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Mathematical modelling of the chlorophyll distribution in the Fraser River Plume, British Columbia De Lange Boom, Bodo Rudolf 1976

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MATHEMATICAL MODELLING OF THE CHLOROPHYLL DISTRIBUTION IN THE FRASER RIVER PLUME* BRITISH COLOMBIA  by  BODO RUDOLF\de LANGE BOOM B,Sc,  U n i v e r s i t y o f V i c t o r i a , 1970  A T h e s i s Submitted  i n P a r t i a l F u l f i l m e n t of  the Requirements f o r the Degree o f Master o f Science i n the Department of Physics and I n s t i t u t e o f Oceanography  We accept t h i s t h e s i s as conforming required  THE  standard  UNIVERSITY OF BRITISH COLUMBIA J u l y , 1976  (c)  t o the  Bodo Rudolf de Lange Boom, 1976  In p r e s e n t i n g t h i s t h e s i s  in p a r t i a l f u l f i l m e n t o f the requirements f o r  an advanced degree at the U n i v e r s i t y of B r i t i s h Columbia, I agree that the L i b r a r y s h a l l make i t f r e e l y a v a i l a b l e f o r r e f e r e n c e and I f u r t h e r agree t h a t p e r m i s s i o n  f o r e x t e n s i v e copying o f t h i s  study. thesis  f o r s c h o l a r l y purposes may be g r a n t e d by the Head of my Department or by h i s  representatives.  It  i s understood that copying o r p u b l i c a t i o n  o f t h i s t h e s i s f o r f i n a n c i a l g a i n s h a l l not be a l l o w e d w i t h o u t my written  permission.  Depa rtment The U n i v e r s i t y o f B r i t i s h Columbia 2075 Wesbrook P l a c e V a n c o u v e r , Canada V6T 1W5  Date  3  ii ABSTRACT The Strait  h o r i z o n t a l c h l o r o p h y l l a d i s t r i b u t i o n observed of Georgia  are  of  developed  distribution  the to  river  discharge.  attempt  to  Mathematical  explain  the  i n terms of such f a c t o r s as the v e l o c i t y  available light  and  the  near the mouth of the Fraser River appears to  r e f l e c t the i n f l u e n c e models  in  the g r a z i n g and  s i n k i n g of the  observed field,  the  phytoplankton  population. A steady upper  s t a t e , two  layer.  modified  The  dimensional  downstream  cross-stream integrated  velocity  (net  equation  is  production  are  considered  of  the  not  as  calculated  eguation-  c o n c e n t r a t i o n by b a l a n c i n g  The  is  modelled  A  for against  minus g r a z i n g and  modelled  directly  the  the  and  vertically integrated chlorophyll  the  source-sink  sinking).  Temperature are  not  model i s s i m p l i f i e d by assuming: a constant  depth  upper  layer,  nutrients  v e r t i c a l entrainment p r o p o r t i o n a l to the  downstream v e l o c i t y , and chlorophyll.  In  a  uniform  vertical  distribution  model I I the l a y e r depth v a r i e s with  from the r i v e r mouth, a more complex r e l a t i o n f o r  employed  the  limiting.  first  entrainment  using a  while  vertically  written advection  from  the  vertical  by an e m p i r i c a l e x p r e s s i o n , is  continuity  conservation  effects  velocity  form of the downstream v e l o c i t y i n a j e t ; the  entrainment i s represented  term  model i s developed f o r  is  for  used the  and  more r e a l i s t i c  horizontal  velocity  the  distance vertical  vertical profiles and  the  of  are  chlorophyll  concentration. Although  the observed downstream maximum i n the h o r i z o n t a l  c h l o r o p h y l l d i s t r i b u t i o n i s not reproduced, the r e s u l t s  indicate  t h a t the v e l o c i t y f i e l d , the a v a i l a b l e l i g h t i n the water column and the value of the maximum  production  rate  {a  water temperature) are the most important parameters the  distribution.  grazing  Sinking  is  of  function  of  influencing  secondary importance while  appears to be r e l a t i v e l y unimportant-  XV  TABLE OF CONTENTS Abstract  ..  .  i ...  i  List  Of T a b l e s  v  List  Of F i g u r e s ........................................... v i  Acknowledgements  x  Chapter  1  1.  General Outline  Background  1  P r o b l e m : The H o r i z o n t a l C h l o r o p h y l l D i s t r i b u t i o n The A p p r o a c h  To The P r o b l e m  ........  7 13  Chapter  2.  The P h y s i c a l Component: The Flow F i e l d  Chapter  3.  The C h l o r o p h y l l C o n s e r v a t i o n E g u a t i o n ......... 25  C h a p t e r 4.  G e n e r a l Method Of S o l u t i o n .................... 28  Chapter  5.  Sources  Chapter  6.  Data  41  C h a p t e r 7.  Model I : F o r m u l a t i o n  50  Chapter  M o d e l I : R e s u l t s .............................. 64  8.  And S i n k s Of C h l o r o p h y l l . . . . . . . . . . . . . . 3 0  Discussion Chapter  9.  Chapter  10.  82 Model I I : Refinements  11.  83  Model I I : R e s u l t s  Discussion Chapter  93  ...................................110 C o n c l u s i o n s ..................................113  References Appendix:  ........ 16  117 Temperature  And S a l i n i t y  Data  120  V  LIST  Table  I-  Evaluation  of  OF  TABLES  entrainment  from  cruise  Gulf 1  data  54  Table I I .  Model  Table I I I . Table IV. Table  V.  I parameters  held constant.  Seasonal v a r i a t i o n Model  o f model I p a r a m e t e r s .  I I parameters h e l d constant-  Seasonal v a r i a t i o n  .............  68  ....  74  ............  96  o f model I I p a r a m e t e r s -  .....  99  LIST OF FIGURES  Fig.  1.  Map  showing the g e n e r a l study area.  F i g . 2.  D e t a i l e d map  F i g . 3.  seasonal  discharge Fig,  4.  The  of the study  2  area  4  v a r i a t i o n of the F r a s e r Hiver d a i l y mean  measured at Hope, B.C.  5  F r a s e r R i v e r plume p o s i t i o n  as  derived  from  a e r i a l photographs, a f t e r Tabata, 1972. F i g . 5.  Horizontal  zooplankton, F i g . 6.  7  d i s t r i b u t i o n of c h l o r o p h y l l a,  (A)  and  (B) i n the S t r a i t of Georgia.  8  Horizontal d i s t r i b u t i o n of c h l o r o p h y l l a-in  terms  of r e l a t i v e f l u o r e s c e n c e ; March, 1973 F i g . 7..  Horizontal  distribution  10  of c h l o r o p h y l l a showing  p a t c h i n e s s ; J u l y , 1973. F i g . 8.  11  Temperature at 1 m as a f u n c t i o n of d i s t a n c e  from  the r i v e r mouth. F i g . 9. Fig.  10.  The  co-ordinate  The  system employed i n the model.  non-dimensionalized  distribution F i g , 11.  14  (LTh/U h ) f o r h = c o n s t a n t . 0  0  C h l o r o p h y l l production  l i g h t i n t e n s i t y , I ; equation Fig.  12.  downstream  ...  velocity  .............. 20  r a t e , P, as a f u n c t i o n  of  (5.3)  Comparison of the curves  33  from equations  (5.4)  and  (5.5) Fig.  13.  35 Location  of  stations,  cruise  Gulf  1;  November, 1971. Fig.  14.  Location  42 of  stations,  cruise  Gulf  2;  February, 1972 Fig.  15.  18  Station  44 positions,  c r u i s e Gulf 3 and  subseguent  cruises.  45  Fig.  16.  Salinity  Fig.  17.  Light  p r o f i l e s from c r u i s e G u l f 1.  intensity  (%  of  surface  46  value)  as  a  f u n c t i o n of depth. Fig.  18.  48  Non-dimensionalized  as a f u n c t i o n of d i s t a n c e from Fig.  19.  A  segment  q u a n t i t i e s used F i g . 20.  egn. F i g . 23.  layer,  49  showing  the 53  distribution  Average zooplankton  The  the r i v e r mouth  upper  (from equation  d i s t a n c e from F i g . 22.  the  0  to d e r i v e Table I.  Elliptical  r = constant F i g . 21.  of  coefficient,jx/JJL ,  extinction  of  (7.16)).  contours  of  .................. 58  d i s t r i b u t i o n as a f u n c t i o n of  the r i v e r mouth. grazing  relation  60 of  model  I,  based  on  (7. 20)  61  Streamline p a t t e r n of  the  horizontal  velocity;  model I with h = 2 m. F i g . 24.  Streamline  65  pattern  of  the h o r i z o n t a l  velocity;  model I with h •= 5 m. F i g . 25.  Variation  model I May F i g . 26.  66  of  M  along  c o n d i t i o n s with h  Variation  of  M  the  axial  = 2 m and h  along  y = 0;  streamline; = 5 m. model  .... I  May  c o n d i t i o n s with f u l l and no d i l u t i o n . F i g . 27.  Variation  conditions  of  showing  M the  along  y = 0;  71 model  I  May  e f f e c t of an i n c r e a s e d s i n k i n g  rate. F i g . 28.  72 V a r i a t i o n of  M  along  y = 0;  model  seasonal v a r i a t i o n . F i g . 29.  69  V a r i a t i o n of M along y = 0; model I  I  showing  ... (May)  73 showing  the  effect  F i g . 30.  of no  grazing  Variation  of  c o n d i t i o n s with the  (Z = 0). M  76  along  effect  of  y = 0;  I  May  velocity  and  model  increased  maximum d i l u t i o n F i g . 31.  77  Horizontal  distribution  of  M  for  model I  May  conditions F i g . 32.  79  Horizontal distribution  c o n d i t i o n s with 0 F i g . 33.  The  F i g . 34.  The  for  model  I  May  0.  81  surface  as a f u n c t i o n  of  r i v e r mouth  84  normalized upper l a y e r  d i s t a n c e from the F i g . 35.  of the  M -1/=  = 2 m/sec and  o  variation  d i s t a n c e from the  of  depth as a f u n c t i o n  of  r i v e r mouth  87  V e r t i c a l p r o f i l e s of c u r r e n t speed, a f t e r  Tabata  et a l . , 1970. F i g . 36.  Comparison of the  on egn. F i g . 37. al., F i g . 38.  89  39.  A 90  V e r t i c a l p r o f i l e s of c h l o r o p h y l l , 1968.  after  Fulton  et  ....  91  Streamline 0  pattern  of  Q  Variation  the  horizontal  velocity;  = 1 m/sec.  94  Streamline pattern of  model I I with U F i g . 40.  of d i f f e r e n t values of  (9.9).  model I I with U Fig.  effect  the  horizontal  velocity;  •= 2 m/sec. of  M  95  along  y = 0  (model II)  showing  seasonal v a r i a t i o n s . F i g . 41.  Variation  of changes i n the F i g , 42.  Variation  of changes i n the  of  98 M along y = 0  upper l a y e r  effect  depth, h  of M along y = 0 velocity  (model I I ) ; the  field.  (model I I ) ; the  101 effect  .....................103  ix F i g . 43.  V a r i a t i o n of M along y •= 0 (model II) ; the e f f e c t  of changes i n the production r a t e . F i g . 44.  V a r i a t i o n o f .8 along y = 0 (model II) ; the e f f e c t  of changes i n the g r a z i n g F i g . 45.  0  o  term.  ....................... 106  V a r i a t i o n of M along y = 0 (model I I ) ; the e f f e c t  of i n c r e a s i n g F i g . 46.  ....105  the s i n k i n g  Horizontal  rate.  distribution  .......................108 of  M  = 1 m/s, x = 10 km.  F i g . 47.  of  II;  ................109  0  Comparison  f o r model  pJVdz/h  f u n c t i o n of l a y e r depth.  and  Jpi/dz/h  as  a  .....112  X  ACKNOWLEDGEMENTS T h i s work was made p o s s i b l e by t h e a s s i s t a n c e o f of  people.  First  gratitude  to  assistance,  and  my  foremost  supervisor  encouragement  I  would  a  number  l i k e t o express  D r . P a u l H. L e B l o n d ,  and p a t i e n c e e n a b l e d  this  my  whose  work t o be  completed. I am g r a t e f u l topic  and  deserves  of  thanks  staff  and  The o f f i c e r s  students  and  crew  f o rtheir cooperation.  the  computer  t h e 0.B.C. C o m p u t i n g Finally  criticism.  this  D r . S. Pond  of  the  Institute  a l s o c o n t r i b u t e d t o t h i s work, p a r t i c u l a r l y  data c o l l e c t i o n -  developing  and  f o r suggesting  f o r h i s comments a n d c r i t i c i s m . the  Oceanography  deserve  D r . T. R. P a r s o n s  f o r h i s assistance  thanks  Many  to  of  the  of  i n the  C.S.S.  Vector  Much i n v a l u a b l e a d v i c e i n  p r o g r a m s was p r o v i d e d by t h e s t a f f o f  Centre.  I wish t o thank  Mary  f o r her  encouragement  and  understandingFinancial  support  N a t i o n a l Research scholarship Centre.  and  f o r this  Council research  of  r e s e a r c h was p r o v i d e d by t h e  Canada  through  a  postgraduate  g r a n t s and by t h e W e s t w a t e r  Research  1 CHAPTER 1.  GENERAL OUTLINE  Background This  work  biological described of  deals  with  processes by  interaction  are  da Lange Boom  possible  the  measure of the the  Fraser  horizontal  the  ecosystem.  distribution  will  be  examined.  effects  on  the  physical  phytoplankton), and the  the  area  of  Island  Columbia  ).  water.  The  north-west  is  the  and  the  south-east  south  via  the north v i a the The large  t y p i c a l estuarine  the  of  estuary  (e.g-  than  advection  the  of  biological  essentially  (1957)  by  one-sided,  and  of  located British  T u l l y S Dodimead  nature of the  and  Access to the t i d a l streams,  The  Pacific is both  Juan de Fuca S t r a i t and  t o Johnson Strait  of  in in  Strait. Georgia  water i n f l o w from v a r i o u s  conditions.  of  S t r a i t of Georgia l i e s i n a  direction.  passages l e a d i n g  amount of f r e s h  present  p h y s i c a l oceanography of t h i s body  the G u l f I s l a n d s  land-locked  the  (a  S t r a i t of Georgia,  through r e s t r i c t e d passes having strong the  and  chlorophyll a  mainland coast  l o n g i t u d i n a l a x i s of the to  number  (e.g. l i g h t a b s o r p t i o n  is  the  Waldichuk  (1957) have d e s c r i b e d  As  b i o l o g i c a l component.  interest  between Vancouver (Fig. 1  parameters  the  and  In t h i s s i t u a t i o n , the  pronounced  interaction  p h y s i c a l a c t i n g on the The  In  of  p h y s i c a l e f f e c t s on the b i o l o g i c a l parameters c h l o r o p h y l l a ) are much more  great  physical  phytoplankton c o n c e n t r a t i o n ) i n  River  physical  (1972), a  between  b i o l o g i c a l components of a marine discussion,  of  i n the ocean on a mathematical b a s i s .  Parsons and  interactions  the  stratification  and  the  r i v e r s leads to is  strongest  in  summer  and weakest i n winter, c o i n c i d i n g with v a r i a t i o n s i n  r i v e r dischargeThe  l a r g e s t r i v e r emptying i n t o the S t r a i t  the F r a s e r R i v e r yearly  (Fig- 3  February  or  magnitude  (Fig. 2 ). ),  March  outflow  maximum  in  m /s.  3  Arm  of  occurring i n  June.  3  The  mean  Both  the  the  yearly  3  I t i s not uncommon f o r t h e discharge to vary by  3  the  of  i / s with a mean y e a r l y d i s c h a r g e of  n e a r l y an order of magnitude between extremes90%  is  of the maxima and minima as w e l l as the date on which  i s about 8.5 x 10  3-2 x 10  generally  outflow  they occur v a r i e s from year t o year. maxima  Georgia  I t s discharge v a r i e s s e a s o n a l l y and  minimum  and  of  Between 80% and  t o t a l outflow of the r i v e r i s v i a the Main  (Giovando and Tabata,  1970)-  At the mouth of the  (South)  Main  Arm  (at Sand Heads), the s u r f a c e v e l o c i t y does not r e f l e c t the l a r g e seasonal  changes  velocity  are  component (Hodgins, of  is  mainly  discharge. tidally  present.  A  Instead the v a r i a t i o n s i n the  induced,  salt  although  wedge  seasonal  i s found i n the r i v e r times  flow.  large , discharge  of  the  Fraser  c o n s i d e r a b l e i n f l u e n c e on the s u r f a c e waters of Georgia,  a  1974), p e n e t r a t i n g as f a r as New Westminster at  low r i v e r The  in  particularly  in  the  vicinity  of  River the  exerts Strait  the r i v e r  a of  delta.  Among t h e more obvious e f f e c t s are the s i l t content of the r i v e r water  (giving the  surface  waters  their  typical  muddy  brown  c o l o u r near the r i v e r ) , the low s a l i n i t y values, and the s u r f a c e velocities levels  due  to  the  momentum of the r i v e r water-  are a l s o low r e l a t i v e to the more  S t r a i t of Georgia-  saline  water  Nutrient o f the  4  400  Jan  Fig.  3.  1  Feb  ,  Mar  1  Seasonal v a r i a t i o n  Apr  1  May  1  Jun  r-  Jul  1  Aug  r—  Sep  1—:  Oct  of the F r a s e r R i v e r d a i l y mean d i s c h a r g e measured a t Hope,  1  Nov  B.C.  l  ~  Dec  The is  s u r f a c e l a y e r of water d i r e c t l y i n f l u e n c e d by the  o f t e n c a l l e d the Fraser R i v e r plume-  the plume i s taken to  the  bottom  of  bottom boundary of  the  being  are harder  to f i x s i n c e there are other r i v e r s d i s c h a r g i n g  strait  of  the order of 2 to 10 m.  halocline,  thickness  the  in  be  The  Georgia  and  mixing  tends  of  the  plume  are  such modifying and  to  smooth out  The  of  pers- com-)-  the  s i l t content  Aside extent  t i d e as w e l l as  dynamical  extent  of  the  plume  i n winter  an  (S. Pond,  extend r i g h t a c r o s s to  ( F i g . 