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Lower Fraser River/Estuary dissolved oxygen dynamics 1976

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LOWER FRASER RIVER/ESTUARY DISSOLVED OXYGEN DYNAMICS by FREDERIC A. KOCH B.A.Sc, U n i v e r s i t y of B r i t i s h Columbia, 1970 A THESIS SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF APPLIED SCIENCE i n the Department of C i v i l Engineering We accept t h i s t h e s i s as conforming to the r e q u i r e d standard THE UNIVERSITY OF BRITISH COLUMBIA September, 1976 @ F r e d e r i c A. Koch In p r e s e n t i n g t h i s t h e s i s i n p a r t i a l f u l f i l m e n t o f t h e r e q u i r e m e n t s f o r an a d v a n c e d d e g r e e a t t h e U n i v e r s i t y o f B r i t i s h C o l u m b i a , I a g r e e t h a t t h e L i b r a r y s h a l l make i t f r e e l y a v a i l a b l e f o r r e f e r e n c e a n d s t u d y . I f u r t h e r a g r e e t h a t p e r m i s s i o n f o r e x t e n s i v e c o p y i n g o f t h i s t h e s i s f o r s c h o l a r l y p u r p o s e s may be g r a n t e d by t h e H e a d o f my D e p a r t m e n t o r by h i s r e p r e s e n t a t i v e s . I t i s u n d e r s t o o d t h a t c o p y i n g o r p u b l i c a t i o n o f t h i s t h e s i s f o r f i n a n c i a l g a i n s h a l l n o t be a l l o w e d w i t h o u t my w r i t t e n p e r m i s s i o n . D e p a r t m e n t o f CZJVIL & A J C S / A j g g r i g / A j <S The U n i v e r s i t y o f B r i t i s h C o l u m b i a 2075 Wesbrook P l a c e Vancouver, Canada V6T 1W5 D a t e Se^pT- 2 7 , /9?G ABSTRACT This i n v e s t i g a t i o n i n t o the nature of d i s s o l v e d oxygen dynamics i n the lower Fraser R i v e r / E s t u a r y has made use of the a p p l i c a t i o n of two mathematical water q u a l i t y models - a t i d a l l y averaged d i s s o l v e d oxygen model and a t i d a l l y v a r y i n g d i s s o l v e d oxygen model. The t i d a l l y averaged model analyzes the i n t e r - t i d a l behaviour of the r i v e r / e s t u a r y , g i v i n g estimates of st e a d y - s t a t e d i s s o l v e d oxygen response. The t i d a l l y v a r y i n g model, on the other hand, analyzes c o n d i t i o n s w i t h - i n the t i d a l c y c l e , thereby d e s c r i b i n g the " r e a l - t i m e " , i n t r a - t i d a l behaviour of the r i v e r / e s t u a r y . Both d i s s o l v e d oxygen models are one- dimensional and make the assumption that the on l y o p e r a t i v e d i s s o l v e d oxygen source/sink processes are deoxygenation due to the o x i d a t i o n of discharged o r g a n i c s and reoxygenation due to atmospheric r e a e r a t i o n . The present high d i s s o l v e d oxygen l e v e l s i n the lower Fr a s e r p r e - clude the accurate c a l i b r a t i o n of the d i s s o l v e d oxygen models. How- ever, an a n a l y s i s of model s e n s i t i v i t i e s i s presented, i n l i e u of v e r i f i c a t i o n , to document model responses. D i s s o l v e d oxygen p r e d i c t i o n s made using the u n v e r i f i e d models i n - d i c a t e t h a t the a s s i m i l a t i v e c a p a c i t y of the lower Fraser R i v e r / Estuary i s c o n s i d e r a b l e , mainly because of the l a r g e freshwater i n - flows which a f f o r d e x t e n s i v e d i l u t i o n as w e l l as r a p i d f l u s h i n g . The " c r i t i c a l p e r i o d " i s l i k e l y to be i n l a t e summer when the combined e f f e c t s of water temperature and freshwater flows r e s u l t i n the lowest d i s s o l v e d oxygen l e v e l s . Future water q u a l i t y impairment i n the main i i channels of the lower F r a s e r , at l e a s t i n s o f a r as d i s s o l v e d oxygen i s concerned, i s considered by t h i s study to be u n l i k e l y , p r o v i d i n g that e x i s t i n g p o l l u t i o n c o n t r o l p o l i c i e s are adhered t o . TABLE OF CONTENTS PAGE LIST OF TABLES v i LIST OF FIGURES v i i ACKNOWLEDGEMENTS i x CHAPTER INTRODUCTION ' 1 1. THE FRASER RIVER 8 1.1 THE FRASER RIVER 8 1.2 FRASER RIVER RUN-OFF CHARACTERISTICS 12 1.3 FRASER RIVER WATER TEMPERATURE CHARACTERISTICS 15 1.4 THE LOWER FRASER RIVER 20 1.4.1 T i d a l E f f e c t s 22 1.4.2 S a l i n i t y I n t r u s i o n 26 2. DISSOLVED OXYGEN DYNAMICS, A REVIEW 28 2.1 DISSOLVED OXYGEN 28 2.2 OXYGEN DEMANDING WASTES 31 2.3 THE OXYGEN BALANCE 34 2.4 DEOXYGENATION • 35 2.4.1 Carbonaceous O x i d a t i o n 38 2.4.2 N i t r i f i c a t i o n 42 2.5 REAERATION 43 2.6 OTHER SOURCES AND SINKS OF OXYGEN 46 2.7 THE STREETERr-PHELPS FORMULATION OF - THE OXYGEN BALANCE IN A STREAM 47 3. DISSOLVED OXYGEN MODELS 50 3.1 STREAM AND RIVER MODELS 50 3.2 ESTUARY MODELS 52 3.3 THE ONE-DIMENSIONAL MASS TRANSPORT EQUATION- 53 3.4 THE STEADY STATE SOLUTIONS TO THE MASS TRANSPORT EQUATION 55 3.4.1 The Continuous S o l u t i o n Approach 58 3.4.2 The F i n i t e S e c t i o n Approach 61 3.5 TIDALLY VARYING SOLUTIONS 66 3.5.1 The Hydrodynamic Sub-Model 67 3.5.2 The T i d a l l y Varying Model 70 i v V CHAPTER PAGE 4. APPLICATION OF DISSOLVED OXYGEN MODELS TO THE FRASER RIVER/ESTUARY 74 4.1 THE MODEL RIVER/ESTUARY 74 4.2 IMPLEMENTATION OF THE MODELS 79 4.2.1 T i d a l l y Averaged Models 79 4.2.2 The T i d a l l y Varying Model 82 4.3 MODEL ASSUMPTIONS 84 4.3.1 General Assumptions 84 4.3.2 D i s s o l v e d Oxygen Assumptions 86 4.4 MODEL COEFFICIENTS 87 4.4.1 D i s s o l v e d Oxygen Model Rate C o e f f i c i e n t s 87 4.4.2 D i s p e r s i o n C o e f f i c i e n t s 89 4.5 WASTE LOADINGS 90 4.5.1 Present Waste Loads 90 4.5.2 P o s s i b l e Future Waste Loads 91 4.6 MODEL OUTPUT 91 5. DISSOLVED OXYGEN MODEL RESULTS 95 5.1 TIDALLY AVERAGED DISSOLVED OXYGEN MODEL RESPONSE 95 5.1.1 E f f e c t of Freshwater Inflow V a r i a t i o n 96 5.1.2 E f f e c t of Waste Loading V a r i a t i o n 99 5.1.3 E f f e c t of D i s p e r s i o n C o e f f i c i e n t V a r i a t i o n 99 5.1.4 E f f e c t of Deoxygenation Rate C o e f f i c i e n t V a r i a t i o n 102 5.1.5 E f f e c t of Reaeration Rate C o e f f i c i e n t V a r i a t i o n 102 5.1.6 E f f e c t of Water Temperature V a r i a t i o n 102 5.1.7 Summary 106 5.2 TIDALLY VARYING DISSOLVED OXYGEN MODEL RESPONSE 106 5.2.1 Hydrodynamic Sub-Model Output 108 5.2.2 T i d a l l y Varying I n i t i a l E f f l u e n t Concentrations 111 5.2.3 I n t r a - T i d a l D i s s o l v e d Oxygen Response 113 5.2.4 V a l i d i t y of T i d a l l y V arying P r e d i c t i o n s 117 5.2.5 Summary 122 • J X\ M r u . t r L u u i j \JC I J V J W E J I V ciutjucv rviviiix/ lioiurvjxi njjmiijnixvE. ±<r.j CAPACITY 6. SUMMARY AND DISCUSSION 132 6.1 DISSOLVED OXYGEN MODELS 132 6.1.1 Summary 132 6.1.2 L i m i t a t i o n s of the P r e d i c t i v e C a p a b i l i t i e s 134 6.1.3 The Modeling Experience 137 6.2 FRASER RIVER/ESTUARY DISSOLVED OXYGEN RESOURCES 139 6.2.1 Summary: An Improved Knowledge Base 139 6.2.2 Future C o n d i t i o n s 142 6.2.3 U n c e r t a i n t i e s 143 7. CONCLUSIONS 146 LIST OF TABLES TABLE PAGE 2.1 C l a s s i f i c a t i o n of R i v e r Q u a l i t y Based on D i s s o l v e d 29 Oxygen Content 2.2 Royal Commission C l a s s i f i c a t i o n of R i v e r s 32 2.3 Average BOD Rate Constants @ 20° C 41 2.4 Summary of Constants f o r the Reaeration Equation 45 4.1 Waste Loadings to the Main Arm/Main Stem, Lower 92 Fraser R i v e r 4.2 Waste Loadings to the North Arm, Lower Fraser R i v e r 93 5.1 Parameters and C o e f f i c i e n t s Used i n S e n s i t i v i t y 96 A n a l y s i s 5.2 DO S a t u r a t i o n Concentrations Used i n A n a l y s i s 128 v i LIST OF FIGURES FIGURE PAGE 1.1 Fraser River Drainage Basin 9 1.2 Average Annual Hydrograph for the Fraser River at 13 Hope (1930-1960) 1.3 D i s t r i b u t i o n of Mean Monthly Flows for the Fraser 14 River at Hope (1913-1970) 1.4 D i s t r i b u t i o n of 7-Day Low Flows for the Fraser 16 River at Hope 1.5 D i s t r i b u t i o n of Minimum Yearly Flows for the Fraser 17 River at Hope 1.6 D i s t r i b u t i o n of Mean Monthly Fraser River Water , 1 8 Temperatures, January to July 1.7 D i s t r i b u t i o n of Mean Monthly Fraser River Water 19 Temperatures, August to December 1.8 The Lower Fraser River 21 1.9 Typical Tides at Point Atkinson 23 1.10 Discharge and Velocity Variation at Steveston Due to 25 Tidal Influence 2.1 Oxygen Sag Curve 36 2.2 Oxygen Uptake of a Wastewater 37 3.1 Subscript Notation of T i d a l l y Averaged Model 63 3.2 The Hydrodynamic Estuary 69 4.1 Numbering Scheme and Network of Stations Used i n the 75 Model River/Estuary 4.2 Variation of Cross-Sectional Parameters i n the Main 77 Arm/Main Stem 4.3 Variation of Cross-Sectional Parameters i n the North 78 Arm and P i t t River 4.4 The Matrix [A] of the T i d a l l y Averaged Model 81 v i i LIST OF FIGURES FIGURE PAGE 5.1 E f f e c t of Freshwater Inflow on Model Response 97 5.2 E f f e c t of Waste Loading on Model Response 100 5.3 E f f e c t of D i s p e r s i o n on Model Response 101 5.4 E f f e c t of Deoxygenation Rate on Model Response 103 5.5 E f f e c t of Reaeration Rate on Model Response 104 5.6 E f f e c t of Temperature on Model Response 105 5.7 P r e d i c t i o n s of T i d a l l y Varying V e l o c i t y 109 5.8 P r e d i c t e d Trace of P a r t i c l e s Released at Various 110 Times from S t a t i o n 40 5.9 P r e d i c t e d I n i t i a l E f f l u e n t D i l u t i o n 112 5.10 T i d a l l y V a r y i n g D i s s o l v e d Oxygen Response: 114 S t a t i o n 20 5.11 T i d a l l y Varying D i s s o l v e d Oxygen Response: 115 S t a t i o n 2 . 5.12 D i s p e r s i o n of a Slug Load 118 5.13 Advection Paths of P a r t i c l e s i n S t r a t i f i e d Model 120 - J n • xx—3 — 1 etna £>a.LO Ll xC n u u c i 5.14 Space-Time P l o t of DO D e f i c i t Concentrations Using 126 10 Year Return P e r i o d Low Flows and High Temperatures 5.15 Space-Time P l o t of DO D e f i c i t Concentrations Using 127 50 Year Return P e r i o d Low Flows and High Temperatures ACKNOWLEDGEMENTS The author would l i k e to express h i s a p p r e c i a t i o n t o the f o l l o w i n g persons, each of whom played a pa r t i n the develop- ment of t h i s t h e s i s . Dr. W.K. Oldham i s to be thanked f o r the p a t i e n t , r e a s s u r i n g support he so k i n d l y o f f e r e d d u r i n g the lengthy p e r i o d r e q u i r e d to complete t h i s study. S p e c i a l thanks go to Dr. C.S. Joy f o r the use of the hydrodynamic and water q u a l i t y models which were developed d u r i n g h i s recent d o c t o r a l s t u d i e s and f o r h i s f r e e l y g i ven a s s i s t a n c e which covered countless hours p l e a s a n t l y spent i n model-related d i s c u s s i o n s . In a d d i t i o n , the author i s deeply indebted to the Westwater Research Centre w i t h whom he was g a i n f u l l y employed du r i n g p a r t s of t h i s study. S p e c i a l thanks are extended there to the D i r e c t o r , P r o f e s s o r I r v i n g K. Fox and to Dr. K.J. H a l l . F i n a l l y , the author g r a t e f u l l y acknowledges the expert a s s i s t a n c e provided by Mr. Itsuo Y e s a k i i n the d r a f t i n g of t h e s i s diagrams, by Mr. Ken Peterson i n e d i t o r i a l suggestions, and by Miss Margaret Scherf who f a i t h f u l l y typed and proof read the t h e s i s manuscript. F i n a n c i a l support during the e a r l y stages of t h i s r esearch was provided by the Water Resources Support Program o f Environment Canada. i x INTRODUCTION "no man stands beside the Fra s e r R i v e r without s e n s i n g the p r e c a r i o u s h o l d of h i s species upon the e a r t h . . . here i t i s t h r u s t upon you w i t h a s p e c i a l c l a r i t y . In t h i s g r i s l y t r e n c h , bored out of s o l i d rock through unimaginable time by the scour of brown water, the long h i s t o r y of l i f e l e s s matter, the p i t i f u l l y b r i e f record of l i f e , the mere moment of man's e x i s t e n c e , are suddenly l e g i b l e . And here, i n t h i s p r o d i g a l waste of energy, nature's war on a l l . . . i s naked, b r u t a l , and ce a s e l e s s . " So begins Bruce Hutchinson's book, The F r a s e r , d e s c r i b i n g the Fraser R i v e r , i t s impact on man, and i t s e f f e c t on h i s environment. He continues to expound the importance of the r i v e r as "one of the b a s i c p o l i t i c a l and economic f a c t s of A m e r i c a . . . l i t t l e understood by governments and seldom mentioned i n h i s t o r y books". Being mindful of the f a c t that the two decade-old d e s c r i p t i o n i s an over d r a m a t i z a t i o n by a n a t i v e B r i t i s h Columbian j o u r n a l i s t does not le s s e n the importance of the Fra s e r R i v e r and the r o l e t h a t i t has played i n B r i t i s h Columbia, i t s h i s t o r i c a l , s o c i a l and economic development. R a i l routes along the F r a s e r passage through the formidable Coast range completed around the turn of the century t i e d B r i t i s h Columbia i n t o the r e s t of the n a t i o n and u l t i m a t e l y l e d to the development of the p o r t c i t y o f Vancouver, the main p o r t and urban centre on the west coast. A t h i r d r a i l r o u t e f o l l o w i n g the upper lengths of the Fraser c o r r i d o r connects Vancouver to the no r t h e r n p a r t s of the pro v i n c e . Vancouver i s thus a major node i n a t r a n s p o r t a t i o n network w i t h two r a i l w a y l i n e s s t r e t c h i n g over the e n t i r e n a t i o n and the - 1 - 2 t h i r d out to the h i n t e r l a n d of the pr o v i n c e . I t i s i r o n i c to see that the development of the urban centres and i n d u s t r y i n i t i a t e d through use of the r i v e r as a t r a n s p o r t a t i o n c o r r i d o r now have the p o t e n t i a l to dest r o y that same r i v e r through t h e i r use of i t as a s i n k f o r t h e i r wastes. Domestic wastes from most of m e t r o p o l i t a n Vancouver, r e p r e s e n t i n g a p o p u l a t i o n i n excess of one m i l l i o n are discharged i n t o the lower Fraser R i v e r and i t s e s t u a r y , as are wastes from many other s m a l l e r urban centres s c a t t e r e d throughout the lower F r a s e r V a l l e y . I n combined t o t a l , the lower Fraser r e c e i v e s the domestic wastes of 1,100,000 persons, which represents about 50 percent of the p o p u l a t i o n of B r i t i s h Columbia. In a d d i t i o n to the domestic waste i n p u t s , l a r g e q u a n t i t i e s of i n d u s t r i a l wastewaters enter the r i v e r from numerous i n d u s t r i e s l o c a t e d on the r i v e r foreshore which, f o r the most p a r t , i s zoned f o r i n d u s t r i a l development. Rapid growth of popula- t i o n i n the lower mainland, which has occurred i n recent y e a r s , along w i t h a s s o c i a t e d expansion i n i n d u s t r i a l and commercial development i s expected to continue. P r o j e c t i o n s have been made, i n d i c a t i n g that by the year 2000, the lower mainland p o p u l a t i o n w i l l be 2,400,000 [LMRPB, 1968] w i t h the major p o r t i o n being concentrated i n and around m e t r o p o l i t a n Vancouver. In recent y e a r s , p o l l u t i o n i n the lower Fraser R i v e r has been an is s u e of p a r t i c u l a r concern. Among other reasons which i n c l u d e d the con- temporary e t h i c of "environmental awareness", p o l l u t i o n has been a p a r t i c u - l a r concern because of the t h r e a t posed by the degradation of water q u a l i t y to the, as y e t , i n t a c t Fraser R i v e r salmon f i s h e r y . This unique, n a t u r a l resource, which has c u l t u r a l as w e l l as economic s i g n i f i c a n c e , has been estimated to have an annual value i n the order of $75 m i l l i o n [ F i s h e r i e s 3 S e r v i c e , 1 9 7 1 ] . D e t e r i o r a t i o n of water q u a l i t y caused by such things as d i s - s o l v e d oxygen d e p l e t i o n due to the a s s i m i l a t i o n of organic waste discharges and the t o x i c o l o g i c a l e f f e c t s of t o x i c discharges has s e r i o u s i m p l i c a t i o n s not o n l y w i t h respect to the salmon f i s h e r y but a l s o w i t h r e s p e c t to other uses o f the r i v e r which may be impaired by p o l l u t e d c o n d i t i o n s . As a r e s u l t o f the genei -al concern over water q u a l i t y i n the lower F r a s e r R i v e r , c o n s i d e r a b l e a t t e n t i o n has been d i r e c t e d towards assessment o f water q u a l i t y c o n d i t i o n s and the f o r m u l a t i o n of water q u a l i t y management p o l i c i e s . An i n v e s t i g a t i o n by the p r o v i n c i a l P o l l u t i o n C o n t r o l Branch [ G o l d i e , 1967] i s worth n o t i n g , p a r t i c u l a r l y because i t formed the b a s i s of adopted pro- v i n c i a l government p o l i c y regarding p o l l u t i o n c o n t r o l on the F r a s e r R i v e r below the town of Hope [PCB, 1968]. The primary o b j e c t i v e of t h i s p o l i c y was "the maintenance of the lower Fraser R i v e r as a multi-purpose water r e - source f o r the people of the province f o r a l l time". More s p e c i f i c a l l y , t h i s o b j e c t i v e was "to maintain the r i v e r f r e e of harmful p o l l u t i o n and t o x i c substances i n areas where the r i v e r i s not so p o l l u t e d . . . a n d . . . t o b r i n g about an improvement i n the s t a t e of the r i v e r i n areas where p o l l u t i o n has a l r e a d y occurred". The f i n d i n g s of the G o l d i e report [1967] on waste d i s p o s a l i n the lower F r a s e r were, i n summary, that d i s s o l v e d oxygen l e v e l s i n the main stem F r a s e r were h i g h and thus the F r a s e r could be regarded as a " c l e a n stream i n terms of BOD" but that b a c t e r i a l contamination was " u n d e s i r a b l y high...and...continues to i n c r e a s e i n some areas". In r e c o g n i t i o n that the lower F r a s e r ' s c a p a c i t y to a s s i m i l a t e wastewater was not s u f f i c i e n t 4 "to accept without danger of impairment the wastes of the fo r e s e e a b l e v a l l e y p o p u l a t i o n and attendant i n d u s t r i e s " and to o f f e r "adequate p r o t e c t i o n a g a i n s t impairment and e x c e s s i v e b a c t e r i a l contamination", the r e p o r t recommended as a general r u l e t h a t " a l l sewage discharges to the lower F r a s e r R i v e r should f i r s t r e c e i v e primary treatment and c h l o r i n a t i o n " . This recom- mendation was, i n l a r g e p a r t , accepted by the P o l l u t i o n C o n t r o l Board as a p r i n c i p a l requirement i n i t s p o l i c y statement [PCB, 1968] to f u l f i l l the general o b j e c t i v e s f o r the lower F r a s e r . The r e s u l t s of more recent research i n v e s t i g a t i o n s i n t o water q u a l i t y i n the lower F r a s e r [BCRC, 1971; Benedict e t a l ^ , 1973; and H a l l e t a l . , 1 9 7 4 ] , i n a d d i t i o n to having more completely d e f i n e d the nature of the water q u a l i t y c o n d i t i o n s , have, i n g e n e r a l , confirmed the f i n d i n g s of the Gol d i e r e p o r t w i t h regard to the d i s s o l v e d oxygen l e v e l s and b a c t e r i a l con- tam i n a t i o n . I t i s the former water q u a l i t y parameter to which t h i s t h e s i s i s addressed. The b a s i c o b j e c t i v e s o f the research d e s c r i b e d i n t h i s t h e s i s were: ( i ) to i n v e s t i g a t e the mechanics of d i s s o l v e d oxygen dynamics i n waterways; ( i i ) to apply these concepts to the development of c a p a b i l i t i e s f o r p r e d i c t i n g d i s s o l v e d oxygen con c e n t r a t i o n s i n the lower F r a s e r R i v e r ; C i i i ) to assess the v a l i d i t y and s u i t a b i l i t y of these p r e d i c t i v e c a p a b i l i t i e s i n t h e i r a p p l i c a t i o n to the F r a s e r R i v e r ; Civ) to assess, through use of the p r e d i c t i v e c a p a b i l i t i e s , the probable impact of v a r i o u s waste discharge p a t t e r n s on d i s s o l v e d oxygen l e v e l s i n the lower Fraser R i v e r . 5 This i n v e s t i g a t i o n i n t o the development, assessment, and u t i l i z a t i o n of p r e d i c t i v e c a p a b i l i t i e s f o r d i s s o l v e d oxygen can be c l a s s e d as a "model study" because i t makes use of d i g i t a l computer "models". The computer programs which form the b a s i s of the d i s s o l v e d oxygen "models" employ mathematical a b s t r a c t i o n s of the r e l e v a n t processes as they seek to emulate the system they represent. Although t h i s procedure of approx- imating a p h y s i c a l system by mathematical a b s t r a c t i o n s i s o f t e n r e f e r r e d to as a " s i m u l a t i o n " of the p h y s i c a l system i t i s s t r e s s e d here that t h i s i s r a r e l y i f ever t r u e . In f a c t the output of a "model" corresponds to the response of the r e a l system o n l y as the model assumptions represent r e a l i t y and the output i s as good as the weakest model assumption. At i t s conception t h i s research p r o j e c t was e n v i s i o n e d as being designed s p e c i f i c a l l y to i n v e s t i g a t e the e f f e c t s of sewage discharge from the proposed treatment f a c i l i t y at Annacis I s l a n d on the oxygen resources of the r i v e r , a " s i s t e r " p r o j e c t to the i n v e s t i g a t i o n undertaken by Rusch [1973] to study £he e f f e c t s of the proposed discharge on b a c t e r i a l e v e l s i n the r i v e r . In the i n t e r i m s i n c e p r o j e c t conception, d u r i n g which the author has been employed w i t h the Westwater Research Centre,at U.B.C. and been a s s o c i a t e d w i t h the development of a number of water q u a l i t y models, the research aims of t h i s p r o j e c t have undergone a degree of metamorphosis to become broader i n scope. Rather than f o c u s i n g on the a n a l y s i s of a s p e c i f i c problem as o r i g i n a l l y intended t h i s t h e s i s has t a c k l e d the more general i s s u e of understanding the nature of d i s s o l v e d oxygen dynamics i n the lower Fraser R i v e r . In doing t h i s i t has remained true to the o r i g i n a l purpose of the research but more completely f u l f i l l e d the s t a t e d o b j e c t i v e s . As w e l l , i t has h o p e f u l l y o f f e r e d some a d d i t i o n a l 6 insights i nto the complex nature of the lower Fraser River and i t s considerable a b i l i t y to assimilate organic wastes that may have gone undetected by the o r i g i n a l project design. The organization of thesis presentation can be thought of as having f i v e d i s t i n c t components - description, theory, a p p l i c a t i o n , results and conclusions. Chapter 1 i s purely d e s c r i p t i v e , presenting information on the d e t a i l s of the Fraser River relevant to dissolved oxygen model studies. These include run-off c h a r a c t e r i s t i c s , water temperature c h a r a c t e r i s t i c s and, for the lower Fraser, the effects of t i d a l influence and saltwater i n t r u s i o n . Chapters 2 and 3 have a more theoretical basis. Chapter 2 presents some of the concepts, theories and mathematical formulations developed to describe dissolved oxygen and the factors which affect i t s dynamic behaviour i n waterways. Chapter 3 discusses methods of applying the fundamental formulations f o r dissolved oxygen to r i v e r s and estuaries i n order to develop modeling c a p a b i l i t i e s . Chapters 4 and 5 are concerned, respectively, with the application of the models to the Fraser River and the results of the modeling exercise. Discussion i n Chapter 4 i s centred around the d e t a i l s of model application and the various assumptions i m p l i c i t i n each of the models. S p e c i f i c results are presented i n Chapter 5 to test the performance of the models. In addition, the re s u l t s of various model runs are presented to enable a preliminary assessment of as s i m i l a t i v e capacity and possible future dissolved oxygen levels i n the lower Fraser River. Chapter 6 summarizes the investigation discussing and assessing the v a l i d i t y of the models, t h e i r u t i l i t y and 7 the r e s u l t s of t h e i r a p p l i c a t i o n . Chapter 7 draws conclusions and suggests ways of improving and strengthening the developed p r e d i c t i v e c a p a b i l i t i e s . CHAPTER 1 THE FRASER RIVER 1.1 THE FRASER RIVER The Fraser River Basin, an area of some 90,000 square miles, i s the largest river basin wholely within the province of British Columbia. Covering approximately one-quarter of the province, the drainage basin occupies the greater portion of the southern half of the province, draining the high central Interior Plateau which i s flanked on the west by the Coast Mountains and by the paralleling Columbia and Rocky Mountains on the east (see Figure 1.1). The Interior Plateau and the rugged mountainous country surrounding i t are characterized by their high elevation with more than 70% of the drainage basin being above 3,000 feet, and 10% being above 6,000 feet. [Fraser River Board, 1958]. The river i t s e l f rises in the Rocky Mountains at one of the most easterly points in the basin near the Yellowhead Pass, descends into the Rocky Mountain Trench, and flows northwesterly for some 250 miles before i t turns south, crossing more than 400 miles of the Interior Plateau. At Lytton, the Fraser forms a spectacular canyon as i t cuts through the formidable Coast Range. Continuing southward to Hope, the river breaks out of the canyon and turns westward, making i t s approach to the sea through 100 miles of the a l l u v i a l , deltaic Lower Fraser Valley. The "mighty" Fraser, by the time i t enters the sea through the Straits of Georgia, has traversed a total length of approximately 850 miles. Of the total Fraser River drainage area, approximately 52,000 - 8 - 9 10 square m i l e s are contained i n t r i b u t a r y sub-basins, the most important of which are shown i n F i g u r e 1.1. The S t u a r t , Nechako, Westroad and C h i l c o t i n R i v e r s d r a i n the w e s t e r l y p o r t i o n s of the I n t e r i o r P l a t e a u and the e a s t e r l y slopes of the Coast Mountains w i t h the Quesnel and Thompson R i v e r s , on the e a s t , d r a i n i n g the remaining p o r t i o n s of the p l a t e a u and the e a s t e r n slopes of the Columbia Mountains. Other than a development d i v e r t i n g 5,400 square m i l e s of the Nechako sub-basin and a minor sub- b a s i n development at Bridge R i v e r , the F r a s e r and i t s t r i b u t a r i e s are n o t , as y e t , dammed, although schemes f o r both f l o o d c o n t r o l and hydro- e l e c t r i c power have been suggested. [Fraser R i v e r Board, 1958; B.C. Energy Board, 1972]. C l i m a t i c c o n d i t i o n s vary c o n s i d e r a b l y over the b a s i n . A l p i n e maritime c l i m a t e c h a r a c t e r i z e s the lower p o r t i o n s of the drainage b a s i n and as one proceeds up the b a s i n c l i m a t i c c o n d i t i o n s change through dry and humid c o n t i n e n t a l to a l p i n e humid c o n t i n e n t a l , c h a r a c t e r i s t i c of the head- waters and e a s t e r l y areas. The extreme n o r t h e r l y p o r t i o n s of the b a s i n border on a l p i n e s u b a r c t i c c l i m a t i c r e g i o n s . Annual p r e c i p i t a t i o n a l s o f l u c t u a t e s markedly throughout the b a s i n , ranging from r a i n f o r e s t p r e c i - p i t a t i o n l e v e l s of over 150 inches per year i n the v i c i n i t y of P i t t Lake i n the Lower Fraser V a l l e y to a r i d and s e m i - a r i d l e v e l s of 5-10 inches per year i n areas of the c e n t r a l p l a t e a u near Kamloops. V a r i a b i l i t y of v e g e t a t i o n i s a l s o extreme. P a r a l l e l i n g p r e c i p i t a t i o n , i t ranges from west coast r a i n f o r e s t to almost d e s e r t - l i k e v e g e t a t i o n c o n s i s t i n g of a r i d and s e m i - a r i d g r a s s l a n d i n the i n t e r i o r . [Fraser R i v e r Board, 1958]. 