water P  10  Ug/1  5 yg/1  • day  4 yg/1  • day  P in phytoplankton 20  yg/1  I n t h i s example the " t u r n o v e r r a t e " between the d i s s o l v e d P0~^ and p h y t o p l a n k t o n  compartment (due  i s 5 yg/1 • day exchange * 10 yg/1  t o u p t a k e by a l g a e and  compartment  consequent growth)  i n the water compartment = 0.5/day.  " t u r n o v e r t i m e " i s the r e c i p r o c a l of 0.5,  The  or two d a y s , w h i c h i s e q u a l t o the  -3 time necessary  f o r a c o m p l e t e t u r n o v e r o f t h e PO^  i n the water.  Now,  if  we l o o k a t t h e o p p o s i t e pathway i n w h i c h 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  compartment, t h e t u r n o v e r r a t e i s 4/20  PO. 4  = 0.2/day, w i t h a t u r n o v e r t i m e o f  f i v e days. Turnover t i m e s between v a r i o u s phosphorus compartments a r e c i t e d i n T a b l e VT> . and a s i m p l i f i e d s c h e m a t i c o f t r a n s f o r m a t i o n s i s  _3 shown i n F i g u r e 5.  The t u r n o v e r t i m e o f 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 o f temperate l a k e s from o l i g o t r o p h i c t o e u t r o p h i c , and l a i n 1968, ing  i n d y s t r o p h i c and bog l a k e s (Chamber-  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 m i n u t e s  summer s t r a t i f i c a t i o n  ( R i g l e r 1973).  dur-  This f l u x i s indicated i n Figure  -3 5 as b e i n g between the s o l u b l e i n o r g a n i c PO^ compartments.  and  phytoplankton-bacteria  R i g l e r n o t e s t h a t s i m i l a r t u r n o v e r t i m e s can be  expected  d u r i n g the p r o d u c t i v e p e r i o d i n l a k e s t h a t have a h i g h r a t i o o f p a r t i c u l a t e phosphorus:orthophosphate. winter  The  considerably longer turnover  time i n  (around one day) can be a t t r i b u t e d to d e c r e a s e d t e m p e r a t u r e , i n c r e a s e d  40  TABLE  VI  TURNOVER TIMES OF PHOSPHORUS FLUX BETWEEN COMPARTMENTS  ORIGINAL COMPARTMENT  Soluble  Soluble  RECEIVING COMPARTMENT  inorganic P (summer) (winter)  phytoplankton  inorganic  soluble  P  bacteria  littoral  TURNOVER TIME  and  0.9  -  REFERENCE  7.3 minutes  Rigler  1964  <30 u 7 minutes 0 . 2 days  organic P vegetation  0.09  days  (Sphagnum) l i t t o r a l vegetation  0.34  days  7 days  R i g l e r 1964 Hayes and P h i l l i p s 1958  (Eriaaulon) l i t t o r a l vegetation and s e d i m e n t s l i t t o r a l sediments Soluble organic P Particulate P  soluble inorganic l i t t o r a l fauna  P  (mussels) deep-water sediments H II  P h y t o p l a n k t o n <30 u Zooplankton (excretion) L i t t o r a l vegetation  soluble  II II  inorganic P  5.4 2.7  1 7 . 0 days  days  0.2  days  2.5  days  C o f f i n et al. 1949 H a y e s et al. 1952 Hayes and P h i l l i p s 1958 it  Kuenzler  H  1961  50 d a y s 100 d a y s 40 - 7 1 d a y s 2.2 days 2 . 1 days  Hutchinson 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  3  Hayes and P h i l l i p s 1958  days  (Erioaulon) Littoral vegetation  3.5  (Sphagnum) Sediments i n u n s t r a - ' t i f i e d lake " " (no b a c t e r i a ) " " (with b a c t e r i a )  39 - 176 d a y s 1 5 . 5 days 3.6 days  days  C o f f i n et al. 1949 Hayes and P h i l l i p s 1958  41  0.2  days-  3-8daysPhytoplankton and bacteria EPILIMNION  2 days JL Zooplankton (herbivores and carnivores) 3-7 weeks  HYPOLIMNION  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  c o n c e n t r a t i o n of orthophosphate and  to the reduced  biomass o f  plankton  ( R i g l e r 1973). -3 The  r e t u r n o f PO^  form i n water i s m a i n l y due phytoplankton;  from the b i o t i c p o o l to the d i s s o l v e d o r t h o t o t h r e e mechanisms:  (2) e x c r e t i o n by z o o p l a n k t o n :  and  (1) d i r e c t  r e l e a s e by  (3) enzymatic h y d r o l y s i s  of o r g a n i c phosphorus compounds e x c r e t e d by organisms o r produced by decompo s i t i o n o f dead p l a n k t o n  ( R i g l e r 1973).  n o t been measured w i t h s u f f i c i e n t d i r e c t r e l e a s e by  While the t h i r d mechanism  s o p h i s t i c a t i o n to determine a  s m a l l p l a n k t o n has been e s t i m a t e d  has  flux,  from t h e r a t e of r e -  32 lease of hr  P from s e s t o n  (suspended p a r t i c u l a t e m a t t e r ) as a v e r a g i n g  ( t u r n o v e r time o f 53 hours or 2.2  zooplankton tude (0.02  has been e s t i m a t e d hr  - 1  )  d a y s j R i g l e r 1973).  0.019  E x c r e t i o n by  from g r a z i n g r a t e s t o be of s i m i l a r magni-  to the r e l e a s e by  small plankton  (Haney 1970,  R i g l e r 1973).  R i g l e r f e e l s t h a t most of the phosphorus e x c r e t e d by z o o p l a n k t o n i s u l t i -3 m a t e l y r e g e n e r a t e d as PO^ , a l t h o u g h a p a r t o f i t may be e x c r e t e d i n o r g a n i c phosphorus compounds. The  s o l u b l e o r g a n i c compartment  (referred  u n r e a c t i v e phosphorus") a c t u a l l y c o n s i s t s of two the r e l a t i o n s h i p of the l a r g e r subcompartment  subcompartments, but  (particle  the c y c l e i s u n c l e a r , F i g u r e 5 shows i t t o be one o r g a n i c and  to by R i g l e r as " s o l u b l e  s i z e 0.1  compartment.  because  - 0.45u) to The  soluble  i n o r g a n i c compartments appear t o exchange phosphorus about  two  -3 o r d e r s of magnitude slower ments, and  Hayes and  R i g l e r notes  than  Phillips  the PO^  and  phytoplankton-bacteria  (1958) r e p o r t a t u r n o v e r  time of f i v e  comparthours.  t h a t the p h y s i c a l - c h e m i c a l n a t u r e o f t h i s compartment i s  l a r g e l y unknown, as i s i t s f u n c t i o n i n the phosphorus economy of the  still tropho-  g e n i c l a y e r . While some of the s o l u b l e o r g a n i c f r a c t i o n i s u n d o u b t e d l y  utilized  43  d i r e c t l y f o r b i o l o g i c growth, the quantity and rate have not been ascertained. Phytoplankton of a size greater than 30y are pictured by R i g ler  (1973) as comprising a large compartment through which phosphorus  cycles r e l a t i v e l y slowly (no rates are given) and from which phosphorus i s l a r g e l y regenerated by decomposition. -3 Movement between the PO^ compartment and l i t t o r a l vegetation i s r e l a t i v e l y 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). P a r t i c u l a t e organic phosphorus i n the form of dead plankton c e l l s sediments to the bottom of lakes at rates  of between 1.0 and  2.5  per cent/day, r e s u l t i n g i n turnover times of between 40 and 100 days (Hutchinson 1941, R i g l e r 1956, Gachter  1968).  The return of phosphorus from the sediments  (or " i n t e r n a l load-  ing") i s an extremely important key to understanding the eutrophication process, and w i l l be dealt with i n considerable d e t a i l i n the section on i n t e r n a l loading.  It w i l l simply be noted here that the turnover time of  t h i s f l u x can vary from days to weeks or longer. of the f l u x between sediment mud  Laboratory measurement -3  (with bacteria) and P0^  i s reported by  Hayes and P h i l l i p s (1958) to be about three days i n both d i r e c t i o n s .  With  no bacteria present, the exchange between the sediment and the water was slowed to 15 days. _3 The importance of bacteria i n determining rates of PO^ i n aquatic ecosystems should not be underestimated.  exchange  Rigler (195 6) surmised  that bacteria might be the primary cause f o r rapid turnover times between  44  plankton and water and noted that they compete very e f f e c t i v e l y with algae _3 for PO^  .  Rhee (1972) studied the competition for phosphates between a  bacterium species (Pseudomonas) found that a l g a l growth was  and an a l g a l species (Scenedesmus),  He  severely limited i n the presence of b a c t e r i a ,  but the growth of bacteria was hardly affected by algae. growth rate of bacteria accounted for the suppressed  The  faster  growth of algae i n  mixed cultures. 3.  The Lake as a P r o d u c t i v i t y Chamber The contrast between biomass and p r o d u c t i v i t y (rate of growth)  i s a very important one for aquatic ecosystems, and stresses the importance of turnover rate i n determining organic growth.  Ketchum (1967) states the  contrast i n t h i s way f o r the marine environment: " I t has been estimated by Ryther (1960) that the plant biomass i n the oceans i s only 0.1% of the t o t a l plant b i o mass on earth, but that t h i s small population contributes 40% of the annual world production of organic matter. The large production which r e s u l t s from such a small standing crop i n the marine environment i s an i n d i c a t i o n of the r a p i d i t y of the turnover of the population. P r a c t i c a l l y a l l of the photosynthesis of the sea i s carried on by microscopic plants which can, under i d e a l conditions, double their population size d a i l y . In contrast to t h i s i t takes 50 years or more to develop a f o r e s t (90.5% of the earth's biomass) and the rate of annual production (25% of the t o t a l ) i s a small f r a c t i o n of the standing crop at any one time." The t o t a l reserve of phosphorus i n a body of water ( i . e . , the quantity of soluble, p a r t i c u l a t e , sestonic, and accessible sedimented phosphorus), i s a pertinent gross parameter because i t indicates the ultimate capacity for biomass synthesis (Stumm and Stumm-Zollinger 1972). authors note that s t o i c h i o m e t r i c a l l y 1 mg of phosphorus w i l l y i e l d  The (on the  45  average) about 100 mg o f a l g a l biomass, which e x e r t s a b i o c h e m i c a l demand o f a p p r o x i m a t e l y 140 mg.  T h i s means t h a t secondary sewage e f f l u e n t  which c o n t a i n s 3-8 mg phosphorus/1 c a n y i e l d 300-800 mg/1 o r g a n i c i n the p r o d u c t i v e  C.  oxygen  environment of a e u t r o p h i c  matter  l a k e such as Skaha.  MODELLING APPROACH Modelling  t h e phosphorus budget and p h y t o p l a n k t o n growth i n a  l a k e i s a s i m u l a t i o n problem. processes  Simulation  o f the p h y s i c a l and b i o l o g i c a l  i n a l a k e has two major g o a l s , one t h e o r e t i c a l and one p r a c t i c a l :  (1) t h e model i n c r e a s e s u n d e r s t a n d i n g of how the l a k e f u n c t i o n s , and (2) the model e n a b l e s p r e d i c t i o n o f e u t r o p h i c a t i o n problems as a response t o varying nutrient inputs. aim  M a t h e m a t i c a l programming, which has the s p e c i f i c  o f maximizing or minimizing  an o b j e c t i v e f u n c t i o n s u b j e c t  i s n o t a p p l i c a b l e t o t h i s problem. made on a minimum s t a n d a r d techniques 1.  At a l a t e r  to c o n s t r a i n t s ,  stage when a d e c i s i o n must be  o f water q u a l i t y w i t h minimum c o s t ,  optimization  may be q u i t e u s e f u l .  Simulation  Modelling  In the s i m u l a t i o n o f a complex system such as a l a k e , i t i s n e c e s s a r y t o make a r e a s o n a b l e model i s too simple,  compromise between s i m p l i c i t y and r e a l i t y .  i t may n o t be a u s e f u l a b s t r a c t i o n o f n a t u r e .  I f the If i t  i s t o o complex and i n c l u d e s too many v a r i a b l e s , more d a t a a r e r e q u i r e d are  a v a i l a b l e . Excessive  complexity  burdens c o m p u t a t i o n a l f a c i l i t i e s as w e l l  as t h e human mind i n the i n t e r p r e t a t i o n o f c a u s a l and M c N e i l accuracy  than  interactions.  As R u s s e l l  (1974) s t a t e , ". . .the aim i s t o produce r e s u l t s o f a c c e p t a b l e  w i t h models o f minimum, c o m p l e x i t y . "  46  C o n s i d e r i n g the e n t s , sediments and and  immense c o m p l e x i t y o f i n t e r a c t i o n s between n u t r i -  b i o t a i n a l a k e , and  the  measuring these i n t e r a c t i o n s , i t i s not  amount of r e a l i s m must be applied  sacrificed.  d i f f i c u l t y of i d e n t i f y i n g s u r p r i s i n g that a c e r t a i n  Walters  (1971) o b s e r v e s t h a t  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 g o a l ,  g e n e r a l i t y are  often  sacrificed for precision.  some degree of p r e c i s i o n the n u t r i e n t f y i n g assumptions must be made.  The  in  realism  In o r d e r to p r e d i c t  relationships within detailed discussion  a lake,  o f the  and with  simpli-  submodels  a m p l i f i e s t h e n a t u r e o f the assumptions made i n t h i s model. (a) Time S c a l e .  The  next s t e p i n model b u i l d i n g  the  time s c a l e t o be  For  i n i t i a l modelling of phosphorus c o n c e n t r a t i o n  it  c o n s i d e r e d , and  r e s o l u t i o n of  i s u s e f u l t o l o o k a t a time span of one  model.  a l g a e i n the  and  predicted  lake,  and  alization  (a l o n g  time s c a l e  r e s u l t i n g a l g a l growth, the  phosphorus  refined u n t i l  actual  time i n t e r v a l ) .  t h i s i n t e r v a l i s too (and  too  cycle short  (a s h o r t  While i t has  time i n t e r v a l ) and  been shown i n the  are  gener-  previous  i n minutes between some compartments i n f o r p r a c t i c a l use  e x p e n s i v e i n computer t i m e ) .  a month) i n t e r v a l would be  of a l g a l m e t a b o l i s m  (or time i n t e r v a l ) i s another com-  between d e t a i l  s e c t i o n t h a t phosphorus can  f o r years  scale.  y e a r i n o r d e r to v e r i f y  the model p r o g r e s s i v e l y  of the  promise, i n t h i s i n s t a n c e  (twice  time  v a l u e s agree r e a s o n a b l y w e l l .  Resolution  a lake,  and  the  Model r e s u l t s are compared w i t h a c t u a l measurements of  and  run  the  i s to d e c i d e  i n a model which w i l l A weekly or  bi-weekly  s a t i s f a c t o r y , except t h a t most c o e f f i c i e n t s  e x p r e s s e d i n the  T h e r e f o r e , a compromise i n t e r v a l of one  l i t e r a t u r e i n u n i t s per  day  i s chosen.  day.  47  (b) Approach  to Mathematical Statement of Relationships.  Two  basic mathematical approaches have been used i n modelling e c o l o g i c a l systems:  (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 i n ecolog i c a l 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 b i o l o g i c a l processes have v a r i a b l e s which do not have continuous, but rather d i s c r e t e values. The only p r a c t i c a l approach i n 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 d a i l y changes i n volume occurring during the  spring s t r a t i f i c a t i o n and autumn d e - s t r a t i f i c a t i o n processes cannot be p r a c t i c a l l y described by a d i f f e r e n t i a l equation, and are more accurately represented by a difference equation.  Difference equations have the advant-  age of being clearer to understand, making the p o s s 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 f o r the equations i n t h i s model.  With t h i s form computations are  performed f o r each time i n t e r v a l according to the following r e l a t i o n s h i p (adapted from Walters 1971):  value of variables now  statement of relationships or rules f o r change  value of variables a f t e r one time period  48  The e s s e n c e o f t h i s t y p e o f systems model i s t h e " s t a t e m e n t of r e l a t i o n s h i p s " or  " r u l e s f o r change" w h i c h d e f i n e t h e way v a r i a b l e s w i l l change  1971).  (Walters  W i t h t h e s e r u l e s i n c o r p o r a t e d i n t h e i n p u t s and o u t p u t s , t h e way  i n w h i c h e a c h v a r i a b l e w i l l change e a c h day can be shown as f o l l o w s  (adapted  from W a l t e r s 1971):  new v a l u e of v a r i.a b, l,e c  =  o l d value o f v a r .i aib_ l, e  +  c  inputs  - o u t p*u t s  With the use o f t h i s input-output format, the problem o f d e v e l o p i n g a systems model i s reduced t o c h o o s i n g r e a s o n a b l e ways t o e x p r e s s t h e change o f t h e i n f l o w s and o u t f l o w s o f t h e system o v e r t i m e ( W a l t e r s 1 9 7 1 ) . Other s e c t i o n s o f t h i s c h a p t e r d i s c u s s t h e d e t a i l s o f t h e s e 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 t h e Phosphorus C y c l e Two b a s i c approaches have been used i n m o d e l l i n g t h e phosphorus  c y c l e i n a q u a t i c systems: (a) t h e "compartment" a p p r o a c h ; and (b) t h e "mass balance" approach. (a)  The Compartment A p p r o a c h .  T h i s a p p r o a c h uses r a d i o p h o s p h o r u s  32 t r a c i n g data (  P) as i t s b a s i s , and emphasizes t h e r a t e o f movement o f  phosphorus between t h e compartments, as d i s c u s s e d i n t h e s e c t i o n on phosphorus c y c l i n g and shown i n F i g u r e 5. the  M o d e l l i n g s e v e r a l compartments and  i n t e r a c t i o n s between each one can be enormously complex.  F o r example,  a phosphorus model w i t h 15 compartments can have as many as 55 pathways o f f l u x between compartments ( K l u e s e h e r 1970).  S i m p l e r compartment models  have been c o n c e i v e d , b u t even a s i x compartment phosphorus model has a t l e a s t 23 I m p o r t a n t f l u x pathways ( F l e m i n g 1971).  49  Rigler  (1973) d i s c u s s e s t h e problems i m p l i c i t i n t h e 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 .  Firstly,  this  method assumes t h e system i s i n a s t e a d y 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 e v e r , met i n a q u a t i c ecosystems (except t h a t d u r i n g summer s t a g n a t i o n a pseudo s t e a d y - s t a t e i s sometimes a c h i e v e d i n some temperate l a k e s ) . 