4 ) , as f a r north as Howe Sound and  A c t i v e Pass, while  the  south  the extent i s much s m a l l e r -  of  Mixing  to winds a c t s t o f u r t h e r decrease the extent of the plume-  Problem: The  Horizontal Chlorophyll Distribution  Chlorophyll phytoplankton,  concentration the  first  Measurements taken i n 1967 LeBrasseur (1969)  (1969)  indicate  concentrations The  and  the  of the water i s not always  In summer the plume can  Gulf Islands  due  the p o s i t i o n , c h a r a c t e r i s t i c s a l s o determined by wind and  into  f a c t o r s as the C o r i o l i s e f f e c t , c e n t r i f u g a l f o r c e  topography-  indication  the  H o r i z o n t a l bounds  d i s t i n g u i s h i n g c h a r a c t e r i s t i c s of the F r a s e r R i v e r plumefrom r i v e r d i s c h a r g e ,  river  and maxima  step and  of  the  aquatic  food  Parsons, LeBrasseur, of  maximum  the mouth of the Main Arm of  of  web.  r e p o r t e d by Parsons, Stephens  chlorophyll a  F u l t o n and and  Kennedy  (Fiq- 5 ).  .appears to form an arc centered the  zooplankton  Fraser  River-  and  zooplankton  a s s o c i a t e d with the F r a s e r R i v e r plume  chlorophyll a  concentrations  i s a measure of the abundance of  The  on  hiqhest  are f u r t h e r from the r i v e r mouth  and t h e r e i s not the d e f i n i t e arc found  in  the  chlorophyll a  7  49°  OO'N  HOURS  /  Mayne^l.') 1 JUNE 1950 POINT ATKINSON 1209  123° 30 W  F i g . 4.  Bands ^""-Foam Mixed Water («M mix)|  ZA Fresh Water  7  Mixed Water (saltiest)  Mixed Water (fresh- 1I| Sea Water est) I23°00'W  The" F r a s e r R i v e r plume p o s i t i o n . a s d e r i v e d from a e r i a l photographs, ".after T a b a t a , 1972.  8  Fig.' 5.:  H o r i z o n t a l d i s t r i b u t i o n o f c h l o r o p h y l l a., CA) and z o o p l a n k t o n , (B) i n the S t r a i t o f G e o r g i a ; a f t e r Parsons, Stephens and L e B r a s s e u r , 1969.  9 distribution.  Further  measurements  taken  a maximum i n the c h l o r o p h y l l d i s t r i b u t i o n r i v e r mouth ( F i g . 6 )  since  •patchy* length  scales  variations  of c h l o r o p h y l l a  phytoplankton  (Fig. 7  1972  a l s o show  with d i s t a n c e from  (unpublished data; Parsons,  The d i s t r i b u t i o n simple  in  the  pers. com.).  i s i n a c t u a l f a c t not so  distributions  are  in  themselves  ) i . e . v a r i a t i o n s i n c o n c e n t r a t i o n occur over  between  are  10  probably  and due  10 to  3  m  (Piatt,  1972).  both p h y s i c a l and  These  biological  processes although no s a t i s f a c t o r y e x p l a n a t i o n as yet e x i s t s . The q u e s t i o n arose as to whether i t was  p o s s i b l e to account  f o r the observed c h l o r o p h y l l d i s t r i b u t i o n  i n terms of the F r a s e r  River outflow as w e l l as such f a c t o r s as  the  grazing  and  sinking.  Biological  factors  available  light,  must be considered  s i n c e c h l o r o p h y l l i s not a c o n s e r v a t i v e property i n the same  way  as s a l i n i t y .  the  The understanding of the r e l a t i o n s h i p between  F r a s e r R i v e r plume and the c h l o r o p h y l l d i s t r i b u t i o n i s important if  the  impact  of man-made changes  R i v e r or d i s c h a r g i n g more e f f l u e n t  (such as damming the Fraser i n t o the  river)  is  to  be  assessed. At  this  features  of  green  it  may  be  phytoplankton.  phytoplankton of  point  in  worth mentioning a few of the Ecologically,  the a q u a t i c environment  plants  in  the  organisms  cellular  the  material  using  zooplankton i n turn grazes on the Phytoplankton organisms,  populations  although  some  role  of  i s e g u i v a l e n t to t h a t  terrestrial  p h o t o s y n t h e s i s , phytoplankton  the  environment.  By  transform n u t r i e n t s i n t o  sun's  energy.  Herbivorous  phytoplankton. are  species  made  up  have  of  single  complex  cell  external,  F i g . 6.  H o r i z o n t a l d i s t r i b u t i o n o f c h l o r o p h y l l a. i n terms o f r e l a t i v e f l u o r e s c e n c e ; March, 1973.  11  123° 30'W  F i g . 7.  Horizontal d i s t r i b u t i o n of chlorophyll a showing patchiness; 1973.  123° 00*  July,  12 structures  (e.g. d i n o f l a g e l l a t e s )  Generally  speaking  immobile.  any motion  exception  to  through  the  this  to  Takahashi,  1973).  well  are  form  almost  long  neutrally  r e l a t i v e to the water i s by rule  water  comparable  they  or  are  using  the  their  phytoplankton  flagellates flagella  sinking  bouyaBt  and  sinking.  An  which can move  and  attain  rates  S i n k i n g r a t e s vary a c c o r d i n g  chains.  speeds  (Parsons to  and  species  as environmental c o n d i t i o n s such as n u t r i e n t l e v e l s .  the motion of phytoplankton i s determined  as Thus  mainly by the movement  of the surrounding water. As one might expect,  light  plays  an  determining the growth of a phytoplankton intensity  at  important f a c t o r  part  population.  any p o i n t depends on s u r f a c e l i g h t  transparency of the water and the Another  important  The  light  intensity,  is  the  nutrient  concentration,  important n u t r i e n t s are n i t r a t e s , phosphates  although  trace  quantities  are  elements also  and  organic  important.  In  and  compounds  The  silicates in  small  the F r a s e r R i v e r e s t u a r y  n i t r o g e n i s the l i m i t i n g n u t r i e n t i n most al.,  the  depth.  with low c o n c e n t r a t i o n s decreasing the p h o t o s y n t h a t i c r a t e . most  in  cases  (Takahashi  et  1973). Temperature  photosynthesis. increasing  is  another  Provided  temperature  an optimum temperature  variable  other  affecting  factors  are  not  the  r a t e of limiting,  i n c r e a s e s the p h o t o s y n t h a t i c r a t e up to (which v a r i e s with s p e c i e s ) , above  which  the r a t e decreases with temperature. / Factors  tending  to  decrease  r e s p i r a t i o n , s i n k i n g and g r a z i n g .  phytoplankton  biomass  are  R e s p i r a t i o n i s the use by the  13 organism  of s t o r e d energy  respiration conditions  rate  t o maintain the l i f e  The  i s not constant but v a r i e s with environmental  (Parsons and  Takahashi, 1973).  r a t e s vary with environmental Grazing  processes.  Similarly,  sinking  conditions.  i s due to zooplankton f e e d i n g and i s dependent on  both the c o n c e n t r a t i o n of the food source and the c o n c e n t r a t i o n of  the  grazers.  As the food supply i n c r e a s e s the g r a z i n g r a t e  ( f r a c t i o n of zooplankton body weight i n g e s t e d by an organism per u n i t time) i n c r e a s e s , a s y m p t o t i c a l l y approaching a maximum r a t e .  The Approach  To The Problem  In order t o make the problem  t r a c t a b l e i t was necessary  q u a n t i f y the f a c t o r s d i s c u s s e d above. consisting  of  mathematical  to  A model was put t o g e t h e r ,  expressions  f o r the r e l a t i o n s h i p s  which t i e d the p h y s i c a l and b i o l o g i c a l components t o g e t h e r , A c o n s e r v a t i o n equation was w r i t t e n f o r c h l o r o p h y l l included  which  a d v e c t i o n as well as sources and s i n k s of c h l o r o p h y l l .  The source term was t h e net p h o t o s y n t h e s i s  which  effect  not c o n s i d e r e d to be  of  respiration.  Nutrients  were  included  the  l i m i t i n g during the time p e r i o d that was modelled  (mid-winter t o  pre-freshet  Takahashi  al.,  1973).  spring)  (Parsons  Similarly  directly.  Temperature  different  values  the was  f o r the  d i f f e r e n t times of the year. scatter  i n t h e temperature  plus the f a c t that the  et  a l , , 1970;  temperature  included maximum  was  not  indirectly  When one c o n s i d e r s the relation  (at any given time)  included  by  photosynthetic  using  rate  at  amount  of  (Takahashi et a l . , the  temperature  plume does not vary more than a few degrees  et  1973)  within  ( F i g . 8 ) , then  TEMPERATURE vs DISTANCE FROM RIVER MOUTH 12-  10-  9H  o  o  0  o T°C  o  e-\  7A  6H  5i  •  •  •  •  ~T~  10  F i g . 8.  D  I  20 r(km)  —r~ 30  40  Temperature a t 1 m as a f u n c t i o n o f d i s t a n c e from t h e r i v e r mouth ( o November, 1971; • F e b r u a r y , 1972; m March, 1972; © May, 1972). . '  M  -P>-  15 t h i s approach The sink possible  terms  losses  be important. was  i s not unreasonable.  not  used  were  grazing  and  sinking.  Other  (such as n a t u r a l m o r t a l i t y ) were assumed not to  Since the zooplankton  itself  modelled,  observational  data,  distribution.  An  had  to  population  certain be  (the grazers)  assumptions,  made  about  the  based  on  zooplankton  a r c - l i k e h o r i z o n t a l d i s t r i b u t i o n was assumed  with the maximum value o c c u r r i n g at some d i s t a n c e from the r i v e r mouth of  (determined from a v a i l a b l e data ) .  phytoplankton  a  x  constant  value  was  For the s i n k i n g used.  The  speed natural  s i t u a t i o n i s t o o complex to j u s t i f y g r e a t e r p r e c i s i o n s i n c e s i z e and shape of the organism  as w e l l  a f f e c t the s i n k i n g speed The  approach  as  environmental  (Parsons and Takahashi,  conditions  1973).  i n modelling was t o use a s l i g h t  modification  of t h e downstream v e l o c i t y i n a  j e t as  (1970).  used along with an experimental  Continuity  expression cross-stream  f o r the  was  then  vertical  component  velocity  discussed  to  Islands  was  not  Wiegel,  calculate  of the h o r i z o n t a l v e l o c i t y .  of the b a r r i e r of the Gulf  by  The e f f e c t  included,  s e m i - i n f i n i t e sea i s assumed i n the h o r i z o n t a l plane.  the  i.e. a  16 CHAPTER 2 . As  the  relative  THE  aim  PHYSICAL COMPONENT: THE  of  this  influences  determining  of  the  shall  which  allow  us  to  interactions.  The  nature  of the  T h e r e i s no outflow water.  a  at  make a number through  the  the  water  of  is  the  factors  in  guantity assumptions  complexities  not  a nearly  a p p l i e d to the  saline  well  critical  internal  flow  pulsed body  of  understood;  out  velocity  the  Fraser.  tidally  s t u d i e s o f t h e r m a l plumes h a v e been directly  of  concern.the  mouth of t h e  stream i n t o a broad case  compare  scalar  most s w e e p i n g a s s u m p t i o n s  steady-state  c a n n o t be  coming o u t  see  a  a d e q u a t e d e s c r i p t i o n o f the  a number o f  they  have t o  biological  of  p a t t e r n i s s u i n g from  fresh  Even t h e  although out,  flow  existing  of  and  distributions  a ) we  various  i s t o examine and  physical  (chlorophyll will  study  FLOW F I E L D  carried  of a  over  river  a  salt  wedge. Nevertheless, flow,  we  1)  net  2) as  the the  shall  out  The  since  relatively  ignorance  o f how this  description  of  first  small  tidal  of  i s independent  v a r i a t i o n s may  of time,  somehow be  time s c a l e i n v o l v e d  corresponding steady-state  to  amplitude.  variations  in  the  assumption  type the  of  study,  varying  may  pattern  considered  not  up  steady be  too are  rapid  and  only  rather  t o work o u t but  a  discharge  the  i n the  w h i c h i s not  plume  the  that  setting  justification  t o a c c o u n t f o r them and  and  prevailing  Neglecting  finds  of  conditions, i . e . , that  short-^period f l u c t u a t i o n s i n r i v e r  important  aim  over the  pattern  conditions.  some r e p r e s e n t a t i o n  assume s t e a d y - s t a t e  influence of t i d a l  distribution  of  first  to obtain  f r e s h water o u t f l o w  averaging  tragic,  i n order  to  in  our  limited a good  study  the  17 response of phytoplankton to the presence of a (mean) c u r r e n t of a reasonable form. In  the absence of a c o r r e c t two-dimensional d e s c r i p t i o n of  r i v e r flow i n t o a the  most  literature.  s a l i n e b a s i n , we chose what  appropriate wiegel  jet  flow . p a t t e r n  we  thought  available  in  (1970) has reviewed the s t u d i e s of j e t s  was the and  r i v e r plumes and we have used a Gaussian j e t flow from h i s work. To  specify  this  flow  C a r t e s i a n c o o r d i n a t e system increasing  downstream  southwards and  z  pattern,  introduce a  (x,y,z) as shown i n F i g . 9 , with  from  positive  v e l o c i t y vector u a r e denoted directions.  l e t us f i r s t  the  river  upwards.  The  mouth,  y  x  positive  components  of  the  by (u,v,w) i n the t h r e e c o o r d i n a t e  The r i v e r plume w i l l be assumed to extend from the  s u r f a c e z = 0 t o some depth z = - h ( x , y ) .  The average  horizontal  v e l o c i t y component over t h a t l a y e r w i l l then be  aiegel  (1970) g i v e s an e m p i r i c a l formula f o r the a x i a l  of an axisymmetric j e t i s s u i n g from an o r i f i c e  of  velocity  diameter  D  0  i n t o an unbounded body of f l u i d :  C  4  i s an experimental c o n s t a n t ,  orifice  in  the  d i s t a n c e from the  downstream jet  axis.  x  is  direction, Results  the and due  distance r to  is  from  the  the r a d i a l  Abraham  (1960)  i n d i c a t e that a s i m i l a r e x p r e s s i o n may be used f o r the d i s c h a r g e  18  F i g . 9.  The c o - o r d i n a t e system employed i n the model.  19 of  a river  y  is  on  the  s u r f a c e o f a body o f r e c e i v i n g  substituted  for  r-  The  which a l l o w s f o r plume s p r e a d i n g with  d i s t a n c e from  U  I.  the  river  =  k  x + x The  upper  mouth  layer  and  parameter x . i s finite  at  x = 0;  jet,  measured  0.38  of  mouth  (x = 0 ) .  also  its  used x  where  small,  water k^  adjusted of  the  The  t o the  river  velocity  k, z  0  (z. 3)  f)  d e c a y s away  from  the  transverse profile-  The  transport  c h o s e n t o make t h e  equal  the value  m ;  =  underneath  value  t o one  remains  width  Gaussian  of  the  falls  to  k i l o m e t e r at the  employed  by  Siegel  river  (1970)  was  96[1.0 + 0. 1 9 ( ^ / ^ w  - 1) 3-2  o  the  of v e l o c i t y  plumeby 0  Since  k j , ^ 96. o  and  depth  U  c  can  then  be  varied  non-dimensionalized o  o  is illustrated  streamline  (t3 /^ w  The h  0  ^  t h a t of  w  "  0  96  ^  v a l u e o f k, at the  i  s  is  centre  V.  t o model v a r i o u s f l o w downstream  i n F i g - 10  p a t t e r n cannot  a s s u m p t i o n s have a l l o w e d component,  and  ~  (x = y = 0) :  of  0h/U h  the  down  Thus  The  distribution  further  value,  For  mouth  conditions.  of  +x  z  between t h e p o i n t s where the  i s well approximated  magnitude  Plots  k f/u  to give a Gaussian  peak  and  slowing  i s t h e d e n s i t y o f t h e d i s c h a r g e d water  0  the s a l t  its  adopt,  be  t r a n s p o r t thus  i t s v a l u e was  = 5 x 103  c  ^  here-  as  i n t r o d u c e d t o i n s u r e t h a t the  c  as  as w e l l  shall  provided  0  downstream  spreads  w h i c h we  mouth, w i l l  exp (-  t  form  water,  be  us t o s p e c i f y  for h =  velocity constant.  constructed the  before  cross-stream  21 The  i n f l u e n c e of the C o r i o l i s f o r c e i s n e g l e c t e d  T h i s assumption may inertial  be t e n a b l e near  the r i v e r  where  terms dominate the flow, but cannot r e a l l y be  to hold f a r downstream, a f t e r the plume has effect  mouth,  entirely.  of  the  slowed  the bottom.  of  layer  F i n a l l y , l a t e r a l f r i c t i o n and entrainment  its  underside  so  as  presence  upper  not c o n s i d e r e d : the plume i s so t h i n compared to i t s area  The  s l o p i n g bottom on the plume i s a l s o i g n o r e d ,  of the s a l t water beneath e f f e c t i v e l y i s o l a t e s the  the  expected  down.  the bottom s l o p e s q u i t e s t e e p l y o f f Sand Heads, and the  from  the  width  are and  l a r g e compared to t h a t of i t s  l a t e r a l edges t h a t i t i s reasonable t o assume t h a t everywhere i n the plume, except  very near the edges, entrainment  w i l l occur only at the bottom of the plume. velocity  distribution  dimensional concerning  flow the  is  field, vertical  given some  by  friction  the downstream  (2.3); to c o n s t r u c t a  assumptions  entrainment  Only  and  have  to  v e l o c i t y found  be  two made  at z = -h.  