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Lower Fraser River/Estuary dissolved oxygen dynamics Koch, Frederic A. 1976

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LOWER FRASER RIVER/ESTUARY DISSOLVED OXYGEN DYNAMICS  by  FREDERIC A. KOCH B . A . S c , 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 , 1970  A THESIS SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF APPLIED SCIENCE  i n t h e Department of C i v i l Engineering  We a c c e p t t h i s t h e s i s as c o n f o r m i n g t o t h e required standard  THE UNIVERSITY OF BRITISH COLUMBIA September, 1976 @  F r e d e r i c A. Koch  In  presenting  an  advanced  the I  Library  further  for  degree shall  agree  scholarly  by  his  of  this  written  thesis  in  at  University  the  make  that  it  thesis  purposes  for  freely  may  be  It  fulfilment of of  British  available for  by  the  understood  gain  for  extensive  granted  is  financial  shall  not  of  University  CZJVIL of  & A J C S / A j g g r i g / A j <S  British  Se^pT-  27,  /9?G  Columbia  the  reference  Head  be  requirements  Columbia,  copying  that  permission.  2075 W e s b r o o k P l a c e V a n c o u v e r , Canada V6T 1W5  Date  partial  permission  representatives.  Department  The  this  of  copying  agree  and  of my  I  this  that  study. thesis  Department or  for  or  publication  allowed without  my  ABSTRACT  This  i n v e s t i g a t i o n i n t o t h e n a t u r e of d i s s o l v e d oxygen dynamics  i n t h e lower F r a s e r R i v e r / E s t u a r y  has made use of t h e a p p l i c a t i o n of  two m a t h e m a t i c a l 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 a n a l y z e s t h e i n t e r - t i d a l b e h a v i o u r of t h e r i v e r / estuary, The  g i v i n g e s t i m a t e s of s t e a d y - s t a t e  d i s s o l v e d oxygen r e s p o n s e .  t i d a l l y v a r y i n g model, on t h e o t h e r hand, a n a l y z e s c o n d i t i o n s  i n t h e 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 " , b e h a v i o u r of t h e r i v e r / e s t u a r y .  intra-tidal  B o t h d i s s o l v e d oxygen models a r e o n e -  d i m e n s i o n a l and make t h e a s s u m p t i o n t h a t t h e o n l y o p e r a t i v e oxygen s o u r c e / s i n k discharged organics The  with-  dissolved  p r o c e s s e s a r e d e o x y g e n a t i o n due t o t h e o x i d a t i o n of and r e o x y g e n a t i o n due t o a t m o s p h e r i c  reaeration.  p r e s e n t h i g h d i s s o l v e d oxygen l e v e l s i n t h e lower F r a s e r  c l u d e t h e a c c u r a t e c a l i b r a t i o n o f t h e d i s s o l v e d oxygen models.  pre-  How-  e v e r , 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 p r e s e n t e d , i n l i e u o f v e r i f i c a t i o n , t o document model r e s p o n s e s . Dissolved  oxygen p r e d i c t i o n s made u s i n g  t h e u n v e r i f i e d models i n -  d i c a t e t h a t t h e a s s i m i l a t i v e c a p a c i t y o f t h e lower F r a s e r Estuary i s considerable,  River/  m a i n l y because o f t h e l a r g e f r e s h w a t e r i n -  flows which a f f o r d extensive  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 t o be i n l a t e summer when t h e combined e f f e c t s o f water t e m p e r a t u r e and f r e s h w a t e r f l o w s r e s u l t i n t h e l o w e s t d i s s o l v e d oxygen l e v e l s .  F u t u r e water q u a l i t y impairment i n t h e main  ii  c h a n n e l s o f the lower F r a s e r , a t 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 c o n c e r n e d , i s c o n s i d e r e d by t h i s s t u d y to be u n l i k e l y , p r o v i d i n g 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 a r e adhered t o .  that  TABLE OF CONTENTS  PAGE LIST OF TABLES  v i  LIST OF FIGURES  v i i  ACKNOWLEDGEMENTS  ix  CHAPTER INTRODUCTION 1.  THE FRASER RIVER 1.1 1.2 1.3 1.4  2.  8  THE FRASER RIVER FRASER RIVER RUN-OFF CHARACTERISTICS FRASER RIVER WATER TEMPERATURE CHARACTERISTICS THE LOWER FRASER RIVER 1.4.1 Tidal Effects 1.4.2 S a l i n i t y I n t r u s i o n  8 12 15 20 22 26  DISSOLVED OXYGEN DYNAMICS, A REVIEW  28  2.1 2.2 2.3 2.4  28 31 34 35 38 42 43 46  2.5 2.6 2.7  3.  ' 1  DISSOLVED OXYGEN OXYGEN DEMANDING WASTES THE OXYGEN BALANCE DEOXYGENATION • 2.4.1 Carbonaceous O x i d a t i o n 2.4.2 N i t r i f i c a t i o n REAERATION OTHER SOURCES AND SINKS OF OXYGEN THE STREETERr-PHELPS FORMULATION OF - THE OXYGEN BALANCE IN A STREAM  47  DISSOLVED OXYGEN MODELS  50  3.1 3.2 3.3 3.4  50 52 53 55 58 61 66 67 70  3.5  STREAM AND RIVER MODELS ESTUARY MODELS THE ONE-DIMENSIONAL MASS TRANSPORT EQUATIONTHE STEADY STATE SOLUTIONS TO THE MASS TRANSPORT EQUATION 3.4.1 The C o n t i n u o u s S o l u t i o n Approach 3.4.2 The F i n i t e S e c t i o n Approach TIDALLY VARYING SOLUTIONS 3.5.1 The Hydrodynamic Sub-Model 3.5.2 The T i d a l l y V a r y i n g Model  iv  V  CHAPTER  PAGE  4.  APPLICATION OF DISSOLVED OXYGEN MODELS TO THE FRASER RIVER/ESTUARY 4.1 THE MODEL RIVER/ESTUARY 4.2 IMPLEMENTATION OF THE MODELS 4.2.1 T i d a l l y Averaged Models 4.2.2 The T i d a l l y V a r y i n g M o d e l 4.3 MODEL ASSUMPTIONS 4.3.1 G e n e r a l Assumptions 4.3.2 D i s s o l v e d Oxygen A s s u m p t i o n s 4.4 MODEL COEFFICIENTS 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 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 4.5 WASTE LOADINGS 4.5.1 P r e s e n t Waste Loads 4.5.2 P o s s i b l e F u t u r e Waste Loads 4.6 MODEL OUTPUT  5.  DISSOLVED OXYGEN MODEL RESULTS 5.1 TIDALLY AVERAGED DISSOLVED OXYGEN MODEL RESPONSE 5.1.1 E f f e c t o f F r e s h w a t e r I n f l o w V a r i a t i o n 5.1.2 E f f e c t o f Waste L o a d i n g V a r i a t i o n 5.1.3 E f f e c t o f 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 5.1.4 E f f e c t o f D e o x y g e n a t i o n Rate C o e f f i c i e n t V a r i a t i o n 5.1.5 E f f e c t o f R e a e r a t i o n Rate C o e f f i c i e n t V a r i a t i o n 5.1.6 E f f e c t o f Water Temperature V a r i a t i o n 5.1.7 Summary 5.2 TIDALLY VARYING DISSOLVED OXYGEN MODEL RESPONSE 5.2.1 Hydrodynamic Sub-Model Output 5.2.2 T i d a l l y V a r y i n g 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 5.2.3 I n t r a - T i d a l D i s s o l v e d Oxygen Response 5.2.4 V a l i d i t y o f 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 5.2.5 Summary • J  X\M  ru.trLu u i j  \JC I J V J W E J I V  ciutjucv  rviviiix/ lioiurvjxi  njjmiijnixvE.  74 74 79 79 82 84 84 86 87 87 89 90 90 91 91 95 95 96 99 99 102 102 102 106 106 108 111 113 117 122 ±<r.j  CAPACITY 6.  SUMMARY AND DISCUSSION 6.1 DISSOLVED OXYGEN MODELS 6.1.1 Summary 6.1.2 L i m i t a t i o n s o f t h e P r e d i c t i v e C a p a b i l i t i e s 6.1.3 The M o d e l i n g E x p e r i e n c e 6.2 FRASER RIVER/ESTUARY DISSOLVED OXYGEN RESOURCES 6.2.1 Summary: An Improved Knowledge Base 6.2.2 F u t u r e C o n d i t i o n s 6.2.3 U n c e r t a i n t i e s  132 132 132 134 137 139 139 142 143  7.  CONCLUSIONS  146  LIST OF TABLES  TABLE  PAGE  2.1  C l a s s i f i c a t i o n o f R i v e r Q u a l i t y Based on D i s s o l v e d Oxygen C o n t e n t  29  2.2  R o y a l Commission C l a s s i f i c a t i o n o f R i v e r s  32  2.3  Average BOD Rate C o n s t a n t s @ 20° C  41  2.4  Summary o f C o n s t a n t s f o r t h e R e a e r a t i o n  4.1  Waste L o a d i n g s t o t h e M a i n Arm/Main Stem, Lower Fraser River  92  4.2  Waste L o a d i n g s t o t h e N o r t h Arm, Lower F r a s e r R i v e r  93  5.1  P a r a m e t e r s 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 Analysis  96  5.2  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  vi  Equation  Used i n A n a l y s i s  45  128  LIST OF FIGURES FIGURE  PAGE  1.1  Fraser River Drainage Basin  1.2  Average Annual Hydrograph f o r the Fraser River at Hope (1930-1960)  13  1.3  D i s t r i b u t i o n of Mean Monthly Flows f o r the Fraser River at Hope (1913-1970)  14  1.4  D i s t r i b u t i o n of 7-Day Low Flows f o r the Fraser River at Hope  16  1.5  D i s t r i b u t i o n of Minimum Yearly Flows f o r the Fraser River at Hope  17  1.6  D i s t r i b u t i o n of Mean Monthly Fraser River Water Temperatures, January to J u l y  , 1 8  1.7  D i s t r i b u t i o n of Mean Monthly Fraser River Water Temperatures, August to December  19  1.8  The Lower Fraser River  21  1.9  T y p i c a l Tides at Point Atkinson  23  1.10  Discharge and V e l o c i t y V a r i a t i o n at Steveston Due to T i d a l Influence  25  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 Model River/Estuary  75  4.2  V a r i a t i o n of Cross-Sectional Parameters i n the Main Arm/Main Stem  77  4.3  V a r i a t i o n of Cross-Sectional Parameters i n the North Arm and P i t t River  78  4.4  The M a t r i x [A] of the T i d a l l y Averaged Model  81  vii  9  LIST OF FIGURES FIGURE  PAGE  5.1  E f f e c t o f F r e s h w a t e r I n f l o w on Model Response  5.2  E f f e c t o f Waste L o a d i n g on M o d e l Response  100  5.3  E f f e c t o f D i s p e r s i o n on Model Response  101  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 Model Response  103  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 Model Response  104  5.6  E f f e c t o f Temperature on Model Response  105  5.7  Predictions  109  5.8  P r e d i c t e d Trace of P a r t i c l e s Released a t Various Times from S t a t i o n 40  110  5.9  Predicted I n i t i a l Effluent 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: S t a t i o n 20  114  5.11  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: Station 2 .  115  5.12  D i s p e r s i o n o f a S l u g Load  118  5.13  A 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 Model  120  - J  n  etna £>a.LO L l  of T i d a l l y Varying V e l o c i t y  •  xC  97  xx—3 — 1  nuuci  5.14  Space-Time 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 10 Year R e t u r n P e r i o d Low Flows and H i g h Temperatures  126  5.15  Space-Time 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 Year R e t u r n P e r i o d Low Flows and H i g h Temperatures  127  ACKNOWLEDGEMENTS  The a u t h o r would l i k e t o e x p r e s s h i s a p p r e c i a t i o n t o t h e f o l l o w i n g p e r s o n s , each o f whom p l a y e d a p a r t i n t h e d e v e l o p ment o f t h i s t h e s i s .  D r . W.K. Oldham i s t o be thanked f o r  t h e p a t i e n t , r e a s s u r i n g s u p p o r t he so k i n d l y o f f e r e d d u r i n g t h e l e n g t h y p e r i o d r e q u i r e d t o complete  t h i s study.  Special  thanks go t o D r . C.S. J o y f o r t h e u s e o f t h e hydrodynamic and water q u a l i t y models w h i c h were d e v e l o p e d d u r i n g h i s r e c e n t 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 v e n a s s i s t a n c e w h i c h c o v e r e d c o u n t l e s s hours p l e a s a n t l y s p e n t i n m o d e l - r e l a t e d discussions. In a d d i t i o n , the author i s deeply indebted t o the Westwater R e s e a r c h C e n t r e w i t h whom he was g a i n f u l l y employed d u r i n g p a r t s of t h i s study.  S p e c i a l thanks a r e extended  t h e r e t o t h e 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 D r . K . J . Hall. F i n a l l y , t h e a u t h o r g r a t e f u l l y acknowledges t h e e x p e r t a s s i s t a n c e p r o v i d e d by Mr. I t s u o Y e s a k i i n t h e d r a f t i n g o f t h e s i s d i a g r a m s , by Mr. Ken P e t e r s o n i n e d i t o r i a l s u g g e s t i o n s , and b y M i s s M a r g a r e t S c h e r f who f a i t h f u l l y t y p e d and p r o o f read the t h e s i s manuscript.  F i n a n c i a l support d u r i n g the e a r l y stages o f t h i s r e s e a r c h was  p r o v i d e d b y t h e Water Resources  Environment  Canada.  ix  Support Program o f  INTRODUCTION  "no man s t a n d s b e s i d e t h e F r a s e r R i v e r w i t h o u t s e n s i n g the p r e c a r i o u s h o l d o f h i s s p e c i e s upon t h e e a r t h . . . h e r e i t i s t h r u s t upon y o u 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 trench, bored out of s o l i d rock through u n i m a g i n a b l e time by t h e s c o u r o f brown w a t e r , t h e long h i s t o r y o f l i f e l e s s matter, the p i t i f u l l y b r i e f r e c o r d o f l i f e , t h e mere moment o f man's e x i s t e n c e , a r e s u d d e n l y l e g i b l e . And h e r e , i n t h i s p r o d i g a l w a s t e o f e n e r g y , n a t u r e ' s war on a l l . . . i s n a k e d , b r u t a l , and ceaseless." So b e g i n s B r u c e H u t c h i n s o n ' s book, The F r a s e r , d e s c r i b i n g t h e F r a s e r R i v e r , i t s i m p a c t on man, and i t s e f f e c t on h i s e n v i r o n m e n t . continues  He  t o expound t h e i m p o r t a n c e o f t h e r i v e r as "one o f t h e b a s i c  p o l i t i c a l and economic f a c t s o f A m e r i c a . . . l i t t l e u n d e r s t o o d b y governments and seldom mentioned i n h i s t o r y b o o k s " . B e i n g m i n d f u l o f t h e f a c t t h a t t h e two d e c a d e - o l d d e s c r i p t i o n i s an o v e r 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 n o t l e s s e n t h e i m p o r t a n c e o f t h e F r a s e r R i v e r and t h e r o l e t h a t i t h a s p l a y e d i n B r i t i s h C o l u m b i a , i t s h i s t o r i c a l , s o c i a l and economic d e v e l o p m e n t .  Rail  r o u t e s a l o n g t h e F r a s e r passage t h r o u g h t h e f o r m i d a b l e C o a s t r a n g e c o m p l e t e d around t h e t u r n o f t h e c e n t u r y t i e d B r i t i s h C o l u m b i a i n t o t h e r e s t o f t h e n a t i o n and u l t i m a t e l y l e d t o t h e development o f t h e p o r t c i t y o f V a n c o u v e r , the main p o r t and u r b a n c e n t r e on t h e west c o a s t .  A t h i r d r a i l route following  the upper l e n g t h s o f t h e F r a s e r c o r r i d o r c o n n e c t s Vancouver t o t h e n o r t h e r n p a r t s o f the province.  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 o v e r t h e e n t i r e n a t i o n and t h e  -  1 -  2  t h i r d out to the h i n t e r l a n d of the p r o v i n c e .  I t i s i r o n i c to see that the  development o f t h e u r b a n c e n t r e s and i n d u s t r y i n i t i a t e d through u s e o f t h e 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 t h e p o t e n t i a l t o d e s t r o y same r i v e r through  that  t h e i r u s e o f i t as a s i n k f o r t h e i r w a s t e s .  Domestic w a s t e s from most o f 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 e x c e s s o f one m i l l i o n a r e d i s c h a r g e d i n t o the l o w e r  Fraser  R i v e r and i t s e s t u a r y , as a r e w a s t e s from many o t h e r s m a l l e r u r b a n c e n t r e s s c a t t e r e d t h r o u g h o u t t h e lower F r a s e r V a l l e y .  I n combined t o t a l , t h e l o w e r  F r a s e r r e c e i v e s t h e d o m e s t i c w a s t e s o f 1,100,000 p e r s o n s , w h i c h about 50 p e r c e n t o f t h e p o p u l a t i o n o f B r i t i s h C o l u m b i a .  represents  I n a d d i t i o n t o the  d o m e s t i c waste i n p u t s , l a r g e q u a n t i t i e s o f i n d u s t r i a l w a s t e w a t e r s e n t e r t h e 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 t h e r i v e r f o r e s h o r e w h i c h , 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. t i o n i n the lower mainland, a s s o c i a t e d expansion to continue.  R a p i d growth o f p o p u l a -  w h i c h has o c c u r r e d i n r e c e n t y e a r s , a l o n g w i t h  i n i n d u s t r i a l and c o m m e r c i a l development i s e x p e c t e d  P r o j e c t i o n s have  been made, i n d i c a t i n g t h a t by t h e y e a r 2000,  t h e l o w e r m a i n l a n d p o p u l a t i o n w i l l be 2,400,000 [LMRPB, 1968] w i t h t h e 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.  I n r e c e n t y e a r s , p o l l u t i o n i n t h e l o w e r F r a s e r R i v e r h a s been an i s s u e of p a r t i c u l a r concern.  Among o t h e r r e a s o n s w h i c h i n c l u d e d t h e c o n -  temporary e t h i c o f " e n v i r o n m e n t a l  awareness", p o l l u t i o n h a s been a p a r t i c u -  l a r c o n c e r n because o f t h e t h r e a t posed by t h e d e g r a d a t i o n o f w a t e r q u a l i t y to t h e , a s y e t , i n t a c t F r a s e r R i v e r salmon f i s h e r y .  This unique,  natural  r e s o u r c e , w h i c h 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 , h a s been estimated  t o have an a n n u a l v a l u e i n t h e o r d e r o f $75 m i l l i o n  [Fisheries  3  Service,  1971].  D e t e r i o r a t i o n o f w a t e r q u a l i t y caused by such t h i n g s as s o l v e d oxygen d e p l e t i o n due and  t o the a s s i m i l a t i o n o f o r g a n i c waste  dis-  discharges  the t o x i c o l o g i c a l e f f e c t s o f t o x i c d i s c h a r g e s has s e r i o u s i m p l i c a t i o n s  n o t o n l y w i t h r e s p e c t t o the salmon f i s h e r y b u t a l s o w i t h r e s p e c t to o t h e r uses o f of  the r i v e r w h i c h may  be i m p a i r e d 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  the g e n e i a l c o n c e r n o v e r w a t e r q u a l i t y i n the l o w e r 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 q u a l i t y c o n d i t i o n s and  water  the f o r m u l a t i o n o f w a t e r 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 w o r t h 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 o f adopted p r o v i n c i a l government p o l i c y r e g a r d i n g 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 b e l o w the town o f Hope [PCB, was  1968].  The  primary  o b j e c t i v e of t h i s p o l i c y  " t h e maintenance o f the lower F r a s e r R i v e r as a m u l t i - p u r p o s e  source  f o r the p e o p l e o f the p r o v i n c e  t h i s o b j e c t i v e was  "to maintain  f o r a l l time".  water r e -  More s p e c i f i c a l l y ,  the r i v e r f r e e of h a r m f u l p o l l u t i o n  t o x i c s u b s t a n c e s i n a r e a s where the r i v e r i s not so  and  polluted...and...to  b r i n g about an improvement i n the s t a t e o f the r i v e r i n a r e a s 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 r e p o r t [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, t h a t d i s s o l v e d oxygen l e v e l s i n t h e main stem F r a s e r were h i g h and s t r e a m i n terms of BOD" high...and...continues  thus the F r a s e r c o u l d be r e g a r d e d  but  that b a c t e r i a l contamination  t o i n c r e a s e i n some a r e a s " .  was  as a " c l e a n "undesirably  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 w a s t e w a t e r was  not  sufficient  4  " t o a c c e p t w i t h o u t danger o f i m p a i r m e n t t h e w a s t e s o f t h e f o r e s e e a b l e p o p u l a t i o n and a t t e n d a n t  valley  i n d u s t r i e s " and t o 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 c o n t a m i n a t i o n " ,  the report  recommended as a g e n e r a l r u l e t h a t " a l l sewage d i s c h a r g e s  t o the lower  R i v e r should f i r s t r e c e i v e primary  treatment  mendation was, i n l a r g e p a r t , a c c e p t e d  and c h l o r i n a t i o n " .  Fraser  T h i s recom-  by t h e 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 r e q u i r e m e n t i n i t s p o l i c y s t a t e m e n t [PCB, 1968] t o f u l f i l l t h e g e n e r a l o b j e c t i v e s f o r t h e lower  Fraser.  The r e s u l t s o f more r e c e n t r e s e a r c h i n v e s t i g a t i o n s i n t o w a t e r q u a l i t y i n t h e lower F r a s e r  [BCRC, 1971; B e n e d i c t 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 t o h a v i n g more c o m p l e t e l y  d e f i n e d the n a t u r e o f the  w a t e r 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 , c o n f i r m e d  the f i n d i n g s of the  G o l d i e r e p o r t w i t h r e g a r d t o t h e 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 c o n tamination.  I t i s t h e former w a t e r q u a l i t y p a r a m e t e r t o w h i c h 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 t h e r e s e a r c h d e s c r i b e d i n t h i s t h e s i s were: ( i ) t o i n v e s t i g a t e t h e mechanics o f d i s s o l v e d oxygen dynamics i n waterways; ( i i ) t o a p p l y t h e s e c o n c e p t s t o t h e development o f 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 c o n c e n t r a t i o n s i n t h e l o w e r Fraser River;  Ciii)  t o a s s e s s the v a l i d i t y and s u i t a b i l i t y o f t h e s e 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 t o the F r a s e r R i v e r ;  Civ) t o a s s e s s , t h r o u g h use o f t h e p r e d i c t i v e c a p a b i l i t i e s , t h e p r o b a b l e impact o f v a r i o u s waste d i s c h a r g e 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 t h e lower F r a s e r R i v e r .  5  T h i s i n v e s t i g a t i o n i n t o t h e development,  assessment, and  u t i l i z a t i o n o f 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 s t u d y " because i t makes use o f d i g i t a l computer  "models".  computer programs w h i c h form t h e b a s i s o f the d i s s o l v e d oxygen  The  "models"  employ m a t h e m a t i c a l a b s t r a c t i o n s o f t h e r e l e v a n t p r o c e s s e s as t h e y seek to  emulate t h e system they r e p r e s e n t . A l t h o u g h t h i s p r o c e d u r e o f approx-  i m a t i n g a p h y s i c a l system by m a t h e m a t i c a l 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 " o f t h e p h y s i c a l s y s t e m i t i s s t r e s s e d h e r e t h a t i s r a r e l y i f ever true. to  this  I n f a c t t h e o u t p u t o f a "model" c o r r e s p o n d s  the r e s p o n s e o f t h e r e a l system o n l y as t h e model a s s u m p t i o n s r e p r e s e n t  r e a l i t y and t h e o u t p u t i s as good as the weakest model a s s u m p t i o n . A t i t s c o n c e p t i o n t h i s r e s e a r c h p r o j e c t was e n v i s i o n e d as b e i n g d e s i g n e d s p e c i f i c a l l y t o i n v e s t i g a t e t h e e f f e c t s o f sewage d i s c h a r g e from the of  proposed treatment f a c i l i t y  a t A n n a c i s I s l a n d on t h e oxygen r e s o u r c e s  t h e r i v e r , a " s i s t e r " p r o j e c t t o t h e i n v e s t i g a t i o n u n d e r t a k e n by  Rusch [1973] t o s t u d y £he e f f e c t s o f t h e p r o p o s e d d i s c h a r g e o n 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 since p r o j e c t conception, during  w h i c h t h e a u t h o r has been employed w i t h t h e Westwater U.B.C. and been a s s o c i a t e d w i t h t h e development  Research Centre,at  o f a number o f w a t e r  q u a l i t y models, t h e r e s e a r c h aims o f t h i s p r o j e c t have undergone of metamorphosis  t o become b r o a d e r i n s c o p e .  a degree  R a t h e r than f o c u s i n g on the  a n a l y s i s o f a s p e c i f i c problem as o r i g i n a l l y i n t e n d e d t h i s t h e s i s has t a c k l e d t h e more g e n e r a l i s s u e o f u n d e r s t a n d i n g the n a t u r e o f d i s s o l v e d oxygen dynamics i n t h e l o w e r F r a s e r R i v e r .  I n d o i n g t h i s i t h a s remained  t r u e to t h e o r i g i n a l purpose o f t h e r e s e a r c h b u t more c o m p l e t e l y f u l f i l l e d the  stated objectives.  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  i n s i g h t s i n t o the complex nature of the lower Fraser River and i t s considerable a b i l i t y to a s s i m i l a t e organic wastes that may have gone undetected by the o r i g i n a l p r o j e c t design. The o r g a n i z a t i o n of t h e s i s presentation can be thought of as having f i v e d i s t i n c t components - d e s c r i p t i o n , theory, a p p l i c a t i o n , r e s u l t s 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 d i s s o l v e d oxygen model s t u d i e s .  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, f o r the lower F r a s e r , the e f f e c t s of t i d a l i n f l u e n c e and s a l t w a t e r i n t r u s i o n . theoretical basis.  Chapters 2 and 3 have a more  Chapter 2 presents some of the concepts, t h e o r i e s  and mathematical formulations developed to describe d i s s o l v e d oxygen and the f a c t o r s which a f f e c t i t s dynamic behaviour i n waterways.  Chapter  3 discusses methods of applying the fundamental formulations f o r d i s s o l v e d oxygen to r i v e r s and e s t u a r i e s i n order to develop modeling c a p a b i l i t i e s . Chapters 4 and 5 are concerned, r e s p e c t i v e l y , w i t h the a p p l i c a t i o n of the models to the Fraser River and the r e s u l t s of the modeling e x e r c i s e . Discussion i n Chapter 4 i s centred around the d e t a i l s of model a p p l i c a t i o n and the various assumptions i m p l i c i t i n each of the models.  Specific  r e s u l t s are presented i n Chapter 5 to t e s t the performance of the models. In a d d i t i o n , the r e s u l t s of various model runs are presented to enable a p r e l i m i n a r y assessment of a s s i m i l a t i v e capacity and p o s s i b l e future 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 .  Chapter 6 summarizes the i n v e s t i g a t i o n  d i s c u s s i n g 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 .  C h a p t e r 7 draws c o n c l u s i o n s and s u g g e s t s  ways o f i m p r o v i n g and s t r e n g t h e n i n g the d e v e l o p e d 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 r i v e r basin wholely within the province of B r i t i s h Columbia. Covering approximately one-quarter of the province, the drainage basin occupies the greater portion of the southern h a l f of the province, draining the high central I n t e r i o r Plateau which i s flanked on the west by the Coast Mountains and by the p a r a l l e l i n g Columbia and Rocky Mountains on the east (see Figure 1.1).  The I n t e r i o r 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 r i v e r i t s e l f r i s e s i n the Rocky Mountains at one of the most easterly points i n the basin near the Yellowhead Pass, descends into the Rocky Mountain Trench, and flows northwesterly f o r some 250 miles before i t turns south, crossing more than 400 miles of the I n t e r i o r Plateau. At Lytton, the Fraser forms a spectacular canyon as i t cuts through formidable Coast Range.  the  Continuing southward to Hope, the r i v e r breaks out  of the canyon and turns westward, making i t s approach to the sea 100 miles of the a l l u v i a l , d e l t a i c Lower Fraser V a l l e y .  through  The "mighty"  Fraser, by the time i t enters the sea through the S t r a i t s of Georgia, has traversed a t o t a l length of approximately  850 miles.  Of the t o t a l Fraser River drainage area, approximately 52,000  -  8 -  9  10  square m i l e s are c o n t a i n e d  i n t r i b u t a r y sub-basins,  w h i c h a r e shown i n F i g u r e 1.1.  The  the most i m p o r t a n t  S t u a r t , Nechako, Westroad and  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 o f the I n t e r i o r P l a t e a u and e a s t e r l y s l o p e s o f the Coast M o u n t a i n s w i t h the Quesnel and R i v e r s , on the e a s t , d r a i n i n g the r e m a i n i n g  Chilcotin  the  Thompson  p o r t i o n s o f the p l a t e a u  the e a s t e r n s l o p e s of the C o l u m b i a M o u n t a i n s .  of  and  Other than a development  d i v e r t i n g 5,400 s q u a r e m i l e s o f t h e Nechako s u b - b a s i n  and a m i n o r  sub-  b a s i n development a t B r i d g e 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 a r e as y e t , dammed, a l t h o u g h  schemes f o r b o t h f l o o d c o n t r o l and  e l e c t r i c power have been s u g g e s t e d .  not,  hydro-  [ F r a s e r R i v e r B o a r d , 1958;  B.C.  Energy B o a r d , 1972]. C l i m a t i c c o n d i t i o n s v a r y c o n s i d e r a b l y o v e r the b a s i n .  Alpine  m a r i t i m e c l i m a t e c h a r a c t e r i z e s the l o w e r p o r t i o n s o f the d r a i n a g e b a s i n as one  p r o c e e d s 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 t h r o u g h d r y  and  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 o f the headw a t e r s and e a s t e r l y a r e a s .  The  extreme n o r t h e r l y p o r t i o n s o f t h e  b o r d e r 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 .  basin  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 m a r k e d l y t h r o u g h o u t the b a s i n , r a n g i n g 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 o f o v e r 150  i n c h e s per y e a r i n the v i c i n i t y of P i t t Lake  i n the Lower F r a s e r V a l l e y t o a r i d and  s e m i - a r i d l e v e l s o f 5-10  y e a r i n a r e a s of the c e n t r a l p l a t e a u n e a r Kamloops. i s a l s o extreme.  inches  V a r i a b i l i t y of  vegetation  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 c o a s t  f o r e s t t o a l m o s t 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 o f a r i d and 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].  