32 Secondly,  P i s i n t r o d u c e d o n l y i n t h e o r t h o p h o s p h a t e compartment, and  w h i l e measurement o f t h e r a t e of movement o f t h e t r a c e r i s c o n s i d e r e d v a l i d , measurement o f t h e q u a n t i t y o f o r t h o p h o s p h a t e i n e a c h compartment i s i n s e r i o u s q u e s t i o n (see p r e v i o u s s e c t i o n ) .  Thirdly,  t h e c h e m i c a l and p h y s i c a l  n a t u r e o f s o l u b l e o r g a n i c ( o r s o l u b l e u n r e a c t i v e ) phosphorus i s s t i l l  largely  unknown, a s i s i t s r o l e i n t h e phosphorus economy o f the t r o p h o g e n i c zone. F o u r t h l y , e x i s t i n g data a r e inadequate t o provide t r u e r a t e constants of phosphorus movement out o f t h e e p i l i m n i o n t o t h e l i t t o r a l and h y p o l i m n i o n . Rigler  ( p e r s o n a l communication) c a u t i o n s a g a i n s t t h e compartment a p p r o a c h  f o r a n a l y s i s o f phosphorus c i r c u l a t i o n between e p i l i m n i o n , h y p o l i m n i o n and  s e d i m e n t s because t h e s e k i n d s o f f l u x d a t a have n o t been q u a n t i f i e d . W h i l e no a t t e m p t s have been made t o f o r m u l a t e even a s i m p l i f i e d  compartment model o f phosphorus f l u x i n a f r e s h w a t e r system, a t l e a s t one a t t e m p t (Pomeroy et al. 1969) has been made i n a s a l t w a t e r marsh.  This  model i n c l u d e s seven compartments (some o f w h i c h a r e d i v i d e d i n t o subcompartments) and a t l e a s t 14 f l u x e s ( r a d i o p h o s p h o r u s t r a c i n g ) between compartments. Because o f t i d a l f l u s h i n g , r o u t e s o f e x p o r t f r o m t h e system c o u l d n o t be evaluated. In summary, i t c a n be c o n c l u d e d t h a t t e c h n i q u e s o f t r a c i n g phosphorus i n a q u a t i c ecosystems have n o t y e t r e a c h e d t h e l e v e l o f s o p h i s t i c a t i o n n e c e s s a r y t o e n a b l e m o d e l l i n g o f t h e 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 i n lakes i s proposed by Vollenweider Extending the e a r l i e r work of B i f f i  (1963) and P i o n t e l l i and T o n o l l i (1964)  Vollenweider begins with the basic mass balance assumption of  (1969).  that the amount  a substance i n a lake i s e s s e n t i a l l y 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 e s s e n t i a l f a c t o r , while P i o n t e l l i and T o n o l l i emphasize the l o s s through sedimentation.  Vollenweider ex-  tends these concepts i n an analysis of the t o t a l phosphorus budgets of eight Swiss lakes, and formulates the following r e l a t i o n s h i p . General form:  change in mass of phosphorus = loading - sedimentation - outflow S p e c i f i c form: dm W  -TT—  dt  for  =  T  J  -  am  w  pm  w  which a steady-state solution i n terms of phosphorus concentration and  s p e c i f i c loading i s :  [m_J  w'  where  =  z " (a+p) L  i s the mass of phosphorus i n the lake (kg); J i s the loading (kg);  a i s an empirically determined  sedimentation c o e f f i c i e n t (years ^~); p i s  the c o e f f i c i e n t of hydrologic flow-through (years ^ ; equal to Q/V, where 3 3 Q i s the outflow discharge (m /year) and V i s the lake volume, m ); [m ] i s w o  _  the mean concentration of phosphorus i n the lake (g/m ); z i s the mean depth of  the lake (m); and L i s the s p e c i f i c loading of phosphorus to the lake  (g/m ). 2  51  Vollenweider accounts f o r the fact that during s t r a t i f i c a t i o n only a part of the e n t i r e lake volume i s involved i n mixing and hydrologic flow-through, and has developed an expression for the "mean exchange e p i l i m nion" during t h i s period.  Vollenweider assumes that the loading r a t e i s  constant and that the concentration of phosphorus i n the outflow i s the same as the average concentration i n the lake. The most d i f f i c u l t part of the analysis i s the formulation of an expression which accurately describes the sedimentation of phosphorus. Vollenweider decided that h i s o r i g i n a l assumption  that phosphorus  sedimenta-  t i o n Was a l i n e a r function of the amount of phosphorus i n the water (c* ^) 11  did not adequately f i t experimental data.  He therefore introduced a co-  e f f i c i e n t , T, which made sedimentation a function of loading as well as the amount of phosphorus i n the water.  The r e s u l t i n g equation produced a  s a t i s f a c t o r y f i t with experimental data when a mean value of 0.39 for T was used:  d [m ] —~— dt w  L  =  t  — — z  loading  L  -  a[m ] - — ( 1 - p ) w — z  -  P[m] w  -  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 d i v i s i o n of  a lake into an epilimnion and hypolimnion, and the introduction of a term to describe the eddy d i f f u s i o n of phosphorus from hypolimnion to epilimnion.  52  O'Melia's mass balance formulation for the epilimnion i s :  dP dt"  d[P ] g  =  W  +  inflow  k  z e-^T A  "  + eddy diffusion  s V  e  "  [ P P ]  - sedimentation  ^ T [ P  -  ]  outflow  With the exception of the eddy d i f f u s i o n term (the second term i n the equat i o n ) , t h i s formulation i s almost i d e n t i c a l to Vollenweider's.  Here P  is  the amount of t o t a l phosphorus i n the epilimnion (kg); W i s the rate of i n put of t o t a l phosphorus from the land (kg/year), a l l of which i s assumed to enter the epilimnion; the term k A d[P ]/dz describes the input of phosphate Z  6  S  to the epilimnion by d i f f u s i o n from the hypolimnion, where  i s the co-  2 e f f i c i e n t of eddy d i f f u s i o n or v e r t i c a l mixing (m /year), A i s the area 2 of the thermocline (m ),.d[P ]/dz i s the gradient of soluble phosphate s across the thermocline  (mg/1); the term sV [PP] i s the sedimentation  where s i s the sedimentation c o e f f i c i e n t epilimnion (m ), and  e  loss,  (years ^ ) , V^ i s volume of the  [PP] i s the concentration of p a r t i c u l a t e phosphorus  in the epilimnion (mg/1); the l a s t term i s the outflow  ( a l l considered to  3 be from the epilimnion) i n which Q lake discharge (m /year) and  [P^] i s  o  the concentration of t o t a l phosphorus in the epilimnion (g/m  ).  O'Melia  does not include a model f o r the mass balance of phosphorus i n the hypolimnion, which i s e s s e n t i a l for the determination of the concentration gradient across the thermocline.  CHAPTER IV  DEVELOPMENT OF A MODEL FOR SKAHA LAKE  The work o f V o l l e n w e i d e r and O'Melia forms t h e e s s e n t i a l base from w h i c h a mass b a l a n c e model f o r an e p i l i m n i o n - h y p o l i m n i o n - s e d i m e n t system c a n be f o r m u l a t e d .  I n t h i s model " t o t a l phosphorus"  t h e b a s i c measure f o r t h e element.  i s considered  The n o r t h and s o u t h b a s i n s o f Skaha  Lake a r e c o n s i d e r e d 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 I n each b a s i n .  S e p a r a t e e q u a t i o n s a r e f o r m u l a t e d f o r t h e e p i l i m n i o n and  hypolimnion.  The b a s i c form o f t h e s e e q u a t i o n s i s d e s c r i b e d i n t h i s  s e c t i o n , w h i l e t h e d e t a i l s o f submodels a r e d e s c r i b e d i n a l a t e r  A.  section.  FUNDAMENTAL INPUT-OUTPUT EQUATION 1.  Form o f t h e E q u a t i o n f o r t h e E p i l i m n i o n I f s t e a d y 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 t h e n u t r i e n t budget o f  a l a k e , t h e 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 : I n p u t - Output = 0  or  Input = Output  However, most l a k e s a c t a s n a t u r a l t r a p s f o r sediments and e x h i b i t a n u t r i e n t g a i n over t i m e .  ( i n c l u d i n g phosphorus)  I n order t o understand  t h e dynamics  o f 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 o u t p u t s must be d e s c r i b e d i n d e t a i l . A l l terms a r e r a t e s i n kg/day. (a) Input Terms.  Input o f phosphorus c a n be d e s c r i b e d by t h e  following equation:  53  54  input = P  where P  L E  + P  + P  E  v  +  P  R E  i s external loading from a l l sources (kg/day), P  i s eddy  d i f f u s i o n from the hypolimnion (kg/day), P^ i s a volume gain of phosphorus (kg/day) as the epilimnion forms and develops following spring mixing, and P  R E  i s regeneration of organic phosphorus from b a c t e r i a l decomposition i n  the l i t t o r a l zone (kg/day). The loading term, P _, i s the summation of natural and c u l t u r a l T  sources of phosphorus.  Natural sources come from d u s t f a l l and p r e c i p i t a t i o n  on the lake surface, streamflow from v i r g i n watersheds, and ground water i n f l u x from natural sources.  C u l t u r a l sources include municipal waste, storm  sewer flows, i n d u s t r i a l waste, a g r i c u l t u r a l return flow, a g r i c u l t u r a l ground water, septic tank ground water, and inputs from disturbed watersheds logging and mining).  (e.g.  The c o l l e c t i o n and r e l i a b i l i t y of these data are d i s -  cussed i n Appendix B. (b) Output Terms.  Output of phosphorus from the epilimnion i s  described by the following equation: Output = P where P^  E  S E  + P  Q  i s the sedimentation to the hypolimnion (kg/day) and P^ i s the  outflow (kg/day). (c) Combined Mass Balance. for  The combined mass balance equation  the epilimnion becomes: P  TE  =P  IE  +P  LE  + P + P + P -P E V RE SE  -P  0  where P^g i s the r e s u l t i n g amount of t o t a l phosphorus (kg) i n the e p i l i m nion at the end of each time period (day) and P  i s the i n i t i a l amount of  55  phosphorus (kg) a t t h e b e g i n n i n g o f each p e r i o d . The o u t f l o w o f phosphorus from the l a k e , P_, 0  i s e q u a l t o QC  , e  3 where Q i s t h e d i s c h a r g e o f water from the l a k e (m /day) and C c o n c e n t r a t i o n of phosphorus i n t h e e p i l i m n i o n (kg/m 2.  Form o f the E q u a t i o n f o r t h e  3  e  i s the  ).  Hypolimnion  As i n t h e e p i l i m n i o n , a mass b a l a n c e f o r t h e h y p o l i m n i o n c o n s i s t s of  i n p u t and o u t p u t terms e x p r e s s e d as r a t e s i n kg/day. (a) Input Terms.  Input t o t h e h y p o l i m n i o n 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 where P  +  L R  P r h  i s l o a d i n g by s e d i m e n t a t i o n from t h e e p i l i m n i o n (kg/day) and  P  LH  RH  i s r e g e n e r a t i o n from the sediments (b) Output Terms.  (kg/day), or " i n t e r n a l  loading."  Output f r o m the h y p o l i m n i o n can be d e s c r i b e d  by t h e f o l l o w i n g e q u a t i o n : Output = P where P  on  S  H  +  P  E  + P  v  +  P  Q  i s t h e s e d i m e n t a t i o n l o s s ( k g / d a y ) , P_ i s t h e eddy d i f f u s i o n h  t o t h e e p i l i m n i o n ( k g / d a y ) , P^ i s a l o s s t o t h e e p i l i m n i o n a s  loss  stratification  o c c u r s a f t e r s p r i n g m i x i n g ( k g / d a y ) , and P^ i s an o u t f l o w l o s s w h i c h  occurs  d u r i n g c o m p l e t e m i x i n g when t h e e n t i r e l a k e i s t r e a t e d as a h y p o l i m n i o n i n t h e model ( k g / d a y ) . (c) Combined Mass B a l a n c e . for  The combined mass b a l a n c e e q u a t i o n  t h e h y p o l i m n i o n becomes: P  TH  = P  IH  + P  LH  +P  RH  -P  SH  - P  E  - P  V  - P  0  where P_ i s the r e s u l t i n g amount o f t o t a l phosphorus (kg/day) i n the hypoIn  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 d a i l y period (equal to P  f o r the previous day). TH  3.  Modification of Mass Balance During Mixing Periods During months when the lake i s completely mixed (mid-November to  mid-April) the hypolimnion model w i l l be used to describe the balance of phosphorus i n the entire lake.  The fact that s l i g h t inverse s t r a t i f i c a t i o n  occurs i n winter when an i c e cover forms on at least part of the lake i s not taken into account, except by adjustment of c o e f f i c i e n t s 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  l y the mixing behavior) of the lake.  (and  consequent-  Instead, thermal data describing the  mixing behavior of the lake i n 1969-70 are used to c a l c u l a t e volumetric changes of the epilimnion, metalimnion  (thermocline) and hypolimnion i n  each basin (Table A - l i n Appendix A).  Area-depth relationships from the  hypsometric curve (Figure 2) and thermal data are used f o r the c a l c u l a t i o n s . The end of the complete mixing period occurs in mid-April when the formation of the epilimnion begins.  As the t o t a l volume of the lake r e -  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 i n volume.  Computation  of these  volume changes takes into account changes i n 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 i s l o s t from the hypolimnion and added to the epilimnion (W. K. Oldham, personal  communication).  This phosphorus exchange i s included i n the mass budget as  and i s  calculated according to the following equation:  V  where P  v  x h  i s the mass of phosphorus l o s t from the hypolimnion and added  to the epilimnion (kg),  i s the volume of water l o s t from the hypolim-  3 nion and added to the epilimnion (m ) and C^ i s the concentration of t o t a l  3 phosphorus i n 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 i s completely absent by mid-March, and vigorous mixing takes place from mid-March to mid-April.  The s t a r t i n g point chosen f o r the model i s mid-  March which could be termed the beginning of the "spring overturn."  The  period of complete mixing i n the autumn ("autumn overturn") begins i n midNovember and l a s t s 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. ber,  During some years an ice cover begins to form i n mid-Decem-  and can remain on at l e a s t part of the lake u n t i l March.  Dissolved  s o l i d s data c o l l e c t e d during two winters (Stein and Coulthard 1971)  indi-  cate l i t t l e v e r t i c a l v a r i a t i o n and r e l a t i v e l y complete mixing during the period of i c e cover. For v a l i d a t i o n purposes mixing data f o r 1969-70 i s used, and for prediction purposes an "average mixing year" i s developed by  computing  58  mean mixing volume v a r i a t i o n s for the years 1967-71.  These are shown i n  Table A - l of Appendix A.  C.  DEVELOPMENT OF SUBMODELS The detailed development of f i v e submodels i s described i n t h i s  section:  eddy d i f f u s i o n , sedimentation,  i n t e r n a l loading, primary  production, and dissolved oxygen. 1.  Eddy D i f f u s i o n Submodel Eddy d i f f u s i o n i s commonly regarded as the main mechanism of  v e r t i c a l heat transport through the water column of a thermally s t r a t i f i e d lake (Mortimer 1942, Hutchinson sidered by Lerman and S t i l l e r  1957).  The same mechanism i s con-  (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 e p i -  limnion can produce high concentrations of phosphorus i n the euphotic zone (O'Melia 1972).  O'Melia c a l c u l a t e s that the v e r t i c a l f l u x of phos-  phate to the epilimnion of the Vierwaldstatersee (Switzerland) can exceed inputs of phosphorus from land runoff during summer stagnation.  For t h i s  2 c a l c u l a t i o n O'Melia assumes an eddy d i f f u s i o n c o e f f i c i e n t of 0.05 cm /sec i n a thermocline 5 m thick with a concentration gradient of 0.02 mg/1 of 2 inorganic phosphorus across the thermocline.  The r e s u l t  (0.6g/m »year) i s  equal to the estimated t o t a l phosphorus loading from the land to the lake, and exceeds the "permissible loading" l e v e l proposed by Vollenweider for a lake of the Vierwaldstatersee's mean depth (104 m).  (1968)  59  (a) Simplifying Assumptions f o r Eddy D i f f u s i o n .  Three major  processes are considered to dominate the eddy d i f f u s i o n process in s t r a t i f i e d lakes: (1) turbulence i s the d r i v i n g force which determines tensity and r a t e of eddy d i f f u s i o n ;  (2) temperature  the i n -  differences between  epilimnion and hypolimnion cause thermal s t r a t i f i c a t i o n which i n h i b i t s eddy d i f f u s i o n ; (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 l a y e r s . Turbulence i s caused mainly by wind which mixes the epilimnion to varying degrees.  Attempts to model thermocline development from wind data have  not been very s a t i s f a c t o r y  (Hutchinson 1957), making turbulence a d i f f i -  c u l t process to quantify i n lakes.  Furthermore,  i n order to v e r i f y a  model f o r turbulence e f f e c t s , d e t a i l e d temperature Unfortunately, v e r t i c a l temperature only twice a month.  records are necessary.  p r o f i l e s from Skaha Lake are a v a i l a b l e  For these reasons, turbulence i s assumed to be con-  stant i n the eddy d i f f u s i o n model, and the epilimnion i s 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 i n t h i s submodel. (b) Equation for Eddy D i f f u s i o n Transport.  An expression d e s c r i b -  ing transport of soluble phosphorus between hypolimnion and epilimnion i s : P  where P  E  = k C A e g t  i s the rate of phosphorus movement by eddy d i f f u s i o n (kg/day); k  i s the c o e f f i c i e n t of eddy d i f f u s i o n (a function C  2 of temperature, m /day);  i s the concentration gradient of soluble and c o l l o i d a l phosphorus across  the thermocline (kg/m  3  *m);  and A  2 i s the area of the thermocline (m ).  The  60  simplifying assumption i s made that turbulence caused by wind mixing i s constant during the s t r a t i f i e d period, and that complete mixing occurs within the  epilimnion.  