Letting w(x,y,-h) =  for  brevity,  w(-h)  we use a r e l a t i o n s h i p obtained  by Keulegan  f o r the v e r t i c a l v e l o c i t y a c r o s s the i n t e r f a c e of a  model  (1966) salt  wedge e s t u a r y :  where m i s a c o n s t a n t ; U  with  c' = c o n s t a n t ,  i>  c  , the c r i t i c a l v e l o c i t y , i s given by  = the  v i s c o s i t y of the lower  layer,A  22  the ^  density  the  for  density  of  the  between  upper  the  layer.  lower  and  Equation  the  upper  (2.4)  layer  i s only  It  field  is  then  by  write  possible  using the  the  to  complete  continuity  horizontal  the  description  equation.  velocity  It  components  will  of  be  where both  we  assume  the  components,  function  must  same  Because  of  course  C*  an  vertical  incompressible  *  of  substituting  dx  / ^  velocity  definitions  profile (2.1),  Y(x,y,z) the  for  profile  h  =  (z.j)  fluid,  integrating from  flow  satisfy  V- u that,  the  the  as  ;  so  valid  convenient  U s tfCx^i) U(x y)  In  and  s u p e r - c r i t i c a l flow, -  to  difference  (2.6)  (2.8) and  (z.s)  = o over  the  upper  layer  depth,  letting  U = (Ucx.y^VCx,/)) we  The  have  surface  vertical  velocity  w(x,y,0)  vanishes  and  (2-9)  may  be  23 i n t e g r a t e d i n t o the form  V-(LIh) The  right  hand  w(-K) + * ( - ^ U ' * f l  =  side  of  this  relation  v e l o c i t y component normal to the s l o p i n g into  the  upper  layer.  Expanding  (2./0)  i s r e c o g n i z e d as the interface  h(x,y)  and  (2.10) and w r i t i n g i t as a  d i f f e r e n t i a l equation f o r V, the t r a n s v e r s e h o r i z o n t a l  velocity,  we have  iV  (z./l)  + f(x,y)V = 3(x,y)  where  ft^y)  =  M-h)  /-  Ak  (2-/2)  and  fi Given  0(x,y)  from  form f o r o'(x,y,z), V(x,y).  Since  to i n t e g r a t e such  as  h  ^x  (2.3) and w (-h) (2.11) becomes a  w(-h)  contains V  (2.11) d i r e c t l y .  2  from  (2.4), and an  differential  explicit  eguation  , i t i s not s t r i c t l y  possible  However, i n areas where  V  2  <  U, 2  near the a x i s of the plume, an i t e r a t i o n technique can  r e a d i l y be used to o b t a i n s u c c e s s i v e l y b e t t e r e s t i m a t e s starting  for  from  V  2  << U , 2  so  that  w (-h) = m(U-0 ). c  approximation f o r s m a l l V i s then found by i n t e g r a t i n g  for  The  V,  first  (2.11);  24  Two models w i l l by  a  more  complex  be considered below: a simple one, f o l l o w e d one.  For  each we s h a l l  specify  explicit  dependences f o r tf(x,y,z) and values o f the constants m  and  c*.  More p r e c i s e estimates of the t r a n s v e r s e flow v e l o c i t y  will  then  be found f o r each one of the models.  25  CHAPTER 3.  THE CHLOROPHYLL CONSERVATION EQUATION  Phytoplankton, to  quantify  and hence the c h l o r o p h y l l c o n c e n t r a t i o n  i t s density,  i s safely  assumed t o be a p a s s i v e  s c a l a r v a r i a b l e , advected by the flow but not any  fashion.  The  used  biological-physical  modifying  i t in  interaction i s i n that  case u n i d i r e c t i o n a l : a l l from the p h y s i c s to the b i o l o g y . Let us w r i t e the c h l o r o p h y l l c o n c e n t r a t i o n n(x,y,z) as  (3./)  n ( x , y , z ) = ^(x,y,2} M ( x , y ) where  C n J.%  M(x,y) = x  (3.2)  \  K  i s then the average c o n c e n t r a t i o n  over  the  upper  layer.  It  f o l l o w s t h a t the p r o f i l e f u n c t i o n l/(x,y,z) must s a t i s f y  CV  <Li = h  (3.3)  A s t e a d y - s t a t e c o n s e r v a t i o n equation  f o r c h l o r o p h y l l may be  w r i t t e n as  V-(un) where Q i s a source  =  Q  (3.4)  s t r e n g t h f u n c t i o n , which may depend on u and  n as w e l l as s p a c e - c o o r d i n a t e s .  The f u n c t i o n Q w i l l i n c l u d e the  growth r a t e , the s i n k i n g r a t e , zooplankton process manner.  grazing and any other  a f f e c t i n g the c h l o r o p h y l l d e n s i t y i n a  non-conservative  26 As we are i n t e r e s t e d i n what happens -h < z < 0, we i n t e g r a t e  Using w(0)  (2.1) = 0,  and  (3.4) over that  (3.1),  Leibnitz's  in  the  upper  layer  layer:  rule,  and  the  condition  (3.5) becomes:  .0  r^  with  ° Q 6  (3.0  4/(-h) =1/(x,y,-h) ana  x i . (x,y) = £  Combining  (2.10)  and  *V  (3.7)  CL^  (3.6) so as to e l i m i n a t e  the v»U  terms  we  find  U-vM  = j _ C°GU* + M  J  U-vK  h  - U-v.ru  )  which i s f u r t h e r a b b r e v i a t e d as  U-vM  = H (M,U,V,x,y)  (3.9)  27 where H (f3 U V,x,y) i s the r i g h t hand s i d e of /  r  As jn_ always t u r n s out example bracket  chosen,  it  p r e f i x e d by  is M/XL  is  net i n c r e a s e then due  to 1)  be  clear  proportional  t h a t the f i r s t  c a n c e l out and  (w(-W  Any  to  (3.8).  to two  h  in  terms i n  or decrease i n the c o n c e n t r a t i o n  (3./0)  of c h l o r o p h y l l  (the Q term) and  through the bottom of the upper l a y e r  the  that  +if(-MU-vO  i n t e r n a l sources  the  (the second  2)  advection  term).  28 CHAPTER 4. Let  t  be  the  time  mouth to some p o i n t pathlines  are  GENERAL METHOD OF SOLUTION  (x y) f  elapsed i n t r a v e l l i n g along a  identical  streamline  i n t h i s steady  from the  river  (streamlines  and  state s i t u a t i o n ) .  The  r a t a of change of p o s i t i o n along a s t r e a m l i n e i s then given by  2ht  =  U (x,y)  (4.l)  =  V(x,y)  (4.2)  3>i 2l  Dt  = uA/<ix •+ V i / ^ y , (3.9)  Since D/Dt  3 M 2>  =  be w r i t t e n as  H(M,U,V,x,y)  (+.3)  t  Given f u n c t i o n a l forms , and is  may  i n i t i a l values f o r 0, V and  p o s s i b l e to i n t e g r a t e the above equations  s t r e a m l i n e s t o o b t a i n a map velocity  and  chlorophyll.  of the  which  a  kind of s c a l a r f i e l d  of  chemical  s p e c i e s , such as observed  a  It  quantitative  sediment load i n the plume, or of c o n c e n t r a t i o n s of  Alternately,  velocity field be  of  M(x,y)  s o u r c e - s i n k f u n c t i o n Q(x,y,z) can be d e f i n e d .  account  might  distribution  T h i s method of s o l u t i o n i s broadly  could f o r example be r e a d i l y a p p l i e d t o provide  (1975).  it  step by step along  horizontal  a p p l i c a b l e i n the above form to any for  M,  the  inverse  which l e a d s to an  attempted using  f o r t r a c e elements by  (4.1)  problem of determining  observed to  Thomas  distribution  (4.3), although  be p o s s i b l e , depending on the form of Q(x,y,z),  the  M(x,y)  i t might not  to f i n d a unique  s o l u t i o n to t h a t  problem.  30 CHAPTER 5.  SOURCES AND SINKS OF CHLOROPHYLL  A number o f i n f l u e n c e s are covered by the function  Q(x,y,z),  and  they  will  source  strength  now be d i s c u s s e d and given  a p p r o p r i a t e p a r a m e t e r i z a t i o n s i n terms o f environmental Three sources and s i n k s of c h l o r o p h y l l i n the c o n s i d e r e d : primary The  occurs  photosynthetic chlorophyll  rate  The  of grams of carbon we  can  transform  conversion factor  of at  particulate a  and  produced  chlorophyll.  layer  are  p r o d u c t i o n , zooplankton g r a z i n g and s i n k i n g .  production  phytoplankton  upper  factors.  rate  P  usually  expressible  per  unit  organic  in  time  matter  by  called'  the  terms  of  gram  of  per  grams  of  existing  usual u n i t s i n which P i s given a r e i n terms f i x e d per unit time per gram o f from  one  s e t of u n i t s t o the other using a  (g c h l o r o p h y l l / g and  an  chlorophyll:  carbon).  light  sensitive  expression  Steele  (1962) and used by Takahashi at  Productivity  originally a l . (1973)  suggested is  is by  employed  here:  (s.i)  T>=*fc7U expO-fcl) P i s the c h l o r o p h y l l p r o d u c t i o n ©< c o n v e r t s  from  carbon  chlorophyll units; b minutes/langley  units,  is a  while  rate,  I  in  constant is  i n units which P with  the  m  (time) , - 1  i s expressed, to  the  light  of  dimensions  of  intensity  in  langleys/minuteIt  i s c l e a r from  an o p t i m a l l i g h t  (5.1) that P has a maximum value  intensity  J  (<<P) m  at  31  Takahashi e t a l . (1973) found experimental  data,  from  a  a value of  (5.2), b = 5.56 min/ly.  best  f i t of  available  = 0.18 l y / m i n , so t h a t from  This d i r e c t l y c a l c u l a t e d  value  for b  g i v e s a b e t t e r f i t t o the experimental curves than that computed by  Takahashi  et  a l . (1973)  (b = 5.37 min/ly)  numerical technique which does not s a t i s f y  by an improper  (5.2).  The maximum r a t e of carbon f i x a t i o n P^_ v a r i e s with, n u t r i e n t availability temperature a  few  and  As  mentioned  earlier  at  any  one time but does vary with the season  Given the s c a t t e r observed by Takahashi et a l . (1973)  i n the P^ (T) o b s e r v a t i o n s i t i s q u i t e  j u s t i f i a b l e t o take  constant  f o r any  everywhere  i n the plume  one  the S t r a i t  of  Georqia  P  m  •=  simulation.  Observations by Parsons e t a l . (1970) show that n u t r i e n t in  the  i n the F r a s e r R i v e r plume does not vary by more than  degrees  (Fig. 8).  temperature.  levels  a r e high enough not to be l i m i t i n g  f a c t o r s i n p r o d u c t i o n , so that we w i l l  completely  neglect  the  dependence o f P^ on n u t r i e n t c o n c e n t r a t i o n s . P o s s i b l e v a l u e s of P^  will  range  from  4.4 x 1Q-*  g carbon/g c h l o r o p h y l l / s e c , depending  to  12.4 x 10-*  on the mean temperature o f  the plume (and thus on the time o f the y e a r ) . To take i n t o account the e f f e c t o f there  exists  a  minimum  energy  respiration  requirement  without growth) the concept of a compensation (Parsons and Takahashi, 1973, p.  t o maintain l i f e light intensity I  64) i s i n t r o d u c e d i n t o  which now becomes  ?=*!>?„, (I-I ) ex 6-fc(I-lj) c  ( i . e . that  P  c  (5.1),  T h i s equation i s v a l i d only f o r I > I .  For I < I , P  c  taken  as e q u a l  Parsons, Stephens from  0.006  t o zero  ( F i g - 11 )- Values of I  and LeBrasseur  t o 0.01 ly/min.  (1969) over  respiration light  implied  measured by  months  (1967),  However,  equation  vary  simulation. the concept  of c o n s t a n t  by (5.3) i s not l i k e l y t o be v a l i d  intensities.  expression,  four  t  be  A constant value c o n s i s t e n t with  those data w i l l be taken f o r any one As i n d i c a t e d by Caperon  will  c  i n the abscence  (5.3)  accounts  for a l l  of a  better  f o r the e f f e c t  of  respiration. The  carbon  vigorously  to chlorophyll  growing  ratio  phytoplankton  been oi  e t a l . , 1963). used  = .025 An  here,  thus  i n n i t r a t e depleted  water  f a i r l y c o n s e r v a t i v e value of 40 has giving  (1961).  a  conversion  factor  The r a t e of c h l o r o p h y l l removal  ("$= mg o f c h l o r o p h y l l / m / t i m e ) 3  Z G  grazing  (5.4)  (wet weight)  d e n s i t y i n mg/m , G the 3  r a t e i n u n i t s of m i l l i g r a m s of c h l o r o p h y l l  m i l l i g r a m o f zooplankton per unit time, d, i s a of m /mg 3  of c h l o r o p h y l l and n(x,y,z)  c o n c e n t r a t i o n as b e f o r e . been used here,  A  nearly  by  i s  (/ - e x f f - c i . r i )  where Z i s the zooplankton  units  of excess  e x p r e s s i o n f o r zooplankton g r a z i n g of phytoplankton has  =  maximum  25 f o r  = 1/40.  been given by I v l e v grazing  A  from  i n t h e presence  n i t r a t e t o 60 f o r unhealthy organisms (Antia  varies  constant  per with  i s the c h l o r o p h y l l  eguivalent  e x p r e s s i o n has  33  P  F i g . 11.  Chlorophyll production I ; equation (5.3).  r a t e , P,  as a f u n c t i o n of l i g h t i n t e n s i t y ,  34  i?=  where  Z  G  (f.f)  n  i s another c o n s t a n t with the dimensions of m i l l i g r a m s  of c h l o r o p h y l l per u n i t volume.  The c h o i c e o f (5.5) i n s t e a d  (5-4)  by  i s primarily  motivated  the f a c t  that  the second  e x p r e s s i o n i s e a s i e r t o i n t e g r a t e over the upper l a y e r vertical  dependences  of n chosen below.  more  e x p r e s s i o n s may selecting  slowly.  Over  be  t o agree  made  the c o n s t a n t  a  limited  (Fig- 12  the  ),  but  range of n, the two  closely  d^; t h i s  for  The e x p r e s s i o n (5-5)  shows a s i m i l a r behaviour t o I v l e v ' s r e l a t i o n increases  of  by  appropriately  i s indeed the case over the  r e g i o n of i n t e r e s t , with n g e n e r a l l y v a r y i n g l e s s than an o r d e r of magnitude al-,  (Parsons, Stephens and LeBrasseur, 1969; Parsons e t  1970). On  the  Takahashi  basis  of  figures  given  by  (1973) a value of d^ = 5 mg/m was used. 3  i n an i n g e s t i o n r a t e o f h a l f the maximum concentrations  rate  Parsons and This  results  f o r chlorophyll  of 5 mg/m and about 0.83 of the maximum r a t e a t 3  25 mg/m . 3  The v o r a c i t y species  of zooplankton  considered  organisms  varies  with the  and with the l i f e stage o f any one s p e c i e s .  F i g u r e s quoted by Parsons and Takahashi (1973) l e d us to use an ingestion Combining 0-2 data  rate  equal  t o 70% of the wet weight  per  day.  t h i s with an average dry t o wet weight r a t i o of about  and a carbon t o dry weight r a t i o of 0.5, as drawn from the given  chlorophyll  by  the same  conversion  authors,  factor  and with  ( o( =  the carbon t o  1/40) used  above,  we  36 c a l c u l a t e G as G  =  X  0>?  O.Z  X  0,5"  X  A somewhat lower value Stephens  variable  As  —  rn^  ZX/0  ^  cUoroplyl/  EoopUhkton-jee  (G - 1 x 1 0 ) i s found i f the r e s u l t s of _a  et a l - (1969) are  conversion-  J[__  40  £4X3600  used  a l l these  for  factors  the  wet  to  are  likely  dry to  be g u i t e  ( e s p e c i a l l y the i n g e s t i o n r a t e ) , we w i l l s t i c k  G = 2 x lO  - 8  weight  to the  mg c h l o r o p h y l l / m g zooplankton-sec value.  The s i n k i n g r a t e i s u s u a l l y w r i t t e n as  f o l l o w i n g R i l e y et a l . . (1949) , with w  s  (1970)  gives  values  r a t e s of l i v i n g species.  of  s  The  phytoplankton, based on o b s e r v a t i o n s on about 25  m/sec to 5.8 x 1 0 local  Smayda  w^ between 0 and 30 m/day f o r s i n k i n g  Values used i n the  1.2 x 10~  a s i n k i n g speed.  source  present  calculations  range  from  m/sec (1 t o 5 m/day).  _ s  s t r e n g t h Q i s then the sum of the above  three e f f e c t s :  Q =  nl  + 3  +  S  (s. ) 7  What i s needed i s the i n t e g r a l of Q over the upper As  the  upper l a y e r i s c o n t i n u o u s l y a g i t a t e d by wind waves  and by i n t e r n a l waves the  upper  few  (Gargett, 1976), the t u r b u l e n c e  meters  is  quite  phytoplankton crop w i l l be c a r r i e d over  a  depth  layer.  range  of  a  few  high, back meters  and and  level  in  the n e a r - s u r f a c e forth  vertically  by mechanical  Besides, phytoplankton from near the s u r f a c e w i l l a l s o  mixing.  gradually  37 s i n k down with a s m a l l v e l o c i t y organism  will  thus  w .  A  s  experience,  typical  over a period of a few hours,  l i g h t c o n d i t i o n s which are averaged  over a  shall  upper  assume  conditions  in  the  light  with  coefficient  intensity  at  experienced The  extinction the  by  surface,  as  use S t r i c k l a n d ' s  The  i s one  radiation  roughness  but  from  closely  population.  in  the  wave  et a l . (1973), we PAR  I  0  with  cloud  at  cover  as computed by Parsons,  the sea  and  sea  Stephens  and  w i l l then denote only the PAR; i t s values The average  value T i s r e a d i l y  (5-8) as  =  (/ - e x p ( - M « )  ofytt have been c a l c u l a t e d  0.3 t o 0.8 m  the  conditions  we can do here i s to use monthly mean  best  0.03 t o 0-10 l y / m i n .  by T.R- Parsons  of  the  T  Values  (PAR) l i e s  that  the l i g h t  a  varies  (1969).  estimated from  and I  intensity  a  range  -1  h a l f the t o t a l s o l a r r a d i a t i o n a t t h e s u r f a c e .  i n s o l a t i o n values f o r l , LeBrasseur  (in m )  F o l l o w i n g Takahashi  (1958) assumption  We  given by  the whole upper l a y e r phytoplankton  range 400-700 nm.  surface  depth.  l a y e r t o be t u r b u l e n t  representative  photosynthetic a v a i l a b l e radiation  length  certain  i n t e n s i t y T,  enough to use the averaged  JUL the  phytoplankton  from  unpublished data  f o r the F r a s e r R i v e r plume i t s e l f These  and range from values  agree  with other measurements i n t h i s r e g i o n (Parsons,  1965).  _1  f o r the p e r i o d of i n t e r e s t .  