per  rain  semi-arid  11  Temperature, along with p r e c i p i t a t i o n , i s a major c l i m a t i c factor which a f f e c t s the hydrology of the basin.  The  temperature at  point i n the basin depends primarily on a l t i t u d e , l a t i t u d e and from the P a c i f i c Ocean.  any  distance  Of p a r t i c u l a r s i g n i f i c a n c e i s the f a c t that  temperature over the whole of the Fraser River basin normally f a l l s below freezing i n the winter months.  With the spring thaw, which usually begins  i n the south and spreads northward, p r e c i p i t a t i o n which has been stored over winter i n the form of snow and i c e i s released, causing freshet conditions which commonly r e s u l t i n flooding. 1948,  Exceptional floods, as i n  are caused when abnormally high spring p r e c i p i t a t i o n combines with  rapid snowmelt.  [Fraser River Board, 1958],  Throughout i t s length the main stem Fraser drops over 4,000 feet i n elevation with a r e l a t i v e l y uniform grade i n d i c a t i v e of a maturing r i v e r , except i n the headwaters where gradients are high, and i n the Lower Fraser Valley where there i s a sharp break i n r i v e r 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 r i v e r deposits  the  major portion of i t s large sediment load, an estimated 25 m i l l i o n tons annually,  [Pretious, 1972]  which, as well as making the r i v e r t u r b i d  and brown i n appearance, has led to the formation valley.  of the a l l u v i a l lower  From Chilliwack downstream to the sea, a distance of 55  miles,  r i v e r grades are very low and as a r e s u l t water slopes and r i v e r stage are affected by t i d e s .  1.2  FRASER RIVER RUN-OFF CHARACTERISTICS The  r u n o f f c h a r a c t e r i s t i c s o f the F r a s e r R i v e r b a s i n a r e  best  d e s c r i b e d by the r e c o r d s o f the g a u g i n g s t a t i o n a t Hope, where the  river  f l o w i s u n a f f e c t e d by  the  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  p e r i o d o f r e c o r d s t r e t c h e s back t o 1912  [Water Survey of Canada,  t o 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 o f the b a s i n , r e p r e s e n t i n g about 87% o f the t o t a l d r a i n a g e estimated  a r e a and  t o t a l r u n o f f o f the F r a s e r R i v e r t o the sea  1913  entire 80% o f  the  [Fraser River  B o a r d , 1958]. An average a n n u a l h y d r o g r a p h o f F r a s e r R i v e r d i s c h a r g e a t 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 r e c o r d i s outdated, i t  shows the o b s e r v e d p a t t e r n o f r u n o f f and r u n o f f regime. mid-June and  Freshet  the i n f l u e n c e o f snowmelt on  t y p i c a l l y b e g i n s n e a r the end o f A p r i l , peaks i n  t a i l s o f f t o base f l o w c o n d i t i o n s i n l a t e f a l l .  low f l o w s o c c u r i n the w i n t e r months, December t o March. extreme f l o w s r e c o r d e d J a n u a r y 8, 1916  The  31, 1948.  out by  w i t h peak f l o w r e a c h i n g an e s t i m a t e d  high  flood  620,000 c f s .  v a r i a t i o n and d i s t r i b u t i o n o f mean m o n t h l y f l o w s f o r the to 1970  i s shown  T h i s summary i n f o r m a t i o n i s b a s e d on f l o w a n a l y s i s c a r r i e d  the Westwater R e s e a r c h C e n t r e [Westwater, u n p u b l i s h e d  each month, median f l o w s , a l o n g w i t h f i v e , t e n and flows-are reported.  \  and  An even l a r g e r  F r a s e r R i v e r a t Hope o v e r the p e r i o d o f r e c o r d from 1913 i n F i g u r e 1.3.  Low  Minimum a n n u a l  a t Hope were 12,000 c u b i c f e e t p e r s e c o n d ( c f s ) on  and 536,000 c f s on May  o c c u r r e d i n 1894,  the  Discharge  data].  f i f t e e n year  For  return  d a t a i n t h i s form a r e u s e f u l n o t o n l y  as  F i g u r e 1.2 Average A n n u a l Hydrograph f o r t h e F r a s e r R i v e r a t Hope (1930-1960)  uisiriDuuon for the  OT iviean Monthly  Fraser  River  at  Mows  Hope  240^  r240  220H  220  •MEAN FLOW -FIVE YEAR LOW FLOW  200-  -200  •TEN YEAR LOW FLOW • FIFTY YEAR LOW FLOW  J"  180-  H80  160-  H60  140 H  1  o 120 H  o  140  120  100-  ICO  80 H  60H  40-  20-  1  IV JAN  1i;  I, FEB  MAR  Distribution  APR  MAY  JUNE  JULY  F i g u r e 1.3 o f Mean Mlonthly F l o w s f o r  AUG  t h eF r a s e r  SEPT  OCT  River  a t Hope  NOV  DEC  d913-1970)  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 s e c t i o n , but a l s o , because the scope of the information i s the broader monthly time base, i t allows f o r a more tempered view of the range of Fraser River flows. Results of an a n a l y s i s o f low flow conditions [Westwater, unpubl i s h e d data] are shown i n Figures 1.4 and 1.5.  Figure 1.4, representing  a n a l y s i s of 7-day low flow data, i s based on a recent p u b l i c a t i o n by the Water Survey of Canada [WSC, 1974].  The 7-day low flow has been recommended  by some researchers as the time p e r i o d most s u i t a b l e f o r study of water q u a l i t y and the examination of water q u a l i t y e f f e c t s [McKee and Wolf, 1963].  The minimum y e a r l y 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 p i c t u r e of low flow data f o r the F r a s e r . 1.3  FRASER RIVER WATER TEMPERATURE CHARACTERISTICS The d i s t r i b u t i o n of water temperature f o r each month at Hope i s  shown i n Figures 1.6 and 1.7 and i s based on mean monthly c o n d i t i o n s f o r seven years of record as published by the Sediment.Survey of Canada [19641970].  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 t h i s i s a reasonable assumption.  Low  temperatures occur during the winter months, w i t h the lowest average temperatures 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 i n f l u e n c e of lower b a s i n cold weather c o n d i t i o n s , t h e i r s e v e r i t y and timing. Higher temperatures are observed i n the summer period w i t h August having the highest average temperature a t 17.7°C.  RECURRENCE INTERVAL in years 10 J  80  PROBABILITY  20 I  9 0 95  5 0 100 I  L  98 99  in percent  F i g u r e 1.4 D i s t r i b u t i o n o f 7-Day Low Flows f o r the F r a s e r R i v e r a t Hope  RECURRENCE  2  1,11  101 'i  I 1 2  INTERVAL  i  i  i  5  i  10  5  '  i  1  20  i — i  40  in years 1  l  60  PROBABILITY  i  t  80  10 2 0 5 0 I0O L  -  1  I  I  9 0 95  1  i  i  98 99  in percent  Figure 1.5 D i s t r i b u t i o n of Minimum Yearly Flows f o r the Fraser River at Hope  18  RECURRENCE  1.01  Ml  INTERVAL  2  in years  5  _i  10 20 i  1  JUNE  IQO  H4  MAY  8  PROBABILITY  in  percent  F i g u r e 1.6 D i s t r i b u t i o n o f Mean M o n t h l y F r a s e r R i v e r Water January t o J u l y  Temperatures  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 o f Mean M o n t h l y F r a s e r R i v e r Water August t o December  Temperatures  1.4  THE LOWER FRASER RIVER The lower Fraser River from Hope to the S t r a i t of Georgia i s  shown i n Figure 1.8. 6,000 square miles.  The drainage area of the lower r i v e r i s  approximately  Although this area represents only some s i x percent of  the t o t a l catchment area, i t can contribute s i g n i f i c a n t l y 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 b r i e f d e s c r i p t i o n of the  various channels of the r i v e r system  delineates the nomenclature used  throughout this paper [taken from Benedict et a l . , 1973 ]. The stretch of r i v e r from Hope to New Main Stem.  At New  entering the S t r a i t of Georgia at  and a minor channel known as the North Arm, In the North Arm,  the Middle Arm,  the  Westminster, the Fraser River branches i n t o a major  channel c a l l e d the Main Arm,  Point Grey.  Westminster i s c a l l e d  Steveston,  which enters the S t r a i t at  b i f u r c a t i o n caused by Sea Island r e s u l t s i n  which enters the S t r a i t over Sturgeon Banks.  A number of  small islands and training walls i n the Main Arm near Ladner r e s u l t formation of side channels,  the major ones being Ladner Reach and  i n the  Sea  Reach, which flow into Canoe Pass, the most southerly e x i t of Fraser River water.  The Main Arm  contributes 85 percent of the discharge that u l t i m a t e l y  enters the S t r a i t and the North Arm, about 5 percent each [Goldie, 1967].  Middle Arm and Canoe Pass contribute  Figure The  Lower  1.8  Fraser  River  22  1.4.1  Tidal Effects.  Tides i n the S t r a i t of G e o r g i a , which i s  c o n n e c t e d t o t h e P a c i f i c Ocean through Juan de Fuca S t r a i t i n t h e s o u t h and J o h n s t o n e S t r a i t s i n t h e n o r t h ( s e e F i g u r e 1.1), a r e o f t h e mixed t y p e , c h a r a c t e r i s t i c o f much o f t h e c o a s t o f n o r t h w e s t e r n  North  America.  That i s , t h e t i d e s a l t e r n a t e from s p r i n g t o neap t i d e s i n a b i - w e e k l y 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 o f t h e c y c l e .  cycle  The t i d a l  range a t S t e v e s t o n 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 a r e shown i n F i g u r e 1.9 f o r P o i n t A t k i n s o n ,  the n e a r e s t H y d r o g r a p h i c 1974].  S e r v i c e s r e f e r e n c e p o r t [Canadian  Hydrographic  Services,  Low r i v e r s l o p e s i n t h e lower F r a s e r R i v e r , as p r e v i o u s l y m e n t i o n e d ,  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 w a t e r s l o p e s and w a t e r 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 t h e mouth. the c o m b i n a t i o n  of unusual  On o c c a s i o n ,  t i d e s and low r i v e r d i s c h a r g e has r e s u l t e d i n  observed  e f f e c t s r e a c h i n g even f a r t h e r upstream t o t h e v i c i n i t y o f R o s e d a l e ,  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 n e a r t h e l i m i t  o f t i d a l i n f l u e n c e a r e r e s t r i c t e d t o minor changes i n s l o p e and e l e v a t i o n and, a l t h o u g h d i s c h a r g e i s a f f e c t e d , e f f e c t s a r e n o t s e v e r e enough t o cause c u r r e n t r e v e r s a l .  C u r r e n t r e v e r s a l has been r e p o r t e d , however, as  f a r u p s t r e a m as M i s s i o n [ B a i n e s , 1952]. Of a d d i t i o n a l i m p o r t a n c e i n u n d e r s t a n d i n g t i d a l e f f e c t s on the h y d r a u l i c b e h a v i o u r  the i n f l u e n c e o f the  o f 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 t h a t t h e P i t t R i v e r - P i t t Lake system i s a t i d a l s t o r a g e Water s u r f a c e e l e v a t i o n s a r e observed  area.  t o v a r y w i t h the t i d e s o v e r t h e f u l l  e x t e n t o f P i t t L a k e , a s u r f a c e a r e a o f some 25 square m i l e s .  This  represents  a l a r g e volume o f . w a t e r s t o r a g e on t h e f l o o d t i d e , w h i c h i s l a t e r r e l e a s e d on t h e ebb t i d e .  There i s a r e v e r s e d e l t a a t the e n t r a n c e  t o P i t t Lake  Neap Tides  Spring Tides 16-1 CD CD  Lu  JZ "cu X CD  •a  1412-  108  6 4  2H 0  l  I  l  I  i  Time in Days F i g u r e 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 o f w a t e r t h a t e n t e r the l a k e [ J o y ,  1974]Low s t u d y by B a i n e s  r i v e r f l o w - h i g h t i d e c o n d i t i o n s were the s u b j e c t o f a [ 1 9 5 2 ] , r e f e r r e d t o i n the p r e c e d i n g  paragraph.  Cubature d i s c h a r g e c a l c u l a t i o n s , based on o n e - h a l f h o u r l y r i v e r s t a g e measurements f o r a day and a h a l f , showed t h a t i n s t a n t a n e o u s  upstream  t i d a l f l o w s i n the v i c i n i t y o f S t e v e s t o n reached n e a r l y 140,000 c f s w i t h downstream t i d a l f l o w s r e a c h i n g o v e r 200,000 c f s f o r a f r e s h w a t e r a t Hope o f 28,400 c f s (see F i g u r e 1.10).  discharge  The v e l o c i t y v a r i a t i o n o v e r from 2.0  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  f e e t p e r second  upstream t o 3.8 f e e t p e r second downstream.  T h i s extreme v a r i a t i o n i n  d i s c h a r g e and v e l o c i t y makes one a c u t e l y aware o f the complex n a t u r e h y d r a u l i c behaviour  of  i n the lower F r a s e r R i v e r .  High r i v e r f l o w c o n d i t i o n s d u r i n g the f r e s h e t tend t o dampen out t i d a l e f f e c t s as t h e f r e s h w a t e r d i s c h a r g e p r e d o m i n a t e s o v e r action.  tidal  D u r i n g t h e s e c o n d i t i o n s t h e r e a r e no r e v e r s a l s o f c u r r e n t and  o n l y m i n o r r i v e r s t a g e v a r i a t i o n even i n the seaward r e a c h e s o f the Although  f l o w s a t t h i s time a r e s t i l l unsteady,  river.  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 r e s e m b l i n g t h a t o f a river. A n o t h e r 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 c o m p l e x i t y and u n s t e a d y n a t u r e o f t h e p h y s i c a l p r o c e s s e s o f m i x i n g 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 p r o c e s s e s ,  although  m i n i m a l , a r e more c o m p l e t e l y 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 a r e t r a n s f e r a b l e from one r i v e r t o a n o t h e r and the p r o c e s s can be  reproduced  26  i n the l a b o r a t o r y , the phenomenon o f t i d a l m i x i n g i n e s t u a r i e s and r i v e r s i s p o o r l y understood.  T h i s i s p a r t l y because i t has  tidal  received less  a t t e n t i o n , b u t m a i n l y 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 o t h e r s t u d i e s do not n e c e s s a r i l y a p p l y . M i x i n g and d i s p e r s i o n p r o c e s s e s been the o b j e c t of a r e c e n t s t u d y by unpublished  data].  Dye  t r a c e r was  on the l o w e r F r a s e r R i v e r have  the Westwater R e s e a r c h C e n t r e [Ward,  r e l e a s e d and  tracked over a  c y c l e t o d e t e r m i n e 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 The  tidal mixing.  r e s u l t s o f 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  o c c u r s r a p i d l y , the r a t e s o f l a t e r a l d i s p e r s i o n a r e much l o w e r . m i x i n g was  Vertical  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 t o be complete w i t h i n the  h o u r a f t e r dye  first  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 m i x i n g  be completed was I t was  normally  estimated  to be more t h a n one  t i d a l c y c l e ( o r 25  hours).  f o u n d , however, t h a t 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  t h e e s t u a r y due  to the p r e s e n c e o f the s a l t wedge, v e r t i c a l m i x i n g was i n -  hibited. 1.4.2  Salinity Intrusion.  S a l t w a t e r i n t r u s i o n i n the  F r a s e r R i v e r has been the s u b j e c t o f much debate i n r e c e n t y e a r s . s p o t measurements were made i n the p a s t [ W a l d i c h u k e t a L , 1968] u n t i l 1973, phenomenon.  was  lower Various  but,  not  any i n t e n s i v e r e s e a r c h i n i t i a t e d t o s t u d y t h i s e s t u a r i n e  F i e l d i n v e s t i g a t i o n s d u r i n g F e b r u a r y - M a r c h , 1973 were under-  taken t o 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 l o w e r F r a s e r R i v e r 1975].  to  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  [Hodgins,  temperature measuring  d e v i c e s were i n s t a l l e d a t t h r e e f i x e d l o c a t i o n s i n the l o w e r r e a c h e s o f  the r i v e r i n an a t t e m p t t o d e t e r m i n e t h e n a t u r e and e x t e n t intrusion.  of the s a l t water  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 movement [ H o d g i n s , 1 9 7 5 ] .  a m a t h e m a t i c a l model o f s a l t w a t e r wedge  The s a l i n i t y m o n i t o r i n g  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 w a t e r wedge was p r e s e n t i n t h e l o w e r r e a c h e s o f t h e r i v e r during  flood tide conditions.  h i g h t i d e , was e s t i m a t e d ,  The tongue o f t h e wedge, j u s t a f t e r  t h r o u g h use o f t h e s a l t w e d g e model, t o e x t e n d  n e a r l y as f a r u p r i v e r as A n n a c i s I s l a n d .  W i t h t h e s u c c e e d i n g s t r o n g ebb  t i d e t h e wedge was washed o u t o f t h e r i v e r t o a p o i n t beyond  Steveston.  Recent s a l i n i t y measurement i n t h e r i v e r has c o n f i r m e d t h a t t h i s i s i n d e e d the case [Ages & Hughes, 1975, and Westwater R e s e a r c h C e n t r e , u n p u b l i s h e d data].  I n d i c a t i o n s a r e t h a t t h e t o e o f t h e wedge c a n e x t e n d u p r i v e r even  as f a r as t h e e a s t e r n  t i p of Annacis I s l a n d .  D u r i n g f r e s h e t , s a l t w a t e r does h o t i n t r u d e u p r i v e r o f S t e v e s t o n due  t o t h e p r e d o m i n a t i n g e f f e c t s o f l a r g e r i v e r f l o w s [Ward, u n p u b l i s h e d  data].  T h i s s i t u a t i o n t h e n , w i t h t h e s a l t w e d g e b e i n g washed o u t o f t h e  r i v e r d u r i n g low f r e s h w a t e r  discharge  river, at a l l during freshet discharge  c o n d i t i o n s and n o t e n t e r i n g t h e c o n d i t i o n s , l e a d s one t o q u e s t i o n  the c l a s s i f i c a t i o n o f t h e l o w e r F r a s e r as an e s t u a r y . estuary  Since  traditional  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 t h e r e be  c o n s i s t e n t p r e s e n c e o f s a l i n i t y , t h e system i s perhaps more p r o p e r l y described 1971].  as a t i d a l r i v e r , as i t has been by some r e s e a r c h e r s  [Callaway,  To account f o r t h e f a c t t h a t s a l i n i t y i n t h e form o f s a l t w a t e r  i n t r u s i o n i s p r e s e n t some o f t h e t i m e , used i n t h i s p a p e r .  t h e term " r i v e r / e s t u a r y " w i l l be  CHAPTER 2 DISSOLVED OXYGEN DYNAMICS, A REVIEW  2.1  DISSOLVED OXYGEN The dissolved oxygen resources of a waterway play a most important  r o l e i n the maintenance of a healthy aquatic ecosystem. one of the most important  Dissolved oxygen,  indicators of water q u a l i t y , i s e s s e n t i a l f o r  support of a balanced aquatic habitat p a r t i c u l a r l y as i t a f f e c t s the s u r v i v a l of f i s h l i f e .  To insure the s u r v i v a l of a healthy f i s h e r y , which w i l l  e s s e n t i a l l y guarantee protection of the entire aquatic community, concentrations 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 s p e c i f i c dissolved oxygen c r i t e r i a for freshwater [F*vPCA, 1972] are given as follows.  fish  For warm water game f i s 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 f o r short periods of time." More stringent requirements  are recommended f o r cold water f i s h e s such as  trout and salmon e s p e c i a l l y i n spawning areas where "DO l e v e l s must not be below 7 mg/1 at any time." For good growth and the general w e l l 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 p r i n c i p a l l y as  migratory routes "DO l e v e l s may be as low as 5 mg/1 for periods up to  -  28 -  6 hours b u t s h o u l d n e v e r be below A mg/1 a t any t i m e o r p l a c e . " A s i d e from b e i n g a n e c e s s a r y r e q u i r e m e n t f o r f i s h  survival,  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 g e n e r a l i n d i c a t o r o f t h e degree o f w a t e r p o l l u t i o n as i t i s l i n k e d w i t h o t h e r w a t e r q u a l i t y  impair-  ments such as t h e n u i s a n c e c o n d i t i o n s c r e a t e d where c o n c e n t r a t i o n s a r e low.  A c l a s s i f i c a t i o n o f 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-  t e n t i s shown i n T a b l e 2.1.  TABLE 2.1 CLASSIFICATION OF RIVER QUALITY BASED ON DISSOLVED OXYGEN CONTENT [KLEIN, 1959] DISSOLVED OXYGEN % OF SATURATION  TYPE OF RIVER WATER Good  -  G r e a t e r t h a n 90  Fair  75-90  Doubtful  50 - 75  Badly p o l l u t e d  L e s s t h a n 50  The amount o f oxygen d i s s o l v e d i n w a t e r from t h e atmosphere i s dependent  on : t e m p e r a t u r e , b a r o m e t r i c p r e s s u r e and t h e amount o f 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 b a r o -  m e t r i c p r e s s u r e and i n v e r s e l y w i t h w a t e r t e m p e r a t u r e and s a l t c o n t e n t . Thus, h i g h w a t e r t e m p e r a t u r e s r e s u l t i n l o w oxygen s o l u b i l i t i e s as does t h e p r e s e n c e o f h i g h s a l t c o n c e n t r a t i o n w h i c h , f o r example, sea w a t e r .  characterizes  The v a l u e s g e n e r a l l y used f o r t h e s o l u b i l i t y o f oxygen i n  30  fresh and s a l t water are those given by the American P u b l i c H e a l t h A s s o c i a t i o n [Standard Methods 1971] and were c a l c u l a t e d by Whipple and Whipple [1911] from gasometric determination c a r r i e d out by Fox  [1909].  More recent i n v e s t i g a t i o n s at the Water P o l l u t i o n Research Laboratory i n England [Truesdale e_t a l . , 1955] have r e s u l t e d i n p u b l i c a t i o n of what may be considered to be more c o r r e c t values as determined by a m o d i f i c a t i o n of the standard Winkler method [Standard Methods, 1971].  These i n v e s t i g a t i o n s  have r e s u l t e d i n the f o l l o w i n g e m p i r i c a l equation r e p r e s e n t i n g the s o l u b i l i t y of oxygen: C  = 14.161 - 0.3943T + 0:007714T - 0.0000646T 2  s  (2.1)  3  where C  i s the s a t u r a t i o n concentration of oxygen i n  s  ppm;  and  T  i s the temperature i n °C.  The e f f e c t s of barometric pressure on s o l u b i l i t y when c o n d i t i o n s are d i f f e r e n t from standard atmospheric are a l s o accounted f o r e m p i r i c a l l y by the f o l l o w i n g : C  s' = s C  JL.  '  760 where C'  i s the s o l u b i l i t y of oxygen at P mm Hg pressure;  C  i s the s o l u b i l i t y of oxygen at 760 mm Hg pressure  s  and g  Saturation concentrations f o r oxygen d i s s o l v e d i n mixtures of freshwater and seawater cannot be reduced to an e m p i r i c a l equation but values have  been t a b u l a t e d [ S t a n d a r d Methods, 1971 and T r u e s d a l e e t a l . ,  2.2  1955].  OXYGEN DEMANDING WASTES When a wastewater i s d i s c h a r g e d i n t o a waterway, t h e b i o d e g r a d -  a b l e o r g a n i c s c o n t a i n e d i n t h a t w a s t e w a t e r e x e r t an oxygen demand on t h e d i s s o l v e d oxygen r e s o u r c e s of t h e stream o r e s t u a r y .  T h i s f a c t was  f i r s t r e c o g n i z e d i n B r i t a i n d u r i n g t h e 1 9 t h c e n t u r y by way o f t h e i n v e s t i g a t i o n s o f t h e R o y a l Commission on Sewage D i s p o s a l , w h i c h was app o i n t e d i n 1898 " t o r e p o r t on methods f o r t h e t r e a t m e n t sewage and t r a d e w a s t e s " .  and d i s p o s a l o f  The Commission p u b l i s h e d a s e r i e s o f t e n  r e p o r t s o v e r 17 y e a r s w h i c h d e s c r i b e d many a s p e c t s o f sewage d i s p o s a l , r a n g i n g from s t a n d a r d s and t e s t s o f sewage and sewage e f f l u e n t s c o n t a m i n a t i o n o f s h e l l f i s h and growth o f weeds i n t i d a l w a t e r s  through t o a com-  p r e h e n s i v e 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 o f sewage and t r a d e w a s t e s . for  implementation  T h i s " m i l e s t o n e " s t u d y l a i d t h e groundwork  o f r e m e d i a l measures i n B r i t a i n where by t h e end o f  t h e 1 9 t h c e n t u r y , t h e w a t e r p o l l u t i o n i n some a r e a s was so bad t h a t " a i l f i s h l i f e and o t h e r a q u a t i c l i f e , a n i m a l and v e g e t a b l e had v i r t u a l l y d i s a p p e a r e d " and " t h e scum i n p a r t s o f t h e 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 h a t b i r d s walked on i t w i t h o u t  thinking".  [Klein,  1962].  The R o y a l Commission s t u d i e s formed t h e b a s i s o f what was u n doubtedly  t h e f i r s t m a j o r w a t e r p o l l u t i o n i n v e s t i g a t i o n and, a s such,  t h e f i n d i n g s have had l o n g l a s t i n g and f a r r e a c h i n g i m p a c t . r e s p e c t , t h e 8 t h Report  i s p a r t i c u l a r l y important.  In this  I t d e a l t w i t h the  q u e s t i o n o f s t a n d a r d s and t e s t s a p p l i e d t o sewage and sewage e f f l u e n t s  b e i n g d i s c h a r g e d t o r e c e i v i n g waterways.  A t e s t o f 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 w a t e r , f i r s t recommended by t h e R o y a l 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 t a k e n up i n 5 days a t 65°F" w h i c h became a s t a n d a r d wastewater and r i v e r water q u a l i t y p a r a m e t e r .  Later  t o be m o d i f i e d s l i g h t l y and re-named, t h e B i o c h e m i c a l Oxygen Demand t e s t was used by t h e R o y a l S o c i e t y i n t h e i r r e p o r t t o c l a s s i f y  (BOD)  rivers  (see T a b l e 2.2).  TABLE  2.2  ROYAL COMMISSION CLASSIFICATION OF RIVERS [KLEIN, 1959] APPROXIMATE 5-DAY BOD (ppm)  CLASSIFICATION  1  Very c l e a n  2  Clean  3  Fairly  5  Doubtful  10  The BOD  @ 65°F  clean  Bad  t e s t has r e t a i n e d i t s i m p o r t a n c e as a measure o f w a s t e -  w a t e r and r i v e r w a t e r q u a l i t y i n s p i t e o f the f a c t t h a t t h e t e s t i s s u b j e c t t o a number o f sometimes  serious errors.  I t s popularity, accept-  ance and w i d e s p r e a d use as a w a t e r q u a l i t y parameter i s i n p a r t due t o the endorsement  i t r e c e i v e d because o f i t s development by t h e p r e s t i g i o u s  R o y a l Commission but m a i n l y because o f i t s v a l u e as a d i r e c t measure o f  oxygen demand as i t i s a t e s t aimed a t r e p r o d u c i n g t h e o x i d a t i o n c o n d i t i o n s o f a n a t u r a l waterway.  Contemporary BOD t e s t i n g i s c o n d u c t e d 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 s e e d i n g a t 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 t e m p e r a t u r e o f 20°C, a l l o f w h i c h a r e aimed a t s t a n d a r d i z i n g t h e BOD t e s t i n o r d e r 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 p r o c e d u r e have  resulted i n increased r e p r o d u c i b i l i t y with minimization o f error.  How-  e v e r , v a g a r i e s i n t r i n s i c t o t h e BOD t e s t r e m a i n . I n c h a r a c t e r , BOD i s d e f i n e d a s " t h e amount o f 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 o r g a n i c m a t t e r u n d e r a e r o b i c conditions"  [Sawyer & M c C a r t y , 1967].  organic decomposition  The oxygen r e q u i r e d d u r i n g t h e  r e s u l t s from t h e a c t i v i t y o f a group o f m i c r o -  o r g a n i s m s , namely t h e a e r o b i c b a c t e r i a , w h i c h u t i l i z e t h e o r g a n i c s a s a f o o d s o u r c e , d e r i v i n g energy from t h e o x i d a t i o n p r o c e s s .  The b i 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 r e p r e s e n t e d 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 w h i c h 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 , t h e amount o f oxygen r e q u i r e d t o c o n v e r t an amount o f any g i v e n o r g a n i c compound t o i t s u l t i m a t e end p r o d u c t s - c a r b o n d i o x i d e , w a t e r and ammonia [Sawyer & M c C a r t y , 1 9 6 7 ] . C H O N n  a  b  c  + (n + -| - y - -| c ) 0 — > n C 0  The r a t e o f o x i d a t i o n o f o r g a n i c m a t t e r  2  2  + (~ - | c ) H 0 + N H 2  C  (2  3  i s governed t o a m a j o r e x t e n t 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 t e m p e r a t u r e . I n t h e BOD t e s t , c o n t r o l o f t h e i n c u b a t i o n t e m p e r a t u r e h a s been standardized.  B u t , however much emphasis i s p l a c e d on " s e e d i n g " t h e t e s t  sample w i t h b a c t e r i a l s e e d , 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  will  be c o n t r o l l e d .  The r o o t of t h i s problem and t h e main drawback of t h e  BOD  t e s t i s t h a t t h e b a c t e r i a , i n many c a s e s , t a k e time t o become a c c l i m a t i z e d t o 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 t h e a c c l i m a t i z a t i o n o f  b a c t e r i a l p o p u l a t i o n s i s not c o n s i d e r e d s e p a r a t e l y i n t h e BOD  test,  o c c u r s o v e r the f i r s t  Thus, t h e  few hours  ( o r d a y s ) o f t h e 5-day t e s t .  amount o f oxygen consumed i n t h e 5-day t e s t p e r i o d may  but  not a c c u r a t e l y  r e f l e c t t h e l o n g term demand e x e r t e d by a p a r t i c u l a r w a s t e b e c a u s e of t h e time t a k e n f o r t h e o x i d a t i o n r a t e t o r e a c h i t s maximum.  This i s true,  i n p a r t i c u l a r , w i t h wastes t h a t 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 t h a n r e a d i l y o x i d i z a b l e o r g a n i c s a s , s a y , a r e p r e s e n t i n an i n d u s t r i a l R e g a r d l e s s of t h e i n h e r e n t i n a c c u r a c i e s of t h e BOD  wastewater.  test, i t i s s t i l l  wide-  l y used as a measure o f t h e s t r e n g t h o f o r g a n i c waste and has been r e l a t e d to the oxygen b a l a n c e i n a s t r e a m .  