11 Temperature, along with precipitation, i s a major climatic factor which affects the hydrology of the basin. The temperature at any point in the basin depends primarily on altitude, latitude and distance from the Pacific Ocean. Of particular significance is the fact that temperature over the whole of the Fraser River basin normally f a l l s below freezing in the winter months. With the spring thaw, which usually begins in the south and spreads northward, precipitation which has been stored over winter in the form of snow and ice i s released, causing freshet con- ditions which commonly result in flooding. Exceptional floods, as in 1948, are caused when abnormally high spring precipitation combines with rapid snowmelt. [Fraser River Board, 1958], Throughout i t s length the main stem Fraser drops over 4,000 feet in elevation with a relatively uniform grade indicative of a matur- ing river, except in the headwaters where gradients are high, and in the Lower Fraser Valley where there is a sharp break in river p r o f i l e . In the v i c i n i t y of Chilliwack, at the break of grade, the river deposits the major portion of i t s large sediment load, an estimated 25 million tons annually, [Pretious, 1972] which, as well as making the river turbid and brown in appearance, has led to the formation of the a l l u v i a l lower valley. From Chilliwack downstream to the sea, a distance of 55 miles, river grades are very low and as a result water slopes and river stage are affected by tides. 1.2 FRASER RIVER RUN-OFF CHARACTERISTICS The runoff c h a r a c t e r i s t i c s of the F r a s e r R i v e r b a s i n are best described by the records of the gauging s t a t i o n at Hope, where the r i v e r flow i s u n a f f e c t e d by t i d e s , the r i v e r c r o s s - s e c t i o n i s s t a b l e and the p e r i o d of record s t r e t c h e s back to 1912 [Water Survey of Canada, 1913 to 1970], As w e l l , t h i s s t a t i o n i n t e g r a t e s the e f f e c t s of the e n t i r e b a s i n , r e p r e s e n t i n g about 87% of the t o t a l drainage area and 80% of the estimated t o t a l r u noff of the F r a s e r R i v e r to the sea [Fraser R i v e r Board, 1958]. An average annual hydrograph of F r a s e r R i v e r discharge at Hope i s shown i n F i g u r e 1.2. Although i t s p e r i o d of record i s outdated, i t shows the observed p a t t e r n of r u n o f f and the i n f l u e n c e of snowmelt on the runoff regime. Freshet t y p i c a l l y begins near the end of A p r i l , peaks i n mid-June and t a i l s o f f to base fl o w c o n d i t i o n s i n l a t e f a l l . Minimum annual low flows occur i n the w i n t e r months, December to March. Low and h i g h extreme flows recorded at Hope were 12,000 cu b i c f e e t per second ( c f s ) on January 8, 1916 and 536,000 c f s on May 31, 1948. An even l a r g e r f l o o d occurred i n 1894, w i t h peak flow reaching an estimated 620,000 c f s . The v a r i a t i o n and d i s t r i b u t i o n of mean monthly flows f o r the F r a s e r R i v e r at Hope over the p e r i o d of record from 1913 to 1970 i s shown i n F i gure 1.3. This summary i n f o r m a t i o n i s based on flow a n a l y s i s c a r r i e d out by the Westwater Research Centre [Westwater, unpublished d a t a ] . For each month, median f l o w s , along w i t h f i v e , ten and f i f t e e n year r e t u r n flows-are reported. Discharge data i n t h i s form are u s e f u l not only as \ Figure 1.2 Average Annual Hydrograph f o r the Fraser R i v e r at Hope (1930-1960) uisiriDuuon OT iviean Monthly Mows for the Fraser River at Hope 240^ 220H 200- 180- 160- J" 140 H o o 120 H 100- 80 H 60H 40- 20- IV 1 I, JAN FEB 1 i; 1 MAR APR MAY •MEAN FLOW -FIVE YEAR LOW FLOW •TEN YEAR LOW FLOW • FIFTY YEAR LOW FLOW r240 220 -200 H80 H60 140 JUNE JULY F i g u r e 1.3 D i s t r i b u t i o n o f Mean M l o n t h l y F l o w s f o r t h e 120 ICO AUG SEPT OCT NOV DEC F r a s e r R i v e r a t Hope d 9 1 3 - 1 9 7 0 ) 15 Input information to the water q u a l i t y models, as w i l l be discussed i n a subsequent section, but also, because the scope of the information i s the broader monthly time base, i t allows for a more tempered view of the range of Fraser River flows. Results of an analysis of low flow conditions [Westwater, unpub- lished data] are shown i n Figures 1.4 and 1.5. Figure 1.4, representing analysis of 7-day low flow data, i s based on a recent publication by the Water Survey of Canada [WSC, 1974]. The 7-day low flow has been recommended by some researchers as the time period most suitable for study of water quality and the examination of water quality effects [McKee and Wolf, 1963]. The minimum yearly low flow d i s t r i b u t i o n presented i n Figure 1.5 has been included to round out the picture of low flow data for the Fraser. 1.3 FRASER RIVER WATER TEMPERATURE CHARACTERISTICS The d i s t r i b u t i o n of water temperature for each month at Hope i s shown i n Figures 1.6 and 1.7 and i s based on mean monthly conditions for seven years of record as published by the Sediment.Survey of Canada [1964- 1970]. D i s t r i b u t i o n was assumed to be normal and i t can be seen that the f i t of the data points suggest that this i s a reasonable assumption. Low temperatures occur during the winter months, with the lowest average temp- eratures being 1.0°C i n January. There i s considerable overlap i n winter monthly mean temperatures between d i f f e r e n t months which r e f l e c t s the influence of lower basin cold weather conditions, t h e i r severity and timing. Higher temperatures are observed i n the summer period with August having the highest average temperature at 17.7°C. RECURRENCE INTERVAL in years 10 2 0 50 100 J I I L 80 9 0 95 98 99 PROBABILITY in percent Figure 1.4 D i s t r i b u t i o n of 7-Day Low Flows f o r the Fraser R i v e r at Hope RECURRENCE INTERVAL in years 101 1,11 2 5 10 20 5 0 I0O ' i i ' 1 L - 1 1 I i i i i 1 i — i l i t I I i i 1 2 5 10 20 40 60 8 0 9 0 95 98 99 PROBABILITY in percent Figure 1.5 Dis t r i b u t i o n of Minimum Yearly Flows for the Fraser River at Hope 18 1.01 RECURRENCE INTERVAL in years Ml 2 5 10 20 _i i 1 IQO J U N E H4 MAY 8 PROBABILITY in percent Figure 1.6 D i s t r i b u t i o n of Mean Monthly Fr a s e r R i v e r Water Temperatures January to J u l y 19 RECURRENCE INTERVAL in years PROBABILITY in percent F i g u r e 1.7 D i s t r i b u t i o n of Mean Monthly Fraser R i v e r Water Temperatures August to December 1.4 THE LOWER FRASER RIVER The lower Fraser River from Hope to the Strait of Georgia i s shown in Figure 1.8. The drainage area of the lower river i s approximately 6,000 square miles. Although this area represents only some six percent of the total catchment area, i t can contribute significantly to the flows i n the lower Fraser River, an estimated 15 percent during the freshet and as much as 50 percent during the winter months [Goldie, 1967]. Terminology used to describe the various stretches of the lower Fraser River i s often confusing. The following brief description of the various channels of the river system delineates the nomenclature used throughout this paper [taken from Benedict et al., 1973 ]. The stretch of river from Hope to New Westminster i s called the Main Stem. At New Westminster, the Fraser River branches into a major channel called the Main Arm, entering the Strait of Georgia at Steveston, and a minor channel known as the North Arm, which enters the St r a i t at Point Grey. In the North Arm, bifurcation caused by Sea Island results i n the Middle Arm, which enters the Strait over Sturgeon Banks. A number of small islands and training walls in the Main Arm near Ladner result in the formation of side channels, the major ones being Ladner Reach and Sea Reach, which flow into Canoe Pass, the most southerly exit of Fraser River water. The Main Arm contributes 85 percent of the discharge that ultimately enters the Strait and the North Arm, Middle Arm and Canoe Pass contribute about 5 percent each [Goldie, 1967]. F i g u r e 1.8 The Lower F r a s e r R i v e r 22 1.4.1 T i d a l E f f e c t s . Tides i n the S t r a i t of Georgia, which i s connected to the P a c i f i c Ocean through Juan de Fuca S t r a i t i n the south and Johnstone S t r a i t s i n the nor t h (see Figure 1.1), are of the mixed type, c h a r a c t e r i s t i c of much of the coast of northwestern North America. That i s , the t i d e s a l t e r n a t e from s p r i n g to neap t i d e s i n a bi-weekly c y c l e r e s u l t i n g i n d i u r n a l i n e q u a l i t i e s most days of the c y c l e . The t i d a l range at Steveston f o r mean and l a r g e t i d e s r e s p e c t i v e l y i s 10 f e e t and 15 f e e t . T y p i c a l t i d e s are shown i n Fi g u r e 1.9 f o r P o i n t A t k i n s o n , the nearest Hydrographic S e r v i c e s reference p o r t [Canadian Hydrographic S e r v i c e s , 1974]. Low r i v e r s lopes i n the lower F r a s e r R i v e r , as p r e v i o u s l y mentioned, r e s u l t i n t i d a l a c t i o n a f f e c t i n g water slopes and water s u r f a c e e l e v a t i o n as f a r upstream as C h i l l i w a c k , some 55 m i l e s from the mouth. On occa s i o n , the combination of unusual t i d e s and low r i v e r discharge has r e s u l t e d i n observed e f f e c t s reaching even f a r t h e r upstream to the v i c i n i t y of Rosedale, although t h i s i s e x c e p t i o n a l [Baines, 1952]. The e f f e c t s near the l i m i t of t i d a l i n f l u e n c e are r e s t r i c t e d to minor changes i n slope and e l e v a t i o n and, although discharge i s a f f e c t e d , e f f e c t s are not severe enough to cause current r e v e r s a l . Current r e v e r s a l has been r e p o r t e d , however, as f a r upstream as M i s s i o n [Baines, 1952]. Of a d d i t i o n a l importance i n understanding the i n f l u e n c e of the t i d a l e f f e c t s on the h y d r a u l i c behaviour of the lower F r a s e r R i v e r i s the r e c o g n i t i o n that the P i t t R i v e r - P i t t Lake system i s a t i d a l storage area. Water s u r f a c e e l e v a t i o n s are observed to vary w i t h the t i d e s over the f u l l extent of P i t t Lake, a surface area of some 25 square m i l e s . This represents a l a r g e volume of.water storage on the f l o o d t i d e , which i s l a t e r r e l e a s e d on the ebb t i d e . There i s a reverse d e l t a at the entrance to P i t t Lake Spring Tides CD CD Lu JZ "cu X CD •a 16-1 14- 12- 10- 8 6 4 2H 0 Neap Tides l I l I i Time in Days Figure 1.9 T y p i c a l Tides at Point Atkinson to which i s evidence of the l a r g e volumes of water that enter the l a k e [Joy, 1974]- Low r i v e r flow-high t i d e c o n d i t i o n s were the s u b j e c t of a study by Baines [1952], r e f e r r e d to i n the preceding paragraph. Cubature discharge c a l c u l a t i o n s , based on one-half h o u r l y r i v e r stage measurements f o r a day and a h a l f , showed that instantaneous upstream t i d a l flows i n the v i c i n i t y of Steveston reached n e a r l y 140,000 c f s w i t h downstream t i d a l flows reaching over 200,000 c f s f o r a freshwater discharge a t Hope of 28,400 c f s (see F i g u r e 1.10). The v e l o c i t y v a r i a t i o n over the same time p e r i o d , a l s o shown i n F i g u r e 1.10, was from 2.0 f e e t per second upstream to 3.8 f e e t per second downstream. This extreme v a r i a t i o n i n discharge and v e l o c i t y makes one a c u t e l y aware of the complex nature of h y d r a u l i c behaviour i n the lower F r a s e r R i v e r . High r i v e r flow c o n d i t i o n s during the f r e s h e t tend to dampen out t i d a l e f f e c t s as the freshwater discharge predominates over t i d a l a c t i o n . During these c o n d i t i o n s there are no r e v e r s a l s of c u r r e n t and only minor r i v e r stage v a r i a t i o n even i n the seaward reaches of the r i v e r . Although flows at t h i s time are s t i l l unsteady, the lower F r a s e r R i v e r behaves h y d r a u l i c a l l y i n a manner more c l o s e l y resembling that of a r i v e r . Another consequence of t i d a l a c t i o n i s the i n c r e a s e d complexity and unsteady nature of the p h y s i c a l processes of mixing and d i s p e r s i o n . U n l i k e the s i t u a t i o n i n a r i v e r where d i s p e r s i o n processes, although minimal, are more completely d e f i n e d because i n s i g h t s and i n f o r m a t i o n are t r a n s f e r a b l e from one r i v e r to another and the process can be reproduced  26 i n the l a b o r a t o r y , the phenomenon of t i d a l mixing i n e s t u a r i e s and t i d a l r i v e r s i s p o o r l y understood. This i s p a r t l y because i t has r e c e i v e d l e s s a t t e n t i o n , but mainly because each s i t u a t i o n i s unique and, as a r e s u l t , the f i n d i n g s from other s t u d i e s do not n e c e s s a r i l y apply. M i x i n g and d i s p e r s i o n processes on the lower F r a s e r R i v e r have been the o b j e c t of a recent study by the Westwater Research Centre [Ward, unpublished d a t a ] . Dye t r a c e r was r e l e a s e d and tracked over a t i d a l c y c l e to determine r a t e s - l a t e r a l , l o n g i t u d i n a l and v e r t i c a l m i x i n g . The r e s u l t s of the dye s t u d i e s i n d i c a t e d t h a t , w h i l e v e r t i c a l m i x i n g normally occurs r a p i d l y , the r a t e s of l a t e r a l d i s p e r s i o n are much lower. V e r t i c a l mixing was c a l c u l a t e d f o r u n s t r a t i f i e d f l o w to be complete w i t h i n the f i r s t hour a f t e r dye i n j e c t i o n , whereas the time r e q u i r e d f o r t r a n s v e r s e mixing to be completed was estimated to be more than one t i d a l c y c l e (or 25 h o u r s ) . I t was found, however, that when p a r t i a l l y s t r a t i f i e d c o n d i t i o n s e x i s t e d i n the estuary due to the presence of the s a l t wedge, v e r t i c a l m i x i n g was i n - h i b i t e d . 1.4.2 S a l i n i t y I n t r u s i o n . S a l t w a t e r i n t r u s i o n i n the lower F r a s e r R i v e r has been the s u b j e c t of much debate i n recent y e a r s . Various spot measurements were made i n the past [Waldichuk e t a L , 1968] b u t , not u n t i l 1973, was any i n t e n s i v e research i n i t i a t e d to study t h i s e s t u a r i n e phenomenon. F i e l d i n v e s t i g a t i o n s during February-March, 1973 were under- taken to d e f i n e the s a l i n i t y p a t t e r n s i n the lower F r a s e r R i v e r [Hodgins, 1975]. I n - s i t u continuous r e c o r d i n g s a l i n i t y and temperature measuring devices were i n s t a l l e d at three f i x e d l o c a t i o n s i n the lower reaches of the r i v e r i n an attempt to determine the nature and extent of the s a l t water i n t r u s i o n . R e s u l t s of t h i s f i e l d i n v e s t i g a t i o n have been i n c l u d e d i n a d o c t o r a l t h e s i s which describes a mathematical model of s a l t water wedge movement [Hodgins, 1975]. The s a l i n i t y m onitoring showed c o n c l u s i v e l y t h a t a s t r a t i f i e d s a l t water wedge was present i n the lower reaches of the r i v e r d u r ing f l o o d t i d e c o n d i t i o n s . The tongue of the wedge, j u s t a f t e r h i g h t i d e , was estimated, through use of the saltwedge model, to extend n e a r l y as f a r u p r i v e r as Annacis I s l a n d . With the succeeding s t r o n g ebb t i d e the wedge was washed out of the r i v e r to a p o i n t beyond Steveston. Recent s a l i n i t y measurement i n the r i v e r has confirmed that t h i s i s indeed the case [Ages & Hughes, 1975, and Westwater Research Centre, unpublished d a t a ] . I n d i c a t i o n s are that the toe of the wedge can extend u p r i v e r even as f a r as the eas t e r n t i p of Annacis I s l a n d . During f r e s h e t , s a l t w a t e r does hot i n t r u d e u p r i v e r of Steveston due to the predominating e f f e c t s of l a r g e r i v e r flows [Ward, unpublished d a t a ] . T h i s s i t u a t i o n then, w i t h the saltwedge bei n g washed out of the r i v e r d u r ing low freshwater discharge c o n d i t i o n s and not e n t e r i n g the r i v e r , at a l l during f r e s h e t discharge c o n d i t i o n s , l e a d s one to q u e s t i o n the c l a s s i f i c a t i o n of the lower Fr a s e r as an es t u a r y . Since t r a d i t i o n a l e stuary c l a s s i f i c a t i o n [Hansen and R a t t r a y , 1966] i m p l i e s t h a t there be c o n s i s t e n t presence of s a l i n i t y , the system i s perhaps more p r o p e r l y described as a t i d a l r i v e r , as i t has been by some resear c h e r s [Callaway, 1971]. To account f o r the f a c t that s a l i n i t y i n the form of s a l t w a t e r i n t r u s i o n i s present some of the time, the term " r i v e r / e s t u a r y " w i l l be used i n t h i s paper. CHAPTER 2 DISSOLVED OXYGEN DYNAMICS, A REVIEW 2.1 DISSOLVED OXYGEN The dissolved oxygen resources of a waterway play a most important role in the maintenance of a healthy aquatic ecosystem. Dissolved oxygen, one of the most important indicators of water quality, i s essential for support of a balanced aquatic habitat particularly as i t affects the survi- val of fish l i f e . To insure the survival of a healthy fishery, which w i l l essentially guarantee protection of the entire aquatic community, concen- trations of dissolved oxygen must generally be above 5 mg/1 (milligrams per l i t r e ) although oxygen requirements may vary depending on the age and species of the f i s h , the temperature and composition of the water, and the presence of toxic substances [Klein, 1962]. More specific dissolved oxygen c r i t e r i a for freshwater f i s h [F*vPCA, 1972] are given as follows. For warm water game fis h "DO concen- trations should be above 5 mg/1 ... (except) under extreme conditions ... the DO may range between 5 mg/1 and A mg/1 for short periods of time." More stringent requirements are recommended for cold water fishes such as trout and salmon especially in spawning areas where "DO levels must not be below 7 mg/1 at any time." For good growth and the general well- being of these species "DO concentrations should not be below 6 mg/1 ... (except) under extreme conditions they may range between 6 mg/1 and 5 mg/1 for short periods." In large streams which serve principally as migratory routes "DO levels may be as low as 5 mg/1 for periods up to - 28 - 6 hours but should never be below A mg/1 at any time or p l a c e . " A s i d e from being a necessary requirement f o r f i s h s u r v i v a l , d i s s o l v e d oxygen c o n c e n t r a t i o n i s a l s o a more gen e r a l i n d i c a t o r of the degree of water p o l l u t i o n as i t i s l i n k e d w i t h other water q u a l i t y i m p a i r - ments such as the nuisance c o n d i t i o n s created where c o n c e n t r a t i o n s are low. A c l a s s i f i c a t i o n of r i v e r q u a l i t y based on d i s s o l v e d oxygen con- tent i s shown i n Table 2.1. TABLE 2.1 CLASSIFICATION OF RIVER QUALITY BASED ON DISSOLVED OXYGEN CONTENT [KLEIN, 1959] DISSOLVED OXYGEN TYPE OF RIVER WATER % OF SATURATION Good - Greater than 90 F a i r 7 5 - 9 0 Doub t f u l 50 - 75 Badly p o l l u t e d Less than 50 The amount of oxygen d i s s o l v e d i n water from the atmosphere i s dependent on :temperature, barometric pressure and the amount of s a l t s present i n the water. S o l u b i l i t y of oxygen v a r i e s d i r e c t l y w i t h baro- m e t r i c pressure and i n v e r s e l y w i t h water temperature and s a l t content. Thus, hi g h water temperatures r e s u l t i n low oxygen s o l u b i l i t i e s as does the presence of high s a l t c o n c e n t r a t i o n which, f o r example, c h a r a c t e r i z e s sea water. The v a l u e s g e n e r a l l y used f o r the s o l u b i l i t y of oxygen i n 30 fresh and s a l t water are those given by the American Public Health Association [Standard Methods 1971] and were calculated by Whipple and Whipple [1911] from gasometric determination carried out by Fox [1909]. More recent investigations at the Water P o l l u t i o n Research Laboratory i n England [Truesdale e_t a l . , 1955] have resulted i n publication of what may be considered to be more correct values as determined by a modification of the standard Winkler method [Standard Methods, 1971]. These investigations have resulted i n the following empirical equation representing the s o l u - b i l i t y of oxygen: C s = 14.161 - 0.3943T + 0:007714T2 - 0.0000646T3 (2.1) C i s the saturation concentration of oxygen i n ppm; s where and T i s the temperature i n °C. The effects of barometric pressure on s o l u b i l i t y when conditions are d i f f e r e n t from standard atmospheric are also accounted f o r e m p i r i c a l l y by the following: C s ' = C s J L . ' 760 where C s' i s the s o l u b i l i t y of oxygen at P mm Hg pressure; and C g i s the s o l u b i l i t y of oxygen at 760 mm Hg pressure Saturation concentrations for oxygen dissolved i n mixtures of freshwater and seawater cannot be reduced to an empirical equation but values have been t a b u l a t e d [Standard Methods, 1971 and Truesdale et a l . , 1955]. 2.2 OXYGEN DEMANDING WASTES When a wastewater i s discharged i n t o a waterway, the biodegrad- able organics contained i n that wastewater exert an oxygen demand on the d i s s o l v e d oxygen resources of the stream or estuary. This f a c t was f i r s t recognized i n B r i t a i n d u r i ng the 19th century by way of the i n - v e s t i g a t i o n s of the Royal Commission on Sewage D i s p o s a l , which was ap- pointed i n 1898 " t o re p o r t on methods f o r the treatment and d i s p o s a l of sewage and trade wastes". The Commission p u b l i s h e d a s e r i e s of ten r e p o r t s over 17 years which d e s c r i b e d many aspects of sewage d i s p o s a l , ranging from standards and t e s t s of sewage and sewage e f f l u e n t s through contamination of s h e l l f i s h and growth of weeds i n t i d a l waters to a com- prehensive t r e a t i s e on methods a v a i l a b l e f o r p u r i f i c a t i o n and d i s p o s a l of sewage and trade wastes. This "milestone" study l a i d the groundwork f o r implementation of remedial measures i n B r i t a i n where by the end of the 19th century, the water p o l l u t i o n i n some areas was so bad that " a i l f i s h l i f e and other a q u a t i c l i f e , animal and vegetable had v i r t u a l l y disappeared" and "the scum i n p a r t s of the R i v e r I r w e l l was so t h i c k and s o l i d t hat b i r d s walked on i t without t h i n k i n g " . [ K l e i n , 1962]. The Royal Commission s t u d i e s formed the b a s i s of what was un- doubtedly the f i r s t major water p o l l u t i o n i n v e s t i g a t i o n and, as such, the f i n d i n g s have had long l a s t i n g and f a r reaching impact. In t h i s r e s p e c t , the 8th Report i s p a r t i c u l a r l y important. I t d e a l t w i t h the question of standards and t e s t s a p p l i e d to sewage and sewage e f f l u e n t s being discharged to r e c e i v i n g waterways. A t e s t of p u r i t y f o r sewage e f f l u e n t s and r i v e r water, f i r s t recommended by the Royal Commission i n t h i s r e p o r t , was the " d i s s o l v e d oxgyen taken up i n 5 days a t 65°F" which became a standard wastewater and r i v e r water q u a l i t y parameter. L a t e r to be modi f i e d s l i g h t l y and re-named, the Biochemical Oxygen Demand (BOD) t e s t was used by the Royal S o c i e t y i n t h e i r r e p o r t to c l a s s i f y r i v e r s (see Table 2.2). TABLE 2.2 ROYAL COMMISSION CLASSIFICATION OF RIVERS [KLEIN, 1959] APPROXIMATE 5-DAY BOD @ 65°F CLASSIFICATION (ppm) 1 Very c l e a n 2 Clean 3 F a i r l y c l e a n 5 D o u b t f u l 10 Bad The BOD t e s t has r e t a i n e d i t s importance as a measure of waste- water and r i v e r water q u a l i t y i n s p i t e of the f a c t t h a t the t e s t i s subject to a number of sometimes s e r i o u s e r r o r s . I t s p o p u l a r i t y , accept- ance and widespread use as a water q u a l i t y parameter i s i n p a r t due to the endorsement i t r e c e i v e d because of i t s development by the p r e s t i g i o u s Royal Commission but mainly because of i t s value as a d i r e c t measure of oxygen demand as i t i s a t e s t aimed at reproducing the o x i d a t i o n c o n d i t i o n s of a n a t u r a l waterway. Contemporary BOD t e s t i n g i s conducted under more c a r e f u l l y c o n t r o l l e d c o n d i t i o n s of n u t r i e n t enrichment, d i l u t i o n water make up and b a c t e r i a l seeding at an i n c r e a s e d , f i x e d i n c u b a t i o n temperature of 20°C, a l l of which are aimed at s t a n d a r d i z i n g the BOD t e s t i n order t o enhance r e p r o d u c i b i l i t y . These improvements i n l a b o r a t o r y procedure have r e s u l t e d i n in c r e a s e d r e p r o d u c i b i l i t y w i t h m i n i m i z a t i o n o f e r r o r . How- ever, v a g a r i e s i n t r i n s i c to the BOD t e s t remain. I n c h a r a c t e r , BOD i s d e f i n e d as "the amount of oxygen r e q u i r e d by b a c t e r i a w h i l e s t a b i l i z i n g decomposable organic matter under a e r o b i c c o n d i t i o n s " [Sawyer & McCarty, 1967]. The oxygen r e q u i r e d d u r i n g the organic decomposition r e s u l t s from the a c t i v i t y of a group o f micro- organisms, namely the ae r o b i c b a c t e r i a , which u t i l i z e the o r g a n i c s as a food source, d e r i v i n g energy from the o x i d a t i o n process. The bi o c h e m i c a l r e a c t i o n may be g e n e r a l l y represented by a q u a n t i t a t i v e r e l a t i o n s h i p which d e f i n e s , on a t h e o r e t i c a l b a s i s , the amount of oxygen r e q u i r e d to convert an amount of any given organic compound to i t s u l t i m a t e end products - carbon d i o x i d e , water and ammonia [Sawyer & McCarty, 1967]. C nH aO bN c + (n + -| - y - -| c ) 0 2 — > n C 0 2 + (~ - | c) H 20 + CNH 3 (2 The r a t e of o x i d a t i o n of organic matter i s governed t o a major extent by two v a r i a b l e s - b a c t e r i a l p o p u l a t i o n and temperature. In the BOD t e s t , c o n t r o l of the i n c u b a t i o n temperature has been standa r d i z e d . But, however much emphasis i s placed on "se e d i n g " the t e s t sample w i t h b a c t e r i a l seed, i t i s u n l i k e l y t h a t b a c t e r i a l p o p u l a t i o n s w i l l be c o n t r o l l e d . The root of t h i s problem and the main drawback of the BOD t e s t i s that the b a c t e r i a , i n many cases, take time t o become a c c l i m a t i z e d to a p a r t i c u l a r wastewater. The time r e q u i r e d f o r the a c c l i m a t i z a t i o n of b a c t e r i a l p o p u l a t i o n s i s not considered s e p a r a t e l y i n the BOD t e s t , but occurs over the f i r s t few hours (or days) of the 5-day t e s t . Thus, the amount of oxygen consumed i n the 5-day t e s t p e r i o d may not a c c u r a t e l y r e f l e c t the long term demand exerted by a p a r t i c u l a r waste because of the time taken f o r the o x i d a t i o n r a t e to reach i t s maximum. T h i s i s t r u e , i n p a r t i c u l a r , w i t h wastes that c o n t a i n e x o t i c m a t e r i a l s o t h e r than r e a d i - l y o x i d i z a b l e organics as, say, are present i n an i n d u s t r i a l wastewater. Regardless of the inherent i n a c c u r a c i e s of the BOD t e s t , i t i s s t i l l wide- l y used as a measure of the s t r e n g t h of organic waste and has been r e l a t e d to the oxygen balance i n a stream. 2.3 THE OXYGEN BALANCE The discharge of organic wastes i n t o a waterway deoxygenates the water. That i s , the b a c t e r i a degrading the o r g a n i c matter consume oxygen, thereby causing a d e p l e t i o n of d i s s o l v e d oxygen i n the r e c e i v i n g water. Simultaneous to the d e p l e t i o n of d i s s o l v e d oxygen i s the occurrence of another process of nature - atmospheric r e a e r a t i o n . During t h i s pro- cess, a d s o r p t i o n of atmospheric oxygen (and other gases) by the water takes place i n order to maintain the e q u i l i b r i u m between the d i s s o l v e d gases and the atmospheric gases according to Dalton's law of p a r t i a l pressures. The net r e s u l t of these two c o u n t e r a c t i n g f o r c i n g f u n c t i o n s i s that an oxygen balance i s e s t a b l i s h e d . This forms the b a s i s of n a t u r a l s e l f - p u r i f i c a t i o n i n waterways. Figure 2.1 shows an i d e a l i z e d form of the balance f o r a s i n g l e major waste discharge showing the zones of degradation and recovery of a p o l l u t e d stream. Three cases are gi v e n : (a) s l i g h t p o l l u t i o n ; (b) heavy p o l l u t i o n ; (c) gross p o l l u t i o n . In each case shown i n F i g u r e 2.1, the curves are the net r e s u l t of deoxygenation and r e a e r a t i o n o c c u r i n g simultaneously w i t h , i n case ( a ) , the oxygen demand being s m a l l enough so that the minimum d i s s o l v e d oxygen d e f i c i t i s s m a l l and t o l e r a b l e ; i n case ( b ) , the oxygen demand being s u f f i c i e n t to deplete the oxygen resources to a minimum; and i n case ( c ) , the oxygen demand being so l a r g e that i t depletes the oxygen to such an extent t h a t s e p t i c c o n d i t i o n s p r e v a i l over a s t r e t c h of the waterway. The oxygen resources of a waterway, i n a constant s t a t e of dynamic e q u i l i b r i u m , are c o n t r o l l e d by the k i n e t i c s of the processes of deoxygenation and r e a e r a t i o n . 