C o l l o i d a l and soluble phosphorus involved i n eddy d i f f u -  sion amount to approximately 30% of the t o t a l phosphorus content i n Skaha Lake (calculated from Stein and Coulthard 1971 and Williams 1972). (c) C o e f f i c i e n t of Eddy D i f f u s i o n .  Estimation of this c o e f f i c i e n t  i s the major t h e o r e t i c a l consideration of t h i s submodel.  Lerman and  Stiller  (1969) review three methods f o r the estimation of the c o e f f i c i e n t , of which the  f i n i t e difference method i s the most applicable f o r modelling on a sea-  sonal basis.  The method i s used extensively i n studies of d i f f u s i o n and heat  movement, and i s based on replacing the d i f f e r e n t i a l s by differences between the  temperature values i n two p r o f i l e s recorded at times t and t+1 (Lerman and  S t i l l e r 1969). six  The following equation expresses the r e l a t i o n s h i p i n terms of  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  where M  X  = x K /x D l2  t  2  i s the thickness of the metalimnion (thermocline) (m);  D x  e  i s the time period chosen (day); = T  1  2  =  ( T  - T z,t  z,t+l  z-l,t  +  T  «-l t+l  )  i  =  2 ( T  z,t  +  +  (  Vl,t  +  Vu.t+l*  where T i s temperature (°C). C o e f f i c i e n t s f o r the s t r a t i f i c a t i o n period of 1969-70 are calculated from temperature p r o f i l e s and presented i n Table A - l i n Appendix A.  The  values are i n the same range of magnitude and v a r i a t i o n as those calculated by  61  O'Melia f o r the Vierwaldstattersee (1972) and by Lerman and S t i l l e r f o r Lake Tiberias (1969).  2.  Sedimentation Submodel This submodel considers only the downward movement of p a r t i c u l a t e  phosphorus by sedimentation.  Regeneration back from lake sediments i s con-  sidered i n the succeeding submodel (internal loading). Sedimentation processes from the epilimnion and hypolimnion are considered to be d i f f e r e n t , and are dealt with separately. (a) Sedimentation from the Epilimnion.  Sedimentation of phosphorus  from the epilimnion occurs i n both inorganic and organic forms. mechanisms predominate  Different  i n 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 p r e c i p i t a t i o n of phosphorus minerals; and (2) adsorp-  tion of phosphate onto the surface of the lake sediment. a. P r e c i p i t a t i o n of Phosphorus Minerals.  There are three  phosphorus mineral groups which may be involved i n inorganic p r e c i p i t a t i o n : 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 i s possible to calculate the equilibrium s t a b i l i t y r e l a t i o n s h i p s  of the apatites, v a r i s c i t e , and strengite using pK values, assuming average concentrations of the cations (Ca, Fe, A l ) , and knowing the pH of the water and concentration of soluble phosphate  (Kramer et al. (1972).  Modelling the sea-  sonal v a r i a t i o n of these variables Is beyond the scope of t h i s i n v e s t i g a t i o n . Furthermore,  i n eutrophic lakes such as Skaha, the sedimentation of organic  phosphorus i s considered q u a n t i t a t i v e l y more important than inorganic  62  phosphorus.  However, an u n d e r s t a n d i n g  o f t h e pathways o f c h e m i c a l  precipi-  t a t i o n o f phosphates i n l a k e s i s p e r t i n e n t t o t h i s d i s c u s s i o n . Stumm (1964) c o n c l u d e s t h a t h y d r o x y a p a t i t e  may l i m i t phosphate  _3 (PO^  ) concentrations  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 t h a t t h e e q u i l i b r i u m c o n c e n t r a t i o n o f phosphate i n contact with hydroxyapatite  i s 0.03 mg/1 a t a pH o f 7, and t h a t a d d i -  t i o n s o f 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 o f h y d r o x y a p a t i t e i n the sediments. and  f i e l d observations  p l a y s an i m p o r t a n t waters."  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  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  r o l e i n t h e e n v i r o n m e n t a l c h e m i s t r y o f phosphate i n n a t u r a l  Lee o b s e r v e s t h a t t h e r e a r e many e u t r o p h i c l a k e s where t h e c o n c e n -  t r a t i o n o f phosphate g r e a t l y exceeds 0.03 mg/1 (the M a d i s o n , W i s c o n s i n l a k e s t y p i c a l l y have 10 t o 50 t i m e s t h i s amount), and h y d r o x y a p a t i t e nant f o r m o f sediment phosphorus.  i s n o t a domi-  P o r c e l l a et al. (1971) c o n c l u d e t h a t w h i l e  Stumm's h y p o t h e s i s may be a p p l i c a b l e t o 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 with the observation  i n e u t r o p h i c l a k e s t h a t phosphate c o n c e n t r a t i o n s  d u r i n g a l g a l a c t i v i t y and do n o t i n c r e a s e a g a i n u n t i l autumn m i x i n g  decrease occurs.  They n o t e t h a t b i o l o g i c a l g r o w t h and d e c o m p o s i t i o n , as w e l l as t h e s e c o n d a r y e f f e c t s o f 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 t h e o b s e r v e d c y c l i n g o f nutrients i n eutrophic  lakes.  E x p e r i m e n t s 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 t a n k 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 t h a t removal o f phosphorus by t h e s e d i m e n t a t i o n o f 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 i m p o r t a n t t a t i o n o f p h o s p h a t e s (Tenney et at. (1972). removal occurs  than the chemical  precipi-  I t was found t h a t no phosphate  i f t h e biomass i s removed from the s u s p e n s i o n and c o n t i n u e d  63  aeration proceeds, even at r e l a t i v e l y high pH values.  It i s concluded that  chemical conditions i n Skaha Lake (maximum recorded pH of 9.2) are not conducive to s i g n i f i c a n t chemical p r e c i p i t a t i o n of insoluble  phosphates.  While Williams (1973) reports that the majority of the phosphorus i n the s u r f i c i a l sediments of Skaha Lake i s i n the form of hydroxyapatite (70%), he concludes that the apatite comes d i r e c t l y from the s o i l and rocks of the watershed, not from chemical p r e c i p i t a t i o n within the lake. e r a l o g i c a l composition of the bedrock supports this hypothesis.  The  min-  The depofii-  t i o n a l pattern of apatite sedimentation shows that the highest concentrations occur i n the northern basin near the inflow of the Okanagan River.  Locally  high apatite concentrations exist near areas of probable erosion and transport from the watershed.  Williams concludes that the hydroxyapatite plays  l i t t l e or no r o l e i n the phosphorus cycle of the lake waters, either before or a f t e r deposition.  Personal communication with Williams confirms that  stream input estimates of phosphorus probably do not include apatite, as i t i s a r e l a t i v e l y heavy mineral not normally sampled with conventional stream sampling techniques.  These findings support the hypothesis that chemical  p r e c i p i t a t i o n of hydroxyapatite has l i t t l e ,  i f any, e f f e c t on the phosphorus  budget of Skaha Lake water. b. Adsorption of Phosphate.  Since t h i s sedimentation  mechanism i s assumed to be s i g n i f i c a n t only during the mixing period (November to March) when the epilimnion does not e x i s t , i t w i l l be discussed i n the section on sedimentation from the hypolimnion. (2) Sedimentation of Organic Phosphorus.  Seasonal v a r i a t i o n i n  the sedimentation of organic phosphorus i s assumed to be a function of p r i -  64  mary production i n the epilimnion, which r e s u l t s i n the sedimentation of organic matter.  Evidence supporting t h i s assumption  comes from many inves-  tigators. In a study of oxygen-nutrient relationships i n the central basin of Lake E r i e , Eurns and Ross (1972) report that high rates of oxygen depletion occur i n the same areas as profuse primary productivity.  They conclude  that since approximately 88 per cent of the hypolimnetic oxygen was consumed i n the decay of organic materials during the summer of 1970,  i t i s probable  that a massive a l g a l bloom was the major cause of anaerobic conditions that subsequently developed i n the hypolimnion. (the  The bloom caused " a l g a l r a i n s "  sedimentation of dead a l g a l c e l l s 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 a l g a l  c e l l s , a portion of which was regenerated back to the hypolimnion following decomposition  (details of t h i s process are discussed i n the next section on  i n t e r n a l loading).  Williams and Mayer (1972) summarize the s i g n i f i c a n c e of  t h i s elegant study: "We now know that the summer months have been marked by a tremendous increase i n the deposition of phosphorus on the sediment-water interface, i n the form of a l gal remains, and that a high proportion of t h i s algal-derived phosphorus i s retained by the sediments during [the aerobic portion of] t h i s period." Hutchinson  (1957) describes an experiment by Elnsele  (1941) i n  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 t o t a l organic (soluble and p a r t i c u l a t e ) phosphorus increased almost as much as the inorganic phosphorus decreased, and i t was evident that phosphate  65  was being taken up very r a p i d l y and sedimented  as p a r t i c u l a t e organic  phosphorus. Sedimentation rates of phosphorus have been measured i n eutrophic lakes during extreme summer s t r a t i f i c a t i o n i n two ways: tracing; and  (2) actual measurement with sediment traps.  method, Hutchinson  (1)  radiophosphorus  Using the former  (1950) found that about two per cent of the t o t a l phos-  phorus i n the trophogenic layersedimented d a i l y , while Rigler (1964) reports a d a i l y loss of about one per cent.  These values are similar to those ob-  tained by Bosch f o r 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 i n the trophogenic layer ended up i n the sediments daily.  Seasonal v a r i a t i o n , and e s p e c i a l l y the response to a l g a l blooms, i s  not reported i n these investigations.  Rigler (1973) observes that these  rates of phosphorus loss are consistent with Hutchinson' s r e s u l t s (1938) showing the hypolimnetic oxygen d e f i c i t i n four lakes to be d i r e c t l y prop o r t i o n a l to the amount of p a r t i c u l a t e organic matter i n the water. The following expression describes sedimentation of organic phosphorus from the epilimnion to l i t t o r a l sediments and the hypolimnion:  POT. = B  c where P  SE  SE  sk pb k re  i s the rate of organic phosphorus sedimentation from the e p i l i m -  nion (kg/day), B  s  i s the rate of sedimentation of phytoplankton c e l l s (bio-  mass) from the epilimnion (kg/day), k ^ Is the c o e f f i c i e n t of phosphorus i n phytoplankton biomass (kg phosphorus/kg dry weight phytoplankton), and k  is  the c o e f f i c i e n t of phosphorus r e c y c l i n g within the epilimnion (dimensionless).  66  T h i s i s a c o n s e r v a t i v e e s t i m a t e o f o r g a n i c phosphorus s e d i m e n t a t i o n , as i t i s o u t s i d e o f t h e scope o f t h i s r e s e a r c h t o a c c o u n t f o r s e d i m e n t a t i o n l o s s e s of  z o o p l a n k t o n and h i g h e r t r o p h i c l e v e l s .  While t h i s e x p r e s s i o n d e s c r i b e s  t h e amount l o s t from t h e e p i l i m n i o n , i t i s i m p o r t a n t t o n o t e t h a t about 17 per c e n t o f t h i s amount ends up i n l i t t o r a l to  sediments and 83 p e r c e n t goes  t h e h y p o l i m n i o n (based on a s u r v e y o f t h e l i t t o r a l a r e a o f Skaha Lake,  S t o c k n e r et al. 1972b).  T h i s I n f o r m a t i o n i s used  i n the f o l l o w i n g  section  on i n t e r n a l l o a d i n g , o r r e g e n e r a t i o n from t h e sediments. The biomass o f p h y t o p l a n k t o n s i n k i n g f r o m t h e e p i l i m n i o n each day  (B ) i s e s t i m a t e d by t h e f o l l o w i n g r e l a t i o n s h i p : BS  p  where B i s t h e biomass o f p h y t o p l a n k t o n i n t h e t r o p h o g e n i c l a y e r ( k g ) and Sp i s t h e r a t e o f s i n k i n g a s c e l l s sediment  o u t o f t h e t r o p h o g e n i c l a y e r (day "*").  Both B and Sp a r e e s t i m a t e d by t h e p r i m a r y p r o d u c t i o n submodel i n a f o l l o w i n g section of t h i s chapter. The c o e f f i c i e n t o f phosphorus i n p h y t o p l a n k t o n biomass ( k ^ ^ ) I s c a l c u l a t e d f r o m t h e a s s u m p t i o n t h a t p h y t o p l a n k t o n have, on the a v e r a g e , a f i x e d c o m p o s i t i o n o f the major elements. f i n e d an average organism  R e d f i e l d et at. (1963) have de-  s t o i c h i o m e t r y o f ^^06^16^1^263^110  t  *  ie  o c e a n s  «  T h i s r a t i o i s v e r y s i m i l a r t o a C:N:P r a t i o i n t h e p a r t i c u l a t e o r g a n i c m a t t e r i n t h e w a t e r above t h e t h e r m o c l i n e i n Lake E r i e o f 122:18:1 (Burns and Ross 1972).  A l t h o u g h a n a l y s e s o f organisms do n o t always agree w i t h t h i s  composi-  t i o n and c a n v a r y due t o " l u x u r y " uptake o f a v a i l a b l e phosphorus (Kramer et al.  1972) i t i s a r e a s o n a b l e a p p r o x i m a t i o n f o r m o d e l l i n g p u r p o s e s .  c u l a r weight o f t h i s average m o l e c u l e  The mole-  ( d r y w e i g h t ) o f o r g a n i c m a t t e r i s 3551  67  g-atoms, and the phosphorus portion weighs 31 g-atoms; the resultant f r a c t i o n of phosphorus i n a mass of organic matter i s 31/3551, or 0.0090.  There-  fore, the c o e f f i c i e n t of phosphorus i n plankton (by weight) i s approximated as 0.009 mg P/mg  dry weight of phytoplankton.  s l i g h t l y higher figure of 0.011  Strickland (1965) reports a  for diatoms i n the ocean.  The c o e f f i c i e n t of r e c y c l i n g , k  » I  s  estimated according to the  quantity of organic matter decomposed within the epilimnion, thereby r e l e a s ing soluble phosphate f o r reuse by plankton and preventing t h i s portion of epilimnion phosphorus from sedimenting to the hypolimnion.  Kajak et al. (1970)  found that 63 per cent of t o t a l primary production i n several P o l i s h lakes was decomposed i n the epilimnion, therefore never sedimenting to the hypolimnion.  Of the remaining 37 per cent which reached the hypolimnion as seston,  19 per cent was decomposed i n the hypolimnion and 18 per cent was decomposed in the sediments.  It i s estimated from these r e s u l t s that approximately 60  per cent of the phosphorus i n organic matter remains and i s decomposed i n the epilimnion, and that the c o e f f i c i e n t of r e c y c l i n g (which indicates that percentage reaching the hypolimnion) i s approximately (b) Sedimentation From the Hypolimnion. from the hypolimnion result from two major mechanisms:  0.4. Sedimentation losses (1) inorganic s e d i -  mentation by adsorption on the bottom sediments; and (2) organic sedimentation of a l g a l c e l l s . (1) Sedimentation of Inorganic Phosphorus. phorus sedimentation during the growing season i s assumed to be  While phosdominated  by organic forms, the assumption i s not v a l i d during the period of complete mixing when low water temperatures and decreased solar r a d i a t i o n cause organic  68  production to be minimal.  During t h i s period (mid-November to mid-April)  soluble inorganic forms of phosphorus are not r a p i d l y taken up by organisms and the concentration of dissolved orthophosphate phorus) increases.  (or soluble reactive phos-  It i s suggested that during t h i s six-month period the  dominant mechanism of phosphorus phate by the sediments.  sedimentation i s adsorption of orthophos-  R e l a t i v e l y complete mixing takes place during t h i s  period (except f o r s l i g h t inverse s t r a t i f i c a t i o n i n mid-winter), r e s u l t i n g i n a reasonably uniform d i s t r i b u t i o n of soluble phosphorus column and enabling sediment-water  throughout the 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 i n c o n t r o l l i n g the exchange of phosphorus between sediments and the overlying water, and many studies i n dicate that  phosphate tends to be r e a d i l y adsorbed to lake sediments (Lee  1970, Golterman 1973, Williams and Mayer 1972).  Williams and Mayer (1972)  report that sorbed phosphorus accounts f o r up to 50 per cent of the t o t a l phosphorus i n the s u r f i c i a l sediments of Lake E r i e .  Eighteen per cent of the  phosphorus i n the s u r f i c i a l sediments of Skaha Lake i s composed o f sorbed phosphorus, which i s the most abundant form after apatite (which accounts f o r 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 i s described as the d i f f e r e n c e 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 p a r t i c u l a r type of a a a  69  sediment and C i s the concentration of orthophosphate i n the water.  Arm-  strong and Gloyna (1967) used a s i m i l a r 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 r  where k and v are constants f o r the sediment and C i s the concentrar r  t i o n of orthophosphate i n the water (mg/1).  The expression f o r net adsorp-  tion (loss from the water to the sediment) i s : net adsorption = gross adsorption - release (a-r) v = k C a  a  where adsorption i s i n mg P/kg of sediment  -  -v k C r  r  (dry weight) (Figure 6)«  It i s  assumed that approximately the upper one mm of sediment i s involved i n 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 g r a v i t y 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 ^ i s the recycling c o e f f i c i e n t f o r organic phosphorus within the e p i limnion (day "^), 0.83 i s the proportion of phosphorus sedimenting from the epilimnion which reaches the hypolimnion, and P i s the rate of sedimentation SE of phosphorus from the epilimnion (kg/day). It i s assumed that a percentage of the organic phosphorus which sediments to the hypolimnion from the epilimnion w i l l decompose i n lower waters  70  Figure 6. Adsorption of phosporus on an oxidized calcerous sediment (Olsen 1958).  