2.3  THE  OXYGEN BALANCE The d i s c h a r g e of o r g a n i c w a s t e s i n t o a waterway  the water.  deoxygenates  That i s , t h e b a c t e r i a d e g r a d i n g t h e o r g a n i c m a t t e r consume  oxygen, t h e r e b y c a u s i n g a d e p l e t i o n of d i s s o l v e d oxygen i n t h e r e c e i v i n g water.  Simultaneous  t o the d e p l e t i o n of d i s s o l v e d oxygen i s t h e o c c u r r e n c e  of a n o t h e r p r o c e s s o f n a t u r e - a t m o s p h e r i c r e a e r a t i o n .  During t h i s pro-  c e s s , a d s o r p t i o n o f a t m o s p h e r i c oxygen (and o t h e r g a s e s ) by t h e w a t e r t a k e s p l a c e i n o r d e r t o m a i n t a i n t h e e q u i l i b r i u m between t h e d i s s o l v e d gases and t h e a t m o s p h e r i c gases a c c o r d i n g t o D a l t o n ' s l a w o f pressures.  partial  The net r e s u l t o f t h e s e 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  t h a t an oxygen b a l a n c e i s e s t a b l i s h e d .  T h i s forms t h e b a s i s o f 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. the  F i g u r e 2.1 shows an i d e a l i z e d form o f  b a l a n c e f o r a s i n g l e major waste d i s c h a r g e showing t h e zones o f  d e g r a d a t i o n and r e c o v e r y o f a p o l l u t e d s t r e a m . (a)  slight pollution;  (b) heavy p o l l u t i o n ;  Three c a s e s a r e g i v e n :  (c) gross p o l l u t i o n .  I n each  c a s e shown i n F i g u r e 2.1, t h e c u r v e s a r e t h e n e t r e s u l t o f d e o x y g e n a t i o n and r e a e r a t i o n o c c u r i n g s i m u l t a n e o u s l y w i t h , i n c a s e ( a ) , t h e oxygen demand b e i n g s m a l l enough so t h a t t h e 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 c a s e ( b ) , t h e oxygen demand b e i n g s u f f i c i e n t t o d e p l e t e t h e oxygen r e s o u r c e s t o a minimum; and i n c a s e ( c ) , t h e oxygen demand b e i n g so l a r g e t h a t i t d e p l e t e s t h e oxygen t o s u c h an e x t e n t  that  s e p t i c c o n d i t i o n s p r e v a i l o v e r a s t r e t c h o f t h e waterway. The oxygen r e s o u r c e s o f a waterway, i n a c o n s t a n t s t a t e o f dynamic e q u i l i b r i u m , a r e c o n t r o l l e d by t h e k i n e t i c s of t h e p r o c e s s e s o f d e o x y g e n a t i o n and r e a e r a t i o n .  2.4  DEOXYGENATION •  .  When m e a s u r i n g t h e oxygen demand of a w a s t e w a t e r o v e r a l o n g p e r i o d o f t i m e , whether w i t h a r e s p i r o m e t e r o r i n a s e r i e s o f BOD b o t t l e s , the  oxygen consumed i s o b s e r v e d t o v a r y i n a manner s i m i l a r t o t h a t  shown i n F i g u r e 2.2.  The t o t a l oxygen demand i s t h e n e t r e s u l t o f two  s e p a r a t e and i n d e p e n d e n t o x i d a t i o n p r o c e s s e s - c a r b o n a c e o u s o x i d a t i o n and nitrification.  During the f i r s t  10 t o 15 d a y s , t h e c a r b o n a c e o u s oxygen  demand, sometime c a l l e d t h e f i r s t s t a g e oxygen demand (FSOD), a c c o u n t s for  most o f t h e t o t a l demand and i s t h e r e s u l t of t h e o x i d a t i o n o f  carbonaceous o r g a n i c m a t t e r .  D u r i n g the subsequent p e r i o d ,  nitrification  Dissolved Oxygen Concentration (Percent O  9 e  Saturation) cn O  O O  Time  (Days)  F i g u r e 2.2 Oxygen Uptake o f a Wastewater  38  o c c u r s a l t h o u g h , i n some i n s t a n c e s , i f t h e wastewater c o n 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 o f ammonia, i t can t a k e p l a c e s i m u l t a n e o u s oxidation.  t o carbonaceous  I n t h i s p r o c e s s , t h e o x i d a t i o n o f ammonia u l t i m a t e l y t o  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 t o as t h e second  s t a g e oxygen demand (SSOD), w h i c h r e s u l t s i n an  i n c r e a s e d 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 m a t h e m a t i c a l l y t h e v a r i a t i o n o f BOD w i t h time t a k e n by p i o n e e r s i n the f i e l d  [ T h e r i a u l t , 1927 and P h e l p s , 1944] made t h e a s s u m p t i o n  t h e o x i d a t i o n was a mono-molecular o r " f i r s t o r d e r " r e a c t i o n .  that  That i s ,  t h e r a t e o f uptake o f oxygen was assumed t o be p r o p o r t i o n a l t o t h e amount o f o x i d i z a b l e o r g a n i c m a t t e r r e m a i n i n g a t any t i m e , e x p r e s s e d  mathematical-  l y as: dL dt  = -KjL  (2.4)  where L r e p r e s e n t s t h e u l t i m a t e FSOD a t any time t ;  i s t h e r a t e c o n s t a n t f o r t h e r e a c t i o n , sometimes r e f e r r e d t o as t h e d e - o x y g e n a t i o n c o e f f i c i e n t . The i n t e g r a t e d form o f t h i s e q u a t i o n i s : L = L e " l K  t  Q  where k° i s t h e i n i t i a l v a l u e o f L a t t = 0. A more c o n v e n i e n t form o f e q u a t i o n (2.5) i s g i v e n by:  (2.5)  39  y =L (l-e-^-^Cl-loV)  (2-6)  0  where y i s the BOD at any time t ; and  L  0  i s the t o t a l or u l t i m a t e FSOD.  (It should be noted t h a t , as i s conventional,  i s the rate constant to  the base e and k^ i s the r a t e 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 r e a c t i o n i s , i n f a c t , not a constant but a v a r i a b l e , the magnitude of which i s governed by a number of important f a c t o r s , i n c l u d i n g 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], i n c r e a s i n g temperatures increased the de-oxygenation constant, the value roughly doubling f o r a temperature increase of 15°C.  The temperature e f f e c t i s  g e n e r a l l y represented by the f o l l o w i n g r e l a t i o n s h i p , derived from van't Hoff's law:  (k ) = (k ) <-V20  ^1 T ;  e  (T_20)  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 t o be 1.047 based on t h e i r e a r l y s t u d i e s , but  40  more r e c e n t  research  temperature  coefficient  temperatures. temperature  range  is  factor  usually  a r e removed, and  rate  ing  phase,  light  on  was' d e v e l o p e d b y Another nature  of  oxidation. of  The  originally  i s comparable  factor  the o r g a n i c  and  phase,  and  growth  present i n the  cellular  oxygen  mass  t a k i n g more  i s some 10  which  (the waste-  f o r auto-  (the "endogenous  t h a n 20  difference  t o 20  times  c o n s t a n t , k^.  average  to the c l a s s i c a l  reaction  to  days, i s  between  D u r i n g the f i r s t , faster  t w o - p h a s e t h e o r y o f BOD rate  the  reactions,  mass i s c o m p l e t e l y o x i d i z e d  usually  [1970], the " o v e r a l l  of  present i n the  f o r energy  of their  t h e BOD  4-20°C.  a l l aerobic  the organic matter  of r e a c t i o n .  rate  low  theorized  During the f i r s t  The main d i s t i n g u i s h i n g rates  at  f o r the  range  p r e s e n t c o n t i n u e to use  residue,  the reaction  Streeter  been  i n fact,  the microrganisms  the meaning  oxidation  i n inaccuracies  I t has  and,  O n l y when t h e c e l l  original  constant i s the a b i l i t y  phases.  hours,  the organisms  complete.  to Eckenfedler  entire  by  cellular  o f endogenous  a new  reactions  distinct  i s the d i f f e r e n t  similation  the rate  When t h e o r g a n i c s  phase).  the o x i d a t i o n  resulting  shown t h e  f o r the temperature  affecting  BOD  has  s u g g e s t s 0 v a l u e s o f 1.056  endogenous metabolism  non-biodegradable  phases  low,  1.135  i n 18-36  phase).  respiration"  two  and  s e p a r a t e and  is utilized  "synthesis"  oxidation  that  complete  wastewater  too  1960]  the organic matter.  1970]  i n two  water  20-30°C  to u t i l i z e  [Eckenfelder, occur  t o be  et a l . ,  S c h r o e p f e r [1960]  Another organisms  [Schroepfer  the  or  as-  than  reaction  the  sheds  However, a c c o r d rate"  form of r a t e  over  the  constant  that  Phelps.  affecting  substrate  the deoxygenation c o n s t a n t i s the  undergoing oxidation.  With  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 t e n d t o be h i g h r e f l e c t i n g t h e ease w i t h which t h e waste c a n be degraded.  After  treatment  w h i c h removes much of t h e o r g a n i c m a t t e r , and i n r i v e r s , where o n l y low concentrations 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.  T h i s c a n be e x p l a i n e d i n terms o f t h e "two-phase" t h e o r y  t h a t , i n t h e s e c a s e s , t h e o x i d a t i o n i s m a i n l y due t o 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 c o n s t a n t s f o r a range o f s u b s t a n c e s  i s shown i n T a b l e 2.3.  TABLE 2.3 AVERAGE BOD RATE CONSTANTS @ 20°C [ECKENFELDER, 1970]  SUBSTANCE  ^1^20  U n t r e a t e d wastewater  0.15-0.28  H i g h r a t e f i l t e r s and a n a e r o b i c c o n t a c t e f f l u e n t  0.12-0.22  H i g h degree b i o t r e a t m e n t 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  o f a p l o t o f e q u a t i o n (2.6) w i t h t h e o b s e r v e d  oxygen u p t a k e o f o r g a n i c m a t t e r 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 t h e f i r s t 8 t o 10 days o f o x i d a t i o n a f t e r w h i c h time t h e BOD c u r v e d i v e r g e s r a d i c a l l y from t h e c o u r s e i t would be e x p e c t e d t o f o l l o w as a u n i m o l e c u l a r r e a c t i o n [Sawyer & 1967].  McCarty,  The main r e a s o n f o r t h e d i v e r g e n c e from t h e t h e o r y a f t e r t h e  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 t h a t t h e e f f e c t s o f n i t r i f i c a t i o n  become  significant. 2.4.2  Nitrification.  g r a d a t i o n , as i n the BOD ammonia and  The  nitrogenous  stage of b i o c h e m i c a l  t e s t , i n c l u d e s c o n v e r s i o n of o r g a n i c n i t r o g e n to  the subsequent o x i d a t i o n o f ammonia u l t i m a t e l y t o n i t r a t e .  O r g a n i c n i t r o g e n i s h y d r o l y z e d t o ammonia, under a e r o b i c o r conditions, without  the u t i l i z a t i o n  l y o x i d i z e d by n i t r i f y i n g organisms n i t r o s o m c n a s I n the BOD lag  of 10-15  The  ammonia i s s u c c e s s i v e -  b a c t e r i a t h r o u g h n i t r i t e t o n i t r a t e by  and n i t r o b a c t e r , r e s p e c t i v e l y .  the  [Wezernak, 1 9 6 8 ] ,  t e s t o f raw wastewater t h e r e i s g e n e r a l l y a pronounced the  T h i s 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 p r o c e s s , and i s i n the o r d e r of one  t h e r e may  of oxygen.  anaerobic  days between the b e g i n n i n g o f carbonaceous o x i d a t i o n and  n i t r i f i c a t i o n step.  In s t r e a m s ,  de-  the two  b a c t e r i a d u r i n g the sewage  treatment  o r two days f o r h i g h l y t r e a t e d samples.  s t a g e s 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  be l a g s i n the n i t r i f i c a t i o n s t a g e i n h i g h l y p o l l u t e d streams o r  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 r e p o r t e d n i t r i f i c a t i o n r a t e s have had  [Courchaine,  1963]  s i g n i f i c a n t e f f e c t s on the oxygen b a l a n c e  streams.  T h i s was  treatment  and a h i g h t e m p e r a t u r e r e c e i v i n g w a t e r b o t h of w h i c h  nitrification.  a t t r i b u t e d t o the c o m b i n a t i o n  I t was  where h i g h of  o f a h i g h d e g r e e of w a s t e favour  found t h a t the h i g h r e c e i v i n g w a t e r t e m p e r a t u r e s  (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 popul a t i o n of n i t r i f y i n g  bacteria.  T h i s , i n t u r n , r e s u l t e d i n an a l m o s t  im-  m e d i a t e u p t a k e of oxygen by t h e s e 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.  I n g e n e r a l , however, e x c e p t  i n high  43  temperature receiving streams, n i t r i f i c a t i o n i s not of much s i g n i f i c a n c e when compared to the e f f e c t s 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 s i g n i f i c a n t [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 r e aeration.  Atmospheric oxygen i s absorbed r e a d i l y by the oxygen d e f i c i e n t  water to maintain the balance of p a r t i a l pressures between the atmosphere and the water which, i n the l i m i t , r e s u l t s i n the saturation of water with dissolved oxygen.  The d r i v i n g force f o r the rate o f oxygenation i s the  dissolved oxygen d e f i c i t , which i s simply the d i f f e r e n c e between the saturation concentration and the e x i s t i n g concentration. Mathematically, t h i s may be expressed as: f  =- 2 K  D  ,  <'> 2  8  where D i s the dissolved oxygen d e f i c i t at any time t ; and K  i s the rate constant, often refered to as the reaeration c o e f f i c i e n t , i n form, s i m i l a r to the deoxygenation constant.  2  Integration of Equation (2.8) r e s u l t s i n : D  =  D e D  - V  =  D  D  10  where Do  i s the i n i t i a l d e f i c i t at t = 0.  ( 2  "  9 )  44  Many f a c t o r s a r e known t o a f f e c t t h e v a l u e o f t h e r e a e r a t i o n c o e f f i c i e n t , k£.  N a t u r a l m i x i n g i n waterways has been found t o be p a r t i c u l a r -  l y i m p o r t a n t as i t e f f e c t s t h e r a t e o f s u r f a c e r e n e w a l a t t h e g a s - l i q u i d i n t e r f a c e where t h e oxygen t r a n s f e r t a k e s p l a c e . [ S t r e e t e r and P h e l p s , and  Early research e f f o r t s  1925] c o n c l u d e d t h a t t h e i n f l u e n c e o f t h e h y d r a u l i c  p h y s i c a l c h a r a c t e r i s t i c s o f a s t r e a m on t h e r e a e r a t i o n c o e f f i c i e n t  c o u l d be d e s c r i b e d k  e m p i r i c a l l y as f o l l o w s :  = aU Hn  2  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 a r e e m p i r i c a l c o n s t a n t s dependent on t h e h y d r a u l i c c o n d i t i o n s and on t h e s l o p e and roughness o f t h e s t r e a m bed. Many r e s e a r c h  i n v e s t i g a t i o n s s i n c e have been d e v o t e d t o t h e d e -  t e r m i n a t i o n o f s t r e a m r e a e r a t i o n r a t e s [Dobbins and O'Connor , 1956;  L a n g b e i n and Durum, 1967; t o name b u t a f e w ] , gations concentrated determining lation  (2.10)).  to the o r i g i n a l Streeter-Phelps  Other r e s e a r c h  the e f f e c t s of surface renewal.  formu-  e f f o r t s a t t e m p t e d a more  t h e o r e t i c a l approach t o 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 and  investi-  on a c c u r a t e l y m e a s u r i n g t h e r e a e r a t i o n r a t e and t h e n  the e m p i r i c a l constants  (Equation  A number o f t h e s e  theories  From t h i s l a t t e r work, t h e r e  appears  t o be a s e m i - t h e o r e t i c a l b a s i s t o t h e e m p i r i c a l f o r m u l a t i o n as a number o f t h e t h e o r e t i c a l approaches have r e s u l t e d i n t h e development o f r e l a t i o n s h i p  45  s i m i l a r t o E q u a t i o n (2.10). given  Some o f t h e v a l u e s f o r t h e e m p i r i c a l c o n s t a n t s  i n t h e l i t e r a t u r e a r e shown i n T a b l e 2.4.  TABLE 2.4 SUMMARY OF CONSTANTS FOR THE REAERATION EQUATION (For U i n f e e t p e r second and H i n f e e t ) REFERENCE  a.  m  n  9.4  0.67  1.85  Owens e t 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 e t a l . , 1962  3.7  1.00  1.50  I s a a c s & Gaudy, 1966  3.3  1.00  1.33  L a n g b e i n & Durum, 1967  Of t h e range o f e m p i r i c a l f o r m u l a e , t h e one g e n e r a l l y  considered  co be most reasonable' f o r t h e e s t i m a t i o n o f reaerat?Lon r a t e s o v e r a w i d e range o f d e p t h 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 o f D o b b i n s  & O'Connor [1956] g i v e n by: . ,.' ...0.5 „-1.50 ^2 = 5.5U H  (2.11)  I n a d d i t i o n t o t h e 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 a r e a l s o a f f e c t e d by w i n d s , waves and c h e m i c a l a g e n t s , such as s u r factants.  The e f f e c t s o f s u r f a c t a n t s a r e m i n i m a l i n n a t u r a l waterways  b e c a u s e , even i f t h e y a r e p r e s e n t , c o n c e n t r a t i o n s the oxygen t r a n s f e r i s not i n h i b i t e d .  a r e u s u a l l y so low t h a t  Wind and wave e f f e c t s , however, can  a t t i m e s be s i g n i f i c a n t as t h e y r e s u l t i n i n c r e a s e d s u r f a c e r e n e w a l due t o w i n d - i n d u c e d shear s t r e s s e s and b r e a k i n g waves.  They a r e u s u a l l y  a c c o u n t e d f o r e m p i r i c a l l y by an a d j u s t m e n t o f r e a e r a t i o n r a t e s a c c o r d i n g t o wind v e l o c i t i e s .  A r e l a t i o n s h i p w h i c h has been s u g g e s t e d i n a r e c e n t  study o f d i s s o l v e d oxygen dynamics  i n t h e Sacremento-San J o a q u i n D e l t a  [DFWPS, 1972], c o n s i d e r e d t o be a d d i t i v e t o t h e r e a e r a t i o n  coefficient  p r e v i o u s l y d i s c u s s e d , i s g i v e n by: Ak  2  -  (Cw)  W  (2.12)  R  where W i s t h e wind v e l o c i t y i n mph; and C  i s t h e wind c o r r e c t i o n f a c t o r r a n g i n g i n v a l u e from 0 t o 0.4.  Temperature Temperature  has a l s o been found t o a f f e c t r e a e r a t i o n r a t e s .  compensation i s made by t h e use o f a t e m p e r a t u r e  correction  f a c t o r , 9, i n a manner s i m i l a r t o t h a t d i s c u s s e d e a r l i e r f o r BOD decay rates. 1.017  2.6  The t e m p e r a t u r e c o r r e c t i o n f a c t o r has been f o u n d t o v a r y from t o 1.044 [ D o b b i n s , 1964] and most commonly i s c h o s e n t o be 1.024.  OTHER SOURCES AND SINKS OF OXYGEN As w e l l a s t h e s o u r c e s and s i n k s o f 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 b i o c h e m i c a l o x i d a t i o n , t h e r e a r e o t h e r s o u r c e / s i n k p r o c e s s e s w h i c h a r e , a t t i m e s , i m p o r t a n t f a c t o r s i n t h e oxygen balance.  A d d i t i o n a l demands a r e o f t e n e x e r t e d on t h e oxygen r e s o u r c e s  o f a waterway by t h e d e c o m p o s i t i o n o f bottom d e p o s i t s o f o r g a n i c m a t t e r ,  t h e r e s p i r a t i o n o f a q u a t i c p l a n t s and t h e immediate c h e m i c a l  oxygen demand  of a wastewater. On t h e o t h e r s i d e o f t h e l e d g e r , oxygen may be added t o a s t r e a m by t h e p r o c e s s  of photosynthesis.  As w e l l , t h e removal o f BOD due  t o s e t t l i n g , w h i c h o c c u r s i n a s l o w moving s t r e a m , i s a p o s i t i v e f a c t o r ; however, t h e amount o f oxygen demand removed by t h i s p r o c e s s w i l l u s u a l l y add 2.7  t o t h e b e n t h i c demand. 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 o f t h e oxygen b a l a n c e  s t r e a m , c i t e d s e v e r a l times above, c a n now be s p e l l e d o u t f u l l y .  ina Their  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 t h e Ohio R i v e r i n t h e 1920's a p p l i e d t h e c o n c e p t s o f d e o x y g e n a t i o n and r e a e r a t i o n t o d e f i n e t h e n a t u r a l s e l f p u r i f i c a t i o n o f waterways. The f o r m u l a t i o n o f t h e oxygen b a l a n c e  ina  s t r e a m , d e v e l o p e d a s a r e s u l t o f t h e i r s t u d i e s , assumed t h a t t h e b i o c h e m i c a l oxygen demand o f a wastewater and r e a e r a t i o n from t h e atmosphere were t h e o n l y two p r o c e s s e s oxygen d e f i c i t .  w h i c h d e t e r m i n e d t h e n e t r a t e of change o f  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 t o as t h e "oxygen-sag c u r v e " , i s g i v e n by:  dD dt  =  K-jL - K D 2  where a l l p a r a m e t e r s a r e 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 :  (2.13)  (2.14) K  2" 1 K  where D i s t h e d i s s o l v e d oxygen d e f i c i t a t any t i m e t ; with L  o  and D  o  b e i n g r e s p e c t i v e l y t h e i n i t i a l u l t i m a t e FSOD and ° r  J  t h e i n i t i a l DO d e f i c i t . Thus, knowing t h e i n i t i a l s t r e a m BOD and DO d e f i c i t and t h e a p p r o p r i a t e d e o x y g e n a t i o n and r e a e r a t i o n c o e f f i c i e n t s , t h e DO d e f i c i t may be a t e d f o r any time t . The r e s u l t a n t p l o t o f DO d e f i c i t v e r s u s q u a n t i t a t i v e s o l u t i o n t o t h e oxygen-sag c u r v e s discussed i n Section  calcul-  time i s a  shown i n F i g u r e 2.1 and  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 e q u a t i o n c a n be expanded t o i n c l u d e t h e e f f e c t s on t h e oxygen b a l a n c e  o f some o f t h e o t h e r oxygen  s o u r c e / s i n k p a r a m e t e r s 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 , t h e s e t t l i n g o u t o f BOD, t h e a d d i t i o n o f BOD t o o v e r l y i n g w a t e r by bottom d e p o s i t s , and p h o t o s y n t h e t i c r e s p i r a t i o n .  The s o l u t i o n t o t h i s more  g e n e r a l form o f t h e oxygen s a g c u r v e w h i c h a c c o u n t s f o r t h e e f f e c t s o f t h e s e a d d i t i o n a l parameters [Camp, 1965] i s g i v e n by: -(K +K )t 1  D = K  2  - K  r 3 K  -K t]  3  2  - e  W •o (K +K ) 1  -K t  -K t  2  2  1 - e (K^+K^) where  K  x  (2.15)  3  +  D  o  e  K.j i s t h e r a t e of BOD  l o s s due t o s e t t l i n g per day;  p  i s t h e r a t e o f BOD  a d d i t i o n from bottom i n ppm p e r day;  a  i s t h e r a t e of p h o t o s y n t h e t i c  oxygen a d d i t i o n i n ppm  a l l o t h e r p a r a m e t e r s a r e as p r e v i o u s l y  defined.  per day;  CHAPTER 3 DISSOLVED OXYGEN MODELS  The mathematical  formulation of the oxygen balance, discussed i n  the previous chapter, forms the b a s i s of the d i s s o l v e d oxygen "model". "model" i s , i n the s t r i c t e s t sense, a formalism - the mathematical  A  express-  i o n of a relevant p h y s i c a l process, or processes, i n t h i s case the n a t u r a l processes of the deoxygenation  and r e a e r a t i o n i n water.  o f t e n used l o o s e l y , has numerous meanings.  The term "model",  I n the most general sense, i t  can mean a very n o n - s p e c i f i c conceptual i d e a l i z a t i o n of a problem o r process, as i n the economists' use of "economic models".  I t can a l s o be used  to mean a simple analog of a r e a l system, examples o f which are the p h y s i c a l models used i n engineering and h y d r a u l i c s . 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 i d e a l i s m , r e f e r s to a mathematical  formulation  together w i t h a technique which allows f o r a s o l u t i o n of the v a r i a b l e s o f 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 r e f e r s to a s p e c i f i c computer program used i n the s o l u t i o n .  It is  a l s o the most appropriate d e f i n i t i o n which can be used to describe the d i s s o l v e d oxygen models which w i l l be discussed i n t h i s chapter. 3.1  STREAM AND RIVER MODELS The b a s i c Streeter-Phelps formulation of the oxygen balance i n  streams and r i v e r s describes a time dependent f u n c t i o n a l r e l a t i o n s h i p between the b a s i c oxygen source and s i n k processes f o r a s i n g l e waste  - 50-  51  discharge.  The a p p l i c a t i o n o f t h i s " c l a s s i c a l " t h e o r y to streams and  r i v e r s i n o r d e r t o 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 a s s u m p t i o n s a r e made: ( i ) c r o s s - s e c t i o n a l m i x i n g i s r a p i d ; ( i i ) r i v e r f l o w s a r e s t e a d y , and ing) e x i s t s .  ( i i i ) " p l u g f l o w " ( l a c k o f l o n g i t u d i n a l mix-  These a s s u m p t i o n s a r e r e a s o n a b l e  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 m i x i n g r a t e s a r e 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 m i x i n g , and a r e low, r e s u l t i n g i n m i n i m a l  l o n g i t u d i n a l mixing  longitudinal dispersion.  n a t u r e of r i v e r and s t r e a m f l o w , a l t h o u g h t h e f l o w may  rates  As f o r t h e  steady  n o t be s t e a d y  over  t h e e n t i r e s t r e a m l e n g t h , i t can be c o n s i d e r e d t o be s t e a d y a t l e a s t  over  g i v e n s t r e t c h e s o f the r i v e r . The a s s u m p t i o n o f s t e a d y r i v e r f l o w a l l o w s s i m p l e : t r a n s p o s a l o f 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 t h e d i s s o l v e d oxygen d e f i c i t equation  ( E q u a t i o n s 2.14  & 2.15)  average v e l o c i t i e s can be o b t a i n e d and V e l o c i t y (V) = D i s t a n c e V/x  to d i s t a n c e - s c a l e s . they may  (DO)  By c o n t i n u i t y ,  be r e l a t e d t o d i s t a n c e as  (x) x Times ( t ) . Thus by s i m p l e s u b s t i t u t i o n of  f o r t i n the oxygen-sag s o l u t i o n , t h e DO d e f i c i t i s e x p r e s s e d  as a  f u n c t i o n o f 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 o f DO  in a  s t r e a m o r r i v e r downstream o f a s i n g l e waste o u t f a l l . t h e r e i s more t h a n one o u t f a l l , a DO  I n the e v e n t t h a t  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 i n p u t and t h e s o l u t i o n s superimposed, the t o t a l DO t h e sum  o f the i n d i v i d u a l d e f i c i t s .  deficit  being  A l s o , i f c o n d i t i o n s of temperature  and  r i v e r f l o w change o v e r 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 b o t h the r e a c t i o n r a t e c o n s t a n t s and  the v e l o c i t y , the s t r e t c h o f r i v e r may  d i v i d e d up i n t o s m a l l e r r e a c h e s o v e r w h i c h c o n d i t i o n s a r e c o n s t a n t .  of  be This  manner o f s e g m e n t a t i o n can be made t o 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 i n r i v e r conditions and a d d i t i o n a l waste inputs can be handled i n one 3.2  step.  ESTUARY MODELS The a p p l i c a t i o n of the " c l a s s i c a l " dissolved oxygen model to  estuaries i s not as simple and straightforward as i t i s i n the case of r i v e r s and streams.  This i s p r i m a r i l y because of the complex, non-uniform  nature of flow patterns i n estuaries which e x i s t as a r e s u l t of t i d a l i n fluence.  Although the natural physical and biochemical  processes involved  are s i m i l a r , the unsteady, o s c i l l a t o r y flows i n estuaries present problems when one attempts to apply a dissolved oxygen model, because of the  difficul-  t i e s encountered i n obtaining the time-histories of d i f f e r e n t parcels of water i n an estuary.  Unlike r i v e r s , where f o r a given set of r i v e r flows  there w i l l be a d i s c r e t e set of r i v e r v e l o c i t i e s f o r every l o c a t i o n along the stream length, v e l o c i t i e s i n an estuary vary with time as w e l l as l o c a t i o n , the temporal v a r i a t i o n s being due to changes i n water surface elevations throughout the estuary during the t i d a l cycle (see Figure 1.10  for  t y p i c a l v a r i a t i o n s i n the lower Fraser River) =- Ths- ussteady nature of v e l o c i t i e s i n estuaries, which are seen to vary "discontinuously" ( i n the sense of direction) makes i t impossible and distance reference frames.  to e a s i l y transpose between time  Thus, the basic Streeter-Phelps  formula-  tions for DO d i s t r i b u t i o n s , 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 d i f f e r s from r i v e r hydraulics and has important implications for the a p p l i c a t i o n of dissolved oxygen models i s increased dispersion and mixing i n estuaries caused by  the  53  o s c i l l a t o r y movement of the w a t e r mass.  S i g n i f i c a n t v e r t i c a l and  lateral  v e l o c i t y g r a d i e n t s , t o g e t h e r w i t h t u r b u l e n t d i f f u s i o n , tend t o e r o d e c o n c e n t r a t i o n peaks from a s l u g d i s c h a r g e ,  s p r e a d i n g and  s o l v e d s u b s t a n c e around the l i n e of mean a d v e c t i v e of  r e d i s t r i b u t i n g the advance.  dis-  T h i s mechanism  l o n g i t u d i n a l m i x i n g , w h i c h 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  t i m e s 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 ignored  i n favour of a "plug f l o w " assumption.  be  I n e s t u a r i e s , however, i t  must be a c c o u n t e d f o r ; i n the case of e s t u a r i e s w i t h z e r o f r e s h w a t e r i n flow, d i s p e r s i o n due  t o t i d a l m i x i n g i s the o n l y mechanism o f  material  transport. As we have s e e n , the n o n - s i m p l e n a t u r e of e s t u a r i n e 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  hydraulics  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 o f the b a s i c S t r e e t e r - P h e l p s oxygen model.  I n o r d e r t o d e v e l o p a d i s s o l v e d oxygen model w h i c h can  a p p l i e d t o e s t u a r i e s , i t i s n e c e s s a r y to go back t o b a s i c mass principles.  