provided  38 The  integrated  value  of  nP  w i l l then  where P i s the p h o t o s y n t h a t i c l i g h t i n t e n s i t y T-  The vertical The  Using  r a t e corresponding to the  average  (3.3),  i n t e g r a l of zooplankton dependence  be  grazing  used f o r n, i . e . on  integrated sinking rate i s  will  depend  on  the  the f u n c t i o n i / ( x , y , z ) .  simply  -Ii  Since the f l u x through the upper s u r f a c e , at z = 0, must be (we  can  i n t e g r a t e to z = 0 + £ , where n (0 + £ )  i s i n the a i r , above the t h a t the f i r s t  =0,  water s u r f a c e , and l e t 6  zero  s i n c e that 0  to  show  term must v a n i s h ) , the net r a t e of s i n k i n g out  of  the upper l a y e r i s  The  i n t e g r a t e d source s t r e n g t h i s then  In  a completely  h o r i z o n t a l l y non-divergent uppar l a y e r  and  39 with h o r i z o n t a l l y independent would  be  local  relative  -j/  (5-12)  , the r i g h t hand side of  the only c o n t r i b u t i o n t o changes i n c h l o r o p h y l l -  zooplankton  importance  of  photosynthetic  growth  g r a z i n g and s i n k i n g would then completely  the d i s t r i b u t i o n of c h l o r o p h y l l a i n the upper l a y e r -  The rate,  determine One c o u l d  then w r i t e ( 5 . 1 2 ) as  C  and  r  Q  M ^Cx,y)  (3-9),  i f ^ (x,y) were a c o n s t a n t , i n t e g r a t e  or r a t h e r i t s  time dependent f o r m u l a t i o n ( 4 - 3 ) t o f i n d M r r M o C X p J ^  The  simple  exponential  readily  understood  source  terms  field,  (5-13)  growth  which  make  may s t i l l  up  course  be  H(M,U,V,x,y)  by  ij> (x,y).  of  the v a r i o u s  In a non-uniform  flow  be regarded as determining i n s t a n t a n e o u s  completely  This purely l o c a l  behaviour  may  masked by the other terms present i n  (eguation 4 . 3 ) , a r i s i n g from the non-homogeneity of  the flow f i e l d obtained  by (5w13) i s  represented  as a r i s i n g from the balance  l o c a l chlorophyll variationsof  (51/3)  The s i m p l e s t example of t h i s masking e f f e c t  comparing  v e r t i c a l a d v e c t i o n term  the s i n k i n g term -Mw (-h) -V (-h) s  Mw(-h) l/(-h) which occurs i n  is  with the (3.8);  i t  i s obvious t h a t the two v e r t i c a l t r a n s p o r t terms are o p p o s i t e i n t h e i r a c t i o n and t h a t s i n k i n g or ascent takes p l a c e a c c o r d i n g t o the  s i g n of (w (-h) ff  r e l a t i v e influence phytoplankton  - w(-h)). of l o c a l  distribution  More d e t a i l e d comparisons sources  will  be  t o flow  of the  divergence  given l a t e r -  on  The obvious  40 lesson that we may expect to learn from solving (4.1) along  pathlines  is  that  play a  very  significant  pattern  of  phytoplankton  thought however, redistribute  that  to  (4.3)  the kinematics of the flow field may role  in  establishing  distribution.  since  the  It  is  advective  the  observed  a comforting  processes  merely  phytoplankton and neither create nor destroy it, a  chlorophyll balance performed over the whole volume of  interest  will be independent of the flow pattern and will reflect the net effect  of  the source term Q, integrated over that volume. Our  assumption of time-independence quantity  of  chlorophyll  in  thus  implies  that  the  total  the volume of water considered is  constant and that, over the whole volume,  a  balance  has been  reached between production, grazing and sinking:  SSjQ' -y>^ x  <** y « k = J  0  Although this is not true over a period in the order of over a few days this is certainly valid.  months,  41 CHAPTER 6. In  order  to o b t a i n r e a l i s t i c values  the model i t was  had  f o r the parameters i n  necessary to make simultaneous measurements  the most important parameters. data  DATA  been  collected  Although q u i t e a l a r g e amount of  i n Georqia S t r a i t , the nature of  problem r e q u i r e d t h a t the b i o l o g i c a l parameters be the F r a s e r  River plume.  downstream  direction  the a x i s of the plume  is  influenced  covered was The The T.R.  Since the i t was  plume.  major v a r i a t i o n s occured i n a  decided  to take measurements along  both wind and  was  Parsons  of  the  as  well  collected-  Temperature  and  distribution We  f l u c t u a t i o n s i n the For the f i r s t plume  had  relayed  to  then occupied of  the  the to  be  Main  measurements. done  no  of  success  of the  same  i n the  profiles  radiation-  were  As part of  zooplankton samples  the  magnitude  using  scatter as  were  made to measure  chlorophyll a since  by  the  in  a the  observed  f l u o r i m e t e r output.. c r u i s e i n the s e r i e s (Gulf 1, November,  position The  salinity  as the p h o t o s y n t h e t i c  c a l i b r a t i o n curve was  aeroplane.  the area  with work being  At a l a t e r date an attempt was  horizontal  fluorimeter.  the  since  I n s t i t u t e of Oceanography, U.B.C-  the b i o l o g i c a l program c h l o r o p h y l l and  the  t i d e and  the v e s s e l used f o r the  data were c o l l e c t e d i n c o n j u n c t i o n  F r a s e r River plume.  also  in  quite large.  C.S.S. Vector  measured  our  measured  T h i s presented some problems by  of  was  determined  boundaries and  the s h i p .  general  visually extent  from  a  of the plume  1971) small were  A s e r i e s of ten s t a t i o n s  (Fig. 13  ) were  as r a p i d l y as p o s s i b l e up to 32 km  from the  mouth  Arm • of  the F r a s e r  River.  For the second c r u i s e  (February, 1972), a d i f f e r e n t method of position  was  use of an  attempted  aircraft.  temperature  s i n c e i t was  The  method  of  to  this  approach  to  take  position  was  salinity  that  start  the  ( F i g . 14  one  the  ).  was  in  main s e r i e s of s t a t i o n s , the plume  may  time  the  ship  T h i s time, a s e r i e s of s t a t i o n s  achieved  Visual observation determining  the  from  in the  plume  The  does not o b t a i n an  occupied along l i n e s r a d i a t i n g out from the mouth of the success  and  is  have changed s i g n i f i c a n t l y .  No  plume  p r o f i l e s i n the upper 20 meters i n a coarse g r i d of  instantaneous p i c t u r e and t h a t , by position  the  not p o s s i b l e to o b t a i n the  was  s t a t i o n s and then deduce the plume drawback  determining  was  river.  f o l l o w i n g the a x i s of the plume. ship  was  p o s i t i o n due  also  unsuccessful  in  to the s m a l l angle between  the l i n e of s i g h t and the water s u r f a c e .  For s i m p l i c i t y ,  later  c r u i s e s occupied s t a t i o n s whose p o s i t i o n s were unchanged f o r the remainder to  of the program.  extend  from  the  These s t a t i o n s  river  ( F i g . 15 ) were chosen  mouth to the north west-  Although  these s t a t i o n s were not always i n the same l o c a t i o n r e l a t i v e the  plume,  and time was  the p o s i t i o n s were c o n s i s t a n t from c r u i s e t o c r u i s e not spent attempting t o l o c a t e the plume each time-  S a l i n i t y and Industrial  temperature  Instruments  profiles  RS 5-  were  The  and  temperature  meter  C°-  with  for  data  are  presented  fitted  were  i n ' the  with a selenium c e l l .  shows  salinity  Appendix.  determined  using  With t h i s  an  these  F i g - 16  p r o f i l e s from c r u i s e G u l f 1, while a l l the  vertical extinction coefficients light  measured  accuracy  measurements i s taken to be ± 0. 1%»and ± 0 - 1 the s a l i n i t y  to  The a  2t<  instrument  the l i g h t i n t e n s i t y a t depth i s compared with the i n t e n s i t y  at  F i g . 14.  L o c a t i o n of s t a t i o n s , c r u i s e G u l f 2; February.,  1972.  45 49°  F i g . 15.  Station positions,  c r u i s e G u l f .3 and  subsequent  cruises.  F i g . 16.  Salinity profiles  from c r u i s e G u l f  1.  the  surface,  hence  The  expected  accuracy  ± 0.05  m -  e x t i n c t i o n c o e f f i c i e n t s may  F i g . 17  -1  of  the  gives  extinction  some  variation  coefficient  the  position  in  e x t i n c t i o n c o e f f i c i e n t , other data.  The  salinity  and  function  of  distance  since  this  from  was  plume.  from one  c r u i s e can  c e r t a i n l y during would  expect  the  the  extinction the  parameters were derived  from  the  the  profiles  r i v e r mouth.  using the data  were plume  The  from  the  magnitude of the  as  a  expressions the  the  Gulf  plume.  1  While  not be r e p r e s e n t a t i v e of a whole year, spring  pre-freshet  characteristics  period  parameters was  one  to remain unchanged-  Hence the same f u n c t i o n s were used f o r the whole p e r i o d but  used to  the only c r u i s e where the s t a t i o n s were  winter and basic  light  from  known to be reasonably c l o s e to the a x i s of data  the  the d e n s i t y , ^ , of the  (described l a t e r ) were f i t t e d cruise  of  is  Aside  temperature  determine the depth, h, and  coefficients  sample p r o f i l e s of the  i n t e n s i t y while F i g . 18 shows the with  be c a l c u l a t e d .  v a r i e d as  modelled  appropriate.  Light Intensity (%  F i g . 17.  Light intensity  of surface value)  (% o f s u r f a c e v a l u e ) as a f u n c t i o n o f depth.  A  "X"  0  18.  10  Non-dimensionalized  20  •  20/3/72  H  11/5/72  I  T r (km)  e x t i n c t i o n coefficient,JJL/JJ.^,  2/l/7l  30  as a f u n c t i o n o f d i s t a n c e  I  40  from t h e r i v e r mouth.  50  CHAPTER  The be  pair  of  considered  hopefully  of  of  in  of The  plays  a  a  MODEL  I:  for  which  first  two  small  FORMULATION  results stages  number  purely  model  is  advective  on  of  the  integrated source  purpose,  situation, easily  where  present the  to  premises  on  together  with  values  for  the  The  next  The current  I  parameters  This  model  clearly  the  various may  be  complex  i s based  are  area  the  of  flow  are  also introduced  set  different  is  idealized  comprehensible parameters  an  basic  section,  consequencesand  is  as  The  in this  Numerical their  choice  interpretation  appear  chapter.  pattern  are  associated  discussed  components  first  with  the  (i-iv),  geometry followed  depth  of  the  upper  layer  i s everywhere  observed  depth  of  the  upper  layer  actually  this  complication  will  plume,  but  model.  In  will  used.  model  I,  and  the  by  the  (v-vii)_  The  be  realistic  considered  listed  their  their  will  i n the  model-  of  and  which  a  areas  a  attempt  more  actual results  parameterizations  biological i)  second, model  of  to  may  greatly idealized  through  with  first  discussion  the  justified.  This  the  which a  us  influence  interpreted.  introduction  The  to  sequence  simplistic:  in a  term.  presented  interactions  overly role  now  steps  biological-physical first  are  in a  of  c o n d i t i o n s , c a r r y i n g phytoplankton  values  in  the  converge  interest.  field  models as  representation  7.  uniform  values  of  be h  the  varies  included between  in 2 m  same:  down the and  the  second 30  m  51  ii)  From  function  X/(x,y,z)  position. the  (7-1)  and  must  Experiments  discharge  of  (2.7),  also  be  performed  hot  water  i t f o l l o w s that the independent  of  horizontal  by Stefan and Schiebe into  a  tank  (1970) on  suggest  a simple  p a r a m e t e r i z a t i o n of the p r o f i l e i n the upper l a y e r i n the r e a d i l y i n t e g r a b l e  p  (^0  (7.2)  exp (-^)  The entrainment  /  s  (7.3)  v e l o c i t y i s simply  which i m p l i e s t h a t the downstream v e l o c i t y the c r o s s - s t r e a m component V, and c r i t i c a l velocity 0 .  of  written  U i s much l a r g e r than  much  larger  are probably  than  the  justifiable  the r i v e r mouth, before t h e r e i s any a p p r e c i a b l e spreading the  plume-  entrainment second  Once  formula  more, (2-4)  the  complexities  of  the  are r e s e r v e d f o r the more  full  realistic  model.  A numerical value of m was of  also  Both assumptions  C  near  of  (2.7) , (^^ must s a t i s f y  <*>k +  iii)  terms  function  = ex In view of equation  profile  the  plume.  along the  axis  entrainment  from  estimated from the s a l t  balance  Assuming that the i n c r e a s e i n s a l i n i t y  observed  of  vertical  the  plume  is  due  uniquely  the lower l a y e r , and not from l a t e r a l  an estimate of the entrainment v e l o c i t y w(-h) follows.  to  may  be  Consider a l o n g i t u d i n a l segment of the upper  mixing,  found  as  layer,  as  52 shown i n F i g - 19 -  The mass balance i s s a t i s f i e d  0, h, •= 0 h 6  by  + w(-h) L  o  and the s a l t balance by U, h, S, = U h S 0  E l i m i n a t i n g U, h  we  U  0  + w(-h)LS  0  find  (7-7)  L  0  S - S 6  0  Estimates of the q u a n t i t i e s e n t e r i n g (7-7)  were  6  the  depth h  0  w(-h)/U  c  (from 1 0  between  pairs  of  varies to  over  a  4 x 10 )-  Due  - 3  Values of  Table  wide  the  that the t h i c k e n i n g of the upper  I  -  range  to the very  at downstream d i s t a n c e s g r e a t e r than about  may  side  of  salinity  s t a t i o n s and of the a p p r o p r i a t e  and s e p a r a t i o n L are shown i n  - 5  hand  made from data gathered by the author on the Gulf 1  c r u i s e a l r e a d y d i s c u s s e d i n Chapter 6. differences  right  low 25 km,  The of  ratio values  stratification i t i s probable  l a y e r observed beyond S t a t i o n 8  be due i n part to wind mixing and not to upward entrainment.  A c c o r d i n g l y , only the f i r s t seven values of Table I were used to form an estimate of m,  f i n d i n g a value of m = 2.4  This  estimate  is  very  x  close  obtained a value of m = 2,12  10-* t o that of Keulegan  x 10  - 4  from experiments  (1966), in a  who  small  s c a l e modelUnder  the  assumptions  (7.1), (7-2) and  h o r i z o n t a l v e l o c i t y components i n the upper s i m p l i f i e d form of  (2.10):  a *  ^y  K  (7-4), the layer  now  average obey  a  L  |-  —  ho So  h.  t  w(-h)  S  F i g . 19.  1  t  b  A segment o f t h e upper l a y e r , showing t h e q u a n t i t i e s used to derive Table I.  54  TABLE I. Stnpair  E v a l u a t i o n of entrainment | Separation | L (m) .  T~  Depth h (m)  from c r u i s e Gulf  (S, -S ) 0  %m  c  (S,  1 data.  -s ) 0  too  1 - 2  4-8  x  103  2  0.4  1. 1  1. 5 x  10-*  2-  3  3-2  x  103  1  0.8  0.7  3.6  10-*  3-  4  3.2  x  103  5  1.2  ~  4-  5  3.2  x  103  5  0-2  1.3  2.4  5-  6  3.2  x  103  5  ~ 0- 01  1.4  ~  6-  7  3-2  x  103  7  1.3  0. 8  3-6  x  10-*  i  3.2  x  103  7  0.2  0.8  5-5  x  10-*  | I 9 - 10 j  3-2  x  103  15  0-7  0. 8  4.1  x  10-3  3-2  x 10 3  30  0-2  1,4  1.3  x  10-3  7-8 8-9  ~  0.01  x  10-s x  10-*  10-5  55  Since U > 0, the pathline source flow  upper  layer  flow  is  everywhere  s e p a r a t i o n i n c r e a s e s downstream and,  terms, the d e n s i t y of any will  decrease  divergent,  i n the absence of  passive s c a l a r c a r r i e d  downstream.  This  decrease  is  by  a direct  consequence of d i l u t i o n with e n t r a i n e d water.  Only i n the  where  upper one  the  lower  layer  is  as  rich  as the  p a s s i v e s c a l a r w i l l there be no d i l u t i o n and  the  case  i n that  hence no downstream  decrease i n c o n c e n t r a t i o n . Choosing w(-h) of  (2.11).  Using  9( #y)# given by x  f <x,y}  independent of V allows  »  (7.1)  and  (2.12) and  o  direct  integration  (7.4), the c o e f f i c i e n t s f(x,y)  (2-13) take e x p l i c i t  3<x,y) =  mU  -  and  forms  \U  (?- )  +  (?")  /0  Hence,  V(x,y> =^ (^mJi "-^-)  In the abscence of the C o r i o l i s f o r c e , V w i l l about  the  downstream  axis,  which f i x e s the constant w r i t t e n i n (2.3),  V(X,y) =  so t h a t we  of i n t e g r a t i o n .  (7.11) becomes  fm In  -h  \  I X +X )  A  0  (x  VUdy  +X<  may  be  antisymmetric  assume V(x,0) =  fiecaliing  U(x,y)  0, as  56 Numerical  values f o r V(x,y) are c a l c u l a t e d  analytic  expression-  r i v e r plume i s now (7.4)  and  The  three  completely  (7-12).  uniform.  ignored and we  (Figs-  In  only  equations  (2.3),  23,24,31,32). y(x,y,z)  i s also  taken  use  justification  simplicity.  