2.4 DEOXYGENATION • . When measuring the oxygen demand of a wastewater over a long p e r i o d of time, whether w i t h a respirometer or i n a s e r i e s of BOD b o t t l e s , the oxygen consumed i s observed to vary i n a manner s i m i l a r to th a t shown i n F i g u r e 2.2. The t o t a l oxygen demand i s the net r e s u l t of two separate and independent o x i d a t i o n processes - carbonaceous o x i d a t i o n and n i t r i f i c a t i o n . During the f i r s t 10 to 15 days, the carbonaceous oxygen demand, sometime c a l l e d the f i r s t stage oxygen demand (FSOD), accounts f o r most of the t o t a l demand and i s the r e s u l t of the o x i d a t i o n of carbonaceous organic matter. During the subsequent p e r i o d , n i t r i f i c a t i o n Dissolved Oxygen Concentration (Percent Saturation) cn O O O O 9 e Time (Days) Figure 2.2 Oxygen Uptake of a Wastewater 38 occurs although, i n some i n s t a n c e s , i f the wastewater con t a i n s s i g n i f i c a n t q u a n t i t i e s of ammonia, i t can take place simultaneous to carbonaceous o x i d a t i o n . In t h i s process, the o x i d a t i o n of ammonia u l t i m a t e l y to n i t r a t e , by n i t r i f y i n g b a c t e r i a , e x e r t s an a d d i t i o n a l oxygen demand, o f t e n r e f e r r e d to as the second stage oxygen demand (SSOD), which r e s u l t s i n an increased t o t a l oxygen uptake. 2.4.1 Carbonaceous O x i d a t i o n . The c l a s s i c a l approach to ex- p r e s s i n g mathematically the v a r i a t i o n of BOD w i t h time taken by pioneers i n the f i e l d [ T h e r i a u l t , 1927 and Phelps, 1944] made the assumption that the o x i d a t i o n was a mono-molecular or " f i r s t o rder" r e a c t i o n . That i s , the r a t e of uptake of oxygen was assumed to be p r o p o r t i o n a l to the amount of o x i d i z a b l e organic matter remaining at any time, expressed mathematical- l y as: dL = -KjL (2.4) dt where L represents the u l t i m a t e FSOD at any time t ; i s the r a t e constant f o r the r e a c t i o n , sometimes r e f e r r e d to as the de-oxygenation c o e f f i c i e n t . The i n t e g r a t e d form of t h i s equation i s : L = L Q e " K l t (2.5) where k° i s the i n i t i a l value of L at t = 0. A more convenient form of equation (2.5) i s given by: 39 y = L 0 ( l - e - ^ - ^ C l - l o V ) (2-6) where y i s the BOD at any time t ; and L 0 is the t o t a l or ultimate FSOD. (It should be noted that, as i s conventional, i s the rate constant to the base e and k^ i s the rate constant to the base 10.) The rate constant, k-p from the c l a s s i c a l formulation of BOD as a continuous f i r s t - o r d e r reaction i s , i n f a c t , not a constant but a var i a b l e , the magnitude of which i s governed by a number of important factors, including temperature, the nature of the organic substrate and the a b i l i t y of the organisms present to u t i l i z e the substrate. Foremost, as was discovered by the pioneers [Streeter and Phelps, 1925], increasing temperatures increased the de-oxygenation constant, the value roughly doubling for a temperature increase of 15°C. The temperature e f f e c t i s generally represented by the following r e l a t i o n s h i p , derived from van't Hoff's law: (k ) = (k ) e(T_20) ^1 ;T <-V20 y (2.7) where (k^)^ i s the value of k^ at any temperature T°C; ( k 1 ) 2 0 i s the value at 20°C; and 0 i s a temperature c o e f f i c i e n t . Streeter and Phelps found 9 to be 1.047 based on t h e i r early studies, but 40 more r e c e n t r e s e a r c h [ S c h r o e p f e r e t a l . , 1960] has shown the o r i g i n a l t e m p e r a t u r e c o e f f i c i e n t to be too low, r e s u l t i n g i n i n a c c u r a c i e s a t low t e m p e r a t u r e s . S c h r o e p f e r [1960] s u g g e s t s 0 v a l u e s of 1.056 f o r t h e t e m p e r a t u r e range 20-30°C and 1.135 f o r t h e temperature range 4-20°C. A n o t h e r f a c t o r a f f e c t i n g t h e r a t e c o n s t a n t i s t h e a b i l i t y o f the organisms t o u t i l i z e t h e o r g a n i c m a t t e r . I t has been t h e o r i z e d [ E c k e n f e l d e r , 1970] t h a t BOD r e a c t i o n s and, i n f a c t , a l l a e r o b i c r e a c t i o n s , o c c u r i n two s e p a r a t e and d i s t i n c t p h a s e s . D u r i n g the f i r s t phase, which i s u s u a l l y complete i n 18-36 h o u r s , t h e o r g a n i c m a t t e r p r e s e n t i n the wastewater i s u t i l i z e d by t h e m i c r o r g a n i s m s f o r energy and growth (the " s y n t h e s i s " p h a s e ) . When the o r g a n i c s o r i g i n a l l y p r e s e n t i n t h e waste- w a t e r a r e removed, the organisms p r e s e n t c o n t i n u e to use oxygen f o r a u t o - o x i d a t i o n and endogenous m e t a b o l i s m o f t h e i r c e l l u l a r mass ( t h e "endogenous r e s p i r a t i o n " p h a s e ) . O n l y when the c e l l mass i s c o m p l e t e l y o x i d i z e d t o n o n - b i o d e g r a d a b l e c e l l u l a r r e s i d u e , u s u a l l y t a k i n g more than 20 d a y s , i s the o x i d a t i o n c o m p l e t e . The main d i s t i n g u i s h i n g d i f f e r e n c e between the two phases i s t h e d i f f e r e n t r a t e s o f r e a c t i o n . D u r i n g the f i r s t , o r a s - s i m i l a t i o n phase, t h e r e a c t i o n r a t e i s some 10 t o 20 times f a s t e r t h a n the r a t e o f endogenous o x i d a t i o n . The two-phase t h e o r y of BOD r e a c t i o n sheds a new l i g h t on t h e meaning of th e BOD r a t e c o n s t a n t , k^. However, a c c o r d - i n g t o E c k e n f e d l e r [1970], t h e " o v e r a l l average r e a c t i o n r a t e " o v e r the e n t i r e o x i d a t i o n i s comparable t o t h e c l a s s i c a l f orm o f r a t e c o n s t a n t t h a t was' d e v e l o p e d by S t r e e t e r and P h e l p s . A n o t h e r f a c t o r a f f e c t i n g t h e d e o x y g e n a t i o n c o n s t a n t i s the n a t u r e o f the o r g a n i c s u b s t r a t e u n d e r g o i n g o x i d a t i o n . W i t h raw sewage, 41 f o r example, average r e a c t i o n r a t e c o n s t a n t s w i l l tend to be h i g h r e - f l e c t i n g the ease w i t h which the waste can be degraded. A f t e r treatment which removes much of the organic matter, and i n r i v e r s , where only low co n c e n t r a t i o n s of organics are present, the r a t e constants are s i g n i f i - c a n t l y lower. This can be explained i n terms of the "two-phase" theory t h a t , i n these cases, the o x i d a t i o n i s mainly due to endogenous r e s p i r - a t i o n which r e s u l t s i n the lower r a t e constants. The v a r i a t i o n i n average BOD r a t e constants f o r a range of substances i s shown i n Table 2.3. TABLE 2.3 AVERAGE BOD RATE CONSTANTS @ 20°C [ECKENFELDER, 1970] SUBSTANCE ^1^20 Untreated wastewater 0.15-0.28 High r a t e f i l t e r s and anaerobic contact e f f l u e n t 0.12-0.22 High degree biotreatment e f f l u e n t 0.06-0.10 R i v e r s w i t h low p o l l u t i o n 0.04-0.08 A comparison of a p l o t of equation (2.6) w i t h the observed oxygen uptake of organic matter w i l l , s u r p r i s i n g l y enough, most o f t e n show a r e l a t i v e l y good " f i t " f o r the f i r s t 8 to 10 days of o x i d a t i o n a f t e r which time the BOD curve d i v e r g e s r a d i c a l l y from the course i t would be expected to f o l l o w as a unimolecular r e a c t i o n [Sawyer & McCarty, 1967]. The main reason f o r the divergence from the theory a f t e r the i n i t i a l p e r i o d of o x i d a t i o n i s that the e f f e c t s of n i t r i f i c a t i o n become s i g n i f i c a n t . 2.4.2 N i t r i f i c a t i o n . The nitrogenous stage of b i o c h e m i c a l de- g r a d a t i o n , as i n the BOD t e s t , i n c l u d e s conversion of organic n i t r o g e n to ammonia and the subsequent o x i d a t i o n of ammonia u l t i m a t e l y to n i t r a t e . Organic n i t r o g e n i s hydrolyzed to ammonia, under a e r o b i c or anaerobic c o n d i t i o n s , without the u t i l i z a t i o n of oxygen. The ammonia i s s u c c e s s i v e - l y o x i d i z e d by n i t r i f y i n g b a c t e r i a through n i t r i t e to n i t r a t e by the organisms nitrosomcnas and n i t r o b a c t e r , r e s p e c t i v e l y . [Wezernak, 1968], In the BOD t e s t of raw wastewater there i s g e n e r a l l y a pronounced l a g of 10-15 days between the beginning of carbonaceous o x i d a t i o n and the n i t r i f i c a t i o n step. This l a g i s l e s s f o r t r e a t e d samples, l i k e l y because of a c c l i m a t i z a t i o n of the n i t r i f y i n g b a c t e r i a d u r i n g the sewage treatment process, and i s i n the order of one or two days f o r h i g h l y t r e a t e d samples. In streams, the two stages f r e q u e n t l y proceed s i m u l t a n e o u s l y , although there may be lags i n the n i t r i f i c a t i o n stage i n h i g h l y p o l l u t e d streams or i n those w i t h low d i s s o l v e d oxygen. [Manhattan C o l l e g e , 1972]. There have been examples reported [Courchaine, 1963] where high n i t r i f i c a t i o n r a t e s have had s i g n i f i c a n t e f f e c t s on the oxygen balance of streams. This was a t t r i b u t e d to the combination of a high degree of waste treatment and a high temperature r e c e i v i n g water both of which favour n i t r i f i c a t i o n . I t was found that the high r e c e i v i n g water temperatures (25-30°C) r e s u l t e d i n the n a t u r a l p r o l i f e r a t i o n of an over-abundant popu- l a t i o n of n i t r i f y i n g b a c t e r i a . T h i s , i n t u r n , r e s u l t e d i n an almost im- mediate uptake of oxygen by these b a c t e r i a when a wastewater' c o n t a i n i n g s i g n i f i c a n t n i t r o g e n was introduced. In g e n e r a l , however, except i n h i g h 43 temperature receiving streams, n i t r i f i c a t i o n i s not of much significance when compared to the effects of carbonaceous demand on stream dissolved oxygen resources. At temperatures below 12 - 2°C, n i t r i f i c a t i o n i s usually not significant [Manhattan College, 1972]. 2.5 REAERATION The deoxygenation of a waterway, due to the degradation of organics, i s counterbalanced by the natural process of atmospheric re- aeration. Atmospheric oxygen i s absorbed readily by the oxygen deficient water to maintain the balance of p a r t i a l pressures between the atmosphere and the water which, in the limit, results in the saturation of water with dissolved oxygen. The driving force for the rate of oxygenation i s the dissolved oxygen d e f i c i t , which i s simply the difference between the saturation concentration and the existing concentration. Mathematically, this may be expressed as: f =- K2 D , <2'8> where and D is the dissolved oxygen de f i c i t at any time t; K 2 i s the rate constant, often refered to as the reaeration coefficient, in form, similar to the deoxygenation constant. Integration of Equation (2.8) results i n : D = D D e - V = D D 10 ( 2 " 9 ) where D o is the i n i t i a l d e f i c i t at t = 0. 44 Many f a c t o r s are known to a f f e c t the value of the r e a e r a t i o n co- e f f i c i e n t , k£. N a t u r a l mixing i n waterways has been found to be p a r t i c u l a r - l y important as i t e f f e c t s the r a t e of sur f a c e renewal at the g a s - l i q u i d i n t e r f a c e where the oxygen t r a n s f e r takes p l a c e . E a r l y r e s e a r c h e f f o r t s [ S t r e e t e r and Phelps, 1925] concluded that the i n f l u e n c e of the h y d r a u l i c and p h y s i c a l c h a r a c t e r i s t i c s of a stream on the r e a e r a t i o n c o e f f i c i e n t could be des c r i b e d e m p i r i c a l l y as f o l l o w s : k 2 = aU nH- m ( 2 ' 1 0 ) where U i s the v e l o c i t y ; H i s the water depth; and a,m.and n are e m p i r i c a l constants dependent on the h y d r a u l i c c o n d i t i o n s and on the slope and roughness of the stream bed. Many resea r c h i n v e s t i g a t i o n s s i n c e have been devoted to the de- t e r m i n a t i o n of stream r e a e r a t i o n r a t e s [Dobbins and O'Connor , 1956; Langbein and Durum, 1967; to name but a few], A number of these i n v e s t i - g a t i o n s concentrated on a c c u r a t e l y measuring the r e a e r a t i o n r a t e and then determining the e m p i r i c a l constants to the o r i g i n a l S t r e e t e r - P h e l p s formu- l a t i o n (Equation (2.10)). Other rese a r c h e f f o r t s attempted a more t h e o r e t i c a l approach to oxygen t r a n s f e r i n v e s t i g a t i n g t h i n f i l m t h e o r i e s and the e f f e c t s of sur f a c e renewal. From t h i s l a t t e r work, there appears to be a s e m i - t h e o r e t i c a l b a s i s to the e m p i r i c a l f o r m u l a t i o n as a number of the t h e o r e t i c a l approaches have r e s u l t e d i n the development of r e l a t i o n s h i p 45 s i m i l a r to Equation (2.10). Some of the val u e s f o r the e m p i r i c a l constants given i n the l i t e r a t u r e are shown i n Table 2.4. TABLE 2.4 SUMMARY OF CONSTANTS FOR THE REAERATION EQUATION (For U i n feet per second and H i n f e e t ) a. m n REFERENCE 9.4 0.67 1.85 Owens et a l . , 1964 5.5 0.50 1.50 Dobbins & O'Connor, 1956 5.0 0.97 1.67 C h u r c h i l l et a l . , 1962 3.7 1.00 1.50 Isaacs & Gaudy, 1966 3.3 1.00 1.33 Langbein & Durum, 1967 Of the range of e m p i r i c a l formulae, the one g e n e r a l l y considered co be most reasonable' f o r the e s t i m a t i o n of reaerat?Lon r a t e s over a wide range of depth and v e l o c i t y c o n d i t i o n s [Thomann, 1971] i s t h a t of Dobbins & O'Connor [1956] given by: . ,.' ...0.5 „-1.50 (2.11) ^2 = 5.5U H In a d d i t i o n to the p h y s i c a l and h y d r a u l i c f a c t o r s , r e a e r a t i o n r a t e s are a l s o a f f e c t e d by winds, waves and chemical agents, such as s u r - f a c t a n t s . The e f f e c t s of s u r f a c t a n t s are minimal i n n a t u r a l waterways because, even i f they are present, c o n c e n t r a t i o n s are u s u a l l y so low th a t the oxygen t r a n s f e r i s not i n h i b i t e d . Wind and wave e f f e c t s , however, can at times be s i g n i f i c a n t as they r e s u l t i n increased s u r f a c e renewal due to wind-induced shear s t r e s s e s and breaking waves. They are u s u a l l y accounted f o r e m p i r i c a l l y by an adjustment of r e a e r a t i o n r a t e s a c c o r d i n g to wind v e l o c i t i e s . A r e l a t i o n s h i p which has been suggested i n a recent study of d i s s o l v e d oxygen dynamics i n the Sacremento-San Joaquin D e l t a [DFWPS, 1972], considered to be a d d i t i v e to the r e a e r a t i o n c o e f f i c i e n t p r e v i o u s l y d i s c u s s e d , i s given by: (Cw) W ( 2 . 1 2 ) where and A k 2 - R W i s the wind v e l o c i t y i n mph; C i s the wind c o r r e c t i o n f a c t o r ranging i n value from 0 to 0.4. Temperature has als o been found to a f f e c t r e a e r a t i o n r a t e s . Temperature compensation i s made by the use of a temperature c o r r e c t i o n f a c t o r , 9, i n a manner s i m i l a r to that discussed e a r l i e r f o r BOD decay r a t e s . The temperature c o r r e c t i o n f a c t o r has been found to vary from 1.017 to 1.044 [Dobbins, 1964] and most commonly i s chosen to be 1.024. 2.6 OTHER SOURCES AND SINKS OF OXYGEN As w e l l as the sources and s i n k s of oxygen p r e v i o u s l y mention- ed, namely r e a e r a t i o n and biochemical o x i d a t i o n , there are other source/ s i n k processes which are, at times, important f a c t o r s i n the oxygen balance. A d d i t i o n a l demands are o f t e n exerted on the oxygen resources of a waterway by the decomposition of bottom d e p o s i t s of o r g a n i c matter, the r e s p i r a t i o n of a q u a t i c p l a n t s and the immediate chemical oxygen demand of a wastewater. On the other s i d e of the ledger, oxygen may be added to a stream by the process of photosynthesis. As w e l l , the removal of BOD due to s e t t l i n g , which occurs i n a slow moving stream, i s a p o s i t i v e f a c t o r ; however, the amount of oxygen demand removed by t h i s process w i l l u s u a l l y add to the benthic demand. 2.7 THE STREETER-PHELPS FORMULATION OF THE OXYGEN BALANCE IN A STREAM The S t r e e t e r - P h e l p s f o r m u l a t i o n of the oxygen balance i n a stream, c i t e d s e v e r a l times above, can now be s p e l l e d out f u l l y . T h e i r i n v e s t i g a t i o n i n t o p o l l u t i o n i n the Ohio R i v e r i n the 1920's a p p l i e d the concepts of deoxygenation and r e a e r a t i o n to d e f i n e the n a t u r a l s e l f - p u r i f i c a t i o n of waterways. The f o r m u l a t i o n of the oxygen balance i n a stream, developed as a r e s u l t of t h e i r s t u d i e s , assumed th a t the b i o - chemical oxygen demand of a wastewater and r e a e r a t i o n from the atmosphere were the only two processes which determined the net r a t e of change of oxygen d e f i c i t . The " c l a s s i c a l " S t r e e t e r - P h e l p s f o r m u l a t i o n , sometimes r e f e r r e d to as the "oxygen-sag curve", i s gi v e n by: dD = K-jL - K 2D (2.13) dt where a l l parameters are as p r e v i o u s l y d e f i n e d . I n t e g r a t i o n of Equation (2.13) r e s u l t s i n : (2.14) K2" K1 where w i t h D i s the d i s s o l v e d oxygen d e f i c i t at any time t ; L and D being r e s p e c t i v e l y the i n i t i a l u l t i m a t e FSOD and o o ° r J the i n i t i a l DO d e f i c i t . Thus, knowing the i n i t i a l stream BOD and DO d e f i c i t and the a p p r o p r i a t e deoxygenation and r e a e r a t i o n c o e f f i c i e n t s , the DO d e f i c i t may be c a l c u l - ated f o r any time t . The r e s u l t a n t p l o t of DO d e f i c i t versus time i s a q u a n t i t a t i v e s o l u t i o n to the oxygen-sag curves shown i n Figure 2.1 and discussed i n S e c t i o n 2.3. The s i m p l i f i e d S t r e e t e r - P h e l p s equation can be expanded to i n - clude the e f f e c t s on the oxygen balance of some of the other oxygen source/sink parameters mentioned i n S e c t i o n 2.3.5, s p e c i f i c a l l y , the s e t t l i n g out of BOD, the a d d i t i o n of BOD to o v e r l y i n g water by bottom d e p o s i t s , and photosynthetic r e s p i r a t i o n . The s o l u t i o n to t h i s more general form of the oxygen sag curve which accounts f o r the e f f e c t s of these a d d i t i o n a l parameters [Camp, 1965] i s given by: D = K 2 - K r K 3 W -•o (K 1+K 3) - ( K 1 + K 3 ) t - K 2 t ] - e (2.15) (K^+K^) K x 1 - e - K 2 t + D o e - K 2 t where K.j i s the r a t e of BOD l o s s due to s e t t l i n g per day; p i s the r a t e of BOD a d d i t i o n from bottom i n ppm per day; a i s the r a t e of photosynthetic oxygen a d d i t i o n i n ppm per day; a l l other parameters are as p r e v i o u s l y d e f i n e d . CHAPTER 3 DISSOLVED OXYGEN MODELS The mathematical formulation of the oxygen balance, discussed i n the previous chapter, forms the basis of the dissolved oxygen "model". A "model" i s , i n the s t r i c t e s t sense, a formalism - the mathematical express- ion of a relevant physical process, or processes, i n t h i s case the natural processes of the deoxygenation and reaeration i n water. The term "model", often used loosely, has numerous meanings. In the most general sense, i t can mean a very non-specific conceptual i d e a l i z a t i o n of a problem or pro- cess, as i n the economists' use of "economic models". I t can also be used to mean a simple analog of a r e a l system, examples of which are the physi- c a l models used i n engineering and hydraulics. Another use of the term "model", which combines the s t r i c t d e f i n i t i o n of formalism and the general d e f i n i t i o n of conceptualized idealism, refers to a mathematical formulation together with a technique which allows for a solution of the variables of concern. This usage i s i m p l i c i t i n the term " d i g i t a l model" which i n some cases refers to a s p e c i f i c computer program used i n the so l u t i o n . I t i s also the most appropriate d e f i n i t i o n which can be used to describe the dissolved oxygen models which w i l l be discussed i n t h i s chapter. 3.1 STREAM AND RIVER MODELS The basic Streeter-Phelps formulation of the oxygen balance i n streams and ri v e r s describes a time dependent functional r e l a t i o n s h i p between the basic oxygen source and sink processes f o r a single waste - 50 - 5 1 discharge. The a p p l i c a t i o n of t h i s " c l a s s i c a l " theory to streams and r i v e r s i n order to s o l v e f o r oxygen-sag i s q u i t e s t r a i g h t f o r w a r d when the f o l l o w i n g assumptions are made: ( i ) c r o s s - s e c t i o n a l mixing i s r a p i d ; ( i i ) r i v e r flows are steady, and ( i i i ) "plug f l o w " ( l a c k of l o n g i t u d i n a l mix- ing) e x i s t s . These assumptions are reasonable f o r most r i v e r s where, i n g e n e r a l , t r a n s v e r s e and v e r t i c a l mixing r a t e s are h i g h , r e s u l t i n g i n r e l a t i v e l y r a p i d c r o s s - s e c t i o n a l mixing, and l o n g i t u d i n a l mixing r a t e s are low, r e s u l t i n g i n minimal l o n g i t u d i n a l d i s p e r s i o n . As f o r the steady nature of r i v e r and stream flow, although the flow may not be steady over the e n t i r e stream l e n g t h , i t can be considered to be steady at l e a s t over given s t r e t c h e s of the r i v e r . The assumption of steady r i v e r flow a l l o w s simple :transposal of r e f e r e n c e frames from the t i m e - s c a l e s used i n the d i s s o l v e d oxygen (DO) d e f i c i t equation (Equations 2.14 & 2.15) to d i s t a n c e - s c a l e s . By c o n t i n u i t y , average v e l o c i t i e s can be obtained and they may be r e l a t e d to d i s t a n c e as V e l o c i t y (V) = Distance (x) x Times ( t ) . Thus by simple s u b s t i t u t i o n of V/x f o r t i n the oxygen-sag s o l u t i o n , the DO d e f i c i t i s expressed as a f u n c t i o n of x g i v i n g a s o l u t i o n for the s p a t i a l d i s t r i b u t i o n of DO i n a stream or r i v e r downstream of a s i n g l e waste o u t f a l l . In the event that there i s more than one o u t f a l l , a DO d i s t r i b u t i o n can be c a l c u l a t e d f o r each waste input and the s o l u t i o n s superimposed, the t o t a l DO d e f i c i t being the sum of the i n d i v i d u a l d e f i c i t s . A l s o , i f c o n d i t i o n s of temperature and r i v e r flow change over s t r e t c h e s of the r i v e r , a f f e c t i n g changes i n both of the r e a c t i o n r a t e constants and the v e l o c i t y , the s t r e t c h of r i v e r may be d i v i d e d up i n t o s m aller reaches over which c o n d i t i o n s are constant. This manner of segmentation can be made to c o i n c i d e , where p o s s i b l e , w i t h waste 52 input locations so that both changes in river conditions and additional waste inputs can be handled in one step. 3.2 ESTUARY MODELS The application of the " c l a s s i c a l " dissolved oxygen model to estuaries is not as simple and straightforward as i t i s in the case of rivers and streams. This is primarily because of the complex, non-uniform nature of flow patterns in estuaries which exist as a result of t i d a l i n - fluence. Although the natural physical and biochemical processes involved are similar, the unsteady, oscillatory flows in estuaries present problems when one attempts to apply a dissolved oxygen model, because of the d i f f i c u l - ties encountered in obtaining the time-histories of different parcels of water in an estuary. Unlike rivers, where for a given set of river flows there w i l l be a discrete set of river velocities for every location along the stream length, velocities i n an estuary vary with time as well as loca- tion, the temporal variations being due to changes in water surface eleva- tions throughout the estuary during the t i d a l cycle (see Figure 1.10 for typical variations i n the lower Fraser River) =- Ths- ussteady nature of velocities in estuaries, which are seen to vary "discontinuously" (in the sense of direction) makes i t impossible to easily transpose between time and distance reference frames. Thus, the basic Streeter-Phelps formula- tions for DO distributions, which depend on a simple time-distance trans- posal, become d i f f i c u l t to implement. Another facet of estuarine hydraulics which differs from river hydraulics and has important implications for the application of dissolved oxygen models is increased dispersion and mixing in estuaries caused by the 53 o s c i l l a t o r y movement of the water mass. S i g n i f i c a n t v e r t i c a l and l a t e r a l v e l o c i t y g r a d i e n t s , together w i t h t u r b u l e n t d i f f u s i o n , tend to erode concen- t r a t i o n peaks from a s l u g d i s c h a r g e , spreading and r e d i s t r i b u t i n g the d i s - s o l v e d substance around the l i n e of mean adv e c t i v e advance. T h i s mechanism of l o n g i t u d i n a l m i x i n g , which i s termed l o n g i t u d i n a l d i s p e r s i o n , i s many times more s i g n i f i c a n t i n e s t u a r i e s than i n r i v e r s where i t s e f f e c t can be ignored i n favour of a "plug f l o w " assumption. In e s t u a r i e s , however, i t must be accounted f o r ; i n the case of e s t u a r i e s w i t h zero f r e s h water i n - flow, d i s p e r s i o n due to t i d a l mixing i s the o n l y mechanism of m a t e r i a l t r a n s p o r t . As we have seen, the non-simple nature of e s t u a r i n e h y d r a u l i c s w i t h d i s p e r s i o n e f f e c t s as w e l l as s p a t i a l and temporal v a r i a t i o n i n v e l o c - i t y , p r o h i b i t s the d i r e c t a p p l i c a t i o n of the b a s i c S t r e e t e r - P h e l p s d i s s o l v e d oxygen model. In order to develop a d i s s o l v e d oxygen model which can be a p p l i e d to e s t u a r i e s , i t i s necessary to go back to b a s i c mass t r a n s p o r t p r i n c i p l e s . This more s o p h i s t i c a t e d approach w i l l u l t i m a t e l y u t i l i z e a l l the b a s i c concepts introduced i n the previous chapter and r e s u l t i n a more g e n e r a l l y a p p l i c a b l e d i s s o l v e d oxygen model. 