dissolved be  transport  T h i s 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 c o n c e p t s i n t r o d u c e d  i n the p r e v i o u s c h a p t e r 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  p o r t of any  b a s i c o n e - d i m e n s i o n a l e q u a t i o n f o r d e s c r i b i n g the mass t r a n s -  d i s s o l v e d s u b s t a n c e i n an u n s t e a d y n o n - u n i f o r m f l o w i s  obtained  by making a mass b a l a n c e o v e r an e l e m e n t a l c r o s s - s e c t i o n a l s l i c e of f l o w f i e l d o f the waterway. p r o c e s s e s of a d v e c t i o n any  and  Mass i s t r a n s p o r t e d d i s p e r s i o n , and  t h r o u g h the s l i c e by  the the  these processes, together w i t h  s o u r c e o r s i n k s o f the s u b s t a n c e w i t h i n the s l i c e , d e t e r m i n e  the  concentration.  The g e n e r a l i z e d form o f t h e o n e - d i m e n s i o n a l  mass b a l a n c e  equation i s given by:  L£ = 2»t  * Fx"  s  -u  E dfA A 3xL  as!  dxJ  "  JL  ^  S  (3.1) i  where s i s t h e c o n c e n t r a t i o n o f 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 t h e r a t e o f p r o d u c t i o n p e r u n i t volume due t o t h e ith s o u r c e - s i n k 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 distance; and t i s the time. The  t h r e e terms on t h e r i g h t hand s i d e o f the e q u a t i o n a r e t h e a d v e c t i v e ,  d i s p e r s i v e and s o u r c e - s i n k t e r m s , r e s p e c t i v e l y . Since Equation  (3.1) i s o n e - d i m e n s i o n a l ,  p a r a m e t e r s a r e c r o s s - s e c t i o n a l l y averaged v a l u e s .  a l l t h e v a r i a b l e s and I n an e s t u a r y , because  o f t i d a l e f f e c t s , t h e p a r a m e t e r s o f t h e e q u a t i o n u, E and A, d e f i n e d by t h e 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 t h e p a r t i c u l a r e s t u a r y , c a n v a r y o v e r b o t h space(x) and t i m e ( t ) .  Thus, i n t h e s o l u t i o n , i t i s n e c e s s -  a r y t o account i n some manner f o r t h e t e m p o r a l  as w e l l as s p a t i a l v a r i a t i o n ,  o f these p a r a m e t e r s . There a r e two types o f s o l u t i o n s w h i c h can be a p p l i e d t o t h e oned i m e n s i o n a l mass t r a n s p o r t e q u a t i o n - t h e " s t e a d y - s t a t e " o r " t i d a l l y a v e r a g e d " s o l u t i o n and t h e " 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 o u t t h e e f f e c t s o f t h e t i d e o v e r t h e t i d a l c y c l e a s s i g n i n g p a r a m e t e r s t h e i r "mean t i d a l " v a l u e .  Because o f t h i s a v e r a g i n g o f  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 t e m p o r a l the  processes  i n v o l v e d b u t , as we s h a l l s e e , i s n o n e t h e l e s s  The second t y p e , t h e t i d a l l y v a r y i n g s o l u t i o n , a c c o u n t s  abstraction of very  useful.  f o r the temporal  v a r i a t i o n i n t h e p a r a m e t e r s by o b t a i n i n g t h e i r v a l u e s i n d e p e n d e n t l y  through  s o l u t i o n o f t h e hydrodynamic e q u a t i o n s w h i c h d e s c r i b e t h e h y d r a u l i c s o f t h e estuary.  The t i d a l l y v a r y i n g s o l u t i o n t o t h e mass t r a n s p o r t e q u a t i o n , a l -  though i t a l l o w s f o r g r e a t e r t e m p o r a l  r e s o l u t i o n and t h e o b s e r v a t i o n o f  " r e a l t i m e " e f f e c t s , demands a much more s o p h i s t i c a t e d a p p r o a c h and g r e a t e r expense o f e f f o r t i n development.  The two t y p e s o f s o l u t i o n s w i l l now be  discussed.  3.4  THE STEADY STATE SOLUTIONS TO THE MASS TRANSPORT EQUATION T h i s method o f s o l v i n g t h e o n e - d i m e n s i o n a l  mass t r a n s p o r t equa-  t i o n , r e f e r r e d t o as t h e " t i d a l l y a v e r a g e d " a p p r o a c h , a s s i g n s p a r a m e t e r s t h e i r mean v a l u e s o v e r a t i d a l c y c l e .  T h i s does n o t a l t e r t h e f o r m o f t h e  mass t r a n s p o r t e q u a t i o n b u t m e r e l y changes t h e i n t e r p r e t a t i o n s o f t h e v a r i a b l e s and p a r a m e t e r s .  F o r example, t h e v e l o c i t y term(u) becomes t h e  t i d a l l y averaged v e l o c i t y ( U ) , w h i c h i s d e t e r m i n e d by t h e f r e s h w a t e r d i s charge t h r o u g h t h e 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  dis-  p e r s i o n c o e f f i c i e n t i s r e p l a c e d by what i s c a l l e d t h e 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 (E) . The  a s s u m p t i o n o f 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 r e s p e c t t o time a r e z e r o .  T h i s means t h a t c o n c e n t r a t i o n s w i l l be a s -  s i g n e d t h e i r mean t i d a l v a l u e and w i l l be seen t o v a r y o n l y w i t h d i s t a n c e  56  along the estuary. Equation  The incorporation of the steady-state assumption reduces  (3..i) s t i l l i n the general case to:  where U i s the t i d a l l y averaged v e l o c i t y  (=Q/A);  E i s the t i d a l l y averaged dispersion c o e f f i c i e n t ; Q i s the fresh water discharge; A i s the t i d a l l y averaged c r o s s - s e c t i o n a l area; and a l l other parameters and variables are as previously defined. Applying Equation t i v e l y straight  (3.2) to dissolved oxygen i n estuaries i s r e l a -  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-  t r i b u t i o n for dissolved oxygen i s given by:  where c i s the dissolved oxygen concentration; c  i s the saturation concentration of dissolved oxygen; s  L i s the BOD  concentration remaining  at any point x;  i s the reaeration rate c o e f f i c i e n t ; i s the BOD  decay rate c o e f f i c i e n t ;  and a l l other parameters and variables are as previously defined.  57  Since the BOD  develop an equation f o r BOD with the DO s o l u t i o n . equation to BOD,  (3.3),  term appears i n Equation  i t i s necessary to  d i s t r i b u t i o n i n an estuary before proceeding  Applying the general steady-state mass transport  assuming point source waste addition with f i r s t order  BOD  removal, r e s u l t s i n :  (3.4)  where L i s the BOD K  r  i s the BOD  concentration remaining at any point x; removal rate c o e f f i c i e n t ;  and a l l other parameters are as previously defined. It should be noted that the BOD removal r a t e (K ) i s the t o t a l r  removal c o e f f i c i e n t which can account f o r removal of BOD  due to s e t t l i n g ,  as w e l l as oxidation, i t being assumed that s e t t l i n g i s approximated f i r s t order k i n e t i c s . then K  r  If BOD  by  removal i s accomplished only by oxidation,  = K . 1 We now have equations to describe, under steady-state conditions,  the d i s t r i b u t i o n s of DO and BOD  i n an estuary.  determined i n part by input from the BOD  Since the DO response i s  s o l u t i o n , Equations  ( 3 . 3 ) and ( 3 . 4 )  are said to be a "coupled" p a i r of equations and the s o l u t i o n must proceed accordingly.  (3.4),  Note that i f E i s set equal to zero i n Equations ( 3 3 ) and V  which would be the case f o r a r i v e r or stream, the resultant solu-  t i o n of the coupled BOD/DO equation would, under the s i m i l a r  assumptions,  be comparable with that derived by way of the Streeter-Phelps formulation.  There are two b a s i c s o l u t i o n 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  o f f e r s continuous s o l u t i o n s to the equations f o r various e s t u a r i a l and boundary c o n d i t i o n c o n f i g u r a t i o n s .  I t can be c r e d i t e d l a r g e l y t o the work  of D.J. O'Connor CO'Connor, 1965-] who has provided s o l u t i o n s f o r a number of s p e c i a l cases.  The advantage o f the continuous s o l u t i o n approach i s  that i t i s designed to handle long r i v e r / e s t u a r y stretches I n a simple, s t r a i g h t f o r w a r d manner. Clhoman, 1965,  The second approach, developed by Robert Thoman  1971], uses f i n i t e  coupled system of equations.  d i f f e r e n c e techniques t o solve the  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 c o n d i t i o n c o n f i g u r a t i o n s , i t i s o f t e n imposing as a s o l u t i o n method because 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 i n v e r s i o n techniques. t i o n of the steady-state 3.4.1  The two approaches t o s o l u -  equations w i l l now be discussed.  The Continuous S o l u t i o n Approach.  I n order t o o b t a i n  continuous s o l u t i o n s by a n a l y t i c a l l y s o l v i n g the BOD/DO equations, i t i s f i r s t necessary t o make assumptions regarding estuary a r e a l c o n f i g u r a t i o n . O'Connor L~1965]J o f f e r s a number of s o l u t i o n s which apply t o e s t u a r i e s with constant as w e l l as v a r i a b l e c r o s s - s e c t i o n p r o v i d i n g that the v a r i a t i o n can be expressed i n terms of l o n g i t u d i n a l distance by l i n e a r , power o r exponent i a l expressions. main stem Fraser  An examination of the c r o s s - s e c t i o n a l geometry of the (see Figure  4-4 ) revealed that the c r o s s - s e c t i o n a l area  increases i n the seaward d i r e c t i o n .  From the r e s u l t s of a l i n e a r regress-  i o n a n a l y s i s , run t o determine the r e l a t i o n s h i p between area and d i s t a n c e , i t was found that a l i n e a r expression  r e l a t i n g c r o s s - s e c t i o n a l area w i t h  59  l o n g i t u d i n a l distance gave a good " f i t " y i e l d i n g values f o r the c o e f f i c i e n t 2 of determination stage.  (r ) which varied from 0.62  to 0.69  depending on r i v e r  Thus O'Connor's a n a l y t i c a l solutions for estuaries with cross-  s e c t i o n a l area increasing l i n e a r l y i n the seaward d i r e c t i o n were appropriate and could be applied to the lower Fraser system. To insure that the d e t a i l s of the working solutions offered by O'Connor were correct, the solutions were re-derived, by way the basic BOD  and DO mass transport equations.  of proof, from  This v e r i f i c a t i o n procedure,  which w i l l not be presented, proved that the a n a l y t i c a l solutions were correct.  The s o l u t i o n f o r BOD  d i s t r i b u t i o n s upstream and downstream of a  single waste discharge at x = X for x<x  for  "Wx " o : 1 (x) = A E o 1 o  X  Wx " o A E o  X  X>X : Q  L^( )= K  X  X  are given  q  by:  V -  (3.5a) o  O  t  V  vr I <qx )K (qx) v  o  (3.5b)  v  o  j  where 2A E o K r  Ni" L^(x) i s the BOD  d i s t r i b u t i o n as a function of distance upstream  of the o u t f a l l l o c a t i o n ; L^(x) i s the BOD  d i s t r i b u t i o n as a function of distance down-  stream of the o u t f a l l l o c a t i o n ; W i s the constant  rate of waste addition;  60  A  o  i s the c r o s s - s e c t i o n a l area a t the o u t f a l l  location;  Q i s the freshwater i n f l o w t o 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 t h e BOD removal r a t e c o e f f i c i e n t ;  I and K a r e m o d i f i e d B e s s e l f u n c t i o n s o f t h e f i r s t and second v v kind o f order v; and 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 estuary. The c o r r e s p o n d i n g  DO d e f i c i t d i s t r i b u t i o n j f o r t h e r e g i o n s up-  s t r e a m and downstream o f a s i n g l e o u t f a l l a t x = "x a r e g i v e n b y : o K f o r x<x : D,(x)= o 1  Wx K (x q)I (xq)-K (x p)l (xp)  A E  v  2 r . o .  K  Wx  f o r x>x : D_(x) = o 2 K.-K A E 2 r o  o  v  v  o  v  (3.6a)  oj  X  T V  I  X  v V (  ) K  v  ( x q )  - v I  ( x  o  p ) I  v  ( x p )  (3.6b)  a  where K  2  D (x) i s t h e DO d e f i c i t d i s t r i b u t i o n a s a f u n c t i o n o f d i s t a n c e 1 upstream o f 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 a s a f u n c t i o n o f d i s t a n c e 2 downstream o f t h e o u t f a l l l o c a t i o n ;  61  K  2  i s the reaeration rate c o e f f i c i e n t ;  and a l l other parameters and variables are as previously defined.  These solutions for BOD  and DO d i s t r i b u t i o n i n an estuary may  at  f i r s t seem somewhat overbearing because they contain a r e l a t i v e l y uncommon mathematical expression, the modified Bessel function.  However, inspection  of the behaviour of modified Bessel functions reveals that they are s i m i l a r to exponentials, with the modified Bessel functions of the f i r s t kind, I ( x ) , v  bx behaving i n a manner analagous to ae K^x),  behave  s i m i l a r l y to ae  b  x  where, as x approaches zero, K (x) v  Equations(3. 5) and  .  Functions of the second kind,  except i n the region of the o r i g i n asymptotically approaches i n f i n i t y .  (3.6) give the BOD  i n an estuary due to a single waste source. present, the d i s t r i b u t i o n s due  to each may  and DO def i c i t  distributions  I f more than one source i s be calculated and, by applying  the p r i n c i p l e of superposition as i s done i n r i v e r s , summed to give the t o t a l d i s t r i b u t i o n of BOD  and DO  deficit.  When applying the continuous  solutions to an estuary i t i s neces-  sary to assume that conditions are constant over the e n t i r e estuary.  Thus  i t i s not possible by this method to account f o r any v a r i a t i o n over the length of the estuary i n 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 F i n i t e Section Approach.  The f i n i t e s e c t i o n approach  i n essence replaces the derivatives i n the mass transport equation with f i n i t e difference approximations. by Thomann CThomann 1965,  1971]  In t h i s method of s o l u t i o n , f i r s t applied to the Delaware Estuary, the estuary i s  62  d i v i d e d i n t o a number o f segments (or boxes) w i t h each segment assumed t o be c o m p l e t e l y processes  mixed.  Assuming t h a t t h e a d v e c t i v e and d i s p e r s i v e t r a n s p o r t  and waste d i s c h a r g e s  m a t e r i a l s balance  to the e s t u a r y a r e steady  i n time, a  can be w r i t t e n around each f i n i t e s e c t i o n o f t h e e s t u a r y .  Writing the mass b a l a n c e  i s e q u i v a l e n t t o r e p l a c i n g the d e r i v a t i v e s i n the  mass t r a n s p o r t e q u a t i o n by t h e i r f i n i t e d i f f e r e n c e a p p r o x i m a t i o n s . balance  over segment i f o r a d i s s o l v e d substance  such as BOD  The mass  undergoing  f i r s t - o r d e r decay g i v e s Drhomann, 19713:  Q  t i-l,i i-l a  C  +  (  1  - i-l,i a  )  c  il  " I>i,i+l i Q  c  +  (  1  - i,i l a  +  )  c  i l] +  (3.7) +  E  x - i , i  (  c  i - r i c  )  +  E  i,i+i< i r i>" i i ± c  c  K  c  v  +  w  +  i -  0  where c^ i s t h e c o n c e n t r a t i o n i n segment i ; V\ i s the volume o f segment i ; W^ i s the mass o f waste substance  discharged  i n t o segment i  per t i d a l c y c l e ; is Q  the decay c o e f f i c i e n t f o r segment i ;  i s the t i d a l l y freshwater  averaged d i s c h a r g e t h r o u g h t h e e s t u a r y (the  discharge);  a.,.,, i s t h e 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 E  i  i,i+l i  i s the " e f f e c t i v e d i s p e r s i v e " t r a n s p o r t between segments  and  (i+1).  The s u b s c r i p t n o t a t i o n o f the v a r i o u s 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 i n 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  In t i d a l flows a i s set  ments from the concentration within each segment. equal to 0.5  seg-  to allow f o r the e f f e c t s of flow r e v e r s a l , whereas i n a r i v e r  flow s i t u a t i o n a i s 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  E  i s given by:  i,i+1 i,i+1 A  ( 3 > 8 )  1,1+1 L  i,i+1  where E. .... i s the e f f e c t i v e c o e f f i c i e n t 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 ( t i d a l l y averaged) of the interface between segments i and  (i+1);  and L  i , i+1  i s the average of the lengths of segments i and  The f i n a l two terms of Equation  (i+1).  (3.7) represent the e f f e c t s of decay and  waste discharge. Equations s i m i l a r to (3.7) can be w r i t t e n f o r each of n segments of an estuary to give a system of n simultaneous  l i n e a r d i f f e r e n c e equations.  These equations can be written i n the general form as: n  £Z where  r  + a. , ,c. .  a..c. ii l  +  a. .,,c.,. l,i+1 l + l  =  W., ij  (3.9)  65  = -a  a  ii a  i  Q - E ; 1-1,1 i - l , i 1,1+1  J L 1  i,i+l  1-1, i *  1-1,1  1  i  - (1-a )Q - E 1,1+1 1,1+1.. H  U s i n g m a t r i x n o t a t i o n , t h e system o f E q u a t i o n s M(c)  i,i+l  (3. 9) c a n be w r i t t e n  = (W)  ( . 3  1 0  )  where C A j 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) a r e ( 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 t h e n o b t a i n e d f o r m a l l y by i n v e r s i o n o f t h e A matrix, i . e . (c)  = CA]"  1  (W)  (3.11)  Thus, t h e problem o f d e t e r m i n i n g t h e s t e a d y - s t a t e , o n e - d i m e n s i o n a l  distri-  b u t i o n o f a waste m a t e r i a l (such as BOD) i n an e s t u a r y r e d u c e s t o s o l v i n g n s i m u l t a n e o u s a l g e b r a i c e q u a t i o n s o r 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 a p p r o x i m a t i o n o r mass b a l a n c e around s e c t i o n s can a l s o be a p p l i e d t o c o u p l e d systems.  finite  S u f f i c e i t t o say here  that- a m a t e r i a l s b a l a n c e f o r DO c a n be w r i t t e n i n a manner s i m i l a r t o t h a t p r e v i o u s l y d e s c r i b e d f o r BOD.  The r e s u l t a n t system o f n s i m u l t a n e o u s ,  l i n e a r e q u a t i o n s f o r DO can be e x p r e s s e d i n m a t r i x forms c o u p l e d w i t h t h e BOD system and s o l v e d by u s i n g m a t r i x i n v e r s i o n t e c h n i q u e s t o o b t a i n t h e s t e a d y - s t a t e , o n e - d i m e n s i o n a l d i s t r i b u t i o n o f DO i n an e s t u a r y 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 o f t h e f i n i t e s e c t i o n approach  t o e s t u a r i e s has  t h e d e c i d e d advantage o f b e i n g more f l e x i b l e t h a n t h e c o n t i n u o u s s t a t e s o l u t i o n i n t h a t i t i s n o t r e s t r i c t e d by assumptions  steady-  regarding  e s t u a r y geometry o r o t h e r boundary c o n d i t i o n c o n f i g u r a t i o n s .  Also,  this  method can e a s i l y be adapted t o a c c o u n t f o r changes o v e r the l e n g t h of the e s t u a r y i n such t h i n g s as w a t e r t e m p e r a t u r e and o f t h e d i s s o l v e d oxygen s o u r c e / s i n k and  the r a t e c o e f f i c i e n t s  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 a p p r o a c h , by i t s main a s s u m p t i o n , r e q u i r e s o n l y t h a t c o n d i t i o n s be h e l d c o n s t a n t  w i t h i n each segment, t h e y may  be a l l o w e d  to  v a r y from segment t o segment t h r o u g h o u t t h e e s t u a r y .  Any  d i s c h a r g e s , each o f w h i c h i s assumed t o be c o m p l e t e l y  mixed i n t o the  segment a d j a c e n t  number of waste  t o i t s l o c a t i o n , can be h a n d l e d s i m u l t a n e o u s l y  as  the  s o l u t i o n method i s d e s i g n e d so t h a t 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 t o t h e o n e - d i m e n s i o n a l 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 t h e s p a t i a l  and  t e m p o r a l v a r i a t i o n s of t h e t i d a l l y v a r y i n g p a r a m e t e r s u, A and E.  In  o r d e r t o 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 n e c e s s a r y 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.  T h i s i s done by a p p l y i n g  a p p r o p r i a t e s e t of hydrodynamic e q u a t i o n s w a t e r mass of the e s t u a r y and tidal cycle.  The  (motion and  s o l v i n g these equations  the  c o n t i n u i t y ) to throughout  the  the  r e s u l t a n t p r e d i c t i o n s of the s p a c e - t i m e h i s t o r y of  t i d a l l y v a r y i n g p a r a m e t e r s s e r v e as i n p u t t o 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 o n e - d i m e n s i o n a l mass t r a n s p o r t e q u a t i o n ,  and as such the h y d r o -  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 ing  scheme of s o l u t i o n .  The  hydrodynamic sub-model w i l l now  I t s h o u l d be noted b e f o r e p r o c e e d i n g  be  vary-  discussed.  that the i n c l u s i o n , i n t h i s t h e s i s ,  of  t h e t i d a l l y v a r y i n g approach t o m o d e l i n g was made p o s s i b l e because o f  an i n v e s t i g a t i o n i n t o e s t u a r y m o d e l i n g on t h e lower F r a s e r R i v e r out by C.S. J o y . H i s d i s s e r t a t i o n [Joy,  [ J o y , 1974] and subsequent  publication  1975], t o which t h e reader i s r e f e r r e d , p r o v i d e comprehensive  coverage o f d e t a i l s i n t h e development the  carried  o f t h e hydrodynamic  sub-model and  t i d a l l y v a r y i n g s o l u t i o n s t o t h e o n e - d i m e n s i o n a l mass t r a n s p o r t  equations.  The e n s u i n g d i s c u s s i o n w h i c h i s b u t a b r i e f summary o f t h o s e  d e t a i l s o f the aforementioned research e f f o r t that a r e p e r t i n e n t t o 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 J o y ' 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 e q u a t i o n s w h i c h  d e s c r i b e t h e hydrodynamic behavour o f t h e water mass i n an e s t u a r y , namely t h e e q u a t i o n s o f m o t i o n and c o n t i n u i t y a r e , a s a p p l i e d t o t h e F r a s e r R i v e r / E s t u a r y , g i v e n by [ D r o n k e r s , 1969]: Su  bt  •bx  ^1  dh  =  8  dx  [uju  _ 8 c  2-  - at  where u i s t h e mean l o n g i t u d i n a l v e l o c i t y ; h i s t h e h e i g h t o f t h e water s u r f a c e above an a r b i t r a r y datum; y i s t h e mean c r o s s - s e c t i o n a l water d e p t h ; 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  acceleration;  level  and C i s Chezy's f r i c t i o n Equations  (3.12) and  factor. (3.13) a r e a c o u p l e d p a i r of p a r t i a l  dif-  f e r e n t i a l e q u a t i o n s 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  F i g u r e 3.2  f o r i l l u s t r a t i o n o f t e r m s ) , independent  parameters  C, b and g.  v a r i a b l e s x and  Note t h a t , as shown i n F i g u r e 3.2,  i n the  t , and hydro-  dynamic e q u a t i o n s 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 e q u a t i o n s x i n c r e a s e s i n t h e downstream d i r e c t i o n . main assumptions  The  made i n d e r i v i n g t h e hydrodynamic e q u a t i o n s were t h a t  t h e t i d a l s t o r a g e w i d t h of t h e r i v e r / e s t u a r y i s e q u a l t o t h e a d v e c t i v e w i d t h , t h e Chezy f o r m u l a a d e q u a t e l y r e p r e s e n t s f r i c t i o n i n t h e e s t u a r y and t h a t t h e e s t u a r y h y d r a u l i c s c o u l d be approximated equations.  These assumptions  by  one-dimensional  a r e , by and l a r g e , r e a s o n a b l e f o r t h e  F r a s e r R i v e r / E s t u a r y except perhaps i n t h e lower r e a c h e s o f t h e r i v e r where the p r e s e n c e may  of t h e s a l t water wedge c a u s i n g a s t r a t i f i e d  a f f e c t b o t h the f r i c t i o n a l e f f e c t s and t h e v a l i d i t y o f t h e  dimensional assumption.  flow  field  one-  ,  N u m e r i c a l s o l u t i o n s t o t h e hydrodynamic e q u a t i o n s can be  ob-  t a i n e d by u s i n g t h e 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 o f 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 o f  super-  i m p o s i n g a g r i d o f " f i x e d " s t a t i o n s a l o n g t h e e s t u a r y and r e p l a c i n g  the  d e r i v a t i v e s i n t h e hydrodynamic e q u a t i o n 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 t e m p o r a l and s p a t i a l v a r i a t i o n s o f t h e  v a r y i n g parameters  u and A may  and t i d a l c o n d i t i o n s .  tidally  be o b t a i n e d f o r s e l e c t e d f r e s h w a t e r f l o w s  I n 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 a r e assumed  69  Figure 3.2 The Hydrodynamic Estuary  to be " q u a s i - s t e a d y "  ( 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 -  w a t e r f l o w s be c o n s t a n t of a n a l y s i s .  and t i d a l p a t t e r n s be i d e n t i c a l o v e r t h e p e r i o d  S i n c e r e s i d e n c e times i n t h e lower F r a s e r a r e n e v e r more  than f o u r t o s i x d a y s , t h i s a s s u m p t i o n i s r e a s o n a b l e . The r e l a t i v e s i g n s o f g r i d s p a c i n g (Ax)  and i n t e g r a t i o n timed  ( A t ) i n t h e s o l u t i o n scheme were s e l e c t e d a c c o r d i n g stability  i n the numerical  integration.  to requirements of  I t was found t h a t a space g r i d  a t 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 o f 90 seconds were s a t i s factory.  D e t a i l s o f t h e network o f s t a t i o n s chosen as a r e s u l t o f t h e s e  c r i t e r i a w i l l be p r e s e n t e d  i n Chapter 4 a l o n g w i t h a d i s c u s s i o n on t h e  a p p l i c a t i o n t o t h e F r a s e r R i v e r / E s t u a r y o f t h e hydrodynamic sub-model. 3.5.2  The T i d a l l y V a r y i n g M o d e l .  Output f r o m t h e hydrodynamic  sub-model y i e l d s i n f o r m a t i o n on t h e space t i m e h i s t o r y o f t h e t i d a l l y v a r y i n g parameters u and A. mass t r a n s p o r t e q u a t i o n  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  can be o b t a i n e d , e q u i v a l e n t i n f o r m a t i o n must be  derived 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). dependent b e h a v i o u r  The t i m e  o f l o n g i t u d i n a l d i s p e r s i o n , b e i n g a complex, p o o r l y  u n d e r s t o o d phenomenon i n f l u e n c e d by such t h i n g s 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 gradients, i s d i f f i c u l t to describe. i n t h i s t h e s i s are one-dimensional,  S i n c e t h e models d i s c u s s e d  t h a t i s , they a r e n o t c o g n i z a n t o f  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 , t h e 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 o f l o n g i t u d i n a l d i s p e r s i o n i s r e p l a c e d by t h e t i d a l l y a v e r a g e d l o n g i t u d i n a l dispersion coefficient. for  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  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 t h e 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 m i x i n g  i s complete.  It  must be s t r e s s e d t h a t t h i s c o e f f i c i e n t i s n o t t h e same as t h e c o e f f i c i e n t o f t i d a l d i s p e r s i o n w h i c h i s used i n t h e s t e a d y - s t a t e o n e - d i m e n s i o n a l mass t r a n s p o r t e q u a t i o n s . two c o e f f i c i e n t s w i l l be d i s c u s s e d  solutions to the  The d i f f e r e n c e s between t h e s e  i n Chapter 4.  Now t h a t t h e s p a t i a l and t e m p o r a l v a r i a t i o n s o f a l l t h e t i d a l l y v a r y i n g p a r a m e t e r s can be accounted f o r , t h e t i d a l l y v a r y i n g mass t r a n s port equation  can be s o l v e d .  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 The  general one-dimensional equation  [ s e e J o y , 1974 f o r d e t a i l s ] .  (Equation  3.1) i s t r a n s f o r m e d  into  i t s c h a r a c t e r i s t i c o r L a g r a n g i a n form,to g i v e :  f  =  u  (3.14)  and dc dt  l  A ' ~3>2C  Equation and  TEA  a  source/sink  dc£ dt  [  a c1 "a^J  . +  T p -  TL  (3.15) i s then s e p a r a t e d  .„  \  ,  ^  (3-15)  i n t o i t s component d i s p e r s i v e  parts to give:  = A  dx  f EA , a c l [ dxj  (3.16)  and n dc d  t  V  =  S  (3.17)  ~  F i n i t e d i f f e r e n c e a p p r o x i m a t i o n s a r e used t o r e p l a c e t h e d e r i v a t i v e s i n Equations (3.14),  (3.16) and (3.17) and n u m e r i c a l  methods  are used t o o b t a i n s o l u t i o n s t o t h e 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 t e c h n i q u e , t h e  mass t r a n s p o r t e q u a t i o n i s s o l v e d a l o n g t h e c h a r a c t e r i s t i c c u r v e s o f t h e advective transport processes.  The main advantage o f t h i s method i s t h a t  i t p r o c e e d s t o 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 t h i n g s as n u m e r i c a l d i s p e r s i o n . processes  As w e l l , by t h i s t e c h n i q u e  each o f t h e  r e l e v a n t t o 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 s o u r c e /  s i n k - a r e handled  independently.  B r i e f l y , t h e mechanics o f t h e s o l u t i o n a r e as f o l l o w s . advective t r a n s p o r t process  i s s i m u l a t e d f i r s t by moving a g r i d o f  " 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 o f d i s s o l v e d s u b s t a n c e time increment  The  fora  o f one hour a c c o r d i n g t o t h e v e l o c i t i e s p r e d i c t e d by t h e  hydrodynamic model.  The c o n c e n t r a t i o n o f each p o i n t i s a d j u s t e d as i t  p a s s e s an e f f l u e n t o u t f a l l .  The second s t e p i n t h e 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 t h e moving g r i d t o 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 i n g t h e time i n c r e m e n t . s i n k e f f e c t s a r e a c c o u n t e d f o r by y e t a n o t h e r tion.  