by  a d d i t i o n , the v e r t i c a l s t r u c t u r e i s  -V = I The  resulting  T y p i c a l flow f i e l d s and s t r e a m l i n e p a t t e r n s  plankton p r o f i l e f u n c t i o n  horizontally  the  dimensional s t r u c t u r e of the  specified  are d e p i c t e d i n the next s e c t i o n iv) The  from  -A < z < o  behind  this  choice  More complex p r o f i l e s , based  (j./z)  is  its  extreme  on data, w i l l be  used  i n model I I . The  integral  of the product of the p r o f i l e f u n c t i o n s , as  d e f i n e d i n (3.7), reduces t o  The  upper-layer c h l o r o p h y l l d e n s i t y equation  the p a r t i c u l a r l y simple  ^y with i/ = 1, as per last  term  (3.8)  f,  fi ^  (7. 13) , and  continuous a c r o s s  on the r i g h t hand s i d e of  terms.  The  role  of  c a r r y p a r c e l s of water through  z = -h,  (7.15) vanishes.  the only c o n t r i b u t i o n to changes i n  source  takes  form  then no d i l u t i o n of c h l o r o p h y l l c o n c e n t r a t i o n due and  then  M  is  to  from  the  There i s  entrainment the  local  the flow f i e l d i s then simply t o areas of v a r y i n g s t r e n g t h of  the  57 source  term-  important  Such an a d v e c t i v e r o l e may  i n determining the o v e r a l l shape  distribution,  since  the  amount  of  p o s i t i v e or negative source s t r e n g t h , concentrations  reached  due  we  time and  there  would  be  the  chlorophyll  spent i n r e g i o n s of hence  strength  might  of  consider  a  the  the  by  the  z < -h-  In  that  a v e l o c i t y dependent d i l u t i o n e f f e c t i n  away from the a x i s of the plume. w i l l provide us  At  will  chlorophyll  (7-15), d e c r e a s i n g with U away from the mouth of the  cases  ultimate  flow-  vertical  with -V = 1 f o r -h < z < 0, -j/ = 0 f o r  profile case,  extreme,  of  extremely  to the e f f e c t of such s o u r c e s ,  depend d i r e c t l y on the l o c a l opposite  of course be  An, examination  river  of both  with an estimate of the r o l e . o f  and  extreme dilution  entrainment. Me now  pass to a d i s c u s s i o n of the b i o l o g i c a l  v) A c o n s i d e r a b l e amount suspension  at  coefficient  u  particulate  the is  matter  mouth  silt  by  the  load  is  usually  presence  found  in  The  extinction  of  suspended  t h i s dependence a f f e c t s the mean l i g h t  i n t e n s i t y I and i n t u r n the average silt  is  of the F r a s e r R i v e r .  increased and  of  parameters,  p h o t o s y n t h e t i c r a t e "P.  The  p i c t u r e d as decreasing away from the r i v e r mouth  a c c o r d i n g to an e l l i p t i c a l d i s t r i b u t i o n i l l u s t r a t e d i n F i g . 20 . Thus i f s (x,y) i s the s i l t  l o a d , i t takes constant values on  the  ellipses X  Z  +  4y2  =  with s(r) a d e c r e a s i n g f u n c t i o n of r . meant  to  reflect  any  observed  This d i s t r i b u t i o n i s  c o n d i t i o n s but- merely  not  gives a  p l a u s i b l e p a t t e r n i n the area of the r i v e r mouthD i r e c t measurements  of  the  extinction  coefficient  were  Fig.  20.  E l l i p t i c a l d i s t r i b u t i o n of c o n t o u r s of r = c o n s t a n t ( f r o m e q u a t i o n  (7.16)).  59 taken  i n the f r a s e r  distribution  River  plume  (Chapter 6 ) and suggest a  of jx a c c o r d i n g t o M = M 0 - _£_)  o ± r < r  0  o  as  shown  o —  i n t i g . l a , wixn r  been taken i n the  range  0  e  = z. o x tu» m-  0.3 m  _1  values or jx nave 9  < jx^ < 0.8 m  based  _l  on the  measurements. vi)  I t has a l r e a d y  semi-annular mouth  been seen i n F i g . 5 that t h e r e i s a  maximum i n the  zooplankton  o f the F r a s e r R i v e r .  distribution  Data c o l l e c t e d  off  the  during the c r u i s e s c  show s i m i l a r  maxima ( F i g . 21 ) .  T h i s kind of d i s t r i b u t i o n  has  been r e p r e s e n t e d by the Gaussian form  z  = z. + z  centered about r, csr  8 x 10 m, with c 3  r as given i n (7.16). vary  seasonally  mid-winter  = 5,0 x 10~ m 8  z  -2  and with  The zooplankton c o n c e n t r a t i o n s Z, and Z  from  minimum  values  o f 15 and 35 mg/m  3  m  in  t o 450 and 1050 mg/m i n May and June. 3  v i i ) The i n t e g r a t e d zooplankton  feeding  term  in  (5.12)  reduces, f o r -J/ = 1, to  3 «*» = - M G Z h  For  the purpose  further lines  of t h i s f i r s t  model, t h i s  (7-/9)  has been  simplified  by approximating the M dependence by a p a i r o f s t r a i g h t  (see F i g . 22 ) , so t h a t the zooplankton feeding term  over  61  F i g . 22.  The g r a z i n g r e l a t i o n of model I, based on eqn.  (7.20).  62 the upper l a y e r i s w r i t t e n as  C°S4» = -Ma'Zn  The  constant  chlorophyll  (7-*°)  -/Sa'Zk  =  a« = 1.35 x 1Q-»;  15a» = G = 2 x 10~«  per mg of zooplankton  per sec, the value  mg  of  introduced  f o r the maximum f e e d i n g r a t e i n Chapter 5. The  average source s t r e n g t h 1/h ^ Q dz then has the form  M( ( P - a ' Z )  -  W.I-MA]  M (? - w U)A) - / s a ' Z  M > is  s  P  i s defined  obtained from  as  in  ^  (5.3), with the average l i g h t  (5.9) and the e x t i n c t i o n  intensity  c o e f f i c i e n t ytt given  by  (7.17). For  the  lower  range  (7.15) i s p r o p o r t i o n a l  to  of  M, the whole r i g h t hand s i d e of  M.  In  i t s time  ( i . e . along a p a t h l i n e ) , that eguation then  DM Dt  dependent  form  reads  = M F U) t  where  is  a  u  k  c  function  of  time  only  3 along  a  pathline  through the  dependence of the c o o r d i n a t e s x and y on the time elapsed moving  along  a  pathline-  while  Thus F, (t) i s the l o c a l e x p o n e n t i a l  63 growth r a t e and M w i l l decay or i n c r e a s e whether  F, (t)  is  negative  or p o s i t i v e .  locally  according  to  The i n f l u e n c e o f each  one of the f a c t o r s a t work i s c l e a r l y i d e n t i f i a b l e i n F (t) and ;  can be estimated For  higher  a t every  p o i n t of t h e f i e l d .  concentrations,  H > 15 mg/m , 3  (7.15)  may be  written  DM = MF ii) z  - /sVZ  with  The c h l o r o p h y l l c o n c e n t r a t i o n i s then subject t o an growth r a t e F (t) and a l i n e a r decay a t a r a t a 9  15a'Z.  exponential  64 CHAPTER 8. Streamline velocity shown  patterns  (2.3)  MODEL I : RESULTS  r e s u l t i n g from the assumed downstream  and the s i m p l i f i e d  entrainment  law  (7.4) a r e  i n F i g . 23 and F i g . 24 f o r two depths o f the upper  h = 2 m and 5 m r e s p e c t i v e l y . spreading  of  value of h.  this  type  I t i s obvious that  the  layer,  rate  of  o f plume i s s t r o n g l y dependent on the  The o r i g i n o f t h i s dependence i s r e a d i l y found.  the a x i s of the plume  (y = 0) we have, from  (2.3)  and  On  (7.9)  (8-')  The  second  term,  due  to  entrainment •, i s a constant and i t s  e f f e c t on the spreading of s t r e a m l i n e s away from the a x i s  does  not  and  decrease  downstream.  With  x  m = 2.4 x 10~ , the divergence term due to 4  the  first  term  x > 15 km  when  appreciable  h = 5 m.  transverse  particles off profile,  f o r x > 3.3 km  U  rapidly  The sign  of  m  but  exceeds only f o r  appearance  of  pushes  an  water  downstream  velocity  the s t r e a m l i n e s  begin t o  For l a r g e r  values  of  h,  this  i s retardedv a r i a t i o n of M along a s t r e a m l i n e i s determined the r i g h t - h a n d - s i d e  M > 15 mg/m ). that  streamline.  of  (7.22)  (or  (7.24)  by the for  Looking a t the growth r a t e as w r i t t e n i n (7.23)  3  we note  ( F i g . 23).  and  3  entrainment  for h = 2 m  the Gaussian  decreases  = 5 x 10  h = 2 m,  premature  velocity  the t o p of  diverge very e a r l y divergence  The  when  0  w (-h) , s  The  h  other  s t r e a m l i n e s a c c o r d i n g to  and ^/ (-h)  do  not change  parameters:  U,  Z  functional  forms  and given  along  a  P* vary along above.  The  0.05  0  F i g . 23.  5  10  x(km)  15  S t r e a m l i n e p a t t e r n of the h o r i z o n t a l v e l o c i t y ; model I w i t h h = 2  20  m.  field  of  H  has been computed f o l l o w i n g  the scheme o u t l i n e d i n  Chapter 4, f o r a range of values of a l l these parameters. ranges correspond t o various in  different  months  presented  (w (-h) ) or The  expected  In  (Vt-h))  rates  and  i n f l u e n c e s of the parameters on the  distribution  below.  dilution  s  grazing.  phytoplankton  such as t o be  of the year and under maximum and minimum  growth r a t e s , s i n k i n g zooplankton  conditions,  These  have  Table  been  II  isolated  and  will  be  , we l i s t t h e values of those  parameters which are not v a r i e d i n the examples d i s c u s s e d  below;  while the v a r i e d parameters w i l l be given f o r each example.  a)  V a r i a t i o n i n upper l a y e r The  has  influence  already  depth.  of the upper l a y e r depth on  been  noted  above.  intensity  sinking Fig.  25  I,  shows  the  (the l a s t  variation  s t r e a m l i n e i n summer c o n d i t i o n s low  sinking  any  chlorophyll  DM/Dt > 0 light  b)  for h  c  dilution  everywhere,  Chlorophyll  the  of  M  but  due  on  two  terms)  along  the  to  e  the  _ s  in  (7.23).  axial  (y = 0)  ) and  entrainment  1,  i s l a r g e r , due t o i n c r e a s e d  i s no  a  average  layer.  concentration  there  with  (-)/(-h) = 1)..  flow.  parameter <f(-h) can take values from 0 t o 1,  When -V(-h) =  average  = 5 m, i n the absence of  d i l u t i o n by the e n t r a i n e d  chlorophyll  field  they a l s o i n f l u e n c e the  ( P^ = 2.2 x 1 0  - 2 m and h  i n t e n s i t y , f o r the t h i n n e r  The on  rate  influence  as given by (5-9);  and d i l u t i o n terms  flow  Changes i n h a l s o a f f e c t the  p h o t o s y n t h e t i c r a t e P through t h e i r light  the  depending  j u s t below the upper l a y e r .  dilution  of  the upper  layer  TABLE I I -  Model I parameters held constantValue  Parameter  96 2-4  x 10-*  5.0 x 10-a (m)  2.5 x 10* 5.0 x 103  b  (min/ly)  5-56 1.35  x  10-9  70 chlorophyll •j/(-h) = 0 ,  content  M;  at  the  extreme  end  one f i n d s a maximum degree of  dilution  of  the  dilution.  i s s u f f i c i e n t to r e v e r s e the growth  That  c) S i n k i n g The  for  May  = 1.  rates.  obvious  effect  of  an  increased sinking r a t e , given  otherwise i d e n t i c a l c o n d i t i o n s i s shown axial  such  trend of M i s seen  from F i g . 26 where M i s p l o t t e d on the downstream a x i s c o n d i t i o n s f o r 1/(-h) = 0 and l/(-h)  range,  streamline.  Under  May  in  F i g . 27  conditions,  entrainment and a 5 m upper l a y e r depth, a  no  along  the  dilution  five-fold  by  increase  i n s i n k i n g r a t e i s s u f f i c i e n t to t r a n s f o r m a net growth t o a net decay o f c h l o r o p h y l l  concentration.  d) Seasonal v a r i a t i o n . The  variation  a x i a l streamline conditions,  of  is  shown  typical  respectively.  phytoplankton c o n c e n t r a t i o n M along the  of  in  the  F i g . 28  months  under  sets  of  of January, March and  May  The v a l u e s of the parameters  three  which  change  from  curve t o curve are shown i n Table I I I . The  main  f a c t o r s which d i f f e r e n t i a t e the three s i t u a t i o n s  are seen from Table I I I to be: 1) The mean  upper  which  to  is  (Fig. 3).  greater  in  late  spring,  due  layer  increased  depth, runoff  An i n c r e a s e d depth would tend t o decrease the r a t e of  growth of M, as seen i n F i g . 25;  the  influence  of  the  upper  layer  depth v a r i a t i o n i s o b v i o u s l y more than overcompensated  other  factors!  January  to  May,  2)  The  zooplankton  corresponding  to  biomass an  increases  increasing  by  from  chlorophyll  27.  V a r i a t i o n o f M a l o n g y = 0; model I, May sinking rate.  conditions  showing the  e f f e c t of an  increased  74  TABLE I I I , 1 j.  Seasonal v a r i a t i o n of model I parameters.  Parameter  ] +  0  o  (m/sec) (m) (m)  Z,  | I  January _ 1-0  2.0 3  i  (mg/m ) 3  (mg/m ) 3  (S8C-1)  J 1 I | 1.1  15 35 X  10-5  J  I  e  I  e  (ly/min) | 0.6 x 10-2 I (ly/min) 1 3.0 x 10"2 0.3  i -j.-  1.0  2. 0  | 8.0 x 10  ~i—  March  8-0 x TO  May 2-0 5.0 1.5 x 10*  3  150  450  350  1050  1-3 x l O "  5  2.2 x 10-5  0,7 x 10-2  1.0 x 10-2  4.0 x 10-2  1.0 x  0.4  10-i  0.8  withdrawal term. importance  this  to the r e l a t i v e  trend  from  that  which  alone.  Again,  winter  to late  would  spring  result  from  Hay, t h r o u g h i n c r e a s e s  the  s u r f a c e waters, and i n I increase  Zooplankton As  in  the  increases  f t  , the input  of the curves  productivity. grazing  compared  the  to  In o r d e r  by i t s e l f ,  axial  (Fig.  29  ).  This  many  of  the  other  that  flow  (0*  o  Fig.  figures  zooplankton  to isolate  velocity, for  the two  At any g i v e n  to  of solar r a d i a t i o n .  It  t h e May c u r v e  the  seasonal  sink  of  M  term  basis  by  the influence  of  F i g . 28  under  zooplankton  show  grazing  during  is  t h e . same  (Z, = Z  = 0)  m  high  the has  rather in  negligible  this  model  on  productivity conditions.  flow. t h e i n f l u e n c e o f the magnitude axial  chlorophyll  different  = 1 m/sec and 2 m/sec) 30 .  of  f i g u r e h a s been p l o t t e d on t h e same s c a l e as  o f t h e mean  order  calculated  the heating  t o estimate  distribution  chlorophyll concentration  Strength  January  o f F i g . 28. .  c o n d i t i o n s b u t i n t h e a b s e n c e o f any  In  with  from  above, i n c r e a s e s i n t h e z o o p l a n k t o n  of zooplankton  f)  markedly  to  zooplankton  (7.25) a r e o v e r c o m p e n s a t e d on a s e a s o n a l  in  influence  opposite  v a r i a t i o n s of  associated  s i n c e the  grazing.  observed  (7.23) o r  m  fundamental  curves,  i n p r o d u c t i v i t y which d e t e r m i n e s  change i n c h a r a c t e r  e)  in P ,  of  i s i n a direction  3) The n e t p r o d u c t i v i t y i n c r e a s e s  this  be  shape o f t h e t h r e e  to  is  f a c t o r cannot  for  distance  river  of  the  concentration  outflow  was  velocities  May  conditions,  as  shown  from  t h e mouth, t h e v a l u e  of  in M  v =0 U " l m / sec 0  10  F i g . 30.  x(km)  20  V a r i a t i o n of M along y = 0; model I, May •and maximum d i l u t i o n .  30  40  conditions with the e f f e c t of increased v e l o c i t y •4  78 is  increased  for  a decreased  e f f e c t of the v e l o c i t y i n absence  of  dilution  a d v e c t i v e r o l e and the  rate  (7.23),  (1/ - 1),  i t  the  Looking  is  clear  flow  field  back at the  that  in  the  p l a y s a purely  t h a t i f the net source-sink term i s  positive  of growth a t any p o i n t i s unchanged by decreasing  flow v e l o c i t y . takes  flow f i e l d .  The v a l u e of M should  longer  to  reach any  the  sink  term  (compare with F i g . 26}. initially  (V=  with  The  because of the  increase  given p o i n t when 0  the case of maximum d i l u t i o n , decreases  then  0), a the  since  in  shown  dilution  rate,  0  In_ also  o  i n F i g . 30  chlorophyll concentration  higher  it  i s reduced.  o  decrease  effect  the  decreases  but  recovers  terms  (7.23) or  a f t e r f a l l i n g to a minimum value.  g) L a t e r a l d i s t r i b u t i o n of c h l o r o p h y l l . Looking  back  once  more  at  the  (7.24), one  n o t i c e s t h a t the v a r i a b l e s U,  along  one  any  streamline  source Z  ~P  and  of  M  along  the  axial  another.  streamline  may  r e p r e s e n t a t i v e of what happens over the r e s t of the Although  M was  vary  because of t h e i r s p a t i a l dependence  w i l l a l s o change i n p a s s i n g from a s t r e a m l i n e to variation  which  The  thus not (x,y)  plane.  c a l c u l a t e d along a number o f s t r e a m l i n e s i n  each  case above f o r which only i t s v a r i a t i o n along the a x i s y = 0 been  displayed,  only two  be  has  types of l a t e r a l d i s t r i b u t i o n emerged  from the i n t e g r a t i o n s . In a l l cases but one, variation The  M  the monotonicity e x h i b i t e d by  along the a x i s was  contours  productivity  May  shown  on  conditions  the  M  mimicked on the other s t r e a m l i n e s . F i g . 31  correspond  h o l d i n g f o r the h  to e  the  high  = 2 m curve of  x  F i g . 31.  H o r i z o n t a l d i s t r i b u t i o n of M f o r model I , May  (km)  conditions.  80 Fig.  25 and to the s t r e a m l i n e  pattern  of  F i g . 23.  In  these  circumstances, the c h l o r o p h y l l c o n c e n t r a t i o n i n c r e a s e s u n i f o r m l y along.each all  s t r e a m l i n e and, i n the (x,y) plane, thus i n c r e a s e s i n  directions  away  from  the  mouth  c h l o r o p h y l l d i s t r i b u t i o n has t h e form  of  of  the r i v e r .  