3.3 THE ONE-DIMENSIONAL MASS TRANSPORT EQUATION The b a s i c one-dimensional equation f o r d e s c r i b i n g the mass t r a n s - p o r t of any d i s s o l v e d substance i n an unsteady non-uniform f l o w i s obtained by making a mass balance over an elemental c r o s s - s e c t i o n a l s l i c e of the f l o w f i e l d of the waterway. Mass i s t r a n s p o r t e d through the s l i c e by the processes of advection and d i s p e r s i o n , and these processes, together w i t h any source o r s i n k s of the substance w i t h i n the s l i c e , determine the c o n c e n t r a t i o n . The g e n e r a l i z e d form of the one-dimensional mass balance equation i s given by: L£ = * s E dfA as! JL (3.1) 2»t - uFx" A 3xL dxJ " ^ S i where s i s the c o n c e n t r a t i o n of any d i s s o l v e d substance; u i s the l o n g i t u d i n a l v e l o c i t y ; E i s the l o n g i t u d i n a l d i s p e r s i o n c o e f f i c i e n t ; A i s the c r o s s - s e c t i o n a l area; S. i s the r a t e of p r o d u c t i o n per u n i t volume due to the i t h s o u r ce-sink p r o c e s s , i = 1,...,n; x i s the l o n g i t u d i n a l d i s t a n c e ; and t i s the time. The three terms on the r i g h t hand s i d e of the equation are the a d v e c t i v e , d i s p e r s i v e and source-sink terms, r e s p e c t i v e l y . Since Equation (3.1) i s one-dimensional, a l l the v a r i a b l e s and parameters are c r o s s - s e c t i o n a l l y averaged v a l u e s . In an e s t u a r y , because of t i d a l e f f e c t s , the parameters of the equation u, E and A, d e f i n e d by the c r o s s - s e c t i o n a l geometry and h y d r a u l i c s f o r the p a r t i c u l a r e s t u a r y , can vary over both space(x) and t i m e ( t ) . Thus, i n the s o l u t i o n , i t i s necess- ary to account i n some manner f o r the temporal as w e l l as s p a t i a l v a r i a t i o n , of these parameters. There are two types of s o l u t i o n s which can be a p p l i e d to the one- dimensional mass t r a n s p o r t equation - the " s t e a d y - s t a t e " or " t i d a l l y averaged" s o l u t i o n and the " t i d a l l y v a r y i n g " s o l u t i o n . The s t e a d y - s t a t e 55 s o l u t i o n averages out the e f f e c t s of the t i d e over the t i d a l c y c l e a s s i g n - i n g parameters t h e i r "mean t i d a l " v a l u e . Because of t h i s averaging of t i d a l c o n d i t i o n s , t h i s s o l u t i o n i s , i n some ways, a temporal a b s t r a c t i o n of the processes i n v o l v e d but, as we s h a l l see, i s nonetheless v e r y u s e f u l . The second type, the t i d a l l y v a r y i n g s o l u t i o n , accounts f o r the temporal v a r i a t i o n i n the parameters by o b t a i n i n g t h e i r v a l u e s independently through s o l u t i o n of the hydrodynamic equations which d e s c r i b e the h y d r a u l i c s of the estua r y . The t i d a l l y v a r y i n g s o l u t i o n to the mass t r a n s p o r t e q u a t i o n , a l - though i t allows f o r gr e a t e r temporal r e s o l u t i o n and the o b s e r v a t i o n of " r e a l time" e f f e c t s , demands a much more s o p h i s t i c a t e d approach and g r e a t e r expense o f e f f o r t i n development. The two types o f s o l u t i o n s w i l l now be di s c u s s e d . 3.4 THE STEADY STATE SOLUTIONS TO THE MASS TRANSPORT EQUATION This method of s o l v i n g the one-dimensional mass t r a n s p o r t equa- t i o n , r e f e r r e d to as the " t i d a l l y averaged" approach, a s s i g n s parameters t h e i r mean values over a t i d a l c y c l e . T h i s does not a l t e r the form o f the mass t r a n s p o r t equation but merely changes the i n t e r p r e t a t i o n s of the v a r i a b l e s and parameters. For example, the v e l o c i t y term(u) becomes the t i d a l l y averaged v e l o c i t y ( U ) , which i s determined by the f r e s h water d i s - charge through the mean t i d a l c r o s s - s e c t i o n a l a r e a . The l o n g i t u d i n a l d i s - p e r s i o n c o e f f i c i e n t i s replaced by what i s c a l l e d the t i d a l d i s p e r s i o n co- e f f i c i e n t (E) . The assumption of s t e a d y - s t a t e a l s o i m p l i e s t h a t any d e r i v a t i v e s w i t h respect to time are zero. This means that c o n c e n t r a t i o n s w i l l be as- signed t h e i r mean t i d a l value and w i l l be seen to vary only w i t h d i s t a n c e 56 along the estuary. The incorporation of the steady-state assumption reduces Equation (3..i) s t i l l in the general case to: where and U is the t i d a l l y averaged velocity (=Q/A); E is the t i d a l l y averaged dispersion coefficient; Q is the fresh water discharge; A is the t i d a l l y averaged cross-sectional area; a l l other parameters and variables are as previously defined. Applying Equation (3.2) to dissolved oxygen in estuaries i s r e l a - tively straight forward i f i t i s assumed that the only source/sink processes are atmospheric reaeration and biochemical oxygen demand, both of which are assumed to be f i r s t order rate processes. The resultant steady-state dis- tribution for dissolved oxygen i s given by: where and c is the dissolved oxygen concentration; c is the saturation concentration of dissolved oxygen; s L i s the BOD concentration remaining at any point x; is the reaeration rate coefficient; is the BOD decay rate coefficient; a l l other parameters and variables are as previously defined. 57 Since the BOD term appears i n Equation ( 3 . 3 ) , i t is necessary to develop an equation for BOD distribution in an estuary before proceeding with the DO solution. Applying the general steady-state mass transport equation to BOD, assuming point source waste addition with f i r s t order BOD removal, results i n : (3.4) where L is the BOD concentration remaining at any point x; K is the BOD removal rate coefficient; r and a l l other parameters are as previously defined. It should be noted that the BOD removal rate (K r) is the total removal coefficient which can account for removal of BOD due to settling, as well as oxidation, i t being assumed that settling i s approximated by f i r s t order kinetics. If BOD removal i s accomplished only by oxidation, then K = K . r 1 We now have equations to describe, under steady-state conditions, the distributions of DO and BOD in an estuary. Since the DO response i s determined i n part by input from the BOD solution, Equations (3.3) and (3.4) are said to be a "coupled" pair of equations and the solution must proceed accordingly. Note that i f E is set equal to zero i n Equations ( 3 V 3 ) and ( 3 . 4 ) , which would be the case for a river or stream, the resultant solu- tion of the coupled BOD/DO equation would, under the similar assumptions, be comparable with that derived by way of the Streeter-Phelps formulation. There are two basic solution techniques for the steady-state coupled BOD/DO system. The f i r s t technique i s an a n a l y t i c a l one which offers continuous solutions to the equations for various e s t u a r i a l and boundary condition configurations. I t can be credited largely to the work of D.J. O'Connor CO'Connor, 1965-] who has provided solutions f o r a number of sp e c i a l cases. The advantage of the continuous solution approach i s that i t i s designed to handle long river/estuary stretches In a simple, straightforward manner. The second approach, developed by Robert Thoman Clhoman, 1965, 1971], uses f i n i t e difference techniques to solve the coupled system of equations. Although t h i s method i s more f l e x i b l e in that i t i s not r e s t r i c t e d by estuary geometry, waste inputs or boundary condition configurations, i t i s often imposing as a solution method be- cause of the large number of l i n e a r equations which must be solved by d i g i t a l computer matrix inversion techniques. The two approaches to solu- t i o n of the steady-state equations w i l l now be discussed. 3.4.1 The Continuous Solution Approach. In order to obtain continuous solutions by a n a l y t i c a l l y solving the BOD/DO equations, i t is f i r s t necessary t o make assumptions regarding estuary areal configuration. O'Connor L~1965]J offers a number of solutions which apply to estuaries with constant as well as variable cross-section providing that the v a r i a t i o n can be expressed i n terms of longitudinal distance by l i n e a r , power or exponen- t i a l expressions. An examination of the cross-sectional geometry of the main stem Fraser (see Figure 4-4 ) revealed that the cross-sectional area increases i n the seaward d i r e c t i o n . From the resu l t s of a l i n e a r regress- ion analysis, run to determine the relationship between area and distance, i t was found that a l i n e a r expression r e l a t i n g cross-sectional area with 59 longitudinal distance gave a good " f i t " yielding values for the coefficient 2 of determination (r ) which varied from 0.62 to 0.69 depending on river stage. Thus O'Connor's analytical solutions for estuaries with cross- sectional area increasing linearly in the seaward direction were appropri- ate and could be applied to the lower Fraser system. To insure that the details of the working solutions offered by O'Connor were correct, the solutions were re-derived, by way of proof, from the basic BOD and DO mass transport equations. This ve r i f i c a t i o n procedure, which w i l l not be presented, proved that the analytical solutions were cor- rect. The solution for BOD distributions upstream and downstream of a single waste discharge at x = X q are given by: for x<x : 1 (x) = o 1 "Wx " X V -o A E X o o t O V (3.5a) for X>X Q: L^(K)= Wx " X v r o A E X o oj I v<qx o)K v(qx) (3.5b) where 2A E o K r N i " L^(x) is the BOD distribution as a function of distance upstream of the outfall location; L^(x) i s the BOD distribution as a function of distance down- stream of the o u t f a l l location; W is the constant rate of waste addition; 60 and A i s the c r o s s - s e c t i o n a l area at the o u t f a l l l o c a t i o n ; o Q i s the freshwater i n f l o w to the e s t u a r y ; E i s the t i d a l d i s p e r s i o n c o e f f i c i e n t ; K r i s the BOD removal r a t e c o e f f i c i e n t ; I and K are modified B e s s e l f u n c t i o n s o f the f i r s t and second v v k i n d of order v; x i s l o n g i t u d i n a l d i s t a n c e along the e s t u a r y . The corresponding DO d e f i c i t d i s t r i b u t i o n j f o r the r e g i o n s up- stream and downstream of a s i n g l e o u t f a l l at x = "x are given by: o f o r x<x : D,(x)= o 1 K 2 r Wx A E . o . oj K v ( x o q ) I v ( x q ) - K v ( x o p ) l v ( x p ) (3.6a) f o r x>x : D_(x) = o 2 K K.-K 2 r Wx A E o X X a T V I v ( V ) K v ( x q ) - I v ( x o p ) I v ( x p ) (3.6b) where K 2 D (x) i s the DO d e f i c i t d i s t r i b u t i o n as a f u n c t i o n o f d i s t a n c e 1 upstream of the o u t f a l l l o c a t i o n ; D (x) i s the DO d e f i c i t d i s t r i b u t i o n as a f u n c t i o n o f d i s t a n c e 2 downstream of the o u t f a l l l o c a t i o n ; 61 K is the reaeration rate coefficient; 2 and a l l other parameters and variables are as previously defined. These solutions for BOD and DO distribution in an estuary may at f i r s t seem somewhat overbearing because they contain a relatively uncommon mathematical expression, the modified Bessel function. However, inspection of the behaviour of modified Bessel functions reveals that they are similar to exponentials, with the modified Bessel functions of the f i r s t kind, I v ( x ) , bx behaving in a manner analagous to ae . Functions of the second kind, K^x), behave similarly to ae b x except in the region of the origin where, as x approaches zero, K v(x) asymptotically approaches i n f i n i t y . Equations(3. 5) and (3.6) give the BOD and DO def i c i t distributions in an estuary due to a single waste source. If more than one source i s present, the distributions due to each may be calculated and, by applying the principle of superposition as is done in rivers, summed to give the total distribution of BOD and DO d e f i c i t . When applying the continuous solutions to an estuary i t i s neces- sary to assume that conditions are constant over the entire estuary. Thus i t i s not possible by this method to account for any variation over the length of the estuary in such things as water temperature or i n the values of parameters describing the dissolved oxygen source/sink and dispersion processes. 3.4.2 The Finite Section Approach. The f i n i t e section approach in essence replaces the derivatives in the mass transport equation with f i n i t e difference approximations. In this method of solution, f i r s t applied by Thomann CThomann 1965, 1971] to the Delaware Estuary, the estuary is 6 2 divided into a number of segments (or boxes) with each segment assumed to be completely mixed. Assuming that the advective and d i s p e r s i v e transport processes and waste discharges to the estuary are steady i n time, a materials balance can be wr i t t e n around each f i n i t e s e c t i o n of the estuary. Writing the mass balance i s equivalent to repla c i n g the d e r i v a t i v e s i n the mass transport equation by t h e i r f i n i t e d i f f e r e n c e approximations. The mass balance over segment i f o r a dissolved substance such as BOD undergoing f i r s t - o r d e r decay gives Drhomann, 19713: Q t a i - l , i C i - l + ( 1 - a i - l , i ) c i l " Q I > i , i + l c i + ( 1 - a i , i + l ) c i + l ] (3.7) + E x - i , i ( c i - r c i ) + E i , i + i < c i + r c i > " K i c i v ± + w i - 0 where c^ i s the concentration i n segment i ; V\ i s the volume of segment i ; Ŵ  i s the mass of waste substance discharged i n t o segment i per t i d a l c y c l e ; i s the decay c o e f f i c i e n t f o r segment i ; Q i s the t i d a l l y averaged discharge through the estuary (the freshwater discharge); a.,.,, i s the t i d a l exchange c o e f f i c i e n t between segments i and l l + l ( i + D ; and i E i s the " e f f e c t i v e d i s p e r s i v e " transport between segments i , i + l i and (i+1). The subscript notation of the various terms i s i l l u s t r a t e d i n Figure 3.1.  64 The f i r s t two terms in Equation (3.7) are the t i d a l l y averaged advective transport into and out of segment i . The factor a i s a weighting factor used to determine the concentration at the interface of two seg- ments from the concentration within each segment. In t i d a l flows a i s set equal to 0.5 to allow for the effects of flow reversal, whereas in a river flow situation a is set equal to 1.0 as the flow i s always downstream. The next two terms of the equation represent the net dispersive transport of i mass into segment i from the neighbouring segments. E is given by: ' . Ei,i+1 Ai,i+1 ( 3 > 8 ) 1,1+1 Li,i+1 where E. .... is the effective coefficient of dispersion over a t i d a l I,x+1 . period at the interface of segments i and (i+1); i s the cross-sectional area (tidally averaged) of the interface between segments i and (i+1); and L i s the average of the lengths of segments i and (i+1). i , i+1 The f i n a l two terms of Equation (3.7) represent the effects of decay and waste discharge. Equations similar to (3.7) can be written for each of n segments of an estuary to give a system of n simultaneous linear difference equations. These equations can be written in the general form as: n r £Z a. , ,c. . + a..c. + a. .,,c.,. = W., i i l l,i+1 l+l ij (3.9) where 65 i a = -a Q - E ; 1-1,1 i - l , i i i 1,1+1 1-1, i * 1-1,1 i , i + l 1 i a J L 1 - (1-a )Q - E i , i + l 1,1+1 H 1,1+1.. Using m a t r i x n o t a t i o n , the system of Equations (3. 9) can be w r i t t e n M ( c ) = (W) ( 3. 1 0) where CAj i s a (nxn) t r i - d i a g o n a l m a t r i x and (c) and (W) are ( n x l ) v e c t o r s . The s o l u t i o n v e c t o r (c) i s then obtained f o r m a l l y by i n v e r s i o n of the A m a t r i x , i . e . (c) = C A ] " 1 (W) (3.11) Thus, the problem of determining the s t e a d y - s t a t e , one-dimensional d i s t r i - b u t i o n of a waste m a t e r i a l (such as BOD) i n an es t u a r y reduces to s o l v i n g n simultaneous a l g e b r a i c equations or i n v e r t i n g an (nxn) t r i - d i a g o n a l m a t r i x . A f i n i t e d i f f e r e n c e approximation or mass balance around f i n i t e s e c t i o n s can a l s o be a p p l i e d to coupled systems. S u f f i c e i t t o say here that- a m a t e r i a l s balance f o r DO can be w r i t t e n i n a manner s i m i l a r to that p r e v i o u s l y described f o r BOD. The r e s u l t a n t system of n simultaneous, l i n e a r equations f o r DO can be expressed i n m a t r i x forms coupled w i t h the BOD system and solved by using m a t r i x i n v e r s i o n techniques to o b t a i n the s t e a d y - s t a t e , one-dimensional d i s t r i b u t i o n of DO i n an estuary L~see Thomann, 1971 f o r d e t a i l s ! ] . The a p p l i c a t i o n of the f i n i t e s e c t i o n approach to e s t u a r i e s has the decided advantage of being more f l e x i b l e than the continuous steady- s t a t e s o l u t i o n i n that i t i s not r e s t r i c t e d by assumptions r e g a r d i n g estuary geometry or other boundary c o n d i t i o n c o n f i g u r a t i o n s . A l s o , t h i s method can e a s i l y be adapted to account f o r changes over the length of the estuary i n such things as water temperature and the r a t e c o e f f i c i e n t s of the d i s s o l v e d oxygen source/sink and d i s p e r s i o n processes. Since the f i n i t e s e c t i o n approach, by i t s main assumption, r e q u i r e s only that con- d i t i o n s be held constant w i t h i n each segment, they may be allowed to vary from segment to segment throughout the estuary. Any number of waste d i s c h a r g e s , each of which i s assumed to be completely mixed i n t o the segment adjacent to i t s l o c a t i o n , can be handled simultaneously as the s o l u t i o n method i s designed so that i t i n t e r i o r l y accommodates the p r i n c i p l e of s u p e r p o s i t i o n . 3.5 TIDALLY VARYING SOLUTIONS T i d a l l y v a r y i n g s o l u t i o n s to the one-dimensional mass t r a n s p o r t equation r e q u i r e , as i n p u t , i n f o r m a t i o n d e s c r i b i n g the s p a t i a l and temporal v a r i a t i o n s of the t i d a l l y v a r y i n g parameters u, A and E. In order to o b t a i n t h i s i n f o r m a t i o n , i t i s f i r s t necessary to "model" the h y d r a u l i c s of Che p a r t i c u l a r estuary. This i s done by a p p l y i n g the a p p r o p r i a t e set of hydrodynamic equations (motion and c o n t i n u i t y ) to the water mass of the estuary and s o l v i n g these equations throughout the t i d a l c y c l e . The r e s u l t a n t p r e d i c t i o n s of the space-time h i s t o r y of t i d a l l y v a r y i n g parameters serve as input to the t i d a l l y v a r y i n g s o l u t i o n s of the one-dimensional mass t r a n s p o r t equation, and as such the hydro- dynamic model i s o f t e n r e f e r r e d to as a "sub-model" i n the t i d a l l y v a ry- i n g scheme of s o l u t i o n . The hydrodynamic sub-model w i l l now be discussed. I t should be noted before proceeding that the i n c l u s i o n , i n t h i s t h e s i s , of the t i d a l l y v a r y i n g approach to modeling was made p o s s i b l e because of an i n v e s t i g a t i o n i n t o estuary modeling on the lower Fraser R i v e r c a r r i e d out by C.S. Joy. His d i s s e r t a t i o n [Joy, 1974] and subsequent p u b l i c a t i o n [Joy, 1975], to which the reader i s r e f e r r e d , provide comprehensive coverage of d e t a i l s i n the development of the hydrodynamic sub-model and the t i d a l l y v a r y i n g s o l u t i o n s to the one-dimensional mass t r a n s p o r t equations. The ensuing d i s c u s s i o n which i s but a b r i e f summary of those d e t a i l s o f the aforementioned r e s e a r c h e f f o r t t h a t are p e r t i n e n t to t h i s d i s s e r t a t i o n has borrowed h e a v i l y from Joy's p u b l i c a t i o n s . 3.5.1 The Hydrodynamic Sub-Model. The b a s i c equations which d e s c r i b e the hydrodynamic behavour of the water mass i n an e s t u a r y , namely the equations of motion and c o n t i n u i t y a r e , as a p p l i e d to the Fraser R i v e r / E s t u a r y , given by [Dronkers, 1969]: Su = d h _ [ u j u bt ^1 8 dx 8 c 2 - •bx - at where u i s the mean l o n g i t u d i n a l v e l o c i t y ; h i s the height of the water surface above an a r b i t r a r y l e v e l datum; y i s the mean c r o s s - s e c t i o n a l water depth; A i s the c r o s s - s e c t i o n a l area; b i s the c r o s s - s e c t i o n a l width; g i s the l o c a l g r a v i t a t i o n a l a c c e l e r a t i o n ; and C i s Chezy's f r i c t i o n f a c t o r . Equations (3.12) and (3.13) are a coupled p a i r of p a r t i a l d i f - f e r e n t i a l equations w i t h dependent v a r i a b l e s u, A and e i t h e r y o r h (see Figure 3.2 f o r i l l u s t r a t i o n of terms), independent v a r i a b l e s x and t , and parameters C, b and g. Note t h a t , as shown i n Figure 3.2, i n the hydro- dynamic equations x i n c r e a s e s i n the upstream d i r e c t i o n whereas i n the mass t r a n s p o r t equations x i n c r e a s e s i n the downstream d i r e c t i o n . The main assumptions made i n d e r i v i n g the hydrodynamic equations were that the t i d a l storage w i d t h of the r i v e r / e s t u a r y i s equal to the a d v e c t i v e width, the Chezy formula adequately represents f r i c t i o n i n the e s t u a r y and that the estuary h y d r a u l i c s could be approximated by one-dimensional equations. These assumptions a r e , by and l a r g e , reasonable f o r the Fraser R i v e r / E s t u a r y except perhaps i n the lower reaches of the r i v e r where the presence of the s a l t water wedge causing a s t r a t i f i e d flow f i e l d may a f f e c t both the f r i c t i o n a l e f f e c t s and the v a l i d i t y of the one- dimensional assumption. , Numerical s o l u t i o n s to the hydrodynamic equations can be ob- t a i n e d by using the f i x e d mesh, e x p l i c i t f i n i t e d i f f e r e n c e method of Dronkers [1969]. By t h i s method, which c o n s i s t s e s s e n t i a l l y of super- imposing a g r i d of " f i x e d " s t a t i o n s along the estuary and r e p l a c i n g the d e r i v a t i v e s i n the hydrodynamic equation w i t h f i n i t e d i f f e r e n c e a p p r o x i - mations, s o l u t i o n s f o r the temporal and s p a t i a l v a r i a t i o n s of the t i d a l l y v a r y i n g parameters u and A may be obtained f o r s e l e c t e d freshwater flows and t i d a l c o n d i t i o n s . In t h i s a n a l y s i s h y d r a u l i c c o n d i t i o n s are assumed 69 Figure 3.2 The Hydrodynamic Estuary to be "quasi-steady" ( i . e . r e p e t i t i v e ) which simply r e q u i r e s that f r e s h - water flows be constant and t i d a l p a t t e r n s be i d e n t i c a l over the p e r i o d of a n a l y s i s . Since residence times i n the lower F r a s e r are never more than four to s i x days, t h i s assumption i s reasonable. The r e l a t i v e s i g n s of g r i d spacing (Ax) and i n t e g r a t i o n timed ( A t ) i n the s o l u t i o n scheme were s e l e c t e d according to requirements of s t a b i l i t y i n the numerical i n t e g r a t i o n . I t was found that a space g r i d at 5,000 f o o t i n t e r v a l s and an i n t e g r a t i o n time of 90 seconds were s a t i s - f a c t o r y . D e t a i l s of the network of s t a t i o n s chosen as a r e s u l t of these c r i t e r i a w i l l be presented i n Chapter 4 along w i t h a d i s c u s s i o n on the a p p l i c a t i o n to the Fraser R i v e r / E s t u a r y of the hydrodynamic sub-model. 3.5.2 The T i d a l l y V a r y i n g Model. Output from the hydrodynamic sub-model y i e l d s i n f o r m a t i o n on the space time h i s t o r y o f the t i d a l l y v a r y i n g parameters u and A. Before a t i d a l l y v a r y i n g s o l u t i o n t o the mass t r a n s p o r t equation can be obtained, e q u i v a l e n t i n f o r m a t i o n must be de r i v e d f o r the c o e f f i c i e n t of l o n g i t u d i n a l d i s p e r s i o n ( E ) . The time dependent behaviour of l o n g i t u d i n a l d i s p e r s i o n , being a complex, p o o r l y understood phenomenon i n f l u e n c e d by such things as l a t e r a l and v e r t i c a l v e l o c i t y g r a d i e n t s , i s d i f f i c u l t to d e s c r i b e . Since the models di s c u s s e d i n t h i s t h e s i s are one-dimensional, that i s , they are not cognizant of any v e r t i c a l and l a t e r a l v a r i a t i o n s , the t i d a l l y v a r y i n g c o e f f i c i e n t of l o n g i t u d i n a l d i s p e r s i o n i s replaced by the t i d a l l y averaged l o n g i t u d i n a l d i s p e r s i o n c o e f f i c i e n t . The t i d a l l y averaged c o e f f i c i e n t i s a p p r o p r i a t e f o r use i n t h i s a p p l i c a t i o n e s p e c i a l l y because i t i s the form b e s t s u i t e d to d e s c r i b i n g d i s p e r s i o n a f t e r c r o s s - s e c t i o n a l mixing i s complete. I t must be s t r e s s e d that t h i s c o e f f i c i e n t i s not the same as the c o e f f i c i e n t of t i d a l d i s p e r s i o n which i s used i n the st e a d y - s t a t e s o l u t i o n s to the one-dimensional mass t r a n s p o r t equations. The d i f f e r e n c e s between these two c o e f f i c i e n t s w i l l be discussed i n Chapter 4. Now that the s p a t i a l and temporal v a r i a t i o n s of a l l the t i d a l l y v a r y i n g parameters can be accounted f o r , the t i d a l l y v a r y i n g mass t r a n s - port equation can be solved. The a p p l i c a b l e s o l u t i o n method employs c h a r a c t e r i s t i c f i n i t e d i f f e r e n c e techniques [see Joy, 1974 f o r d e t a i l s ] . The general one-dimensional equation (Equation 3.1) i s transformed i n t o i t s c h a r a c t e r i s t i c or Lagrangian form,to g i v e : f = u (3.14) and dc dt l a TEA a c 1 . T p - .„ , ^ A ' ~3>2C [ "a^ J + TL \ (3-15) Equation (3.15) i s then separated i n t o i t s component d i s p e r s i v e and source/sink p a r t s to g i v e : dc d £ = f EA , a c l (3.16) t A d x [ d x j and n dc = V S (3.17) d t ~ F i n i t e d i f f e r e n c e approximations are used to r e p l a c e the d e r i v a t i v e s i n Equations (3.14), (3.16) and (3.17) and numerical methods are used to o b t a i n s o l u t i o n s to the t i d a l l y v a r y i n g mass t r a n s p o r t equation throughout the t i d a l c y c l e . By t h i s s o l u t i o n technique, the mass t r a n s p o r t equation i s solved along the c h a r a c t e r i s t i c curves of the adv e c t i v e t r a n s p o r t processes. The main advantage of t h i s method i s that i t proceeds to a s o l u t i o n d i r e c t l y and a c c u r a t e l y , e l i m i n a t i n g such things as numerical d i s p e r s i o n . As w e l l , by t h i s technique each of the processes r e l e v a n t to mass t r a n s p o r t - a d v e c t i o n , d i s p e r s i o n and source/ s i n k - are handled independently. B r i e f l y , the mechanics of the s o l u t i o n are as f o l l o w s . The advective t r a n s p o r t process i s simulated f i r s t by moving a g r i d of " p o i n t s " , each c o n t a i n i n g a c o n c e n t r a t i o n of d i s s o l v e d substance f o r a time increment of one hour according to the v e l o c i t i e s p r e d i c t e d by the hydrodynamic model. The c o n c e n t r a t i o n of each p o i n t i s adjusted as i t passes an e f f l u e n t o u t f a l l . The second step i n the s o l u t i o n i n v o l v e s a c o n c e n t r a t i o n adjustment f o r each p o i n t on the moving g r i d to account f o r d i s p e r s i o n a l e f f e c t s d u r ing the time increment. F i n a l l y , the source/ s i n k e f f e c t s are accounted f o r by yet another readjustment of concentra- t i o n . These three steps are repeated i n sequence f o r the next time i n - crement and so on. The s o l u t i o n thus passes through time, h o u r l y read- j u s t i n g c o n c e n t r a t i o n s on the g r i d of moving p o i n t s . Moving p o i n t s are added to and removed from the model estuary at i t s boundaries as they are needed. At the end of each hour, con c e n t r a t i o n s are e x t r a p o l a t e d o f f the g r i d of moving p o i n t s onto the f i x e d g r i d of s t a t i o n s used i n the hydrodynamic model. In order to use the t i d a l l y v a r y i n g model to p r e d i c t BOD and DO co n c e n t r a t i o n s i n the estuary, i n a d d i t i o n to the t i d e and r i v e r flow i n f o r m a t i o n which i s needed f o r the hydrodynamic sub-model, i n f o r - mation i s r e q u i r e d d e s c r i b i n g the l o c a t i o n and q u a n t i t y of e f f l u e n t d i s - charges as w e l l as the values of the r a t e constants which govern the source/sink r e a c t i o n s and the d i s p e r s i o n process. The e f f l u e n t i n f o r - mation i s fed i n t o the model as quasi-steady hourly discharge r a t e s over a 25 hour t i d a l c y c l e at any of up to 40 d i f f e r e n t l o c a t i o n s on the f i x e d grid.. CHAPTER 4 APPLICATION OF DISSOLVED OXYGEN MODELS TO THE FRASER RIVER/ESTUARY The implementation of d i s s o l v e d oxygen models c o n s i s t s of the f o l l o w i n g s t e p s : making an a b s t r a c t i o n of the p h y s i c a l - h y d r a u l i c system to f i t the b a s i c model f o r m u l a t i o n s ; making assumptions about the v a r i o u s processes i n v o l v e d ; a p p l y i n g a p p r o p r i a t e c o e f f i c i e n t s to each of these processes; e n t e r i n g v a r i o u s waste discharge p a t t e r n s ; and observing the p r e d i c t e d r e s u l t s . The a p p l i c a t i o n of the t i d a l l y averaged and t i d a l l y v a r y i n g d i s s o l v e d oxygen models to the Fraser R i v e r / E s t u a r y w i l l now be considered i n l i g h t o f the b a s i c elements o f model implementation. 