These t h r e e s t e p s a r e r e p e a t e d  crement and so on.  F i n a l l y , the source/  readjustment  of concentra-  i n sequence f o r t h e next  The s o l u t i o n t h u s p a s s e s t h r o u g h  j u s t i n g c o n c e n t r a t i o n s on t h e g r i d of moving p o i n t s .  time, hourly  read-  Moving p o i n t s a r e  added t o and removed from t h e model e s t u a r y a t i t s b o u n d a r i e s a r e needed.  time i n -  as they  A t t h e end o f each hour, c o n c e n t r a t i o n s a r e e x t r a p o l a t e d  o f f t h e g r i d o f moving p o i n t s o n t o t h e f i x e d g r i d o f s t a t i o n s used i n t h e hydrodynamic model. I n o r d e r t o use t h e 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 c o n c e n t r a t i o n s i n t h e e s t u a r y , i n a d d i t i o n t o t h e t i d e and r i v e r  f l o w i n f o r m a t i o n w h i c h i s needed f o r t h e hydrodynamic  sub-model,  infor-  m a t i o n i s r e q u i r e d d e s c r i b i n g t h e l o c a t i o n and q u a n t i t y o f e f f l u e n t d i s c h a r g e s as w e l l as the v a l u e s o f t h e r a t e c o n s t a n t s source/sink  r e a c t i o n s and the d i s p e r s i o n p r o c e s s .  m a t i o n i s f e d i n t o t h e model as q u a s i - s t e a d y  which govern the The e f f l u e n t i n f o r -  hourly discharge  r a t e s over  a 25 hour t i d a l c y c l e a t any o f up t o 40 d i f f e r e n t l o c a t i o n s on t h e f i x e d grid..  CHAPTER 4  APPLICATION OF DISSOLVED OXYGEN MODELS TO THE FRASER RIVER/ESTUARY  The  i m p l e m e n t a t i o n o f d i s s o l v e d oxygen models c o n s i s t s o f t h e  following steps:  making an a b s t r a c t i o n o f t h e p h y s i c a l - h y d r a u l i c system  t o f i t t h e b a s i c model f o r m u l a t i o n s ; making assumptions about t h e v a r i o u s processes involved; applying appropriate processes;  c o e f f i c i e n t s t o each o f these  e n t e r i n g v a r i o u s waste d i s c h a r g e  predicted results.  p a t t e r n s ; and o b s e r v i n g t h e  The a p p l i c a t i o n o f t h e 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 t o the F r a s e r R i v e r / E s t u a r y w i l l now be considered  4.1  i n l i g h t o f the b a s i c e l e m e n t s o f model  THE MODEL RIVER/ESTUARY The  Joy  implementation.  "model r i v e r / e s t u a r y " used i n t h i s study was d e v e l o p e d by  [1974] i n h i s i n v e s t i g a t i o n s o f e s t u a r i n e h y d r a u l i c b e h a v i o u r .  covers  It  t h e l o w e r F r a s e r R i v e r system from t h e S t r a i t o f G e o r g i a t o  C h i l l i w a c k and i n c l u d e s t h e t h r e e p r i n c i p a l c h a n n e l s - t h e M a i n Arm/Main Stem, t h e N o r t h Arm and t h e P i t t R i v e r system.  The s c h e m a t i c l a y o u t o f  the model r i v e r / e s t u a r y i s shown i n F i g u r e 4.1 a n d , as mentioned i n S e c t i o n 3.5.1, was f i r s t d e v e l o p e d by J o y [1974] t o be u t i l i z e d w i t h i n t h e hydrodynamic sub-model o f t h e 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 t h e t i d a l l y averaged model. As t h e model r i v e r / e s t u a r y e x t e n d s t o c o v e r t h a t p o r t i o n o f t h e l o w e r 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 , t h e upstream boundary was chosen t o be i n t h e v i c i n i t y  o f C h i l l i w a c k , t h e commonly a c c e p t e d l i m i t o f  -  74 -  Main Arm  Figure 4.1 Numbering Scheme and Network of Stations Used i n the Model River/Estuary  76  t i d a l influence.  Downstream model boundaries are the exits of the River to  the S t r a i t 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 i n the model.  I t should be noted,  however, that t h e i r presence has been accounted f o r i m p l i c i t l y by a r e a l adjustments of the Main Arm and North Arm e x i t s .  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 i n Figure 4.1. chosen to be 5,000 f e e t . Chilliwack Mountain  Segment length was  arbitrarily  The Main Arm/Main Stem extends from Steveston to  (station numbers 1 to 62); the North Arm, from Point  Grey to New Westminster  (station numbers 101 to 118) where i t j o i n s 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 l o c a l low water depth, cross-sectional area, and r i v e r width f o r each station were obtained from hydrographic charts supplied by the Department of Public Works [DPW,  1970] .  These parameters were ad-  justed to compensate f o r the presence of major side channels as was the case i n the Main Arm and North Arm e x i t s of the r i v e r and also to f i t the advective flow core.  Figures 4.2 and 4.3 show the v a r i a t i o n of the  gross and advective values of these parameters along each of the three channels considered by the models.  Gross  Values  Advective  30 Stations Figure 4.2 V a r i a t i o n of Cross-Sectional Parameters i n the Main Arm/Main Stem  Values  78  DEPTHS AND AREAS  Relative to local low water. Gross  Values  Advective  Norm  i  Arm  Values  Pitt River  _40,000 CM  £30,000 §20,000 10,000 i  i  1  i  l  I  0 _i  I  i  i  l  i  I  i  0 40 30 CL  20  a 10  3.000  i O  d Z CO  i  I  m O  l£) o  z  co  V  i  3;  o  in m  z  d Z  z  o  o  CO  CO  CO  CO  d  Figure 4.3 V a r i a t i o n of Cross-Sectional Parameters i n the North Arm and P i t t River  4.2  IMPLEMENTATION OF THE MODELS In Chapter 3 the general theory, formulations and s o l u t i o n o f  estuary d i s s o l v e d oxygen models were discussed.  The implementation of  these models as they apply to the lower Fraser R i v e r / E s t a r y i s now considered. 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 S e c t i o n 3.4: tinuous s o l u t i o n approach and the f i n i t e s e c t i o n approach.  the con-  Of these, only  the l a t t e r could be a p p l i e d t o the f u l l extent of the lower Fraser R i v e r . The implementation  of the continuous a n a l y t i c a l s o l u t i o n s which o f f e r e d  advantages over the f i n i t e s e c t i o n approach both i n terms of ease of development and the s t r a i g h t f o r w a r d manner of s o l u t i o n was found to be impossible.  The a n a l y t i c a l s o l u t i o n s f o r estuarine BOD and DO d i s t r i -  butions contained modified Bessel f u n c t i o n s (see S e c t i o n 3.4.1). When the a p p l i c a t i o n of these s o l u t i o n s t o a steady-state Fraser R i v e r d i s solved oxygen model was f i r s t considered, i t was known t h a t s o l u t i o n s o f these f u n c t i o n s were r e a d i l y a v a i l a b l e i n the form of package programs i n the Computing Centre General L i b r a r y [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 c r o s s - s e c t i o n a l area w i t h distance i n the Fraser system, the arguments of the modified Bessel f u n c t i o n s u t i l i z e d i n the s o l u t i o n proved to be much l a r g e r over most o f the model extent than the l i m i t s allowed by the Bessel f u n c t i o n package programs. the modified Bessel functions were indeterminate.  As such, the values of  80  Although  i t s h o u l d be p o s s i b l e t o 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 w e l l beyond the a u t h o r ' s  the l i m i t s of the arguments, t h i s  capabilities.  Thus the c o n t i n u o u s  a p p r o a c h t o the s t e a d y - s t a t e d i s s o l v e d oxygen model was  was  solution  abandoned i n f a v o u r  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 m o d e l i n g 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 t h e l o w e r  Fraser  system u s i n g the segmented r e p r e s e n t a t i o n o f the r i v e r / e s t u a r y shown i n F i g u r e 4.1.  T h i s s t a t i o n arrangement r e s u l t e d i n a t o t a l o f 92 segments i n  the t h r e e b r a n c h e s o f the r i v e r / e s t u a r y w h i c h r e q u i r e d the s o l u t i o n o f a system o f 93 s i m u l t a n e o u s  l i n e a r equations.  The  solution for solving this  l a r g e system o f e q u a t i o n s 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 p r o c e d u r e s  was  c o m p l i c a t e d by the b r a n c h e d c o n f i g u r a t i o n o f the r i v e r / e s t u a r y . The  usual  s o l u t i o n technique  suggested  by Thomann [1971] had  t o a l l o w f o r the c o u p l i n g of the N o r t h Arm A p r o c e d u r e was  developed  t o be m o d i f i e d  slightly  and P i t t R i v e r t o the M a i n Stem.  w h i c h a l l o w e d f o r m a t r i x s o l u t i o n t o the  three  component system o f e q u a t i o n s w i t h o u t h a v i n g  to r e s o r t to techniques  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 .  a c h i e v e d by u s i n g a s i n g l e  I t was  involv-  m a t r i x w i t h a d d i t i o n a l terms p l a 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 t o 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 o f E q u a t i o n  as a p p l i e d t o the l o w e r F r a s e r s y s t e m , shown i n F i g u r e 4.4,  3.11  i n effect i s  p a r t i t i o n e d i n t o t h r e e s e p a r a t e b l o c k s each of w h i c h r e p r e s e n t s a s i n g l e channel.  The b l o c k s are u n c o u p l e d e x c e p t a t 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 t e r m w h i c h d i f f e r s  from the main e l e m e n t s o f the m a t r i x i n t h a t i t i s n o t  tri-diagonal.  81  Figure  4.4  The M a t r i x D O o f t h e T i d a l l y A v e r a g e d Model  82  The  t i d a l l y averaged model was programmed t o FORTRAN, making use o f  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 by d i g i t a l  computer. 4.2.2  use  [UBC M a t r i x , 1973] f o r s o l u t i o n  The T i d a l l y V a r y i n g M o d e l .  J o y [1974 and 1975] , t h r o u g h  o f 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 t o t h e  mass t r a n s p o r t e q u a t i o n s w h i c h he a p p l i e d t o t h e l o w e r F r a s e r Estuary  River/  t o form t h e 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).  J o y ' 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 discharge  of conservative  As  c a u s e d by t h e  s u b s t a n c e s , a l l t h a t remained was t o implement  the c o u p l e d BOD-DO system t o t h e t i d a l l y v a r y i n g model and a p p l y  t h e model  t o t h e purpose o f t h i s r e s e a r c h , namely, t h e p r e d i c t i o n o f d i s s o l v e d oxygen levels.  The f o l l o w i n g i s a b r i e f summary o f t h e i m p l e m e n t a t i o n o f t h e  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 t o d i s s o l v e d oxygen m o d e l i n g . The  hydrodynamic sub-model, t h e o p e r a t i o n  of which i s p r e l i m i n a r y  t o t h e mass t r a n s p o r t model, y i e l d s o u t p u t i n t h e f o r m o f h a l f - h o u r l y p r e d i c t e d 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 a r e a o v e r a t i d a l c y c l e f o r any  of t h e s t a t i o n s i n the model e s t u a r y  water discharge  (see F i g u r e 4.1) g i v e n  the f r e s h -  c o n d i t i o n s a t 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  I n a p p l y i n g t h e hydrodynamic m o d e l , a d e s i g n selected freshwater  discharge  Steveston.  t i d a l c y c l e s p e c i f y i n g the  a t 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 a t  S t e v e s t o n i s chosen a l o n g w i t h assumed i n i t i a l v a l u e s o f v e l o c i t y and w a t e r surface elevations.  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 o f t h e s e i n i t i a l v a l u e s to the " t r u e " values  o f v e l o c i t y and w a t e r s u r f a c e  f o r the given c o n d i t i o n s .  elevation  During the s o l u t i o n , i t i s  83  assumed t h a t the r i v e r d i s c h a r g e the p e r i o d o f a n a l y s i s . both  and t i d a l c o n d i t i o n s a r e q u a s i - s t e a d y  over  T h e hydrodynamic model has been c a l i b r a t e d under  h i g h t i d e - l o w f l o w and h i g h t i d e - h i g h f l o w c o n d i t i o n s and found t o  adequately  reproduce water s u r f a c e e l e v a t i o n s [Joy, 1 9 7 4 ] ,  An  accurate  v e r i f i c a t i o n o f p r e d i c t e d v e l o c i t i e s has n o t been p o s s i b l e b e c a u s e o f t h e l a c k o f t h e necessary observations to  be  f i e l d measurements.  However,  based on p e r s o n a l  and i s o l a t e d f i e l d measurements, t h e p r e d i c t e d v e l o c i t i e s  reasonable.  It  s h o u l d be n o t e d t h a t t h e hydrodynamic s u b - m o d e l , w h i c h  d o e s n o t a c c o u n t f o r t h e p r e s e n c e o f t h e s a l t wedge, may v e l o c i t i e s during certain t i d a l conditions.  This  underestimate  was p o i n t e d o u t i n more  recent r e s e a r c h i n t o h y d r a u l i c modeling of the F r a s e r [Hodgins,  appear  River/Estuary  1975]. Selected  output  from t h e hydrodynamic sub-model i n t h e f o r m o f  h o 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 a r e a s a l o n g w i t h i n d e p e n d e n t e s t i m a t e s o f d i s p e r s i o n i s used as i n p u t t o t h e 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 h e model a d v e c t s w a t e r p a r c e l s a l o n g t h e e s t u a r y r e -  a d j u s t i n g h o u r l y Che  c o i ' 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, t o a c c o u n t f o r t h e e f f e c t s o f waste a d d i t i o n and d i s p e r s i o n . I n o r d e r t o use t h e 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 t o t h e b a s i c S t r e e t e r Phelps  to  equation  ( s e e S e c t i o n 2.7) a r e i n c o r p o r a t e d i n t h e s o l u t i o n scheme  r e a d j u s 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 h o u r l y a c c o r d i n g t o t h e BOD  c o n c e n t r a t i o n and t h e v a l u e s o f t h e d e o x y g e n a t i o n and r e a e r a t i o n coefficients.  T h e r e s u l t a n t model o u t p u t  rate  gives a t i m e - h i s t o r y of dissolved  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 a r e 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  4.3  computer.  MODEL ASSUMPTIONS A l t h o u g h the model assumptions were d i s c u s s e d i n the c h a p t e r on  d i s s o l v e d oxygen model development,  t h e y w i l l be b r i e f l y r e v i e w e d h e r e i n a  comparative context. 4.3.1  General Assumptions.  The b a s i c and, p e r h a p s , most  r e s t r i c t i v e a s s u m p t i o n w h i c h a p p l i e s t o b o t h the t i d a l l y a v e r a g e d and v a r y i n g models i s t h a t o f a p p r o x i m a t i n g the mass t r a n s p o r t (and p r o c e s s by one d i m e n s i o n a l e q u a t i o n s .  cross-sectionally  Thus the models a r e n o t a b l e t o " s e e " v a r i a t i o n s o v e r t h e  w i d t h o r d e p t h of the r i v e r ; changes direction.  hydrodynamic)  The one d i m e n s i o n a l space a s s u m p t i o n  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 a s s i g n e d t h e i r averaged v a l u e s .  tidally  a r e " s e e n " o n l y i n the l o n g i t u d i n a l  By t h i s a s s u m p t i o n the s a l t w a t e r wedge e f f e c t s a r e i g n o r e d .  w e l l , t h i s a s s u m p t i o n r e q u i r e s waste i n p u t s t o the models t o be  As  treated  as b e i n g " c o m p l e t e l y mixed", e i t h e r o v e r t h e c r o s s - s e c t i o n o r , as I s t h e 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 o f t i m e , the models v i e w 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 w h i c h i n essence e l i m i n a t e s the time v a r i a b l e , a r e a t e m p o r a l a b s t r a c t i o n o f the  p h y s i c a l system.  As a l l p a r a m e t e r s a r e a s s i g n e d t h e i r average  tidal  v a l u e s , the models do n o t " s e e " " r e a l t i m e " e f f e c t s such as c u r r e n t r e v e r s a l w h i c h o c c u r w i t h i n the t i d a l c y c l e .  The  t i d a l a v e r a g i n g p r o c e s s may  thought of as a r e p r e s e n t a t i o n o f the response o f the e s t u a r y o v e r a  be  85  number o f t i d a l c y c l e s a n d , as s u c h , models based on t h i s a p p r o a c h a r e o f t e n r e f e r r e d t o 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 t h e e s t u a r y i s r e p l a c e d by a f r e s h w a t e r f l o w f i e l d and a t i d a l d i s p e r s i o n term w h i c h a c c o u n t s f o r c u r r e n t 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, t h e 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 , a l t h o u g h n o t " s e e n " by the  t i d a l l y averaged models, a r e t a k e n 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  o u t p u t from the models, w h i c h i s i n t h e form o f t i d a l l y a v e r a g e d  con-  c e n t r a t i o n s , may be thought o f as i n t e g r a t i n g o v e r a t i d a l c y c l e t h e r e a l response o f t h e e s t u a r y . The t i d a l l y v a r y i n g model does n o t s u f f e r f r o m l a c k o f t e m p o r a l resolution.  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 a r e a c c o u n t e d f o r  i n the hydrodynamic  sub-model,  t h i s model a t t e m p t s t o more a c c u r a t e l y  r e p r e s e n t the true nature o f response i n the e s t u a r y .  By a p p r o x i m a t i n g  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 " s e e " changes t h a t o c c u r 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 t o as a " r e a l t i m e " or  "intra-tidal"  model.  Because o f t h e a f o r e m e n t i o n e d d i f f e r e n c e s i n t e m p o r a l r e s o l u t i o n , waste d i s c h a r g e i n f o r m a t i o n i s h a n d l e d d i f f e r e n t l y i n each o f t h e models. In  the t i d a l l y averaged models, e f f l u e n t d i s c h a r g e s a r e f e d i n as average  daily loadings.  I n t h e t i d a l l y v a r y i n g m o d e l s , however, i n o r d e r t o keep  a l l p r o c e s s i n f o r m a t i o n c o m p a t i b l e , waste d i s c h a r g e i n f o r m a t i o n i s f e d 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 t o v a r y d i s c h a r g e 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 t h e i n v e s t i g a t i o n o f s h o r t term l o a d i n g s such as s l u g l o a d s from s t o r m w a t e r o v e r f l o w o r a c c i d e n t a l spills.  86  4.3.2  D i s s o l v e d Oxygen A s s u m p t i o n s .  I n the a p p l i c a t i o n o f  d i s s o l v e d oxygen models t o the l o w e r F r a s e r R i v e r i t has been assumed t h a t o n l y two f a c t o r s a f f e c t the oxygen b a l a n c e : matter  and a t m o s p h e r i c  reaeration.  biochemical o x i d a t i o n of  organic  O t h e r oxygen s o u r c e / s i n k p r o c e s s e s  assumed t o 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  are  significance  compared t o the main p r o c e s s e s , and as such have not been c o 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 p r o d u c t i o n has n o t been c o n s i d e r e d  to  be i m p o r t a n t because o f t h e h i g h n a t u r a l t u r b i d i t y o f F r a s e r R i v e r w a t e r w h i c h b l o c k s the p e n e t r a t i o n o f l i g h t .  The  e f f e c t s o f 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 i g n o r e d because o f 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  for s i n k processes,  b e n t h i c oxygen demands have been assumed t o 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 l o w e r F r a s e r , 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 o f suspended m a t e r i a l .  T h i s a s s u m p t i o n 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 a n o t h e r oxygen s i n k  p r o c e s s w h i c h has not been i n c l u d e d i n the d i s s o l v e d oxygen m o d e l s .  This  p r o c e s s i s u s u a l l y a s s o c i a t e d o n l y w i t h h i g h w a t e r t e m p e r a t u r e s and,  as  n o t e d i n S e c t i o n 2.4.2, the e f f e c t s o f n i t r i f i c a t i o n a r e 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 a t w a t e r t e m p e r a t u r e s below 12 ± 4°C.  A l s o , u n l e s s wastes  a r e h i g h l y t r e a t e d , t h e r e 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 . (see F i g u r e s 1.6  and 1.7)  As w a t e r t e m p e r a t u r e s i n the F r a s e r a r e except  low  d u r i n g the summer months when r e s i d e n c e  time i n the e s t u a r y i s g e n e r a l l y l e s s than 2 days and because w a s t e w a t e r s r e c e i v e the e q u i v a l e n t of o r l e s s than p r i m a r y  treatment,  i t is  reasonable  87  to assume that n i t r i f i c a t i o n e f f e c t s can be ignored.  Atmospheric reaeration  was assumed to be the only oxygen source process, that i s , wind and surface wave e f f e c t s , etc. were ignored. 4.4  MODEL COEFFICIENTS 4.4.1  Dissolved Oxygen Model Rate C o e f f i c i e n t s .  The s e l e c t i o n  and evaluation of model rate c o e f f i c i e n t s i s the most c r u c i a l step i n model a p p l i c a t i o n . As the c o e f f i c i e n t s to a large extent c o n t r o l model output response, t h e i r 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 p h y s i c a l system.  T r a d i t i o n a l l y , the appropriate  dissolved oxygen model c o e f f i c i e n t s f o r deoxygenation and reaeration are selected by a c a l i b r a t i o n procedure during which model response i s "tuned" to f i t the system response by adjustment of the c o e f f i c i e n t s .  Usually the  reaeration rate c o e f f i c i e n t s are calculated from p r e d i c t i o n equations based on hydraulic considerations and then, with a l l inputs to the models equivalent to t h e i r counterparts i n the p h y s i c a l system, the BOD decay rates are obtained during the model c a l i b r a t i o n , a procedure known as "verification". Model v e r i f i c a t i o n requires, f i r s t l y , that there be a measurable dissolved oxygen response i n the p h y s i c a l system and, secondly, s u f f i c i e n t data be a v a i l a b l e to f u l l y document this response.  that In the  a p p l i c a t i o n of dissolved oxygen models to the lower Fraser River/Estuary, the c a l i b r a t i o n and v e r i f i c a t i o n procedures are extremely d i f f i c u l t .  At  present, Fraser River, dissolved oxygen l e v e l s are generally a t o r near saturation, which means that there i s l i t t l e or no observable  response  88  i n t h e oxygen dynamics o f t h e system t o p r e s e n t waste d i s c h a r g e p a t t e r n s . I n a d d i t i o n , d u r i n g t h o s e 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 t h e 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 , u n p u b l i s h e d d a t a , 1 9 7 0 ] , the a v a i l a b l e  documentation  o f t h e e s t u a r y d i s s o l v e d oxygen response i s o f i n s u f f i c i e n t s p a t i a l and t e m p o r a l r e s o l u t i o n t o be o f 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 n o t p r a c t i c a b l e t o o b t a i n t h e 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 o f F r a s e r 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 o f  model c o e f f i c i e n t s was c a r r i e d o u t s o l e l y by e s t i m a t i o n . I n t h i s s t u d y , 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 a r e based on the p r e d i c t i v e e q u a t i o n ( E q u a t i o n 2.11) o f Dobbin and O'Connor u s i n g a t e m p e r a t u r e c o r r e c t i o n f a c t o r (0) o f 1.024.  [1956]  The a p p r o p r i a t e form  o f v e l o c i t y t o be used i n a p p l y i n g t h i s f o r m u l a t o e s t u a r i e s i s , a c c o r d i n g t o Thomann [1971], t h e mean t i d a l v e l o c i t y w h i c h i n t h e l o w e r F r a s e r R i v e r ranges from 0.4 t o 8.0 f e e t p e r second.  Assuming an average depth o f  25 f e e t , t h e r e a e r a t i o n c o e f f i c i e n t ( K ) i s found t o v a r y from 0.07 t o 0.30 2  p e r day. I n a t t e m p t s t o e v a l u a t e t h e r a t e c o e f f i c i e n t s o f BOD decay a p p r o p r i a t e f o r t h e l o w e r 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 o f BOD r e s p o n s e were c o n d u c t e d . Westwater  These s t u d i e s w h i c h were c a r r i e d o u t i n c o n j u n c t i o n w i t h the  R e s e a r c h C e n t r e as p a r t o f an i n v e s t i g a t i o n d e s i g n e d t o e v a l u a t e  r a t e c o e f f i c i e n t s and d e t e r m i n e temperature and s a l i n i t y e f f e c t s on b a c t e r i a l d i e - o f f , as w e l l as BOD decay i n F r a s e r R i v e r w a t e r , y i e l d e d i n conclusive results  [Westwater R e s e a r c h C e n t r e , u n p u b l i s h e d d a t a ] .  Consequently,  89  the rates chosen f o r use i n t h i s research had to be taken from the l i t e r a t u r e which described other i n v e s t i g a t i o n s of d i s s o l v e d 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 t o be appropriate f o r 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 t o 0.20 per day.  A temperature c o r r e c t i o n f a c t o r (0) of 1.135 was used. 4.4.2  Dispersion C o e f f i c i e n t s .  Because the view taken of  estuarine d i s p e r s i o n processes i s d i f f e r e n t i n each of the models, a b r i e f d i s c u s s i o n of d i s p e r s i o n c o e f f i c i e n t s i s deemed necessary i n order t o r e s o l v e p o s s i b l e confusion which might e x i s t over the use o f the terms.  In the  t i d a l l y averaged models 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 , by design, accounts f o r a l l t i d a l e f f e c t s i n c l u d i n g upstream water movement and t i d a l mixing. Thus, i t bears l i t t l e resemblance t o the term used to describe l o n g i t u d i n a l d i s p e r s i o n 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 " d i s p e r s i o n phenomena, the processes by which concentration peaks are eroded and mass i s r e d i s t r i b u t e d i n an estuary due to the e f f e c t s 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 d i s p e r s i o n c o e f f i c i e n t is- an a b s t r a c t i o n of  true estuarine mixing phenomena, i t has no r e a l t h e o r e t i c a l b a s i s and, although s e v e r a l s e m i - t h e o r e t i c a l formulations have been p o s t u l a t e d , 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  coefficients  are u s u a l l y evaluated e m p i r i c a l l y through use of some observable t r a c e r I n the estuary such as s a l i n i t y or c h l o r i d e concentration.  Values of 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 l i s t e d by Thomann [1971] f o r various e s t u a r i e s range from 1 to 20 square miles per day w i t h a mean value of about 10 square miles per day. In the lower Fraser River/Estuary i t i s impracticable to e s t a b l i s h  90  e m p i r i c a l values of 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 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 p o s s i b l e through use of presently a v a i l a b l e 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 . c o e f f i c i e n t must be used.  Therefore assumed values of t h i s  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 d i s c u s s i o n , 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 d i s p e r s i o n coefficient. 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 d i s p e r s i o n has been assumed to be zero, that i s , a l l d i s p e r s i v e e f f e c t s have been ignored.  The reasons f o r doing t h i s are twofold.  F i r s t l y , i t has  been e s t a b l i s h e d from the r e s u l t s of the recent dye t r a c e r 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 c o n d i t i o n s , 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 d a t a ] .  Thus, ignoring the e f f e c t s of l o n g i t u d i n a l d i s p e r s i o n  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 p r e d i c t e d concentration to approximate Fraser River/Estuary c o n d i t i o n s .  Secondly, as t h i s assumption  e l i m i n a t e s the d i s p e r s i v e e f f e c t s of e r o s i o n and r e d i s t r i b u t i o n of conc e n t r a t i o n peaks, i t w i l l r e s u l t i n an exaggeration of concentration peaks, g i v i n g a c l e a r e r p i c t u r e of i n t r a - t i d a l response i n the r i v e r / e s t u a r y . 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 Arm/Main Stem and Table 4.2  f o r the North Arm.  expressed i n terms of pounds of BOD  f o r the Main  Average loading rates  per day are tabulated according  to  l o c a t i o n w i t h i n the model r i v e r / e s t u a r y as s p e c i f i e d by model segment numbe These waste loading estimates are based on e f f l u e n t 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]. BOD  The  loading to the lower Fraser t o t a l s some 250,000 pounds of BOD  present  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 4.5.2  sources.  P o s s i b l e Future Waste Loads.  An i n v e s t i g a t i o n of the  p o s s i b l e impact of future waste discharge patterns on the d i s s o l v e d oxygen dynamics of the lower Fraser River/Estuary  requires assumptions of p o s s i b l e  future waste loads.  