an  elongated  The rising  trough o r i e n t e d along the a x i s o f the flow. The  corresponding  distribution  uniform decrease i nfli s found larger  sinking  rate  curve  f o r those  (the V = 0 curve o f f i g .  of  26; the  F i g . 27; the March and January  curves o f F i g . 28) i s not i l l u s t r a t e d . is  c a s e s where a  The s p a t i a l  distribution  very s i m i l a r t o t h a t shown f o r u n i f o r m l y i n c r e a s i n g M, except  t h a t there i s now a descending r i d g e . The only case where along  any  a  streamlines  was  non-monotonic  f o r the f u l l d i l u t i o n  c o n d i t i o n s curve shown i n F i g . 26 and flow  behavior  F i g . 30.  was  (•!/ = 0) May  For  the  r a t e (0 = 2 m/sec) a uniform decrease i n M i s found  initial  diminution  of  streamlines  chlorophyll  ( F i g . 32  concentration  high there  o  only along the a x i s ; on the other  )  an  i s always  f o l l o w e d by an e v e n t u a l recovery and an i n c r e a s e i n M. to  found  I n order  see whether t h e mimimum i n M on t h e n o n - a x i a l s t r e a m l i n e s i s  associated  with  zooplankton  d e n s i t y i s a maximum, a c c o r d i n g t o (7.18), has  traced  a  as  zooplankton  thin  g r a z i n g , t h e e l l i p s e on which the  dotted l i n e on F i g . 32.  I f the zooplankton  were r e s p o n s i b l e f o r the c h l o r o p h y l l d e p l e t i o n , one would the minima  of  streamlines, not the case. along  M,  to  as fall  indicated  by  crosses  on or near the e l l i p s e -  I t seems most l i k e l y that  the  been  on  the  expect various  This i s c l e a r l y diminution  of M  the s t r e a m l i n e segments l y i n g near the a x i s i s a s s o c i a t e d  I  0  F i g . 32.  I  10  I  15  H o r i z o n t a l d i s t r i b u t i o n o f M f o r model I, May  i  20 x (km)  conditions with U  I  25  G  i 30  = 2 m/sec and v =  0,  82 with  the diluting  water  from  since  i t  e f f e c t of the entrainment  below. i s  The d i l u t i o n  proportional  according  t o the Gaussian  position  of  the  axis  t h e minima  strongly  i s most  t o 0,  form  chosen  this  chlorophyll-free  pronounced  and f a l l s  of M along  supports  of  rapidly  for  curves  near  U  o f f the axis  i n  which  the axis  (2.3).  The  nearly  parallel  the  relative  interpretation.  Discussion The  simple  effects  of  model many  concentration. variation through This  i s  fact  the  the  weak  density;  productivity  parameters in  well  model  'in  constructing refined, dynamic  F i g .5,  as presented effects.  of  the M curves  chlorophyll the  seasonal  i n productivity  the  I n view  i t .  are almost  i n none  below,  of  upper  More  zooplankton  and dynamic  a feature  t h e model.  that  by c h a n g e s  to confirm  i n d i c a t i o n of the formation  appears  affecting  layers.  known a n d i t i s c e r t a i n l y n o t w o r t h  influence  factors  shown  particular  determined  entrainment. . Furthermore, any  has  i n s o l a t i o n and warming  a numerical  very  explored  appears  i s of course  chlorophyll by  of  primarily  increased  constructing is  It  just  factors  such  o f a downstream we  of  this  mainly  grazing  uniquely  o f t h e above  which  surprising on t h e  determined  as  dilution  r e s u l t s i s there maximum  i n M,  as  set forth to explain i n the  to yield  model  better  has  been  estimates of  0  83  CHAPTER  In  order  to  agreement  with  the  cruises,  a  have  been  forms  for  the  layer,  and  density,  have  i)  for  with  m =  m /sec.  was  2.4  arrested  pools.  The  in  were  and  are  in  and  Gulf  to  closer Gulf  3  used  appropriate  depth  of  and  the  upper  chlorophyll  below.  form of  1  more  velocity  i n terms  into  simplifications  the  presented  (2.5).  model  deemed  of  simplified  expressed  the  the  function,  profiles  the  given  of  (7.4), the the  entrainment  complete  Repeating  these  expression expressions  x  10~*  as  before;  (1966)  salt  g i v e s two  wedges,  latter  g =  value  9.8  m/sec  values  f o r c»:  the  other  (c' =  5.6)  was  chosen  here  as  the  lower  V  and  2  -  z  one  10  - 6  (c* =  7.3)  for stagnant  salt  more  appropriate to  plume. The  layer into  used of  Keulegan  2  the  What  entrainment  as  premises  approximations  abandoned.  been  c  .REFINEMENTS  convenience,  where  for  U  of  vertical  w(-h)  the  II:  observations taken  Instead  velocity (2.4),  the  MODEL  bring  number  above  9-  density  contrast  diminishes account.  surface plotted  as  The a  downstream, variation  function  i n F i g . 33  AO^ b e t w e e n  from  of data  and  of ^  this (c£  distance taken  and  variation =  (^  -  from  i n Gulf  1.  1)  has x  the The  the  upper  been  taken  10 )  at  3  river  mouth  fitted  the i s  curve  22  H  ® —A-  Q—•  -A-  '  G  21-  0 20  A  H o  19-  / o  V  °t  o  /  18"  /  A  /  17H  © Observed A Fitted Curve  / 16  H  V  15  33.  0  1  10  ,  x (km)  The v a r i a t i o n o f t h e s u r f a c e  r  20  1  30  ~  «^ as a f u n c t i o n o f d i s t a n c e from t h e r i v e r mouth.  I  40  —I  85  with  k = 0.935 x 1 0  i s a l s o shown i n F i g . 33.  - 4  T h i s curve was  chosen f o r i t s s i m p l i c i t y ; ' the o v e r a l l f i t of (9.3) t o the points  is  tolerable,  although  (9.3)  o b s e r v a t i o n a l v a l u e s f o r 12 < x < 25 km.  is  well  above  In the lower  data the  layer  a  constant d e n s i t y of ^, = 1.0235 was used. Now  that  w(-h) i n c l u d e s V, (2.10) becomes n o n - l i n e a r i n V  and i s no l o n g e r simply i n t e g r a t e d to terms  of  0.  The  velocity  f o l l o w i n g procedure. c o n t i n u i t y equation  for a  the f o l l o w i n g i t e r a t i v e  given  value  from  =  w(x,0,-h)  which  i n (9.2), the V,  with  the  process.  (9.1). i t was  assumed  that  allows the c a l c u l a t i o n of V(x,£)  (2.10). 3-  using the computed V, an updated value of w(x,£,-h) was  c a l c u l a t e d from 4the  c  of x and s t a r t i n g on y = 0 (where  at a point o f f the a x i s , y = £,  w(x,£,-h)  for V in  was now computed u s i n g the  (2.10) was i n t e g r a t e d t o f i n d  V = 0} , w(x,0,-h) was evaluated from 2-  (7.12)  Given U(x,y) i n (2.3) and U  h e l p of (9.1), through 1-  field  yield  (9-1).  at y = 2&, w(x,2&,-h) was found by  values  of v e r t i c a l v e l o c i t i e s at y = 0 and y = &-  i s then c a l c u l a t e d from 5-  extrapolation  from  V(x,2£)  (2.10).  an updated w(x,2&,-h) i s  estimated  from  (9.1)  using  V(x,2c06-  at  y = 3&, w(x,3&,-h) i s obtained by e x t r a p o l a t i o n and  the process c o n t i n u e s . The values  velocity f i e l d of £.  was mapped i n t h i s f a s h i o n  A value o f & = 10 m was found,  f i n e r g r i d computations,  to g i v e s u f f i c i e n t  for  various  by comparison with  accuracy.  86 In r o u t i n e i n t e g r a t i o n of the b i o l o g i c a l - p h y s i c a l model, an even s i m p l e r method of  integration  (x,y),  w(x,y,-h)  was  estimated from  V = 0.  V(x,y) was  then c a l c u l a t e d from  w(-h).  The  r e s u l t s of  this  ( 3 . 8 ) , w(-h)  biological calculations  ii)  The  depth of the  depth  of  bottom  the  of  the  r a p i d l y around x = 25 km. F i g . 16,  in  with r e s p e c t to h  method  deepening  agreed  for  updated  |v|  with  < U.  the  In the  with the  value  upper l a y e r , i d e n t i f i e d with the halocline,  frequently  From the s a l i n i t y  increases  p r o f i l e s f o r Gulf 1  the t h i c k n e s s of the upper l a y e r  of  and  f o r t h a t value of  (normalized  = 15 m) have been p l o t t e d i n F i g . 34  6  point  with U = U(x,y)  (2.10)  was  any  (9.1).  of V s u b s t i t u t e d back i n t o  rapid  (9.1)  simpler  at  used.  process o u t l i n e d above w i t h i n IS  iteration  shown  was  the upper l a y e r has been modelled  .  The  with  the  curve  with r as given by was  always  B = 3.5.  (7.17).  chosen  at  r  The o r i g i n of the h y p e r b o l i c tangent d  = 25  km  and  the  steepness  factor  For r >> r , 0  h (f 0  (  + D  while f o r r << r,  K  K  (f,  "  From which  f,  In  most  runs,  h^  was  kept  constant  at 2 m and only h  +  was  88 varied. The r a p i d change o f expected  to  depth  have some important  embodied  in  (9.4)  should  consequences on the flow  and on the c h l o r o p h y l l c o n c e n t r a t i o n .  field  I f h increases rapidly i n  (2.3), U w i l l decrease a c c o r d i n g l y , thereby decreasing the of  entrainment  and  a l s o l e a d s , from  profiles al.  In of  (1970)  An i n c r e a s e d mixed l a y e r  (5.9), t o a decreased mean l i g h t  thus to decreased iii)  dilution.  attempt  and  were  rate depth  intensity  and  productivity.  an  u  be  v,  to  i n c l u d e more r e a l i s t i c  current  examined.  meter  data  from  vertical  Tabata  et  These are shown i n F i g . 35 together  with a f i t t e d curve of the form  The  value  of  A was a d j u s t e d t o provide the best v i s u a l f i t t o  the c u r r e n t p r o f i l e s . shown  in  Fig.  Curves of X f o r v a r i o u s values of  36  A  are  A = 1 gave the best f i t and i s the curve  shown i n F i g - 35. The requirement  (2.7) that the i n t e g r a l o f tf(z) equal  the  depth o f the upper l a y e r imposes the r e l a t i o n  R Thus, f o r A = 1, K=  1-434.  Examples o f v e r t i c a l c h l o r o p h y l l v a r i a t i o n -j/(x,y,z) i n the region  of i n t e r e s t  shown i n F i g . 37 .  were drawn from F u l t o n e t a l . (1968) and are Once more a curve of  A = 1 p r o v i d e s a good Using  these  the  form  (9.9)  with  fit.  forms  for X  and V ,  the f u n c t i o n xi.(x,y) as  89  Tf(z,h)  0  .5  1.0  15  z/h  F i g . 35.  V e r t i c a l p r o f i l e s of c u r r e n t speed; the curve r e p r e s e n t s (9.9) w i t h A = 1, ( a f t e r Tabata e t a l . , 1970).  eqn.  90  0  0.5  * ' ( z  h ]  |.0  1.5  z/h  Fig.  36.  Comparison o f the e f f e c t o f d i f f e r e n t v a l u e s o f A on eqn.  (9.9).  -Mz.h)  4^  5^  Fig.  37.  V e r t i c a l p r o f i l e s o f c h l o r o p h y l l , the c u r v e r e p r e s e n t s eqn. (9.9) w i t h A = 1, ( a f t e r F u l t o n et a l . , 1968).  92 d e f i n e d i n (3-7)  becomes  -a- = J_ [  (/+  f*nJ>(j.+ /))  and the c o n s e r v a t i o n equation  K  (3-8)  foil)  takes the form  3  have an a n a l y t i c e x p r e s s i o n f o r 4/(x,y,z) ,  the i n t e g r a l i n the g r a z i n g Using  C3  /.oi4n  K (  i v ) Since we now  evaluated.  eii -  (9.9)  =  term  of  equation  (5-12)  can  be  we o b t a i n  (fl+ U cosh (A + A^)  K  - U  cosh  Pl j  («5./3)  t  where  R^ =  Hence equation  \  (trctctnr)  (5.12) becomes  ftU X  V  2  + aM)(  - t» cosn fyj - ( - K ) ^ ( - n ) ^  (?./5")  Wi  Equations values  of  M  (9,12) and alonq  i n c r e a s e or decrease term  (the  dilution  Q  term-  (9.15) may  pathlines.  then be used to  The  concentration  depending on wether the  solve  of M w i l l  integrated  term) i s l a r g e enough to overcome the  for  source  entrainment  93 CHAPTER  10.  MODEL I I : RESULTS  D i r e c t comparison of the s t r e a m l i n e s in  model I I with those  of model I  is  (pathlines) c a l c u l a t e d  difficult.  The  problem  a r i s e s from the f a c t t h a t c a l c u l a t e d v e l o c i t i e s are dependent h(x,y); away  i n model I, h i s constant  from  the  streamlines and  U  f o r two  mouth.  the  (2.11), (2.3)  F i g . 38  different i n i t i a l  (9-9)  axis and  we  of  (2.4)  the and  plume  F i g . 39  that  the  rate  rate  of  (y = 0)  = 1  m/sec  - 1/>^ > 0. of  Thus we  The  increase  v a r i a t i o n of M along  of the r i g h t - h a n d - s i d e entrainment  Hence we when  U  of M was  It  F i g . 39.  Similarly  spreading.  can  be  seen  model I I parameters.  constant  are given i n Table  influences  of  the  that  different  the  Since most of  (9.15) vary along a s t r e a m l i n e ,  calculated for  various  expect  thus U) i s  easy to determine t h e i r net e f f e c t on M.  the f i e l d  would  a s t r e a m l i n e depends upon the s i g n  (9.12).  (9.12) and  we  (and  0  d i l u t i o n term i s always a l o s s term.  the parameters i n not  of  Also  depends not only on the l a y e r  the g r a d i e n t of h. to  have d i v e r g e n t  (10.1) i s always >-0.  of spreading  spreading  < U, V(x,0) = 0  a l a r g e r value of h would decrease the r a t e of  I,  0  show the  we can w r i t e , using  i n c r e a s e d , as i s demonstrated by F i g . 38 and  is  U  velocities,  c  know t h a t X(-h)  depth, h, but a l s o on the  and  r e c a l l i n g that U  flow s i n c e the r i g h t - h a n d - s i d e see  while i n model I I , h i n c r e a s e s  = 2 m/sec.  6  On  From  river  on  As  it  with model  values  of  the  For model I I , the parameters held IV  varied  .  We  will  parameters  on  now the  discuss  the  chlorophyll  96  TABLE IV.  Model I I parameters h e l d constanti  Parameter (mg/m ) 3  d  l  3  5.0  B  3.5  c'  5.6  *t  (m /sec)  k  (in- )  2  1  -1  Value  1.002 9.35  x  10~  6  x 10-s  96 m  2.4 x 10-*  c  z  (ffl-2)  5.0 x 10-a  r  o  (m)  2. 5 x 10*  (m)  5.0 x  x  e  b a  (min/ly) 1  10  3  5.56 1.35  x  10-9  97 distribution.  a)  Seasonal v a r i a t i o n The  variation  illustrated  in  of  M  F i g . 40  along  the  axial  f o r conditions  streamline  r e p r e s e n t a t i v e of the  months of January, March and May r e s p e c t i v e l y . the all  For each  curve,  values of parameters which v a r i e d are given i n Table three cases a s i n k i n g speed  of  v  $  is  = 1.2 x 1 0  V.  m/sec  - 5  In was  used. Refering  to  Table  V  ,  i t can  be  seen that the b a s i c  d i f f e r e n c e s i n the three cases a r e : 1) i n c r e a s e d i n l a t e s p r i n g which i n c r e a s e s the v e l o c i t y , the upper l a y e r depth near the mouth  l a y e r deepens l e s s r a p i d l y downstream).  the  maximum  radiation,  I ,  towards  0  productivity  is  rate,  P^,,  summer.  counterbalanced  discharge  and  increases  d  (due to i n c r e a s e d  the  production  U  river  and  The by  2) The i n c r e a s e of  the  incident  resultant an  stability  solar  increase  increase  in  in the  compensation l i g h t i n t e n s i t y , I , and the e x t i n c t i o n c o e f i c i e n t , e  JJL . 0  3) The i n c r e a s e d Of  coupled  the  effects,  with a more gradual  increase values  above  zooplankton g r a z i n g towards summer.  the  chlorophyll  of U , I , 0  e  the  of  P_ and I„ when  i n c r e a s e i n the l a y e r depth tends t o concentration  while  the  The curves shown i n F i g - 40  the balance a t t a i n e d by the source and s i n k terms i n the  c h l o r o p h y l l equation.  The r e s u l t s i n d i c a t e t h a t except f o r May,  a l l the curves show a steady decrease of c h l o r o p h y l l the  increased  and the l a y e r depth near the mouth tend t o  i n c r e a s e the c h l o r o p h y l l sink term. reflect  increase  river  mouth-  In  May there  away  from  i s an i n i t i a l decrease with a  TABLE Vi  j  I j h i  Seasonal v a r i a t i o n of model I I paramaters.  Parameter  (m)  c  J f,  i  | U  0  (m/sec)  | P  m  (sec-*)  I I  I I  I  j I 1  i u I  ]  |  j. I I I i  |  15-0  i  l  j  (. J  T  I  May  ^  1.0  |  I  I  |  1.13  J  5.00  j  |  1-0  j  2.0  J  l  I  x  I  I  I  lo-s j  2.2 x 10~s j  I  I  I  I  i  I  i  I  c  (ly/min)  j 0.6 x 10~* I 0.7 x 10-* I 1-0 x 1Q-* J  0  (ly/min)  | 3.0 x 10~* j 4.0 x 1 0 - 2 j 1.0 x 1Q-»  0  I I I  (m-M  I  i (mg/m ) 3  m  j  I  I r, (m) :  March  | 1. 1 x 10-s j 1.3  j  1  1.0  I  3  I  1.13  1  |  ^  15.0  I  I Z, (mg/m ) J Z  3  January  I  0.3  |  I  I  15  150  I I  35  I  J 8.0 x 10 3 J  0.4  I  0.8 450  I 350  j 8.0 x 1Q3 J  i J i j  I  i J I j  I 1050  I  I  j 1.5 x 10* J I  J  1  100 minimum a t about 25 km, then there i s a gradual  increase.  The  d i s c u s s i o n which f o l l o w s shows the e f f e c t of varying some of the parameters i n d i v i d u a l l y . The  reference  curve  obtained by choosing terms  i n the d i s c u s s i o n  parameter values  and minimize the sink terms.  M i n c r e a s e s with i.e. similar  increasing  below  t o maximize  i s that  the source  T h i s produces a curve where  distance  from  the r i v e r  t o the comparison curve of model I.  mouth,  The e f f e c t o f  changes i n the parameter values i s then demonstrated by changing one o f the parameters i n the r e f e r e n c e curve and resulting  curve with the r e f e r e n c e curve.  