4.1 THE MODEL RIVER/ESTUARY The "model r i v e r / e s t u a r y " used i n t h i s study was developed by Joy [1974] i n h i s i n v e s t i g a t i o n s of e s t u a r i n e h y d r a u l i c behaviour. I t covers the lower F r a s e r R i v e r system from the S t r a i t of Georgia to C h i l l i w a c k and i n c l u d e s the three p r i n c i p a l channels - the Main Arm/Main Stem, the North Arm and the P i t t R i v e r system. The schematic layout of the model r i v e r / e s t u a r y i s shown i n Figure 4.1 and, as mentioned i n Sec t i o n 3.5.1, was f i r s t developed by Joy [1974] to be u t i l i z e d w i t h i n the hydrodynamic sub-model of the t i d a l l y v a r y i n g model. This s t a t i o n arrange- ment i s a l s o used f o r the t i d a l l y averaged model. As the model r i v e r / e s t u a r y extends to cover that p o r t i o n of the lower F r a s e r R i v e r i n f l u e n c e d by t i d a l e f f e c t s , the upstream boundary was chosen to be i n the v i c i n i t y of C h i l l i w a c k , the commonly accepted l i m i t of - 74 - Main Arm Figure 4.1 Numbering Scheme and Network of Stations Used in the Model River/Estuary 76 t i d a l influence. Downstream model boundaries are the exits of the River to the Strait of Georgia at Steveston on the Main Arm and Point Grey on the North Arm. Other outlets of the lower Fraser River, the Middle Arm and Canoe Pass, have not been considered in the model. It should be noted, however, that their presence has been accounted for implicitly by areal adjustments of the Main Arm and North Arm exits. The P i t t River system was included within the bounds of the model because of i t s importance as a t i d a l storage area. The numbering scheme and network of stations used i n the model river/estuary are also shown in Figure 4.1. Segment length was a r b i t r a r i l y chosen to be 5,000 feet. The Main Arm/Main Stem extends from Steveston to Chilliwack Mountain (station numbers 1 to 62); the North Arm, from Point Grey to New Westminster (station numbers 101 to 118) where i t joins the Main Stem; and the P i t t River from the Main Stem junction to P i t t Lake (station numbers 140 to 155). In a l l cases only the main core of advective flow of the major channels has been considered. Values of local low water depth, cross-sectional area, and river width for each station were obtained from hydrographic charts supplied by the Department of Public Works [DPW, 1970] . These parameters were ad- justed to compensate for the presence of major side channels as was the case in the Main Arm and North Arm exits of the river and also to f i t the advective flow core. Figures 4.2 and 4.3 show the variation of the gross and advective values of these parameters along each of the three channels considered by the models. Gross Va lues Advec t i ve Va lues 30 Stations Figure 4.2 Variation of Cross-Sectional Parameters in the Main Arm/Main Stem 78 DEPTHS AND AREAS Relative to local low water. _40,000 CM £ 3 0 , 0 0 0 §20 ,000 10,000 0 40 30 20 10 0 3.000 C L a O d Z CO m O o z co l£) d z CO Gross Values Advective Values Norm Arm i Pitt River i i 1 i l I _i I i i l i i i I I i V i 3; d Z CO o o z CO i n m o CO Figure 4.3 Variation of Cross-Sectional Parameters in the North Arm and Pitt River 4.2 IMPLEMENTATION OF THE MODELS In Chapter 3 the general theory, formulations and sol u t i o n of estuary dissolved oxygen models were discussed. The implementation of these models as they apply to the lower Fraser River/Estary i s now con- sidered. 4.2.1 T i d a l l y Averaged Models. Two approaches to t i d a l l y averaged, steady-state modeling were discussed i n Section 3.4: the con- tinuous solution approach and the f i n i t e section approach. Of these, only the l a t t e r could be applied to the f u l l extent of the lower Fraser River. The implementation of the continuous a n a l y t i c a l solutions which offered advantages over the f i n i t e section approach both i n terms of ease of development and the straightforward manner of solution was found to be impossible. The a n a l y t i c a l solutions for estuarine BOD and DO d i s t r i - butions contained modified Bessel functions (see Section 3.4.1). When the application of these solutions to a steady-state Fraser River d i s - solved oxygen model was f i r s t considered, i t was known that solutions of these functions were readily available i n the form of package programs i n the Computing Centre General Library [UBC Function, 1973]. The develop- ment of the model was i n i t i a t e d and i t was not u n t i l the programming was completed that problems were encountered. Because of the r e l a t i v e l y small changes i n cross-sectional area with distance i n the Fraser system, the arguments of the modified Bessel functions u t i l i z e d i n the sol u t i o n proved to be much larger over most of the model extent than the l i m i t s allowed by the Bessel function package programs. As such, the values of the modified Bessel functions were indeterminate. 80 Although i t should be p o s s i b l e to reprogram the m o d i f i e d B e s s e l f u n c t i o n s o l u t i o n s to extend the l i m i t s of the arguments, t h i s was w e l l beyond the author's c a p a b i l i t i e s . Thus the continuous s o l u t i o n approach to the s t e a d y - s t a t e d i s s o l v e d oxygen model was abandoned i n favour of the f i n i t e s e c t i o n t i d a l l y averaged model. The f i n i t e s e c t i o n s o l u t i o n approach t o modeling e s t u a r i n e mass t r a n s p o r t (see S e c t i o n 3.4.2) was s u c c e s s f u l l y a p p l i e d to the lower F r a s e r system u s i n g the segmented r e p r e s e n t a t i o n of the r i v e r / e s t u a r y shown i n Figure 4.1. This s t a t i o n arrangement r e s u l t e d i n a t o t a l of 92 segments i n the three branches of the r i v e r / e s t u a r y which r e q u i r e d the s o l u t i o n of a system of 93 simultaneous l i n e a r equations. The s o l u t i o n f o r s o l v i n g t h i s l a r g e system of equations w h i c h - i n v o l v e d m a t r i x i n v e r s i o n procedures was complicated by the branched c o n f i g u r a t i o n of the r i v e r / e s t u a r y . The u s u a l s o l u t i o n technique suggested by Thomann [1971] had to be m o d i f i e d s l i g h t l y to a l l o w f o r the c o u p l i n g of the North Arm and P i t t R i v e r to the Main Stem. A procedure was developed which allowed f o r m a t r i x s o l u t i o n to the three component system of equations without having to r e s o r t to techniques i n v o l v - i n g s o l u t i o n of i n d i v i d u a l m a t r i c e s . I t was achieved by u s i n g a s i n g l e m a t r i x w i t h a d d i t i o n a l terms pla c e d i n a p p r o p r i a t e l o c a t i o n s to account f o r mass t r a n s p o r t through the j u n c t i o n s t a t i o n s . The m a t r i x A of Equation 3.11 as a p p l i e d to the lower F r a s e r system, shown i n F i g u r e 4.4, i n e f f e c t i s p a r t i t i o n e d i n t o three separate b l o c k s each of which represents a s i n g l e channel. The b l o c k s are uncoupled except at the j u n c t i o n s t a t i o n s where c o u p l i n g i s accomplished through the use of an a d d i t i o n a l term which d i f f e r s from the main elements of the m a t r i x i n that i t i s not t r i - d i a g o n a l . 81 Figure 4.4 The M a t r i x D O of the T i d a l l y Averaged Model 82 The t i d a l l y averaged model was programmed to FORTRAN, making use of package program m a t r i x i n v e r s i o n r o u t i n e s [UBC M a t r i x , 1973] f o r s o l u t i o n by d i g i t a l computer. 4.2.2 The T i d a l l y Varying Model. Joy [1974 and 1975] , through use of a hydrodynamic sub-model, d e r i v e d t i d a l l y v a r y i n g s o l u t i o n s to the mass t r a n s p o r t equations which he a p p l i e d to the lower F r a s e r R i v e r / Estuary to form the b a s i c t i d a l l y v a r y i n g model (see S e c t i o n 3.5). As Joy's i n v e s t i g a t i o n d e a l t w i t h c o n d i t i o n s i n the e s t u a r y caused by the discharge of co n s e r v a t i v e substances, a l l t h a t remained was t o implement the coupled BOD-DO system to the t i d a l l y v a r y i n g model and apply the model to the purpose of t h i s r e s e a r c h , namely, the p r e d i c t i o n of d i s s o l v e d oxygen l e v e l s . The f o l l o w i n g i s a b r i e f summary of the implementation of the t i d a l l y v a r y i n g mass t r a n s p o r t model and i t s a p p l i c a t i o n to d i s s o l v e d oxygen modeling. The hydrodynamic sub-model, the ope r a t i o n of which i s p r e l i m i n a r y to the mass t r a n s p o r t model, y i e l d s output i n the form of h a l f - h o u r l y p r e d i c t e d values of v e l o c i t y and c r o s s - s e c t i o n a l area over a t i d a l c y c l e f o r any of the s t a t i o n s i n the model estuary (see Figure 4.1) g i v e n the f r e s h - water discharge c o n d i t i o n s at C h i l l i w a c k and t i d a l v a r i a t i o n a t Steveston. In a p p l y i n g the hydrodynamic model, a design t i d a l c y c l e s p e c i f y i n g the s e l e c t e d freshwater discharge at C h i l l i w a c k and t i d a l c o n d i t i o n s at Steveston i s chosen along w i t h assumed i n i t i a l v a l u e s of v e l o c i t y and water sur f a c e e l e v a t i o n s . Running the model f o r s e v e r a l t i d a l c y c l e s r e s u l t s i n convergence of these i n i t i a l v a l u e s of v e l o c i t y and water s u r f a c e e l e v a t i o n to the " t r u e " values f o r the given c o n d i t i o n s . During the s o l u t i o n , i t i s 83 assumed that the r i v e r discharge and t i d a l c o n d i t i o n s are quasi-steady over the p e r i o d of a n a l y s i s . The hydrodynamic model has been c a l i b r a t e d under b o t h high t i d e - l o w flow and high t i d e - h i g h flow c o n d i t i o n s and found to adequately reproduce water surface e l e v a t i o n s [Joy, 1974], An accurate v e r i f i c a t i o n of p r e d i c t e d v e l o c i t i e s has not been p o s s i b l e because of the l a c k of the necessary f i e l d measurements. However, based on personal observations and i s o l a t e d f i e l d measurements, the p r e d i c t e d v e l o c i t i e s appear to be reasonable. I t should be noted that the hydrodynamic sub-model, w h i c h does n o t account f o r the presence of the s a l t wedge, may underestimate v e l o c i t i e s d u r i ng c e r t a i n t i d a l c o n d i t i o n s . T h i s was p o i n t e d out i n more recent research i n t o h y d r a u l i c modeling of the F r a s e r R i v e r / E s t u a r y [Hodgins, 1975]. S e l e c t e d output from the hydrodynamic sub-model i n the form of ho u r l y v a l u e s o f v e l o c i t y and c r o s s - s e c t i o n a l areas along w i t h independent estimates of d i s p e r s i o n i s used as inp u t to the t i d a l l y v a r y i n g mass tr a n s p o r t model. The model advects water p a r c e l s along the es t u a r y r e - a d j u s t i n g h o u r l y Che coi ' i Genu* r a t i o n s o f ally d i s s o l v e d Substance, i n t h i s case BOD, to account f o r the e f f e c t s of waste a d d i t i o n and d i s p e r s i o n . In order to use the t i d a l l y v a r y i n g mass t r a n s p o r t model t o p r e d i c t d i s s o l v e d oxygen c o n c e n t r a t i o n s , a n a l y t i c a l s o l u t i o n s to the b a s i c S t r e e t e r - P h e l p s equation (see S e c t i o n 2.7) are i n c o r p o r a t e d i n the s o l u t i o n scheme to r e a d j u s t d i s s o l v e d oxygen con c e n t r a t i o n s h o u r l y a c c o r d i n g to the BOD c o n c e n t r a t i o n and the values of the deoxygenation and r e a e r a t i o n r a t e c o e f f i c i e n t s . The r e s u l t a n t model output gives a t i m e - h i s t o r y of d i s s o l v e d 84 oxygen c o n c e n t r a t i o n throughout the e s t u a r y . The hydrodynamic sub-model and the t i d a l l y v a r y i n g mass t r a n s p o r t model are programmed i n h i g h speed FORTRAN f o r s o l u t i o n by d i g i t a l computer. 4.3 MODEL ASSUMPTIONS Although the model assumptions were discussed i n the chapter on d i s s o l v e d oxygen model development, they w i l l be b r i e f l y reviewed here i n a comparative context. 4.3.1 General Assumptions. The b a s i c and, perhaps, most r e s t r i c t i v e assumption which a p p l i e s to both the t i d a l l y averaged and t i d a l l y v a r y i n g models i s that of approximating the mass t r a n s p o r t (and hydrodynamic) process by one dimensional equations. The one dimensional space assumption r e q u i r e s t h a t a l l v a r i a b l e s and parameters be assigned t h e i r c r o s s - s e c t i o n a l l y averaged v a l u e s . Thus the models are not able to "see" v a r i a t i o n s over the width or depth of the r i v e r ; changes are "seen" only i n the l o n g i t u d i n a l d i r e c t i o n . By t h i s assumption the s a l t w a t e r wedge e f f e c t s are i g n o r e d . As w e l l , t h i s assumption r e q u i r e s waste inputs to the models to be t r e a t e d as being "completely mixed", e i t h e r over the c r o s s - s e c t i o n o r , as Is the case i n the f i n i t e s e c t i o n s t e a d y - s t a t e model, w i t h i n a segment. In terms of time, the models view c o n d i t i o n s d i f f e r e n t l y . The t i d a l l y averaged models, w i t h the assumption of " s t e a d y - s t a t e " c o n d i t i o n s which i n essence e l i m i n a t e s the time v a r i a b l e , are a temporal a b s t r a c t i o n of the p h y s i c a l system. As a l l parameters are assigned t h e i r average t i d a l v a l u e s , the models do not "see" " r e a l time" e f f e c t s such as c u r r e n t r e v e r s a l which occur w i t h i n the t i d a l c y c l e . The t i d a l averaging process may be thought of as a r e p r e s e n t a t i o n of the response of the estuary over a 85 number of t i d a l c y c l e s and, as such, models based on t h i s approach are o f t e n r e f e r r e d to as " i n t e r - t i d a l " . The complex, o s c i l l a t o r y f l o w f i e l d i n the estuary i s replaced by a freshwater flow f i e l d and a t i d a l d i s p e r s i o n term which accounts f o r current r e v e r s a l as w e l l as t i d a l m i x i n g . Thus, the r e a l time e f f e c t s caused by t i d a l a c t i o n , although not "seen" by the t i d a l l y averaged models, are taken i n t o c o n s i d e r a t i o n i m p l i c i t l y and the output from the models, which i s i n the form of t i d a l l y averaged con- c e n t r a t i o n s , may be thought of as i n t e g r a t i n g over a t i d a l c y c l e the r e a l response of the e s t u a r y . The t i d a l l y v a r y i n g model does not s u f f e r from l a c k of temporal r e s o l u t i o n . As r e a l time e f f e c t s caused by t i d a l a c t i o n are accounted f o r i n the hydrodynamic sub-model, t h i s model attempts to more a c c u r a t e l y represent the true nature of response i n the e s t u a r y . By approximating c o n d i t i o n s h o u r l y , the t i d a l l y v a r y i n g model can "see" changes t h a t occur w i t h i n the t i d a l c y c l e and as such i s o f t e n r e f e r r e d to as a " r e a l time" or " i n t r a - t i d a l " model. Because of the aforementioned d i f f e r e n c e s i n temporal r e s o l u t i o n , waste discharge i n f o r m a t i o n i s handled d i f f e r e n t l y i n each of the models. In the t i d a l l y averaged models, e f f l u e n t discharges are f e d i n as average d a i l y l o a d i n g s . In the t i d a l l y v a r y i n g models, however, i n o r d e r to keep a l l process i n f o r m a t i o n compatible, waste discharge i n f o r m a t i o n i s fed i n as h o u r l y l o a d i n g s . As a r e s u l t , i t i s p o s s i b l e to vary discharge r a t e s w i t h i n the t i d a l c y c l e , thus making p r a c t i c a b l e the i n v e s t i g a t i o n of short term l o a d i n g s such as s l u g loads from storm water overflow o r a c c i d e n t a l s p i l l s . 86 4.3.2 D i s s o l v e d Oxygen Assumptions. In the a p p l i c a t i o n of d i s s o l v e d oxygen models to the lower F r a s e r R i v e r i t has been assumed that only two f a c t o r s a f f e c t the oxygen balance: b i o c h e m i c a l o x i d a t i o n of o r g a n i c matter and atmospheric r e a e r a t i o n . Other oxygen s o u r c e / s i n k processes are assumed to be e i t h e r i n o p e r a t i v e o r , i f p r e s e n t , of l i t t l e s i g n i f i c a n c e compared to the main processes, and as such have not been co n s i d e r e d i n the models. P h o t o s y n t h e t i c oxygen pr o d u c t i o n has not been c o n s i d e r e d t o be important because of the h i g h n a t u r a l t u r b i d i t y of F r a s e r R i v e r water which b l o c k s the p e n e t r a t i o n of l i g h t . The e f f e c t s of oxygen p r o d u c t i o n by a q u a t i c p l a n t s and weeds have been ignored because of the n o t i c e a b l e absence of a q u a t i c p l a n t growth on the r i v e r b a n k s . As f o r s i n k processes, b e n t h i c oxygen demands have been assumed to be i n s i g n i f i c a n t because the h i g h t i d a l v e l o c i t i e s i n the lower Fraser, g e n e r a l l y p r o h i b i t s e t t l i n g of suspended m a t e r i a l . This assumption a l s o r e s u l t s i n the e x c l u s i o n of s e t t l i n g e f f e c t s as a s i n k of BOD. N i t r i f i c a t i o n i s another oxygen s i n k process which has not been i n c l u d e d i n the d i s s o l v e d oxygen models. T h i s process i s u s u a l l y a s s o c i a t e d only w i t h h i g h water temperatures and, as noted i n S e c t i o n 2.4.2, the e f f e c t s of n i t r i f i c a t i o n are c o n s i d e r e d t o be i n s i g n i f i c a n t at water temperatures below 12 ± 4°C. A l s o , u n l e s s wastes are h i g h l y t r e a t e d , there g e n e r a l l y i s a l a g of 5 - 10 days b e f o r e i t s e f f e c t s become p r e v a l e n t . As water temperatures i n the F r a s e r are low (see F i g u r e s 1.6 and 1.7) except during the summer months when residence time i n the estuary i s g e n e r a l l y l e s s than 2 days and because wastewaters r e c e i v e the e q u i v a l e n t of or l e s s than primary treatment, i t i s reasonable 8 7 to assume that n i t r i f i c a t i o n effects can be ignored. Atmospheric reaeration was assumed to be the only oxygen source process, that i s , wind and surface wave effects, etc. were ignored. 4.4 MODEL COEFFICIENTS 4.4.1 Dissolved Oxygen Model Rate Coefficients. The selection and evaluation of model rate coefficients is the most crucial step in model application. As the coefficients to a large extent control model output response, their s u i t a b i l i t y ultimately determines the a b i l i t y of the models to represent the physical system. Traditionally, the appropriate dissolved oxygen model coefficients for deoxygenation and reaeration are selected by a calibration procedure during which model response i s "tuned" to f i t the system response by adjustment of the coefficients. Usually the reaeration rate coefficients are calculated from prediction equations based on hydraulic considerations and then, with a l l inputs to the models equivalent to their counterparts in the physical system, the BOD decay rates are obtained during the model calibration, a procedure known as "verification". Model verification requires, f i r s t l y , that there be a measurable dissolved oxygen response in the physical system and, secondly, that sufficient data be available to f u l l y document this response. In the application of dissolved oxygen models to the lower Fraser River/Estuary, the calibration and verification procedures are extremely d i f f i c u l t . At present, Fraser River, dissolved oxygen levels are generally at or near saturation, which means that there i s l i t t l e or no observable response 88 i n the oxygen dynamics of the system to present waste discharge p a t t e r n s . In a d d i t i o n , during those i s o l a t e d i n s t a n c e s when s u b s t a n t i a l oxygen d e p l e t i o n s have been measured, as was the case i n June and J u l y , 1970 [ F i s h e r i e s S e r v i c e , unpublished d a t a , 1970], the a v a i l a b l e documentation of the estuary d i s s o l v e d oxygen response i s of i n s u f f i c i e n t s p a t i a l and temporal r e s o l u t i o n to be of use i n model c a l i b r a t i o n . As a r e s u l t , i t i s not p r a c t i c a b l e to o b t a i n the model c o e f f i c i e n t s by v e r i f i c a t i o n of Fraser R i v e r d i s s o l v e d oxygen models. Consequently, the e v a l u a t i o n of model c o e f f i c i e n t s was c a r r i e d out s o l e l y by e s t i m a t i o n . In t h i s study, the r e a e r a t i o n r a t e c o e f f i c i e n t s are based on the p r e d i c t i v e equation (Equation 2.11) of Dobbin and O'Connor [1956] using a temperature c o r r e c t i o n f a c t o r (0) of 1.024. The a p p r o p r i a t e form of v e l o c i t y to be used i n a p p l y i n g t h i s formula to e s t u a r i e s i s , a c c o r d i n g to Thomann [1971], the mean t i d a l v e l o c i t y which i n the lower F r a s e r R i v e r ranges from 0.4 to 8.0 feet per second. Assuming an average depth of 25 f e e t , the r e a e r a t i o n c o e f f i c i e n t (K 2) i s found to vary from 0.07 to 0.30 per day. In attempts to evaluate the r a t e c o e f f i c i e n t s of BOD decay a p p r o p r i a t e f o r the lower F r a s e r , l a b o r a t o r y i n v e s t i g a t i o n s of BOD response were conducted. These s t u d i e s which were c a r r i e d out i n c o n j u n c t i o n w i t h the Westwater Research Centre as par t of an i n v e s t i g a t i o n designed to evaluate r a t e c o e f f i c i e n t s and determine temperature and s a l i n i t y e f f e c t s on bac- t e r i a l d i e - o f f , as w e l l as BOD decay i n Fra s e r R i v e r water, y i e l d e d i n - c o n c l u s i v e r e s u l t s [Westwater Research Centre, unpublished d a t a ] . Consequently, 89 the rates chosen for use i n this research had to be taken from the l i t e r a t u r e which described other investigations of dissolved oxygen dynamics. The range of BOD decay c o e f f i c i e n t s (K^) used i n the models and considered to be appropriate for r i v e r s with low p o l l u t i o n such as the Fraser i s 0.09 to 0.20 per day. A temperature correction factor (0) of 1.135 was used. 4.4.2 Dispersion Coefficients . Because the view taken of estuarine dispersion processes i s d i f f e r e n t i n each of the models, a b r i e f discussion of dispersion c o e f f i c i e n t s i s deemed necessary i n order to resolve possible confusion which might exist over the use of the terms. In the t i d a l l y averaged models the t i d a l dispersion c o e f f i c i e n t , by design, accounts for a l l t i d a l effects including upstream water movement and t i d a l mixing. Thus, i t bears l i t t l e resemblance to the term used to describe longitudinal dispersion i n the t i d a l l y varying model as t h i s c o e f f i c i e n t i s based on theories which describe " r e a l " dispersion phenomena, the processes by which concentration peaks are eroded and mass i s redistributed i n an estuary due to the effects of turbulent d i f f u s i o n and v e r t i c a l and l a t e r a l v e l o c i t y gradients. Since t h e ' t i d a l dispersion c o e f f i c i e n t is- an abstraction of true estuarine mixing phenomena, i t has no r e a l t h e o r e t i c a l basis and, although several semi-theoretical formulations have been postulated, t h e i r use i s questionable [Thomann, 1971]. As a r e s u l t , t i d a l mixing c o e f f i c i e n t s are usually evaluated empirically through use of some observable tracer In the estuary such as s a l i n i t y or chloride concentration. Values of the t i d a l dispersion c o e f f i c i e n t l i s t e d by Thomann [1971] for various estuaries range from 1 to 20 square miles per day with a mean value of about 10 square miles per day. In the lower Fraser River/Estuary i t i s impracticable to establish 90 empirical values of the t i d a l dispersion c o e f f i c i e n t because of the unsteady s t r a t i f i e d nature of s a l i n i t y i n t r u s i o n (see Section 1.4.2) and since i t i s not possible through use of presently available data to define a r e l i a b l e steady-state s a l i n i t y d i s t r i b u t i o n . Therefore assumed values of t h i s c o e f f i c i e n t must be used. I t should be noted, however, that as the lower Fraser River/Estuary i s "freshwater dominated", as w i l l become evident i n subsequent discussion, the t i d a l l y averaged model response i s r e l a t i v e l y i n s e n s i t i v e to assumptions regarding the values of t i d a l dispersion c o e f f i c i e n t . In the t i d a l l y varying model, the c o e f f i c i e n t of l o n g i t u d i n a l dispersion has been assumed to be zero, that i s , a l l dispersive effects have been ignored. The reasons for doing t h i s are twofold. F i r s t l y , i t has been established from the results of the recent dye tracer study that due to the i n h i b i t o r y e f f e c t of s t r a t i f i e d flow conditions, l o n g i t u d i n a l d i s - persion c o e f f i c i e n t s i n the lower Fraser River/Estuary are low [P. Ward, unpublished data]. Thus, ignoring the effects of l o n g i t u d i n a l dispersion should not severely r e s t r i c t the a p p l i c a b i l i t y of predicted concentration to approximate Fraser River/Estuary conditions. Secondly, as t h i s assumption eliminates the dispersive e f f e c t s of erosion and r e d i s t r i b u t i o n of con- centration peaks, i t w i l l result i n an exaggeration of concentration peaks, giving a clearer picture of i n t r a - t i d a l response i n the river/estuary. 4.5 WASTE LOADINGS 4.5.1 Present Waste Loads. Estimates of present waste loadings entering the lower Fraser River/Estuary are shown i n Table 4.1 for the Main Arm/Main Stem and Table 4.2 for the North Arm. Average loading rates expressed i n terms of pounds of BOD per day are tabulated according to location within the model river/estuary as specified by model segment numbe These waste loading estimates are based on effluent discharge permit i n - formation supplied by the lower mainland d i s t r i c t o f f i c e of the P o l l u t i o n Control Branch, New Westminster [PCB, unpublished data, 1973]. The present BOD loading to the lower Fraser t o t a l s some 250,000 pounds of BOD per day, of which approximately two-thirds i s contributed by municipal sources and the remaining one-third by i n d u s t r i a l sources. 4.5.2 Possible Future Waste Loads. An i n v e s t i g a t i o n of the possible impact of future waste discharge patterns on the dissolved oxygen dynamics of the lower Fraser River/Estuary requires assumptions of possible future waste loads. Instead of attempting to forecast the magnitudes and locations of future waste loads, hypothetical waste loads w i l l be used i n t h i s study. These loadings w i l l be arranged i n a manner that, rather than typifying- what might be expected as a future condition,, w i l l show what can be considered a severe future impact. B a s i c a l l y t h i s involves locating the waste o u t f a l l s at positions i n the river/estuary where the discharges w i l l have an exaggerated e f f e c t . 