to forecast the magnitudes and  Instead of attempting  l o c a t i o n s of future waste loads, h y p o t h e t i c a l 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 t h a t , r a t h e r than  typifying- what might be expected as a future condition,, w i l l show what can be considered a severe future impact.  Basically t h i s involves locating  the waste o u t f a l l s at p o s i t i o n s i n the r i v e r / e s t u a r y 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 d i s s o l v e d oxygen, i t i s not  TABLE 4.1 WASTE LOADINGS TO THE MAIN ARM/MAIN STEM, LOWER FRASER RIVER  MODEL SEGMENT 1 2 3 4 6 7 11 14 15 16 17 18 20 21 23 24 25 29 30 31 32 37 46 47 51  PRESENT BOD LOADING (LBS/DAY) 720 1,730 52,470 1,760 50 3,490 5,040 13,780 3,300 810 7,350 990 37,420 5,470 2,550 2,520 50 600 20 1,800 3,690 2,410 380 1,500 8,780  TABLE 4.2 WASTE LOADINGS TO THE NORTH ARM, LOWER FRASER RIVER  MODEL SEGMENT  PRESENT BOD LOADING (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 a t t h i s t i m e t o v a l i d a t e d i s s o l v e d oxygen model o u t p u t . of observable way  The  lack  system response t o w h i c h model r e s p o n s e c o u l d be compared by  o f v e r i f i c a t i o n p r o h i b i t s a c c u r a t e c a l i b r a t i o n o f the d i s s o l v e d oxygen  models.  As s u c h , the r e s u l t s from the m o d e l s , p r e s e n t e d  Chapter 5 ,  and  discussed i n  s h o u l d 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 m o d e l o u t p u t i s  at best considered p o s s i b l e outcomes,  t o be o n l y a s e r i e s o f 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 o f  CHAPTER 5 DISSOLVED OXYGEN MODEL RESULTS  S i n c e t h e t r a d i t i o n a l model c a l i b r a t i o n p r o c e d u r e s a r e n o t a p l i c a b l e t o t h e lower F r a s e r  River/Estuary  d i s s o l v e d oxygen m o d e l s , v e r i -  f i c a t i o n o f t h e models i s n o t p r e s e n t l y p o s s i b l e .  I t follows  therefore,  t h a t model p r e d i c t i o n s cannot be viewed w i t h c o m p l e t e c o n f i d e n c e .  In  o r d e r t o a l l e v i a t e t h o s e doubts a s s o c i a t e d w i t h t h e mechanics o f t h e model, a s e n s i t i v i t y a n a l y s i s c a n be c a r r i e d o u t t o document model r e s p o n s e over t h e e x p e c t e d range o f i n p u t parameter v a r i a t i o n f o r t h e f u l l range o f c o n c e i v a b l e  model c o e f f i c i e n t s .  I f , b y t h i s a n a l y s i s , model  r e s p o n s e i s found t o be r e a s o n a b l e , t h e mechanics o f t h e models c a n be a c c e p t e d a s b e i n g v a l i d and t h e r e m a i n i n g d o u b t s a s t o t h e a c c u r a c y and v a l i d i t y o f model p r e d i c t i o n s l i e i n c h o o s i n g t h e 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 , a s w e l l a s b e i n g a " c h e c k "  of model v a l i d i t y , i s a l s o u s e f u l i n t h a t i t b r i n g s  t o l i g h t some o f t h e  d e t a i l s p e c u l i a r t o t h e n a t u r e o f l o w e r F r a s e r d i s s o l v e d o x y g e n dynamics. Thus i t i s more t h a n j u s t a n e c e s s a r y p r e l i m i n a r y  to the ensuing  discus--  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 a s w e l l a s d e t e r m i n i n g i f t h e models a r e " w e l l behaved", i t a l s o a f f o r d s us w i t h a f o c u s upon w h i c h t o base i n i t i a l lower F r a s e r  5.1  discussions  on t h e a s s i m i l a t i v e c a p a c i t y  of t h e  River/Estuary.  TIDALLY AVERAGED DISSOLVED OXYGEN MODEL RESPONSE .. A s t u d y o f model r e s p o n s e c h a r a c t e r i s t i c s t h r o u g h i n v e s t i g a t i o n  of t h e s e n s i t i v i t y o f model o u t p u t t o v a r i a t i o n s i n i n p u t p a r a m e t e r s and  - 95 -  96  model c o e f f i c i e n t s i s best carried out by holding a l l parameters and coe f f i c i e n t s constant except for the p a r t i c u l a r element of concern, which i s allowed to vary within the expected range of values.  Repeating this pro-  cedure for each parameter and c o e f f i c i e n t i n 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 e f f e c t s of v a r i a t i o n i n s i x parameters were considered - freshwater flow, waste loading, dispersion, reaeration rate, deoxygenation rate and temperature.  The values used i n the analysis are  s p e c i f i e d i n Table 5.1.  TABLE 5.1 PARAMETERS AND COEFFICIENTS USED IN SENSITIVITY ANALYSIS  Parameter Freshwater flow (Q) Waste loading (W) Dispersion C o e f f i c i e n t  Constant Value  (E)  ucoAygcudtiuu L u c n i C i e u t  Reaeration C o e f f i c i e n t (K ) Temperature (T) 2  .  40,000 c f s 1,000,000 l b 10 sq. miles/day  Range of Values 10,000 to 60,000 100,000 to 1,000,000 0 to 30  u.z/aay  u.x  0.2/day 10.0°C  0.0 to 0.4 5.0 to 20.0  to  0.6  The response of the model over the Main Stem reach of the r i v e r with waste discharge location at Station 40 i n the upstream portion of the model  w i l l be used throughout the a n a l y s i s . 5.1.1  E f f e c t of Freshwater Inflow V a r i a t i o n .  to flow v a r i a t i o n i s shown i n Figure 5.1.  The model response  The e f f e c t of increases i n  freshwater flow i n the river/estuary can be seen to r e s u l t i n reduced concentration  BOD  and increased DO concentration as would be expected due to  K, = K = 0.2/day at 20° C 2  E = 10 mi /day 2  T= I0°C Q is variable  W= 1,000,000 '  Q O  CD  e to c o  c <u o c o O  11.0 •o  10.OH O  a 9.0  8.0  "  ,  , 20  30  River/ Estuary Figure Ef f e c t  of Freshwater  Section  5 .1  Inflow  dn M o d e l  Response  lb/day Riv  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 h i g h e r f l o w s . l a r I n t e r e s t i s observed  An e f f e c t o f p a r t i c u -  f o r the l o w e s t 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 c a s e , i n c o n t r a s t to the o t h e r s , i s s e e n t o r e a c h a c l e a r l y d e f i n e d minimum i n the v i c i n i t y o f s t a t i o n 25 a f t e r w h i c h i t begins  t o 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 o f 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 o b s e r v e d  f o r the h i g h e r r i v e r f l o w s i t i s  e v i d e n t t h a t a c c o r d i n g t o model r e s p o n s e ,  i t i s only during extremely  f l o w s w h i c h r e s u l t i n i n c r e a s e d f l u s h i n g times and h i g h BOD t h a t the c o n d i t i o n o f maximum DO d e f i c i t i s reached  concentrations  w i t h i n the  channelized  s t r e t c h o f the r i v e r / e s t u a r y . A t the h i g h e r r i v e r f l o w s the b u l k o f oxygen demand i s presumably f l u s h e d out i n t o the S t r a i t o f  low  the  Georgia.  A l s o e v i d e n t f o r d e c r e a s i n g r i v e r f l o w s i s the i n c r e a s i n g dominance o f t i d a l i n f l u e n c e as e v i d e n c e d  by the i n c r e a s e d u p s t r e a m  e f f e c t s f o r b o t h BOD  t h a t i f the f r e s h w a t e r i n f l o w t o  and DO.  I t i s noted  the e s t u a r y were z e r o , the s t e a d y s t a t e BOD  and DO d e f i c i t  would be d i s t r i b u t e d n o r m a l l y about the o u t f a l l l o c a t i o n .  concentrations The  i n f l u e n c e of  f r e s h w a t e r i n f l o w i s s e e n t o 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 downs t r e a m d i r e c t i o n w i t h o n l y the maximum  BOD  concentration s t i l l occurring  a t the o u t f a l l l o c a t i o n as the p o i n t o f maximum DO  d e f i c i t i s s h i f t e d down-  stream.  d i s t r i b u t i o n i s skewed  I t can be seen i n F i g u r e 5.1  t h a t the BOD  s i g n i f i c a n t l y and t h a t the p o i n t o f maximum DO  d e f i c i t f o r any e x c e p t  low r i v e r f l o w i s d i s p l a c e d out o f the model! r i v e r / e s t u a r y , thus the p r e d o m i n a t i n g  i n f l u e n c e of freshwater i n f l o w .  data].  indicating  Note t h a t the minimum  low f l o w f o r the F r a s e r R i v e r a t C h i l l i w a c k i s e s t i m a t e d CWestwater R e s e a r c h C e n t r e , u n p u b l i s h e d  very  t o be 18,000 c f s  99  5.1.2  E f f e c t of Waste Loading V a r i a t i o n .  various waste loadings i s shown i n Figure 5.2.  The model response to  Increases i n BOD and  DO  d e f i c i t concentrations are found to be r e l a t e d l i n e a r l y to increases i n waste loading rates i n d i c a t i n g that the p r i n c i p l e of s u p e r p o s i t i o n i s adhered 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 a l s o observed  up-  stream of the waste discharge l o c a t i o n w i t h t h i s e f f e c t , due to t i d a l d i s p e r s i o n , again being found to be r e l a t e d l i n e a r l y to increases i n waste loadings. 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 .  In the t i d a l l y  averaged model a l l t i d a l e f f e c t s are accounted f o r by the t i d a l d i s p e r s i o n coefficient.  I t accounts f o r current r e v e r s a l and the e f f e c t s of upstream  water movement as w e l l as t i d a l mixing.  The e f f e c t 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 d i s p e r s i o n which converts the estuary model i n t o a model app 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 e f f e c t 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 i n f l o w and i t s e f f e c t s i n the lower Fraser River/Estuary.  The e f f e c t s of v a r y i n g t h i s model co-  e f f i c i e n t , although minor, are observable.  In the case of zero d i s p e r s i o n ,  no e f f e c t s 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 cont 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 d i s p e r s i o n  c o e f f i c i e n t i s increased, upstream e f f e c t s become evident and are of i n creasing s i g n i f i c a n c e i n terms both of magnitude of BOD and DO  deficit  concentrations and extent of t h e i r upstream i n f l u e n c e as the c o e f f i c i e n t  K,= K = 0.2/day at 20° C 2  T= I0°C Q= 40,000 cfs E is variable W = 1,000,000  I  lb/day  River  5.0-i  4.0  3.0 1  -  "  2.0  E= 30 square miles/day —  I.OH  E= 20 square miles/day  Jh'  — — E = 10 square miles/day  jl\ •  —-E=  ;U •  0  square miles/day  0 10' 11.4  ft*  Saturation  20  l!o~  40  50  40  50  ~60~  Concentration  11.2-  11.0 -  10.8  I0.6H  10  20  30  River/Estuary Figure Effect  GO  Section 5.3  of D i s p e r s i o n on Model  Response  102  approximates the e f f e c t s of water movement i n the r i v e r / e s t u a r y .  I n 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 d i s p e r s i o n c o e f f i c i e n t have the opposite e f f e c t , that i s , BOD concentrations are reduced as f a r 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 t h i s region 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 operates  In the manner of the " t r u e " d i s p e r s i o n 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  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 .  The  e f f e c t o f 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 r i v e r / e s t u a r y s t r e t c h downstream of the waste discharge l o c a t i o n (see Figure 5.4). Increases i n the r a t e c o e f f i c i e n t are observed to r e s u l t i n increased deoxygenation as evidenced by reduced oxygen l e v e l s and corresponding decreases i n BOD concentrations as a g r e a t e r port i o n of the oxygen demand i s s a t i s f i e d . response of t h i s c o e f f i c i e n t .  This i s t y p i c a l o f the expected  Note that at the assumed water temperature of  10°C, t h e _ e f f e c t i v e r a t e s of deoxygenation w i l l be somewhat lower than the magnitudes shown, which are the values a t 20°C. . 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 .  Model  response due to v a r i a t i o n i n the r e a e r a t i o n c o e f f i c i e n t i s shown i n Figure 5.5 w i t h the only e f f e c t being the decrease i n DO c o n c e n t r a t i o n evident f o r decreases i n r e a e r a t i o n r a t e .  Again, as the water temperature  i s held at 10°C the e f f e c t i v e r a t e s of r e a e r a t i o n w i l l be. somewhat lower than t h e i r s p e c i f i e d values which are f o r 20°C. 5.1.6  E f f e c t o f Water Temperature V a r i a t i o n .  e f f e c t s on model response are shown i n Figure 5.6.  Water temperature  The obvious e f f e c t i s  seen as a lower s a t u r a t i o n concentration f o r i n c r e a s i n g temperature.  As  103  K = 0.2/day at  20° C  2  E = 10 midday T = 10° C Q = 40,000 cfs  W= 1,000,000  K| Is variable  lb/day  ^  R\ver  4.0  a o ca  2.0  E tn c  o c o c o o  11.4 H  <U  11.2  XI  11.0  a>  Saturation Concentration  10.8O Q  10.610.4  10.2-1 io!o 9.8 0  10  20  30  40  River/Estuary Figure Effect  of Deoxygenation  50  60  Section  5.4  Rate  on M o d e l  Response  104  K,= 0.2/day at 20° C E= 10 m i / d a y 2  T = 10° C Q= 40,000 cfs K  is variable  2  W =1,000,000  lb/day  5.0 n  4.0 H  Q O  3.0-^  ca  2.0 £  1.0  tn c o  <u o c o O  0 11.4  10  20  30  40  50  60  40  50  60  Saturation Concentration  T3  11.2 0>  1.01  o o 10.8  10.6  10.4  —i—  0  10  20  30  River/Estuary Figure Effect  of Reaeration  Rate  Section  5.5 on M o d e l  Response  K, =K = 0.2/day at 20°C E= 10 mi /day Q= 40,000 cfs T is variable 2  2  W= 1,000,000 4  lb/day Rive  f  a o 03  40  50  60  sat, cone, at 5_° C  12.04 sat, cone, at 1 0 ° C 11.0  •  o a  1  sat. cone, at  15° C  10.0 ^  0  ^ ^ '  i sat. cone, at 2 0 ° C  9.0 T = 2 0 ^ 8.0  0  10  ;  20  30  40  R i v e r / Estuary Figure Effect  of Temperature  50  60  Section  5 .6 on Model  Response  w e l l , increased deoxygenation as evidenced by decreases i n BOD concentrat i o n and increases i n DO d e f i c i t with increasing temperature show the e f f e c t of temperature compensation  (9 i n this case i s 1.135) on the det-20  oxygenation rate c o e f f i c i e n t ( K = K T  2 q  9  ).  The corresponding tempera-  ture e f f e c t on reaeration rate, not observable d i r e c t l y , i s l e s s severe (6 being 1.024) and thus i t s e f f e c t s are seen to be outweighed by i n creased deoxygenation. 5.1.7  Summary.  The s e n s i t i v i t y analysis has shown that the  t i d a l l y averaged dissolved oxygen model response i s reasonable over the range of input parameters and model c o e f f i c i e n t s considered by the analysis, that i s , model mechanics appear to be sound.  Thus the model  can be considered to be v a l i d at l e a s t i n the sense that model response i s i n the d i r e c t i o n i t should be.  As w e l l , the analysis has pointed out  some i n t e r e s t i n g - d e t a i l s regarding - lower Fraser dissolved oxygen dynamics. Foremost, the predominating influence of freshwater inflow which minimizes the e f f e c t s of t i d a l dispersion i s seen to f l u s h oxygen demand out of the river/estuary to be exerted i n the S t r a i t of Georgia.  In a d d i t i o n , the  b e n e f i c i a l e f f e c t s of low water temperatures have become evident i n t h e i r dual r o l e 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 i n i t s a b i l i t y to describe the i n t r a - t i d a l behaviour of modeled parameters.  Thus, the  t i 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 i n the  lower F r a s e r R i v e r / E s t u a r y  i n t h a t i t w i l l a l l o w an assessment  t o be made  o f i n t r a - t i d a l d i s s o l v e d oxygen r e s p o n s e . B e f o r e we can a c c e p t 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 a s s u r e d t h a t i t s manner o f r e s p o n s e i s r e a s o n a b l e .  Although i t  would be d e s i r a b l e t o 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 o f t h e s e n s i t i v ities  of model r e s p o n s e as was done w i t h the t i d a l l y averaged model,  i s p r e c l u d e d by o p e r a t i o n a l l i m i t a t i o n s i n h e r e n t i n the t i d a l l y  this  varying  d i s s o l v e d oxygen model w h i c h 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, u n w i e l d y  n a t u r e o f t h e s o l u t i o n s , w h i c h a r e c o s t l y , not o n l y i n terms o f computing t i m e , b u t a l s o i n terms of expense o f e f f o r t because a l l sub-models  must  be reprogrammed each t i m e an i n p u t parameter o r model c o e f f i c i e n t i s altered.  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 o f t h i s  model's r e s p o n s e o v e r the r e q u i r e d range of i n p u t 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 . f a c t a l s o p o i n t s out a d e f i n i t e s h o r t c o m i n g o f the t i d a l l y  This  varying  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 b e h a v i o u r o f t h e 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 flexibility. 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 t o i n v e s t i g a t e the b e h a v i o u r o f the t i d a l l y d i s s o l v e d oxygen model p r e d i c t i o n s t o see how the t i d a l l y averaged model. as a s u i t a b l e framework  varying  t h e y compare t o r e s u l t s from  T h i s c o m p a r a t i v e assessment w i l l a l s o s e r v e  f o r p o i n t i n g out some of t h e d e t a i l s of r i v e r /  e s t u a r y b e h a v i o u r t h a t cannot be o b s e r v e d t h r o u g h use o f t h e 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  deal separately with  each  component o f t h e 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 t o i l l u s t r a t e a l l aspects  of model o u t p u t .  As i n i t s p r e s e n t  s t a t e a l l components o f  the t i d a l l y v a r y i n g model a r e 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  t h e v a l i d i t y o f t h e v a r i o u s l e v e l s o f model  o u t p u t and t o 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 t h e 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 freshwater  i n f l o w of 40,000 c f s a t C h i l l i w a c k and t i d a l r a n g e o f 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  e s t u a r y a r e shown a c c o r d i n g Steveston.  the r i v e r /  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  Note t h a t the n e g a t i v e v e l o c i t i e s i n d i c a t e f l o w i n t h e down-  stream d i r e c t i o n . stations.  for a  Current  r e v e r s a l i s predicted to occur at a l l three  The t i m i n g o f i t s o c c u r e n c e i s seen t o v a r y from t h r e e h o u r s  a f t e r l o c a l low w a t e r (LLW) a t S t a t i o n 2 t o f o u r and f i v e h o u r s a f t e r LLW a t S t a t i o n s 20 and 40, r e s p e c t i v e l y .  The d e s i g n  tidal configuration  i s a l s o seen t o r e s u l t i n an extended p e r i o d o f e s s e n t i a l l y s l a c k w a t e r around hour 12 i n t h e t i d a l c y c l e . The a d v e c t i v e  transport of p a r t i c l e s released at v a r i o u s  from S t a t i o n 40 on t h e M a i n Arm/Main Stem of t h e r i v e r / e s t u a r y t o 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  times according 5.8.  P a r t i c l e s 1 and 2 r e l e a s e d a t h o u r s 8 and 14, r e s p e c t i v e l y a r e seen t o e x i t d u r i n g t h e s t r o n g ebb a t a p p r o x i m a t e l y  70 h o u r s .  Particle 3 re-  l e a s e d a t hour 20 and p a r t i c l e 4 r e l e a s e d a t hour 26 a r e n o t s e e n t o  Q= 40,000 cfs Tidal  Range  at  at  Chilliwack  Steveston  10 feet  109  Q= 40,000  cfs at Chilliwack  Tidal Range at Steveston  10 feet  Particle No. Release Time (hrs) 1 2 3  8 14 20  Residense Time (hrs) 61 56 72  Hours F i g u r e 5.8 P r e d i c t e d T r a c e of- P a r t i c l e s Released a t V a r i o u s Times From S t a t i o n 40  e x i t u n t i l t h e ebb o f t h e f o l l o w i n g t i d a l c y c l e a t 90 h o u r s w h i c h 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 r e s i d e n c e times f o r t h e s e 5.2.2  particles.  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 d i s c h a r g e d i n t o an e s t u a r y t h e o s c i l l a t o r y movement o f t h e 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 F i g u r e 5.9).  T h i s i s caused by t h e 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 p o i n t of e f f l u e n t d i s c h a r g e . to  I n p a r t , t h i s i s due  t h e phenomenon o f " m u l t i p l e d o s i n g " w h i c h o c c u r s when a p a r c e l o f  w a t e r r e c e i v e s a s l u g o f e f f l u e n t as i t f i r s t  moves p a s t t h e d i s c h a r g e  p o i n t i n t h e downstream d i r e c t i o n d u r i n g an ebb f l o w ; another  slug of  e f f l u e n t as i t moves upstream p a s t t h e o u t f a l l on t h e f l o o d t i d e ; and yet another succeeding  s l u g o f e f f l u e n t as t h e w a t e r p a r c e l moves downstream on t h e ebb t i d e .  Thus f l o w r e v e r s a l can r e s u l t i n a w a t e r p a r c e l  b e i n g "dosed" a number o f times by t h e same e f f l u e n t d i s c h a r g e .  Also,  any p e r i o d o f extended s l a c k o r slow moving w a t e r r e s u l t s i n d e c r e a s e d e f f l u e n t d i l u t i o n which again causes i n c r e a s e d e f f l u e n t c o n c e n t r a t i o n . An e x a m i n a t i o n  o f F i g u r e 5.9 shows t h r e e c o n c e n t r a t i o n " s p i k e s " i n t h e  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  i n c r e a s e d c o n c e n t r a t i o n s a t h o u r s z e r o and f o u r r e s u l t from t h e f l o w r e v e r s a l s w h i c h o c c u r a t those t i m e s t i o n " s p i k e " observed moving w a t e r .  a t hour 12 i s due t o an extended p e r i o d o f slow  T h i s l a t t e r " s p i k e " i s seen t o be t h e h i g h e s t BOD c o n c e n -  t r a t i o n , being approximately concentration (B0D ). t a  to  ( s e e F i g u r e 5.7). The c o n c e n t r a -  s i x times h i g h e r than t h e t i d a l l y a v e r a g e d  I t was p o i n t e d out by J o y [1974] t h a t , a c c o r d i n g  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 c o u l d be up t o  Q = 40,000 cfs at Chilliwack Tidal Range at  Steveston 10 feet  Continuous Waste Discharge at Station 40 Predicted Initial BOD Concentrations  Hours  F i g u r e 5.9 Predicted  Initial  Effluent Dilution  ten times higher 5.2.3  than the t i d a l l y a v e r a g e v a l u e s .  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 t h e  i n t r a - t i d a l r e s p o n s e of d i s s o l v e d oxygen i n a manner t h a t a l l o w s f o r comp a r i s o n t o the t i d a l l y averaged r i v e r / e s t u a r y r e s p o n s e , e q u i v a l e n t estuary  and waste d i s c h a r g e  c o n d i t i o n s were chosen:  e q u a l t o 40,000 pounds of BOD of 10°C; day  decay (K^)  at 20°C.  The  and  waste  discharge  per hour at S t a t i o n 40; w a t e r t e m p e r a t u r e  reaeration  (K ) 2  c o e f f i c i e n t s e q u a l t o 0.2  r i v e r / e s t u a r y r e s p o n s e as p r e d i c t e d by the  v a r y i n g d i s s o l v e d oxygen model i s shown i n F i g u r e s downstream S t a t i o n s 20 and  2, r e s p e c t i v e l y .  p r e d i c t e d v a r i a t i o n i n BOD  ( B 0 D ) and tv  DO  5.10  and  per  tidally 5.11  for  These f i g u r e s i l l u s t r a t e  deficit  t v  two m i n o r e f f l u e n t " s p i k e s " t h a t had been d i s t i n c t i n the  i n i t i a l e f f l u e n t d i l u t i o n c u r v e (see F i g u r e 5.9) and r e s u l t i n the m i n o r BOD  peak a t hour one  have " b l e n d e d "  i n F i g u r e 5.10.  d i s t i n g u i s h between them. F i g u r e s 5.10  and  5.11  the major i n i t i a l BOD  That i s to  are a r b i t r a r y .  The  p a r c e l of w a t e r w h i c h  " s p i k e " i s seen to have moved downstream t h e n p a r t way  one  f o r the two major BOD  and  two  peaks of DO  s l u g s are r e s p o n s i b l e d e f i c i t are  since  the  be n o t e d t h a t the t i m e s c a l e s i n  p a s t S t a t i o n 20 at hour f o u r and  5.10  together  e v e n t s w i t h i n the hour i t i s u n a b l e t o  I t should  s l u g of w a t e r i s r e s p o n s i b l e  values.  predicted  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 t i d a l l y v a r y i n g model cannot " s e e "  the  ( D 0 ) which, although  shown t o be c o n t i n u o u s curves, a r e a c t u a l l y a p p r o x i m a t e d by h o u r l y The  river/  contained completely  back around hour 14.  f o r the minor peak.  Thus  peaks i n F i g u r e Corresponding  observed.  At S t a t i o n .2 (see F i g u r e 5.11)  the same phenomenon i s o b s e r v e d  114  Q= 40,000 cfs at Tidal Range at  Chilliwack  Steveston  Continuous  Waste  Predicted  BOD and  10 feet  Discharge DO  at  Station  Concentrations  40 at  Station  20  £*30-|  24  F i g u r e 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 Model Response: S t a t i o n 20  Hours  115  Q= 40,000 cfs  at Chilliwack  Tidal Range at  Steveston  10 feet  2  Continuous  Waste  Predicted  BOD  Discharge and DO  at  Station  Concentrations  40 at  Station 2  F i g u r e 5.11 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 Response: Station 2  o n l y i n t h i s case t h e major BOD peak i s f l u s h e d o u t o f t h e model r i v e r / e s t u a r y a t hour s i x .  This i s evident  b e c a u s e . t h e BOD and DO d e f i c i t  con-  c e n t r a t i o n s a r e o b s e r v e d t o be z e r o between hours s i x and t w e n t y , w h i c h means t h a t s e a water w h i c h i s assumed t o be u n p o l l u t e d  has moved i n t o t h e  river/estuary. A c o m p a r i s o n o f peak t i d a l l y v a r y i n g DO d e f i c i t t i d a l l y averaged d e f i c i t  (DO  ) to the  (DO. ) r e v e a l s t h a t a t b o t h s t a t i o n s t h e t i d a l l y ra  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 t h e maximum r a t i o i n each case b e i n g around s i x .  The f a c t t h a t t h e r a t i o o f peak DO^^ t o D 0  e q u a l t o t h e peak B O D  t o BOD  tv  ta  r e s i d e n t times,  That i s f o r e q u a l  and e q u a l c o e f f i c i e n t s and r o u g h l y  comparable  t h e r e l a t i v e s i z e o f DO d e f i c i t c o n c e n t r a t i o n s  mined by t h e S t r e e t e r - P h e l p s  oxygen s a g e q u a t i o n  (Equation  as deter-  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 t o t h e r e l a t i v e magnitude o f i n i t i a l BOD tions.  is  r a t i o i s t o be e x p e c t e d because o f t h e  l i n e a r n a t u r e o f t h e d i s s o l v e d oxygen s o l u t i o n s . i n i t i a l d e f i c i t s , constant  t a  concentra-  Note t h a t t h e 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  t i m e of a w a t e r p a r c e l i n t h e r i v e r / e s t u a r y i s m i n i m a l  w i t h t h e 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 o f 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 t h e i m p o r t a n c e o f 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 v a l u e s  u l t i m a t e l y d e t e r m i n e what t h e t i d a l l y  d i s s o l v e d oxygen r e s p o n s e w i l l be.  I t should  varying  be n o t e d t h a t t h e 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 c a s e , 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 , t h e e f f e c t would have been t o erode t h e " s p i k e s " t h e r e b y r e d i s t r i b u t i n g BOD,  117  the n e t r e s u l t b e i n g d e c r e a s e d maximum DO d e f i c i t ing  concentrations.  Accord-  t o J o y [1974], who i n v e s t i g a t e d t h e p r e d i c t e d d i s p e r s i o n o f a s l u g l o a d  released  i n t h e upstream r i v e r / e s t u a r y r e a c h e s , t h e r e i s a f i v e - f o l d de-  c r e a s e i n peak c o n c e n t r a t i o n w i t h i n t h e f i r s t 24 hours a f t e r r e l e a s e (see F i g u r e 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  c o e f f i c i e n t s used by J o y were l i k e l y  that  t o o l a r g e [ P . Ward, u n p u b l i s h e d d a t a ]  t h e degree t o w h i c h t h i s a f f e c t s t h e r e s u l t s i s n o t e a s i l y d e t e r m i n e d . i s recognized  t h a t t h e e f f e c t s o f 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  i n Sections  gradients.  V a l i d i t y of T i d a l l y Varying  Predictions.  I t was p o i n t e d o u t  4.2.2 and 5.2 t h a t due t o i t s s o p h i s t i c a t e d a p p r o a c h t h e t i d a l -  l y v a r y i n g model must, o f n e c e s s i t y , u t i l i z e a s t a g e d , 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, t h e 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 w a t e r s u r f a c e e l e v a t i o n s t h r o u g h o u t t h e r i v e r / e s t u a r y f o r given r i v e r discharge formation,  and t i d a l c o n d i t i o n s .  i n a d d i t i o n t o data d e s c r i b i n g waste d i s c h a r g e s ,  This i n -  i s used i n  t u r n as i n p u t t o t h e g e n e r a l mass t r a n s p o r t model w h i c h u l t i m a t e l y p r e d i c t s the time-varying Within  #  w i l l be somewhat l e s s t h a n i n t h e c a s e o f a s l u g l o a d  because of t h e reduced c o n c e n t r a t i o n 5.2.4  It  d i s t r i b u t i o n o f BOD and DO t h r o u g h o u t t h e e s t u a r y .  