f o r the r e f e r e n c e curve are those f,  = 2.00,  I  = 1.0 x 1 0 - i  0  U  = 1 m/sec,  e  ly/min,  Z^ = 35 mg/m and w 3  $  P I  c  The parameter  of Table  IV  and h  0  = 3.1 x 10~ sec-- , 5  m  comparing the  = 0.6 x 10-*  = 1.2 x 1 0  - 5  1  JJL  ly/min,  = 5 m,  0.3 m - i ,  -  0  values  Z, = 15 mg/m , 3  m/sec.  b) Changes i n upper l a y e r depth In  F i g . 41 the e f f e c t o f changes i n the depth of the upper  l a y e r are compared. the  chlorophyll  With a l l other f a c t o r s being  distributions  p r o f i l e s are compared: which  gives  0  < h < 30m; and  2m  < h < 12m. is  (C)  clear  from  h  Q  upper  constant,  layer  depth  = 5 m, f, - 2.00 (reference curve)  5m < h < 15m; (B)  2m  It  (&) h  f o r three  kept  h  0  = 5 m,  equations  - 15 m, f, = 1.13 which g i v e s f, - 1.40  (9.12)  which  and  (9.15)  gives  that  v a r i a t i o n s i n the depth of the upper l a y e r are i n s i g n i f i c a n t i n the  local  production  variations in  h  occurs  and g r a z i n g  terms.  The main e f f e c t of  i n the hydrodynamic  dilution  terms  3H  2H  O)  E  I  5  F i g . 41.  10  x  I km)  15  A  ho=5m , ^=2.00; 5<h<15  B  ho^lSm, f f l . 1 3 ; 2<h<30  C  h =5m, f p l . 4 0 ; 2<h<12 0  20  25  V a r i a t i o n o f M a l o n g y = 0 (model I I ) ; t h e e f f e c t o f changes i n t h e upper l a y e r d e p t h  102 (proportional  to  1/h)  i n (9.12).  Comparing curves A and C f o r where h a* c o n s t a n t , the  example, i t i s c l e a r that f o r x < 15 km, c h l o r o p h y l l growth r a t e of curve A should that of curve C s i n c e 1/h  < 1/h  fl  steep  gradient  rapid  than  On the other hand, once the reached  (x as 15 - 25 km) , curve C catches up and passes curve A  because  f, = 2.00  the  more  is  (with  of  .  c  be  for  A,  g r a d i e n t sink-term O-yh behavior  of  curves  i  as  layer  depth  compared to 1.40  f o r curve C)  l a r g e r i n A than i n C.  s  B  upper  and  C  The  dilution  by  f,  f o r curve C) , o u t d i s t a n c e s C  = 1.40  relative  i s s i m i l a r a t s m a l l x s i n c e the  o r i g i n a l upper l a y e r depths are e q u a l ; curve B, with divergence  the  term  (f, = 1.13 in  a  for  B  the  region  smaller  compared of  to ,the  upper l a y e r depth g r a d i e n t .  c) V a r i a t i o n s i n the v e l o c i t y In  r i g . 42  velocity f i e l d of  parameters  (upper)  the  results  of  are i l l u s t r a t e d . U  d  = 1 m/sec  curve) ,  U  illustrates  changing the s t r e n g t h of the  The curves compared have values  and  x  = 5 x 10  0  = 1 m/sec and x  0  and U„ = 2 m/sec and x curve  field  e  = 5 x 10  the  3  effect  v e l o c i t y at the r i v e r mouth; such discharge increases,.  e  = 1 x 10  m (lower of  by  m  (the m  4  as  The  the  happens  reference  (middle  curve) .  increasing  when  curve) lower  downstream the  river  The s i t u a t i o n f o r a l e s s r a p i d decrease i n  U downstream i s i l l u s t r a t e d by the middle The  3  curve.  l e s s r a p i d i n c r e a s e of a with d i s t a n c e can be e x p l a i n e d  the f a c t t h a t ; 1) the d i l u t i o n by e n t r a i n e d water from below  i s i n c r e a s e d , 2) with the organism  spends  less  increased  time  in  velocity  transit  and  a  phytoplankton  for s i m i l a r  local  i 0  5  n  :  10  i  i  r  15  20  25  x(kmi) . 42.  Variation  o f M along y = 0 (model I I ) ; the e f f e c t o f changes i n the v e l o c i t y  field.  104 growth r a t e s , would not a t t a i n e q u a l l y high c o n c e n t r a t i o n s a t a given d i s t a n c e downstream.  d) V a r i a t i o n s i n the production term The changing  production  term  has been  varied  i n two ways; by  the value of the maximum production  changing  the value  o f the e x t i n c t i o n  rate,  P  m  c o e f f i c i e n t , j^ .  in  curve  = 3. 1 x 10~ s e c , jA -  has values  of P  while the middle curve has and the bottom curve has P Although amount  both  P m  m  F i g . 43  The r e f e r e n c e 0.3 m  _1  JA - 0.8 m  _1  - 1  a  = 3.1 x 1 0  = 1.1 x 1 0  _ s  - 5  sec  sec  - 1  ,  - 1  ,  0  j i - 0.3 m . -1  0  and ju. were changed by about the same 0  (just l e s s than a f a c t o r of 3 ) ,  appeared  , s  m  The  g  r e s u l t i n g curves are i l l u s t r a t e d (top)  and by  the d i s t r i b u t i o n  of M  l e s s s e n s i t i v e t o changes i n jx than to changes i n P . 0  I n c r e a s i n g JJ. decreased 0  m  M as d i d decreasing  P , m  as one would  expect.  e) V a r i a t i o n s i n the grazing term F i g . 44  illustrates  the e f f e c t of i n c r e a s i n g the g r a z i n g  r a t e by i n c r e a s i n g the zooplankton The  top  curve  Z  m  = 35 mg/m )  Z  m  - 1050  while  3  is  a  is  mg/m ) has  large  3  the  reference  the  bottom  (Z, = 15 mg/m ; 3  curve  c o n c e n t r a t i o n o f M, 3  between  those  o f 30.  (Z, = 450 mg/m ; 3  Although  there  chlorophyll  very much.  x = 1 km) i s i n c r e a s e d t o 3 mg/m lies  factor  i n c r e a s e i n the grazer p o p u l a t i o n , the  when the i n i t i a l  0  curve  the i n c r e a s e d g r a z i n g term.  c o n c e n t r a t i o n i s not decreased  M/M  biomass by a  M  e  = M(1,y)  (ie. at  from 1 mg/m then the curve of  f o r the above  3  two cases.  Thus i t  10  F i g . 43.  x(km)  15  20  25  V a r i a t i o n s o f M a l o n g y = 0 (model I I ) ; the e f f e c t o f changes i n t h e p r o d u c t i o n r a t e by v a r i a t i o n s i n P and JJL m  0  107 appears  that the g r a z i n g term i s not one of the  more  important  terras.  f)  v a r i a t i o n s i n the s i n k i n g The  w  $  phytoplankton  = 1 m/day of the  curves  are  shown  r e f e r e n c e curve.  rate  sinking  reference in  rate  curve  F i g . 45  was  to  with  w  5  the  increased  from  = 5 m/day.  top  These  curve being the  The i n c r e a s e d s i n k i n g r a t e r e s u l t s i n  a  much  reduced c h l o r o p h y l l c o n c e n t r a t i o n .  g) L a t e r a l d i s t r i b u t i o n of c h l o r o p h y l l To  illustrate  have chosen x  0  = 10 km).  Fig. of  the  42  case  The  l a t e r a l d i s t r i b u t i o n of c h l o r o p h y l l illustrated  parameters  in  are the same as the middle curve of  distributions  are  not  locii  resembles  The most  F i g . 31 of model  increase  decrease,  of constant M are convex towards p o s i t i v e  x, i e . the  of p o i n t s (x,y) of M = constant are l o c a t e d such t h a t as x  from  F i g . 46  decreases.  The  the  river  mouth  few  cases  are those where t h e r e i s f i r s t  and then an i n c r e a s e i n M with d i s t a n c e from Near  completely  or  i n c r e a s e s the magnitude of y differ  two  found f o r model I I .  Provided M shows e i t h e r a monotonic lines  (the a x i s  field).  common p a t t e r n f o r model I I ( F i g . 46)  the  we  (U,, - 1 m/sec,  c o n t r a s t to model I (Figures 31 and 32)  distinct  I.  F i g . 46  which shows the d i s t r i b u t i o n of M along y = 0  the v e l o c i t y In  the  the  that  a decrease  river  mouth.  (where a i s decreasing) the contours of  constant M are c l o s e d , while i n the r e g i o n where M i s i n c r e a s i n g the contours of M = constant resemble  those of F i g . 46.  If  one  46.  H o r i z o n t a l d i s t r i b u t i o n o f M f o r model I I ; s o l i d l i n e s a r e s t r e a m l i n e s , dashed l i n e s a r e c o n t o u r s of M = c o n s t a n t , U = 1 m/sec, x = 10 km. e  e  110 looks  just  at  the  region  where  M i s d e c r e a s i n g , then the M  contours look s i m i l a r to those of F i g . 32 of model I.  Discussion Model I I , which has essentially  the  same  been  discussed  results  in  greater most  d i f f e r e n c e between the two models i s the v a r i a t i o n of model  II,  since  both the v e l o c i t y f i e l d and the p r o d u c t i o n term.  the same parameter M  produced  Probably the s i n g l e  the upper l a y e r t h i c k n e s s with x and y i n affects  has  as model I , even though  r e a l i s m was i n t r o d u c e d i n t o model I I , important  above,  the  second  it  Using  values i n both models l e d to lower values model  of  when l o o k i n g at s e a s o n a l d i f f e r e n c e s .  Again i t became apparent that the a v a i l a b l e l i g h t , the magnitude of P  m  and the a d v e c t i o n by the  important  parameters  while  l i t t l e i n f l u e n c e on M. possible study  to  In  velocity  field  were  zooplankton grazing, had none  of  the  model  the  most  relatively  runs  was  it  produce a downstream maximum such as we set out to  ( F i g , 5). The reduced v a l u e s of M i n the second model (as compared to  model I) can be e x p l a i n e d i n part by the i n c r e a s e i n  the  layer  depth which decreases the average l i g h t i n t e n s i t y , thus reducing the  size  of  the . p r o d u c t i o n  term.  Another  factor  f o r m u l a t i o n used f o r the depth i n t e g r a t e d production will  be  periods  that  are  It  Thus  we  used  vertically  mixed  over  s h o r t r e l a t i v e to the growing time, so  that l i g h t of v a r y i n g i n t e n s i t i e s i s depths.  term.  the  r e c a l l e d t h a t one of the assumptions used i n the model  i s that the phytoplankton p o p u l a t i o n i s time  is  a  experienced  depth-averaged  light  at  different  intensity in  111  equation  (5.3).  compared  pj-vdz/h to  coefficient,^, of  To check  the  and  the  ^Pj/ dz/h  effect  of  this  assumption  f o r v a r i o u s values of  become s u f f i c i e n t l y  l a r g e , so t h a t the average  enough, does the assumption  of the production  term.  I(z)/I  Thus the lower  0  < 0.027.  a t t r i b u t e d , at l e a s t the light  assumption intensity.  that  The  curves  diverge  depth  plankton experience a  seen  coefficient intensity  under-estimate noticeably  values of M i n modal I I can  p a r t l y , to the l a y e r the  light  l e a d to an  Some  I t can be  t h a t only when the l a y e r t h i c k n e s s or the e x t i n c t i o n  decreases  extinction  v a r i o u s values of l a y e r t h i c k n e s s , h.  r e s u l t i n g curves are shown i n F i g . 4 7 .  we  variation  for be and  depth-averaged  113 CHAPTER 11. The  CONCLUSIONS  two models d i s c u s s e d above have given an i n d i c a t i o n of  the r e l a t i v e importance o f t h e v a r i o u s parameters that determine the c h l o r o p h y l l d i s t r i b u t i o n . the  chlorophyll  The two most important  conservation  equation  appear  to  the  sinking  production term and the advection term, with being  of  least  important. The  somewhat  production  turbidity maximum  of  the  water,  in  the  layer thickness water  rate  by  the  input)  be the term  insolation,  the  the depth of the upper l a y e r and the (through  water  temperature).  i n c i d e n t r a d i a t i o n , the decrease  (through  in  importance and the g r a z i n g term the  term i s a f f e c t e d  production  increase  fresh  lesser  terms  increased  stability  The  i n the upper  due  to  and the i n c r e a s e i n the maximum  greater  production  r a t e a l l tend t o i n c r e a s e production as winter changes t o s p r i n g and  summer.  decrease  On the other hand t h e i n c r e a s e d t u r b i d i t y  tends  to  the a v a i l a b l e l i g h t i n the water column, decreasing the  production term. The  advection  term  also  varies  from  discharge  i n c r e a s e the v e l o c i t y components,  to  to  the season; r i v e r  discharge i n c r e a s i n g tends  winter  with summer.  The  increased (u,v,w),  g i v i n g r i s e t o a g r e a t e r f l u s h i n g r a t e (shorter r e s i d e n c e and  increased  mixing  mixing  and entrainment.  i s i n h i b i t e d somewhat by the  time)  However, the i n c r e a s e d  greater  stability  of the  water column as r u n o f f i n c r e a s e s . It  appears that the n a t u r a l s t a b i l i t y of the phytoplankton  p o p u l a t i o n i n the S t r a i t o f Georgia f a c t t h a t although  insolation,  may  be  attributed  t o the  the upper l a y e r t h i c k n e s s and the  114 production  r a t e serve  as  changes  sinter  advection  work  the blooms. increase (or  to i n c r e a s e the c h l o r o p h y l l  to  summer,  i n the opposite  Only when an  in  the  population.  could  increased  occurs  is  the  there  One  mechanism f o r t h i s  be  patchiness.  r e s u l t s of these s t u d i e s point  be  turbidity  direction, limiting  imbalance  perhaps a r e s u l t of i t ) may The  the  concentration  to  further  s i z e of a  large  imbalance  work  done to improve the r e a l i s m of the model.  and  that  It i s f e l t  t h a t the s i n g l e most important step i s to develop a b e t t e r model of the  velocity f i e l d  River.  for river estuaries  such  It  has  been shown that advection  determining  the  chlorophyll  further not  modelling  prove very  Fraser by  without  useful.  appear  modulation. to  rather  1/x  decay as  more slowly  A  the  not  variations) population required  very since  to  to  of  downstream  attempt  model would  flow  the r i v e r discharge velocity  in is  Further  the  pulsed  does  work on  not but this  underway at t h i s I n s t i t u t e .  second d e f i c i e n c y of the present  is  Fraser  (as the analogy with j e t s suggests)  time dependent changes are This  measurements  (S. Pond, pers. com-).  problem i s p r e s e n t l y  hence  a better v e l o c i t y f i e l d  Recent  Also  the  i s very important i n  distribution,  River plume have shown how  tidal  as  not  models i s the  included  in  the  fact  that  formulation.  important f o r long time s c a l e s  (eg-  the  phytoplankton  achieve  f o r the long  time  required  'equilibrium  for  is  the  seasonal  much s h o r t e r than t h a t  period v a r i a t i o n s to  be  felt.  However,  when such t h i n g s as the d i u r n a l v a r i a t i o n of the i n s o l a t i o n , the diurnal  vertical  migration  induced v a r i a t i o n s i n  the  of  zooplankton  velocity  field  and are  the  tidally  considered  in  115 conjunction  with  chlorophyll  conservation  present  models  the n o n - l i n e a r i t y of some of the terms i n the  can  be  g r a z i n g i s about 180° photosynthetic Spatial  eguation,  the  appreciated,  ( i . e . 1/2  limitations  particularly  day)  out  of  the  with  the  production. inhomogeneity  vertical  must  also  be c o n s i d e r e d . the  Me have  effect  of  s t r u c t u r e of the c h l o r o p h y l l d i s t r i b u t i o n and  the  a v a i l a b l e l i g h t d i d not i n t r o d u c e l a r g e  errors..  However,  combined e f f e c t of the v e r t i c a l c h l o r o p h y l l d i s t r i b u t i o n and vertical  migration  of  the  investigated i n conjunction  zooplankton  biological  parameters.  time.  variations Another  is  between that  different  results  simple  to r e s o l v e .  one  than  values  that  laboratory field  is  measurements  studies.  However,  due  it  may  to  give  The problem i s not a  indicates  that  realistic  s t u d i e s i n the p a r t i c u l a r  study the problems of s h e l f - s h a d i n g and n u t r i e n t they  for  parameters  of i n t e r e s t i n order t o choose the c o r r e c t parameter v a l u e s .  were not c o n s i d e r e d ;  be  s p e c i e s , g e o g r a p h i c a l areas and i n  models must have i n p u t from f i e l d  our  the  formulation.  choosing  Part of  the  must  Most of the b i o l o g i c a l  can take on a l a r g e range of values. natural  population  with a time-dependent  Last but not l e a s t i s the problem of the  the  since  phase  shown i n Chapter 10 t h a t , i n g e n e r a l , averaging the  of  would become  more  important  area In  limitation at  the  higher c h l o r o p h y l l concentrations. In  summary,  although  it  was  not p o s s i b l e to produce the  downstream maximum i n the d i s t r i b u t i o n of set  out t o e x p l a i n , i t was  water  column,  the  value  chlorophyll  that  we  shown t h a t the l i g h t a v a i l a b l e i n the of  P  m  and  the  velocity  field  are  116  important i n effect  of  determining  changes  the  chlorophyll  distribution.  