4.6 MODEL OUTPUT Since present organic discharges are absorbed by the lower Fraser without causing s i g n i f i c a n t depletion of dissolved oxygen, i t i s not TABLE 4.1 WASTE LOADINGS TO THE MAIN ARM/MAIN STEM, LOWER FRASER RIVER PRESENT BOD LOADING MODEL SEGMENT (LBS/DAY) 1 720 2 1,730 3 52,470 4 1,760 6 50 7 3,490 11 5,040 14 13,780 15 3,300 16 810 17 7,350 18 990 20 37,420 21 5,470 23 2,550 24 2,520 25 50 29 600 30 20 31 1,800 32 3,690 37 2,410 46 380 47 1,500 51 8,780 TABLE 4.2 WASTE LOADINGS TO THE NORTH ARM, LOWER FRASER RIVER PRESENT BOD LOADING MODEL SEGMENT (LBS/DAY) 106 10,250 107 1,040 108 4,450 109 3,120 110 11,690 111 120 112 4,950 114 1,000 115 10 116 4,850 p o s s i b l e at t h i s time to v a l i d a t e d i s s o l v e d oxygen model output. The l a c k of observable system response to which model response c o u l d be compared by way of v e r i f i c a t i o n p r o h i b i t s accurate c a l i b r a t i o n of the d i s s o l v e d oxygen models. As such, the r e s u l t s from the models, presented and d i s c u s s e d i n Chapter 5 , should be viewed w i t h c a u t i o n s i n c e u n v e r i f i e d model output i s at best considered to be o n l y a s e r i e s of s c e n a r i o s r e p r e s e n t i n g s e t s of p o s s i b l e outcomes, CHAPTER 5 DISSOLVED OXYGEN MODEL RESULTS Since the t r a d i t i o n a l model c a l i b r a t i o n procedures are not ap- l i c a b l e to the lower Fraser R i v e r / E s t u a r y d i s s o l v e d oxygen models, v e r i - f i c a t i o n of the models i s not p r e s e n t l y p o s s i b l e . I t f o l l o w s t h e r e f o r e , that model p r e d i c t i o n s cannot be viewed w i t h complete co n f i d e n c e . In order to a l l e v i a t e those doubts a s s o c i a t e d w i t h the mechanics of the model, a s e n s i t i v i t y a n a l y s i s can be c a r r i e d out t o document model response over the expected range of input parameter v a r i a t i o n f o r the f u l l range of conceivable model c o e f f i c i e n t s . I f , by t h i s a n a l y s i s , model response i s found to be reasonable, the mechanics of the models can be accepted as being v a l i d and the remaining doubts as to the accuracy and v a l i d i t y of model p r e d i c t i o n s l i e i n choosing the c o r r e c t v a l u e f o r each model c o e f f i c i e n t . The s e n s i t i v i t y a n a l y s i s , as w e l l as being a "check" of model v a l i d i t y , i s a l s o u s e f u l i n that i t b r i n g s to l i g h t some of the d e t a i l s p e c u l i a r to the nature of lower Fraser d i s s o l v e d oxygen dynamics. Thus i t i s more than j u s t a necessary p r e l i m i n a r y to the ensuing d i s c u s - - s i o n on d i s s o l v e d oxygen model p r e d i c t i o n s , because as w e l l as determining i f the models are " w e l l behaved", i t a l s o a f f o r d s us w i t h a focus upon which to base i n i t i a l d i s c u s s i o n s on the a s s i m i l a t i v e c a p a c i t y of the lower Fraser R i v e r / E s t u a r y . 5.1 TIDALLY AVERAGED DISSOLVED OXYGEN MODEL RESPONSE .. A study of model response c h a r a c t e r i s t i c s through i n v e s t i g a t i o n of the s e n s i t i v i t y of model output to v a r i a t i o n s i n input parameters and - 95 - 96 model coefficients i s best carried out by holding a l l parameters and co- efficients constant except for the particular element of concern, which is allowed to vary within the expected range of values. Repeating this pro- cedure for each parameter and coefficient in turn, enables one to obtain a complete documentation of model response for the f u l l range of a n t i c i - pated input values. In analyzing the behaviour of the t i d a l l y averaged dissolved oxygen model, the effects of variation in six parameters were considered - freshwater flow, waste loading, dispersion, reaeration rate, deoxygenation rate and temperature. The values used in the analysis are specified in Table 5.1. TABLE 5.1 PARAMETERS AND COEFFICIENTS USED IN SENSITIVITY ANALYSIS Parameter Constant Value Range of Values Freshwater flow (Q) 40,000 cfs 10,000 to 60,000 Waste loading (W) 1,000,000 lb 100,000 to 1,000,000 Dispersion Coefficient (E) . 10 sq. miles/day 0 to 30 u c o A y g c u d t i u u L u c n i C i e u t u.z/aay u.x to 0.6 Reaeration Coefficient (K 2) 0.2/day 0.0 to 0.4 Temperature (T) 10.0°C 5.0 to 20.0 The response of the model over the Main Stem reach of the river with waste discharge location at Station 40 in the upstream portion of the model w i l l be used throughout the analysis. 5.1.1 Effect of Freshwater Inflow Variation. The model response to flow variation is shown in Figure 5.1. The effect of increases in freshwater flow in the river/estuary can be seen to result in reduced BOD concentration and increased DO concentration as would be expected due to K, = K2= 0.2/day at 20° C E = 10 mi2/day T= I0°C Q is variable W= 1,000,000 lb/day ' Riv Q O CD e to c o c <u o c o O •o O a 11.0 10.OH 9.0 E f f 8.0 " , , 20 30 River/ Estuary Section F i g u r e 5 .1 e c t o f F r e s h w a t e r I n f l o w dn M o d e l R e s p o n s e 98 the i n c r e a s e d d i l u t i o n a f f o r d e d by the higher f l o w s . An e f f e c t of p a r t i c u - l a r I n t e r e s t i s observed f o r the lowest r i v e r f l o w (Q = 10,000 c f s ) . The DO d i s t r i b u t i o n i n t h i s case, i n c o n t r a s t to the o t h e r s , i s seen to reach a c l e a r l y defined minimum i n the v i c i n i t y of s t a t i o n 25 a f t e r which i t begins to i n c r e a s e i n the seaward d i r e c t i o n - the c h a r a c t e r i s t i c s of a t y p i c a l oxygeh-sag curve. As t h i s e f f e c t i s not observed f o r the higher r i v e r f lows i t i s evident that according to model response, i t i s only during extremely low flows which r e s u l t i n increased f l u s h i n g times and high BOD c o n c e n t r a t i o n s that the c o n d i t i o n of maximum DO d e f i c i t i s reached w i t h i n the channelized s t r e t c h of the r i v e r / e s t u a r y . At the higher r i v e r flows the b u l k of the oxygen demand i s presumably f l u s h e d out i n t o the S t r a i t of Georgia. A l s o evident f o r decreasing r i v e r flows i s the i n c r e a s i n g dominance of t i d a l i n f l u e n c e as evidenced by the i n c r e a s e d upstream e f f e c t s f o r both BOD and DO. I t i s noted that i f the freshwater i n f l o w to the estuary were zero, the steady s t a t e BOD and DO d e f i c i t c o n c e n t r a t i o n s would be d i s t r i b u t e d normally about the o u t f a l l l o c a t i o n . The i n f l u e n c e of freshwater i n f l o w i s seen to skew the r e s p e c t i v e d i s t r i b u t i o n s i n the down- stream d i r e c t i o n w i t h only the maximum BOD c o n c e n t r a t i o n s t i l l o c c u r r i n g at the o u t f a l l l o c a t i o n as the p o i n t of maximum DO d e f i c i t i s s h i f t e d down- stream. I t can be seen i n Figure 5.1 that the BOD d i s t r i b u t i o n i s skewed s i g n i f i c a n t l y and t h a t the p o i n t of maximum DO d e f i c i t f o r any except very low r i v e r flow i s d i s p l a c e d out of the model! r i v e r / e s t u a r y , thus i n d i c a t i n g the predominating i n f l u e n c e of freshwater i n f l o w . Note that the minimum low f l o w f o r the F r a s e r R i v e r at C h i l l i w a c k i s estimated to be 18,000 c f s CWestwater Research Centre, unpublished d a t a ] . 99 5.1.2 Effect of Waste Loading Variation. The model response to various waste loadings i s shown i n Figure 5.2. Increases i n BOD and DO d e f i c i t concentrations are found to be related l i n e a r l y to increases i n waste loading rates indicating that the p r i n c i p l e of superposition i s ad- hered to by the t i d a l l y averaged model. A s l i g h t increase i n BOD concentra- t i o n and a corresponding decrease i n DO concentration i s also observed up- stream of the waste discharge location with t h i s e f f e c t , due to t i d a l d i s - persion, again being found to be related l i n e a r l y to increases i n waste loadings. 5.1.3 Effect of Dispersion Coefficient V a r i a t i o n . In the t i d a l l y averaged model a l l t i d a l effects are accounted for by the t i d a l dispersion c o e f f i c i e n t . I t accounts for current reversal and the e f f e c t s of upstream water movement as we l l as t i d a l mixing. The effect on model response f o r a range of values of t h i s c o e f f i c i e n t i s shown i n Figure 5.3. Included i s the case of zero dispersion which converts the estuary model into a model ap- p l i c a b l e to r i v e r s . Note that i n t h i s case the t i d a l exchange c o e f f i c i e n t (a) must be set equal to 1.0. I t i s evident that v a r i a t i o n of t h i s coef- f i c i e n t has a rather l i m i t e d effect on both BOD and DO d i s t r i b u t i o n s . This i s again evidence of the predominance of freshwater inflow and i t s e f f e c t s i n the lower Fraser River/Estuary. The effects of varying t h i s model co- e f f i c i e n t , although minor, are observable. In the case of zero dispersion, no effects upstream of the o u t f a l l are evident i n d i c a t i n g that flow Is con- t i n u a l l y i n the downstream d i r e c t i o n . As the magnitude of the dispersion c o e f f i c i e n t i s increased, upstream effects become evident and are of i n - creasing significance i n terms both of magnitude of BOD and DO d e f i c i t concentrations and extent of t h e i r upstream influence as the c o e f f i c i e n t  K,= K2= 0.2/day at 20° C T= I0°C Q= 40,000 cfs E is variable W = 1,000,000 lb/day I 5.0-i 4 .0 3.0 1 - " 2.0 I.OH River E= 30 square miles/day ft* — E= 20 square miles/day Jh' ——E= 10 square miles/day jl\ • — - E = 0 square miles/day ;U • 0 11.4 11.2- 11.0 - 10.8 I0.6H 10' 20 l!o~ 40 50 Saturation Concentration 10 50 ~60~ GO 20 30 40 River/Estuary Section Figure 5.3 Effect of Dispersion on Model Response 102 approximates the effects of water movement i n the river/estuary. In contrast to t h i s , downstream of the o u t f a l l increases i n the t i d a l dispersion coef- f i c i e n t have the opposite e f f e c t , that i s , BOD concentrations are reduced as far upstream as the o u t f a l l and DO d e f i c i t concentrations are reduced i n the downstream reaches. In th i s region the t i d a l dispersion c o e f f i c i e n t operates In the manner of the "true" dispersion c o e f f i c i e n t as i t seeks to r e d i s - t r i b u t e mass by minimizing concentration gradients. 5.1.4 Effect of Deoxygenation Rate Coefficient V a r i a t i o n . The effect of v a r i a t i o n of deoxygenation rate c o e f f i c i e n t s on models can be seen to be evident only i n the river/estuary stretch downstream of the waste discharge location (see Figure 5.4). Increases i n the rate c o e f f i c i e n t are observed to re s u l t i n increased deoxygenation as evidenced by reduced oxygen lev e l s and corresponding decreases i n BOD concentrations as a greater por- t i o n of the oxygen demand i s s a t i s f i e d . This i s t y p i c a l of the expected response of th i s c o e f f i c i e n t . Note that at the assumed water temperature of 10°C, the_effective rates of deoxygenation w i l l be somewhat lower than the magnitudes shown, which are the values at 20°C. . 5.1.5 Effect of Reaeration Rate Coefficient V a r i a t i o n . Model response due to v a r i a t i o n i n the reaeration c o e f f i c i e n t i s shown i n Figure 5.5 with the only effect being the decrease i n DO concentration evident for decreases i n reaeration rate. Again, as the water temperature i s held at 10°C the effec t i v e rates of reaeration w i l l be. somewhat lower than t h e i r specified values which are for 20°C. 5.1.6 Effect of Water Temperature Var i a t i o n. Water temperature effects on model response are shown i n Figure 5.6. The obvious e f f e c t i s seen as a lower saturation concentration for increasing temperature. As 103 K2 = 0.2/day at 20° C E = 10 midday T = 10° C Q = 40,000 cfs K| Is variable W= 1,000,000 lb/day ^ R\ver 4.0 a o ca E tn c o c o c o o <U X I a> 2.0 O Q 11.4 H 11.2 11.0 10.8- 10.6- 10.4 10.2-1 io!o 9.8 Saturation Concentration 0 10 20 30 40 50 60 River/Estuary Section F i g u r e 5.4 E f f e c t o f D e o x y g e n a t i o n R a t e on M o d e l R e s p o n s e 104 K,= 0.2/day at 20° C E= 10 mi 2 /day T = 10° C Q= 40,000 cfs K 2 is variable Q O ca £ tn c o <u o c o O T 3 0 > o o W =1,000,000 lb/day 5.0 n 4.0 H 3.0-̂ 2.0 1.0 11.4 11.2 1.01 10.8 10.6 10.4 0 10 20 30 Saturation Concentration 40 50 60 — i — 0 10 20 30 40 50 River/Estuary Section 60 F i g u r e 5.5 E f f e c t o f R e a e r a t i o n R a t e on M o d e l R e s p o n s e K, =K2= 0.2/day at 20°C E= 10 mi2/day Q= 40,000 cfs T is variable W= 1,000,000 lb/day 4 R i v e f a o 03 o a 12.04 11.0 10.0 9.0 8.0 40 50 60 sat, cone, at 5_° C • 1 sat. cone, at 15° C ^ 0 ^ ^ ' i sat. cone, at 2 0 ° C T = 2 0 ^ ; 0 10 20 30 40 50 60 River/ Estuary Section F i g u r e 5 .6 E f f e c t o f T e m p e r a t u r e on M o d e l R e s p o n s e sat, cone, at 10°C well, increased deoxygenation as evidenced by decreases in BOD concentra- tion and increases in DO de f i c i t with increasing temperature show the effect of temperature compensation (9 in this case i s 1.135) on the de- t-20 oxygenation rate coefficient ( K T = K 2 q 9 ). The corresponding tempera- ture effect on reaeration rate, not observable directly, i s less severe (6 being 1.024) and thus i t s effects are seen to be outweighed by i n - creased deoxygenation. 5.1.7 Summary. The sensitivity analysis has shown that the ti d a l l y averaged dissolved oxygen model response i s reasonable over the range of input parameters and model coefficients considered by the analysis, that i s , model mechanics appear to be sound. Thus the model can be considered to be valid at least i n the sense that model response i s in the direction i t should be. As well, the analysis has pointed out some interesting-details regarding - lower Fraser dissolved oxygen dynamics. Foremost, the predominating influence of freshwater inflow which minimizes the effects of tidal dispersion i s seen to flush oxygen demand out of the river/estuary to be exerted in the Strait of Georgia. In addition, the beneficial effects of low water temperatures have become evident i n their dual role of retarding biochemical oxidation and at the same time increase the dissolved oxygen saturation concentration. 5.2 TIDALLY VARYING DISSOLVED OXYGEN MODEL RESPONSE The u t i l i t y of a t i d a l l y varying model l i e s in i t s a b i l i t y to describe the in t r a - t i d a l behaviour of modeled parameters. Thus, the ti d a l l y varying dissolved oxygen model affords us with an opportunity to more f u l l y investigate the nature of dissolved oxygen resources in the lower F r a s e r R i v e r / E s t u a r y i n that i t w i l l a l l o w an assessment to be made of i n t r a - t i d a l d i s s o l v e d oxygen response. Before we can accept the r e s u l t s from t h i s u n v e r i f i e d model we must be assured that i t s manner of response i s reasonable. Although i t would be d e s i r a b l e to c a r r y out a r i g o r o u s i n v e s t i g a t i o n of the s e n s i t i v - i t i e s of model response as was done w i t h the t i d a l l y averaged model, t h i s i s precluded by o p e r a t i o n a l l i m i t a t i o n s inherent i n the t i d a l l y v a r y i n g d i s s o l v e d oxygen model which r e s u l t from the complex, m u l t i p l e model s o l u t i o n format. The main l i m i t a t i o n a r i s e s from the awkward, unwieldy nature of the s o l u t i o n s , w h i c h are c o s t l y , not only i n terms of computing time,but a l s o i n terms of expense of e f f o r t because a l l sub-models must be reprogrammed each time an input parameter or model c o e f f i c i e n t i s a l t e r e d . Thus an i n v e s t i g a t i o n of the complete s e n s i t i v i t i e s of t h i s model's response over the r e q u i r e d range of input parameter and model c o e f f i c i e n t v a r i a t i o n i s h i g h l y i m p r a c t i c a l , i f at a l l p o s s i b l e . This f a c t a l s o p o i n t s out a d e f i n i t e shortcoming of the t i d a l l y v a r y i n g model, namely i t s r a t h e r s o p h i s t i c a t e d a b i l i t y to d e s c r i b e the d e t a i l e d behaviour of the r i v e r / e s t u a r y has s e v e r e l y r e s t r i c t e d o v e r - a l l model f l e x i b i l i t y . Even though a thorough s e n s i t i v i t y a n a l y s i s i s not p o s s i b l e , i t w i l l . s t i l l be u s e f u l to i n v e s t i g a t e the behaviour of the t i d a l l y v a r y i n g d i s s o l v e d oxygen model p r e d i c t i o n s to see how they compare to r e s u l t s from the t i d a l l y averaged model. This comparative assessment w i l l a l s o serve as a s u i t a b l e framework f o r p o i n t i n g out some of the d e t a i l s of r i v e r / estuary behaviour t h a t cannot be observed through use of the t i d a l l y averaged model. The f o l l o w i n g d i s c u s s i o n w i l l d eal s e p a r a t e l y w i t h each component of the m u l t i p l e model t i d a l l y v a r y i n g s o l u t i o n to i l l u s t r a t e a l l aspects of model output. As i n i t s present s t a t e a l l components of the t i d a l l y v a r y i n g model are e s s e n t i a l l y u n v e r i f i e d , i t w i l l a l s o be worthwhile to b r i e f l y assess the v a l i d i t y of the v a r i o u s l e v e l s of model output and to i n d i c a t e how i n a c c u r a c i e s might u l t i m a t e l y have an e f f e c t on the v a l i d i t y of t i d a l l y v a r y i n g d i s s o l v e d oxygen p r e d i c t i o n s . 5.2.1 Hydrodynamic Sub-Model Output. T y p i c a l output from the t i d a l l y v a r y i n g hydrodynamic sub-model i s shown i n F i g u r e 5.7 f o r a freshwater i n f l o w of 40,000 c f s at C h i l l i w a c k and t i d a l range of 10 f e e t at Steveston. P r e d i c t e d v e l o c i t i e s f o r three s t a t i o n s along the r i v e r / e stuary are shown according to t h e i r r e l a t i o n w i t h t i d a l stage a t Steveston. Note that the negative v e l o c i t i e s i n d i c a t e flow i n the down- stream d i r e c t i o n . Current r e v e r s a l i s p r e d i c t e d to occur at a l l three s t a t i o n s . The t i m i n g of i t s occurence i s seen to vary from t h r e e hours a f t e r l o c a l low water (LLW) at S t a t i o n 2 to f o u r and f i v e hours a f t e r LLW at S t a t i o n s 20 and 40, r e s p e c t i v e l y . The design t i d a l c o n f i g u r a t i o n i s a l s o seen to r e s u l t i n an extended p e r i o d of e s s e n t i a l l y s l a c k water around hour 12 i n the t i d a l c y c l e . The advective t r a n s p o r t of p a r t i c l e s r e l e a s e d at v a r i o u s times from S t a t i o n 40 on the Main Arm/Main Stem of the r i v e r / e s t u a r y a c c o r d i n g to hydrodynamic sub-model v e l o c i t y p r e d i c t i o n s i s shown i n F i g u r e 5.8. P a r t i c l e s 1 and 2 r e l e a s e d at hours 8 and 14, r e s p e c t i v e l y are seen to e x i t d u r i n g the strong ebb at approximately 70 hours. P a r t i c l e 3 r e - leased at hour 20 and p a r t i c l e 4 r e l e a s e d at hour 26 are not seen to Q= 40,000 cfs at Chilliwack Tidal Range at Steveston 10 feet 109 Q= 40,000 cfs at Chilliwack Tidal Range at Steveston 10 feet Particle No. Release Time Residense Time (hrs) (hrs) 1 8 61 2 14 56 3 20 72 Hours Figure 5.8 P r e d i c t e d Trace of- P a r t i c l e s Released at Various Times From S t a t i o n 40 e x i t u n t i l the ebb of the f o l l o w i n g t i d a l c y c l e at 90 hours which r e s u l t s i n a s i g n i f i c a n t i n c r e a s e i n residence times f o r these p a r t i c l e s . 5.2.2 T i d a l l y Varying I n i t i a l E f f l u e n t Concentrations. When an e f f l u e n t i s discharged i n t o an estuary the o s c i l l a t o r y movement of the water mass r e s u l t s i n a v a r i a b l e i n i t i a l e f f l u e n t c o n c e n t r a t i o n (see Figure 5.9). This i s caused by the v a r i a t i o n s i n magnitude and d i r e c t i o n of t i d a l flows at the point of e f f l u e n t discharge. In p a r t , t h i s i s due to the phenomenon of " m u l t i p l e d o s i n g " which occurs when a p a r c e l of water r e c e i v e s a s l u g of e f f l u e n t as i t f i r s t moves past the dis c h a r g e p o i n t i n the downstream d i r e c t i o n d u r i n g an ebb flow; another s l u g of e f f l u e n t as i t moves upstream past the o u t f a l l on the f l o o d t i d e ; and yet another s l u g of e f f l u e n t as the water p a r c e l moves downstream on the succeeding ebb t i d e . Thus flo w r e v e r s a l can r e s u l t i n a water p a r c e l being "dosed" a number of times by the same e f f l u e n t discharge. A l s o , any p e r i o d of extended s l a c k or slow moving water r e s u l t s i n decreased e f f l u e n t d i l u t i o n which again causes increased e f f l u e n t c o n c e n t r a t i o n . An examination of Fi g u r e 5.9 shows three c o n c e n t r a t i o n " s p i k e s " i n the p r e d i c t e d i n i t i a l t i d a l l y v a r y i n g BOD c o n c e n t r a t i o n p r o f i l e ( B 0 D t v ) . The increased c o n c e n t r a t i o n s at hours zero and four r e s u l t from the flow r e v e r s a l s which occur at those times (see Figure 5.7). The concentra- t i o n " s p i k e " observed at hour 12 i s due to an extended p e r i o d of slow moving water. This l a t t e r " s p i k e " i s seen to be the highest BOD concen- t r a t i o n , being approximately s i x times higher than the t i d a l l y averaged c o n c e n t r a t i o n (B0D t a). I t was pointed out by Joy [1974] t h a t , according to model p r e d i c t i o n s , peak t i d a l l y v a r y i n g c o n c e n t r a t i o n s could be up to Q = 40,000 cfs at Chilliwack Tidal Range at Steveston 10 feet Continuous Waste Discharge at Station 40 Predicted Initial BOD Concentrations Hour s P r e d i c t e d F i g u r e 5.9 I n i t i a l E f f l u e n t D i l u t i o n ten times higher than the t i d a l l y average v a l u e s . 5.2.3 I n t r a - T i d a l D i s s o l v e d Oxygen Response. To i n v e s t i g a t e the i n t r a - t i d a l response of d i s s o l v e d oxygen i n a manner that a l l o w s f o r com- p a r i s o n to the t i d a l l y averaged r i v e r / e s t u a r y response, e q u i v a l e n t r i v e r / estuary and waste discharge c o n d i t i o n s were chosen: waste discharge equal to 40,000 pounds of BOD per hour at S t a t i o n 40; water temperature of 10°C; decay (K^) and r e a e r a t i o n (K 2) c o e f f i c i e n t s equal to 0.2 per day at 20°C. The r i v e r / e s t u a r y response as p r e d i c t e d by the t i d a l l y v a r y i n g d i s s o l v e d oxygen model i s shown i n Fi g u r e s 5.10 and 5.11 f o r downstream S t a t i o n s 20 and 2, r e s p e c t i v e l y . These f i g u r e s i l l u s t r a t e the p r e d i c t e d v a r i a t i o n i n BOD (B0D t v) and DO d e f i c i t ( D0 t v) which, although shown to be continuous curves, are a c t u a l l y approximated by h o u r l y v a l u e s . The two minor e f f l u e n t " s p i k e s " that had been d i s t i n c t i n the p r e d i c t e d i n i t i a l e f f l u e n t d i l u t i o n curve (see F i g u r e 5.9) have "blended" together and r e s u l t i n the minor BOD peak at hour one i n F i g u r e 5.10. That i s to say, the " s p i k e s " a r r i v e at S t a t i o n 20 w i t h i n the same hour and s i n c e the t i d a l l y v a r y i n g model cannot "see" events w i t h i n the hour i t i s unable to d i s t i n g u i s h between them. I t should be noted that the time s c a l e s i n F i g u r e s 5.10 and 5.11 are a r b i t r a r y . The p a r c e l of water which contained the major i n i t i a l BOD " s p i k e " i s seen to have moved downstream completely past S t a t i o n 20 at hour four and then p a r t way back around hour 14. Thus one s l u g of water i s r e s p o n s i b l e f o r the two major BOD peaks i n F i g u r e 5.10 and two slugs are r e s p o n s i b l e f o r the minor peak. Corresponding peaks of DO d e f i c i t are observed. At S t a t i o n .2 (see Figure 5.11) the same phenomenon i s observed 114 Q= 40,000 cfs at Chilliwack Tidal Range at Steveston 10 feet Continuous Waste Discharge at Station 40 Predicted BOD and DO Concentrations at Station 20 £ * 3 0 - | 2 4 H o u r s Figure 5.10 T i d a l l y Varying D i s s o l v e d Oxygen Model Response: S t a t i o n 20 115 Q= 40,000 cfs at Chilliwack Tidal Range at Steveston 10 feet 2 Continuous Waste Discharge at Station 40 Predicted BOD and DO Concentrations at Station 2 Figure 5.11 T i d a l l y Varying D i s s o l v e d Oxygen Model Response: S t a t i o n 2 only i n t h i s case the major BOD peak i s f l u s h e d out of the model r i v e r / e s t u a r y a t hour s i x . This i s evident because.the BOD and DO d e f i c i t con- c e n t r a t i o n s are observed to be zero between hours s i x and twenty, which means that sea water which i s assumed to be unp o l l u t e d has moved i n t o the r i v e r / e s t u a r y . A comparison of peak t i d a l l y v a r y i n g DO d e f i c i t (DO ) to the t i d a l l y averaged d e f i c i t (DO. ) r e v e a l s that at both s t a t i o n s the t i d a l l y r a v a r y i n g d e f i c i t i s s i g n i f i c a n t l y g r e a t e r w i t h the maximum r a t i o i n each case being around s i x . The f a c t that the r a t i o of peak DO^^ to D 0 t a i s equal to the peak BOD t v to BOD t a r a t i o i s to be expected because of the l i n e a r nature of the d i s s o l v e d oxygen s o l u t i o n s . That i s f o r equal i n i t i a l d e f i c i t s , constant and equal c o e f f i c i e n t s and roughly comparable r e s i d e n t times, the r e l a t i v e s i z e of DO d e f i c i t c o n c e n t r a t i o n s as d e t e r - mined by the St r e e t e r - P h e l p s oxygen sag equation (Equation 2.3) w i l l be d i r e c t l y p r o p o r t i o n a l to the r e l a t i v e magnitude of i n i t i a l BOD concentra- t i o n s . Note that the r e l a t i v e d i f f e r e n c e between t i d a l l y averaged and " a c t u a l " residence time of a water p a r c e l i n the r i v e r / e s t u a r y i s minimal w i t h the d i f f e r e n c e becoming p r o p o r t i o n a l l y of l e s s e r s i g n i f i c a n c e as residence time i n c r e a s e s . T h i s p o i n t s out the importance of p r e d i c t e d i n i t i a l e f f l u e n t d i l u t i o n s as t h e i r values u l t i m a t e l y determine what the t i d a l l y v a r y i n g d i s s o l v e d oxygen response w i l l be. I t should be noted that the above a n a l y s i s was made n e g l e c t i n g l o n g i t u d i n a l d i s p e r s i o n . Thus i t represents an extreme case, i n t h a t , had d i s p e r s i v e e f f e c t s been i n c l u d e d , the e f f e c t would have been to erode the " s p i k e s " thereby r e d i s t r i b u t i n g BOD, 117 the net r e s u l t being decreased maximum DO d e f i c i t c o n c e n t r a t i o n s . Accord- i n g to Joy [1974], who i n v e s t i g a t e d the p r e d i c t e d d i s p e r s i o n of a s l u g load r e l e a s e d i n the upstream r i v e r / e s t u a r y reaches, there i s a f i v e - f o l d de- crease i n peak c o n c e n t r a t i o n w i t h i n the f i r s t 24 hours a f t e r r e l e a s e (see Figure 5.12). Although recent f i e l d i n v e s t i g a t i o n s have e s t a b l i s h e d that c o e f f i c i e n t s used by Joy were l i k e l y too l a r g e [P. Ward, unpublished data] the degree to which t h i s a f f e c t s the r e s u l t s i s not e a s i l y determined. I t i s recognized that the e f f e c t s of d i s p e r s i o n on e f f l u e n t peaks produced by # a steady discharge w i l l be somewhat l e s s than i n the case of a s l u g load because of the reduced c o n c e n t r a t i o n g r a d i e n t s . 