71  before reaching the sediment.  The r e c y c l i n g c o e f f i c i e n t , ^ » r n  r e f l e c t s 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  r e s u l t s indicate that about half of the organic matter reaching the hypolimnion i s decomposed i n the water before f a l l i n g to the sediment, and thus the r e c y c l i n g c o e f f i c i e n t f o r the hypolimnion i s approximated  as 0.5/day.  Not a l l of the phosphorus sedimenting from the epilimnion reaches the hypolimnion.  Assuming horizontal homogeneity of t o t a l phosphorus i n the  water, a percentage equal to the area of the l i t t o r a l zone w i l l sediment i n the l i t t o r a l .  Since the area of the l i t t o r a l zone i s 17 per cent of the t o t a l  area (Stockner et al. 1972b), 17 per cent of phosphorus sedimenting from the epilimnion w i l l end up i n the l i t t o r a l and the remainder reach hypolimnetic waters.  Therefore, 83 per cent of P  (83 per cent) w i l l w i l l reach the hypo-  SE  limnion. (3) Resulting Expression f o r Sedimentation From the  Hypolimnion.  The following expression describes sedimentation of inorganic and organic phosphorus from the hypolimnion: P  SH  = adsorption loss + organic sedimentation -  where P  (k C a  V a  -k C r  V r  )S  d +  k  r h  (0.83)P  S E  i s the sedimentation of phosphorus from the hypolimnion on  and Sj i s the dry weight of sediment involved i n adsorption (kg).  (kg/day)  72 3.  I n t e r n a l Loading  Submodel  I n t e r n a l l o a d i n g o f phosphorus i n a l a k e i s the amount from the sediments f o l l o w i n g t h e i n i t i a l sedimentation loading  regenerated  gross  sedimentation  process.  c o u l d be c o n c e p t u a l i z e d a s g r o s s  sedimentation  minus i n t e r n a l  (regeneration).  Although  net s e d i m e n t a t i o n  i s t h e amount o f  Net  import-  ance t o " e u t r o p h i c a t i o n l i m n o l o g i s t s " , the mechanisms i n v o l v e d i n g r o s s sedimentation  and subsequent r e g e n e r a t i o n a r e q u i t e d i f f e r e n t and  m o d e l l e d s e p a r a t e l y i f an a c c u r a t e e s t i m a t e  of n e t s e d i m e n t a t i o n  must be i s t o be  achieved. The  importance of i n t e r n a l l o a d i n g t o t h e phosphorus budget o f l a k e s  can be g r e a t , e s p e c i a l l y d u r i n g a n a e r o b i c generate  c o n d i t i o n s when the sediments may r e -  more phosphorus t o t h e l a k e than incoming streams and groundwater (ex-  ternal loading) contribute. the e u t r o p h i c B a l d e g g e r s e e  During  two summers of h y p o l i m n e t i c  (Switzerland) gained  f o u r times a s much phosphorus  from sediment r e g e n e r a t i o n than from e x t e r n a l s u r f a c e l o a d i n g cited  i n Vollenweider  1968).  conditions,  (Bachofen,  The s i t u a t i o n r e v e r s e d d u r i n g a e r o b i c c o n d i t i o n s  when more phosphorus was taken up (on a d a i l y r a t e ) by t h e sediments than had been r e l e a s e d d u r i n g a n a e r o b i c c o n d i t i o n s . In t h e c e n t r a l b a s i n o f Lake E r i e i n t e r n a l phosphorus l o a d i n g d u r i n g anaerobic  c o n d i t i o n s c o n t r i b u t e d 1.1 times  (Burns and Ross 1972).  During  t h e amount from e x t e r n a l l o a d i n g  a e r o b i c c o n d i t i o n s t h e sediments s t i l l  phorus t o t h e o v e r l y i n g water, but the amount was o n l y 25 p e r c e n t t e r n a l l o a d i n g d u r i n g t h e same p e r i o d . phosphorus which r e t u r n e d  lost  phos-  of t h e ex-  The p e r c e n t a g e o f sedimented  organic  to t h e water under a e r o b i c c o n d i t i o n s was 25 per cent  (a f i g u r e c o i n c i d e n t a l w i t h t h e p r e c e e d i n g  25 p e r c e n t ) .  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 p o s s i b l e explanation f o r the low percentage of phosphorus regeneration (25 per cent) during aerobic conditions i s that most of the orthophosphate produced xides.  regenerated from b a c t e r i a l decomposition i s  on the lake bottom i n close proximity to p r e c i p i t a t e d f e r r i c  hydro-  This s i t u a t i o n 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 SedimentWater Interface.  Five major mechanisms control the transfer of nutrients from  sediments to the hypolimnion: diffusion;  (1) physical disturbance and mixing;  (3) b i o l o g i c a l uptake;  (2) physical  (4) anaerobic chemical regeneration; and  (5)  decomposition regeneration. (1) Physical Disturbance and Mixing. on the exchange of dissolved substances between mud  In h i s c l a s s i c a l papers  and water, Mortimer (1941,  1942) observed that ordinary processes of molecular d i f f u s i o n were extremely slow i n transmitting material between sediments and water.  Physical processes  that speed up transmission are mixing during overturn periods, horizontal movement of water over the benthos (which increases eddy d i f f u s i o n ) , convection currents under winter ice cover, and movement of benthic organisms 1941).  (Mortimer  Seiche action would also contribute to eddy d i f f u s i o n at the i n t e r -  face (T.G. Northcote, personal communication). quantify.  These losses are d i f f i c u l t to  74  Following a period of high winds on Lake E r i e , Kramer et al. (1970) report increases i n 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 a g i t a t i o n of the sediment a f t e r storms caused a 100-fold orthophosphate increase i n the overlying water.  U i t h i n 18 hours of the storm the orthophos-  phate concentration was halved.  Regeneration of phosphorus by t h i s mechanism  i s of more significance f o r l i t t o r a l zones and shallow.lakes than f o r deep lakes because of greater e f f e c t s on the sediments due to wind, wave and current action. A c t i v i t y by benthic organisms, such as t u b i f i c i d worms, results in  phosphorus loss from sediments (Whitten and Goodnight 1967).  feeding  Bottom-  f i s h such as carp and perch species deplete the sediment of organic  forms of phosphorus.  The s i g n i f i c a n c e of these losses from the sediments,  although not q u a n t i f i e d , i s probably not great (Williams and Mayer 1972). (2) Physical D i f f u s i o n .  Regeneration to the water can occur  as a r e s u l t of d i f f u s i o n of soluble phosphorus out of the sediments due to a difference i n 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).  soluble  phosphorus regenerated may form through diagenesis of sedimented par-  t i c u l a t e phosphorus within the sediments. the  The  The rate of d i f f u s i o n depends on  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 c i r c u l a t i o n 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 i n c o n t r o l l i n g regeneration has not been adequately  75  evaluated. Although i t has been suggested that the microzone acts as a b a r r i e r 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 b a r r i e r i s e f f e c t i v e when the microzone i s unconsolidated. Diagenetic formation of hydroxyapatite within sediments (an important process i n the sediments of Skaha Lake) i s a mechanism which acts i n opposition to the d i f f u s i o n of soluble phosphate into overlying water (Williams and Mayer 1972). +2 Ca  For Lake E r i e and Lake Ontario sediments, the concentration of soluble -3  , PO^ , and OH  ions i n the i n t e r s t i t i a l water of the sediments corresponds  very c l o s e l y to the s o l u b i l i t y product of hydroxyapatite (Sutherland et al. 1966, Williams and Mayer 1972).  Hydroxyapatite, once formed, i s very u n l i k e l y to  participate in regeneration reactions. Due to the d i f f i c u l t y  i n modelling the d i f f u s i o n process, the l a c k  of necessary data (especially the phosphorus concentration of i n t e r s t i t i a l s e d i ment water), and the lack of knowledge concerning i t s quantitative r o l e i n the nutrient budget of lake sediments, modelling t h i s mechanism w i l l not be attempted. (3)  B i o l o g i c a l Uptake.  Radiophosphorus studies show that l i t t o r a l  vegetation (especially macrophytes) can take up phosphorus from sediments d i r e c t l y , 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 i n the s u r f i c i a l ments of a s a l t water marsh and Spavtina  (marsh grass).  sedi-  Uptake of s o l u b i l i z e d  sediment phosphorus by macrophytes and epiphytic algae probably takes place i n the  l i t t o r a l zone of Skaha Lake (Stockner et al. 1972a), thereby preventing a  percentage of s o l u b i l i z e d 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 t h i s process would tend to diminish the amount of net uptake by the vegetation (Hayes and P h i l l i p s 1958, Confer 1969).  For modelling purposes i t w i l l be considered that net movement of  phosphorus from sediments to water through b i o l o g i c a l uptake i s not s i g n i f i cant i n the o v e r a l l phosphorus budget of the lake. (4) Anaerobic Chemical Regeneration. Mortimer (1941, 1942) r e 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 p r e c i p i t a t e d as i n -  soluble f e r r i c phosphate under aerobic conditions at the sediment-water i n t e r face, becomes soluble when the oxygen i s depleted i n the hypolimnion. The r e sult of the change to anerobic conditions can be a massive increase i n soluble phosphate i n the hypolimnion of a lake (e.g. Lake E r i e , Burns and Ross 1972). Although much of this soluble phosphate may r e p r e c i p i t a t e when autumn mixing reoxygenates the hypolimnion, i t may be only a portion of the phosphorus l o s t from the sediments during the anaerobic period.  Burns and Ross (1972) report  that the soluble r e a c t i v e 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 p a r t i c u l a t e form.  These r e s u l t s indicate that a s i g n i f i c a n t part of the s o l -  uble phosphorus (both organic and inorganic) regenerated under anaerobic cond i t i o n s ultimately re-enters the b i o l o g i c a l cycle of Lake E r i e .  Although  anaerobic hypolimnetic conditions have not yet occurred i n 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 i n  returning soluble nutrients to the water i n lakes i s 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 s t a t e . " This i s accomplished by the mineralization of organic nitrogen as NH*  or  NO^,  -3 and organic phosphorus as PO^  .  McCoy and  balanced mixture of bacteria i s present  Sarles point out that a w e l l -  i n temperate lakes to carry out degra-  dation of c h i t i n , c e l l u l o s e , pectins, proteins and other complex organic compounds.  Measurement of the f l u x between sediment mud  (including bacteria)  and soluble phosphate i s reported by Hayes and P h i l l i p s (1958) to be about three days i n both d i r e c t i o n s . sediment and water was  With no bacteria present the exchange between  slowed to 15 days.  Although phosphorus can be regenerated from phytoplankton c e l l s by a u t o l y s i s i n addition to b a c t e r i a l decomposition, the r e l a t i v e importance of the processes has not been adequately evaluated  (Hooper 1973).  the assumption i s made that most of the regeneration  Therefore,  occurs through b a c t e r i a l  decomposition. The assumption i s made that b a c t e r i a l growth i s proportional to a l g a l growth, and that b a c t e r i a l growth i s l i m i t e d by the same factors of temperature and nutrients that l i m i t primary production; assumed that as a l g a l populations  therefore i t w i l l be  increase during the growing season, b a c t e r i a l  populations w i l l increase proportionally and w i l l have the c a p a b i l i t y , under optimum temperature conditions, of decomposing much of the organic matter produced by primary production.  Evidence for t h i s assumption comes from the work  78  bf Thomas (1969) showing that i n the Swiss Ziirichsee the same growth factors that stimulate most freshwater algae also stimulate bacteria associated with them.  Thomas shows that increases i n b a c t e r i a l density are d i r e c t l y propor-  t i o n a l to the phosphate content of the water at 20°C.  As w i l l be shown  i n the submodel on primary production, s i m i l a r r e l a t i o n s h i p s are true f o r a l g a l production and phosphorus. On the sediment surface of an aerobic lake with an abundant supply of dead organic matter Skaha), temperature  ( a reasonable assumption  i n a eutrophic lake such as  w i l l probably be the most important factor c o n t r o l l i n g  the decomposition process.  McCoy and Sarles state that i n a northern temp-  erate climate a low rate of b a c t e r i a l a c t i v i t y i s maintained by r e l a t i v e l y cold water temperatures  f o r about two-thirds of the year; during the summer  months, however, there i s a " f l u s h " of b a c t e r i a l a c t i v i t y which noticeably increases the b a c t e r i a l decomposition of o r g a n i c a l l y held phosphorus. The relationship between temperature  and b a c t e r i a l  decomposition  processes i s reported f o r the b a c t e r i a l community i n the sediments of eutrophic Lake Wingra, Wisconsin (Boylen and Brock 1973).  The r e s u l t s show that the  heterotrophic bacteria i n Lake Wingra sediments do not adapt to the low temperatures (1.0 - 1.5°C) which p r e v a i l i n winter.  Using the rate of glucose  uptake and C O 2 evolution as a measure of the difference i n decomposition Boylen and Brock (1973) show that at the optimum temperature  rate,  (25° C) under aero-  b i c conditions, decomposition rates were f o u r - f o l d to 14-fold higher than at the low temperature.  The authors conclude that a consequence of t h i s i s that  b a c t e r i a l decomposition processes should occur at a much slower rate during winter than during summer (and i n the colder sediments of the hypolimnion),  79  and plant material that had not decomposed before cold weather set i n w i l l decompose at l e a s t four times more slowly than i n warm sediments. The r e s u l t s of Boylen and Brock indicate a nearly l i n e a r r e l a t i o n ship between decomposition rates at 5°C and 25°C, and t y p i c a l curves i n d i cate that decomposition occurs approximately four times f a s t e r at the higher temperature than at the lower.  The l i n e a r i t y of the r e l a t i o n s h i p makes  possible the mathematical formulation of a c o e f f i c i e n t of decomposition, k^. If we assume that k^ = 1 at 25°C, we can r e l a t e k^ to temperature by:  k, = .04T d  where T i s sediment temperature in o  ,  C  Now i t i s possible to say that i n 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 decompose four times faster than i n the hypolimnetic sediments where the temperature 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 concent r a t i o n i n the l i t t o r a l sediments supports t h i s assumption (b) Formulation of Internal Loading Submodel.  (Williams 1973).  The assumption i s  made that i n a eutrophic lake such as Skaha Lake, regeneration of phosphorus from the sediments i s best r e f l e c t e d i n 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 i n 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. summer temperatures i n the l i t t o r a l sedimented phosphorus  The assumption i s made that at  (20 - 25°C) b a c t e r i a l decomposition of  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 devoid of organic matter i n the summer ( J . G. Stockner, personal communication).  The conclusion drawn' from t h i s evidence i s that the organic phos-  phorus which accumulates i n 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 t o t a l area of the lake, the following submodel i s proposed:  P  RL  °'  =  1 7 P  SE d k  where P i s the regeneration of phosphorus from the l i t t o r a l RL D T  (kg/day); P SE  i s the sedimentation of phosphorus from the epilimnion (kg/day), and k^ i s the c o e f f i c i e n t 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.  cient of decomposition.  The lower temperature r e s u l t s i n a lower c o e f f i -  The following expression describes regeneration from  deep water sediments:  P  where P  RH  = k P d SHorg  i s the regeneration of phosphorus from hypolimnetic sediments  k, i s the c o e f f i c i e n t of decomposition, and P„„ d SHorg r  i s the amount of organic  phosphorus sedimenting to the bottom of the hypolimnion (kg/day; the sedimentation submodel, equal to 0.83 P ,k_ ). OT:  u  (kg/day);  &  according to  81  4.  Primary Production Submodel The primary production submodel i s formulated f o r the prediction  of the biomass of phytoplankton i n the trophogenic layer, or the upper 8 m of the lake.  In addition to being of great interest i n the study of the  eutrophication problem, the p r e d i c t i o n of phytoplankton i s a necessary v a r i able i n the sedimentation submodel. Marked seasonal v a r i a t i o n i n population density i s a characterist i c feature of phytoplankton i n northern temperate  lakes (Odum 1971).  