i n these parameters must be c o n s i d e r e d  e v a l u a t i n g the r e s u l t s of n a t u r a l or  man-made  system, such as damming the Fraser River, power p l a n t or d i s c h a r g i n g  changes  constructing  possible pollutants.  The when  t o the a nuclear  REFERENCES  Abraham, G. , 1960. J e t d i f f u s i o n i n l i q u i d of g r e a t e r d e n s i t y . D i v . , Proc. ASCE 86, HY6, 1-13.  J_. Hyd.  A n t i a , N.J., C D . M c A l l i s t e r , T.R. Parsons, K. Stephens and J.D.H. S t r i c k l a n d 1963. 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Boatwright J r . , ed. Academic P r e s s , N.Y. 454 pp.  120 APPENDIX: TEMPERATURE AND SALINITY DATA  A b b r e v i a t i o n s used: CRN  —  c r u i s e number, G f o r Gulf  HR  --  time o b s e r v a t i o n s t a r t e d  STN DY  s t a t i o n number —  date, (day/month/year)  Note: The f i r s t correspond  (GMT)  to  the  5 s t a t i o n s of c r u i s e 2 ( p r o f i l e s single  s t a t i o n s preceded by a  2  number in  stations  F i g . 14  c r u i s e 2 s t a t i o n s with p r o f i l e s t o 50 m-  in  correspond  to  20 m)  F i g - 14. to  the  The 14  -J  1  I  CRN: G- 1 STN: ..  01  HR: DY:  +  1814  |  02/11/71  Temp. | S a l . (0 ) C  i  (%•)  CRN: G- 1  |  STN:  r  +  Depth (m)  I I  DY:  -i  02/11/71 1  Depth I Te mp. | I (°C) (m) 1  Sal. (%o)  0  8.7  |  20.4  0  .j |  8.8  1  24.3  1  9.2  |  25.6  1  I  8.9  I  25-5  2  9.3  j  27.0  2  |  8.8  i  26.0  3  9.0  |  26.4  5  |  9.0  |  26.3  5  9.2  I  26.6  10  |  10.0  |  28.5  7  9.3  !  28.4  15  J  9.8  J  28.8  10  9.2  I  28.7  20  |  9.7  |  28.6  15  9.4  j  29.1  30  |  9.7  I  30.1  20  9.2  j  29.4  50  |  9.7  I  30.3  30  9.4  |  30.1  75  J  9,7  1  30.8  1  50 .1  02  Hfi: 1856  9.4 1  i 1  30.2 I  1  1  1  122  CRN: G- 1 STN: 03 Depth (m)  HR: 1922 DY: 0 2/11/71  CRN: G- 1 STN: 04  HR: 1948 DY; 02/11/71  Temp. <°C)  Sal.  0  8.8  24. 6  0  8.7  ]  24.3  1  8. 9  27.0  1  8.6  |  24.2  2  8. 8  26.9  2  8.8  |  25.7  5  9.0  27.5  5  9.3  i  27.3  7  9. 2  27.9  7  !  9-2  i  27.3  10  9. 5  28.7  10  1  9-3  |  27.5  15  9,5  29.0  15  20  9. 6  29.0  20  30  9.6  29.5  50  9.8  75  9.7  Depth (m)  Temp. | (°C) i  Sal. <%. )  9.5  i  27.9  1  9.6  ]  28.4  30  1  9.6  j  29.3  30.5  50  1  9.5  |  30.2  30.9  75  1  9.8  j  30.9  CRN: G- 1 STN: 05  HR: 2014 DY: 02/11/71  Depth | Temp, (ffl) I (°C)  CRN: G- 1 STN: 06 Depth (m)  HR: 2047 DY: 02/11/71  Temp. (°C)  Sal-  0  I  8.7  24.2  0  9.0  25.7  1  J  8.6  24.4  1  8.8  25.8  2  |  8.5  24.7  2  8.8  26.0  5  |  9.0  27.4  5  8.9  26. 1  7  |  9. 1  27.6  7  9.2  27.5  10  j  9.2  28.4  10  9.2  27.9  15  j  9.4  29.3  15  9.8  28.9  20  I I I i ]  9.4  29.5  20  9.6  29.4  9.4  29.8  30  9.6  29.6  9.1  30.2  50  9.4  30.3  75  9.7  30-7  30 50  r-  ••  | CRM: G- 1  DI: 0 2 / 1 1 / 7 1  j STN: 0 7  j i  HR: 2 1 1 6  Depth | Temp. I S a l . (m)  i  | i  o  i i  1  i  2  J  5  I  (OC)  I  (%«)  9.0  |  27.0  »  i  i  i J  4  -  —3  1  | CRN; G- 1 1 STN; 0 8  i I  i  HR: 2 1 4 1 J DY: 0 2 / 1 1 / 7 1  J  Depth ! Temp. j I (m) i (°C)  Sal. |  8.9  J  27.3 J  i1  i o  {%• )  I  I 1  1  8.8  I  27.4 |  9.0  |  27-6  !  !  8. 9  J  27.3  i  j  2  8.8  I  27.6 }  8-9  |  27.6  !  i  5  8.8  I  27.7 J  7  !  8.8  |  28-0  J  7  8.8  I  27.7 1  |  10  I  9.0  |  J  10  8.9  j  27.7 |  I  15  9. 2  I  28.5  j  15  9-2  1  28-5 |  |  20  9.7  |  28.8 i  |  20  9-2  i  28-6 J  i  30  9. 4  j  29-9  J  30  9.6  I  29.4 )  I  50  !  !  9. 2  |  30.2  i  |  50  9.4  i  30,3 |  I  75  ]  9.8  |  30.8 j  I  75  9.8  I  30.8 J  !  !  !  I I  i 28.2 1 !  125  CRN: G- 1 STN: 09  HR: 2212  CRN; G— 1 STN: 10  DY: 02/11/71  + Temp,  Sal.  (OC)  j |  0  9.0  |  28. 1  0  1  9.0  |  28. 1  2  9.0  |  5  9.0  7  Depth (m)  Depth (m)  +-  HR; 2236  DY; 02/11/71 -h Sal, Temp« (°C) (%o) 9.0  28. 1  1  8.9  28.2  28.2  2  8.8  28.3  |  28.2  5  8.8  28.4  8.9  |  28.2  7  8.8  28,4  10  9.1  |  28.4  10  8.8  28.6  15  9.2  j  28.6  15  9.0  28.9  20  9- 1  |  28.9  20  9.0  28.9  30  9.4  I  29.4  30  9.3  29.5  50  9.3  |  30-4  50  9.3  30.5  75  9.6  |  31.0  75  9.5  31.0  CRN: G- 1 STN: Depth (m)  1  HR: 0041 DY: 03/11/71  Temp (°C)  Sal.  0  8. 1  23.3  1  8,0  23. 2  2  8.0  23.5  5  8.4  25.7  7  8.7  28-4  10  8.8  28-6  (%o)  CRN: G- 2 STN: 01 Depth (m)  HR; 2120 DY: 09/02/72  Temp. (°C)  Sal. 4  (X.)  CRN: G- 2 STN: 02 Depth (a)  HR: 2220 DY: 09/02/72  Temp. (°C)  Sa 1.  0  5.4  30. 1  1  5.4  30. 1  5.2  | 27.2 i i 27.3 I ! 28.9  2  5.5-  30.2  3  5.5  |  29.9  3  5.5  30-3  5  5.6 J  30.5  5  5. 5  30.3  7  5.6  |  30.5  7  5.5  30.3  10  5.8  |  30.8  10  5.6  30.4  15  6.0  |  30.9  15  5.8  30.6  20  6.2  J  30.9  20  6.0  0  5.0  1  5.0  2  CRN: G- 2 STN; 03  HS: 2322 DY: 09/02/72  Temp. | S a l . (°C) | (%•)  30.9 -A  i  CRN: G- 2 STN: 04  HR: 0025 DY: 10/02/72  127  | CRN: G- 2 | ST H j  I  DY; 10/02/72 i  05  Sal. J  Depth | Temp. i  (m)  I  o  I  1  I  2  I  3  I  :  HE: 0220 i  5  I  7  |  10  |  14  j  19  |  ....  T  !  I I ! !  I I  (OC)  i  L  .  (*•) 1  | CRN: G- 2  I STN: 01 j  I  HR: 1205 | DY: 10/0 2/72 |  Depth  Sal. J  Temp.  {%•)  (°C)  (m)  I  j  1  4.0  r I i J I  4.1  i  22.6 |  I  2  5.4  I  30.3 |  4.3  1  25.9 |  I  3  5.6  I  30.6 |  30.2 |  I  5  5.8  30.5 I  I  7  6. 3  3. 1  i  1 i I  12.9 |  I  o  4.3  22.0 |  I  1  5. 1  I  27.4 |  I  5.1 5.8  1  1 1 i  1 1 1  !  24.0 |  30.7 | 31-0 |  I !  5.6  J  30.5 |  |  10  6.4  5.7  1 1  30.6 j  I  15  5,9  6.1  1  31.0 | •  |  20  5.7  !  31.4 |  |  29  5.7  i  31.4 j  J  38  5.7  !  31.4 j  J  48  i  i  1  i  I  5.5  j  31-0 | 31.4 |  31.4 J  128  CRN: G- 2  HE: 1250~1  1  HR; 1333 |  | CBN; G- 2  I I j STN: 0 2 DY; 10/02/72 i | ^ S a l . Temp. | Depth (in) (°C) I (*•)  j 1  0  3.9  j  19.8  1  o  |  3.3  1  3.9  |  20. 1  |  1  j  4.0  2  4. 5  |  24. 1  I  2  1  4.2  3  4.6  |  25. 5  I  3  I  5.0  5  5.2  |  29.7  I  5  j  5.2  7  5.4  j  30. 1  I  7  i  5.3  10  5.9  j  31. 1  j  10  J  5.6  15  6. 1  j  31. 2  |  15  |  5.8  20  6.2  |  31. 2  J  20  i  5,8  30  6. 4  |  31.3  I  30  I  6.1  40  6. 4  |  31. 3  j  40  |  6.1  5.8  |  31.3  1  50  |  6.1  f  L  50  r  | 1  I  J  DY: 10/02/72 J  J STN: 03  i  i  Depth 1 Temp(m) 1 (°C)  j  1  I  Sal.. | (%o) I  1  15.8  J  20.6 J  ! !  ,  23.3 1 28.5 |  1  30.1 J  ! ! ! ! ! !  30.5 J 31.0 J 31.2 | 31.3 | 31-3 J 31.4  I  31.4 | _  . i  129  i —  CRN; G- 2 STN: 04  HR: 1409 DI: 10/02/72  I  • •  CRN:  —9  G-  j STN: 05 1  Hfi: 1440 j  2  JL  DY;  10/02/72 |  1  Depth | Temp. 1 (m) 1 (°C) 1  j  1 1  o  1  4.8  I  1  !  J  2  I  I  •-+-  Sal. (-oo  )  1  .  1  25.8 J  5.0  |  28.1 j  5.0  |  28.1 j  3  ! .5.3  J  30.3 |  i  5  I  5.3  I  30.3 J  j  7  !  5.5  I  30.5 J  I  10  !  5.6  i  30.5 I  i  15  5.8  i  30.7 j  1  20  1 5.9  i  30.7 |  1  30  6.1  I  30.9 |  |  40  6.3  J  31.0 i  I  31.2 j  k L  50 _  ! !  I J  6.6  . .!„,_ , _.  J  |  CfiN: G- 2 STN: 06  HE: 1511 DY: 10/02/72  Depth } Temp. J (m) (°C)  Sal.  0  5.1  I  29.2  1  5.3  |  29. 2  2  5.0  |  29.0  3  5. 1  |  29.0  5  5. 3  j  29.9  7  5.4  j  30.3  10  5.4  J  30.4  15  5.5  !  30.5  20  5.8  I  30. 9  30  6.3  |  31.0  40  6.7  J  31.3  50  6.9  I  31.3  CfiN: G- 2 STN: 07  HH: 1553 DY;  10/02/72  CRN:  G- 2  STN:  08  HR: 1622  CRN:  G- 2  DY: 10/02/72  STN:  09  Temp, (OC)  Sal. (%.)  0  4.8  27.2  1  5.0  2  DY: 10/02/72 Temp. (°C)  Sal.  0  4.7  28.9  29.5  1  5.0  29.2  5.0  29. 1  2  5.0  29. 1  3  5. 1  29. 5  3.  5.1  29.3  5  5. 1  29.9  5  5.2  30. 1  7  5.2  30. 2  7  5.2  30. 1  10  5.4  30.3  10  5.2  30.1  15  5.5  30.4  15  5.2  30.2  19  5.6  30.5  20  5.4  30.5  29  5.9  30.9  30  6.1  30.9  39  6.3  31. 0  40  6.5  31.2  48  6. 8  31.3  50  6.7  31.3  Depth (m)  Depth (m)  HR; 1648  (%• )  1  CRN:  G- 2  STN:  10  Depth (m)  HR: 1720 DY: 10/02/72  Temp, (0 ) C  Sal. (%.)  -i  "  | CRN: G- 2 1  1 J j  STN: 11  HH: 1 7 4 7 | DY; 1 0 / 0 2 / 7 2 l  +-  D e p t h j Temp- J 1 (m) | (°C)  Sal. | (%o) 1  0  3.3  17.8  1  0  1  4.2  J  23.5 j  1  4.8  26.7  1  1  I  4.8  1  26.8  |  2  5. 1  28.7  i  2  |  4.8  J  27.3  J  3  5. 1  28-8  1  3  |  5.0  J  28.1 I  5  5. 2  29.5  !  5  |  5.5  |  30.0  7  5.3  29.9  1  7  1  5.5  I  30.2 J  10  5. 5  30. 2  1  10  J  5.5  J  30.5 J  15  5.6  30.5  1  15  i  5.5  j  30.7 \  20  5.8  31.0  I  20  |  6.1  j  31.3  |  30  6.0  31.4  I  30  1  6.6  j  31.4  |  40  6.0  31,4  I  40  i  6.5  i  31.6  |  50  6.0  31.4  1 i  50  I  6-2  J  31.6  |  i  , 4,  {  - , - J  CRN: G- 2 STN:  12  Depth (m)  DI:  HR: 1816  | CRN: G- 2  10/02/72  | STN: 13  Temp.  Sal.  J I  <°C)  HS: 1846 J DI: 10/02/72 j Temp. I <°C) i  Depth (m)  4.5  I  25-5 |  1  4.7  I  25.2 |  I  2  5. 1  J  30.1 |  30.3  J  3  5.2  i  30.0 j  5. 8  31.0  I  5  5-4  i  30.2 |  7  6. 1  31. 0  I  7  5.4  i  30.2 I  10  6. 2  31.4  I  10  5.4  i  30.2 |  15  6.2  |  31.5  1  15  5.8  i  30.6 |  20  6.3  I  31-5  |  20  6.0  i  30.7 1  30  5.9  |  31.5  |  30  6.0  i  30.9 1  40  5.7  |  31.6  }  40  6-0  1  31.1 1  50  5.7  |  31.5  j  50  6.3  1  31.1 |  0  3.5  15.6  I  o  1  5.0  27.4  j  2  5.5  30.2  3  5.4  5  |  Sal. | (%o) I  I  I  j CRN: G- 2 HR: 1921 I | STN: 14 DY: 10/02/72 j. j Depth j Temp. | S a l . (m) i%o) (0 ) j C  r  j  4.7  |  26.6  1  5.2  |  27.6  2  5.4  |  30.0  3  5.5  |  30.1  5  5.5  |  30.2  7  5.5  j  30.2  10  5.5  I  30.2  15  5.5  |  30.2  20  5.5  I  30.4  30  5.9  |  30.6  40  6.4  |  30.9  50  6.8  |  31,1  0  135  1  I I  | I  HR: 1910 |  CRN: G- 3 SIN: 01  DT: 2 0 / 0 3 / 7 2 | 1  Depth 1 Temp. (m) 1 ( ° C )  r  I  o  1  1  I  2  I  3  i  5  |  20  «  „..  1  l  6,7  6.8  I  23.6  1  2  I  6.6  6.8  1  24.1 j  I  6.7  1  26.8  1  6.7  1  28.1 I  6.6  1  28,6  6.4  1  29.9 j  l 1 1 1 1 1 1  1  , „  6.3  23.0  30.4  G-  STN:  03  |  |  |  ]  |  r  ! !  I ! ! |  0  3 5 7 10 15 20  i  i.  CRN:  1 r  1  iI  15  On)  (°C)  23.0 |  1  3  Depth | Temp. (m) j (°C)  ! !  j  2025  j  CRN: G - 3  20/03/7 2  J  STN: 04  Sal.  | i  HH; DY:  I i I  -r-  |  Sal. I  Depth 1 Temp.  1  1 f1  I  L  1  20/03/72 *  7.0  1 1  10  I  DY:  i  1  J  L  STN: 02  HR: 1 9 5 8 |  7.2  i  7  •  Sal. | (%*) !  i  CRN: G- 3  +J l 1  !  t •  6.7  6.5 6.5 6.5 6.4 6.2 6.5  j 1  !  !  ! !  (%•) I 25,6  |  25.8  |  26. 1 | 27.0  |  27.4  |  27.4  |  27.9  |  30.0  |  _[_  30.2  |  HR;  2055 1  I  !  I  It  DY: 2 0 / 0 3 / 7 2 {  Depth 1 Temp, j (m) 1 (°C) i  Sal.  |  (%o)  1  6.9  24.8  1  o  I  7.5  1  18.5 I  6. 8  25.0  I  1  i  7.0  1  22.1 J  2  6.7  27. 4  I  2  1  7.1  i  22.7 j  3  6. 6  27.8  |  3  |  6.8  I  23.4 |  5  6. 5  27.7  |  5  I  6,6  j  26.0 I  7  6.4  28.6  1  7  I  6.8  I  28.4 I  10  6. 3  28. 8  |  10  |  6.7  J  29. 1 i  15  6. 4  29.9  ]  15  |  6.3  |  29.9 J  20  6.5  30.3  I  20  |  6.3  J  30.4 |  0  1  I  A  ...i.  I  136  J  ~\  | CRN: S- 3 HR: 2115 I I STN: 05 DY: 20/03/72 | I b ; f -J | Depth J Temp- J S a l . | I (m) | (°C) | (So) i I  +  1  i  :  i  1  { CRN: G- 3 HS: -2149 J I STN: 06 DY: 20/03/72 | I J{i | Depth I Temp- | S a l - | | (m) | (OC) j (%.) I -I  I  r  -4  I  0  |  7.1  |  15.7 ]  |  0  j  6.9  |  17.8 |  I  1  |  6.7  j  20.8 J  |  1  |  6.9  |  19.9 |  I  2  j  6.5  |  21.6 J  I  2  j  7.1  J  20.0 |  |  3  |  6.6  1  22.1 |  I  3  |  7.1  j  21.4 |  I  5  |  6.6  |  26.8 |  |  5  |  6.7  J  26.3 |  I  7  |  6.8  |  28.8 j  I  7  J  6.7  J  29.7 |  I  10  |  6.6  J  29.9 |  |  10  |  6.8  |  29.7 |  i  15  |  6.4  J  30.4 |  1  15  |  6.7  j  30.5 |  I  20  J  6.5  |  30.5 I  |  20  |  6.7  J  30.9 |  i  1  J  CRN: G- 3  J  STN: 07  j J  i  1  HR: 2 2 1 5 I DY: 2 0 / 0 3 / 7 2 J  Depth | Temp. | (m) I <°C) I  Sal- J i%o) J  I  I  \ CRN:  G-  3  | STN: 0 8  j  J  i  HR:  2247  DY: 2 0 / 0 3 / 7 2 1  j__ Temp. Depth | (°C) (a) 1 0 i 5. 5  1,  .... ... i  Sal. j {*.) 1 6.8 J  1  o  |  7.0  J  16.4 J  | 1 I  i  1  |  7.2  |  18-6 |  I  1  I  5,4  I  6.9  1  J i  |  |  2  I  7. 1  J  20.0 |  I  2  i  5-6  i  8.5 1  I  3  I  7. 1  1  20.3  J  I  3  i  5.7  1  14.6 |  I  5  |  6.6  j  29.0  I  I  ^  j  6. 1  j  23.7  I  I  7  |  6- 6  |  29-2 |  I  6  |  6.5  |  27.5  J  |  10  |  6.6  j  30-0 j  i  8  6.6  j  30.7 !  I  15  |  6-8  |  30. 3 j  I  12  |  6.5  j  30.9 i  |  20  I  6.7  \  30.4  I  15  1  6.4  |  30.7 | . J  i  I  t  J  i_  i  CRN:  G- 4  STN; 01  HR: DY;  +  Depth (m)  17/04/72 h  | Temp. | S a l . (°C) 1 (%o)  I  |  1  I i I  6.9  1 1 1 i i  6.9 6.9  j  6.8  1 | i  6.8  | i 1 j i i 1  6.8  i  6.7  i 1 1 i l  3 5 7 10 15 20  CRN: GSTN: 03  6.9  i i 1 i i i i  0  2  1840  |  \  i  1 1 • 1  i  1 1  CRN:  G- 4  HR:  1915  STN: 02  DY:  17/04/72  Depth  Temp. <°C)  Sal.  (%o)  27-3  0  6.9  27.7  27.6  1  6.9  27.6  27.8  2  6.9  27.6  27.5  3  6.9  27.6  27.6  5  6.9  27.7  27. 8  7  6.9  27.8  28.2  10  6.9  28.2  29.1  15  6.6  29.5  29.6  20  6.6  30.0  i  i  6.6  4  l  i  HR: DY:  2000  17/04/72  CRN: G- 4 STN: 04  Depth (m)  -+-  HR: DY:  2025  17/04/72  Temp,  Sal.  0  7.1  28.2  1  7.0  28.3  2  6.9  28.2  3  6.9  28. 1  5  6.7  28. 1  7  6.9  28. 1  10  6.8  28.3  15  7.0  28.5  20  6.6  30.3  CRN:  G-  S T N : 05 Depth  (n)  CRN:  DY: 17/04/72 | Temp. I (°C)  0  7. 3  1  7.2  2  j Sal. | (%»)  4  G-  Hfi:  STN: 06  DY:  17/04/72  Depth (m)  Temp. {°C)  Sal.  0  7.5  26.9  J  27. 1  1  7.4  27.0  7.2  |  27.0  2  7.3  27.3  3  7.2  }  27.1  3  7.0  27.6  5  6.9  J  27.4  5  6.9  27.8  7  6.8  I  27.9  7  6.9  27.8  10  6.8  27.9  10  6.8  28.3  15  6.7  28.1  15  6.6  30.0  20  6.7  29.3  20  6.7  30.4  4  CRN: G-  j S T N : 07  }  i I  2150 |  HE: DY:  17/04/72  |  , |  CRN: G-  |  STN:  4  08  Hfi: DY:  J_  |  1  1  D e p t h 1 Temp. 1 (°C) (m)  o  |  7.6  i 1  |  |  {%•>  !  1  25.0  |  1  o  25.8 J  1  1  1 i i 1 1  25.2 J  I  2  25.5 |  I  3  1 1  26.0 J  i  5  27. 1 |  I  7  29.3 |  j  10  30.0  |  15  I  20  L I  1  Sal. .  Depth (m)  i  |  1  |  7. 5  I  1 l  I  2  ]  7.5  i  3  |  7.5  I  5  |  7. 2  1I  1  I  7  1  6.9  |  10  |  6.7  I I I i  i  15  1  6.6  |  20  j  6.6  i.  2124  27. 1  1  |  HR: 2059  4  _ _  i  1 i 1  1  1  |  30.1 J  i  1 Temp.  17/0 4/72 | i r  ! ! !  I  ! ! !  I  J  5.8 5.8 6.3 6.5 6.7 6.8 6.7 6.7 6.7  .i  Sal.  |  (35.) i  1 (°C) I  ,  2241 J  I  ! !  I  !  i  ! ! ! I  2.0 J 6.7 J 17.3 j 21.3 1 23.9  j  28.9 J 29.3 J 29.7 1 30.1 J 1  139  HR: 1815  j CRN: G- 5 j STN: 01 , Depth  DY: 1 /05/72  STN: 02  DY: 11/05/72  +  HR; 1847  CRN: G- 5  +  Temp. | S a l .  Depth  I  (IQ)  (OC)  (a)  0  9.5  1  (%o )  „j  Temp. (°C)  0  9.6  4-  Sal. (».) 11. 1  I  10.6  9.6  |  13.8  1  10. 1  18.6  2  10.5  |  24.7  2  10. 1  18-7  3  10.6  j  26.0  3  10.3  22.3  5  1 0.3  \  27.0  5  10.0  27.5  7  8.8  |  27.8  4  9.5  27.8  10  7.7  j  28-9  10  8.5  28.4  15  7.5  I  29.5  15  7.5  29.3  20  7.4  |  29.6  20  7-2  29.9  CRN: G- 5 STN: 03 Depth (m)  HR: 1925 DY: 11/05/7 2  Temp, (°C)  Sal. i%o)  • •• —i r 5 HR: 2000 I I CRN: G| STN: 04 DY: 11/0 5/72 | Depth | Temp. I 1 (m) I ( O Q  j I i ?  .,  , ,i i 10.7  Sal. <%o)  | |  i  7.0 |  I 10.6  1  12.3 J  2  I 10.8  i  16.4 J  I  3  | 10.5  I  21.9 |  27.0  I  5  I 10.3  1  26.9 i  9. 9  27. 1  I  7  | 10.2  i  27.3 |  10  8. 8  27.7  I  10  I  9.0  j  27.8 I  15  7. 9  28.7  |  15  i  7-5  i  29.1 |  20  7.3  29. 3  I  20  |  7.1  1  29.9 |  0  10.7  1  10. 8  2  7.5  1  o  10.4  !  1  10.6  18.2  i  3  10.4  22. 1  5  10. 1  7  t  1  J  140  I  } S T N : 05 , |  I  ,  J  T  | CRN: G- 5 |_  HE: 2020  J  j CRN: G- 5  |  I  1 Sal.1 | {%*) 1 j.  I  DY: 1 1 / 0 5 / 7 2  D e p t h j Temp(m) | (°C) 1-  }.  j  L  I  4  S T N : 06  +  HE: 2 0 4 2 DY: 1 1 / 0 5 / 7 2  j-  D e p t h | Temp(m) | (°C) . -j  J  i j-  ?  j  |  j  J  Sal(%o)  |  j  j  0  I  11.1  |  14.4 |  I  0  | 11,0  |  12.9 |  I  1  J11.1  I  15.2 |  |  1  | 11,0  |  13.0 |  |  2  I  |  15.9 |  1  2  | 11.1  |  12.7 |  |  3  | 11.0  i  17.1 I  |  3  I  11.3  |  15.0 J  1  5  i  10.5  J  26-8 |  |  5  | 10.9  J  24.8 J  j  7  |  9.7  |  27.3 |  I  7  | 10.4  |  27.2 |  11.1  |  10  1  8.2  J  28.2 |  |  10  J  9.7  |  27.5 |  |  15  j  7.7  j  28.9 |  |  15  |  7.6  J  29.2 |  j  20  j  7.1  |  29.7 J  |  20  |  7.2  |  29.7 |  i  i  i  j  I  i  "1  3 CRN: G- 5 3 STN: 07  HR:  t  I  2100 J  DY: 1 1 / 0 5 / 7 2  i  1  3  I CRN; G- 5  I i  I STN: 08 I 1  \  1-  1  |  I  D e p t h 1 Temp, (m) i (°C)  | j  r  +  +  i  I  Sal.1 J  | |  Depth (m)  HE: 2 1 3 0 j  DY; 1 1 / 0 5 / 7 2 i-  | Temp. J {°C)  1  I  J f  | i  Sal, (%e)  J  i  |  0  I  10.4  |  13,7 I  I  0  J  8.2  |  0.0 J  |  1  | 10.7  3  16.5 j  i  1  |  7.8  |  0.0 J  |  2  I  10.7  J  19.4 |  |  2  I  9.4  1  15.8 j  |  3  j 10.7  |  21.5 |  1  3  | 10.1  J  21.2 1  J  5  1  9.8  |  26.7 |  1  1  7.5  J  29.6 1  1  7  J  8.7  |  28. 1 J  \  1  J  7.3  \  29.7 |  |  10  I  7.4  |  28.7 j  |  10  |  7.3  J  29.8 |  J |  15 20  J \  7.0 6.8  | |  29.7 j 30.2 j  | i  15 16  I 1  7.2 7.2  | 1  29.8 3 29.9 |  i  j  i  i  .  i  5  J  i  i  |  

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