5.2.4 V a l i d i t y of T i d a l l y Varying P r e d i c t i o n s . I t was p o i n t e d out i n Sections 4.2.2 and 5.2 that due to i t s s o p h i s t i c a t e d approach the t i d a l - l y v a r y i n g model must, of n e c e s s i t y , u t i l i z e a staged, m u l t i p l e model s o l u t i o n format. The b a s i c model, the hydrodynamic sub-model, p r e d i c t s t i d a l l y v a r y i n g v e l o c i t i e s and water surface e l e v a t i o n s throughout the r i v e r / e s t u a r y f o r given r i v e r discharge and t i d a l c o n d i t i o n s . T h i s i n - formation, i n a d d i t i o n to data d e s c r i b i n g waste d i s c h a r g e s , i s used i n tu r n as input to the general mass t r a n s p o r t model which u l t i m a t e l y pre- d i c t s the time-v a r y i n g d i s t r i b u t i o n of BOD and DO throughout the es t u a r y . Within the framework of the general mass t r a n s p o r t model the hydrodynamic i n f o r m a t i o n i s used to perform two b a s i c f u n c t i o n s . F i r s t l y , the v e l o c i t y f i e l d p r e d i c t i o n s are used as the b a s i s f o r r o u t i n g p a r t i c l e s r e l e a s e d at v a r i o u s times and l o c a t i o n s i n the r i v e r / e s t u a r y , thereby s i m u l a t i n g advec- t i v e t r a n s p o r t and d e f i n i n g a t r a c e of the t i m e - h i s t o r y of v a r i o u s water and/or e f f l u e n t p a r c e l s . Secondly, the p r e d i c t e d v e l o c i t y i n f o r m a t i o n i n combination w i t h the c r o s s - s e c t i o n a l a r e a , which i s d e r i v e d from water / 118 Q= 40,000 cfs at Chilliwack Tidal Range at Steveston 10 feet 40 oser RWer. Slug Discharge at Station 40 Predicted Erosion of Effluent Spike surface e l e v a t i o n p r e d i c t i o n s , i s used to c a l c u l a t e t i d a l f lows which are used i n t u r n to o b t a i n estimates of i n i t i a l e f f l u e n t d i l u t i o n . Thus the accuracy of p r e d i c t e d t i d a l l y v a r y i n g d i s s o l v e d oxygen response depends to a l a r g e extent on the v a l i d i t y of the hydrodynamic sub-model; s p e c i f i c a l l y on the accuracy of t i d a l l y v a r y i n g v e l o c i t y p r e d i c t i o n s as they are used to determine residence times as w e l l as i n i t i a l e f f l u e n t c o n c e n t r a t i o n s . With regards to p o s s i b l e i n a c c u r a c i e s i n the magnitudes of v e l o c i t i e s as they might e f f e c t residence times, i t appears t h a t these could be s u b s t a n t i a l , p a r t i c u l a r l y i n the lower r i v e r / e s t u a r y s t r e t c h e s where flo w s t r a t i f i c a t i o n e f f e c t s e x i s t due to the i n t r u s i o n of s a l t w a t e r (see S e c t i o n 1.4.2). Hodgins [1974] developed a m o d i f i e d hydrodynamic model which could account f o r the s a l t w a t e r wedge e f f e c t s . He found that the main e f f e c t of the s a l t w a t e r l a y e r was to i n c r e a s e the freshwater ebb v e l o c i t i e s which r e s u l t e d i n s u f f i c i e n t l y d i f f e r e n t r a t e s of p a r t i c l e a d vection. A comparison of the a d v e c t i o n paths as they are p r e d i c t e d by the s t r a t i f i e d model and the b a r o t r o p i c model r e v e a l s that the e f f e c t s of v e l o c i t y underestimation are t w o - f o l d . F i r s t l y there i s a s u b s t a n t i a l e r r o r i n p r e d i c t e d residence time. For example, co n s i d e r p a r t i c l e s r e - leased from Annacis I s l a n d ( p a r t i c l e s 3 and 4 i n F i g u r e 5.13). P a r t i c l e 3 i n the s t r a t i f i e d model i s seen to be f l u s h e d out of the r i v e r / e s t u a r y approximately nine hours f a s t e r than i t s counterpart p a r t i c l e 4 i n the b a r o t r o p i c model, a r e d u c t i o n i n residence time of over 30 p e r c e n t . The second e f f e c t evident from the t r a c e of p a r t i c l e s 1 and 2 i n F i g u r e 5.12 i s that the underestimation of v e l o c i t i e s r e s u l t s i n a g r e a t e r degree of m u l t i p l e "dosing", i n t h i s case, four separate dosings as compared w i t h only two i n the s t r a t i f i e d model. 120 F i g u r e 5.13 d v e c t i o n P a t h s o f P a r t i c l e s i n S t r a t i f i e d M o d e l and B a r o t r o p i c M o d e l Consider now the e f f e c t s of v e l o c i t y e r r o r s on p r e d i c t e d i n i t a l e f f l u e n t d i l u t i o n . Of c r i t i c a l importance here are those v e l o c i t y pre- d i c t i o n s which determine the major e f f l u e n t s p i k e s , namely p r e d i c t e d values around the slackwater p e r i o d s . I t i s c r u c i a l that the p r e d i c t e d values be accurate not only i n terms of magnitude but as the l e n g t h of the slackwater p e r i o d i s important, they must a l s o be accurate i n t i m i n g . Before one can a p p r e c i a t e the s i g n i f i c a n c e of n e a r - s l a c k - t i d e v e l o c i t y e r r o r s i t i s necessary to understand the method used i n the t i d a l l y v a r y - in g mass t r a n s p o r t model to c a l c u l a t e i n i t i a l e f f l u e n t c o n c e n t r a t i o n s . Estimates of i n i t i a l d i l u t i o n are obtained by d i l u t i n g the e f f l u e n t mass discharged over one hour i n t o the volume which flows by the d i s c h a r g e p o i n t d u r i n g the same p e r i o d . Although t h i s method i s acceptable when average t i d a l flows are non-zero, i t i s i n a p p r o p r i a t e when the net h o u r l y flow approaches zero as i n t h i s case i n i t i a l e f f l u e n t c o n c e n t r a t i o n s become indeterminate and the i n i t i a l d i l u t i o n curve becomes d i s c o n t i n - uous. To prevent the occurrence of t h i s slackwater d i s c o n t i n u i t y , the net h o u r l y flow has been con s t r a i n e d so that i t can never reach zero. Thus i n the event that the zero f l o w c o n d i t i o n o c c u r s , the v a l u e of i n i t i a l instream waste c o n c e n t r a t i o n i s determined by the a r b i t r a r i l y chosen minimum flow r a t e . This weakness, inherent i n the t i d a l l y v a r y i n g model, cannot e a s i l y be overcome. P o s s i b l y by i n c r e a s i n g the temporal r e s o l u t i o n of the model so that i t would approximate r i v e r / e s t u a r y c o n d i t i o n s u s i n g smaller time increments ( i . e . i n the order of minutes i n s t e a d of one hour), the e f f e c t could be minimized. Although the zero t i d a l f l o w c o n d i t i o n might s t i l l occur, because of the f i n e r time increment, i t s impact i n 122 the s i m u l a t i o n would be reduced as each time increment would then r e p r e - sent a smaller f r a c t i o n of the t i d a l p e r i o d and thus r e c e i v e l e s s weight i n d e f i n i n g the t i d a l l y v a r y i n g response. Another important f a c t o r that i n f l u e n c e s the v a l i d i t y of the t i d a l l y v a r y i n g p r e d i c t i o n s i s the f a c t that l o n g i t u d i n a l d i s p e r s i o n has been ignored. This was done p u r p o s e f u l l y to exaggerate the i n t r a - t i d a l r i v e r / e s t u a r y response, however i t may have d r a s t i c a l l y e f f e c t e d the v a l i d i t y of the p r e d i c t e d r e s u l t s . In p a r t i c u l a r , s i n c e the d i s p e r s i o n process i s time dependent, i t w i l l e x h i b i t I t s most severe e f f e c t s on c o n c e n t r a t i o n spikes i n e f f l u e n t p a r c e l s which have extended r e s i d e n c e times, p r e c i s e l y the same c o n d i t i o n s that r e s u l t i n the most s i g n i f i c a n t DO d e p l e t i o n s . In t h i s study, although i t has not been p o s s i b l e to f u l l y de- termine the extent to which t h i s e f f e c t might a l t e r the v a l i d i t y of the t i d a l l y v a r y i n g p r e d i c t i o n s , i t i s considered t h a t l o n g i t u d i n a l d i s p e r s i o n a f t e r any extended p e r i o d ( i . e . more than one t i d a l c y c l e ) w i l l r e s u l t i n a two to f i v e f o l d r e d u c t i o n i n any c o n c e n t r a t i o n s p i k e . 5.2.5 Summary. In summary, the r e s u l t s from the t i d a l l y v a r y - i n g d i s s o l v e d oxygen model show an increased DO d e f i c i t during p o r t i o n s of the t i d a l c y c l e . Although t h i s e f f e c t i s t y p i c a l of estuary d i s s o l v e d oxygen response i t may not be an accurate r e p r e s e n t a t i o n of t r u e r i v e r / estuary response. Concern has been expressed over the v a l i d i t y of the t i d a l l y v a r y i n g p r e d i c t i o n s ; f i r s t l y , because the mechanics of the s o l u t i o n method are s e n s i t i v e to the c o n d i t i o n s causing the i n c r e a s e d d e f i c i t s , namely the v e l o c i t y p r e d i c t i o n s around s l a c k w a t e r , and secondly, because the assumption of zero d i s p e r s i o n may also d r a s t i c a l l y a f f e c t the conditions of maximum d e f i c i t . Because of the concern that the t i d a l l y varying model may not be e n t i r e l y appropriate f o r use i n de s c r i b i n g the i n t r a - t i d a l behaviour of dissolved oxygen parameters, i t w i l l not be used e x p l i c i t l y i n the assessment of lower Fraser a s s i m i l a t i v e capacity. I t w i l l be used, however, to exemplify i n t r a - t i d a l response thereby augment- ing and tempering the following assessment of lower Fraser d i s s o l v e d oxygen dynamics. 5.3 AN ANALYSIS OF LOWER FRASER RIVER/ESTUARY ASSIMILATIVE CAPACITY The following prefactory comments are of f e r e d p r i o r to making a preliminary assessment of lower Fraser River/Estuary a s s i m i l a t i v e capacity Their purpose i s to inform the reader as to the int e n t of the ensuing d i s - cussion and, at the'same time, to o f f e r the r a t i o n a l e behind i t . When i t comes time to u t i l i z e the c a p a b i l i t i e s of a study such as t h i s , a d e c i s i o n must be made regarding the mode of attack. Since i t i s possible through the use of mathematical models to i n v e s t i g a t e an i n - v e r i t a b l e i n f i n i t u d e of d i f f e r e n t input combinations and permutations, the d e c i s i o n must take into account the l i m i t s of p r a c t i c a l i t y as w e l l as the objective at hand. The most appropriate use to be made of the pre- d i c t i v e c a p a b i l i t i e s f o r the purposes of t h i s study i s to bring to l i g h t some of the main features of lower Fraser oxygen dynamics. To do t h i s the analysis has made use of s p e c i f i c a l l y chosen hypothetical s i t u a t i o n s , thus r e t a i n i n g an a i r of gen e r a l i t y i n i t s approach. I t f a l l s f a r short of being completely d e f i n i t i v e and, therefore, has d e l i b e r a t e l y r e f r a i n e d from making s p e c i f i c forecasts of future conditions. However, what i t doe o f f e r i s some i n d i c a t i o n of how the models have been u s e f u l i n h e l p i n g i n o b t a i n i n g an improved understanding of the nature of a s s i m i l a t i v e c a p a c i t y i n the lower Fraser R i v e r / E s t u a r y . The a n a l y s i s i s based mainly on r e s u l t s from the t i d a l l y averaged model. S e n s i t i v i t y a n a l y s i s has shown t h i s model to be w e l l behaved i n i t s p r e d i c t e d response (see Sectio n 5.1) and t h e r e f o r e i t i s considered to be more r e l i a b l e i n terms of the v a l i d i t y of i t s p r e d i c t i o n s . Some use w i l l be made of t i d a l l y v a r y i n g model r e s u l t s but because s e r i o u s concerns have been expressed about i t s v a l i d i t y as a p p l i e d i n t h i s i n v e s t i g a t i o n (see Section 5.2), i t s use w i l l be r e s t r i c t e d to e x e m p l i f y i n g the expected e f f e c t of i n t r a - t i d a l d i s s o l v e d oxygen response; thereby q u a l i f y i n g to some extent the o v e r a l l assessment of a s s i m i l a t i v e c a p a c i t y . As the f o l - lowing a n a l y s i s i s based on u n v e r i f i e d d i s s o l v e d oxygen models, a l l con- c l u s i o n s drawn out of i t must be considered to be t e n t a t i v e . In the i n v e s t i g a t i o n of t i d a l l y averaged model response i n d i - c a t i o n s were t h a t , according to model p r e d i c t i o n s , the d i s s o l v e d oxygen dynamics of the lower Fraser R i v e r / E s t u a r y were to a l a r g e e x t e n t governed by two f a c t o r s : the i n f l u e n c e of freshwater i n f l o w and the e f f e c t of water temperature. As c o n d i t i o n s i n the lower F r a s e r are such t h a t low flows occur during the p e r i o d January to March when water temperatures are low, and conv e r s e l y , that high temperatures occur d u r i n g h i g h e r f l o w p e r i o d s , i t i s not p o s s i b l e to e a s i l y d e f i n e a " c r i t i c a l p e r i o d " d u r i n g which d i s s o l v e d oxygen c o n c e n t r a t i o n s would be most s e r i o u s l y a f f e c t e d by waste water discharges. In attempts to e s t a b l i s h t h i s c r i t i c a l p e r i o d and a l s o to o b t a i n some i n d i c a t i o n as to the e f f e c t on d i s s o l v e d oxygen l e v e l s of a l a r g e waste l o a d i n g , there being no observable response using a c t u a l waste l o a d i n g s , a s e r i e s of model runs was made using the t i d a l l y average DO model t o s t i m u l a t e c o n d i t i o n s f o r each month of the year. A h y p o t h e t i c a l waste load of 1,000,000 pounds of BOD per day (approximately four times the present t o t a l BOD load) was discharged a t S t a t i o n 40 i n the model r i v e r / e s t u a r y , the l o c a t i o n chosen to be i n the upstream reaches so t h a t a gre a t e r oxygen response would be observed w i t h i n the model boundaries. Monthly mean low flows and high temperatures (see Se c t i o n s 1.2 and 1.3) r e p r e s e n t i n g c o i n c i d e n t events w i t h ten and f i f t y year r e t u r n periods were chosen f o r use i n the a n a l y s i s as these c o n d i t i o n s would represent an extreme d i s s o l v e d oxygen response i n the r i v e r / e s t u a r y . I t i s recognized that the simultaneous occurrence of these two events i s h i g h l y improbable. Assumed values f o r the d i s s o l v e d oxygen model co- e f f i c i e n t s (see S e c t i o n 4.4) were used. The r e s u l t s of the s i m u l a t i o n are shown i n F i g u r e s 5.14 and 5.15, the former r e p r e s e n t i n g a n a l y s i s u s i n g ten year r e t u r n p e r i o d con- d i t i o n s w h i l e the l a t t e r represents f i f t y year c o n d i t i o n s . These "space- time" p l o t s are a u s e f u l means of p r e s e n t i n g l a r g e q u a n t i t i e s of data i n summary form. I t should be noted that they are not t r u e space-time p l o t s because the s i m u l a t i o n , i n t h i s i n s t a n c e , has made use of mean monthly c o n d i t i o n s . Since these diagrams represent expected d e f i c i t c o n c e n t r a t i o n s per 1,000,000 pounds of BOD discharged at S t a t i o n 40, they can a l s o be thought of as " u n i t response diagrams". For example, i f the waste load at S t a t i o n 40 were to be doubled, the d e f i c i t c o n c e n t r a t i o n s throughout the r i v e r / e s t u a r y would be found to double according to the l i n e a r i t y of K| = K2= 0.2/day at 20°Cj E = 10 mi2/dayt W= 1,000,000 lb/day at Stn. 40 River/Estuary Section Figure 5.14 Space-Time P l o t of DO D e f i c i t C oncentrations Using 10 Year Return P e r i o d Low Flows and High Temperatures K, = K 2= 0.2/day at 20° C •, E = I0 mi/day; W= 1,000,000 lb/day at Stn. 40 River/ Estuary Section F i g u r e 5.15 S p a c e - T i m e P l o t , o f DO D e f i c i t C o n c e n t r a t i o n s U s i n g 50 Y e a r R e t u r n P e r i o d Low F l o w s and H i g h T e m p e r a t u r e s the s u p e r p o s i t i o n p r i n c i p l e . From F i g u r e s 5.14 and 5.15 i t i s evident t h a t , a c c o r d i n g to model p r e d i c t i o n s , the d i s s o l v e d oxygen response i n the lower F r a s e r i s minimal even when a c o n s i d e r a b l y l a r g e waste load i s di s c h a r g e d i n the upstream reaches. The maximum DO d e f i c i t c o n c e n t r a t i o n s , 0.6 mg/1 and 0.9 mg/1, r e s p e c t i v e l y f o r the ten and f i f t y year c o n d i t i o n s , are seen i n both i n s t a n c e s to occur during the low flow p e r i o d i n March. Thus, i n terms of oxygen d e p l e t i o n s , the e f f e c t s of low flows outweighed the e f f e c t s of low water temperatures. S l i g h t DO d e p l e t i o n s upstream of the o u t f a l l l o c a t i o n are observed f o r a l l months of the year except d u r i n g the high flow months - May, June and J u l y . In order to determine d i s s o l v e d oxygen c o n c e n t r a t i o n s from the r e s u l t s of t h i s s i m u l a t i o n , mean monthly DO s a t u r a t i o n c o n c e n t r a t i o n s are r e q u i r e d f o r the temperature c o n d i t i o n s used i n each set of analyses. These are shown i n Table 5.2. TABLE 5.2 DO SATURATION CONCENTRATIONS USED IN ANALYSIS Ten Year F i f t y Year Month Return P e r i o d Return P e r i o d January 13.9 13.8 February 13.8 13.6 March 13.2 13.0 A p r i l 12.4 12.2 May 11.4 11.2 June 10.5 10.3 J u l y 9.9 9.7 August 9.7 9.6 September 10.0 9.9 October 11.2 11.0 November 12.5 12.3 December 13.2 12.9 I t i s evident from a review of Table 5.2 t h a t , even though the maximum DO d e f i c i t s occur i n March, minimum d i s s o l v e d oxygen concentra- t i o n s w i l l occur i n the.period of J u l y to September because of reduced DO s a t u r a t i o n c o n c e n t r a t i o n s . This i n d i c a t e s t h a t , according to model r e s u l t s , the c r i t i c a l p e r i o d f o r d i s s o l v e d oxygen i n the lower F r a s e r i s l a t e summer or e a r l y f a l l , the c o n t r o l l i n g f a c t o r being the i n f l u e n c e of water temperature on oxygen s a t u r a t i o n l e v e l s . In terms of the magnitude of DO d e p l e t i o n s , the r e s u l t s of model analyses show that f o r the most extreme combinations of low r i v e r flows and high water temperatures and an extremely l a r g e waste discharge i n the upper reaches, the d i s s o l v e d oxygen response observable i n the estuary w i l l be minimal. I t i s noted that f o r a d i s t r i b u t e d l o a d of the same t o t a l magnitude, or the s i m i l a r l a r g e load l o c a t e d i n the lower r i v e r / e s t u a r y reaches, the e f f e c t on d i s s o l v e d oxygen response w i l l be even l e s s . To demonstrate the s i z e a b l e a b i l i t y of the lower F r a s e r to as- similate- o r g a n i c waste 1 d i s c h a r g e s ; consider the prsdic-te-d e f f e c t s of a r i d i c u l o u s l y extreme waste l o a d i n g . I f there were a f o u r - f o l d i n c r e a s e i n the h y p o t h e t i c a l discharge l o c a t e d at S t a t i o n 40 ( t h i s r e p r e s e n t s a s i n g l e p o i n t source discharge w i t h a p o p u l a t i o n e q u i v a l e n t o f 20 m i l l i o n ) , u s i n g the f i f t y year extreme c o n d i t i o n s , the p r e d i c t e d , minimum d i s s o l v e d oxygen co n c e n t r a t i o n s are s t i l l above 7.5 mg/1 i n August and over 9 mg/1 i n March. At t h i s j u n c t u r e a caveat to the for e g o i n g a n a l y s i s i s appro- p r i a t e . Up to t h i s p o i n t , the assessment has been based s o l e l y on t i d a l l y averaged p r e d i c t i o n s . Although t h i s should be a good i n d i c a t i o n of average c o n d i t i o n s i t does not f u l l y r e f l e c t the t r u e nature of r i v e r / estuary d i s s o l v e d oxygen response. In the a n a l y s i s of t i d a l l y v a r y i n g d i s s o l v e d oxygen response (see S e c t i o n 5.2) i t was noted that due to the o s c i l l a t o r y movement of the water mass i n e s t u a r i e s , i n i t i a l instream e f f l u e n t c o n c e n t r a t i o n s vary throughout the t i d a l c y c l e , being c h a r a c t e r - i z e d by c o n c e n t r a t i o n spikes formed during slackwater p e r i o d s . This t i d a l l y v a r y i n g e f f l u e n t p r o f i l e r e s u l t s i n a t i d a l l y v a r y i n g d i s s o l v e d oxygen p r o f i l e . I n d i c a t i o n s were that during the low f l o w p e r i o d when t h i s e f f e c t i s most pronounced, i n the absence of l o n g i t u d i n a l d i s p e r - - s i o n , peak t i d a l l y v a r y i n g d i s s o l v e d oxygen d e f i c i t c o n c e n t r a t i o n s could be up to s i x to ten times higher than t i d a l l y averaged d e f i c i t s (see S e c t i o n 2.3). By making the c o n s e r v a t i v e assumption that a two-fold decrease i n c o n c e n t r a t i o n f o r extended residence times w i l l account f o r the e f f e c t s of d i s p e r s i o n (see S e c t i o n 5.2.4), the r a t i o of peak t i d a l l y v a r y i n g to t i d a l l y averaged DO d e f i c i t would be reduced to the order of three to f i v e . The a p p l i c a t i o n of t h i s "expected" i n t r a - t i d a l DO d e f i c i t r a t i o to temper t i d a l l y averaged p r e d i c t i o n s w i l l g i v e some i n d i c a t i o n of the s i g n i f i c a n c e of t i d a l l y v a r y i n g response. I n the case of the hypo- t h e t i c a l waste l o a d i n g of 1,000,000 pounds per day a t S t a t i o n 40 by t h i s c a l c u l a t i o n there would be a maximum low flow t i d a l l y v a r y i n g d e f i c i t of 1.8 mg/1 to 3.0 mg/1 using the ten year extreme c o n d i t i o n s and a 2.7 mg/1 to 4.5 mg/1 d e f i c i t u s i n g the f i f t y year c o n d i t i o n s . However, even i n the worst i n s t a n c e , minimum DO c o n c e n t r a t i o n s would s t i l l be above 8.5 mg/1. I t should be noted that the e f f e c t s of i n t r a - t i d a l DO response w i l l become more s i g n i f i c a n t f o r l a r g e wastewater di s c h a r g e s . For example, consider the extremely l a r g e waste discharge (20 m i l l i o n p o p u l a t i o n e q u i v a l e n t s ) at S t a t i o n 40: whereas the minimum t i d a l l y averaged DO was approximately 9 mg/1 u s i n g the f i f t y year c o n d i t i o n s , the minimum t i d a l l y v a r y i n g con- c e n t r a t i o n by t h i s a n a l y s i s w i l l be l e s s than 2.5 mg/1. Thus, f o r l a r g e discharges the t i d a l l y averaged model may not be a good i n d i c a t i o n of r i v e r / e s t u a r y behaviour. This was one of the major c o n c l u s i o n s of Joy's i n v e s t i g a t i o n where he used loads of 25 m i l l i o n pounds per day [Joy, 1974]. Although no r e s u l t s u s i n g the t i d a l l y v a r y i n g model a r e a v a i l - able from the c r i t i c a l , l a t e summer p e r i o d , there i s every reason to b e l i e v e that a s i m i l a r r e l a t i o n s h i p between the t i d a l l y v a r y i n g and t i d a l l y averaged r e s u l t s h o l d . Thus, one would expect that the e f f e c t of waste water discharges on d i s s o l v e d oxygen would be exacerbated by the i n - f l u e n c e of t i d a l a c t i o n which, although reduced due to higher freshwater f l o w s , would nonetheless be s i g n i f i c a n t . In summary, according to the r e s u l t s of t h i s a n a l y s i s , the lower Fraser R i v e r / E s t u a r y would seem to have an e x c e p t i o n a l l y l a r g e a s s i m i l a t i v e c a p a c i t y . P r i m a r i l y t h i s i s because of the combined i n f l u e n c e o f l a r g e freshwater flows and low water temperatures. The a n a l y s i s has shown th a t the c r i t i c a l p e r i o d f o r d i s s o l v e d oxygen i s i n the l a t e summer i n s p i t e of the f a c t that maximum d i s s o l v e d oxygen d e p l e t i o n s are observed d u r i n g the low flow p e r i o d i n March. A cursory examination of i n t r a - t i d a l d i s s o l v e d oxygen response has i n d i c a t e d that i t i s an important determinant of lower Fraser d i s s o l v e d oxygen dynamics and that i t w i l l become more important as waste loadi n g s to the r i v e r are i n c r e a s e d . CHAPTER 6 SUMMARY AND DISCUSSION Given the r e s u l t s from the d i s s o l v e d oxygen models as o u t l i n e d i n the previous chapter i t now remains to b r i e f l y review and d i s c u s s the f i n d i n g s of t h i s study. A t t e n t i o n w i l l be devoted to the i m p l i c i t as w e l l as e x p l i c i t d e t a i l s of the re s e a r c h i n an e f f o r t to glean as much as p o s s i b l e from the r e s u l t s of t h i s attempt at water q u a l i t y modeling. This chapter w i l l c o nsider s e p a r a t e l y two aspects of t h i s r e s e a r c h : f i r s t - l y , the development of the d i s s o l v e d oxygen models i n c l u d i n g an assessment of t h e i r p r e d i c t i v e c a p a b i l i t i e s and, secondly, the r e s u l t s of the a p p l i - c a t i o n of the models to an assessment of the a s s i m i l a t i v e c a p a c i t y of the lower F r a s e r R i v e r / E s t u a r y . This s u b d i v i s i o n i s u s e f u l i n th a t i t sepa- r a t e s the d i s c u s s i o n i n t o two s e c t i o n s , one which d e a l s w i t h the models themselves'and the other which deals w i t h the d i s s o l v e d oxygen resources of the lower Fraser. 6.1 DISSOLVED OXYGEN MODELS 6.1.1 Summary. A review was made of the v a r i o u s oxygen source/ s i n k processes which a f f e c t the oxygen balance i n waterways. I n l i g h t of c o n d i t i o n s i n the lower F r a s e r R i v e r / E s t u a r y i t was determined that f o r the purposes of t h i s study the two b a s i c processes - deoxygenation due to the degradation of discharged organic matter and reoxygenation due to atmospheric r e a e r a t i o n - were the p r i n c i p a l f a c t o r s to be c o n s i d e r e d i n the development of a d i s s o l v e d oxygen p r e d i c t i v e c a p a b i l i t y . Because - 132 - of the complex nature of estuary h y d r a u l i c s which i s c h a r a c t e r i z e d by un- steady, o s c i l l a t o r y water movement due to the i n f l u e n c e of t i d e s , the a p p l i c a t i o n of the b a s i c oxygen balance concepts to the modeling of d i s - solved oxygen i n e s t u a r i e s i s many times more d i f f i c u l t than i n the analagous r i v e r s i t u a t i o n . However, i n s p i t e of t h i s high degree of h y d r a u l i c complexity, mass t r a n s p o r t and water movement can be modeled. In t h i s study two d i f f e r e n t s o l u t i o n methods were u t i l i z e d : a t i d a l l y averaged approach and a t i d a l l y v a r y i n g approach. The t i d a l l y averaged approach by making use of s t e a d y - s t a t e assumptions s i m p l i f i e s the problem of e l i m i n a t i n g the time v a r i a b l e . In essence, the unsteady, estuary f l o w f i e l d i s r e p l a c e d by a steady f r e s h - water flow f i e l d and a t i d a l d i s p e r s i o n component which can i n d i r e c t l y account f o r the e f f e c t s of t i d a l a c t i o n . A l l parameters and v a r i a b l e s by t h i s s o l u t i o n approach are assigned t h e i r mean t i d a l v a l u e s . " The second approach to modeling mass t r a n s p o r t , the t i d a l l y v a r y - i n g approach, does not e l i m i n a t e the time v a r i a b l e . Thus i t attempts to d e s c r i b e " r e a l time" estuary h y d r a u l i c behaviour and can account d i r e c t l y f o r such t i d a l e f f e c t s as cur r e n t r e v e r s a l . The i n c o r p o r a t i o n of the b a s i c d i s s o l v e d oxygen balance formula- t i o n s i n t o each of the two mass t r a n s p o r t models has formed the b a s i s of the two d i s s o l v e d oxygen models used i n t h i s study: the t i d a l l y averaged d i s s o l v e d oxygen model and the t i d a l l y v a r y i n g d i s s o l v e d oxygen model. To some extent the two models are complementary i n t h e i r view of r i v e r / estuary c o n d i t i o n s . The former model a l l o w s an a n a l y s i s to be made of average c o n d i t i o n s over a number of t i d a l c y c l e s whereas the l a t t e r by p r o v i d i n g a grea t e r degree of temporal r e s o l u t i o n a l l o w s an a n a l y s i s to be made of i n t r a - t i d a l r i v e r / e s t u a r y behaviour. 