Odum  gives the following d e s c r i p t i o n of a t y p i c a l phytoplankton growth season, and the r e l a t i o n s h i p with temperature, l i g h t and nutrients:  "Very high densities which appear quickly and p e r s i s t for a short time are c a l l e d "blooms" or phytoplankton "pulses." In the northern United States ponds and lakes often exhibit a large early spring bloom and another, usually smaller, pulse i n the autumn. The spring pulse, which limnologists sometimes c a l l the "spring flowering", t y p i c a l l y involves the diatoms and i s apparently the r e s u l t of the following combination of circumstances. During the winter, low water temperatures and reduced l i g h t r e s u l t i n a low rate of photosynthesis so that regenerated nutrients accumulate unused. With the advent of favorable temperature and l i g h t conditions the phytoplankton organisms, which have a high b i o t i c p o t e n t i a l , increase r a p i d l y since nutrients are not l i m i t i n g f o r the moment ( i . e . , the spring bloom). Soon, however, nutrients are exhausted and the bloom disappears. When nutrients again begin to accumul a t e , n i t r o g e n - f i x i n g blue-green algae, such as Anabaena, often are responsible for autumn blooms, these organisms being able to continue to increase r a p i d l y despite a reduct i o n of dissolved nitrogen — that i s , u n t i l phosphorus, low temperature, or some other factor becomes l i m i t i n g and halts the population growth." As the combination of temperature,  l i g h t and nutrient supply changes  seasonally, phytoplankton populations change q u a l i t a t i v e l y as well as quantitatively.  P e a r s a l l (cited i n Hutchinson 1967) a t t r i b u t e s the spring maxima  of diatoms i n English lakes to a temporarily high concentration of S i which  82  comes with the spring freshet.  He concludes that i n d i v i d u a l species have  d i f f e r e n t nutrient requirements, and succeed each other as the waxing popul a t i o n reduces the a v a i l a b l e supply.  The interactions of changing l i g h t  and temperature conditions along with changes i n nutrient supply r e s u l t i n a very complex s i t u a t i o n .  Dinobryon  divergens  often replaces diatoms at the  end of the spring bloom when Ca and S i l e v e l s drop and the N:P r a t i o r i s e s . 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 i n summer) mixing  with epilimnetic waters (Tucker 1957, c i t e d i n Hutchinson 1967). (a) Other Phytoplankton Models.  An early model by Fleming, formu-  lated i n 1939, i s described by Patten (1968).  Fleming emphasized grazing  losses i n the following equation to describe the spring diatom bloom i n 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 r e s u l t i n g from zooplankton grazing. The work of R i l e y and h i s co-workers  (1946, 1949, 1963, 1965) i n  modelling plankton populations i n the ocean represents the f i r s t attempt to deal q u a n t i t a t i v e l y with the problem.  realistic  According to Patten (1968),  R i l e y , 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 s i m p l i f i e d form, R i l e y ' s formulation i s : HP  ~ = (PH - R - G - S + T)P dT where P i s the rate of change i n phytoplankton density; PH i s the rate of  83  photosynthesis (growth); R i s the rate of r e s p i r a t i o n ; G i s the grazing rate (loss to zooplankton); S i s the sinking rate of dead c e l l s ; and T i s the rate of upward movement due to turbulent eddies.  Riley's contribution  i s to r e l a t e the growth rate, r e s p i r a t i o n rate and grazing rate to basic environmental variables —  temperature, r a d i a t i o n , the e x t i n c t i o n c o e f f i c i e n t  of l i g h t i n water, and nutrient concentration. This r e s u l t s i n timev a r i a b l e c o e f f i c i e n t s , as the environmental components change throughout the year.  Respiration i s determined by temperature, and photosynthesis i s  l i m i t e d by temperature, l i g h t and phosphate concentration. In general, R i l e y found that observed values f o r phytoplankton density were within 25 per cent of the calculated values during one annual cycle i n the waters at Georges Bank o f f the coast of New England. Steele (1956, 1964) proposed similar models to predict plankton production i n the Gulf of Mexico and Fladen Ground.  He reports that a steady  state assumption does not e x i s t f o r shallow and deep layers i n the ocean, and considers each of the two layers to have d i f f e r i n g inputs and outputs. Steele uses a d i f f e r e n t expression than R i l e y to describe l i g h t penetration and introduces a v e r t i c a l eddy d i f f u s i o n term, but r e l i e s on the same type of mass balance formulation. More recent models consider three major interdependent  systems:  n u t r i e n t s , phytoplankton and zooplankton (Chen 1970, D i Toro et al. 1971). External environmental parameters advective flow.  considered are temperature,  radiation and  Parker (1972) adds f i s h as a fourth major component to h i s  model of Kootenay Lake, but uses the same mass balance approach as Chen and Di Toro.  84  (b) B a s i c P h y t o p l a n k t o n E q u a t i o n . posed  A d i f f e r e n c e equation i s pro-  to d e s c r i b e p h y t o p l a n k t o n dynamics on a d a i l y b a s i s .  rate coefficients of a d a i l y  f o r p l a n k t o n growth are d a i l y r a t e s , making the c h o i c e  time s c a l e p a r t i c u l a r l y u s e f u l .  The  p r e s s i o n d e s c r i b e s the biomass o f p h y t o p l a n k t o n  B vesultinq biomass  = =  B  I initial biomass T  +  (G  -  p  a v o w t } l  R  p  f o l l o w i n g g e n e r a l i z e d exi n the t r o p h o g e n i c zone:  —  Z  —  p  ( k g ) ; B^  at the b e g i n n i n g o f the time p e r i o d ( k g ) ; G^  (day ^ ) ; R^  (day "*");  out of the t r o p h o g e n i c l a y e r ( d a y ^ ) ; and 0^  radi-  i s the g r a z i n g as  i s the r a t e o f  Each o f these terms  discussed i n d e t a i l . (c) P h y t o p l a n k t o n  p l a n k t o n dynamics i s the f a c t  Growth.  A b a s i c problem  As D i Toro et al.  i n m o d e l l i n g phyto-  that d i f f e r e n t s p e c i e s r e a c t d i f f e r e n t l y  the t h r e e most i m p o r t a n t e n v i r o n m e n t a l v a r i a b l e s : and l i g h t .  temperature,  to  nutrients,  (1971) p o i n t o u t :  "The a v a i l a b l e i n f o r m a t i o n i s not s u f f i c i e n t l y d e t a i l e d to s p e c i f y the growth k i n e t i c s f o r i n d i v i d u a l phytoplankton species i n n a t u r a l environments."  T h e r e f o r e , the pragmatic  approach  I  i n a loss  i s the r a t e of s i n k i n g  a d v e c t i v e l o s s from the o u t l e t o f the l a k e (day ^ ) . is  p  , ~, outflow  n u t r i e n t s and  i s endogenous r e s p i r a t i o n r a t e which r e s u l t s  r a t e o f zooplankton  0 )B  i s the d a i l y  o f o r g a n i c c a r b o n i n the p h y t o p l a n k t o n p o p u l a t i o n (day ^ ) ; Z^  c e l l s sediment  —  p  i s the i n i t i a l biomass o f  growth r a t e o f p h y t o p l a n k t o n , dependent on temperature, ation  S  ,, . , . . . ,. ~ r>esp%vat%on - grastng - stnHng -  where B i s biomass o f p h y t o p l a n k t o n phytoplankton  Many p u b l i s h e d  o f D i Toro et al.  i s adopted, which i s to  85  ignore the problem of d i f f e r i n g species requirements f o r temperature, nutr i e n t s , and l i g h t .  The basic unit of kg of dry weight of phytoplankton  in the trophogenic zone (computed from concentrations i n mg/1) i s used for the e n t i r e population, and average c o e f f i c i e n t s for growth and loss are taken from the l i t e r a t u r e . (1) Temperature Dependency.  I f nutrients and l i g h t are not  l i m i t i n g , the temperature of the water i s the s i g n i f i c a n t parameter l i m i t i n g the growth rate of phytoplankton (Di Toro et al. 1971).  D i Toro et al. have  reviewed 22 experiments i n the l i t e r a t u r e which examine maximum growth rates as a function of temperature, and conclude that a s t r a i g h t - l i n e f i t i s a reasonable approximation of the data r e l a t i n g the maximum growth rate K^day to temperature T(°C)(Figure 7):  K  T  =  k l  T  where k^ has values i n the range 0.10±0.025/day  • °C. The c o e f f i c i e n t 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 1971).  of b i o l o g i c a l growth rates (Di Toro et al.  The upper water temperature range i n Skaha Lake (near freezing to  25°C) f i t s i n t h i s range well enough for modelling purposes. (2) Light Dependency.  The relationship between l i g h t  and photosynthesis i n water i s w e l l known: l i g h t at low i n t e n s i t y (e.g.  photosynthesis i s limited by  during the winter), whereas the optimum i n -  tensity photosynthetic production i s limited by other factors (e.g. ature and nutrients) (Vollenweider 1965).  temper-  Vollenweider (1965) has reviewed  86  o •o  Temperature  °C  F i g u r e 7. Growth r a t e o f p h y t o p l a n k t o n as a f u n c t i o n o f temperature ( a f t e r D i Toro e t 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 p h o t o s y n t h e s i s on  the b a s i s  1952,  of p r i m a r y p r o d u c t i o n  T a i l i n g 1957,  Ryther and  and  light  Y e n t s c h 1957,  measurements  obtained  from  in situ  f l u x i n water Steele  (Steemann  and  the a t t e n u a t i o n  coefficient  day)  of  (m "*") .  (1964, 1965)  uses a somewhat more e m p i r i c a l  the r e l a t i o n s h i p between l i g h t and  photosynthesis,  appropriate  f o r t h i s model because i t r e q u i r e s  l e s s d a t a and  growth i n h i b i t i o n a t h i g h K  L  l i g h t i n t e n s i t y (Figure  I = —  formulation which seems accounts f o r  8):  I exp(l m  ing  •  photosynthetically  to d e s c r i b e  where  These  the 3  r a t e a t l i g h t optimum (g carbon/m  (dimensionless);  layer  Nielson  1960).  2 (g carbon/m ) w i t h  experiments); a f u n c t i o n o f the  active incident l i g h t light  production  trophogenic  V o l l e n w e i d e r 1958,  models c a l c u l a t e the r a t e o f p r i m a r y p r o d u c t i o n  following information:  i n the  —) m  i s the r e l a t i v e r a t e o f p h o t o s y n t h e s i s  (a c o e f f i c i e n t between 0 and  1, day  ; I  when n u t r i e n t s are not  limit-  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  and  i s the l i g h t  I  (langleys/day).  i n the f o l l o w i n g s e c t i o n ,  langleys/day);  i n t e n s i t y a t which p h y t o p l a n k t o n growth i s maximum  Steele  assumes t h a t I  i s a p p r o x i m a t e l y 0.5  I  i n winter  in a i n summer, w h i l e R y t h e r (1956) c o n s i d e r s 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 t o be p h o t o s y n t h e t i c a l l y a c t i v e (making I = 0.5 I ) . Di m a and  0.3  Toro et  I  al.  (1971) use  a f i g u r e of 300  langleys/day  for I . m  88  tn in  d> si  —  100  200  300  Light  400  500  600  700  Intensity ( ly/day)  Figure 8. Relative photosynthesis rate (percent of maximum) as a function of l i g h t i n t e n s i t y (langleys/day). Theoretical curve from equation by Steele (1956) and data points from Manning and Juday (the response of a variety of phytoplankton populations; c i t e d i n Edmonson 1956).  800  89  The preceding equation includes the symbol I , which represents the average l i g h t i n t e n s i t y i n the trophogenic layer. The well-known BeerLambert r e l a t i o n describes the decrease of l i g h t i n t e n s i t y with depth i n water:  1 = 1 z where I  z  o  exp(-k z) e v  i s the l i g h t i n t e n s i t y (langleys/day) at depth z(m); I  cident incoming radiation (langleys/day); k (m \  &  o  i s the i n -  i s the extinction c o e f f i c i e n t  explained below); and z i s the depth (m).  This r e l a t i o n has been i n -  tegrated for the photosynthetic layerby Riley (1946) to produce an expression describing the average photosynthetic l i g h t i n t e n s i t y i n the trophogenic layer: I  I a =ck z"(l " exp(- ek z)) 2  r v  g  where I  i s the average l i g h t i n t e n s i t y i n the trophogenic layer (langleys/ a.  day) and z i s the depth of the trophogenic layer (8 m i n this case). This expression i s also used by Parsons and Takahashi (1973) i n comparing  growth  rates of two phytoplankton species of d i f f e r i n g c e l l aize. The extinction c o e f f i c i e n t , k , i s a function of two major facg  tors:  (1) dissolved coloured material and p a r t i c u l a t e inorganic matter, and  (2) phytoplankton c e l l s , both of which reduce l i g h t i n t e n s i t y , thereby i n h i b i t i n g photosynthesis (Chen 1971, Di Toro et al. 1971).  I f the phytoplank-  ton concentration i s large, the e x t i n c t i o n c o e f f i c i e n t i s 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 e x t i n c t i o n c o e f f i c i e n t as a function of these two causes (Chen 1970, Di Toro et al. 1971):  k  e  = k + k ew ep  where k i s the r e s u l t of e x t i n c t i o n from coloured dissolved ew l a t e inorganic matter (m "*") and k (m ^/mg/1 phytoplankton).  and p a r t i c u -  i s a result of phytoplankton  While i t i s d i f f i c u l t to completely  shading separate  the two f a c t o r s , a measurement of l i g h t absorption during the winter (not under i c e cover) when production i s minimal i s a good i n d i c a t i o n of k ew Edmondson (1956) describes a method for converting Secchi-disk measurements to e x t i n c t i o n c o e f f i c i e n t s : ew  D  where C i s an e m p i r i c a l l y determined dimensionless i s the Secchi-disc transparency  constant of 1.7 and D  (m). The maximum Secchi-disc transparency  i n Skaha Lake i n 1971 was 7 m, which indicates an e x t i n c t i o n c o e f f i c i e n t of 1.7/7 = 0.24/m. The r e l a t i o n s h i p between a l g a l c e l l density and l i g h t absorption i s reported by Azad and Borchardt  (1969).  These results are interpreted by  Chen (1970) and D i Toro et al. (1971) i n the following formulation of k k  ep  = 0.17 B c  where B^ i s the concentration of phytoplankton  i n mg/1.  The e x t i n c t i o n co-  e f f i c i e n t , k , therefore has been given the following form: e  k  e  :  = 0.24 + 0.17 B c  91  The biomass of phytoplankton i n the trophogenic layer(B, kg) i s 3  converted to concentration (B^, kg/km ) through d i v i s i o n by the volume of 3  the trophogenic layer(km ). *  (Concentration i n kg/km  3  i s converted to con-  , -6 centration i n mg/1 through m u l t i p l i c a t i o n 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 km . 3  (3) Nutrient Dependency.  The r e l a t i o n s h i p between phyto-  plankton growth and nutrient concentration i s most often expressed by a Michaelis-Menton 1967,  (or Monod growth k i n e t i c s ) expression (Ketchum 1939, Ketchum  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:  .  y  -  (  "S\ K  [ N ]  ^  + [N]  )  where y i s the average daily growth r a t e (day ^) ; K^, i s the maximum d a i l y growth rate (dependent on temperature  and defined i n a previous section, day ^ ) ;  [N] i s the concentration of the l i m i t i n g nutrient i n the trophogenic layer (mg/1); and K^ i s the Michaelis-Menton, or h a l f - s a t u r a t i o n constant f o r phytoplankton growth with the l i m i t i n g nutrient (Figure 9). The h a l f - s a t u r a t i o n constant i s defined as the nutrient concentration at which growth i s h a l f 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 l i m i t i n g nutrient (Fuhs e_t a l . 1972). Growth rates are shown at varying p^ values with a h a l f - s a t u r a t i o n constant of approximately 1 ug/1 phosphate.  93 According to Di Toro et al.  (1971),  "There exists an increasing body of experimental evidence to support the use of this funct i o n a l form IMichaelis and Menton] for the dependence of the growth rate on the concentration of e i t h e r phosphate, n i t r a t e , or ammonia i f only one of these nutrients i s i n short supply." It w i l l be assumed that phosphorus i s the nutrient i n short supply i n Skaha Lake, and that approximately h a l f of the supply of t o t a l phosphorus i n the trophogenic layer i s " b i o l o g i c a l l y a c t i v e , " and therefore p o t e n t i a l l y available f o r growth (Gachter 1971 makes a s i m i l a r assumption Swiss lakes). assumption  According to J . G. Stockner (personal communication),  the  that phosphorus i s the l i m i t i n g nutrient f o r most of the season  i n Skaha Lake i s a reasonable one. al.  for several  Although bioassay r e s u l t s (Stockner et  1972c) show nitrogen to be more l i m i t i n g than phosphorus during two per-  iods of 1971, phosphorus probably became l i m i t i n g l a t e r i n the summer during a bloom of blue-green algae {Gleotrichia').  I t i s u n l i k e l y that blue-green  algae, of which many species possess the c a p a b i l i t y to f i x nitrogen d i r e c t l y from the molecular form i n the trophogenic layer, would be limited by n i t r o gen.  High rates of nitrogen f i x a t i o n have been correlated with high produc-  tion rates of blue-green algae, primarily Anabaena, menon (Brezonik 1972).  G l e o t r i c h i a , and  Aphanizo-  Phosphorus, there fore, i s generally regarded to be the  most important l i m i t i n g nutrient to the growth of blue-green algae. gerald (1972) notes that: ". . . i f bioassays are carried out with mixtures of n i t r o g e n - f i x i n g and nonnitrogen-fixing phytoplankton, i t might be d i f f i c u l t to interpret the r e s u l t s , since the n i t r o g e n - f i x i n g species could be phosphorus limited and the nonfixing algae could be nitrogen l i m i t e d but have surplus phosphorus. . .  Fitz-  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 d i f f e r e n t times." The Michaelis-Menton  c o e f f i c i e n t for phytoplankton  growth with  phosphorus as the l i m i t i n g n u t r i e n t i s known to vary for d i f f e r e n t a l g a l species.  Di Toro et al. (19 71) have interpreted the r e s u l t s of  s i x i n v e s t i g a t i o n s , and report a v a r i a t i o n between 0.006 and 0.025 mg/1 phosphorus.  