t h e framework o f t h e g e n e r a l mass t r a n s p o r t model t h e hydrodynamic  i n f o r m a t i o n i s used t o p e r f o r m two b a s i c f u n c t i o n s .  Firstly,  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 a r e used as t h e 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 a t v a r i o u s t i m e s and l o c a t i o n s i n t h e r i v e r / e s t u a r y , t h e r e b y s i m u l a t i n g advect 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 o f t h e t i m e - h i s t o r y o f v a r i o u s w a t e r 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 with the c r o s s - s e c t i o n a l area, which i s derived  from water  118 /  Q= 40,000 cfs  at Chilliwack  Tidal Range at Steveston  10 feet  40  Slug Discharge at Station 40 Predicted Erosion of  Effluent Spike  oser  RWer.  s u r f a c e e l e v a t i o n p r e d i c t i o n s , i s used t o c a l c u l a t e t i d a l f l o w s w h i c h a r e used i n t u r n t o o b t a i n e s t i m a t e s  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 t h e  a c c u r a c y 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 r e s p o n s e depends t o a l a r g e e x t e n t on t h e v a l i d i t y of the hydrodynamic sub-model;  specifically  on t h e a c c u r a c y 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 t h e y a r e used to determine residence  t i m e s 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 .  W i t h r e g a r d s to p o s s i b l e i n a c c u r a c i e s i n t h e m a g n i t u d e s of v e l o c i t i e s as they might e f f e c t r e s i d e n c e  times, i t appears t h a t  these  c o u l d 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 l o w e r r i v e r / e s t u a r y s t r e t c h e s where f l o 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 (see S e c t i o n 1.4.2).  to the i n t r u s i o n of  Hodgins [1974] d e v e l o p e d a m o d i f i e d  hydrodynamic  model w h i c h c o u l d a c c o u n t f o r the s a l t w a t e r wedge e f f e c t s . 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  He  found that  t o i n c r e a s e the f r e s h w a t e r  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 advection.  saltwater  ebb  particle  A c o m p a r i s o n of the a d v e c t i o n p a t h s as t h e y a r e 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 t h a t t h e 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 .  error i n predicted residence  time.  F i r s t l y there i s a s u b s t a n t i a l  For example, c o n s i d e r p a r t i c l e s r e -  l e a s e d from A n n a c i s 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).  Particle  3 i n t h e s t r a t i f i e d model i s seen t o be f l u s h e d out o f 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  b a r o t r o p i c model, a r e d u c t i o n i n r e s i d e n c e second e f f e c t e v i d e n t  o n l y two  t i m e of o v e r 30 p e r c e n t .  from the t r a c e of p a r t i c l e s 1 and  i s that the underestimation m u l t i p l e "dosing",  p a r t i c l e 4 i n the  2 i n Figure  The 5.12  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 d e g r e e of  i n t h i s case, four separate  i n the s t r a t i f i e d model.  d o s i n g s as compared w i t h  dvection  120  Figure Paths  of P a r t i c l e s  5.13  in Stratified  Model  and  Barotropic  Model  C o n s i d e r now effluent dilution.  t h e 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 Of c r i t i c a l  d i c t i o n s which determine  importance  inital  h e r e a r e those v e l o c i t y  pre-  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  v a l u e s around the s l a c k w a t e r p e r i o d s .  I t i s c r u c i a l t h a t the p r e d i c t e d  v a l u e s be a c c u r a t e not o n l y i n terms o f magnitude but as the l e n g t h o f t h e s l a c k w a t e r p e r i o d i s i m p o r t a n t , t h e y must a l s o be a c c u r a t e i n t i m i n g . B e f o r e 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 o f n e a r - s l a c k - t i d e v e l o c i t y errors i t i s necessary  to understand  the method used i n the t i d a l l y  vary-  i n g mass t r a n s p o r t model t o 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 . E s t i m a t e s o f i n i t i a l d i l u t i o n a r e o b t a i n e d by d i l u t i n g the e f f l u e n t mass d i s c h a r g e d o v e r one hour i n t o t h e volume w h i c h f l o w s 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  average t i d a l f l o w s a r e non-zero,  t h i s method i s a c c e p t a b l e when  i t i s i n a p p r o p r i a t e when t h e n e t h o u r l y  f l o w approaches z e r o 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 i n d e t e r m i n a t e and the i n i t i a l d i l u t i o n c u r v e becomes d i s c o n t i n uous.  To p r e v e n t  t h e o c c u r r e n c e of t h i s s l a c k w a t e r d i s c o n t i n u i t y ,  net h o u r l y f l o w has been c o n s t r a i n e d so t h a t i t can n e v e r r e a c h  the  zero.  Thus i n t h e event t h a t the z e r o 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 i n s t r e a m waste c o n c e n t r a t i o n i s d e t e r m i n e d  by the  arbitrarily  chosen minimum f l o w r a t e . T h i s weakness, i n h e r e n t i n t h e t i d a l l y v a r y i n g m o d e l , 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 t h e t e m p o r a l r e s o l u t i o n o f  the model so t h a t i t would a p p r o x i m a t e 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 s m a l l e r time i n c r e m e n t s  ( i . e . i n the o r d e r of m i n u t e s i n s t e a d o f one  t h e e f f e c t c o u l d be m i n i m i z e d .  Although  hour),  the z e r o t i d a l f l o w c o n d i t i o n  might s t i l l o c c u r , because o f the f i n e r time i n c r e m e n t , i t s impact  in  122  the s i m u l a t i o n would be reduced as each t i m e increment would t h e n r e p r e sent a s m a l l e r f r a c t i o n of t h e t i d a l p e r i o d and  thus r e c e i v e l e s s w e i g h t  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 r e s p o n s e . Another important  f a c t o r t h a t i n f l u e n c e s the v a l i d i t y o f  the  t i d a l l y varying 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 been i g n o r e d .  T h i s was  done p u r p o s e f u l l y to e x a g g e r a t e the  r i v e r / e s t u a r y r e s p o n s e , however i t may v a l i d i t y of t h e p r e d i c t e d r e s u l t s .  has  intra-tidal  have d r a s t i c a l l y e f f e c t e d  the  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  p r o c e s s i s t i m e dependent, i t w i l l e x h i b i t I t s most s e v e r e e f f e c t s on c o n c e n t r a t i o n s p i k e s i n e f f l u e n t p a r c e l s w h i c h have extended  residence  t i m e s , p r e c i s e l y t h e same c o n d i t i o n s t h a t r e s u l t i n t h e most s i g n i f i c a n t DO  depletions. In t h i s study, although  i t has not been p o s s i b l e t o f u l l y  de-  t e r m i n e t h e e x t e n t t o w h i c h t h i s e f f e c t might a l t e r t h e v a l i d i t y of  the  t i d a l l y varying p r e d i c t i o n s , i t i s considered  that l o n g i t u d i n a l dispersion  a f t e r any extended p e r i o d ( i . e . more t h a n one  t i d a l cycle) w i l l result i n  a two  t o f i v e f o l d r e d u c t i o n i n any 5.2.5  Summary.  concentration  spike.  I n summary, t h e r e s u l t s from the t i d a l l y  i n g d i s s o l v e d oxygen model show an i n c r e a s e d DO d e f i c i t d u r i n g of the t i d a l c y c l e .  estuary response.  portions  A l t h o u g h t h i s e f f e c t i s t y p i c a l of e s t u a r y  oxygen r e s p o n s e i t may  not be an a c c u r a t e  vary-  dissolved  r e p r e s e n t a t i o n of t r u e r i v e r /  Concern has been e x p r e s s e d over the v a l i d i t y of  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 t h e mechanics of 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 c a u s i n g  the  the  the  increased  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 t h e assumption o f zero d i s p e r s i o n may a l s o d r a s t i c a l l y a f f e c t the conditions  o f maximum d e f i c i t .  Because o f the c o n c e r n t h a t  v a r y i n g model may n o t be e n t i r e l y a p p r o p r i a t e i n t r a - t i d a l behaviour of d i s s o l v e d explicitly  the t i d a l l y  f o r use i n d e s c r i b i n g t h e  oxygen p a r a m e t e r s , i t w i l l n o t be used  i n t h e assessment of lower F r a s e r  assimilative capacity.  It  w i l l be used, however, to e x e m p l i f y i n t r a - t i d a l r e s p o n s e t h e r e b y augmenti n g and tempering t h e f o l l o w i n g assessment o f lower F r a s e r  dissolved  oxygen dynamics.  5.3  AN ANALYSIS OF LOWER FRASER RIVER/ESTUARY ASSIMILATIVE CAPACITY The  preliminary  following prefactory  assessment o f lower F r a s e r  T h e i r purpose i s t o i n f o r m cussion  comments a r e o f f e r e d p r i o r t o making a River/Estuary  assimilative  capacity  the r e a d e r as t o t h e i n t e n t o f the e n s u i n g  and, a t the'same time, t o o f f e r t h e r a t i o n a l e behind i t . When i t comes time t o u t i l i z e t h e c a p a b i l i t i e s o f a s t u d y  as  dis-  t h i s , a d e c i s i o n must be made r e g a r d i n g  t h e mode o f a t t a c k .  such  Since i t  i s p o s s i b l e through t h e use of m a t h e m a t i c a l models t o 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  c o m b i n a t i o n s and p e r m u t a t i o n s ,  the d e c i s i o n must take i n t o account t h e l i m i t s o f p r a c t i c a l i t y a s w e l l as the o b j e c t i v e a t hand.  The most a p p r o p r i a t e  use t o be made o f t h e 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 t h e purposes o f t h i s study i s t o b r i n g some o f t h e main f e a t u r e s  o f lower F r a s e r  the a n a l y s i s has made use o f s p e c i f i c a l l y  oxygen dynamics.  of b e i n g c o m p l e t e l y d e f i n i t i v e and, from making s p e c i f i c  To do t h i s  chosen h y p o t h e t i c a l  thus r e t a i n i n g an a i r o f g e n e r a l i t y i n i t s approach. therefore,  to l i g h t  It falls  situations, f a r short  has d e l i b e r a t e l y r e f r a i n e d  f o r e c a s t s of f u t u r e c o n d i t i o n s .  However, what i t doe  o f f e r i s some i n d i c a t i o n o f how t h e 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 u n d e r s t a n d i n g o f t h e n a t u r e o f 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  River/Estuary.  The a n a l y s i s i s based m a i n l y on r e s u l t s from t h e t i d a l l y model.  averaged  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 t o be w e l l behaved i n i t s  p r e d i c t e d r e s p o n s e ( s e e S e c t i o n 5.1) and t h e r e f o r e i t i s c o n s i d e r e d more r e l i a b l e i n terms o f t h e v a l i d i t y o f i t s p r e d i c t i o n s .  t o be  Some use w i l l  be made o f t i d a l l y v a r y i n g model r e s u l t s b u t because s e r i o u s c o n c e r n s have been e x p r e s s e d 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 ( s e e S e c t i o n 5.2), i t s use w i l l be r e s t r i c t e d t o e x e m p l i f y i n g  the expected  e f f e c t o f i n t r a - t i d a l d i s s o l v e d oxygen r e s p o n s e ; t h e r e b y q u a l i f y i n g t o some e x t e n t  t h e o v e r a l l assessment  of a s s i m i l a t i v e capacity.  As t h e f o l -  l o w i n g 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 m o d e l s , a l l c o n c l u s i o n s drawn out o f i t must be c o n s i d e r e d  t o be t e n t a t i v e .  I n t h e i n v e s t i g a t i o n o f t i d a l l y averaged model r e s p o n s e c a t i o n s were t h a t , a c c o r d i n g dynamics  indi-  t o model p r e d i c t i o n s , t h e d i s s o l v e d oxygen  o f the l o w e r F r a s e r R i v e r / E s t u a r y were t o a l a r g e e x t e n t  by two f a c t o r s :  the i n f l u e n c e of freshwater  water t e m p e r a t u r e .  governed  i n f l o w and t h e e f f e c t o f  As c o n d i t i o n s i n t h e l o w e r F r a s e r a r e s u c h t h a t low  f l o w s o c c u r d u r i n g t h e p e r i o d J a n u a r y t o March when w a t e r are l o w , and c o n v e r s e l y ,  temperatures  that high temperatures occur d u r i n g h i g h e r  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 "  flow  during  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 d i s c h a r g e s .  I n attempts t o e s t a b l i s h t h i s c r i t i c a l  period  and a l s o t o o b t a i n some i n d i c a t i o n as t o t h e e f f e c t o n d i s s o l v e d oxygen  l e v e l s o f a l a r g e waste l o a d i n g , t h e r e b e i n g no o b s e r v a b l e r e s p o n s e u s i n g a c t u a l waste l o a d i n g s , a s e r i e s o f model runs was  made u s i n g t h e 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 o f t h e y e a r .  A  h y p o t h e t i c a l waste l o a d o f 1,000,000 pounds o f BOD p e r day ( a p p r o x i m a t e l y f o u r t i m e s t h e p r e s e n t t o t a l BOD l o a d ) was d i s c h a r g e d 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 , t h e l o c a t i o n chosen t o be i n t h e u p s t r e a m  reaches  so t h a t a g r e a t e r oxygen r e s p o n s e would be o b s e r v e d w i t h i n t h e model boundaries.  M o n t h l y mean low f l o w s and h i g h t e m p e r a t u r e s ( s e e S e 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 e v e n t s w i t h t e n and f i f t y  year  r e t u r n p e r i o d s were chosen f o r use i n t h e a n a l y s i s as t h e s e c o n d i t i o n s would r e p r e s e n t an extreme d i s s o l v e d oxygen r e s p o n s e i n t h e r i v e r / e s t u a r y . I t i s r e c o g n i z e d t h a t t h e s i m u l t a n e o u s o c c u r r e n c e o f t h e s e two e v e n t s i s h i g h l y improbable. efficients  Assumed v a l u e s f o r t h e d i s s o l v e d oxygen model c o -  (see S e c t i o n 4.4) were used. The r e s u l t s o f t h e s i m u l a t i o n a r e shown i n F i g u r e s 5.14 and  5.15,  t h e 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 t e n y e a r 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 r e p r e s e n t s f i f t y year c o n d i t i o n s .  These "space-  t i m e " p l o t s a r e a u s e f u l means o f 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 o f d a t a i n summary form.  I t s h o u l d be n o t e d t h a t they a r e n o t t r u e s p a c e - t i m e p l o t s  because t h e 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 o f mean m o n t h l y conditions.  S i n c e t h e s e diagrams r e p r e s e n t e x p e c t e d 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 o f BOD d i s c h a r g e d a t S t a t i o n 40, t h e y can a l s o be thought o f as " u n i t r e s p o n s e diagrams".  F o r example,  i f the waste  load  a t S t a t i o n 40 were t o be d o u b l e d , t h e d e f i c i t c o n c e n t r a t i o n s t h r o u g h o u t the  r i v e r / e s t u a r y would be found t o d o u b l e a c c o r d i n g t o t h e l i n e a r i t y o f  K| = K = 0.2/day 2  at  20°Cj E = 10 mi /day 2  t  River/Estuary  W=  1,000,000  lb/day  at  Stn. 40  Section  F i g u r e 5.14 S p a c e - T i m e P l o t o f DO D e f i c i t R e t u r n P e r i o d Low Flows  C o n c e n t r a t i o n s U s i n g 10 Y e a r and H i g h T e m p e r a t u r e s  K, = K = 0.2/day 2  at 20° C •, E = I0 mi/day; W= 1,000,000 lb/day at Stn. 40  R i v e r / Estuary Figure Space-Time  Plot,  Return  o f DO  Period  Deficit  Low  Flows  Section 5.15  Concentrations and  High  Using  Temperatures  50  Year  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 e v i d e n t t h a t , a c c o r d i n g t o model p r e d i c t i o n s , t h e d i s s o l v e d oxygen r e s p o n s e i n t h e l o w e r F r a s e r i s m i n i m a l even when a c o n s i d e r a b l y l a r g e waste l o a d i s d i s c h a r g e d upstream r e a c h e s .  i n the  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 t h e t e n and f i f t y y e a r c o n d i t i o n s , a r e seen i n both i n s t a n c e s t o occur d u r i n g the low flow p e r i o d i n March.  Thus,  i n terms o f oxygen d e p l e t i o n s , t h e e f f e c t s o f low f l o w s o u t w e i g h e d t h e e f f e c t s o f low water temperatures.  S l i g h t DO d e p l e t i o n s u p s t r e a m o f t h e  o u t f a l l l o c a t i o n a r e o b s e r v e d f o r a l l months o f t h e y e a r e x c e p t d u r i n g the h i g h f l o w months - May, June and J u l y . I n o r d e r t o d e t e r m i n e d i s s o l v e d oxygen c o n c e n t r a t i o n s f r o m t h e r e s u l t s o f t h i s s i m u l a t i o n , mean m o n t h l y 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 a r e r e q u i r e d f o r t h e t e m p e r a t u r e c o n d i t i o n s used i n each s e t o f a n a l y s e s . These a r e shown i n T a b l e 5.2. TABLE 5.2 DO SATURATION CONCENTRATIONS USED IN ANALYSIS  Month  Ten Y e a r Return Period  F i f t y Year Return P e r i o d  January February March April May June July August September October November December  13.9 13.8 13.2 12.4 11.4 10.5 9.9 9.7 10.0 11.2 12.5 13.2  13.8 13.6 13.0 12.2 11.2 10.3 9.7 9.6 9.9 11.0 12.3 12.9  I t i s evident  from a r e v i e w o f T a b l e 5.2 t h a t , even though t h e  maximum DO d e f i c i t s o c c u r i n March, minimum d i s s o l v e d oxygen c o n c e n t r a t i o n s w i l l occur i n the.period saturation concentrations.  This i n d i c a t e s that, according  r e s u l t s , the c r i t i c a l period l a t e summer o r e a r l y f a l l ,  o f J u l y t o September because o f r e d u c e d DO t o model  f o r d i s s o l v e d oxygen i n t h e l o w e r F r a s e r i s  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  w a t e r t e m p e r a t u r e on oxygen s a t u r a t i o n l e v e l s . I n terms o f t h e magnitude o f DO d e p l e t i o n s ,  the r e s u l t s of  model a n a l y s e s show t h a t f o r t h e most extreme c o m b i n a t i o n s o f l o w r i v e r f l o w s and h i g h w a t e r t e m p e r a t u r e s and an e x t r e m e l y l a r g e waste d i s c h a r g e i n t h e upper r e a c h e s , t h e d i s s o l v e d oxygen r e s p o n s e o b s e r v a b l e i n t h e e s t u a r y w i l l be m i n i m a l .  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 o f the  same t o t a l magnitude, o r t h e s i m i l a r l a r g e l o a d l o c a t e d i n t h e l o w e r r i v e r / e s t u a r y r e a c h e s , t h e e f f e c t on d i s s o l v e d oxygen r e s p o n s e w i l l be even l e s s . To demonstrate t h e s i z e a b l e a b i l i t y o f t h e l o w e r F r a s e r similate- o r g a n i c waste d i s c h a r g e s 1  ;  r i d i c u l o u s l y extreme waste l o a d i n g .  consider  to as-  t h e prsdic-te-d e f f e c t s o f a  I f t h e r e were a f o u r - f o l d  increase  i n t h e h y p o t h e t i c a l d i s c h a r g e l o c a t e d a t S t a t i o n 40 ( t h i s r e p r e s e n t s s i n g l e point source discharge w i t h a population  equivalent  a  o f 20 m i l l i o n ) ,  u s i n g t h e f i f t y y e a r extreme c o n d i t i o n s , t h e p r e d i c t e d , minimum 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 r e s t i l l above 7.5 mg/1 i n August and o v e r 9 mg/1  i n March. At t h i s j u n c t u r e a c a v e a t t o t h e f o r e g o i n g priate.  a n a l y s i s i s appro-  Up t o t h i s p o i n t , t h e 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 .  A l t h o u g h t h i s s h o u l d be a good i n d i c a t i o n o f  a v e r a g e 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 e s t u a r y d i s s o l v e d oxygen r e s p o n s e .  i t was  i z e d by c o n c e n t r a t i o n s p i k e s formed d u r i n g s l a c k w a t e r  oxygen p r o f i l e . this  varying to  the  instream  v a r y t h r o u g h o u t the t i d a l c y c l e , b e i n g  t i d a l l y varying effluent profile  river/  n o t e d t h a t due  movement of the w a t e r mass i n e s t u a r i e s , i n i t i a l  effluent concentrations  of  I n the a n a l y s i s of t i d a l l y  d i s s o l v e d oxygen response (see S e c t i o n 5.2) oscillatory  the t r u e n a t u r e  periods.  characterThis  results i n a t i d a l l y varying dissolved  I n d i c a t i o n s were t h a t d u r i n g the low f l o w p e r i o d when  e f f e c t i s most pronounced, i n the absence o f 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 be up t o s i x t o ten t i m e s h i g h e r S e c t i o n 2.3).  concentrations  than t i d a l l y averaged d e f i c i t s  By making the c o n s e r v a t i v e a s s u m p t i o n t h a t a  d e c r e a s e i n c o n c e n t r a t i o n f o r extended r e s i d e n c e  three to f i v e . ratio  The  (see  two-fold  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 v a r y i n g t o t i d a l l y averaged DO  could  of peak t i d a l l y  d e f i c i t would be r e d u c e d t o the o r d e r  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  of  deficit  t o 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 r e s p o n s e . thetical  I n t h e c a s e o f t h e hypo-  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  this  c a l c u l a t i o n t h e r e would be a maximum low f l o w 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  mg/1  t o 4.5  t o 3.0 mg/1  mg/1  u s i n g the t e n y e a r extreme c o n d i t i o n s and  d e f i c i t u s i n g the f i f t y y e a r c o n d i t i o n s .  w o r s t i n s t a n c e , minimum DO  a 2.7  However, even i n the  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 s h o u l d be n o t e d t h a t the e f f e c t s of i n t r a - t i d a l  DO  r e s p o n s e 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 w a s t e w a t e r d i s c h a r g e s .  F o r example, c o n s i d e r  the e x t r e m e l y  l a r g e waste d i s c h a r g e  a t S t a t i o n 40:  (20 m i l l i o n p o p u l a t i o n  whereas t h e minimum t i d a l l y averaged DO was  equivalents) approximately  9 mg/1 u s i n g t h e f i f t y y e a r c o n d i t i o n s , t h e minimum 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 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  d i s c h a r g e s t h e t i d a l l y averaged model may n o t be a good i n d i c a t i o n o f r i v e r / e s t u a r y behaviour.  T h i s was one o f t h e major c o n c l u s i o n s o f J o y ' s  i n v e s t i g a t i o n where he used l o a d s o f 25 m i l l i o n pounds p e r day [ J o y , 1974]. Although  no r e s u l t s u s i n g t h e t i d a l l y v a r y i n g model a r e a v a i l -  a b l e from t h e c r i t i c a l , l a t e summer p e r i o d , t h e r e i s e v e r y r e a s o n t o b e l i e v e t h a t a s i m i l a r r e l a t i o n s h i p between t h e 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 e x p e c t t h a t t h e e f f e c t o f  waste water d i s c h a r g e s on d i s s o l v e d oxygen would be e x a c e r b a t e d fluence of t i d a l a c t i o n which, although f l o w s , would n o n e t h e l e s s  reduced due t o h i g h e r  by t h e i n freshwater  be s i g n i f i c a n t .  I n summary, a c c o r d i n g t o t h e r e s u l t s of t h i s a n a l y s i s , t h e l o w e r F r a s e r R i v e r / E s t u a r y would seem t o 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 capacity.  P r i m a r i l y t h i s i s because o f t h e combined i n f l u e n c e o f l a r g e  freshwater  f l o w s and l o w w a t e r t e m p e r a t u r e s .  The a n a l y s i s has shown t h 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 t h e l a t e summer i n s p i t e o f the f a c t t h a t maximum d i s s o l v e d oxygen d e p l e t i o n s a r e o b s e r v e d d u r i n g t h e low f l o w p e r i o d i n March.  A cursory examination  of i n t r a - t i d a l  oxygen r e s p o n s e has i n d i c a t e d t h a t i t i s an i m p o r t a n t  dissolved  determinant of  lower F r a s e r d i s s o l v e d oxygen dynamics and t h a t i t w i l l become more important  as waste l o a d i n g s t o t h e r i v e r a r e i n c r e a s e d .  CHAPTER 6 SUMMARY AND DISCUSSION  G i v e n t h e r e s u l t s from t h e d i s s o l v e d oxygen models a s o u t l i n e d i n t h e p r e v i o u s c h a p t e r i t now remains t o b r i e f l y r e v i e w and d i s c u s s t h e f i n d i n g s of t h i s study. as e x p l i c i t  A t t e n t i o n w i l l be d e v o t e d t o t h e i m p l i c i t a s w e l l  d e t a i l s o f t h e r e s e a r c h i n an e f f o r t t o g l e a n a s much as  p o s s i b l e from t h e r e s u l t s o f t h i s attempt a t w a t e r q u a l i t y  modeling.  T h i s c h a p t e r w i l l c o n s i d e r s e p a r a t e l y two a s p e c t s o f t h i s r e s e a r c h :  first-  l y , t h e development o f t h e 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, s e c o n d l y , t h e r e s u l t s o f t h e a p p l i -  c a t i o n o f t h e models t o an assessment o f t h e a s s i m i l a t i v e c a p a c i t y o f t h e lower F r a s e r R i v e r / E s t u a r y .  T h i s s u b d i v i s i o n i s u s e f u l i n t h a t i t sepa-  r a t e s t h e d i s c u s s i o n i n t o two s e c t i o n s , one w h i c h d e a l s w i t h t h e models themselves'and of  6.1  t h e o t h e r which d e a l s w i t h t h e d i s s o l v e d oxygen r e s o u r c e s  the lower Fraser.  DISSOLVED OXYGEN MODELS 6.1.1  Summary.  A r e v i e w was made o f t h e v a r i o u s o x y g e n s o u r c e /  s i n k p r o c e s s e s w h i c h a f f e c t t h e oxygen b a l a n c e i n waterways. c o n d i t i o n s i n t h e l o w e r F r a s e r R i v e r / E s t u a r y i t was d e t e r m i n e d t h e purposes to  I n l i g h t of that f o r  o f t h i s s t u d y t h e two b a s i c p r o c e s s e s - d e o x y g e n a t i o n due  t h e d e g r a d a t i o n o f d i s c h a r g e d o r g a n i c m a t t e r and r e o x y g e n a t i o n due t o  a t m o s p h e r i c r e a e r a t i o n - were t h e p r i n c i p a l f a c t o r s t o be c o n s i d e r e d i n t h e development o f 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 .  -  132 -  Because  of  t h e complex n a t u r e o f e s t u a r y h y d r a u l i c s w h i c h i s c h a r a c t e r i z e d by u n -  s t e a d y , o s c i l l a t o r y w a t e r movement due t o t h e i n f l u e n c e o f t i d e s , t h e a p p l i c a t i o n o f t h e b a s i c oxygen b a l a n c e c o n c e p t s t o t h e m o d e l i n g o f d i s s o l v e d oxygen i n e s t u a r i e s i s many t i m e s more d i f f i c u l t t h a n i n t h e analagous r i v e r s i t u a t i o n .  However, i n s p i t e o f t h i s h i g h degree o f  h y d r a u l i c c o m p l e x i t y , mass t r a n s p o r t and w a t e r movement can be modeled. In t h i s s t u d y 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 tidally  averaged approach and a t i d a l l y v a r y i n g a p p r o a c h . The t i d a l l y averaged a p p r o a c h by making u s e o f s t e a d y - s t a t e a s s u m p t i o n s s i m p l i f i e s t h e problem o f e l i m i n a t i n g t h e t i m e v a r i a b l e .  In  e s s e n c e , t h e u n s t e a d y , e s t u a r y f l o w f i e l d i s r e p l a c e d by a s t e a d y f r e s h water f l o w f i e l d and a t i d a l d i s p e r s i o n component w h i c h can i n d i r e c t l y account f o r t h e e f f e c t s o f t i d a l a c t i o n .  A l l p a r a m e t e r s and v a r i a b l e s  by t h i s s o l u t i o n approach a r e a s s i g n e d t h e i r mean t i d a l  values."  The second approach t o m o d e l i n g mass t r a n s p o r t , t h e t i d a l l y v a r y ing  a p p r o a c h , does n o t e l i m i n a t e t h e t i m e v a r i a b l e .  Thus i t a t t e m p t s t o  d e s c r i b e " r e a l t i m e " e s t u a r y h y d r a u l i c b e h a v i o u r and c a n a c c o u n t d i r e c t l y for  such t i d a l e f f e c t s as c u r r e n t  reversal.  The i n c o r p o r a t i o n o f t h e b a s i c d i s s o l v e d oxygen b a l a n c e f o r m u l a t i o n s i n t o each of t h e two mass t r a n s p o r t models has formed t h e b a s i s o f the  two d i s s o l v e d oxygen models used i n t h i s s t u d y :  the t i d a l l y  averaged  d i s s o l v e d oxygen model and t h e 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. some e x t e n t t h e two models a r e complementary estuary conditions.  i n t h e i r view of r i v e r /  The former model a l l o w s an a n a l y s i s t o be made o f  average c o n d i t i o n s o v e r a number o f t i d a l c y c l e s whereas t h e l a t t e r by  To  p r o v i d i n g a g r e a t e r degree o f t e m p o r a l 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 t o be made o f i n t r a - t i d a l r i v e r / e s t u a r y b e h a v i o u r . 6.1.2  L i m i t a t i o n s o f t h e 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 t h e 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 t h r e e s p a t i a l , t e m p o r a l and c a l i b r a t i o n a l .  