6.1.2 L i m i t a t i o n s of the P r e d i c t i v e C a p a b i l i t i e s . The l i m i t a t i o n s of the d i s s o l v e d oxygen models can be c l a s s i f i e d i n t o three c a t e g o r i e s : s p a t i a l , temporal and c a l i b r a t i o n a l . Of these only the f i r s t a p p l i e s i n a s i m i l a r degree to both the t i d a l l y averaged and t i d a l l y v a r y i n g models. This l i m i t a t i o n a r i s e s from the assumption that a l l parameters and v a r i a b l e s can be-approximated by t h e i r c r o s s - s e c t i o n a l l y averaged v a l u e s . Choosing t h i s one-dimensional assumption which g r e a t l y s i m p l i f i e d the s o l u t i o n s of the mass t r a n s p o r t equations has r e s u l t e d i n the models being cognizant only of v a r i a t i o n along the l e n g t h of the r i v e r / e s t u a r y . The models are unable to d e a l w i t h v a r i a b i l i t y over the r i v e r / e s t u a r y c r o s s - s e c t i o n s and thus are r e s t r i c t e d i n a p p l i c a t i o n to only the main core flow of the main r i v e r channels. Thus the models cannot be a p p l i e d to the a n a l y s i s of l o c a l i z e d problems such as might occur i n the immediate v i c i n i t y of an o u t f a l l or i n the sm a l l s i d e channels and slough areas adjacent to the main r i v e r . A l s o by the one-dimensional assumption waste i n p u t s to the models are "completely mixed" e i t h e r over the c r o s s - s e c t i o n as i s the case i n the t i d a l l y v a r y i n g model or w i t h i n a 5,000 foot segment as i s the case i n the t i d a l l y averaged model. T h i s " i n s t a n t m i x i n g " c o r o l l a r y to the main assumption has as i t s l i m i t a t i o n the f a c t that m i x i n g i s n e i t h e r instantaneous nor n e c e s s a r i l y complete. I t i s estimated [P. Ward, unpublished data] t h a t at l e a s t two t i d a l c y c l e s are r e q u i r e d i n the lower r i v e r / e s t u a r y reaches (with c o n s i d e r a b l y more time being r e q u i r e d i n the upper reaches) f o r mixing to be completed. S t r a t i f i c a t i o n e f f e c t s due to the presence of the s a l t w a t e r wedge may at times i n h i b i t v e r t i c a l m i x i n g , preventing complete mixing i n the v e r t i c a l plane. Another .. s t r a t i f i c a t i o n e f f e c t i s the sometimes s i g n i f i c a n t i n c r e a s e i n f r e s h - water flow v e l o c i t i e s which r e s u l t from the freshwater f l o w i n g out over top of the s a l t w a t e r l a y e r . The presence of the s a l t w a t e r wedge i s not taken i n t o account i n e i t h e r of the models used i n t h i s study. The second c l a s s of model l i m i t a t i o n s are those i n v o l v i n g the degree to which the models are a temporal a b s t r a c t i o n of the r e a l , r i v e r / , e stuary s i t u a t i o n . The t i d a l l y averaged model i s a severe a b s t r a c t i o n i n the sense that i t considers only " s t e a d y - s t a t e " c o n d i t i o n s , a s s i g n i n g a l l parameters and v a r i a b l e s t h e i r t i d a l l y averaged v a l u e s . Although to some extent t h i s , i n e f f e c t , r e p r e sents an i n t e g r a t i o n over a number of t i d a l c y c l e s , the. averaged c o n d i t i o n s have no " r e a l time" meaning. The t i d a l l y v a r y i n g model represents a l e s s e r temporal a b s t r a c t i o n as i t attempts to simulate " r e a l time" c o n d i t i o n s by a s s i g n i n g a l l v a r i a b l e s t h e i r average h o u r l y values. Although t h i s method of s i m u l a t i o n i s the t i d a l l y v a r y i n g model's strong p o i n t , i t i s not without i t s i n h e r e n t weakness. The c h i e f l i m i t a t i o n i s the manner of c a l c u l a t i o n used t o estimate i n i t i a l e f f l u e n t d i l u t i o n r a t e s . During the p e r i o d around s l a c k - water, the method used i s i n a p p r o p r i a t e because i t r e s u l t s i n a d i s c o n - tinuous i n i t i a l d i l u t i o n curve; the i n i t i a l e f f l u e n t d i l u t i o n becoming zero as the t i d a l l y v a r y i n g v e l o c i t y approaches zero. Although c o n s t r a i n t s w i t h i n the model p r o h i b i t the p r e d i c t e d r e s u l t s from ever reaching t h i s extreme c o n d i t i o n , the model p r e d i c t i o n s are nonetheless extremely s e n s i t i v e to the magnitude as w e l l as the t i m i n g of occurence of slackwater v e l o c i t i e s . As the slackwater p e r i o d r e s u l t s i n maximum BOD conc e n t r a t i o n s which i n t u r n u l t i m a t e l y determine maximum DO d e p l e t i o n s i t must be s t r e s s e d that t h i s l i m i t a t i o n w i t h i n the t i d a l l y v a r y i n g model may d r a s t i c a l l y a l t e r the v a l i d i t y of p r e d i c t e d r e s u l t s . F i n a l l y , there i s the o v e r r i d i n g l i m i t a t i o n that the d i s s o l v e d oxygen models cannot p r e s e n t l y be c a l i b r a t e d . Because of the l a c k of any s i g n i f i c a n t d i s s o l v e d oxygen d e p l e t i o n s i n the lower F r a s e r R i v e r / Estuary, t r a d i t i o n a l c a l i b r a t i o n procedures were of no use. Consequently the d i s s o l v e d oxygen response c o e f f i c i e n t s used i n t h i s study were s e l e c t e d s o l e l y from e m p i r i c a l r e l a t i o n s h i p s d e s c r i b e d i n the l i t e r a t u r e . A side from the f a c t that the d i s s o l v e d oxygen c o e f f i c i e n t s may not be ap p r o p r i a t e , a number of other l i m i t a t i o n s of a c a l i b r a t i o n a l nature e x i s t . With regard to the t i d a l l y averaged model, because of the p e c u l i a r nature of s a l i n i t y v a r i a t i o n i n the lower Fraser, i t was not p o s s i b l e to estimate the value of the t i d a l l y averaged d i s p e r s i o n c o e f f i c i e n t (E). As such, values used were chosen on a pu r e l y a r b i t r a r y b a s i s . C o n s i dering the c a l i b r a t i o n a l l i m i t a t i o n s of the t i d a l l y v a r y i n g model, i t has not been p o s s i b l e to v e r i f y hydrodynamic sub-model v e l o c i t y p r e d i c t i o n s . Hence the accuracy of these p r e d i c t i o n s , i n terms of both magnitude and t i m i n g , i s not known. This i s an important l i m i t a t i o n s i n c e v e l o c i t y p r e d i c t i o n s serve as the b a s i s f o r e s t i m a t i n g t i d a l l y v a r y i n g mass t r a n s p o r t . As w e l l , l o n g i t u d i n a l d i s p e r s i o n was neglected i n analyses u s i n g the t i d a l l y v a r y i n g model. This can be considered as a c a l i b r a t i o n a l l i m i t a t i o n s i n c e d i s p e r s i o n can be accounted f o r through use of a non-zero l o n g i t u d i n a l d i s p e r s i o n c o e f f i c i e n t . 137 6.1.3 The Modeling Experience. To t h i s p o i n t i n the d i s c u s s i o n i t may seem that the l i m i t a t i o n s of the models have been over-emphasized. This has been done p u r p o s e f u l l y . The author f e e l s s t r o n g l y t h a t the l i m i - t a t i o n s and weaknesses inherent i n the models must be r e a l i z e d as a necessary p e r l i m i n a r y to o b t a i n i n g a t r u e a p p r e c i a t i o n of the models' c a p a b i l i t i e s . Only by l e a r n i n g the l i m i t a t i o n s can one a p p r e c i a t e the s t r e n g t h of the modeling e x e r c i s e ; i t s o v e r a l l s t r e n g t h being determined by the s t r e n g t h of the weakest assumption. A l l too o f t e n modeling s t u d i e s o v e r s t r e s s the strengths and c a p a b i l i t i e s of the e x e r c i s e w h i l e g l o s s i n g over i t s weaknesses which when uncovered p o i n t out s e r i o u s shortcomings i n methodology and/or i n t e r p r e t a t i o n . Seldom i s any attempt made from w i t h i n the study or from the o u t s i d e to c r i t i c a l l y assess the net r e s u l t and over- a l l u t i l i t y of the modeling e x e r c i s e . Because of the author's concern over the importance of t h i s o f t e n neglected aspect of the modeling exper- i e n c e , the f o l l o w i n g i s included i n t h i s d i s c u s s i o n . In recent years the i d e a of u s i n g mathematical models as an a i d i n the p l a n n i n g and management of r i v e r systems has a t t a i n e d u n i v e r s a l acceptance. At the outset of most planning/management s t u d i e s the q u e s t i o n i s no longer " S h a l l we use a model?" but r a t h e r "Which model(s) s h a l l we use?" Encouraged by those who seek an e a s i e r means of d e a l i n g w i t h the i n c r e a s i n g c o m p l e x i t i e s of water management and spurred on by r a p i d developments i n d i g i t a l computer technology, vast numbers of models of v a r y i n g d i s c i p l i n e s have p r o l i f e r a t e d t e c h n i c a l l i t e r a t u r e . I t Is not un- f a i r to say that the m a j o r i t y e x i s t i n a h i g h l y t h e o r e t i c a l s t a t e , un- 138 t e s t e d i n a p p l i c a t i o n and unproved by use. Of those s t u d i e s which have a p p l i e d water q u a l i t y modeling concepts to the development of a usable p r e d i c t i v e c a p a b i l i t y , very few have been subjected to i n t e n s i v e c r i t i c a l reviews. A r e c e n t l y published case study e n t i t l e d The U n c e r t a i n Search f o r Environmental Q u a l i t y [Ackerman et_ a l . , 1974] has made such a review of the Delaware Estuary Comprehensive Study (DECS), c r i t i c a l l y a n a l y z i n g a number of t e c h n i c a l aspects and c r i t i c i z i n g the water p o l l u t i o n p o l i c y d e c i s i o n s made by the Delaware R i v e r Basin Commission as a v r e s u l t of the DECS f i n d i n g s . In p a r t i c u l a r , the water q u a l i t y modeling s t u d i e s c a r r i e d out by DECS using Thomann's ste a d y - s t a t e BOD-DO model ( s i m i l a r to the t i d a l l y averaged model used i n t h i s i n v e s t i g a t i o n ) came under heavy a t t a c k . Shortcomings were pointed out i n the DECS model study i n i t s f a i l u r e to d e a l adequately, i f at a l l , w i t h u n c e r t a i n t i e s r e g a r d i n g model response c o e f f i c i e n t s , stormwater and t r i b u t a r y l o a d i n g s and b e n t h i c oxygen demand. Ackerman concludes t h a t as a r e s u l t of these inadequacies the DECS study gave m i s l e a d i n g , perhaps f a u l t y , i n f o r m a t i o n on the b e n e f i t s which would be d e r i v e d from a "clean-up" program on the Delaware. He goes on to say that i n s p i t e of the a c c l a i m given DECS, la u d i n g the s o p h i s t i c a t - ed e f f o r t which employed i n n o v a t i v e c o n c e p t i o n a l and i n s t i t u t i o n a l t o o l s , i t was i n the end "unequal to the t a s k " and l e d to "a f a i l u r e i n modern p o l i c y making". The main reason f o r t h i s , according to Ackerman, i s th a t i n t h e i r enthusiasm the DECS s t a f f had f a i l e d to impart a r a t i o n a l sense of p e r s p e c t i v e along w i t h t h e i r f i n d i n g s . In p r e s e n t i n g t h e i r achievements "the research s t a f f emphasized the accuracy of the numbers i t s model 1 3 9 generated", o f f e r i n g an a n a l y s i s that was "conspicuously devoid of cautions (to the d e c i s i o n makers) about the l i m i t a t i o n s of i t s p r e d i c t i o n s " . Thus although the s c i e n t i f i c m e r i t s of the study were undeniable, i t s u t i l i t y as an a i d to d e c i s i o n making was q u e s t i o n a b l e , s p e c i f i c a l l y because of misconceived perceptions regarding the accuracy of the water q u a l i t y model. In t h i s i n v e s t i g a t i o n , because of f o r t u i t o u s circumstances which l e d t o employment w i t h an i n t e r d i s c i p l i n a r y research team, the author has been f o r c e d throughout to view the r e s u l t s of t h i s modeling e x e r c i s e i n l i g h t of t h e i r meaning and adequacy as a i d s to an understanding which could be communicated to persons from d i f f e r e n t d i s c i p l i n e s . T h i s has been f o r t u n a t e i n that i t has r e s u l t e d i n the development of a more balanced sense of p e r s p e c t i v e i n t h i s study than would have otherwise occurred. H o p e f u l l y t h i s sense of p e r s p e c t i v e has been e f f e c t i v e l y com- municated and has r e s u l t e d i n a strengthening of t h i s i n v e s t i g a t i o n . <C O r D A C f D D T V T 7 D / T 7 C T T T A . D V TXT C C r i T V C T l n w r i ? ) ) OTT C n i T T J f p C 6.2.1 Summary: An Improved Knowledge Base. I t can be s t a t e d almost without exception that d i s s o l v e d oxygen l e v e l s i n the lower Fraser R i v e r / E s t u a r y are h i g h , g e n e r a l l y being 90 to 100 percent of s a t u r a t i o n v a l u e s . In combination w i t h the c h a r a c t e r i s t i c a l l y low water tempera- t u r e s , t h i s r e s u l t s i n d i s s o l v e d oxygen con c e n t r a t i o n s of 8 to 12 mg/1 throughout the year; more than enough to support even the most s e n s i t i v e a q u a t i c organisms. I t i s not d i f f i c u l t to a s c e r t a i n why the d i s s o l v e d oxygen resources of the lower Fraser are p r e s e n t l y i n t h e i r h e a l t h y s t a t e . P r i m a r i l y i t i s because, r e l a t i v e to i t s s i z e and d i l u t i o n a l a b i l i t y , the. lower F r a s e r r e c e i v e s very l i t t l e i n the way of discharged organic wastes. T h i s can best be i l l u s t r a t e d by way of example. Consider the Delaware Estuary i n the e a s t e r n United States where there has been s e r i o u s oxygen d e p l e t i o n problems. Average freshwater i n f l o w s there are approximately 11,000 c f s w h i l e the average estimated organic waste discharge i s i n ex- cess of 1,300,000 pounds of BOD per day [DECS, 1968]. Compare that to the lower F r a s e r where average freshwater flows are approximately 93,000 c f s w h i l e the estimated BOD l o a d i s p r e s e n t l y i n the order of 250,000 pounds per day; a s i t u a t i o n where r i v e r flows are on an average a p p r o x i - mately nine times higher and t o t a l waste l o a d i n g s are lower by a f a c t o r of f i v e . In. a d d i t i o n to the c o n s i d e r a b l e d i f f e r e n c e i n the r e l a t i v e magnitude of waste l o a d i n g s , the s i t u a t i o n i n the lower Fraser has the added advantage that the bulk of the t o t a l BOD l o a d i n g i s discharged from the Greater Vancouver area l o c a t e d on the seaward reaches of the r i v e r / e stuary. In the Delaware a l a r g e p o r t i o n of the t o t a l l o a d (at l e a s t 45 percent) i s discharged i n the v i c i n i t y of P h i l a d e l p h i a near the head end of the e s t u a r y , whereas the major p o r t i o n of the t o t a l BOD l o a d (over 80 percent) enters the lower F r a s e r downstream of the Port Mann Bridge w i t h i n 20 m i l e s of the S t r a i t of Georgia. A number of other f a c t o r s p l a y an important r o l e i n the d i s - solved oxygen dynamics of the lower F r a s e r . Assessment made through use of the d i s s o l v e d oxygen models has shown that two i n p a r t i c u l a r are im- portant i n d e f i n i n g the nature of the lower F r a s e r ' s r a t h e r e x t e n s i v e 141 a s s i m i l a t i v e c a p a c i t y . These are the c h a r a c t e r i s t i c a l l y low water temp- er a t u r e s and l a r g e freshwater f l o w s . With regard to the l a r g e r i v e r f l o w s , not only do they a f f o r d c o n s i d e r a b l e d i l u t i o n to e f f l u e n t d i s c h a r g e s , but they a l s o minimize residence times of e f f l u e n t p a r c e l s i n the r i v e r / e s tuary. In s p i t e of the r e t a r d i n g i n f l u e n c e of t i d a l a c t i o n , a major p o r t i o n of the oxygen demand even f o r waste discharges i n the upper reaches of the r i v e r i s f l u s h e d out of the channelized s e c t i o n s of the r i v e r / estuary to be exerted i n the S t r a i t of Georgia. The low water temperatures, i n a d d i t i o n to p r o v i d i n g high d i s s o l v e d oxygen s a t u r a t i o n c o n c e n t r a t i o n s , a l s o reduce the e f f e c t i v e r a t e s of deoxygenation which again r e s u l t s i n a s m a l l e r p o r t i o n of the t o t a l oxygen demand being s a t i s f i e d w i t h i n the r i v e r / e s t u a r y . In terms of seasonal v a r i a t i o n a complementary p a t t e r n e x i s t s i n the lower F r a s e r t y p i c a l of n o r t h l a t i t u d e s where low f l o w s occur i n the winter months when water temperatures are a l s o low. Thus during the p e r i o d when t i d a l e f f e c t s are most pronounced and r e s i d e n c e times are maximum, deoxygenation r a t e s are low and s a t u r a t i o n l e v e l s h i g h . In the summer months the s i t u a t i o n i s reversed w i t h high flow c o u n t e r a c t - i n g the e f f e c t of higher water temperatures on s a t u r a t i o n c o n c e n t r a t i o n s and deoxygenation r a t e s . A n a l y s i s made usin g the oxygen models to simu- l a t e c o n d i t i o n s f o r a l l months of the year has shown that the c r i t i c a l p e r i o d f o r d i s s o l v e d oxygen i n the lower F r a s e r i s i n l a t e summer. A l - though maximum DO d e p l e t i o n s would t h e o r e t i c a l l y occur during the winter months, the predominating i n f l u e n c e of water temperature e f E e c t s on s a t u r a t i o n c o n c e n t r a t i o n r e s u l t s i n the lowest DO l e v e l s o c c u r r i n g i n August and September. Another aspect of lower F r a s e r d i s s o l v e d oxygen dynamics brought to l i g h t i n t h i s i n v e s t i g a t i o n i s the f a c t that t i d a l a c t i o n can cause a t i d a l l y v a r y i n g d i s s o l v e d oxygen response. This s i t u a t i o n a r i s e s as a r e s u l t of the o s c i l l a t o r y water movement i n the r i v e r / e s t u a r y which produces a t i d a l l y v a r y i n g i n i t i a l e f f f l u e n t c o n c e n t r a t i o n p r o f i l e , c h a r a c t e r i z e d by e f f l u e n t spikes formed during p e r i o d s of slackwater. P r e l i m i n a r y i n d i c a t i o n s are that these c o n c e n t r a t i o n peaks co u l d be s i x to ten times higher than the t i d a l l y averaged e f f l u e n t c o n c e n t r a t i o n s . Although i t has not been p o s s i b l e to determine the exact nature of i n t r a - t i d a l d i s s o l v e d oxygen response, cur s o r y i n v e s t i g a t i o n has shown that peak t i d a l l y v a r y i n g DO. d e f i c i t s could be three to f i v e times g r e a t e r than t i d a l l y averaged DO d e f i c i t s . In summary, the d i s s o l v e d oxygen models which were developed i n t h i s study have shown to be u s e f u l i n h e l p i n g to d e f i n e the nature of d i s s o l v e d oxygen dynamics i n the lower Fraser R i v e r / E s t u a r y . T h e i r c h i e f u t i l i t y has been as an a i d to improving .the understanding and f u r t h e r i n g 6.2.2 Future C o n d i t i o n s . " Since the d i s s o l v e d oxygen models c o u l not be c a l i b r a t e d , a great d e a l of u n c e r t a i n t y e x i s t s r e g a r d i n g the accura- c i e s of t h e i r p r e d i c t i o n s . In order to d e a l w i t h t h i s u n c e r t a i n t y and to a l l e v i a t e some of the doubt (the author's included) surrounding the v a l i d i t y of p r e d i c t i o n s , t h i s study has made use only of very c a u t i o u s analyses choosing the most c o n s e r v a t i v e estimates. As w e l l , t h i s study has d e l i b e r a t e l y r e f r a i n e d from the u s u a l p r a c t i c e of making assessments of f u t u r e c o n d i t i o n s which are based on s p e c i f i c s e t s of p o s s i b l e f u t u r e 143 waste l o a d i n g p a t t e r n s . Instead, emphasis was placed on improving the extent and depth of the knowledge base. Assessment of f u t u r e c o n d i t i o n s has been made i n d i r e c t l y by o u t l i n i n g i n an i l l u s t r a t i v e manner the c o n s i d - e r a b l e magnitude of the a s s i m i l a t i v e c a p a c i t y of the lower F r a s e r . Stated simply, t h i s i n v e s t i g a t i o n has shown that i n the conceivable f u t u r e there w i l l not be any s i g n i f i c a n t d e t e r i o r a t i o n of water q u a l i t y i n the main stem, lower Fraser R i v e r / E s t u a r y , at l e a s t i n s o f a r as concerns average l e v e l s of d i s s o l v e d oxygen. The nature of d i s s o l v e d oxygen dynamics i n the lower F r a s e r , coupled w i t h present c o n s e r v a t i v e p o l l u t i o n c o n t r o l p o l i c y , should be s u f f i c i e n t to guarantee that d i s s o l v e d oxygen concen- t r a t i o n s are maintained at t h e i r present high l e v e l s . P o l l u t i o n c o n t r o l requirements as they a f f e c t d i s s o l v e d oxygen i n the lower F r a s e r may, i n f a c t , be more s t r i n g e n t than they need be. However t h i s i s indeed a sma l l p r i c e to pay f o r the adequate p r o t e c t i o n and maintenance of a very v a l u a b l e n a t u r a l resource. 6.2.3 U n c e r t a i n t i e s . H o p e f u l l y the r e s u l t s of t h i s research i n v e s t i g a t i o n * lias c l e a r e d up a number of u n c e r t a i n t i e s t h a t p r e v a i l e d at the time of i t s conception. However, upon i t s completion there remain a number of areas of concern which have e i t h e r not been covered completely or adequately by t h i s i n v e s t i g a t i o n , or have a r i s e n out of i t . Some o f these w i l l now be b r i e f l y d i s c u s s e d . The main area of u n c e r t a i n t y i n v o l v e s the f a c t that the d i s s o l v e d oxygen models used i n t h i s i n v e s t i g a t i o n were not c a l i b r a t e d . Hence, a l l p r e d i c t i o n s must be viewed w i t h c a u t i o n and a l l c o n c l u s i o n s must be regarded as being t e n t a t i v e . With respect to the t i d a l l y averaged model, i t s mech- a n i c s appear to be sound as evidenced by i t s manner of response during the s e n s i t i v i t y a n a l y s i s . Uncert a i n t i e s w i t h t h i s model l i e i n the values of the c o e f f i c i e n t s used. These u n c e r t a i n t i e s could be a l l e v i a t e d by a more exact determination of model c o e f f i c i e n t s , t h e o r e t i c a l l y p o s s i b l e but prac t i c a l l y , very d i f f i c u l t to accomplish. With the t i d a l l y v a r y i n g model, on the other hand, i t was not p o s s i b l e to f u l l y i n v e s t i g a t e the s e n s i t i v i t i e s of i t s response and, more i m p o r t a n t l y , there was concern expressed that some of the mechanics o f s o l u t i o n method may not be e n t i r e l y a p p r o p r i a t e . I t was beyond the scope of t h i s i n v e s t i g a t i o n to become i n v o l v e d w i t h m o d i f i c a t i o n s to t h i s very s o p h i s t i c a t e d model and, as a r e s u l t , i t was pr-obably not u t i l i z e d to i t s f u l l p o t e n t i a l . Consequently, a great d e a l of u n c e r t a i n t y e x i s t s r e g a r d - i n g the t i d a l l y v a r y i n g aspects of lower F r a s e r d i s s o l v e d oxygen dynamics. Some of t h i s u n c e r t a i n t y could be c l e a r e d up by a f u t u r e study, more s p e c i f i c than t h i s one, that would o b t a i n b e t t e r estimates of some parameters, f o r example, l o n g i t u d i n a l d i s p e r s i o n , or would t e s t the model response u s i n g f i e l d i n v e s t i g a t i o n s . Then i t would be pos- s i b l e to more f u l l y assess the s i g n i f i c a n c e of i n t r a - t i d a l d i s s o l v e d oxygen response as w e l l as the e f f e c t s of short term s i t u a t i o n s such as stormwater discharges or combined sewer overflows which may, sooner or l a t e r , become important. One other major area of concern should be mentioned and th a t i s the water q u a l i t y i n bays, sloughs and other backwater areas i n the lower F r a s e r . This q u e s t i o n has not been addressed i n t h i s research as the models were r e s t r i c t e d i n t h e i r a p p l i c a t i o n to the main core f l o w . However, there i s evidence to i n d i c a t e t h a t , i n some cases, s i t u a t i o n s i n v o l v i n g s i g n i f i c a n t oxygen d e p l e t i o n s already e x i s t [Westwater, un- published d a t a ] . What w i l l be the e f f e c t s on these areas, some of which are very s e n s i t i v e , of l a r g e discharges that may have no s i g n i f i c a n t e f f e c t on main stem d i s s o l v e d oxygen l e v e l s ? I n summary, a con s i d e r a b l e u n c e r t a i n t y e x i s t s , upon c o n c l u s i o n of t h i s i n v e s t i g a t i o n , i n v o l v i n g a number of aspects of the d i s s o l v e d oxygen resources of the lower Fraser R i v e r / E s t u a r y . Some of these have been b r i e f l y discussed and deserve f u t u r e study. CHAPTER 7 CONCLUSIONS The p r i n c i p a l conclusions which emerge from t h i s i n v e s t i g a t i o n are l i s t e d summarily, as f o l l o w s . F i r s t l y , w i t h regard to the d i s s o l v e d oxygen models, i t can be concluded t h a t : (1) V e r i f i c a t i o n of the models i s not p r e s e n t l y p o s s i b l e because of the absence of any s i g n i f i c a n t d i s s o l v e d oxygen d e p l e t i o n s which has precluded model c a l i b r a t i o n ; (2) In a n . a n a l y s i s of the s e n s i t i v i t i e s of the t i d a l l y averaged model i t s manner of response was found to be reasonable and " w e l l behaved" over the expected range of input parameter v a r i a t i o n . Therefore, i t i s considered to be r e l i a b l e i n i t s p r e d i c t i o n s , i n s p i t e of the f a c t that i t could not be v e r i f i e d ; (3)* There are r e s e r v a t i o n s about the v a l i d i t y of the t i d a l l y v a r y i n g model i n t h i s a p p l i c a t i o n as i t s s e n s i t i v i t i e s could not be f u l l y t e s t e d and, i n a number of r e s p e c t s , i t i s considered to be i n a p p r o p r i a t e ; (4) The t i d a l l y averaged model o f f e r s a number of d i s t i n c t advantages over the t i d a l l y v a r y i n g model i n terms of the s i m p l i c i t y of i t s approach, the s t r a i g h t f o r w a r d n e s s of i t s development and the f l e x i b i l i t y of i t s a p p l i c a t i o n ; (5) The u t i l i t y of the h i g h l y s o p h i s t i c a t e d t i d a l l y v a r y i n g model i s s e v e r e l y r e s t r i c t e d because,as a r e s u l t o f i t s complex, multi-model s o l u t i o n format, i t i s o p e r a t i o n a l l y , both cumbersome and c o s t l y ; (6) O'Connor's s t e a d y - s t a t e , continuous s o l u t i o n model could not be a p p l i e d i n t h i s i n v e s t i g a t i o n due to computing problems which r e s u l t e d from the p a r t i c u l a r form of c r o s s - s e c t i o n a l geometry v a r i a t i o n that c h a r a c t e r i z e s the lower Fraser R i v e r / E s t u a r y ; (7) The l i m i t a t i o n s of model s t u d i e s must be s t r e s s e d along w i t h t h e i r c a p a b i l i t i e s so that the modeling experience i s e f f e c t i v e l y communicated i n the l i g h t of a proper p e r s p e c t i v e . - 146 - 147 Secondly, as a p p l i e s to the lower Fraser R i v e r / E s t u a r y , through use of the d i s s o l v e d oxygen models, i t can be concluded t h a t : (1) An improved general understanding of the nature of d i s s o l v e d oxygen dynamics i n the lower Fraser R i v e r / Estuary has been achieved; (2) An a p p r e c i a t i o n of the consi d e r a b l e magnitude of the lower F r a s e r ' s a s s i m i l a t i v e c a p a c i t y has been gained, although i t s accurate q u a n t i f i c a t i o n i s not p r e s e n t l y p o s s i b l e because the d i s s o l v e d oxygen models cannot be v e r i f i e d ; (3) The " c r i t i c a l p e r i o d " f o r d i s s o l v e d oxygen i n the lower Fraser i s l i k e l y to be i n l a t e summer; (4) T i d a l l y averaged d i s s o l v e d oxygen l e v e l s i n the main channels of the lower Fraser R i v e r / E s t u a r y w i l l not be s e r i o u s l y impaired i n the conceivable f u t u r e . In f a c t , e x i s t i n g p o l l u t i o n c o n t r o l requirements, as they p e r t a i n to d i s s o l v e d oxygen, may be more s t r i n g e n t than needs be; (5) As BOD loadin g s to the lower Fraser i n c r e a s e , there w i l l be b r i e f periods w i t h i n the t i d a l c y c l e , p a r t i c - u l a r l y d u r i ng the low flow p e r i o d s , when d i s s o l v e d oxygen con c e n t r a t i o n s w i l l be reduced below t i d a l l y averaged l e v e l s . However, i n t h i s i n v e s t i g a t i o n , the s i g n i f i c a n c e of t h i s e f f e c t could not be f u l l y assessed. REFERENCES Ages, A. B. and Hughes, G. C. [1975], Salinity and Temperature Measurements in the lower Fraser River, 1966-1968, 1970-1973, Unpublished Manuscript, P a c i f i c Marine Science Report No. 75-2, I n s t i t u t e of Ocean Sciences, P a t r i c i a Bay, V i c t o r i a . Baines, W. D. [1952]. 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