Fuhs et al. (1972) report lower values near 0.001 mg/1 f o r  two species of diatoms. (4) F i n a l Growth Rate Expression.  The growth rate of phyto-  plankton i s assumed to depend on temperature, l i g h t , and n u t r i e n t s , and the preceeding formulations separately describe the e f f e c t s of these three limiting factors.  Each of the three formulations can be considered a  "reduction f a c t o r " since each one reduces the t h e o r e t i c a l maximum growth rate.  Therefore, i t i s r a t i o n a l to multiply the three formulations t o -  gether to arrive at a f i n a l growth rate expression.  The same r a t i o n a l e i s  followed by Ketchum (1939) i n dealing with two n u t r i e n t s , and by Riley (1965), Chen (1970) and D i Toro et al, (1971) i n dealing with temperature, l i g h t and nutrients.  Following t h i s procedure,  G P  the growth rate expression becomes:  x maximum t h e o r e t i c a l growth rate dependent on temperature  I I j — exp(l - ~ ) m m reduction factor for light  x  [P] reduction factor for phosphorus  95  where [P] i s the concentration of " b i o l o g i c a l l y a c t i v e " phosphorus  (mg/1).  Other terms have been defined previously. (d) Phytoplankton Losses.  The loss of phytoplankton c e l l s 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-  s u l t s i n degradation of a l g a l protoplasm to supply energy f o r s u r v i v a l (McKinney 1962).  The chemistry of endogenous metablism i s the same as  the f a m i l i a r one f o r r e s p i r a t i o n :  c  c  7 o H  <A>  Q  N  + 6.25 0  5.7 C0 + NH. + 3.4 H„0  o  o  McKinney notes that the demand f o r oxygen i n the absence o f sunlight f o r photosynthesis can be as great as the photosynthetic production of oxygen. Using data from Riley et al. (1949), D i Toro et al. (1971) have established the following r e l a t i o n s h i p f o r a l g a l r e s p i r a t i o n 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, c i t e d i n Di Toro et a l . 1971).  96  Di  Toro et al. conclude that a straight l i n e adequately f i t s these data,  which can be formulated as:  R = K_T P 2 where R^ i s the endogenous r e s p i r a t i o n rate (day "*"),  i s a constant which  i s approximately 0.005 ± 0.001, and T i s °C. (2) Grazing by Zooplankton. ing in  Loss of phytoplankton by graz-  can be the most s i g n i f i c a n t factor reducing phytoplankton biomass. s i t u method of measuring  An  the grazing rate of the zooplankton community  (excluding animals less than 70 u) i n a eutrophic lake i s reported by Haney (1970; c i t e d i n Rigler 1973). Results show that organisms (.Pseudomonas), yeast (Rhodotorula),  such as bacteria  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 f r a c t i o n o f small algae eaten each day) i f zooplankton are 100 per cent e f f i c i e n t at a s s i m i l a t i n g t h e i r food. Based on studies of the a s s i m i l a t i o n e f f i c i e n c y of zooplankton (Marshall and Orr 1953, Corner et al. 1967, and Conover 1964, 1966; c i t e d i n Rigler 1973), Rigler (1973) assumes that a reasonable estimate ciency i s approximately 60 per cent.  of e f f i -  The a s s i m i l a t i o n e f f i c i e n c y i s probably  lower i f blue-green algae make up a s i g n i f i c a n t part of the t o t a l a l g a l population.  The resistance of blue-green algae to grazing i s one reason f o r  large blue-green blooms (Odum 1971).  I t i s suggested that the a s s i m i l a t i o n  e f f i c i e n c y i s h a l f (30 per cent) when blue-green algae dominate the population.  The following expression describes the loss o f algae by grazing:  Z =(K )(K ) p  where Z  p  G  A  i s the rate of grazing loss by zooplankton (day  K  grazing rate with 100 per cent e f f i c i e n c y (0.79 day "*"), and K  i s the i s the  c o e f f i c i e n t of a s s i m i l a t i o n e f f i c i e n c y (0.3 to 0.6). (3) Sinking of Phytoplankton C e l l s .  Sinking rates of dead  c e l l s vary according to the s i z e , shape, and chemical  composition  of the  c e l l s , and are therefore a function of the c h a r a c t e r i s t i c s of the algal species.  For example, some species of blue-green algae contain gas vacuoles  which slow their sinking rates (Morris 1967, B e l l a 1970), and some diatom species sink f a s t e r 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).  B e l l a (1970) r e -  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. 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 data i t appears that a reasonable  Lund (1959)  species.  From these  estimate of the sinking rate i s between  0.5 and 1.0 m/day. Using t h i s estimate, the d a i l y loss of algae from the trophogenic layerby sinking would be s i x to 12 per cent (e.g. 0.06/day).  0.5 m/day * 8 m =  An expression describing the rate of sinking losses i s :  S = V IT p s' t  98  where S i s the rate of sinking losses (day p toplankton sinking (m/day), and T  ), V  s  i s the v e l o c i t y of phy-  i s the thickness of the trophogenic  layer(m) . (4) Advection Losses.  Because of the r e l a t i v e non-motility  of phytoplankton, some loss w i l l occur through hydrologic flow at the outl e t of the lake (Uhlmann 1972).  The following expression describes this  rate of l o s s :  Where Op i s the rate of outflow loss of phytoplankton  (day  ), Q i s the  3  d a i l y discharge from the outlet of the lake (m /day), and V  i s the volume  3  of the Crophogenic layer(m ). 5.  Hypolimnetic Dissolved Oxygen Submodel Although i t i s not necessary to predict dissolved oxygen i n  the hypolimnion i n order to model phosphorus and phytoplankton, this i n f o r mation serves as a useful check on other parts of the model. status of hypolimnetic water has great importance  The oxygen  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 i s a v a i l a b l e to formu-  l a t e a s i m p l i f i e d 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 i s  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 f o r the i n i t i a l conditions.  Except for a minor amount  of eddy d i f f u s i o n of oxygen from the epilimnion (ignored i n this  submodel),  the beginning of s t r a t i f i c a t i o n i s o l a t e s 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 d i r e c t function of the amount of organic matter sedimenting i n t o the region below the thermocline.  The conclusion of Burns and Ross (1972) that approximately 88 per  cent of the hypolimnetic oxygen of Lake E r i e was consumed i n the decay of organic matter supports t h i s assumption.  Decomposition of organic matter  i s assumed to proceed according to the following r e a c t i o n (Fogg 1953):  C  5  ?  H  Q  g  0  2 3  N + 6.25 0  2  -> 5.7 C0 + NK^ + 3.4 H 0 2  2  Therefore, f o r 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 f o r each 129 g-atoms of phytoplankton decomposed, 200 g-atoms o f oxygen are used.  Converting to a simpler r a t i o ,  for each gram of phytoplankton decomposed, 1.55 g of oxygen i s used. The following formulation describes the use of oxygen through decomposition i n the hypolimnion:  100  DO  (.4 B S  dc  C F  phytoplankton sinking from epilimnion  where D0^  c  .83)  (1.55) coefficient of oxygen use  coefficient of decomposition  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^ i s the concentration of phytoplankton biomass i n the epilimnion (mg/1); S  p  i s 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  i s the stoichiometric  c o e f f i c i e n t of oxygen use per mg of phytoplankton decomposed; k^ i s the temperature-dependent c o e f f i c i e n t of decomposition (defined i n the regeneration submodel); and  i s 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 v e r i f i c a t i o n of the model:  (1) the t o t a l phosphorus concentration  i n the upper mixed layer of the lake (the whole lake during mixing); (2) the phytoplankton concentration i n the trophogenic layer; and the minimum dissolved oxygen concentration i n the hypolimnion.  (3)  Collec-  tion and analysis of these limnological data are discussed i n Appendix B. During the year of simulation (March 1969 to March 1970), the t o t a l input phosphorus from a l l known sources was  24,500 kg (see Table  A-3) of Appendix A f o r percentages of d i f f e r e n t sources).  Variations  of input and output of phosphorus to and from Skaha Lake during the simulation year are shown i n Figure 11. t r a t i o n i n March 1969 was 27 yg/1  The i n i t i a l phosphorus  concen-  (conditions of complete mixing; Stein  and Coulthard 1971). 1.  Total Phosphorus Concentration (a) Upper Mixed Layer.  In the process of mathematically simulating  a n a t u r a l system, the modeller generally learns something of h i s basic assumptions.  about the v a l i d i t y  While the i n i t i a l simulation of the phosphorus  concentration i n the upper mixed layer (Figure 12) indicates a reasonable  The following r e s u l t s pertain to the north basin, except where the south basin i s s p e c i f i c a l l y discussed. 101  102  500  120 180 240 TIME(DAYS)  300  Figure 11. Loading rate of phosphorus to Skaha Lake, 1969-70 (upper curve) and phosphorus outflow rate (lower curve).  360  103  0  60  120 180 240 TIME(DAYS)  300  F i g u r e 12. Phosporus c o n c e n t r a t i o n i n s u r f a c e water o f Skaha Lake, 1969-70, w i t h no m o d i f i c a t i o n o f o r i g i n a l assumptions ( c i r c l e s i n d i c a t e o b s e r v e d v a l u e s and s o l i d l i n e s i m u l a t e d values).  360  104  fit  to the shape of the r e a l data, there are two s i g n i f i c a n t discrepancies.  The f i r s t i s that minimum simulated concentrations i n midsummer are consistently 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 i s underestimated; or (2) the rate of eddy d i f f u s i o n of phosphorus from the hypolimnion to the epilimnion i s overestimated. To evaluate the f i r s t , the c o e f f i c i e n t of eddy d i f f u s i o n was reduced by 20 per cent (a maximum reasonable margin of e r r o r ) , but no appreciable difference was observed i n the simulated phosphorus concentration.  However, when the sedimentation of phosphorus from the e p i l i m -  nion was doubled  (Figure 13), the f i t was considerably improved  midsummer minimum values.  f o r the  Doubling the phosphorus sedimentation i s a  reasonable change i n the o r i g i n a l assumption  f o r the following reasons.  The sedimentation submodel i s d i r e c t l y dependent on the biomass of phytoplankton i n the trophogenic layer (Chapter IV).  As stated i n Chapter IV,  this i s a conservative estimate of sedimentation loss because other organisms (bacteria, zooplankton, fish) also sediment the amount of phosphorus i n the upper layer.  to the bottom and decrease  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 p r e c i p i t a t i o n of inorganic phosphorus minerals l i k e apatite (Golterman 1973).  (Rates of phosphorus loss by sedimentation from  the epilimnion are shown i n Figure 14. The lower curve represents regeneration from l i t t o r a l sediments by b a c t e r i a l decomposition).  105  100  Q_ CO  o zn  CL.  0  60  120 180 240 TIME(DAYS]  300  Figure 13. Phosphorus concentration i n surface water of Skaha Lake, 1969-70, with the sedimentation rate from the epilimnion doubled ( c i r c l e s indicate observed values and s o l i d l i n e simulated values).  360  106  500  o 200 |  150 1  P  100 t  Q_  120 180 240 TIME(DRYS)  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).  360  107  The second discrepancy apparent i n the simulated r e s u l t s of Figure 13 shows the lake l o s i n g phosphorus between the mixing period of March 1969 (day 1) and the same period i n March o f 1970 (day 360). The simulated curve shows the lake with a f i n a l concentration of 26 yg/1, whereas a n a l y t i c a l data showed that the lake a c t u a l l y increased i n concentration to 33 yg/1.  A p l a u s i b l e 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 i n a f i n a l concentration o f 35 yg/1. A correct simulated concentration of 33 yg/1 was achieved by increasing the regeneration rate 3.5 times  (Figure 15).  Apparently, b a c t e r i a l decom-  p o s i t i o n 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 d i f f u s i o n , turbulent mixing, and chemical r e generation are discussed i n Chapter IV. Estimated sedimentation  losses from the hypolimnion  ation are shown i n Figure 16 (estimates according to revised  and regenerassumptions).  The sedimentation losses are divided i n t o organic and inorganic components i n Figure 17. Organic sedimentation  i s a dynamic function o f phytoplank-  ton production, while inorganic sedimentation by adsorption i s shown as a r e l a t i v e l y constant process. (b) Hypolimnion Phosphorus.  During 1969-70 phosphorus determinations  were made to a depth of only 20 m i n Skaha Lake, which has a maximum depth of 57 m.  As phosphorus concentrations often tend to increase i n the hypo-  108  100  120 180 240 TIME(DRYS)  300  Figure 15. Phosphorus concentration i n surface water of Skaha Lake, 1969-70, with the sedimentation rate from the epilimnion doubled and the regeneration rate from deepwater sediments X 3.5 ( c i r c l e s indicate observed values and s o l i d l i n e simulated values).  360  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  F i g u r e 17. S i m u l a t e d s e d i m e n t a t i o n r a t e s o f o r g a n i c phosphorus (upper curve) and i n o r g a n i c phosphorus (lower curve) from the h y p o l i m n i o n o f Skaha Lake, 1969,-70.  Ill  limnion of deep lakes during summer s t r a t i f i c a t i o n  (Golterman 1973), the  measurements from Skaha are not considered s u f f i c i e n t for v a l i d a t i o n purposes.  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 o f peaks could not be p r e c i s e l y predicted.  The simulated peak  of the f i r s t bloom lagged 20 to 30 days behind the r e a l peak, and could not be modified by manipulation of growth c o e f f i c i e n t s (within l i m i t s reported i n the l i t e r a t u r e ) .  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 r a t e , losses from grazing are underestimated phytoplankton 3.  a t high  production.  Dissolved Oxygen i n the Hypolimnion According to the submodel i n Chapter IV, dissolved oxygen i n the  hypolimnion  i s d i r e c t l y dependent on phytoplankton  of 20 to 30 days between  production, and the l a g  real and simulated values (Figure 20) i s a r e f l e c -  tion of the lag i n the phytoplankton  simulation.  Agreement between real  and simulated values at the end of summer stagnation (about 6 mg/1) i s r e l a t i v e l y close.  Because oxygen use i n the hypolimnion  i s an i n d i r e c t mea-  sure of the amount of organic matter produced i n the lake and sedimented to  the hypolimnion,  the values a t the end of summer stagnation are an  approximate i n d i c a t i o n of the sum of organic productivity during the growing  season.  112  CD  o cx  100 90 I 80 70 • 60 ••  y  501  o  40 -  CO  30 ••  g 20} m o_ 10 co o 0 IE CL 0  ——I  60  1  1  1  1  1  h—i  1  1  1  1—  H  120 180 240 TIME(DAYS)  1  1  1  (-  300  Figure 18. Simulated phosphorus concentration i n the hypolimnion of Skaha Lake, 1969-70.  360  113  Figure 19. Phytoplankton biomass i n the trophogenic layer of Skaha Lake, 1969-70 (dashed l i n e indicates observed values and s o l i d l i n e simulated values).  114  F i g u r e 20. D i s s o l v e d oxygen c o n c e n t r a t i o n i n the hypol i m n i o n o f Skaha Lake, 1969-70 ( c i r c l e s i n d i c a t e o b s e r v e d v a l u e s and s o l i d l i n e s i m u l a t e d v a l u e s ) .  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 i s 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 f o r the north basin are 0.517 p o t e n t i a l than the north basin.  km  and 28 m), has greater eutrophic  In addition, p r e v a i l i n g north winds i n  summer b r i n g f l o a t i n g a l g a l matter from the north basin to the south. V e r i f i c a t i o n of simulated values f o r the south basin was  simi-  l a r to v e r i f i c a t i o n f o r the north basin (no figures are presented).  More  eutrophic conditions i n the south basin are evidenced by more measured phosphorus at the end of the year (37 yg/1 compared to 33 yg/1 f o r 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 5.  compared to 6.6 mg/1  f o r the north basin).  V e r i f i c a t i o n for 1970-71 and 1972-73 During the next year (March 1970  hydrologic conditions occurred.  to March 1971),  quite d i f f e r e n t  While 1969-70 was nearly an average hydro-  l o g i c year (11 per cent higher than the average discharge from Skaha Lake; Table A-4 i n 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-  l o g i c 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 i n March 1970  to 53 yg/1 i n March 1971.  This predic-  tion i s within 12 per cent of the measured concentration of 60 yg/1 for A p r i l 1971  (Williams 1972).  No phytoplankton or dissolved oxygen data are  116  available f o r the summer of 1970. No data i s a v a i l a b l e f o r the spring and summer of 1972, making i t impossible to v e r i f y the model f o r 1971-72.  During this period hydro-  l o g i c conditions were average (14 per cent higher than 1969-70), and phosphorus loading was approximately the same as i n the previous  two years.  During the period March 1972 to March 1973 s i g n i f i c a n t changes occurred i n both phosphorus loading and hydrologic flow.  This was the  f i r s t year the phosphorus removal system i n the Penticton sewage treatment plant was operating e f f e c t i v e l y , r e s u l t i n g i n 50 to 60 per cent removal o f phosphorus from municipal sources (Haughton et al. 1974).  This resulted i n  an o v e r a l l loading decrease of approximately 33 per cent from the previous year.  