categories:  Of t h e s e o n l y t h e f i r s t a p p l i e s i n  a s i m i l a r degree t o b o t h t h e t i d a l l y averaged and t i d a l l y v a r y i n g models. T h i s l i m i t a t i o n a r i s e s from t h e a s s u m p t i o n t h a t a l l p a r a m e t e r s and v a r i a b l e s can b e - a p p r o x i m a t e d 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 t h e s o l u t i o n s o f the mass t r a n s p o r t e q u a t i o n s has r e s u l t e d i n t h e models b e i n g only o f 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 .  cognizant  The models a r e  u n a b l e t o d e a l w i t h v a r i a b i l i t y o v e r t h e 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 a r e r e s t r i c t e d i n a p p l i c a t i o n t o o n l y t h e main c o r e f l o w o f t h e main r i v e r channels.  Thus t h e models cannot be a p p l i e d t o t h e a n a l y s i s o f  l o c a l i z e d problems such as might o c c u r i n t h e immediate v i c i n i t y o f an o u t f a l l o r i n t h e s m a l l s i d e c h a n n e l s and s l o u g h main r i v e r .  areas adjacent to the  A l s o by t h e o n e - d i m e n s i o n a l a s s u m p t i o n w a s t e i n p u t s t o t h e  models a r e " c o m p l e t e l y  mixed" e i t h e r o v e r t h e c r o s s - s e c t i o n as i s t h e  case i n t h e t i d a l l y v a r y i n g model o r w i t h i n a 5,000 f o o t segment as i s the c a s e i n t h e t i d a l l y averaged model.  This "instant mixing" c o r o l l a r y  t o t h e main a s s u m p t i o n has as i t s l i m i t a t i o n t h e f a c t t h a t 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,  u n p u b l i s h e d d a t a ] t h a t a t l e a s t two t i d a l c y c l e s a r e r e q u i r e d i n t h e l o w e r r i v e r / e s t u a r y r e a c h e s ( w i t h c o n s i d e r a b l y more t i m e b e i n g i n t h e upper r e a c h e s ) f o r m i x i n g t o be c o m p l e t e d .  required  Stratification effects  due  t o t h e p r e s e n c e o f t h e s a l t w a t e r wedge may a t t i m e s i n h i b i t  m i x i n g , p r e v e n t i n g complete m i x i n g  i n the v e r t i c a l plane.  vertical  A n o t h e r ..  s t r a t i f i c a t i o n e f f e c t i s t h e 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 f l o w v e l o c i t i e s w h i c h r e s u l t from t h e f r e s h w a t e r top o f t h e s a l t w a t e r l a y e r .  f l o w i n g out o v e r  The p r e s e n c e o f t h e s a l t w a t e r wedge i s n o t  t a k e n i n t o a c c o u n t i n e i t h e r o f t h e models used i n t h i s The  study.  second c l a s s o f model l i m i t a t i o n s a r e those i n v o l v i n g t h e  degree t o w h i c h t h e models a r e a t e m p o r a l a b s t r a c t i o n o f t h e r e a l , r i v e r / , estuary s i t u a t i o n . in  The t i d a l l y averaged model i s a s e v e r e a b s t r a c t i o n  t h e sense t h a t i t c o n s i d e r s o n l y " 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 p a r a m e t e r s 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 . some e x t e n t  t h i s , i n e f f e c t , represents  Although to  an i n t e g r a t i o n o v e r a number o f  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 t i m e " meaning. t i d a l l y v a r y i n g model r e p r e s e n t s  The  a l e s s e r t e m p o r a l a b s t r a c t i o n as i t  a t t e m p t s t o s i m u l a t e " r e a l t i m e " 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 v a l u e s .  A l t h o u g h t h i s method o f s i m u l a t i o n i s t h e  t i d a l l y v a r y i n g model's s t r o n g p o i n t , i t i s n o t w i t h o u t weakness. estimate  i t s inherent  The c h i e f l i m i t a t i o n i s t h e manner o f c a l c u l a t i o n used t o i n i t i a l effluent d i l u t i o n rates.  D u r i n g t h e p e r i o d around s l a c k -  w a t e r , t h e 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 c u r v e ; t h e 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 t h e t i d a l l y v a r y i n g v e l o c i t y approaches z e r o .  Although  c o n s t r a i n t s w i t h i n t h e model p r o h i b i t t h e p r e d i c t e d r e s u l t s f r o m e v e r reaching  t h i s extreme c o n d i t i o n , t h e model p r e d i c t i o n s a r e n o n e t h e l e s s  e x t r e m e l y s e n s i t i v e t o t h e magnitude as w e l l as t h e t i m i n g o f o c c u r e n c e  of s l a c k w a t e r v e l o c i t i e s .  As t h e s l a c k w a t e r p e r i o d r e s u l t s  BOD c o n c e n t r a t i o n s w h i c h i n t u r n u l t i m a t e l y  i n maximum  d e t e r m i n e maximum DO  d e p l e t i o n s i t must be s t r e s s e d t h a t 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 t h e v a l i d i t y o f p r e d i c t e d F i n a l l y , there i s the overriding  l i m i t a t i o n that the dissolved  oxygen models cannot p r e s e n t l y be c a l i b r a t e d . any  s i g n i f i c a n t dissolved  Because o f t h e l a c k o f  oxygen d e p l e t i o n s i n t h e l o w e r F r a s e r R i v e r /  E s t u a r y , t r a d i t i o n a l c a l i b r a t i o n p r o c e d u r e s were o f no use. the d i s s o l v e d  results.  Consequently  oxygen r e s p o n s e c o e f f i c i e n t s used i n t h i s s t u d y 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  relationships  A s i d e from t h e f a c t t h a t t h e d i s s o l v e d  described i n the l i t e r a t u r e .  oxygen c o e f f i c i e n t s may n o t be  a p p r o p r i a t e , a number o f o t h e r l i m i t a t i o n s o f a c a l i b r a t i o n a l n a t u r e exist.  W i t h r e g a r d t o t h e t i d a l l y averaged model, because o f t h e 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 t h e l o w e r F r a s e r , i t was n o t p o s s i b l e t o  e s t i m a t e t h e v a l u e o f t h e 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  s u c h , v a l u e s used were chosen on a p u r e l y a r b i t r a r y  basis.  Considering 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 varying model, i t has n o t been p o s s i b l e t o v e r i f y hydrodynamic sub-model v e l o c i t y predictions.  Hence t h e a c c u r a c y o f t h e s e p r e d i c t i o n s ,  magnitude and t i m i n g , i s n o t known. since velocity predictions v a r y i n g mass t r a n s p o r t .  i n terms o f b o t h  T h i s i s an i m p o r t a n t l i m i t a t i o n  s e r v e as t h e b a s i s f o r e s t i m a t i n g As w e l l , l o n g i t u d i n a l  i n a n a l y s e s u s i n g t h e t i d a l l y v a r y i n g model.  tidally  d i s p e r s i o n was n e g l e c t e d T h i s can be c o n s i d e r e d 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 c a n be a c c o u n t e d f o r through use  o f a non-zero l o n g i t u d i n a l  dispersion  coefficient.  137  6.1.3 may  The M o d e l i n g E x p e r i e n c e .  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  seem t h a t the l i m i t a t i o n s of the models have been o v e r - e m p h a s i z e d .  T h i s has been done p u r p o s e f u l l y .  The  a u t h o r f e e l s s t r o n g l y t h a t the  limi-  t a t i o n s and weaknesses i n h e r e n t i n the models must be r e a l i z e d as a n e c e s s a r y p e r l i m i n a r y t o 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 o f the models' capabilities.  Only by l e a r n i n g the l i m i t a t i o n s can one  appreciate  s t r e n g t h of t h e m o d e l i n g 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 b e i n g by the s t r e n g t h of the weakest a s s u m p t i o n .  the  determined  A l l too o f t e n m o d e l i n g s t u d i e s  o v e r s t r e s s t h e s t r e n g t h s 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 o v e r i t s weaknesses w h i c h when u n c o v e r e d p o i n t out s e r i o u s s h o r t c o m i n g s 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 s t u d y o r from the o u t s i d e t o c r i t i c a l l y a s s e s s a l l u t i l i t y of the m o d e l i n g e x e r c i s e .  the net r e s u l t and  over-  Because of t h e a u t h o r ' s c o n c e r n  o v e r the i m p o r t a n c e of t h i s o f t e n n e g l e c t e d  a s p e c t of the m o d e l i n g e x p e r -  i e n c e , the f o l l o w i n g i s i n c l u d e d i n t h i s d i s c u s s i o n . I n r e c e n t y e a r s the i d e a of u s i n g m a t h e m a t i c a l 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 acceptance.  attained universal  At the o u t s e t of most planning/management s t u d i e s t h e  question  i s no l o n g e r " S h a l l we use a model?" but r a t h e r "Which m o d e l ( s ) s h a l l use?"  Encouraged by t h o s e who  seek an e a s i e r means o f d e a l i n g w i t h  i n c r e a s i n g c o m p l e x i t i e s of w a t e r management and developments i n d i g i t a l  we  the  s p u r r e d on by r a p i d  computer technology, v a s t 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 I s not  f a i r to say t h a t 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-  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 t h o s e s t u d i e s w h i c h have  a p p l i e d w a t e r q u a l i t y m o d e l i n g c o n c e p t s t o t h e development o f a u s a b l e p r e d i c t i v e c a p a b i l i t y , v e r y few have been s u b j e c t e d t o i n t e n s i v e c r i t i c a l reviews. for  A r e c e n t l y p u b l i s h e d case s t u d y e n t i t l e d The U n c e r t a i n  Environmental  Search  Q u a l i t y [Ackerman et_ a l . , 1974] has made s u c h a r e v i e w  of t h e Delaware E s t u a r y Comprehensive Study (DECS), c r i t i c a l l y a n a l y z i n g a number o f t e c h n i c a l a s p e c t s and c r i t i c i z i n g  the water p o l l u t i o n  policy  d e c i s i o n s made by t h e Delaware R i v e r B a s i n Commission as a r e s u l t o f t h e v  DECS f i n d i n g s .  I n 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 u s i n g Thomann's s t e a d y - s t a t e BOD-DO model ( s i m i l a r t o t h e 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 attack.  Shortcomings were p o i n t e d o u t i n t h e DECS model s t u d y i n i t s  f a i l u r e t o deal adequately,  i f a t 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  r e s p o n s e 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 c o n c l u d e s  t h a t as a r e s u l t o f t h e s e  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 t h e b e n e f i t s w h i c h would be d e r i v e d from a " c l e a n - u p "  program o n t h e D e l a w a r e .  He goes  on t o s a y t h a t i n s p i t e o f t h e a c c l a i m g i v e n DECS, l a u d i n g t h e s o p h i s t i c a t ed e f f o r t w h i c h 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 i t was i n t h e end " u n e q u a l t o t h e t a s k " and l e d t o "a f a i l u r e  tools,  i n modern  p o l i c y making". The main r e a s o n f o r t h i s , a c c o r d i n g t o Ackerman, i s t h a t i n t h e i r e n t h u s i a s m t h e DECS s t a f f had f a i l e d t o i m p a r t a r a t i o n a l s e n s e o f perspective along w i t h t h e i r f i n d i n g s .  I n p r e s e n t i n g t h e i r achievements  " t h e r e s e a r c h s t a f f emphasized t h e a c c u r a c y  o f t h e numbers i t s model  139  generated",  o f f e r i n g an a n a l y s i s t h a t was  " c o n s p i c u o u s l y d e v o i d of  cautions  ( t o t h e d e c i s i o n makers) about the l i m i t a t i o n s o f i t s p r e d i c t i o n s " . although  the s c i e n t i f i c m e r i t s o f the study were u n d e n i a b l e ,  as an a i d t o d e c i s i o n making was misconceived  Thus  its utility  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  p e r c e p t i o n s r e g a r d i n g the a c c u r a c y  of the water q u a l i t y  model. I n t h i s i n v e s t i g a t i o n , because o f f o r t u i t o u s c i r c u m s t a n c e s  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 r e s e a r c h team, t h e a u t h o r  has  been f o r c e d t h r o u g h o u t t o v i e w the r e s u l t s o f t h i s m o d e l i n g 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 t o an u n d e r s t a n d i n g c o u l d be communicated t o p e r s o n s from d i f f e r e n t d i s c i p l i n e s .  which  This  has  been f o r t u n a t e i n t h a t 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  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-  m u n i c a t e d and has r e s u l t e d i n a s t r e n g t h e n i n g o f t h i s  <C  O  otherwise  r D A C f D  D T V T 7 D  6.2.1  / T 7 C T T T A . D V  Summary:  TXT  C C r i T  V C T l  n w r i ? ) )  OTT  CniTTJ f p  investigation.  C  An Improved Knowledge Base.  I t can be s t a t e d  a l m o s t w i t h o u t e x c e p t i o n t h a t d i s s o l v e d oxygen l e v e l s i n the l o w e r  Fraser  R i v e r / E s t u a r y a r e h i g h , g e n e r a l l y b e i n g 90 t o 100 p e r c e n t o f s a t u r a t i o n values.  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 c o n c e n t r a t i o n s o f 8 to 12 t h r o u g h o u t the y e a r ; more than enough t o 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  t o a s c e r t a i n why  mg/1  the d i s s o l v e d oxygen  r e s o u r c e s of the lower F r a s e r a r e p r e s e n t l y i n t h e i r h e a l t h y  state.  P r i m a r i l y i t i s b e c a u s e , r e l a t i v e t o 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 , l o w e r F r a s e r r e c e i v e s v e r y l i t t l e i n the way T h i s can b e s t be i l l u s t r a t e d by way  the.  of d i s c h a r g e d o r g a n i c w a s t e s .  of example.  Consider  the Delaware  E s t u a r y i n the e a s t e r n U n i t e d S t a t e s where t h e r e has been s e r i o u s oxygen d e p l e t i o n problems.  Average f r e s h w a t e r i n f l o w s t h e r e a r e  approximately  11,000 c f s w h i l e the average e s t i m a t e d o r g a n i c waste d i s c h a r g e i s i n exc e s s o f 1,300,000 pounds o f BOD  per day  [DECS, 1968].  Compare t h a t t o  t h e lower F r a s e r where average f r e s h w a t e r f l o w s a r e a p p r o x i m a t e l y c f s w h i l e the e s t i m a t e d BOD  93,000  l o a d i s p r e s e n t l y i n the o r d e r o f 250,000  pounds per day; a s i t u a t i o n where r i v e r f l o w s a r e on an average a p p r o x i m a t e l y n i n e times h i g h e r and t o t a l waste l o a d i n g s a r e l o w e r by a of f i v e .  factor  In. a d d i t i o n t o 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 l o w e r F r a s e r has added advantage t h a t t h e b u l k of the t o t a l BOD  loading i s discharged  t h e G r e a t e r Vancouver a r e a l o c a t e d on the seaward r e a c h e s o f t h e estuary. percent)  the from  river/  I n 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 ( a t l e a s t  45  i s d i s c h a r g e d i n the v i c i n i t y o f P h i l a d e l p h i a n e a r the head  o f the e s t u a r y , whereas the major p o r t i o n o f the t o t a l BOD  end  l o a d (over  80  p e r c e n t ) e n t e r s the l o w e r F r a s e r downstream o f the P o r t Mann B r i d g e w i t h i n 20 m i l e s o f the S t r a i t of  Georgia.  A number o f o t h e r f a c t o r s p l a y an i m p o r t a n t s o l v e d oxygen dynamics of the l o w e r F r a s e r .  r o l e i n the d i s -  Assessment made t h r o u g h  of the d i s s o l v e d oxygen models has shown t h a t two  i n p a r t i c u l a r are  use im-  p o r t a n t i n d e f i n i n g the n a t u r e o f the l o w e r F r a s e r ' s r a t h e r e x t e n s i v e  141  assimilative capacity.  These a r e the c h a r a c t e r i s t i c a l l y low w a t e r temp-  e r a t u r e s and l a r g e f r e s h w a t e r f l o w s .  W i t h r e g a r d t o the l a r g e r i v e r  flows,  not o n l y 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 t o e f f l u e n t d i s c h a r g e s , they a l s o m i n i m i z e estuary.  r e s i d e n c e t i m e s of e f f l u e n t p a r c e l s i n the  but  river/  I n s p i t e o f the r e t a r d i n g i n f l u e n c e o f t i d a l a c t i o n , a major  p o r t i o n o f the oxygen demand even f o r waste d i s c h a r g e s i n the u p p e r r e a c h e s of the r i v e r i s f l u s h e d out of the c h a n n e l i z e d s e c t i o n s of the e s t u a r y t o be e x e r t e d i n the S t r a i t of G e o r g i a .  The  river/  low w a t e r  temperatures,  i n a d d i t i o n t o p r o v i d i n g h i g h 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 o f d e o x y g e n a t i o n  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 t h e t o t a l oxygen demand b e i n g s a t i s f i e d w i t h i n the river/estuary.  I n terms of s e a s o n a l 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 t h e l o w e r F r a s e r t y p i c a l o f n o r t h l a t i t u d e s where l o w  flows  o c c u r i n the w i n t e r months when w a t e r t e m p e r a t u r e s a r e a l s o low. d u r i n g the p e r i o d when t i d a l e f f e c t s a r e most pronounced and times a r e maximum, d e o x y g e n a t i o n  r a t e s a r e low and  Thus  residence  saturation l e v e l s high.  I n the summer months the s i t u a t i o n i s r e v e r s e d w i t h h i g h f l o w c o u n t e r a c t i n g the e f f e c t of h i g h e r w a t e r t e m p e r a t u r e 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 s and d e o x y g e n a t i o n  rates.  A n a l y s i s made u s i n g t h e oxygen models t o s i m u -  l a t e c o n d i t i o n s f o r a l l months o f the y e a r has shown t h a t the  critical  p e r i o d f o r d i s s o l v e d oxygen i n the l o w e r F r a s e r i s i n l a t e summer.  Al-  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 o c c u r d u r i n g t h e w i n t e r months, t h e p r e d o m i n a t i n g  i n f l u e n c e of water temperature e f E e c t s  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 l o w e s t DO August and  September.  on  levels occurring in  A n o t h e r a s p e c t o f lower F r a s e r d i s s o l v e d oxygen dynamics b r o u g h t t o 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 t h a t 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 r e s p o n s e .  T h i s s i t u a t i o n a r i s e s as a  r e s u l t o f 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 w h i c h 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 c h a r a c t e r i z e d by e f f l u e n t s p i k e s formed d u r i n g p e r i o d s of  profile, slackwater.  P r e l i m i n a r y i n d i c a t i o n s a r e t h a t t h e s e c o n c e n t r a t i o n peaks c o u l d be s i x t o t e n t i m e s h i g h e r t h a n 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 t o d e t e r m i n e the e x a c t n a t u r e  of  intra-  t i d a l d i s s o l v e d oxygen r e s p o n s e , c u r s o r y i n v e s t i g a t i o n has shown t h a t peak t i d a l l y v a r y i n g DO.  d e f i c i t s c o u l d be t h r e e t o f i v e t i m e s g r e a t e r t h a n  t i d a l l y averaged DO  deficits.  I n summary, the d i s s o l v e d oxygen models w h i c h were d e v e l o p e d i n t h i s study have shown t o be u s e f u l i n h e l p i n g to d e f i n e the n a t u r e d i s s o l v e d oxygen dynamics i n the lower F r a s e r R i v e r / E s t u a r y . u t i l i t y has been as an a i d to i m p r o v i n g .the u n d e r s t a n d i n g  6.2.2  of  Their chief  and f u r t h e r i n g  F u t u r e C o n d i t i o n s . " S i n c e 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 g r e a t d e a l o f 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 t h e c i e s of t h e i r p r e d i c t i o n s .  I n o r d e r t o d e a l w i t h t h i s u n c e r t a i n t y and  a l l e v i a t e some o f the doubt ( t h e a u t h o r ' s  included) surrounding  v a l i d i t y of p r e d i c t i o n s , t h i s s t u d y has made use o n l y o f v e r y analyses choosing  accura-  the most c o n s e r v a t i v e e s t i m a t e s .  to  the cautious  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 a s s e s s m e n t s of f u t u r e c o n d i t i o n s w h i c h are based on s p e c i f i c s e t s o f 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 .  I n s t e a d , emphasis was p l a c e d on i m p r o v i n g t h e  e x t e n t and d e p t h o f t h e knowledge base.  Assessment o f 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 t h e c o n s i d e r a b l e magnitude o f t h e a s s i m i l a t i v e c a p a c i t y o f t h e l o w e r F r a s e r . s i m p l y , t h i s i n v e s t i g a t i o n has shown t h a t i n t h e c o n c e i v a b l e  Stated  future there  w i l l n o t 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 o f w a t e r q u a l i t y i n t h e main stem, lower F r a s e r R i v e r / E s t u a r y , a t l e a s t i n s o f a r as c o n c e r n s a v e r a g e l e v e l s o f d i s s o l v e d oxygen.  The n a t u r e o f d i s s o l v e d oxygen dynamics i n  the lower F r a s e r , c o u p l e d w i t h p r e s e n t  conservative p o l l u t i o n control  p o l i c y , s h o u l d be s u f f i c i e n t t o g u a r a n t e e t h a 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 are maintained  at t h e i r present high l e v e l s .  Pollution control  r e q u i r e m e n t s as they a f f e c t d i s s o l v e d oxygen i n t h e 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 t h e y need be.  However t h i s i s i n d e e d a  s m a l l p r i c e t o pay f o r t h e adequate p r o t e c t i o n and maintenance o f a v e r y valuable n a t u r a l resource. 6.2.3  Uncertainties.  Hopefully 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 o f 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 t i m e o f i t s c o n c e p t i o n .  However, upon i t s c o m p l e t i o n  there remain  a number o f a r e a s o f c o n c e r n w h i c h have e i t h e r n o t been c o v e r e d or adequately  by t h i s i n v e s t i g a t i o n , o r have a r i s e n o u t o f i t .  these w i l l now be b r i e f l y  completely Some o f  discussed.  The main a r e a o f u n c e r t a i n t y i n v o l v e s t h e f a c t t h a t t h e 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 n o t 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 v i e w e d 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 as b e i n g t e n t a t i v e .  regarded  W i t h r e s p e c t t o t h e t i d a l l y averaged m o d e l , i t s mech-  a n i c s appear t o be sound as e v i d e n c e d by i t s manner o f response sensitivity analysis. the c o e f f i c i e n t s used.  during the  U n c e r t a i n t i e s w i t h t h i s model l i e i n the v a l u e s o f These u n c e r t a i n t i e s c o u l d be a l l e v i a t e d by a more  e x a c t d e t e r m i n a t i o n o f 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 b u t p r a c t i c a l l y , very d i f f i c u l t to accomplish. W i t h the t i d a l l y v a r y i n g model, on t h e o t h e r hand, i t was n o t p o s s i b l e t o f u l l y i n v e s t i g a t e t h e s e n s i t i v i t i e s o f i t s response i m p o r t a n t l y , t h e r e was concern e x p r e s s e d  and, more  t h a t some o f the mechanics o f  s o l u t i o n method may n o t be e n t i r e l y a p p r o p r i a t e .  I t was beyond t h e scope  o f t h i s i n v e s t i g a t i o n t o 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 t o t h i s v e r y s o p h i s t i c a t e d model a n d , as a r e s u l t , i t was pr-obably n o t u t i l i z e d t o i t s f u l l potential.  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 regard-  i n g t h e t i d a l l y v a r y i n g a s p e c t s o f lower F r a s e r d i s s o l v e d oxygen dynamics. Some o f t h i s u n c e r t a i n t y c o u l d be c l e a r e d up by a f u t u r e s t u d y , more s p e c i f i c than t h i s one, t h a t w o u l d o b t a i n b e t t e r e s t i m a t e s o f some p a r a m e t e r s ,  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 , o r w o u l d t e s t  the model response  using f i e l d investigations.  Then i t w o u l d be p o s -  s i b l e t o more f u l l y a s s e s s t h e s i g n i f i c a n c e o f 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 t h e e f f e c t s o f s h o r t term s i t u a t i o n s  such  as stormwater d i s c h a r g e s o r combined sewer o v e r f l o w s w h i c h may, sooner o r l a t e r , become i m p o r t a n t . One o t h e r m a j o r a r e a o f c o n c e r n s h o u l d be mentioned and t h a t i s the w a t e r q u a l i t y i n b a y s , s l o u g h s and o t h e r b a c k w a t e r areas i n the lower F r a s e r .  T h i s q u e s t i o n has n o t been a d d r e s s e d  i n t h i s r e s e a r c h 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 t h e main c o r e f l o w .  However, t h e r e i s e v i d e n c e t o i n d i c a t e t h a t , i n some c a s e s , 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 a l r e a d y e x i s t [Westwater, unpublished data].  What w i l l be t h e e f f e c t s on t h e s e a r e a s , some o f w h i c h  are very s e n s i t i v e , of l a r g e discharges  t h a t 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 c o n 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 o f a s p e c t s o f t h e d i s s o l v e d oxygen r e s o u r c e s  o f t h e lower F r a s e r R i v e r / E s t u a r y .  been b r i e f l y d i s c u s s e d and d e s e r v e f u t u r e  study.  Some o f t h e s e have  CHAPTER 7 CONCLUSIONS  The p r i n c i p a l c o n c l u s i o n s w h i c h 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 s u m m a r i l y , as f o l l o w s .  F i r s t l y , w i t h regard  t o the d i s s o l v e d  oxygen models, i t can be c o n c l u d e d t h a t : (1)  V e r i f i c a t i o n o f the models i s n o t p r e s e n t l y p o s s i b l e because o f 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 w h i c h has p r e c l u d e d model c a l i b r a t i o n ;  (2)  I n 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 o f the t i d a l l y averaged model i t s manner of r e s p o n s e was found t o be r e a s o n a b l e and " w e l l behaved" o v e r the e x p e c t e d range of i n p u t parameter v a r i a t i o n . T h e r e f o r e , i t i s c o n s i d e r e d t o 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 o f the f a c t t h a t i t c o u l d not be v e r i f i e d ;  (3)*  There a r e 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 c o u l d n o t be f u l l y t e s t e d and, i n a number o f r e s p e c t s , i t i s c o n s i d e r e d t o 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 o f d i s t i n c t advantages o v e r the t i d a l l y v a r y i n g model i n terms o f the s i m p l i c i t y o f i t s a p p r o a c h , the s t r a i g h t f o r w a r d n e s s o f i t s development and the f l e x i b i l i t y o f 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, m u l t i - m o d e l s o l u t i o n f o r m a t , i t i s o p e r a t i o n a l l y , b o t h cumbersome and c o s t l y ;  (6)  O'Connor's s t e a d y - s t a t e , c o n t i n u o u s s o l u t i o n model c o u l d 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 t o computing problems which r e s u l t e d from the p a r t i c u l a r form o f c r o s s s e c t i o n a l geometry v a r i a t i o n t h a t c h a r a c t e r i z e s the lower Fraser River/Estuary;  (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 a l o n g w i t h t h e i r c a p a b i l i t i e s so t h a t the m o d e l i n g e x p e r i e n c e i s e f f e c t i v e l y communicated i n the l i g h t o f a p r o p e r perspective.  -  146  -  147  S e c o n d l y , as a p p l i e s t o t h e lower F r a s e r R i v e r / E s t u a r y , use o f t h e d i s s o l v e d oxygen models, i t c a n be c o n c l u d e d  through  that:  (1)  An improved g e n e r a l u n d e r s t a n d i n g o f t h e n a t u r e o f d i s s o l v e d oxygen dynamics i n t h e lower F r a s e r R i v e r / E s t u a r y has been a c h i e v e d ;  (2)  An a p p r e c i a t i o n of t h e c o n s i d e r a b l e magnitude o f t h e 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 g a i n e d , a l t h o u g h i t s a c c u r a t e 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 t h e 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 t h e lower F r a s e r i s l i k e l y t o be i n l a t e summer;  (4)  T i d a l l y a v e r a g e d d i s s o l v e d oxygen l e v e l s i n t h e main c h a n n e l s o f t h e lower F r a s e r R i v e r / E s t u a r y w i l l n o t be s e r i o u s l y i m p a i r e d i n t h e c o n c e i v a b l e f u t u r e . I n 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 t o 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 l o a d i n g s t o t h e lower F r a s e r i n c r e a s e , t h e r e w i l l be b r i e f p e r i o d s w i t h i n t h e 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 n g t h e low f l o w p e r i o d s , when d i s s o l v e d oxygen c o n 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 o f t h i s e f f e c t c o u l d n o t 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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