An unusually heavy snowpack resulted i n the highest yearly flow on 8  record through Skaha Lake:  10.4 X 10  3 m  (884,000 a c r e - f t ) , o r approxi-  mately twice the flow of 1969-70 (an average year). With these new loading and hydrologic conditions, the model predicts a t o t a l phosphorus concentration of 16 yg/1 for the spring of 1973 i n the north basin, a large decrease from 42 yg/1 the previous spring.  Lake data  for the spring of 1973 indicates a concentration o f 13 yg/1 i n the north basin (B.C. P o l l u t i o n Control Branch, courtesy of E. R. Haughton).  The  modelled value i s therefore within 23 per cent of the a n a l y t i c a l value. Based on this low spring phosphorus concentration, the model predicts s i g n i f i c a n t l y lower phytoplankton growth during the summer of 1973 (peak of 2.9 mg/1), probably not i n the bloom category. munication) confirms during 1973.  A. M. Thomson (personal com-  that there were no serious a l g a l problems i n Skaha Lake  117  B.  SENSITIVITY ANALYSES Two  types of s e n s i t i v i t y are important  i n this simulation.  The  f i r s t i s the s e n s i t i v i t y of the model to the major " f o r c i n g functions": phosphorus loading and hydrologic discharge.  The second i s the s e n s i t i v i t y  of the model to changes i n the 15 p h y s i c a l and b i o l o g i c a l c o e f f i c i e n t s  (con-  stants) used i n the submodels.  1.  S e n s i t i v i t y of Phosphorus Loading and Hydrology Simulation results of the three trophic i n d i c a t o r s (phosphorus,  phytoplankton,  and hypolimnetic dissolved oxygen) are shown i n Figure  21a.  For comparison with subsequent simulations, a key value of each i n d i c a t o r i s chosen:  (1) the concentration of t o t a l phosphorus at the end of the  year; (2) the peak value of phytoplankton  biomass; and  concentration of dissolved oxygen i n the hypolimnion. 21a) these values are: dissolved oxygen 6.6  (3) the minimum For 1969-70 (Figure  phosphorus 33 yg/1, phytoplankton  4.6 mg/1,  and  mg/1.  Simulations at varying loading and hydrologic discharge are presented i n Figures 21b - 21f.  Figure 21b shows the indicators with the phos-  phorus loading doubled (49,000 kg/year).  The e f f e c t of this hypothetical  loading i s to increase the phosphorus concentration to 64 yg/1 to increase the phytoplankton  peak to 6.3 mg/1  the hypolimnetic dissolved oxygen to 1.9 mg/1  (from 33),  (from 4.6), and to decrease (from  6.6).  Simulation at h a l f of the o r i g i n a l loading (12,250 kg/yr) (Figure 21c) indicates quite d i f f e r e n t trophic conditions.  Phosphorus concentration  decreases to 19 yg/1 by the end of the year, the phytoplankton  peak i s 3.2  118  (b) Loading doubled  (a) Loading and discharge for 1969-70  Q_ tn o X Q.  60  120 180 240 TIME(DflYS)  60  300  120 180 240 TIME(DAYS)  300  360  (d) Discharge doubled  (c) Loading halved  60  120 180 240 TIME(DAYS)  300  360  (e) Discharge halved -I 15  60  120 180 240 TIME(DAYS)  300  (f) Loading halved and discharge doubled  360  15  o u  cn ZD  ce o X Qin o X 0-  60  120 180 240 TIME(DAYS)  300  360  60  120 180 240 TIME(DAYS)  300  Figure 21. Simulated phosphorus ( s o l i d l i n e ) , phytoplankton (short dashes) and hypolimnetic dissolved oxygen (long dashes) with varying phosphorus loading and hydrologic discharge, Skaha Lake, 1969-70.  360  119  mg/1, and hypolimnetic dissolved oxygen decreases only to 9.4 mg/1. Trophic conditions s i m i l a r to effects of halving the loading are simulated by doubling the hydrologic discharge (Figure 21d; the o r i g i n a l loading of 24,500 kg i s maintained). 22 yg/1, the phytoplankton oxygen  Phosphorus concentration decreases to  peak i s 3.5 mg/1, and the hypolimnetic dissolved  minimum i s 9.0 mg/1.  Halving the discharge  (while maintaining  origi-  n a l loading) produces simulated conditions s i m i l a r to the e f f e c t s of doubling the loading (Figure 21e):  phosphorus increases to 47 yg/1,  phytoplankton  concentration peaks a t 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 s i g n i f i c a n t l y 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. I t i s s i g n i f i c a n t that large changes i n trophic status may theoret i c a l l y occur i n only one year as a r e s u l t o f variations i n hydrology and phosphorus loading.  This theory was tested during 1972-73 (as described i n  the previous s e c t i o n ) , and the r e s u l t s show that although s i g n i f i c a n t changes did occur during the year of high runoff and decreased impact was evident during the following year.  loading, an even larger  Hence, the hydrologic and  loading condit ions occurring from March 1972 to March 1973 resulted In a decrease i n spring phosphorus concentration of 26 yg/1 (from 42 to 16). The lower phosphorus concentration resulted i n  s i g n i f i c a n t l y lower phytoplank-  ton production during the summer of 1973, and no serious a l g a l blooms.  120  2. S e n s i t i v i t y of P h y s i c a l and B i o l o g i c a l  Coefficients  The s e n s i t i v i t y of 15 physical and b i o l o g i c a l c o e f f i c i e n t s 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 c o e f f i c i e n t as reported  in the l i t e r a t u r e (Chapter IV) i s shown i n column 2, and the value used i n the simulation i s shown i n column 3.  The simulated  phosphorus concentra-  tion (using the c o e f f i c i e n t values i n column 3) i s shown i n column 4.  The  r e s u l t i n g phosphorus concentration when the c o e f f i c i e n t i s set at i t s minimum value (with a l l other c o e f f i c i e n t s remaining the same) i s shown i n column 5, and the concentration with the c o e f f i c i e n t at i t s maximum value i s shown i n column 6.  The maximum per cent deviation from the simulated concentration  (33 yg/1) i s shown i n column 7. position  The analysis shows the c o e f f i c i e n t o f decom-  (k^) to be the most s e n s i t i v e , with a maximum p o s i t i v e deviation of  15 per cent.  This s i m p l i f i e d s e n s i t i v i t y analysis does not explore the  i n t e r a c t i v e s e n s i t i v i t y o f the 15 c o e f f i c i e n t s as they vary with respect to each other, but i t does give an approximate index of r e l a t i v e s e n s i t i v i ties . Table VIII explores the s e n s i t i v i t i e s of the same c o e f f i c i e n t s with respect to the phytoplankton peak, and indicates much greater deviations than with respect to phosphorus concentration. cient appears to be the Michaelis-Menton  The most sensitive  half-saturation  constant  coeffi(K^), which  can cause an increase of 56 per cent i n simulated phytoplankton biomass when the minimum value reported i n the l i t e r a t u r e i s used i n the model. ing v e l o c i t y  The sink-  (Vg) i s apparently the second most sensitive c o e f f i c i e n t , caus-  ing a maximum positive deviation of 39 per cent i n phytoplankton biomass.  TABLE V I I SENSITIVITY OF COEFFICIENTS ON PHOSPHORUS CONCENTRATION  COEFFICIENT  RANGE REPORTED IN LITERATURE  VALUE USED  SIMULATED CONCENTRATION FOR VALUES IN COLUMN 3  CONCENTRATION USING MINIMUM VALUE  CONCENTRATION USING MAXIMUM VALUE  MAXIMUM PECENTAGE DEVIATION FROM COLUMN 4  I  d k  k  d  k  rh  V T  K  v  pb  G  s  2 k k  Z  «H kl re k  1  .03 - .05 80 - 120 .4 - .6 • ±20% .15 - .19 .007-.015 150-300 .4 - .7 .6 - .9 .5 - 1.5 .004- .006 .15 - .25 .001 -.03 .075 -.125 .3 - .5  .04 100 .5 .17 .009 200 .6 .79 1.0 .005 .20 .01 .10 .4  33 33 33 33 33 33 33 33 33 33 33 33 33 33 33  29 36 34 34 32 33 32 32 33 33 33 33 33 33 33  38 30 32 33 34 32 33 33 33 33 33 33 33 33 33  +15 + 9 + 3 + 3 ± 3 - 3 - 3 - 3 0 0 0 0 0 0 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 a d s o r p t i o n 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 a d s o r p t i v e r e l e a s e k , = c o e f f i c i e n t o f phosphorus i n biomass 1^ = l i g h t i n t e n s i t y o f maximum growth K = c o e f f i c i e n t o f zooplankton a s s i m i l a t i o n A  K  G  re  coefficient of grazing v e l o c i t y of s i n k i 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 o f l i g h t e x t i n c t i o n f o r p l a n k t o n biomass Michaelis-Menton h a l f - s a t u r a t i o n coefficient c o e f f i c i e n t o f 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 e p i l i m n i o n  TABLE VIII SENSITIVITY OF COEFFICIENTS ON PHYTOPLANKTON PRODUCTION  COEFFICIENT 1  A hi  l pb G k k . re k k  k  K  e p  d 2 k a vr h a k  k  k  n  RANGE REPORTED IN LITERATURE ? .001 .5 .4 150 .075 .007 .6 .15 .3  - .03 - 1.5 - .7 - 300 - .125 - .015 - .9 - .25 - .5 ±20% .03 - .05 .004 - .006 80 - 120 .4 - .6 .15 - .19  VALUE USED 3  .01 1.0 .6 200 .10 .009 .79 .20 .4 .04 .005 100 .5 .17  SIMULATED CONCENTRATION FOR VALUES IN COLUMN 3 4  4.56 4.56 4.56 4.56 4.56 4.56 4.56 4.56 4.56 4.56 4.56 4.56 4.56 4.56 4.56  CONCENTRATION USING MINIMUM VALUE  CONCENTRATION USING MAXIMUM VALUE  ' MAXIMUM PERCENTAGE DEVIATION FROM COLUMN 4  5  6  7  7.13 6.35 5.99 5.24 3.62 5.04 5.56 5.26 5.11 4.09 4.34 4.69 4.65 4.60 4.52  2.51 3.39 4.12 3.29 5.69 3.55 4.18 4.01 4.11 4.13 4.78 4.43 4.47 4.52 4.60  +56 +39 +31 -28 +25 -22 +22 +15 +12 -10 ±5 ±3 ±2 ±1 ±1  123  C.  EDDY DIFFUSION Eddy d i f f u s i o n of phosphorus from the hypolimnion to the e p i -  limnion cannot be v e r i f i e d , as t h i s movement cannot be d i r e c t l y measured. According to the eddy d i f f u s i o n submodel (Chapter IV), "loading" of phosphorus to the epilimnion by eddy d i f f u s i o n 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 d i f f u s i o n .  During t h i s time the predicted  concentration  difference between the epilimnion and hypolimnion reached a maximum of AO yg/1.  124  500 450  I  H  1  1  120 180 240 TIME(DAYS)  1  1  1  1  300  1  1  H  360  Figure 22. Loading rate of phosphorus from external sources to Skaha Lake, 1969-70 (upper curve) and simulated " i n t e r n a l loading" to the epilimnion by eddy d i f f u s i o n (lower curve).  CHAPTER VI  DISCUSSION  A.  INTERPRETATIONS AND  LIMITATIONS  The s e d i m e n t a t i o n submodel assumes a d i r e c t tween p h y t o p l a n k t o n p r o d u c t i o n and phosphorus IV).  This  relationship  s e d i m e n t a t i o n (Chapter  r e l a t i o n s h i p i s e v i d e n t i n midsummer when the s e d i m e n t a t i o n  of dead o r g a n i c m a t t e r r e s u l t s  i n low v a l u e s of t o t a l phosphorus  c e n t r a t i o n i n the e p i l i m n i o n d u r i n g the peak o f the growing ( F i g u r e 13).  Because t o t a l phosphorus  phate i s m o d e l l e d ,  r a t h e r than d i s s o l v e d  and not s i m p l y l o s s e s  by organisms.  d e s c r i b e a l a k e which  The  uses the phosphorus  orthophos-  through uptake o f s o l u b l e  r e c e i v e s phosphorus  to  i n a form a v a i l a b l e f o r growth a v a i l a b l e through d e c o m p o s i t i o n ) ,  i n the p r o d u c t i o n o f o r g a n i c matter, and then s e d i -  ments a p o r t i o n of the dead p a r t i c u l a t e o r g a n i c phosphorus. sense, the t o t a l phosphorus  curve ( F i g u r e 13)  f o r s o l u b l e o r t h o p h o s p h a t e , which  1973);  season  low v a l u e s d u r i n g the summer appear  (or makes incoming p a r t i c u l a t e phosphorus  d u r i n g the growing  con-  these low v a l u e s must r e f l e c t s e d i m e n t a t i o n o f p a r -  t i c u l a t e phosphorus, phosphate  be-  that t o t a l phosphorus  d u r i n g the h e i g h t of the growing  this  i s s i m i l a r to the curve  u s u a l l y reaches n o n - d e t e c t a b l e l e v e l s  season i n a p r o d u c t i v e l a k e  But the f a c t  In  season may  (Hutchinson 1957,  remains a t d e t e c t a b l e l e v e l s make i t a more u s e f u l  c a t o r than orthophosphate of p o t e n t i a l primary p r o d u c t i o n .  125  Rigler  indi-  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 i n several possible ways.  F i r s t , i t could be assumed that sedimentation of phosphorus by  a l g a l organisms accounts for only half of the actual amount, and that sedimentation by other organisms (bacteria, zooplankton, f i s h ) must at least double the amount.  This assumption  was made i n f i t t i n g the simulated  curve to the r e a l data (Chapter V). Secondly, i t i s possible that other mechanisms are responsible for sedimentation of p a r t i c u l a t e phosphorus from the epilimnion. One p o s s i b i l i t y i s that p r e c i p i t a t i o n of phosphorus minerals such as apatite takes place.  Because no chemical p r e c i p i t a t i o n submodel was formulated  (for the reasons discussed i n Chapter IV), this p o s s i b i l i t y cannot be quantitatively explored.  Adsorption losses from the epilimnion to s e d i -  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 i n contact with 2.  sediments.  Regeneration of Phosphorus from Deep-water Sediments A s u r p r i s i n g 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 b a c t e r i a l  decomposition.  Several explanations are possible, the most obvious one being that much of the phosphorus sedimenting through the hypolimnion did not reach the sediments i n the f i r s t place, and was decomposed en route or chemical mechanisms.  by b i o l o g i c a l  This explanation would mean that the c o e f f i c i e n t  127  of recycling f o r the hypolimnion  (k j )  1 S  considerably higher than the  0.5/day value (±0.1) reported i n the l i t e r a t u r e (Chapter IV). A second explanation i s that sedimented phosphorus i s regenerated three to four times faster to the water than can be explained by processes of b a c t e r i a l decomposition.  Other mechanisms, such as d i f f u -  sion, p h y s i c a l disturbance by benthic organisms, turbulence during mixing periods, and chemical s o l u b i l i z a t i o n are p o s s i b i l i t i e s (discussed i n d e t a i l i n Chapter IV).  Regeneration  through turbulence during mixing  periods does not appear l i k e l y , however, as r e a l 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, l i g h t and nutrient conditions) exceeds the loss rate (a function of grazing, r e s p i r ation, sinking, and advection losses from the south end of the lake). i n i t i a l exponential growth phase i s temporarily reversed  The  around day 90 by  phosphorus deficiency caused by sedimentation of phosphorus-bearing a l g a l c e l l s , and by self-shading e f f e c t s .  The major probable reason that the  simulated r e v e r s a l i s not as great as the r e a l data indicates i s the omission of a dynamic zooplankton during high a l g a l growth.  submodel which would increase grazing losses  The lack of adequate zooplankton  data f o r Skaha  Lake precludes the v a l i d a t i o n of such a submodel. The second simulated growth phase (peak at day 100) i s terminated again by^phosphorus sedimentation  and self-shading, but at this higher  128  growth l e v e l the effects are more severe.  A t h i r d peak occurs around  day 150 because of continuing favorable conditions of temperature, and nutrients.  light  Losses by sinking and advection exceed growth after this  peak, and no net growth occurs a f t e r day 210 when temperature and l i g h t conditions become unfavorable. The e f f e c t s of phosphorus on the growth rate are separated from those of temperature and l i g h t i n Figure 23.  This analysis excludes  the e f f e c t s of losses (grazing, r e s p i r a t i o n , 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 l i g h t , while assuming that there i s an abundance of a v a i l able phosphorus.  The lower curve represents the growth rate with a l l  three l i m i t i n g factors included.  I f the assumption  i s accepted that  phosphorus i s the l i m i t i n g nutrient f o r most of the growing season, the difference between the two curves indicates the s p e c i f i c e f f e c t of phosphorus l i m i t a t i o n on phytoplankton growth. Several simplifying assumptions  have been made i n the formula-  t i o n of the primary production submodel which l i m i t diction.  i t s accuracy of pre-  D i f f e r e n t rates of phosphorus uptake, sinking, and grazing pre-  ference by zooplankton f o r d i f f e r e n t 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 p h y t o f l a g e l l a t e s , while the second was dominated by blue-green species.  Differences i n  the Michaelis-Menton h a l f - s a t u r a t i o n constant f o r phosphorus uptake, sinking rate, and grazing rate can be s i g n i f i c a n t between diatoms and  129  Figure 23. Simulated phytoplankton growth rates showing the l i m i t i n g effects of temperature and l i g h t (upper curve) and the l i m i t i n g effects of temperature, l i g h t and phosphorus (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 r e a l and simulated values could probably  be achieved by modelling the two a l g a l groups separately. Given these l i m i t a t i o n s and s i m p l i f y i n g assumptions,  the results  indicate that t o t a l phosphorus can be used as a measure of the most l i m i t ing nutrient i n the simulation of phytoplankton production i n Skaha Lake. The assumption  that approximately h a l f of the t o t a l phosphorus i s a v a i l a b l e  for growth (Gachter 1971)  appears to be reasonable.  In order to investigate  the e f f e c t s of other possible l i m i t i n g nutrients on phytoplankton production (e.g.  B.  nitrogen, carbon), a d d i t i o n a l models would have to be formulated.  APPLICATION TO MANAGEMENT OF THE EUTROPHICATION PROBLEMS OF SKAHA LAKE In this section an assessment i s made of the hypothetical long-  range (20-year) e f f e c t s of four d i f f e r e n t phosphorus management p o l i c i e s on the eutrophication of Skaha Lake. I.  The four management p o l i c i e s are:  No phosphorus removal and no growth i n the Penticton region  II.  60 per cent phosphorus removal (approximately the removal with chemical p r e c i p i t a t i o n 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 F i n a l 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 i r r i g a t i o n system of municipal waste disposal)  Policy IV assumes that 60 per cent of the phosphorus loading to Skaha Lake i s from Penticton municipal wastes (Haughton et a l . 1974), and  131 that the remaining  40 per cent from a g r i c u l t u r a l and n a t u r a l sources r e -  mains at a constant l e v e l .  The annual population growth estimates of  three per cent and 1.5 per cent r e s u l t i n a yearly increase i n phosphorus input of approximately  two per cent and one per cent, as only 60 per cent  of the annual input comes from municipal sources. Canada-British Columbia Okanagan  As reported i n the  Basin Agreement F i n a l 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-  c a l of the Okanagan Basin, outflow discharges from Skaha Lake for the 20-year period preceeding the year of simulation (1949-1969) are used. O  period yearly flows varied from 2.29 X 10 m  During t h i s  O  Q  (187,000 acre-ft) to 7.95  X 10 m  (646,000 a c r e - f t ) (see Table A-5 of Appendix A). The 20-year simulations of the four management p o l i c i e s 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 v a r i a t i o n s of the next 20 years are impossible to  predict.  Secondly,  the s i m p l i f y i n g assumptions and l i m i t a t i o n s inherent i n  the submodels make future predictions a risky exercise.  These simulations  are, therefore, only an attempt to show general trends that might be  ex-  pected i n the trophic indicators with the hydrologic v a r i a t i o n 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: phosphorus concentration of 33 yg/1, a phytoplankton hypolimnetic dissolved oxygen minimum of 6.6 mg/1.  peak of 4.6 mg/1,  a final and a  These same trophic i n d i -  cators are then modelled for a 20-year period with each of the four management p o l i c i e s .  132  The results of p o l i c y I (no treatment  and no growth) appear to  keep the lake i n as high or higher trophic state than i t was i n 1970 (Figure 24).  Except during r e l a t i v e l y 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 u n t i l the occurrence  of four r e l a t i v e l y dry years (years 12 - 15).  The  low flow causes the modelled concentration to exceed 60 yg/1, with associated 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 Coulthard 1971), phytoplankton  peaks appear to i n d i c a t e bloom conditions during  each of the 20 years. The r e s u l t s of p o l i c y II (high growth and 60 per cent removal; Figure 24) show at f i r s t an  improvement i n trophic conditions, but  by year 12 the s i t u a t i o n returns to the i n i t i a l eutrophic s t a t e .  By year  20 conditions have become nearly the same as the trophic state i n year 20 for p o l i c y I. Under p o l i c y I I I (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 s i t u a t i o n i s back to  the i n i t i a l trophic s t a t e .  The dry period does not appear to a f f e c t  the lake as s e r i o u s l y as with the higher loading rates of p o l i c y I I , but a l g a l growth appears to remain i n the bloom category. To investigate the e f f e c t s of removing a l l of the phosphorus from municipal sources (e.g. spray i r r i g a t i o n ) , a 20-year period with a 60 per cent reduction (no growth) was simulated (Figure 24).  Trophic con-  133  NO PHOSPHORUS REMOVAL AND NO  GROWTH  I e ^ o E  14  A A-  Phosphorus Phvtoolanhton Di s o l v e d o x y g e n  12 g  Iroli  I  \  /\  V'/  — V *  —  i  S  60  — •  |  ,'\  1/ o  40  i  i  PhosphofuS  O 8  60% PHOSPHORUS REMOVAL AND HIGH GROWTH  70  Phytoplankton Dissolved  A  /  y  x> > —  6  |  8  3  0  •6 4  v \  V  /  /  8  10 tn  12  y . a r i  14  — °"  \ ,'  —  n6  IB  a  A  \  V  10  o >•  o Tim*  I  K  v  ^  2  A  oxygen  s  0  10  20 in  12  14  yt a r t  Figure 24. Hypothetical effects of four different phosphorus management p o l i c i e s on the long-range eutrophication of Skaha Lake.  IS  18  \  134  d i t i o n s show s i g n i f i c a n t improvement: occur and phytoplankton  growth appears to remain at a tolerable l e v e l  during most of the period. when the phytoplankton  no low dissolved oxygen conditions  Even during an exceptionally dry year  (15)  peak reaches a l e v e l that could be considered a  minor bloom, the peak i s only h a l f of the i n i t i a l value. These simulations support the predictions of Stockner  and  Pinsent (1974) concerning the r e l a t i o n s h i p 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, d i s -  solved oxygen depletion, and other limnological data. above the " c r i t e r i a " area i n d i c a t e a moderate  Values within and  to high trophic s t a t e , and  the p r o b a b i l i t y of moderate to serious a l g a l blooms during most years. With phosphorus removal by advanced ("tertiary") treatment,  Stockner  and  Pinsent predict the p r o b a b i l i t y of frequent a l g a l blooms f o r moderate, high, and low population growth rates (I, I I , and III) after 1980.  With complete  removal of municipal phosphorus ("land treatment"), an acceptable trophic state with infrequent a l g a l blooms i s predicted.  This "steady s t a t e " s i t u a -  tion could, however, be upset i f phosphorus loading from Okanagan Lake i n creased s i g n i f i c a n t l y .  C.  SUITABILITY OF THE MODEL FOR OTHER LAKES The model has been formulated  for a lake with r e l a t i v e l y high  primary production, making i t more s u i t a b l e for eutrophic than o l i g o t r o p h i c lakes.  The key assumption of the sedimentation  submodel i s that sedimenta-  135  O  I  I 1970  I 1980  1 : 1990  I 2000  I 2010  I 2020  YEAR  Figure 25. Predictions of the trophic status of Skaha Lake with present phosphorus loading p o l i c i e s , t e r t i a r y treatment f o r phosphorus removal, and land disposal of sewage. Each policy i s considered f o r three projected growth scenarios. The area within and above the " c r i t e r i a " zone i s considered moderately to highly eutrophic (from Stockner and Pinsent 1974).  136  tion of phosphorus  i s a d i r e c t function of primary production i n the tropho-  genic layer, thus ignoring possible sedimentation by chemical p r e c i p i t a t i o n . While i t seems reasonable to assume that much of the soluble phosphorus i n a eutrophic lake such as Skaha i s u t i l i z e d i n . the production of organic matter, this may not be the case i n oligotrophic lakes such as Okanagan or Kalamalka.  Chemical p r e c i p i t a t i o n of phosphorus minerals such as apatite  probably plays a greater r o l e i n the phosphorus c e l l a et al. 1972, Lee 1970).  cycle of such lakes (Por-  Therefore, this model appears to be more  suited to eutrophic lakes such as Osoyoos.  A chemical p r e c i p i t a t i o n sub-  model would probably be a necessary addition f o r application of the model to an oligotrophic lake such as Kalamalka.  CHAPTER VII  SUMMARY AND  CONCLUSIONS  A simulation model of the phosphorus cycle i n eutrophic  Skaha  Lake shows t o t a l phosphorus to be a u s e f u l indicator for the p r e d i c t i o n of trophic states.  Difference equations and  a d a i l y 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 t i o n regime of the lake. T o t a l phosphorus movement between epilimnion, hypolimnion, and sediments i s detailed i n a series of submodels. submodel predicts loading  An eddy d i f f u s i o n  from the hypolimnion to the epilimnion which can  equal external loading for short periods of the summer.  A phosphorus s e d i -  mentation submodel predicts organic sedimentation on the basis of primary production and inorganic sedimentation from adsorption regeneration submodel considers  considerations.  A  the temperature-dependent decomposition  rates of sedimented phosphorus. A primary production submodel accounts for temperature, l i g h t and phosphorus dependency, as w e l l as r e s p i r a t i o n , grazing, sinking and  advection losses.  tions were necessary i n the formulation succeeded i n simulating  of detailed submodels, the model  three key trophic indicators reasonably w e l l .  on known phosphorus loading and agreement was  Although many s i m p l i f y i n g assump-  Based  three years of limnological data, reasonable  found between r e a l and simulated t o t a l phosphorus concentra-  t i o n , phytoplankton biomass, and hypolimnetic dissolved oxygen.  137  136  The model i s considered applicable to other eutrophic lakes, but not to o l i g o t r o p h i c lakes without ing sedimentation losses from  the i n c l u s i o n of a submodel d e s c r i b -  phosphorus mineral p r e c i p i t a t i o n .  The i n -  clusion of a submodel describing regeneration of phosphorus by d i f f u s i o n from sediments could improve p r e d i c t a b i l i t y , as r e s u l t s show that three to four times more phosphorus apparently returns to the lake from deepwater sediments than possible by b a c t e r i a l decomposition  alone.  This f i n d -  ing shows the model to be a u s e f u l research tool f o r i n d i c a t i n g areas needing further research.  Improved simulation of phytoplankton  production  could probably be achieved with the i n c l u s i o n of a zooplankton  submodel  and extension to include the s p e c i f i c growth dynamics of more than one a l g a l group.  The Michaelis-Menton  h a l f - s a t u r a t i o n constant appears to be  the most s e n s i t i v e c o e f f i c i e n t i n the primary production submodel. The probable e f f e c t s of four phosphorus management p o l i c i e s are assessed using 20 years of hydrologic data (1949-69) and the eutrophic conditions of 1970 as a s t a r t i n g point.  While no attempt i s made to pre-  d i c t the trophic status of the lake for the next 20 years, d e f i n i t e trends are apparent.  With no phosphorus removal and no increase i n loading over  the hypothetical 20-year period, phytoplankton  blooms increase i n i n t e n s i t y  and hypolimnetic dissolved oxygen approaches zero, while phosphorus concentrations are greater than 60 yg/1.  With 60 per cent removal of municipal  phosphorus and conditions of either low or high economic growth i n the Pent i c t o n region, the eutrophic conditions of 1970 are again reached within 12 to 14 years.  Algal blooms and hypolimnetic dissolved oxygen d e f i c i t s are  p a r t i c u l a r l y serious during dry years.  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No. 18 (Suppl. 1), 75 p.  APPENDIX A  INPUT DATA FOR SKAHA LAKE  TABLE A - l MIXING AND EDDY DIFFUSION DATA (North Basin)  D  A  T  E  EPILIMNION VOLUME (km ) 3  15 March 1969 1 A p r i l 1969 15 A p r i l 1969 1 May . 1969 15 May 1969 1 June 1969 15 June 1969 1 July 1969 15 July 1969 1 August 1969 15 August 1969 1 September 1969 15 September 1969 1 October 1969 15 October 1969 1 November 1969 15 November 1969 .1 December 1969 15 December 1969 1 15 1 15 1  January 1970 January 1970 February 1970 February 1970 March 1970  HYPOLIMNION VOLUME (km ) 3  THERMOCLINE VOLUME (kin )  THERMOCLINE THICKNESS (m)  COEFFICIENT OF EDDY DIFFUSION (cm /sec) 2  0 0 .024 .048 .070 .080 .090 .106 .114 .120 .125 .144 .160 .184 .210 .280 .517 0 0  .517 .517 .459 .415 .377 .35 7 .337 .315 .307 .303 .302 .285 .273 .253 .233 .187 0 .517 . .517  0 0 .034 .054 .070 .080 .090 .096 .096 .094 .090 .088 .084 .080 .074 .050 0 0 0  0 0 2.0 3.0 5.0 5.0 6.0 5.0 5.0 5.0 5.0 7.0 7.0 7.0 6.0 2.0 0 0 0  0 0 .077 .077 .051 .077 .020 .077 .077 .077 .077 .154 .077 .077 .077 .077 0 0 0  0 0 0 0 0  .517 .517 .517 .517 .517  0 0 0 0 0  0 0 0 0 0  0 0 0 0 0  \  TABLE A - l (Continued) MIXING;DATA (South Basin)  DATE 15 1 15 1 15 1 15 1 15 1 15 1 15 1 15 1 15 1 15  March 1969 A p r i l 1969 A p r i l 1969 May 1969 May 1969 June 1969 June 1969 July 1969 July 1969 August 1969 August 1969 September 1969 September 1969 October 1969 October 1969 November 1969 November 1969 December 1969 December 1969  1 15 1 15 1  January 1970 January 1970 February 1970 February 1970 March 1970  EPILIMNION VOLUME (km ) 0 0 .002 .014 .014 .014 .014 .014 .014 .014 .014 .014 .018 .024 .030 .036 .041 0 0 0 0 0 0 0  HYPOLIMNION VOLUME (km ) 3  .041 .041 .036 .022 .016 .016 .016 .016 .016 .016 .016 .016 .012 .008 .006 .003 0 .041 .041 .041 .041 .041 .041 .041  THERMOCLINE VOLUME (km ) 3  0 0 .003 .013 .011 .011 .011 .011 .011 .011 .011 .011 .011 .009 .005 .002 0 0 0 0 0 0 0 0  THERMOCLINE THICKNESS (m) 0 0 1.0 2.0 4.0 6.0 6.0 6.0 6.0 6.0 6.0 6.0 6.0 6.0 3.0 2.0 0 0 0 0 0 0 0 0  155  TABLE A-2 RADIATION AND EPILIMNION TEMPERATURE  NET RADIATION* (langleys/day; average f o r month)  DATE  15 1 15 1 15 1 15 1 15 1 15 1 15 1 15 1 15 1 15  March 1969 A p r i l 1969 A p r i l 1969 May 1969 May 1969 June 1969 June 1969 July 1969 July 1969 August 1969 August 1969 September 1969 September 1969 October 1969 October 1969 November 1969 November 1969 December 1969 December 1969  1 15 1 15 1  January 1970 January 1970 February 1970 February 1970 March 1970  315 361 553 569 579 500 312 203 89 47 82 163  EPILIMNION TEMPERATURE (°C)  1.8 3.0 5.8 8.4 11.3 14.8 18.6 20.2 20.4 20.6 20.6 18.4 15.2 13.0 11.2 9.6 7.8 5.8 4.0 3.0 2.4 1.8 1.2 1.4  1 langley = 1 g calorie/cm^; measured,with Eppley 180 Pyranometer at Summerland, B.C.; reported i n 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  Municipal sewage (Penticton) Okanagan Lake (via Okanagan River) Tributary streams (natural sources) Septic tanks ( v i a ground water) D u s t f a l l and p r e c i p i t a t i o n Agriculture ( v i a streams) Septic tanks (via streams) Ground water (natural sources) Industry Storm sewers Ground water (other sources) TOTAL  PERCENTAGE  59.7 21.9 7.6 5.3 3.5 0.7 0.4 0.3 0.3 0.2 0.1 100.0% (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  15 March - 31 March April May June July August September October November December January February 1 March - 15 March TOTAL  DISCHARGE (Acre-ft)  32,800 51,300 85,000 40,600 37,200 34,800 34,100 31,700 22,900 19,800 15,100 14,300 4,800 426,000  Although monthly values are shown here, d a i l y values were used i n computing inflow and outflow of phosphorus (from Surface Water Summary f o r B r i t i s h Columbia, Gov. of Canada, Dept. Transport). The average discharge for 48 years of record i s 386,000 a c r e - f t / y r .  158  TABLE A-5  YEARLY OUTFLOW HYDROLOGY FROM SKAHA LAKE, 1949 to 1973 (15 March to 15 March of the following year)  YEAR  1949 1950 1951 1952 1953 1954 1955 1956 1958 1959 1960 1961 1962 1963 1964 1965 1966 1967 1968 1969 1970 1971 1972  DISCHARGE (acre-ft/yr)  450.2 524.0 635.6 417.3 416.8 530.9 456.2 436.6 408.4 646.0 337.1 341.6 286.8 187.2 446.2 432.2 243.6 313.0 418.2 426.0 182.9 486.1 844.0  * From Surface Water Summary f o r B r i t i s h Columbia, Gov. of Canada, Dept. Transport  APPENDIX B  COLLECTION AND ANALYSES OF LIMNOLOGICAL DATA  During 1969-70 sampling of phosphorus, phytoplankton oxygen i n Skaha Lake was bimonthly  and dissolved  from 1 May to 15 September and monthly  the remainder of the year (Stein and Coulthard 1971).  Water samples f o r  chemical and b i o l o g i c a l analyses were taken i n two transects: the north basin and one across the south basin. data from each transect was averaged  one across  For use i n the model,  to give one value f o r 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 1.  f o r an epilimnion concentration. Total Phosphorus T o t a l phosphorus i n the lake was determined  method described by Gales et al. (1966).  according to the  This method involves a c o l o u r i -  metric determination a f t e r treatment with s u l f u r i c acid and p e r s u l f a t e . A s i m i l a r method was used to determine t o t a l phosphorus i n the Okanagan River inflow to Skaha Lake.  This method i s described by Fee (1971):  . . .a colourimetric determination on an auto-analyser with ammonium molybdate and stannous chloride a f t e r 30 minutes i n an autoclave with s u l f u r i c acid and potassium p e r s u l f a t e ; determination done on shaken sample." 11  159  160  2.  Phytoplankton Water samples for a l g a l analyses were counted with a Sedgwick-  Rafter counting chamber and 100X magnification with a compound (Coulthard and Stein 1969).  A l g a l biomass was  microscope  reported i n units of c e l l s / m l .  For c o l o n i a l or filamentous algae i t was not f e a s i b l e to count i n d i v i d u a l cells,  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 C y o l o t e l l a glomevata Bachm. Cymbella sp. Melosira spp. Naviaula sp. Pinnularia sp. Stephanodisous sp. T a b e l l a r i a sp.  8 1 1 1 1 1 1 1  Chlorophyceae (green algae) Mougeotia sp.  12-15  Chrysophyceae (chrysophtes) Dinobryon sp.  1 cell  = 1 unit  Cryptophyceae (cryptomonads) Cryptomonas ovata Ehrbg.  1 cell  = 1 unit  Cyanophyceae (blue-green algae) Anabaena flos-aquae (lyngb.) Breb. Bos toe sp. Oscillatoria acutissima Kuff Dinophyceae ( d i n o f l a g e l l a t e s ) Certa-ium k i v u n d i n e l l a (O.F. Mull.) Duj.  cells cell cell cell cell cell cell cell  = = = = = = = =  1 1 1 1 1 1 1 1  unit unit unit unit unit unit unit unit  c e l l s = 1 unit  12-15 12-15  cells cells  12-15  c e l l s = 1 unit  1 cell  1 unit 1 unit  = 1 unit  Phytoplankton biomass was converted from c e l l s / m l to dry weight concentration i n mg/1.  This conversion can be v a r i a b l e depending on the  species of phytoplankton, and an  average value of 100 c e l l s / m l =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 l e a s t one set of determinations i n each transect was made using the modified Winkler method.  

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